Economic Development and the Division of Labor

ECONOMIC DEVELOPMENT AND THE DIVISION OF LABOR with a foreword by Jeffrey D. Sachs ECONOMIC DEVELOPMENT AND THE DIVISI...

Author: Xiaokai Yang | Jeffrey D. Sachs

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ECONOMIC DEVELOPMENT AND THE DIVISION OF LABOR with a foreword by Jeffrey D. Sachs

ECONOMIC DEVELOPMENT AND THE DIVISION OF LABOR

To Xiaojuan Wu

ECONOMIC DEVELOPMENT AND THE DIVISION OF LABOR with a foreword by Jeffrey D. Sachs

© 2003 by Xiaokai Yang 350 Main Street, Malden, MA 02148-5018, USA 108 Cowley Road, Oxford OX4 1JF, UK 550 Swanston Street, Carlton South, Melbourne, Victoria 3053, Australia Kurfürstendamm 57, 10707 Berlin, Germany The right of Xiaokai Yang to be identiﬁed as the Author of this Work has been asserted in accordance with the UK Copyright, Designs, and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs, and Patents Act 1988, without the prior permission of the publisher. First published 2003 by Blackwell Publishing Ltd Library of Congress Cataloging-in-Publication Data Yang, Xiaokai. Economic development and the division of labour / Xiaokai Yang. p. cm. Includes bibliographical references and index. ISBN 0-631-22003-8 (alk. paper) – ISBN 0-631-22004-6 (pb. : alk. paper) 1. Development economics. 2. Economic development. I. Title. HD75.S23 2003 338.9–dc21 2001018137 A catalogue record for this title is available from the British Library. Set in 10/11.5pt Ehrhardt by Graphicraft Ltd, Hong Kong Printed and bound in the United Kingdom by TJ International, Padstow, Cornwall For further information on Blackwell Publishing, visit our website: http:/www.blackwellpublishing.com

CONTENTS

List of Figures

xiii

List of Tables

xv

Foreword by Jeffrey D. Sachs

xvii

Preface

xxi

1 Introduction 1.1 Classical Development Economics and Capitalist Economic Development 1.2 The Breakdown of the First Global Capitalist System and Neoclassical Development Economics 1.3 A Return to Classical Development Economics 1.4 The Scientiﬁc Approach to Development Economics Key Terms and Review Further Reading Questions Notes

PART I: GEOGRAPHY AND MICROECONOMIC MECHANISMS FOR ECONOMIC DEVELOPMENT 2

1 1 6 10 15 19 19 20 31

35

Geography and Economic Development

37

2.1 Uneven Economic Development in Different Parts of the World Questions to Ask Yourself when Reading this Chapter 2.2 Geography and Division of Labor 2.3 Empirical Linkages of Geography and Economic Development 2.3.1 Geographical correlates of economic development 2.3.2 Geography and levels of per capita income 2.3.3 Geography and growth of per capita income 2.3.4 Geographical effects on economic policy choices Key Terms and Review

37 41 41 44 44 47 48 52 53

vi

3

C ONTENTS

Further Reading Questions Notes

54 54 56

Driving Force I – Exogenous Comparative Advantage and Trading Efﬁciency

57

3.1

4

5

Use of the Concept of General Equilibrium to Figure Out Mechanisms for Economic Development Questions to Ask Yourself when Reading this Chapter 3.2 A Ricardian Model with Exogenous Comparative Technological Advantage and Transaction Costs 3.3 Analysis of Decisions versus Equilibrium Analysis of Development 3.4 Per Capita Real Income, GDP, GNP, and PPP 3.5 Economic Development and Trade Policy 3.6 Comparative Endowment Advantage and Transaction Efﬁciency Key Terms and Review Further Reading Questions Exercises

61 67 74 76 83 90 91 91 95

Driving Force II – Endogenous Comparative Advantage and Trading Efﬁciency

98

57 61

4.1 Endogenous versus Exogenous Comparative Advantages Questions to Ask Yourself when Reading this Chapter 4.2 Conﬁgurations and Corner Solutions in a Smithian Model 4.3 How the Market Coordinates Division of Labor to Utilize Network Effects and Promote Economic Development 4.4 More Examples 4.5 Pattern of Trade Key Terms and Review Further Reading Questions Exercises

98 100 100 109 116 121 123 123 124 128

Driving Force III – Economies of Scale and Trading Efﬁciency

131

5.1 Economies of Scale and Economic Development Questions to Ask Yourself when Reading this Chapter 5.2 General Equilibrium Models of Economic Development with Trade-offs between Economies of Scale, Consumption Variety, and Transaction Costs 5.3 The Ethier Model with Transaction Costs 5.4 The Murphy–Shleifer–Vishny (MSV) Model of Big-push Industrialization 5.5 The Sachs and Yang Model with Economies of Scale, Endogenous Degree of Industrialization, and Transaction Costs Key Terms and Review Further Reading Questions

131 132 132 138 144 147 151 152 152

C ONTENTS vii

6

7

Exercises Notes

154 156

Coexistence of Endogenous and Exogenous Comparative Advantages and Patterns of Development and Trade

157

6.1 Underdevelopment and a Dual Structure with Underemployment Questions to Ask Yourself when Reading this Chapter 6.2 A Smithian Model with a Dual Structure in the Transitional Stage of Economic Development 6.3 General Equilibrium and its Inframarginal Comparative Statics 6.4 Trade Pattern in the Presence of Both Endogenous and Exogenous Comparative Advantages, and the Relationship between Income Distribution and Development 6.5 Development Strategies and Trade Patterns 6.5.1 A consumer’s decision 6.5.2 Possible trade structures 6.5.3 Production of agricultural good z 6.5.4 Production of ﬁnal manufactured good y 6.5.5 Production of intermediate goods 6.5.6 Local equilibrium in structure A 6.5.7 Local equilibrium in structure C 6.5.8 Local equilibrium in structure D 6.5.9 Local equilibrium in structure E 6.5.10 Local equilibrium in structure F 6.6 General Equilibrium and Inframarginal Comparative Statics 6.7 A Comparison with the Conventional Wisdom based on Models with CRS Key Terms and Review Further Reading Questions Exercises Notes

167 169 170 170 171 171 172 172 173 174 176 176 177 179 183 184 184 188 192

Structural Changes, Trade, and Economic Development

193

Endogenous Trade Theory and an Endogenous Number of Consumer Goods Questions to Ask Yourself when Reading this Chapter 7.2 A Model of Economic Development with Fixed Learning Costs 7.3 How Are Demand and Supply Functions Determined by Individuals’ Levels of Specialization? 7.4 Inframarginal Comparative Statics of Optimum Decisions 7.5 How is the Level of Division of Labor in Society Determined in the Market? 7.6 Inframarginal Comparative Statics of General Equilibrium and Many Concurrent Development Phenomena 7.7 Emergence of International Trade from Domestic Trade 7.8 Co-movement of Division of Labor and Consumption Variety 7.9 The Emergence of Professional Middlemen and Trade Patterns 7.10 The Trade-off between Economies of Specialization and Coordination Costs

157 158 159 162

7.1

193 195 195 198 201 201 204 209 210 214 216

viii

C ONTENTS

Key Terms and Review Further Reading Questions Exercises Note

PART II: 8

9

THE INSTITUTION OF THE FIRM, ENDOGENOUS TRANSACTION COSTS, AND ECONOMIC DEVELOPMENT

217 218 218 223 225

227

Economic Development, the Institution of the Firm, and Entrepreneurship

229

8.1 What is the Institution of the Firm? Questions to Ask Yourself when Reading this Chapter 8.2 Why are Claims to Residual Rights of the Firm Essential for Nurturing Entrepreneurship? – The Story behind the Model 8.3 The Emergence of the Firm from the Evolution of Division of Labor 8.3.1 Economies of roundabout production 8.3.2 The corner equilibria in four structures 8.3.3 General equilibrium structure of transactions and residual rights 8.4 The Distinction between ex ante and ex post Production Functions, and the Role of the Institution of the Firm in Economic Development 8.5 The Coase Theorem and Other Theories of the Firm Key Terms and Review Further Reading Questions Exercises

229 231

Endogenous Transaction Costs, Contracts, and Economic Development

254

9.1 Endogenous Transaction Costs and Economic Development Questions to Ask Yourself when Reading this Chapter 9.2 Endogenous Transaction Costs Caused by Moral Hazard 9.3 Game Models and Endogenous Transaction Costs 9.3.1 Game models 9.3.2 Nash equilibrium 9.3.3 Subgame perfect equilibrium 9.3.4 Bayes equilibrium 9.3.5 Sequential equilibrium 9.4 The Role of Nash Bargaining Games in Reducing Endogenous Transaction Costs caused by Trade Conﬂict 9.5 Endogenous Transaction Costs caused by Information Asymmetry and Holding Up 9.5.1 Economic development and endogenous transaction costs caused by adverse selection 9.5.2 An alternating-offer bargaining game in a model of endogenous specialization 9.5.3 Economic development and endogenous transaction costs caused by holding up 9.5.4 How can endogenous transaction costs be eliminated by consideration of reputation? 9.6 The Grossman–Hart–Moore Incomplete Contract Model

254 257 257 270 270 270 272 274 275

231 233 234 235 239 241 242 245 245 246 251

278 281 281 283 285 287 288

C ONTENTS

9.7 Noncredible Commitment and Soft Budget Constraint Key Terms and Review Further Reading Questions Exercises 10 Transaction Risk, Property Rights, Insurance, and Economic Development 10.1 Uncertainties in Transactions and the Economics of Property Rights Questions to Ask Yourself when Reading this Chapter 10.2 Economic Development and the Trade-off between Economies of Division of Labor and Coordination Reliability 10.3 Endogenization of Coordination Reliability in Each Transaction and Substitution between Competition and Better Enforced Property Rights 10.4 Why Can Insurance Promote Economic Development? 10.5 Economic Development and Endogenous Transaction Costs Caused by Moral Hazard Key Terms and Review Further Reading Questions Exercises

ix

291 293 293 294 298 302 302 306 307 310 319 324 331 332 332 336

PART III: URBANIZATION AND INDUSTRIALIZATION

339

11 Urbanization, Structural Duality between Urban and Rural Areas, and Economic Development

341

11.1 Why and How Cities Emerge from the Division of Labor Questions to Ask Yourself when Reading this Chapter 11.2 The Fujita–Krugman Model of Urbanization based on a Trade-off between Economies of Scale and Transaction Costs 11.3 Emergence of a Structural Duality of Urban and Rural Areas from the Division of Labor 11.4 Why Can the Geographical Concentration of Transactions Improve Transaction Efﬁciency? 11.5 Simultaneous Endogenization of Level of Division of Labor, Location Pattern of Residences, Geographical Pattern of Transactions, and Land Prices Key Terms and Review Further Reading Questions Exercises Notes 12 Industrialization, Structural Changes, Economic Development, and Division of Labor in Roundabout Production 12.1 The Features of Industrialization Questions to Ask Yourself when Reading this Chapter 12.2 Industrialization and the Evolution of Division of Labor in Roundabout Production

341 343 344 346 349 355 366 366 367 368 369 370 370 375 375

x

C ONTENTS

12.3 Corner Equilibria and the Emergence of New Industry 12.4 General Equilibrium, Industrialization, and Structural Changes 12.4.1 Changes in the employment shares of the industrial and agricultural sectors 12.4.2 The number of possible structures of transactions increases more than proportionally as division of labor evolves in roundabout production 12.5 Evolution in the Number of Producer Goods and Economic Development Key Terms and Review Further Reading Questions Exercises Notes

377 379 381

383 386 391 391 391 396 398

PART IV: DYNAMIC MECHANISMS FOR ECONOMIC DEVELOPMENT

399

13 Neoclassical Models of Economic Growth

401

13.1 Exogenous versus Endogenous Growth Questions to Ask Yourself when Reading this Chapter 13.2 The Ramsey and AK Models 13.3 R&D-based Endogenous Growth Models Key Terms and Review Further Reading Questions Exercises Notes 14 Economic Development Generated by Endogenous Evolution of Division of Labor 14.1 Economies of Specialized Learning by Doing and Endogenous Evolution in Division of Labor Questions to Ask Yourself when Reading this Chapter 14.2 A Smith–Young Dynamic Model with Learning by Doing 14.3 Optimum Speed of Learning by Doing and Evolution of Endogenous Comparative Advantage 14.3.1 The function of contracts 14.3.2 An individual’s dynamic decision problem 14.3.3 Dynamic equilibrium 14.4 Endogenous Evolution of the Extent of the Market, Trade Dependence, Endogenous Comparative Advantages, and Economic Structure 14.5 Empirical Evidence and Rethinking Endogenous Growth Theory Appendix 14.1: The Relationship between the Control Theory and Calculus of Variations Key Terms and Review Further Reading Questions Exercises Notes

401 403 403 410 416 416 417 418 420

421 421 423 424 425 425 426 427 437 438 444 445 445 446 447 448

C ONTENTS

15 Social Experiments and the Evolution of Knowledge of Development 15.1 How Does Organizational Knowledge Acquired by Society Determine Economic Development? Questions to Ask Yourself when Reading this Chapter 15.2 A Static Model with a Roundabout Production Chain of Endogenous Length and an Endogenous Division of Labor 15.3 Interactions between Dynamic Decisions and Evolution in Organizational Information 15.4 Walrasian Sequential Equilibrium and Concurrent Evolution in Organizational Information and Division of Labor Key Terms and Review Further Reading Questions Exercises

xi

449 449 453 454 456 459 468 468 468 470

PART V: THE MACROECONOMICS OF DEVELOPMENT

473

16 Investment, Saving, and Economic Development

475

16.1 Classical Theory of Investment and Saving Questions to Ask Yourself when Reading this Chapter 16.2 Neoclassical General Equilibrium Models of Self-saving and Interpersonal Loans 16.3 The Smith–Young Theory of Investment and Savings 16.3.1 The model 16.3.2 Conﬁguration and structure sequences 16.3.3 Dynamic corner equilibria in 16 structure sequences 16.4 Investment, Capital, and Division of Labor in Roundabout Production 16.4.1 Dynamic general equilibrium 16.4.2 Nontopological properties of economic growth and the sudden decline of interest rates 16.4.3 An endogenous decision horizon and effect of liberalization on opportunities for lucrative investment Key Terms and Review Further Reading Questions Exercises Note 17 Money, Division of Labor, and Economic Development 17.1 Neoclassical and Classical Theories of Money Questions to Ask Yourself when Reading this Chapter 17.2 A Smithian Model with an Endogenous Monetary Regime and Economic Development 17.3 Possible Structures and Monetary Regimes Key Terms and Review Further Reading Questions Exercises Notes

475 478 478 482 482 483 485 488 489 492 494 495 495 496 497 497 498 498 501 501 503 509 510 510 511 512

xii C ONTENTS

18 Endogenous Business Cycles, Cyclical Unemployment, and Endogenous Long-run Growth 18.1 Rethinking Macroeconomic Phenomena in Economic Development Questions to Ask Yourself when Reading this Chapter 18.2 Long-run Regular Efﬁcient Business Cycles, Cyclical Unemployment, Long-run Economic Growth, and Division of Labor in Producing Durable Goods 18.3 A Smithian Dynamic Equilibrium Model of Business Cycles, Unemployment, and Economic Development 18.4 Cyclical and Noncyclical Corner Equilibria 18.4.1 Regime speciﬁcation, conﬁgurations, and market structures 18.4.2 The dynamic corner equilibrium in autarky 18.4.3 Market structure C 18.4.4 Market structure P 18.4.5 Welfare and policy implications of the model 18.5 General Price Level, Business Cycles, and the Unemployment Rate 18.6 The Emergence of Firms and Fiat Money from the Division of Labor Key Terms and Review Further Reading Questions Exercises Note 19 Economic Transition 19.1 Understanding Economic Transition Questions to Ask Yourself when Reading this Chapter 19.2 The Socialist System and Evolution in Division of Labor 19.3 Driving Mechanisms for Transition 19.4 Market-oriented Reforms Associated with the Transition of Constitutional Rules 19.5 Market-oriented Reforms in the Absence of Constitutional Order 19.6 Trade-offs between Reliability and the Positive Network Effects of Division of Labor, and between Incentive Provision and Stability Key Terms and Review Further Reading Questions Exercises Notes

513 513 519 519 523 525 525 526 527 529 531 531 534 536 537 537 539 543 544 544 546 547 555 557 561 572 577 578 578 582 583

References

586

Index

617

FIGURES

2.1 World GDP per capita 1995 3.1 Economies of division of labor based on exogenous technical comparative advantage 3.2 Conﬁgurations and structures 3.3 Possible trade structures 4.1 Economies of division of labor based on endogenous absolute and comparative advantage 4.2 Indirect utility functions and corner equilibrium-relative price 4.3 Partition of parameter space 4.4 Autarky and division of labor 5.1 Economic development based on economies of scale 5.2 Structural changes, industrialization, and economic development in the Ethier model 6.1 Dual structures in economic development 6.2 Economies of division of labor based on endogenous and exogenous comparative advantage 6.3 Different patterns of development and trade 7.1 Economies of division of labor generated by ﬁxed learning costs 7.2 Evenly dispersed individuals’ residence location 7.3 Multiple general equilibria 7.4 Exogenous evolution in division of labor 7.5 Emergence of new technology and new consumption goods 8.1 Emergence of the ﬁrm from the division of labor 9.1 Risk aversion and a strictly concave utility function 9.2 The extensive form of the alternating-offer bargaining game 10.1 Different degrees of competition in equilibrium 11.1 Emergence of cities from evolution of division of labor 11.2 Dispersed and concentrated location patterns of transactions 11.3 Evolution of division of labor and location pattern of residences and transactions 12.1 Various industrial structures 12.2 Structures with ﬁrms 12.3 Industrialization and evolution of division of labor in the Sun–Lio model

38 64 64 83 101 110 114 115 133 143 160 166 171 196 203 204 205 214 232 259 273 316 347 351 364 377 384 387

xiv

13.1 13.2 14.1 14.2 14.3 14.4 14.5 15.1 15.2 15.3 16.1 16.2 16.3 17.1 17.2 17.3 18.1 18.2 18.3 18.4 19.1

F IGURES

Phase diagram of the Ramsey model Phase diagram of the Romer model Different market structures in the early development stage Intervals of a that divide between various growth patterns Various growth patterns of nt and per capita real income Endogenous evolution in division of labor Sequential divergence and convergence Conﬁgurations and structures in the static model An individual’s dynamic programming problem in period 0 Walrasian sequential equilibrium Conﬁgurations and market structures Investment and evolution of division of labor in roundabout production Nontopological properties of evolution in division of labor and economic growth The absence of double coincidence of demand and supply based on ex ante differences between individuals Emergence of money and evolution of division of labor Market structures and monetary regimes Aggregate transformation curve for M = 3 An individual’s organization utility under equilibrium prices Growth patterns with and without business cycles and unemployment Structures with and without business cycles The trade-off between sensitive incentive and stability of the feedback mechanism

407 414 428 433 434 436 441 455 457 462 485 485 492 499 500 504 515 516 521 525 576

TABLES

2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 4.5 6.1 6.2 6.3 6.4 7.1 8.1 8.2 8.3 9.1 9.2 9.3 9.4a 9.4b 9.5 9.6 9.7

Geographical characteristics of selected regions Levels of GDP GDP growth Levels and changes in malarial prevalence between 1966 and 1994, by ecozone Four corner equilibria in the Ricardian model General equilibrium and its inframarginal comparative statics of the Ricardo model Corner equilibrium solutions General equilibrium and its inframarginal comparative statics Proﬁles of zero and positive values of the 6 decision variables Three corner solutions Two corner equilibria Corner solutions based on the CES utility function Trade pattern in a model of endogenous comparative advantage Indirect utility functions Corner equilibria General equilibrium structure: inframarginal comparative statics Equilibrium structure (economies of specialization in producing one good for all countries) Corner equilibria in ﬁve structures Corner equilibria in four structures Candidates for equilibrium structure General equilibrium and its inframarginal comparative statics Corner solutions in seven conﬁgurations Corner equilibria in four structures General equilibrium and its inframarginal comparative statics The strategic form of the Nash tariff game in structure Ba The strategic form of the Nash tariff game in structure C The strategic form of the game to compete for ﬁrst mover advantage Probabilities for four contingent states The equilibrium structure of ownership and inframarginal comparative statics

40 47 49 50 67 70 77 88 103 106 111 117 122 163 163 164 168 215 238 239 240 267 268 269 271 271 285 288 291

xvi

10.1 10.2 10.3 11.1 11.2 11.3 11.4 11.5 12.1 12.2 15.1 15.2 15.3 15.4 15.5 16.1 16.2 17.1 17.2 19.1

T ABLES

Equilibrium reliability and degree of competition Expected real incomes in seven structures General equilibrium and its inframarginal comparative statics Eight corner solutions Corner equilibria in four structures General equilibrium and its inframarginal comparative statics Interactions between geographical patterns of transactions, transaction efﬁciency, and level of division of labor General equilibrium and its inframarginal comparative statics Corner equilibria Emergence of new industry and evolution in division of labor Three corner equilibria Static general equilibrium and its inframarginal comparative statics Optimum dynamic decisions in period 0 Adjusted optimum dynamic decisions in period 1 Inframarginal comparative dynamics of Walrasian sequential equilibrium Total discounted per capita real incomes in seven structure sequences Dynamic general equilibrium and its inframarginal comparative dynamics Corner equilibria in eight structures Inframarginal comparative statics of general equilibrium and emergence of money from evolution in division of labor Corner solutions in four conﬁgurations

315 327 328 347 348 348 354 354 378 380 455 455 459 461 464 488 490 506 508 575

FOREWORD Jeffrey D. Sachs

It is a great pleasure and honor for me to write a Foreword for Xiaokai Yang’s remarkable text on Economic Development and the Division of Labor. Yang is one of the world’s most penetrating and exacting economic theorists, and one of the most creative minds in the economics profession. He is a major contributor to the modern theory of economic development, especially to the microeconomic foundations of development theory. He is also, without doubt, one of the most profound and bold analysts of the social transformation of his homeland China. In a powerful body of work stretching over nearly two decades, Yang has sought to reconstruct general equilibrium economic analysis based on Adam Smith’s fundamental insights on the role of the division of labor as an essential progenitor of economic development and growth. Yang recognized early on that this bold research program would require a new mathematical framework, and that indeed the lack of such a mathematical framework had frustrated earlier pioneers in economic theory, including great analysts of the division of labor such as Alfred Marshall, Allyn Young, and George Stigler. Yang rose to the challenge by adopting rigorous tools of inframarginal analysis based on nonlinear programming techniques. A key milestone in this research program was the path-breaking study Specialization and Economic Organization, co-authored with Yew-Kwang Ng (North-Holland, 1993). Yang appreciated that a careful general equilibrium model of the division of labor would serve two basic goals. It would provide a research tool for new scientiﬁc discoveries, and it would also provide a canonical framework for teaching, so that teachers and students throughout the worldwide economics profession would have a common set of models and tools with which to discuss and investigate the division of labor. This new textbook will provide another important contribution to the dual agendas of research and teaching. Yang stresses throughout his work how the conceptual and mathematical simpliﬁcations of standard development and growth theory in the post-Second World War era gravely misled both theorists and practitioners about the key determinants of economic development. The simplest models tended to deal with a single “representative good” and a single “representative agent,” often invoking the solitary ﬁgure of the shipwrecked Robinson Crusoe as a relevant “model” of economic development. Rather than studying the social context of the economy – how different individuals and ﬁrms relate to each other through markets, organizations, and social and political relationships – the postwar models focused mainly on the patterns of saving and investment by a representative household and ﬁrm. According to such models, the biggest development challenge was raising the rate of capital accumulation. Robinson Crusoe’s income on the island rises in such models according to the productive capital that he accumulates.

xviii

FOREWORD

Development economics thereby turned its attention to saving rates, incremental capitaloutput ratios, budget balances, and other indicators of capital accumulation, as the central tools of analysis for many decades. The socialist economies – including the Soviet Union and China – took the emphasis on capital accumulation to the extreme, by employing various forms of compulsion, including extreme suppression of peasant incomes, to raise national saving rates in order to speed industrialization and development. Alas, the savings-led model of development proved to be inadequate both in theory and in practice. It is one thing to accumulate capital, but quite another to raise living standards on a sustained basis. For that, the economy needs to enjoy rising productivity, and for that, it requires an increasingly sophisticated division of labor, just as Adam Smith had stressed more than two centuries ago. The rule of law and market forces are much more powerful than coercion in promoting rising living standards. One of the great insights of Smith, Young, and other followers is that the division of labor depends on the extent of the market, while at the same time the division of labor helps to determine the extent of the market. Yang’s models vividly illuminate this two-way causation, and with a mathematical rigor never before achieved on these issues. Yang also illuminates the fundamental determinants of the division of labor – how the extent of the market is inﬂuenced by the costs of transactions between economic agents, and how those transaction costs reﬂect a combination of physical and technological constraints (e.g. shipping costs) as well as contractual costs determined by the legal environment. Smith himself gave stress both to physical geography and government policy in determining the extent of the market, and Yang follows in this tradition. Yang’s models also put the gains from trade on a much richer and more profound footing than standard notions of comparative advantage. Yang’s models have the important and realistic property that international trade is a source of productivity gain even when the trading economies are essentially the same in their basic endowments and capabilities, a result that is also familiar from the “new trade theory,” though in Yang’s case the underpinnings are through the division of labor, rather than through the assumption of increasing returns to scale at the level of the ﬁrm and imperfect competition at the level of the industry as in most of the new trade theory. Trade, as Smith ﬁrst explained and Yang’s models make clear, permits gains from an increasingly sophisticated division of labor. Once the proper focus is put on the productivity gains from an increasingly reﬁned division of labor, Yang’s models underscore the self-defeating, indeed hopeless, course of trade autarky that has enticed, and entrapped, many poor countries over the years. Protectionism is the surest way to destroy the beneﬁts of specialization and the division of labor, an argument that also goes back to Smith’s original conception. Many strands of modern economic theory, including the imperfect competition and new trade theory models of Stiglitz, Dixit, Krugman, and others, share some of the results of Yang’s models of the division of labor. The imperfect competition models also help us to understand trade ﬂows between similarly endowed economies; the beneﬁts of agglomeration and urbanization; and the determinants of the number of ﬁrms and industries in an economy (and how economic productivity depends on the number of industries). The two approaches indeed look similar. Yet, there is much to be gained from Yang’s relentless focus on transaction costs and the division of labor. In many circumstances Yang’s approach will provide a much sounder basis for empirical understanding, and can address many phenomena that cannot be handled well in the new trade theory, such as specialization at the individual level, the degree of market integration, and the deep microeconomics of network economies such as the use of money as an instrument of trade. Yang’s emphasis on the division of labor helps us to understand the growth of productivity from economic integration even when – as is often the case – there are no evident increasing returns to scale at the ﬁrm (or industry) level and when imperfect competition at the industry level is unrealistic. Yang’s approach thereby gives us the

FOREWORD xix

deepest tools to date for understanding the networks of economic interactions that arise under conditions that favor specialization. This textbook will be a take-off point for many new directions of research. The emerging global network of regional economies under globalization will be fruitfully studied using Yang’s modeling approach. The diffusion and innovation of technologies also depend on specialization and networks of economic interaction, and thus are logical directions for future research. The empirical validation of the linkages between physical geography, transaction costs, and the extent of the market is yet to be undertaken, but the preliminary results discussed in chapter 2 of the text are very promising. And Yang’s conjectures about the tradeoffs of network complexity and network reliability pose many issues for advanced research. Yang’s work will also mesh very well with the increasingly sophisticated modeling of networks based on rapid advances in graph theory (such as the advent of “small world” models). Network models try to explain the “emergent behavior” (macro-scale characteristics) of a system as a function of the topology of the underlying networks of interactions. These models are increasingly used in sociology, epidemiology, and engineering design. Since both Yang and the network modelers put great stress on the micro-features of interactions among agents, there is much that can be learned in economics from the new network theories, and Yang’s work will provide a vital bridge and framework. Finally, as Yang stresses throughout, the emphasis on transaction costs puts Yang’s models squarely in the context of the modern economic history approaches of North and colleagues, who emphasize how changes in economic institutions regarding property rights and contracting have helped to shape the extent of division of labor, and thus the processes of overall economic growth. I must also say some words about Xiaokai Yang as an individual, not just because he is brave and dedicated and steadfast, but also because his personal experience helps to shed light on his search for the foundations of economic analysis. Yang grew up in the People’s Republic of China, in a revolutionary period of great turmoil and human suffering. Of course, the newly established People’s Republic of China adopted a socialist economic system. As Yang has insightfully described, the very limited division of labor in the Chinese industrial sector was achieved in large part by copying the patterns of industrialization of the more advanced economies. In fact, even this rudimentary industrialization affected only a small part of the population and economy in the ﬁrst decades of the new state. Yang grew up in a society in which the overwhelming proportion of the population lived in subsistence conditions in rural areas. As a young man, like tens of millions of his generation, Yang got caught up in the turmoil of the Cultural Revolution. It was during the extreme dislocations of his personal life and formal education that Yang ﬁrst undertook his economic studies – often using books and journals that circulated informally or learning in improvised settings from intellectuals who were also thrown into the turmoil of the times. Many of his “professors” never returned to the University, dying of torture or neglect or duress. But out of these conditions, Yang was led to explore the very deepest questions about his own society, and eventually about economic life more generally. Without any glitter of the latest academic fads, or the small issues that can loom so large in the academic milieu, Yang asked probing questions about China’s impoverishment, the relationship of the city and the countryside, the role of specialization and expert knowledge, and other lifeand-death issues posed by Mao’s disastrous Cultural Revolution. It is in this probing, I believe, that Yang came to fashion his future research program, with all its boldness and insight. His graduate and postgraduate studies in China and the United States after the Cultural Revolution gave Yang the formal theoretical tools for analysis, but by then Yang was already taking on the most basic and probing questions in economic science. I came to know Xiaokai Yang during the 1990s, when I turned some of my own research to China’s remarkable economic reforms and their implications for economic development strategies

xx

FOREWORD

in other parts of the world. Yang and I discussed at length the nature of China’s economic transformation, and the comparison of China’s reform path with the reform paths in Eastern Europe and the former Soviet Union. We saw eye to eye on many crucial points: that China was on its way to a full market economy integrated into global markets; and that serious analytical comparisons of China and Eastern Europe needed to take into account the fundamentally different conditions in the two places (such as differences in the extent of urbanization and industrialization, and even differences in the physical geography and access to world markets). We also concurred that the integration of China and other transition economies into the world economy was a fundamental aspect of transition. Our fruitful discussions led to Xiaokai’s visit to the Center for International Development at Harvard University during 1998–2000, and to our collaboration on many projects and coauthorship of many papers. At that point, we decided to write a book together on economic development and the division of labor. Xiaokai dutifully carried out a mountain of research and writing, while I became increasingly absorbed by many advisory assignments, the start-up of a new research institute at Harvard, and the currents of my own research initiatives on globalization and development. Xiaokai returned to Monash University with a draft manuscript delivered to Blackwell Publishers with both of our names as author. And while the manuscript reﬂected many joint ideas and shared approaches, it overwhelmingly reﬂected Xiaokai’s own substantive research triumphs as well as his unique voice. I promised that I would rectify the balance in the coming year through work on the manuscript, but in the end could not do so. Not only was my own schedule increasingly daunting, especially with new leadership assignments at the World Health Organization, United Nations Headquarters, and elsewhere, but I also found that editing the manuscript simply diluted Xiaokai’s own voice without adding sufﬁcient beneﬁt of my own. In essence, the book was truly Xiaokai’s – a ﬁtting and superb reﬂection of his long-standing research program – and while there were many reﬂections of my own concerns and preoccupations, there were far from enough to justify joint authorship. As usual, Xiaokai would hear nothing of it – he insisted on joint authorship with his usual grace, charm, generosity, and most of all stubborn persistence. In the end, though, bilateral stubbornness has led to the correct outcome. This is Xiaokai’s book, with my good fortune to be author of this Foreword, as well as Xiaokai’s continuing colleague and committed friend.

PREFACE

The core of classical mainstream economics represented by William Petty and Adam Smith was development economics. Classical development economics differed from neoclassical development economics in two aspects: it focused on development implications of the division of labor and it emphasized the role of the market (the “invisible hand”) in exploiting productivity gains from the division of labor. As shown in this textbook, inframarginal analysis of individuals’ networking decisions is essential for formalizing classical development economics. Here inframarginal analysis is the total cost–beneﬁt analysis across corner solutions in addition to the marginal analysis of each corner solution. If the optimum value of a decision variable takes on its upper or lower bound, the optimal decision is a corner solution. Formally, it relates to nonlinear programming, mixed integer programming, dynamic programming, the control theory, and other nonclassical mathematical programming. The ﬁrst decision that you have to make when you get into a university is to choose a major. If you choose economics as your major, you do not then attend chemistry and physics classes, but rather take classes in microeconomics, macroeconomics, and econometrics. Such a decision is called an inframarginal decision, since the values of decision variables discontinuously jump between zero and interior values as you shift between majors. After you have chosen a major, you allocate your limited time between the ﬁelds in this major. This type of resource allocation decision for a given major (or occupation) is called a marginal decision, since standard marginal analysis is applicable to it. The aggregate outcome of all students’ choices of majors in a university generates division of students among majors and ﬁelds, which is analogous to a structure of division of labor in society. But when Alfred Marshall formalized classical economics within a mathematical framework at the end of the nineteenth century, he had no knowledge of inframarginal analysis. He made an assumption of dichotomy between pure consumers’ decisions and ﬁrms’ decisions to avoid inframarginal analysis of corner solutions. Within the neoclassical framework, each pure consumer must buy all goods from the market and cannot choose her level of selfsufﬁciency or its reciprocal, level of specialization. Hence, the focus of economics shifted from inframarginal analysis of problems of economic development concerning how the degree of scarcity can be reduced by division of labor in society, to marginal analysis of problems of resource allocation for a given degree of scarcity. Neoclassical development economics departs, by following the neoclassical framework, from classical development economics. Hence, neoclassical development economics loses the central position that classical development economics occupied in the economics mainstream. Some neoclassical developmental economists also

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depart from classical development economics by their advocacy of state-planned industrialization and development. Since the 1950s, economists have applied inframarginal analysis to various decision problems. However, many economists still follow Marshall’s assumption of a dichotomy between pure consumers and ﬁrms, under which the corner solution is exceptional and the interior solution is the rule. Hence, the implications of formal inframarginal analysis for investigating effects of network size of division of labor on economic development could not be fully explored until the late 1970s. This text will show that if a Smithian framework is adopted, the interior solution is never optimal and corner solution is the rule rather than the exception. Hence, marginal analysis is not enough and inframarginal analysis is essential for exploring the implications of the division of labor for economic development. The recent renaissance of classical development economics not only revives the spirit of the classical development economics, but also provides new frameworks for inframarginal analysis of the network of division of labor. Hence it creates an opportunity for bringing development economics back to the core of modern mainstream economics. The new thinking of development economics is associated with the literature of the economics of property rights, transaction costs, and institutions; the literature of the “new economic history” school; the formal models of endogenous transaction costs; the formal models of high-development economics (general equilibrium models with economies of scale); endogenous growth models; and the literature of endogenous specialization. The formal general equilibrium models of division of labor and transaction costs also echo recent rethinking of development policies represented by Bhagwati, Krueger, Srinivasan, and the World Bank. The current text organizes the literatures under an overarching framework with emphasis on inframarginal analysis of the network of division of labor and related transaction costs. It seeks to simplify complex ideas and tie them together. The structuralist views of Lewis (1955) and Chenery et al. (1986), the neoclassical views of economic development, and many nonmainstream views, such as those of Alizadeh (1984), Bacha (1978), Emmanuel (1972), Frank (1995), Myrdal (1957), Nelson (1956), Palma (1978), Prebisch (1988), and Smith and Toye (1979), are reassessed here using inframarginal analysis and formal models. Despite the innovative structure of the text, standard topics on population (chapters 2, 5, 7, 11, 13), income distribution (chapters 3, 5, 6), human capital (chapters 14, 16), entrepreneurship (chapter 8), dual structure/structural changes (chapters 3, 5, 6, 12), industrialization (chapter 12), and urbanization (chapter 13) in development economics are covered by comparing new and old models. In addition, empirical evidence for or against the new and old models is reviewed (for instance in chapters 1, 2, 5, 7, 11, 12, 13, 14, 16). Since the main purpose of the text is to teach theories of development economics in a systematic and coherent way and to bring considerable analytic machinery to bear on important problems of economic development, it reviews empirical research rather than covering details of regressions. The coverage of empirical research is selective; for instance, a large part of recent empirical research on microeconomic development problems (see e.g. Case and Deaton, 1998, 1999a/b, and Deaton and Paxson, 1998a/b) is not covered in this text. This text can be used at two different levels. Since each chapter includes the descriptive intuition behind the formal models and mechanisms at work, with the aid of graphical illustrations, the text can be used for third- or fourth-year courses in development economics. The focus for an undergraduate course is on training in economic thinking. If the text is used for that purpose, questions for assignments and examinations can be chosen from those at the end of each chapter, and difﬁcult algebra in the text and exercises at the end of each chapter could then be skipped. The questions not only expose students to different ideas and controversies, they also include important readings from the documentation of economic history, classic pieces, empirical ﬁndings, and interesting debates. Teachers will ﬁnd that the graphs used in

P REFACE xxiii

the text to describe topological properties (the number of trade connections between individuals and the number of goods involved in the division of labor) of the evolution of division of labor in the Smithian models are much more intuitive than conventional demand and supply curves. Hence, if a teacher can use demand and supply curves to teach neoclassical development economics without mathematics, she will certainly feel more comfortable teaching materials in this text using graphs of the evolution of division of labor without mathematics. This text could also be used for a course in development economics at the graduate level. The focus for a graduate course is on formal basic training as well as on innovative, creative, and critical economic thinking. For basic training, students should pay more attention to duplication of major models in the text and work on the main exercises at the end of each chapter. One hour spent on duplicating the models is as effective as eight hours spent listening and reading. The formal training is characterized by strong accumulation effects. If each model covered in the lectures is duplicated and well understood, study will become increasingly easy. But if one of the major models cannot be duplicated or a lecture is missed out, study may become increasingly difﬁcult later on. For training in creative and critical thinking, students are asked to pay more attention to the trial-and-error process in designing models and in choosing one from many possible frameworks. Not only must all original ideas stand the tests of rigorous deduction, of logical consistency, and of empirical evidence, but we should also encourage insights that might be too sophisticated to be formalized by any available mathematical instruments. Questions and exercises at the end of each chapter include many good thesis topics for masters and Ph.D. programs. Free assistance can be obtained for such programs from the author upon request. You may contact the author at [email protected]. The website www.inframarginal.com provides updated information on research, teaching, and dissertations, contact information for economists in the ﬁeld, and details on conferences related to this text. This text is a response to increasing demand for a text and a survey from which the technical substance of the inframarginal analysis of economic development can be systematically learned. It covers many new research results in inframarginal analysis and compares it with the conventional marginal analysis of economic development. Some of the new research results are published here for the ﬁrst time. I hope that the reader will experience an exciting intellectual adventure and discover inframarginal analysis to be a bridge between mainstream economics and this era of networking and globalization. Many individuals and institutions contributed to this project. I am ﬁrst very grateful to my teachers at Princeton University: Hugo Sonneschein, who taught me the theory of general equilibrium; Edwin Mills, who taught me development economics and urban economics; Gene Grossman and Avinash Dixit, who taught me trade theory and new general equilibrium models with increasing returns; Gregory Chow, Whitney Newey, Angus Deaton, and Richard Quandt, who taught me econometrics; Joseph Stiglitz, Barry Nalebuff, and Sandy Grossman who taught me information economics and game theory; Alan Blinder and John Taylor who taught me macroeconomics; and William Baumol, Michael Katz, and Robert Willig who taught me industrial organization. I am also greatly indebted to my co-authors of various research papers which are covered in this text: Jeff Borland, Been-Lon Chen, Wen-Li Cheng, John Gallup, Ben Heijdra, Geoff Hogbin, Chien-fu Lin, Monchi Lio, Mong-Chun Liu, Pak-Wai Liu, Siang Ng, Yew-Kwang Ng, Katharina Pistor, Steven Radelet, Bob Rice, Jeff Sachs, He-Ling Shi, Guangzhen Sun, Jianguo Wang, Ian Wills, Kar-yiu Wong, Wing Thye Woo, Shuntian Yao, Dingsheng Zhang, Yiming Zhao, and Lin Zhou. In particular chapter 1 draws heavily on Sachs and Warner (1995a) and Sachs (1998), and chapter 2 draws heavily on Gallup and Sachs (1998). I appreciate that Gallup, Warner, and Sachs kindly allowed me to use their research results.

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I have beneﬁted immensely from comments and criticisms on research papers and books that relate to this text from Olivier Blanchard, Gary Becker, Avner Ben-Ner, Steven Cheung, Cyrus Chu, Eric van Damme, Herbert Dawid, Jürgen Eichberger, Karl Farmer, Robyn Frandson, John Gallup, Robert Gilles, Gene Grossman, Oliver Hart, Michael Kremer, Heinz Kurz, Lachie McGregor, Douglas North, Eric Maskin, Yingyi Qian, Lloyd Reynolds, Peter Ruys, Jeff Sachs, Andre Shleifer, Hugo Sonnenschein, Sherwin Rosen, Donald Smythe, Willy Spanjers, Guoqiang Tian, Yingjiang Wang, Andrew Warner, Chenggang Xu, Gang Yi, Weiying Zhang, and the participants at numerous seminars and conference sessions. Many students at Harvard University, Monash University, Peking University, the Chinese University of Hong Kong, University of Hong Kong, the National University of Taiwan, and the University of Louisville provided useful feedback on the teaching of the materials covered in this text. Special thanks go to Jeff Borland, Monchi Lio, Yingyi Qian, Sherwin Rosen, Mei Wen, and Julan Du for drawing several references cited in the text to my attention. Lijun Chen, Mei Wen, and Yiming Zhao have done an excellent job on research assistance related to this text. My gratitude also goes to Andrew Warner, the anonymous reviewers of the draft of this text for their helpful comments, and Blackwell’s editors. The ﬁnancial support for this project and related research from the Center for International Development at Harvard University, Australian Research Council, National Taiwan University, Institute of Economics of Academia Sinica, the National Sciences Council of the Republic of China, Guanghua School of Management of Peking University, and the Centre for Economic Research at Tilburg University is gratefully acknowledged. Last, but not least, without the love, patience, and strong support of my family, it would have been hard to complete this book. I hereby express my deepest love and thanks to Xiaojuan Wu, Xiaoxi, James, and Edward. Of course, any remaining errors are solely my own responsibility. Xiaokai Yang

NOTE ON THE TEXT Equations are numbered only when they are referred to in the text.

C HAPTER 1: I NTRODUCTION

INTRODUCTION

1.1

1

1

CLASSICAL DEVELOPMENT ECONOMICS AND CAPITALIST ECONOMIC DEVELOPMENT

The focus of classical mainstream economics, represented by William Petty, A. R. J. Turgot, Adam Smith, and others, is on the development implications of division of labor.1 In a sense, the core of classical mainstream economics is development economics. This core includes the Smith theorem: Division of labor is the mainspring of economic progress (1776, ch. 1 of bk. I), division of labor is dependent on the extent of the market (ch. 3 of bk. I), and the extent of the market is determined by the transportation condition (pp. 25–32). Also, Smith’s conjecture on the intrinsic relationship between specialization and the use of money (p. 37), his theory of capital according to which investment is a vehicle for increasing division of labor in roundabout production (p. 371), and his conjecture on the role of the invisible hand in coordinating the network of division of labor are part of this core. In addition, this core comprises Petty’s theory of urbanization according to which cities can promote the division of labor by reducing transaction costs (Petty, 1683, pp. 471–2), and Turgot’s conjecture on the relationship between the division of labor, the introduction of money, the extension of commerce, and the accumulation of capital (Turgot, 1766).2 We refer to this core of classical mainstream economics as classical development economics. The policy prescription of classical development economics is represented by this statement by Smith, which is consistent with Britain’s liberal policy regime in the seventeenth to nineteenth centuries, as well as with liberalization policy reforms in nineteenth-century western Europe:3 “Little else is requisite to carry a state to the highest degree of opulence from the lowest barbarism, but peace, easy taxes, and tolerable administration of justice; all the rest being brought about by the natural course of things” (cited in Jones, 1981, p. 235). We call the development experience that is associated with classical development economics capitalist economic development. Max Weber (1927), Rosenberg and Birdzell (1986), Braudel (1984), and North (1981) have stressed that capitalist economic development is a result of capitalist institutions. The capitalist institutions affect the level of division of labor and the related extent of the market via their effects on trading efﬁciency, while the level of division of labor and the extent of the market affect development performance, which in turn drives institutional changes. Also, the geographical and physical environment in western Europe and the north Atlantic were favorable for the evolution of institutions and division of labor. Many

2 C HAPTER 1: I NTRODUCTION

historians consider the driving force of the development of capitalist institutions as the absence of a single overarching political power in Europe and the rivalry between hostile sovereignties, which created the opportunity for social experiments with a great variety of institutions within a relatively short period of time. This rivalry also created great pressure for rulers to creatively mimic those institutions that enhance economic performance and, thereby, their power. Baechler (1976, p. 79) states: “Fundamental springs of capitalist expansion are, on the one hand, the coexistence of several political units within the same cultural whole and on the other, political pluralism which frees the economy.” McNeil (1974, p. 125) also indicates that “The political pluralism of early modern Europe was, I think, fundamental and distinctive. When all the rest of the civilized world reacted to the enhanced power cannon gave to a central authority by consolidating vast, imperial states, the effect in western and central Europe was to reinforce dozens of local sovereignties, each consciously competing with its neighbors both in peace and, most especially, in war. Such a political structure acted like a forced draft in a forge, fanning the ﬂames of rival ideologies and nurturing any spark of technical innovation that promised some advantage in the competition among states.” Hall (1987), Mokyr (1990), Jones (1981, pp. 226–35), Braudel (1984, pp. 128–9), Weber (quoted in MacFarlane, 1988, pp. 186–7), and Laslett (1988, p. 235) also support this view. Baechler (1976, pp. 77–113) indicates that the probability that such a pluralist geopolitical structure could be sustained for a long period of time in the absence of any political hegemonism is very low, since all power tends toward the absolute. Several explanations for the occurrence of this improbable phenomenon are proposed. One is to attribute it to particular geographical conditions of western Europe and the Mediterranean that are favorable for long-distance trade between city-states and unfavorable for a uniﬁcation war (Baechler, 1976 and Mokyr, 1990, 1993). Around the Mediterranean and the English Channel, a great portion of highly populous areas were either coastal or island. The favorable conditions for trade were crucial for the emergence and evolution of capitalist institutions ( Jones, 1981, p. 233). This pluralism in an international arena ensured that several cultures and sovereignties could challenge each other on a nearly equal footing. In contrast, east Asian geopolitical structures ensured the hegemonism of Chinese culture prior to the invasion by Occidental cultures. No other culture could challenge it. The Japanese, Mongolians, and Manchurians were conquered culturally by the Chinese, regardless of whether they were subordinated to, or were rulers of, China. China is a mainland country, so it is easy to win a uniﬁcation war and very expensive for inland trade. Hence, the variety of institutional experiments in east Asia was much smaller than that in western Europe until Japan’s Meiji Restoration. In particular, Britain’s geographic conditions ensured that she could avoid war with other countries, had lower defense expenses, a transportation advantage for trade; the evolution of its unique Anglo-Saxon culture and common law tradition. The pursuit of riches was legitimated under the prevailing ideology, so that talents were diverted from military, religious, and bureaucratic careers to business activities prior to and during the Industrial Revolution (Baechler, 1976, pp. 93–5). Competition among crown, local, and Church courts in Britain and amongst the state, the Church, and the decentralized feudal system also probably were conducive to the checks and balances on the top of the political arena in the western Europe (Baechler, 1976, pp. 78–80). Another unique feature of western Europe was the development of free cities prior to the formation of nation-states. The free cities and related international trade became the cradle of capitalist institutions and economic development. In contrast, cities were princely fortresses in ancient Asia. The particular conditions nurtured the political and legal institutions in Britain in the eighteenth century, then the institutions spread to the rest of western Europe via creative imitations and revisions in the nineteenth century. These fundamental institutions provided

C HAPTER 1: I NTRODUCTION 3

conditions for the emergence of many important economic institutions, which signiﬁcantly reduced transaction costs and therefore promoted the evolution of division of labor. Structural changes caused by this evolution are called industrialization, which includes increases in the income share of industrial output and in investment rate and saving rate (Lewis, 1955, Chenery, 1979, Kaldor, 1957, Kuznets, 1966). According to classical development economics, the increase in income share of industrial output is a transition from a self-sufﬁcient society, where no division between agriculture and industry exists and each individual produces all industrial and agricultural goods for herself, to a high level of division of labor between professional farmers and manufacturers (Lewis, 1954 and Ranis, 1988, p. 88). Increases in the income share of the sector producing producer goods and in related investment imply the development of division of labor in roundabout production, which endogenously generates technical progress. This industrialization process increases aggregate productivity and individuals’ utilities (real income). The development performance then, in turn, affects the evolution of ideology and related institutions in a competitive arena between rival sovereignties. Hence, capitalist economic development can be analyzed at ﬁve levels. At ﬁrst, we consider geopolitical structure, such as the absence of an overarching political power in Europe. This structure determines the evolution of ideology, norms, moral codes, and political and legal institutions at the second level, which determines the evolution of commercial institutions, industrial organization, and business practices at the third level, which determines the evolution of division of labor and related economic structure at the fourth level, which determines aggregate productivity and welfare at the ﬁfth level, which in turn affects the evolution of ideology, norms, and institutions (North, 1994). The second and third levels of analysis (institutions) have received substantial attention from the literature of property rights and the “new school of economic history.” According to the literature, the evolution of capitalist institutions has the following features.4 1) The government’s credible commitment to constitutional order with due process emerged from the signiﬁcant variety of institutional experiments in western Europe. The legal basis for private property rights and state enforcement of private contracts based on rational procedure emerged from this constitutional order. Also, predictable laws and a professional bureaucratic administration were conducive to the reduction of transaction costs. Under this credible commitment mechanism, the rational state not only provided many services, such as standard measures of weight and distance, currency, and infrastructure (the highway system, the census, etc.), but also the state itself was governed by law (constitutional and public law). Automatic registration of private ﬁrms replaced the approval system and government monopoly for enterprise. The licensing system has not been subject to state opportunism since free association became a legitimate ideology and practise in western Europe in the nineteenth century. State taxation power became subject to the approval of representatives, and the king’s coffer was separated from the Bank of England (Huang, 1991 and Pipe, 1999). These new institutions effectively restricted state opportunism. Also, Equity Law created a mechanism under which new cases could override outdated cases in the presence of justice, which made common law very adaptive to a changing world (Huang, 1991). This very adaptive legal system spontaneously created many rules to protect private property rights, in particular rights to residual returns and control of ﬁrms, business names, and brands. According to Mokyr (1990, 1993), the legal protection of residual rights was more important than patent laws for technical and managerial inventions and innovation. This institutional evolution in Britain and western Europe in the seventeenth to nineteenth centuries created an opportunity for solving the paradox of state power: how to tame the Leviathan. Legitimate and powerful state violence could then be used to protect individuals’ rights via checks and balances at the top level of the political arena (MacFarlane, 1988, pp. 189–91).5

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2) A special government policy regime of laissez faire and many government institutional innovations emerged in Britain after the Glorious Revolution and were later mimicked by other western European countries. Under this regime, mercantilist industrial policies, interventionist trade policy, and medieval regulations were abolished. This is represented by unilateral free trade in the UK in 1846, and by the 1860 Cobden Chevalier Treaty (Sachs and Warner, 1995a). Many innovative government institutions, such as the central bank system (for instance, the Bank of England as the ﬁrst central bank, 1694), bankruptcy laws, the postal system, the government library system, the public school system, the publicly funded highway system, and national galleries and museums emerged from the rivalry between national governments. The tradition of free migration in western Europe also created great pressure for enhancing government’s capacity for managing public affairs. 3) In this institutional environment, a set of market institutions emerged and developed. Private contracting for labor, land, capital, and other properties gradually substituted for nonmarket institutions. For instance, the labor market substituted for serfdom, slavery, and corvée. Private ownership of land and related markets substituted for, hereditary, non-alienable, and patrimonial land relationships, common ﬁelds, and estates with servile obligations. The capital market took the place of government’s predatory, monopolistic, and interventionist role in money lending (for instance, the repeal of usury laws in Britain). Also, the market for technology and intellectual property superceded the government monopoly on technology and its infringement upon intellectual property rights (for instance, the Statute of Monopolies of 1624 in Britain). Many commercial institutional innovations emerged from this liberal institutional environment. They include modern double-entry accounting and bookkeeping, commercial instruments such as loans, stock shares, mortgages, bills of exchange, deeds of trust, insurance, power of attorney, franchising, and joint stock companies with limited liability. Capitalist institutions spread on a global scale in the nineteenth century. The ﬁrst episode of global capitalism, of course, came about as much through the instruments of violent conquest and colonial rule as through economic reform and development of international institutions. Starting around 1840, western European powers wielded their superior industrial, and hence military, power to challenge traditional societies around the world. France began to colonize north Africa in the 1830s and 1840s; Britain forced its way into China in the Opium Wars, 1839–42; Britain and France defeated Russia in the Crimean War, 1854–6; and Britain completed the conquest of India in 1857. Among the populous societies of Asia and the Near East, only Japan was able to mobilize social and political institutions to support market reforms, implementing the ﬁrst “shock therapy” reforms following the 1868 Meiji Restoration.6 By the 1870s, a global market had begun to take shape along the following economic lines. Western Europe and the United States constituted the main industrial powers. A major push toward industrialization, especially in east-central Europe, followed the uniﬁcation of Germany. Russia began a period of rapid industrialization, partly through the building of foreign-ﬁnanced railways across Russian Eurasia. Japan had begun its dramatic opening to the world economy through the adoption of capitalist institutions and free trade. Note that early Japanese industrialization took place entirely under free trade, since the dominant Western powers imposed low Japanese tariff levels through “unequal treaties” that lasted until the end of the century. Latin America, after a half century of post-independence upheaval, ﬁnally settled into market-based, export-led growth in the 1870s, based on raw materials exports and capital imports (primarily for railroad construction). Africa, which lagged farthest behind, was gobbled up by the western European powers in an orgy of imperialist competition that reached its height between 1880 and 1910. Trade barriers remained low among these economies for several decades, from the 1860s to 1914.7 As in the late twentieth century, the emergence of the ﬁrst global capitalist system was based on the interaction of technology and economic institutions. Long-distance transport and

C HAPTER 1: I NTRODUCTION 5

communications achieved breakthroughs similar to those in the present (Headrick, 1981). The Suez Canal, completed in 1869, and the Panama Canal, completed in 1914, dramatically cut international shipping times, as did the progressive development of faster and larger steamships from the 1840s. New railways in India, Russia, the United States, and Latin America, often built with foreign ﬁnance, opened vast, fertile territories for settlement and economic development. The spread of telegraph lines and transoceanic cables from the 1850s linked the world at electronic speed. Military innovations, particularly the breach-loading riﬂe introduced in the 1840s, combined with mass production made possible by industrialization, decisively shifted the military advantage to Europe. Medical advances, particularly the use of quinine as a preventative against malaria, played a pivotal role in the spread of European settlements, domination, and investment, especially in Africa. Without a doubt, these technological breakthroughs were as revolutionary in underpinning the emerging global system as those of our own age. On the economic level, key institutions similarly spread on a global scale. International gold and silver standards became nearly universal after the 1870s, eventually embracing North and South America, Europe, Russia, Japan, and China, as well as other European colonies and independent countries. By 1908, roughly 89 percent of the world’s population lived in countries with convertible currencies under the gold or silver standard.8 Basic legal institutions, such as business and commercial codes, were widely adopted. These were based on European models, mainly the Napoleonic Code, which absorbed some important features of Common Law. New multilateral institutions were established, such as the Universal Postal Union in 1878. The system was highly integrative, as in the present. A network of bilateral trade treaties kept protectionism in check in most countries (the United States and Russia, where tariff rates were relatively high, being the exceptions). Nations as diverse as Argentina and Russia struggled to adjust their economic policies, and especially their ﬁnancial policies, to attract foreign investment, particularly for railway building. The adoption of a stable currency tied to gold was seen as a key step in the strategy of international integration. In Russia, Count Witte recalled how he outmaneuvered the conservative tsarist court to introduce the gold standard at the end of the nineteenth century (Owen, 1997, pp. 15–16). In Latin America, liberal market regimes stabilized under both democratic (Argentina and Chile) and authoritarian (Brazil and Mexico) political regimes. In all four cases, overall growth of GDP and exports was very rapid, indeed historically unprecedented. India similarly enjoyed rapid export growth between 1870 and 1914 under British rule. In a series of important papers, Jeffrey Williamson and his collaborators have shown that the open international system at the end of the nineteenth century produced an era of economic convergence ( Jeffrey Williamson, 1992, 1993, and O’Rourke and Williamson, 1994). Peripheral countries in Europe, such as Ireland and the Scandinavian countries, experienced rapid growth that narrowed the gap in real wages with the more advanced countries, the United Kingdom, France, and Germany. Former European colonies in Latin America and the South Paciﬁc (Australia and New Zealand) similarly achieved convergent growth rates based on export-led growth. In a massive study of long-term growth in 41 developing countries, Lloyd Reynolds similarly found that the open international economy of 1850–1914 was crucial in promoting the onset of rapid economic growth in much of the developing world outside of Europe and North America (Reynolds, 1985). Reynolds noted that “politics apart, the main factor determining the timing of turning points has been a country’s ability to participate effectively in the trade opportunities opened by expansion of the world economy” (Reynolds, 1985). He then pointed out the wide range of countries that were indeed able to avail themselves of the burgeoning trade opportunities, including almost all of Latin America (with the exception of Venezuela); much of Asia, including but not limited to Ceylon, Burma, Malaya, Thailand, Japan, Taiwan,

6 C HAPTER 1: I NTRODUCTION

and the Philippines; and parts of Africa, including Algeria, Nigeria, Ghana, the Ivory Coast, Kenya, Uganda, Tanganyika, and Southern Rhodesia (Reynolds, 1985, pp. 34–5). Capitalist economic development has spread mainly as capitalist institutions have spread around the world from their home base in western Europe. This diffusion process is driven by challenges and competition between different societies, which might be associated with war, conquest, and colonization. Hence, the spread of capitalist institutions could be either a creative imitation process or a painful imposition process.

1.2

THE BREAKDOWN OF THE FIRST GLOBAL CAPITALIST SYSTEM AND NEOCLASSICAL DEVELOPMENT ECONOMICS

Keynes (1971) rightly intuited in 1919 that the Humpty Dumpty of world markets and shared institutions would not soon be put back together in the harsh peace that followed the First World War. Indeed, the war and its aftermath laid waste to the emergent global capitalist system for more than half a century. The ﬁnancial underpinnings of the late nineteenthcentury liberal order were not reestablished. British dominance in the international ﬁnancial system was ended by the Great War, and neither US leadership nor international cooperation took its place (Kindleberger, 1973, Eichengreen and Flandreau, 1994). Financial instability and the failure of the gold standard rocked the 1920s and contributed to the Great Depression of the 1930s. The export-led growth of the primary producers in Latin America and elsewhere was undermined by low and unstable commodities prices in the 1920s, and then was devastated by the Great Depression, which brought about the utter collapse of the terms of trade, intense protectionism in Europe and the United States, and the end of capital inﬂows. Political upheaval accompanied economic and military upheaval. Most important was the Bolshevik Revolution in Russia in 1917, and the emergence of fascist states in Italy and Germany in the 1920s and 1930s, respectively. In Latin America, the traditional political power of the landholders and mine owners was undermined by the collapse in the terms of trade. The free trade regimes of the late nineteenth century were replaced by a revolutionary regime in Mexico and authoritarian regimes in Argentina, Brazil, and Chile that were heavily inﬂuenced by the state planning of the communist and fascist regimes in the Soviet Union and Europe.9 Throughout the world, state planning, authoritarianism, and militarism competed with limited government and market-based economies. Whether or not economic theory offered insights and predictions about these alternative strategies, political leaders felt compelled to push for new and radical experimentation. Two events prior to the Second World War strengthened the tendency of economics to move away from classical development economics. One is the Great Depression in 1930; the other is the relatively successful industrialization of the Soviet Union in the 1930s. Krueger (1995) indicates that the two events and Keynes’ advocacy for state intervention and investment fundamentalism were crucial for the formation of the spirit of neoclassical development economics. According to an inframarginal analysis of the trade-off between the positive network effect of division of labor on aggregate productivity and the reliability of a larger network of transactions in chapter 10, as transaction conditions are improved and the risk of coordination failure for each transaction declines, the beneﬁt of a larger network of division of labor outweighs the increased aggregate transaction risk. Hence, the equilibrium network size of division of labor and the equilibrium aggregate risk of coordination failure of the whole network increase side by side. This implies, on the one hand, a greater degree of industrialization and higher aggregate productivity, and on the other hand, greater likelihood of a coordination failure in the larger

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network of division of labor. Hence, to a certain degree, the Great Depression is a “crisis of success” and a sort of cost of successful industrialization and globalization that we had to pay. This is similar to choosing a higher risk of being killed when we choose to drive on a freeway. The decision is rational and efﬁcient as long as the expected beneﬁt from doing so outweighs the higher risk of being injured or killed in a trafﬁc accident. If people really understood this mechanism for economic development, they would not turn to communism and distrust of the market mechanism when such an event takes place.10 Also, as the cobweb model in chapter 19 will show, when globalization and liberalization develop, the sensitivity of the feedback mechanism in response to a coordination failure will increase. The efﬁcient balance of the trade-off between stability and sensitivity of the market feedback mechanism implies that the stability of the larger network of division of labor will decrease and the risk of devastating crisis will increase. When Keynes did not understand the trade-off, he suggested we go back to the autarchic state to avoid the risk of a great crisis.11 We would conjecture that if development economics had been better able to explain the mechanism behind the Great Depression, the thinking in the 1950s on state-planned development would not have been as inﬂuential.12 In chapter 10 we cover general equilibrium models that explain the development mechanism with concurrent increases in aggregate productivity and in aggregate risk for coordination failure. The complicated trade-offs among moral hazard, transaction costs, and the positive effect of insurance on the reliability of the network of division of labor are investigated in connection with the recent Asian ﬁnancial crisis. These models formalize Sachs’ (1998) seemingly paradoxical notion of a “crisis of success.” They show that as transaction conditions are improved, the equilibrium network of division of labor expands and the efﬁcient aggregate risk for coordination failure increases because of trade-offs among economies of division of labor, reliability of the network of transactions, and transaction costs. Insurance can be used to enlarge the scope for trading-off one against the other conﬂicting forces, at the cost of increasing moral hazard. Hence, there is a trade-off between the positive effect of insurance on the reliability of the network of division of labor and the distortions caused by moral hazard. The complicated trade-offs imply that simply reducing moral hazard or following a simple slogan of liberalization will not necessarily ensure the efﬁcient balance of these trade-offs. Repeating the overreaction to the Great Depression by resorting to communism, central planning, protectionism, or interventionism is also not the right way out. An inframarginal analysis of the general equilibrium mechanism of the crisis in chapter 10 will provide a balanced comprehension of new development phenomena generated by globalization. The second event that reversed the tide came from the industrialization experience of the Soviet Union in the 1930s and that of China in the 1950s. This is a special pattern of stateplanned, big-push industrialization. The major features of this pattern are as follows.13 China and the Soviet Union mimicked successful patterns of industrialization in developed capitalist economies, such as a high saving rate, an increasing income share of heavy industry producing capital goods, the Taylor scientiﬁc management approach, mass production, standardization, comprehensive investment programs, and internal organizational patterns of large capitalist corporations. However, the mimicry was not associated with a market and private property rights, as happened in Taiwan and South Korea in the 1960s and 1970s. Instead, the imitation was conducted by the central planning system through infringements upon the private property rights which created the industrialization patterns in capitalist economies. The precondition for the success of state-planned big-push industrialization is to mimic whatever succeeds in a capitalist economy. Many economists predicted that such a system could not succeed, since it destroyed the incentive mechanism that created the successful industrialization pattern (see, for instance, von Mises, 1922). But they were surprised by the relatively successful industrialization in the Soviet Union in the 1930s.

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The short-run success impressed the leaders of many newly independent countries, who were busy with the task of state building. In particular, they believed that in a reverse engineering of capitalist institutions, they could repeat industrialization by mimicking capitalist industrial patterns and by ignoring fundamental capitalist institutions, including the legal system, constitutional order, behavior norms, and moral codes. Mainstream thinking on economic development converted from liberalism to the convictions of state-planned economic development and industrialization. Since classical development economics did not establish a sound theoretical foundation, economists could not really comprehend the mechanism of modern economic development and the real reason for the Soviet Union’s short-run success. They were easily converted to ideas of state-planned industrialization. Despite the short-run success of Sovietstyle big-push industrialization, the fall of the Soviet Union announced the long-run failure of state-planned economic development, compared to Hong Kong’s pattern of market-led industrialization, which is a modern version of Britain’s development pattern. As Britain’s original capitalist development experience spread to Europe in the nineteenth century, Hong Kong’s capitalist development experience was followed by Taiwan, South Korea, Thailand, and China. As Sachs (1996) suggests, the fatal long-run negative effects of Soviet-style industrialization will outweigh its short-run positive effect on economic development once the potential for mimicking has been exhausted. The disintegration of the Soviet Union, along with reforms in China and other developing countries, symbolize a shift in development policy regime, which is associated with a shift of development economics back to its classical origin. The ﬁnal support for a move away from classical development economics came from the idea that a great variety of institutional experiments might be helpful for discovering the institutions that are most conducive to economic development. Keynes (e.g. 1933) stressed that countries simply demanded the right to experiment with new economic models, since the old ones no longer commanded respect and assent. He joined the chorus for experimentation, vividly exemplifying the end of intellectual faith in global capitalism by the 1930s. His point was that there is no prospect for the next generation of a uniformity of economic systems throughout the world, such as existed, broadly speaking, during the nineteenth century; that we all need to be as free as possible of interference from economic changes elsewhere in order to make out own favorite experiments towards the ideal social republic of the future; and that a deliberate movement towards greater national self-sufﬁciency and economic isolation would make our task easier, insofar as it can be accomplished without excessive economic cost (Keynes, 1933, p. 241). This line of thinking is supported by documentation of the fact that experiments with a more active government role and different institutions in the US and on the European continent generated growth performance superior to Britain’s in the second half of the nineteenth century (see Craft, 1997).14 In response to these events, the term “development economics” was coined after the Second World War, when it became a ﬁeld of applied economics relevant only to less-developed or underdeveloped countries.15 We call this version of development economics neoclassical development economics; it pays more attention to the fourth and ﬁfth levels of analysis of development (structural changes, such as an increase in income share of industrial output, and productivity progress). Neoclassical development economics rejects the universal applicability of classical development economics and the capitalist development experience. It does not pay much attention to the intimate relationships between the evolution of division of labor and the institutional evolution that affects transaction costs, and between the evolution of division of labor and structural changes. It is characterized by the following features: the belief in protectionist trade policy (import substitution) to provide shelter for infant industries and industrialization; distrust of private entrepreneurship, the market, and related international trade; speciﬁc and comprehensive government industrial policies and investment programs; the belief that government,

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as a paternalistic benevolent planner, and state-owned ﬁrms should take the leading role in development (state-planned industrialization); pessimism that exports from developing countries could grow (the theories justifying worries about a shortage of foreign investment and a shortage of foreign exchange); investment fundamentalism (i.e., a high saving rate is the engine of growth); speciﬁc and sometime comprehensive planned targets for development;16 urban-biased price controls and other interventionist policies; marginal analysis; and partial equilibrium or disequilibrium analysis (see Krueger, 1995, 1997 and Behrman and Srinivasan, 1995 for a critical assessment of development strategies). We call economic development guided by neoclassical development economics state-planned economic development. The shift from capitalist economic development to state-planned development was associated with the shift of development economics from the core of mainstream economics to its periphery. The latter shift started with Alfred Marshall (1890). Chapters 8–12 of book IV in Marshall’s keystone text are full of insights into the development implications of division of labor. He described the network of division of labor as an economic organism. Unfortunately, Marshall could not formalize his insights into development economics in a mathematical framework. This formalization must specify an individual’s decision in choosing her occupation and her level of specialization. Choosing a professional occupation is a yes-or-no decision. If you choose economics as your major during your college education, you do not go to classes in chemistry and physics; you go to classes in micro- and macroeconomics and econometrics. To say “yes” to a major and say “no” to other majors is an inframarginal decision, in the sense that decision variables discontinuously jump between zero and a positive value as one shifts between majors. For a given major which you have chosen, you compare the relative marginal cost and relative marginal beneﬁt between two ﬁelds to choose the optimum allocation of your limited time between different ﬁelds in the major that you have chosen. This is called a marginal decision. In terms of mathematics, marginal analysis is classical mathematical programming, and inframarginal analysis is associated with linear and nonlinear programming and other kinds of nonclassical mathematical programming. Inframarginal analysis is a total beneﬁt–cost analysis across corner and interior solutions, in addition to marginal analysis of each corner and interior solution.17 When you compare your life with the lives of secondary-school classmates who currently specialize in other occupations, you can see that an inframarginal decision is often more important than a marginal decision. Inframarginal analysis is essential for formalizing classical development economics. But Marshall did not know how to handle inframarginal analysis when he tried to formalize classical mainstream economics within a mathematical framework. Hence, it is not surprising that Marshall could not formalize his insights into classical development economics within a mathematical framework. In order to get around the corner solution, he made the very unrealistic assumption that society is divided between pure consumers, who do not make production decisions, and ﬁrms, which are exogenously given. This dichotomy, together with the assumptions of a quasi-concave utility function and a convex production set, ensure that interior solutions may occur in equilibrium.18 Then, marginal analysis of interior solutions can work. Within this neoclassical framework of marginal analysis, pure consumers have to buy all goods from the exogenously given market and ﬁrms, and cannot choose their level of self-sufﬁciency or its reciprocal, the level of specialization. Thus the focus has shifted from the development implications of division of labor to marginal analysis of demand and supply. Marginal analysis cannot be used to investigate individuals’ decisions in choosing their occupation patterns and levels of specialization. It cannot explain the emergence and evolution of markets as a result of the evolution of division of labor. The fatal ﬂaw in this framework is that the equilibrium and Pareto optimum allocation of resources are always associated with an exogenously given production possibility frontier (PPF).

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Hence, we cannot use this framework to address the classical question of economic development: why aggregate productivity can be increased by an increase in the level of division of labor in the absence of changes in production functions and endowments, and how the invisible hand coordinates division of labor to promote economic development. Since it cannot predict the emergence and evolution of markets, it is not applicable to studies of economic development and a decrease of the degree of scarcity. Marshall was aware of the fatal ﬂaw in neoclassical marginal analysis of demand and supply. He suggested the use of the concept of external economies of scale to describe the effects of social division of labor on economic development. However, Allyn Young (1928, p. 533) argued that use of a notion of large-scale production misses the phenomenon of economies of division of labor. He emphasized Smith’s classical general equilibrium view of the network of division of labor: “The mechanism of increasing returns is not to be discerned adequately by observing the effects of variations in the size of an individual ﬁrm or of a particular industry, for the progressive division of labor and specialization of industries is an essential part of the process by which increasing returns are realized. What is required is that industrial operations be seen as an interrelated whole” (p. 539). However, Marshall’s formalization of marginal analysis of demand and supply established the neoclassical economic mainstream in the following sense. Marshall’s mathematical structure of marginalism gives the teaching of economics a well-organized structure. Within this structure, not only can different generations of economists and students share a common dictionary, but teachers can also set up good questions and exercises in classrooms and in examinations for which unique, correct answers are expected. What teachers demonstrate on the blackboard can be exactly duplicated by many students. This common mainstream facilitates division of labor between different generations of economists and between different ﬁelds of economics. Unfortunately, the neoclassical mainstream does not carry the core of classical mainstream thinking on the development implications of division of labor. As an unexpected consequence of Marshall’s success in formalizing marginal analysis of demand and supply, the core of classical economics concerning economic development has been forgotten. As indicated by Young (1928, pp. 538–40), the “possibility of economic progress” can not be fully understood without this core. The failure of the Soviet-style experiment with the socialist system shows that it is impossible to have successful social experiments if the rights for experimentation are monopolized by a totalitarian government and if individuals have no rights to experiment with various institutions via voluntary trade of property rights in the free market and under a fair constitutional order. The conviction that less-developed countries can catch up by mimicking the legal and economic systems of capitalist developed countries in the absence of a constitutional order was challenged by the defeat of Nazi Germany and Japan in the Second World War. It has been challenged again by the transition of Taiwan, South Korea, and other Asian countries from an authoritarian regime to democracy.

1.3

A RETURN TO CLASSICAL DEVELOPMENT ECONOMICS

There were scattered efforts to keep classical development economics alive when it shifted from liberalism to advocacy for state-planned development. Rosen (1983, p. 44) suggests that Young (1928) was “the zenith of the analysis of the connection between specialization and economic development.” Young criticized technological fundamentalism, which claimed that exogenous technological progress was the engine of economic development, and investment fundamentalism, which claimed an if-and-only-if positive relationship between current saving and future productivity. He considered increases in per capita capital as increases in division of

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labor in roundabout production. This view of capital is consistent with Smith’s classical view of investment, that investment is a vehicle for increasing division of labor in roundabout production (Smith, 1776, p. 371). According to Young and Smith, society’s capacity to create and absorb new knowledge and to invent new technology is determined by the extent of the market, which is in turn determined by the level of division of labor. Marshall (1890, p. 256) also attributed the invention of the steam engine by Boulton and Watt to a deep division of labor in inventing activities. Young proposed the Young theorem: “The securing of increasing returns depends on the progressive division of labor”; “Not only the division of labor depends upon the extent of the market, but the extent of the market also depends upon the division of labor”; “Demand and supply are two sides of the division of labor” (this is also known as the reciprocal law of demand). The Young theorem implies that, in the absence of a sufﬁciently high level of division of labor and a related sufﬁciently extensive market, not only can new technology not be invented but also, even if it were invented, it would be a commercially nonviable luxury. Houthakker (1956) formalizes Smith’s concept of endogenous absolute advantage using a graph. He shows that this concept might be more general than Ricardo’s concept of exogenous comparative advantage, and that the trade-off between economies of specialization and transaction costs may be used to explain the endogenous progress of aggregate productivity. But as Stigler (1976, pp. 1209–10) notes, “The last of Smith’s regrettable failures is one for which he is overwhelmingly famous – the division of labor. How can it be that the famous opening chapters of his book, and the pin factory he gave immortality, can be considered a failure? Are they not cited as often as any passages in all economics? Indeed, over the generations they are. The failure is different: almost no one used or now uses the theory of division of labor, for the excellent reason that there is scarcely such a theory . . . there is no standard, operable theory to describe what Smith argued to be the mainspring of economic progress. Smith gave the division of labor an immensely convincing presentation – it seems to me as persuasive a case for the power of specialization today as it appeared to Smith. Yet there is no evidence, so far as I know, of any serious advance in the theory of the subject since his time, and specialization is not an integral part of the modern theory of production.” The scattered efforts to keep classical development economics alive gradually became an increasingly more inﬂuential ﬂow of thought. Several separate literatures contributed to this development. First, the literature on the economics of property rights, transaction costs, and institutions, represented by Coase, pioneered the renaissance of classical development economics. The literature of new school of economic history, represented by North, and the literature of constitutional economics and new political economics, represented by Buchanan, pushed this line of thinking further. The literature of formal models of transaction costs and contracts then consolidated the position of this research line in mainstream economics. Second, criticisms of state-planned development since the 1980s by World Bank and prominent development economists, such as Krueger and Srinivasan, put this tendency into policy practice.19 Finally, a recent surge in the literature of general equilibrium models of high development economics, represented by Fujita, Krugman, Venables, Murphy, Shleifer, and Vishny, the literature of endogenous growth, represented by Aghion and Howitt, Lucas, Grossman and Helpman, and Romer, and the literature of endogenous specialization, represented by Becker, Murphy, Rosen, and Yang, provides sophisticated technical vehicles for formalizing classical development economics. The main purpose of this text is to systematically cover all of the new literatures that resurrect classical development economics in a modern body of formalism. We call the synthesis of the new literatures new development economics. In what follows, we brieﬂy outline the new literatures one by one. A group of economists who study the economics of property rights, transaction costs, and institutions consider their theories as the inheritor of classical development economics. They

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are very critical of neoclassical development economics. Among them, Coase (1946, 1960) and Buchanan and Stubblebine (1962) have proposed the notion of inframarginal analysis.20 Cheung (1970, 1983), Coase (1937, 1960), and Barzel (1982, 1985) apply this inframarginal analysis to criticism of Pigou’s marginal analysis of externality and public goods. Their theory of the endogenous degree of externality suggests that this degree is determined by the efﬁcient tradeoff between transaction costs in specifying and enforcing property rights, and the distortions caused by inaccurate speciﬁcation and enforcement. The theory is later formalized by models of Holmstrom and Milgrom (1994), Milgrom and Roberts (1992), and Yang and Wills (1990) in the literature of endogenous externality. In particular, Yang and Ng (1993) and Lio (1996) explore the intimate relationship between distortions, transaction costs, aggregate productivity, and the level of division of labor. Many models of the principal–agent relationship, general equilibrium models with transaction costs and endogenous specialization, and game models with strategic interactions have formalized ideas about property rights, transaction costs, contracts, and institutions. Milgrom and Roberts (1992), Hart (1995), Bolton and Scharfstein (1998), Gibbons (1998), Holmstrom and Roberts (1998), Maskin and Xu (1999), and Yang and S. Ng (1998) have provided reviews of the literatures. Also, the new school of economic history represented by North (1981, 1990), Mokyr (1990, 1993), and others has echoed the new development of the economics of property rights, transaction costs, and institutions. It shows that the development experience of eighteenthand nineteenth-century Britain and western Europe, and the classical thinking of economic development, are very relevant to currently developing countries. According to exponents of this approach, impediments to economic development consist of various transaction costs that are caused by state opportunism and deﬁcient institutions. In particular, North spells out the intimate relationship between the evolution of division of labor, transaction costs, institutions, and economic development. Recently, many general equilibrium models of endogenous specialization and transaction costs have formalized ideas proposed by the new school of economic history. We shall cover this line of rethinking of development economics, comprising the literature of endogenous transaction costs caused by opportunism and the models formalizing the ideas of the new school of economic history, in Part III.21 Even if the new literatures can be dismissed as the voices of those who are outside the ﬁeld of development economics, the critique of neoclassical development economics by policymakers, represented by the World Bank (1996, 1997) and by the prominent development economists Krueger (1995, 1997) and Behrman and Srinivasan (1995), can hardly be ignored. According to these critics, governments’ predatory and expropriative policies, their noncredible commitment to constitutional order, their distrust of the market (domestic as well as international), state opportunism that takes economic development as a hostage of the vested interests of the privileged class, rather than market failure, are real obstacles for economic development. More precisely, a great deal of market failure in developing countries is indeed caused by state opportunism and the absence of constitutional order (Sachs and Pistor, 1997 and Sachs and Woo, 1999). Again, their new policy prescriptions are quite similar to those suggested by the successful development experience of eighteenth-century Britain and nineteenth-century western Europe and advocated by Smith and other classical development economists. The distinctive feature of our era is that capitalist institutions have spread to virtually all of the world for the ﬁrst time in history. In addition, the new political economics, represented by Buchanan (1991), develops the research on the effects of constitutional rules on rent-seeking and state opportunism, which affect economic development in the developed countries. This literature shows that the political-economic mechanism dictating the evolution of constitutional rules is much more important than the political-economic mechanism that determines policy-making under given constitutional rules.

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Some ideas in the rethinking of development policies and in the literature of new political economics have been formalized by models of the commitment game (surveyed in Maskin and Xu, 1999) and other game models, which will be covered later in this text. Development economics has come full circle. This circle suggests that if we did not really understand the development mechanism underlying the early successful development experience of Britain and western Europe along with new development phenomena such as the Great Depression, previous mistakes will be repeated again and again and useful lessons cannot be exploited. Although many economists since the 1950s have become familiar with the technical substance of inframarginal analysis (nonlinear programming), which is essential for formalizing classical development economics, economists did not apply the new tools to formalization until the end of the 1970s. Since then, three literatures have stimulated the rethinking of development economics. They provide the technical substance for formalizing classical development economics. All three research lines feature general equilibrium analysis of the network of division of labor. This text will cover all three of the lines of rethinking and synthesize them with the above three literature areas (economics of property rights and transaction costs, the new school of economic history, and studies of liberal reforms and political economy). In chapter 3, inframarginal analysis is applied to the Ricardian model and the Heckscher– Ohlin model. It is shown that equilibrium aggregate productivity can endogenously increase as a result of the evolution of the network of division of labor. This inframarginal analysis of the Ricardian model and the Heckscher–Ohlin model identiﬁes a general equilibrium mechanism of economic development. The equilibrium and efﬁcient aggregate productivity are not on the PPF if the transaction cost coefﬁcient for a unit of goods traded is very large. As transaction conditions are improved, the equilibrium network of division of labor expands and aggregate productivity becomes closer to the PPF. The interesting feature of this model is that the equilibrium aggregate productivity increases as the equilibrium network of division of labor and the related extent of the market expand, even if economies of scale are absent. This type of increasing returns to a larger network of division of labor in the absence of economies of scale is called by Young (1928) “social increasing returns,” by Buchanan (1994) “generalized increasing returns,” and by Rosen (1978) “superadditivity.” Also, this general equilibrium mechanism for economic development implies that aggregate productivity increases as an outcome of the interactions between self-interested decisions. In the two types of model, as the equilibrium network of division of labor expands in response to improvements in transaction conditions, the following development phenomena concur. The equilibrium level of specialization for each individual or each country increases, the extent (or thickness) of the market increases, and the degree of market integration, degree of production concentration, and variety of occupation conﬁgurations increase. The degree of commercialization and trade dependence, degree of interpersonal dependence, and aggregate productivity increase. The inframarginal analysis can also explore a general equilibrium mechanism that simultaneously determines the interdependent policy regime and the level of division of labor. In chapters 4 and 7 we formalize Smith’s notion of endogenous comparative advantage, which means that differences in productivities between various specialists are consequences rather than causes of division of labor (Smith, 1776, p. 28). The notion of endogenous absolute advantage may be more general than Ricardo’s notion of exogenous comparative advantage, since the former may exist between ex ante identical individuals, while the latter does not exist if all individuals are identical in all aspects. The Smith–Young models of endogenous comparative advantage are used to investigate the equilibrium mechanism of economic development. This equilibrium analysis of economic development suggests that aggregate productivity and the degree of endogenous comparative advantage will increase in response to improvements in transaction conditions even if tastes (demand side) and production conditions (supply side) do not change.

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In Part III, the Smith–Young models of endogenous comparative advantage are used to explore the implications of entrepreneurship and the institution of the ﬁrm for economic development. There we also investigate how endogenous transaction costs caused by opportunism prevent the realization of economic development and evolution in division of labor. In chapter 11, several Smith–Young models with endogenous urbanization formalize Petty’s idea with regard to the intimate relationship between urbanization and division of labor. In chapter 12, Young’s idea about the relationship between industrialization and division of labor in roundabout production is formalized. Chapter 14 uses a Smith–Young dynamic general equilibrium to formalize Young’s idea on the spontaneous coevolution of network of division of labor and extent of the market. In chapter 15, a Walrasian sequential equilibrium model formalizes Austrian theory of entrepreneurial discovery and bounded rationality. It predicts spontaneous coevolution in organization information acquired by the society via social experiments and in division of labor. In chapters 16, 17, and 18, Smith, Turgot, and other classical economists’ ideas on the relationship among investment, money, business cycles, economic development, and division of labor are formalized. In particular, technology and saving fundamentalisms are criticized using dynamic general equilibrium models. All of the Smith–Young models suggest that as soon as the right tool of the trade for formalizing classical development economics is at the command of economists, the spirit of classical mainstream economics can be resurrected in a modern body of inframarginal analysis, and development economics can then be brought back to the core of modern mainstream economics. In chapters 5, 6, 11, and 13, general equilibrium models with economies of scale and economies of variety of goods (Dixit–Stiglitz, 1977, Ethier, 1982, Krugman, 1979, 1980, Krugman– Venables, 1995, 1996, Murphy–Shleifer–Vishny, 1989, Fujita–Krugman, 1995, Romer, 1987, 1990) are used to formalize the high-development economics of Rosenstein-Rodan (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), Myrdal (1957), and Hirschman (1958). These models show that as economists have gained a command of the technical substance of general equilibrium models with economies of scale, many development problems, such as the network effects of industrial linkage, circular causation, and interdependent decisions in different sectors, industrialization, dual structure, and urbanization can be much better investigated using general equilibrium analysis. These models show that not only is the degree of industrialization dependent on the degree of urbanization, but the latter is also determined by the former. Also, the number of goods, the network size of industrial linkage, productivity, and the extent of the market are interdependent. Some of the models show that each player’s decision in choosing her trade network is dependent on the size of the network of trade and industrial linkage, while the network size is determined by all players’ participation decisions. The Romer models (1987, 1990) and other dynamic equilibrium models of economic development in chapter 13 formalize Young’s conjecture about the spontaneous evolution of the number of producer goods, which Young (1928) called the “qualitative aspect of division of labor,” and the interdependence between the emergence of new goods and the evolution of the extent of the market. All of the models of high-development economics show that the very function of the market is to network self-interested decision-makers in order to utilize the gains from economic development, though the function might be imperfect. All of the formal general equilibrium models focus on the classical question of economic development (namely, why one county is wealthier than others or how scarcity can be reduced by the division of labor) rather than on the neoclassical question of what the resource allocation is in a market for a given degree of scarcity. In many of the new development models, symmetry is assumed, so that resource allocation is too trivial to be interesting at all: the quantities of all goods consumed and produced are the same in a model with ex ante identical

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individuals and symmetric tastes and production and transaction conditions. But very interesting stories of economic development, such as the evolution of division of labor and the related extent of the market, structural changes, and industrialization, can be told by the models. Asymmetries are introduced in chapters 6, 8, 11, 17, and 18 to tell stories about urbanization, the emergence of dual structure, cities, money, business cycles, and the institution of the ﬁrm from the evolution of division of labor.

1.4

THE SCIENTIFIC APPROACH TO DEVELOPMENT ECONOMICS

All of the new models of economic development and transaction costs share a common feature: they are based on a scientiﬁc approach to development economics. This approach divides economic analysis between four levels in a hierarchical structure. At the bottom level of the hierarchy, the mathematical concepts of functions and sets are used to describe the environment of economic development. For instance, utility functions are used to describe individuals’ preferences, and production functions and production sets are used to describe production conditions. The notions of budget constraint and related ownership structure and pricing rules, or more general game rules in game models, are used to describe the institutional environment. At the second level of the hierarchy, mathematical programming is used to describe individuals’ self-interested decisions. The results of the analysis at this level are referred to as the comparative statics of a decision in a static model, or the dynamics and comparative dynamics of a decision in a dynamic model. Such results explain individuals’ self-interested decisions by prices and the development environment, which encompasses preferences, production conditions, and institutional arrangements. At the third level of the hierarchy, more sophisticated mathematical tools are used to describe the outcome of interactions between self-interested decisions. The results of the analysis at this level are called comparative statics of general equilibrium in a static model, and the dynamics and comparative dynamics of general equilibrium in a dynamic model. Such results explain how the outcomes of interactions between self-interested decisions and related development performance change in response to changes in the economic environment. Development economists pay particular attention to those comparative statics or dynamics that predict changes in equilibrium aggregate productivity. In this text, the equilibrium models that formalize classical development economics are used to predict evolution in division of labor and related structural changes. All analysis at the three levels just described is referred to as positive analysis of economic development. When development economists conduct positive analysis, they do not ask what is good or bad, or what should be done to change matters, for they are not then concerned with value judgments. What they are trying to do is to use thought experiments to ﬁgure out what is going to happen under certain conditions and what is the mechanism for economic development. The following process is typical of such thought experiments. Beginning with some assumptions about intangible preferences and behaviors, economists use rigorous mathematics to establish connections between the intangible and tangible phenomena. One example of such a tangible phenomenon is the structural change whereby the income share of the industrial sector increases with per capita income. They can thus infer intangible relationships from the tangible. If the observed phenomena are consistent with their predictions based on the established connection, then their assumptions about the intangible are accepted as working hypotheses, which can be used to explain development phenomena. If the thought experiment generates predictions concerning tangible phenomena that are incompatible with observations, the hypothesis underlying the thought experiment is then rejected.

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Some conjectures can never be falsiﬁed. For example, consider the statement: “An increase in inequality of income distribution will decrease the welfare of a country.” Here, the inequality can be measured by the Gini coefﬁcient or the variance of income distribution. Most economists accept the Pareto rankable measurement of welfare (see the deﬁnition of Pareto optimum in chapter 3). But if economic development generates changes that are not Pareto rankable, for instance, increases of some individuals’ utilities are at the cost of others’ utilities, then it is nearly impossible to ﬁnd a measure of a country’s welfare that is accepted by all economists. This is not only because utility is intangible and cannot be directly measured and compared between individuals, but also because economists cannot ﬁnd a universally accepted functional form or set of weights to specify a country’s welfare as a function of all individuals’ utilities. Without a well-deﬁned measurement of the country’s welfare, there is no way to test or falsify the above statement. On the other hand, the following statement can be falsiﬁed. “Deterioration of a country’s terms of trade is associated with a decrease in per capita income in this country.” Data on a country’s terms of trade and per capita income can be collected. If the average price of all goods exported in terms of the average price of all goods imported decreases, while per capita real income increases, then the statement is falsiﬁed. P. Sen (1998) uses data to falsify this statement. He has also found that deterioration of the terms of trade and dramatic increases in trade volume and in total factor productivity may concur. In chapters 3 and 6, we shall use inframarginal analysis of general equilibrium models to show that the concurrent phenomena may take place if positive productivity gains from an enlarged network of division of labor caused by improvements in transportation conditions outweigh the negative effects of deteriorated terms of trade. This general equilibrium view about the relationship between economic development and the terms of trade can be intuitively illuminated by the following fact. The terms of trade of the computer sector have deteriorated dramatically in the past two decades, while productivity progress in this sector far outweighs the deterioration of terms of trade. Hence, an increase in the income share and productivity of this sector and the deterioration of its terms of trade concur. Falsiﬁcation of a hypothesis does not invalidate the chain of mathematical logic linking the assumption and the prediction in the hypothesis, provided of course that the process of deduction is mathematically correct. Hence, rejection of the hypothesis may be attributable to unrealistic assumptions, or it may be attributable to a problem with the analytical framework itself. Thus, by safeguarding against incorrect logic in the thought experiment that generates a hypothesis, mathematics can help us to narrow down the list of possible explanations for the empirical rejection of that hypothesis. This enables us to focus our attention on the assumptions and the analytical framework. This text will review emerging empirical research that tests new development economics against observations. For instance, North (1958) provides empirical evidence for a positive correlation between the employment share of the transaction sector and economic development. Barro (1997), Easton and Walker (1997), Frye and Shleifer (1997), Gallup and Sachs (1998), and Sachs and Warner (1995a, 1997) provide empirical evidence for the positive effects of transaction conditions on economic development. Yang, Wang, and Wills (1992) provide empirical evidence for a positive correlation between the evolution of division of labor, improvements in transaction conditions, and economic development. As Albert Einstein suggested, however, “It is quite wrong to try founding a theory on observable magnitudes alone. . . . It is the theory which decides what we can observe” (quoted in Heisenberg, 1971, p. 31). The new development economics covered in this text might challenge many conventional interpretations of empirical observations and may develop new concepts that lead to unconventional observations. At the fourth level of the hierarchical structure of development economics, economists raise questions that involve value judgments, such as, “Is the outcome of interactions between self-interested decisions (equilibrium) in a competitive market based on the private ownership

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system good for society as a whole?” The analysis at this level is referred to as welfare or normative analysis of economic development. The following examples explain why the scientiﬁc approach to analyzing economic development is useful. First, we consider a striking feature of ideas of state-planned economic development which is inconsistent with the scientiﬁc approach. In the 1950s, normative analysis of economic development received a great deal of attention from development economists when a sound theoretical foundation for the positive analysis of general equilibrium mechanism of economic development was yet to be established. Many indices were suggested to measure the effects of development on welfare (see Sen, 1988), and many policy prescriptions were made to pursue what was believed to be the best for society in the absence of sound positive analysis. This was partly because development economists were not familiar with the technical substance of inframarginal analysis and general equilibrium models. Also, it was based on the assumption that economists, or the governments for which some economists work, are benevolent central planners who can make value judgments on behalf of individual citizens. Even if the assumption is valid, this approach is naive, since it ignores complicated trade-offs between many variables associated with the indices in raising utility and complicated interactions between conﬂicting self-interested decisions that somehow trade-off the utility of one person against another’s utility. Hence, in this text, we do not follow this approach. Instead, we follow a scientiﬁc approach. That is, we ﬁrst make assumptions about the environment for economic development, then use mathematics to ﬁgure out the general equilibrium development mechanism and establish a connection between intangible behaviors and tangible development phenomena. Then we test the hypothesis generated by thought experiments against observations. We can thus recommend to decision-makers those equilibrium mechanisms that are compatible with empirical observations as working hypotheses. In chapters 3 and 4, we will show that with localized increasing returns and network effects of division of labor the equilibrium network size of division of labor that emerges in the decentralized market is Pareto optimal. The very function of the market is to coordinate self-interested decisions to fully utilize the network effects of division of labor net of transaction costs. In chapters 5, 6, 11, and 13 we will investigate the coordination difﬁculty of the efﬁcient network of industrial linkage which may occur when global economies of scale exist in a neoclassical framework with a dichotomy between pure consumers and ﬁrms, though the market can utilize most of the network effects of industrialization and urbanization. Part III will focus on the endogenous transaction costs caused by interest conﬂicts and opportunism and their effects on economic development. We will establish the connection between intangible endogenous transaction costs and utility on the one hand, and tangible per capita income and trade volume on the other. Hence, we can use a sophisticated way to infer intangible endogenous transaction costs and distortions and their effects on economic development from tangible development phenomena. Since economic transition and reforms are considered as a subﬁeld of development economics (Roland, 2000), we will apply the theories covered in this text to economic transition in chapter 19. The scientiﬁc approach to development economics is based on the extensive application of mathematics. This application can facilitate the division of labor between different generations of economists and students or between specialized ﬁelds of economics by raising communication efﬁciency in debating, teaching, and research. From the point of view of classical development economics, Marshall’s insights into the development implications of division of labor are far superior to his marginal analysis of demand and supply. But the former is not in modern mainstream economics, while the latter is part of the core of modern mainstream economics, because the former is not but the latter is formalized within a mathematical framework. This illustrates the implications of mathematical formalism for the formation of mainstream economics.

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In addition, as Debreu (1991) indicates, mathematics not only provides better tools of the trade for economics, but also may affect economists’ framework for thinking in a profound way. The history of the theory of labor surplus and the literature of high-development economics illustrates his point. According to Lewis (1988) and Ranis (1988), Lewis’s original motivation for developing the theory of labor surplus was to explore the development mechanism that generates evolution in division of labor. According to this idea, the dual structure is between self-sufﬁcient production of goods and commercialized and specialized production of goods, rather than between the agricultural and industrial sectors. But Lewis could not ﬁnd the right tool to formalize his original idea. We know today that this right tool is the inframarginal analysis of decisionmaking in choosing the level of specialization. As Krugman (1995) points out, proponents of the labor surplus model could not even play with a tractable general equilibrium model with increasing returns. In the 1950s and 1960s, most development economists could only barely manage general equilibrium models with constant returns to scale. They were not familiar with inframarginal analysis of this kind of model either. Hence, Lewis, Fei, and Renis used marginal analysis of the model with constant returns to scale to formalize their ideas. As a result, their ﬁnal models are far away from classical development economics and from their own original thinking. The ad hoc assumption of disequilibrium in the labor market and exogenous technical progress or capital accumulation in the industrial sector becomes the driving force of economic development in their models. We shall show in chapters 3, 4, and 6 that their original ideas can be appropriately formalized using inframarginal analysis of the Ricardian and Smithian models with endogenous specialization. Krugman (1995) indicates that high-development economics about circular causation, coordination problems of the network of industrial linkages, and economies of scale was more interesting than the model of labor surplus. But economists could not manage general equilibrium models with economies of scale to formalize high-development economics in the 1950s. Krugman attributes the success of the labor surplus model compared to high-development economics to the latter’s low level of analytical formalism. In this text, we will show that many ideas of high-development economics can be formalized using general equilibrium models with increasing returns. Stories based on the models are much more interesting than those based on labor surplus models. This history of development economics demonstrates that some insightful ideas may not be included in mainstream development economics if they are not appropriately formalized within a mathematical framework. A limited capacity in managing mathematical formalism was very often a bottleneck in development economics. Since the application of mathematics in the research of economic development is a gradual evolutionary process, usually the most simple and thereby very unrealistic mathematical models are developed before more sophisticated and realistic ones. Hence, it is common that very ingenious ideas are too complicated to be formalized by any mathematical models that can economists’ command, while tractable models are too simple and naive. Therefore the following two extremes are inappropriate: One is to worship mathematical formalism and ignore nonmathematical insights into economic development. The other is to totally ignore the implications of mathematical formalism. As development economics becomes part of the core of modern mainstream economics, it becomes universally applicable. This implies, on the one hand, that it is applicable not only to less-developed countries, but also to developed countries. On the other hand, the economic mechanisms that drove economic development in Britain, western Europe, and the US in the eighteenth and nineteenth centuries are, to a great extent, the same as those driving the economic development of east Asia and other currently developing countries. Poverty in sixteenth- and seventeenth-century Britain, in eighteenth-century France, and in nineteenth-century Japan was, to a great extent, the same as that in currently less-developed countries. Chapters 3 to

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6 and 19 will use inframarginal analysis of evolution of division of labor to investigate the advantages and disadvantages of the latecomer to industrialization and their evolution over different development stages. The relationship between income distribution, endogenous transaction costs, and economic development will be examined in chapters 3 to 6 and 9. The general equilibrium analysis yields some predictions that are substantially different from the economics of underdevelopment which was quite popular in the 1950s and 1960s. Many new development phenomena caused by globalization and the information revolution are the very features of economic development in the developed world. The questions at the end of this chapter give several examples of new features that can be analyzed by the new development economics. We can not only ﬁgure out the mechanism that enables the poor to catch up to the wealthy, but also predict some of the megatrends of future economic development. Examples of the megatrends given in the questions are the increasing income share of the resource cost in handling noise in information transmission, and the higher risk of coordination failure in an increasingly more integrated and larger network of division of labor and exchanges. This trend causes increases in frustration and mental pressure, which might enlarge the market for counseling and psychoservices in the new century. Since this text resurrects the spirit of classical development economics in a modern body of analytical formalism, its spirit is older and its body is younger than neoclassical development economics. The new development economics is, we hope, particularly powerful in analyzing the new development phenomena of networking and globalization.

Key Terms and Review • • • •

Classical development economics vs. neoclassical development economics The scientiﬁc approach to development economics Positive, normative, and empirical analyses of economic development Why is general equilibrium analysis essential for understanding the mechanisms for economic development? • Marginal analysis vs. inframarginal analysis of economic development • Why is inframarginal analysis essential for formalizing classical development economics?

Further Reading Classical development economics: Turgot (1766), Groenewegen (1977), Lewis (1988), Sen (1988), Petty (1671, 1683), Marshall (1890), Smith (1776), Meier and Seers (1984), Robbins (1968), North and Thomas (1970); Neoclassical development economics: Sen (1983), Arndt (1989), Bliss (1989), Bhagwati (1984), Lewis (1955, 1984), Livingstone (1983), Meier and Seers (1984), Adelman (1961), Meier (1994), Stern (1989), Rosenstein-Rodan (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), Fei and Renis (1964), Myrdal (1957), Hirschman (1958), Chenery (1979), Kuznets (1966), Kaldor (1957); Criticisms of neoclassical development economics: Stiglitz (1989), Bhagwati (1984), Stigler (1976), Kornai (1991, 1992), Young (1928), Krueger (1995, 1997), Behrman and Srinivasan (1995), World Bank (1991, 1996, 1997), Cheung (1970), Coase (1960); Economics of property rights and transaction costs: Coase (1937, 1946, 1960), Cheung (1970, 1983), Barzel (1982, 1985, 1997), Buchanan (1975), Milgrom and Roberts (1992), Hart (1995), Bolton and Scharfstein (1998), Gibbons (1998), Holmstrom and Roberts (1998), Yang and Wills (1990), Maskin and Xu (1999); The new school of economic history: North (1981, 1990, 1994), McNeill (1974), Mokyr (1990, 1993), Landes (1998), Rosenberg and Birdzell (1986), MacFarlane (1988), Braudel (1984), Fairbank (1992), Weber (1927, 1961, 1968), Baechler (1976), Chandler (1990), Pipe (1999); General

20 C HAPTER 1: I NTRODUCTION equilibrium models with economies of scale: Murphy, Shleifer, and Vishny (1989), Krugman (1991, 1995), Fujita and Krugman (1995), Krugman and Venables (1995); Literature of endogenous growth: Judd (1985), Lucas (1993), Romer (1987, 1990, 1993), Grossman and Helpman (1995), Barro and Sala-i-Martin (1995), Aghion and Howitt (1998); Literature of endogenous specialization: Young (1928), Stigler (1951, 1976), Houthakker (1956), Rosen (1978, 1983), Becker (1981), Yang and S. Ng (1998); Constitutional economics: Buchanan (1989, 1991).

QUESTIONS Classical development economics 1

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Following Marshall, Young (1928) described the technical progress associated with division of labor as a development in which a production process becomes fragmented and disintegrates into specialized tasks while new machinery is introduced to perform these tasks. In his comment on Knight (1921), he stated clearly that: “You [Knight] miss the point, I fear, of Marshall’s ‘external economies.’ They are the economies (in general) of greater specialization and div. of labor” (quoted in Blitch, 1983, p. 362). See also Blitch (1995) for a detailed account of Young’s perspectives on external economies. Compare this defense of Marshall to Young’s criticism of Marshall’s notion of external economies of scale, and discuss the connection and differences between economies of division of labor and economies of scale. Use the following examples to criticize technology fundamentalism and saving and investment fundamentalism. China’s telecommunications market is monopolized by the state telecommunications company. Hence, despite very advanced technology and equipment, which are superior even to those in many developed countries, the prices of telecommunications services are 2 to 600 times those in the US. Due to weak protection and enforcement of intellectual property, many Chinese software companies are unable to survive, despite a large population size that might be associated with a very large market for Chinese software. Automobile manufacturing technology is now available to the Chinese as it was to Ford in 1903 (when the Ford Motor Company was established). Currently, per capita income in China is not lower than it was in the US in 1908 (when the Ford Model T came onto the market). But why couldn’t a Chinese counterpart to the Ford Motor Company appear in the twentieth century? You may assume that Mr. Ford is now in China, at the age of 16. The following conditions indicate that he cannot set up his company, and cannot make a fortune from his Model T. Use this example to illustrate whether the policy prescriptions of classical development economics are relevant to the currently developing country. a) Mr. Ford was a country boy when he moved to Detroit, Michigan in 1879. If the young Ford were now in rural China and wanted to move to a city, he would not be able to get permanent residential registration in a Chinese city. Without this registration, he would have to pay a much higher rent for housing, and would even be unable to get housing at all in some large Chinese cities. Also, an automobile manufacturing company would be ﬁned severely by the government if it hired him. Hence, his chances of learning automobile manufacturing skills would be very slim. Suppose that Mr. Ford had already set up his Ford Motor Company in a Chinese city. He would have to bribe the government ofﬁcers for urban residential registration of his employees from rural areas.

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The rationing of houses and a state-monopolized land distribution system mean that he would have a very difﬁcult time providing housing for his employees. b) Mr. Ford could successfully sell his Model T in the 1910s because of his dealer franchise network, which created a high level of division of labor between production and distribution and between franchisees at different localities. But in China, any private wholesale and retail network cannot operate without a license issued by a government committee, which is usually headed by the government ofﬁcer who monopolizes the local wholesale and retail network. The interest conﬂict between any private wholesale and retail network and the state monopoly in that wholesale and retail network implies that Mr. Ford would have a very slim chance of approval for his dealer franchise network from the government committee. In the US at the beginning of the twentieth century, more than a hundred start-ups of motor vehicle manufacturing companies created a competitive environment that nurtured Mr. Ford’s success. There is no such free entry into automobile manufacturing in China. China has an approval system for setting up ﬁrms. In other words, the automatic registration system which has been institutionalized in the Western world since the nineteenth century is not available in China. In addition, in China there is a list of sectors in which domestic private ﬁrms are not allowed to operate. This list includes banking, automobile manufacturing, telecommunications, railroad, and freeway construction. Hence, Mr. Ford would be unable to set up his company at all if he were an entrepreneur in China in the 1990s. c) State opportunism and a predatory government policy in China engender a government monopoly in the capital market, imposing arbitrary fees and expropriatory taxes on private ﬁrms. This implies that even if Mr. Ford got the chance to set up his Ford Motor Company, he might be unable to get adequate capital and to make a proﬁt. The state-monopolized banking system implies that personal checks and many other mediates of exchanges are not available to many ordinary Chinese. This substantially limits the market for Ford’s cars. d) Ford’s lobbying campaign to promote a better infrastructure under a democratic system utilizes “externality” associated with infrastructure. But the state monopoly on constructing infrastructure in China and restriction on free association generate a lot of rent-seeking activities and opportunistic behavior. Mr. Ford would not have much of a chance to promote a motor-related infrastructure in China. e) In China, local government monopoly in many sectors fragments the Chinese market. Local governments’ monopolistic distribution systems carry out a protection policy that restricts the sale of goods produced by those ﬁrms that are not under local government control. Mr. Ford would have a hard time penetrating the fragmented local markets. Some economists treat the study of specialization and division of labor as a subﬁeld of economics. Comment on this view in connection to Houthakker’s assertion (1956, p. 182) that “there is hardly any part of economics that would not be advanced by a further analysis of specialization.” Use some examples to discuss his points. Smith and Turgot used the general equilibrium view of division of labor and economic development to criticize the mercantilists’ partial equilibrium view on the relationship between trade and development. According to this mercantilists’

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view, a great trade surplus would contribute to a country’s wealth. Hence, the government should manipulate the terms of trade by using tariff and other trade policies. According to Smith’s general equilibrium view, as domestic division of labor within a country or international division of labor between countries increases, wealth will be increased. Since demand and supply are two sides of division of labor, worries on trade deﬁcit and shortages of foreign exchange are groundless, provided the gains from division of labor and trade are not outweighed by transaction costs. The policy based on this view of development is intended to reduce the barriers of trade and transaction costs and let the invisible hand play its role in coordinating division of labor. Use this example to discuss why the notion of division of labor is a general equilibrium concept, and why Young (1928) considered marginal analysis of demand and supply that is separated from the analysis of decisions in choosing levels of specialization as a partial view. The new school of economic history 6

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Compare the British experience of successful development in the seventeenth to nineteenth centuries with the following facts. In some less-developed countries, government behavior is predatory and expropriatory. Government ofﬁcers use the coercive power of the government apparatus and their taxing power to steal citizens’ property. A typical example is the Duvalier government’s behavior in Haiti during the 1950s and 1960s. According to the World Bank (1997, p. 149), the economic pillars of Haiti’s predatory state were expropriation, extortion, tax inﬂation, and corruption. Signiﬁcant resources were devoted to protecting Duvalier himself – 30 percent of total government expenditures during the ﬁrst half of the 1960s. Agriculture, particularly coffee, was heavily taxed. Some sources estimate that Duvalier transferred more than US$7 million a year out of Haiti for personal purposes. Large-scale bribing also took place, through deals with foreign investors on projects that often never materialized. Extortion under the veil of “voluntary” donations was institutionalized under some political movements. According to Summers (1992), in a sub-Saharan African country, the government pursued a patronage recruitment policy for government employment and favoritism in issuing trade licenses. Then it purposely distorted exchange rates and prices in favor of the relatives’ trade businesses. In China during the 1960s and 1970s, the government used its monopoly in the banking sector, in the distribution network, in the urban real estate sector, and in other important sectors to pursue tangible and intangible rents. The approval system for setting up private ﬁrms, the strict licensing system for setting up ﬁrms for foreign trade, and the monopolized job assignment system were used by the government to discriminate against private businesses. A procurement system that compelled peasants to sell underpriced agricultural goods to government agents, and the residential registration system, which restricted rural residents’ mobility, were used to pursue the interests of urban residents, including the government elite, at the expense of rural residents (see Yang, Wang, and Wills, 1992). In this process, industrialization and economic development became hostages to state opportunism. North (1958, 1981, p. 166) observes that “productivity increase as a result of declining transaction costs had been going on since at least 1600, when the Dutch ﬂute [a specialized merchant cargo ship] was used in the Baltic trade and subsequently adopted on other routes. The declining transaction costs – a result of reduced piracy,

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increases in size of ships, growing trade, and reduced turnaround time – led to substantial productivity growth beginning 150 years (at least) before the Industrial Revolution; and they, more than technological change, were responsible for productivity increases.” Compare this view of technical progress to technology and investment fundamentalism, which claims that investment in research and development is the main engine of economic development. Comment on Landes’ (1998, p. 31) discussion on the institutional conditions for economic development: “It has been suggested that this end to danger from without launched Europe on the path of growth and development. Others would argue that freedom from aggression is a necessary but not sufﬁcient condition. Growth and development call for enterprise, and enterprise is not to be taken for granted. Besides, medieval Europe did not lack for impediments to such initiatives. . . . Linked to the opposition between Greek democracy and oriental despotism was that between private property and ruler-owns-all. Indeed, that was the salient characteristic of despotism, that the ruler who was viewed as a god or as partaking of the divine, thus different from and far above his subjects, could do as he pleased with their lives and things, which they held at his pleasure. And what was true for the ruler was true for his henchmen. The martial aristocracy typically had a monopoly of weapons, and ordinary folk were careful not to offend them, arouse their cupidity, or even attract their attention; to look them in the eye was an act of impudence that invited severest punishment.” Use the following documentation of the differences between China and Europe to explain the differences in their development performances in the seventeenth to nineteenth centuries. Landes (1998, pp. 34–6): “The concept of property rights went back to biblical times and was transmitted and transformed by Christian teaching. The Hebrew hostility to autocracy, even their own, was formed in Egypt and the desert.” “Despotisms abounded in Europe, too, but they were mitigated by law, by territorial partition, and within states, by the division of power between the center (crown) and local seigneurial authority. Fragmentation gave rise to competition, and competition favored good care of good subjects. Treat them badly, and they might go elsewhere. Ecumenical empires did not fear ﬂight, especially when, like China, they deﬁned themselves as the center of the universe. There was no other place to go.” Fairbank (1992): “Oriental societies, organized under centralized monolithic governments in which the bureaucracy was dominant in almost all aspects of large-scale activity – administrative, military, religious, and economic – so that no sanction for private enterprise ever became established . . .” Imperial governments carried out the industrial policy of limiting commerce and promoting agriculture. Fairbank (1992, p. 179): “The merchant was kept in check by the ofﬁcial as an ally whose activities could be used and milked in the interest of either the ofﬁcials personally or of the state. As Etienne Balazs pointed out, commercial transactions were always subject to the superintendence and taxation of the ofﬁcials. Government monopolies of staple articles, like salt and iron in ancient times, or like tea, silk, tobacco, salt, and matches more recently, expressed the overriding economic prerogatives of the state. No merchant class had been allowed to rise independently and encroach upon these prerogatives. This was ensured in practice by the ofﬁcial disregard for private property. This meant that ofﬁcial patronage and support were necessary to protect any big commercial undertaking. The result was a close community of interest between the merchant and the ofﬁcial. . . . In short, capitalism

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failed to prosper in China because the merchant was never able to become established outside the control of the landlord gentry and their representatives in the bureaucracy. In feudal Europe the merchant class developed in the towns. Since the landed ruling class were settled in their manors upon the land, the European towns could grow up outside the feudal system instead of being integrated in it.” Analyze the driving force of the evolution of capitalist institutions with connection to the following historical facts. Weber (1968, pp. 1212–64): Trade and cities are the progenitors of modern capitalism. Towns precede princes. Occidental cities had the following unique features. Cities emerged before the nation states. They had fortiﬁcations, markets, their own courts of law, and in part, autonomous law, association structure, partial autonomy (privileges, corporate rights). In Asia, cities were princely fortresses. In the Occident, “urban landed property was always alienable without restriction, inheritable, unencumbered with feudal obligations or obligated only to ﬁxed rental payments . . . In Asia and in the ancient world, this distinctive treatment of urban land settlement cannot be observed with similar regularity.” Magical caste was absent in Occidental cities. The city as an institutionalized association and a “territorial corporation” protected properties from the sovereign. It provided, under merchant governance, freedom for serfs, religious minorities, and new ideas. According to McNeill (1974), the lack of an overarching sovereign under feudalism led to horizontal contractual relations. Strong monarchies in England and France consolidated after the rise of towns (also, certainly, in German lands). The rise of the limited state implies that monarchs were too weak to snuff out dissent, opposition, and countervailing pressures. The increasing consolidation of states (England, France, Prussia, Hapsburg Spain) was generally not enough to undermine internal pluralism, corporate intermediaries, etc. Hence, state consolidation generally expanded internal markets. “As a general rule, a measure of expansion in foreign trade preceded the laborious uniﬁcation of the internal market.” An expanding internal market supported the commercialization of agriculture (specialization within agriculture). Hoffman and Norberg (1994, p. 305) comment, “In sum, all of the monarchs of early modern Europe had to confront powerful obstacles to their will; none raised revenue without negotiation, consultation, and sometimes bribery.” “Absolutist regimes despite their pretentions were not able to borrow or tax at will. Only governments with strong representative institutions could extract huge revenues and borrow large sums. Taxation and despotism were in the end incompatible.” “In the end, liberty was a necessary precondition for the emergence of a strong state, a state of wealth and power” (p. 310). Discuss the institutional conditions for economic development using the following documentation of the differences between Britain and France. Letters from England by Voltaire (in exile in England, 1726–9) already revealed the differences between England and France. Letter 9, “On the Government”: “A man is by no means exempt from paying certain taxes here simply because is a noble or because is a priest. All taxes are ﬁxed by the House of Commons which, though only second in rank [to the House of Lords], is ﬁrst in prestige. The Lords and the Bishops may well reject the Bill from the Commons for taxation, but they may not change anything in it; they must either pass or reject it out of hand. When the Bill is conﬁrmed by the Lords and approved by the King, then everybody pays. Everyone gives, not according to his rank (which is absurd) but according to his income. There is no arbitrary tax or capitation, but a real tax on landed property.” Letter 10, “On Commerce”: “In France, [the Marquis] loftily despises a business man, and the business man so

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often hears people speak disparagingly of his profession that he is foolish enough to blush.” According to Mokyr (1990, pp. 234–50), the differences between Britain’s patent laws and the French government prize system for invention, and between people-made Common Law and government-made civil laws explain the differences in development performance between Britain and France in the eighteenth century. Landes (1998) also notes more limited private rights to land in France than in Britain in the seventeenth century. A forthcoming manuscript by North and Weingast on the comparison between North American and Latin American growth over the last three centuries suggests that state opportunism (predatory and expropriatory taxation and authoritarian regimes) in Latin America explains the great difference in the development performance between North America and Latin America. Comment on their view. Use Landes’ (1998, p. 222) following discussion to assess technology and saving fundamentalism of economic development in connection with Young’s view on the relationship between technological progress, the extent of the market, and division of labor. “The contribution of high consumption to technological progress struck contemporaries, and more of them as the British advance grew. Without taking a course in Keynesian economics, French merchants understood that mechanization made for high wages, that high wages made for increased demand for manufactures, and that effective demand made for increased prosperity. ‘Thus, by the working of a system that seems paradoxical, the English have grown rich by consuming’ [Daniel Defoe, 1728]. Paradoxical indeed: such dispendious habits ran against the old wisdom that counseled thrift and abstemiousness, habits congenial to French peasants compelled to avarice. One result was a manufacture that aimed at a large national and international market and focused on standardized goods of moderate price – just the kind that lent themselves to machine production. ‘The English,’ wrote Charles marquis de Biencourt, ‘have the wit to make things for the people, rather than for the rich,’ which gave them a large and steady custom.” According to North and Weingast (1989), the Constitutional Monarch and parliamentary democracy that emerged from the British Glorious Revolution in 1688 provided a credible government commitment to a constitutional order. This signiﬁcantly reduced the government’s predatory behavior. Hence, endogenous transaction costs caused by rent-seeking and opportunism were reduced and long-term political stability could be secured. North argues (1981, pp. 158–68) that “Toynbee wrote, ‘The essence of the industrial revolution is the substitution of competition for the medieval regulations which had previously controlled the production and distribution of wealth.’ It is true that the decline in mercantilist restrictions including repeal or reform of the Statute of Artiﬁcers, poor laws, acts of settlement, usury laws, navigation acts, [corn laws], and so forth is part of the story. Particularly signiﬁcant to the development of more efﬁcient markets, however, is the better speciﬁcation and enforcement of property rights over goods and services; and in many cases much more was involved than simply removing restrictions on the mobility of capital and labor – important as those changes were. Private and parliamentary enclosures in agriculture, the Statute of Monopolies establishing a patent law, and the immense development of a body of common law to better specify and enforce contracts also are part of the story.” According to Mokyr (1993, p. 47), “Many of the obsolete laws and regulations that encumbered progress (for example by mandating precise technological practices in detail) were revoked. In 1809 Parliament revoked a sixteenth

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century law prohibiting the use of gig mills in the wool-ﬁnishing trade, and ﬁve years later it did away with one of the pillars of regulation, the Statutes of Artiﬁcers and Apprentices.” As he notes (Mokyr, 1990, p. 268; 1993), secured rights to residual returns of ﬁrms reduced transaction costs in setting up ﬁrms and encouraged specialized entrepreneurial activities, and secured rights to intellectual property directly improved transaction conditions for technological progress and encouraged specialized invention of new technology. When patent laws were not enough to protect entrepreneurial ideas and rights to inventions, the institution of the ﬁrm was used to protect intellectual rights via residual rights of the ﬁrm and trade secrets. A stable and nonpredatory tax system and the government’s laissez faire policy encouraged business activities and the evolution of division of labor. The liberation of civil society with respect to the State and the separation of Crown’s coffer from the Bank of England enriched the creativity of society and restrained rent-seeking. Free association (i.e., setting up private ﬁrms needed no approval or license from the government) improved transaction conditions for the evolution of the institution of the ﬁrm. Hence, transaction costs were signiﬁcantly reduced, the level of division of labor in inventing and other activities increased, and new producer goods and related new technology emerged. Is the development experience of Britain in the seventeenth and eighteenth centuries relevant to currently developing countries? Why did neoclassical development economists not pay enough attention in the 1950s to this successful development experience? Neoclassical development economics 15

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Some development economists argue that mainstream economics on the function of the market is not applicable to developing countries because of the nonexistence of many markets in less-developed countries. Lio (1998; see ch. 10 below) shows that if inframarginal analysis is used to formalize classical development economics, the equilibrium number of active markets and degree of marketization can be endogenously determined by the equilibrium level of division of labor and trading efﬁciency. Use this example to discuss the relationship between classical development economics and neoclassical development economics. Some development economists suggest using many direct measures of welfare to assess the development performance of a country. Use the scientiﬁc approach to assess this method in connection with the following discussion. India’s per capita GNP is higher but life expectancy is lower than in China. Which country’s people have higher utility? This is a question that has no well-deﬁned, unique answer. According to one index of the living standard which is a weighted average of per capita GNP, house affordability, pollution, trafﬁc congestion, the crime rate, and other variables that affect welfare, Japan has the highest welfare and the US is ranked number seven, behind Australia. But many Americans who have experience of Japan would not agree with this ranking. In other words, there are a lot of possible substitutions (trade-offs) between each pair of development indices. Only an individual knows her own utility maximization problem which efﬁciently trades off one against the others among these indices. Such a utility maximization problem is intangible to the government decision-maker. The trade-off between an individual’s utility and that of others’ is even more complicated. Not only is the government planner unable to ﬁgure it out, but even if she can, it is impossible for her to balance them in a

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benevolent way. Olsen (1996) and Dowrick and Nguyen (1989) use the net ﬂow of migrants between the two countries to identify per capita utility difference between them. Analyze under what conditions this approach to assessing development performance is more reliable than the neoclassical approach discussed above. The infant industry argument claims that protectionist tariffs are essential for industrialization of a less-developed country because of economies of scale, learning by doing, and the network effect of industrial linkage. But some economists argue that the infant industry argument boils down to the argument of an imperfect capital market. In the absence of a developed capital market, protectionist tariffs are essential for industrialization. Comment on these views in connection with Hume’s (1748, “Of Money,” pp. 34–5) following the classical view on investment. “There seems to be a happy concurrence of causes in human affairs, which checks the growth of trade and riches, and hinders them from being conﬁned entirely to one people; as might naturally at ﬁrst be dreaded from the advantages of an established commerce. Where one nation has gotten the start of another in trade, it is very difﬁcult for the latter to regain the ground it has lost; because of the superior industry and skill of the former, and the greater stocks of which its merchants are possessed, and which enable them to trade on so much smaller proﬁts. But these advantages are compensated in some measure, by the low price of labor in every nation which has not an extensive commerce, and does not much abound in gold and silver. Manufactures therefore gradually shift their places, leaving those countries and provinces which they have already enriched, and ﬂying to others, whither they are allured and are again banished by the same cause.” Dodzin and Vamvakidis (1999) have found empirical evidence for a positive correlation between the degree of openness and the income share of the industrial sector in developing agricultural economies. Use this evidence to assess the theory of the infant industry, which claims that protectionist tariffs are essential for industrialization of an agricultural society. Recent equilibrium models of saving and credit (see chapter 16 below) show that the rationale for saving, investment, and interpersonal loans is based on the gains from the intertemporal trade of goods. Saving and investment cannot take place if transaction costs (moral hazard, adverse selection, and other types of transaction costs) outweigh the gains from intertemporal trade. Use this general equilibrium view to analyze worries about the shortage of investments in developing countries and capital ﬂight from less-developed countries. An ingredient of failed development policies prevailing in the 1950s was reliance on state-owned enterprises for industrialization. This policy failure was generated by ignorance of the function of private residual rights of ﬁrms, which has been explored by the new theory of the ﬁrm and transaction costs discussed in chapters 8 and 9 below. A comprehensive government investment program based on Harrod– Domar’s investment fundamentalism and input–output analysis is evidence for the ignorance of the function of the market in coordinating division of labor, which is investigated in chapters 4, 7, and 8 below. A discriminatory development policy that promotes industrialization at the cost of rural residents’ welfare was due to state opportunism that took economic development hostage in pursuing the interests of the elite at the cost of the powerless. Analyze the mechanism of political economy for this policy prescription in connection with Krueger’s related analysis of rentseeking (1995, 1997).

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Krueger (1995, p. 2511) indicates that the pessimism of many neoclassical development economists over the contribution of trade to economic development is based on the argument of elasticity, which implies that the income share of demand for primary goods from less-developed countries declines due to an income elasticity of less than 1. Krueger argues that protectionist tariffs based on this pessimism are a self-fulﬁlling prophecy. The model in chapter 4, below, shows that regardless of the income elasticity of demand for any good, as the transaction cost coefﬁcient for a traded good increases, the general equilibrium jumps from a structure with trade and high aggregate productivity to autarky with low aggregate productivity. Use this result to analyze why the elasticity argument is not a general equilibrium view of development, and why it might be misleading. Why did neoclassical development economics pay no attention to the difference between the successful development experience of Britain and the relatively unsuccessful development experience of France in the eighteenth century? (See Mokyr, 1990, pp. 234–50 and 1993 for comparison of the two.) Many policy prescriptions suggested by neoclassical development economics are similar to mercantilism, which was rejected by the successful development experience of Britain in the eighteenth century and by classical development economics as represented by Smith. Why was the mercantilists’ mistake repeated in the 1950s and 1960s? In the 1950s, many development economists worried about the capability of developing countries in obtaining foreign exchange and investment. If the developing country concerned was a large one (such as India or China), they worried that the world market could not absorb goods exported from this country. Why are the worries groundless from a general equilibrium view? In the 1950s, the governments in Soviet Union, China, and India set up many speciﬁc development targets, such as increases in per capita income, life expectancy, literacy, medical aid, public utilities, output levels of steel, machine tools, and grain; per capita consumption of cloth, education, housing, and investment; increases in nutrition levels, and decreases in infant mortality (see, for instance, Behrman and Srinivasan, 1995). Early development economics generally followed this central planning idea of economic development. Some indices to measure economic development, such as the indices of inequality of income distribution, of illiteracy, of infant mortality, and of life expectancy, were developed in accordance with this idea. Is such thinking about economic development consistent with scientiﬁc analysis? Some neoclassical development economists claim that many markets are absent in less-developed countries, so that distortion in the latter is greater than in developed countries. But according to the economics of property rights and endogenous externality (see ch. 10 below), the trade-off between economies of division of labor and transaction costs implies that better transaction conditions in developed countries may generate more transactions and more aggregate distortion in society as a whole. Use this example to discuss why we need inframarginal analysis of the general equilibrium network of division of labor to investigate the development mechanism. Some development economists argue that the experience of capitalist economic development in eighteenth- and nineteenth-century western Europe is not sufﬁcient for successful economic development. They point to Egypt, India, Indonesia, and Latin America as examples of unsuccessful capitalist economic development. Use the differences in institutions between these countries and Britain to assess this argument. For instance, the longtime political monopoly of the ruling party in

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Egypt generates state opportunism, while India’s state-planned industrialization encourages rent-seeking and other opportunism. The applicability of development economics to developed countries 27

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According to Buchanan (1991), state opportunism is not only an obstacle for economic development in developing countries, but also a burden of economic development in developed countries. He argues that the game between constitutionalists, who are concerned with constitutional rules based on a collective decision that pursues long-term social welfare, and rent-seekers who pursue the short-term interests of a particular group at the cost of long-term social welfare under given democratic rules, dictates the evolution of constitutional rules, which determine policy-making. An individual may play dual roles as a constitutionalist and a rent-seeker. Use the debates on trade policies, the education systems and the healthcare system in a democratic developed country (the US or Britain) to analyze the effect on economic development in that country of the “super game” in forming constitutional rules and in policy-making. Naisbitt (1990) predicts several megatrends: franchising will be a major business form in the US in the twenty-ﬁrst century, the income share of counseling and psychoservices will increase, and individuals will be increasingly less specialized. Discuss the possibilities for using new development economics to predict such megatrends and modernization phenomena in developed countries. One of Bill Gates’ 12 rules for the digital revolution is to read all of one’s email (Time Magazine, March 22, 1999, p. 72). This is certainly not an optimum economic decision because of the trade-off between information gains and resource cost in acquiring information. Several Smithian models in this text predict that the income share of information cost increases as information technology improves and negative network effect increases more rapidly than the positive network effect of division of labor and information exchange as the network expands. This implies that increasingly more resources are used for screening and deleting useless information or jargon messages. More importantly, society’s capacity to handle and absorb information increases as what each member knows, as a proportion of the total information that the society knows, decreases. Hence, the simple slogan “information era” may mislead people to think that the more information that one knows, the better. A new development feature in the US in the twenty-ﬁrst century might be that it becomes increasingly difﬁcult to make decisions to achieve an efﬁcient trade-off between the positive and negative network effects of information exchange. Comment on this view in connection with the dramatic and rapid negative network effects of the computer virus on modern economic life. A striking development phenomenon in developed countries, documented in Lio (1996), is the concurrent increase in market leisure time and working time, and decrease in self-sufﬁcient working time. This phenomenon implies that as individuals are more specialized in their professional jobs, they increase the purchase of services that used to be self-provided. This tendency is associated with increasing income from the market. According to the Franchise Annual 1999, this will make the sector that offers time-saving services to the two-income family the fastest growing sector in the next 30 years. Explain why the Lio model predicts the concurrent development phenomena as a consequence of the expansion of the network of division of labor.

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An interesting development phenomenon in developed countries is documented by a survey in The Economist (Sept. 5–11, 1998, pp. 4 –7). The survey found that the probability that a motorist gets in a trafﬁc jam is higher in the US cities which are upgrading their transportation infrastructure the fastest. North (1958, 1986) also ﬁnds empirical evidence for this phenomenon, that income share of transaction costs increases as transaction conditions are improved. This implies that as communication technology is improved and productivity of the computer sector increases, the income share of expenditure on computers and communications increases rather than decreases. This implies that increasingly more time and resources will be consumed in handling jargon and in searching and screening. Use classical ideas on network effects of division of labor to analyze this modern development phenomenon. A development phenomenon noted by Naisbitt (1990) is the rapid development of franchise networks in the US and other developed economies. He claims: “Franchising is the single most successful marketing concept ever.” According to the International Franchise Association (1997), “More than 550,000 franchise businesses dot the American landscape, generating more than $800 billion in sales, with a new franchise business opening somewhere in the US every 8 minutes each business day.” Among three types of franchise – a products franchise, a brand name franchise, and a business format franchise – the last one grows much faster than the other two. In 1999, 4,177 business format franchises in the US are listed in Franchise Annual. Most of them were franchised after 1960. One of them has 20,000 to 22,000 units. It seems that classical development economics can explain this phenomenon very well. Most business format franchises (the fast food franchise networks McDonald’s and Kentucky Fried Chicken are two of them) involve the division of labor between thinking and doing. The franchiser specializes in providing know-how (intangible intellectual property, which is very commonly associated with an operation manual and training programs). The franchisee specializes in providing tangible goods or services, buying intangible know-how from the franchiser. Sometimes, a franchise network involves deep division of labor between the sector providing roundabout production equipment and the sector providing ﬁnal services. For instance, the know-how (McDonald’s “bible”) provided by the McDonald’s franchiser includes the purchase of very specialized cooking equipment that can utilize a high level of division of labor between the roundabout sector and the ﬁnal sector to improve productivity. Also, the know-how provided by the Precision Tune franchiser includes the purchase of very specialized equipment for testing and ﬁxing car engines. If Smith applied his theory to analyze the franchise, he might say something as follows. The high level of division of labor within a particular franchise network generates high productivity on the one hand, and high transaction costs of tangible and intangible properties on the other. The common opportunism in the network is that the franchisee no longer wants to pay a franchise fee once she has acquired the necessary know-how. The franchise contract uses a hostage mechanism to restrict such opportunism. The typical franchise contract has a special clause allowing the franchiser to unilaterally terminate the contract if the franchisee does not pay the franchise fee, which might be 9 percent of the sales revenue of the franchise. Within a certain period of time after the termination, the franchisee is not allowed to compete with the franchiser in a speciﬁed territory and in speciﬁed activities. This hostage mechanism signiﬁcantly reduces the transaction costs caused by infringement

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upon the intellectual property rights of the franchiser, so that productivity gains from a larger network of division of labor become more likely to outweigh transaction costs. From this point of view, the boom of franchise networks in the developed countries is the evolution of division of labor between the production of intellectual property and of tangible services. This new development phenomenon has the same economic mechanism as that for Smith’s pin factory. This boom of franchise networks is associated with the recently popular business practices of downsizing, disintegration, outsourcing, contracting out, and focusing on core competencies, which are considered puzzling, since their concurrence to performance progress is incompatible with the neoclassical concept of economies of scale. In chapter 8 of this text, we will use a Smithian model to explain concurrent increases in productivity and division of labor and the decrease in the average size of ﬁrms. Up to 1999, more than a thousand new business practices in Internet commerce (e-commerce) have been granted patents. One of them pays reviewers for clicking on Internet messages. This generous pricing policy makes money from a rapid expansion of network connections which repays the company in a roundabout way. The variety of possible pricing structures of a business network increases more than proportionally as the network of transactions expands, since the number of pricing structures is nm where m is the number of traded goods and n is the number of goods directly priced in this network. Marginal cost pricing does not work for choosing the efﬁcient one from many pricing structures since decision variables and prices discontinuously jump between different pricing and network conﬁgurations. Use this example to illustrate why inframarginal analysis is essential for understanding many of the new development phenomena in the networking and globalization era.

Notes 1 According to Lewis (1988), “The theory of economic development established itself in Britain in the century and a half running from about 1650 to Adam Smith’s The Wealth of Nations (1776).” Hagen (1980, p. 72) also claims that “Adam Smith was a growth theorist.” Sen (1988, p. 10) indicates that “Petty is regarded, with justice, as one of the founders of modern economics and speciﬁcally a pioneer of quantitative economics. He was certainly also a founder of development economics. Indeed, in the early contributions to economics, development economics can hardly be separated out from the rest of economics, since so much of economics was, in fact, concerned with problems of economic development. This applies not only to Petty’s writings, but also to those of the other pioneers of modern economics, including Gregory King, François Quesnay, Antoine Lavoisier, Joseph Louis Lagrange, and even Adam Smith. An Inquiry into the Nature and Causes of the Wealth of Nations was, in fact, also an inquiry into the basic issues of development economics.” 2 Petty (1671, I, pp. 260–1) noted that specialization contributes to skillful clothmaking and pointed out that the Dutch could convey goods cheaply because each of their ships was specialized for a speciﬁc function. In another place, Petty gave a more striking example of the division of labor in the manufacture of a watch. Turgot (1751, pp. 242–3) linked the development of division of labor with concurrent increases in inequality of income distribution and in living standards for even the humblest member of society. 3 According to North (1981, pp. 158–68) and Groenewegen (1977), Britain’s domestic liberal policy regime and France’s liberal reforms under Turgot preceded Smith’s advocacy for the role of the invisible hand which was followed by Britain’s liberal international trade regime. 4 Economists agree to disagree about the theory of economic history. Hence, the hypotheses on development history reviewed in this chapter are only a sample of many competing ones.

32 C HAPTER 1: I NTRODUCTION 5 According to La Porta, Lopez-de-Silanes, Shleifer, and Vishny (forthcoming), common law, which emerges spontaneously from litigation rather than being made by government, is more conducive than civil (continental) law, which is government created, to economic development. However, since major west European countries have increasingly imitated the constitutional judiciary ( judicial review) in the US, the constitutional orders of common law and the continental system have been converging. 6 See Beasley (1995) for a detailed analysis of the economic, political, and social reforms of the Meiji period. 7 The era of nineteenth-century free trade is usually dated from 1846, when Britain unilaterally liberalized by repealing the Corn Laws. In fact, liberalization had begun earlier, with the abolition of export duties in 1842 and the reduction of import duties in 1842 and 1845. The next decisive step was the Cobden–Chevalier Treaty of 1860, which liberalized British–French trade. The new German Reich was established by Bismarck on free trade principles and low tariffs in 1879. It is often suggested that this free trade era ended in 1879 with a renewed wave of protectionism, starting with Bismarck’s acceptance of the famous tariff on bread and iron, which raised import duties on agriculture and steel. Higher tariffs soon followed in France and Italy. In fact, even with these tariff increases, average tariff rates remained low until the First World War, and nontariff barriers (for example, quotas and exchange controls) were virtually non-existent. According to data assembled by Capie (1983, table 1.3, p. 8), average tariff revenues as a percentage of total imports stayed below 10 percent in France, Germany, and the United Kingdom; between 10 and 20 percent in Italy; between 20 and 30 percent in the United States; and between 20 and 40 percent in Russia. 8 See Eichengreen and Flandreau (1994, p. 9). The countries on the gold or silver standards in 1908 included, in Europe: the United Kingdom, France, Belgium, Switzerland, Italy, Germany, the Netherlands, Portugal, and Romania; in North America: the United States and Canada; in Central America: Mexico, Nicaragua, Guatemala, Honduras, Salvador, and Costa Rica; in South America: Peru, Chile, Brazil, Venezuela, and Argentina; in Asia and the Middle East: the Ottoman Empire, Egypt, and Persia. The national currencies were convertible into gold in all cases except the following: Italy, Austria, Spain, Portugal, Nicaragua, Guatemala, Peru, Chile, Brazil, and Venezuela. The Italian and Australian currencies were stable though not convertible. 9 See Thorp (1984) for very insightful essays on the country-by-country experience. 10 Just as Baechler (1976) considers the rivalry between sovereignties as the driving force of the evolution of capitalist institutions in the seventeenth to nineteenth centuries, Krueger (1995) considers the rivalry between governments in the international arena as the driving force for the return to liberalization reforms in the late twentieth century. 11 The changing zeitgeist is captured by Keynes in his remarkable lecture “National SelfSufﬁciency,” delivered in Ireland in 1933, when the world was in the depths of the Great Depression (Keynes, 1933). In the lecture, Keynes rejects the commitment to free trade and the international harmonization of institutions, declaring the late nineteenth-century experience a massive, and apparently inevitable, failure. In Keynes’ view, the international system led to war by stoking competition among the leading powers: “The protection of a country’s existing foreign interests, the capture of new markets, the progress of economic imperialism – these are a scarcely avoidable part of a scheme of things which aims at the maximum geographical diffusion of capital wherever its seat of ownership” (Keynes, 1933, p. 236). For this reason, countries are best linked by ideas and culture, not economic and ﬁnancial entanglements. Keynes writes: “I sympathise, therefore, with those who would minimise, rather than with those who would maximise, economic entanglements between nations. Ideas, knowledge, art, hospitality, travel – these are the things which should of their nature be international. But let goods be homespun whenever it is reasonably and conveniently possible; and, above all, let ﬁnance be primarily national” (Keynes, 1933, p. 236). 12 In comparison to communism and fascism, the welfare state was a much more successful response to the Great Depression. 13 Zaleski (1980) documents Soviet planners’ mimicry of Western production patterns. Lenin’s works, for instance (1939), indicate that he was very familiar with the features of industrialization in a developed capitalist economy. 14 Sachs and Warner (1995a) document the surge of protectionism at the end of the nineteenth century. Chapter 3 in this text uses the Ricardian model to explain the phenomenon; the inframarginal analysis has simultaneously endogenized trade regime and the equilibrium level of market integration.

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For instance, Arndt (1989), Bliss (1989), Bhagwati (1984), Hirschman (1958), Lewis (1984), Livingstone (1983), Meier and Seers (1984), Sen (1983), and Stern (1989) consider development economics as a ﬁeld which applies economics to less-developed countries. In the 1950s the governments in the Soviet Union, China, and India set many speciﬁc development targets, such as increases in per capita income, life expectancy, literacy, medical aid, accessibility of public utilities, output levels of steel, machine tools and grain, per capita consumption of cloth, education, housing, investment, and nutrition levels; see, for instance, Behrman and Srinivasan (1995). The optimum solution to a decision problem is a corner solution if some decision variables take on their upper or lower bound values. The optimum solution is an interior solution if all decision variables do not take on the bound values. Marshall assumed concavity (diminishing marginal utility), which implies but is not implied by quasi-concavity of a utility function. Though neoclassical marginal analysis is used by many economists to criticize the state-planned development strategies proposed by early neoclassical development economics, our text will show that inframarginal analysis can provide a much more powerful analytical vehicle. Coase (1946, p.173) noted “a consumer does not only have to decide whether to consume additional units of a product; he has also to decide whether it is worth his while to consume the product at all rather than spend his money in some other direction.” He applies this inframarginal analysis to criticize marginal cost pricing rule (1946) and Pigou’s marginal analysis of externality (Pigou, 1940 and Coase, 1960). Buchanan and Stubblebine (1962) coined the term “inframarginal analysis.” Koopman (1957) and Arrow, Enthoven, Hurwicz, and Uzawa (1958) are among those economists who initiated formal inframarginal analysis in economics. Becker (1981) and Rosen (1977) are among those economists who initiated formal inframarginal analysis of specialization and division of labor. The application of inframarginal analysis to a decision problem can be found in Kendrick (1978), Little and Mirrless (1980), Becker (1981), and Rosen (1983). Its application to the theory of incomplete contracts can be found in Grossman and Hart (1986) and Hart (1995). The application of inframarginal analysis to general equilibrium models can be found in Yang and Wills (1990), Yang and Borland (1991), Dixit (1987, 1989), Yang and Shi (1992), Yang and Ng (1993), and in chapters in this text. Yang and S. Ng (1998) provide a recent survey of inframarginal analysis of division of labor. Recent development economics texts, for instance Ray (1998) and Meier (1995), cover part of the literature on endogenous transaction costs, such as Stiglitz’s models of moral hazard and tenancy. But they do not cover the literature of endogenous externality, commitment game models, the economics of property rights and transaction cost, and the new school of economic history.

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PART I Geography and Microeconomic Mechanisms for Economic Development

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GEOGRAPHY AND ECONOMIC DEVELOPMENT

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2.1 UNEVEN ECONOMIC DEVELOPMENT IN DIFFERENT PARTS OF THE WORLD Two centuries after the start of modern economic growth, a large portion of the world remains mired in poverty. Some beneﬁts of modern development, especially gains in life expectancy and reduced infant mortality, have spread to nearly all parts of the world, though huge and tragic discrepancies remain in even these areas. In material well-being, however, as measured by gross domestic product (GDP) per capita adjusted for purchasing power parity (PPP), the yawning gaps are stunning and show few signs of amelioration. According to the valuable data assembled by Angus Maddison for the Organization of Economic Cooperation and Development (1995), western Europe outpaced Africa in average per capita GDP by a factor of around 2.9 in 1820, and by a factor of 13.2 by 1992. More stunningly, Madison puts the African per capita income in 1992 at $1,284 dollars (measured in 1990 PPP adjusted dollars), which is essentially identical to Maddison’s estimate of the average GDP per capita in western Europe in 1820, $1,292. One area of the developing world, Asia, showed signiﬁcant progress during the past thirty years, with average incomes rising from around $1,212 in 1965 to $3,239 in 1992 on the Maddison data.1 In Africa, however, the levels of income in the 1990s were about the same as in 1970. (Maddison puts Africa’s average income at $1,289 in 1971 and $1,284 in 1992.) In Latin America and the Caribbean, average income levels in 1992 ($4,820) were only 6.6 percent higher than in 1974 ($4,521). Figure 2.1 (from Gallup and Sachs, 1998) shows the global map of GDP per capita as of 1995 (using PPP-adjusted estimates from World Bank 1997). Two geographical correlates of economic development are unmistakable. First, the countries in the geographical tropics are nearly all poor.2 Almost all high-income countries are in the mid- and high latitudes. Second, coastal economies are generally higher income than the landlocked economies. Indeed, outside of Europe, there is not a single high-income landlocked country, though there are 29 nonEuropean landlocked countries. In the next chapter, we will analyze the relationship between individuals’ utilities (per capita real income), per capita GDP, the extent of the market, aggregate productivity, and the equilibrium level of division of labor. We shall show that GDP relates closely to the notion of extent of the market which coevolves with the level of division of labor. Per capita GDP overstates per capita real income (utility) not only because it ignores effects of general price level, but also it includes transaction costs that reduce utility. On the

Figure 2.1 World GDP per capita 1995

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other hand per capita GDP also understates per capita real income because it excludes most of self-sufﬁcient or noncommercial income. This underestimation negatively relates to the level of division of labor. Gallup and Sachs (1998) have also made three observations about population density from data compiled in their research. First, there is no simple relationship between population density and income level. They ﬁnd densely populated regions that are rich (western Europe) and poor (India, Indonesia, and China), and sparsely populated regions that are both rich (Australia and New Zealand) and poor (the Sahel of Africa). Second, the coastlines and areas connected to the coast by navigable rivers are more densely populated than the hinterlands (we will use this term to refer to regions more than 100 km from the coast or from an oceannavigable waterway). If we multiply GDP per capita and population density, we can calculate GDP density, measured as GDP per km2. As shown by Gallup and Sachs, the coastal, temperate, Northern Hemisphere economies have the highest economic densities in the world. Four of these areas – western Europe, northeast Asia (coastal China, Japan, and Korea), and the eastern and western seaboards of the US and Canada – are the core economic zones of the modern world. These regions are the overwhelming providers of capital goods in global trade, the world’s ﬁnancial centers, and the generators of a large proportion of global production. If we take the regions within the US, western Europe, and temperate-zone east Asia that lie within 100 km of the coastline, these areas account for a mere 3 percent of the world’s inhabited land area, 13 percent of the world’s population, and at least 32 percent of the world’s GDP measured at purchasing power parity. According to recent data of the World Trade Organization (1995), just 11 countries in North America, western Europe, and east Asia, with 14 percent of the world’s population, account for remarkable 88 percent of global exports of capital goods (machinery and transport equipment). For purposes of discussion, we deﬁne a tropical country as one in which half or more of the land area is within the geographical tropics. There are 72 tropical countries, with 41 percent of the world population, and 78 nontropical countries, with 59 percent of the world population. Among the tropical countries, the simple average of 1995 GDP per capita (not weighted by country population) is $3,326. Among the nontropical countries, the average is $9,027, or nearly three times greater. It is convenient to divide the nontropical countries into two subgroups, the temperate-zone economies and the subtropical economies. For our purposes, we deﬁne subtropical as countries in which half or more of the land area is tropical or subtropical ecological zones, but in which the country’s land area is more than half outside of the geographical tropics. There are 15 subtropical economies, and 63 temperate-zone economies. While the tropical countries have mean income of $3,326, the subtropical countries have mean income of $7,874, and the temperate-zone economies have a mean income of $9,302. Among the economies that were not socialist in the postwar period, the geographical divide is even sharper: nonsocialist tropics, $3,685; nonsocialist subtropics, $9,248; and nonsocialist temperate, $14,828. Of the top thirty countries ranked by 1995 PPP-adjusted GDP per capita, only two are tropical, and these two are tiny: Hong Kong and Singapore. Four are subtropical, and 23 are temperatezone. The two tropical countries account for a mere 1.0 percent of the combined population of the top 30 countries. Using geographic information system data, we can also examine the proportion of the population living in the geographical tropics in the top 30 countries, taking into account that four of the top thirty countries that we have not counted as tropical (Australia, Chile, Taiwan, and the United Arab Emirates) have a part of their populations in the tropical region. Making this adjustment, the tropical share of the top-30 population is 2.3 percent. Nearly all landlocked countries in the world are poor, except for a handful in western and central Europe which are deeply integrated into the regional European market, and connected by low-cost trade.3 (Even mountainous Switzerland has the vast bulk of its population in the

40 P ART I: D EVELOPMENT M ECHANISMS Table 2.1 Geographical characteristics of selected regions

Continent GDP/PC Total population 2

Sub-Saharan Africa

Western Europe

East Asia

South Asia

Transition economies

Latin America

1,865

19,230

580

383

10,655

1,471

3,902

5,163

1,819

1,219

400

472

Total land area (million km )

24

3

14

4

24

20

Land in tropics (%)

91

0

30

40

0

73

Population w/in 100 km of coast (%)

19

53

43

23

9

42

Population w/in 100 km of coast or river (%)

21

89

60

41

55

45

Landlocked population (%) Distance to core market (km)

28

4

0

2

21

3

6,237

922

3,396

5,744

2,439

4,651

Coastal density (pers/km2)

40

109

381

387

32

52

Interior density (pers/km2)

22

125

91

287

16

18

low-elevation cantons north of the Alps, and these population centers are easily accessible to the North Atlantic by land and river-based trafﬁc.) There are 35 landlocked countries in the world with population greater than 1 million, of which 29 are outside of western and central Europe. Of these 29 countries, the richest is 38th(!), Botswana, which owes its pride of place to well-managed diamond mines. The second richest is 68th, Belarus. The difference in means is striking: the landlocked countries outside of western and central Europe have an average income of $1,771, compared with the non-European coastal countries, which have an average income of $5,567. Of course, geography is not everything. Even geographically favored countries, such as temperate-zone, coastal North Korea, or well-located Czechoslovakia, failed to thrive under a socialist economic and political system. Nonetheless, development surely seems to be favored among the temperate-zone economies, especially the subset that: (1) is in the Northern Hemisphere; (2) has avoided socialism; and (3) has avoided being ravaged by war. In total, there are 78 nontropical economies, of which 7 are in the Southern Hemisphere: Argentina, Australia, Chile, Lesotho, New Zealand, South Africa, and Uruguay (all in the temperate zone). Gallup and Sachs (1998) classify 46 countries as socialist during the postwar period, of which 31 are in the North temperate zone, and four are in the North subtropical zone. They also classify 12 nontropical countries as war-torn. There are 12 nontropical landlocked countries outside of Europe, of which 10 were socialist and 2 were not. With these deﬁnitions, Gallup and Sachs ﬁnd the following. There are 23 countries with the most favored combination of geography and politics – Northern Hemisphere, temperate zone, coastal, nonsocialist, and nonwar-torn – with an average income of $18,000. In fact, 21 of these countries have an average GDP per capita above $10,000, with Turkey and Morocco being the only exceptions.4 Using a multiple regression estimate for the 78 nontropical countries, average incomes per capita are reduced by an estimated $4,785 for being in the subtropics; $3,590 for being in the Southern hemisphere; $10,053 for being socialist; and $5,190 for being landlocked. A summary of geographical characteristics by major region is shown in table 2.1. For each region, they show the average GDP per capita, total population and land area, and several key variables that we will ﬁnd to be closely related to economic development: the extent of land in the geographical tropics, the proportion of the region’s population within 100 km of the

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E CONOMIC D EVELOPMENT 41

coastline or within 100 kilometers of the coastline or ocean-navigable river,5 the percentage of the population that lives in landlocked countries, the average distance by air (weighted by country populations) of the countries within the region to the closest “core” economic areas,6 the density of human settlement (population per km2) in the coastal region (within 100 km of the coastline) and the interior (beyond 100 km from the coastline). Some important characteristics are the following. First, sub-Saharan Africa, the poorest region, has several characteristics closely associated with low income in general: a very high concentration of land in the tropics, a population heavily concentrated in the interior (only 19 percent within 100 km of the coast); with more than a quarter of the population in landlocked countries (the highest of any region); very far from the closest “core” markets in Europe; and with low population densities in the coastal and interior regions. By contrast, western Europe, the richest region shown, is nontropical; heavily concentrated near coastal areas; with almost no population in landlocked regions; and with moderate population density. South Asia and the transition economies (of eastern Europe and the former Soviet Union) are, like sub-Saharan Africa, also heavily concentrated in the interior rather than the coast. India’s great mass of population, for example, lives in the Gangetic valley, often hundreds of kilometers from the coast. South Asia is, of course, partly tropical and densely populated (indeed the most densely populated in the world), while the transition economies are nontropical and also the least densely populated region. Latin America is the other highly tropical region, with low population densities, and with a moderately coastal population. The United States has two enormous advantages for development: a relatively high proportion of population near the coast (38 percent within 100 km of the coast, and a remarkable 67 percent if oceannavigable river systems are included), and a temperate-zone landmass. These patterns prompt the following questions. How much has geography mattered for economic growth, once we control for economic policies and institutions? What is the general equilibrium mechanism for economic development that involves the interplay between geography, urbanization, institutions, and evolution of division of labor? If geography mattered in the past, what difference does it still make via the equilibrium mechanism today? Based on the evidence provided by Gallup and Sachs (1998), we believe that geography continues to be of importance for economic development, alongside the importance of economic and political institutions. From an analytical point of view, we believe that geographical considerations should be reintroduced into development economics, which so far has almost completely neglected geographical themes. This chapter is organized as follows. Section 2.2 discusses a range of theoretical approaches linking geography and economic development. Section 2.3 provides cross-country empirical evidence for the linkages.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n n

What is the relationship between geographic conditions, transaction costs, level of division of labor, and per capita real income of a country? What is the relationship between geographic conditions, quality of public institutions, government policy regime, and development performance of a country?

2.2 GEOGRAPHY AND DIVISION OF LABOR While geography has been much neglected in the past decade of formal econometric studies of cross-country performance, economists have long noted the crucial role of geographical factors.

42 P ART I: D EVELOPMENT M ECHANISMS

Indeed, though Adam Smith (1776) is most remembered for his stress on economic institutions, Smith also gave deep attention to the geographic correlates of growth. (Smith should also be remembered for his recognition that Europe’s ﬁrst-mover military advantage gave it an ability to impose huge costs on other parts of the world.7) Smith saw geography as the crucial accompaniment of economic institutions in determining the division of labor. Smith’s logic, of course, started with the notion that productivity depends on specialization, and that specialization depends on the extent of the market. The extent of the market in turn depends both on the freedom of markets as well as the costs of transport. And geography is crucial in transport costs: As by means of water-carriage a more extensive market is opened to every sort of industry than what land-carriage alone can afford it, so it is upon sea-coast, and along the banks of navigable rivers, that industry of every kind naturally begins to subdivide and improve itself, and it is frequently not till a long time after that those improvements extend themselves to the inland part of the country. (p. 25)

In view of the crucial role of transport costs, Smith notes that: All the inland parts of Africa, and that part of Asia which lies any considerable way north of the Euxine [Black] and Caspian seas, the antient Sycthia, the modern Tartary and Siberia, seem in all ages of the world to have been in the same barbarous and uncivilized state in which we ﬁnd them at present. The sea of Tartary is the frozen ocean which admits of no navigation, and though some of the greatest rivers in the world run through that country, they are at too great a distance from one another to carry commerce and communication through the greater part of it. There are in Africa none of those great inlets, such as the Baltic and Adriatic seas in Europe, the Mediterranean and Euxine seas in both Europe and Asia, and the gulphs of Arabia, Persia, India, Bengal, and Siam, in Asia, to carry maritime commerce into the interior parts of that great continent . . . (p. 25)

Great thinkers such as Braudel (1972, 1981–4) and McNeill (1963, 1974), and important recent historians such as E. L. Jones (1981) and Crosby (1986), have placed the geography and climate of Europe at the center of their explanations for Europe’s preeminent success in economic development. Braudel points to the key role of the Mediterranean-based and northAtlantic coastal economies as the creative centers of global capitalism after the ﬁfteenth century. McNeill similarly stresses Europe’s great advantages in coastal trade, navigable rivers, temperate climate, and suitable disease patterns as fundamental conditions for European takeoff and eventual domination of the Americas and Australasia. Crosby details the advantages of the temperate zones in climate, disease ecology, and agricultural productivity. Two important essays, one by the Council on Foreign Relations (Lee, 1957), and one a generation later by Kamarck (1976) for the World Bank, synthesized these arguments in excellent surveys on Tropical Development, which have been largely ignored by the formal modelers of economic development. Historians have also stressed the changing nature of geographical advantage over time, as technology changes. In early civilizations, when transport and communications were too costly to support much interregional and international trade (and virtually any oceanic trade), geographical advantage came overwhelmingly from agricultural productivity rather than from access to markets. Therefore, early civilizations almost invariably emerged in highly fertile river valleys such as the Nile, Indus, Tigris, Euphrates, Yellow and Yangtze rivers. These civilizations produced high-density populations that in later eras were actually disadvantaged by their remoteness from international trade. Northern Europe could not be densely settled before the discovery of appropriate technologies (e.g. the moldboard plow in the Middle Ages) and tools to fell the great northern forests (Landes, 1998). Similarly, as the advantages of overland trade and coastal-based trade between Europe and Asia gave way to oceanic commerce in the

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sixteenth century, economic advantage shifted from the Middle East and eastern Mediterranean, to the north Atlantic. In the nineteenth century, the high costs of transport of coal for steam power meant that early industrialization almost invariably depended on proximity to coal ﬁelds. This advantage of course disappeared with the discoveries of petroleum reﬁning, oil and hydro-based electricity production, and reduced cost of bulk transport. Railroads, automobiles, and air transport, as well as all forms of telecommunications, surely reduced the advantages of the coastline relative to the hinterland, but according to the evidence below, the advantages of sea-based trade remained. To summarize, we can say that leading historians and economists have long recognized geography as a crucial scaffolding for economic development, even though geography has been neglected in most recent empirical studies of comparative development. Leading thinkers have pointed to four major areas in which geography will play a fundamental and direct role in economic development: transport costs, human health, agricultural productivity (including animal husbandry); and proximity and ownership of natural resources (including water, minerals, hydrocarbon deposits, etc.). The factors may also have indirect effects, if ﬁrst-mover advantages or population densities affect subsequent growth dynamics through agglomeration economies or other feedback mechanisms.8 The models in this text have formalized Smith’s ideas that geography affects transportation cost, which determines the extent of the market, which determines the level of division of labor, which determines in turn productivity and development performance. We develop Smithian static and dynamic equilibrium models to explore the intimate relationships between geography, trading efﬁciency, the equilibrium network size of division of labor, the extent of the market, urbanization, and productivity. In the models, the equilibrium network size of division of labor is determined by all individuals’ networking decisions. The networking decisions determine each player’s numbers of traded goods and trade partners. The tradeoff between transaction costs and positive network effects of division of labor on aggregate productivity determines the equilibrium level of division of labor and equilibrium aggregate productivity. Coastal areas and areas that are close to navigable rivers have a greater scope for trading-off economies of specialization against transaction costs than landlocked areas, so that the extent of the market and the equilibrium level of division of labor are greater in the former than in the latter. In chapter 11 we shall develop several Smithian models of urbanization. These models show that the geographical conditions that are favorable for transportation will generate great economies of agglomeration. This implies a fast coevolution of urbanization and division of labor. In chapter 12, several Smithian models with an endogenous number of producer goods and endogenous degree of production roundaboutness show that geographical conditions that are favorable for transportation will generate a larger equilibrium number of producer goods, a greater degree of production roundaboutness, and more outsourcing trade. In chapter 14, a Smithian dynamic general equilibrium model shows such favorable geographical conditions can speed up spontaneous coevolution of division of labor and the extent of the market. It predicts that those countries in islands or coastal areas will enter takeoff stage of economic development earlier than hinterland or landlocked areas do. The prediction of the models is consistent with the empirical observation documented in Radelet and Sachs (1998b) that only those developing countries with good transport access to world markets have been able to establish assembly-type industries and to adopt laborintensive export-oriented industrialization patterns. So far we have stressed that geography may inﬂuence economic development directly through transportation efﬁciency and level of division of labor. Geography can have another potent effect by affecting the choice of economic policies and institutions. Countries with favorable geographical conditions for transportation, for example, may choose more open trade policies

44 P ART I: D EVELOPMENT M ECHANISMS

than countries with unfavorable geographical conditions for transportation. The Ricardian model with transaction costs and an endogenous trade policy regime in chapter 3 provides a formal general equilibrium mechanism that predicts the relationship between geography and government policies. In that model, there is a trade-off between the positive network effect of division of labor on aggregate productivity, transportation costs, and distortions caused by tariffs. As transportation efﬁciency is improved, the general equilibrium discontinuously jumps from autarky ﬁrst, to the partial division of labor where one country produces two goods and the other country completely specializes in producing one good, then to the complete division of labor where each country produces only its comparative advantage good. For the partial division of labor, the terms of international trade are determined by the domestic terms of trade in the less-developed country which is not completely specialized. In the absence of tariffs, all gains from trade will go to the developed country that completely specializes. Hence, the less-developed country can use import tariffs to obtain most gains from trade by altering the terms of international trade. But the developed country will hurt itself by imposing any positive tariffs. Hence, in this transitional stage of economic development, unilateral free trade in the developed country coexists with unilateral protection tariffs in the less-developed country. As transportation efﬁciency is improved, the equilibrium is associated with the complete division of labor in which two countries have incentive to engage in Nash tariff bargaining, in order to avoid a tariff war which will exhaust gains from trade. Such Nash tariff negotiation will generate bilateral free trade. This general equilibrium mechanism which simultaneously determines the trade policy regime and level of division of labor can tell the following story about the relationship between geography and policy regime. Transportation efﬁciency is higher in an island or coastal economy than in a hinterland or landlocked economy. Hence, the equilibrium level of division of labor is higher in the former than in the latter. The higher level of division of labor is associated with a free trade policy regime, while the low level of division of labor is associated with unilateral protectionist tariffs. If two countries, such as Britain and France, are coastal, their favorable geographical conditions for transportation generate a high level of division of labor between them. As a result, each country can increase the share of gains from trade that it receives by increasing import tariffs to manipulate terms of trade. Such a tariff war will generate deadweight that exhausts all gains from trade. Therefore, both countries will have an incentive to adopt a multilateral free trade regime via Nash tariff negotiations. In chapter 3, we will extend the Ricardian model with two countries to the case with three countries. It will be shown that favorable geographical conditions for transportation will increase the number of countries that might be involved in international trade. This increase in the number of potentially trading countries creates pressure to exclude the country with higher tariffs from trade even if this country has a comparative advantage in producing a good. This implies that favorable geographical conditions will increase the potential number of trading countries and thereby press all countries to adopt free trade policy.

2.3

EMPIRICAL LINKAGES OF GEOGRAPHY AND ECONOMIC DEVELOPMENT

2.3.1 Geographical correlates of economic development The basic theories in this volume point to two broad categories of geographical factors of deep signiﬁcance: transport costs, and production condition parameters that affect the degree of comparative advantage. Consider ﬁrst the transport costs. Remarkably, despite the likely

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importance of transport costs for economic development, there are no adequate measures of transport costs for a large sample of developed and developing countries. The best that we could obtain for a large number of countries is the IMF estimates of the CIF/FOB margins in international trade. These margins measure the ratio of import costs inclusive of insurance and freight (CIF) relative to import costs exclusive of insurance and freight (FOB). There are several problems with these measures, the most important being that: (1) they are only crudely estimated by the IMF staff; and (2) they depend on the composition of imports, and thus are not standardized across countries. Nonetheless, the CIF/FOB margins are informative, and predictive of economic development. The CIF/FOB margin for 1995 is 3.6 percent for the US, 4.9 percent for western Europe, 9.8 percent for east Asia, 10.6 percent for Latin America, and a whopping 19.5 percent for sub-Saharan Africa.9 Gallup and Sachs estimate an equation relating the CIF/FOB band to the distance of the country to the “core” areas of the world economy (Distance, measured in thousands of kilometers), and to the accessibility of the country to sea-based trade, by including a dummy variable for non-European landlocked countries (Landlocked): CIF/FOB = 1.06 + 0.010 Distance (1,000 km) + 0.11 Landlocked (84.9) (3.0) (2.4) N = 83, R2 = 0.32[10] As expected, there is a penalty both for distance from the core economies and for being landlocked. Each 1,000 km raises the CIF/FOB margin by 1.0 percentage points; being landlocked raises the CIF/FOB margin by 11.1 percentage points. We will show later that the CIF/FOB margin is indeed predictive of income levels and economic development. Regressing CIF/FOB on the proportion of the population within 100 km of the coast (Pop100km), Gallup and Sachs also ﬁnd a negative effect, but when they include both Pop100km and Landlocked, Landlocked has more explanatory power. The coefﬁcient on Pop100km remains negative, as expected, but drops in magnitude and is statistically insigniﬁcant. We saw in table 2.1 that the various regions in the world differ markedly in locations of their populations relative to the seacoast and navigable rivers. African populations especially are far from the coastline, while Europe is overwhelmingly coastal. Indeed, Africa has the highest proportion of landlocked population of any continent in the world, and especially in east Africa, the populations are heavily in the interior (beyond 100 km of the coast) even in countries with coastlines such as Kenya (coastal population equals 6 percent of the total), Mozambique (40 percent), Sudan (2 percent), and Tanzania (16 percent). The situation is made worse by the fact that Africa’s interior regions are not accessible by ocean-navigable vessels, since the river systems in Africa almost all face impassable barriers (e.g. cataracts, shallows, etc.) that prevent the entry of ocean-going vessels into the interior of the continent. The notion that the coastal access has a large effect on trade and development is plausible given what we know about the growth patterns of the most successful developing countries in the period after 1965. Almost without exception, fast-growing developing countries have based their rapid growth on labor-intensive manufacturing exports. And almost without exception, such activities have expanded in port cities or export zones close to ports. As shown in Radelet and Sachs (1998b), almost all countries with macroeconomic success in labor-intensive manufacturing exports have populations almost totally within 100 km of the coast. Geographical conditions affect the equilibrium degree of urbanization and the equilibrium level of division of labor via their effects on transportation conditions (see chapter 11). Most large cities other than garrison towns or administrative capitals typically grow up on coastlines or ocean-navigable rivers. Therefore, countries with neither coastlines nor navigable rivers

46 P ART I: D EVELOPMENT M ECHANISMS

tend to have less urbanization, and less growth. A simple regression estimate for 149 developed and developing countries in 1995 shows that more ocean-accessible regions in the world are indeed also more urbanized, as are economies closer to the economic core regions. In a simple regression Gallup and Sachs ﬁnd: %Urban = 132.3 + 17.1 Pop100km − 10.8 LDistance (10.8) (3.6) (7.1) N = 149, R2 = 0.29 where %Urban is population share of urban residents, Pop100km is the proportion of the population within 100 km of the coast, and LDistance is the log of the distance to the core areas. A second major dimension of productivity linked to geography is the prevalence of infectious disease. As shown in Gallup and Sachs (1998), malaria, with an estimated incidence of between 200 and 500 million cases per year (WHO, 1997a), is almost entirely concentrated in the tropics. There is no effective prophylaxis or vector control for malaria in the areas of high endemicity, especially sub-Saharan Africa. Earlier methods of vector control are losing their effectiveness because of increased resistance of the mosquitoes to insecticides. Standard treatments are also losing effectiveness because of the spread of resistance to chloroquine and other antimalarial drugs. The geographical extent of malaria is determined mostly by the ecology of the parasites (different species of malaria Plasmodia) and the vectors (different species of Anopheles mosquitoes). Malaria was brought under control since 1945 mainly in temperate-zone and subtropical environments, where the foothold of the disease (both in terms of the mosquito population and the parasite endemicity) was more fragile. Gallup and Sachs (1998) also show the extent of endemic malaria in 1946, 1966 and 1994, with its gradually retreat to the core tropics. Using data from the World Health Organization, they construct a measure of malaria intensity. A simple regression of malarial intensity on ecological zones shows that it is most intense in the tropics and somewhat less in the subtropics (relative to all other ecozones). There is also a strong “sub-Saharan Africa” effect. Malarial Intensity (scale 0 to 1) = −0.01 + 0.3 Wet Tropics + 0.5 Dry Tropics + 0.4 Wet Subtropics + 0.2 Dry Subtropics (0.7) (2.0) (4.9) (3.9) (1.5) +0.5 sub-Saharan Africa, (6.7)

N = 148, R2 = 0.74

The pattern for malaria is common for a range of infectious diseases, whose vectors of transmission depend on the tropical climate. Many diseases that are carried by mosquitoes (dengue, yellow fever, and lymphatic ﬁlariasis in addition to malaria), mollusks (e.g. schistosomiasis), and other arthropods (onchocerciasis, leishmaniasis, trypanosomiasis, Chagas’ disease, and visceral ﬁlariasis), are endemic in the tropical ecological zones and nearly absent elsewhere. While data on disease burdens by country are generally not available, the recent massive study by Murray and associates on the burden of disease (Murray and Lopez, 1996), conﬁrms the heavy tropical concentration of infectious disease as a cause of death. A third major correlate of geography and productivity is the link of climate and agricultural output. Gallup’s (1998) estimates of agricultural productivity suggest a strong adverse effect of tropical ecozones on the market value of agricultural output, after controlling for inputs such as labor, tractors, fertilizer, irrigation and other inputs. Gallup (1998) suggests that tropical agriculture suffers a productivity decrement of between 30 and 50 percent compared with temperate-zone agriculture, after controlling as well as possible for factor inputs.

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2.3.2 Geography and levels of per capita income Gallup and Sachs (1998) have examined the linkage of output to geography both in levels and rates of change of GDP. They start with the simplest speciﬁcation, writing the log level of per capita income as a function of three underlying geographical variables: (1) Tropicar, the percentage of land in the geographical tropics; (2) Pop100km, the proportion of the population within 100 km of the coastline; and (3) LDistance, the minimum log-distance of the country to one of the three core regions, measured speciﬁcally as the minimum log-distance to New York, Rotterdam, or Tokyo. This relationship are estimated three times: for Maddison’s GDP estimates for 1950 and 1990, and for the World Bank’s PPP GDP estimates for 1995 on the subset of countries for which Maddison’s data are available. In all three regression estimates, reported in Table 2.2 output is a positive function of Pop100km, and a negative function of Tropicar and LDistance. The magnitude of the effects tends to increase over time, as expected. In 1950, the “penalty” for Tropicar was −0.69, signifying that tropical areas were only 50 percent (= exp(−0.69)) of per capita income of the nontropical areas controlling for the other factors. By 1995, the effect has risen to −0.99 (or 37 percent of the nontropical areas). Similarly, the beneﬁt of a coastal population rose from 0.73 in 1950 to 1.17 in 1995. The suggestion is that being tropical, landlocked and distant was bad already in 1950, and adverse for growth between 1950 and 1995. Table 2.2 Levels of GDP

Tropical area (%) Pop100km (%) LDistance

(1) lgdp50

(2) lgdp90

(3) lgdp95

−0.69 (4.13)

−0.99 (5.78)

−0.99 (5.10)

0.71 (4.02)

1.00 (5.43)

1.09 (5.27)

−0.22 (2.56)

−0.39 (4.39)

−0.34 (3.41)

(4) lgdp95

0.85 (3.63)

(5) lgdp95 (non-Africa)

1.21 (4.17)

(6) lgdp95

0.36 (2.53) 0.03 (0.55)

Shipping Cost (CIF/FOB)

−2.28 (2.32)

−13.50 (4.66)

Malaria index 1994 (0–1)

−1.55 (6.60)

−1.26 (2.69)

−1.15 (7.65)

Log hydrocarbons per person

0.01 (1.84)

0.01 (1.75)

0.01 (1.85)

Socialism

−0.05 (0.31)

New state (0–3)

−0.06 (0.98)

Trade Openness (0–1)

0.23 (7.38)

Public Institutions (0–10)

0.55 (3.17)

Constant

9.07 (13.58)

11.19 (16.26)

10.98 (14.10)

10.84 (9.82)

22.64 (7.42)

6.71 (11.06)

Observations R2

129 0.38

129 0.58

129 0.50

83 0.69

52 0.56

97 0.88

Note: Absolute value of t-statistics in parentheses.

48 P ART I: D EVELOPMENT M ECHANISMS

We now turn in more detail to the 1995 data, for which we have a wider range of possible explanatory variables. This simple level equation for GDP per capita on a PPP-basis in 1995 is ﬁrst estimated, for the 150 countries with population greater than 1 million. Then growth equations for the period 1965–90 are considered. The explanatory variables are grouped into three broad categories: (1) variables related to transport costs and proximity to markets; (2) variables related to ecological zone; and (3) variables related to economic and political institutions. In regression (4) of table 2.2, the explanatory variables are limited to a parsimonious set of four variables closely linked to geography: the prevalence of malaria; transport costs as measured by the CIF/FOB margin; the proportion of the country’s population near the coastline; and the endowment of hydrocarbons per capita. These four variables alone account for 69 percent of the cross-country variation in per capita income, and are all with the expected sign and statistically signiﬁcant (hydrocarbons only at the 10 percent level). High levels of GDP per capita are associated with the absence of malaria; low transport costs; a coastal population; and a large endowment of hydrocarbons per capita. Of course, these associations are hardly a proof of causality. Not only might the explanatory variables be proxies for left out variables (e.g. malaria may be proxying for a range of tropical diseases or other liabilities), but there could also be reverse causation, in which high incomes lead to the control of malaria, or to a reduction of transport costs. In regression (6), variables related to political and economic institutions are included: Socialism, which is a dummy variable for socialist economic institutions; New State, which measures the proportion of time under colonial rule; Public, which measures the quality of governmental institutions; and Open, which measures the proportion of time between 1965 and 1990 that the country is open to international trade. These variables relate to endogenous transaction costs. The relationships between endogenous transaction costs, institutions, evolution in division of labor, and economic development will be investigated in chapters 8, 9, and 10 in Part II. It is found, in line with many recent studies, that openness and quality of public institutions are highly correlated with the level of income. The socialist variable is not signiﬁcant, probably because of the strong collinearity with Open and because of the smaller data set once Gallup and Sachs include the Public variable (since that variable is not available for most of the socialist economies). Newly independent countries also do not have signiﬁcantly lower income levels. If the malaria index is not included, the new state variable is highly signiﬁcant, which suggests the possibility that the heavy burden of disease in tropical Africa and Asia made these regions more susceptible to colonization. Gallup and Sachs ﬁnd, importantly, that both policy and geography variables are strongly correlated with the level of 1995 per capita GDP. Remember that geography may be even more important than suggested by this equation, since there are reasons to believe that favorable geography plays a role in inducing growth-promoting institutions such as open trade and an efﬁcient public bureaucracy. We examine this linkage, brieﬂy, below.

2.3.3 Geography and growth of per capita income We now examine the forces of convergence and divergence by estimating a cross-country growth equation that allows for the possibility of catching-up effects. Gallup and Sachs (1998) have run a Barro regression. They estimate a model of average annual growth during 1965–90 conditional on per capita income levels in 1965. The dates are determined by data availability. For the purposes of the growth equations, they use the Penn World Tables for measures of PPP-adjusted GDP per capita. They test whether growth is affected by the initial income level (negatively in the case of convergence, positively in the case of divergence), as well as by geographical variables holding constant the initial income and other policy and institutional variables.

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E CONOMIC D EVELOPMENT 49

Table 2.3 GDP growth (1) gr6590

(2) gr6590

(3) gr6590

(4) gr6590

(5) gr6590 (TSLS)

(6) gr6590

(7) gr6590

GDP p.c. 1965

−2.3 (7.70)

−2.4 (8.02)

−2.5 (8.06)

−2.6 (7.87)

−2.7 (7.60)

−2.3 (7.41)

−2.4 (7.09)

Years of secondary schooling

0.3 (1.75)

0.2 (1.77)

0.2 (1.32)

0.2 (1.34)

0.2 (1.15)

0.1 (0.81)

0.1 (0.89)

Log life expectancy 1965

6.6 (7.23)

5.5 (6.21)

4.3 (4.45)

3.3 (3.60)

2.4 (1.79)

4.1 (4.53)

3.4 (3.89)

Trade openness 1965–90 (0–1)

1.9 (5.49)

1.9 (4.79)

1.7 (4.79)

1.7 (4.70)

1.7 (4.39)

1.8 (4.79)

1.8 (4.66)

Public institutions (0–10)

0.3 (3.08)

0.3 (2.63)

0.3 (3.32)

0.4 (3.92)

0.5 (3.66)

0.3 (3.20)

0.4 (3.47)

LDistance

0.0 (0.24)

Pop100km (%)

1.0 (3.07)

0.9 (3.01)

0.8 (2.64)

0.6 (1.91)

−0.9 (2.28)

−0.6 (1.35)

−0.5 (1.09)

−0.4 (0.82)

−0.7 (1.89)

−0.5 (1.44)

−1.2 (2.15)

−2.0 (3.60)

−2.6 (3.87)

−0.9 (1.86)

−1.6 (2.89)

−2.5 (3.93)

−4.5 (2.12)

Tropical area (%) Malaria index 1966 dMal6694

−1.9 (2.94)

Log coastal density

0.3 (4.91)

0.2 (4.34)

Log inland density

−0.1 (2.26)

−0.1 (1.60)

Constant

−8.9 (2.90)

−4.1 (1.17)

1.3 (0.34)

5.9 (1.57)

9.8 (1.76)

0.7 (0.19)

4.1 (1.08)

Observations R2

75 0.71

75 0.75

75 0.77

75 0.80

75 0.78

75 0.80

75 0.82

Note: Absolute value of robust t-statistics in parentheses.

They start with a baseline equation similar to those in Barro and Sala-i-Martin (1995), in which average annual growth between 1965 and 1990 is a function of initial income in 1965; the initial level of education in 1965 (measured by average years of secondary school in the population); the log of life expectancy at birth in 1965; the openness of the economy to international trade; and the quality of public administration (regression (1) of table 2.3). Evidence for conditional convergence, and standard results for the other variables are found: average growth rate is an increasing function of education, life expectancy, openness, and the quality of public administration. In regression (2) of table 2.3, Tropicar and Pop100km are highly signiﬁcant and of the expected sign. All other things equal, annual growth is 0.9 percentage points lower in tropical countries than in nontropical countries. Landlocked countries (Pop100km = 0) experienced 1.0 percentage points slower growth than coastal economies. Interestingly, the LDistance variable is not signiﬁcant. This suggests that distance to the core may be endogenously determined by openness and quality of public institutions

50 P ART I: D EVELOPMENT M ECHANISMS Table 2.4 Levels and changes in malarial prevalence between 1966 and 1994, by ecozone Predominant ecozone Temperate (N = 57)

Malaria index 1966 (0 –100)

Average change 1966–94

0.2

−0.2

27.8

−8.8

Subtropical (N = 42)

61.7

−5.0

Tropical (N = 21)

64.9

0.5

Desert (N = 23)

Note: Countries are classiﬁed by their predominant ecozone from the following groupings: Temperate (temperate, boreal, and polar ecozones), Desert (tropical and subtropical deserts), Subtropical (nondesert subtropical), and Tropical (nondesert tropical). The index and average reduction are unweighted averages over countries.

during the period. If those two variables are dropped, then LDistance has the expected negative sign with statistical signiﬁcance (not shown). In regression (3) of table 2.4, Ldistance is dropped and a measure of malaria at the beginning of the period is added. Initial malaria incidence has a dramatic correlation with poor economic performance. Countries that had severe malaria in 1966 grew 1.2 percentage points per year slower than countries without falciparum malaria, even after controlling for life expectancy. The estimated effect of being in the tropics becomes smaller than it was without the malaria variable, and insigniﬁcant. Clearly, the malaria variable is picking up the explanatory power of the tropics variable. The effect of initial life expectancy is also reduced, though still large and signiﬁcant. In fact, none of the countries in the sample with 100 percent of their land area subject to falciparum malaria were able to eradicate it completely over this period. The reductions in malaria were largest in the countries with the least malaria in 1966. The temperate ecozones were effectively free of falciparum malaria in 1966. The reductions in malaria occurred in the desert (nontemperate) regions, and the subtropics. There was a small increase in the malaria index for countries in tropical ecozones. The change in malaria incidence could be partly due to economic growth if growth provided countries with the economic resources and institutional wherewithal to carry out effective control programs. To account for the possible impact of economic growth on malaria reduction, Gallup and Sachs instrument the malaria change with four subtropical ecozone variables and two desert tropical ecozone variables. Regression (5) shows that the estimated impact of malaria on growth increases when change in malaria is instrumented. There is no indication that faster growth is the cause of malaria reduction. Some of the countries that have had the largest increases in malaria, like India and Sri Lanka, have had steady, if unspectacular, economic growth over this period. Likewise some countries with dramatic decreases in malaria, like Namibia, had almost no economic growth. It is only after controlling for other relevant variables that the effect of malaria reduction on growth becomes apparent. The index of malaria, and malaria change, may be more than just a measure of malaria. It may be picking up the incidence of other tropical diseases not well indicated by the average life expectancy and tropical area. Among tropical diseases, malaria is widely recognized to be the most important, but the malaria index may also be a proxy for scourges like onchocerciasis, ﬁlariasis, and trypanosomiasis. Malaria occurs throughout the tropics, but severe malaria is heavily concentrated in subSaharan Africa. Africa currently has 90 percent of the estimated cases of malaria each year (WHO, 1997a), and it is the only region of the world where falciparum malaria predominates.

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In regression (6) agglomeration effects are tested. The basic idea is to see how economic growth depends on the extent of the market which is associated with the level of division of labor according to Young (1928). A plausible measure of extent of the market is GDP per km2 within the economy in the initial year, 1965. Gallup and Sachs (1998) separate GDP per km2 on the coast and GDP per km2 in the interior, for reasons discussed earlier: high population density on the coast is likely to be associated with an increased division of labor due to a favorable transport condition, while high population density in the interior is likely to be associated with disintegrated economy and low level of division of labor due to an unfavorable transport condition. Note that ln(GDP density) = ln(GDP per km2) = ln(GDP per capita) + ln(Population per km2), and since ln(GDP per capita) is already a regressor, population density or GDP density can enter interchangeably into the regression. For countries in which the entire population is within 100 km of the coast, the interior population density is put at zero. For countries in which the entire population is farther than 100 km from the coast, the coastal population density is put at zero. Pop100km is also dropped as a separate regressor, since Pop100km is highly collinear with the two population density variables. The 1994 measures of Pop100km and the 1965 population levels for the country are used as a whole to calculate the population densities in the coastal and interior regions. The regression estimate is revealing. It shows that higher coastal population density is associated with faster growth, while higher interior population density is associated with lower growth. Thus, there appear to be economies of agglomeration, which are generated by network effects of division of labor, at play in the coastal regions. Large populations appear to be a net disadvantage for inland economies since adverse transportation conditions generate a low level of division of labor and a low level of market integration. Hence, a large population is divided among isolated local economies with inferior development performance. The Smith–Young models in chapters 7, 11, and 12 provide theoretical prediction of this phenomenon. With separate inland and coastal agglomeration effects in regression (6), the estimated effect of malaria becomes less precise, slipping to a 7 percent signiﬁcance level. On the other hand, if initial malaria and malaria change are included as in regression (7), they are both strongly signiﬁcant, but the diminishing returns of interior population density loses statistical signiﬁcance. The limits of the degrees of freedom in data are pushed, but the results suggest that both malaria prevalence and inland population concentrations are detrimental to growth. General conclusions from the growth equations are as follows. First, both institution and geography variables matter. There is no simple “geographic determinism” nor a world in which only good institution matters. The tropics are adverse for growth, while coastal populations are good for growth. The tropical effect seems to be strongly related to the prevalence of malaria. This could be the true direct and indirect effect of that disease, or more likely, a proxy for a range of tropical maladies geographically associated with malaria. The access to coast seems to matter in lowering transport costs and in allowing for agglomeration economies and related division of labor. A dense coastal population is actually seen to be favorable to economic growth during 1965–90, while a dense interior population is adverse. If we summarize the implications on a region by region basis, we conclude the following. Africa is especially hindered by its tropical location; by its high prevalence of malaria; by its low proportion of the population near the coast; and by the low population density near the coast. Europe, North America, and east Asia, the core regions, by contrast, are favored on all three counts. South Asia is burdened by a high proportion of the population in the interior, a very high interior population density, and a large proportion of the land area in the tropics. The transition economies of eastern Europe and the former Soviet Union, many of which are landlocked, are burdened by a very low proportion of the population near the coast and very low population density near the coast, but these countries are beneﬁted by lack of exposure to tropical disease. Finally, Latin America is moderately coastal, but with relatively low coastal

52 P ART I: D EVELOPMENT M ECHANISMS

population densities. Also, Latin America has a moderate exposure to the problems of tropics, including the prevalence of malaria.

2.3.4 Geographical effects on economic policy choices We have noted in the theoretical section that geography may affect economic policy choices by altering the trade-offs facing government. Two coastal countries may prefer high levels of specialization, so that they face a tariff war between countries with high levels of specialization since they can both manipulate terms of trade using tariff policies. This generates incentives for both countries to achieve bilateral free trade via Nash tariff negotiations. As a result, coastal governments may choose a free trade regime. An inland country may choose a low level of specialization due to adverse transportation conditions. As a result, a revenuemaximizing inland sovereign may choose to impose harsh trade taxes, thereby getting more gains from trade by manipulating terms of trade. In this section, we brieﬂy explore this idea with the data at hand, focusing on the choice of openness versus closure to trade in the period 1965–90 as affected by geography. The ﬁrst step is to check the underlying notion: that the responsiveness of growth to openness actually depends on geography. So far, Open and the geography variables are entered in a linear manner, not allowing for interactions. To check the possibility of interactions, Gallup and Sachs estimate the basic regression equation for three sets of countries: all, coastal (Pop100km ≥ 0.5), and hinterland (Pop100km < 0.5), and check the coefﬁcient on the Open variable. Since degrees of freedom in this exercise are lost, Gallup and Sachs estimate the barebones growth equation, in which annual average growth between 1965 and 1990 is a function of initial income, Openness, malaria in 1966, the change in malaria between 1966 and 1995, and the log of life expectancy in 1965. The results for the Open coefﬁcient (β) are as follows (robust t-statistics in parentheses): All economies (N = 92), β = 2.6 (6.8); coastal economies (N = 46), β = 3.3 (6.5); hinterland economies (N = 46), β = 1.4 (2.5). We see that the growth responsiveness to trade seems to be more than twice as high in coastal economies. The next step is to see whether more coastal economies in fact choose more open trade policies. This Gallup and Sachs do by regressing the extent of openness during 1965–90 on the proportion of land within 100 km of the coast (Land100km), Tropicar, and the initial income level: Open6590 = −1.12 + 0.23 Land100km − 0.18 Tropicar + 0.19 lnGDP1965 (3.2) (2.1) (2.0) (4.5) N = 106, R2 = 0.44 There does indeed seem to be something to this line of reasoning, though the results are at best suggestive, and should be tested more carefully in later work. The early liberalizers, on the whole, were the coastal economies. This is certainly evident in east Asia, where countries such as Korea, Malaysia, Taiwan, Thailand, all opened their economies to trade early in the 1960s, much before the other developing countries. Two important geographical characteristics affect coevolution of division of labor and institutions via their impacts on transportation condition and trading efﬁciency. Coastal regions, and regions linked to coasts by ocean-navigable waterways, are strongly favored in development relative to the hinterlands. Landlocked economies may be particularly disadvantaged by their lack of access to the sea, even when they are no farther than the interior parts of coastal economies, for at least three reasons: (1) cross-border migration of labor is more difﬁcult than

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internal migration; (2) infrastructure development across national borders is much more difﬁcult to arrange that similar investments within a country; and (3) coastal economies may have military or economic incentives to impose costs on interior landlocked economies. All of the three factors affect the trading efﬁciency of a landlocked country, so that as predicted in chapter 3, coevolution of division of labor and institutions is slower in such a country. High population density seems to be favorable for economic development in coastal regions with good access to internal, regional, and international trade. This may be the result of the interplay between increasing returns in construction of transportation infrastructure, network effects of division of labor, and transportation efﬁciency. Gallup and Sachs’ results show population density in the hinterland has no such advantages, and a net disadvantage. As shown in the Chu model (see exercise 14 in chapter 7), the coexistence of a high population density and favorable geographic conditions for transportation will reduce per capita investment in transport infrastructure and increase demand for infrastructure. This will make a professional infrastructure sector emerge from enlarged scope for trading-off the beneﬁt of increasing infrastructure expenditure against its cost in terms of reducing resources allocated to direct production. The professional infrastructure raises trading efﬁciency, thereby enlarging the scope for trading-off the positive network effect of division of labor on aggregate productivity against transaction costs. This leads to a larger network of division of labor, higher aggregate productivity, a greater degree of trade dependence, a greater market extent, more market integration, and higher aggregate productivity. Also, several general equilibrium mechanisms developed in chapters 7 and 11 show that if geographical conditions are favorable for transportation, then a high population density is associated with an integrated market and a high level of division of labor, so that aggregate productivity is high. If geographical conditions are unfavorable for transportation, then a high population density is associated with many separated local markets and a low level of division of labor, so that aggregate productivity is low. We thus see that economies are likely to bifurcate on two pathways. The hinterland will be characterized by a negative correlation between economic development and population growth. The coastline will be characterized by a positive correlation between economic development and population growth. The two systems will interact through ever-greater pressures on migration from the hinterland to the coast. As we have discussed, tropical regions are hindered in development relative to temperate regions, probably because of higher disease burdens and limitations on agricultural productivity. Chapters 3, 4, 5, and 11 will explore general equilibrium mechanisms that predict the phenomena. In those chapters we shall draw the distinction between endogenous and exogenous comparative advantage and analyze the effect of exogenous differences in geographic conditions on economic development and urbanization. Endogenous comparative advantage may emerge between ex ante identical individuals or countries. We shall show that the interplay between endogenous and exogenous comparative advantages generates very complicated stories about effects of geography on economic development and urbanization.

Key Terms and Review • The effects of the following geographic conditions on economic development: temperate zones, tropics, landlocked regions, coastal regions, regions close to ocean-navigable waterways • The relationship between geographical conditions, transaction costs, quality of institutions, the level of division of labor, and development performance

54 P ART I: D EVELOPMENT M ECHANISMS

Further Reading Gallup and Sachs (1998), Gallup (1998), Capie (1983), Kindleberger (1973), Reynolds (1985), Jeffrey Williamson (1992, 1993), Smith (1776), Yang and Borland (1991), Sachs, Yang, and Zhang (1999), Cheng, Sachs, and Yang (2000), Braudel (1972, 1981–4), Crosby (1986), E. Jones (1981), Kamarck (1976), Lee (1957), McNeill (1963, 1974), Murray and Lopez (1996), Radelet and Sachs (1998b), WHO (1997), World Bank (1997), CIA (1996, 1997), Curtin (1989).

QUESTIONS 1 According to E. L. Jones (1981, pp. 226–7), Europe’s very considerable geological, climatic, and topographical variety endowed it with a dispersed portfolio of resources. This conduced to long-distance, multilateral trade in bulk loads of utilitarian goods. Taxing these goods was more rewarding than appropriating them. Bulk trade was also favored by an abnormally high ratio of navigable routeways to surface area. Use the theories reviewed in this chapter to explain this historical fact. 2 Many scholars agree to the claim that “Fundamental springs of capitalist expansion are, on the one hand, the coexistence of several political units within the same cultural whole and, on the other, political pluralism which frees the economy” (see chapter 1). Several explanations are proposed for the ability of this geopolitical structure to persist for a long period of time. One is to attribute it to particular geographical conditions of western Europe and the Mediterranean which are favorable for long-distance trade between city-states and unfavorable for uniﬁcation wars. Around the Mediterranean and the English Channel, a great portion of highly populated areas were either coastal or island. The favorable conditions for trade were crucial for the emergence and evolution of capitalist institutions ( Jones, 1981, p. 233). In contrast, east Asian geopolitical structures ensured the hegemonism of Chinese culture prior to the invasion of Occidental cultures. Use the historical facts to analyze the relationship between political pluralism, the absence of overarching political power, institutional experiments, economic development, and geography. 3 Baechler (1976, pp. 93–5) surmises that Britain’s geographic condition ensured that it could avoid war with other countries, had low defense expenses, was able to preserve its unique Anglo-Saxon culture and common law tradition, and had transportation advantage for trade. Use this hypothesis to speculate on why Japan, Taiwan, and other island countries enter takeoff stage earlier than many inland countries. Find some counterexamples (for instance, Cuba). Use the counterexamples to analyze the effects of institutions and geographical conditions. 4 Explain why Singapore has a much better development performance than other tropic countries. 5 Smith did not discuss culture and economic development in any detail in The Wealth of Nations, but it seems clear that, in line with much thinking of the Scottish Enlightenment, he viewed human nature as universal, and did not view culture as a primary differentiating factor in economic development. After all, Smith saw the “propensity to truck, barter, and exchange one thing for another” as universal, not culturally speciﬁc. For example, Smith never bemoans the lack of entrepreneurial zeal in one place or another as an explanation for poor economic performance. Later

C HAPTER 2: G EOGRAPHY

6

7

8 9

10

11

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E CONOMIC D EVELOPMENT 55

thinkers such as Max Weber attributed the formation of the capitalist spirit to Protestant moral codes. Landes (1998) attributes Judaic-Christian culture to formation of the concept and institutions of private property. Recent empirical evidence for effects of culture on economic development can be found in La Porta, Lopezde-Silanes, Shleifer, and Vishny (forthcoming). They suggest that the Catholic tradition has a negative effect and Protestant tradition has a positive effect on development performance, and that the common law tradition has a positive and civil law tradition a negative effect on development performance. Discuss possible development mechanisms for coevolution of culture, institutions, and per capita real income. In connection with the discussion on the relationship between geopolitical structure and institutional evolution in western Europe, analyze why landlocked Austria and Switzerland have a much higher per capita income than other landlocked countries. Bearing in mind that the relationship between socialist experiment and economic development is analyzed in chapter 19, consider why landlocked Austria and Switzerland have much higher per capita income than the landlocked Czech Republic, Hungary, the Former Yugoslav Republic of Macedonia, Slovakia, and Russia. Analyze how geographical conditions affect the transition performance of ex-socialist economies in connection with the analysis in chapter 19. Though Gallup and Sachs (1998) did not ﬁnd strong evidence that distance from the core markets is endogenously determined by other variables, it is still subject to speculation that the formation of the core markets is endogenously determined by other geographical conditions and coevolution of institutions and division of labor. Bearing in mind the models in chapters 3, 7, 11, 12, and 14, conduct thought experiments about possible development mechanisms that may explain the formation of core markets. In chapters 5, 11, and 13, we will see that several general equilibrium models of high development economics with economies of scale predict that a large population will generate a higher degree of urbanization, a higher degree of industrialization, a higher productivity, a larger average size of ﬁrms, a higher per capita real income, a larger number of available goods, and a higher growth rate of per capita real income. But the Smith–Young models we consider in chapters 4, 7, 11, 12, and 14 show that if transport conditions are good, a large population size is associated with a high level of division of labor and a highly integrated market, so that productivity, degree of urbanization, industrialization and trade dependence, per capita real income and its growth rate are high, and the number of available goods is large. If transport conditions are not good, a large population size is associated with a low level of division of labor and many segregated local markets, so that productivity, degree of urbanization, industrialization and trade dependence, per capita real income, and its growth rate are low, and the number of available goods is small. Use the empirical evidence in this chapter to test these theoretical hypotheses. You may want to relate your discussion to the empirical evidence for rejecting various scale effects in Liu and Yang (2000), Y. Zhang (1999), the National Research Council (1986), Dasgupta (1995), C. Jones (1995a, b), reported in chapters 5, 13, and 14. Design a regression of reform performance on the geographical conditions of different provinces in China, different countries in eastern Europe, or other newly independent states. Test the claims made in this chapter.

56 P ART I: D EVELOPMENT M ECHANISMS

Notes 1 These ﬁgures refer to the unweighted average of per capita GDP of nine countries: China, Korea, Taiwan, Hong Kong, Singapore, the Philippines, Malaysia, Indonesia, and Thailand. 2 The geographical tropics refers to the area between the Tropic of Cancer (23.45 N latitude) and the Tropic of Capricorn (23.45 S latitude), the band in which the sun is directly overhead at some point during the year. 3 The landlocked countries in western and central Europe are Austria, the Czech Republic, Hungary, the Former Yugoslav Republic of Macedonia, Slovakia, and Switzerland. 4 Morocco is just on the borderline of classiﬁcation as a subtropical country, with 48 percent of the population in the tropical and subtropical ecozones. 5 Using geographical information system (GIS) data, the coastal population is calculated in two ways. First, all land area within 100 kms of the open sea, except for coastline in the arctic and subarctic region above the winter extent of sea ice (National Geography Society (NGS), 1995) are taken, and the population within that area is measured. Additionally, river systems that accommodate oceangoing vessels on a regular basis (e.g. the Saint Lawrence Seaway and the Mississippi River) are identiﬁed, and land areas within 100 kms of such navigable rivers are added. Since data of direct costs of transport for these river systems are not available, there are inevitably difﬁculties in classiﬁcation, as some ostensibly ocean-navigable rivers impose very high costs for such transport. Due to the classiﬁcation difﬁculties and the greater empirical relevance of coastal access alone, the population and land area near navigable rivers are not used in the rest of the chapter. 6 Gallup and Sachs (1998) experimented with a number of distance measures, all of which produced similar outcomes. They therefore chose the simplest: the smallest distance of the country’s capital city to one of the following three cities: New York, Rotterdam, or Tokyo. 7 He noted that “all the commercial beneﬁts” to the East and West Indies that might have resulted from increased trade “have been sunk and lost in the dreadful misfortunes” occasioned by European military advantage, which enabled the Europeans “to commit with impunity every sort of injustice in those remote countries.” 8 See chapter 11 for the deﬁnitions of various types of agglomeration economies and their relationship with the equilibrium level of division of labor. 9 The data refer to unweighted country averages for the respective regions for the countries for which IMF data are available. 10 Absolute values of t-statistics are in parentheses below the coefﬁcients, and N is the number of observations.

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DRIVING FORCE I – EXOGENOUS COMPARATIVE ADVANTAGE AND TRADING EFFICIENCY

3

3.1 USE OF THE CONCEPT OF GENERAL EQUILIBRIUM TO FIGURE OUT MECHANISMS FOR ECONOMIC DEVELOPMENT The ﬁrst question that development economics must address is: why can the wealth of a nation increase for a ﬁxed amount of an available resource or why can the degree of scarcity be reduced by individuals’ decisions in choosing their pattern of organization? Many economists have answered these questions by pointing to exogenous technical progress, which is deﬁned as technological changes that raise productivity and are independent of individuals’ decisions. In the Solow model (1956), the driving force of long-run growth in per capita income is such progress. A necessary condition for increases in productivity, per capita income, and output share of industrial goods in the Fei–Renis model (1964) is exogenous technical progress in the industrial sector. This method of explaining economic development is not interesting because we have known since Adam Smith that individuals’ decisions in choosing their levels of specialization can endogenously determine the wealth and productivity of a nation. Smith made a vague guess about the mechanism for economic development. He proposed the well-known Smith theorem: (1) division of labor is the mainspring of economic progress (1776, ch. 1, bk. I); (2) division of labor is dependent on the extent of the market (ch. 3, bk. I); and (3) the extent of the market is determined by transportation conditions (bk. I, pp. 31–2). If we specify a state equation that entails a positive relationship between productivity and transaction conditions, then it is not an interesting economic model, since this is equivalent to specifying total factor productivity as a function of time, as in the Solow model. An economic model of development must specify some trade-offs in decision-making, such that the efﬁcient balance of the trade-offs endogenously determines productivity. In other words, a very high productivity, like a very low productivity, is not efﬁcient because of the trade-offs, which imply that there are costs for the extremely high productivity. Hence, in order to formalize Smith’s conjecture, our job is to formalize some trade-off in individuals’ decisions of their levels of specialization. This task is not easy, since individuals’ decisions in choosing their levels of specialization involve corner solutions. Moreover, in order to understand a mechanism of economic development

58 P ART I: D EVELOPMENT M ECHANISMS

for society as a whole, we have to use a concept of general equilibrium that involves corner solutions to ﬁgure out the trade-offs in the marketplace. The equilibrium as a consequence of interactions between individuals’ decisions is, of course, much more complicated than individuals’ decisions. There are several reasons that the concept of general equilibrium is essential for investigating mechanisms for economic development. First, economic development involves interactions between prices and quantities. Not only are all individuals’ decisions in choosing quantities produced and consumed determined by prices, but market prices are also determined by all individuals’ decisions about quantities. In addition, there are interdependencies between markets for different goods and factors and between different individuals’ decisions. These interdependencies relate to circular causation, network effects of industrial linkages, and related decisions in different sectors that concern high-development economists. There are inﬁnite feedback loops between each pair of endogenous variables. For instance, as the price of a ﬁnal good changes, the demand curve for labor will shift. This shift will change the price of labor, which will shift the demand curve for that ﬁnal good. That shift will in turn change the price of that good, thereby shifting the demand curve for labor again. This feedback between the two markets will continue endlessly, though feedback effects attenuate after each round of feedback. Marshall’s partial equilibrium analysis considers only interactions between price and quantity in the market for a single good or factor and ignores all of the feedback loops, therefore generating misleading predictions. Hence, a partial equilibrium model is not a good vehicle for investigating mechanisms of economic development. Some partial equilibrium model of urban–rural migration is an example of this point. In the model, structural changes and migration between the rural and urban areas are explained by the wage differential between the two areas. But the wage differential is exogenously ﬁxed. The feedback loops between wage, income, demand, and supply are all ignored. We cannot tell from this model why there is such a wage differential, nor what the mechanism is for economic development. The second reason for using a general equilibrium model to investigate mechanisms for economic development relates to network effects of division of labor. Adam Smith considered division of labor to be a main driving force of economic development. But as Young (1928) and Yang and Ng (1998) indicate, the beneﬁts of division of labor are network effects. An individual’s decision in choosing her level of specialization determines not only her productivity, but also the extent of the market for others’ produce, thereby putting a constraint on others’ decisions in choosing their levels of specialization. The concept of network is by nature intimately related to the concept of general equilibrium. We cannot understand network effects by looking only at part of the network. In this chapter, we will show that a network of division of labor involves individuals’ corner solutions. Hence, marginal analysis for the interior solution does not work and inframarginal analysis is essential for investigating mechanisms of economic development. Either a static or dynamic general equilibrium model can be used to study the mechanism for economic development. Comparative statics of the static general equilibrium model explain changes in endogenous variables by changes in parameters representing tastes and the technical, natural, and social environments. Endogenous variables may include prices, productivity, economic structure, and some institutional features of the economy. Some parameters may represent exogenous institutional conditions as well. If productivity increases and economic structure changes in response to changes in some parameters, the chain of causation based on comparative statics of general equilibrium can explain the mechanism of economic development as the consequence of interactions between self-interested decisions (behavior). Simple partial equilibrium models cannot count all feedback loops based on such interactions. Simple decision models cannot explain the consequence of all direct and indirect interactions between selfinterested decisions.

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 59

If dynamic general equilibrium models are used to study mechanisms for economic development, some dynamics of general equilibrium may generate economic development in the absence of exogenous changes in parameters. Comparative dynamics of general equilibrium can be used to investigate changes in dynamics in response to changes in parameters. Hence, dynamic general equilibrium models may have a higher degree of endogenization, which is supposed to imply more explanatory power. However, dynamic general equilibrium models are more difﬁcult to manage than static general equilibrium models. In order to solve for dynamics or comparative dynamics of general equilibrium, stronger assumptions are essential for keeping the models tractable. This implies that the tractable dynamic general equilibrium models may have a lower degree of endogenization than do tractable static general equilibrium models. Therefore, we have a trade-off between advantages and disadvantages of static and dynamic general equilibrium models. This text will show that static general equilibrium models may be more powerful for investigating mechanisms of economic development that involve interesting and sophisticated structural changes. In this chapter, we use inframarginal analysis of the Ricardian and Heckscher–Ohlin models to investigate a general equilibrium mechanism for economic development. The story behind the formal model runs as follows. There are technological comparative advantages between two types of individuals. This implies that even if one type of individual is less productive in producing all goods than an individual of another type, the productivity difference between the two types is not the same across goods. Thus, the second type of individual can specialize in producing a good with a smaller productivity difference, so that all individuals may gain from a division of labor and trade that generates a higher aggregate productivity than in autarky. We deﬁne comparative advantage based on ex ante differences of production conditions between individuals as exogenous comparative advantage. In this text, ex ante means “before individuals have made decisions” and ex post means “after individuals have made decisions, and the economy has settled down in equilibrium.” If all individuals prefer diverse consumption, then there is a tension between utilization of comparative advantages and diverse consumption. Some individuals must specialize in producing one good in order to exploit exogenous comparative advantage. But the specialization of production and diversiﬁcation of consumption imply that individuals must trade. If trade involves transaction costs, then there is a trade-off between transaction costs and economies of division of labor generated by comparative advantages. The trade-off can be used to endogenize productivity. The production possibility frontier (PPF) is achieved when at least one type of individual completely specializes in producing one good. If a transaction cost coefﬁcient for one unit of goods traded is large, then transaction costs caused by trade outweigh productivity gains from it. Hence, the equilibrium is autarky where production takes place below the aggregate PPF, since the marginal rates of substitution and marginal rates of transformation must be equalized for each individual. If the transaction cost coefﬁcient is small, then productivity gains outweigh transaction costs caused by the division of labor, so that the equilibrium is the division of labor which is associated with the PPF. Since the trade-off between exploitation of comparative advantage and transaction costs can be used to explain the equilibrium aggregate productivity by the trading efﬁciency parameter, the aggregate productivity is endogenized even if the production function does not change. This general equilibrium approach to explaining productivity changes is much more interesting than technological fundamentalism, which explains productivity progress by changes in production functions, for it explains productivity changes as a consequence of interactions between self-interested decisions. If governments are introduced into this simple model, it can be used to predict their behavior in choosing tariff rates and in choosing amongst unilateral protectionist tariffs, unilateral laissez faire policy, and tariff negotiation. As transaction conditions are improved, the general equilibrium

60 P ART I: D EVELOPMENT M ECHANISMS

shifts from autarky to the partial division of labor, where one country completely specializes in producing one good and the other country produces two goods, then to the complete division of labor, where each country completely specializes in producing one good. For the partial division of labor, terms of international trade are determined by the production conditions in the country producing two goods. Hence, gains from trade all go to the country producing one good in the absence of tariffs. Thus, the country producing two goods can use tariffs to manipulate terms of trade in order to get a greater share of the gains. But the country producing one good will only hurt itself by imposing tariffs on imported goods, since this will increase the price of goods purchased by domestic residents. This implies that when the partial division of labor occurs in equilibrium, unilateral protectionist tariffs in the country producing two goods coexists with a unilateral laissez faire policy in the country producing one good. If the complete division of labor occurs in equilibrium, each country can get a greater share of gains from trade by increasing tariffs. But as the tariff rates in the two countries become sufﬁciently high, gains from trade can be exhausted by the deadweight caused by the tariff in the rent-seeking game. Hence, both countries may prefer tariff negotiation in a Nash bargaining game that generates trade liberalization. This explains the coexistence of unilateral protectionist tariffs and a unilateral laissez faire policy regime in the early stages, and tariff negotiation that generates bilateral trade liberalization in the later stages, of economic development. The driving force of this shift in trade policy is the improvements in transaction conditions that can be achieved via a better legal system, a better transportation infrastructure, urbanization, or a better banking system. The shift of trade policy from protectionist tariffs to trade liberalization is sometimes referred to as a shift from an import substitution to an export substitution strategy (see Bruton, 1998). Some development economists (for instance Palma, 1978, Bauer and Yamey, 1957) call the phenomenon of increasing income difference between the two countries as the equilibrium shifts from autarky to the partial division of labor, “underdevelopment.” Protectionist tariffs are often suggested as a policy instrument to avoid underdevelopment. But the Ricardian model with transaction costs and tariffs indicates that improvements of transaction conditions can shift equilibrium from the partial division of labor to the complete division of labor, which not only generates more gains from trade but also a more equal distribution of gains from trade. Many economists try to ﬁnd empirical evidence for or against the claim that terms of trade are worsening for developing economies. Some of them try to measure adverse effects of worsening terms of trade on economic development (see, for instance, Morgan, 1970 and Kohli and Werner, 1998). Recent empirical evidence provided by Sen (1998) shows that economic development and deteriorating terms of trade may concur. We shall show that in the process of moving to a high level of division of labor, a country may receive more gains from trade even if its terms of trade deteriorate. This is because an expansion of the network size of division of labor can generate productivity gains that outweigh the adverse effect of the terms of trade deterioration. This story can be extended to the Heckscher–Ohlin model with comparative endowment advantage and transaction costs. If the ex ante difference in production conditions comes from differences in production functions between individuals, then we say there is exogenous comparative technological advantage, which will be investigated in sections 3.2–3.5. If it comes from differences in factor endowments between individuals, then we say there is exogenous comparative endowment advantage, which will be studied in section 3.6. If two countries have different factor endowments, then they can employ the difference to increase equilibrium aggregate productivity. But if transaction efﬁciency is low, the efﬁcient trade-off between exploitation of comparative endowment advantage and transaction costs entails autarky and low productivity. As transaction conditions are improved, the equilibrium aggregate productivity and level of division of labor increase.

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 61

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n n

n n n n n n

n n

What are the differences between the general equilibrium mechanism and partial equilibrium mechanism for economic development? What are the differences between economic development caused by exogenous technological changes and economic development caused by individuals’ decisions in choosing their patterns of specialization? What is the distinction between absolute and comparative advantages? How can we measure division of labor and economies of division of labor? How can evolution of division of labor and related structural changes take place? What are the differences between the structural changes caused by evolution of division of labor and structural changes caused by exogenous technical changes? Why may unilateral protectionist tariffs and a unilateral laissez faire regime coexist in a transitional period from autarky to a high level of international division of labor? Why may an income differential between countries ﬁrst increase and then decline as the economy develops from autarky to an intermediate level of trade dependence, then to a high level of trade dependence? What is the distinction between a comparative technological advantage and a comparative endowment advantage? What is the driving force for a policy shift from protectionist tariffs to trade liberalization?

3.2

A RICARDIAN MODEL WITH EXOGENOUS COMPARATIVE TECHNOLOGICAL ADVANTAGE AND TRANSACTION COSTS

Before David Ricardo, economists did not pay attention to the distinction between absolute and comparative advantages. An individual has absolute advantage in producing good i if her labor productivity in good i is greater than that of the other individual. Ricardo (1817) drew economists’ attention to the distinction between this measure and the concept of comparative advantage. If person 2 is absolutely less productive than person 1 in producing both goods x and y, but the difference in productivity between the two individuals is greater for good y than for good x, then person 2 has a comparative advantage in producing good x, since her absolute disadvantage is relatively smaller in producing x than in producing y. Ricardo argued that as long as such a comparative advantage exists, a country having no absolute advantage in producing any good nonetheless can gain from trade, as can the other country which enjoys absolute advantage in all lines of production. Ricardo’s theory of comparative advantage is regarded as the foundation of modern trade theory. However, the Ricardian model has not attracted the attention it deserves. This lack of attention is attributable to the fact that conventional marginal analysis is not applicable to the Ricardian model because of corner solutions. There are two ways to set up the Ricardo model. One is to specify a dichotomy between pure consumers and ﬁrms. However, in the Ricardian model each country is a consumer as well as a producer. Hence, the corner solution may be chosen by a country. This speciﬁcation will entail multiple general equilibria based on several structures of corner and interior solutions of countries. Since in the Walrasian regime, ﬁrms’ proﬁt is always zero in each and every structure, ﬁrms do not care about choice of structure. Pure consumers cannot choose the structure of production. Therefore, the local equilibrium in each structure can be a general equilibrium. This multiplicity of general equilibria renders comparative statics analysis of general equilibrium impossible (see Dixit and Norman, 1980, p. 38).

62 P ART I: D EVELOPMENT M ECHANISMS

The second way to set up the Ricardian model is to use a Smithian framework. In this framework, each individual is speciﬁed as a consumer-producer, so that each individual can choose her level of specialization. In this framework, the general equilibrium is one of several corner equilibria, which efﬁciently trades-off economies of division of labor generated by exogenous technical comparative advantage against transaction costs. Hence, an inframarginal comparative statics of general equilibrium will generate very rich and interesting stories about economic development and trade. If the Ricardian model is speciﬁed within the neoclassical dichotomy between pure consumers and ﬁrms, domestic trade and international trade are not based on the same rationale: domestic trade is always necessary, while international trade is induced by exogenous comparative advantage. If the transaction efﬁciency coefﬁcient for domestic trade and that for international trade are the same, then international trade is always Pareto superior to autarky. The framework of consumer-producers not only avoids multiple equilibria, but also allows the model to explain international trade by individuals’ choices of their patterns of specialization. Within this framework, even when the domestic and international transaction cost coefﬁcients are the same, individuals still choose whether or not to engage in international trade, and autarky can be the unique general equilibrium structure when the transaction cost coefﬁcient is large. There are many ways to deﬁne transaction costs. One general deﬁnition of transaction costs is to assume a delivery function of goods such that the amount of goods that arrives at the destination is a function of the amount of goods that departs from the origin, and of other inputs essential for the delivery (see Hahn, 1971 and Kurz, 1974). The delivery function describes the technical conditions governing transactions. The difference between the amounts of goods at the origin and at the destination, together with any inputs employed in the delivery process, can be considered as transaction cost. This speciﬁcation of transaction costs involves a notoriously unmanageable set of indices of destinations and origins. This index set, compounded with corner solutions, makes it impossible to work out comparative statics of general equilibrium. Thus the general equilibrium implications of transaction costs in the models with this otherwise appealing speciﬁcation of transaction costs cannot be explored. Hence, a speciﬁcation of so-called “iceberg” transaction cost is often used to work out the general equilibrium implications of transaction costs. In a system involving iceberg transaction costs, an individual receives the fraction k when she buys one unit of a good, or pays one dollar when she buys goods with value of k dollars, where k ∈[0, 1]. If sellers of goods pay transaction costs, then they receive the fraction k of each dollar paid by the buyers. These speciﬁcations imply that the fraction 1 − k of goods or their value disappears in transit because of transaction costs. These transaction costs can take the form, for example, of transportation costs, costs in implementing transactions, storage costs, and costs caused by nonpunctual delivery. However, the transaction cost coefﬁcient 1 − k is considered an exogenous transaction cost that can be seen before individuals have made their decisions. There are two common deﬁnitions of endogenous transaction cost. According to the more general deﬁnition, all transaction costs are considered endogenous whose levels can be seen only after individuals have made their decisions. In the consumer-producer models with iceberg transaction costs, although the transaction cost coefﬁcient 1 − k is exogenous, the total transaction cost for each consumer-producer, and thus for society, is endogenous in terms of this general deﬁnition, since the number of transactions is endogenized in the model of consumer-producers. The second, narrower, deﬁnition of endogenous transaction cost relates to a speciﬁc type of endogenous transaction costs, namely those that are caused by a departure of general equilibrium from the Pareto optimum. Hereafter, we will adopt this second deﬁnition of endogenous transaction cost unless otherwise indicated. Endogenous transaction cost is the focus of chapters 9 and 10.

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 63

Example 3.1: The Ricardian model with exogenous comparative technological advantage and transaction costs. Consider a world consisting of country 1 and country 2. The set of consumerproducers is assumed to be a continuum with mass M1 + M2 where Mi is the measure of individuals in country i. This assumption implies that the population size is very large, so that we would not have an integer problem when individuals are divided between different occupation conﬁgurations. Example 9.10 in chapter 9 will show that, for a ﬁnite set of consumerproducers, Walrasian equilibrium may not exist. For that case, Nash bargaining might be essential for coordinating the division of labor. The individuals within a country are assumed to be identical. Hence, two countries may be considered as two groups of ex ante different individuals. As consumer-producers, the individuals consume two goods, x and y, and decide their own conﬁgurations of production and trade activities. The utility function for each individual of group i or in country i is: Ui = (xi + kx id )β( yi + ky id )1−β

(3.1)

where xi, yi are quantities of goods x and y self-provided, x id, y id are quantities of the goods bought from the market, and k is the transaction efﬁciency coefﬁcient. Assume that the production functions for a consumer-producer in country i are: x ip ≡ xi + x is = aix lix

and

yip ≡ yi + y is = aiyliy

(3.2)

where x ip and y ip are respective output levels of the two goods produced by a person in country i and lij is a type i-individual’s amount of labor allocated in producing good j. We call lij the level of specialization of a type i-individual in producing good j. aij is a type i-individual’s labor productivity in producing good j. The labor endowment constraint for a person in country i is lix + liy = 1. Let country 1 have comparative advantage in producing good x, thus

a1x a2 x > a1 y a2 y

(3.3)

The individuals’ transformation curves for a1x = 2, a1y = 1, a2x = 3, a2y = 4 are drawn in ﬁgure 3.1. CD is the transformation curve of an individual in country 1 and AB is the transformation curve of an individual in country 2. Here, an individual in country 2 has absolute advantage in producing both goods. The consumption, production, and trade decisions for an individual in country i involve choosing six variables xi, x is, x di , yi, y is, y id ≥ 0. Since zero values are allowed, there are 26 = 64 combinations of zero and positive values of the 6 variables. Since buying and selling the same good incur unnecessary transaction costs, x is and x di cannot both be positive, and y is and y id cannot both be positive. Thus, the budget constraint is either px x is = py y id or px x di = py y is. Hence, we ﬁrst rule out 48 combinations that satisfy any of the following conditions, which violate the budget constraint. x is = 0 and y id > 0; x is > 0 and y id = 0; x id = 0 and y is > 0, x di > 0 and y is = 0. Four more combinations that involve selling and buying the same good can be ruled out. Then from the remaining 12 combinations, we use the positive utility constraint (Ui = (xi + kx id)β( yi + ky id )1−β > 0) to rule out 7 combinations that involve xi = x di = 0 or yi = y id = 0. We will show later that 2 combinations that involve specialization in an individual’s comparative disadvantage good cannot occur in general equilibrium. Now we are left with 3 types of conﬁgurations, listed as follows: Conﬁguration A i (autarky) is shown in ﬁgure 3.2. This conﬁguration is deﬁned by xi , yi > 0, x is = x id = y is = y id = 0, i = 1, 2, which implies self-providing all goods. If all individuals choose conﬁguration A, this social pattern of organization is called structure A.

64 P ART I: D EVELOPMENT M ECHANISMS y E

F

A

C

H

0

D

B

G

x

Figure 3.1 Economies of division of labor based on exogenous technical comparative advantage

y1

A1

x1

x

x1 (xy/y)1

y2

A2

y1

x2

x2

x

x

(xy/x)2

(x/y)1

y2

y country 1 country 2 Structure Ba

Structure A

x1

( y/x)2

y

y2

y

y2

country 1 country 2 Structure Bb

( y/x)2

(x/y)1 x1 country 1

country 2 Structure C

Figure 3.2 Conﬁgurations and structures

The conﬁguration of partial specialization in the comparative advantage good, denoted by (xy/y)1 and (xy/x)2, is shown in ﬁgure 3.2. Conﬁguration (xy/y)1 is relevant for individuals in country 1 and is deﬁned by x1, y1, x 1s, y 1d > 0, x 1d = y 1s = 0, which implies self-providing goods x and y, selling good x, and buying good y; conﬁguration (xy/x)2 is relevant to individuals in country 2 and is deﬁned by x2, y2, x 2d, y 2s > 0, x 2s = y 2d = 0, which implies self-providing goods x and y, selling good y, and buying good x. The conﬁguration of complete specialization in the comparative advantage good, denoted by (x/y)1 and (y/x)2, is shown in ﬁgure 3.2. Conﬁguration (x/y)1 is deﬁned by x1, x 1s, y 1d > 0, x 1d = y1 = y 1s = 0, which implies self-providing and selling good x and buying good y; conﬁguration (y/x)2 is deﬁned by y2, y 2s , x 2d > 0, y 2d = x2 = x 2s = 0, which implies self-providing and selling good y and buying good x. The notion of occupation conﬁguration can be virtualized from the Dictionary of Occupational Titles. In its 1939 edition, there were 17,500 occupational titles. In 1977, 2,100 occupational

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 65

titles were added, and 840 more were added in 1996. In 1991, a new section including many computer-related occupations was added. As population is divided among the occupation conﬁgurations, a certain structure of division of labor for society as a whole occurs. For a two-country-two-good economy, we may deﬁne division of labor as a structure where, at least, individuals in one country choose a pattern of specialization and the conﬁgurations of individuals in the two countries are not the same. This deﬁnition implies that specialization is not sufﬁcient for the division of labor. If population is divided between conﬁgurations (y/x)1 and (y/x)2 (two types of person specialize in producing y), this is not associated with division of labor. Similarly, specialization of two types of person in producing good x involves specialization, but no division of labor. There are two structures involving partial division of labor. Structure Ba consists of (xy/y)1 and (y/x)2 and structure Bb is composed of (x/y)1 and (xy/x)2. The structure of complete division of labor, C, consists of conﬁgurations (x/y)1 and (y/x)2. Suppose there is only one person in each country. The aggregate production schedules for the four structures are shown in ﬁgure 3.1. We will show later that if autarky occurs in equilibrium, the aggregate production schedule occurs on the line EG. For structure Ba, an individual in country 1 completely specializes in producing x and an individual in country 2 produces two goods. The aggregate transformation curve for this structure is the segment EF in ﬁgure 3.1. This segment can be obtained by moving individual 2’s transformation curve CD up to point E on the vertical axis. The aggregate transformation curve for structure Bb is FG, which can be obtained by moving individual 1’s transformation curve AB to the right to point G on the horizontal axis. The aggregate production for structure C is point F in ﬁgure 3.1. Production schedule EHG is associated with the division of labor with comparative disadvantage. Later we will show this production schedule never takes place in equilibrium. To understand the distinction between occupation conﬁguration and structure of division of labor, you may consider the university where you are studying. The ﬁrst decision that you have to make when you get into the university is to choose a major. If you choose economics as your major, then you do not go to chemistry and physics classes, but instead take classes in microeconomics, macroeconomics, and econometrics. This decision chooses an occupation conﬁguration. We call such a decision an inframarginal decision, since decision variables are not continuous between occupation conﬁgurations. They discontinuously jump between 0 and a positive value as you shift between majors. After you have chosen a major, you allocate your limited time between the ﬁelds in this major. The resource allocation decision for a given occupation conﬁguration is called a marginal decision, since standard marginal analysis can be applied to this type of decision. The aggregate outcome of all students’ choices of majors in a university generates a division of students among majors and ﬁelds, which is equivalent to a structure of division of labor in our model. The general equilibrium of the world economy is deﬁned as a resource allocation and a structure of trade network that satisfy the following: (1) each individual maximizes utility at a given set of prices with respect to conﬁgurations and quantities of production, trade, and consumption; (2) the set of prices clears the market. The individuals make their utility maximization decisions based on inframarginal analysis. Inframarginal analysis means that for each conﬁguration, individuals apply marginal analysis to solve for the optimum quantities of consumption, production, and trade, and then apply total cost–beneﬁt analysis to compare their utilities across all conﬁgurations and choose the conﬁguration that gives the highest utility. Here, the marginal analysis is your decision to allocate your time between different ﬁelds after you have chosen a major and the total cost–beneﬁt analysis is your decision to choose a major. Marginal analysis is about “how much” and total cost–beneﬁt analysis is about “yes or no.” If you say “yes” to a major, you spend time studying it. If you say

66 P ART I: D EVELOPMENT M ECHANISMS

“no” to a major, you do not allocate any time to it. There is a local or corner equilibrium for a given structure and the general equilibrium is one of the four corner equilibria. Because of the complexity of inframarginal analysis, we need a two-step approach to solve for equilibrium. We ﬁrst apply nonlinear programming to solve the individuals’ utility maximization problems and use the market clearing condition to ﬁnd the local equilibrium for each of the four structures, we then use total cost–beneﬁt analysis to identify the general equilibrium. For instance, given structure Ba, the decision problem for individuals choosing conﬁguration (xy/y)1 in country 1 is: Max

x1 , x1s y1 , y1d , l1x , l1 y

s.t.

U1 = x1β( y1 + ky 1d)1−β x1 + x 1s = a1x l1x ,

y1 = a1y l1y

y = px ,

l1x + l ly = 1

d 1

s 1

where all decision variables can be positive or zero and p ≡ px /py is the price of x in terms of y. Note that variables underneath the symbol Max are decision variables. Inserting all constraints into the utility function to eliminate x1, y1, y 1d, l1x yields: U1 = (a1x l1x − x 1s)β [a1y(1 − l1x) + kpx 1s ]1−β. It is not difﬁcult to see that ∂U1/∂l1x > 0 for any positive l1x if p > a1y /ka1x and if the optimum value of x 1s is given by ∂U1/∂x 1s = 0. This implies that the utility can always be increased by increasing l1x if p > a1y /ka1x, or the optimum value of l1x is at its upper-bound value. Due to the endowment constraint of working time, this implies that an individual should not produce y and should specialize in producing x if p > a1y /ka1x. That is, individuals in country 1 should choose conﬁguration (x/y)1 instead of conﬁguration (xy/y)1 if p > a1y /ka1x. Following a similar reasoning, it can be shown that individuals in country 1 will choose conﬁguration A1 instead of (xy/y) if p < a1y /ka1x. Hence, individuals in country 1 will choose (xy/y)1 only if the market relative price satisﬁes p = a1y /ka1x. This condition is analogous to the zero-proﬁt condition in a standard general equilibrium model with constant returns to scale. With the condition, the ﬁrst-order condition ∂U1/∂x 1s = 0 yields the optimum value of x 1s as a function of l1x. Inserting it into the constraints in the original decision problem, we have: p = a1y /ka1x, y1 = a1y (1 − l1x),

x1 = βa1x,

x1s = a1x (l1x − β),

y1d = a1y (l1x − β)/k

Let us work out the intuition behind this nonlinear programming. If the price of x in terms of y, discounted by transaction cost in the world market, is lower than a type-1 individual’s marginal rate of transformation a1y /a1x in autarky, then the optimum decision is to choose autarky, producing both x and y. If p > a1y /ka1x, then utility of l1x always increases as l1x increases. Hence, the optimum decision is to specialize in producing x. But for p = a1y /ka1x, the individual is indifferent between autarky and conﬁguration (xy/y)1. Hence, conﬁguration (xy/y)1 will be chosen if the market clearing condition in equilibrium ensures that demand and supply of occupation conﬁguration (xy/y)1 can be realized. In conﬁguration (xy/y)1 there is a trade-off between the quantity of x self-provided x1 and quantity sold x 1s. The former directly contributes to utility and the latter indirectly increases utility by increasing more good y that is exchanged from x 1s. The efﬁcient balance of the trade-off is determined by the ﬁrst-order condition which implies that the marginal direct utility cost of x 1s equals the marginal indirect utility of x 1s.

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 67 Table 3.1 Four corner equilibria in the Ricardian model Structures

A

Relative price (px/py)

Relevant parameter interval

N.A.

Per capita real income (utility) Country 1

Country 2 U2(A) ≡

U1(A) β

≡ (βa1x) [(1 − β)a1y] Ba

k < k1 ≡

a1y/ka1x

1−β

U1(A)

k < k2 ≡

U2(A) (k2a2y a1x/a2x a1y)β

M1a1y(1 − β)/βM2a2y < 1 Bb

(βa2x)β[(1 − β)a2y]1−β

U1(A)(k2a2y a1x/a2x a1y)1−β

U2(A)

βM2a2y

U1(A)[βkM2a2y

U2(A)[(1 − β)kM1a1x

÷ M1a1x(1 − β)

÷ M1a1y(1 − β)]1−β

÷ M2a2xβ]β

ka2y/a2x

M2a2xβ/(1 − β)M1a1x < 1 C

In this solution, the optimum value of l1x is indeterminate. Its equilibrium value will be determined by the market clearing condition. This is analogous to a standard equilibrium model with constant returns to scale technology where the zero-proﬁt condition determines prices, and the market clearing condition, together with demand functions, determines equilibrium quantities. The decision problem for an individual in country 2 is:

Max U2 = (kx 2d )βy21−β d s

x 2 y2 , y 2

s.t.

y2 + y 2s = a2y,

y 2s = px 2d

The ﬁrst-order conditions imply: x2d =

ka2 y a1x a1 y

β,

y2 = (1 − β)a2y,

y 2s = px 2d = βa2y

where p = a1y /ka1x is the equilibrium price of good x in terms of good y. From the market clearing condition M1x 1s = M2x 2d, we obtain l1x = (ka2y M2β/a1y M1) + β, which is less than 1 (an individual’s endowment of labor) if and only if (or iff for short) a2y /a1y < M1(1 − β)/M2βk. That is, structure Ba can be chosen iff a2y /a1y < M1(1 − β)/M2βk. Using the same approach as we used above, we can ﬁnd the corner equilibria for Structure A, Bb and C. The results are summarized in table 3.1.

3.3

ANALYSIS OF DECISIONS VERSUS EQUILIBRIUM ANALYSIS OF DEVELOPMENT

A general equilibrium is the outcome of interactions between individuals’ self-interested decisions which might be in conﬂict with others’. In a standard equilibrium model, individuals choose quantities of goods to be produced, traded, and consumed for given prices, while equilibrium prices are themselves determined by all individuals’ decisions on quantities of goods and factors. A general equilibrium is a consequence of the interactions between prices

68 P ART I: D EVELOPMENT M ECHANISMS

and quantities of goods and factors. In a model of endogenous specialization, each individual’s decision problem involves multiple conﬁgurations, as there are many possible combinations of these individual conﬁgurations. Hence, the model of endogenous specialization features multiple corner equilibria. Since each individual chooses only the optimal of the multiple corner solutions, the general equilibrium is one of multiple corner equilibria. The notion of general equilibrium in the model of endogenous specialization relates not only to all interactions between prices and quantities, between the markets for different goods, and between individuals’ self-interested decisions, but also to the mechanism that simultaneously determines the size of the network of division of labor, demand and supply as two aspects of that network, productivity, and per capita real incomes. Network effect relates to the following phenomenon. In a system comprising many interdependent subsystems, the efﬁciency of the whole system is determined not only by each individual’s productivity, but also by the number of participants in the network. Each individual’s decision-making is dependent on the number of participants in a network, which is in turn determined by all individuals’ decisions of participation in the network, though this interdependence may occur indirectly through the price system. It was, indeed, the network effects of the division of labor that Smith and Young focused on in their classic works. Smith was more interested in the function of the invisible hand in coordinating the division of labor, in utilizing the network effects, and in promoting economic development than in its function in allocating resources for a given pattern of division of labor and given productivity. Young (1928) emphasized several times that the beneﬁts of division of labor are network effects rather than effects of the scale of a ﬁrm or a sector. The effects can be analyzed only by taking the division of labor as a whole. The economic analysis that separates the investigation of demand and supply from that of decisions in choosing patterns of specialization does not help us in understanding the development implications of division of labor. From the model in this chapter, it can be seen that if each individual, as a consumer, prefers diverse consumption, then the individual cannot specialize if all other individuals choose autarky. In this situation, the person cannot sell what she wants to sell and cannot buy consumption goods that she does not produce. This implies that each individual’s level of specialization determines not only her own productivity, but also the extent of the market for the produce of others, thereby determining the others’ productivities and levels of specialization. This is a typical network effect. The focus of the current chapter is on how the price system simultaneously sorts out the network size of division of labor, the extent of the market, productivity, and per capita real income. In daily life, we hear many managers and other decision-makers stating that demand is dependent on per capita real income. According to Young, this is a one-sided view that misses the nature of the network of division of labor. From a complete view of network effects, we can see that the extent of the market (effective demand) determines productivity and thereby per capita real income too. Certainly the question whether the network size of division of labor determines an individual’s decision in participating in the trade network and prices, or each individual’s participation decision determines the network size of trade and prices, or prices determine all individuals’ participation decisions and network size of trade, is analogous to the question: did the egg generate the hen, or the hen the egg? The notion of general equilibrium is a powerful device for illuminating the mechanism that simultaneously determines all of the interdependent phenomena. This chapter provides a framework within which the development implications of the network effects of the division of labor can be understood. In order to study the function of the price system, consideration of an individual’s decisionmaking, as in the previous section, is not enough since price is a social phenomenon, the consequence of a spontaneous social invention of an institution. It was invented by the invisible hand. The invisible hand here implies interaction of many individuals’ self-interested decisions.

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Hence, there is no suggestion that the invisible hand is not affected by individuals’ decisions. What is implied, rather, is that the invisible hand is determined by all individuals’ selfinterested decisions. However, no single individual decision-maker can determine the outcome of the interactions between myriad individual decisions in a free market environment. Economists call the outcome, as we have observed already, general equilibrium, or equilibrium for short. In many cases, the notion of equilibrium is associated with the market clearing condition (demand equals supply). But it is not necessarily so. For instance, a sequential equilibrium in Qian’s game model (1994) is associated with shortage. Also, equilibrium may not necessarily imply a steady state. In chapters 13, 14, and 15, the notion of dynamic equilibrium will be used to show that an equilibrium as the outcome of interactions of individuals’ dynamic optimum decisions generates spontaneous evolution in endogenous variables. From the concept of conﬁguration, we can see that for society as a whole, combinations of conﬁgurations may generate many structures of division of labor. The market clearing condition in each structure yields a corner equilibrium and the general equilibrium is only one of them. Each corner equilibrium sorts out the resource allocation problems for a given structure of division of labor and given productivity, while the general equilibrium sorts out the efﬁcient structure of division of labor and problems of economic development. Economic development relates to the concept of equilibrium since the former is a consequence of interaction between individuals’ decisions. We shall show that discontinuous jumps of the general equilibrium between corner equilibria as a result of changes in parameters will generate economic development. Hence the distinction between corner equilibrium and general equilibrium is essential for investigating microeconomic mechanisms of economic development. A general equilibrium is a corner equilibrium in which no individual has an incentive to deviate from the conﬁguration that she chooses under the corner equilibrium-relative prices. Now, we apply the total cost–beneﬁt analysis and the deﬁnition of general equilibrium to prove that a structure where the countries export their comparative disadvantage good cannot be a general equilibrium structure. Consider the structure where individuals in both countries completely specialize in their comparative disadvantage good, i.e., individuals in country 1 export good y (choose conﬁguration (y/x)1), and individuals in country 2 export good x (choose conﬁguration (x/y)2). For this structure to occur in general equilibrium, conﬁguration (y/x)1 must be most preferred by individuals in country 1, and conﬁguration (x/y)2 most preferred by individuals in country 2, that is, the following conditions must hold: U1( y/x) > U1(x/y) which holds iff p < (a1y /a1x)k 2β−1

and

U2(x/y) > U2( y/x) which holds iff p > (a2y /a2x)k 2β−1 The two inequalities jointly imply (a2x /a2y) > (a1x /a1y) which contradicts the assumption (a2x /a2y) < (a1x /a1y). Similarly, it can be shown that other structures involving specialization in comparative disadvantage goods cannot occur in general equilibrium. Next, we apply the total cost–beneﬁt analysis and the deﬁnition of general equilibrium again to ﬁnd out under what conditions each of the structures listed in table 3.1 occurs in general equilibrium. Consider structure Ba ﬁrst. Structure Ba is the general equilibrium structure if the following three conditions hold. First, under the corner equilibrium-relative price in this structure p = a1y /ka1x, individuals in country 2 prefer specialization in y (conﬁguration ( y/x)) to the alternatives, namely autarky (conﬁguration A) and specialization in x (conﬁguration (x/y)). In other words, the following conditions hold: U2(y/x) ≥ U2(A) which holds iff k ≥ k0 ≡ [(a2x /a2y)/(a1x /a1y)]0.5

(3.4a)

U2(y/x) ≥ U2(x/y) which holds iff k ≥ k3 ≡ [(a2x /a2y)/(a1x /a1y)]

(3.4b)

0.5/β

70 P ART I: D EVELOPMENT M ECHANISMS Table 3.2 General equilibrium and its inframarginal comparative statics of the Ricardo model Parameter Intervals

Equilibrium structure

k > k0

k < k0

A

M1/M2 > (a2x a2y /a1x a1y)0.5β/(1 − β)

M1/M2 < (a2x a2y /a1x a1y)0.5β/(1 − β)

k ∈(k0, k1)

k ∈(k1, 1)

k ∈(k0, k2)

k ∈(k2, 1)

Ba

C

Bb

C

where k0 ≡ (a2x a1y /a1x a2y)0.5, k1 ≡ (1 − β)a1y M1/βa2y M2, k2 ≡ βa2x M2/(1 − β)a1x M1.

Second, general equilibrium requires that all individuals in country 1 prefer conﬁguration (xy/y) to the alternatives, that is: U1(xy/y) ≥ U1(x/y) which holds iff a1y /a1x ≥ kp = a1y /a1x

(3.5a)

U1(xy/y) ≥ U1( y/x) which holds iff 1 ≥ k

(3.5b)

Third, no individual in country 1 is completely specialized in x, i.e.: l1x < 1, which holds iff k < k1 ≡ a1y M1(1 − β)/a2y M2β As k3 ≥ k0, it follows that conditions (4.4)–(4.6) hold if k ∈(k0, k1). Since k0 < k1 holds iff M1(1 − β)/M2β > [(a2x a2y)/(a1x a1y)]0.5, the corner equilibrium in structure Ba is the general equilibrium if k ∈(k0, k1) and M1(1 − β)/M2β > [(a2x a2y)/(a1x a1y)]0.5, where k1 ≡ a1y M1(1 − β)/ a2y M2β. Similarly, we can identify the conditions for other structures to occur in general equilibrium. These conditions are summarized in table 3.2. Table 3.2 reads that if k < k0, the general equilibrium structure is autarky (structure A). If k > k0 and M1 /M2 > (a2x a2y/a1x a1y)0.5β/(1 − β), the general equilibrium occurs in structure Ba if k < k1, and in structure C if k > k1. If k > k0 and M1 /M2 < (a2x a2y /a1x a1y)0.5β/(1 − β), the general equilibrium occurs in structure Bb if k < k2, and in structure C if k > k2. It is important to note that the structures are compared within relevant parameter subspaces. For instance, structure Ba can be chosen only if M1 /M2 < (a2y /a1y)β/(1 − β). In this text we deﬁne level of division of labor for society by all individuals’ levels of specialization and diversity of occupation conﬁgurations. If all individuals’ levels of specialization in a structure are not lower than their levels of specialization in another structure, and some individuals have higher levels of specialization in the former than in the latter, we say that the level of division of labor in the former structure is higher than in the latter. If all individuals’ levels of specialization are not lower in a structure than in another structure, but the diversity of occupation conﬁgurations in the former is greater than in the latter, we say that the level of division of labor is higher in the former than in the latter. If some individuals’ levels of specialization in a structure are higher than in another structure, but other individuals’ levels of specialization in the former are lower than in the latter, then it is much more difﬁcult to compare the levels of division of labor in the two structures. A more rigorous deﬁnition of level of division of labor that is applicable to the comparison can be found in Yang (2000). Table 3.2 implies that as the transaction efﬁciency coefﬁcient increases from a small value to k0, and then to k1 or k2, the general equilibrium jumps from autarky to partial division of labor, then to complete division of labor. Whether the transitional structure is Ba or Bb depends on the relative size of the two countries compared to relative tastes and relative productivity. Such discontinuous jumps of equilibrium structure and endogenous variables across corner equilibria

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 71

in response to changes of parameter are referred to as inframarginal comparative statics of general equilibrium. Since we assume (a1x /a2x) > (a1y /a2y) or country 1 has comparative advantage in producing good x, we can take r = r1r2 ≡ (a1x /a2x)/(a1y /a2y) as a measure of the degree of exogenous technical comparative advantage. A derivative of k0, k1, k2 with respect to r1 and r2 yields: ∂k0/∂r1, ∂k0/∂r2,

∂k1/∂r2, ∂k2/∂r1 < 0

This implies that for a given value of k, the greater the degree of comparative advantage, the more likely k > ki (i = 0, 1, 2) or the more likely the equilibrium level of division of labor is higher. A close examination of all conditions for structure C to be the general equilibrium indicates that they require either that 1 > k1 and M1/M2 > (a2x a2y/a1x a1y)0.5β/(1 − β), or that 1 > k2 and M1 /M2 < (a2x a2y /a1x a1y)0.5β/(1 − β). The two conditions imply that the requirement for C to be equilibrium is either: (a2y /a1y)β/(1 − β) > M1 /M2 > (a2x a2y /a1x a1y)0.5β/(1 − β)

or

(a2y /a1y)β/(1 − β) < M1 /M2 < (a2x a2y /a1x a1y) β/(1 − β) 0.5

This implies that the relative population size of the two countries is neither too large nor too small. Since individuals in one country have a higher level of specialization in structure C than in structure Ba or Bb and since the level of division of labor positively relates to individuals’ levels of specialization, structure C has a higher level of division of labor than structure Ba or Bb. Our result implies that the more the relative population size is in balance with relative tastes and relative productivity, the more likely the equilibrium level of division of labor is higher. Now we consider the implications of inframarginal comparative statics for development economics. To this end, we need to work out a production schedule in autarky. If autarky is the general equilibrium, then marginal rate of substitution equals marginal rate of transformation for each individual. This implies: βyi/(1 − β)xi = aiy /aix

or

(x1/a1x)/( y1/a1y) = β/(1 − β) = (x2/a2x)/( y2/a2y)

where the subscript i represents country i. This, together with the production functions xi = aix liy , yi = aiy liy, and the endowment constraint lix + liy = 1 imply that l1x = l2x = β, l1y = l2y = 1 − β. Using all of the conditions to eliminate taste parameter β, or using the production functions, the endowment constraints, and the conditions l1x = l2x and l1y = l2y, we can then show that the equilibrium production schedule in autarky must satisfy: Y = y1 + y2 = (a1y + a2y)[1 − X/(a1x + a2x)],

where X = x1 + x2.

This is the line EG in ﬁgure 3.1. The slope of this line is dY/dX = −(a1y + a2y)/(a1x + a2x), which is between −a1y /a1x and −a2y /a2x. In other words, this line is ﬂatter than line FG and steeper than line EF in ﬁgure 3.1. Hence, production takes place at a point on EG if autarky is the general equilibrium. The exact position of the equilibrium production schedule on EG is dependent on the value of taste parameter. From ﬁgure 3.1, we can see that the aggregate production possibility frontier (PPF) is EFG. Since straight line EG is lower than the PPF, the aggregate productivity in autarky is lower than that for the division of labor which is associated with the PPF. As transaction conditions are improved, the equilibrium aggregate productivity will discontinuously jump from line EG to the PPF. The difference between EFG and line EG can then be deﬁned as economies of division of labor.

72 P ART I: D EVELOPMENT M ECHANISMS

It is interesting to see that there exist economies of division of labor even if there are no economies of scale or the aggregate production set is convex in the Ricardian economy. The aggregate production set is the area enclosed by the vertical and horizontal axes, lines EF and FG and its boundaries in ﬁgure 3.1. This implies productivity chosen by the decision-makers in the equilibrium will endogenously increase as transaction conditions are improved. If transaction efﬁciency is low, then the high productivity associated with the PPF is not Pareto efﬁcient because of the trade-off between economies of division of labor and transaction costs. Rosen (1978) calls economies of division of labor superadditivity, which is a kind of economies of interpersonal complementarity. It implies that equilibrium aggregate productivity for society increases as the equilibrium network size of division of labor increases. Buchanan (1994) calls this “generalized increasing returns” and Allyn Young (1928) calls it “social increasing returns,” which may exist in the absence of economies of scale. Individuals’ levels of specialization and the diversity of individuals’ occupation conﬁgurations are two aspects of the network. The inframarginal comparative statics of general equilibrium provides a general equilibrium mechanism for economic development. In this mechanism, exogenous comparative advantage and trading efﬁciency are driving forces of economic development. Exogenous changes in production functions or endowments are not needed for the economic development if transaction conditions are improved. Also, exogenous changes in tastes are not needed for structural changes in this economic development process. Suppose that transaction efﬁciency is improved from a level lower than k0 to a level higher than k0, then to a value of k greater than k1 or k2. Then the general equilibrium jumps from autarky, to the partial division of labor, then to the complete division of labor. In autarky each individual produces all goods that she consumes and there is no division between different occupations, such as that between farmers and manufacturers. As transaction conditions are improved, different professional occupations emerge from the evolution of division of labor. This process can be considered as structural change. Suppose x is food and y is cloth. Since the number of professional farmers in structure C is smaller than the number of individuals producing food, which is the population size in autarky, the structural change caused by evolution of division of labor looks like a transfer of labor from the traditional agricultural sector to the industrial sector. But in essence the structural change is a process in which each individual’s level of specialization increases and the degree of diversity of occupation conﬁgurations increases, the degree of market integration increases, the number of markets for different goods increases, new traded goods emerge, the degree of interpersonal dependence and connection increases, the extent of the market and related network size of division of labor rise, the degree of production concentration increases, and productivity increases. As the general equilibrium jumps from Ba to C due to improvements in transaction conditions, occupation conﬁguration (xy/y), is replaced with new occupation conﬁguration (x/y), which has a higher level of specialization than (xy/y). This process of destructive creation (Schumpeter, 1934) – a further example of which would be the replacement of craftsmen by specialized workers in large ﬁrms as described by Rosenberg and Birdzell (1986, pp. 145– 84), Mokyr (1990, 1993, pp. 26–110), and Marx (1867), involves emergence of new occupations and the disappearance of old ones. It can be quite painful if the transitional costs are considered. We now consider the received wisdom that as the terms of trade of a country deteriorate, the gains that this country receives from trade will fall. Many development economists consider worsening terms of trade to be a cause of underdevelopment. The inframarginal comparative statics of our model show that this is not a general equilibrium view and might be misleading. Consider tables 3.1 and 3.2. Suppose that M1/M2 > (a2xa2y /a1x a1y)0.5β/(1 − β) and the initial value of k is k′ ∈((a2x a1y /a1x a2y)0.5, (M1/M2)(a1y /a2y)β/(1 − β)). Hence, the equilibrium structure is Ba where country 1 exports x and imports y at the relative price px /py =a1y/k′a2y. Assume now that

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 73

the transaction efﬁciency is improved, so that the value of k is k″ > (M1 /M2)(a1y /a2y)β/(1 − β), which is greater than k′. Hence, the equilibrium jumps to structure C where the relative price is (M2/M1)(a2y /a1x)β/(1 − β). This implies that country 1’s terms of trade deteriorate as the improvement in transaction efﬁciency drives the equilibrium to jump from Ba to C, if k′ < (M1/ M2)(a1y /a2y)(1 − β)/β. It is straightforward that the parameter subspace for such a structural change is not empty. Therefore, as transaction efﬁciency is improved within this parameter subspace, country 1’s per capita real income increases from autarky level despite deteriorated terms of trade. This is because improvements in transaction conditions will expand network of division of labor and raise equilibrium aggregate productivity, so that productivity gains might outweigh the deterioration of terms of trade. The inframarginal comparative statics of the general equilibrium can be summarized in the following proposition. Proposition 3.1: The general equilibrium structure is determined by the two countries’ relative productivity, relative preference, relative population size and the level of transaction efﬁciency. Given other parameters, improvements in transaction efﬁciency can make the general equilibrium structure jump from autarky to partial division of labor and then to complete division of labor. For given transaction conditions, relative population size, and relative tastes for the two goods, the greater the degree of comparative advantage, the more likely the equilibrium level of division of labor is higher. For given transaction conditions, the more the relative population size is in balance with relative tastes and relative productivity, the more likely the equilibrium level of division of labor is higher. As the equilibrium level of division of labor increases, the equilibrium aggregate productivity for society as a whole increases. In the process of moving to a higher level of division of labor, a country may receive more gains from trade even if its terms of trade deteriorate. It is interesting to note that the general equilibrium market price may not be determined by the conventional marginal cost pricing rule in the model with exogenous comparative advantage. When structure Ba (or Bb) is the general equilibrium, the market price of good x in terms of y equals country 1’s (or country 2’s) marginal opportunity cost including (or excluding) transaction cost. When structure C is the general equilibrium, the market price of x in terms of y is determined by the total demand and supply in both countries and does not equal either country’s marginal opportunity cost of producing x. This observation substantiates Coase’s argument (1946) that one should use total cost–beneﬁt analysis in addition to marginal analysis in price determination. Other examples of nonmarginal cost pricing can be found in chapter 4 in this text, in the literature of industrial organization (see Tirole, 1989, ch. 3), and in the labor contract literature (Azariadis, 1975, Baily, 1974, and Gordon, 1974). In the Ricardian model, an increase in k (or a decrease in the transaction cost coefﬁcient 1 − k) can increase total transaction costs because the increase in k can generate a jump of the general equilibrium from a low level to a high level of division of labor and increase the number of transactions. This implication of transaction costs can be used to explain why the income share of transaction costs increases as transaction efﬁciency is improved. North (1986) has found empirical evidence for this phenomenon. In order to formalize Smith’s conjecture that the invisible hand can efﬁciently coordinate individuals’ decisions in choosing their patterns of specialization, we must prove that the general equilibrium is Pareto optimal. The Pareto optimum is a resource allocation and a network structure of division of labor in which no individual can increase her utility without reducing others’ utilities. A revealed preference argument can be used to prove that in the Ricardo economy with consumer-producers, the general equilibrium is Pareto optimal. The logic of the proof can be outlined as follows.

74 P ART I: D EVELOPMENT M ECHANISMS

We may use an argument of negation to establish the ﬁrst welfare theorem. Suppose that the equilibrium is not Pareto optimal, so that there exists a feasible resource allocation that is Pareto superior to the general equilibrium resource allocation. This implies that at least one individual’s utility is greater in this alternative allocation than in equilibrium, and other individuals are at least indifferent between the equilibrium and the alternative allocation. We now specify artiﬁcial budget constraints for all individuals’ consumption, production, and trade ﬂows given by the alternative allocation under the equilibrium prices. The person receiving greater utility in the alternative allocation must pay more than her income in the alternative allocation under the equilibrium prices since, by the deﬁnition of optimization, her optimum decision under the equilibrium prices cannot achieve more utility than in the equilibrium. All other individuals must have a binding budget in the alternative allocation under the equilibrium prices. By aggregating all individuals’ artiﬁcial budget constraints and canceling prices, it can be shown that the aggregate endowment constraint is violated. Hence, the alternative allocation is infeasible. This establishes the ﬁrst welfare theorem. The ﬁrst welfare theorem implies that the most important function of the market is to coordinate all individuals’ decisions in choosing their patterns of specialization to utilize positive network effect of division of labor net of transaction costs. Zhou, Sun, and Yang (1998) have proved an existence theorem of general equilibrium for a general class of models of endogenous specialization. In their model, the set of ex ante different consumer-producers is a continuum, preferences are rational, continuous, and increasing, and both constant returns and local increasing returns are allowed in production. The Ricardian model in this chapter and the Smithian model with economies of specialization in chapter 4 are just special cases of their model. They have also established the ﬁrst welfare theorem and the equivalence between the set of competitive equilibria and economic core for this general class of models of endogenous specialization. The results imply that if transaction costs outweigh exogenous comparative advantage in a structure or if the corner equilibrium in this structure is not Pareto optimal, then there is coordination difﬁculty in getting self-interested decision-makers to choose the constituent occupation conﬁgurations in this structure. In that case a set of relative prices to support individuals’ Walrasian decisions choosing constituent occupation conﬁgurations in this structure does not exist. The ﬁrst welfare theorem implies not only resource allocation for a given structure of division of labor is efﬁcient, but also the structure of division of labor is efﬁcient in equilibrium. We call a corner equilibrium an efﬁcient resource allocation for a given structure of division of labor, and call the general equilibrium structure of division of labor an efﬁcient organization or organism. The concept of organization efﬁciency relates to inframarginal analysis of economic development. The concept of allocation efﬁciency relates to marginal analysis of resource allocation. It can be shown that for the model of endogenous specialization, general equilibrium may not exist if the number of individuals is not a continuum because of an integer problem (see example 9.10 in chapter 9).

3.4

PER CAPITA REAL INCOME, GDP, GNP, AND PPP

Many development economists measure development performance by per capita gross domestic product (GDP) or per capita gross national product (GNP) and their growth rates. GDP is the market value of an economy’s domestically produced goods and services. GNP equals GDP plus the net factor income from abroad. Many development economists are critical of using per capita GNP as a measure of development performance. They suggest using some social index that includes life expectancy, the literacy rate, infant mortality, and inequality of income distribution. There are many problems with this measurement method. First, unequal income

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distribution might be caused either by distortions or by evolution in division of labor. For instance, government monopoly power in the banking sector and many other sectors generates an inefﬁcient level of division of labor and a related narrow extent of the market, which is associated with extremely unequal income distribution, as in, for instance, China. But under a constitutional order and fair competition, the evolution of division of labor may generate a new professional occupation of entrepreneurial activity. The professional entrepreneurs’ job is to experiment with various patterns of economic organizations and to take the risk of the experimenting (see chapter 15). Entrepreneurs may make a fortune and they may go bankrupt. Bankruptcy implies a negative income (maybe negative inﬁnity, in the case of committing suicide), while a successful venture may make the entrepreneur very rich, despite the fact that the expected income of the entrepreneur is nearly same as it would be in other lower risk occupations. Hence, inequality of income distribution will increase as the professional entrepreneur emerges from a high level of division of labor. As long as free entry and free pricing prevail, such an increase in inequality might be welfare enhancing for society as a whole. The index of life expectance, the literacy rate, and infant mortality are problematic gauges of welfare since there are many possible trade-offs between each pair of the variables. Individuals’ welfare maximization relates to the efﬁcient balance of the trade-offs rather than maximization or minimization of the value of any single one of them. The ultimate concern of welfare analysis is individuals’ utilities. Hence, we deﬁne utility as per capita real income. We now use our simple Ricardian model to show that per capita real income differs from per capita GNP, so that measuring development performance by per capita GNP might be misleading. Suppose parameter values are within the subspace deﬁned by k ∈ (k0, k1) and M1/M2 > (a2x a2y /a1x a1y)0.5β/(1 − β), such that structure Ba occurs in equilibrium. In this simple model per capita GNP is the same as per capita GDP because of the absence of trade in labor. Following common practice in calculating GNP, most self-provided services are not counted as part of GNP. Hence, per capita GNP in terms of good y in country 1 is I1 = px 1s = (M2a2yβ/M1) − (a1y β/k), where the equilibrium value of p is given in table 3.1 and x 1s = a1x (l1x − β) is given by the decision problem for conﬁguration (xy/y)1 and the equilibrium value of l1x = (ka2y M2β/a1y M1) is given by the market clearing condition for structure Ba. Per capita GNP in country 2 is I2 = y 2s = a2yβ, given by the decision problem for conﬁguration (y/x)2. Similarly, we can ﬁnd per capita GNP in structure C: I1 = M2a2yβ/M1 and I2 = a2yβ. From table 3.1, it is easy to determine that per capita real incomes in the two countries in structure Ba are: U1(Ba) = (βa1x)β[(1 − β)a1y]1−β,

U2(Ba) = (βa2x)β[(1 − β)a2y]1−β(k2a2y a1x /a2x a1y)β

U1(C) = (βa1x)β[(1 − β)a1y]1−β[βkM2 a2y /M1a1y(1 − β)]1−β U2(C) = (βa2x)β[(1 − β)a2y]1−β[(1 − β)kM1a1x /M2 a2x β]β It is not difﬁcult to verify that when equilibrium occurs in structure Ba, U1(Ba) > U1(C), I1(Ba) < I1(C)

and

U2(Ba) > U2(C), I2(Ba) = I2(C).

In other words, welfare comparison between different patterns of division of labor in terms of per capita real income (utility) is inconsistent with that in terms of per capita GNP. This shows that the analysis of development performance based on the notion of per capita GNP might be misleading. There are two reasons for misinformation of the calculation of welfare from per capita GNP. First, this notion does not count or it understates self-provided services. Hence, it may overstate welfare in a country with a high level of division of labor in comparison to a country with a low level of division of labor, which is associated with a high level of self-provided services. Second, transaction cost has a negative effect on per capita real income.

76 P ART I: D EVELOPMENT M ECHANISMS

But transaction costs and the income of the sector providing transaction services are counted as part of per capita GNP. Hence, per capita GNP overstates the welfare of a country with a high level of division of labor that is associated with a high level of transaction cost. For instance, the per capita GNP of the US was 40 percent higher than that of Australia in 1997. Also, we can see that the level of division of labor in the US was higher than in Australia. As an example, many writers in the US depend on specialized publicity agents for publishing business, while such a specialized service is not much available in Australia. But the difference in per capita real income between the two countries is much smaller than the ﬁgures of per capita GNP suggest, according to many individuals who had experience of living in both countries in 1997. This is partly because the ﬁgure misses some noncommercialized real incomes in Australia which are commercialized in the US and partly because it ignores the fact that each individual in the US pays more transaction costs (caused by a higher level of division of labor in the US) than each Australian. This higher transaction cost is counted as part of per capita GNP, but has a negative direct effect on per capita real income (utility). The real wages in terms of good y are different between the two countries in a structure with trade. Consider structure Ba. Let the value of x produced by a person in country 1 in terms of y be equal to wage; we have p(x1 + x 1s ) = w1l1x where w1 is the wage rate in country 1. This, together with equilibrium values of p, x1, x 1s, l1x, yield the equilibrium wage rate in country 1, w1 = a1y /k. Similarly, we can ﬁnd the equilibrium wage rate in terms of good y in country 2, w2 = a2y. It can be shown that w1(Ba) > w1(C) for k ∈(k0, k1) and w2(Ba) = w2(C). Recalling that U1(Ba) > U1(C), I1(Ba) < I1(C) and U2(Ba) > U2(C), I2(Ba) = I2(C) when equilibrium occurs in structure Ba, or when k ∈(k0, k1), we can see that welfare analysis in terms of wage rates is closer than that in terms of per capita GNP to that in terms of per capita real income. In this general equilibrium model, we can consider the nominal exchange rate between the two countries as 1 if they use the same currency. We can consider w1/w2 as a real exchange rate in terms of the price difference in labor between the two countries. If the wage rate in a country is adjusted by this exchange rate, then the price of labor would be the same in the two countries. This kind of adjustment is referred to as an adjustment according to purchasing power parity (PPP). Hence, the adjustment of per capita GNP according to PPP in Maddison (1995) makes the adjusted per capita GNP closer to per capita real income. But as we have shown in this example, adjusted per capita GNP according to PPP is still different from per capita real income. Our discussion here does not consider the effects of inﬂation on measurement of development performance. We will consider this in chapter 17, which introduces money into a Smithian general equilibrium model.

3.5

ECONOMIC DEVELOPMENT AND TRADE POLICY

In the early stages of economic development in the sixteenth century, the governments of some European countries used protectionist tariffs as a vehicle for rent-seeking in international trade (see, for instance, Ekelund and Tollison, 1981). This mercantilism was replaced by a free trade regime in some European countries in the eighteenth and nineteenth centuries. According to Smith (1776), a laissez faire regime is more conducive to economic development than protectionist tariffs. But after the Second World War, many governments in developing countries still used protectionist tariffs as a means to increase their share of gains from trade by manipulating the terms of trade. This trade policy is sometimes referred to as import substitution strategy. In contrast, the governments in Hong Kong, Taiwan, and other developing countries use tax holidays, export-processing zones, and other policy instruments to reduce tariffs. This trade liberalization policy is sometimes referred to as an export-oriented development strategy. Many economists argue that trade liberalization which involves tariff reduction is a powerful

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 77 Table 3.3 Corner equilibrium solutions Structure

A Ba

Price px/py

Relevant parameter subspace

N.A. a1y(1 + t1)/k1a2x

k1 < D1(1 − β)a1y M1

Individual utility Country 1

Country 2

(βa1x)β[(1 − β)a1y]1−β

(βa2x)β[(1 − β)a2y]1−β

≡ U1(A)

≡ U2(A)

[(1 + L1xt1)/(1 + β)t1]U1(A)

[k1k2(a1x a2y) ÷ (a1y a2x)]βT 1βU2(A)

÷ βa2y M2 Bb C

k2a2y/(1 + t2)a2x

k2 < D2βa2x M2

[k1k2(a1x a2y)

U2(A)[1 + (1 − L2x)t2]

÷ (1 − β)a1x M1

÷ (a1y a2x)]1−βT 1−β 2 U1(A)

÷ [(1 − β)t2]

(1 + βt1)βa2y M2

[k1T3 βa2y M2/(1 −

[k2T4(1 − β)a1x M1

÷ (1 − β)[1 +

β)a1y M1]1−βU1(A)

÷ βa2x M2]βU2(A)

(1 − βt2)]a1x M1 where D1 ≡ (1 + t1)[1 + (1 − β)t2]/(1 + βt1),

D2 ≡ (1 + βt1)(1 + t2)/[1 + (1 − β)t2],

L1x ≡ β + (1 + βt1)k1βa2y M1/a1y M2[1 + (1 − βt2)](1 + t1) > β, T1 ≡ {(1 + t2)/[1 + (1 − β)t2]}(1−β)/β/(1 + t1)[1 + (1 − β)t2)], L2x ≡ β − [1 + (1 − β)t2]k2(1 − β)a2x M1/a1x M2(1 + t2)(1 + βt1)] < β, T2 ≡ [(1 + t1)/(1 + βt1)]β/(1−β)/(1 + t2)(1 + βt1), T4 ≡ {(1 + t2)/[1 + (1 − β)t2]}

T3 ≡ [(1 + t1)/(1 + βt1)]β/(1−β)/[1 + (1 − β)t2],

/(1 + βt1).

(1−β)/β

engine of economic development (Krueger, 1997; World Bank, 1996). Recently, bilateral and multilateral tariff negotiations have become a driving force for trade liberalization. The question is, why is free trade difﬁcult to realize, and trade negotiation essential for trade liberalization, if free trade is mutually beneﬁcial? Why do some governments choose unilateral protectionist tariffs but others a unilateral laissez faire regime? How can we use general equilibrium models to explain government policy shifts from protectionist tariffs to free trade or tariff negotiation that leads to trade liberalization? This section will introduce government tariffs into the Ricardian model to address these questions. Example 3.2: A Ricardian model with an endogenous trade regime (Cheng, Sachs, and Yang, 2000). Based on the model in section 3.2, suppose that the government in country i (i = 1, 2) imposes an ad valorem tariff of rate ti, and transfers all tariff revenue equally to all individuals in country i. In this case, individuals’ budget constraint, for instance, for conﬁguration (x/y), changes from px x s = py y d to px x s + Ri = (1 + ti)py y d, where ti is the tariff rate in country i and Ri is the tariff revenue received by each resident in country i. Individuals take the amount of transfer as given. At equilibrium, the total transfer equals total tariff revenue. Also, we assume that the transaction efﬁciency coefﬁcient for country i is ki , which may be different between countries. Using the same procedure as in section 3.3, we can solve for the corner equilibrium for each structure. The corner equilibrium solutions are presented in table 3.3. It is easy to see that if t1 = t2 = 0 and k1 = k2, table 3.3 reduces to table 3.1. If t1 = t2 = 0, the Ricardian model predicts that the country that produces both goods does not get any gains from trade. This result can be clearly seen in table 3.1 – when the general equilibrium occurs in structure Ba (or Bb), individuals in country 1 (or country 2) that produces both goods x and y get the same level of utility as they do in autarky.

78 P ART I: D EVELOPMENT M ECHANISMS

The story is different when tariffs are introduced. With reference to table 3.3, if the general equilibrium occurs in structure Ba (or Bb), individuals in the country producing both goods get a higher utility than they do in autarky. Moreover, in structure Ba, ∂U1/∂t1 > 0 (or in structure Bb, ∂U2/∂t2 > 0), that is, given the tariff rate of the country producing one good, the country producing two goods can improve its own welfare by raising its tariff rate. This is because the latter country determines the terms of trade and can improve them by imposing a tariff, thereby obtaining a larger share of the gains from trade. The country producing two goods gains at the expense of its trading partner, and it can be shown that ∂U2 /∂t1 < 0 in structure Ba and ∂U1/∂t2 < 0 in structure Bb. If the country producing two goods imposes a sufﬁciently high tariff, the other country may want to withdraw from trade, in which case both countries are hurt. In contrast to the country producing two goods, the completely specialized country has no inﬂuence on the terms of trade. As a result, it only hurts itself by imposing a tariff, as can be derived from table 3, ∂U2/∂t2 < 0 in structure Ba and ∂U1/∂t1 < 0 in structure Bb. If both countries can inﬂuence the terms of trade (as in structure C), then the gains of trade are shared between the two countries. However, since ∂U1/∂t1 > 0 and ∂U2/∂t2 > 0 in structure C, i.e., each country can beneﬁt from raising its own tariff given the other country’s tariff rate, each country will be tempted to raise its own tariff as much as possible. But if they both raise their tariff, both may be worse off. It can be shown that in structure C ∂U1/∂t2 < 0 and ∂U2/∂t1 < 0, and that U1 converges to 0 as t2 tends to inﬁnity and U2 converges to 0 as t1 tends to inﬁnity. This implies that, as a country sufﬁciently increases its tariff, the other country will not only be marginally worse off, but will also discontinuously (inframarginally) jump from trade to autarky. The above analysis is conducted within the Walrasian regime. To analyze the behavior of the governments in the two countries, we examine two other regimes: a Nash game and a Nash tariff bargaining game. (If you are not familiar with the two concepts, you might refer to sections 9.3 and 9.4 in chapter 9 below.) Suppose ﬁrst that the governments in the two countries play a Nash game. Each government chooses its own tariff rate to maximize home residents’ utility, taking as given the tariff rate in the foreign country and the Walrasian decisions of all individuals. For each structure (A, Ba, Bb, or C), a Nash corner equilibrium can be calculated. The Nash general equilibrium is one of four Nash corner equilibria. Consider structure Ba ﬁrst. Since ∂U2/∂t2 < 0 in this structure, the equilibrium strategy of country 2’s government is to impose zero tariff. Since ∂U1/∂t1 > 0 and ∂U2/∂t1 < 0, the equilibrium strategy of country 1’s government is to impose as high a tariff as possible, provided each individual in country 2 will not deviate from conﬁguration (y/x). If the Nash corner equilibrium in structure Ba is the Nash general equilibrium, each individual in country 2 is slightly better off than in autarky and most gains from trade go to country 1. In other words, the Nash corner equilibrium in the tariff game in this structure generates a distribution pattern of gains from trade that is opposite to the distribution in the absence of a tariff, where all the gains go to country 2. This Nash corner equilibrium is not Pareto optimal because of the deadweight loss caused by the tariff. But the distortion caused by the tariff converges to zero as gains from trade net of transaction costs go to zero. If each government can choose any level of tariff (including a zero tariff ), the Walrasian equilibrium with no tariff will not occur when structure Ba is chosen in general equilibrium, because country 1’s government has an incentive to deviate from that “equilibrium” by increasing the tariff. Since structure Bb is symmetric to Ba, we can obtain a similar result: a Nash tariff game will reverse the distribution pattern of gains from trade and will generate distortions. Now, consider structure C. Since ∂U1/∂t1 > 0, ∂U2/∂t1 < 0, ∂U1/∂t2 < 0, ∂U2/∂t2 > 0 in this structure, the Nash corner equilibrium strategy of each government in this structure is to

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 79

impose as high a tariff as possible, provided the individuals in the other country will not deviate from their specialization conﬁgurations. This implies that the gains from the complete division of labor in this structure will be almost exhausted by the deadweight loss caused by the tariff war. If the Nash general equilibrium occurs in this structure, this equilibrium may generate a very signiﬁcant welfare loss to both countries. This is a typical prisoners’ dilemma: mutually beneﬁcial gains cannot be realized because of coordination difﬁculty between self-interested rational decisions (see section 9.5 in chapter 9). Now suppose the two governments play a Nash tariff bargaining game. This game maximizes a Nash product of the net gains of the two countries with respect to the tariff rates of the two countries. Each country’s net gain is the difference between each individual’s realized utility and her utility at a disagreement point. The Nash tariff negotiation equilibrium can be solved in two steps: (1) a restricted Nash bargaining game is solved for a given structure, taking another structure as a disagreement point; (2) the two governments bargain over the choice of structure. The Nash product in structure C, with autarky as a disagreement point, is V = V1V2 = [U1(C) − U1(A)][U2(C) − U2(A)] where Ui (C) and Ui (A) are given in table 3.3. The Nash bargaining corner equilibrium in structure C is given by maximizing V with respect to t1 and t2. The two ﬁrst-order conditions ∂V/∂t1 = ∂V/∂t2 = 0 generate (1 + t1)(1 + t2) = 1. Since t1, t2 ≥ 0, the condition generates the solution of the Nash tariff negotiation game: t *1 = t 2* = 0. This implies that the Nash tariff negotiations will generate a bilateral laissez faire regime. But this regime cannot be achieved in the absence of tariff negotiations because of conﬂict of interest. Although in this Nash bargaining game no risk is speciﬁed, the players’ attitude towards risk “plays a central role” (Osborne and Rubinstein, 1990, p. 10). As long as uncertainty exists about other players’ behavior, there is a chance that negotiations will break down. Thus, each government intends to maximize its expected utility gain in the negotiation. In fact, the Nash product can be interpreted as a player’s expected utility gain, with the probability of reaching an agreement being approximated by the utility gain(s) of the other player(s). According to this view of Nash (1950), the Nash bargaining solution is the outcome of a noncooperative game despite the fact that the gains are shared fairly among players. If each government can decide whether or not to participate in a tariff negotiation game, then it is clear that when structure Ba or Bb occurs in general equilibrium, it must be a Nash equilibrium with no tariff negotiation, since the country producing two goods can get the most gain from a unilateral tariff. When structure C occurs in general equilibrium, the general equilibrium must involve tariff negotiation since both governments prefer tariff negotiation to tariff war. Clearly, the two countries receive more net gains in the tariff negotiation game than in the tariff war since the Nash tariff bargaining equilibrium, which coincides with the Walrasian equilibrium with no tariff, is Pareto optimal. This result explains why it is difﬁcult to realize a laissez faire regime even if it is good for all countries. When the sovereignty of a country can be used to seek rent in international trade via taxation power, the coordination difﬁculty of a prisoners’ dilemma makes tariff negotiation essential for fully exploiting the mutually beneﬁcial gains from trade. Following the method in the previous section, we can show that in the model with an endogenous choice of regimes, the general equilibrium discontinuously jumps from autarky to structure Ba or Bb, then to structure C as the transaction efﬁciency coefﬁcient k increases. From the column within a relevant parameter subspace in table 3.3, we can see that in the transitional stage from A to C, the country with low transaction efﬁciency and/or a large population produces two goods. This provides a formal theory that predicts the positive correlation between favorable geographic conditions for transportation and the openness of government policy, reported in chapter 2.

80 P ART I: D EVELOPMENT M ECHANISMS

Summarizing the above analysis, we have: Proposition 3.2: In a model with two governments that can choose tariff levels and decide whether or not to participate in tariff negotiations, if partial division of labor occurs in equilibrium, that equilibrium is a Nash tariff equilibrium with no tariff negotiations. Most gains from trade go to the country producing both goods and having lower transaction efﬁciency. If complete division of labor occurs in equilibrium, it is a Nash tariff negotiation equilibrium that generates a bilateral laissez faire regime. Proposition 3.2 may be used to explain two phenomena. First, despite the distortions caused by tariffs, they may be used by a government in a less-developed economy with low transaction efﬁciency to get a larger share of gains from trade, since the Walrasian equilibrium terms of trade with no tariffs may be very unfavorable to that country. Second, when transaction conditions are inadequate, so that the equilibrium is associated with an intermediate level of division of labor, a country (which has a low transaction efﬁciency and does not completely specialize) may prefer a unilateral tariff, whereas the other country (which has a higher transaction efﬁciency and completely specializes) may prefer a unilateral laissez faire regime. But as transaction conditions improve, all countries may prefer tariff negotiations to a unilateral tariff. In the sixteenth century, unilateral tariffs were advocated by Mercantilists as a means of rent-seeking in international trade. They gave way to trade liberalization in the eighteenth and nineteenth centuries in some European countries. However, even after the Second World War, many governments in developing countries still adopted unilateral tariff protection. More recently, tariff negotiations have become increasingly prevalent. Some economists use the Walrasian model to explain the emergence of laissez faire regimes, but the model cannot explain why other trade regimes persisted in many countries for a long period of time. Other economists use the theory of import and export substitution to explain the transition from unilateral tariffs to trade liberalization (see, for instance, Balassa, 1980), but the theory cannot explain why a laissez faire regime was unstable even between developed countries; why unilateral protectionist tariffs and a laissez faire regime may coexist; or why tariff negotiations may be necessary for free trade and for the exploitation of the gains from trade. Proposition 3.2 in this chapter seems to offer a more plausible response to the above questions, as well as to why unilateral tariffs prevailed in the early stages of economic development; and why trade liberalization is preferred in the later stages of economic development. In the next example, we extend the simple 2 × 2 Ricardian model to include a third country, country 3, to show that a country may be excluded from trade despite the existence of a comparative advantage between that country and another country. Example 3.3: A Ricardo model with three countries. Let’s assume that transaction conditions are different from country to country such that k1, k3 > k2, where ki is the transaction efﬁciency coefﬁcient in country i. We intend to show that a country that does not have a comparative advantage over two other countries in any single good, and/or that has a low transaction efﬁciency, can be excluded from trade. Suppose that the production functions in country i (i = 1, 2, 3) are the same as in (3.2) and that (a3x /a3y) < (a2x /a2y) < (a1x /a1y), i.e., country 1 has a comparative advantage in producing good x relative to the other two countries; country 2 has a comparative advantage in producing x relative to country 3 and a comparative advantage in producing good y relative to country 1; and country 3 has a comparative advantage in producing y relative to the other two countries. We will consider only the case where the trading countries are completely specialized. For reasons similar to those discussed in example 3.2, all structures involving trade in comparative

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 81

disadvantage goods cannot occur in general equilibrium. We now prove that if a structure involves trading between only two of the three countries, the two trading countries must be country 1 and country 3. In other words, the country with the lowest transaction efﬁciency and/or no comparative advantage over the other two countries in any single good may be excluded from trade. We ﬁrst prove that it is impossible either that only country 1 and country 2 trade, or that only country 2 and country 3 trade. To do so, we use the argument of negation. Suppose that only countries 1 and 2 trade. This can occur in general equilibrium only if individuals in country 2 prefer specialization in y (or conﬁguration ( y/x)) to autarky and individuals in country 3 prefer autarky to specialization in y. That is, the following inequalities hold: U2(y/x) > U2(A) which holds iff p < (a2y /a2x)k2

and

U3(y/x) < U3(A) which holds iff p > (a3y /a3x)k3. where the indirect utility functions for different conﬁgurations are from table 3.1. The two inequalities jointly imply (a2x /a2y k2) < (a3x /a3y k3), which contradicts the assumption (a2x /a2y) > (a3x /a3y) and k2 < k3. Suppose, instead, that only countries 2 and 3 trade. This can occur in general equilibrium only if: U2(x/y) > U2(A) which holds iff p > a2y /a2x k2

and

U1(x/y) < U1(A) which holds iff p < a1y /a1x k1. The two inequalities jointly imply (a1y /a1x k1) > (a2y /a2x k2), which contradicts the assumption (a1x /a1y) > (a2x /a2y) and k2 < k1. Hence, if only two countries trade, they must be countries 1 and 3. Next, we examine the conditions under which the structure involving trade between only countries 1 and 3 occurs in general equilibrium. The conditions are: U1(x/y) > U1(y/x) which holds iff p > (a1y /a1x)k 12β−1, U1(x/y) > U1(A) which holds iff p > a1y /a1x k1, U2(x/y) < U2(A) which holds iff p < a2y /a2x k2, U2(y/x) < U2(A) which holds iff p > (a2y /a2x)k2, U3(y/x) > U3(A) which holds iff p < (a3y /a3x)k3, U3(y/x) > U3(x/y) which holds iff p < (a3y /a3x)k 32β−1, where p = a3y M3β/a1x M1(1 − β) is the corner equilibrium-relative price in this structure. The six inequalities together imply Min{a2y /a2x k2, (a3y /a3x)k3} > a3y M3β/a1x M1(1 − β) > Max{a1y /a1x k1, (a2y /a2x)k2}. The parameter subspace satisfying this condition is certainly not empty. For instance, if k2 is sufﬁciently close to 0 and k1 and k3 are sufﬁciently close to 1, then the above condition becomes (a3y /a3x)k3 > a3y M3β/a1x M1(1 − β) > a1y /a1xk1, or (a1x /a3x)k3 > M3β/M1(1 − β) > a1y /a3y k1, which holds only if k3k1[(a1x /a1y)/(a3x /a3y)] > 1. This condition can be satisﬁed if the relative population size is not too far away from a balance with relative tastes, if the two countries’ transaction conditions are sufﬁciently good, and if the degree of comparative advantage (measured by (a1x /a3x)(a3y /a1y)) between the two countries is great.

82 P ART I: D EVELOPMENT M ECHANISMS

Summarizing the above analysis, we obtain: Proposition 3.3: In a 3 × 2 Ricardian model within a certain parameter subspace, it is possible that the country that has no comparative advantage in producing any good over both of its potential trading partners and/or that has very low transaction efﬁciency will be excluded from trade. This proposition can accommodate the opinions expressed by both sides in a recent debate on international competitiveness. Krugman (1994) argues that a nation should focus on promoting free trade and that an emphasis on international competitiveness can be “a dangerous obsession.” Sachs (1996) and Prestowitz (1994), on the other hand, contend that international competitiveness plays an essential role in improving national welfare. If international competitiveness is measured by a country’s transaction efﬁciency, then proposition 3.3 conﬁrms that competitiveness matters: it implies that comparative advantage is not enough for realizing gains from trade. A country can be excluded from trade even if it has comparative advantage over another single country when its transaction efﬁciency is low and/or it has no comparative advantage to both of its other potential partners in producing the same good. However, the proposition also supports Krugman’s argument that a country should focus on promoting free trade and improving transaction efﬁciency. In our model, the promotion of free trade can be done through reducing tariff and nontariff barriers to trade so as to improve transaction efﬁciency k. If k is extremely low, no trade occurs and absolute and comparative advantage does no good for trade. Since in our model the improvement of the transaction efﬁciency coefﬁcient through trade liberalization policies can generate a jump of general equilibrium from a low to a high level of division of labor, the argument for free trade is even stronger than the conventional marginal analysis suggests. Therefore, international competitiveness and free trade are important factors contributing to a country’s welfare. Krugman’s emphasis on trade liberalization is particularly relevant if the pursuit of international competitiveness is used as an excuse for impeding free trade. Introducing tariffs into the model in this section, it can be shown that when all governments are allowed to choose their tariff level and when the partial division of labor occurs in general equilibrium, the country with a higher tariff and/or a worse transaction condition (a small value of k) will be excluded from trade. Hence, in a world economy with many governments, each country will reduce tariffs to avoid exclusion from trade. This implies that, even in a partial division of labor, tariff rates will be reduced by competition between governments in similar countries. On the other hand, since a greater value of k will increase the number of countries involved in international trade, which will in turn ensure a multilateral free trade regime even if the partial division of labor occurs in general equilibrium, a sufﬁciently great increase in k in the country that was excluded from trade can then ensure a zero tariff rate for all countries, even if the general equilibrium is associated with the partial division of labor. This result implies that there are two possible explanations for a shift of trade regime from protectionist tariffs to trade liberalization. The ﬁrst is to attribute such a shift to the increase in the level of division of labor (a shift from partial to complete division of labor), which is caused by improvements in transportation conditions. The second is to attribute such a shift to the increase in the number of countries that are involved in international trade, which is caused by improvements of the transaction conditions in those countries which were excluded from trade. An increase in k can be generated by improvements in transportation conditions (the emergence of new transportation technology or the development of transportation infrastructure) and/or by institutional changes (the emergence of a legal system that more effectively protects property rights or the emergence of a more competitive and efﬁcient banking system).

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 83

3.6

COMPARATIVE ENDOWMENT ADVANTAGE AND TRANSACTION EFFICIENCY

In this section we consider the Heckscher–Ohlin (HO) model with two countries differing in endowments and transaction conditions. The HO model can be used to show that in the absence of Ricardo’s technical comparative advantage, economies of division of labor may arise from exogenous differences in endowment between countries. Some core neoclassical trade theorems can be based on the HO model. In this section, we work out an inframarginal as well as marginal comparative statics of general equilibrium of the HO model to show that as transaction conditions are improved, the equilibrium levels of division of labor and productivity increase. In particular, comparative statics that relate to the Heckscher–Ohlin (HO) theorem, the Stolper– Samuelson (SS) theorem, and the factor price equalization (FPE) theorem are examined. Example 3.4: The HO model with transaction costs. Consider the HO model with transaction costs and with comparative endowment advantages between two countries. Perfect competition prevails in both goods and factor markets, and factors are mobile within a country but immobile between countries. Country i (i = 1, 2) is endowed with labor Li and capital Ki, which can be used to produce two consumer goods x and y. The decision problem of a representative consumer in country i is: Max: Ui = X iθ Y 1−θ i ,

pix xi + pjx xji + piy yi + pjy yji = wi Li + ri Ki

s.t.

where Xi ≡ xi + ki xji and Yi ≡ yi + ki yji are respective amounts of the two goods consumed, pst is the price of good t in country s, xi and yi are respective amounts of the two goods purchased from the domestic market in country i, xji and yji are respective amounts of the two goods, purchased from a foreign country, or delivered from country j to country i, wi and ri are wage rate and rental of capital in country i, respectively. xi , xji , yi , yji may be 0, or corner solutions are allowed. Because of transaction costs, the prices of the same good may differ between the two countries. The price of imported good t to country s, pst, can be considered as CIF (import price inclusive of insurance and freight) and the price of exported good t from country s, pst, can be considered as FOB (import price exclusive of insurance and freight) to the importing country. Since corner solutions are allowed, a consumer’s decision is conﬁguration dependent as in previous sections. In addition to autarky, there are 8 different trade structures in the HO model. Using the ﬁrst letter to denote goods produced by country 1, the second letter to denote goods produced by country 2, and the subscript i to denote country i, we have the following structures, as shown in ﬁgure 3.3: x1 y2 (country 1 produces x and country 2 produces y); y1x2 (country 1 produces y and country 2 produces x); xy1 y2 (country 1 produces both goods and country 2 produces y);

xy

xy

x y yx1xy2 y x xy1 yx2

xy

xy

xy

y

x y xy1 y2 y x y1xy2

Figure 3.3 Possible trade structures

y

x

xy

xy

x y x1xy2 y x xy1x2

xy

x

x

y

x y x1 y2 y x y1x2

y

x

84 P ART I: D EVELOPMENT M ECHANISMS

xy1x2, x1xy2, y1xy2, yx1xy2 (each country produces two goods and country 1 exports x and imports y); xy1 yx2 (each country produces two goods and country 1 exports y and imports x). The last two structures are referred to as interior structures since they are based on interior solutions for each country. The ﬁrst six structures involve the corner solutions of at least one country, and are thus referred to as corner structures. Our concept of interior structure relates to the concept of the diversiﬁcation cone, developed in the 1950s (see Lerner, 1952, and McKenzie, 1955). It is deﬁned as the range of factor endowments within which a country produces both goods for given prices. We ﬁrst consider structure yx1xy2 where x21 = y12 = 0. The ﬁrst-order conditions for the decision problems of representative consumers in the two countries (∂u1/∂x1)/(∂u1/∂y1) = p1x /p1y,

(∂u1/∂x1)/(∂u1/∂y21) = p1x /p2y,

(∂u2/∂x2)/(∂u2/∂y2) = p2x /p2y,

(∂u2/∂x12)/(∂u2/∂y2) = p1x /p2y,

yield: p2y = k1 p1y = k1,

p1x = k2 p2x.

We assume that good y produced in country 1 is the numeraire, so that p1y = 1 and denote p = p1x, so that p2x = p/k2 and p2y = k1. Assume that the production functions for x and y in country i are: x is = L αix K ix1−α;

yis = L iyβ K iy1−β

where x is and y is are the respective output levels of the two goods, Lij (i = 1, 2; j = x, y) is the amount of labor and Kij is the amount of capital allocated to produce good j in country i. Constrained by its production technology, the representative ﬁrm producing x in country i maximizes its proﬁt, i.e., Max πix = pix x is − wi Lix − ri Kix = pix L αix K1−α ix − wi Lix − ri Kix. Lix , K ix

The decision problem for the representative ﬁrm producing y is similar. Because of the constant returns to scale, the optimum quantities of both goods supplied and factors demanded are indeterminate. But the ﬁrst-order conditions for the four decision problems of the two types of ﬁrms in the two countries ∂πi/∂L ij = wi ,

∂πi/∂Kij = ri ,

i = 1, 2, j = x, y

can be used to express factor prices and relative factor allocation as functions of relative prices of goods: w1/r1 = (a1y B/a1x Ap)1/(β−α)

and

w2/r2 = (a2x Ap/a2y Bk1k2)1/(β−α).

(3.6)

where A ≡ αα(1 − α)1−α, B ≡ ββ(1 − β)1−β. The market clearing conditions for factors in each country Lix + Liy = Li

and

Kix + Kiy = Ki ,

i = 1, 2,

together with the ﬁrst-order conditions for ﬁrms’ decisions, can then be used to solve resource allocations also as functions of the relative prices of goods:

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 85

Lix = [αβri Ki /(β − α)wi] − [α(1 − β)Li /(β − α)],

Kix = [(1− α)wi Lix /αri],

Liy = [αβ/(β − α)]{[(1 − α)Li/α] − (riKi /wi)},

Kiy = [(1 − β)wi Liy /βri].

where the relative prices of factors are functions of the relative price of goods, p, as given in (3.6). The world market clearing condition for good x x1 + x2 + x12 = x 1s + x 2s then determines the equilibrium relative price of goods, p. Note that the market clearing condition for good y is independent of this equation due to Walras’s law. Without loss of generality, we assume that β > α. It is easy to show that in the equilibrium, Kix /Lix > Kiy/Liy iff β > α. Hence, the assumption implies that the x industry is capital-intensive and the y industry is labor-intensive. We assume also that country 1 is relatively capital abundant, or that K2/L2 < K1/L1. We ﬁrst consider the world general equilibrium in structure yx1xy2, then consider structure xy1 yx2, and identify the parameter subspaces for autarky and corner structures to be general equilibrium. The interior equilibrium in structure yx1xy2 is summarized as follows: Xi = A[βKi − (1 − β)Li/γ]γ α/(β − α), Yi = B[(1 − α)(Li/γ) − αKi]γ β/(β − α), Lix = [α/(β − α)][βKiγ − (1 − β)Li], (3.7a)

Liy = [β/(β − α)][(1 − α)Li − αKiγ], Kix = (1 − α)Lixwi/ri α, p = Bγ

(β−α)

/A,

Kiy = (1 − β)Liy wi/riβ,

r1/w1 = (Ap/B)1/(β−α),

r2/w2 = (Ap/k1k2B)1/(β−α),

where A ≡ αα(1 − α)1−α, B ≡ ββ(1 − β)1−β, γ≡

[1 − β + (β − α)θ]L1 + [1 − β + (β − α)θ/k2 ](k1k2 )(1− α )/(β − α ) L 2 [β(1 − θ) + αθ]K1 + [β − (β − α)θ/k2 ](k1k2 )(1− α )/(β − α )K2

,

(3.7b)

Xi and Yi are respective amounts of the two goods consumed by the representative consumer in country i, that is, X1 = x1, X2 = x2 + k2x12, Y1 = y1 + k1 y21, Y2 = y2. The HO theorem (Heckscher, 1919; Ohlin, 1933) states that a country exports the goods whose production uses its abundant factor intensively. In terms of the model in this section, the HO theorem, together with the assumption that β > α (the x sector is capital intensive), implies that country 1 exports good x and imports y if K1/L1 > K2/L2. Considering all possible structures, this implies that structure yx1xy2, xy1 y2, x1xy2, or x1 y2, as shown in ﬁgure 3.3, occurs at general equilibrium. Letting the equilibrium values of Lix and Liy be greater than or equal to 0, we can partition the nine-dimension space of parameters β, α, θ, Ki, Li, and ki into subspaces. For instance, letting Lix , Liy > 0 for i = 1, 2, we can identify the parameter subspace for an interior structure as the general equilibrium structure, and letting Lix, L1y > 0 and L2y = 0, we can identify the parameter subspace for structure xy1x2 as the general equilibrium structure. All possible trade structures are illustrated in ﬁgure 3.3, where the left circle in each panel represents country 1 and the right circle represents country 2; lines between circles represent goods ﬂows. In ﬁgure 3.3 the distinction is drawn between the interior structure xy1 yx2, in which country 1 exports y and country 2 exports x, and the structure yx1xy2, in which country 1 exports x and

86 P ART I: D EVELOPMENT M ECHANISMS

country 2 exports y. The two structures are interior structures, but the former is inconsistent with the HO theorem. Structures xy1x2, y1xy2, y1x2 are incompatible with the HO theorem; in those cases, the capital-abundant country 1 exports the labor-intensive good y. We ﬁrst identify the condition under which the parameter subspaces that enable the three structures to be general equilibrium structures are empty. Letting Lix, L1y > 0 and L2y ≤ 0 in (3.7a), we can see that structure xy1x will be chosen only if K2/L2 > K1/L1, which contradicts the assumption K2/L2 < K1/L1. Hence, we can see that the parameter subspace for structure xy1x2 to be chosen is empty if: K2/L2 < K1/L1

and

β > α.

(3.8)

Similarly, we can prove that structures y1xy2, y1x2, which are incompatible with the HO theorem, cannot be general equilibrium structures if (3.8) holds. We can also show that the parameter subspaces for other structures as equilibrium structures are not empty if (3.8) holds. For an interior structure to occur in equilibrium, it must be true that L1x > 0; L1y > 0; L2x > 0; L2y > 0. These conditions are equivalent to: γ ∈((1 − β)L1/βK1, (1 − α)L1/αK1), which holds only if β > α

(3.9a)

γ/(k1k2) ∈ ((1 − β)L2/βK2, (1 − α)L2/αK2), which holds only if β > α

(3.9b)

γ ∈((k1k2)

(1 − β)L2/βK2, (1 − α)L1/αK1), which holds only if (1 − α)L1/αK1 > (k1k2)1/(β−α)(1 − β)L2/βK2

(3.9c)

γ ∈((1 − β)L1/βK1, (k1k2)1/(β−α)(1 − α)L2/αK2), which holds only if (k1k2)1/(β−α)(1 − α)L2/αK2 > (1 − β)L1/βK1

(3.9d)

1/(β−α)

where γ is given in (3.7b) and ∂γ/∂k1 > 0 and ∂[γ/(k1k2)]/∂k2 < 0. (3.9a) implies that k1 is neither too great nor too small, and (3.9b) implies that k2 is neither too great nor too small. (3.9c) implies that transaction efﬁciencies in two countries (k1k2) are not too great and comparative endowment advantage K1L2/L1K2 is not too great compared to other parameters. (3.9d) implies that transaction efﬁciency (k1k2) is not small and comparative endowment advantage K1L2/L1K2 is not small. Hence, structure yx1xy2 occurs in equilibrium if transaction efﬁciencies in two countries are neither too great nor too small and if comparative endowment advantages are neither too signiﬁcant nor too trivial. Now we consider the dividing line between structure yx1xy2 and autarky. Since both structures satisfy Lij > 0 for i = 1, 2 and j = x, y, we have to calculate the domestic excess demand for x and y to identify the dividing line. Inserting the equilibrium prices into the domestic demand and supply functions for goods yields: x 1s ≥ X1 iff γ ≥ γ1 ≡ [(β − α)θ + 1 − β]L1/K1[β(1 − θ) + αθ]

(3.10a)

y 2s ≥ Y2 iff γ ≤ γ2 ≡ [(β − α)θ + 1 − β](k1k2)1/(β−α)L2/K2[β(1 − θ) + αθ]

(3.10b)

The two semi-inequalities imply that: γ2 ≥ γ ≥ γ1 which holds only if γ2 ≥ γ1

(3.11)

It is not difﬁcult to see that γ2 > γ1 iff η ≡ (k1k2)1/(β−α)μ = (k1k2)1/(β−α)(K1L2/K2L1) > 1,

(3.12)

C HAPTER 3: E XOGENOUS C OMPARATIVE A DVANTAGE 87

where η is a product of transaction efﬁciencies in the two countries and μ which represents the degree of comparative endowment advantage. It is obvious for k1k2 = 1, γ2 > γ1 iff (3.8) holds. Hence, if (3.8) holds and transaction costs in two countries do not outweigh comparative endowment advantage, then structure yx1xy2 may occur in equilibrium. As k1 and k2 decrease from 1, γ2 tends to γ1. If k1 and k2 are sufﬁciently small, it will be true that γ2 = γ1, which implies γ2 ≥ γ ≥ γ1 holds only if γ = γ1 = γ2. Recalling (3.10), this implies that the domestic excess demand in both countries is 0, or that autarky occurs in equilibrium. Hence, the dividing line between structure yx1xy2 and autarky is η = (k1k2)1/(β−α)(K1L2/K2L1) = 1. For η ≤ 1, autarky occurs in equilibrium. (3.12), together with (3.9c), imply that structure yx1xy2 occurs in equilibrium only if β(1 − α)/α(1 − β) > η > 1. Alternatively, we can verify that autarky occurs in equilibrium if transaction efﬁciency in either country is sufﬁciently low. First, note the facts that dγ/dk1 > 0 and for k1k2 = 1, γ > γ1. This implies that as k1 decreases from 1 to 0, γ monotonously decreases from a value greater than γ1 toward γ1. As γ reaches γ1, the equilibrium price in structure yx1xy2 becomes the same as that in autarky. Hence, as k1 becomes sufﬁciently close to 0, country 1 chooses autarky and, therefore, the general equilibrium is autarky. Similarly, we can prove that as k2 becomes sufﬁciently close to 0, country 2 chooses autarky and, therefore, the general equilibrium is autarky. Therefore, if transaction efﬁciency in either country is too low, the general equilibrium will be autarky. As transaction efﬁciencies increase, the general equilibrium jumps from autarky to a structure with trade. In order to rule out structure xy1 yx2, we assume x12, y21 = 0 and x21, y12 > 0 in the consumer’s decision problem. Following the same procedure for solving for the local equilibrium in structure yx1xy2, we can show that the equilibrium prices in this structure are p1y = 1, p1x = p, p2x = k2, p2y = k1 p and that domestic excess demand for x in country 1 and for y in country 2 are positive only if μ = (K1L2/K2L1) < (k1k2)1/(β−α), which is incompatible with the assumption (3.8) for ki ∈[0, 1] and β > α. This implies that the parameter subspace for structure xy1 yx2 to occur in equilibrium is empty, or that this structure is ruled out from the set of candidates for equilibrium structures. Following this method, we can show that the parameter subspace for structure x1xy2 to occur in equilibrium is given by: (1 − α)L1/αK1 < γ < (1 − α)L2(k1k2)1/(β−α)/αK2 (1 − α)L2/αK2 > γ/(k1k2)

1/(β−α)

> (1 − β)L2/βK2.

and

(3.13a) (3.13b)

(3.13a) holds only if k1k2 is sufﬁciently large and the degree of comparative endowment advantage, K1L2/L1K2, is not too great compared to other parameters. Since d[γ/(k1k2)1/(β−α)]/dk2 < 0, (3.13b) implies that k2 is neither too great nor too small, and the degree of comparative endowment advantage, K1L2/L1K2, is not too small compared to other parameters. Hence, the general equilibrium occurs in structure x1xy2 if transaction efﬁciency in country 2 and comparative advantage are neither too high nor too low, while the transaction efﬁciency is great in country 1. In other words, country 1 completely specializes and country 2 produces two goods if k1 is great compared to k2. Since international terms of trade are determined by the domestic terms of trade in country 2 in this structure, most gains from trade go to the country producing one good.

88 P ART I: D EVELOPMENT M ECHANISMS Table 3.4 General equilibrium and its inframarginal comparative statics η

<1

∈[1, β(1 − α)/α(1 − β)]

k

k1 and/or k2 are small

k1 is great, k2 is neither great nor small

k1 and k2 are neither great nor small

k2 is great, k1 is neither great nor small

k1 is great, k2 is neither great nor small

k1 and k2 are great

k2 is great, k1 is neither great nor small

Autarky

x1xy2

yx1xy2

yx1 y2

x1xy2

x1 y2

yx1 y2

Equilibrium structure

> β(1 − α)/α(1 − β)

The parameter subspace for structure xy1 y2 to occur in equilibrium is given by: (1 − β)L1/βK1 < γ < (1 − α)L1/αK1

and

(1 − α)L2(k1k2)1/(β−α)/αK2 > γ > (1 − β)L1/βK1.

(3.14a) (3.14b)

(3.14b) holds only if k1k2 is sufﬁciently large and the degree of comparative endowment advantage, K1L2/L1K2, is not too small. Since dγ/dk1 > 0, (3.14a) implies that k1 is neither too great nor too small, and the degree of comparative endowment advantage, K1L2/L1K2, is not too great. Hence, the general equilibrium occurs in structure xy1 y2 if the transaction efﬁciency in country 1 and comparative advantage are neither too high nor too low, while the transaction efﬁciency is great in country 2. In other words, country 1 produces two goods and country 2 completely specializes if k2 is great compared to k1. Following this method, we can identify the parameter subspace necessary for each structure to be an equilibrium structure, as summarized in table 3.4, where η ≡ (k1k2)1/(β−α)μ = (k1k2)1/(β−α)(K1L2/K2L1), and β(1 − α)/α(1 − β) > 1 > α(1 − β)/β(1 − α) > 0. η is a product of transaction efﬁciencies in the two countries and μ, which represents the degree of comparative endowment advantage. Table 3.4 suggests that under our assumption (3.8), autarky and four different trade patterns can occur in equilibrium depending on parameter values. All four trade patterns feature country 1 exporting good x. (It can be shown that if we reverse our assumption (3.8), the other four trade patterns will occur in equilibrium, each featuring country 1 exporting good y.) All corner structures in table 3.4 are consistent with the HO theorem. For instance, in structure xy1 y2, capital-abundant country 1 exports the capital-intensive good x and laborabundant country 2 exports labor-intensive good y, as shown in ﬁgure 3.3. We can see that for each corner structure, the market clearing condition ensures a trade pattern that is unambiguous about which country exports which good. This implies that the HO theorem holds for all corner structures in table 3.4, even if parameter values shift between the parameter subspaces that demarcate the structures. Following the same approach to analyzing the Ricardian model in the previous sections, it can be shown that the equilibrium production schedule in autarky is lower than the PPF, since autarky imposes the constraint that marginal rate of substitution and marginal rate of transformation must be equalized within each country. Hence, as transaction conditions are improved, the aggregate productivity jumps as a result of an increase in the equilibrium levels of division of labor and trade. Another general equilibrium mechanism for economic development is: as transaction conditions are improved, equilibrium productivity increases due to exploitation of more comparative endowment advantages between countries or between different groups of individuals. You are asked in exercise 8 below to introduce comparative technological

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advantages into the HO model to reestablish proposition 3.4, and to prove that the HO theorem may not hold in the model with comparative technological and endowment advantages and transaction costs. The inframarginal comparative statics are summarized as follows. Proposition 3.4: If transaction efﬁciency is sufﬁciently low in any country and/or comparative endowment advantage is small, autarky occurs in equilibrium. If transaction efﬁciencies in two countries are slightly improved and/or the degree of comparative advantage slightly increases, the equilibrium shifts to a low level of division of labor with each country producing two goods. If the transaction efﬁciency is further improved in one country and/or the degree of comparative advantage increases further, the equilibrium shifts to a dual structure wherein this country completely specializes and gets the most gains from trade, while the other country produces two goods. As transaction efﬁciencies in two countries and/or the degree of comparative advantage are sufﬁciently increased, the equilibrium jumps to a high level of division of labor, where each country produces only one good and gains from trade are shared by the two countries. This evolution in division of labor and trade dependence increases the equilibrium aggregate productivity. Table 3.4 and (3.7) show that for k1 = k2 = 1, international trade will make factor prices in the trading countries equalize, even though the factors themselves are immobile across countries (Samuelson, 1948), if the comparative endowment advantage and transaction efﬁciencies in the two countries are neither great nor small, or if the interior structure yx1xy2 occurs in equilibrium. It is easy to show that the factor price equalization does not hold if k1 and k2 are not 1 (transaction cost is not zero). In addition, the factor price may not be equal if a corner structure occurs at equilibrium or if transaction efﬁciency in any country and/or comparative endowment advantage are too great or too small. In exercise 11 (below) you are asked to show that if total factor productivity is different from country to country and from good to good, then relative factor price may be different even in the interior structure yx1xy2 in the absence of transaction costs. The SS theorem was derived from an interior structure in the HO model, in which both countries produce both goods and the commodity price is assumed to be exogenous. The theorem states that if the price of the capital-intensive (or labor-intensive) good rises, the price of capital (or labor) rises, and in greater proportion to the commodity price increase, while the price of labor falls (or that of capital rises), but necessarily in greater proportion to the commodity price increase (Stolper and Samuelson, 1941). The theorem is wildly at odds with empirical evidence. (Grossman and Levinsohn (1989) show that the speciﬁc factors model captures reality more closely than the SS theorem for many US industries.) Since the price of a country’s comparative advantage good rises with the opening-up of international trade, a corollary of the SS theorem is that international trade beneﬁts a country’s abundant factor and hurts its scarce factor, so that a tariff beneﬁts a country’s scarce factor. This prediction is inconsistent with the common sense that the protection of labor-intensive industries may shift the distribution of income marginally in favor of workers, but will lower overall income, and on balance, therefore, will normally hurt them. On this view, the SS theorem provides a theory to explain the income distribution effect of international trade. The inframarginal comparative statics in table 3.4 imply that common sense might be closer to reality than the SS theorem. Our iceberg transaction cost is equivalent to a tax system that uses all tax revenue to pay the bureaucrats who collect the tax. Hence, our model can be used to analyze the effects of a tariff that incurs signiﬁcant bureaucratic costs. The SS theorem ignores the possible inframarginal effect of tariff and transaction costs on a discontinuous shift of trade structure. As shown in

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table 3.4, tariff and associated transaction costs may generate jumps between autarky and structures x1 y2 and yx1xy2 that may be inconsistent with the SS theorem. Proposition 3.4 implies that as the transaction efﬁciency in a country unilaterally decreases compared to another country, the general equilibrium may shift from structure x1 y2 to an asymmetric structure where this country produces two goods and most of the gains from trade go to the other country. This is because in an asymmetric structure, terms of international trade are determined by terms of domestic trade in the country producing two goods. This formalizes the common sense that even if a tariff may marginally change terms of trade and increase income of scarce factors, it may inframarginally hurt all home residents by reducing level of trade and associated gains. Finally, we prove that even within the interior structure, the SS theorem may not hold if price movements are caused by changes in transaction conditions. Suppose that the equilibrium occurs in structure yx1xy2 so that the equilibrium prices are given by (3.7). Country 2’s terms of trade are P ≡ p2y /p1x = k1/p, where p2y is the price of good y in country 2 in terms of good y in country 1, and p ≡ p1x is the price of good x in terms of good y in country 1. The differentiation of (6d) yields: d(r2/w2)/dk2 = ∂(r2/w2)/∂k2 + [∂(r2/w2)/∂P](dP/dk2) where ∂(r2/w2)/∂k2 < 0, ∂(r2/w2)/∂P < 0, and dP/dk2 = −k1dp/p2dk2 is ambiguous, since dp/dk2 is positive within a parameter subspace and negative within the other subspace. If dp/dk2 > 0, the sign of ∂(r2/w2)/∂k2 is opposite to that of [∂(r2/w2)/∂P](dP/dk2). Therefore, the SS theorem may not hold if the indirect effect of a change in k2 on r2/w2 dominates the direct effect. The prediction of the SS theorem even within the diversiﬁcation cone may be wrong if price movements are caused by changes in transaction conditions, because some feedback loops between price differentials, transaction conditions, production, and consumption in the two countries are ignored by the SS theorem. In exercises 12–16 you are asked to prove that the SS theorem may not hold even within the diversiﬁcation cone if price movements are caused by changes in nonneutral technological changes, or by changes in total factor productivity in a model with comparative technological and endowment advantages. Also, you are asked to verify that the SS theorem may not hold in a corner structure and may not hold if price movements are caused by inframarginal shifts of trade structure.

Key Terms and Review • Absolute vs. comparative advantages • Level of specialization and level of division of labor • Economies of division of labor generated by exogenous comparative productivity advantage • Economies of division of labor generated by exogenous comparative endowment advantage • Comparative statics of decisions vs. comparative statics of general equilibrium • Marginal comparative statics vs. inframarginal comparative statics • Why may a country receive more gains from trade even if its terms of trade deteriorate? • Implications of inframarginal analysis of the Ricardian model and the HO model • The HO theorem, the SS theorem, the factor price equalization theorem, and the conditions under which these hold

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Further Reading Ricardian model: Dixit and Norman (1980), Ethier (1988), Gomory (1994), Cheng, Sachs, and Yang (2000). Mercantilism, import substitution, and export-oriented development: Ekelund and Tollison (1981), Balassa (1980), and Bruton (1998), and references there. Theory of dependence and underdevelopment: Palma (1978), Meier (1995, p. 109), Bauer and Yamey (1957), and references there. Inframarginal analysis and rejection of marginal cost pricing: Buchanan and Stubblebine (1962), Coase (1946, 1960), Rosen (1978, 1983), Yang and Ng (1993), Azariadis (1975), Baily (1974), Liebowitz and Margolis (1994), Tirole (1989). Neoclassical trade theory and core (HO, SS, RY, FPE) theorems: Dixit and Norman (1980), Dornbusch and Samuelson (1977), Ethier (1988), Deardorff and Stern (1994), Jones (1965), Heckscher (1919), McKenzie (1955), Lerner (1952), Ohlin (1933), Rybczynski (1955), Samuelson (1948, 1953), Stolper and Samuelson (1941), Uzawa (1959). The Ricardian model with economies of scale: Gomory (1994), Sachs, Yang, and Zhang (1999a), Cheng, Liu, and Yang (2000). The debate about competitiveness: Krugman (1994a,b), Prestowitz et al. (1994), Sachs (1996a,b). The relationship between trade and income distribution: Sachs (1996c), Krugman (1995). Political economics of trade policy, and strategic trade models: Cheng, Sachs, and Yang (2000), Krueger (1974, 1997), World Bank (1996, 1997), Conybeare (1987), Grossman and Richardson (1986), Grossman and Helpman (1995a,b), Johnson (1954), Krugman (1986), Pincus (1975), Riezman (1982), Mayer (1981, 1984). The Nash bargaining game: Nash (1950), Osborne and Rubinstein (1990). Trade policy and dual structure: Murphy, Shleifer, and Vishny (1989), Yang (1991, 1994, 1996), Cheng, Sachs, and Yang (2000). Deteriorated terms of trade and development: Dudley (1986), Sen (1998), Morgan (1970), Kohli and Werner (1998). Empirical tests of the core trade theorems: Bowen, Leamer, and Sveikauskas (1987), Treﬂer (1993, 1995), Grossman and Levinsohn (1989), Leamer (1984), Leontief (1956). “Anything possible” theorem: Debreu (1974), Mantel (1974), Sonnenschein (1973), or see Mas-Collell et al. (1995, ch. 17).

QUESTIONS 1 An economics student claims that the extent of the market and demand are determined by income. Why did Allyn Young criticize this as a partial view? Why did he argue not only that division of labor depends upon the extent of the market, but also that the extent of the market depends on the level of division of labor? What is the relationship between the Young theorem and the notion of network effect, and why is the notion of general equilibrium essential for formalizing the Young theorem? 2 What is the difference between the concept of economies of division of labor and economies of scale? What is the network effect of division of labor? 3 From the model in example 3.1, we can see that if the partial division of labor occurs in equilibrium, the country with lower transaction efﬁciency and/or larger population size will produce two goods (see the column of relevant parameter subspaces in table 3.3). This implies that the country will receive no gains from trade in the absence of tariffs and will have an incentive to pursue unilateral protectionist tariffs. There are many ways to interpret this result. For instance, the US is a large country, so that it can use tariffs to get a greater share of gains from trade if asymmetric partial division of labor occurs between the US and a smaller country. As another example, New Zealand is a small country with a low transaction efﬁciency (because it is far away from other countries). Hence, for either of the two cases, the US or New Zealand can use protectionist tariffs to get more gains from trade. But after the Second World War, the US opened its market to Japan, South Korea, Taiwan, and China, so that the international division of labor among these countries developed drastically, and the US and these other countries gained tremendously from free trade. New Zealand does not pursue protectionism either.

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Use the possible evolution from partial division of labor to complete division of labor in the model in this chapter to explain the success of these countries’ trade policies. The Lewis model (1955) and the Fei and Renis model (1964) explain economic development as a process in which labor is transferred from the agricultural to the industrial sector. Compare this view of economic development to Lewis’s original idea, formalized by the Ricardian model in this chapter, that economic development is an evolutionary process of commercialization. An increase in each person’s level of specialization and an increase in the diversity of occupation conﬁgurations are two aspects of this evolution. There is a debate between Krugman (1994a,b) and Prestowitz et al. (1994) about the international competitiveness of countries (see also Sachs, 1996). One side of the debate argues that according to Ricardo’s theory of comparative advantage, competitiveness which relates to absolute advantage does not matter in exploiting gains from trade. Assume in example 3.1 that (1 − β)M1/βM2 = 1, and show that structure C cannot be general equilibrium if one country has no absolute advantage, even if k = 1 (there is no transaction cost). Under this condition, Ba or Bb is the equilibrium where one country obtains no gain from trade. Discuss possible trade conﬂicts and related distortions, and the implications of absolute advantage for avoiding such endogenous transaction costs. According to Jones (1981, pp. 226–7), Europe’s considerable geological, climatic, and topographical variety endowed it with a dispersed portfolio of resources. This conduced to long-distance, multilateral trade in bulk loads of utilitarian goods. Taxing these was more rewarding than appropriating them. An abnormally high ratio of navigable routes to surface area also favored bulk trade. Use the model in this chapter to elaborate this historical fact. France imposed high protectionist tariffs on goods imported from Britain prior to its industrialization, and gave preferential trade status to less-developed trade partners after its industrialization in the nineteenth century (see Landes, 1998). Many developed countries currently use this policy to promote their trade with lessdeveloped countries. Use the model in example 3.2 to explain why this policy might be good for both developed and less-developed countries. According to Mokyr (1990, p. 254; 1993, p. 34), Britain had a comparative advantage in entrepreneurial and skilled production activities, and thus imported inventions and inventors from, and exported entrepreneurs and technicians to, the industrializing enclaves of the Continent in the eighteenth and nineteenth centuries. In addition to the inventions that Britain imported from the Continent, it imported some inventors, including Isambard Brunel, Friedrich Koenig, and the Swiss engineer J. G. Bodmer. E. Jones (1981) and Baechler (1976) indicate that the comparative advantage of British entrepreneurs was created by a variety of political systems in Europe, some of which encouraged entrepreneurial activities while others encouraged sciences. Such a created comparative advantage is called an endogenous comparative advantage (see chapters 4 and 5 below). The comparative advantage studied in this chapter is exogenous comparative advantage. Give some examples in which comparative advantages appear to be exogenous, but may be endogenously created by a variety of institutions and cultures. One way to specify increasing returns to scale based on the neoclassical dichotomy between consumers and ﬁrms in the Ricardian model can be found in Gomory

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(1994). That speciﬁcation causes Pareto rankable multiple general equilibria, since pure consumers cannot choose between occupation patterns, while pure producers do not care about the choice because of zero proﬁt in all structures. Discuss the implications for trade theory of the difference between the Smithian framework and the neoclassical framework with a dichotomy between pure consumers and ﬁrms. Some economists argue that the statement that improvements in transaction conditions can increase trade sounds like a tautology. Use the model in this chapter to show that the exact formula for substitution between relative population size, relative tastes, relative productivity, and transaction efﬁciency in raising the equilibrium level of division of labor and productivity can be worked out from the inframarginal comparative statics of the general equilibrium model with comparative advantage and transaction costs. Also, use the fact that improvements in transaction efﬁciency may increase total transaction costs to comment on the above argument. Conduct the following thought experiment. Suppose many goods are introduced into the Ricardian model in example 3.1. Each of the two countries has two types of individuals. Under what conditions might international trade emerge from domestic trade? Baran (1957; see also Palma 1978) argued that the integration of developing economies into the world economy is necessarily achieved through an interminable metropolis–satellite chain, in which the surplus generated at each stage is successively drawn off toward the center. “If it is satellite status which generates underdevelopment, then a weaker or lesser degree of metropolis–satellite relations may generate less deep structural underdevelopment and/or allow for more possibility of local development.” Use the evolution of division of labor from autarky to the partial division of labor, where gains from trade go to one country, then evolve to the complete division of labor, in the model in this chapter, to predict the underdevelopment phenomenon, which implies divergence of income difference between countries in the transitional stage. Comment on the theory of dependence and underdevelopment. Recently, North used the difference in institutions and policies between North America and Latin America to explain the difference of development performance between the two regions. You might use the cases of Taiwan, Australia, and New Zealand in connection with the Ricardian and HO models to explain why a peripheral position may be associated with successful economic development based on globalization and liberalization. In the sixteenth and seventeenth centuries Britain and France were developing economies. In the eighteenth and nineteenth centuries, the US, Australia, Canada, and New Zealand were less-developed economies in a peripheral position compared to Britain and France. What are their development experiences? Are they applicable to currently less-developed economies? Why do many development economists ignore these development experiences? Assume that in the models in this chapter there are two types of individuals in each country. Use the models to explain dual structure, and sequential divergence and convergence of income distribution between the two types of individuals in the economic development process. Compare this explanation to the theory of labor surplus (Lewis, 1955) which explains dual structure by disequilibrium in the labor market caused by institutionally ﬁxed wages. The Indian and Chinese governments carried out the following import substitution strategy in the 1950s and 1960s. They imposed a high tariff on imported manufactured consumer goods, manipulated terms of trade using trade quota, trade licenses,

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and other instruments, and overvalued the local currency in favor of importing capital goods and of exporting primary goods. These governments restrict the role of the market in facilitating economic development through various regulations, government planning, state ownership of ﬁrms, and monopoly of ﬁrms owned or backed by the government in many important businesses. The Japanese government carried out an export promotion policy before the Second World War, manipulating tariffs and local currency exchange rates to promote importation of producer goods and exportation of manufactured consumer goods. South Korea likewise followed this so-called export-oriented development strategy in the 1960s and 1970s. Such a policy regime is very similar to the mercantilism of sixteenth-century Europe. The government of Hong Kong, on the other hand, followed a laissez faire policy which is very similar to the British government’s policy regime in the eighteenth and nineteenth centuries. The Taiwanese government instituted various policies, such as tax holidays and duty-free and tariff exemption processing zones, to promote export of manufactured goods and import of related inputs. Use the models set out in this chapter to assess the beneﬁts and costs of these different strategies for economic development. Analyze the roles of policy, institutional experimentation, and competition between different governments in discovering policies and institutions that are conducive to economic development. According to the models in this chapter, economic development is a process of evolution of the market network and the emergence of new markets for new traded goods. Bearing the models in mind, comment upon the following statement: In developing economies there is not a perfect market system, so that development experiences in market economies in western Europe and the US are not applicable to developing economies. Use the Ricardian model to explain why new markets emerged and the market system evolved in eighteenth- and nineteenth-century Britain, and why market expansion is difﬁcult in some sub-Saharan economies. Why is the concept of economies of scale neither sufﬁcient nor necessary for the existence of economies of division of labor? Sometimes the HO theorem is proved under the assumptions that the interior structure is the general equilibrium and factor prices are exogenously given. Discuss the legitimacy of these assumptions in a general equilibrium analysis. Although we can prove that the SS theorem may not hold even if each country produces two goods, our proof is based on a speciﬁc version of the HO model with Cobb– Douglas utility and production functions. Use the “everything possible” theorem, which states that it is impossible to identify comparative statics of general equilibrium in the absence of the explicit speciﬁcation of a model (Sonnenschein, 1973, Mantel, 1974, and Debreu), to discuss the trade-off between the generality of functional forms and the predictive power of the model that is based on comparative statics of general equilibrium. Use the HO model to analyze dual structure in a transitional period from autarky to a trade structure with complete specialization of each country. Can the feature of a transitional dual structure be used to explain the so-called underdevelopment phenomenon, which implies that the relative position of the less-developed country deteriorates as international trade and productivity increase? Per capita gross national product (GNP) and its growth rates have been used as one of the major measures of development performance. Assess the appropriateness of this measure in connection with the models in this chapter.

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EXERCISES 1 Prove that the equilibrium production schedule in autarky equilibrium occurs on line EG in ﬁgure 3.1. 2 Assume a dichotomy between pure consumers and ﬁrms in each country in the Ricardian model in example 3.1. Then solve for equilibrium. Discuss the implications of this speciﬁcation for multiple general equilibria. Identify the conditions under which the Pareto optimum equilibrium is the same as the general equilibrium in the Ricardian model in example 3.1. 3 Assume that transaction conditions differ between the two countries in example 3.1. Solve for the inframarginal comparative statics of general equilibrium. Show that the country with a lower transaction efﬁciency receives no gains from trade in a structure with the partial division of labor. Identify the parameter subspace within which improvements in transaction conditions may generate concurrence of deteriorated terms of trade of a country and an increase of gains that this country receives from trade. If a country’s trading efﬁciency ki is considered to be a measure of its competitiveness, use your result to assess Krugman’s claim that competitiveness does not matter for exploiting gains from trade. 4 Assume that the utility function in example 3.1 is U = ln(x + kx d ) + aln( y + ky d ). Solve for the general equilibrium and its inframarginal comparative statics. Analyze the impact of transaction conditions on the equilibrium level of division of labor and productivity. 5 Assume that k1 = k2, a1x = 2, a1y = a2x = M1/M2 = β/(1 − β) = 1 in the model in example 3.2. Explicitly solve for the inframarginal comparative statics of general equilibrium. Analyze the impact of the interplay between governments’ decisions and the market on the equilibrium level of division of labor and welfare. If each government maximizes the total utility instead of the per capita utility of all its home residents, will your results change? (Hint: the exponentially weighted Nash product with each country’s population shares as weights will be maximized in this case.) 6 Assume that aij is the total factor productivity of good j in country i. Work out comparative statics of general equilibrium and show that the HO theorem holds if country 1 has both comparative technological and endowment advantage in producing good x, or if its comparative endowment advantage dominates its comparative technological disadvantage. Use your results to analyze why the prediction of the HO theorem is inconsistent with empirical ﬁndings 50 percent of the time (Treﬂer, 1995). 7 Assume that k = 1 in the model in example 3.4, but the government taxes each dollar used to import goods from the foreign country and then distributes the tariff revenue equally among all domestic residents. Solve for the general equilibrium and its inframarginal comparative statics. Analyze the impact of the tax on the equilibrium level of division of labor, productivity, and welfare. 8 Assume that in the HO model, the production functions and endowment constraints are speciﬁed for each consumer-producer. Solve for the general equilibrium and its marginal and inframarginal comparative statics. Analyze the implications of the difference between this version and the original version of the HO model. 9 Consider the HO model in example 3.4. Assume that Kij is a sector j speciﬁc capita in country i and its amount is a given constant. Solve for the general equilibrium of the speciﬁc factor model and its inframarginal comparative statics.

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The SS theorem states that if the price of a capital-intensive (or labor-intensive) good rises, the price of capital (or labor) rises. Use the model in example 3.4 to show that the theorem holds within the diversiﬁcation cone if the changes in prices are caused by changes in taste or endowment parameters. Suppose ki = 1 and aij is the total factor productivity of good j in country i in the HO model. Verify the solutions of local equilibria in several structures. Autarky: pi = (aiy/aix)(ri/wi)β−α/A, ri/wi = Li μ/Ki, xi = aix A(βμ − 1 + β)L αi K 1−α i /(β − α)μ, yi = aiy β(1 − α − αμ)L iβK1−β i /(β − α)μ, Kix = (1 − α)(βμ − 1 + β)Ki/(β − α)μ, Kiy = (1 − β)(1 − α − αμ)Ki/(β − α)μ, Lix = αKix ri/wi(1 − α), Liy = βKiy ri/wi(1 − β); structure x1 y2: p = θa2y L2β K 21−β/a1x Lα1 K 21−α(1 − θ), r1/w1 = (1 − α)L1/αK1, w1 = αθa2y L 2βK 1−β 2 / L1(1 − θ), r2/w2 = (1 − β)L2/βK2, w2 = βa2y (K2 /L2)1−β, x1 = a1x L 1αK 1−α , y 1 2 = −α/(β−α) K1(a1x Ap)β/(β−α) − a2y L 2βK1−β 2 , structure xy1 y2: p is given by F ≡ (a1y B) (1/μ)(a1y B)(1−α)/(β−α)L1(a1xAp)(β−1)/(β−α) − {θ(β − α)/[β − θ(β − α)]}a2y L 2βK1−β 2 = 0, r1/w1 = (a1x Ap/a1y B)1/(β−α), w1 = a1x Ap(a1y B/a1x Ap)(1−α)/(β−α), r2/w2 = (1 − β)L2/K2β, w2 = a2y B[βK2/L2(1 − β)]1−β. Also in structure xy1 y2, it can be shown that ∂F/ ∂p > 0, ∂F/∂θ > 0, ∂F/∂a1x > 0, ∂F/∂a1y < 0, ∂F/∂a2y < 0, dp/dθ = −(∂F/∂θ)/ (∂F/∂p) < 0, dp/da1x = −(∂F/∂a1x)/(∂F/∂p) < 0, dp/da1y = −(∂F/∂a1y)/(∂F/∂p) > 0, dp/da2y = −(∂F/∂a2y)/(∂F/∂p) > 0, dp/dKi < 0, dp/dLi > 0 for i = 1, 2. Here, μ ≡ [(β − α)θ + 1 − β]/[β − θ(β − α)] > 0, and A ≡ αα(1 − α)1−α and B ≡ ββ(1 − β)1−β. Based on your result in the previous exercise, prove that for ki = 1 and aij = 1 the SS theorem may not hold within the interior structure if changes in prices are caused by a change in α. Then assume that aij ≠ 1 and prove that the SS theorem may not hold within the interior structure if price movements are caused by changes in aij. Prove that for ki = 1, the SS theorem may not hold when equilibrium jumps from autarky to structure x1 y2 or from structure yx1xy2 to structure x1 y2, but that the theorem always holds when equilibrium jumps from autarky to an interior structure with partial international division of labor. Prove that if a corner equilibrium with the complete specialization of each country is the general equilibrium, then changes in the parameters of taste, production, and endowments can generate movements of price that are inconsistent with the SS theorem. If a corner equilibrium with a dual structure is the general equilibrium, then changes in the relative factor price in the country producing both goods, and in the relative commodity price, that are caused by changes in the taste parameter are consistent with the SS theorem. But the corresponding unchanged relative factor price in the specialized country is inconsistent with the SS theorem. There exists a parameter subspace such that changes in production parameters and endowments will generate movements of prices within this corner structure that are inconsistent with the SS theorem. The Rybczynski (RY) theorem is derived within the interior structure (diversiﬁcation cone) and assuming exogenous commodity prices. It states that at given commodity prices, if the endowment of some resource increases, the industry that uses that resource most intensively will increase its output, while the other industry reduces its output (Rybczynski, 1955). Assume ki = 1 in the HO model in example 3.4. Prove that the RY theorem does not hold in the interior structure and that the output of both industries can increase in response to an increase in the endowment of some factor. Deﬁne type I partial equilibrium analysis as analysis assuming exogenous prices of goods (or factors) and investigating changes in factor prices (or output) in response to changes in prices of goods (or endowment parameters). Deﬁne type II

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partial equilibrium analysis as analysis conﬁned within the interior structure and ignoring discontinuous jumps of general equilibrium between different trade patterns. Use your answers in the previous exercises to analyze why type I and type II partial equilibrium analyses could be misleading. Bhagwati and Dehejia, 1994 – factor reversal theorem: Assume that the production functions in example 3.4 are x is = (L αix + K αix)1/α and y is = (L βiy + K βiy)1/β. Show that the equilibrium-relative factor in producing a good may be reversed (a good changes from capital intensive to labor intensive) as the relative price of goods changes.

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DRIVING FORCE II – ENDOGENOUS COMPARATIVE ADVANTAGE AND TRADING EFFICIENCY

4

4.1 ENDOGENOUS VERSUS EXOGENOUS COMPARATIVE ADVANTAGES William Petty (1671, I, pp. 260–1) noted that specialization contributes to skillful clothmaking and pointed out that the Dutch could convey goods cheaply because they specialized each ship for a speciﬁc function. In another place, Petty gave a more striking example of the division of labor in the manufacture of a watch. Joseph Harris (1757) and Josiah Tucker (1755, 1774) referred directly to the productivity implications of the division of labor, the possibilities for the subdivision of labor, and the intimate relationship among a greater variety of goods, production roundaboutness, and a higher level of division of labor. Before Smith, a number of works recognized the advantages of division of labor in improving the skill (or human capital, in modern terms) of individual workers in reducing the time and effort involved in having to switch from one production operation to another, and in facilitating the invention of machinery. They also recognized the role of the market and population size in permitting specialization. These included the works of Denis Diderot (1713), an anonymous author (1701, p. 591), Henry Maxwell (1721, p. 33), and Josiah Tucker (1755, 1774). Smith (1776) called public attention to the central role of specialization and division of labor in economic analysis by systematically investigating their implications for economic development and prosperity. All the classical ideas about the development implications of specialization relate to the concept of absolute advantage, as deﬁned in the previous chapter. Since Ricardo (1817) proposed the concept of comparative advantage, many economists have believed that the concept is more general than that of absolute advantage. But as Yang and Borland (1991) and Yang (1994) have pointed out, Smith’s absolute advantage is endogenous, and can exist between ex ante identical individuals in the absence of Ricardian exogenous comparative advantage. According to Smith (1776, p. 28), the differences in productivity between individuals in producing different goods are the consequence, rather than the cause, of division of labor. This chapter will focus on the development implications of endogenous absolute and comparative advantages. It is not difﬁcult to perceive the importance of specialization and division of labor for economic development. In the absence of social division of labor, you would have to produce

C HAPTER 4: E NDOGENOUS C OMPARATIVE A DVANTAGE 99

all of the food, housing, furniture, cars, television sets, and airplanes whose services you wished to consume. What a crazy world it would be. Productivity in such a world would be as low as in an ancient society. Indeed, productivity would be zero in the case of such technologically complex items as cars, TV sets, and airplanes, which could not be produced by one person. The most important difference between a developed economy and a less-developed economy is that the former has a much higher level of division of labor than the latter. This implies that in a developed economy, most individuals are more “professional” or more specialized than their counterparts in a less-developed country. The degree of commercialization (the ratio of consumption purchased from the market to total consumption, including self-provided consumption) is higher in the former than in the latter. For instance, the degree was 0.3 in rural China prior to reform, and is now higher than 0.8 (see Yang, Wang, and Wills 1992). The ratio of transaction volume to income was 0.2 in 1869, and was 9.28 in 1997 in the US (US Department of Commerce, 1975, 1998). (Transaction volume comprises domestic wholesale and retail trade, foreign trade, and ﬁnancial transactions.) This implies that an average American who conducted business transactions of $0.2 in 1869 would have to have conducted transactions of $9.28 in 1998 to get $1 in income. This increase in the ratio certainly reﬂects an increase in division of labor that raises transaction volume faster than income. Also, in a less-developed economy, the diversity of different occupations is much smaller than in a developed economy. If you check commercial telephone directories in any state in the US in the past ﬁfty years, you can see that the variety of occupations has been drastically increasing. Many new occupations, such as those related to computing, emerge every year. When Kang Youwei, a leading reformist during China’s Qian dynasty, visited Europe at the end of the nineteenth century, his ﬁrst impression of the difference between industrialized Europe and less-developed China was that each European individual bought and sold much more than did her Chinese counterpart. In other words, he was impressed by the high degree of commercialization in European countries (see Kang, reprinted in 1980, pp. 12–13). In terms of Smith’s academic jargon, the ﬁrst difference Kang perceived between developed and less-developed economies was the difference in level of division of labor. In this chapter, we use a simple Smithian model with endogenous comparative advantage to formalize the Smithian mechanism for economic development. The assumption of a very large population size, together with the further assumption that economies of specialization are localized increasing returns, imply that a Walrasian regime prevails in the economy. All decision-makers are price takers, and equilibrium prices are sorted out by a Walrasian auction mechanism. The assumption that individuals are ex ante identical is a very strong one, since we rarely see two persons exactly the same in the real world. However, as Smith suggested, many differences between specialists that appear to be ex ante differences are, in fact, ex post differences, which are acquired as individuals choose different occupations. The assumption that individuals are ex ante identical helps to highlight the development implications of endogenous comparative advantages. In the Ricardian model in the preceding chapter, if all individuals are ex ante identical in all aspects, the economic stories will be too trivial to make any sense to us (i.e., the economy is always in autarky and all individuals’ consumption and production plans are exactly the same). But we shall show that in the Smithian model, even if all individuals are ex ante identical in all aspects, ex post differences will emerge endogenously from the evolution of division of labor. This enables many interesting stories to be told that cannot be predicted by the Ricardian model, such as the emergence of professional middlemen, money, business cycles, unemployment, the ﬁrm, and a hierarchical structure of production and transactions. These all result from the evolution of division of labor, even in the absence of ex ante differences among individuals. The implications of ex ante cum ex post differences between individuals for economic development will be explored in chapter 5.

100 P ART I: D EVELOPMENT M ECHANISMS

In section 4.2, the model is speciﬁed and many possible conﬁgurations of specialization are examined. Section 4.3 investigates individuals’ decisions, their comparative statics, and general equilibrium and its comparative statics. In section 4.4, we use more examples to further investigate the features of the Smithian model. In section 4.5, we investigate determinants of trade pattern in a model of endogenous comparative advantage.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n

n n n n n n n n

Why is the decision problem of choosing an occupation conﬁguration and level of specialization much more complicated than the decision problem to allocate resources for a given occupation conﬁguration? Why are demand and supply two sides of the division of labor? Why is it inappropriate to separate the analysis of demand and supply from the analysis of individuals’ decision-making in choosing levels of specialization? What is the difference between marginal analysis of problems of resource allocation and inframarginal analysis of problems of economic development? Why did Young claim that the extent of the market and level of division of labor are two sides of the same coin? What are the network effects of division of labor and their implications for economic development? How does the market coordinate the division of labor, utilize the network effects of the division of labor, and solve problems of economic development? Why are scarcity and productivity endogenous in Smithian equilibrium models? Why do markets for many goods and services not exist in a less-developed economy, and under what conditions will the markets emerge from the economic development process?

4.2 CONFIGURATIONS AND CORNER SOLUTIONS IN A SMITHIAN MODEL Example 4.1: A simple Smithian model with endogenous comparative advantage. Example 9.10 in chapter 9 will show that for a ﬁnite set of consumer-producers, Walrasian equilibrium may not exist. In that chapter, we shall investigate the function of Nash bargaining in eliminating endogenous transaction costs caused by the integer problem in a Walrasian regime. In this chapter, we assume that the set of consumer-producers is a continuum with mass M. This implies that the population size in the economy is very large. Hence, we will not have an integer problem with the numbers of different specialists. Each consumer-producer has the following utility function: u = (x + kxd )( y + ky d )

(4.1)

where x and y are respective amounts of goods x and y that are self-provided, x d and y d are respective amounts of the two goods that are purchased from the market, 1 − k is the iceberg transaction cost coefﬁcient, or k is an exogenous trading efﬁciency coefﬁcient, which represents the conditions governing transactions. k relates to infrastructure conditions, degree of urbanization, transportation conditions, and the general institutional environment. Each consumer-producer’s production functions and endowment constraint are: x p = x + x s = l xa , lx + ly = 1

y p = y + y s = l ya ,

a>1

(4.2a) (4.2b)

C HAPTER 4: E NDOGENOUS C OMPARATIVE A DVANTAGE

101

y 2 E H

F

1 A J

C

I G 0

B

1

2

x

Figure 4.1 Economies of division of labor based on endogenous absolute and comparative advantage

where x p and y p are respective amounts of the two goods produced, x s and y s are respective amounts of the two goods sold, and li is an individual’s share of labor allocated to the production of good i and thus represents her level of specialization in producing good i. Here, we assume that all individuals are ex ante identical, and that they have the same production functions for every good and the same endowment of working time. This implies that there is no exogenous comparative advantage. Let x ip denote individual i ’s output of good x, y ip individual i ’s output of good y, and lij individual i ’s level of specialization in producing good j. We say that there are economies of specialization for an individual in producing a good if her labor productivity increases with her level of specialization in producing that good. Since a > 1, it is easy to see that there are economies of specialization for each individual in producing each good. Consider the transformation curves for two individuals. On the basis of (4.2), we work out the transformation function for individual i as follows: y ip = (1 − x ip 1/a)a,

xip, y ip ∈[0, 1]

The ﬁrst- and second-order derivatives of y ip with respect to x ip indicate that the transformation curve AB is downward sloping (negative ﬁrst-order derivative) and convex (positive secondorder derivative), as shown in ﬁgure 4.1. Diminishing marginal opportunity costs and increasing marginal rate of transformation are the features of this transformation curve. This implies that the amount by which y must be decreased for each marginal unit increase of x diminishes as x increases. Alternatively, it implies that each unit of y can be transformed into increasingly larger increments of x. Now let us draw the aggregate production schedules for different structures in the economy for two individuals. Since all individuals are ex ante identical, they must have the same labor allocation pattern if each of them self-provides all goods in autarky. The aggregate production schedule for autarky in this model, which is deﬁned by (4.2) and l1x = l2x , l1y = l2y , can be drawn as curve ECG in ﬁgure 4.1. A point J of curve ECG can be obtained by letting OJ = 2OI along ray OH. All such points constitute curve ECG. If one individual completely specializes in producing y and the other produces any mix of x and y, then the aggregate transformation curve is shown by curve EF. Similarly, we can work out the aggregate transformation curves FG for a structure where an individual completely specializes in producing x and the other produces any mix of x and y. The aggregate transformation curve for the division of labor is

102 P ART I: D EVELOPMENT M ECHANISMS

thus curve EFG. Economies of division of labor are then the difference between curve EFG and curve ECG, shown as the shaded area. Figure 4.1 provides a basis for deﬁning endogenous absolute and comparative advantage. In this model, all individuals are ex ante identical, so that there is no ex ante difference in productivity or endowment between the two individuals, that is, there is no exogenous comparative advantage. If the two individuals are in autarky, then the production pattern is the same for both. Therefore, their productivity for each good is the same. But if they choose complete division of labor (point F in ﬁgure 4.1), for instance, if individual 1 produces only x and individual 2 produces only y, then x 1p = 1, y 1p = 0, x 2p = 0, y 2p = 1. This implies that person 1’s labor productivity in producing x is greater than person 2’s, and person 2’s labor productivity in producing y is greater than person 1’s. These ex post productivity differences between ex ante identical individuals result from their decisions to choose different production patterns. Such differences in productivity, arising from individuals’ choices concerning patterns of specialization, represent endogenous comparative advantage. For this speciﬁc example, the endogenous comparative advantage is also endogenous absolute advantage. On the one hand, a person’s economies of specialization in producing a good are positively related to diseconomies in her scope of activities. On the other hand, a ﬁrm’s operation scope and its members’ levels of specialization can increase at the same time if all individuals’ levels of specialization, the number of different specialists, and the number of different specialties within the ﬁrm increase simultaneously. Since specialization and diversity of professional activities are two sides of the division of labor, simultaneous increases in levels of specialization of all individuals and in the number of different professional jobs within a ﬁrm can be seen as an increase in the level of division of labor within the ﬁrm. Hence, if a ﬁrm’s higher productivity is generated by a higher level of division of labor associated with higher levels of specialization of all members (entailing a narrower scope of each individual’s activities) and a greater variety of professional jobs within the ﬁrm (entailing a broader scope of the ﬁrm’s activities), then it can be said that there exist economies of division of labor. An individual’s budget constraint is: px x s + py y s = px x d + py y d

(4.3)

where pi is the price of good i. Hence, the left-hand side of (4.3) is income from the market and the right-hand side is expenditure. Since corner solutions are allowed, we have the nonnegativity constraint: x, x s, x d, y, y s, y d, lx , ly ≥ 0

(4.4)

This constraint distinguishes the nonlinear programming from the classical mathematical programming. Each consumer-producer maximizes utility in (4.1) with respect to x, x s, x d, y, y s, y d, lx , ly subject to the production conditions given by (4.2), the budget constraint (4.3), and the nonnegativity constraint (4.4). Since lx and ly are independent of the values of the other decision variables, each of the 6 decision variables can take on 0 and positive values. When a decision variable takes on a value of 0, a corner solution is chosen. Table 4.1 lists several possible proﬁles of zero and positive values of the 6 decision variables. The number of all possible proﬁles is 26 = 64. Since the optimum values of the decision variables are discontinuous across the proﬁles, there is no method that can solve for the optimum decision in only one step. A general procedure in solving for this kind of nonlinear programming problem is as follows. First, the Kuhn–Tucker theorem and other conditions for the optimum decisions are used to rule out as many proﬁles as possible. Then, marginal analysis is applied to each of the remaining candidates for the optimum decision. Finally, the local maximum values of the objective function are compared across the candidates to identify the globally optimum

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103

Table 4.1 Proﬁles of zero and positive values of the 6 decision variables x

xd

xs

y

yd

ys

+ 0 0 + • + 0

+ + + 0 • 0 0

+ + 0 0 • 0 0

+ 0 0 0 • 0 0

+ + + + • 0 0

+ + + + • + +

decision. This is referred to as inframarginal analysis. Let us take the ﬁrst step, which is to prove the following theorem: Theorem 4.1: The optimum decision can be achieved by selling not more than one good. It does not involve selling and buying the same good, and does not involve buying and producing the same good. This theorem is referred to as the Wen theorem. Wen proves this theorem for a class of the Smithian general equilibrium models with general utility and production functions (see Wen, 1998). We will use the theorem frequently in this text. Proof: Claim 1: The optimum decision does not involve selling and buying the same good. Substituting the budget constraint (4.3) for x s in (4.2a) and eliminating x in (4.1) with (4.2a) yields: u = {l xa − [x d + py( y d − y s )/px] + kx d }( y + ky d ). Differentiating this expression with respect to x d yields:

∂u <0 ∂x d

∀x d > 0.

According to the Kuhn–Tucker condition, this implies that when x, x s > 0, the optimum value of x d is 0. This is intuitive: the optimum value of x d must be 0 if u always decreases as x d increases. Hence, x d and x s cannot be positive at the same time. Following the same deduction, but eliminating y s and y instead of x s and x from the above expression of u, it can be shown that y d and y s cannot be positive at the same time. Claim 2: The optimum decision does not involve buying and producing the same good. Suppose x d > 0. It follows from claim 1 that x s = 0. From the budget constraint, it follows that y s > 0, if x s = 0. We can use claim 1 again to obtain that y d = 0, if y s > 0. A positive utility requires y > 0. Now, plugging the budget constraint and the production function of y into the utility function yields: a ⎧ 1 ⎡⎛ ⎤ p ⎫⎪ ⎞ ⎪ a ⎢ u = ⎨x + k ⎜1 − x ⎟ − y⎥ y ⎬ y ⎠ ⎢⎣⎝ ⎥⎦ px ⎪ ⎪⎩ ⎭

Differentiating u twice yields: ∂2u >0 ∂x 2

∀x > 0.

104 P ART I: D EVELOPMENT M ECHANISMS

This violates the second-order condition of the interior maximum point of x. Hence, the optimum x is at a corner: either x = 0, or x = l xa = 1. x = 1 is incompatible with a positive y which is required by a positive utility. Therefore, the optimum value of x is zero if x d > 0. Claim 3: An individual sells at most one good. We use the argument of negation. Suppose claim 3 does not hold. An individual sells two goods, that is, x s, y s > 0. It follows from claim 1 that x d = y d = 0. This violates the budget constraint, since the individual sells but does not buy. Therefore, it is impossible that x s, y s > 0. Claims 1–3 sufﬁce to establish Theorem 4.1. Q.E.D. Theorem 4.1 is intuitive. Selling and buying the same good involve unnecessary transaction costs and therefore are inefﬁcient. Selling two goods is also inefﬁcient because it prevents the full exploitation of economies of specialization. Theorem 4.1, together with the budget constraint and the requirement that utility be positive, can be used to radically reduce the number of candidates for the optimum decision from 64 to only 3. For instance, the ﬁrst proﬁle of zero and positive values of the 6 decision variables in table 4.1 is associated with the unique interior solution. This proﬁle, which involves selling and buying the same good, obviously violates the Wen theorem. This implies that in the Smithian model, an interior solution cannot be optimal, so that the marginal analysis for the interior solution is not applicable. The second, third, and fourth proﬁles violate claim 1 in the Wen theorem, while the ﬁfth and sixth proﬁles violate the budget constraint and the requirement for a positive utility level. We call a proﬁle of zero and positive decision variables that satisﬁes the Wen theorem a conﬁguration. For each conﬁguration, there is a corner solution. Each individual applies marginal analysis to solve for a corner solution in a conﬁguration. Each corner solution gives the optimum resource allocation for a given level and pattern of specialization. Then each individual conducts total beneﬁt–cost analysis across conﬁgurations to choose the optimum corner solution. To choose the optimum conﬁguration is to choose the optimum level and pattern of specialization. This involves the decision of whether or not to engage in a certain activity. This is a decision about “yes” or “no.” The marginal analysis for each corner solution is to allocate resources between those activities an individual has already decided to engage. It is a decision about “how much,” after you have already said “yes” to the ﬁrst type of question. As your career develops, you will see that your peers will have very different lives from one another according to their different occupations. To choose an occupation and a level of specialization in that chosen occupation is to choose a conﬁguration. There are three conﬁgurations that an individual needs to consider: Autarchy, or conﬁguration A, is deﬁned by x, y, lx, ly > 0, x s = x d = y s = y d = 0. This conﬁguration implies that all quantities of goods that are self-provided are positive and all quantities of goods that are traded are zero. The decision problem for conﬁguration A is:

i)

ii)

Max: u = xy

x, y, lx , l y

s.t.

x = l xa ,

y = l ya,

lx + ly = 1

(4.5a)

Those letters that do not denote decision variables are parameters. Here, we have used the production function and working time constraint in (4.2). Inserting all constraints into the utility function, (4.5a) can be converted to the following nonconstrained maximization problem: Max: u = l xa(1 − lx)a lx

(4.5b)

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105

The ﬁrst-order condition for an interior optimum:

du = al xa−1(1 − lx)a − al xa(1 − lx)a−1 = 0 dlx yields that the optimum lx is 1/2. In terms of natural language, the marginal condition for the marginal analysis implies that the efﬁcient trade-off between the quantity of labor allocated to produce x and that allocated to produce y are achieved if the marginal direct utility of an increase in lx equals its indirect marginal cost in terms of utility loss caused by a decrease in y. The marginal analysis is relevant only if a conﬁguration is given. It does not work for solving for the optimum conﬁguration. Inserting lx = 1/2 into u = l xa (1 − lx )a yields the maximum value of utility that can be achieved in autarky, namely u(A) = 2−2a, where u(A) is called per capita real income in autarky. The ﬁrst-order condition tells you that lx = 1/2 is the interior extreme point, but does not tell you if it is the interior maximum or minimum point. If the curve of u is convex rather than concave, then the ﬁrst-order condition gives a minimum rather than a maximum point. For the nonconstrained maximization problem, the second-order condition is that at lx = 1/2, which is given by the ﬁrst-order condition: ⎤ ⎡ ⎛ 1 − lx lx ⎞ a−1 a−1 ( 1 ) ( 1 ) = − − + − 2 al l a a ⎥ < 0. ⎢ x x ⎜ ⎟ 1 − lx ⎠ dl 2x ⎝ lx ⎥⎦ ⎢⎣

d2 u

This condition implies that the function u = l xa (1 − lx )a is concave at lx = 1/2. It is easy to verify that the above inequality holds for lx = 1/2. If the utility function is associated with the convex curve, then the second-order condition cannot hold. In terms of natural language, this means that there is no real trade-off for the decision problem, that is, the optimum decision is a corner solution in which all labor is allocated to the production of either x or y. In the real world, some resource allocation problems for a given level and pattern of division of labor do not actually involve a real trade-off despite appearances to the contrary, because the second-order condition for the interior optimum may not be satisﬁed. In this circumstance, the compromise between the conﬂicting forces that is given by the ﬁrst-order condition may be too conservative and may not be efﬁcient. Even if the second-order condition for a local maximum is satisﬁed, a local maximum may not be the global maximum. For instance, an individual may achieve higher productivity and utility if she chooses complete specialization lx = 0, or lx = 1. Hence, we consider the two conﬁgurations of specialization next. The ﬁrst conﬁguration with specialization is (x/y), implying specialization in producing good x, selling x, and buying y. It is deﬁned by x, x s, y d, lx > 0, x d = y s = y = ly = 0. This deﬁnition, together with (4.1) to (4.4), can be used to specify the decision problem for this conﬁguration: Max: u = xky d x, x s, x d

s.t.

x + x s = l xa, py y = px x d

lx = 1

s

(production conditions) (budget constraint)

Plugging the constraints into the utility function to eliminate lx, x, and y d yields the nonconstrained maximization problem:

Max: u = (1 − x s ) k x

s

px x s py

106 P ART I: D EVELOPMENT M ECHANISMS Table 4.2 Three corner solutions Conﬁguration

Corner demand

Corner supply

Self-provided quantities

Level of specialization

Indirect utility function

A (x/y) (y/x)

0 y d = px/2py x d = py/2px

0 x s = 1/2 y s = 1/2

x = y = 1/2 x = 1/2 y = 1/2

lx = ly = 1/2 lx = 1, ly = 0 lx = 0, ly = 1

uA = 2−2a ux = kpx/4py uy = kpy/4px

The decision problem involves the trade-off between two opposite effects of an increase in x s. The individual’s utility increases with x s through an increase in revenue generated by the sale of good x, while her utility decreases with x s through a decrease in the self-provided quantity of good x. The optimum decision maximizes utility by efﬁciently trading off the beneﬁt against the cost. The ﬁrst-order condition for marginal analysis, du/dx s = 0, gives the optimum decision for conﬁguration (x/y) as follows.

1 xs = , 2

yd =

py 1 kp , x s = , ux = x . 2 px 2 4 py

It is easy to verify that the second-order condition for the interior maximum is satisﬁed, that is, d2u/d(x s )2 < 0 when the ﬁrst-order condition holds. Here, the quantity demanded is a decreasing function of the price of goods purchased and an increasing function of the price of goods sold. Also, demand is an increasing function of supply. This last feature of demand and supply is referred to by Young (1928) as the law of reciprocal demand, which implies that demand and supply are two sides of the division of labor. If individuals choose autarky, there are no demand and supply in the marketplace, since selfdemand is self-supply. If an individual chooses specialization in producing x, then she demands good y and supplies good x. According to Young, an analysis of demand and supply that is separated from the analysis of individuals’ decisions in choosing their levels of specialization is only a partial view, incompatible with the concept of general equilibrium and therefore often misleading. Following the procedure used in solving for the corner solution for conﬁguration (x/y), the corner solution for conﬁguration (y/x) can be solved as follows: 1 ys = , 2

xd =

py , 2 px

uy =

kpy 4 px

From the corner solutions for the two occupation conﬁgurations, we have seen that the utility of a specialist producer of a good increases with the price of this good and decreases with the price of the good she buys. This is referred to as the law of specialization. An individual’s demand and supply functions are ultimately determined by her decision in choosing the optimum one from many corner solutions. Since the optimum values of all decision variables are discontinuous across conﬁgurations, an individual must compare locally maximum utility levels in all corner solutions to ﬁnd the optimum corner solution. Table 4.2 summarizes the information of three corner solutions. On the basis of this information, an individual compares utility levels across conﬁgurations. She will choose conﬁguration (x/y), that is, specialization in x, if: ux ≥ uA and ux ≥ uy

or

kpx /py ≥ 22(1−a) and px /py ≥ 1.

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107

She will choose conﬁguration (y/x), that is, specialization in y, if uy ≥ uA and uy ≥ ux

kpy /px ≥ 22(1−a) and py /px ≥ 1.

or

The two conditions can hold simultaneously only if k > k0 ≡ 22(1−a)

and

py /px = 1.

(4.6)

Since the division of labor can be realized only if both occupation conﬁgurations (x/y) and (y/x) are chosen, and because of network effect of specialization, an individual will choose specialization only if (4.6) holds. When the relative price satisﬁes this condition, individuals are indifferent between the two conﬁgurations, since utility would be the same in both. In equilibrium, utility equalization between different occupations must hold, since individuals are ex ante identical in all aspects. The individual will choose conﬁguration A, that is, autarky, if ux < uA

and

uy < uA

or if

k22(a−1) <

px 22 (1−a ) < py k

(4.7)

which holds only if k < k0 ≡ 22(1−a) In other words, if k < k0 ≡ 22(1−a), there is no relative price that ensures both professional occupations being chosen. Therefore, the optimum corner solution is autarky where no market exists. The optimum corner solution is specialization in either x or y if the transaction efﬁciency coefﬁcient k is greater than the critical value k0 and py /px = 1, so that the market emerges from specialization. This result implies that the core of classical mainstream economics is about under what condition does the market emerge from the division of labor, and how can the market coordinate individuals’ decisions of specialization to utilize network effects of division of labor? As the core of classical mainstream economics is formalized, we no longer claim that mainstream economics is not applicable to developing countries, where many markets are absent. The very purpose of mainstream economics is to explain why markets do not exist under a certain condition, as well as how they emerge from the division of labor under other conditions. (4.6) and (4.7) imply that specialization will be chosen if px /py = 1 and k > k0, and autarky will be chosen if k < k0. Here, we ignore ex ante differences in transaction and production conditions that generate unequal real incomes between individuals. We will consider this in chapter 5. However, the utility equalization condition is more realistic than it appears. Take a businessman and his secretary as an example. Nominal incomes between them are very unequal. Everybody knows that the businessman (if successful) can make more money, so that competition to get into business school is much more intensive than that for entry to a school for secretarial training. The more intensive competition generates intangible disutility, as well as a greater ﬁnancial burden since business schools rarely provide scholarships. More importantly, the businessman takes a considerable risk of bankruptcy, which may even cause suicide (implying an inﬁnitely large negative real income). If you count all the tangible and intangible beneﬁts and costs, the difference in real income between the businessman and his secretary is much smaller than it seems to be.

108 P ART I: D EVELOPMENT M ECHANISMS

If there is free entry into every occupation, utility equalization will hold. Inserting px /py = 1 into the indirect utility function ux or uy yields: ux = uy = uD =

k 4

where uD is per capita real income for the division of labor, which depends on the transaction efﬁciency parameter k but does not depend on relative price. Hence, an individual’s demand and supply functions are given by the corner solution in conﬁguration A if k < k0, and are given by the corner solutions in conﬁguration (x/y) or (y/x) if k > k0. As k increases from a value smaller than k0 to a value greater than k0, demand and supply discontinuously jump from 0 to positive levels as functions of relative prices due to an increase in individuals’ levels of specialization. This is referred to as the Smithian law of demand, which is distinguished from the neoclassical law of demand. The analysis of the discontinuous shift of optimum decisions between conﬁgurations in response to changes of parameters is called inframarginal comparative statics of decision problems, which are distinguished from marginal comparative statics of the decisions. The inframarginal comparative statics of demand and supply are based on total cost–beneﬁt analysis between corner solutions. For a given conﬁguration, marginal analysis generates marginal comparative statics of the decisions. For instance, in conﬁguration (y/x): dx d/d(px /py) = −0.5( px /py)−2 < 0. This implies that as the price of good x increases relative to that of good y, the quantity demanded of good x by each specialist in y falls. This is referred to as the neoclassical law of demand. The analysis of how the optimum decisions continuously change within a given conﬁguration in response to changes in parameters is called marginal comparative statics of decisions. The marginal comparative statics of the decisions are concerned with changes in the efﬁcient resource allocation for a given conﬁguration of specialization in response to changes in parameters within a given parameter subspace that demarcates this conﬁguration. The inframarginal comparative statics of the decisions relate to changes in the efﬁcient conﬁguration of specialization as parameters shift between the subspaces that demarcate the conﬁgurations. In summary, marginal comparative statics of the decisions relate to marginal analysis, resource allocation, demand, and supply for a given conﬁguration of specialization, and given aggregate demand. In contrast, inframarginal comparative statics of the decisions relate to inframarginal analysis of the level of specialization, which determines the extent of the market, the size of the network of division of labor, and aggregate demand (which will be deﬁned later on). Problems of resource allocation closely relate to marginal analysis of relative quantities of goods produced and consumed and relative prices for a given network size of division of labor and related productivity. Problems of economic development relate to the question of how equilibrium productivity or its reciprocal (the degree of scarcity) is determined by individuals’ decisions in choosing their patterns of specialization and by the interactions of decisions in the marketplace. Hence, inframarginal comparative statics relate to the problems of economic development. A common practice in neoclassical economics is to separate the analysis of demand and supply from the analysis of individuals’ decisions in choosing their levels and patterns of specialization. As discussed before, this is because economists were not familiar with the mathematical tools for handling corner solutions, which are essential for the endogenization of individuals’ levels of specialization, when Marshall formalized classical economic thinking within a mathematical framework based on marginal analysis and on the dichotomy between pure consumers and ﬁrms. Unfortunately, many economists still show remarkable insistence

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on maintaining the neoclassical dichotomy and marginal analysis, despite the fact that many mathematical instruments for handling corner solutions are now available and the neoclassical framework is no longer essential for mathematical modeling. This chapter shows that we can abandon the neoclassical dichotomy and apply inframarginal analysis to study individuals’ decisions in choosing their levels and conﬁgurations of specialization. The spirit of classical analysis of demand and supply as two sides of division of labor can then be resurrected in the body of Smithian general equilibrium models.

4.3 HOW THE MARKET COORDINATES DIVISION OF LABOR TO UTILIZE NETWORK EFFECTS AND PROMOTE ECONOMIC DEVELOPMENT Combinations of the three conﬁgurations considered in the preceding section generate two organization structures, or structures for short. A conﬁguration is equivalent to a major that a university student chooses and a structure is equivalent to the division of students among majors in the university. All individuals choosing conﬁguration A (autarky) constitute a structure involving no market, no prices, no interdependence, and no interaction between individuals. The division of M individuals between conﬁgurations (x/y) and (y/x) constitutes a structure with division of labor, denoted D, where there are two markets for two goods sold by two types of specialists. Let the number of individuals choosing (x/y) be Mx and the number choosing (y/x) be My. Strictly speaking, when the set of individuals is a continuum, we should call the number of a particular type of specialists the measure of this type of specialists. There is a corner equilibrium for each structure. A corner equilibrium is deﬁned by the relative price of the two traded goods px /py, and the numbers of the two types of specialists, Mx and My, that satisfy the market clearing condition and utility equalization condition for a given structure. In a corner equilibrium, individuals maximize their utility with respect to conﬁgurations in the given structure and with respect to quantities of goods produced, traded, and consumed for the given corner equilibrium-relative price and the numbers of individuals selling the two goods. According to the deﬁnition of corner equilibrium, the corner solution in conﬁguration A chosen by M individuals is the corner equilibrium in structure A, where the market clearing condition always holds, since self-demand and self-supply are two sides of self-provided quantities in the structure. In structure D, free choices between conﬁgurations (occupations) and utility maximizing behavior will establish the utility equalization condition. From table 4.2, it can be seen that the indirect utility function of a specialist in x is an increasing function of px /py , and the indirect utility function of a specialist in y is a decreasing function of px /py, as shown in ﬁgure 4.2 where p ≡ px /py. Hence, the utility equalization condition is associated with the intersection point E in ﬁgure 4.2. The upward-sloping straight line in ﬁgure 4.2 is an x specialist’s indirect utility function, which looks like a supply curve. The downward-sloping curve is a y specialist’s indirect utility function, which looks like a demand curve. The corner equilibrium-relative price in structure D is determined by the intersection point between the two curves. If the relative price px /py is at point B, then the utility of a specialist in x is greater than that of a specialist in y, so that all individuals will specialize in x and nobody will specialize in y. This implies that the corner equilibrium in structure D cannot be established. Therefore, the utility equalization condition determines the corner equilibrium-relative price of traded goods in structure D, that is: ux = kpx /4py = uy = kpy /4px

or

px /py = 1.

110 P ART I: D EVELOPMENT M ECHANISMS

ux

uy

ux = kpx /4py

E

u*

uy = kpy /4px

0

p*

B

px /py

Figure 4.2 Indirect utility functions and corner equilibrium-relative price

We will show that if the model is not symmetric, then the corner equilibrium-relative price is determined by relative tastes and relative production and transaction conditions. In structure D, the market demand for good x is: X d ≡ My x d = My py /2px ,

(4.8a)

while the market supply of good x is: X s ≡ Mx x s = Mx /2

(4.8b)

where x d = py /2px, and x s = 1/2 are given by table 4.2. The market demand function for x not only exhibits the demand law (i.e., the quantity demanded of a good decreases as its price increases relative to that of the good sold by the buyer), but is also an increasing function of the number of specialists in y. The market supply function of x is an increasing function of the number of specialists of x. If the C–D utility function is replaced with the constant elasticity of substitution (CES) utility function as shown in section 4.4, then the market supply function will exhibit the supply law (i.e., the quantity supplied of a good increases with the price of this good relative to that of the good bought by the seller). In a Walrasian regime, prices are determined by a Walrasian auction mechanism. The Walrasian auctioneer calls a set of relative prices of all traded and nontraded goods. All individuals report to the auctioneer their optimum quantities of goods to be traded for the given set of prices. Then the auctioneer adjusts relative prices according to excess demands, raising or lowering the price of a good according to whether its excess demand is positive or negative. This tatonnement process continues until the excess demands for all goods tend to 0. This is referred to as a centralized pricing mechanism. The Walrasian auction mechanism will establish the market clearing condition for good x: X d = My py /2px = X s = Mx /2,

or

px /py = My /Mx

(4.8c)

This equation implies that competition in the market and free choice of conﬁgurations establish an inverse relationship between the relative prices of goods x and y and the relative numbers of individuals selling goods x and y.

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Table 4.3 Two corner equilibria Structure

Relative price

A

dy/dx = 1

D

px /py = 1

Number of specialists

Mx = My = M/2

Quantities of goods

Per capita real income

x = y = 0.5a

2−2a

x = y = xs = ys = xd = y d = 1/2,

k/4

Free choice with respect to conﬁgurations (occupations), together with free choice of quantities to produce, trade, and consume, are the driving forces that establish a corner equilibrium. Summing up all individuals’ budget constraints, we can express the excess demand for x as a function of the excess demand for y even if the market is not cleared. Hence, the market clearing condition for good y is not independent of that for good x. Thus, we do not need to consider that market clearing condition. This is referred to as Walras’s law which states that for n traded goods and factors, there are only n − 1 independent market clearing conditions. The market clearing condition for x, the utility equalization condition, and the population equation Mx + My = M yield the corner equilibrium in structure D: px /py = 1,

Mx = My = M/2.

Inserting the corner equilibrium-relative price of traded goods back into demand and supply functions and indirect utility functions yields the corner equilibrium quantities to produce, trade, and consume and the corner equilibrium utility level, which we call per capita real income, denoted by uD. The corner equilibrium values of endogenous variables are no longer functions of prices. Due to symmetry, per capita real income depends only upon the parameter k. x = y = x s = y s = x d = y d = 1/2,

uD = k/4.

For an asymmetric model, all the endogenous variables will depend upon the parameters of relative transaction and production conditions and relative tastes for the two goods. We call the corner equilibrium values of endogenous variables, including the relative price of traded goods and the numbers of individuals selling different goods, a resource allocation for a given structure. A corner equilibrium sorts out resource allocation for a given structure. In the Smithian framework, there are multiple corner equilibria, and the general equilibrium is only one of these. All the information about the two corner equilibria in structures A and D is summarized in table 4.3. We distinguish per capita real income, which is the corner equilibrium value of the indirect utility function in a structure, from the indirect utility function, which is the optimum value of utility for a conﬁguration. We now further examine the nature of the pricing mechanism in the Walrasian regime in the Smithian model. Though we use a Walrasian auction mechanism to describe the pricing mechanism, this centralized pricing mechanism is not essential in the Smithian framework. The Walrasian pricing mechanism in the Smithian framework can be decentralized. In the Smithian framework, prices are determined by all individuals’ self-interested decisions in choosing their occupation conﬁgurations. In principle, individuals are allowed to choose prices. But interactions between self-interested decisions in choosing occupation conﬁgurations will nullify any attempts to manipulate prices, as long as nobody can manipulate the numbers of individuals choosing various occupation conﬁgurations. As shown in (4.8c), the market relative

112 P ART I: D EVELOPMENT M ECHANISMS

price of the two traded goods is inversely determined by the corresponding relative number of individuals selling the two goods and the relative outputs of individual sellers. Since an individual’s output level is trivial compared to the very large number of individuals who can choose any occupation conﬁguration, the relative price cannot be manipulated by an individual’s output level as long as the relative number of different specialist producers cannot be manipulated. This justiﬁes the price-taking behavior for each individual, despite the assumption that each individual is allowed to choose prices. In the Smithian model, the tatonnement process is a negative feedback mechanism. Suppose that the relative price px /py is higher than the equilibrium price. Then it must be true that ux > uy, so that individuals will shift from conﬁguration (y/x) to conﬁguration (x/y). This reduces My/Mx , and therefore reduces px /py through (4.8c). This adjustment will continue until the equilibrium is established. A general equilibrium is deﬁned by a set of relative prices of traded goods, a set of numbers of individuals choosing different conﬁgurations that constitute a structure, and individuals’ quantities of goods produced, traded, and consumed that satisfy the following conditions: (i) each individual’s decision with regard to quantities and conﬁguration maximizes her utility for the given equilibrium-relative prices of traded goods and the given equilibrium numbers of individuals choosing different conﬁgurations; (ii) the set of relative prices of traded goods and numbers of individuals choosing different conﬁgurations clear markets for all traded goods and equalize all individuals’ utilities. It is easy to see that a corner equilibrium satisﬁes these two conditions for a general equilibrium, except that individuals’ choices of conﬁgurations are conﬁned within a given structure. Hence, the general equilibrium is the corner equilibrium, in which each constituent conﬁguration is preferred by those choosing it over alternative conﬁgurations. From (4.6) and (4.7), we can see that individuals prefer either of the two specialization conﬁgurations to autarky if k > k0 and p = 1. Also, (4.6) and (4.7) imply that if k < k0, a relative price does not exist that ensures higher utility in both conﬁgurations of specialization than in autarky. Hence, the division of labor between two types of professional occupations is impossible to be coordinated via a relative price. This implies that the general equilibrium is autarky if k < k0. In summary, our two-step procedure to solve for a general equilibrium in the Smithian model runs as follows. A corner equilibrium is ﬁrst solved for each structure. Then individuals’ utilities under the corner equilibrium prices are compared between conﬁgurations to identify a parameter subspace within which each constituent conﬁguration of this structure is at least as good as any other alternative conﬁguration. Within this parameter subspace, this corner equilibrium is a general equilibrium. As the parameter space is partitioned, we can identify within each of the parameter subspaces which corner equilibrium is the general equilibrium. It can be seen that as the number of goods increases, the number of possible structures increases more than proportionally. As a result, the two-step approach to solving for general equilibrium becomes very cumbersome. Sun, Yang, and Yao (1999) have generalized the Smithian model to the case with very general preferences and production and transaction conditions, and have developed a much simpler two-step approach to solving for general equilibrium. Their two-step procedure needs the concept of Pareto optimum corner equilibrium, which is the corner equilibrium with the greatest per capita real income. They have shown that general equilibrium exists if the set of consumer-producers is a continuum, and that a general equilibrium is the Pareto optimum corner equilibrium. Hence, we can solve for corner equilibrium for each feasible structure, then compare per capita real incomes between corner equilibria to identify the general equilibrium. The following theorem is the theoretical foundation of this two-step approach. Yang (1988) proves this theorem for a speciﬁc Smithian model. Sun, Yang, and Yao have proved this theorem for a general class of Smithian models with ex ante identical consumer-producers. For simplicity, we call it the Yao theorem.

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Theorem 4.2 (Yao theorem): For an economy with a continuum of ex ante identical consumer-producers with rational, continuous, and convex preferences, and production functions displaying economies of specialization, and individual speciﬁc limited labor, a Walrasian general equilibrium exists, and it is the Pareto optimum corner equilibrium. Proof of the Yao theorem: Since the proof of the existence of equilibrium is very cumbersome, we provide here only the proof of the second part of the Yao theorem (i.e., the general equilibrium is the Pareto optimum corner equilibrium). Without loss of generality, we may assume that goods {1, . . . , n} are traded at any corner equilibrium. Denote this corner equilibrium E. Here, n ≤ m, and m is the number of all traded and nontraded goods. Assume that the values of prices for these traded goods are ( p1, . . . , pn ) in this corner equilibrium and the general Now without loss of generality, we may equilibrium values of the prices are ( p *, 1 . . . , p *). n assume that: p */p 1 1 = max{p*/p j j, j = 1, . . . , n} j

which implies for j = 1, . . . , n, *j ≥ p1/pj . p */p 1

(4.9)

The Wen theorem implies that an individual does not sell other goods if she sells good 1. Also, we have noted that the indirect utility function is an increasing function of the price of a good sold and a decreasing function of the prices of goods purchased. This together with (4.9) imply that the utility for selling good 1 under p* is not lower than that under p. Thus, under p*, an individual can do at least as well as those individuals selling good 1 at the corner equilibrium under p if she chooses the same production and trade plan as theirs. It follows that: u1( p*) ≥ u1( p) = u( p),

(4.10)

where u1( p*) is an individual’s utility from a conﬁguration in the corner equilibrium E under the general equilibrium prices, u1( p) is her utility from this conﬁguration under the corner equilibrium prices in E, and u( p) is the per capita real income in the corner equilibrium E. The last equality in (4.10) is due to utility equalization in any corner equilibrium. But by the deﬁnition of general equilibrium, any conﬁguration chosen by any individual in general equilibrium generates at least the same utility as in any alternative conﬁguration under the general equilibrium prices. This implies: u( p*) ≥ u1( p*)

(4.11)

where u( p*) is per capita real income in general equilibrium. (4.10) and (4.11) together imply u( p*) ≥ u( p), that is, per capita real income in general equilibrium is not lower than in any corner equilibrium. In other words, the general equilibrium is the Pareto optimum corner equilibrium. Q.E.D. We will use the Yao theorem frequently in this text. For the model in this section, the Yao theorem implies the following inframarginal comparative statics. Proposition 4.1: The general equilibrium is the corner equilibrium in structure D if uD > uA, or if k > k0 ≡ 22(1−a), and is autarky if k < k0.

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k

1 k = 22−2a k > k0 k < k0 0

1

a

Figure 4.3 Partition of parameter space

Since economies of specialization are individual speciﬁc, or increasing returns are localized, we can apply the argument of revealed preferences used in chapter 3 to prove that a general equilibrium in this model is Pareto optimal. The rigorous proof of the ﬁrst welfare theorem for a broad class of general equilibrium models allowing endogenous as well as exogenous comparative advantages can be found in Zhou, Sun, and Yang (1998). This result implies that the most important function of the market is to coordinate individuals’ decisions in choosing their patterns of specialization, in order to fully exploit positive network effect of division of labor net of transaction costs. If transaction costs outweigh economies of division of labor, coordination of the division of labor between various occupations will fail, so that the general equilibrium is autarky. If economies of division of labor outweigh transaction costs, the market can always utilize positive network effect of division of labor. Hence, in this model, coordination failure of division of labor comes from transaction costs. According to the ﬁrst welfare theorem, either in the case of coordination failure or in the case of coordination success of division of labor, we have market success, due to the trade-off between economies of division of labor and transaction costs. Proposition 4.1 has partitioned a two-dimensional space of parameters k and a into two subspaces, as shown in ﬁgure 4.3. Since we assume k ∈[0, 1] and a ≥ 1, the feasible space of parameters is the region below horizontal line k = 1, above the line k = 0, and on the right side of the vertical line a = 1, including the boundaries of the region in ﬁgure 4.3. The curve k = 22−2a partitions the parameter space into two subspaces, one of them above the curve and the other below the curve. If values of parameters are within the ﬁrst subspace, the corner equilibrium in structure D is the general equilibrium; if values of parameters are within the second subspace, the corner equilibrium in autarky is the general equilibrium. Figure 4.4 provides an intuitive illustration of proposition 4.1. Panel (a) denotes two representative individuals choosing autarky and panel (b) denotes two representative individuals choosing (x/y) and (y/x), respectively. The circles denote individuals; directed lines denote ﬂows of goods. As transaction efﬁciency k increases from a value smaller than k0 to a value larger than k0, the general equilibrium jumps from autarky to the division of labor between two specialists. Such a jump in turn generates discontinuous jumps of all endogenous variables, emergence of markets for two goods, and of demand and supply from the division of labor, and an increase in the size of the network of the market. We call this phenomenon exogenous evolution in division of labor, since it never takes place in the absence of an exogenous change in parameters. An increase in individuals’ specialization and an increase in diversity between different occupation conﬁgurations are two facets of the evolution.

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y

A

x y

y

A

x

(a) Structure A, autarky

ys

yd

xd

xs

x/y

y/x

115

x

(b) Structure D, division of labor

Figure 4.4 Autarky and division of labor

As a result of this evolution, aggregate demand jumps from 0 to a positive value, the total transaction cost for society jumps from 0 to (1 − k)(Mx y d + My x d ) = (1 − k)M/2, and the aggregate production schedule jumps from a lower to a higher position, as indicated in ﬁgure 4.1, while the level of specialization of each individual increases from 1/2 to 1. An individual’s labor productivity of the good sold increases from 0.5a−1 (< 1) to 1, and her labor productivity of the good purchased decreases from 0.5a−1 to 0. But all individuals’ productivities in each good are the same in autarky, which is the general equilibrium for k < k0. This implies that productivity difference between ex ante identical individuals may emerge if they choose different levels of specialization in producing a good. Hence, we use the term endogenous comparative and absolute advantage to describe the difference in productivity between the buyer and seller of a good caused by the difference in their levels of specialization in producing that good. If the ex ante identical individuals choose the same level of specialization in producing a good, there is no endogenous comparative advantage. Of course, endogenous comparative advantage is not conﬁned to cases involving ex ante identical individuals. The exogenous evolution of division of labor is based on inframarginal comparative statics of general equilibrium. Inframarginal comparative statics of general equilibrium are analogous to the inframarginal comparative statics of individuals’ decisions. That is, the general equilibrium discontinuously jumps between corner equilibria as values of parameters shift between parameter subspaces. The marginal comparative statics of general equilibrium characterize changes of relative prices, of relative quantities of goods and factors, and of utility in response to those changes in parameters that take place within the parameter subspace demarcated by the inframarginal comparative statics. For instance, if k > k0, the general equilibrium is the corner equilibrium in D. If k is increased, equilibrium per capita real income uD = k/4 will increase. For k < k0, the general equilibrium is the corner equilibrium in A. As a is decreased within the parameter subspace k < k0, the equilibrium values of x = y = 0.5a will change. All such changes in the equilibrium values of endogenous variables are marginal comparative statics of general equilibrium. These are changes in equilibrium resource allocation in response to parameter changes for a given structure of division of labor, since each corner equilibrium determines resource allocation for a given structure. The inframarginal comparative statics of general equilibrium deal with changes in the structure of division of labor in response to parameter changes, since the general equilibrium determines the equilibrium network structure of division of labor. If there exists a parameter subspace within which a corner equilibrium is the general equilibrium, then within this subspace the marginal comparative statics of general equilibrium are the comparative statics of the corner equilibrium. We deﬁne a proﬁle of quantities of goods produced, traded, and consumed by all consumerproducers for a given structure as an allocation of resource for a given structure of division of labor. A corner equilibrium in the Smithian framework sorts out resource allocation for a given structure of organization. We deﬁne the task of determining a structure of division of labor as a problem of development, which relates to all individuals’ conﬁgurations of specialization, the size of the network of division of labor, variety between different occupation conﬁgurations, and productivity.

116 P ART I: D EVELOPMENT M ECHANISMS

The general equilibrium sorts out problems of development. The analysis of resource allocation relates to the marginal comparative statics of general equilibrium, while the analysis of economic development relates to the inframarginal comparative statics of general equilibrium.

4.4 MORE EXAMPLES Example 4.2: A general equilibrium model with the CES utility function. In the previous sections, supply functions in conﬁgurations with specialization are independent of prices, because of the unitary elasticity of substitution of the C–D utility function. Unitary elasticity of substitution implies that the substitution effect and the income effect cancel each other out in a consumerproducer setting. In this subsection, we use a constant elasticity of substitution (CES) utility function to illustrate the implications of the elasticity of substitution for the law of supply. The CES utility function is speciﬁed for each consumer-producer: u = [(x c)ρ + ( y c)ρ]1/ρ,

xc ≡ x + kx d,

yc ≡ y + ky d

where ρ ∈(0, 1) is a parameter of elasticity of substitution. The following features distinguish the CES utility function from the C–D utility function. For the C–D function, the quantity of each consumption good must be positive for maintaining a positive utility. For the CES function, utility is positive even if the quantity of a consumption good is 0, as long as the quantity of at least one of the other consumption goods is positive. The elasticity of substitution is deﬁned as the percentage change of relative quantity for one percentage change of relative marginal utility of two goods. The elasticity of substitution of the CES function can be calculated as follows:

⎛ ∂u/∂y c ⎞ d( x c/y c ) ⎜ ⎟ d ln(x c/y c ) 1 ⎝ ∂u/∂x c ⎠ = . = E= c c ⎛ ∂u/∂y ⎞ 1 − ρ ⎛ ∂u/∂y ⎞ c c d⎜ d ( / ) ln x y ⎟ ⎜ ⎟ ⎝ ∂u/∂x c ⎠ ⎝ ∂u/∂x c ⎠ This formula implies that relative quantities of the two goods consumed will decrease by 1/(1−ρ) percent when the relative price of the two goods increases by one percent. Since the elasticity of substitution is an increasing function of ρ, or dE/dρ > 0, the greater the value of ρ, the greater the elasticity of substitution. Since an individual’s desire for variety in consumption diminishes as the elasticity of substitution increases, the degree of desire for a variety in consumption can be deﬁned by 1/ρ. If we let x c = y c, it is not difﬁcult to see that consumption of two goods always generates a greater level of utility than consumption of a single good, that is, 21/ρx c > x c. We need the assumption ρ ∈(0, 1) to ensure diverse consumption in equilibrium, since ρ < 0 or ρ > 1 implies specialized consumption in autarky equilibrium. Now that you are more familiar with the use of mathematical language in specifying economic models, we can quickly specify an individual’s decision problem based on the CES utility function as follows: Max: u = [(x c )ρ + ( y c )ρ]1/ρ s.t.

x ≡ x + kx c

x+x =l s

d

(utility function)

y ≡ y + ky c

y+y =l

a x

s

lx + ly = 1

(deﬁnition of quantities to consume) (production function) (endowment constraint)

px x + py y = px x + py y s

a y

d

s

d

d

(budget constraint)

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Table 4.4 Corner solutions based on the CES utility function Conﬁguration

Quantities self-provided

Corner supply functions

Corner demand functions

Corner indirect utility functions

A1

x=1

0

0

1

0

0

2

xs yd = p

ρ ⎡ ⎤ ⎢1 + ⎛ k ⎞ 1− ρ ⎥ ⎜ ⎟ ⎢ ⎝ p⎠ ⎥ ⎢⎣ ⎥⎦

a

A2

⎛ 1⎞ x= y=⎜ ⎟ ⎝ 2⎠

(x/y)

ρ ⎤ ⎡ ⎛ k ⎞ 1− ρ ⎥ ⎢ x = ⎢1 + ⎜ ⎟ ⎥ ⎝ p⎠ ⎢⎣ ⎥⎦

(y/x)

ρ ⎡ ⎤ y = ⎢1 + (kp) 1− ρ ⎥ ⎢⎣ ⎥⎦

−1

−1

ρ ⎡ ⎤ ⎛ p ⎞ 1− ρ ⎥ ⎢ s x = 1+⎜ ⎟ ⎢ ⎝ k⎠ ⎥ ⎥⎦ ⎣⎢ −ρ ⎡ ⎤ y = ⎢1 + (kp) 1− ρ ⎥ ⎢⎣ ⎥⎦ s

−1

−1

x = py d

s

1 − aρ ρ

ρ ⎤ ⎡ ⎢1 + (kp) 1− ρ ⎥ ⎥⎦ ⎢⎣

1− ρ ρ

1− ρ ρ

where x, x s, x d, y, y s, y d, lx, ly are decision variables and px, py are price parameters. According to the Wen theorem, 5 conﬁgurations need to be considered. There are three autarky conﬁgurations: A1, in which one good is consumed; A2, in which two goods are consumed; and a third, which is symmetric to A1. The two conﬁgurations with specialization are (x/y) and (y/x). The optimum decisions in the various conﬁgurations are summarized in table 4.4, where p ≡ py /px is the relative price. To familiarize yourself with inframarginal analysis, you should follow the procedure of the previous sections to solve for the optimum decisions in table 4.4. Let us ﬁrst consider the marginal comparative statics of the decisions. For a given conﬁguration of specialization, differentiation of the corner supply functions in table 4.4 yields:

dx s < 0, dp

dy s >0 dp

This is referred to as the neoclassical supply law, i.e., the quantity of a good supplied increases with the price of that good. Since p ≡ py /px, the neoclassical supply law implies that the quantity of a good that is supplied not only increases with the price of that good, but also decreases with the price of the good purchased by the specialist supplier. This is consistent with the feature of classical demand and supply analysis: demand and supply are two sides of specialization. It is easy to verify from table 4.4 that neoclassical demand law holds for this model based on the CES utility function.

dx d > 0, dp

dy d <0 dp

Next, consider the inframarginal comparative statics of the decisions, which require a comparison of per capita real income across conﬁgurations. It can be shown that both conﬁgurations of specialization will be chosen only if p = 1. For p = 1, a comparison between specialization and conﬁguration A1 implies that specialization is always better than A1. Hence, A1 will not be chosen. A comparison between specialization and conﬁguration A2 indicates that individuals will choose specialization if k > k1 ≡ (2(1−aρ)/ρ − 1)(1−ρ)/ρ,

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and will choose A2 (autarky) if k < k1. As transaction efﬁciency increases from a value smaller than k1 to the one larger than k1, the general equilibrium will jump from autarky to the division of labor. Example 4.3: An asymmetric model. In the model we have discussed, there are too many symmetries. Hence, equilibrium values of endogenous variables are independent of relative tastes and relative production conditions. In this example, we examine the implications of relative tastes and relative production conditions for the equilibrium resource allocation and the level of division of labor. Assume that all ex ante identical consumer-producers have the following utility and production functions: u = (x + kx d )α( y + ky d )1−α, x + x s = l xa,

α ∈(0, 1)

y + y s = l yb .

The corner equilibrium-relative price in structure D is py/px = k1−2α. Its derivative with respect to k is positive when α < 1/2, and is negative when α > 1/2. The corner equilibrium-relative number of the two types of specialists is Mx/My = αk1−2α/(1 − α). Its derivative with respect to k has similar features. The general equilibrium is the division of labor if: 1

⎛ ⎞ 2 α (1− α ) (α a)α a [b(1 − α)]b(1−α ) k > k2 ≡ ⎜ ⎟ ⎝ [αa + (1 − α)b]α a+(1−α )b α α (1 − α)1−α ⎠ and autarky if k < k2. The equation k = k2, which involves four parameters, partitions the fourdimensional space of parameters a, b, α, and k into the two subspaces. You should follow the procedure in chapters 3 and 4 to solve for individuals’ decisions, the marginal and inframarginal comparative statics of the decisions, the two corner equilibria, the general equilibrium, and ﬁnally, for the marginal and inframarginal comparative statics of the general equilibrium. Comparative statics of general equilibrium describe how the consequences of interactions between self-interested decisions change in response to changes in environment. They differ from comparative statics of decisions. From the corner solutions in table 4.2, we can see that the decisions for a given conﬁguration are functions of relative prices and parameters of production and transaction. For instance, the neoclassical demand law for a given conﬁguration dy d/d( py /px) = − 0.5( px /py)2 is part of the marginal comparative statics of decisions. From the corner solution for a given conﬁguration in example 4.2, we can see that the optimum decision, which is a corner solution in a conﬁguration, is also a function of parameters of tastes and production. If the maximum amount of working time is a parameter rather than a speciﬁc number, then the optimum decision is a function of the endowment parameter as well. The inframarginal comparative statics are associated with discontinuous jumps of the optimum decisions between conﬁgurations as parameters of prices, tastes, endowments, and production and transaction conditions shift between the parameter subspaces that demarcate different conﬁgurations. Hence, the marginal and inframarginal comparative statics of decisions explain the optimum quantities of consumption, production, trade, and the optimum conﬁguration of specialization by parameters of prices, tastes, endowments, and production and transaction conditions. From table 4.2, we can see that comparative statics of decisions may be represented by the following mapping: Parameters of tastes, transaction and production conditions, endowments, prices, numbers of different specialists

⇒

Quantities demanded and supplied, resource allocation, utility, conﬁguration of specialization

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Recalling table 4.3 and proposition 4.1, we can see that the general equilibrium-relative price, numbers of different specialists, and quantities of consumption, production, and trade are determined by parameters of tastes, endowments, population size, and production and transaction conditions. The marginal and inframarginal comparative statics of general equilibrium explain relative price, numbers of different specialists, structure of division of labor, per capita real income, and resource allocation by the parameters as summarized by the following mapping: Parameters of tastes, endowment, production and transaction conditions, population size

⇒

Quantities demanded and supplied, relative prices, numbers of specialists, structure of division of labor

Hence, prices and numbers of individuals choosing different conﬁgurations are explaining parameters in comparative statics of decisions, while in comparative statics of general equilibrium, they are endogenous variables, themselves explained by parameters of tastes, endowments, production and transaction conditions, and population size. It should be noted that comparative statics of decisions relate only to individuals’ occupation conﬁgurations, since an individual cannot choose a structure of division of labor for society. Comparative statics of general equilibrium relate to the structure of division of labor for society as a whole, since the general equilibrium is the outcome of interactions among all individuals’ optimizing decisions. It is not difﬁcult to see that inframarginal comparative statics of general equilibrium are a rich source of the explaining power of economic development and related structural changes. The model in example 4.1 is similar to the model in the previous chapter, in that the production possibility frontier (PPF) may not be associated with the Pareto optimum. The general equilibrium structure is A, which is Pareto optimal if k < k0. But the PPF is associated with structure D, not with structure A (recall ﬁgure 4.1). The trade-off between economies of division of labor and transaction costs implies that the Pareto optimum that is associated with the utility frontier is not the same as the PPF if transaction efﬁciency is low. As transaction efﬁciency is improved, the general equilibrium and the Pareto optimum move closer to the PPF. The endogenization of aggregate productivity implies that the degree of scarcity is endogenously explained by individuals’ decisions concerning their levels of specialization, and is ultimately determined by trading efﬁciency. Hence, problems of economic development occupy a central place in the model of endogenous network of division of labor. Although the model in the current chapter is a static model, inframarginal comparative statics of general equilibrium can explain not only productivity progress, increases in per capita real income and consumption, and other “growth phenomena,” but can also explain the emergence of the market, increases in diversity of economic structure and in the extent of the market, and other “development phenomena.” From ﬁgure 4.1, we can see that if transaction efﬁciency is low, the general equilibrium is the corner equilibrium in autarky and the production takes place on curve ECG, which is lower than the PPF (EFG). As transaction efﬁciency is sufﬁciently improved, production schedule jumps from ECG to point F. This generates productivity progress and an increase in the network size of division of labor, which are two aspects of economic development. Example 4.4: Effects of a tax on allocation and organization efﬁciencies. Consider the Smithian model of example 4.1 with k = 1, and with taxation introduced. A benevolent and efﬁcient government imposes a tax rate t on each dollar of goods sold, then evenly distributes the tax revenue among M consumer-producers. Hence, the income transfer that each individual receives from the government is r = t(Mx x s + My y s)/M if the structure D is the general equilibrium.

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Applying inframarginal analysis and using the symmetry of the model, we can solve for the corner solutions in the three conﬁgurations A, (x/y), and (y/x). Then the utility equalization and market clearing condition in structure D yields the corner equilibrium in D, as follows: px /py = 1,

Mx = My = M/2,

x = y = 1/(2 − t),

x = y = x = y = (1 − t)/(2 − t), s

s

d

d

uD = (1 − t)/(2 − t)2,

r = (1 − t)t/(2 − t)

where uD is per capita real income in structure D, which is a monotonically decreasing function of the tax rate t. This implies that the tax causes a distortion resulting in a reduction of utility. The Pareto optimum tax rate is 0. But the corner equilibrium-relative price in structure D is the same as in the corner equilibrium with no tax. Aggregate relative resources allocated to the production of the two goods, Mx /My = 1, and aggregate relative consumption and production of the two goods, (Mx x + My x d)/(Mx y d + My y) = 1, are Pareto optimal. However, each individual’s relative consumption of the two goods is not Pareto optimal. The relative consumption is x/y d = 1/(1 − t) > 1 for an x specialist, and is x d/y = 1 − t < 1 for a y specialist. Also, you can verify that each individual’s resource allocation is inconsistent with the ﬁrst-order condition for the Pareto optimum problem that maximizes the x specialist’s utility for a constant utility of the y specialist. The tax encourages individuals to allocate too much resource for self-provided consumption, and correspondingly discourages production for and consumption from the market. Hence, this allocation inefﬁciency may also cause organization inefﬁciency. Since, by deﬁnition, autarky does not involve trade, no tax revenue can be collected in autarky, so per capita real income in autarky is the same as in example 4.1. The general equilibrium will be the corner equilibrium in structure D in the absence of tax when k = 1. But a sufﬁciently high tax rate will make uD smaller than per capita real income in autarky, 2−2a even if k = 1. If k < 1, then we can show that the critical value of k, which ensures that division of labor will be the general equilibrium, is smaller in the absence of tax than when the tax is imposed. Hence, if k is between the two critical values, then the general equilibrium in the absence of tax is the division of labor, while the general equilibrium in the presence of tax is autarky. This example illustrates the interdependence between allocation efﬁciency and organization efﬁciency. The allocation inefﬁciency caused by the tax also causes an inefﬁcient general equilibrium level of division of labor and an inefﬁcient productivity level. The next example illustrates the conﬂict between allocation efﬁciency and organization efﬁciency in a Smithian model. Example 4.5: Conﬂict between allocation efﬁciency and organization efﬁciency. Suppose that in the model in example 4.1, the utility function is u = (x + kx d )α( y + ky d )1−α. Then we can solve for corner equilibria in autarky and in structure D as follows: uA = [αα(1 − α)1−α ]a uD = [αα(1 − α)1−α ]k2α(1−α), Mx = αk1−2αM/(1 − α + αk1−2α),

px /py = k2α−1, My = (1 − α)M/(1 − α + αk1−2α)

The general equilibrium is the division of labor iff k > k1 ≡ [αα(1 − α)1−α](a−1)/2α(1−α). It is easy to show that the critical value k1 is minimized with respect to α at α = 1/2, and that Mx = My = M/2 at α = 1/2. That is, as the difference between α and 1/2 increases, k1 increases. For a larger

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k1, k is more likely to be smaller than k1, so that autarky instead of the division of labor is more likely to occur in equilibrium. In other words, as the differential in tastes for different goods tends to 0, the general equilibrium is more likely to be the division of labor. This indicates a possible conﬂict between organization efﬁciency, which relates to higher productivity and economic development, and efﬁciency of resource allocation, if one good is more preferred than the other. Under this circumstance, in order to accommodate taste differential, a high level of division of labor and related high productivity may have to be sacriﬁced. Example 4.6: Free entry and free pricing. In a Smithian model, the power to manipulate the relative numbers of different specialists has a more crucial impact on efﬁciencies of resource allocation and organization than does the power to manipulate relative prices. This result can be used to criticize Lange’s theory of market socialism, which emphasizes the importance of price ﬂexibility in achieving allocation efﬁciency. According to the theory of market socialism, the government adjusts prices according to excess demand and directs managers of state enterprises to choose proﬁt-maximizing quantities of outputs and inputs. Many economists have pointed out that self-interested government ofﬁcials have no incentive to price commodities in accordance with excess demand because of the absence of residual claimants of proﬁts. According to our model in this chapter, even if a system of ﬂexible prices clears the market, self-interested government ofﬁcials may still manipulate the relative numbers of different specialists, for instance, restricting free entry into the state banking sector and into entrepreneurial activities, such that the market clearing prices of the services provided by the ofﬁcials are high. This form of market socialism is not much better than the Soviet-style socialist system, under which governmentcontrolled prices do not clear the market and the great excess demand becomes the source of the power of the central planning authorities. The government ofﬁcials gain a great deal of tangible and intangible beneﬁt from that power.

4.5 PATTERN OF TRADE In this section, we examine the trade pattern in a Smith–Young model of endogenous comparative advantage. In both the Ricardo and Heckscher–Olin models of exogenous comparative advantage in the preceding chapter, the equilibrium pattern of trade is determined by exogenous comparative technology and endowment advantages. But in the Smith–Young model of endogenous comparative advantage, all individuals are ex ante identical in all aspects, so that the equilibrium trade pattern cannot be explained by exogenous comparative advantage. In this section, we specify a Smith–Young model with three goods and show that if not all goods are involved in the division of labor, those goods which have more signiﬁcant economies of specialization in production and/or higher transaction efﬁciencies are more likely to be involved in trade. Example 4.7: A model of endogenous comparative advantage with three goods. Consider a model with M ex ante identical consumer-producers. Each of them has the following utility function, production functions, and endowment constraint of labor: u = (x + kx x d )( y + ky y d )(z + kzz d ), x + x s = Max{lx − a, 0}, lx + ly + lz = e

y + y s = Max{ly − b, 0},

z + z s = Max{lz − c, 0},

122 P ART I: D EVELOPMENT M ECHANISMS Table 4.5 Trade pattern in a model of endogenous comparative advantage Structure

Corner equilibrium prices

Corner equilibrium per capita real income [(e − a − b − c)/3]3

A Pxy

px/py = (kx/ky )0.5[(e − b − c)/(e − a − c)]1.5

(kx ky)0.5[(e − b − c)(e − a − c)]1.5/33

Pxz

px/pz = (kx/kz )0.5[(e − b − c)/(e − a − b)]1.5

(kx kz)0.5[(e − b − c)(e − a − b)]1.5/33

Pyz

py/pz = (ky/kz ) [(e − a − c)/(e − a − b)]

(kz ky)0.5[(e − b − a)(e − a − c)]1.5/33

D

px/py = (kx/ky )1/3(e − b)/(e − a), pz/py = (kz/ky )1/3(e − b)/(e − c)

(kx ky kz)2/3(e − a)(e − b)(e − c)/33

0.5

1.5

where a, b, and c are ﬁxed learning and training costs in producing goods x, y, and z, respectively. The ﬁxed learning cost generates economies of specialization, which implies that average labor productivity increases with a person’s level of specialization in producing a good. Each individual is endowed with e units of labor. The transaction efﬁciency coefﬁcient for good i is ki. It is assumed that a > b > c and kx > ky > kz. Applying inframarginal analysis, we can solve for the inframarginal comparative statics of general equilibrium, which indicate that the general equilibrium jumps from autarky to the partial division of labor with two traded goods, and then to the complete division of labor with three traded goods as trading efﬁciency k i improves. There are three corner equilibria for the partial division of labor. In one, denoted as structure Pxy , goods x and y are traded; in structure Pxz, goods x and z are traded; and in structure Pyz, goods y and z are traded. Denoting the complete division of labor D and autarky A, information about the corner equilibria in the ﬁve structures is summarized in table 4.5. Applying inframarginal analysis to each individual’s decision in choosing a conﬁguration, it can be shown that under the assumptions that a > b > c, kx > ky > kz, and kx, ky are neither too great nor too small, the general equilibrium structure is Pxy. Individuals have incentives to deviate from their conﬁgurations in structure Pxz or Pyz under the corner equilibrium prices in either of the two structures. The inframarginal comparative statics of general equilibrium can also be obtained by directly applying the Yao theorem to information in table 4.5. If taste parameters are different across goods, it can be shown that if not all goods are traded, then those goods that are more desirable are more likely to be traded (see exercise 21). The results are summarized in the following proposition about trade pattern in a model of endogenous comparative advantage. Proposition 4.2: If transaction efﬁciencies are neither too high nor too low, not all goods are traded in equilibrium. Those goods which have more signiﬁcant economies of specialization in production or higher transaction efﬁciencies, or are more desirable, are more likely to be traded. This proposition can be used to explain why markets for some goods do not exist. The nonexistence of many markets in developing economies is often used to justify development economics as a ﬁeld separate from standard microeconomics. The inframarginal analysis of the Ricardian model and the HO model in chapter 3, and the Smith–Young model in this chapter, suggests that the number of active markets in equilibrium can be endogenized in a standard microeconomic framework. Hence, inframarginal analysis can explain why the markets for many goods and services do not exist in a developing economy, and under what conditions the markets will emerge from economic development process.

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Key Terms and Review • Conﬁguration and corner solutions. • Why the decision problem that involves a corner solution is much more complicated than the interior decision • Implications of the Wen theorem for inframarginal analysis • Trade-off in allocating resources for a given conﬁguration of specialization versus trade-off in choosing a conﬁguration of specialization • Marginal analysis of the problem of resource allocation versus inframarginal analysis of the problem of economic development • Relationship between the trade-off in decision-making and the second-order condition • Corner demand function, corner supply function, and corner indirect utility function versus demand function, supply function, and indirect utility function • Demand law, supply law, and the law of specialization • The difference between marginal and inframarginal analyses of demand and supply • Marginal comparative statics versus inframarginal comparative statics of decisions • Network effect of division of labor • How the market coordinates division of labor and utilizes network effect of division of labor • Structure based on conﬁgurations and corner equilibrium based on corner solutions • General equilibrium versus corner equilibrium • Marginal versus inframarginal comparative statics of general equilibrium • The difference between an individual’s demand and supply functions, total market demand and supply functions, and aggregate demand and supply functions • Implications of Walras’s law for solving for a corner equilibrium • Implications of free pricing and free choice between occupation conﬁgurations for coordination of the network of division of labor • Why marginal cost pricing may not work in a Smithian general equilibrium model • Allocation efﬁciency versus organization efﬁciency • The implications of institution for the equilibrium level of division of labor through its effect on transaction efﬁciency • Why the Pareto optimum may not be associated with the production possibility frontier • Implications of transaction efﬁciency for the disparity between the Pareto optimum and the PPF, and for reducing scarcity • Implications of the trade-off between economies of division of labor and transaction costs for endogenizing productivity, network size of division of labor, and trade dependence • The relationship between decisions in choosing an occupation conﬁguration and the size of network of division of labor • The Smithian aggregate demand law • Relationship between production and transaction conditions and trade pattern in a Smith–Young model of endogenous comparative advantage

Further Reading The classical literature of specialization: Arrow (1979), Petty (1671), Tucker (1755, 1774), Smith (1776), Turgot (1751), Babbage (1832), Rae (1834), Walker (1874), Groenewegen (1987), Meek and Skinner (1973), Rashid (1986), Stigler (1951, 1976), Anonymous (1701); Inframarginal analysis: Buchanan and Stubblebine (1962),

124 P ART I: D EVELOPMENT M ECHANISMS Coase (1946, 1960), Young (1928), Houthakker (1956), Wen (1998), Yang and Y.-K. Ng (1993), Yang (1994), Rosen (1978, 1983), Becker (1981), Hadley (1964); Marginal analysis of endogenous specialization: Baumgardner (1988), Becker and Murphy (1992), Tamura (1991), Locay (1990), Kim (1989). Network effects: Buchanan and Stubblebine (1962), Farrell and Garth (1985), Katz and Shapiro (1985, 1986), Liebowitz and Margolis (1994); Criticism of marginal cost pricing: Coase (1946, 1960), Yang and Y.-K. Ng (1993, ch. 2), Yang (1988, 1994); Neoclassical general equilibrium models with transaction costs and constant returns to scale technology: Hahn (1971), Karman (1981), Kurz (1974), Mills and Hamilton (1984), Schweizer (1986).

QUESTIONS 1 In the last decade, many shops specializing in changing engine oil have emerged in the US. They are usually organized through franchise networks, which reduce transaction costs caused by a deep division of labor between the franchiser and the franchisees. The franchiser specializes in planning, advertising, designing the operation manual, choosing specialized equipment, and management, while the franchisee specializes in changing engine oil. Since the franchiser specializes in producing intangible intellectual properties, it is very easy for the franchisee to infringe upon the franchiser’s property. (For instance, the franchisee refuses to pay the franchise fee as soon as she has acquired the know-how in the operation manual provided by the franchiser.) Thus, a special form of contract has evolved, which gives the franchiser great discretionary power to terminate the contract, and which increases the degree of speciﬁcity of the franchisee’s investment in the business. (For instance, within 15 years after the termination of the contract, the franchisee is not allowed to engage in the engine oilchanging business within a certain territory.) Such clauses provide a mechanism of hostage, which signiﬁcantly enhances transaction efﬁciency of intellectual properties of the franchiser. Use the model in this chapter to explain why this type of contract is essential for deepening the division of labor within the sector providing engine oil-change services, and between this sector and the rest of the economy. 2 Rosenberg and Birdzell (1986, pp. 163–5) provide historical evidence for endogenous comparative advantage and related endogenous productivity progress. According to data on trade and production between 1720 and 1900, it wasn’t simply the case that British production responded to demand from overseas markets, but in addition trade stimulated productivity progress, which created more demand. Use the notion of general equilibrium and the model in this chapter to explain this historical fact. 3 According to E. Jones (1981, p. 267) and North (1981), trade based on exogenous comparative advantage prior to the Industrial Revolution generated endogenous comparative advantage and more trade. Design a model to formalize the interactions between endogenous and exogenous comparative advantages (see chapter 6). 4 Compare the Smithian model in this chapter with the neoclassical model based on the dichotomy between consumers and ﬁrms. 5 A businessman found that many hotel and restaurant managers need taped music for their customers, but the latter do not have time to keep track of the constantly changing musical tastes of customers. The businessman specialized in identifying the most popular music, added a margin to the price of the tapes he had chosen, and then sold them to the managers. His business became very successful. Use the model in this chapter to explain how the businessman created demand and supply for professional services by deepening division of labor. If you use neoclassical analysis

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of demand and supply to consider this case, how would you explain the demand and supply of music tapes? Why can’t that analysis predict created demand and supply based on an endogenous level of specialization and productivity, which is the most interesting feature of modern entrepreneurism and economic development? When Lady Thatcher retired as Prime Minister of Britain, she was worried about whether her humble pension would be enough to support the very expensive life-style to which she had been accustomed. She was approached by a company which specializes in cultivating public relations. The contract between her and the agent helped her to make so much money from public speaking throughout the world that she was able to earn much more than she made as Prime Minister. Explain why the division of labor between specialized agents and specialized movie stars, public ﬁgures, and singers occurs in the marketplace. Explain why many writers in New York use agencies to ﬁnd publishers and to sign publication contracts for their commercial books on their behalf, while the division of labor between academic writers and specialized publication agents is not common. In particular, why do academics never use professional publication agents for submitting research papers to refereed journals on their behalf ? What are network effects of division of labor? What is the difference between network effects of division of labor and economies of scale? Why can we not understand demand and supply if we do not understand the network effects of division of labor? Chenery (1979) and Kuznets (1966) explain structural changes by increases in per capita income. Use the concept of network effect of division of labor to analyze interdependencies between structural changes and increases in per capita incomes and between the extent of the market and level of division of labor in connection to Chenery’s and Kuznets’ theory. Before the 1830s, economists rarely used the concept of economies of scale. The notions they used were beneﬁts and costs of specialization and division of labor, which relate, in essence, to the economies of interpersonal complementarity and the network effect of division of labor. At the end of the nineteenth century, the notion of economies of scale became popular. Use the model in this chapter to illustrate why coordination failure caused by economies of scale disappears if the notion of economies of scale is replaced by the notion of economies of specialization and division of labor. Use the model in this chapter to explain why Allyn Young claimed that demand and supply are two sides of division of labor, and why we cannot understand what demand and supply are if we do not understand how individuals choose their levels and patterns of specialization. Use the Wen theorem, which helps to keep inframarginal analysis tractable, to explain why, in the late nineteenth and twentieth centuries, the analysis of demand and supply shifted from inframarginal analysis of decision-making in choosing a level of specialization which is essential for economic development, to marginal analysis of resource allocation for a given level of specialization and productivity. Why is the notion of general equilibrium a powerful vehicle for analyzing the development implications of the network effects of division of labor? What is the difference between the interdependence between quantities of goods chosen by individuals for given prices and the market equilibrium prices, and the interdependence between individuals’ decisions in choosing their levels of specialization? In the models in this chapter, improvements in transaction conditions can generate evolution in division of labor. This evolution is associated with structural changes. For instance, the number of professional farmers (producing food x) in structure D

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is smaller than the number of all individuals producing x, which is the population size in autarky. If the general equilibrium jumps from autarky to D because of an improvement in transaction conditions, the resulting structural change appears to be a transfer of labor from the traditional agricultural sector to the industrial sector producing cloth y. Compare this equilibrium mechanism for economic development and structural changes with that in the theory of labor surplus of Lewis (1955) and Fei and Renis (1964). (According to the theory of labor surplus, as technology in the industrial sector exogenously changes or as capital accumulates, labor is transferred from the traditional agricultural sector to the industrial sector.) Suppose a student raises a concern about coordination failure in utilizing the network effects of division of labor in the model in this chapter. She suggests that if there is no central planner, the market cannot select the Pareto optimum corner equilibrium from the multiple corner equilibria. Analyze the coordination mechanism in the marketplace and address her concern. Use your daily experience to explain how the decentralized market coordinates individuals’ decisions in choosing occupation conﬁgurations and levels of specialization to utilize the network effect of division of labor. If economies of division of labor outweigh transaction costs, but nobody is willing to choose some occupation conﬁguration, how can the market sort out the coordination problem? Many individuals prefer the occupation conﬁgurations of medical doctors, lawyers, and high executive positions in large companies to those of doormen, janitors, and garbage collectors. If all individuals refuse to choose occupations in the latter group, then coordination failure of division of labor occurs. How can the market sort out this coordination problem? In neoclassical marginal analysis, the function of free pricing in equilibriating demand and supply is used to explain how the market coordinates conﬂicting self-interested decisions. In addition to free pricing, our analysis in this text also emphasizes free choice of occupation conﬁgurations in coordinating the division of labor, and inframarginal analysis across occupation conﬁgurations in utilizing the network effects of division of labor. Discuss the implications of the difference between inframarginal analysis and marginal analysis of demand and supply. Many development economists argue that due to network effects of industrial linkage, market failure will retard industrialization. Hence, a government policy to pursue big-push industrialization may overcome such coordination failure. Use the model in this chapter to analyze this view. Network effect is a basic feature of division of labor. Smith and Young emphasized the function of the market in coordinating the network of division of labor, though they did not use the word “network.” Why did economists until recently pay no attention to this feature of the market and the function of the invisible hand in coordinating division of labor? Why was network effect not the focus of economics in the nineteenth century nor in most of the twentieth century? Some economists argue that inframarginal analysis of specialization is relevant only to the evolution of division of labor that occurred before the Industrial Revolution. They claim that in a modern economy, each individual is completely specialized and buys everything from the market, so that the assumption of an exogenous level of specialization of individuals is acceptable. Comment on this view in connection with the following cases: a) The emergence of CNN (the Cable News Network) is very much a modern phenomenon. According to the model in this chapter, an improvement in

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transaction efﬁciency (which might be caused by new telecommunications facilities) or a spontaneous evolution of division of labor will make commercially viable a higher level of division of labor between specialized media. The corner equilibrium that involves the ﬁner division of labor between CNN (which specializes in reporting news through TV networks) and other media will be the general equilibrium. Whether or not the demand for and supply of CNN’s professional services are “effective” depends on the general equilibrium level of division of labor, since demand and supply are two sides of the division of labor. But this in turn is determined by the efﬁcient balance point between the economies of specialization and transaction costs. b) The Wall Street Journal (“Manufacturers Use Supplies to Help Them Develop New Products,” Dec. 19, 1994, p. 1; see also “Enterprise: How Entrepreneurs Are Reshaping the Economy and What Big Companies Can Learn?” Business Week, Oct. 22, 1993, and “Management Focus,” The Economist, March 5, 1994) reported that each wave of mergers between modern corporations is associated with more specialization and division of labor. In particular, the latest wave of rationalization in the corporate sector has the characteristic that many companies have moved to separate some of their functions from their core business. Services that were once self-provided are now bought from more specialized suppliers. This phenomenon, in the business community variously called deintegration, downsizing, outsourcing, contracting out, and focusing on core competencies, relates to evolution in division of labor. c) The recent boom in franchise networks in the US (see question 1 in chapter 1). d) The development of the market for the automatic toothbrush is a modern phenomenon, one that converts self-sufﬁcient production and consumption of tooth brushing to specialized production of the automatic toothbrush and commercialized consumption. You may analyze the commercialization of the robot. If the production cost of robot has been signiﬁcantly reduced so that each family can afford to use the robot for housekeeping. Then you may ﬁnd that the income share of the commercialized housekeeping will be higher than the income share of food or automobiles. Discuss why Young’s insights into the limitations of the concept of economies of scale were not formalized and taught in mainstream textbooks until recently. Why can’t the Herﬁndahl index of specialization, which is the output share of the main industry of a city or a sector, reﬂect the level of division of labor of the city or sector? According to Chandler (1990), the economic growth of the United States at the end of the nineteenth century and in the early twentieth century was generated by economies of scale and scope. Clarify this statement, using the concept of economies of division of labor that you have learned in this chapter. Specialization has many adverse effects on human life. It can lead to boredom and to narrowing of the mind. It prevents full exploitation of economies of complementarity between different production activities. (For instance, teaching economics generates beneﬁts for economic research.) Nevertheless, we observe that the level of specialization still increases, and companies increasingly use slogans like “We are professional” in their advertisements. Explain this phenomenon. Some economists claim that economies of specialization represent a special case of economies of scale, since the former reﬂect economies of scale for an individual’s labor. Use what you have learned from this chapter to assess this statement.

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EXERCISES 1 Suppose a < 1 in the production functions (4.2). Draw the transformation curve for each individual, two individuals’ aggregate transformation curves for autarky, and for the division of labor in the x–y plane. Use the graphs to deﬁne diseconomies of division of labor. 2 Assume that a = 1 in the production functions (4.2). In the x–y plane, draw the transformation curve for each individual, and the aggregate transformation curves for the respective cases of autarky and division of labor. Use the graphs to deﬁne constant returns to division of labor. 3 Suppose a ≤ 1 for good x and a > 1 for good y in the production functions (4.2). In the x – y plane, draw the transformation curve for each individual and the aggregate transformation curves for the respective cases of autarky and division of labor. Use the graphs to identify the condition under which economies of division of labor exist. 4 Use exercise (3) to demonstrate the following propositions: a) Economies of specialization in producing a good are neither necessary nor sufﬁcient for the existence of economies of division of labor. b) Economies of division of labor cannot exist in the absence of economies of specialization in producing all goods. c) Economies of division of labor cannot exist if the diseconomies of specialization in producing x dominate the economies of specialization in producing y. d) Economies of division of labor must exist if economies of specialization exist in producing all goods. e) Economies of division of labor exist if economies of specialization in producing good y dominate diseconomies of specialization in producing x. In this case, economies of specialization are external economies to the sector producing x. Show that external economies cannot exist if there are no economies of specialization in all sectors. Use your analysis to address the debate between Marshall, Young, and Young’s student Frank Knight. You will recall that Marshall argued that external economies of scale relate to the beneﬁts of division of labor, that Young argued that the concept of economies of scale is a misrepresentation of that beneﬁt, and that Knight argued that economies of scale that are external to all ﬁrms constitute an “empty box.” 5 Assume that three individuals have the production system given in (4.2). Follow the method used in ﬁgure 4.1 to draw aggregate production schedules for autarky, for the case wherein two people are not completely specialized, for the case in which one person is completely specialized, and for the case in which two persons are completely specialized. 6 Consider production function x ay b = L, where a, b > 0, and L is the amount of labor used to produce goods x and y. Use the implicit function theorem to show that for a constant L, dy/dx < 0 and d2y/dx 2 > 0, i.e., the transformation curve is convex to the origin. The production function has no deﬁnition at x = 0 and y = 0. Explain why this production function is not suitable for describing economies of specialization. 7 Explain why the neoclassical Cobb–Douglas production function y = K aLb is not suitable for describing economies of specialization.

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8 Assume that the production functions in (4.2) are x p = Max{lx − a, 0} and y p = Max{ly − b, 0}. Draw an individual’s transformation curve and the twopersons’ aggregate production schedules for autarky and division of labor. Are there economies of division of labor if b = 0? 9 Assume that the production functions in (4.2) are x p = Max{l xα − a, 0} and y p = Max{l yα − b, 0}. Draw an individual’s transformation curve and the two persons’ aggregate production schedules for autarky and division of labor. Analyze the difference between the case with α > 1 and the case with α < 1. Identify the condition for the existence of economies of division of labor. 10 Becker 1981, Rosen 1983: An individual maximizes the difference between beneﬁts and costs of learning. V = w1k1t + w2k2(1 − t) − C(k1, k2) with respect to t, which is the time allocated to produce good 1, and ki, which is the learning and training level in activity i, where C is the total learning and training cost, 1 − t is the amount of time allocated to produce good 2, and wi is a given beneﬁt coefﬁcient for activity i. Solve for two corner solutions with specialization and the interior solution with no specialization. Draw the distinction between technical complementarity (∂2C/∂k1∂k2 > 0) between two learning activities in producing two goods and social complementarity based on economies of specialization. Investigate the conditions under which economies of division of labor exist in the model with both technical and interpersonal complementarity. 11 Assume that the decision problem is the same as in examples 4.2 and 4.3, but that k = 1 and that the government taxes each dollar of goods sold at the rate t, then evenly distributes the tax revenue among the population. Solve for all corner solutions and identify the conditions under which each of them is the optimum decision. Use marginal and inframarginal comparative statics to analyze the effect of the tax. 12 Assume that the production functions in (4.2) of example 4.1 are x + x s = l xa, y + y s = l yb , a ≠ b. Solve for equilibrium and its inframarginal comparative statics. 13 Assume that in exercise 12, k = 1 and the government taxes each dollar of good x that is purchased, then evenly distributes the tax revenue among the buyers of good x. Use the marginal and inframarginal comparative statics to analyze the effect of the tax on demand and supply. Compare your answer to that of exercise 11. 14 Consider the model in example 4.7. Identify the parameter subspace within which improvements in transaction conditions generate concurrence of deteriorated terms of trade of an occupation conﬁguration and an increase in gains that an individual choosing this occupation receives from trade. 15 Lio 1998: Suppose that the utility and the production functions are the same as in (example 4.1). But there is a minimum consumption amount for good x, given by x + kx d ≥ x0, x0 ∈(0, 1 − a). How many conﬁgurations must be considered? Solve for the corner solution for each of them. 16 Suppose that in the equilibrium model in example 4.1, the production functions are x p = lx − a and y p = lx − b, and the utility function is u = (x + kx d )α( y + ky d )1−α where i p is the output level of good i. Solve for the general equilibrium and its inframarginal comparative statics. 17 Suppose that in the equilibrium model in this chapter, the utility function is of the CES type and the time endowment constraint is lx + ly = 1 − c if an individual consumes one good, and is lx + ly = 1 − 2c if an individual consumes two goods. Solve for the general equilibrium and its inframarginal comparative statics.

129

130 P ART I: D EVELOPMENT M ECHANISMS

18

19

20 21

Assume that in example 4.1 the transaction efﬁciency coefﬁcient for good i is ki and 1 > kx > ky > 0. Solve for the general equilibrium and its inframarginal comparative statics. Analyze the implications of the difference in transaction efﬁciency for the equilibrium-relative price. Why is the effect of the difference in transaction efﬁciency different from the effect of the difference in tax rate on the equilibriumrelative price? Chu and Wang, 1998, Ng and Yang, 2000: Suppose that in exercise 16, α = 0.5 and the production function of x is modiﬁed as x p = lx − a − s∑ y p where s is an externality parameter. This speciﬁcation implies that there is a negative externality of production of y on production of x. Suppose that the government taxes sales of good y at the tax rate t, then returns the tax revenue to the buyers of y. Solve for the corner equilibrium for structure D, then solve for an individual’s utility value when she chooses specialization (or autarky) and all other individuals choose D (or A). Then solve for the corner equilibrium in a structure where the population is divided among autarky and specialization in x and y. Find general equilibrium and its inframarginal comparative statics. Show that within a certain parameter space, Pareto improving Pigouvian tax does not exist. Use your answer to justify Coase’s claim that Pigou’s marginal analysis of effects of tax on the distortions caused by externality is misleading and inframarginal analysis is essential for the analysis of the distortions. Work out the algebra for proving proposition 4.2. Suppose that a = b = c in example 4.7, but the respective taste parameters for the three goods are α > β > γ, where α + β + γ = 1. Solve for inframarginal comparative statics of general equilibrium.

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DRIVING FORCE III – ECONOMIES OF SCALE AND TRADING EFFICIENCY

5

5.1 ECONOMIES OF SCALE AND ECONOMIC DEVELOPMENT When Marshall (1890) and other economists tried to formalize classical economics concerning development implications of division of labor, they could not ﬁnd the analytical tools appropriate to well deﬁne division of labor. As discussed in chapter 3, the concept of level of division of labor is analogous to the concept of utility, which can be deﬁned only as a function of several variables. Level of division of labor is deﬁned in chapter 3 as a function of all individuals’ levels of specialization and the diversity of occupation conﬁgurations. The notion of economies of division of labor is even more difﬁcult to deﬁne. Marshall used a one-dimensional variable, the scale of a ﬁrm or a sector, to formalize the classical notion of division of labor. He was aware of the inappropriateness of the concept of economies of scale for representing the notion of economies of division of labor; he proposed a new concept of external economies of scale, and argued that external economies of scale are generated by division of labor in society as a whole rather than by the scale of a ﬁrm or a sector.1 External economies of scale imply that a ﬁrm’s productivity increases as the size of the whole economy or of a sector increases. But according to Allyn Young (1928), Marshall’s concept of external economies of scale is a misrepresentation of the classical concept of economies of division of labor. Since the end of the 1970s there has been a revival of the thinking based on the concept of economies of scale, represented by Dixit and Stiglitz (1977), Ethier (1982), Krugman (1979), Judd (1985), Romer (1986, 1990), Grossman and Helpman (1989, 1990), and Murphy, Shleifer, and Vishny (1989; hereafter designated “MSV”). Some of these works (such as some of Romer’s and Ethier’s models) follow Marshall’s idea about external economies of scale. But most of these works use the concepts of internal economies of scale and monopolistic competition. Internal economies of scale exist if a ﬁrm’s productivity increases as the size of the ﬁrm increases. Although the concept of economies of scale was considered misleading by Young, the research built upon the concept of economies of scale has achieved relative success in explaining many development phenomena, in comparison to conventional development models with constant returns to scale. In the new development models, the trade-off between economies of scale and beneﬁts of a greater variety of goods is used to explain productivity progress in the absence of any exogenous technological changes. A consequence of this trade-off is that an increase in population size or in the size of the economy can enlarge the scope for trading-off economies of scale against the variety of goods in the market, so that both the variety of goods

132 P ART I: D EVELOPMENT M ECHANISMS

and productivity may increase. In particular, Murphy, Shleifer, and Vishny (1989, 1991), Ciccone and Matsuyama (1996), and Matsuyama (1991) use this approach to analyze dual economies and industrialization. Their results, based on general equilibrium models with economies of scale and an endogenous number of goods, are more powerful than labor surplus models, and other general equilibrium models with constant returns to scale, in explaining dual economies, structural changes, and industrialization. Recently, Yang (1994), Krugman and Venables (1995), Fujita and Krugman (1995), Baldwin and Venables (1995), Puga and Venables (1998), and Wong and Yang (1998) have introduced transaction costs into general equilibrium models with economies of scale and endogenous number of goods. They show that the trade-off between economies of scale, economies of complementarity, and transaction costs can be used to explain dual economy, structural changes, industrialization, urbanization, productivity progress, and other development phenomena in the absence of exogenous technical changes. Murphy, Shleifer, and Vishny (1989) have developed general equilibrium models with economies of scale to explore the implications of multiplicity of equilibria for formalizing the ideas on big-push industrialization in the literature of high-development economics. Kelly (1997) and Sachs and Yang (1999) have introduced transaction costs into the MSV model to endogenize the number of modern versus traditional sectors. In this chapter, we study major models of these two types and compare them to conventional development models of structural duality, labor surplus, industrial linkage externality, and balanced versus unbalanced industrialization. This family of new general equilibrium models of economic development will also be compared with models in chapter 4 in connection to empirical evidence. Section 5.2 uses a simpliﬁed version of the Dixit–Stiglitz model to demonstrate basic algebra and illustrate intuition. Section 5.3 uses the Ethier model with transaction costs to analyze structural changes, industrial linkage, and other development phenomena. Section 5.4 uses a version of the MSV model to analyze the implications of multiple equilibria and economies of scale for big-push industrialization. Section 5.5 uses the Sachs–Yang model with transaction costs to study the relationship between evolution in the degree of industrialization and economic development.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n n

n n

What are the differences between economies of scale and network effects of division of labor, and the implications of the differences for studies of economic development? What are the differences among the model of labor surplus with constant returns to scale, the equilibrium models with economies of scale and an endogenous number of goods, and the Smithian models with endogenous network size of division of labor? What are the relationships among circular causation, network effects of industrial linkage, big-push industrialization, and the notion of general equilibrium? What are various scale effects and why are they rejected by empirical observations?

5.2 GENERAL EQUILIBRIUM MODELS OF ECONOMIC DEVELOPMENT WITH TRADE-OFFS BETWEEN ECONOMIES OF SCALE, CONSUMPTION VARIETY, AND TRANSACTION COSTS The Dixit and Stiglitz (DS) model (1977) is a general equilibrium model that endogenizes the number of consumption goods on the basis of the trade-off between economies of scale and consumption variety. The story behind this kind of model runs as follows. Consider an

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Japan

1

2

3

4

x

y

x

y

2

1

(a) Two separate markets

US

x

3

z

4

y

(b) An integrated market

Figure 5.1 Economic development based on economies of scale

economy in which pure consumers prefer diverse consumption, while there are global economies of scale for pure producers (ﬁrms) in the production of each good. With the CES utility function, each good individually is not a necessity, so that the number of consumption goods is endogenized in equilibrium. A larger number of consumption goods, on the one hand, implies a higher level of direct utility because of the preference for diverse consumption; but on the other hand, the larger number may imply a lower level of indirect utility because of the higher prices of goods that are associated with smaller scales of production. The trade-off between economies of scale and consumption variety can be used to endogenize the number of consumption goods. As the size of the economy is increased, the scope for trading-off economies of scale against consumption variety is enlarged, so that the number of goods and per capita real income may increase concurrently. If the increase in the size of the economy is interpreted as the merging of two countries into an integrated market, or as the ad hoc opening of international trade between the two countries, then comparative statics of the neoclassical general equilibrium can be used to explore the implications of international trade for productivity, welfare, and consumption variety. We now use the following graph to illustrate the story. In ﬁgure 5.1 there are two countries: Japan and the US. In each country there are two individuals. Circles 1 and 2 represent two Japanese and circles 3 and 4 represent two Americans. In panel (a), there is no international trade between the two countries, and in each country there are two ﬁrms producing goods x and y, respectively. Each of the two ﬁrms sells its produce to each and every domestic consumer and hires one worker. In panel (b), the two countries have merged to form an integrated market, where a Japanese ﬁrm sells good x to each and every consumer in both countries, an American ﬁrm sells good y to each and every consumer in both countries, and a multinational ﬁrm sells a new good z to each and every consumer in both countries. Firm x hires 4/3 Japanese, ﬁrm y hires 4/3 Americans, and ﬁrm z hires 2/3 Japanese and 2/3 Americans. Hence, the average size of the ﬁrm in panel (b) is larger than in panel (a). This implies that the productivity of each ﬁrm in panel (b) is higher than in panel (a) because of global economies of scale in production. Also, each consumer in panel (b) consumes three goods, while each consumer in panel (a) consumes only two goods. Hence, international trade may increase per capita real income through two possible channels. It may increase the number of consumption goods for each consumer, and it may improve productivity and thereby reduce prices of all goods through the utilization of economies of scale.2 Gains from trade can arise between two ex ante identical countries in the absence of exogenous comparative advantage in technology and in endowments, and in the absence of differences in tastes between them. However, in order to realize those gains from trade, the two countries have to accept the shifting of workers between different sectors, which may cause temporary

134 P ART I: D EVELOPMENT M ECHANISMS

unemployment in the transitional period. For instance, a Japanese who in panel (a) produces good y before international trade is opened up will lose her job as a producer of good y, and will take a new job in producing good z or x after international trade is opened up in panel (b). Symmetrically, an American who produces good x before the opening of international trade will lose her job as a producer of good x, and will take a new job to produce good z or y after the opening of international trade. Suppose the government, or some interest group, does not want to see the emergence of the new sector or the associated reallocation of labor, because they generate temporary unemployment in the transitional period. If the Japanese government implements an interventionist policy to protect the ﬁrm producing good y from bankruptcy caused by international trade, or if an American interest group successfully lobbies Congress to implement a similar policy, then coordination failure in utilizing the gains from international trade will take place. The function of the market, and of a liberalization policy that allows the market to fully play its role, is to avoid such coordination failure. Example 5.1: The Dixit–Stiglitz model with the trade-offs between economies of scale and consumption variety. Consider an economy with M identical consumers. Each of them has the following neoclassical decision problem for consumption: ⎛ n ⎞ Max: u = ⎜ ∑ xiρ ⎟ ⎝ i =1 ⎠

1/ρ

(utility function) (5.1)

n

∑px

s.t.

i i

=1

(budget constraint)

i =1

where pi is the price of good i in terms of labor, xi is the amount of good i that is consumed, n is the number of consumption goods, ρ ∈(0, 1) is the parameter of elasticity of substitution between each pair of consumption goods, and u is utility level. To avoid an integer problem, which may render differentiation impossible, many writers assume that the set of goods is a continuum. If the set of goods is a continuum, all signs for summation should be understood as those for integration. If we take the ﬁrst-order condition for a continuous number of goods as a proxy for the ﬁrst-order condition for the integer programming in the model with goods 1, 2, . . . , m, the result based on our discrete speciﬁcation is equivalent to that based on a continuum of goods. It is assumed that each consumer is endowed with one unit of labor, which is the numeraire. Hence, each consumer’s income from selling one unit of labor is 1, her expenditure on good i n pi xi. Each consumer is a price taker and her decision is pi xi, and her total expenditure is ∑ i=1 variable is xi. It is assumed that the elasticity of substitution 1/(1 − ρ) > 1. It is easy to see that if the quantity of each good consumed is the same, then utility is an increasing function of the number of consumption goods, that is, u = (nx iρ)1/ρ and ∂u/∂n = (1/ρ)n(1−ρ)/ρxi > 0. We need the assumption ρ ∈(0, 1), since for ρ < 0, which implies 1/(1 − ρ) < 1, utility will be a decreasing function of the number of consumption, indicating that individuals do not prefer diverse consumption. If ρ > 1, it can be shown that the ﬁrst-order conditions for the optimum decisions and market clearing conditions will yield a negative number of goods (see equation 5.8). The ﬁrst-order conditions for the consumer’s decision problem are: (∂u/∂xi)/(∂u/∂xj) = pi/pj

and

(5.2a)

n

∑px

i i

i =1

=1

(5.2b)

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(5.2a) is the rule that relative marginal utility equals relative price, which implies the Gossen rule (i.e., the marginal utility of a dollar spent on different goods is the same) as well as the rule that the marginal rate of substitution equals the relative price. Concretely, (5.2a) is: xj p −ρ/(1−ρ) pi xi = p1/(1−ρ) j i Summing up the two sides of the equation with respect to i, and using the budget constraint (5.2b), yields: 1 = ∑ pi xi = p1j/(1−ρ) xj ∑ pi−ρ/(1− ρ) i

i

From this equation, the demand function for good j can then be solved: ⎡ ⎤ xj = 1/ ⎢ p1j/(1− ρ) ∑ p iρ/(ρ −1) ⎥ = 1/np ⎢⎣ ⎥⎦ i

(5.3)

where the second equality is obtained by using the symmetry condition pj = pi for all i, j = 1, 2, . . . , n. This can be expressed as:

ln xj = − [ln pj /(1 − ρ)] − ln ∑ p ρi /(ρ −1) i

where ∑ i p iρ/(ρ−1) includes one pj. Hence, the own price elasticity of demand for good j is: ∂ ln x j /∂ ln pj = − [1/(1− ρ)] − ∂ ln ∑ p ρi /(ρ −1) /∂ ln pj i

⎧ = − [1/(1−ρ)] − ⎨[ρ/(ρ − 1)] p1j /(1− ρ) ⎩

∑p i

ρ /( ρ −1) i

⎫ ⎬ ⎭

Using the symmetry condition pj = pi for all i, j = 1, 2, . . . n again, we obtain the Yang–Heijdra (YH, 1993) formula for the own price elasticity of demand in the DS model: ∂ ln xi/∂ ln pi = −[1/(1 − ρ)] + [ρ/(1 − ρ)n] = −(n − ρ)/(1 − ρ)n.

(5.4)

Dixit–Stiglitz (1977) made an ad hoc assumption that the number of goods is inﬁnitely large, and accordingly ignored the term ρ/(1 − ρ)n, so that their expression for the elasticity is −1/(1 − ρ). Their assumption is not legitimate, since the number of goods in this model is endogenous and is very large only for a certain range of parameter values. The negative effect of international trade on prices cannot be worked out with their formula for the own price elasticity of demand. In exercise 6, you are asked to show that if the production function is homogeneous in the DS model, then the DS formula for own price elasticity of demand entails nonexistence of equilibrium. But if the YH formula is used, a well-deﬁned equilibrium exists for a particular parameter subspace. Next, we consider the pure producers’ decision problems. Because of global increasing returns to scale, only one ﬁrm can survive in the market for a good. If there are two ﬁrms producing the same good, one of them can always increase output to reduce price by utilizing further economies of scale, thereby driving the other ﬁrm out of the market. Therefore, the

136 P ART I: D EVELOPMENT M ECHANISMS

monopolist can manipulate the interaction between quantity and price to choose a proﬁtmaximizing price. Freedom to produce new goods, however, is assumed. This will drive to zero the proﬁt of a marginal ﬁrm that has the lowest proﬁt. Any positive proﬁt of the marginal ﬁrm will invite a potential entrepreneur to set up a new ﬁrm to produce a differentiated good. For a symmetric model, this condition implies zero proﬁt for all ﬁrms. This signiﬁcantly simpliﬁes the algebra and makes the DS model attractive. Assume that the production function of good j is: Xj = (Lj − a)/b, so that the labor cost function of good j is: Lj = bXj + a

(5.5)

The ﬁrst-order condition for the monopolist to maximize proﬁt with respect to output level and price implies that: MR = pj[1 + 1/(∂lnxi/∂lnpi)] = MC = b where MR and MC stand for marginal revenue and marginal cost, respectively. Inserting the expression for the own price elasticity of demand ∂lnxi /∂lnpi, given in (5.4), into the ﬁrst-order condition yields: pj = b(n − ρ)/ρ(n − 1).

(5.6)

The zero-proﬁt condition implies: pj Xj = bXj + a.

(5.7)

The general equilibrium is given by (5.3a), (5.6), (5.7), and the market clearing condition Mx = X, which involve the unknowns p, n, x, X. Here, the subscripts of variables are skipped because of symmetry. Hence, the general equilibrium and its comparative statics are: n = ρ + [M(1 − ρ)/a],

dn/dM > 0,

dn/dt < 0

p = bM/ρ[M − a],

dp/dM < 0,

dp/dt > 0

x = ρ[M − a]/bM[(1 − ρ)M + (1 + t)ρ],

dx/dt < 0

X = Mx,

dX/dt < 0

dX/dM > 0,

u = ρ{[(1 − ρ)M/a] + ρ}

[M − a]/bM,

(1−ρ)/ρ

(5.8)

du/dM > 0.

It can be shown that the equilibrium labor productivity of each good is the reciprocal of the equilibrium price of each good. Comparative statics substantiate the story presented in the ﬁrst part of this section, that is, the equilibrium number of consumption goods, productivity of each good, and per capita real income increase and the price of each good falls as the size of the economy increases. Now, let us compare the DS model with the neoclassical models with constant returns to scale and with the Smithian models in chapter 4. First, the DS model can generate gains from trade even if all countries are ex ante identical, or even if exogenous comparative advantage is

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absent. The gains from trade based on economies of scale are referred to by Grossman and Helpman (1990) as acquired comparative advantage. Hence, Krugman (1979) applies the DS model to explain the Linder pattern of trade, which suggests that trade volume between ex ante similar developed countries is much greater than that between ex ante different developed and less-developed economies. The Linder pattern of trade is inconsistent with the neoclassical trade model with constant returns to scale and with the theory of exogenous comparative advantage, which predicts that trade volume is greater between ex ante different countries than between similar countries. Second, the DS model predicts that an increase in population size has positive effects on economic development because of economies of scale. This prediction is referred to as type I scale effect. Type I scale effect is consistent with the data of the early economic development of the US, Australia, and New Zealand, and with Hong Kong’s data after the Second World War. In contrast, Solow’s neoclassical growth model and other neoclassical models with constant returns to scale predict that an increase in population will have a negative impact on economic growth. This prediction is consistent with the data of many African countries and with the prereform data in China and India. The National Research Council (1986) and Dasgupta (1995) reject the type I scale effect on the grounds of empirical evidence. The model can simultaneously explain the equilibrium number of goods and per capita real income by the size of an economy, and has more explanatory power than many neoclassical models with a ﬁxed number of goods. If we deﬁne the extent of the market as the product of per capita aggregate market demand for all goods and population size, then the DS model has endogenized the extent of the market. Since each pure consumer’s aggregate demand for all goods is determined by the number of goods, the DS model has endogenized the extent of the market by endogenizing the number of goods. Many economists use this feature of the DS model to explain aggregate demand and related macroeconomic phenomena. If we deﬁne the level of division of labor by each individual’s level of specialization, the number of traded goods in society, and the degree of production roundaboutness, then the DS model has endogenized one aspect of division of labor: the number of traded goods. However, it has not endogenized individuals’ levels of specialization and production roundaboutness. Let us examine the implications of the difference between the DS model and the Smithian model. Assume, in ﬁgure 5.1(a), that each of consumers 1 and 2 sells half her labor to each of the two Japanese ﬁrms. Since obviously, this implies that each individual is not specialized, we call this allocation of labor a pattern of nonspecialization. Suppose, alternatively, that each of the two consumers sells all her labor to a ﬁrm. Since now each individual is completely specialized, we call this allocation of labor a pattern of complete specialization. In the general equilibrium of the DS model, the two patterns of labor allocation generate the same values of all endogenous variables (relative prices, output levels, productivity of each good, and consumption of each good by each person), since the two patterns of division of labor generate the same scale of each ﬁrm. In other words, individuals’ levels of specialization in equilibrium are not well-deﬁned, so that individuals’ levels of specialization have no productivity implications. In this kind of model, productivity is determined by the scale of ﬁrms rather than by individuals’ levels of specialization. Hence, the DS model cannot explain individuals’ levels of specialization. As a result, many interesting development phenomena that are explained by the Smithian models, such as evolution in division of labor and specialization and the emergence of the ﬁrm, money, and business cycles, cannot be predicted by the DS model. In the DS model, separate markets, as indicated in ﬁgure 5.1(a), can never exist in equilibrium if transaction conditions are the same between all individuals, because of the positive effect of population size on per capita real income, and because of the fact that each pure consumer will buy all goods that are produced. Hence, the DS model cannot endogenize the degree of market integration. In contrast, Smithian models in examples 7.1 and 7.2 have endogenized the degree

138 P ART I: D EVELOPMENT M ECHANISMS

of market integration and the emergence of international trade from domestic trade. Therefore, the Smithian model is referred to by Smythe (1994) as endogenous trade theory. Moreover, the population size does not play an active and positive role in promoting productivity in a Smithian model, where productivity is determined by the level of division of labor, which is determined by transaction efﬁciency. Hence, high transaction efﬁciency, due to a good legal system, explains productivity progress in Hong Kong, the US, and Australia, where population growth passively provides more scope for evolution in division of labor (i.e., the number of different occupations cannot exceed population size). The low transaction efﬁciency in prereform China and India and in some African countries explains the low per capita real income that coexists with a large population size. In a Smithian model, productivity progress and the emergence of new goods and technology in equilibrium can be achieved by the merging of many separate local communities into an increasingly more integrated network of division of labor, even if the population size is ﬁxed. Hence, the Smithian model does not have a scale effect. Empirical evidence against the DS model is provided by Liu and Yang (2000), who show that productivity increases and the average size of ﬁrms decreases in many countries. In contrast, the DS model predicts that productivity goes up if and only if the average size of ﬁrms increases. This is referred to as type II scale effect. But the DS model may be extended to endogenize the degree of market integration by appropriately specifying a ﬁxed transaction cost in setting up a trade connection or by specifying differences of transaction conditions between international and domestic trade, between countries, or between ﬁrms. Example 6.3 illustrates how this can be done. Ethier extends the DS model to endogenize the number of producer goods and productivity by specifying a tradeoff between economies of scale in producing producer goods and economies of complementarity between the producer goods in raising productivity of the ﬁnal good. This kind of model can be used to explain dual economy and structural changes in economic development. The next section illustrates how this can be achieved.

5.3 THE ETHIER MODEL WITH TRANSACTION COSTS Before you become mired in the algebra and lose your capacity for economic thinking, let us ﬁrst outline the story behind the model. There are two ﬁnal consumption goods in an economy with M identical consumers. One of them is food that is produced by labor, with constant returns to scale technology. The other is a manufactured good that is produced from a composite producer good and labor, with a production function of constant returns to scale. The composite producer good is a CES function of quantities of many producer goods. There are economies of complementarity between the producer goods in raising productivity of the ﬁnal manufactured good. Hence, total factor productivity of the ﬁnal manufactured good is an increasing function of the number of producer goods employed. There are global economies of scale in producing each producer good. The markets for the two ﬁnal goods are competitive, while the market for producer goods is monopolistically competitive. If transaction costs are introduced into the economy, there is a trade-off between economies of scale and transaction costs, in addition to the trade-off between economies of scale and economies of complementarity. As the population size increases, the scope for trading-off one against others among economies of scale, economies of complementarity, and transaction costs is enlarged in the market. Hence, the number of producer goods increases, productivity of producer goods increases, and per capita real income increases. In particular, through the linkage between the ﬁnal manufacturing sector and the intermediate sector, the labor price of the ﬁnal manufactured

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good declines, the total factor productivity of the manufactured good rises, and the relative output level of the manufacturing sector to the agricultural sector increases. Due to the tradeoff between economies of scale and transaction cost, improvements in transaction conditions will generate a decrease in the labor price of the manufactured good and an increase in relative output of the manufacturing and agricultural sectors. The effects of an increase in population size on the general equilibrium productivity and relative output of the industrial and agricultural sectors are similar to development implications of labor surplus in the labor surplus model. However, an exogenous change in technology in the industrial sector and the ad hoc disequilibrium labor price are essential for structural changes in the labor surplus model. In contrast, in the Ethier model, structural changes can take place in the absence of any exogenous technical changes and of disequilibrium labor price. Compared to rough conjecture on the role of linkage between different sectors in economic development, the Ethier model explores the general equilibrium nature of economic linkage between the ﬁnal manufacturing sector and the intermediate sector, as well as the implications of the linkage for economic development and structural changes. In many rough conjectures on the role of industrial linkages in industrialization (see, for instance, Rosenstein-Rodan 1943, Nurkse 1953), demand and supply of a sector depend on production conditions in another sector. The “external effects” of the linkage may be ignored by the market, or cannot be utilized because of coordination failure in a decentralized market. Hence, the government’s industrial policies may promote industrialization and economic development. In the general equilibrium model of this section, we shall show not only that demand and supply of each sector depend on demand and supply of each other sector, but also that prices and quantities are interdependent. In addition, there are inﬁnite feedback loops between sectors, between prices and quantities, and between decisions of all players. The very function of the market is to transmit information about the interdependencies based on industrial linkages. The function of the market is much more powerful than we realize, and much more powerful than the government’s capacity to ﬁgure out the implications of the linkages. This prediction of the Ethier model is different from conventional wisdom related to debates on balanced versus unbalanced industrialization. Some development economists argue that because of interdependencies of different industrial sectors, government policy should promote balanced and big-push industrialization (see Lewis 1955, Nurkse 1953, Rosenstein-Rodan 1943, Scitovsky 1954, Thirwall 1994). Other development economists argue that because of the effects of linkage, a policy to promote unbalanced industrialization should be adopted (see Streeten 1959, Hirschman 1958). If we interpret the increase in productivity and in the number of industrial sectors as industrialization, then the Ethier model shows that the essential conditions for successful industrialization are a large population size in an integrated world market and favorable transaction conditions. These conditions can be provided through liberalization, internalization, and open-door policies. If transaction conditions are unfavorable and the population size in the integrated world market is small, then the equilibrium productivity is low and the number of professional industrial sectors is small, because of the trade-offs between economies of scale, economies of linkage complementarity, and transaction costs. According to this model, many conventional industrial policies that manipulate industrial structure via increasing transaction costs are detrimental to economic development. Example 5.2: The Ethier model with an endogenous number of producer goods and transaction costs. Consider an economy with M identical consumers. A representative consumer’s decision problem is: Max: u = (kz)1−α (ty)α

s.t.

py y + pz z = 1

(5.9)

140 P ART I: D EVELOPMENT M ECHANISMS

where u is a consumer’s utility level, y is the quantity of the agricultural good consumed (such as food), z is the quantity of the manufactured consumption good (such as a car), and k and t are respective transaction efﬁciency coefﬁcients of the agricultural and manufactured goods. Each consumer is endowed with one unit of labor, which is the numeraire. The size of the labor force (which is the population size as well) is M and the price of good i in terms of labor is pi. The demand functions for the two goods are: Y d = My d, y d = α/py,

Z d = Mz d, z d = (1 − α)/pz

(5.10)

where Z d and Y d are respective market demand and z d and y d are respective individual demand for the two goods. A representative ﬁrm of food producers maximizes the following proﬁt subject to a given set of prices of goods and factors and a production function with constant returns to scale: Max: πy = pyY s − L yd ,

s.t.

Y s = AL yd

(5.11)

where Y s is the output level of y, and L yd is the amount of labor allocated to the production of food. The equilibrium conditions in the market for z are: p *y = 1/A

(zero-proﬁt condition for good y)

Y* = Y s = Y d = α AM

(equilibrium quantity of y)

L = αM

(equilibrium quantity of labor employed to produce y)

d y

(5.12)

where Y s is market supply, which is determined by market demand Y d, Y* is the equilibrium quantity of good y, L dy is the equilibrium quantity of labor employed to produce y, and p*y is the equilibrium labor price of good y. A representative car manufacturer maximizes the following proﬁt, subject to a given set of prices of goods and factors and a production function displaying constant returns to scale and economies of complementarity between different producer goods employed to produce cars: β/ρ

n

Max: πz = pz Z − ∑ pi xi − Lz , i =1

s.t.

⎤ ⎡n Z = ⎢∑ (kxi )ρ ⎥ L1z−β ⎥⎦ ⎢⎣ i =1

(5.13)

where k is the transaction efﬁciency coefﬁcient of each producer good, xi can be considered as all kinds of professional machine tools, and the elasticity of substitution 1/(1 − ρ) is assumed to be larger than one, that is, ρ ∈(0, 1). Since the total factor productivity of z increases with the number of specialized machine tools n, this production function displays economies of complementarity between producer goods employed to produce z. The elasticity of substitution increases with ρ and the degree of economies of complementarity between different producer goods inversely relates to the elasticity of substitution. Hence, 1/ρ can be interpreted as the degree of economies of complementarity. For the decision problem with constant returns to scale, only two of the zero-proﬁt condition and the two ﬁrst-order conditions for xi and Lz are independent. We can use the two ﬁrst-order conditions, ∂πz/∂Lz = ∂πz/∂xi = 0, to establish the connection between the quantity of labor demanded and the quantity of x demanded. Lzd = (1 − β)pxnx/β

(5.14)

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T RADING E FFICIENCY 141

where the symmetry of the model is used. Using the zero-proﬁt condition in producing z and (5.14), we can obtain an expression of pz Z in terms of px x: pz Z = px nx/β.

(5.15)

Using the production function of z and (5.14), we can obtain another expression of pz Z pz Z = pz nβ(1−ρ)/ρ(kx)β[(1 − β)px nx/β]1−β.

(5.16)

Let the two expressions be equal. We can then establish a connection between the equilibrium prices of z and x. pz = p xβ/n β(1−ρ)/ρ(1 − β)1−β(kβ)β.

(5.17)

If this condition is not satisﬁed, then the ﬁrm will either not produce z or demand an inﬁnitely great amount of labor, which is incompatible with equilibrium due to limited supply of labor. Using (5.15) and the demand function for y in (5.10), we have: px nx = β(1 − α)M

(5.18)

where M is the population size. The ﬁrm selling producer good i maximizes the following proﬁt with respect to the price and quantity of good i, subject to a given production function with global economies of scale: Max: πix = pi Xi − Lix,

s.t.

Xi = (Lix − a)/b,

or

Lix = a + bXi

(5.19)

where Xi is the quantity of good i supplied by the monopolist and Lix is the amount of labor hired by the ﬁrm producing good i. All decision problems for ﬁrms selling other n − 1 producer goods are symmetric to (5.19). Due to the complete symmetry of the model, we will skip subscript i when no confusion is caused. The market for producer goods is monopolistically competitive. Using Yang–Heijdra’s formula in (5.4), the own price elasticity of the demand for producer good i is: E ≡ ∂ log xi /∂ log pi = −(n − ρ)/(1 − ρ)n. The ﬁrst-order condition MR = MC for a producer of a producer good yields MR = px[1 + (1/E )] = b = MC, or: px = (n − ρ)b/(n − 1)ρ.

(5.20)

This, together with the zero-proﬁt condition AC = [(a/X ) + b] = px, yields: nX = (n − 1)ρa/b(1 − ρ).

(5.21)

Letting x in (5.18) equal X in (5.21), the two equations yield: px = β(1 − α)(1 − ρ)bM/a(n − 1)ρ.

(5.22)

142 P ART I: D EVELOPMENT M ECHANISMS

(5.20) and (5.22) imply: n = ρ + β(1 − α)(1 − ρ)M/a.

(5.23)

Inserting (5.23) back into (5.22) yields the equilibrium value of px. Plugging this value into (5.17) yields the equilibrium labor price of z. Differentiating this expression of the equilibrium price of z with respect k and M, respectively, we have: dpz/dM < 0

and

dpz/dk < 0.

(5.24)

We are interested in the effects of changes in the population size M and transaction efﬁciency k on the number of producer goods n, prices of goods, relative size of the manufacturing and agricultural sectors, productivity, and per capita real income. Let us use (5.10) to (5.24) to work out the equilibrium expressions of the variables: Rzy = Y/Z = (1 − α)/αApz,

n = ρ + β(1 − α)(1 − ρ)bM/a, TFPz = nβ/ρ,

LPy = A,

px = β(1 − α)bM/ρ[bMβ(1 − ρ)(1 − α) − a],

LPx = X/(a + bX) = ρ(n − 1)/b(n − ρ) = ρ[β(1 − ρ)(1 − α)M − a]/β(1 − α)bM,

(5.25)

u = (αtA)α[k(1 − α)/p1−α z ] where TFPz is the total factor productivity of good z, LPj is the labor productivity of producer good j, Rzy is relative output level of ﬁnal manufactured goods and agricultural good, and u is equilibrium per capita real income (i.e., utility). Comparative statics of the equilibrium are summarized as follows: dpx/dM < 0, dpz/dM < 0,

(5.26a) dpz/dk < 0,

(5.26b)

dpy/dM = 0,

(5.26c)

dn/dM > 0,

(5.26d)

dTFPz /dM = (dTFPz /dn)(dn/dM) > 0, dRzy /dM = (dRzy/dpz)(dpz/dM) > 0, du/dM = (du/dpz)(dpz/dM) > 0,

dLPx /dM > 0,

(5.26e)

dRzy /dk = (dRzy /dpz)(dpz/dk) > 0,

(5.26f)

du/dk = (∂u/∂pz)(dpz/dk) + (∂u/∂k) > 0,

(5.26g)

where (5.26d) is used to derive (5.26e), and (5.26b) is from (5.24) and is used to derive (5.26f) and (5.26g). (5.26) yields the following proposition. Proposition 5.1: The equilibrium labor prices of the industrial goods (z and x) decrease, the equilibrium total factor productivity of the manufactured good and labor productivity of producer goods increase, the equilibrium relative output level of the industrial and agricultural sectors increases, and the equilibrium level of per capita real income increases as the population size increases. The labor price of the manufactured good decreases, and relative output level of the industrial and agricultural sectors and per capita real income increase as transaction efﬁciency of industrial goods is improved.

C HAPTER 5: E CONOMIES

x1

x2 x1

y y y

x2

x3

S CALE

AND

T RADING E FFICIENCY 143

x1

x2

x3

x4

x2

z z y

x1

OF

y z

(a) n = 2

z

z

y

z (b) n = 3

y

z (c) n = 4

Figure 5.2 Structural changes, industrialization, and economic development in the Ethier model

If we interpret the increase in the number of producer goods and related productivity progress and emergence of new goods as industrialization, the model is more powerful than conventional development models in explaining economic development, industrialization, and related structural changes. It can predict the following concurrent phenomena of economic development as transaction conditions are improved or as the population size in the integrated world market increases. Productivity of the ﬁnal manufactured goods and intermediate goods increases, the number of producer goods increases as new producer goods emerge, relative output of the industrial and agricultural sectors increases, relative price of the industrial and agricultural goods decreases, and per capita real income increases. According to this model, the best policy to promote industrialization and economic development is to pursue liberalization, internalization, and openness, which improve transaction conditions, reduce trade barriers, and increase the population size in the integrated world market. The topological properties of the linkage network in the Ethier model cannot be appreciated from standard graphs of demand and supply curves. Hence, we use ﬁgure 5.2 to highlight economic development and structural changes predicted by that model. In ﬁgure 5.2, each circle with xi represents workers producing a producer good, a circle with z represents farmers producing the agricultural good, a circle with y represents workers producing the ﬁnal manufactured good, thin lines represent goods ﬂows, and thick lines represent the path of structural change in economic development caused by an increase in population size in the integrated world market or by improvements in transaction conditions. From the graphs and the speciﬁcation of the model, it is clear that the whole economy is always integrated and each individual’s level of specialization is not endogenized. This model cannot explain the following development phenomena. From (5.12), (5.15), and (5.18), it can be shown that the income shares of the ﬁnal manufacturing sector, the intermediate sector, and agricultural sector in terms of value of labor are (1 − α)(1 − β), (1 − α)β, and α, respectively. They are independent of transaction condition, population size, and production conditions. Hence, the process of transferring labor from the agricultural sector to the industrial sector as an aspect of industrialization cannot be predicted by the model in the absence of changes of relative tastes. Note that relative physical output Rzy in (5.25) and (5.26) is different from relative value and relative employment. The former can be explained by transaction conditions and population size, but the latter does not change in the absence of exogenous changes in relative tastes in the model. More importantly, the equilibrium degree of market integration, individuals’ levels of specialization, and the degree of commercialization never change in this model. Similar to the DS model, this model generates type I scale effect that is rejected by empirical evidence. Casual observations indicate that there are increasing returns to specialization and division of labor in the agricultural sector. The level of division of labor in the agricultural sector evolves over time, although this evolution is slower than in the industrial sector. It is ad hoc to assume that

144 P ART I: D EVELOPMENT M ECHANISMS

agricultural production does not have increasing returns and cannot use roundabout productive machines and tractors. Hence, the model in this section does not provide a convincing description of a mechanism for economic development. It has a higher degree of endogenization than do the conventional development models, but it cannot formalize Smith’s conjecture about the intimate relationship between an increase in income share of the industrial sector and evolution of division of labor. According to Smith, this increase is not caused by relative taste change or by exogenous technical changes. Rather, it is caused by a faster evolution of division of labor in the industrial sector, which has lower transaction costs and seasonal coordination costs than does the agricultural sector. We will formalize this conjecture in chapter 12.

5.4 THE MURPHY–SHLEIFER–VISHNY (MSV) MODEL OF BIG-PUSH INDUSTRIALIZATION Murphy, Shleifer, and Vishny (1989) are among the economists who ﬁrst realized the implications of the equilibrium model with global economies of scale for exploring the coordination problem in industrialization process pertinent to the work of Rosenstein-Rodan (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), and others. Their model of big-push industrialization has two distinct features: (a) Each good can be produced using either a cottage technology with constant returns to scale or a modern technology with a ﬁxed cost that generates global economies of scale. This implies that the price of any good is determined by the zero-proﬁt condition for the cottage ﬁrm, so that prices cannot transmit information about modern ﬁrms’ production conditions to consumers. This price misinformation may generate distortions. (b) All ﬁrms choosing modern technology make a decision on entry into production, given other modern ﬁrms’ entry decisions. Two equilibria may coexist. In one of them, all modern ﬁrms are active, so that their proﬁt creates income for owners who can sustain the market for goods produced by all modern ﬁrms. In the other, all modern ﬁrms are inactive, so that income from zero proﬁt cannot support a sufﬁciently large market for any good produced by a single modern ﬁrm. Hence, staying out of the market is the optimum decision for each modern ﬁrm. In other words, the expectation of others’ decisions is self-fulﬁlled. Example 5.3: The Murphy–Shleifer–Vishny model of big-push industrialization. There is a continuum of goods with mass 1. Two types of production functions are available to any ﬁrm in producing each good. Xj = Lj is a traditional technology in producing good j. Xj = (Lj − F)/b is a modern technology in producing good j, where Xj is the output level and Lj is the amount of labor employed in producing good j. F is a ﬁxed production cost and b is a variable labor cost in producing a good. A worker in a cottage ﬁrm has the decision problem: Max: uc = exp

1

ln x(q)dq] 0

1

subject to the budget constraint

p(q)x(q)dq = yc = (Π/L) + wc ,

0

where each consumer is endowed with one unit of labor, yc is a cottage worker’s income, and wc is her wage rate. Assume that the cottage worker’s labor is the numeraire, so that wc = 1. Π is the total dividend, which equals the total proﬁt of n modern ﬁrms. It is assumed that ownership of ﬁrms is equally distributed among the population. Here, n ∈[0, 1] and Π = nπ, where π is each active modern ﬁrm’s proﬁt. The population size is assumed to be L. The decision problem for a worker in a modern ﬁrm is:

C HAPTER 5: E CONOMIES

⎡ Max: um = exp ⎢ ⎢ ⎣

1

0

OF

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T RADING E FFICIENCY 145

⎤ ln x(q)dq⎥ − v, ⎥ ⎦

1

subject to the budget constraint

p(q)x(q)dq = ym = (Π/L) + w,

0

where ym is a modern worker’s income and w is her wage rate relative to a cottage worker’s wage rate, and v is a utility loss when one works in the modern sector. The two utility maximization problems generate indirect utility functions for the two types of workers. Let the indirect utility functions be equal. We can then obtain equation (6) in MSV (1989a, p. 1011). Hence, we have: w = 1 + v,

yc = (Π/L) + 1,

ym = (Π/L) + w.

Let the amount of labor allocated to a modern ﬁrm be Lm. The amount of labor allocated to cottage production is then Lc = L − nLm, where L is total labor supply or population size. The demand function for each good is: x = y/p = y = Lc yc + nLm ym. Because of constant returns to scale for a cottage ﬁrm, and free entry for any cottage ﬁrm into the production of any good, an active cottage ﬁrm receives zero proﬁt, and the price of any good in terms of a cottage worker’s wage rate is p = 1. A modern ﬁrm maximizes: π = px − wLm = y(α − 1 − v) − F(1 + v) = (Lm − F)(α − 1 − v) − F(1 + v), where p = 1, x = α(Lm − F) is the production function, x = y is aggregate demand for the good produced by a modern ﬁrm, w = 1 + v, and y is aggregate income. This is equation (6) in MSV (1989a, p. 1012). To see the feedback loop between proﬁt, income, demand, and production, note that y = Lc yc+ nLm ym = Lc[(πn/L) + 1] + nLm[(πn/L) + w] = L + πn + nLmv. This implies that income depends on proﬁt, while the above expression of proﬁt suggests that proﬁt depends on demand, which is in turn determined by income. The following features of the MSV model differentiate it from other equilibrium models with global economies of scale and monopolistic competition. In the MSV model, global economies of scale in a modern sector imply that each active modern ﬁrm is a monopolist. But this monopolist takes the price of its produce as given because of the existence of a competitive fringe of ﬁrms. In the MSV model, there are inﬁnite equilibria within a certain parameter subspace. If all other modern ﬁrms choose not to produce, a modern ﬁrm’s optimum decision is not to produce. Hence, no industrialization is an equilibrium. If all other modern ﬁrms choose to operate, a modern ﬁrm’s optimum decision is to operate. This is another equilibrium of complete industrialization. Finally there is a zero-proﬁt equilibrium in which a measure of modern ﬁrms n ∈ (0, 1) produce positive quantities of their goods. Since which ﬁrms produce and which do not in any of this kind of zero-proﬁt equilibria is indeterminate and the number of ﬁrms is a continuum, there are inﬁnite equilibria. We now consider the three types of equilibria one by one. Suppose that Lm = 0 and n = 0 (i.e., no industrialization), so that each consumer receives one unit of income and y = L. Hence, proﬁt is negative if and only if: L < Fα(1 + v)/(α − 1 − v).

(5.27)

146 P ART I: D EVELOPMENT M ECHANISMS

This implies that if (5.27) holds, any individual modern ﬁrm that unilaterally industrializes receives negative proﬁt, provided all other modern ﬁrms are not active. Hence, the equilibrium is n = 0 (no industrialization) if (5.27) holds. If all modern ﬁrms produce, then nLm = L, Lc = 0, n = 1, and the proﬁt becomes: π = px − wLm = α(L − F) − L(1 + v) which is positive, if and only if L > Fα/(α − 1 − v). This implies that for n = 1 (i.e., complete industrialization), any individual modern ﬁrm’s proﬁt is positive if L > Fα/(α − 1 − v). But there is no more room for further industrialization, because the upper bound of n is 1. Therefore, for L ∈(Fα/(α − 1 − v), Fα(1 + v)/(α − 1 − v)), there are at least two equilibria. One of them is n = 0 and π = 0, and the other is n = 1 and π > 0. Since the equilibrium prices of all goods are the same between the two equilibria, but per capita income is higher in complete industrialization than in the equilibrium with nonindustrialization, it can be shown that for L ∈(Fα/(α − 1 − v), Fα(1 + v)/(α − 1 − v)), the equilibrium with n = 1 is Pareto superior to the equilibrium with n = 0. Indeed, there are many other equilibria that generate zero proﬁt for all ﬁrms. Letting the proﬁt equal 0 yields: Lm = Fα/(α − 1 − v).

(5.28)

Using the labor market clearing condition Lc + nLm = L, we can ﬁnd: Lc = [(α − 1 − v)L − Fnα]/(α − 1 − v).

(5.29)

Inserting Lm, given by (5.28), into the production function for a modern ﬁrm x = α(Lm − F) yields the quantity supplied by the modern ﬁrm. Inserting (5.28) and (5.29) into the demand function for a good, x = y = Lc yc + nLm ym, we can get the quantity demanded, where yc = (Π/L) + 1 = 1 and ym = (Π/L) + (1 + v) = 1 + v. Letting demand equal supply, we can ﬁnd the zeroproﬁt equilibrium: n = [(1 + v)/v] − [(α − 1 − v)L/vFα], which is between 0 and 1 if L ∈(Fα/(α − 1 − v), Fα(1 + v)/(α − 1 − v)). The zero-proﬁt equilibrium generates the same welfare as in the equilibrium of non-industrialization, since the cottage worker receives the same utility in the two equilibria and utility is equalized between the two types of workers in the zero-proﬁt equilibrium. The existence of the multiple equilibria can be used to tell the story of big-push industrialization. Murphy, Shleifer, and Vishny suggest that if the government coordinates simultaneous investment in all modern sectors, the development trap (i.e., bad equilibrium) can be avoided. This model does not suggest the necessity of government intervention. It implies that the theory cannot predict which equilibrium will occur. If the good equilibrium occurs, government intervention is not needed. It cannot explain why the bad equilibrium has occurred in some African countries while the good one occurred in Britain, which reduced government regulations in the nineteenth century. The possibility for a Pareto inefﬁcient equilibrium to occur is due to the misinformation of price signals in this model. The equilibrium price is determined by the zero-proﬁt condition of cottage ﬁrms, so that it cannot transmit information on the production conditions of modern ﬁrms to consumers. Hence, consumers may allocate too much of their income to buy goods produced by cottage ﬁrms. If the population size is large enough to overcome the misinformation or if L > Fα(1 + v)/ (α − 1 − v), then government intervention is not needed, since unique good equilibrium is n = 1 for that case. As population size increases from a low level to reach the threshold value Fα/(α − 1 − v), the equilibrium degree of industrialization may discontinuously jump from n = 0

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to n = 1 (i.e., big-push industrialization). Consider the parameter subspace L ∈(Fα/(α − 1 − v), Fα(1 + v)/(α − 1 − v)), within which there are multiple equilibria. This kind of multiple equilibria and associated inefﬁciencies are substantially different from the coordination problems in the prisoners’ dilemma or other models with interest conﬂicts between decision makers. (See chapters 3 and 9 for models with interest conﬂicts that generate endogenous transaction costs.) Here, there is no interest conﬂict between self-interested decisions. Nobody beneﬁts from a bad equilibrium. Nobody suffers, and all consumers and modern ﬁrms gain, from a good equilibrium. Hence, a simple talk between entrepreneurs in an industrial association is enough to sort out the coordination problem. And hence, the government’s job is to ensure free association, so that such talk can spontaneously occur. There are many other ways to avoid multiplicity of equilibria. If a modern ﬁrm can differentiate its produce from that produced by a cottage ﬁrm, the misinformation of price signals can be avoided, so that multiplicity of equilibria may also be avoided. Second, the number of active modern sectors is not endogenized in the MSV model. If that number is endogenized by specifying that the trade-off is between economies of scale and transaction costs, multiplicity of equilibrium may be avoided. Murphy, Shleifer, and Vishny (1989a, p. 1003) suggest that transaction cost may be a cause of the development trap. Kelly introduces transaction costs into the MSV model and uses the zero-proﬁt condition to endogenize the number of active modern sectors and the degree of market integration. But because of the zero-proﬁt condition, consumers cannot obtain information from the feedback loop between positive dividend earnings and economies of scale. Hence, consumers’ utility will not increase as the number of active modern sectors increases. In other words, beneﬁts from industrialization are completely eaten up by transaction costs. Sachs and Yang (1999) have devised a method to specify the zero-proﬁt condition for the marginal modern ﬁrm and to keep positive proﬁts for other active modern ﬁrms. This can endogenize the number of active modern sectors, while keeping the original ﬂavor of the feedback loop between dividend earnings and economies of scale which can be exploited in the MSV model.

5.5 THE SACHS AND YANG MODEL WITH ECONOMIES OF SCALE, ENDOGENOUS DEGREE OF INDUSTRIALIZATION, AND TRANSACTION COSTS Example 5.4: The Sachs and Yang Model (1999). Following MSV, we assume that the set of consumption goods produced by the industrial sector is a continuum with mass M. Each of L consumer-worker-owners has the same CES utility function. Their decision problem is:

⎡ Max: u = ⎢ ⎢ ⎣

m

0

⎤ x( j )ρ dj ⎥ 1/ρ, s.t. ⎥ ⎦

m

p( j )x( j )dj = I = (π + w)

0

where j ∈[0, m] is an industrial good, x( j) is the quantity of good j consumed, and p( j) is the price of good j. Each consumer endowed with one unit of labor has income I, which consists of dividend earning π and wage income w. Labor is assumed to be the numeraire, so that w = 1. Ownership of all ﬁrms is equally shared by all consumers. As in the MSV model, p( j) = 1 for all j in equilibrium. Hence, the optimum quantity demanded of good j is the same for all j. Using the symmetry, the solution to the consumer’s decision problem can be found as follows: x = I/m.

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The total market demand is: X d = IL/m = (Π + L)/m,

Π = πL,

(5.30)

where Π is total dividend earning, which is equal to total proﬁt. We now consider the production of x. For each industrial good, there are two available technologies. The modern one exhibits economies of scale, and the traditional one displays constant returns to scale. Because of the existence of the traditional technology, the labor prices of all industrial goods are always 1, so that the quantity demanded is the same for all industrial goods. The production function of the modern sector producing good j is: xj = (Lj − Fj)/b,

F0 = δ,

Fj = γ j > δ for j ∈(0, m)

(5.31)

where xj is the quantity supplied, Lj is the amount of labor allocated to the production of the industrial good, and Fj is the ﬁxed production cost of good j. We assume that the ﬁxed cost differs across modern sectors and that the industrial goods are indexed according to their ﬁxed costs. Industrial good 0 has the smallest ﬁxed cost δ, which is a very small positive number, industrial good m has the largest ﬁxed cost γm, and for j ∈(0, m), Fj = γ j ∈(δ, γm). Here, γ can be considered as a general production condition parameter. As γ decreases, the ﬁxed costs for any modern sector j decrease. A large value of Fj implies that the modern sector j needs a high investment in ﬁxed costs before a positive output can be produced. Hence, index j can be considered as an index of capital intensity of the modern sectors. We assume further that there is a variable transaction cost for each modern ﬁrm. The transaction condition differs across countries. The transaction cost incurred by a modern ﬁrm in country i is: Ci = ci xj ,

c1 = s,

ci = μi > s for i = 2, 3, . . . , M,

(5.32)

where i = 1, 2, . . . ; M is an index of countries; s, a very small positive number, is the transaction cost coefﬁcient for country 1; and xj is the output level of modern sector j, which is the same in any country and in any sector, as we have shown. The speciﬁcation implies that two factors determine the transaction cost coefﬁcient: a general transaction condition μ, and a country-speciﬁc transaction condition represented by index i. For a larger i, the transaction cost coefﬁcient ci is larger. A country’s geographical condition and institutional and cultural tradition determine its ranking index i. For any given i, the transaction cost coefﬁcient ci decreases as μ decreases. A decrease in μ can be caused by worldwide changes in transportation technology or institutions. We may consider country 1 as the most developed country and country M as the most underdeveloped country. The proﬁt of ﬁrm j in country i is: πij = xj − Lj − cixj = (1 − μi − b)xj − γ j

(5.33)

where xj = X d/(1 − ci) is determined by the market clearing condition and demand function given in (5.30). Total dividend earning is equal to total proﬁt of n active modern ﬁrms: n

Π=

π dj ij

(5.34)

0

where n ∈(0, m) is endogenously determined. Plugging this expression for total dividend earning into (5.30), total market demand for the good produced by modern ﬁrm j can be found as:

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xj = (Π + L)/m

(5.35)

where the number of all industrial goods is m, and the number of active traditional sectors is m − n. (5.33) to (5.35) nicely capture the feedback loop between income, demand, and production conditions. They also capture the idea of big-push industrialization. If the transaction cost is 0, then as more modern ﬁrms operate (i.e., n increases), dividend earning and income increase and demand increases, which makes more modern ﬁrms proﬁtable. Hence, as population size reaches a threshold level, the equilibrium number of modern sectors, n, jumps from 0 to its upper bound m. But in our model, transaction costs counteract the positive feedback between the extent of the market and economies of scale that can be exploited, so that industrialization may occur gradually as the transaction conditions are improved. Inserting (5.35) into (5.33), then inserting the resulting expression into (5.34), we can conduct integration and then express total income Π + L as a function of n: Π + L = (L − 0.5γn2 )m/[m − αn(1 − b − μi )]

(5.36)

where L − 0.5γ n2 > 0 and m − αn(1 − b − μi)] > 0 are required by positive income. We now consider the zero-proﬁt condition for the most capital-intensive active modern sector n. Letting j equal n in (5.33) and πn = 0, we get the zero-proﬁt condition, πn = (1 − b − μi)xj − γn = 0. Inserting the demand function, given in (5.35), into the zero-proﬁt condition for the marginal active modern ﬁrm generates another expression of Π + L: Π + L = γmn/(1 − b − μi)

(5.37)

where 1 − b − μi > 0 is required by positive income. (5.36) and (5.37) together generate the following equation, which gives the equilibrium number of active modern ﬁrms n as a function of parameters γ, μ, L, b, i. f (n, α, γ, μ, L, b, i ) = An2 − bn + D = 0

(5.38)

where A ≡ 0.5αγ [1 − b/(1 − μi )], B ≡ γm, D ≡ αL[1 − b/(1 − μi)] are positive. The graph of this quadratic equation of n in the ﬁrst and fourth quadrants of the n–f coordinates is a convex curve cutting the vertical axis above the horizontal axis, since f (0) = D > 0, f ′(0) = −B < 0, f ″(n) = 2A > 0. The unique minimum point n = B/2A > 0 of this curve is given by f ′(n) = 0. Hence, this curve may have two cutting points on the right half horizontal axis, which deﬁnes two equilibria, given by f (n*) = 0. The two solutions of f (n) = 0 are called n1 and n2, respectively, with n2 > n1. Hence, we can see that f ′(n1) < 0 and f ′(n2) > 0 for a convex curve with the unique minimum point that is below the horizontal axis. But we can show that for a positive income, ∂f/∂n = (α/n)[1 − b/(1 − μi )](0.5γn2 − L) < 0 must hold, since positive income in (5.36) requires 1 − b/(1 − μi) > 0 and 0.5γn2 − L < 0. This implies that n2 cannot be an equilibrium. We have then established the claim that there is only one equilibrium in this model. Differentiating (5.38) and using the implicit function theorem, we can identify the comparative statics of the equilibrium number of active modern ﬁrms: dn/dL = −(∂f/∂L)/(∂f/∂n) > 0,

dn/dμ = −(∂f/∂μ)/(∂f/∂n) < 0,

dn/db = −(∂f/∂b)/(∂f/∂n) < 0,

dn/di = −(∂f/∂i)/(∂f/∂n) < 0

(5.39)

where ∂f/∂n = (α/n)[1 − b/(1 − μi)](0.5γn2 − L) < 0 and ∂f/∂γ < 0 if (5.38) holds, ∂f/∂b, df/di, ∂f/∂μ < 0, ∂f/∂L > 0. (5.39) implies that there is substitution between transaction conditions and population size in promoting industrialization. For a given μ, a larger population size

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generates a higher degree of industrialization. For a given L, better general transaction conditions generate a higher degree of industrialization. dn/di < 0 implies that the degree of industrialization is lower for a country with the larger transaction cost coefﬁcient, which implies a larger i. This implies that a large country may have a low degree of industrialization if its transaction conditions are very bad. The general equilibrium in country i is summarized as follows: px = 1,

X d = α(Π + L)/m, n

Lx =

{[bα(Π + L)/(1 − c)m] + γ j}dj = [bα(Π + L)n/(1 − c)m] + 0.5γ n

2

0

R ≡ Lx/L,

α(1−ρ)/ρ

u=m

α

(5.40)

α [θ(1 − α)] [(Π/L) + 1], 1−α

(Π/L) + 1 = γmn(1 − μi)/α(1 − b − μi )L, and n is given by (5.38) where u is per capita real income (i.e., equilibrium utility level), (Π/L) + 1 is per capita income in terms of labor, Lx is the amount of labor allocated to all active modern ﬁrms, and R ≡ Lx /L is the income share of the modern sector. Differentiating u in (5.40) and using (5.38) and (5.39), it can be shown that: du/dL > 0,

and

du/dμ < 0,

dn/dL > 0,

dn/dμ < 0,

d(m − n)/dL = −dn/dL < 0,

dR/dL > 0,

dR/dμ < 0,

dn/db < 0, d(m − n)/dμ = −dn/dμ > 0.

It is straightforward that the number of active traditional sectors m − n decreases as the population size increases and/or as transaction conditions are improved. Hence, the duality of economic structure is endogenized. Comparative statics can be summarized in the following proposition. Proposition 5.2: As population size increases and/or as general transaction conditions are improved, the equilibrium number of active modern sectors, the degree of capital intensity of active modern ﬁrms, productivity, and per capita real income increase. For a given general transaction condition and population size, the country with the better country-speciﬁc transaction condition has a higher degree of industrialization than do other countries. Suppose general transaction conditions are very bad in the initial time. Then no modern ﬁrm operates in any country. As time goes by, general transaction conditions are improved, so that some modern ﬁrms operate in the country with the smallest transaction cost coefﬁcient c1 = s. But other countries are not industrialized. As general transaction conditions are further improved, those countries with a slightly larger transaction cost coefﬁcient start industrializing, and the number of active modern ﬁrms in each of the industrializing countries increases. As general transaction conditions are further improved, those countries with the worse transaction conditions are eventually industrialized. This process goes on until all countries and all sectors in each country are industrialized. In this model, not only each modern ﬁrm’s decision to be active depends on the number of active modern ﬁrms, but the equilibrium number of active modern ﬁrms is also determined by such decisions. The general equilibrium mechanism simultaneously determines the interdependent variables. Sachs and Yang (1999) have extended this model to the case with many countries. They have shown that not only each country’s decision to participate in international trade is dependent on the network size of international trade and degree of industrialization

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in this network, but also that the network size is determined by all countries’ decisions of participation in the network. Kelly (1997) speciﬁes the time dimension and introduces uncertainty to the transaction condition for setting up a trade connection. His model has endogenized the evolution of the degree of market integration. But this kind of model generates the scale effect. It predicts that productivity goes up if and only if the average size of the ﬁrm increases. Empirical evidence in Liu and Yang (2000) rejects the type II scale effect. Also, the National Research Council (1986) and Dasgupta (1995) reject the type I scale effect predicted by this model. As Krugman (1995, p. 21) noted, this kind of model cannot explain the transfer of beneﬁt of economies of scale between sectors through price mechanism and industrial linkages, since prices of all goods are always constant. Although empirical evidence has rejected scale effects predicted by the models in this chapter, there is a lot of empirical evidence that conﬁrms the positive effects of transaction efﬁciency on economic development and structural changes. This prediction is veriﬁed by historical evidence documented in North (1958) and North and Weingast (1989), and by empirical evidence provided in Barro (1997), Easton and Walker (1997), Frye and Shleifer (1997), Gallup and Sachs (1998), and Sachs and Warner (1995a, 1997). North shows that the continuous fall of ocean freight rates signiﬁcantly contributed to early economic development in Europe. He and Weingast show that it was the institution (i.e., a constitutional monarch and parliamentary democracy) established after the English Glorious Revolution (1688) that ensured the credible commitment of the British government to the constitutional order and that signiﬁcantly reduced endogenous transaction costs caused by rent-seeking, corruption, and state opportunism. Hence, economic development could take off in the UK in the eighteenth and nineteenth centuries. Barro uses a data set of 100 countries in the period 1965–90 to establish the positive effect of an index of rule of law, which affects transaction conditions on growth rates of per capita real GDP. Easton and Walker use cross-country data to show that growth performance is positively affected by an index of economic freedom. Frye and Shleifer use survey data from Poland and Russia to establish a negative correlation between growth performance and government violation of private property rights. Gallup and Sachs use cross-country data to show that the geographical conditions that affect the transportation efﬁciency of a country have a very signiﬁcant impact on per capita income. Sachs and Warner use a data set of 83 countries in the period 1965–90 to establish a positive correlation between growth performance and indices of openness and quality of institutions that affect transaction conditions. Krugman (1995) argues that the ideas about the external effects of industrial linkage, circular causation, and big-push industrialization should be formalized by models with economies of scale. The general equilibrium models with economies of scale in this chapter have successfully captured the general equilibrium ﬂavor of the ideas. But they are not so successful in standing the empirical test because of their emphasis on economies of scale.

Key Terms and Review • Relationships between circular causation, big-push industrialization, network effects of industrial linkages, the notion of general equilibrium • High-development economics and different ways to formalize it • Why various scale effects are rejected by empirical evidences • Differences between the models of labor surplus, the equilibrium models with economies of scale, and the Smithian models of division of labor • Differences between the DS models of monopolistic competition and the MSV models of economies of scale

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Further Reading Early ideas on big-push industrialization, balanced versus unbalanced industrialization, linkage externality: Rosenstein-Rodan (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), Myrdal (1957), Hirschman (1958), Sheahan (1958), Sutcliffe (1964), Streetern (1956), Krugman (1992, 1995); Dual structure: Ranis (1988), Lewis (1955), Fei and Ranis (1964); Formal general equilibrium models of structural changes and dual economy with economies of scale: Ciccone and Matsuyama (1996), Krugman and Venables (1995), Baldwin and Venables (1995), Puga and Venables (1998), Gans (1998), Matsuyama (1991), Yang (1994), Weitzman (1994), Wong and Yang (1994, 1998), Yang and Heijdra (1993), Dixit and Stiglitz (1977), Ethier (1982), Krugman (1979, 1980, 1981, 1995), Murphy, Shleifer, and Vishny (1989), Kelly (1997), Sachs and Yang (1999); Talking to solve coordination problems: Matsui (1991), Bhaskar (1995), Blume, Kim, and Sobel (1993), Kim and Sobel (1995), Mailath (1998); Empirical evidence against scale effects: Liu and Yang (2000), National Research Council (1986), Dasgupta (1995); Empirical evidence for the positive relationship between development performance and transaction efﬁciency: Gallup and Sachs (1998), Sachs and Warner (1995, 1997), North (1958), North and Weingast (1989), Barro (1997), Easton and Walker (1997), Frye and Shleifer (1997).

QUESTIONS 1 To what extent can the models in this chapter formalize the Smith theorem, which states that the extent of the market is determined by transportation efﬁciency and that the division of labor is limited by the extent of the market? 2 Discuss the differences between the development implications of transaction costs in the Ricardian model and the Smithian model and that in the models in this chapter. 3 According to one line of argument about infant industry (see, for instance, Scitovsky, 1954), if there are economies of scale, externalities of linkage, and learning by doing, a tariff to protect the infant sector from international competition will improve social welfare and speed up industrialization. Use the models in this chapter to assess the argument in connection with the effect of population size and transaction condition on prices of goods with economies of scale in production. 4 Consider the model in example 5.2. Assume that there are job shifting costs, so that an individual who has just changed jobs is not as productive, at least for a time, as person who has not changed jobs. Suppose that the oil crisis has suddenly reduced transaction efﬁciency. Analyze what will happen to the equilibrium network size of division of labor and the equilibrium number of goods. Then discuss the possible effects on short-run unemployment, which some economists (such as Friedman) call natural unemployment, and and others call structural unemployment. 5 Many development economists (for instance, Myrdal, 1957) believe that high population growth rates impede economic development in the less-developed countries. But Schultz (1974) argued that in a free market system, individuals’ rational decisions will take care of population growth. Thus, the negative effect of population growth on economic development must be associated with deﬁcient institutions in lessdeveloped economies. For instance, an egalitarian institution of land allocation in the absence of private ownership and free trade of land in China creates incentives for a high birth rate among farmers. Discuss the two different views in connection with the models in chapters 4 and 5, and the empirical evidence that there is a

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positive correlation between population density and development performance in those countries with favorable geographical conditions for transportation, and a negative correlation between the two variables in those countries with unfavorable geographical conditions (see chapter 2). In the model in example 5.2, as transaction efﬁciency is improved, the production functions of some new goods emerge from the evolution of division of labor. This looks like endogenous technical progress. Analyze the difference between this approach to explaining endogenous technical progress, which is dependent on a large-size market network and on the merging of separate local business communities into an increasingly integrated market, and the neoclassical approach to explaining technical progress by investment, which is independent of the evolution of the network size of division of labor. Rosenstein-Rodan (1943) argues that an investment is likely to be unproﬁtable in isolation, but proﬁtable if accompanied by similar investments in many other industries. Hirschman (1958) argues that an industry creates a backward linkage when its demand enables an upstream industry to be established at least at minimum economic scale. The strength of an industry’s backward linkage is to be measured by the probability that it will, in fact, push other industries over the threshold of proﬁtability. This is called the effect of backward linkage. Forward linkage is also deﬁned by Hirschman as involving an interaction between scale and market size. It involves the ability of an industry to reduce the costs of potential downstream users of its products and thus, again, to push them over the threshold. Use the models in this chapter to formalize these vague ideas about industrialization and economic development. Nurkse (1952) proposed a concept of virtuous circles of development, which implies that the demand and supply of different sectors are interdependent. Use the general equilibrium model in this chapter to formalize his vague idea. Scitovsky (1954) drew a clear distinction between technological and pecuniary external economies and made the point that, in competitive equilibrium, the market will take care of pecuniary external effects. (Pecuniary external effects are those interdependencies between endogenous variables that are registered in price signals.) Use the concept of general equilibrium to analyze how interactions between self-interested decisions in the market take into account the beneﬁt of economies of scale and interdependencies between sectors. Most of these early development economists did not mention economies of scale. Use the model in chapter 3 to analyze why the network effect of industrial linkage can exist in the absence of economies of scale. Fleming (1955) argues that the “horizontal” external economies of Rosenstein-Rodan are less important than the “vertical” external economies. The former relate to interdependency between the different sectors at the same link of a roundabout production chain, while the latter relate to interdependency between different links. Use the distinction between the DS model and the Ethier model to formalize the distinction between vertical and horizontal economies. You may relate your analysis to the model in chapter 12, which endogenizes the number of industrial links in a roundabout production chain. Draw the distinction between dual economy in the Ricardian model in chapter 3, in the Ethier model, in Lewis’s labor surplus model, and in the Sachs and Yang model. More dual structures will be predicted by the models in chapters 6, 11, and 12. Compare all the different deﬁnitions of dual economy.

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11 12

13

If big-push industrialization is beneﬁcial to all ﬁrms, under what conditions can private ﬁrms use the ﬁnancial market to organize it, just as businessmen in Hong Kong did after the Second World War? How can the coordination problem of industrialization in the MSV model be avoided by cheap talk, industrial associations, and other business practices in the absence of government intervention? How can we reﬁne the notion of equilibrium and develop new research approaches to avoid the multiplicity of equilibria and to increase the predictive power of the models (see chapter 9)? Specify the market clearing condition for labor in example 5.1 and use Walras’s law to check if the equilibrium solution in example 5.1 is correct.

EXERCISES 1 Interpret the utility function in example 5.1 as a production function of the ﬁnal consumption good (or agricultural good). Each consumer’s utility equals the quantity of this good consumed. xi is intermediate good i employed to produce the consumption goods. Suppose that the government sales tax rate for intermediate goods is s and all tax revenue is evenly distributed among consumers. Work out the general equilibrium and its comparative statics. Will the equilibrium-relative output and relative price of the industrial and agricultural sectors change as relative tax rates t and s change? Use this model to analyze the government’s discriminatory tax policy with regard to the agricultural sector and the dual structure in the economic development process. 2 Yang and Heijdra, 1993: Delete the equality condition between marginal revenue and marginal cost in example 5.1. Then all endogenous variables can be expressed as a function of the number of goods, n, using a zero-proﬁt condition and consumer demand functions. Suppose a central planner maximizes a consumer’s utility with respect to n. Then a Pareto optimum value of n can be solved. Compare this Pareto optimum value of n with the equilibrium value, and analyze under what condition it is greater or smaller than the equilibrium value of n for production functions Xj = (Lj − a)/b and Xj = L aj , respectively. Nobody gains from the distortions in a monopolistically competitive market. Analyze why such distortions occur in a decentralized market. In your opinion, how can such distortions be avoided? 3 Assume that the economy in example 5.2 is initially in equilibrium. An oil crisis reduces transaction efﬁciency from k1 to k2, so that the equilibrium number of goods decreases. Assume that as the equilibrium shifts, there is a job shifting cost when individuals change jobs, so that those who lose their jobs are not as competitive as those who do not change jobs. Thus, unemployment will take place. Compute the unemployment rate caused by the oil crisis. 4 Replacing the production function in example 5.1 with Xj = L ja, solve for equilibrium and its comparative statics. If the DS formula for the own price elasticity of demand, 1/(1 − ρ), is used in this new model, what is going to happen? If the production function is still Xj = (Lj − a)/b, what is the solution based on the DS formula for the own price elasticity of demand? Analyze the results based on the DS formula in comparison with the results based on the YH formula.

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5 Wong and Yang, 1994: Suppose that in the DS model in example 5.1, the tax rate t is imposed on sales of consumption goods. The tax revenue is evenly distributed among consumers. Solve for equilibrium and its comparative statics. Then replace the production function with Xj = L ja and solve for equilibrium and its comparative statics. Analyze the sensitivity of the results to the speciﬁcation of who is paying the transaction costs and to the speciﬁcation of production function. 6 Suppose that in example 5.1, parameter a, b, or M changes. Show that the equilibrium average size of ﬁrms and labor productivity of each good in the DS model will change in the same direction in response to each of these changes in parameters. Use your analysis to establish the claim that the DS model will be rejected if data show a negative correlation between changes in the average size of ﬁrms and changes in productivity. Use data to test the hypothesis generated by the DS model. 7 Assume that in a simpliﬁed version of the model in example 5.2, each consumer’s utility function is u = yz where y and z are two consumption goods. There is no transaction cost other than government tax. The government imposes a consumption tax on goods y and z. The tax revenue is evenly distributed among manufacturers of goods z and x. Solve for equilibrium and its comparative statics. What are the effects of the tax on economic development and structural changes? Will this policy to tax the agricultural sector and subsidize the industrial sector increase productivity and per capita real income? 8 Consider another version of the MSV model, in which each consumer maximizes her total discounted utility over two periods. U = [∫ 10 xγ1(q)dq]θ/γ + β[∫ 01 x 2γ (q)dq]θ/γ, subject to the budget constraint ∫ 01 x 1γ (q)dq + ∫ 10 xγ2 (q)dq = L + β*(L + nπ), where β is a subjective discount factor, β* is the equilibrium discount factor, 1/(1 − θ) is the intertemporal elasticity, 1/(1 − γ ) is the elasticity of substitution between goods, n is the number of active modern ﬁrms, π is proﬁt of each active modern ﬁrm, and the wage rate in each period is assumed to be 1. Each good q in the ﬁrst period must be produced using a constant returns to scale technology, converting one unit of labor into one unit of output. Each sector q has a potential monopolist who can invest F units of labor in period 1 and then produce α > 1 units of output per unit of labor in period 2. Each modern ﬁrm maximizes its total discounted proﬁt over two periods π = [β*(α − 1)y2/α] − F. It will operate if this total discounted proﬁt is positive. Identify the parameter subspace within which there are two equilibria, one of which is n = 0 and the other is n = 1. 9 Calculate the relative income share of the modern to traditional sector in the Sachs and Yang model. Identify whether it increases or decreases as the transaction cost coefﬁcient c decreases or as population size L increases. Suppose the variable cost coefﬁcient b decreases or the ﬁxed production cost F decreases. What will happen to the equilibrium degree of industrialization n? Use this model to explain industrialization and the evolution of dual structure of the economy. 10 Specify the market clearing condition for labor in example 5.4 and show that Walras’s law holds in this model. (Hint: do not forget transaction costs in terms of labor incurred to each active modern ﬁrm.) 11 Show that the equilibrium in the Sachs and Yang model is not Pareto optimal. Is the equilibrium degree of industrialization higher or lower than the Pareto optimum one? What causes the distortions and how can they be reduced? 12 Extend the Sachs and Yang model in example 5.4 to a case with intermediate goods. Assume that consumers’ utility functions are U = yαz1−α and the production functions for goods z and y are z = [∫ 0m x( j)ρd j]β/ρL1−β y and y = Lz, respectively,

156 P ART I: D EVELOPMENT M ECHANISMS

13 14 15

16

17

where z is the manufactured consumption good, y is food, x( j ) is the quantity of intermediate good j, and Ly and Lz are the respective amounts of labor allocated to the production of goods y and z. The production function is the same as in example 5.4. Solve for the equilibrium and its comparative statics. Why are the equilibria in the DS, Ethier, and Sachs and Yang models unique? Why are there multiple equilibria in the MSV model? Suppose in example 5.3 that the government imposes a tax on sales of goods produced from traditional technology with constant returns to scale. What are the effects of the tax rate on economic development and dual structure? Specify a general equilibrium model of Lewis’s theory (1955) with the following features. In an economy with two goods, the agricultural good is produced out of labor with decreasing returns to scale technology, and the industrial good is produced out of labor and capital with constant returns to scale technology. There are two periods. In period 1, all proﬁt is used to produce the capital good used in period 2. A unit proﬁt in terms of labor can be converted to a unit of capital available in the next period. Suppose the discount rate is zero and a central planner maximizes a representative consumer’s total utility in two periods. If there is an institutional wage lower than the market wage in the agricultural sector, then absorption of surplus labor from the agricultural sector by the industrial sector takes place in the development process. Compare the development mechanism in this model with those in the models of economies of scale in this chapter. Specify a general equilibrium model of the Fei–Ranis model (1964) with the following features. An institutional wage in the agricultural sector is higher than its market level, generating labor surplus. An exogenous increase of productivity in the industrial sector starts the process that absorbs labor surplus. Compare this model with the models in this chapter. Assume that the Ethier model in example 5.2 is asymmetric. The production functions for intermediate goods are the same as in example 5.4 and the number of intermediate goods is a continuum. Solve the asymmetric Ethier model and compare its comparative statics with that in examples 5.2 and 5.4.

Notes 1 To defend Marshall’s concept of external economies, Young (1928) argued that in addition to preserving the observed compatibility between competition and increasing returns, Marshall proposed this concept because the beneﬁts from social division of labor are not limited by the ﬁrm size. There are two reasons. First, a production process can be subdivided and performed by a number of different ﬁrms. Second, a further division of labor usually accompanies a further diversiﬁcation of intermediate goods, and alters qualities as well as quantities of undertakings of the production process. The size of ﬁrm is too simple a variable to characterize changes in producers’ conﬁgurations (Blitch, 1995). 2 Note that if production functions are homogeneous, then it is possible that the number of goods will not increase as the size of an economy increases. For this case, gains from trade come solely from the fall of prices of all goods. See exercise 6 at the end of this chapter.

C HAPTER 6: C OMPARATIVE A DVANTAGE

COEXISTENCE OF ENDOGENOUS AND EXOGENOUS COMPARATIVE ADVANTAGES AND PATTERNS OF DEVELOPMENT AND TRADE

157

6

6.1 UNDERDEVELOPMENT AND A DUAL STRUCTURE WITH UNDEREMPLOYMENT If we introduce endogenous comparative advantage into the Ricardian model in chapter 3, introduce exogenous comparative advantage into the Smith–Young model in chapter 4, or introduce differences in transaction conditions between countries into the models of highdevelopment economics in chapter 5, we can develop more realistic models to explain development and trade phenomena. This kind of model can predict dual structures in economic development and a trade pattern in which a country exports goods with exogenous comparative disadvantage, if this disadvantage is dominated by endogenous comparative advantage. Inframarginal comparative statics can be used to predict the emergence, evolution, and disappearance of dual structures. In addition, the models can be used to analyze development strategies and trade policies that relate to the literature of import substitution and export-led industrialization. Lewis (1955) noted the development implications of a dual structure of commercialized versus noncommercialized sectors and evolution of commercialization. But he could not ﬁnd the right way to model the evolution of division of labor, which is associated with the reallocation of resources from the noncommercialized and self-sufﬁcient sector to the commercialized modern sector. He did not know how to use the general equilibrium model with increasing returns to describe the evolution of dual structures, nor could he command an inframarginal analysis of division of labor. Hence, he used neoclassical marginal analysis of a model with constant returns to scale and disequilibrium in the labor market to investigate the development implications of evolution in division of labor. Ranis (1988, p. 80) emphasized that the guiding principle of organizational dualism is “commercialized” as against “noncommercialized,” rather than

158 P ART I: D EVELOPMENT M ECHANISMS

“agricultural” as against “non-agricultural.” Also, the notions of disequilibrium and institutionally rigid wages are not essential in this analysis. Chenery (1979) used market disequilibrium to explain structural changes in order to avoid a general equilibrium analysis of structural changes. Recently, three kinds of equilibrium models have been developed to analyze dual structure and the underdevelopment phenomenon. Khandker and Rashid (1986) and Din (1996) have developed general equilibrium models of a dual structure in which the wage rate that is higher than market clearing level is still exogenously ﬁxed. In the emerging literature of formal models of high-development economics, equilibrium models with economies of scale are used to predict the evolution of dual structures (see Krugman and Venables, 1995, 1996, and Fujita and Krugman, 1995). The equilibrium models with an endogenous geographical location of economic activities – Krugman and Venables (1995), Puga and Venables (1998), and Baldwin and Venables (1995) – attribute the emergence of dual structures to the geographical concentration of economic activities in economic development that marginalizes peripheral areas. Kelly (1997) develops a dynamic general equilibrium model that predicts the spontaneous evolution of a dual structure between the modern sector with economies of scale and the traditional sector with constant returns technology. As transaction conditions are sufﬁciently improved, the level of division of labor increases and dual structure disappears. In the growing literature of endogenous specialization, inframarginal analysis of the Smithian models with endogenous and exogenous comparative advantages is used to explain the emergence, evolution, and disappearance of dual structure. This literature pays more attention to the effects of the evolution of individuals’ levels of specialization and the coexistence of exogenous and endogenous comparative advantages on the emergence and evolution of dual structure. Here, dual structure not only implies unequal distribution of gains from trade between developed and less-developed countries, which relates to underdevelopment phenomenon (examined in chapter 3) or a division between the industrial and agricultural sectors (examined in chapter 5), but also implies a dual structure between the commercialized sector, which is involved in international trade, and self-sufﬁcient individuals who appear to be in underemployment in a less-developed economy. In sections 6.2, 6.3, and 6.4, we use a Smithian model with endogenous and exogenous comparative advantage to illustrate how dual structure can be analyzed using the third kind of general equilibrium model. In section 6.5, we then use an extended Krugman–Venables model with economies of scale to illustrate how dual structure can be analyzed using the second kind of general equilibrium model. In section 6.6, this model is used to analyze import substitution, export-led industrialization, and coordination problems of the industrial linkage network. In these two kinds of model, evolution of dual structure is treated as an equilibrium phenomenon in the absence of an ad hoc disequilibrium wage rate. Also, the coexistence of increasing returns and ex ante differences between individual decision-makers are common features of these two kinds of model of dual structure.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n

n n

What are the differences between industrial/agricultural dual structure, a dual structure with unequal distribution of gains from trade, and a dual structure of commercialized and self-sufﬁcient sectors? What are the differences between dual structure caused by disequilibrium in the labor market and dual structure in the transitional stage of evolution of division of labor? What are the effects of coexistence of endogenous and exogenous comparative advantages on the emergence, evolution, and disappearance of dual structure?

C HAPTER 6: C OMPARATIVE A DVANTAGE n

n

159

What are the effects of coexistence of economies of scale, industrial linkages, and differences in transaction conditions between countries on the emergence, evolution, and disappearance of dual structures? What is underdevelopment? What is dual structure with underemployment? Under what conditions do they occur in the development process?

6.2 A SMITHIAN MODEL WITH A DUAL STRUCTURE IN THE TRANSITIONAL STAGE OF ECONOMIC DEVELOPMENT Example 6.1: A Smithian model with endogenous and exogenous comparative advantages (Sachs, Yang, and Zhang, 1999). Consider a world consisting of country 1 and country 2, each with a continuum of consumer-producers of mass Mi (i = 1, 2). The individuals within a country are assumed to be identical. The utility function for individuals in country i is: ui = (xi + ki x id)β( yi + ki y id )1−β

(6.1)

where xi, yi are quantities of goods x and y produced for self-consumption, xdi , y id are quantities of two goods bought from the market, and ki is the transaction efﬁciency coefﬁcient in country i. The transaction cost is assumed to take an iceberg form: for each unit of goods bought, a fraction 1 − ki is lost in transit; the remaining fraction ki is received by the buyer. The production functions for a consumer-producer in country i are: b , x1 + x 1s = L 1x

x2 + x 2s = aL2x,

y1 + y 1s = L1y, c y2 + y 2s = L2y ,

(6.2a) (6.2b)

where x is, y is are respective quantities of the two goods sold by a person in country i, Lij is the amount of labor allocated to the production of good j by an individual in country i, and Lix + Liy = B > 1. For simplicity, we assume that B = 2. It is assumed that a, b, c > 1. This system of production functions and endowment constraint displays economies of specialization in producing good x for an individual in country 1 and in producing good y for an individual in country 2. It exhibits constant returns to specialization for an individual in country 1 to produce good y and for an individual in country 2 to produce good x. But an individual in country 2 has higher productivity in producing good x than an individual in country 1 has in producing good y. Suppose that b = c = 2. If all individuals allocate the same amount of labor to the production of each good, then an individual in country 1 has the same average labor productivity of good x as an individual in country 2 has in producing good y. But the average labor productivity of good x for an individual in country 2 is higher. This is similar to the situation in a Ricardian model with exogenous comparative advantage. Country 1’s productivities are not higher than country 2’s in producing all goods, but country 1 may have exogenous comparative advantage in producing good y. But if an individual in country 1 allocates much more labor to the production of x than an individual in country 2, then her productivity is higher than that of the latter. Similarly, if an individual in country 2 allocates at least the same amount of labor as that allocated in country 1 to the production of good y, her productivity of good y will be higher. This is referred to as endogenous comparative advantage, since individuals’ decisions on labor allocation determine the difference in productivity between them. But an individual in country 1 has no endogenous comparative advantage in producing good y and an individual in

160 P ART I: D EVELOPMENT M ECHANISMS x

x

x/y

x/y

y

A

x

A

y country 1

x

(1) Structure AA y

x A

x x

x

x

A y country 2

y/x

y

y/x y

A

y country 1

y

x country 2

(7) Structure PC −

country 1

country 2

x

x x/y y x y

x/y

y/x

country 2

country 1

(8) Structure CD+

country 2

(9) Structure DC+

y y/x

y

y country 1

x y/x

y

country 2

(10) Structure CC+

y y/x

country 1

x/y x country 2

(11) Structure CC−

x

y

x

y

x

x/y x

x x/y

y

y/x

y

x

A

y

(4) Structure PC+

x

x x/y

x

y country 1

x y

country 1

x/y

y country 2

x x/y

(5) Structure CP+

y

x

y

y/x

x

(6) Structure CP−

A

(3) Structure DA

x

A

y y/x

y country 1

y

y country 2

country 1

y country 2

x x/y

x

y/x

(2) Structure AD

x/y

x

x

y/x

y country 1

y country 2

y y/x

x

y

y country 1

y/x country 2

(12) Structure CD−

Figure 6.1 Dual structures in economic development

country 2 has no endogenous comparative advantage in producing good x, since respective productivities never change, independent of their labor allocation. Figure 6.1 depicts the three conﬁgurations from which the individuals can choose. Self-sufﬁciency. Conﬁguration A, where an individual produces both goods for selfconsumption. This conﬁguration is deﬁned by:

C HAPTER 6: C OMPARATIVE A DVANTAGE

xi, yi > 0,

xis = x id = y is = y id = 0,

161

i = 1, 2.

Specialization in producing good x. Conﬁguration (x/y), where an individual produces only x and sells x in exchange for y, is deﬁned by: xi, x is, y id > 0,

xdi = yi = y is = 0.

Specialization in producing good y. Conﬁguration (y/x), where an individual produces only y and sells y in exchange for x, is deﬁned by: yi, y is, x id > 0,

yid = xi = xis = 0.

There are 13 feasible structures that can satisfy market clearing and other conditions for a general equilibrium. Structure AA, as shown in panel (1) of ﬁgure 6.1, is an autarky structure, where individuals in both countries choose self-sufﬁciency (conﬁguration A). Structure AD, shown in panel (2), is asymmetric between the two countries: all individuals in country 1 choose autarky conﬁguration A, while some individuals in country 2 choose conﬁguration (x/y) and others choose conﬁguration (y/x). Hence, there is domestic division of labor and related domestic trade in country 2, but no international division of labor and related international trade. Structure DA is symmetric to structure AD: country 1 has domestic division of labor and country 2 is in autarky. This structure involves a type 1 dual structure between countries. Structure PC+, shown in panel (4), involves a type 2 dual structure between the two countries as well as in country 1. Some individuals in country 1 choose conﬁguration (x/y), the rest of the population choose autarky, and all individuals in country 2 choose conﬁguration (y/x). There is a dual structure between professional individuals choosing (x/y) and selfsufﬁcient individuals in country 1, despite their ex ante identical characteristics. The professional individuals in country 1 are involved in international trade with country 2. Structure CP+ is symmetric to structure PC+. Structure PC−, shown in panel (6), is the same as structure PC+, except that professional individuals in country 1 choose conﬁguration (y/x) instead of (x/y) and individuals in country 2 choose conﬁguration (x/y) instead of ( y/x). Structure CP− is the same as structure CP+, except that individuals in country 1 choose conﬁguration (y/x) instead of (x/y) and professional individuals in country 2 choose conﬁguration (x/y) instead of (y/x). Structure DC+, shown in panel (9), is the same as structure PC+, except that those individuals choosing autarky in country 1 in structure PC+ choose conﬁguration (y/x) instead in structure DC+. Hence, in structure DC+ all individuals completely specialize, but country 1 is involved in both domestic and international trade, whereas country 2 is involved only in international trade. Also, country 1 exports good x and country 2 exports good y. Structure DC− is the same as structure DC+, except that country 1 exports good y instead of good x and country 2 exports good x instead good y. Structure CD+, shown in panel (8), is symmetric to structure DC+: country 1 has only international trade, whereas country 2 has both international and domestic trade, and country 1 exports good x and country 2 exports good y. Structure CD− is the same as CD+, except that country 1 exports good y instead of x, and country 2 exports good x instead of y. Structure CC+, shown in panel (10), is international complete division of labor between two countries, in which all individuals in country 1 choose conﬁguration (x/y) and all individuals in country 2 choose conﬁguration (y/x). Structure CC− is symmetric to structure CC+: all individuals in country 1 choose conﬁguration (y/x) and all individuals in country 2 choose conﬁguration (x/y).

162 P ART I: D EVELOPMENT M ECHANISMS

6.3 GENERAL EQUILIBRIUM AND ITS INFRAMARGINAL COMPARATIVE STATICS According to Zhou, Sun, and Yang (1998), a general equilibrium exists and is Pareto optimal for the Smithian models with endogenous and exogenous comparative advantages in this chapter under the following assumptions. The set of individuals is a continuum, and preferences are strictly increasing and rational. Both local increasing returns and constant returns are allowed in production and transactions. Also, they have proved that the set of equilibrium allocations is equivalent to the set of core allocations. The deﬁnition of equilibrium is the same as in chapters 3 and 4. We will follow the two-step approach to inframarginal analysis developed in chapters 3 and 4. For simplicity, assume that M1 + M2 = 1, M1 = M2 = 0.5, and β = 0.5. Let the number (measure) of individuals in country i choosing conﬁguration (x/y) be Mix, that choosing (y/x) be Miy, and that choosing A be MiA. In the ﬁrst step, we consider a structure. Each individual’s utility maximizing decision is solved for the given structure. The utility equalization condition between individuals choosing different conﬁgurations in the same country and the market clearing condition are used to solve the corner equilibrium-relative price of traded goods and number (measure) of individuals choosing different conﬁgurations. According to the deﬁnition, a general equilibrium is a corner equilibrium in which all individuals have no incentive to deviate, under the corner equilibrium-relative price, from their chosen conﬁgurations. Hence, in the second step, we can plug the corner equilibrium-relative price into the indirect utility function for each constituent conﬁguration in this structure, then can compare corner equilibrium values of utility across conﬁgurations. The total cost–beneﬁt analysis yields the conditions under which the corner equilibrium utility in each constituent conﬁguration of this structure is not smaller than any alternative conﬁguration. This system of inequalities can thus be used to identify a subspace of parameter space within which this corner equilibrium is a general equilibrium. With the existence theorem of general equilibrium proved by Zhou, Sun, and Yang (1998), we can completely partition the parameter space into subspaces, within each of which the corner equilibrium in a structure is a general equilibrium. As parameter values shift between the subspaces, the general equilibrium will discontinuously jump between structures. The discontinuous jumps of structure and all endogenous variables are inframarginal comparative statics of general equilibrium. We now take the ﬁrst step of the inframarginal analysis. As an example, we consider structure CP+. Assume that in this structure, M2y individuals choose conﬁguration (y/x) and M2A individuals choose autarky in country 2, where M2y + M2A = M2 = 0.5. M1 = 0.5 individuals in country 1 choose conﬁguration (x/y). Since all individuals in the same country are ex ante identical in all aspects, the maximum utilities in conﬁgurations A and (y/x) must be the same in country 2 in equilibrium. Marginal analysis of the decision problem for an individual in country 2 choosing autarky yields the maximum utility in conﬁguration A: U2A = (a2c+1γ)0.5, where γ ≡ c c/(c + 1)c+1. Marginal analysis of the decision problem for an individual in country 2 choosing conﬁguration (y/x) yields the demand function x 2d = 2c−1/p, the supply function y 2s = 2c−1, and the indirect utility function U2y = 2c−1(k2/p)0.5. The utility equalization condition U2y = U2A yields p ≡ px/py = k22c−3/aγ. Similarly, the marginal analysis of the decision problem of an individual choosing conﬁguration (x/y) in country 1 yields the demand function y 1d = 2b−1/p, the supply function x 1s = 2b−1, and the indirect utility function U1x = 2b−1(k1 p)0.5. Inserting the corner equilibrium-relative price into the market clearing condition for good x, M1x 1s = M2y x 2d, yields the number of individuals selling good y, M2y = 0.5k2/23−caγ, where M1 = 0.5

C HAPTER 6: C OMPARATIVE A DVANTAGE

163

Table 6.1 Indirect utility functions Conﬁgurations

Indirect utility functions (x/y)

(y/x)

A

Country 1

u1x = 2b−1 (k1 p)0.5

u1y = (k1/p)0.5

u1A = (2b+1αγ )0.5

Country 2

u2x = a(k2 p)0.5

u2y = 2c−1(k2/p)0.5

u2A = (2c+1aγ )0.5

where α ≡ b b/(1 + b)b +1, γ ≡ c c/(1 + c)c +1. Table 6.2 Corner equilibria Structure

Relative price of x to y

Numbers of individuals choosing various conﬁgurations M1A = M2A = 0.5

AA AD

c−1

2 /a

M1A = 0.5, M2x = M2y = 1/4

DA

21−b

M2A = 0.5, M1x = M1y = 1/4

PC+

23−bα/k1

M2y = 0.5, M1A = 0.5(1 − k12 c−3/α), M1x = 0.5k12c−3/α

CP+

2c−3k2/γa

M1x = 0.5, M2A = 0.5(1 − k22 b−3/γa), M2y = 0.5k22b−3/γa

CP−

2c+1γ/ak2

M1y = 0.5, M2x = 0.5k22−c−1/γ, M2A = 0.5(1 − k22−c−1/γ)

CC+

2c−b

M1x = M2y = 1/2

CD+

2c−1/a

M1x = 0.5, M2y = (1 + 2b−1/a)/4, M2x = (1 − 2b−1/a)/4

CD−

c−1

M1y = 0.5, M2x = 0.25 + 2−c−1, M2y = 0.25 − 2−c−1

2 /a

by assumption. Indirect utility functions for individuals choosing various conﬁgurations in the two countries are listed in table 6.1. Following this procedure, we can solve for the corner equilibrium in each structure. The solutions of all corner equilibria are summarized in table 6.2. Then we can take the second step to carry out a total cost–beneﬁt analysis for each corner equilibrium and to identify the parameter subspace within which the corner equilibrium is a general equilibrium. Consider the corner equilibrium in structure CP+ as an example again. In this structure, M1 individuals choose conﬁguration (x/y) in country 1, and in country 2, M2y individuals choose conﬁguration (y/x) and M2A individuals choose autarky. For an individual in country 1, equilibrium requires that her utility in conﬁguration (x/y) is not smaller than in conﬁgurations (y/x) and A under the corner equilibrium-relative price in structure CP+. Also, equilibrium requires that all individuals in country 2 are indifferent between conﬁgurations (y/x) and A and receive a utility level that is not lower than in conﬁguration (x/y). In addition, this structure occurs in equilibrium only if M2y ∈(0, 0.5). All the conditions imply: u1x ≥ u1y,

u1x ≥ u1A,

u2A = u2y ≥ u2x,

M2y ∈(0, 0.5),

where indirect utility functions in different conﬁgurations and corner equilibrium-relative price are given in tables 6.1 and 6.2. The conditions deﬁne a parameter subspace: k1k2 ≥ 26−b−caαγ, a < 24−b−c,

k2 ∈(24−b−caγ, Min{4γ, aγ23−b}),

k1 > Max{24− b−caα, α23−c},

164 P ART I: D EVELOPMENT M ECHANISMS Table 6.3 General equilibrium structure: inframarginal comparative statics k2 ∈(0, 4γ ) k1 ∈ (0, 4α)

k2 ∈(4γ, 1)

a < 2b+c−2

a > 2b+c−2

a < 2b+c−2

k1k2 < aαγ2 6−b−c

k1k2 > aαγ26−b−c

k1k2 < αγ2b+c+2/a

a < 2b−1

a > 2 b−1

k1 < α2b+c/a

AA

a < 2b−1

AA

k1 < aα24−b−c

AD

AD

k1 ∈ (aα24 −b−c, α23−c)

k1 > aα24 −b−c

k1 ∈ (α2b+c/a, 4α)

k1k2 > αγ2b+c+2/a

PC+

CD+

CD−

CP−

k1 > α23−c CC+

k2 < γ2b+c/a

a < 2b−1

a > 2b−1

CD−

CC+

CD+

a > 2b−1

k1 < α2 PC+

3−c

k2 < aγ23−b CP+

CP+

k1 > α23−c k2 > aγ23−b CC+ k1 ∈ (4α, 1)

a > 2b+c−2

a < 2b−1

a > 2b−1

k2 < aγ2 DA

4−b−c

DA

k2 ∈(aγ2 , aγ23−b) CP+

k2 > aγ2

k2 > γ2b+c/a

k2 > aγ23−b CC+

CP+

CD−

4−b−c

4−b−c

where α ≡ b b/(1 + b)b+1 and γ ≡ c c/(c + 1)c+1. Within this parameter subspace, the corner equilibrium in structure CP+ is the general equilibrium. Following this procedure, we can do total cost– beneﬁt analysis for each structure. The total cost–beneﬁt analysis in the second step and marginal analysis of each corner equilibrium in the ﬁrst step yields the inframarginal comparative statics of general equilibrium, summarized in table 6.3. From this table, we can see that the parameter subspace for structure DC+, DC−, or CC− to occur in general equilibrium is empty. In table 6.3, α ≡ b b/(1 + b) b+1, γ ≡ c c/(1 + c)c+1. C stands for complete specialization in a country, D stands for the domestic division of labor in a country, A stands for autarky in a country, P stands for the partial division of labor where the population in a country is divided between autarky and specialization, subscript + stands for a pattern of trade in which country 1 exports good x and imports good y, and subscript − stands for a trade pattern in which country 1 exports good y and imports good x. Hence, structure AA involves autarky in both countries, structures AD and DA involve autarky in one country and division of labor in the other, structures PC and CP involve complete specialization in one country and coexistence of autarky and complete specialization in the other. The country with the lower transaction efﬁciency in this structure appears to be underdeveloped in the sense that it receives none of the gains from trade, and the income differential between it and the other country with higher transaction efﬁciency increases as a result of a shift of equilibrium from autarky to this structure. Also, ex ante identical individuals in the less-developed country in this structure are divided between a professional occupation that trades with the foreign country and those who are self-sufﬁcient and not involved in commercialized production. These self-sufﬁcient individuals appear to be in underemployment, since they cannot ﬁnd a job to work for the market. All individuals completely specialize in structures CD and CC. But CC involves complete specialization of both countries in the absence of domestic trade, whereas CD involves complete

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165

specialization in country 1 and domestic division of labor in country 2. Figure 6.1 illustrates the equilibrium structures.1 We say that the level of division of labor increases if the occurrence of letters A or P decreases or the occurrence of letters D or C increases in a structure. Recall from chapters 3 and 4 that endogenous comparative advantage is the productivity difference between individuals that is caused by individuals’ labor allocations, and exogenous comparative advantage is the productivity difference between individuals that is independent of their labor allocation. Since in this model, marginal and average productivity never change as labor allocation alters for a production function with constant returns to scale, these deﬁnitions imply that in this model endogenous comparative advantages come from economies of specialization, and exogenous comparative advantages come from exogenous difference of production conditions with constant returns. Parameter b represents the degree of endogenous comparative advantage for a person in country 1 producing good x since, as b increases, increases in productivity become more responsive to an increase in the amount of labor allocated to the production of x. Similarly, c represents the degree of endogenous comparative advantage for a person in country 2 producing good y. If b = c = 1, then country 2 has exogenous absolute and comparative advantage in producing good x and country 1 has exogenous comparative advantage in producing good y, since a > 1 in (6.2). This implies that a represents the degree of exogenous comparative advantage. With the deﬁnitions, we can now have a close look at table 6.3, which consists of four blocks. The northwest block is associated with low transaction efﬁciencies in both countries. The northeast block is associated with low transaction efﬁciency in country 1 and high transaction efﬁciency in country 2. The southwest block is associated with low transaction efﬁciency in country 2 and high transaction efﬁciency in country 1. The southeast block is associated with high transaction efﬁciencies in both countries. As parameter values move from the northwest toward the southeast, the occurrence of letter A, representing autarky, and letter P, representing partial division of labor, decreases and the occurrence of letters D and C, representing complete division of labor, increases. Hence, as transaction conditions are improved, the level of domestic and international division of labor increases because of the trade-off between economies of division of labor generated by endogenous and exogenous comparative advantages and transaction costs. If the transaction efﬁciency is low in one country and high in the other (northeast or southwest block), the country with the lower transaction efﬁciency has a dual structure (P) or in autarky (A) in a structure with asymmetric division of labor between countries (AD, DA, PC, or CP). If the transaction efﬁciencies are high in both countries, then complete division of labor occurs and dual structure disappears in equilibrium. Each block consists of three sections. If the degree of exogenous comparative advantage a is small compared to the degree of endogenous comparative advantage (b, c), each country exports the good with economies of specialization in production. This is denoted by subscript +. Otherwise, a country exports the good with constant returns and exogenous comparative advantage. From the table we can see that if b and c are sufﬁciently large, country 1 imports its good of exogenous comparative advantage, y. One such case is that structure CP+ occurs in equilibrium when k1 ∈(0, 4α), k2 ∈(0, 4γ), a < 2b+c−2, k1k2 > aαγ26−b−c, a > 2b−1. In structure CP+, country 1 exports x and imports y, but country 1 has exogenous comparative advantage in producing y. All the results on evolution of division of labor, dual structure, and trade pattern are summarized in the following proposition, illustrated in ﬁgure 6.1 where large arrows indicate the direction of the evolution in division of labor. Proposition 6.1: As transaction efﬁciency increases from a very low to a very high level, the equilibrium level of domestic and international division of labor increases from complete autarky in both countries to the complete division of labor in both countries. In the transitional

166 P ART I: D EVELOPMENT M ECHANISMS y

6 E F

4A G 2C

0 2

B D 2a 4

H 4 + 2a

x

Figure 6.2 Economies of division of labor based on endogenous and exogenous comparative advantage

stage, two types of dual structure may occur. In a type 1 dual structure, the country with the lower transaction efﬁciency is in autarky, and the other has domestic division of labor and higher productivity and per capita real income. In a type 2 dual structure, the country with higher transaction efﬁciency completely specializes and obtains all the gains from trade, and the other country has a domestic dual structure between the commercialized sector and the selfsufﬁcient sector (autarky) which appears to be in underemployment. The dual structures of the two types disappear as individuals in all countries are involved in international and domestic division of labor. Each country exports goods of exogenous comparative advantage if exogenous comparative advantage dominates endogenous comparative advantage in producing this good. Otherwise, each country exports goods with endogenous comparative advantage and economies of specialization in production. The inframarginal comparative statics of general equilibrium can be used to establish two corollaries. The ﬁrst is that the evolution in division of labor generated by improvements in transaction conditions will raise equilibrium aggregate productivity. In order to establish the above statement, we consider the aggregate PPF for individual 1 (from country 1) and individual 2 (from country 2). As shown in ﬁgure 6.2, where b = c = 2, the PPF for individual 1 is curve AB, and that for individual 2 is curve CD. In autarky, the two persons’ optimum decisions for taste parameter β ∈(0, 1) are x1 = [4β/(1 + β)]2, x2 = 2aβ/(2 − β), y1 = 2(1 − β)/(1 + β), y2 = [4(1 − β)/(2 − β)]2. Let β change from 0 to 1; we can calculate values of Y = y1 + y2 and X = x1 + x2 as functions of β. The values of X and Y for different values of β constitute curve EGH in ﬁgure 6.2. The equilibrium aggregate production schedule in structure AA is a point on the curve, dependent on the value of β. But the aggregate PPF for the two individuals is the curve EFH. Since in structure CC, CD, or DC the equilibrium production schedule is point F, which is on the aggregate PPF, the aggregate productivity in a structure with the complete division of labor is higher than in structure AA. The difference between EFH and EGH can be considered as economies of division of labor. Following the same reasoning, we can prove that the equilibrium aggregate productivity in structures AD, DA, PC, or CP is lower than the PPF. Hence, proposition 6.1 implies that as transaction efﬁciencies are improved, the equilibrium level of division of labor and equilibrium aggregate productivity increase side by side. The second corollary is that deterioration of a country’s terms of trade and increase of gains received by this country from trade may concur. Suppose that the initial values of parameters

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167

satisfy k1 ∈(0, 4α), k2 ∈(0, 4γ), and k1k2 > aγα26−b−c, which implies, from table 6.3, that we are considering the northwest block. Suppose that the initial value of k2 satisﬁes k 2′ < aγ23−c, so that the equilibrium structure is CP+ in which country 2 exports y and imports x, and its terms of trade, from table 6.2, are 1/p = 23−caγ/k 2′. Now the value of k2 increases to k 2″ > aγ23−c, which implies, from table 6.3, that the general equilibrium jumps from CP+ to structure CC+ in which country 2’s terms of trade, from table 6.2, are 23−c. It can then be shown that country 2’s terms of trade deteriorate as a result of the change in k2. But this shift of the equilibrium from CP+ to CC+ increases the utility of each individual in country 2 from the autarky level. This has established the claim that the deterioration of a country’s terms of trade and an increase of gains that this country receives from trade may concur. There are other parameter subspaces within which changes in parameters may generate concurrence of the deterioration of one country’s terms of trade and an increase in its gains from trade. Although an equilibrium in this model is always Pareto optimal, it generates interesting implications, from the perspective of economic development and trade, for income distribution. It is straightforward that as the equilibrium jumps from a structure in which at least some individuals in a country are in autarky (structure AD, DA, PC, CP) to a structure in which all individuals are involved in trade and division of labor, then all individuals’ utilities in this country will be increased. Hence, immiserizing development never occurs for a less-developed economy in our model, since all individuals in our model of endogenous specialization can choose occupation conﬁgurations, and they will not choose trade if autarky makes them better off. But the effects of trade and development on the utility of an individual in the developed economy are not monotonic. As the equilibrium jumps from autarky to the partial division of labor (AD, DA, PC, or CP), the developed country gets all the gains from trade and development. But as the equilibrium jumps, say, from PC+ to CC+, it is possible that the utility of a person in the developed country may decline. It can be shown that this takes place within the parameter subspace in the southwest block in table 6.3. This prediction is consistent with the fact, documented in Krugman and Venables (1995, pp. 857–8), that in the 1970s the general view was that the integration of world markets produced a rise in the living standards of rich nations at the expense of the poor. Now, in the twenty-ﬁrst century, it is believed that the rise of Third World manufacturing nations has had serious adverse impacts on developed economies. But according to our model, this reverse of the tide is just compensation to the less-developed economies, which did not receive gains from trade in the early development stage. Also, in our model there exists some parameter subspace within which such immiserizing development never occurs. This is the case when the improvements in the transaction efﬁciency of the developed country keep pace with those of the less-developed country.

6.4 TRADE PATTERN IN THE PRESENCE OF BOTH ENDOGENOUS AND EXOGENOUS COMPARATIVE ADVANTAGES, AND THE RELATIONSHIP BETWEEN INCOME DISTRIBUTION AND DEVELOPMENT Since the inframarginal comparative statics change with the speciﬁcation of the system of production functions, we report the sensitivity analysis of our result. Example 6.2: A model with economies of specialization in one activity for all individuals. The system of production functions in (6.2) displays economies of specialization in production of good x by a person in country 1 and in production of good y by a person in country 2. We now assume that there are economies of specialization for all individuals in producing x, but constant returns prevail in the production of good y. Hence, the system of production functions in (6.2) is replaced by:

168 P ART I: D EVELOPMENT M ECHANISMS Table 6.4 Equilibrium structure (economies of specialization in producing one good for all countries) k2 ∈(0, 4γ) k1 ∈ (0, 4α)

a > 2c−b k1k2 < αγ2c−b+4/a

k1k2 > αγ2c−b+4/a

a < 2c−b

a > 2c−b

a < 2c−b

k1k2 < aαγ24+b−c

2c−b > 1

AA

k1 < α22+c−b/a

AD k1 < α22+c−b/a CC+

k1 > aα22+b−c CD− CD−

2c−b < 1

CP+

k1k2 > aαγ2 CP−

k1 > α2 CD+

k2 < γ22+b−c/a DA

k2 < aγ22+b−c DA

2c−b > 1

2c−b < 1

k2 > γ22+b−c/a CP+

k2 > aγ22+b−c CP−

CD+

CC+

AA k1 ∈ (4α, 1)

k2 ∈ (4γ, 1)

4+b−c

2+c−b

/a

k1 < aα22+b−c AD

where α ≡ b b/(1 + b)b+1, γ ≡ c c/(1 + c)c+1.

x1 + x 1s = L b1x,

y1 + y 1s = L1y,

x2 + x 2s = L c2x,

y2 + y 2s = aL2y.

The corresponding inframarginal comparative statics of general equilibrium are summarized in table 6.4 and proposition 6.2. Proposition 6.2: As transaction efﬁciency is improved, the equilibrium level of division of labor and aggregate productivity increase. The country with lower transaction efﬁciency and/or insigniﬁcant economies of specialization has a dual structure with underemployment in the transitional stage of economic development. If a country has endogenous comparative advantage and exogenous comparative disadvantage in producing a good, it exports this good when the former dominates the latter. Otherwise, it imports this good. In exercise 1 at the end of this chapter, you are asked to replace the production functions in (6.1) with the one displaying economies of specialization for individuals in one country and constant returns for individuals in the other country. Then you can show that the essence of propositions 6.1 and 6.2 would not be changed. Proposition 6.2 can provide a theoretical explanation for recent empirical evidence that shows signiﬁcant effects of geographical conditions on a country’s performance of development and trade. Gallup and Sachs (1998; and see ch. 2 in this text) have used cross-country and crossregion data to show that countries with favorable geographical conditions for transportation have a better development performance. This analysis is different from the DS and Ethier models in chapter 5, as well as the Yang model (1991; example 4.7 above), which explain economic development, structural changes, and trade pattern by economic changes in the absence of ex ante differences between decisionmakers. It is different from conventional trade theory and development economics concerning only exogenous comparative advantages (see chapter 3). We explain complicated development and trade phenomena by the coexistence of endogenous and exogenous comparative advantages. The Smithian models can be extended to investigate the relationship between economic development and inequality of income distribution. Theories and empirical evidence for a positive correlation between economic development and inequality of income distribution in developing countries can be found in Banerjee and Newman (1993), Lewis (1955), Palma

C HAPTER 6: C OMPARATIVE A DVANTAGE

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(1978), and Li and Zou (1998), for instance. Theory and empirical evidence for a negative correlation between inequality and international trade, which relate to economic development, can be found in Alesina and Rodrik (1994), Galor and Zeira (1993), Thompson (1995), Fei, Ranis, and Kuo (1979), Frank (1977), Aghion, Caroli, and Garcia-Pena Losa (1999), and Balassa (1986), for instance. Not only are data from developing and newly industrialized countries contradictory, but data from developed countries also generate controversies. Kuznetz (1955) proposed the hypothesis of the inverted U-curve of the relationship between inequality and per capita income and provided some support for it from US data. Krugman and Venables (1995) use a general equilibrium model with global economies of scale to predict such an inverted U-curve of inequality. Greenwood and Jovanovic (1990) use a dynamic equilibrium model to predict the inverted U-curve. Some theories and data show that there is a negative or insigniﬁcant correlation between trade or development and inequality in developed countries (see, for instance, Krugman and Lawrence, 1994, Katz and Murphy, 1992). Others show a positive correlation between trade and inequality in developed countries (see, for instance, Grossman, 1998, Murphy and Welch, 1991, Borjas, Freeman, and Katz, 1992, Karoly and Klerman, 1994, Sachs and Shartz, 1994). But Ram (1997) provides new empirical evidence for an uninverted-U pattern in developed countries, taking into account data since the Second World War. Jones (1998, p. 65) also ﬁnds that the ratio of GDP per worker in the ﬁfth richest country to GDP per worker in the ﬁfth poorest country ﬂuctuated from 1960 to 1990. In exercise 12 (below), Yang and Zhang (1999) extend the model in example 6.1 to the case with two types of individuals in each country. They show that as transaction conditions are improved, different countries and different types of individual in each country get involved one by one in an increasingly higher level of division of labor. The group of individuals with better transaction conditions is involved in a higher level of specialization and commercialization than other groups. As the former group chooses a higher level of specialization, leaving other groups behind, inequality of income distribution and aggregate productivity go up side by side. As the other groups catch up to the leaders, inequality decreases while aggregate productivity increases. As the leading group chooses an even higher level of specialization and commercialization, leaving the other groups behind again, inequality increases again. The next catch-up process will reduce inequality again. Hence, this ratcheting process of inequality and equality of income distribution generates ﬂuctuation in inequality. This invalidates monotonic positive or negative correlation between inequality and economic development, and it also invalidates Kuznetz’s inverted U-curve of inequality and per capita income. Recent empirical evidence in Deininger and Squire (1996) strongly supports Yang and Zhang’s model. In chapter 9 we will investigate the negative effects on economic development of endogenous transaction costs, which distort income distribution.

6.5 DEVELOPMENT STRATEGIES AND TRADE PATTERNS Example 6.3: An extended Krugman and Venables model of a dual economy (Sachs, Yang, and Zhang 2001). Krugman and Venables’ (KV) model (1995) and many similar models are extensions of the Ethier model in example 5.2 in chapter 5, above. We now introduce ex ante differences between two countries into the KV model. The transaction efﬁciency coefﬁcient for country i is ki (i = 1, 2). In Krugman and Venables’ original version of this model, zero transaction cost for the agricultural good is unrealistically assumed. Consider two countries. Population size in country i is Mi. Migration between countries is prohibitively expensive. Agricultural good z is produced from labor. Industrial good y is produced from labor and n intermediate goods.

170 P ART I: D EVELOPMENT M ECHANISMS

6.5.1 A consumer’s decision A representative consumer’s decision problem in country i is: Max: ui = ( yi + ki yji)α(zi + ki zji)1−α

s.t.

piy yi + pjy yji + pizzi + pjzzji = wi

where ui is a consumer’s utility level in country i, yi and zi are the respective quantities of the manufactured consumption good (such as a car), and the agricultural good (such as food) is purchased from the domestic market in country i. yji and zji are the respective quantities of the two goods imported by an individual in country i from the other country. pis is the price of good s in country i. The price of imported good t to country s, pst, can be considered as CIF (import price inclusive of insurance and freight) and the price of exported good t from country s, pst, can be considered as FOB (import price exclusive of insurance and freight) to the importing country. It is assumed that each individual is endowed with one unit of labor, and labor in country 1 is the numeraire, so that w1 = 1 and w2 = w. Iceberg transaction cost is assumed, so that 1 − ki ∈[0, 1] is the transaction cost coefﬁcient and ki the transaction efﬁciency coefﬁcient for importing one unit of ﬁnal consumption goods in country i.

6.5.2 Possible trade structures As we introduce the ex ante differences in transaction conditions between the two countries into the model, corner solutions are possible. Hence, standard marginal analysis for interior solutions does not work. We ﬁrst apply the Kuhn–Tucker condition to identify the conditions under which a particular trade structure occurs in equilibrium. These conditions are dependent on relative prices. Second, for a given structure, we solve for a local equilibrium using marginal analysis. We can plug the equilibrium prices into the conditions identiﬁed in the ﬁrst step. We can then partition parameter space into subspaces, within each of which a particular structure occurs in equilibrium. Let us take the ﬁrst step in the inframarginal analysis. The Kuhn–Tucker condition for the two representative consumers’ decision problems in the two countries indicates that some trade structures never occur in equilibrium, and that each of the feasible trade structures occurs in equilibrium only if relative prices and the relative transaction condition in the two countries satisfy a certain condition. Later, we can obtain a similar result for a trade pattern of intermediate goods using the Kuhn–Tucker condition for the decision of a ﬁrm producing the ﬁnal manufactured good. The two sets of the Kuhn–Tucker condition yield the following conditions for a particular trade pattern to occur in equilibrium, where xi is the amount of an intermediate good purchased from the domestic market in country i, xji is the amount of an intermediate good imported from country j in country i, and ti is the transaction efﬁciency coefﬁcient of importing intermediate goods in country i. Let’s label all of these conditions “6.3”: (A) (C1) (C2) (D0)

If k1 and t1 and/or k2 and t2 are sufﬁciently small, the optimum decision requires that zji = xji = yji = 0 and xi, yi, zi > 0, which implies that no trade occurs between the countries, or that autarky structure, shown in ﬁgure 6.3(a), occurs in equilibrium. For p1y/p2y < k2 and p1z /p2z > 1/k1, the optimum decision requires z12 = x12 = y21 = z1 = y2 = 0 and x1, y1, z2, x21, z21, y12 > 0. This structure of trade (C1) is shown in ﬁgure 6.3(c). For p1y /p2y > 1/k1 and p1z/p2z < k2, the optimum decision requires z21 = x21 = y12 = z2 = y1 = 0 and x2, y2, z1, x12, z12, y21 > 0. This structure of trade C2 is symmetric to C1. For p1y/p2y ∈ (k2, 1/k1) and p1z/p2z ∈(k2, 1/k1), the optimum decision requires z12 = y12 = z21 = y21 = 0 and x1, y1, z1, x2, y2, z2, x12, x21 > 0. This structure of trade (D0) is shown in ﬁgure 6.3(d).

C HAPTER 6: C OMPARATIVE A DVANTAGE x

y

z

z x

1

y

x

z

2 z

(d) Structure D0

x

x

x

z

x

2

y 1

z

z

y

x

y 1

y

x

x

2

z

y

x

(b) a structure that does not occur in equilibrium x

x 1

1

z

y y (a) Structure A (autarky)

x

y y

2

171

z 2

z

(c) Structure C1

x

y 1

y

z x

2

z (e) Structure E1

(f ) Structure F1

Figure 6.3 Different patterns of development and trade

(D1) (D2) (E1) (E2) (F1) (F2)

For p1y/p2y ∈ (k2, 1/k1) and p1z/p2z < k2, the optimum decision requires y12 = z21 = y21 = z2 = 0 and x1, y1, z1, x2, y2, x12, x21, z12 > 0. This structure of trade is called D1. For p1y/p2y ∈ (k2, 1/k1) and p1z/p2z > 1/k1, the optimum decision requires y21 = z12 = y12 = z1 = 0 and x2, y2, z2, x1, y1, x21, x12, z21 > 0. This structure of trade D2 is symmetric to D1. For p1y/p2y < k2 and p1z/p2z ∈ (k2, 1/k1), the optimum decision requires x12 = z12 = y21 = z21 = x2 = y2 = 0 and x1, y1, z1, x21, y12, z2 > 0.This trade structure is called E1, shown in panel (e). For p1y/p2y > 1/k1 and p1z/p2z ∈(k2, 1/k1), the optimum decision requires x21 = z21 = y12 = z12 = x1 = y1 = 0 and x2, y2, z2, x12, y21, z1 > 0. This trade structure E2 is symmetric to E1. For p1y/p2y < k2 and p1z/p2z < k2, the optimum decision requires x12 = y21 = z21 = x2 = z2 = y2 = 0 and x1, y1, z1, x21, y12, z12 > 0. This trade structure is called F1, shown in panel (f). For p1y/p2y > 1/k1 and p1z/p2z > 1/k1, the optimum decision requires x21 = y12 = z12 = x1 = z1 = y1 = 0 and x2, y2, z2, x12, y21, z21 > 0. This trade structure is called F2. (6.3)

It can also be shown that the pattern of trade in panel (b) and other trade structures do not occur in equilibrium, except for some razor-edge cases, where some of the inequalities involving relative prices in (6.3) become equalities.2 The markets for goods y and z are competitive because of constant returns to scale in production. But the market for intermediate goods is monopolistically competitive.

6.5.3 Production of agricultural good z The production function of food in country i is: Zi = θi Liz where Zi is the output level of z and Liz is the amount of labor allocated to the production of food in country i. For simplicity, we assume that θ2 = 1 and θ1 = θ > 1. This implies that country 1 has exogenous comparative advantage in producing food, since in the next two subsections the production function of industrial goods y and x is assumed to be the same for the two countries.

6.5.4 Production of ﬁnal manufactured good y The production function for a representative car manufacturer’s production function in country i is:

172 P ART I: D EVELOPMENT M ECHANISMS

Yi = [ni x iρ+ (n − ni)(ti xji)ρ]β/ρL1−β iy where Yi is the output level of good y produced by a representative ﬁrm in country i, ni and n − ni are the respective numbers of intermediate goods purchased by country i from the domestic market and from the other country, xi is the amount of an intermediate good purchased by the ﬁrm in country i from the domestic market to produce good y, xji is that purchased by the ﬁrm in country i from the other country, and ti is the transaction efﬁciency coefﬁcient for country i importing an intermediate good from the other country. x can be considered as all kinds of professional machine tools, and the elasticity of substitution 1/(1 − ρ) is assumed to be larger than one, that is, ρ ∈(0, 1). We have used the symmetry and omit the index of intermediate goods when no confusion is caused.

6.5.5 Production of intermediate goods The production function for the monopolist producer of an intermediate good in country i is: Xi = (Li − a)/b, where Xi is the quantity of an intermediate good supplied by the monopolist in country i and Li is the amount of labor hired by the ﬁrm to produce the intermediate good. Again, we have used the symmetry, and omit the index of intermediate goods when no confusion is caused. As shown in (6.3), ten market structures may occur in equilibrium in this model. We consider the local equilibrium in each of them.

6.5.6 Local equilibrium in structure A We ﬁrst consider structure A, where xi, yi, zi > 0, xij = yij = zij = 0. A consumer’s decision yields demand functions for goods y and z. Each consumer supplies one unit of labor, and total supply of labor in country i is Mi. The zero-proﬁt condition for the ﬁrm producing z gives the price of good z in terms of labor in country i, piz. The symmetry implies that quantities supplied or employed are the same for ni intermediate goods. The zero-proﬁt condition and a ﬁrst-order condition for the decision problem of the ﬁrm producing y yields the equilibriumrelative quantity of labor and intermediate goods and an equation that determines the equilibrium piy/pix. Using the production and demand functions of y, the market clearing conditions for y and labor, and the ﬁrst-order conditions for the decision problem of the ﬁrm producing y, we can ﬁnd the demand function for x. Using the Dixit–Stiglitz formula for own price elasticity E = 1/(1 − ρ), we can then work out the ﬁrst-order condition for the decision problem for the monopolist producer of an intermediate good. Then the zero-proﬁt condition for this ﬁrm yields the equilibrium ni. The local equilibrium and its marginal comparative statics in this structure are summarized as follows: wi = 1,

p1z = 1/θ, β−1

p2z = 1,

pix =b/ρ,

β/ρ

piy = (1 − β) [a/(1 − ρ)β] [(1 − ρ)b/ρa]β (αMi )β(1−1/ρ), ni = Mi βα(1 − ρ)/a, u1 = [θ(1 − α)](1−α)ααp 1y−α, dpiy /dMi < 0,

−α u2 = (1 − α)(1−α)αα p 2y ,

dni /dMi > 0,

dui /dMi > 0

C HAPTER 6: C OMPARATIVE A DVANTAGE

173

where i = 1, 2. The marginal comparative statics imply that as the population in an integrated market increases, the equilibrium price of ﬁnal manufactured goods decreases and the equilibrium number of intermediate goods and per capita real income increase. Since total factor productivity of the ﬁnal manufactured good is an increasing function of the number of intermediate goods, this productivity increases with population size, too. The result is similar to that in the Ethier model in chapter 5, except that we assume there is no transaction cost for domestic trade.

6.5.7 Local equilibrium in structure C Next, we consider structure C1 where x1, y1, z2, y12, x21 > 0, x12 = y21 = z12 = 0. The procedure to solve the corner equilibrium in this structure is the same as that for structure A, except that the markets for x, y, z are jointly cleared for both countries. The corner equilibrium in this structure is summarized as follows: w = t 1ρ,

p1z = 1/θ,

p2z = t 1ρ,

p1x = b/ρ,

p2x = t 1ρb/ρ,

p1y = (1 − β)β−1β−β/ρ (b/ρ)β [(1 − ρ)α(M1 + k 1ρM2)/a] β(1−1/ρ), n1 = [(1 − ρ)/a][M1(βα + 1 − α) − α(1 − β)t 1ρM2], n2 = [(1 − ρ)/a][M2α − (1 − α)t1−ρM1], u1 = B(θk1)1−αt1−ρ(1−α)(M1 + t 1ρM2)αβ (1−ρ)/ρ,

u2 = Bt 1ραk α2 (M1 + t 1ρM2)αβ(1−ρ)/ρ

where B ≡ (1 − α)(1−α)αα[(1 − β)1−β ββ/ρ(ρ/b)β]α[α(1 − ρ)/a]αβ(1−ρ)/ρ. The differentiation of the solutions yields marginal comparative statics of the local equilibrium in structure C1. dni/dMi > 0,

dni/dMj < 0,

dn2/dt1 > 0,

dn1/dt1 < 0,

dn/dt1 > 0, if (1 − α)M1/α(1 − β)M2 > t , 2ρ 1

dn/dM1 > 0 iff t1 > [(1 − α)/αβ + 1 − α]1/ρ, dn/dM2 > 0,

(6.4)

dw/dt1 > 0, dui/dMj > 0, dui/dki > 0, dui/dt1 > 0 where i, j = 1, 2 and n = n1 + n2 is the number of all intermediate goods available in the two countries. The marginal comparative statics of the local equilibrium imply that as the transaction condition in country 1 improves, the production of intermediate goods will shift from country 1 to country 2. This relocation of industrial production increases utility levels in the two countries, although the nominal income in country 2 relative to that in country 1, which is w, increases as well. The improvement of the transaction condition in country 2 has no effects on industrial structure and the location of industrial production, though it increases the utility of each individual in country 2. An increase in population size in country 1 will shift the production of producer goods from country 2 to country 1. But an increase in the population size in country 2 has the opposite effect on location of industrial production. However, an increase in population size in either country will raise per capita real income in both countries. As n1 or n2 tends to zero, the production of all intermediate goods becomes concentrated in country 2 or 1. A careful examination of the local equilibrium solutions in structure C1 yields the following conditions for such concentration: n1 = n and n2 = 0 if t1 < ta ≡ [M1(1 − α)/M2α]1/ρ n1, n2 ∈(0, n) if t1 ∈(ta, tb), where tb ≡ [M1(αβ + 1 − α)/M2α(1 − ρ)]1/ρ n2 = n and n1 = 0 if t1 > tb,

(6.5)

174 P ART I: D EVELOPMENT M ECHANISMS

where ta < tb always holds. The marginal comparative statics of the local equilibrium in structure C1 are summarized in the following proposition. Proposition 6.3: If the transaction efﬁciency of intermediate goods is very low in country 1, country 2 specializes in producing the agricultural good in the absence of industrialization. The production of all ﬁnal and intermediate manufactured goods is located in country 1. As the transaction condition is improved in country 1, country 2 starts industrialization, which relocates the production of intermediate goods from country 1 to country 2. The smaller the population size of country 1 relative to country 2, the faster the relocation process. Per capita real incomes in both countries increase as a result of the relocation, although the wage rate in country 2 increases compared to that in country 1. The wage difference between the two countries converges to 0 as transaction cost tends to 0. The per capita real income in country 1 is more likely to be higher than in country 2, the greater the income share of the ﬁnal manufactured good, and/or the greater the elasticity of substitution between intermediate goods, and/or the higher the relative transaction efﬁciency of country 1 to country 2. An increase in the population size of a country will move the production of intermediate goods to this country from the other country, increasing per capita real income in both countries. The local equilibrium in structure C2 is symmetric to that in C1. Hence, a similar proposition can be obtained from comparative statics of that local equilibrium.

6.5.8 Local equilibrium in structure D We now consider structure D0, in which country 1 produces ﬁnal goods y and z and n1 intermediate goods. It exchanges the intermediate goods for n2 intermediate goods produced by country 2, which self-provides goods y and z as well. Hence, for this structure we have xi , yi , zi , xij > 0, yij = zij = 0. The local equilibrium in this structure is summarized as follows: w is given by f = M1 + t 1ρ/(1−ρ) [M2w−ρ/(1−ρ) − M1w−1/(1−ρ) − M2w−(1+ρ)/(1−ρ) t 2−ρ/(1−ρ)] = 0 p1z = 1/θ,

p2z = 1, β

ρ/(ρ−1) 1

p1y = A(M1/t1) [(t

p1x = b/ρ, −t

ρ/(1−ρ) 2

)/(1 − t

p2x = wb/ρ, ρ/(1−ρ) 2

w1/(1−ρ))]β[M1t 11/(ρ−1) + M2wρ/(ρ−1)]−β/ρ

p2y = wAM 2β [(t 1ρ/(ρ−1) − t 2ρ/(1−ρ))/(t 1ρ/(ρ−1)w1/(1−ρ) − 1)]β[M1t 1/(1−ρ) + M2wρ/(ρ−1)]−β/ρ 2 ni = β(1 − ρ)Mi /a, u1 = [θ(1 − α)]1−αααp 1y−α,

u2 = (1 − α)1−ααα ( p2y /w)−α

where A ≡ (1 − β)β−1αβ[a/(1 − ρ)β]β/ρ [(1 − ρ)b/aρ]β. The market clearing conditions for intermediate goods and the ﬁrst-order conditions for producers of good y in the two countries require: w ∈(t 1ρ, t 2−ρ) where t 1ρ < t 2−ρ always holds. It is obvious that w converges to 1 as t1 and t2 tend to 1. The differentiation of the solutions yields: dw/dt1 = −(∂f/∂t1)/(∂f/∂w) > 0, dw/dt2 = −(∂f/∂t2)/(∂f/∂w) < 0 where ∂f/∂t1 > 0, ∂f/∂t2 < 0, ∂f/∂w < 0. The result implies that relative per capita nominal income of country 2 to country 1 increases as the transaction condition in country 1 improves or as the transaction condition in country 2 worsens.

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Similar results can be obtained for the relationship between per capita real income in a country and the transaction conditions in the two countries. It can be shown that: du1/dt1 = (∂u1/∂t1) + (∂u1/∂w)(dw/dt1) < 0,

(6.6a)

du2/dt2 = (∂u2/∂t2) + (∂u2/∂w)(dw/dt2) < 0

where dw/dt1 > 0, dw/dt2 < 0, ∂u1/∂w < 0, ∂u2/∂w > 0, ∂u1/∂t1 < 0, ∂u1/∂t2 < 0, ∂u2/∂t2 < 0. Other marginal comparative statics in this structure are: dui/dMi > 0,

dui/dMj > 0,

dni/dMi > 0,

dni/dρ < 0,

dni/da < 0,

(6.6b)

where i ≠ j. The Kuhn–Tucker condition for a producer of good y indicates that the ﬁrst-order derivative of proﬁt with respect to the quantity of an imported intermediate good is always negative if the transaction efﬁciency coefﬁcient is zero in this country. Hence, the equilibrium will jump to another structure if t is sufﬁciently close to 0 in either country. If 1 − ti is interpreted as the import tariff rate in country i and all tariff revenue is exhausted by the bureaucrats who collect it, then the marginal comparative statics in (6.6) imply that each country has an incentive to impose tariffs, which increase per capita real income in the home country. Proposition 6.4: As the population size or import tariff rate increases in a country, the per capita real income in that country increases. Also, the number of intermediate goods produced in a country increases with its population size. The wage difference between the two countries converges to 0 as transaction cost tends to 0. The local equilibrium in structure D1 is: w is given by f = αβM1 − (1 − α)wM2 − αβt 1ρ/(1−ρ)w−1/(1−ρ)M1 + w−ρ/(1−ρ)[(1 − α + αβ)M2t 1ρ/(1−ρ) + (1 − α)M2t 2−ρ/(1−ρ) − (1 − α + αβ)M2w−(1+ρ)/(1−ρ)t ρ/(1−ρ) t 2−ρ/(1−ρ) ] = 0 1 p1z = 1/θ,

p2z = 1,

p1x = b/ρ,

p2x = wb/ρ,

− k 2ρ/(1−ρ))/(1 − t 2ρ/(1−ρ)w1/(1−ρ))]β[M1t 1/(ρ−1) + M2wρ/(ρ−1)]−β/ρ p1y = A(M1/t1)β [(t ρ/(ρ−1) 1 1 p2y = wAMβ2 [(t 1ρ/(ρ−1) − t 2ρ/(1−ρ))/(t 1ρ/(ρ−1)w1/(1−ρ) − 1)]β[M1t 1/(1−ρ) + M2wρ/(ρ−1)]−β/ρ 2 n1 = [αβM1 − (1 − α)wM2](1 − ρ)/a, α −α 1y

u1 = [θ(1 − α)] α p , 1−α

n2 = (1 − α + αβ)M2(1 − ρ)/a,

u2 = (1 − α) αα(p2y /w)−α 1−α

where A ≡ (1 − β)β−1αβ[a/(1 − ρ)β]β/ρ[(1 − ρ)b/aρ]β. The market clearing conditions for intermediate goods and the ﬁrst-order conditions for producers of good y in the two countries require: w ∈(t 1ρ, t −ρ 2 ) where t 1ρ < t −ρ 2 always holds.

176 P ART I: D EVELOPMENT M ECHANISMS

The local equilibrium in structure D2 is symmetric to that in D1. Marginal comparative statics in structure D1 or D2 are similar to that in D0.

6.5.9 Local equilibrium in structure E The local equilibrium in structure E1 is: w = p2z = t ρ1 ,

p1z = 1/θ,

β−1 −β/ρ

p1y = (1 − β) β

p1x = b/ρ,

β

p2x = wb/ρ,

(b/ρ) [(1 − ρ)α(M1 + M t )/a]−β(1−ρ)/ρ ρ 2 1

p2y = (1 − β)β−1β−β(b/ρ)β[(1 − ρ)αM2/a]−β(1−ρ)/ρ n1 = [αβM1 − (1 − β)αt 1ρM2](1 − ρ)/a, u1 = θ1−αB(M1 + t 1ρM2)αβ(1−ρ)/ρ

n2 = αM2(1 − ρ)/a,

u2 = B(M1 + t 1ρM2)αβ(1−ρ)/ρk 2αt 1αρ

where B ≡ αα(1 − α)1−α[(1 − β)1−β(ρ/b)βββ/ρ]α[α(1 − ρ)/a]αβ(1−ρ)/ρ. The marginal comparative statics in this structure are: dui/dMi > 0,

dui/dMj > 0,

dui/dt1 > 0,

dni/dMi > 0,

dn1/dM2 < 0,

dn1/dt1 < 0,

du2/dk2 > 0

(6.7)

where i ≠ j. The local equilibrium in structure E2 is symmetric to that in E1. The marginal comparative statics in the two structures are summarized in the following proposition. Proposition 6.5: As transaction efﬁciency and population size increase in either country, per capita real incomes in both countries increase. The number of intermediate goods produced in a country increases with the population size in that country. The number of intermediate goods produced by a country importing intermediate goods decreases with the population size in the other country and with the transaction efﬁciency coefﬁcient in the ﬁrst country.

6.5.10 Local equilibrium in structure F The local equilibrium in structure F1 and its marginal comparative statics are: w = p2z = t 1ρ,

p1z = 1/θ,

p1x = b/ρ,

p2x = wb/ρ,

p1y = (1 − β)β−1(b/ρ)ββ−β/ρ[(1 − ρ)α(M1 + t 1ρM2)/a] p2y = (1 − β)β−1β−β(b/ρ)β[(1 − ρ)M2/a]−β(1−ρ)/ρ n1 = [αβM1 − (1 − αβ)t 1ρM2](1 − ρ)/a, ρ 1

αβ(1−ρ)/ρ

u1 = θ B(M1 + t M2) 1−α

,

n2 = M2(1 − ρ)/a, ρ 1

u2 = B(M1 + t M )

dui/dMi > 0,

dui/dt1 > 0,

du2/dk2 > 0

dni/dMi > 0,

dn1/dM2 < 0,

dn1/dt1 < 0

(6.8)

αβ(1−ρ)/ρ ρ 2 1 2

t k.

where B ≡ αα(1 − α)1−α[(1 − β)1−β(ρ/b)βββ/ρ]α[α(1 − ρ)/a]αβ(1−ρ)/ρ. The local equilibrium in structure F2 is symmetric to that in F1. The marginal comparative statics in the two structures are consistent with proposition 6.5.

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6.6 GENERAL EQUILIBRIUM AND INFRAMARGINAL COMPARATIVE STATICS Inserting the local equilibrium values of prices into (6.3), we can partition the parameter space of 12 dimensions (θ, b, a, ρ, M1, M2, α, β, t1, t2, k1, k2) into subspaces, within each of which a local equilibrium is the general equilibrium. This analysis needs the equilibrium value of the domestic price of some good in a country that does not produce this good in some structure. But we can calculate the shadow price of this good in this country from the ﬁrst-order condition of a ﬁrm, assuming that ﬁrm is active in producing this good. This analysis yields the following inframarginal comparative statics of general equilibrium: (6.9a)

The local equilibrium in structure A is the general equilibrium if either k1 and t1 or k2 and t2 are sufﬁciently small.

(6.9b)

Suppose that M1 is not too small compared to M2 and that k2 and t1 are not too small. The local equilibrium in structure C1 is the general equilibrium if t 1ρ < k1/θ. The local equilibrium in structure E1 is the general equilibrium if t 1ρ ∈(k1/θ, 1/θk2). The local equilibrium in structure F1 is the general equilibrium if t 1ρ > 1/θk2.

(6.9bI) (6.9bII) (6.9bIII) (6.9c) (6.9cI) (6.9cII) (6.9cIII) (6.9d) (6.9dI) (6.9dII) (6.9dIII)

Suppose that M1 is close to M2 and t1 is close to t2. The local equilibrium in structure D0 is the general equilibrium if k1 < θt 1ρ and k2 < t 2ρ/θ. The local equilibrium in structure D1 is the general equilibrium if k2 > 1/θt 1ρ. The local equilibrium in structure D2 is the general equilibrium if k1 > θ/t 2ρ. Suppose that M2 is not too small compared to M1 and that t2 and k1 are not too small. The local equilibrium in structure C2 is the general equilibrium if t ρ2 < θk2. The local equilibrium in structure E2 is the general equilibrium if t 2ρ ∈(θk2, θ/k1). The local equilibrium in structure F2 is the general equilibrium if t 2ρ > θ/k1.

Here, we have used the upper and lower bound of the local equilibrium value of w to ﬁnd sufﬁcient conditions for Di to occur in equilibrium, since the local equilibrium value of w in Di cannot be solved analytically. But these conditions may not be necessary. Hence, the parameter subspace (6.9c) is not completely partitioned. In other words, the inframarginal comparative statics state that three factors determine trade patterns: exogenous technological comparative advantage (its degree is represented by θ); endogenous comparative advantage (its degree is represented by 1/ρ which is the degree of economies of variety of producer goods as well); exogenous comparative advantages in transactions, which relate to relative transaction efﬁciencies of ﬁnal and intermediate goods in country 1 compared to these in country 2 (ki/kj, ti/tj, ki/ti, kj/tj) and the absolute level of transaction efﬁciency. Here, we consider economies of variety of producer goods to be equivalent to endogenous comparative advantage since two countries have the same production conditions in producing y and x (i.e. no exogenous comparative advantage exists between them in producing y and x) and the equilibrium total factor productivity and variety of producer goods positively relate to 1/ρ. If the absolute level of transaction efﬁciency is low for all goods, autarky is equilibrium. As transaction efﬁciency is improved, the general equilibrium jumps from autarky to a structure with trade. It is the interplay between exogenous and endogenous comparative advantage in production and transactions that determines to which structure the equilibrium will jump.

178 P ART I: D EVELOPMENT M ECHANISMS

In order to understand the complicated comparative statics, we take a three-step analysis. We ﬁrst consider inframarginal analysis between structures, then marginal analysis for each structure. For inframarginal analysis, we ﬁrst compare cases (6.9b), (6.9c), and (6.9d), then compare between different structures in each case. The comparison of the cases indicates that when transaction conditions of intermediate goods are similar in the two countries, each country exports and imports intermediate goods, that is, structure D occurs in equilibrium. Otherwise, the country with the better transaction conditions of intermediate goods imports such goods. This is case (6.9b) or (6.9d). Case (6.9b), in which only country 1 imports intermediate goods, is more likely to occur in equilibrium than case (6.9d), in which country 2 imports intermediate goods, if the transaction efﬁciency of intermediate goods relative to that of ﬁnal goods is higher in country 1 than in country 2 and/or if the population size in country 1 is larger. We now take the second step. We consider case (6.9b) ﬁrst. Suppose that the transaction conditions and exogenous comparative advantage change in the following way. k1 decreases and/or k2 increases, and/or θ (degree of exogenous comparative advantage) increases, and t1 increases over three periods of time. Hence, in period 1, k1 > t 1ρθ, which implies that country 1’s transaction efﬁciency of ﬁnal goods is high, its transaction efﬁciency of intermediate goods is low, and exogenous comparative advantage is not signiﬁcant. Therefore, the local equilibrium in structure C1 is the general equilibrium (see (6.9bI)). In this structure, country 1 imports z and x and country 2 imports y. Then, these parameters change: k1 decreases, θ increases, and/or t 1ρ increases such that in period 2, t 1ρk2θ < 1 < t 1ρθ/k1. Hence, the equilibrium jumps to structure E1, where country 1 no longer imports the ﬁnal good z (see (6.9bII)). In period 3, k2 increases, and/or t 1ρ, θ further increase, such that k2θt 1ρ > 1. Then the equilibrium jumps to structure F1, where country 2 imports one more ﬁnal good z (see (6.9bIII)). This implies that as the degree of exogenous comparative advantage increases and as country 2’s relative transaction efﬁciency of importing ﬁnal and intermediate goods increases compared to that for country 1, the equilibrium trade pattern shifts to increase country 2’s imported ﬁnal goods compared to country 1. Also, the equilibrium trade pattern shifts from exporting goods with exogenous comparative disadvantage in production to exporting goods with exogenous comparative advantage. Repeating this analysis for other cases, we can obtain similar results. In summary, if exogenous and endogenous comparative advantages in production and transactions go in the same direction, then a country exports its comparative advantage goods. If it has endogenous comparative advantage in production and exogenous comparative advantage in transactions, but exogenous comparative disadvantage in production for exporting a good, then it will export this good if the advantage dominates the disadvantage. Otherwise, it imports this good. In other words, a country exports a good with net comprehensive endogenous and exogenous comparative advantage in production and transactions. It will use substitution between trade of different types of goods to avoid trade with low transaction efﬁciency. Putting together marginal comparative statics for structure C, given in (6.4), and inframarginal comparative statics, given in (6.9), we can see that if the local equilibrium in structure C1 is the general equilibrium, then the conditions for dn/dt1 > 0 and dn/dM1 > 0, given in (6.4), are satisﬁed. Hence, dn/dt1 > 0 and dn/dM1 > 0 hold if structure C1 occurs in equilibrium. All marginal and inframarginal comparative statics are summarized in the following proposition. Proposition 6.6: 1) If transaction efﬁciencies for all goods are low, then the autarky structure is equilibrium, in which no international trade occurs though the number of intermediate goods, productivity, and per capita real income in each country increase with population size. As transaction efﬁciency is improved, the equilibrium jumps to a structure with trade. In an equilibrium trade pattern, a country exports goods with net endogenous and exogenous

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comparative advantages in production and transactions. It exports a good if its endogenous comparative advantage in production and exogenous comparative advantage in transactions outweigh its exogenous comparative disadvantage in producing this good. Otherwise, it imports this good. Each country will exploit the substitution between trades of different types of goods to avoid trading goods that are associated with low transaction efﬁciency. 2) If a country exports the agricultural good and imports the ﬁnal manufactured good (structure C), then as the transaction efﬁciency of intermediate goods in the other country increases from a very low to a high level, this country shifts from specialization in producing the agricultural good to exporting increasingly more intermediate goods. Changes in relative population size will shift the production of producer goods to the country with increased relative population size. Improvements in transaction conditions of ﬁnal goods beneﬁt both countries, too. Improvements in transaction conditions and increases in population size raise per capita real incomes in both countries and raise the total number of producer goods in the whole economy. 3) If a country specializes in producing producer goods (structures E or F occurring in equilibrium), an increase in population size and/or in transaction efﬁciency in either country raises per capita real income. But an increase in a country’s transaction efﬁciency or in population size in the other country will relocate the production of producer goods from the former country to the latter. 4) If the two countries trade producer goods (structure D occurring in equilibrium), then an increase in the transaction efﬁciency in a country may reduce its per capita real income, although increases in population size may have positive effects on industrialization and per capital real income. This implies that the government in each country may have an incentive to impose a tariff (reducing transaction efﬁciency for importing goods) to improve terms of trade and raise home residents’ per capita real income.

6.7 A COMPARISON WITH THE CONVENTIONAL WISDOM BASED ON MODELS WITH CRS In this section, we compare the analysis of patterns of trade and economic development in example 6.3 with the wisdom in the conventional theories of trade and economic development. We ﬁrst compare the result from example 6.3 with the core theorems of neoclassical trade theory, and then compare it with neoclassical development economics based on models with constant returns to scale (CRS). We ﬁrst compare the result from example 6.3 with the HO theorem. It is interesting to see that our comparative statics may generate a prediction that is empirically equivalent to rejecting the HO theorem. If we interpret intermediate goods as capital or producer goods, then empirically, the aggregate output level of intermediate goods in our model can be considered to be the total value of capital. With this interpretation, good y is capital intensive and z is labor intensive (i.e., z needs no capital goods for production). Hence, as the number of intermediate goods endogenously increases in response to improvements in transaction condition or to population growth, the capital intensity of good y increases. There is no reason that the country producing a lot of capital goods must export good y in our model. Hence, it is perfectly reasonable that from empirical observation, a country producing a lot of capital goods exports labor-intensive goods z and imports capital-intensive goods y. This analysis is consistent with the proposition made by Bhagwati and Dehejia (1994), that as increasing returns and intermediate goods are introduced, the neoclassical core trade theorems may not hold.

180 P ART I: D EVELOPMENT M ECHANISMS

Next, we compare our results with the SS theorem. Using the results in subsections 6.5.7 to 6.5.10, it can be shown that if structures C, E, or F occur in equilibrium, we have: d(pix/wi)/dti = 0 and d(piy/piz)/dti < 0 d(pix/wi)/dMi = 0 and d(piy/piz)/dMi < 0 d(pix/wi)/dMj = 0 and d(piy/piz)/dMj < 0. Also, if structure D occurs in equilibrium: d(pix/wi)/dtj = 0 and d(piy/piz)/dtj < 0 d(pix/wi)/dMi = 0 and d(piy/piz)/dMi < 0 d(pix/wi)/dMj = 0 and d(piy/piz)/dMj < 0. All these marginal comparative statics imply that as relative prices of goods and inputs change in response to changes in parameters, the direction of the changes of relative prices are inconsistent with the SS theorem. Here, the ﬁnal manufactured good y is capital intensive and the agricultural good is labor intensive. As the relative price of the two ﬁnal goods decreases in response to changes of transaction conditions, the relative price of capital goods to labor does not change. It is well known that the SS theorem does not hold outside of the diversiﬁcation cone. Hence, if we consider inframarginal comparative statics that involve discontinuous jumps of equilibrium across structures, then the SS theorem can easily be invalidated. The SS theorem has been used to show that tariffs can be employed to redistribute income toward the scarce factor. But common sense is inconsistent with the prediction of the SS theorem: the former says that as tariffs increase in a country that exports capital-intensive goods and imports labor-intensive goods, labor will marginally beneﬁt. But tariffs mean the country has forgone the opportunity to increase productivity by expanding the trade network. Hence, net effect that determines whether labor can beneﬁt from the increased tariffs. Our model substantiates this common sense. From (6.9b), we can see that if k2 and t1 are large, structure C1 occurs in equilibrium. Assume that country 1 is the US and country 2 is Taiwan. Now, the government in the US increases the import tariff rate, so that t1 decreases. Its inframarginal effect is to make the equilibrium jump to autarky. From subsections 6.5.6 and 6.5.7, we can see that the relative wage rate of the US to Taiwan is 1/t ρ1 > 1 in C1, and is 1 in autarky. Hence, the inframarginal effect of the tariff increase is to reduce the relative wage in the US. But the marginal effect of a decrease in t1 is to raise the relative wage rate in the US, since d(1/w) = d(1/t 1ρ)/dt1 < 0. Also, from subsection 6.5.7, the terms of trade of the US, p1y/p2z, marginally increase as t1 decreases (or as tariff rates in the US increase). These are the positive marginal effects of this tariff increase on terms of trade and wage rates in the US. But it generates negative marginal effects by reducing the trade and productivity gains that can be exploited. The net marginal effect of this tariff increase is represented by resulting changes in per capita real incomes (equilibrium utility). From (6.4), it is obvious that this net marginal effect is negative, since per capita real income decreases as a result of the tariff increase in the US (du1/dt1, du2/dt1 > 0). If we take into account the negative inframarginal effect of the tariff increase, which reduces the relative wage rate of the US, the total net effect of the tariff increase is to hurt labor in the US. We can conduct a similar analysis for the other structures C, E, and F and obtain similar results. It is interesting to see that in this example, labor in the US beneﬁts from a decrease in tariff rates, even if this tariff reduction marginally deteriorates the US’s terms of trade. This is because productivity gains from the expanded network size of trade (an increase in the number of traded intermediate goods n) may outweigh the negative effect of deteriorated terms of trade.

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The analysis of structure D suggests that the net marginal effect of a tariff increase in the US is positive (u1 increases as t1 decreases), though it marginally deteriorates terms of trade p1x/p2x and relative wage 1/w. But total net marginal and inframarginal effect could still be negative. It is straightforward from the local equilibria in C, D, E, and F that the factor price equalization does not hold in general since the equilibrium value of w is not 1 in general, though it tends to 1 as transaction costs go to 0. Hence, transaction costs explain the difference in factor prices between the countries. As transaction conditions are improved, the factor price tends to be equal for a given structure. A generalized FPE theorem may then be considered: as transaction conditions are improved, factor prices tend to be equalized. But inframarginal comparative statics (jumps of equilibrium between structures) will invalidate the generalized FPE theorem. For instance, as k2 increases, the equilibrium may jump from D0 to C1, which may cause an increase in the difference in wage rates between the two countries. It is easy to see that the RY theorem may not hold in this example. But it is not appropriate to directly compare comparative statics with the core trade theorems in the HO model because of different speciﬁcations of model structures. Hence, we should pay more attention to the distinct features of comparative statics of the model in example 6.3, which are summarized in propositions 6.3 to 6.6. The effects of changes in transaction conditions on the number of traded and intermediate goods (the degree of industrialization), productivity, per capita real income, and on discontinuous jumps of trade patterns are much more important than their effects on the structure of relative prices. In general in example 6.3, not much regularity of comparative statics relating to changes of the structure of relative prices stands out. Anything is possible, even if a speciﬁc model is explicitly speciﬁed. The regularity of comparative statics as they relate to price structure is not only model speciﬁc, but also trade-structure speciﬁc (or parameter-subspace speciﬁc). Hence, it is inconsequential to try to ﬁnd the counterparts of the SS theorem and RY theorem in the model with economies of scale. We now turn to a comparison between our comparative statics and the conventional wisdom in development economics. We ﬁrst consider the development trap, then the relationship between industrialization, income distribution, and evolution of a dual structure; and ﬁnally, development strategy. Assume that food z is a necessity and its minimum per capita consumption must not be smaller than 1 for subsistence. Suppose all labor is allocated to the production of z. Then per capita output, and therefore per capita consumption, of z is θi, which is not greater than 1 if and only if θi ≤ 1. Hence, for a value of θi small enough to be close to 1, the equilibrium number of intermediate goods must be at its minimum value 1. In other words, each intermediate good is not individually a necessity for the production of the ﬁnal manufactured good y, and therefore labor must be concentrated in the production of food, rather than dispersed in producing many intermediate goods, if productivity of food is very low. If transaction efﬁciency for international trade is also very low, then importing food is not an optimum choice. Thus a country with very low transaction efﬁciency and low agricultural productivity will be locked in the development trap associated with autarky structure A, where the number of available producer goods is very small, productivity of the ﬁnal manufactured goods is low, and trade dependence and per capita income is low. This provides a formal equilibrium theory that predicts the empirical evidence in chapter 2, that tropical regimes are in a development trap due to unfavorable geographical conditions that cause low agricultural productivity. It is not difﬁcult to show that as transaction conditions are improved, the relative output of industrial goods x and y to the agricultural good z increases, though the income share of industrial goods is always a constant, regardless of the degree of industrialization. Here, industrialization relates to an increase in the number of intermediate goods and to a decrease of price of ﬁnal manufactured goods (which is associated with an increase in the total factor productivity of ﬁnal manufactured goods). As industrialization continues, changes in the differences in per capita real income between countries do not have much general regularity.

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Suppose structure C1 occurs in equilibrium. Then from subsection 6.5.7, we can see that per > (k2t2)α. capita real income in country 1 is higher than in country 2 if and only if (θk1)1−αt 1−ρ−α 1 Suppose this inequality holds, and the difference in per capita real income between the two countries increases with θ and k1 and decreases with k2 and a. Its relationship with t1 is ambiguous. Hence, there are many determinants of the relationship between trade and inequality of income distribution between countries. Suppose industrialization and increases in trade are driven by improvements in transaction conditions. The relative change speed of transaction conditions in the two countries affects changes in the difference in per capita real income between the two countries. There is no monotonic correlation, nor is there a simple, inverted U-curve between the difference and trade, which increases with transaction efﬁciency and industrialization. If marginal comparative statics in other structures and inframarginal comparative statics are considered, our conclusion will be strengthened: little general regularity of the relationship between inequality and economic development and related trade exists. This prediction is supported by recent empirical evidence in Ram (1997) and Deininger and Squire (1996) which show that no monotonic correlation between inequality of income distribution and economic development exists. We now consider the implications of comparative statics for development strategies. Again, we may take country 1 to be the US and country 2, Taiwan. Suppose transaction efﬁciency for international trade in the initial period of time is very low in both countries, then autarky occurs in equilibrium. Assume further that the US has quite a large autarky equilibrium number of intermediate goods (quite a high degree of industrialization) due to its relatively large population size, and that Taiwan is in the development trap. Now we consider the two cases. In case (a), Taiwan is in the development trap due to the low relative productivity of the agricultural sector (bad climatic conditions and limited arable land). In case (b), the relative productivity of Taiwan’s agricultural sector is high, but its population size is too small. Assume that in period 2, transaction efﬁciency for international trade is slightly improved. The equilibrium will jump to structure F1 for case (a), since (6.9a) and (6.9bIII) indicate that for a large θ (country 2’s relative productivity of the agricultural good is low), as transaction conditions are slightly improved, the equilibrium jumps from autarky to F1. For case (b), as transaction conditions are improved, the equilibrium jumps from autarky to structure C1, since (6.9bI) indicates that for a small θ (country 2’s relative productivity of the agricultural good is high), structure C1 is more likely to occur in equilibrium. Suppose that the slight improvement in transaction conditions is not enough to ensure t1 > ta, so that n2 = 0 as shown in (6.5). This implies that Taiwan completely specializes in producing and exporting the agricultural good (without industrialization), though it can gain from exogenous comparative advantage in production. In period 3, Taiwan has several options, dependent on the transaction cost coefﬁcient or tariff rate in the US, which is 1 − t1. Suppose 1 − t1 decreases over time due to liberalization reforms or a preferential tariff rate to Taiwan in the US. Then Taiwan starts industrialization. The production of intermediate goods relocates from the US to Taiwan, increasing per capita real incomes in both countries and the relative wage rate in Taiwan (see (6.4) and (6.5)). This shift from C1 with a small n2 to C1 with a large n2 looks like an export oriented development pattern pursued by Taiwan from the 1960s to the 1980s. The driving forces of this industrialization are the open-door policy of the US (an increase in t1 and k1; see (6.4) and (6.9bI)) and Taiwan’s liberalization and internalization policy (a large k2, see (6.9b)). In the literature of development economics, structure C1 with a small n2 is sometimes called the development pattern of dependence (see Myrdal, 1957, Nelson, 1956, and Palma, 1978, for instance). But if k2 is small compared to t1 and t2 because of a high tariff of imported ﬁnal goods and a low tariff of imported producer goods in Taiwan, then the equilibrium will jump from C1 with a small n2 to D0 as Taiwan lowers its import tariff on producer goods. This policy regime is just like the import substitution strategy carried out in Taiwan in the 1950s (see for instance

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Balassa, 1980, Chenery, Robinson, and Syrquin, 1986, Meier, 1989, pp. 297–306, and Bruton, 1998). The jump from C1 with a small n2 to D0 is just like an import substitution process. The difference between export-oriented and import substitution development patterns lies in the ideas set out in propositions 6.3 to 6.5, that all countries have incentives to raise import tariff rates in structure D0, which will reduce per capita real incomes in both countries, while in structures C, E, or F, both countries have incentives to reduce tariff rates. In other words, if a government manipulates their tariff structure to pursue structure D (import substitution), D itself will justify a more distorted tariff structure which impedes economic development. Hence, this distorting tariff policy could generate a particular type of development trap. In the absence of such a distorting tariff, structure D may occur naturally in equilibrium as a consequence of certain patterns of endogenous and exogenous comparative advantages in production and transactions. Since the utilities of both countries increase with transaction efﬁciencies in structures C, E, and F, liberalization and internationalization policy is easier to carry out in these structures. This explains why an export-oriented development pattern is more successful than a pattern of import substitution. But the notion of import substitution is inaccurate, since this pattern of trade and development relies on increases in imported intermediate goods, though it promotes domestic production of ﬁnal manufactured goods. Another interesting difference in development patterns is that between structures E1 or F1 and structure E2. F1 indicates that the less-developed country (country 2) imports ﬁnal goods and exports parts and components of the ﬁnal manufactured goods. Taiwan does not export automobiles, but exports a lot of automobile and computer parts and components. In structure E2, the less-developed country imports intermediate goods and exports ﬁnal manufactured goods, similar to Hong Kong’s development pattern in the 1970s and 1980s. However, if E1 or F2 occurs in equilibrium in the absence of government intervention, which of them actually takes place is determined by natural endogenous and exogenous comparative advantage in production and transactions. It is counterproductive to pursue a particular one by using tariff policy. Any improvements in transaction efﬁciencies will promote productivity progress and increase per capita real income, regardless of which one, E or F, occurs in equilibrium. The Krugman–Venables model and the model in example 6.3 predict type II scale effects (manufacturing productivity goes up if and only if the average size of manufacturing ﬁrms increases). The type II scale effects are rejected by empirical evidence provided by Liu and Yang (2000) and Y. Zhang (2000). There are two ways to avoid these scale effects. One is to specify local economies of scale. This makes the algebra very complicated due to feedback loops between positive proﬁt and consumers’ demand functions. The other way is to develop Smithian models with intermediate goods and ﬁrms: these are presented in chapter 12.

Key Terms and Review • Dual structure between the industrial and agricultural sectors, dual structure with unequal distribution of gains from trade, and dual structure between commercialized and self-sufﬁcient sectors • Dual structure caused by disequilibrium in the labor market versus dual structure in the transitional stage of evolution of division of labor • Effects of coexistence of endogenous and exogenous comparative advantages on the emergence, evolution, and disappearance of dual structure • Underdevelopment and dual structure with underemployment • Why the deterioration of terms of trade of a country and increases in gains that it receives from trade may concur

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• Effects of economies of scale, industrial linkages, and differences in transaction conditions between countries, on the evolution of dual structure and on income distribution • Immiserizing development • Coordination problems, caused by multiple equilibria, of the industrial linkage network • Type II scale effect • The relationship between inequality of income distribution, economic development, trade, and evolution in division of labor

Further Reading Smithian models with both endogenous and exogenous comparative advantages: Gomory (1994), Liu (1999), Cheng, Liu, and Yang (2000), Zhou, Sun, and Yang (1998); Existence theorem and ﬁrst welfare theorem in a general class of Smithian models: Sun, Yang, and Yao (1999), Zhou, Sun, and Yang (1998); Underdevelopment: Bauer and Yamey (1957), and Kindleberger (1958), Myrdal (1957), Nelson (1956), Palma (1978); Dual economies and structural changes: Ranis (1988), Lewis (1955), Fei and Ranis (1964), Chenery (1979, 1986), Khandker and Rashid (1995), Dixit (1968); Equilibrium models of dual economies and economies of scale: Din (1996), Murphy, Schleifer, and Vishny (1989), Gans (1998), Kelly (1997), Fujita and Krugman (1995), Baldwin and Venables (1995), Puga and Venables (1998), Krugman and Venables (1995); Deteriorated terms of trade: Sen (1998), Cypher and Dietz (1998), Kohli and Werner (1998), Morgan (1970); Variable returns to scale: Young (1991), Panagariya (1983), Kemp (1991); Empirical evidence for the coexistence of exogenous and endogenous comparative advantage: Gallup and Sachs (1998), Sachs and Warner (1995, 1997); Development strategies of import and export substitution: Hirschman (1968), Krueger (1984), Balassa (1980), and Bruton (1998); Unequal distribution of gains from trade and deteriorated terms of trade: United Nations Economic Commission for Latin America (ECLA) (1950), Spraos (1983), Sapsford (1985), Singer (1984), Kravis and Lipsey (1981), Emmanuel (1972), Bacha (1978), Smith and Toye (1979), Alizadeh (1984), Thirwal (1986), Evans (1987); Positive correlation between inequality and growth: Banerjee and Newman (1993), Lewis (1955), Palma (1978), Li and Zou (1998), Grossman (1998), Murphy and Welch (1991), Borjas, Freeman, and Katz (1992), Karoly and Klerman (1994), Sachs and Shatz (1995); Negative correlation between inequality and growth: Alesina and Rodrik (1994), Galor and Zeira (1993), Thompson (1995), Fei, Ranis, and Kuo (1979), Aghion, Caroli, and Garcia-Pena Losa (1999), Frank (1977), Balassa (1986); Immiserizing growth: Bhagwati (1969), Sachs, Yang, and Zhang (1999a); Inverted U-curves for inequality and per capita income: Kuznetz (1955), Krugman and Venables (1995); Fluctuation of inequality: Yang and Zhang (1999), Ram (1997), Jones (1998, p. 65), Deininger and Squire (1996); Surveys of the relationship between inequality, trade, and economic development: Cline (1997), Jeffrey Williamson (1998), Burtless (1995).

QUESTIONS 1 Gallup and Sachs (1998) have found empirical evidence that different geographical conditions are responsible for development performance differences between countries. Those countries, which are located in temperate zones and have better geographical conditions for transportation, also have better long-term development performance. Use the model with endogenous and exogenous comparative advantages in examples 6.1 and 6.3 to explain the empirical evidence. 2 There are several different deﬁnitions of dual economy. Lewis (1955) and Fei and Renis (1964) take dual economy as a structure with division of population between the modern industrial sector and the traditional agricultural sector. In chapter 3, we

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3 4

5

6

7

185

consider a structure with unequal incomes between two groups of ex ante different individuals to be a dual structure. Compare the dual structure in example 6.1 to these deﬁnitions and discuss the effects of the coexistence of endogenous and exogenous comparative advantage on dual structure. Relate your discussion to the notions of underemployment and underdevelopment. Emmanuel (1972), Bacha (1978), Smith and Toye (1979), Prebisch (1988), Frank (1995), and Alizadeh (1984) argue that international trade transfers wealth from the poor countries to the rich ones. Use the models in this chapter to assess that argument. John Stuart Mill (1848) emphasized the importance of “the tendency of every extension of the market to improve the processes of production.” He argued that “a country which produces for a larger market than its own can introduce a more extended division of labour, can make greater use of machinery, and is more likely to make inventions and improvements in the processes of production.” Use the models in this chapter to formalize his ideas. The United Nations, Department of Economic Affairs (1950, pp. 7, 13–24) and Lewis (1952, p. 118) argue, based on the measurement of prices of the United Kingdom’s commodity terms of trade or the terms of trade between primary products and manufactured products, that international market forces have transferred income from poor to rich nations through deterioration in the terms of trade of less-developed countries. Meier (1989, pp. 390–2) argues that this does not provide a sufﬁciently strong statistical foundation for any adequate generalization about the terms of trade of poor countries. The import price index conceals the heterogeneous price movements within and among the broad categories of foodstuffs, raw materials, and minerals; no allowance is made for changes in the quality of exports and imports; there is inadequate consideration of new commodities, and the recorded terms of trade are not corrected for the substantial decline in transportation costs. The introduction of new products and qualitative improvements have been greater in manufactured products than in primary products, and a large proportion of the fall in British prices of primary products can be attributed to the great decline in inward freight rates. Even if it were true that the less-developed country experienced a secular deterioration in their commodity terms of trade, this deterioration may have been caused by productivity progress in the export sector. Hence, as long as productivity in export industries is increasing more rapidly than export prices are falling, the single-factoral terms of trade (commodity terms corrected for changes in productivity in producing exports) may increase, and the country’s real income can rise despite the deterioration in the commodity terms of trade. Use the model in example 6.1 to formalize this analysis. Many economists argue that deterioration of terms of trade for less-developed countries hinders economic development in these countries. Other economists try to ﬁnd empirical evidence for or against the fact that terms of trade for developing countries have been worsening, or to measure the adverse effects of the worsening terms on economic development (see for example Morgan, 1970, and Kohli and Werner, 1998). Sen (1998) reports that from 1990 to 1995, Thailand’s GDP increased by 49 percent, its export prices increased by 18 percent, and its import prices by 21 percent. During the same period, Singapore’s GDP increased by 49 percent, its export prices decreased by 18 percent, and its import prices decreased by 9 percent. Use the model in example 6.1 to explain this fact. Murphy, Shleifer, and Vishny (1989) show that if income distribution is very unequal, a limited market will adversely affect economic development. Compare

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this theory on the relationship between dual structure and economic development to the Smithian mechanism for economic development in example 6.1. 8 Lewis (1955) argues that an exogenously ﬁxed wage rate that is higher than the market clearing level generates a labor surplus in the traditional agricultural sector. As capital accumulates over time in the modern industrial sector, marginal productivity of labor relative to capital in the industrial sector increases, so that this sector can absorb surplus labor and grow at no cost to the agricultural sector. Compare this development/dual economy mechanism to the Smithian mechanisms in examples 6.1 and 6.2. Find empirical evidence to test one mechanism against the other. 9 Chenery et al. (1986, pp. 13–32), used models with disequilibrium and changes of taste to explain structural changes in an economy. According to them, “Given imperfect foresight and limits to factor mobility, structural changes are most likely to occur under conditions of disequilibrium; this is particularly true in factor markets. Thus a shift of labor and capital from less productive to more productive sectors can accelerate growth.” Use the equilibrium models in this and previous chapters to explain structural changes and dual structures, and discuss the differences between the two approaches. Which of them is analytically more powerful, and why? 10 Chenery et al. (1986) emphasize the effects of changes to the demand side on structural change in the economic development process. For instance, they argue that changes in preferences and in income alter the expenditure share of agricultural goods. Other economists pay more attention to effects of changes to the supply side on structural change – for instance, changes in technology alter the income share of industrial output. Use the general equilibrium analysis in this text to explain why the separation between demand and supply analyses is inconsistent with the notion of general equilibrium. For example, income is determined by productivity and network size of division of labor, which are in turn determined by the extent of the market, which relates to aggregate income. Also, use models in this chapter to explain why economic structure may change endogenously in the absence of changes in production functions and in preferences. 11 Lewis (1955) uses a model with disequilibrium in the labor market to analyze dual structure. Use the approach developed in chapter 13 (below) to specify a formal dynamic general equilibrium model with constant returns to scale technology in two sectors. One of the sectors needs capital and labor as inputs, and the other sector needs only labor as an input in production. Show that in the absence of exogenous technical changes and of disequilibrium in the labor market, the equilibrium-relative size of the two sectors can evolve over time. Use this example to discuss the effects of economists’ limited capacity to manage general equilibrium models on the economic thinking in the 1950s and 1960s. 12 Lewis (1955) considers economic development and structural change to be a process of transformation of the traditional sector with a low degree of exchange to a modern sector with a high degree of exchange. Use the models in this chapter to formalize his conjecture. 13 Compare the policy implications of the model in example 6.1 with the view that underdevelopment is caused by the exploitation of less-developed economies by capitalist developed economies (Myrdal, 1957, Nelson, 1956, Palma, 1978). 14 Use the inframarginal comparative statics in table 6.3 to analyze a recent debate on competitiveness. Show that a country with low transaction efﬁciency cannot receive

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15 16 17 18

19

20

21

22

23

187

gains from trade in the transitional stage of economic development. Verify the following statements. From the northwest block of table 6.3, we can see that if the degree of economies of specialization in country 1, b, which negatively relates to α, is small relative to c, which negatively relates to γ, or k1 < α23−c, then structure PC is the equilibrium where this country is in an inferior position in the transitional stage. If c is small relative to b, or k2 < aγ23−b, structure CP occurs in equilibrium, where country 2 is in an inferior position in the transitional state. You may interpret absolute level of transaction efﬁciency and degree of economies of specialization for a country in producing a good as degree of competitiveness. Compare the dual economy model in example 6.1 with the Ethier model of dual economy in example 5.2 and the Sachs and Yang dual economy model in example 5.4. Compare the dual economy model in example 6.1 with the model in example 6.3, analyze the empirical implications of the differences, and design a method to test the two types of model against data. Use the model in example 6.3 to show that the notions of import substitution and export substitution may be misleading. Use this model to analyze the welfare effects of industrial and trade policies. Some economists argue that imperialism and colonialism are detrimental to economic development because they deter the expansion of a variety of industrial sectors in the less-developed country. Use the models in this chapter to assess this statement. In your analysis, compare and contrast division of labor, diversity of professional occupations, and individuals’ specialization. Compare Taiwan’s development pattern, which does not promote domestic production of automobiles, but promotes exports of components and parts produced by many small companies, with South Korea’s development pattern, which promotes domestic production of automobiles and other ﬁnal manufactured goods. Use the extended KV model in example 6.3 to assess the effects of the two different development patterns. Use the extended KV model in example 6.3 to comment on the following statements: “Any industrial and trade policies are harmful for economic development and exploitation of gains from trade.” “Industrial and trade policies can be used to enhance a developing country’s performance of trade and development and thereby signiﬁcantly enhance the welfare of the country.” Use the model in example 6.3 to analyze the differences between three types of coordination problem in an industrial linkage network. The ﬁrst two types are caused by multiplicity of equilibria. One of them involves interest conﬂicts between the countries (in a Ricardo model with dichotomy between pure consumers and ﬁrms). The other does not (the MSV model in example 5.3). The ﬁnal type is caused by a particular kind of distortion in the equilibrium models of monopolistic competition that are not beneﬁcial to any decision-makers (in the DS model in example 5.1 and the Ethier model in example 5.2; see also example 2 in ch. 5). Hirschman (1958) argues that forward (to downstream sectors) and backward (to upstream sectors) linkages to the sectors with economies of scale in production are more important than terms of trade for a developing country to gain from trade. Use the models in this chapter to formalize this idea. Some economists argue (see Meier, 1989, pp. 381–93) that if income elasticity of demand for goods exported by a developing country is low, export-led industrialization may not beneﬁt the economic development of the country. Compare the

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24

25

26

general equilibrium analysis with this analysis of demand. Why is the marginal analysis of demand often very misleading? Some economists argue that the demonstration effects of international trade will increase the desire for consumption and reduce saving and investment. This will be detrimental for economic development. Use the model in example 6.3 to show that as the taste parameter for imported ﬁnal manufactured goods increases in country 1, economic development may be speeded up in structure C1. Ram (1997), Jones (1998, p. 65), and Deininger and Squire (1996) have found empirical evidence that inequality ﬂuctuates as an economy develops. Yang and Zhang (1999, and see exercise 13) specify different types of individuals in each country in example 6.1 and show that inequality of income distribution ﬂuctuates as different groups are sequentially involved in an increasingly higher level of division of labor. Use that model to explain the empirical evidence. Discuss the effect of a change in analytical framework on the interpretation of empirical observation in connection with the Albert Einstein’s statement as follows: “It is quite wrong to try founding a theory on observable magnitudes alone. . . . It is the theory which decides what we can observe” (quoted in Heisenberg, 1971, p. 31). Why is marginal analysis not enough for managing the model in example 6.3?

EXERCISES 1 Following the method used to draw ﬁgure 6.2, draw individual PPFs, the aggregate production schedule for autarky, and the aggregate PPF in the model in example 6.2. Show that there are economies of division of labor in this model. 2 Suppose that b = c = 2 in example 6.1. Show that the inframarginal comparative statics are given by the table below. Interpret the results.

0 < k1 ≤ 16/27 0 < k2 ≤ 16/27 k1k2 < 4a(2/3)6 AA

16/27 < k1 ≤ 1

k1k2 > 4a(2/3)6

k1 < k1 ∈ k1 > 8/27 4a/27 (4a/27, 8/27)

k1 < 8/27 k2 < k1 < 8/27, 8a/27: k2 < 8a/27: PC CP CC AC

16/27 ≤ k2 < 1 k2 < 4a/27 k2 ∈ (4a/27, 8/27): CA CP

k2 > 8/27

PC

CC

Structure CC

CC

3 Show that in the previous exercise, if k2″ > k2′, k2′ ∈(4a/27, 16/27), k1 ∈(16/27, 1), a < 4, k2″ ∈(16/27, 1) and if k2′ < 8/27, then as k2 increases from k2′ to k2″, country 2’s terms of trade deteriorate. Meanwhile, each individual’s utility in country 2 increases from autarky to a higher level. 4 If we assume that there are economies of specialization only for individuals in country 1 in producing two goods, whereas constant returns prevail in country 2 in producing the two goods, the system of production functions is then:

C HAPTER 6: C OMPARATIVE A DVANTAGE b , x1 + x1s = L1x

c y1 + y 1s = L 1y ,

x2 + x 2s = aL 2x,

y2 + y 2s = L2y

Draw individual PPFs, the aggregate production schedule for autarky, and the aggregate PPF. Show that the inframarginal comparative statics of general equilibrium are given in the table below. k2 < 1

k2 = 1

k1 ∈ a > 2b−c (0, 4θ) k1k2 > θ2b−c+2/a k1k2 < θ2b−c+2/a a > 2b−1

AA

a < 2b−c

a > 2b−c

k1k2 < aθ2c−b+2

a > 2b−1

a < 2b−1 AA

k1 < θ2 /a CP+ PC− b+1

k2 < 21−c CP−

k1k2 > aθ2c−b+2 PC+

k1 > θ2b+1/a k2 > 21−c CC− k1 ∈ a > 2b−1 (4θ, 1) k2 < 2b−c/a k2 ∈ (2b−c/a, 21−c) CD− k2 > 2

1−c

a < 2b−c a < 2b−1

k1 < θ2c−b+2/a k1 ∈(θ2 θ2b+1/a) PC−

k1 < aθ2c−b+2 AD

AD

/a, k1 > k1 > aθ2c−b+2 θ2c−b+2/a PC− PC+

c−b+2

k1 > θ2b+1/a CC−

a < 2b−1

k2 < a2 c−b

DA

DA

k2 > 2 /a

k2 > a2c−b

DC−

DC+

b−c

a > 2b−1

a < 2 b−1

CC−

DC−

DC+

CC−

where θ ≡ bbcc/(b + c)b+c.

5 Suppose b = c = 2 in the model in example 6.1. A value tax rate t is imposed on each dollar of imported goods, and the total tax revenue is evenly distributed among the buyers of the goods. Solve for the general equilibrium and its inframarginal comparative statics. Compare the results to the solutions in exercise 1 in chapter 4. Discuss the different implications of tax and transaction costs in a neoclassical equilibrium model and in a Smithian equilibrium model. 6 Liu, 1999: Consider the Ricardian model with endogenous cum exogenous comparative advantage, in which the number of type 1 persons is M1 and the number of type 2 persons is M2. Assume that all individuals have the same Cobb–Douglas utility function with the same taste for the two goods. The production functions for type i persons are: xi + x is = Max{lix − bix, 0} yi + y is = Max{liy − biy, 0}. Solve for the Walrasian general equilibrium and its inframarginal comparative statics. Use your results to analyze the relationship between international and

189

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domestic trade and dual structure in the transitional period from autarky to a high level of division of labor. 7 Suppose the production functions in the previous exercise are: xi + x is = Max{aix (lix − b), 0} yi + y is = Max{aiy (liy − b), 0} Solve for the Walrasian general equilibrium and its inframarginal comparative statics. 8 Suppose the production functions in exercise 6 are: x1 + x 1s = Max{l1x − b, 0}, y1 + y 1s = l1y,

x2 + x 2s = Max{l2x − c, 0},

y2 + y 2s = al2y.

Solve for the Walrasian general equilibrium and its inframarginal comparative statics. Use the model to explain pattern of trade with transaction and production conditions in two countries. 9 Draw the equilibrium production schedule in autarky and the PPF and identify economies of division of labor in example 6.1. 10 Find the parameter subspace within which a country’s terms of trade deteriorate and its gains from trade increase as the equilibrium shifts from structure PC to structure CC in example 6.1. 11 Liu (1999) introduces intermediate goods and tariffs into the Smithian model in example 6.1 to analyze the development patterns of import and export substitution. Design such a model and examine the different implications of it and the model in example 6.3 for the analysis of development patterns. 12 Yang and Zhang, 2000: Introduce tariffs into the model in example 6.1, and allow the Nash tariff game and Nash tariff negotiation. (See chapter 3 for the two regimes.) Analyze under what conditions unilateral protection tariffs and unilateral laissez fairism coexist and under what conditions Nash tariff negotiation occurs in equilibrium. 13 Yang and Zhang, 1999: Assume that in the model in example 6.1, there are two types of individuals in country 1. Type a persons and type b persons are distinguished by their transaction conditions. We assume that ka = k, kb = t, and k > t. In other words, each type a person has higher transaction efﬁciency than each type b person. Also, we assume that in country 2, k2 = k. This implies that country 2 is a developed country which has better transaction conditions. Country 1 is a less-developed country, where some residents (who might be urban or coastal residents) have the same transaction condition as in a developed country, but the rest of the population have a lower transaction efﬁciency. The production conditions are the same for all individuals in the same country, but different between the countries. Hence, the production functions for a type i consumerproducer are xj + x js = L cjx, yj + y js = Ljy, j = a, b. x2 + x2s = L c2x, y2 + y2s = rL2y, where x is, y is are respective quantities of the two goods sold by a type i person, Lis is the amount of labor allocated to the production of good s (= x, y) by a type i person, and Lix + Liy = 2. It is assumed that r, c > 1. Solve for equilibrium and its inframarginal comparative statics. Show that as transaction conditions are improved, the level of division of labor increases and inequality of income distribution ﬂuctuates. 14 Yang and Zhang, 1999: Assume that in the developed country there are also two types of individual. Show that as more individuals are sequentially involved in

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15

16

17

18

19

the division of labor, some individuals achieve a higher level of specialization before others do. This increases inequality. As the latecomers catch up, inequality decreases. As the leading group goes to an even higher level of specialization, leaving the others behind, inequality increases again. Show how such a ratcheting process generates the ﬂuctuation of inequality. Prove that in the model in example 6.3, the following structures cannot occur in equilibrium for ki ∈(0, 1): A structure in which each country produces y, z, x, and one of them exports y, x and the other exports z, x; A structure in which each country produces all goods, and imports and exports of all goods cannot occur in equilibrium. (Clue: use the ﬁrst-order conditions for the decision problems of consumers in two countries to show that equilibrium requires k1k2 = 1, which contradicts ki ∈(0, 1).) Puga and Venables, 1998: Suppose that in example 6.3, the production function for the agricultural sector is a Cobb–Douglas function of labor and land. Solve for local equilibria in all possible market structures. Use the model to analyze the effects of geographical concentration of industrial production on dual structure. Introduce tariffs into the KV model to analyze the effects of trade policy on development pattern. Assuming that the two governments can choose between a Nash tariff game and Nash tariff negotiations, as in the Ricardian model in chapter 3, what policy regime will occur if structure D takes place in equilibrium? Consider the model in example 6.3. Prove that the structure in ﬁgure 6.3(b) cannot occur in equilibrium. (Clue: use the market clearing conditions to show that equilibrium requires x11 = k1x21, x12 = k1(k1k2)ρ/(1−ρ)x22, x11 + x12 = x1, x21 + x22 = x2, which contradicts ki ∈(0, 1)), where xij is the amount of an intermediate good produced in country i and sold in country j.) Show that the corner equilibrium in structure C2 is: w = k2−ρ,

p1z = 1, β−1 −β/ρ

p2y = (1 − β) β

p2x = bw/ρ,

p1x = b/ρ,

β −ρ 2

(b/ρ) k [(1 − ρ)α(M2 + k 2ρM1)/a]β(1−1/ρ),

n1 = [(1 − ρ)/a] [M1β − (1 − β)k2−ρM2], n2 = [(1 − ρ)/a] [M2αβk 2−ρ − (1 − α)βM1], −α u1 = Bk1αp 2y ,

20

21 22

−α u2 = Bk1−α−ρ p 2y , 2

where B ≡ (1 − α)(1−α)αα. Prove a proposition for this structure similar to proposition 6.3. In the original version of the KV model, the transaction cost for the agricultural good is 0 and transaction conditions for industrial goods y and x are the same in the two countries. Prove that for this version of the KV model, the local equilibrium in the structure in ﬁgure 6.3(b) is indeterminate, the equilibria n1 and n2 are indeterminate, and equilibrium values of xij , yij , and zij are indeterminate. Assume that in the KV model, country 1’s total productivity of good λ is θ > 1. Solve for local equilibria in all possible structures and their comparative statics. Then compare your results with the results in example 6.3. Use the model in example 6.3 to formalize Chenery and Meier’s idea that exporting ﬁnal manufactured and importing intermediate goods can be a development pattern, which may evolve into the pattern of exporting producer goods.

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Notes 1 It can be shown that there are multiple equilibria in some razor-edge cases with inequalities replaced by equalities. For instance, if 2b−1 > a, 0 < k1 < 4α, k1 < aα24−b−c, and k2 = 4γ, multiple equilibria occur. 2 The complete partition of the parameter space when the razor-edge cases are considered is very cumbersome. But the essence of our results here would not be changed under such circumstances.

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7

7.1 ENDOGENOUS TRADE THEORY AND AN ENDOGENOUS NUMBER OF CONSUMER GOODS Smith explained domestic and international trade by individuals’ decisions in choosing their levels of specialization. Hence, his rationale for both international and domestic trade was the same: economies of division of labor. But within the neoclassical framework, the dichotomy between pure consumers and ﬁrms implies that the rationale for domestic trade differs from that for international trade. Domestic trade is essential for pure consumers even if comparative advantage, economies of scale, and differences in taste between individuals are absent, since pure consumers do not produce and will die from starvation in the absence of domestic trade between them and ﬁrms. However, international trade will not take place if these elements are not present, since each country has ﬁrms, or each country is a consumer-producer. Therefore, neoclassical trade theory cannot explain why and how international trade emerges from domestic trade. The ﬁrst purpose of this chapter is to use a Smithian model to illustrate the intimate relationship between economic development, trade, structural changes, and evolution of division of labor. This model explains international and domestic trade by way of individuals’ decisions in choosing their levels of specialization, and explains the emergence of international trade from domestic trade by way of evolution in division of labor and evolution in endogenous comparative advantage between ex ante identical individuals. Since the number of goods in the models in this chapter is a parameter or a variable instead of a speciﬁc number, structural changes and their relationship with evolution of division of labor and economic development can be more thoroughly investigated. In section 7.2, we specify a Smithian model with endogenous specialization and the number of goods as a parameter. In section 7.3, individuals’ decisions in choosing their patterns of specialization and resource allocation are solved. Then the inframarginal comparative statics of the decisions are analyzed in section 7.4. Section 7.5 is devoted to the analysis of the general equilibrium network of division of labor. Then inframarginal comparative statics of general equilibrium are used to analyze many concurrent phenomena of structural changes as different aspects of economic development. Section 7.5 analyzes how international trade emerges from domestic trade. In section 7.6, we combine the approach of endogenizing individuals’ levels of specialization with the approach of endogenizing the number of all available goods, to investigate the role of the development of division of labor in accounting for the emergence of new goods. More than

194 P ART I: D EVELOPMENT M ECHANISMS

two centuries ago, Josiah Tucker (1755, 1774) noted that the development of division of labor creates the conditions for the emergence of new goods. Casual observations indicate that in an autarchic society without much division of labor, the variety of available goods is small, whereas in a developed economy with a high level of division of labor and specialization, the variety of available goods is large. Does this positive correlation between specialization and variety of available goods happen by coincidence? Or is it generated by some economic mechanism that is essential for understanding economic development? We can guess. Assume that there are economies of specialization, transaction costs, and economies of consumption variety or economies of complementarity between consumption goods because of individuals’ preferences for diverse consumption. Assume further that the calculation cost of the optimum decision increases with the number of consumption goods and accordingly counteracts the economies of consumption variety. Therefore, there are several trade-offs among four elements: economies of specialization, transaction costs, economies of consumption variety, and the management costs of consumption variety. The efﬁcient trade-offs are, of course, dependent on the parameters of transaction efﬁciency, the degree of the economies of consumption variety, the management cost of consumption variety, and the degree of economies of specialization. For a sufﬁciently low transaction efﬁciency, each person has to choose autarky. The narrow scope for trading-off among economies of specialization, economies of consumption variety, and the management cost of consumption variety, due to each individual’s limited time endowment in autarky, may force individuals to produce few goods. It would not be feasible in autarky for individuals to self-provide cars, trains, airplanes, computers, television sets, telephones, and various detergents. However, as transaction efﬁciency is improved, the scope for trading-off economies of specialization against transaction costs is enlarged, so that the level of division of labor is increased. The increased division of labor enlarges the scope for trading-off economies and diseconomies of consumption variety, so that each individual’s level of specialization and the number of available consumption goods can be simultaneously increased through a higher level of division of labor between specialists who produce different goods. Thus, in a Smithian model with a CES utility function, the number of consumption goods and the level of division of labor can be endogenized simultaneously if a trade-off between economies and diseconomies of consumption variety is speciﬁed in addition to the trade-off between economies of specialization and transaction costs. The endogenization of the number of goods is associated with the endogenization of emergence of new goods, which is considered by many economists as endogenous technical progress. If transaction efﬁciency is low, then the production functions of some goods cannot be seen in equilibrium. As transaction efﬁciency is improved, the production functions of new goods emerge from a greater scope for trading-off economies of specialization against transaction costs and economies of consumption variety. Hence, in our model of endogenous specialization with an endogenous number of goods, productivity progress is associated with the emergence of the production functions of new goods. This view of endogenous technical progress differs from the conventional view that attributes technical progress to investment in research and development. According to our view of endogenous technical progress, investment in R&D alone is not sufﬁcient for emergence of new goods and related new production functions. It is essential for the emergence of new goods that the size of the network of division of labor and the related extent of the market are sufﬁciently large to create the condition for the commercialization of new technology. But a sufﬁciently high transaction efﬁciency is essential for a large size of the network of division of labor. In section 7.9, we consider a model with an endogenous level of specialization in trading activities. If individuals are allowed to choose levels of specialization in trading activities and if there are economies of specialization and transaction costs in the trading activities, then transaction efﬁciency is endogenously determined by the level of division of labor between

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production and transactions and within the professional trading sector. Hence, the level of division of labor is determined by transaction efﬁciency, which is determined by the level of specialization in the trading sector, which is in turn determined by the efﬁcient trade-off between economies of specialization in the trading sector and the transaction cost of trading services. Therefore, we can use a Smithian model to explain the equilibrium level of division of labor and productivity by the transaction conditions of transaction services, and investigate the effects of institutions and government policies on economic development via their effects on the transaction conditions of transaction services. In this general equilibrium model, transaction efﬁciencies, the network size of division of labor, the extent of the market for transaction services, the level of division of labor within the transaction sector, the emergence of professional middlemen, productivity, and per capita real income are interdependent. The notion of general equilibrium is powerful for working out a development mechanism that simultaneously determines all of them. Finally, section 7.10 presents the Becker–Murphy model, with a trade-off between economies of specialization and coordination costs, which can explain evolution of division of labor by improvements of coordination efﬁciency in the absence of increases in population size.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n n n n

n n n n

Why can ﬁxed learning costs generate economies of division of labor? What are the differences between the neoclassical and Smithian theories of demand? What are the differences between neoclassical trade theory and Smithian trade theory? Why does evolution in division of labor generate concurrent increases in the following variables: the degree of commercialization, trade dependence, the degree of interpersonal dependence, the extent of the market, the number of types of markets, productivity, the extent of endogenous comparative advantage, the degree of diversity of economic structure, individuals’ levels of specialization, the degree of production concentration, and the degree of market integration? How does international trade emerge from domestic trade? Why is endogenous comparative advantage a more important determinant of trade dependence and economic development than exogenous comparative advantage? Why does the development of division of labor create conditions for a greater consumption variety and the emergence of new goods? What are the development implications of the emergence of professional middlemen?

7.2 A MODEL OF ECONOMIC DEVELOPMENT WITH FIXED LEARNING COSTS Example 7.1: A Smithian trade model with ﬁxed learning costs (Yang, 1996). As in the previous chapters, we assume that the set of consumer-producers is a continuum of mass M. The set of consumer goods is either a ﬁnite set {1, 2, . . . , m} or a continuum with mass m. As shown by Zhou, Sun, and Yang (1998), the assumption of a continuum of goods is not essential for the existence of equilibrium in this kind of model, though it may simplify the algebra of a symmetric model by avoiding an integer problem. If the set of goods is considered as a continuum, then symbols for summation Σ and multiplication Π should be viewed as integration. If the set of goods is ﬁnite, then all derivatives with respect to the number of goods in the ﬁrst-order condition for maximization should be considered as the approximation of the ﬁrst-order condition for integer programming. The self-provided amount of good i is xi. The

196 P ART I: D EVELOPMENT M ECHANISMS x2 2(1 − A) M 2 − 3A C 2 − 4A D 1−A E 1 − 2A

A

K B

F

G

0

H I J L 1 − 2A 1 − A 2 − 4A 2 − 3A 2(1 − A) x1

Figure 7.1 Economies of division of labor generated by ﬁxed learning costs

amount of good i sold in the market is x is. The amount of good i purchased in the market is x id. The transaction cost coefﬁcient for a unit of goods bought is 1 − k. Thus, kx id is the amount an individual obtains when she purchases x id. The amount consumed of good i is thus x ic ≡ xi + kx id. The utility function is identical for all individuals: m

u = ∏ x ic = x1c , x2c , . . . xmc

(7.1)

i =1

The system of production for each consumer-producer is: x ip ≡ xi + x is = Max{Li − A, 0}

∑L

i

= L 1 + L 2 + . . . + Lm = 1

i = 1, . . . , m

(7.2a) (7.2b)

i

where x ip is the output level of good i, Li is an individual’s level of specialization in producing good i, and A is a ﬁxed learning and training cost in producing each good. This system of production displays economies of specialization for each individual in producing each good. For Li > A, the average labor productivity, (xi + x is )/Li = 1 − (A/Li), increases with an individual’s level of specialization in producing good i, Li. Houthakker (1956) uses a graph to illustrate the development implications of the ﬁxed learning cost. A similar graph in ﬁgure 7.1 shows that economies of division of labor exist for the production condition deﬁned in (7.2) with m = 2. An individual’s transformation curve is EFGH in ﬁgure 7.1. The aggregate transformation curve for the two persons when each of them produces two goods, with no division of labor, is segment DI. The aggregate transformation curve for the division of labor, which implies at least one person producing only one good, can be obtained in the following way. Suppose that an individual produces only good 1. Her output level is represented by the vertical line HK. Assume that another individual can choose any production conﬁguration, so that his transformation curve is still EFGH. If we move the individual transformation curve horizontally to the right by distance 1 − A, the aggregate transformation curve we obtain for the two individuals is KBJL. Suppose now, alternatively, that she produces only good 2 instead

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of good 1, while he can still choose any production pattern. Now the aggregate transformation curve is MCAK. Therefore, in the simple two-good-two-person case, the aggregate transformation curve for the division of labor, where at least one individual produces only one good, is MCAKBJL. It is obvious that the aggregate transformation curve for the division of labor is higher than the aggregate transformation curve for autarky, even if the two persons are ex ante identical and even if exogenous comparative advantage is absent. This is because each individual’s total learning cost is 2A if she produces both goods, and her total learning cost is reduced to A if she produces only one good. That is, her time for production increases from 1 − 2A to 1 − A as she reduces the number of goods produced from two to one. Hence, the total learning cost for the economy with two individuals is 4A in autarky, 3A for partial division of labor (segments CA and BJ), and 2A for complete division of labor (point K) in an economy with two individuals. The economies of division of labor are represented by the difference between the transformation curve for the division of labor, MCABJL (which is also the PPF), and the transformation curve for autarky, DI. In section 7.6 we will show that as transaction efﬁciency is improved, the equilibrium aggregate production schedule jumps from line DI to point K, generating economic development. Charles Babbage (1832, pp. 170–4) noted this phenomenon more than a century ago, pointing out that division of labor can save on ﬁxed learning costs by avoiding duplicated learning and training. Becker (1981), Barzel and Yu (1984), and Rosen (1983) have formalized the idea that division of labor can increase the utilization rate of a ﬁxed learning and training investment. Tamura (1992) and Yang (1996) have explored the general equilibrium implication of ﬁxed learning costs for the endogenization of individuals’ levels of specialization. Economies of division of labor are, of course, generated by endogenous comparative advantage. When ex ante identical individuals choose different levels of specialization in an activity, a specialist endogenously acquires a higher productivity than a novice. Consider the two-persontwo-goods example in ﬁgure 7.1, where the two individuals choose complete division of labor. If person 1 specializes in producing good 1 (accordingly choosing L1 = 1), her labor productivity in that good is Max{(L1 − A)/L1, 0} = 1 − A. For person 2, specializing in good 2 (and thus choosing L1 = 0), labor productivity in good 1 is Max{(L1 − A)/L1, 0} = Max{−∞, 0} = 0. The difference in productivity between the specialist and novice is endogenous comparative advantage. The following story should give you a sense of how division of labor is generated by ﬁxed learning costs. Suppose there are two individuals: a professor and a secretary. If they do not have division of labor, then each of them must engage in both research and secretarial support work. The ﬁrst type of work requires education at the Ph.D. level, while the second type requires education in a secretarial school. Hence, each of them must get two types of education to do the two kinds of jobs. If the professor specializes in research and the secretary specializes in secretarial work, the professor can avoid the cost of training at secretarial school and the secretary can avoid the cost of training for a Ph.D. For each of them, the utilization rate of the investment in specialized learning increases as they spend more time in their specialties. The beneﬁt of division of labor can be reaped by both of them. The secretary is able to begin working several years earlier than he could if he were in school during those additional years, so that his lifetime income is increased. Similarly, specialization increases the professor’s productivity in research and in the utilization rate of her learning investment in a Ph.D. program, and reduces her total ﬁxed learning cost. Economies of division of labor based on ﬁxed learning cost are more ubiquitous than they seem, since ﬁxed learning cost can be caused by a trial-and-error process that is common in all production activities. The next section investigates how the market sorts out the efﬁcient trade-off between transaction costs and economies of division of labor based on a ﬁxed learning cost.

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7.3 HOW ARE DEMAND AND SUPPLY FUNCTIONS DETERMINED BY INDIVIDUALS’ LEVELS OF SPECIALIZATION? It can be shown that the Wen theorem (see theorem 4.1 in section 4.2, chapter 4 above) is applicable to the model in this chapter. An individual does not simultaneously buy and sell the same good; nor simultaneously buy and self-provide the same good; and she sells at most one good. This implies that the decision conﬁguration of each consumer-producer who sells good i satisﬁes the following conditions: xi > 0,

xis > 0,

xid > 0,

xr = x = Lr = 0, xj, Lj > 0,

Li = 0

x > 0,

s r

∀r ∈R,

d r

x = x = 0, s j

d j

(7.3)

∀j ∈J

where R is the set of n − 1 goods that are purchased from the market, and J is the set of m − n nontraded goods. ∀ means “for any,” ∈ means “an element of.” In words, the conditions imply the following propositions: for each good i that is sold, its self-provided quantity, its quantity for sale, and the level of specialization in producing it are positive, while its quantity purchased is 0; for each good r that is purchased, its self-provided quantity, its quantity for sale, and the level of specialization in producing it are 0, while its quantity purchased is positive; for each nontraded good j, its self-provided quantity and the amount of labor allocated to produce it are positive, while its quantities sold and bought are 0. According to these conditions, the decision problem of an individual selling good i can be set out as follows:

Max: u i = x ic ∏ x rc ∏ x cj = x i (∏ kx rd ) ∏ xj r ∈R

j ∈J

r ∈R

j ∈J

s.t. x ≡ xi + x = Max{Li − A, 0}, p i

s i

x = x ≡ xj = Max{Lj − A, 0}, c j

p j

(production function for good i) ∀j ∈J

(production function for good j)

Li + ∑ L j = 1

(endowment constraint for time)

j ∈J

p i x is = ∑ p r x rd

(budget constraint)

r ∈R

where pi is the price of good i, x rc ≡ kx rd and x ic ≡ xi are respective quantities of goods r and i that are consumed, xi, x is, x rd, Li, xj, Lj, and n are decision variables. Having inserted all constraints into ui , we can express ui as a function of Li, Lj, x is, x rd, and n. One of all x rd can be eliminated using the budget constraint, and one of all Lj can be eliminated using the endowment constraint for time. Hence, we can convert the original constrained maximization problem to a nonconstrained maximization problem:

Max: ui = xic xsc ∏ xrc ∏ x jc = xi kxsd (∏ kxrd )(Lt − A)∏(L j − A) r

where

j

r

x ic = xi = Max{Li − A, 0} − x is xsd = ( pi xis − ∑ pr xrd )/ps

s, r ∈R, s ≠ r

r

Lt = 1 − Li − ∑ L j j

t, j ∈J, t ≠ j

j

(7.4)

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The ﬁrst-order conditions for problem (7.4) are: ∂ui/∂x rd = 0 ∂ui/∂x is = 0 ∂ui/∂Lj = 0 ∂ui/∂Li = 0 ∂ui/∂n = 0

(7.5a) (7.5b) (7.5c) (7.5d) (7.5e)

Since (7.5a) holds for all r ∈R, and (7.5c) and for all j ∈J, they can be used to prove that pr x rd is the same for any r ∈R and that xj is the same for any j ∈J, respectively. Using this result and the constraint in (7.4), utility can be expressed as: ⎛ kx s p ⎞ u i = (Li − A − x ) ⎜ i i ⎟ ⎝ pr ⎠ ∂u i ∂u i = =0 ∂Li ∂x is s i

n−1

⎛ 1 − Li ⎞ ⎜ m − n − A⎟ ⎝ ⎠

m− n

.

yields the optimum values of Li and x is. This, together with (7.4), yields: Li = A + n[1 − (m − n + 1)A]/m x is = (n − 1)[1 − (m − n + 1)A]/m Lj = [1 + (n − 1)A]/m, xi = xj = [1 − (m − n + 1)A]/m, x rd = pir x is /(n − 1) = pir[1 − (m − n + 1)A]/m, ∀r ∈R

(7.6)

where pir ≡ pi/pr. As shown in chapter 4, the neoclassical supply function in (7.7a) is independent of prices because of the unitary elasticity of substitution of the Cobb–Douglas utility function in this model. Inserting the solution into (7.4) yields the indirect utility function: ui = αβ = ui (n, A, k, pir),

(7.7)

where α ≡ {[1 − (m − n + 1)A]/m}m, β ≡ (kpi) n−1(∏ r∈R p -1r ). (7.6) and (7.7) are neoclassical optimum decisions for a given level of specialization. The neoclassical decision sorts out resource allocation for a given level of specialization. Here, an individual’s level of specialization in producing the good sold is uniquely determined by the number of traded goods n. In (7.7), [1 − (m − n + 1)A]/m is per capita output of each good, where 1 − (m − n + 1)A is each person’s amount of time allocated for production after total ﬁxed learning cost (m − n + 1)A is deducted. This amount of time is allocated to produce m − n nontraded goods and one good that is sold in exchange for n − 1 goods purchased. Hence, this amount is ultimately used to obtain m consumption goods. Since marginal labor productivity of each good is 1, the total output of m goods produced out of the amount of time is 1 − (m − n + 1)A. Thus, per capita consumption of each good, which equals per capita output of each good, is [1 − (m − n + 1)A]/m. As the number of traded goods n increases, the total learning cost incurred in producing m − n nontraded goods, (m − n)A, will be reduced, so that the amount of time available for production increases and, therefore, per capita consumption of each good increases. α in ui can be considered as the product of the per capita consumption amounts of each and every good, which is an increasing function of n, while n determines an individual’s level of specialization. kn−1 in β decreases as n increases, since k is between 0 and 1. β can then be considered as a term through which utility is reduced by an increase in the number of transactions and related transaction costs. Since the Smithian optimum decision sorts out the optimum level of specialization that relates to n, the Smithian optimum decisions are given by (7.6) to (7.7) and the following condition:

200 P ART I: D EVELOPMENT M ECHANISMS

(∂ui /∂α)(dα/dn) = −(∂ui /∂β)(dβ/dn)

(7.8)

Since n can represent an individual’s level of specialization in the symmetric model, the left-hand side of the equation is the marginal utility of an increase in an individual’s level of specialization. The right-hand side is marginal transaction cost in terms of utility loss caused by an increase in an individual’s level of specialization. Hence, (7.8) implies that the optimum level of specialization is determined by equality between marginal beneﬁt of specialization and marginal transaction cost. This law of optimum level of specialization was ﬁrst proven by Yang (1984) and then conﬁrmed by Becker and Murphy (1992; see example 7.4 below). Plugging the optimum value of n, given by (7.8), back into (7.6) to (7.7) yields the optimum resource allocation. Hence, (7.6) to (7.8) give the complete optimum decisions, which sort out optimum organization, which in turn relates to optimum productivity and economic development, as well as optimum resource allocation. Since n − 1 is the number of each individual’s trade partners, the optimum level of specialization determines the optimum network size of each person’s trade partners. However, this is an impersonal networking decision since each person does not care about who her partners are. She cares only about how many partners she has. An impersonal network decision is associated with price taking behavior. It should be noted that although (7.8) looks like a marginal condition for an interior solution, it is only an approximation of realistic inframarginal analysis. Strictly speaking, when the set of goods is ﬁnite rather than a continuum, we need integer programming to solve for the optimum integer n. As n jumps between the integers, all endogenous variables discontinuously jump. More importantly, if the model is asymmetric, we must use marginal analysis to solve for many corner equilibria, and then use total cost–beneﬁt analysis to identify the general equilibrium from among them. If a symmetric model is assumed, a decision to choose one from many conﬁgurations, and a procedure to identify one from many corner equilibria, turns out to be equivalent to choosing a value of n. There are two integer values of n, n1 and n2, such that n1 < n′ < n2, where n′ is the value of n that is given by (7.8). The optimum value of n* of the integer programming is determined by Max{u(n1), u(n2)}. But for a large value of m, n′ is a good approximation of n*. In this text, we will use n′ to represent n* in all symmetric Smithian models. Since all of n traded goods are produced only if all occupations generate the same utility level for the ex ante identical individuals, the inframarginal analysis between conﬁgurations establishes the utility equalization conditions: u1 = u2 = u3 = . . . = un

(7.9)

(7.8) and (7.9) are completely symmetric between conﬁgurations selling different goods. Hence, they hold at the same time if and only if pi = pr

∀i, r = 1, 2, . . . , n

(7.10)

and n is the same for all individuals. Using the information about the equilibrium-relative prices of traded goods and the equilibrium number of traded goods, each individual’s optimum decision can be solved as follows: n = m + 1 − (1/A) − [m/ln(kpir)] Li = [1 − (ln kpir)−1 + (A − 1)mA]/(−ln kpir) x is = A[m − (1/A) − (m/ln kpir)]/(−ln kpir) xi = xj = −A/(ln kpir) j ∈J d x r = pir A/(−ln kpir) ∀r ∈R ui = (kpir)m−(1/A)−(m/ln kpir)[1 + (1/A) + (m/ln kpir)]/m

(7.11)

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where pir ≡ pi /pr is the price of a good sold in terms of a good purchased. Since the optimum values of all decision variables are no longer functions of n, we call them Smithian optimum decisions, which differ from the neoclassical optimum decisions in (7.7). The distinction between the neoclassical decisions and the Smithian decisions formalizes Young’s idea that demand and supply are two sides of specialization. The optimum decisions that generate individuals’ demand and supply are ultimately determined by the optimum level of specialization, which is determined by n in a symmetric model.

7.4 INFRAMARGINAL COMPARATIVE STATICS OF OPTIMUM DECISIONS As discussed in chapter 4, the marginal comparative statics differ from the inframarginal comparative statics of optimum decisions. From the neoclassical optimum decisions in (7.7), you can see that the level of specialization Li and the neoclassical supply function are independent of relative prices. But the optimum level of specialization and the Smithian supply function are dependent on prices. The distinction between decisions before and after the level of specialization is chosen was ﬁrst noted by Stigler (1951) and received attention later from Rosen (1978). Suppose that parameters m, A, and k are ﬁxed. Differentiation of the Smithian optimum decisions with respect to the relative price pir yields: dn/dpir > 0

dLi/dpir > 0

(7.12a)

dx is/dpir > 0

(7.12b)

dxi/dpir = dxj/dpir > 0

(7.12c)

dx /dpir < 0

(7.12d)

d i

where (7.12b) is called the law of supply, and (7.12d) is called the law of demand. Certainly, comparative statics of the Smithian optimum decisions differ from comparative statics of the neoclassical optimum decisions given in (7.7). The distinction between the marginal and the inframarginal comparative statics of the optimum decisions highlights the point that we cannot really understand demand and supply if we do not understand individuals’ decisions in choosing their levels of specialization. The neoclassical demand and supply functions and their marginal comparative statics for a given value of n are only a half-way house. Since the choice of n determines productivity, there is an intimate relationship between inframarginal analysis of demand and supply and the analysis of economic development.

7.5 HOW IS THE LEVEL OF DIVISION OF LABOR IN SOCIETY DETERMINED IN THE MARKET? Assume that the numbers of individuals selling goods i and r are respectively Mi and Mr. The total market supply of good i is Mi xis. The market demand for good r by individuals selling good r is Mr x id. The total market demand for good i is then ∑r ∈R Mr x id. The market clearing conditions are thus:

M i x is = ∑ M r x id , r ∈R

i = 1, 2, . . . , n

(7.13)

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This system comprises n equations. One of them is independent of the other n − 1 due to Walras’s law. The n − 1 equations and the population equation ∑ i Mi = M determine the numbers of individuals selling n traded goods. The market clearing conditions, together with the utility equalization condition (7.9), yield the ﬁnal solution of the general equilibrium: Li = A + A[1 − m(ln k)−1][1 − m−1 − (Am)−1 − (ln k)−1], x is = A[m − (1/A) − (m/ln k)]/(−ln k), xi = x rd = xj = −A/ln k,

∀r ∈R,

pir = 1,

for

Mr = M/n,

∀j ∈J r = 1, . . . , n

(7.14)

ui = kn−1{[1 − (m − n + 1)A]/m}m n = m + 1 − (1/A) − (m/ln k) where i = 1, 2, . . . , n. The equilibrium value of utility can be considered as the absolute price of labor. We call ui (n) in (7.14) the Smithian utility function, which is a function of the number of traded goods that relates to an individual’s level of specialization and the level of division of labor for society. The Smithian utility function differs from the indirect utility function, since the former is not a function of prices, whereas the latter is a function of the prices of traded goods. Usually, we can work out the analytical expression of the Smithian utility function only for a completely symmetric model. For asymmetric models, we must work out the corner equilibrium per capita real income in each structure, where the level and pattern of division of labor, equivalent to n here, is exogenously ﬁxed. Then a total cost–beneﬁt analysis can sort out the equilibrium level and pattern of division of labor. The absolute price of labor is associated with the equilibrium levels of division of labor and productivity. But the relative prices of traded goods, and the relative numbers of individuals choosing different conﬁgurations, are determined by relative tastes and relative production and transaction conditions. A corner equilibrium for a given n sorts out resource allocation, relative prices, and numbers of different specialists, while the general equilibrium sorts out the absolute price of labor and the levels of division of labor and productivity. Hence, in a Smithian model, a corner equilibrium sorts out problems of resource allocation and a general equilibrium sorts out problems of economic development. Now we assume that individuals’ residential locations are exogenously given. They reside at the vertices of a grid of triangles with equal sides, as shown in ﬁgure 7.2. In order to save transaction costs, each individual will trade ﬁrst with those closest. But as the number of each individual’s traded goods increases, she will trade with those who are further away. Because of symmetry, the number of traded goods, n, is the same for all individuals and for society. Thus, there is a local business community around each individual. The members of the local community are trade partners of the individual who sells a good to, and buys a good from, each of them. Therefore, for n traded goods, each individual has n − 1 trade partners, while there are n members of the community. If the local communities do not overlap, then M individuals will be divided among N = M/n local communities. If the local communities overlap, N is the number of producers of each traded good, and can be considered as a measure of the fragmentation of the economy, since there is no trade between individuals who sell the same good or choose the same conﬁguration (occupation). We may say that structure B has a higher level of division of labor than structure A, if the levels of specialization of all individuals are higher in B than in A and the number of distinct conﬁgurations in B is larger than in A. Later, we shall show that in the model, each individual’s optimum level of specialization is an increasing function of her number of traded goods n. Also, the number of traded goods is positively related to the number of distinct conﬁgurations in a structure. Hence, n represents the level of division of labor for the symmetric model.

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Figure 7.2 Evenly dispersed individuals’ residence location

According to the ﬁrst welfare theorem proved by Zhou, Sun, and Yang (1998), a general equilibrium with consumer-producers in this chapter (which is different from the Arrow– Debreu model with a dichotomy between consumers and ﬁrms) is Pareto optimal. For a given value of n, a corner equilibrium is allocation efﬁcient, while the general equilibrium is both allocation efﬁcient and organization efﬁcient. Here, organization efﬁciency is associated with the efﬁcient productivity that balances the trade-off between productivity gains from the division of labor and transaction costs. Thus organization efﬁciency is a central notion for the analysis of problems of economic development. Two points need more attention. It is not difﬁcult to show that the second-order condition for the optimum n is satisﬁed, that is, the second-order derivative of ui in (7.4) with respect to n is negative. Also, it can be shown that the partial derivative of ui with respect to n is always negative for any positive n if k is sufﬁciently close to 0. According to the Kuhn–Tucker theorem, this implies that the equilibrium level of division of labor will be its minimum value, n = 1, which means that the number of goods purchased n − 1 = 0 (autarky), if k is sufﬁciently close to 0. The second point to note is the problem of multiple equilibria. Because of symmetry, which bundle of goods is to be traded is indeterminate in equilibrium. Hence, n combinations of m factors generate many general equilibria with the same per capita real income and the same value of n, but with different bundles of traded goods (type I multiplicity of equilibrium). There are still more possible general equilibria, since who specializes in producing which good is indeterminate, too. Exchanges of choices of conﬁgurations between each pair of different specialists will generate more general equilibria with the same value of n and the same per capita real income, but with different choices of conﬁguration by each individual (type II multiplicity of equilibrium). Finally, the case in which the number of society’s traded goods does not equal each individual’s number of traded goods may incur more general equilibria with the same per capita real income (type III multiplicity of equilibrium). Figure 7.3a shows an example of the case where individual 1 sells good 1 to individual 2, who sells good 2 to individual 3, who sells good 3 to individual 1. Each individual in this structure trades two goods, but the whole society trades three goods. For the symmetric model, the equilibrium in this structure generates the same per capita real income as does the structure in ﬁgure 7.3b. For the symmetric static model, the two types of structures have symmetric properties of equilibrium, except that in the case of ﬁgure 7.3(a) the number of traded goods for an individual is smaller than that for society. Since comparative statics of general equilibrium are

204 P ART I: D EVELOPMENT M ECHANISMS 2 1

3 3

1

3

1 1

1 1

2

1 3

2

2 2

3

2 3

2 (a) Different individuals trade different bundles of goods

(b) All individuals trade the same bundle of goods

Figure 7.3 Multiple general equilibria

easier to handle for those structures with an equal number of traded goods for each individual and for society, we focus on this type of structure. A slight difference in tastes or in production and transaction conditions between different goods will rule out type I and type III multiplicities of general equilibrium. A slight difference in taste and/or production and transaction conditions between individuals will rule out a type II multiplicity of general equilibrium.

7.6 INFRAMARGINAL COMPARATIVE STATICS OF GENERAL EQUILIBRIUM AND MANY CONCURRENT DEVELOPMENT PHENOMENA Since choosing a structure of division of labor is also choosing a certain network of transactions, many economic phenomena can be generated by inframarginal comparative statics of the general equilibrium as different aspects of the size and structural features of the network of division of labor. These structural changes are generated by a coherent mechanism of economic development. Hence, we ﬁrst examine the change in the equilibrium level of division of labor, n, in response to changes in transaction efﬁciency, k, and in ﬁxed learning cost, A. Differentiation of the equilibrium value of n in (7.14) yields: dn*/dk > 0

dn*/dA > 0

(7.15)

This implies that the equilibrium level of division of labor increases as transaction efﬁciency is improved or as ﬁxed learning cost increases. This formalizes the Smith theorem that division of labor is dependent on the extent of the market (Smith, 1776, ch. 3 of bk. I) and that the extent of the market is determined by transportation conditions (Smith, 1776, pp. 31–2). Total differentiation of the equilibrium level of per capita real income in (7.14) yields: du/dk = (∂u/∂n)(dn/dk) + (∂u/∂k) = ∂u/∂k > 0

(7.16a)

where the ﬁrst-order condition for the optimum level of specialization ∂u/∂n = 0 is used. (7.16a) is referred to as the envelope theorem, which states in words that the total derivative of the optimum value of the objective function with respect to a parameter equals the partial derivative of the objective function with respect to the parameter at the optimum values of the endogenous variables. Application of the envelope theorem to u in (7.4) with respect to parameter A yields: du/dA = ∂u/∂A < 0.

(7.16b)

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4

1

1 2

A

4 3

3

2 4 3 (a) Autarky

1

2 2

2

A 3

3 4

2 1

3

3

2 2

3

2 (b) Partial division of labor

2

2 4

1

3 2

4

1

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1

4

1

T RADE

1

2 1

1 A

4

1

4

3

1 4

2

AND

4

4

2

1 3

3 4 3 (c) Complete division of labor

Figure 7.4 Exogenous evolution in division of labor

(7.16) implies that there are two different ways to increase the equilibrium level of division of labor. The ﬁrst is to improve transaction efﬁciency and the second is to increase the ﬁxed learning cost of each activity. The ﬁrst approach increases while the second decreases per capita real income as it raises the level of division of labor. The ﬁrst method perhaps relates to the development of an efﬁcient banking system, the improvement of the legal system, government liberalization policies, and urbanization, all of which reduce the transaction cost coefﬁcient 1 − k. The second method perhaps relates to a stiff licensing fee and other entry barriers that decrease per capita real income and increase the equilibrium level of division of labor. Figure 7.4 gives an intuitive illustration of the inframarginal comparative statics of general equilibrium where the number of goods is assumed to be 4. The lines denote goods ﬂows. The small arrows indicate the directions of goods ﬂows. The numbers beside the lines signify the goods involved. A circle with the number i denotes a person selling good i. Panel (a) illustrates the case of autarky, where each person self-provides 4 goods, due to an extremely low transaction efﬁciency. Panel (b) shows how an improvement in transaction efﬁciency leads to partial division of labor, where each person sells one good, buys one good, trades two goods, and selfprovides three goods. Panel (c) shows how a very high transaction efﬁciency results in complete division of labor, where each person sells and self-provides one good, buys three goods, and trades four goods. If we suppose that the transaction efﬁciency coefﬁcient k continuously and exogenously evolves from 0 to 1, then the inframarginal comparative statics of general equilibrium predict that the equilibrium level of division of labor will evolve as illustrated in ﬁgure 7.4. This exogenous evolution in division of labor differs from the exogenous evolution of productivity and per capita real income generated by an exogenous change in the total factor productivity parameter in the Solow model (1956), which is a state equation that does not involve individual decision-making. In our model the exogenous evolution in division of labor is based on individuals’ decisions in choosing their levels of specialization and on interactions between those decisions. The evolution of division of labor will generate economic development associated with jumps of productivity from a low level to a high level in the absence of changes in production conditions (production functions and endowment constraints). Making a close examination of ﬁgure 7.1 in connection with ﬁgure 7.4, you can see that as transaction efﬁciency is improved, the general equilibrium jumps from the aggregate transformation curve DI to MCAKBJL. The novelty of the Smithian model is that it can predict many phenomena of structural change, some of them seemingly contradictory to each other, as different aspects of a coherent development mechanism. Let us now examine the phenomena one by one.

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Concurrent increases in each person’s level of specialization, degree of commercialization, trade dependence, and decrease in the degree of self-sufﬁciency as results of an increase in the level of division of labor Each individual’s level of specialization, Li is given in (7.7) and (7.14). It isn’t difﬁcult to see that dLi/dk = (dLi/dn)(dn/dk) > 0,

(7.17)

where dLi/dn = [1 − (m − 2n + 1)A]/m > [1 − (m − n + 1)A]/m > 0. The last inequality can be obtained by inserting the equilibrium value of n into the expression of the derivative. dn/dk > 0 is given by (7.16a). In this simple model, the amount of labor allocated to producing a good can be considered as the price of the good in terms of labor. Hence, the equilibrium value of Li is a measure not only of each individual’s level of specialization, but also of the value, in terms of labor, of all goods that she purchases, which equals her income from the market. The total value of consumption, including self-provided consumption and consumption from the market, in terms of labor is 1. Thus, the ratio of consumption purchased to total consumption, which is called the degree of commercialization, is Li/1 = Li. Also, trade dependence can be deﬁned by total trade volume divided by total income, including commercialized and self-provided income. It is apparent that the degree of trade dependence equals twice the degree of commercialization in the simple model, since trade volume equals double commercialized income. (7.17) implies that the degrees of commercialization and trade dependence increase as an improvement in transaction efﬁciency raises the level of division of labor. (1 − Li)/1 = 1 − Li is the degree of self-sufﬁciency, which is deﬁned as the ratio of the value of self-provided income in terms of labor to total income in terms of labor. Thus, (7.17) shows the negative relationship between the degree of self-sufﬁciency and transaction efﬁciency, and between it and the level of division of labor.

The extent of the market and the level of division of labor are two sides of the same coin (Young, 1928) Let E denote the extent of the market; then E equals the product of population size and per capita aggregate demand. An individual’s aggregate demand is the total demand of that individual for all traded goods. Market aggregate demand is the sum of all individuals’ aggregate demand for all traded goods. It is what we call the extent of the market and it differs from total market demand for a particular good. Total market demand for a good is a microeconomic or disaggregated concept, while market aggregate demand is a macroeconomic concept, which relates to the level of division of labor and the related size of the market network. From (7.7) and (7.14), the extent of the market can be calculated as follows. E = Mx is = M(n − 1)[1 − (m − n + 1)A]/m dE/dk = (dE/dn)(dn/dk) > 0

(7.18)

(7.15) and (7.18) imply that the equilibrium extent of the market and the equilibrium level of division of labor increase concurrently as transaction efﬁciency is improved. Smith (1776) conjectured that the level of division of labor is determined by the extent of the market, which is in turn determined by transaction efﬁciency. Some economists have misinterpreted this as meaning that division of labor is determined by the size of an economy (population size or resource size). Young (1928) criticized this interpretation. According to him, the extent of the

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market is determined not only by population size, but also by per capita effective demand, which is determined by income, which is determined by productivity, which in turn is determined by the level of division of labor. The interdependence of the level of division of labor and the extent of the market is analogous to the interdependence of prices and quantities demanded and supplied. The notion of general equilibrium is a powerful vehicle to sort out the mechanism that simultaneously determines the interdependent endogenous variables. In the Smithian general equilibrium model, the equilibrium level of division of labor and the equilibrium extent of the market are two sides of the equilibrium size of the market network. They are simultaneously determined by transaction efﬁciency. The driving force of the mechanism is, of course, the trade-off between economies of division of labor and transaction costs. In chapter 14, we shall use dynamic general equilibrium models to show that a dynamic mechanism can generate endogenous evolution in division of labor in the absence of exogenous changes in parameters.

Productivity progress The labor productivity of traded and nontraded goods, x is/Li and xj/Lj, can be worked out from (7.14). It can be shown that d(x is/Li)/dk > 0,

d(xj/Lj)/dk > 0.

(7.19)

This implies that the labor productivity of each good increases as the level of division of labor is raised by improvements in transaction efﬁciency. This formalizes Smith’s thought that productivity progress and national wealth are generated by evolution in division of labor and that the development implications of division of labor should be at the core of mainstream economics. Hence, if we formalize classical economic thought about the development implications of division of labor within the Smithian framework, then trade theory, which is concerned with trade dependence, and development economics, which is concerned with productivity progress, are two aspects of the core of economics. The development implications of evolution of division of labor can be better appreciated by looking at ﬁgure 7.1, which shows that as division of labor evolves, the equilibrium production schedule will discontinuously jump to be closer to the PPF.

Evolution in endogenous comparative advantage We deﬁne the extent of endogenous comparative advantage as the difference in productivity of a good between its sellers and its buyers. Since in our model the buyer of a good stops producing it, her labor productivity of that good is zero. But a seller’s labor productivity of the good increases as transaction efﬁciency is improved, as indicated in (7.19). Hence, the extent of endogenous comparative advantage increases as improvements in transaction efﬁciency drive division of labor to evolve. This formalizes Smith’s idea that the difference in productivity between a specialist and a novice is a consequence, rather than the cause, of division of labor.

Development of diversity of economic structure and of interpersonal dependence From the foregoing comparative statics of general equilibrium, we can see that when individuals choose autarky, all individuals’ conﬁgurations of production and consumption are the same, and their productivities in all activities are the same; thus, there is no diversity of economic structure. As improvements in transaction efﬁciency drive division of labor to evolve, the number of distinct occupation conﬁgurations and kinds of market increases. As the degree of self-sufﬁciency falls, each pair of different specialists shares a progressively smaller number

208 P ART I: D EVELOPMENT M ECHANISMS

of common self-provided production activities, so that the degree of difference between each pair of individuals choosing different conﬁgurations increases. We deﬁne the degree of diversiﬁcation by reference to the degree of this difference and the number of different traded goods, n. We deﬁne the degree of interpersonal dependence as the number of trading partners for each individual, which is n − 1. Hence, both the degree of diversiﬁcation of economic structure and the degree of interpersonal dependence increases as division of labor evolves.

Increases in the degree of production concentration and in the degree of market integration In the symmetric model, the number of producers of each traded good is N = M/n, where M is population size and n is the number of traded goods. The number of separate local business communities is also N = M/n. The degree of production concentration can then be deﬁned as 1/N = n/M. The degree of market integration can also be deﬁned by 1/N. Hence, the degrees of production concentration and market integration increase as improvements in transaction efﬁciency raise the equilibrium level of division of labor n.

Changes in industrial structure If good 1 is the agricultural good, and other goods are industrial goods, then the model predicts structural changes, which look like an increase in the employment share of the industrial sector and a decrease in the employment share of the agricultural sector. If transaction efﬁciency is low, autarky is the general equilibrium where each individual self-provides agricultural and industrial goods. This looks like a traditional agricultural society where all individuals are farmers. As transaction efﬁciency is improved, some individuals become professional farmers and others become professional manufacturers of industrial goods. But the number of professional farmers is much smaller than the number of all individuals producing agricultural goods in autarky. Hence, this looks like a structural change that transfers labor from the traditional agricultural sector to the industrial sector. In essence, this is a process of evolution of division of labor in which each individual’s level of specialization increases, natural agents who used to self-provide everything for themselves become different specialist producers, and new professions emerge. These are the structural changes and economic development in which Smith was interested.

Evolution of degree of information asymmetry In the Walrasian model, it is assumed that each individual does not know the others’ utility and production functions, endowments, and transaction conditions. She does not even know the distribution functions of the characteristics of others. Since all individuals are ex ante identical in our model and each of them has exactly the same ex post production and consumption pattern in autarky equilibrium, then each of them actually knows all the detailed production and consumption plans of the others if autarky occurs in equilibrium. As transaction conditions are improved, the equilibrium level of division of labor increases. The population is divided between different occupations. All individuals choosing the same occupation have the same ex post production, trade, and consumption pattern, which is different from those of other occupations. Hence, each individual actually knows 1/n information about the detailed production, trade, and consumption plans of n occupations. This implies that in a Walrasian model of endogenous specialization, the equilibrium degree of information asymmetry increases as division of labor evolves.1 The inframarginal comparative statics of general equilibrium can be summarized in the following proposition.

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Proposition 7.1: As transaction efﬁciency is improved, the level of division of labor increases. The following concurrent phenomena are different aspects of the evolution in division of labor. Each individual’s level of specialization, productivity, and trade dependence increases. The degree of commercialization, the extent of endogenous comparative advantage, the degrees of production concentration and market integration, and the degree of diversity of economic structure all increase. The number of traded goods, the number of markets, and the degree of information asymmetry increase, while the degree of self-sufﬁciency falls. This process transfers the traditional agricultural economy, where everybody self-provides everything to a modern economy with a high level of division of labor between professional farming and industrial manufacturing. Compared to the structural changes analyzed by Chenery (1979) and Kuznets (1966), the Smithian model predicts more structural changes, such as increases in the degree of market integration, degree of commercialization, extent of the market, extent of endogenous comparative advantage, degree of production concentration, and degree of structural diversity. More importantly, this model predicts co-movement of all the structural changes, rising productivity, and increasing per capita real income. This prediction implies that all of the endogenous variables are simultaneously determined by a general equilibrium mechanism. It does not make sense to explain some of them by others of them. Hence, regression of structural variables, such as the income share of the industrial sector or expenditure share of food consumption, on income may establish correlation, rather than a one-way causation chain, between the variables. The Smithian model in this chapter explores a coherent general equilibrium mechanism that explains all of the development phenomena by transaction conditions. Preliminary empirical work that relates to this hypothesis can be found in Barro (1997), North (1958), North and Weingast (1989), Gallup and Sachs (1998), Sachs and Warner (1995), Easton and Walker (1997), Gwartney, Lawson, and Block (1996), Frye and Shleifer (1997), and Yang, Wang, and Wills (1992). They use indices of freight fee (North), quality of institution (Sachs and Warner), rule of law (Barro), economic freedom (Easton and Walker, and Gwartney, Lawson, and Block), and violation of private property (Frye and Shleifer), or an index of transaction efﬁciency in specifying and enforcing property rights (Yang, Wang, and Wills), to approximate transaction conditions.

7.7 EMERGENCE OF INTERNATIONAL TRADE FROM DOMESTIC TRADE Now we use our model to address the questions: Why and how does international trade emerge from domestic trade, and what is the distinctive contribution of the Smithian framework to trade theory? Suppose that in the symmetric model, the number of individuals is an integer and that there are 100 countries in the world and the population size of each country is 10 million. Assume further that the number of goods m and the population size of the world are both 1 billion, and that transaction efﬁciency is inﬁnitesimally greater for trade within the same country than for trade across countries. Then our theory tells a story of trade as follows. If transaction efﬁciency is extremely low, then autarky for each person is equilibrium, and therefore domestic and international trade are not needed. If transaction efﬁciency is improved such that the equilibrium n = 1,000, then 10,000 local markets emerge from the division of labor in each country. The equilibrium number of business communities is M/n where M is the population size of the economy and n is the number of traded goods as well as the population size of a local business community. Each member of a local business community sells one traded good to the other 999 individuals and buys one traded good from each of them. Under the assumption that trade occurs ﬁrst with those closest, there is no trade between the local communities and therefore a national market does not exist. Suppose that transaction

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efﬁciency is further improved such that n* = 10,000,000. Then the national market emerges from the higher level of division of labor, but international trade does not exist. As n* increases to 100 million due to an improvement in transaction efﬁciency, such as that caused by the invention of the steam engine, the world is divided into 10 common markets. In each of these, 10 countries have an integrated market, and international trade emerges from domestic trade, but no trade occurs between the 10 common markets. However, if transaction efﬁciency becomes extremely high, an integrated world market will emerge from the complete division of labor. The difference between this story and the Dixit–Stiglitz model with economies of scale in example 5.1 is obvious. For the Dixit–Stiglitz, international trade instead of autarky is always the equilibrium in the absence of government intervention. But for our model, autarky for each individual or for each country may be the equilibrium in the absence of government intervention. If there are many goods, many different types of individuals in each country, and many countries in the Ricardian model in chapter 3 (above), emergence of international trade from domestic trade can also be explained by transaction conditions. But the Ricardo model with many goods and many different types of individuals is extremely difﬁcult to manage. In particular, endogenous comparative advantages in the Smithian model can be endogenously determined by individuals’ decisions, whereas exogenous comparative advantages in the Ricardo model and HO model are not affected by decisions. Hence, the Smithian model is referred to by Smythe (1994) as the theory of endogenous trade.

7.8 CO-MOVEMENT OF DIVISION OF LABOR AND CONSUMPTION VARIETY This section uses a new classical model with an endogenous number of consumer goods and ﬁxed learning costs to illustrate the general equilibrium mechanism that simultaneously determines the network size of division of labor, the number of traded goods, and the number of all goods (including nontraded ones). Example 7.2: A Smithian model with the CES utility function (Yang, 1996). The production functions and time endowment constraint for each consumer-producer are the same as in the previous sections. xip ≡ xi + x is = Max{li − A, 0}

i = 1, 2, . . . , m

m

∑l

i

= 1,

(7.20)

li ∈[0, 1]

i =1

where li is an individual’s level of specialization in producing good i, x ip is the output level of good i, xi is the amount of good i self-provided, x is is the amount of good i sold, and A is a ﬁxed learning cost in producing each good. In contrast to the previous sections, m, the number of consumption goods, is each individual’s decision variable rather than a given parameter. Each individual’s utility function is: 1 /ρ

V = (1 − cm)u,

⎤ ⎡m u = ⎢∑ (xic) ρ ⎥ ⎥⎦ ⎢⎣ i =1

(7.21)

where x ic ≡ xi + kx id is the amount of good i that is consumed, x id is the amount of good i that is purchased, and k is the transaction efﬁciency coefﬁcient. Following the method introduced in example 4.2, we can calculate the elasticity of substitution between any pair of consumption goods as 1/(1 − ρ). Since there is an inverse relationship between the elasticity of substitution

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and the degree of economies of complementarity, and a positive relationship between the elasticity of substitution and parameter ρ, we can use 1/ρ to represent the degree of economies of complementarity between each pair of consumption goods, or the degree of economies of consumption variety. Taking account of the Wen theorem and the budget constraint, each consumer-producer’s decision problem is Max: Vi = (1 − cm)ui, s.t.

⎤ ⎡ u i = ⎢x ρi + ∑ (kx rd ) ρ + ∑ x ρj ⎥ ⎥⎦ r ∈R j ∈J ⎢⎣

1/ρ

xi + xis = Max{Li − A, 0}, xj = Max{Lj − A, 0}∀j ∈J (production function) Li + ∑ L j = 1

(endowment constraint)

p i x is = ∑ p r x rd

(budget constraint)

(7.22)

j ∈J

r ∈R

where pi is the price of good i, and xi, x is, x rd, Li, xj, Lj, n, m are decision variables. Each decision variable can be zero or a positive value. R is the set of goods purchased and J is the set of nontraded goods. We assume that the calculation of the optimum decision will generate more disutility as the number of ﬁrst-order conditions for the optimum decision increases with the number of consumption goods m. This disutility is referred to as the management cost of consumption variety. Let c be the management cost coefﬁcient of a particular consumption good, measured as a fraction of utility that is lost. The total management cost of m consumption goods in terms of the fraction of utility that is lost is then cm. This implies that the fraction of utility ultimately enjoyed from the consumption of m goods is (1 − cm). From the decision problem, the individual’s level of specialization, her demand and supply functions, and her indirect utility function can be solved as follows. Li = {(n − 1)[1 −A(m − n)] + K}/[n − 1 + (m − n + 1)K ] x is = (n − 1)[1 − A(m − n + 1)]/[n − 1 + K(m − n + 1)] xi = x rd = xj = K[1 −A(m − n + 1)]/[n − 1 + K(m − n + 1)],

∀r ∈R, ∀j ∈J

n = 1 + {(A − c)(1 − K ) + ρ[A − (1 − K ) ]}/cA(1 + ρ)(1 − K ) 2 2

(7.23)

m = [A + cρ(1 − K)]/c(1 + ρ) Vi = (1 − cm)(akpi/pr)[1 − A(m − n + 1)][n − 1 + K(m − n + 1)](1−ρ)/ρ where K ≡ ( pr/kpi)ρ/(1−ρ) is a decreasing function of pi and k and an increasing function of pr , good i is sold and good r is purchased. Note that the demand and supply functions in (7.23) are neoclassical demand and supply functions if n is exogenously given, but are Smithian demand and supply functions if n is endogenized. In exercise 5, you are asked to work out the own price elasticity of the neoclassical and Smithian demand and supply functions, and to examine the differences between these functions. The utility equalization and market clearing conditions V1 = V2 = . . . Vn

M i x is = ∑ M r x id r ∈R

for all

i = 2, 3, . . . , n

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yield n − 1 relative prices of n traded goods and n − 1 relative numbers of individuals selling different goods. All of the relative prices and relative numbers are 1 because of symmetry. Note that we have not used the market clearing condition for good 1, since it is independent of the other n − 1 market clearing conditions. The equilibrium numbers of individuals selling different traded goods can be solved from the market clearing conditions and the population equation ∑i Mi = M. The equilibrium values of the relative prices of traded goods and of the numbers of individuals selling different traded goods are pi/pr = 1,

r, i = 1, 2, 3, . . . , n

Mi = Mr = M/n,

r, i = 1, 2, 3, . . . , n

Inserting the equilibrium values of the relative prices of traded goods into the optimum decision (7.23) yields the equilibrium values of the endogenous variables. Let K ≡ ( pr/kpi)ρ/(1−ρ) = kρ/(ρ−1) in (7.23). Then (7.23) becomes the equilibrium values of an individual’s optimum decisions. Differentiation of the equilibrium values of the number of consumption goods m and the number of traded goods n (which represents the level of division of labor) with respect to transaction efﬁciency k and the management cost coefﬁcient of consumption variety c yields the main results of the inframarginal comparative statics of general equilibrium. dn*/dk > 0,

dn*/dc < 0

dm*/dk > 0,

dm*/dc < 0,

d(m* − n*)/dk < 0, d(cm*)/dk > 0,

(7.24a) dm/dρ < 0,

d(m* − n*)/dc > 0, d(cm*)/dc < 0,

(7.24b) (7.24c) (7.24d)

where cm* is the fraction of utility that is lost because of the management costs of consumption variety. It is an interesting result that total management cost cm* increases as the management cost coefﬁcient c decreases. This implies that management cost as a proportion of real income increases as management efﬁciency is improved. (7.24a, b) implies that the equilibrium number of traded goods (or the level of division of labor), n, and the equilibrium number of all consumption goods, m, increase concurrently as transaction efﬁciency, k, and/or management efﬁciency, 1/c, is improved. (7.24c) implies that n increases more quickly than m does, so that the number of traded goods will eventually equal the number of all consumption goods, that is, all goods are eventually involved in the division of labor as transaction efﬁciency and/or management efﬁciency are continuously improved. Let us now consider the second-order conditions for the interior solutions of n and m. Recalling the second-order condition for a nonconstrained maximization problem from, for instance, Chiang (1984), we know the solutions given by the ﬁrst-order conditions are maximization solutions if the following conditions are satisﬁed. ∂2V/∂n2 < 0,

∂2V/∂m2 < 0,

(∂ V/∂n )(∂ V/∂m ) − (∂ V/∂n∂m) > 0. 2

2

2

2

2

(7.25a) (7.25b)

where m and n are valued at their equilibrium values. Let pi/pr = 1 in (7.23); then differentiation of V with respect to n and m indicates that (7.25a) holds when n and m equal their equilibrium values. But for pi/pr = 1 and the equilibrium values of m and n, (7.25b) holds if and only if f (k, ρ) ≡ k − [ρ/(1 + ρ − ρ2)](1+ρ)2ρ > 0

(7.26)

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where ∂f/∂ρ < 0. This implies that the second-order condition holds only if the degree of economies of consumption variety (or of complementarity between consumption goods), 1/ρ, is sufﬁciently great in comparison with transaction efﬁciency. If economies of consumption variety are not signiﬁcant, then the equilibrium m takes on one of two corner values, either n = m or m = ∞. Since m = ∞ is incompatible with the endowment constraint, the general equilibrium entails n = m if economies of consumption variety are not signiﬁcant, or if the second-order condition is not satisﬁed. If n = m, then the results in (7.24) become irrelevant. For this case, in order to determine the general equilibrium and its comparative statics, we should ﬁrst let m = n in each individual’s decision problem, and then solve for each individual’s optimum decision. It can be shown that if (7.26) does not hold, or if economies of consumption variety are not signiﬁcant in comparison to transaction efﬁciency, then the general equilibrium and its inframarginal comparative statics are given as follows: m* = n* = [(1 − ρ)/c] + ρ(1 − kρ/(ρ−1)) dm*/dk > 0,

dm*/dc < 0.

(7.27)

(7.24), (7.26), and (7.27) together yield the following proposition. Proposition 7.2: As transaction efﬁciency k and/or management efﬁciency 1/c are improved, the equilibrium level of division of labor, n, and the equilibrium number of all consumption goods, m, increase concurrently, with the former increasing more quickly than the latter, so that all goods are eventually traded and the complete division of labor will be achieved. If economies of consumption variety are not signiﬁcant in comparison to transaction efﬁciency, the number of traded goods always equals the number of all consumption goods. They simultaneously increase as transaction efﬁciency and management efﬁciency are improved. In addition, all concurrent development phenomena listed in proposition 7.1 take place as different aspects of the evolution in division of labor. Figure 7.5 gives an intuitive illustration of the inframarginal comparative statics of general equilibrium. The difference between the development mechanism in this chapter and that in chapter 5 is as follows. In the Smithian model, there is not a scale effect. The population size plays a very passive role: the number of occupations cannot exceed the population size. Compared to the Dixit–Stiglitz and Ethier models, the model in this chapter has endogenized individuals’ levels of specialization and degree of market integration. Hence, the following structural changes can be predicted as different aspects of economic development: increases in the degree of commercialization and in the extent of endogenous comparative advantage, and a decrease in each individual’s degree of self-sufﬁciency. If transaction efﬁciency is very low, a large population will be divided into many separate local communities which do not trade with each other, and productivity and per capita real income will be very low in such an economy (for instance, in pre-reform India). As transaction efﬁciency is improved, separate local communities merge into an increasingly integrated market, thereby generating economic development. Sachs and Warner (1995) use cross-country data to establish a positive correlation between economic development, trade dependence, the degree of openness, and quality of institution, all as they affect transaction conditions. Gallup and Sachs (1998) use cross-country data to show that geographical conditions, such as population share in coastal regions, have signiﬁcant impacts on per capita income in a country. The empirical evidence supports the theoretical models in this chapter.

214 P ART I: D EVELOPMENT M ECHANISMS (a) Autarky, n = 1, m = 2

(b) Partial division of labor with n = 2, m = 3

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3 4 3 (d) Complete division of labor with n = m = 4

3 3

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3 (c) Complete division of labor with n = m = 3

Figure 7.5 Emergence of new technology and new consumption goods

7.9 THE EMERGENCE OF PROFESSIONAL MIDDLEMEN AND TRADE PATTERNS Example 7.3: A Smithian model allowing for specialization in trading a particular good. In the previous sections, specialization in trading activities is not allowed, so that transaction efﬁciency is exogenous. In order to explore this issue, we now specify a new model as follows. Max: u = [x + (rx + kxr xd)xd][ y + (ry + kyr yd )yd ][z + (rz + kzr zd )z d ] s.t.

x + xs = Max{0, Lx − a}, z + zs = Max{0, Lz − a}, rx + r xs = Max{Lrx − a, 0}, rz + r zs = Max{Lrz − a, 0}

y + y s = Max{0, Ly − a}, ry + r ys = Max{Lry − a, 0},

(production function) (transaction condition)

Lx + Ly + Lz + Lrx + Lry + Lrz = 1

(endowment constraint)

prx(r xs − r xd) + pry(r ys − r yd) + prz(r zs − r zd) + px(xs − xd) + py( ys − yd) + pz(zs − zd) = 0

(budget constraint)

where a is a ﬁxed learning or training cost in each production and transacting activity, transacting services r for different goods are distinguished by subscript i (i = x, y, z), Lri is labor allocated to the production of transaction services in delivering good i, ki is the transaction efﬁciency coefﬁcient for delivering transaction services for good i, and pri is the price of the transaction services in delivering good i. In this model, although transaction efﬁciency for goods is endogenized, the transaction efﬁciency coefﬁcient for transaction services, ki, is exogenously given. Hence, we can use ki to explain all endogenous variables through comparative statics analysis of general equilibrium.

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Table 7.1 Corner equilibria in ﬁve structures Structure A

P

C

PT

CT

Relative price

pi /pj = 1

py /px = pz/px = 1

pri /prj = pi /pj = (ki /kj)1/4; pi /pri = [44(1 − 2a)/55]1/3

pri/prj = (ki /kj)1/6 pi /pj = (kj/ki)1/6 pi /pri = 5(1 − a)1/5/66/5

Real income

(1 − 3a)3 ÷ 27 (1 − 3a)4 ÷ 44

(1 − 3a)5 ÷ 55 (1 − 2a)13/3(ki kj).5 ÷ (55/348/3)

(1 − a)27/5(kxkykz)2/3 ÷ (53612/5)

Following the two-step approach, we can solve for the corner equilibria in 5 structures: A (autarky), P (partial division of labor in production, where two goods are traded), PT (partial division of labor in production and transactions, where two goods and transaction services for the two goods are traded), C (complete division of labor in production where three goods are traded), and CT (complete division of labor in production and transactions where all goods and transaction services for all goods are traded), as shown in table 7.1 (where pri is the price of transaction service for good i). Because of symmetry, which goods are traded is indeterminate in structures P and C. Each middleman in the two structures in example 7.3 only provides transaction services for one good. Comparisons between per capita real incomes in the ﬁve types of structure indicate that structures P and C cannot be equilibrium structures. If transaction efﬁciency of transaction services is sufﬁciently low, autarky is the general equilibrium, whereas if that efﬁciency is sufﬁciently high the general equilibrium is the complete division of labor in production and transactions (structure CT) involving three types of middlemen. Each type of middleman completely specializes in producing transaction services for one type of good. If the transaction efﬁciency of transaction service ki is neither too large nor too small, then the general equilibrium is structure PT, where only two goods are traded and transaction services for delivering each of the two goods are provided by middlemen. As indicated in table 7.1, the per capita real income for this structure is uPT = (1 − 2a)13/3(kikj)0.5/55/348/3, where ki and kj are the transaction efﬁciency coefﬁcients of transaction services for goods i and j, respectively. Hence, the corner equilibrium that trades the two goods with the larger transaction efﬁciency coefﬁcients of transaction services generates a greater per capita real income. This, together with the Yao theorem, implies that if not all goods are traded in the general equilibrium, those will be traded that have the larger transaction efﬁciency coefﬁcients for transaction services. Also, table 7.1 shows that the relative price of the two traded goods in the corner equilibrium trading only two goods is pi/pj = (ki/kj)1/4 where ki/kj is the relative transaction efﬁciency of transaction services for the two goods. Our results about the implications of relative transaction conditions for trade pattern are summarized as follows. Proposition 7.3: The general equilibrium includes as traded goods those with larger transaction efﬁciency coefﬁcients of transaction services if not all goods are traded. The higher the transaction efﬁciency of transaction services for a good, the higher the equilibrium price of this good in terms of other goods. As transaction efﬁciency for transaction services is improved, the general equilibrium evolves from autarky to the partial division of labor between production and transactions, followed by the complete division of labor between production and transactions.

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This result implies that those goods that involve inferior transaction conditions may be excluded from the network of division of labor and related trade. Even if such a good is involved in trade, its equilibrium price will be lower than that of other goods with the same production and consumption conditions. This explains why the market price is lower for those houses that are subject to government rent and trade restrictions than for other similar houses that can be freely traded. This also explains why there is no market for some goods. For instance, no market exists for clear air because of the extremely low transaction efﬁciency in trading this. In many textbooks, the absence of such markets is exogenously given. But in our models, this is endogenously determined by the trade-off between positive network effects of division of labor and transaction costs. In chapters 9 and 10 below, the existence of markets for different goods is endogenized by specifying more complicated trade-offs among endogenous transaction costs, exogenous transaction costs, coordination reliability of the network of division of labor, and economies of division of labor. Because of economies of specialization assumed in our models, the inframarginal comparative statics of equilibrium also imply that productivities and equilibrium quantities produced and consumed are greater for the traded goods with the higher transaction efﬁciency of transaction services than for the nontraded goods, even if production and consumption conditions are exactly the same for the two types of goods. This explains why the income share of the sectors manufacturing automobiles, refrigerators, and computers can dramatically increase despite the fact that they do not generate direct use-value for ﬁnal consumption. These sectors specialize in producing goods that can be used to improve transaction efﬁciency, so that they can promote the division of labor in all sectors. This, in turn, enlarges the market for all goods, including those produced by these sectors.

7.10 THE TRADE-OFF BETWEEN ECONOMIES OF SPECIALIZATION AND COORDINATION COSTS Example 7.4: The Becker–Murphy model of endogenous specialization (1992). Consider a production team consisting of n ex ante identical agents. This team undertakes a continuum of activities with mass 1 to produce good y. The production function of y is Y = Min Y (s), s ∈[ 0 ,1]

(7.28a)

where Y(s) is the contribution of activity s to the ﬁnal output Y. The Leontief relationship between Y and Y(s) implies that each activity is essential for obtaining the ﬁnal output. Each team member has a production function in activity s: Y(s) = AT hθ(s)T 1−θ w (s)

(7.28b)

where Th(s) is her total amount of time devoted to acquiring activity-speciﬁc skills and Tw(s) is time devoted to production in activity s. Each agent is endowed with one unit of time. This implies that if each agent disperses her limited time among many activities, duplicated investment in acquiring activity-speciﬁc skills will generate inefﬁcient aggregate output. Hence, in an efﬁcient team, each team member specializes in a certain range of activities that are different from other members’ activities. Suppose that the number of agents in the team is n; then each member undertakes a range of activities with measure 1/n. Therefore, (7.28b) is the production function of the agent who specializes in activity s as well as the team’s aggregate production function in this activity.

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Let each agent’s total amount of time allocated to learning and production in each activity be T(s). Then each person’s time endowment constraint is (1/n)T(s) = 1, where 1/n is her range of activities. This implies that T(s) = n. Hence, each agent will maximize (7.28b), subject to the time endowment constraint Th(s) + Tw(s) = T(s) = n. The optimum solution of this decision problem, together with the production function (7.28a), yields Y* = B(n) ≡ Anθθ(1 − θ)1−θ.

(7.29)

Hence, the optimum aggregate ﬁnal output of the team is an increasing function of the team size n. But a larger team size generates greater coordination cost. Assume that the coordination cost in terms of ﬁnal output among team members is C(n), C′(.) > 0,

C″(n) > 0,

(7.30)

then the optimum team size can be determined by maximizing the net output B(n) − C(n). The ﬁrst-order condition is dB(n)/dn = dC(n)/dn

(7.31)

that is, the marginal beneﬁt of division of labor equals the marginal coordination cost. Here, 1/n is the scope of each team member’s activities and n can be interpreted as each team member’s level of specialization as well as the level of division of labor within the team. Suppose C(n) = cn2. The efﬁcient team size given by (7.31) is n = α/2c, where α ≡ Aθθ(1 − θ)1−θ. This result implies that even if the population size for the society is ﬁxed, the level of division of labor increases as the transaction condition is improved (c decreases). Suppose the population size is M. Then for a very large c, the efﬁcient team size n = α/2c is small, so that the economy is divided into a large number (M/n) of separated teams. There is no connection between the teams. As c decreases, the efﬁcient team size increases and the separate teams merge into an increasingly integrated coordination network. As Becker and Murphy (1992) indicate, the relationships between members within the same team could be either relationships within a ﬁrm or market relationships between ﬁrms. Dynamic versions of this model of endogenous specialization can be found in Tamura (1991, 1992).

Key Terms and Review • Economies of division of labor generated by ﬁxed learning costs • The differences between decision rules in choosing the optimum resource allocation for a given conﬁguration and decision rules in choosing the optimum conﬁguration of specialization • Differences between neoclassical and Smithian demand and supply functions • The relationship between resource allocation and relative prices of traded goods versus the relationship between the level of division of labor and the absolute price of labor • The Young theorem: demand and supply are two sides of the division of labor; the extent of the market and the level of division of labor are two sides of the same coin • Extent of the market and the distinction between total market demand for a good and aggregate demand (the extent of the market or the thickness of the market) • The difference between effects of an increase in transaction efﬁciency and an increase in ﬁxed learning costs on the level of division of labor

218 P ART I: D EVELOPMENT M ECHANISMS

• The mechanism that generates the following concurrent phenomena: increases in the degree of commercialization, in trade dependence, in the degree of interpersonal dependence, in the extent of the market, in the number of types of markets, in productivity, in the extent of endogenous comparative advantage, in the degree of diversity of economic structure, in individuals’ levels of specialization, in the degree of production concentration, and in the degree of market integration • The mechanism generating the Linder pattern of trade • The relationship between evolution of division of labor, an increase in consumption variety, and emergence of new goods • Economies of consumption variety • Differences between the Smithian and neoclassical approaches to endogenizing the number of goods and the degree of market integration

Further Reading Smithian models with endogenous specialization: Houthakker (1956), Chu (1997), Chu and Wang (1998), Lio (1997, 1998), Sun (1999), Wen (1997), Yang and Y.-K. Ng (1993, ch. 5), Smith (1776), Yang (1991, 1994), Yang and S. Ng (1998), S. Ng (1995), Rosen (1983), Becker (1981), Becker and Murphy (1992), Barzel and Yu (1984), Young (1928); Models with an endogenous number of goods: Dixit–Stiglitz (1977), Krugman (1979, 1980), Ethier (1981); Smithian models with an endogenous number of goods: Yang and Shi (1992), Yang and Y.-K. Ng (1993, ch. 8), Yang (1996), Sun and Lio (1996); Emergence of professional middlemen: Yang (1991), Carter (1995), Bolton and Dewatripont (1994), Yang and Ng (1993, ch. 6).

QUESTIONS 1 In the early part of the twentieth century, Ford pioneered the use of mass production techniques featuring production lines. The new methods of management and production substantially reduced the prices of, and drastically increased demand and supply of, automobiles. This made the US the ﬁrst country “on the wheelers.” Not only did the income share of the automobile industry and related sectors drastically increase, but also many new specialized sectors emerged from the better transportation conditions provided by cheap automobiles. (For instance, presentday supermarkets might not survive market competition in the absence of cheap automobiles.) Many economists call this phenomenon “economies of scale and economies of scope” (Chandler, 1990). However, Young claimed that the notion of economies of scale misses the phenomenon of division of labor, and in particular misses the qualitative aspect of division of labor. Use the notion of positive network effect of division of labor and the trade-off between economies of division of labor and transaction costs to explain the phenomenon. Discuss the implications of the production line, the geographical concentration of production of automobiles, the standardization of parts, and the division of labor between manufacturing and Ford’s dealer franchise network for reducing coordination costs (a type of transaction cost) and for increasing the efﬁcient level of division of labor within the automobile industry. Then analyze the implications of cheap automobiles for an increase in the level of division of labor for society as a whole and for the extent of

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the market for automobiles. Use the notion of general equilibrium to ﬁgure out the mechanisms that simultaneously determine all of these interdependent phenomena. Use Marshall’s idea, that a ﬁner division of labor in production creates more scope for the division of labor in management, to explain the emergence of Taylor’s scientiﬁc approach to management from mass production and industrialization. How does the market simultaneously determine the demand and supply of management services as two aspects of the division of labor between production and management? The Smithian model in example 7.1 explains structural changes as evolution of division of labor, in which self-sufﬁcient individuals transform into increasingly more professional individuals as the number of professional occupations increases. If the increase in employment share of the tertiary sector is interpreted as the increase in employment share of the professional transaction sector, as in North (1986), can you use the Smithian models in this chapter to explain this data as evolution of division of labor? Reprocess data according to your theory (for instance, counting all sectors that relate to the production of automobiles and computers as part of the transaction sector) and then test your theory against empirical observations. Many economists cite the Smith theorem, that division of labor is dependent upon the extent of the market, to argue that population size determines the extent of the market, which determines the level of division of labor. Use the Young theorem to critically assess the statement. Young argued that the approach that separates the analysis of demand from the analysis of individuals’ decisions in choosing their levels of specialization is misleading. The Young theorem (1928, pp. 539, 534) consists of three statements: (a) Not only is the level of division of labor dependent upon the extent of the market, but also the extent of the market is determined by the level of division of labor, so that they are two sides of the same coin; (b) Demand and supply are two aspects of division of labor from a general equilibrium view; (c) Increasing returns depends on the progressive division of labor. Use the new classical models in this chapter to explain the Young theorem. Smith claimed that the extent of a market is determined by transportation efﬁciency (1776, pp. 31–2) and that division of labor is limited by the extent of the market (1776, ch. 3 of bk. I). Use the models in this chapter to formalize the Smith theorem in connection with the Young theorem. In ancient Europe and China there was a debate about the role of commerce in comparison to production in determining the wealth of a nation. One side in the debate argued that commerce is nonproductive, makes no positive contribution to the wealth of a nation, and should be restricted. The other side argued that commerce is a driving force of economic development which positively contributes to the wealth of a nation. Use the Smithian models in this chapter, and the notion of the general equilibrium network of division of labor, to assess these views. Transaction costs in the Smithian models can be interpreted as costs caused by unpunctual delivery of traded goods and unpunctual transmission of information. It follows that the development of the watch, the refrigerator, the automobile, the computer, the Internet, the inventory facility, and the standardization of goods and services have had very important inﬂuences on the size of the general equilibrium network of division of labor. Use statistical data on the income shares of all sectors that are directly and indirectly related to transaction conditions to verify this theory.

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8 Consider the Smithian model with an endogenous number of consumption goods in example 7.2. Assume that there are job shifting costs, so that an individual who has just changed jobs is not as productive, at least for a time, as a person who has not changed jobs. Suppose that the oil crisis has suddenly reduced transaction efﬁciency. Analyze what will happen to the equilibrium network size of division of labor and the equilibrium number of goods. Then discuss the possible effects on short-run unemployment, which some economists (such as Friedman) call natural unemployment while others call it structural unemployment. Analyze the intimate relationship between the equilibrium network size of division of labor before such a shock and the unemployment rate after the shock. (You could start from two extreme cases: (a) Before the shock, the equilibrium is autarky; (b) Before the shock, the equilibrium is the complete division of labor, where each person produces only one good and completely depends upon the market for other goods.) 9 It is said that specialization should be restricted because it conﬂicts with diversiﬁcation, which is good for society. Marx and other economists argued that specialization makes individuals’ lives dull and boring, and should be restricted. Managers of Japanese companies emphasize diversifying the experience of their employees, rather than skill specialization. In contrast, American managers have paid more attention to specialization since Taylor’s scientiﬁc approach to management was developed. Similarly, American universities emphasize the diversity of undergraduate education, while ﬁne specialization occurs at the level of graduate education. In contrast, the German technical training system and the Russian tertiary education system introduce specialization at quite early stages of education. Analyze these cases to identify the conditions for different efﬁcient balance points between specialization and diversiﬁcation. Draw a distinction between the following two kinds of economies of diversity in your analysis. One is the economies of variety of inputs, which is considered in this chapter and in chapters 18 and 19. The diversity of each person’s inputs and the specialization of their output can increase side by side as the network size of division of labor evolves, as shown in this chapter and in chapters 18 and 19. The other type of economies of diversity is a certain technical complementarity between activities in which a person engages. For instance, a person’s teaching experience of economics may help her research in economics – a kind of technical complementarity not considered in this chapter. Do some thought experiments about the possible general equilibrium implications of the latter in the Smithian framework. Refer to Rosen (1983) for an analysis of the trade-off between economies of specialization and this type of economy of technical complementarity. 10 Many economists use the notion of economies of scope to describe diseconomies of specialization. Use an example similar to that following to illustrate that the notion of economies of scope may be misleading. In the example, there are two ﬁrms, A and B. A hires 3 employees who all engage in exactly the same 3 activities. B hires 10 workers. Each of them engages in an activity that is distinct from the activities of the others. B has a larger scale of operation as well as a greater scope of activities than A. But a higher productivity of B than A may be due to a higher level of specialization of each worker in B and a higher level of division of labor in B than in A. Use your example to illustrate why the Herﬁndal index, which uses the output share of a sector, a city, or a region as a measure of the level of specialization, is misleading. According to this index, many large American cities, such as Los Angeles, Chicago, San Francisco, and New York, have lower levels of specialization than, say,

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Albany, Gary, and Norfolk (see Diamond and Simon, 1990, pp. 180–3). But from casual observation, we can perceive that the four large cities certainly have a much higher level of division of labor than the three small cities, because of their higher degree of diversity of occupations as well as the higher levels of specialization of many professionals. This is veriﬁed by Baumgardner’s (1988b) empirical evidence that individuals in a larger city are more specialized than those in small towns. In the Smithian model in example 7.2, as transaction efﬁciency is improved, the production functions of some new goods emerge from evolution of division of labor. This looks like endogenous technical progress. Analyze the difference between this approach to explaining endogenous technical progress, which is dependent on a large size of market network and on the merging of separate local business communities into an increasingly integrated market, and the neoclassical approach to explaining technical progress by investment, which is independent of the evolution of the network size of division of labor. Yang, Wang, and Wills (1992) have tested the concurrent evolution of the degree of commercialization (one aspect of division of labor) and per capita real income, generated by improvements in a transaction efﬁciency index, which is determined by institutional changes, against China’s data. Find other ways to test the theory developed in this chapter. For instance, you may test concurrent evolution in commercialization and in the number of available goods or concurrent evolution in commercialization and in the degree of market integration and production concentration. Casual observations suggest that individuals in a very developed and highly commercialized economy are often frustrated by the disutility caused by management of a great variety of goods and services. Use the statistical data of cases of psychosis caused by complexity in managing a great variety of goods in a highly commercialized society to test the theory developed in example 7.2. Design a method to test the model in example 7.2, which predicts a neutral role of population size in promoting per capita real income, in contrast to the DS model in example 5.1, which predicts a positive effect of population size on per capita real income against empirical data. The former has endogenized the degree of market integration and the latter has not. Design a statistical approach to test the comovement of all concurrent phenomena of structural changes predicted by the models in this chapter. From our daily experience, we can perceive that coordination costs for specialization are increasingly more signiﬁcant as specialization is increased. For instance, an expert on the Russian military system can provide professional knowledge that nobody else can provide. But the value of her professional knowledge is very low in peacetime (though she may become a star in TV shows when there is a possibility of war between Russia and another country). Smith noted the trade-off between coordination costs and economies of division of labor. Becker and Murphy have formalized the trade-off in a decision model (see example 7.4). How does the market sort out the efﬁcient balance of this trade-off ? How should you ﬁnd the efﬁcient trade-off when you choose your professional career? Use the Smithian models in this chapter to explain the Linder pattern of trade, which suggests that trade volume between ex ante similar developed countries is much greater than that between ex ante different developed and less-developed economies. Discuss the difference between the Smithian way and Krugman’s way (using the DS model) to explain the Linder pattern of trade.

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18

19

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Many development economists compare the cases of India, Bangladesh, some African countries, and the east Asia in the nineteenth century, with the development experience of western Europe in the eighteenth and nineteenth centuries, to argue that population growth has negative effects on economic development. Hence, they say, birth control is essential for economic development. Other economists use the early development experience of the US, Australia, and New Zealand, and the development experience of Hong Kong and Japan in the twentieth century, to argue that population size has a positive effect on economic development. Use the Smithian models in this chapter to assess the two opinions in relation to the effects of transaction conditions on economic development. Rosenberg and Birdzell (1986, p. 168) ﬁnd that “The agricultural revolution came after 1880 (increased use of fertilizers, machines, improved seeds, improvements in methods of cultivation and animal husbandry) as a consequence of improved transportation, the development of regional specialization in agriculture.” Use the model in this chapter to explain this historical fact. Mokyr (1993, p. 31) indicates that “Many authors maintain that the challenge imposed by resource scarcities stimulates invention. Thus the deforestation of Britain is alleged to have led to a rise in timber prices, thus triggering Britain into adopting a novel and ultimately far more efﬁcient set of techniques using fossil fuels.” Use the model in exercise 13 to analyze the conjecture. Under what conditions would the frightening forecast of crises due to an energy shortage and a population explosion make sense, and under what conditions would it be nonsense? In the model in exercise 14, the transaction efﬁciency coefﬁcient k is equivalent to “public goods.” According to Pigou and Samuelson, the output level of public goods is not Pareto efﬁcient in the Walrasian regime with no government intervention. Use the Chu model (exercise 13) to assess under what condition this claim is wrong in relation to the following facts. Early economic development in the US in the last century was driven by the development of infrastructure. But the infrastructure (canals, railways, and early freeways) was developed largely by private companies. The development of freeways by private companies in Malaysia is much more successful than in China, where the government monopolizes the construction of freeways. According to Coase (1960), the market and the private sector are able to take care of so-called “public goods,” and Pigou and Samuelson’s notion of distortion being caused by externality and public goods is misleading. Use the Chu model to assess Coase’s view. Kremer (1993) argues that population density has a positive effect on long-run economic growth. But Jones (1981, p. 232) provides historical evidence of the negative effect of population density on early economic development in India, China, the Ottoman empire, and Europe in the period 1500–1800. Use the model in this chapter to analyze the opposite opinions. Many development economists argue that mainstream economics on the function of the market is not applicable to developing countries because of the non-existence of many markets in these countries. Use the models in this chapter to show that if classical mainstream economics pertaining to development implication of division of labor are formalized, their core purpose is to explain the emergence of markets and the evolution of marketization. Hence, the development experience of eighteenthand nineteenth-century Britain in improving transaction conditions becomes applicable to currently developing countries.

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EXERCISES 1 Let the equilibrium number of traded goods in the model in example 7.1 be n ≥ 1. Then identify the parameter space within which the solution given by the ﬁrst-order condition is relevant. If the parameter values are not within this subspace, what is going to happen to general equilibrium and its inframarginal comparative statics? Check the second-order condition for maximizing utility with respect to n and discuss the feature of the general equilibrium when the second-order condition is not satisﬁed. 2 S. Ng, 1995: Consider the model in example 7.1 with m = 3. Suppose that there are two countries. Each of them has M citizens and transaction efﬁciency k differs from country to country, so that utility equalization may not hold between countries. Solve for the general equilibrium and analyze under what conditions international trade emerges from domestic trade. Suppose k is the same between the two countries, but is larger for domestic trade than for international trade. Identify the condition for international trade emerging from domestic trade and trade pattern. 3 Suppose there are two countries and only two goods in the model in example 7.1. The utility function is u = (xc )α ( yc)1−α. The population size for each country is an integer M. Identify the conditions for international trade to emerge from domestic trade. 4 Show that the Nash bargaining equilibrium in example 7.1 or 7.2 is the same as the Walrasian equilibrium. 5 Work out the own price elasticities of the neoclassical and Smithian demand and supply functions in example 7.2, and examine the differences between them. 6 Suppose that the government taxes sales of goods at rate t and then equally distributes the tax revenue among individuals in the model in example 7.1. Solve for the general equilibrium and its inframarginal comparative statics, and analyze the implications of the tax for the equilibrium network size of division of labor and other related variables. 7 Yang and Shi, 1992: Assume that the production function in (7.1) is x ip = l ia, a > 1. Solve for the general equilibrium and its inframarginal comparative statics. Check the second-order condition where the equilibrium number of traded goods is n ∈(1, m), and analyze the implications of the second-order condition. Then work out the general equilibrium and inframarginal comparative statics when the second-order condition is not satisﬁed. 8 Assume that in the model in example 7.2, transaction efﬁciency k = 1, but the government imposes a tax rate t on each dollar of sales, then equally distributes the tax revenue among all individuals. Solve for general equilibrium and its comparative statics. Analyze the implications of the tax for the equilibrium network size of division of labor and number of available goods. 9 Assume that in example 7.3, transaction service is not good-speciﬁc, so that transaction service for one good is the same as that for another good. Solve for the inframarginal comparative statics of general equilibrium. In some developing countries, such as China, the government monopolizes both the wholesale and retail networks. The government uses the licensing system and other regulations to deter free entry of private businessmen into trading businesses, in particular

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into importing, exporting, and wholesale. Use your answer to analyze the effects of such institutions and regulations on economic development. Assume that the economy in example 7.2 is initially in equilibrium. An oil crisis reduces transaction efﬁciency from k1 to k2, so that the equilibrium number of goods decreases. Assume that as the equilibrium shifts from a corner equilibrium to another corner equilibrium, there is a job shifting cost when individuals change jobs, so that those who lose their jobs are not as competitive as those who do not change jobs, giving rise to unemployment. Compute the unemployment rate caused by the oil crisis. Lio, 1998: Each ex ante identical consumer-producer’s utility function is: V = ∑ mi=1 ln(xI + x id ) + β ln H, where xi, x di , and k have the same meanings as in example 7.1. H = 1 − L is the amount of time allocated for leisure, L is the amount of time allocated for the production of goods, and β is a parameter representing the desire for leisure. It is assumed that the total amount of available time for each individual is 1, so that the production functions and the endowment constraint for time are xI + x id = Max{0, lI − a}, i = 1, 2, . . . , m, ∑ mi=1 lI ≡ L, L + H = 1. Solve for comparative statics of general equilibrium. Show that as transaction efﬁciency k or the degree of desire for leisure β increases, the equilibrium level of division of labor n, productivity, and per capita demand from the market, which equals per capita supply x id, increase. Lio (1996) ﬁnds empirical evidence that productivity, per capita real income, and leisure time increase, while working time for self-provided consumption decreases as division of labor evolves. Why do productivity and the level of division of labor increase as the degree of desire for leisure increases? Assume a CES utility function. Will your result change? (Hint: see Lio.) Wen, 1997b: Consider an economy with M ex ante identical consumer-producers. Each individual’s utility is speciﬁed as a function of the quantities of two goods that are consumed, u = (x + kx d )( y + ky d ), where all variables have the same meanings as in example 4.1. Each individual has the following production functions for the two consumption goods. x + x d = Max{0, (lx − a)(sx − b)}, y + y d = Max{0, (ly − a)(sx − b)}, where li is the individual’s level of specialization in producing good i, si is the amount of primary resource allocated to produce good i, a is a ﬁxed learning cost in producing a good, and b is a ﬁxed amount of the resource that is essential for the production of each good. ly + ly = 1 and sy + sy = s0 where s0 is each individual’s initial endowment of the resource, which can be coal, iron ore, or land. Solve for the inframarginal comparative statics of general equilibrium, and show that as per capita endowment of the resource s0 decreases due to population expansion or depletion of the resource, the equilibrium level of division of labor and productivity increases. Explain why labor surplus caused by population expansion, and an energy crisis caused by the depletion of energy, can increase the level of division of labor and productivity under good transaction conditions. (Hint: work out the critical value of k that divides autarky and the division of labor, as a function of s0, then show that the derivative of this critical value with respect to s0 is negative.) Compare the results with Sachs and Warner’s (1995b) empirical evidence that shortage of resources is positively correlated with growth performance for open economies. Chu, 1997: Consider an economy with M ex ante identical consumer-producers, where transaction efﬁciency k is determined by the level of specialization in producing transaction infrastructure. For an individual who does not produce infrastructure, the decision problem is:

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Max: u = (x + kx d)( y + ky d ); s.t.

y + ys = 1 − α

(production function of y)

Lx + Ly = 1

(endowment constraint of time)

1 ⎧ ⎪1 − M k=⎨ k ⎪k ⎩0

if

Mk > 1

if

Mk ≤ 1

px x s + py y s = px x d + py y d + pk

(transaction conditions) (budget constraint)

where x and y are respective quantities of two goods that are self-provided, xd and yd are respective quantities of the two goods purchased from the market, xs and ys are respective quantities of the two goods sold, and Li is the individual’s level of specialization in producing good i. k is the transaction efﬁciency coefﬁcient, which is an increasing function of the number of individuals producing infrastructure, Mk. If the number is 0, that is, no professional infrastructure sector exists, then k = k0. xd (i = x, y) is the price of good i, and pk is a fee for the use of infrastructure paid by each individual. Assume that individuals compete for the right to construct the infrastructure in an auction. The bidder who collects the lowest per capita fee will get the right. If no infrastructure exists, that is, Mk = 0, then pk is irrelevant and k = k0. For an individual choosing to be a specialist in the infrastructure sector, her decision problem is: Max: u = kxdkyd s.t. px xd + py yd = pk(Mx + My)/Mk where (Mx + My)/Mk is the ratio of the number of specialists producing goods to those producing infrastructure, so that pk(Mx + My )/Mk is the earnings that an infrastructure specialist receives from the production of infrastructure. Because of the assumptions that individuals are ex ante identical and that a competitive bidding process determines distribution of the rights to produce infrastructure, the earnings must be the same between the infrastructure specialists. Solve for the inframarginal comparative statics of general equilibrium, and show that the level of division of labor between the production of goods and the production of infrastructure is more likely to be higher if the population size M is larger. Use your result to formalize Boserup’s idea (1975) that the per capita investment cost of a canal system, a railway network, a freeway network, an airport system, and other infrastructure decreases with the population density, so that a high population density may be favorable for evolution in division of labor and economic development. Why can a competitive bidding procedure for rights to develop infrastructure, plus free choice of occupation conﬁgurations, avoid distortion in producing infrastructure (public goods)? (Hint: the corner equilibrium Mk is implicitly given by an equation. Use the envelope theorem and the implicit function theorem to show that the corner equilibrium utility in the structure with specialists producing infrastructure is greater as the population size M increases.)

Note 1 According to Hurwicz (1973), the Walrasian model has more information asymmetry than most game models, and the Walrasian equilibrium can efﬁciently utilize information in a society when each agent has minimum information.

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PART II The Institution of the Firm, Endogenous Transaction Costs, and Economic Development

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ECONOMIC DEVELOPMENT, THE INSTITUTION OF THE FIRM, AND ENTREPRENEURSHIP

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8

8.1 WHAT IS THE INSTITUTION OF THE FIRM? In the Smithian models of chapters 4, 6, 7, there is no labor trade, and there are no ﬁrms. You may wonder if this kind of model can only describe economic development before the Industrial Revolution. But it is one of the advantages of the Smithian framework over the neoclassical that only the ex ante players are consumer-producers, and there are no ﬁrms before individuals have made their decisions. The institution of the ﬁrm is a particular way of organizing transactions that are required by the division of labor. It may emerge from the division of labor only as a consequence of individuals’ decisions in choosing their levels of specialization and manner of organizing transactions. If the transaction cost coefﬁcient for labor is smaller than that for goods, then the institution of the ﬁrm will be chosen to organize the division of labor and to promote economic development as trade and pricing of goods are replaced by the corresponding trade and pricing of labor. An example of the replacement of goods trade with labor trade is trade between a professor and his housekeeper. Outputs of services provided by housekeepers are prohibitively expensive to price because of such a great variety of services, generating an extremely high cost in measuring quality and quantity of the services item by item. Hence, trade in labor that involves pricing of the housekeeper’s labor inputs will substitute for trade in her outputs. The professor pays the housekeeper according to her working hours, rather than according to quantity and quality of each and every service item she provides. However, we do not take trade between the professor and the housekeeper to be associated with the institution of the ﬁrm. The division of labor between the professor and the housekeeper, and the replacement of trade in outputs of the housekeeper with trade in her labor, are two necessary but not sufﬁcient conditions for the emergence of the ﬁrm from the division of labor. Before we study the sufﬁcient conditions for the existence of the ﬁrm, a rigorous deﬁnition is needed for the institution of the ﬁrm. The institution of the ﬁrm is a structure of transactions based on the division of labor that satisfy the following three conditions. i) There are two types of trade partner who are associated with a ﬁrm: the employer and the employee. There is an asymmetric distribution of control rights or authority. The employer has control rights to use the employee’s labor. The latter must do what he is told to do, if

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his boss so demands. That is, the ultimate rights to use the employee’s labor are owned by the employer, subject to the employee’s freedom to quit the job and to other terms of the labor contract. ii) The contract that is associated with the asymmetric relationship between the employer and the employee never speciﬁes how much the employer receives from the relationship, but only how much the employee receives from the relationship. The employer claims the residual returns, deﬁned as the revenue of the ﬁrm net of the wage bill and other expenses. The employer is referred to as the owner of the ﬁrm. One of the most important components of the ownership of a modern ﬁrm is the entitlement to the business name of the ﬁrm. The exclusive rights to the business name are enforced through a business name search process when the ﬁrm is registered with the government and through recognition of the name in legal cases in the judicial process. The exclusive rights are also enforced through laws governing brands. iii) A ﬁrm must involve a process that transforms employees’ labor into something that is sold in the market by the owner of the ﬁrm. In the process, what is produced by the employee is owned by the employer (residual returns). The relationship between the professor and the housekeeper does not involve the institution of the ﬁrm, since it does not involve such a resale process. The professor directly consumes what the housekeeper produces and never resells it to the market. If an individual hires a broker to conduct stock transactions, the relationship involves asymmetric authority and rights to residual returns. But the relationship does not involve the ﬁrm since it does not satisfy condition (iii). Suppose that in the model in chapter 4, with consumption goods only, a specialist producer of x buys the labor of a specialist producer of y, directs that employee to specialize in producing y within the ﬁrm, and then sells y to the specialist producer of y in the market for y. Such roundabout transactions involve unnecessary transactions in labor. If the producer of y must buy his own produce from the market, why would he not directly sell y to the specialist producer of x in exchange for good x? The latter structure of transactions is exactly the same as the former, except that the former involves more trade in labor and therefore creates unnecessary transaction costs. This implies that the institution of the ﬁrm will not be chosen in a model with ex ante identical individuals if there is no producer good or service. In this chapter, we shall show that the institution of the ﬁrm may be used to save on transaction costs if there is division of labor between the production of the ﬁnal goods and the production of the intermediate goods. The rationale behind our story of the ﬁrm may not seem very plausible. Human history has been troubled by the question of the fairness of asymmetric relationships between employer and employee. In a free enterprise system, employees have the freedom to become employers by using the free capital market and a legal system that protects free association. They also have the freedom to quit their jobs. Hence, an asymmetric relationship between the employer and the employee in a free market system differs from the relationship between a master and his slave or the feudal relationship between a lord and his servant. Notwithstanding this, many people (from Karl Marx to modern trade union activists) are still concerned with the following questions. Why must the employee do what he is told to do rather than what he likes to do? Why shouldn’t the employee have rights to the residual returns that perhaps are making a fortune for the employer? Such questions were at least partly responsible for the Russian Revolution in 1917 and the Chinese Revolution in 1949 that changed the lives of a billion people over the course of more than half of the twentieth century, and generated very serious consequence for economic development in many current and ex-socialist economies. (According to a conservative estimate in Forbes (March 23, 1998, p. 80), the cost of the social experiment with the communist economic system in Cuba was $31.5 billion in 1995. In other words, without this communist system, Cuba’s GDP in 1995 would be $31.5 billion more than its realized value.)

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Russia and East Europe have already abandoned the disastrous social experiments that were inspired by such questions, and China shows every prospect of doing so in the near future. However, we need a well-developed theory to explain why a communist government’s infringement of the residual rights of private ﬁrms is harmful for economic development; and to address the following questions. What is the role of multinational ﬁrms and foreign direct investment in economic development? What are the effects on the development of entrepreneurship, which is crucial for economic development, of a legal system that protects the residual rights of owners of private ﬁrms? Why is the average size of ﬁrms declining (downsizing, outsourcing, contracting out, disintegration)? This chapter will address such questions. In section 8.2, we outline the story behind the model. In section 8.3, we set out a general equilibrium model of endogenous specialization and endogenous emergence of the ﬁrm. We then solve individuals’ decisions, corner equilibria in various structures, general equilibrium, and its inframarginal comparative statics. Sections 8.4 and 8.5 explore the development implications of the institution of the ﬁrm.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n n n

n

What is the institution of the ﬁrm? What are the necessary and sufﬁcient conditions for the emergence of the ﬁrm? What is the function of the institution of the ﬁrm and what are the implications of the internal organization of the ﬁrm for the equilibrium level of division of labor and productivity? What is the relationship between the legal system that protects the residual rights of owners of private ﬁrms; entrepreneurship; and economic development?

8.2 WHY ARE CLAIMS TO RESIDUAL RIGHTS OF THE FIRM ESSENTIAL FOR NURTURING ENTREPRENEURSHIP? – THE STORY BEHIND THE MODEL We will outline the intuition behind the formal model, before you become mired in the algebra of the model and lose your capacity for economic thinking, by telling a story about the role of the institution of the ﬁrm in economic development. Our story of the ﬁrm runs as follows. Each individual as a consumer must consume a ﬁnal good, called cloth, the production of which requires an intermediate good, called management service, as an input. There is a tradeoff between economies of specialization and transaction costs. If transaction efﬁciency is high, then division of labor will occur at equilibrium. Otherwise, autarky will be chosen as the equilibrium. There are three different structures of residual rights which can be used to organize transactions required by the division of labor. Structure D, shown in ﬁgure 8.1(b), comprises markets for cloth and management services. Specialist producers of cloth exchange that product for the specialist services of management. For this market structure, residual rights to returns and authority are symmetrically distributed between the trade partners, and no ﬁrms or labor market exist. Structure E, shown in ﬁgure 8.1(c), comprises the market for cloth and the market for labor hired to produce the management service within a ﬁrm. The producer of cloth is the owner of the ﬁrm and specialist producers of management services are employees. Control rights over employees’ labor and rights to the ﬁrm’s residual returns are asymmetrically distributed between the employer and her employees. The employer claims the difference between revenue and the wage bill, has control rights over her employees’ labor, and sells goods that are produced from employees’ labor. Structure F, shown in ﬁgure 8.1(d), comprises the market for cloth and the market for labor hired to produce cloth within a ﬁrm. The professional manager is the owner of the ﬁrm and specialist producers of cloth are

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xd

x

y/lx x

ys l

A y

x/ly

y

ys

d x

y ys

lyd

x xs

(a) Autarky

yd

lsx

yd

lsy

yd

x/y

lx/y

ly/x

(b) Structure D

(c) Structure E

(d) Structure F

Figure 8.1 Emergence of the ﬁrm from the division of labor

employees. For the ﬁnal two structures of residual rights, the ﬁrm emerges from the division of labor. Compared with structure D, these involve a labor market but not a market for management services. As Cheung (1983) argues, the ﬁrm replaces the market for intermediate goods with the market for labor. Although both structures E and F involve a ﬁrm and an asymmetric structure of residual rights, they entail different ﬁrm ownership structures. Suppose that transaction efﬁciency is much lower for management service than for labor. This is very likely to be the case in the real world, since the quality and quantity of intangible entrepreneurial ideas are prohibitively expensive to measure. Potential buyers of intellectual property in entrepreneurial ideas may refuse to pay by claiming that these are worthless as soon as they are acquired from their specialist producer. Under these circumstances, the institution of the ﬁrm can be used to organize the division of labor more efﬁciently because it avoids trade in intangible intellectual property. Suppose further that transaction efﬁciency for labor hired to produce management services is much lower than for labor hired to produce cloth because it is prohibitively expensive to measure the efforts exerted in producing intangible management services. (Can you tell if a manager sitting in the ofﬁce is pondering business management or his girlfriend?) Then the division of labor can be more efﬁciently organized in structure F than in structure E. This is because structure F involves trade in cloth and in labor hired to produce cloth, but not trade in management services nor in labor hired to produce management services, while structure E involves trade in cloth and in labor hired to produce management services. Hence, structure F will occur at equilibrium if the transaction efﬁciencies for labor hired to produce cloth and for cloth are sufﬁciently high. The manager’s claim to the residual returns of the ﬁrm is the indirect price of management services. Therefore, the function of the asymmetric structure of residual rights is to get the activity with the lowest transaction efﬁciency involved in the division of labor while avoiding direct pricing and marketing of the output and input of that activity, thus promoting the division of labor and productivity. In a sense, the function of the asymmetric structure of residual rights is similar to that of a patent law that enforces rights to intangible intellectual property, thereby promoting the division of labor and productivity in producing the intangible. However, the asymmetric structure of residual rights to returns and control can indirectly price those intangible intellectual properties which are prohibitively expensive to price even through a patent law. Intuitively, there are two ways to do business if an individual has an idea for making money. The ﬁrst is to sell the entrepreneurial idea in the market. This is very likely to create a situation in which everybody can steal the idea and refuse to pay for its use. The second way of proceeding is for the entrepreneur to hire workers to realize the idea, while keeping the idea to

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herself as a business secret. Then she can claim as her reward the residual returns to the ﬁrm, which represent the difference between revenue and the wage bill. If the idea is a good one, then the entrepreneur will make a fortune. If the idea is a bad one, she will become bankrupt. The residual return is the precise price of the idea, and the entrepreneur gets what she deserves, so that stealing and over- or under-pricing of intellectual property is avoided. To understand this, you might imagine that Bill Gates did not set up a company to hire others to realize his entrepreneurial ideas about how to make money from computer software. Instead, he sold his ideas as consultant services. Would anybody pay a billion dollars (which is the real market value of the ideas, indicated by Gates’ residual returns) to buy the ideas? This theory is referred to as the theory of indirect pricing, which is formalized by the Yang– Ng model (1995). It also formalizes the Cheung–Coase theory of the ﬁrm (Coase, 1937 and Cheung, 1983), which suggests that the institution of the ﬁrm can save on transaction costs by replacing trade in intermediate goods with trade in labor if the former involves higher transaction costs than the latter. The model does not endogenize transaction costs if these are deﬁned as a departure from the Pareto optimum. However, if endogenous transaction costs are deﬁned as those transaction costs whose value is endogenously determined by individuals’ decisions and the equilibrium process, then the Yang–Ng model has endogenized transaction costs. This is because the number of transactions for individuals and for the economy as a whole is endogenized in this model due to the trade-off between economies of specialization and transaction costs. With this theory, it is not difﬁcult to understand the role that the institution of the ﬁrm plays in economic development. If the legal system in a country does not protect the residual rights of the owners of private ﬁrms, then there will be a shortage of entrepreneurial activity. This is because entrepreneurial knowledge is very intangible, and can be indirectly priced only through claims to the residual rights of private ﬁrms. In the former Soviet Union, the government could arbitrarily infringe upon the residual rights of private ﬁrms, and monopolized rights to found ﬁrms. The Constitution of the People’s Republic of China regards earnings via the residual rights of private ﬁrms as a source of exploitation. According to Barro (1997), Easton and Walker (1997), and Frye and Shleifer (1997), for example, such infringement of residual rights is very harmful to the nurturing of entrepreneurship and for economic development. Also, using the theory of indirect pricing, we can explain why large companies in the developed economies use the institution of the multinational ﬁrm to export intangible management know-how rather than directly exporting it to less-developed countries. Again, management know-how is very intangible. It is very easy to under- or over-price it in direct trading. But the multinational company is an effective way to indirectly price such intangibles. It encourages division of labor and trade between professional producers of intangibles and tangibles, thereby promoting economic development. This theory has an interesting empirical implication. It predicts that the equilibrium size of the ﬁrm should decrease as division of labor evolves, if the transaction conditions are improved faster for goods than for labor (see exercise 11 below). Empirical evidence to support the hypothesis can be found in Liu and Yang (2000), who show that productivity, level of division of labor, and per capita real income increase, and the average size of ﬁrms declines concurrently, as improvements in transaction conditions for goods outpace those for labor.

8.3 THE EMERGENCE OF THE FIRM FROM THE EVOLUTION OF DIVISION OF LABOR In subsection 8.3.1, the model is elaborated and the concept of economies of roundabout production is deﬁned. In subsection 8.3.2, the corner equilibria in all structures of organizations

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and transactions are solved for. Finally, the general equilibrium and its comparative statics are solved in subsection 8.3.3.

8.3.1 Economies of roundabout production Example 8.1: A Smithian-Coasian model of the institution of the ﬁrm. As discussed in section 8.1, the existence of intermediate goods is essential for explaining the emergence of the ﬁrm from the division of labor. People produce intermediate goods because they can be used to improve the productivity of the ﬁnal goods. There are economies of roundabout production if the productivity of a good can be improved by employing intermediate goods. There are three types of economies of roundabout production. Type A relates to the quantity of an intermediate good that is employed to produce the ﬁnal goods. Type B relates to the number of intermediate goods at a link of the roundabout production chain. Type C relates to the number of links in the roundabout production chain. In this chapter we study type A economies of roundabout production. Type B are studied in chapter 6, and will be studied again in chapter 12. Type C will also be investigated in chapter 12. The development of division of labor since the Industrial Revolution has been taking place mainly in roundabout production of these three types. In the model in this chapter, each consumer-producer has the following system of the production involving economies of roundabout production. y + y s = (x + tx d )cl ya, x+x =l s

(8.1a)

b x

lx + ly = 1,

(8.1b) y, y , x, x , x , lx, ly ≥ 0 s

d

s

(8.1c)

where li is an individual’s level of specialization as well as her amount of labor allocated to the production of good i. x and y are respective quantities of the intermediate and consumption goods self-provided, x s and y s are respective quantities of the two goods that are sold, x d is the quantity of intermediate goods bought, t is the transaction efﬁciency coefﬁcient for the intermediate goods, and a and b are parameters of production conditions. x + tx d is the quantity of the intermediate good that is employed to produce the ﬁnal good. The exponentially weighted average of this quantity and the amount of labor employed, (x + tx d)c/(c+a)l ya/(c+a), is called the total factor input in producing good y. The ratio of output y + y s to total factor input is called total factor productivity (TFP), given by TFP = [(x + tx d )cl ya ](a+c−1)/(a+c). The TFP increases with an individual’s level of specialization in producing y if a + c > 1. A production function of a good with two inputs displays economies of specialization if the total factor productivity increases with an individual’s level of specialization in producing the good. A production function of a good displays type A economies of roundabout production if the total factor productivity of the good increases with the quantity of the intermediate good employed. In this chapter, the parameter c(a + c − 1)/(a + c) can be considered the degree of type A economies of roundabout production, and parameter a(a + c − 1)/(a + c) can be considered the degree of economies of specialization in producing the ﬁnal good. We assume that a = c for simplicity in the rest of the chapter, so that TFP increases with the quantity of the intermediate good employed and with the level of specialization in producing good y if a > 0.5. Hence, a can be considered the degree of economy of roundaboutness, as well as the degree of economy of specialization in producing y. Suppose that the transaction efﬁciency coefﬁcient for the ﬁnal good y is k, and that all ex ante identical consumer-producers have the following utility function: u = y + ky d, where the set of individuals is a continuum.

(8.2)

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8.3.2 The corner equilibria in four structures The Wen theorem can be reestablished and reﬁned for a model with intermediate goods. Hence, an individual sells at most one good and does not buy and self-provide the same good. She self-provides the consumer good if she sells it. Since intermediate goods do not directly contribute to utility, she does not self-provide the intermediate good unless she produces the ﬁnal good. Structure A (autarky), where each individual chooses a conﬁguration with x s = y s = x d = y d = 0, as shown in ﬁgure 8.1(a): The decision problem for each individual in this structure is: Max: u = y = x al ya = l xab(1 − lx)a and its solution is: lx = b/(1 + b),

ly = 1/(1 + b),

x = [b/(1 + b)]b (8.3a)

uA = y = [bb/(1 + b)1+b]a

where per capita real income in structure A, uA, is per capita output of the consumption good as well. Structure D, comprising conﬁgurations (x/y) and (y/x), as shown in ﬁgure 8.1(b): There is no asymmetric distribution of residual rights in this structure. Individuals exchange goods for goods in the absence of the institution of the ﬁrm and a related labor market. Conﬁguration (x/y) is deﬁned by x = y = y s = ly = 0 and x s, lx, y d > 0. Inserting the values of the variables and the budget constraint into the utility function yields the decision for this conﬁguration. Indeed, there is no scope for adjusting the values of the decision variables, which are ﬁxed by the deﬁnition of the conﬁguration and the budget constraint. Here, the specialist producer of good x does not self-provide x, which is not a consumption good. Conﬁguration ( y/x) is deﬁned by x = x s = y d = lx = 0 and x d, y, y s, ly > 0. Marginal analysis of the conﬁguration yields the corner solution. The corner solutions for the two conﬁgurations are summarized as follows: (x/y): x s = 1,

yd = px/py,

ux = kpx/py

(y/x): x d = (at apy /px)1/(1−a),

ys = (at apy /px)1/(1−a)px/py,

uy = (atpy/px)a/(1−a)(1 − a) where ui is the indirect utility function of an individual selling good i. Having considered the market clearing and utility equalization conditions and the population size equation Mx + My = M in structure D, we can solve for the corner equilibrium in that structure as follows: py /px = [k/(1 − a]1−a/(at)a,

Mx =

akM , 1 − a + ak

My =

uD = aa(1 − a)1−a(tk)a

(1 − a)M 1 − a + ak

(8.3b)

where Mi is the number of individuals selling good i, and uD is the per capita real income in structure D. Per capita real income is per capita consumption of the ﬁnal good, and its reciprocal is the absolute price of labor, which includes labor allocated to the production of both ﬁnal and intermediate goods.

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Structure E, comprising conﬁgurations (lx/y) and (y/lx), as shown in ﬁgure 8.1(c): (y/lx) denotes a specialist producer of y who hires workers and directs them to specialize in producing x within the ﬁrm. (lx/y) denotes a worker who is hired to produce the intermediate good and who buys the ﬁnal good. The decision problem of the employer choosing (y/lx) is: Max: uy = y s.t.

y + y s = (x dly) a, x = (slx) , s

b

x = Nx d

ly = 1,

lx = 1,

s

(production conditions for specialist of y) (production conditions for specialist of x) (equality between quantities of x produced and employed)

py y = wNlx = wN s

(budget constraint)

where N is the number of workers hired by the employer, w is the wage rate, and 1 − s is the transaction cost coefﬁcient for each unit of labor hired. The quantity of labor employed in production is thus slx. Nlx is the employer’s demand for labor. Each worker in the ﬁrm produces x s = (slx)b = s b when he is directed to specialize in producing x (lx = 1). Hence, the employer receives intermediate good x d = Nx s. Superscripts s and d denote supply and demand for inputs and outputs within the ﬁrm. Note that lx is an employee’s quantity of labor, but is the employer’s decision variable. This is what we mean by residual control rights or asymmetric distribution of authority. However, the employee always has the right to quit the job and to ﬁnd another employer. More important than this, he can use the free markets for capital, labor, and goods to choose to become an employer himself and to found his own enterprise. This distinguishes the asymmetric relationship between employer and employee in a capitalist ﬁrm from the asymmetric relationship between master and slave or the feudal relationship between lord and servant. The employer’s rights to residual returns relate to the difference between the output level of y within the ﬁrm and the quantity of y that is sold by the ﬁrm. Note that the production function of good x is still speciﬁed for each worker. It displays economies of specialization for each worker rather than economies of the scale of labor in the ﬁrm. All individual workers, production functions, and the employer’s production function are aggregated as the production function for the ﬁrm, which is y + y s = (x dly) a = (Ns bly) a. This production function displays local economies of scale to x d and ly for ly ≤ 1 and a ∈ (0.5, 1). But, there also are economies of specialization in producing y for the employer and in producing x for each worker. Hence, the local economies of scale for the ﬁrm are associated with economies of division of labor within the ﬁrm, which cannot be obtained by simply pooling labor together in the absence of specialization and division of labor. Note that the total factor is (x d )0.5l y0.5. This formalizes the distinction, drawn by Young (1928), between economies of scale generated by pooling labor within a ﬁrm and economies of specialization. If a > 1, the production of the ﬁrm displays global economies of scale to employed labor, N, that is, total factor productivity increases as the employer hires more workers. For a > 1, the Kuhn–Tucker condition for the interior optimum number of workers is not satisﬁed, so that the optimum value of N is as large as possible. Hence, a corner equilibrium with ﬁrms doesn’t exist. With a ∈(0.5, 1), the solution of the decision problem for conﬁguration (y/lx) is N = (s abapy/w)1/(1−a),

ys = (saba)1/(1−a)(py/w)a/(1−a)

uy = y = (1 − a)(s bapy/w)a/(1−a) where uy is the employer’s indirect utility function. Note that the interior solution of N is relevant only for a < 1.

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Each worker’s decision is simple. He sells all his labor, so that the budget constraint is py y d = wl xs where l xs = 1 is the labor supply. The worker’s utility is thus ux = ky d = kw/py. Let the number of individuals choosing (y/lx) be My; then the market supply of good y is My y s and the market demand for labor is My N. Let the number of individuals choosing (lx/y) be Mx; then the market demand for good y is Mx y d and the market supply of labor is Mx. The market clearing conditions for good y and for labor are equivalent to each other due to Walras’s law. Hence, we consider only one of them. Together with the utility equalization condition and two corner solutions, we have Mx y s = My y d,

y s = (saba)1/(1−a)(py /w)a/(1−a),

ux = uy

kw/py = (1 −a)(sbapy /w)a/(1−a)

or

yd = w/py

This yields the corner equilibrium in structure E as follows:

N = Mx /M y =

ak 1− a

w/py = [(1 − a)/k]1−a(sba)a

(8.3c)

uE = (s ka) (1 − a) b

a

1−a

where uE is the per capita real income in structure E. Its reciprocal is also the absolute labor price of the ﬁnal good. Structure F, comprising conﬁgurations (ly/x) and (x/ly), as shown in ﬁgure 8.1(d): (x/ly) denotes a specialist producer of x who hires workers and directs them to specialize in producing y using her produce x within the ﬁrm. (ly/x) denotes a worker who is hired to produce the ﬁnal good, using the intermediate good, and who buys the ﬁnal good. The decision problem of the employer choosing (x/ly) is: Max: ux = Y Y + Y s ≡ Ny s y s = (x drly) a,

(total output of y for a ﬁrm) ly = 1

x = x /N d

s

x s = l xb,

(quantity of x employed by each employee) lx = 1

pyY = wly N = wN s

(production condition for each employee)

(production condition of employer) (budget constraint)

where the upper-case letters represent output levels for the ﬁrm, and the lower-case letters represent quantities of goods for each individual. Y + Y s is the total output of the ﬁnal good for the ﬁrm, Y is the residual return to the employer, Y s is the total amount sold by the ﬁrm, y s is the output level of the ﬁnal good produced by each employee, x d is the amount of the intermediate good used by each employee to produce y, and r is the transaction efﬁciency coefﬁcient for the labor of employees. Because of the transaction cost of labor, the employer receives rly when she buys ly. N is the number of workers hired by each employer and xs is the amount of the intermediate good produced by the employer. The superscripts d and s for the lower-case letters represent internal demand for inputs and supply of outputs within the ﬁrm,

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while the superscripts d and s for the upper-case letters represent demand and supply in the marketplace. The solution of the decision problem is: Y s = ( py/w)(1−a)/ar(1 − a)1/a,

N = r[(1 − a)py /w]1/a,

ux = Y = ar[(1 − a)py /w](1−a)/a, where ux is the employer’s indirect utility function. The decision problem of a specialist worker producing y is simple. He sells all of his labor to exchange for good y. Hence, from the utility function uy = ky d and the budget constraint py y d = wly = w, we obtain his indirect utility function: uy = kw/py. The market clearing and utility equalization conditions yield the corner equilibrium in structure F:

N = M y /Mx =

w/py = (ar/k)a(1 − a)1−a,

k (1 − a) a

(8.3d)

uF = (ar)a [k(1 − a)]1−a where uF is the per capita real income in this structure. Let us put all information relating to the four corner equilibria together in table 8.1.

Table 8.1 Corner equilibria in four structures Structure

A

D

E 1− a

Relative price

py ⎛ k ⎞ = px ⎜⎝ 1 − a ⎟⎠

Number of specialists

Mx =

akM 1 − a + ak

My =

(1 − a)M 1 − a + ak

Demand function

w ⎛1 − a⎞ =⎜ ⎟ py ⎝ k ⎠

a

(as b ) −a

akM 1 − a + ak (1 − a)M My = 1 − a + ak

aM (1 − a)k + a k(1 − a)M My = (1 − a)k + a 1

p ⎞ 1−a ⎛ N d = ⎜ s ab a y ⎟ w⎠ ⎝

y d = px/py

y d = w/py

y =a

⎛ p y ⎞ 1−a ⎜t ⎟ ⎝ px ⎠

1

⎛ p (1 − a) ⎞ a N = r⎜ y ⎟ ⎝ w ⎠ y d = w/py d

a

a

1 1− a

w ⎛ ar ⎞ = ⎜ ⎟ (1 − a)1−a py ⎝ k ⎠

Mx =

p ⎞ 1−a ⎛ x d = ⎜ at a y ⎟ px ⎠ ⎝

s

⎛ bb ⎞ ⎜ (1 + b)1+b ⎟ ⎝ ⎠

1−a

Mx =

1

Supply function

Real income

(at ) − a

F

y =a s

1 1− a

⎛ s b p y ⎞ 1−a s ⎜ w ⎟ lx ⎝ ⎠

⎛p ⎞ Y = (1 − a) ⎜ y ⎟ ⎝w⎠ s

1 a

xs = 1

=1

l ys = 1

(tka)a(1 − a)1−a

(s bka)a(1 − a)1−a

(ar)a[k(1 − a)]1−a

a

1− a a

r

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8.3.3 General equilibrium structure of transactions and residual rights Per capita real incomes in the four structures are dependent on the transaction efﬁciency parameters t, s, k, the degree of economies of specialization b, and the degree of economies of roundabout production a. According to the Yao theorem, all we have to do in solving for the general equilibrium in a model with ex ante identical individuals is to identify the Pareto optimum corner equilibrium from the four corner equilibria. Letting per capita real incomes in each pair of structures be equal, we will obtain several equations that partition the parameter space of ﬁve dimensions into several subspaces. Our job is then to identify which structure is the general equilibrium structure within each of the subspaces. Essentially, this amounts to solving for a system of simultaneous inequalities – for which there is no standard procedure. Experience and skill in ruling out Pareto inefﬁcient structures as far as possible through identifying incompatibility of and contradictions between inequalities are crucial for ﬁnding the solution. From working with many of the models in this text, you should gain skills in manipulating such systems of inequalities. For the current model, let us solve for the system of simultaneous inequalities in two steps. First, we compare per capita real incomes in structures D, E, and F. We have: uE > uD iff t < s b.

(8.4a)

uE > uF iff k > k8 ≡ (r/s b)a/(2a−1)

(8.4b)

uD > uF iff k > k7 ≡ (r/t)

(8.4c)

a/(2a−1)

(8.4a) can be used to partition the parameter space into two subspaces ﬁrst. For t < s b, structure D can be ruled out due to (8.4a). We need to compare only between structures E and F. Hence, only k8 and (8.4b) are relevant. For the case with t > s b, structure E is ruled out. Only k and (8.4c) are relevant. Structure D generates the greatest per capita real income if k > k7; Structure F generates the greatest per capita real income if k < k7; Structure E cannot be general equilibrium since uE < uD for any k. Putting the information together and considering per capita real income in autarky yields table 8.2. Comparisons between per capita real incomes in each pair of structures for the parameter subspace in table 8.2 yield the general equilibrium and its inframarginal comparative statics, as shown in table 8.3. If you use the constraints that all critical values ki are between 0 and 1, you can partition the parameter space further. We leave this as an exercise to you.

Table 8.2 Candidates for equilibrium structure t > sb

t < sb k < k8

k > k8

k < k7

k > k7

F, A

E, A

F, A

D, A

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Table 8.3 General equilibrium and its inframarginal comparative statics Values of t and s Value of k Relative to r, t, s, a Equilibrium structure

t < sb

t > sb

k < k8

k > k8

k < k7

k > k7

< k11

> k11

< k10

> k10

< k11

> k11

< k9

k > k9

A

F

A

E

A

F

A

D

Where k7 ≡ (r/t)a/(2a−1) is given by uD = uE, k8 ≡ (r/sb)a/(2a−1) is given by uE = uF, k9 ≡ (1 − a)(a−1)/ab b/ta(1 + b)1+b is given by uA = uD, k10 ≡ (1 − a)(a−1)/ab b/asb(1 + b)1+b is given by uA = uE, k11 ≡ [bb/ar(1 + b) 1+b]a/(1−a)/(1 − a) is given by uA = uF.

In terms of intuition, table 8.3 tells the following story. I) The structure with division of labor and the producer of y as the employer (structure E) cannot be general equilibrium if the transaction efﬁciency for labor employed to produce the intermediate good (s) is low compared to that for the intermediate good (t), or if t > s a, since structure E must trade labor employed to produce the intermediate good. I.a) Under this circumstance, if the transaction efﬁciencies for the ﬁnal and intermediate goods (k and t) are sufﬁciently high, compared to the transaction efﬁciency for labor employed to produce the ﬁnal good (r), or if k > k7, the structure with the division of labor and the producer of x as the employer (structure F) cannot be general equilibrium either, since F must trade labor employed to produce the ﬁnal good. Note the relationship between this statement and the formula for k7. Hence, only structures A and D are candidates for the equilibrium structure. If the transaction efﬁciencies for the ﬁnal and intermediate goods are high, D is the equilibrium; otherwise, A is the equilibrium. I.b) If the transaction efﬁciency for the intermediate good (t) is low compared to the transaction efﬁciency for labor employed to produce the ﬁnal good (r), or if k < k7, the structure with the division of labor and with no ﬁrms (structure D) cannot be general equilibrium, since D must trade the intermediate good. Hence, only structures A and F are candidates for the equilibrium structure. If the transaction efﬁciencies for the ﬁnal good and the labor hired to produce the ﬁnal good are high, F is the equilibrium; otherwise, A is the equilibrium. II) Structure D cannot be equilibrium if t is small compared to s, or if t < s a, since structure D must trade the intermediate good that involves a small t. II.a) If k and s are sufﬁciently large compared to r, or if k > k8, structure F cannot be equilibrium since F is associated with r. Hence, only structures A and E are candidates for the equilibrium structure. If k and s are sufﬁciently large (or k > k10), E is the equilibrium; otherwise, A is the equilibrium. II.b) If s is small compared to r, or if k < k8, structure E cannot be equilibrium since E is associated with s. If k and r are sufﬁciently large, F is the equilibrium; otherwise, A is the equilibrium. The inframarginal comparative statics of general equilibrium are summarized in the following proposition. Proposition 8.1: The general equilibrium is autarky if transaction efﬁciency is low, and it is the division of labor if transaction efﬁciency is high. The division of labor is coordinated through the institution of the ﬁrm and the labor market if the transaction efﬁciency for labor

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is higher than that for intermediate goods. Otherwise, it is organized through the markets for the intermediate and ﬁnal goods. When the general equilibrium is associated with the ﬁrm, the specialist producer of the ﬁnal good is the owner of the ﬁrm if the transaction efﬁciency for labor employed to produce the intermediate good is higher than that for labor employed to produce the ﬁnal good. Otherwise, the specialist producer of the intermediate good is the owner of the ﬁrm. The institution of the ﬁrm can get the activity with the lowest transaction efﬁciency involved in the division of labor while avoiding the direct pricing and marketing of the outputs and inputs of that activity. The residual returns claimed by the employer are the indirect price of her efforts. The essence of the theory of indirect pricing can be summarized as follows. If individuals engage in division of labor in producing two goods x and y, trade in two of the four elements comprising outputs x, y, and inputs lx, ly can be used to organize the division of labor. Hence, there are six possible structures of transactions (2 combinations of 4 elements) which can be used to organize the division of labor: x and y (structure D), y and lx (structure E), y and ly (structure F), x and lx (not feasible, since a specialist of x who must consume y cannot buy y), x and ly (also not feasible), ly and lx (a structure that may be seen in some collective organization with a direct exchange of labor, but is rarely seen in the real world). Hence, individuals can at least consider three of the structures and choose one of them to avoid trade that involves the lowest transaction efﬁciency. Later we shall show that as the number of traded goods and the level of division of labor increase, the number of possible structures of transactions increases more than proportionally. This implies that, as division of labor develops, the choice of transaction structure is increasingly more important for economic development than the choice of production structure and resource allocation for a given structure of production. This is why, in a highly commercialized society (with a high level of division of labor), there are more opportunities for entrepreneurs to make fortunes from manipulating transaction structures.

8.4 THE DISTINCTION BETWEEN EX ANTE AND EX POST PRODUCTION FUNCTIONS, AND THE ROLE OF THE INSTITUTION OF THE FIRM IN ECONOMIC DEVELOPMENT For inframarginal analysis, the equilibrium system of production functions discontinuously jumps across structures as parameters shift between the subspaces that demarcate structures. This feature of the Smithian system of production generates important implications for endogenous productivity progress. Hence, it is important to draw the distinction between the ex ante production function, which is the production function speciﬁed before individuals have made their decisions, and the ex post production function, which is observed only after individuals have chosen conﬁgurations and the economy has settled down in a structure. The ex ante production functions are speciﬁed in (8.1). Since all decision variables are allowed to take on zero and positive values, there are multiple production conﬁgurations for different proﬁles of zero and positive values of decision variables. As individuals choose different conﬁgurations and the economy settles down in different structures, each individual’s system of production differs from conﬁguration to conﬁguration, while the system of production for society differs from structure to structure. If an individual chooses autarky (x, y, lx, ly > 0, x s, y s, x d, y d = 0), then her ex post production function of y is y = xal ya = l xab(1 − lx) a = (1 − ly) abl ya ,

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where the endowment constraint is used. The marginal productivity of y and the derivative of the marginal productivity are

dy = ay(bl x−1 − l y−1) dly d 2y <0 dl y2

when

dy = 0. dly

This implies diminishing marginal labor productivity of y within the neighborhood of the corner solution in conﬁguration A. But if structure E is chosen, then the ex post production function of a ﬁrm in producing y is given in (8.7). It is y + y s = (x dly) a = (Ns b ) a. As discussed in the previous subsection, this ex post production function for the ﬁrm displays economies of specialization in producing y if a > 0.5; and exhibits global increasing returns to scale of labor, N, if a > 1, and local economies of scale if a ∈(0.5, 1). Thus the ex post production function for the ﬁrm may emerge from the division of labor as the general equilibrium shifts from autarky to structure E. The ex post production function in E is not only different from the ex post production function in autarky, but also different from the ex ante production functions in (8.1), which do not involve the ﬁrm and its economies of scale. Rosen (1978) was the ﬁrst economist to spell out the distinction between ex ante and ex post production functions. George Stigler (1951) noted the discontinuous jumps of cost functions which are based on the production function and which are a result of changes in the level of specialization for the ﬁrm. In the Smithian framework, the production function for the ﬁrm may emerge from individuals’ decisions in choosing a certain structure of transactions required by the division of labor. In particular, the production function for a ﬁrm is a combination of many individuals’ production functions. An owner of a ﬁrm combines her system of production with all employees’ systems of production to arrive at a composite. This implies that in the Smithian framework, the ﬁrm is no longer a black box represented by an ad hoc production function. The theory of the ﬁrm in this chapter has looked at how the production function for the ﬁrm emerges, and at the development implications of the internal organization of the ﬁrm.

8.5 THE COASE THEOREM AND OTHER THEORIES OF THE FIRM From the discussion in the previous subsections, we can see that division of labor is necessary but not sufﬁcient for the existence of the ﬁrm. This proposition was ﬁrst proposed by Coase (1937). As Cheung (1983) argues, the other necessary condition for the existence of the ﬁrm is that the transaction efﬁciency for intermediate goods must be lower than that for labor employed to produce the intermediate goods. Cheung’s theory reﬁnes Coase’s idea about the ﬁrm. Coase argues that the institution of the ﬁrm is used to replace the market with administration within the ﬁrm. But, according to Cheung, the institution of the ﬁrm replaces the market for intermediate goods with the market for labor, instead of replacing the market with a nonmarket institution.

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Coase (1960) claims that the structure of ownership makes no difference to the efﬁciency of the market if the transaction cost is zero, and that the market will choose a structure of ownership to maximize the beneﬁt of division of labor, net of transaction costs (the Coase theorem). Our model substantiates the Coase theorem. From table 8.1, it is obvious that structures D, E, F generate the same per capita real income if t = k = s = r = 1 (no transaction costs). The structure of ownership of the ﬁrm makes a difference only if transaction costs are not zero. Also, proposition 8.1 implies the second statement in the Coase theorem, that the market will choose the most efﬁcient structure of ownership and property rights. We have reﬁned Coase’s ideas about transaction costs, which he claims the institution of the ﬁrm can be used to reduce. But our proposition 8.1 implies that as transaction efﬁciency is improved, total transaction costs will be increased as the general equilibrium shifts from autarky to structure E or F. Hence, the institution of the ﬁrm may increase transaction costs when it promotes division of labor, as long as increased economies of division of labor outweigh the increased transaction costs. From table 8.2, we can see that for t < s a and k9 > k > k8, k10, the institution of the ﬁrm in structure E generates the highest per capita real income and productivity, while the division of labor in structure D generates a lower per capita real income than in autarky. Hence, if ﬁrms are not allowed, the division of labor will not be chosen while autarky with low productivity will be. If ﬁrms are allowed, then individuals will choose the division of labor and associated high productivity in structure E. Hence, ﬁrms can promote the division of labor and economic development by reducing transaction costs compared to D and by increasing transaction costs compared to autarky. And hence, a good legal system that protects the residual rights of owners of private ﬁrms is a very important driving force of economic development. Recent literature on the theory of the ﬁrm comprises three subﬁelds. One of them is represented by the Hart–Grossman–Moore model of incomplete contract and two-sided moral hazard (see chapter 9 below and Hart 1995). As pointed out by Holmstrom and Roberts (1998, pp. 79–82), the incomplete contract model simultaneously addresses the beneﬁts and the costs of ownership. Markets are identiﬁed with the right to bargain and, when necessary, to exit with the assets owned. This greatly clariﬁes the market’s institutional role, as well as its value in providing entrepreneurial incentives. On the other hand, ﬁrms are poorly deﬁned in the model. Further, it cannot explain the difference between contractual arrangements in Japanese and US companies. It cannot explain the complex network of contracts in the new high-tech sector which does not use integration to restrain opportunism. Such opportunism often occurs when the investment is locked in a relationship-speciﬁc business. The incomplete contract model has recently been criticized by Maskin and Tirol (1999a,b), who show that unforeseeable contingencies (which are often invoked in order to justify contractual incompleteness) and sequential rationality (parties must foresee the payoff consequences of contracts and investments) are incompatible. They show that even ex ante undescribability is often irrelevant, since sophisticated mechanisms can be used to implement the same payoff outcomes as if contingencies were describable. Our model in this chapter shows that a theoretical foundation for investigating the emergence and evolution of the institution of the ﬁrm and related structures of residual rights can be established in the absence of undescribability. However, the labor contract in the model in this chapter can be interpreted as incomplete in the sense that it requires the employee to do whatever he is told to do rather than specifying exactly what he is supposed to do. The second research line in this literature is represented by Holmstrom and Milgrom (1994). Related to this research line, many models of multiple layers of principal–agent relationships have been developed (see Gibbons, 1998 and Bolton and Scharfstein, 1998 for recent reviews). Holmstrom and Milgrom argue that the function of ﬁrms cannot be properly under-

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stood without considering additional incentive instruments that can serve as substitutes for outright ownership. Employees, for instance, typically own no assets, yet they often do work quite effectively. In these theories, asset ownership gives access to many incentive instruments and the role of the ﬁrm is to coordinate the use of them all. That may also explain why noninvesting parties, including the ﬁrm itself, own assets. They use BskyB, a satellite broadcasting system in Rupert Murdoch’s media empire, as an example to motivate their model (see Holmstrom and Roberts, 1998, p. 85). This company is an example of a highly successful organization that has created its wealth not by owning physical assets, but by crafting ingenious contracts that have given it inﬂuence over an effective network of media players. Satellite broadcasting requires a variety of highly complementary activities, including acquisition and development of programming, provision of the distribution system (satellites, transmitters, and home receivers), and development of encryption devices (to limit reception to those who pay), all of which must be carried out before the service can be offered. An example of how the agency issue can affect the boundaries of an organization is whether a ﬁrm employs its sales force directly or uses outside sales agents. The best-known example here involves electronic parts companies, some of which hire their own sales agents while others sell through separate supply companies (see Holmstrom and Roberts, 1998, p. 86). Originally, it was expected that the observed variation in this choice would relate to the degree of asset speciﬁcity; for example, the extent to which investment by sales people with knowledge about products was speciﬁc to a particular company. Instead, measurement costs and agency concerns turned out to be central. An employee sales force is used when individual performance is difﬁcult to measure and when nonselling activities (like customer support or gathering information about customers’ needs) are important to the ﬁrm; otherwise, outside companies are used. Holmstrom and Milgrom (1991, 1994) rationalize this pattern with a model of a multitask agency in which salespeople carry out three tasks: making current sales, cultivating long-term customer satisfaction, and gathering and relaying information on customer needs. If the latter two activities are important and if the three activities compete for the agent’s time, then the marginal rewards to improved performance on each must be comparable in strength; otherwise, the ill-paid activities will be slighted. Because performance in nonselling activities is arguably hard to measure, it may be best to provide balanced, necessarily lower-powered incentives for all three activities. Offering weak incentives to an outside sales agent can be problematic, however, because the agent may then divert all effort to selling the products of other ﬁrms, which come with stronger rewards for sales. With an employee, this problem can be handled with a salary and a low commission rate, because the employee’s outside activities are more easily constrained, and promotion and other broader incentives can be used within the ﬁrm to inﬂuence the agent’s behavior. One of the Holmstrom and Milgrom models is presented in example 9.3. See exercise 17 in chapter 9 for a synthesis of the theory in this chapter, Hart’s theory of incomplete contract, and Maskin, Tirole, Milgrom, and Holmstrom’s criticisms thereof. The model in this chapter complements the Holmstrom and Milgrom model with the trade-off between stronger incentive and greater measurement costs. Our model explains why the residual rights of the entrepreneur who designs contractual arrangements that efﬁciently trade off incentive provision against measurement costs, are essential for her to have the right incentive to sort out the efﬁcient trade-off. Her entrepreneurial services are intangible intellectual properties that can be indirectly priced only via residual rights, the institution of the ﬁrm, and the related labor market. The case of the franchise network in question 32 of chapter 1 shows that when the transaction efﬁciency of intangible intellectual properties can be effectively priced via a hostage mechanism, the division of labor between the production of intellectual

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properties and the production of tangible services can be organized by market relationships between the franchiser and franchisees. The third subﬁeld in this literature focuses on the pyramidal structure of hierarchies – a recent survey of this subﬁeld can be found in Borland and Eichberger (1998). The pyramidal hierarchy investigated in this literature may not necessarily be related to asymmetric residual rights to returns and control, which are essential for the existence of the institution of the ﬁrm. Shi and Yang (1998) and Yang (2000, ch. 20) relate the theory of the ﬁrm in this chapter to hierarchical transaction structures, division of labor, and residual rights. Finally, a literature on the reliability of economic systems has been developed to address the problems that relate to the theory of the ﬁrm. This literature is more relevant to the problems of economic development which we address below in chapter 10, and we will discuss it in that chapter. Recent reviews of this literature can be found in Sah (1991), Kremer (1993), Blanchard and Kremer (1997), and Lio (1998).

Key Terms and Review • The institution of the ﬁrm • Economies of specialization in producing a good requiring more than one input factor • The relationship between economies of specialization in producing a good, economies of division of labor, and economies of the institution of the ﬁrm • The distinction between ex ante and ex post production functions • Necessary and sufﬁcient conditions for the emergence of the ﬁrm from division of labor • The function of the institution of the ﬁrm and implications of the internal organization within the ﬁrm for the level of division of labor and economic development • The relationship between individuals’ production functions and the production function of a ﬁrm • The difference between rights to residual returns and rights to residual control, and the relationship between those residual rights and the function of the institution of the ﬁrm • The role of freedom of choice of profession conﬁguration and freedom of enterprise in enabling the institution of the ﬁrm to function • The signiﬁcance of a legal system that protects the residual rights of the owners of the ﬁrm in enabling the institution of the ﬁrm to function

Further Reading Theory of the ﬁrm: Cheung (1983), Coase (1937, 1991), Alchian and Demsetz (1972), Jensen and Meckling (1976), Knight (1925), Stigler (1951); Theory of incomplete contracts: Hart (1995), Grossman and Hart (1986), Hart and Moore (1990, 1999), Maskin and Tirole (1999a,b), Tirole (1999), Segal (1999); Theory of the ﬁrm and endogenous specialization: Bolton and Dewatripont (1994), Carter (1995), Shi and Yang (1998), Yang and Y.-K. Ng (1993, ch. 9; 1995), Borland and Yang (1995), Yang (1988); Models with a trade-off between incentive provision and measurement costs: Bolton and Scharfstein (1998), Holmstrom and Milgrom (1991, 1994), Holmstrom and Roberts (1998); Theory of the ﬁrm and endogenous transaction costs: Milgrom and Roberts (1990, 1992), Kreps (1990), Lewis and Sappington (1991), Aghion and Tirole (1997),

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Gibbons (1998); Theory of the ﬁrm and commitment games: Dewatripont and Maskin (1995), Dewatripont and Roland (1995), Roland (2000), Dewatripont (1988), Qian (1994b); Hierarchy: O. Williamson (1967), Tirole (1986), Bolton and Dewatripont (1994), Borland and Eichberger (1998), Yang and Ng (1993, ch. 14), Yang (2000, ch. 20), Van Zandt (1995), Bac (1996), Bag (1997), Calvo and Wellisz (1978, 1979), Keren and Levhari (1982), MacLeod and Malcomson (1988), Qian (1994a), Radner (1992, 1993); Empirical evidence against the type II scale effect: Aiginger and Tichy (1991), Loveman and Sengenberger (1991), Liu and Yang (2000), Murakami, Liu, and Otsuka (1996), Y. Zhang (1999), Berger and Ofek (1995), Bhagat, Shleifer, and Vishny (1990), Comment and Jarrell (1995), Fauver, Houston, and Naranjo (1998), Kaplan and Weisbach (1992), Lang and Stulz (1994), Servaes (1996).

QUESTIONS 1 Alchian and Demsetz (1972) indicate that the claim of the owner of the ﬁrm to its residual returns is the distinguishing feature of the capitalist ﬁrm. If the marginal productivities of the members of the production team are interdependent, then each member does not count the effect of her effort on others’ productivity if her pay is determined by her marginal productivity in the market, thereby resulting in distortions. Hence, a monitor is essential to measure the efforts of the members and pay them according to their effects in the productivity of the entire team. But by what mechanism can effort levels of the monitor be efﬁciently determined? According to Alchian and Demsetz, the residual returns to the owner-monitor of the ﬁrm are the efﬁcient institution for achieving this. Without a claim on the residual returns, nobody will have an incentive to ensure the efﬁcient management of the ﬁrm. Hence, so-called “X-inefﬁciency,” which means that productivity potential cannot be exploited even if it is technically easy to achieve, will emerge from the absence of claimants to the residual returns of the ﬁrm. This is why all state-owned ﬁrms, which have no individual residual rights claimants, are associated with signiﬁcant X-inefﬁciencies. There are two major criticisms of Alchian and Demsetz’s theory. One is proposed by Grossman and Hart (see chapter 9 below), who argue that the capitalist ﬁrm is distinguished not only by the asymmetric distribution of residual returns, but also by the asymmetric distribution of residual control, which implies that the owner of the ﬁrm has rights to dispose of the assets and labor of the ﬁrm. In chapter 9, the rationale for the asymmetric distribution of residual control rights will be investigated. The second criticism is that if the pricing of the effort level of the monitor is highly efﬁcient, the production team can pay the monitor according to her performance. Interdependence of the marginal productivities of members in a production team does not necessarily imply that residual returns are the only way to resolve the problem. It is because the pricing efﬁciency of the monitor’s effort is even lower than the pricing efﬁciency of the efforts of the team members that the claim to residual returns emerges as an institution to indirectly price the effort level of the monitor. Comment on these criticisms of the Alchian– Demsetz argument. 2 Rosenberg and Birdzell (1986, pp. 145–83) have documented the history of the emergence and evolution of the ﬁrm. Use the model in this chapter, in connection with the model in chapter 11, to analyze the historical fact (pp. 145, 159, 167, 179, 183): “Starting about 1750, the factory system of production gradually became

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dominant in most of Western industry. It changed relationships in the workplace and, probably with more drastic social effect, changed the location of the workplace from the household to the factory. The shift to the factory was practically complete by 1880, but most commercial and industrial enterprises continued to be organized as individual proprietorships, with the exception of banks and railways. Between 1750 and 1880, the respect of the Western governments for the autonomy of the economic sphere became virtually an ideology. Apart from such sporadic intrusions as the British Factory Acts and Bismarck’s system of social insurance, governments were content to assist only when asked. Peacetime taxes were small and currencies comparatively stable.” “The textile industry led factory development during the ﬁrst decades of the Industrial Revolution, not only in England but also in the United States. Richard Arkwright, inventor of a spinning machine, came to be known as the ‘father of the English factory system,’ owing to the numerous cotton spinning mills he promoted. The early textile mills were also a principal object of the public agitation that led to the ﬁrst English factory legislation. Arkwright’s patent for a spinning machine supplies an approximate date, 1769, for the beginning of the conversion. In the British textile industry, ﬁrms tended to specialize in a single step in the process of producing cotton cloth. Instead of building fully integrated plants of the type used in the iron and steel industry and in ceramics, the British textile makers located highly specialized plants close to each other. The development of these regional textile complexes was facilitated by the substitution of steam for water power.” “The pioneer of factory production was Josiah Wedgwood. At his works at Etruria, he divided his factory into departments by type of product and, within each department, workers were classiﬁed according to numerous specialties. N. L. Clow describes the division of labor at Etruria as follows. ‘The gradual multiplication of the processes whereby ceramic products could be produced led, as in other industries, to a marked division of labour in Josiah Wedgwood’s Etruria, where the principle of specialization was ﬁrst introduced, was divided into departments according to the type of ware produced: useful, ornamental, jasper, basalt, and so on. In 1790 some 160 employees were engaged in the “useful” branch, in the following categories: slip-house, clay-beaters, throwers and their attendant boys, plate makers, dish makers, hollow-ware pressers, turners of ﬂat-ware, turners of hollow-ware, handlers, biscuit-oven ﬁremen, dippers, brushers, placers and ﬁremen . . . , girl colourgrinders, painters, enamellers and gilders, and, in addition, coal getters, modellers, mould makers, saggar makers, and a cooper.’ The ceramic industry was typical of later industries in its elimination of any easily visible connection between what a worker does and the marketable product of the worker’s efforts.” “Recently, Marglin, in comparing factory work to work under the puttingout system, principally as practiced in the British textile industry, has speciﬁed the following advantages of the factory to its owners: (1) stealing of materials and work in process by workers could be reduced; (2) unskilled women and children were capable of doing the narrowly specialized factory jobs and accepted lower wages for equivalent output than the more highly skilled adult male labor used in the putting-out system; (3) factory hands could be induced, by the threat of dismissal for absenteeism, to work regularly for a full week instead of working the partial and uncertain week common among cottage workers.” “By 1880, the change to market relations was substantially complete. By then, terms of employment were determined

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by employer offers of terms and employee acceptances, and, as in any other market, both offers and acceptances were inﬂuenced by the state of the supply of, and the demand for, labor.” John bought from James a copying shop at $110,000, which did not include the rental of the real estate and copy machines. Each year John can make up to $40,000 as proﬁt net of all rents for real estate, copy machines, other equipment, and the wage bill for the machine keepers and for himself. James told John that the goodwill of the business, embodied in the client base that he had cultivated over the years, as well as his planning in putting together in the right way his client base, the location of the shop, the machines, and other factors were worth more than $110,000. This was veriﬁed by the fact that by his fourth year in the business, John had repaid his investment of $110,000 and interest, and started to make a net proﬁt. Use this case to analyze why the shop could make a net proﬁt and why the intellectual property of James could not be appropriately priced in the absence of the institution of the ﬁrm. Use the model in this chapter to analyze increases in labor and capital shown in statistical data. According to neoclassical economics, observed increases in labor and capital inputs are simply increases in production factors employed in production. But according to the theory in this chapter, an increase in trade of labor is the result of the development of the institution of the ﬁrm, while an increase in trade of capital goods is the result of the development of division of labor in roundabout production between ﬁrms and individuals. The two phenomena can take place in the absence of increases in the total amounts of primary factors employed in production for society as a whole. Discuss the implications of the difference between these two interpretations of the data. In the nineteenth century, France, Germany, and other major European countries followed Britain in enacting laws guaranteeing the right of free association. Analyze the implications of these laws, in conjunction with patent laws, the automatic registration of companies, and laws that protect private property rights, for economic development and the evolution of division of labor. In Japan and China such laws did not exist until the end of the nineteenth century. Emperors were extremely sensitive to unofﬁcial free associations and tended to arbitrarily infringe the residual rights of the owners of ﬁrms. Use that institutional feature, in relation to the theory in this chapter, to explain the following historical fact documented by Elvin (1973). Song China (960 –1270 ad) possessed both the scientiﬁc knowledge and the mechanical ability to have experienced a full-ﬂedged industrial revolution some four centuries before it occurred in Europe. The Chinese developed very elaborate contracts and sophisticated commercial organizations, but failed to have an industrial revolution at that time. Under a regime of free association, any individual can set up a ﬁrm by registering it with the local government. But in many less-developed countries residents need to apply for approval from the government to set up a ﬁrm. When setting up a company engaging in foreign trade, for instance, a government license can be essential. Also, the government agency which has such approval power has vested interests in the business in which the applicant wants to engage. For example, in each Chinese city there is a government committee with power to approve the setting up of wholesale and retail ﬁrms. This committee is also the owner of the government

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monopoly wholesale and retail network in the city. Analyze the development implications of such an approval system in connection with the theory of the ﬁrm in this chapter. 7 Apply the theory of the ﬁrm in this chapter to analyze the role of multinational ﬁrms and foreign direct investment (FDI) in economic development. Under what conditions can multinational ﬁrms more efﬁciently protect the right to intellectual property (know-how) than direct trade in the intellectual properties? In many developing countries the governments require that the foreign ownership share of ﬁrms not exceed a certain percentage. What are the effects of such regulation on economic development? In many joint-venture businesses between foreign companies and Chinese government, the government has control rights and owns more than 50 percent of the businesses. But joint ventures between a government agency and foreign private ﬁrms are very unusual in a free market economy. Analyze the implications of the institutional difference for economic development in connection with the theory in this chapter. 8 In all Soviet-style economies, there are no laws that protect residual rights to ﬁrms. Due to Marx’s ideology, in a Soviet-style socialist country such residual rights are considered to be exploitative. Also, a Soviet-style government prohibits unofﬁcial free association (including free enterprise) for political reasons. Apply the theory of the ﬁrm to analyze the implications for economic development of these institutional features of the Soviet-style economy. Many development economists argue that entrepreneurship is essential for economic development (see, for instance, Bauer and Yamey, 1957, and Kindleberger, 1958). Use the theory in this chapter to analyze the conditions which nurture entrepreneurship. 9 Apply the theory of indirect pricing in this chapter to analyze why it is the shareholders rather than the managers of a company who are the owners when the division of labor between portfolio management and production management emerges. 10 In the Soviet-style economic system, land cannot be privately owned or traded. Only pricing according to working effort is legitimate. Making income from the ownership of assets, including land and shares in a ﬁrm, is regarded as exploitation. Analyze why, under these institutional arrangements, intangible services in managing real estate will be underpriced and short of supply. 11 Many economists claim that the function of the institution of the ﬁrm is to internalize externalities. Coase also claims that ﬁrms replace market transactions with the nonmarket arrangement of centralized planning within the ﬁrm. Apply the theory of indirect pricing to comment on this view. Relate your discussion to Cheung’s view that the institution of the ﬁrm replaces the market for intermediate goods with the labor market. 12 Apply the model in this chapter to substantiate Cheung, Coase, Stigler, and Young’s arguments that ﬁrm size is irrelevant to the realization of returns from the division of labor. The widely cited thesis of Coase (1937) states that the ﬁrm and the market are substitutes for each other in organizing division of labor. Cheung (1983) further suggests that the ﬁrm should be viewed as one type of contract under which a factor owner surrenders a delimited set of rights to use his or her factor in exchange for income. Therefore, a clear distinction is drawn between the ﬁrm size and the scale of division of labor. On the one hand, an increase in the ﬁrm size simply indicates that the number of one type of contract increases. As this can be achieved by decreasing

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the number of other types of contracts, there exists the possibility that the ﬁrm size increases but the level of division of labor remains the same or even decreases. On the other hand, since factory owners can choose different types of contracts to coordinate division of labor, economies of division of labor do not always lead to large ﬁrms. As Cheung (pp. 5–6) clearly puts it, “Could it be that specialization, coordination, and economy of scale achieved by pooling input resources from many owners will yield higher income for all, so that each chooses to join a ﬁrm . . . the answer is no . . . beneﬁts arising from specialization and coordination can be realized without the ‘factor market’ – the right to decide and use one’s input need not be delegated to some agent or entrepreneur, because in a product market the input owner will receive a payment for every contribution.” There have been many reports in the media in the 1980s and recently (see, for instance, “Enterprise: How Entrepreneurs are Reshaping the Economy and What Big Companies Can Learn,” Business Week, Oct. 22, 1993; Special Issue, “Management Focus,” The Economist, March 5, 1994, p. 79; and “Manufacturers Use Supplies to Help Them Develop New Products,” Wall Street Journal, 19 Dec., 1994, p. 1) about deintegration, focusing on core competence, increasing specialization, contracting out or outsourcing, which feature recent changes of company structure. Use the theory in this chapter to explain the phenomena. Use the theory of the ﬁrm in this chapter to analyze the implications of minimum wage laws. Then compare your results to the neoclassical analysis of the effects of such laws. Holmstrom and Roberts (1998, p. 78) indicate that according to the Hart–Grossman– Moore model, as investment by the buyer B becomes more important relative to investments by the seller S, B should be given more assets. If an asset has no inﬂuence on B’s investment, it should be owned by S. For this reason, no outsider should ever own an asset that would waste bargaining chips that are precious for incentive provision. For the same reason, joint ownership, meaning that both parties have the right to veto the use of the asset, is never optimal. As a consequence, assets that are worthless unless used together should never be separately owned. Extend the model in this chapter to predict that outside shareholders should own a ﬁrm if the division of labor between portfolio management and production management occurs, and if the transaction efﬁciency for input and output of portfolio management is lower than that for other activities. Specializations in producing x and y are complementary. Each of occupations (x/y) and (y/x) has no value if it is not matched up by the other. But in the model in this chapter, separate ownership of x and y may occur in equilibrium. Use this to discuss the difference between the model in this chapter and the Hart–Grossman model in chapter 9 below.

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EXERCISES 1 Assume that there is no transaction cost in the model in this chapter. But the government imposes a value tax rate t on goods sold and then returns to the sellers of goods the tax revenue collected from them. Solve for the general equilibrium and its inframarginal comparative statics. Analyze the impact of the tax rate on the equilibrium level of division of labor and productivity, and the equilibrium structure of residual rights. 2 Assume that in the model in exercise 1, a fraction of tax revenue 1 − s is used to maintain the government bureaucratic apparatus, so that only a fraction s of tax revenue goes back to the sellers of goods. Solve for the general equilibrium and its inframarginal comparative statics again. Analyze the impact of the bureaucracy efﬁciency coefﬁcient s on the equilibrium level of division of labor and productivity. 3 Now suppose that in the model in exercise 1, the government imposes a value tax on the sale of labor instead of on the sale of goods. Then it returns all tax revenue to the sellers of labor. Solve for the general equilibrium and its inframarginal comparative statics. Analyze the impact of the tax on the equilibrium level of division of labor and productivity. Compare your answer here to that in exercise 1. Then analyze the impacts of different tax regimes on the equilibrium structure of transactions, residual rights, and ownership of the ﬁrm. 4 Assume that in the model in exercise 3, a fraction of tax revenue 1 − θ is used to maintain the government bureaucratic apparatus, so that only the fraction θ of the tax revenue goes back to the sellers of labor. Solve for the general equilibrium and its inframarginal comparative statics again. Analyze the impact of the bureaucracy efﬁciency coefﬁcient θ on the equilibrium level of division of labor and productivity. Compare your answer here to that in exercise 2. Then analyze the impacts of bureaucracy efﬁciency θ and different tax regimes on the equilibrium structure of transactions, residual rights, and ownership of the ﬁrm. 5 Analyze the impact of various tax regimes in exercises 1 and 3 on trade volume of labor and intermediate goods, which can be observed from statistical data. Explain why, within the Smithian framework, an increase in labor trade implies the development of division of labor within the ﬁrm or the replacement of the market for intermediate goods with the institution of the ﬁrm as a vehicle to organize the division of labor, while an increase in capital trade may be associated with the development of division of labor in a roundabout production chain. Both phenomena can occur in the absence of changes of total endowments for society as a whole. 6 Suppose that transaction cost is 0 in the model in this chapter, but the government enforces a minimum wage law which requires the wage rate to be higher than a constant θ. Analyze the general equilibrium implications of the minimum wage. 7 Assume that the production function in (8.1b) is replaced with x + x s = lx − b. Solve again for the general equilibrium and its inframarginal comparative statics. 8 Yang, 1988: Add one more consumption good to the model in this chapter, so that the utility function becomes u = ( y + ky d)(z + kz d), where z is the new consumption good. The production function of z is z + z s = lz − b. Solve for the general equilibrium and inframarginal comparative statics. Note that in this model lemma 8.1 may not hold.

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9 Assume that the production function (8.1a) is replaced with y + y s = Min{x + tx d, ly}. Solve for the general equilibrium and inframarginal comparative statics. Add a ﬁxed learning cost to the production function, so that y + y s = Min{x + tx d, ly − a}. How will your answer change? 10 Yang and Ng, 1995: Assume that in the model in this chapter the transaction cost of labor is speciﬁed as a loss of goods produced by the employee in transit from the employee to the employer. The algebra can be signiﬁcantly simpliﬁed. Solve for the general equilibrium and inframarginal comparative statics. 11 Consider the Liu and Yang model (2000), where each of M ex ante identical consumer-producers has the utility function u = z + kz d, where good z is food. Her system of production is z + z s = (x + rx d )1/2Lz, x + x s = ( y + ty d )1/2Lx, y + y s = L 2y, Lz + Lx + Ly = 1, Li ∈[0, 1], i = z, x, y. x is the hoe used to produce food and y is the steel used to produce the hoe. If we ignore differences in the ownership structure of the ﬁrm, then there are 9 structures. Structure A is autarky. Structure with partial division of labor P(y) consists of conﬁgurations (zx/y), selling z, selfproviding x, and buying y, and (y/z), selling y and buying z. Structure with partial division of labor P(x) consists of conﬁgurations (xy/z), selling x, selfproviding y, and buying z; and (z/x), selling z and buying x. Structure with partial division of labor and the ﬁrm FP(y) consists of conﬁgurations (zx/Ly), selling z, self-providing x, and buying labor Ly; and (Ly /z), selling labor Ly and buying z. Structure with partial division of labor and the ﬁrm FP(x) consists of conﬁgurations (Lx /z), selling labor Lx and buying z; and (z/Lx), selling z and buying labor Lx. Structure with the complete division of labor C consists of conﬁgurations (z/x), (y/z), and (x/yz). Structure with the complete division of labor and the ﬁrm FC(y) consists of conﬁgurations (Lx/z), (y/z), and (z/Lx y) selling z and buying y and Lx. Another structure with the complete division of labor and the ﬁrm, FCL, consists of conﬁgurations (Lx/z), (Ly /z), and (z/Lx Ly), selling z and buying Lx and Ly. Solve for the general equilibrium and its inframarginal comparative statics. Show that a complete division of labor structure, with the producer of x hiring labor to produce y within the ﬁrm and buying z from an independent specialist of z, cannot be a general equilibrium structure if t < s. Solve for eight corner equilibria, the general equilibrium, and its inframarginal comparative statics. Show that if the following evolutionary paths take place as transaction efﬁciency is improved over time, evolution in division of labor is associated with decreasing size of the ﬁrm: A ⇒ P(y) ⇒ FP(x) ⇒ C, A ⇒ P(y) ⇒ FP(x) ⇒ FC(y), A ⇒ FP(y) ⇒ FP(x) ⇒ C, A ⇒ FP(y) ⇒ FP(x) ⇒ FC(y). Under what conditions will trade of producer goods, which may be recorded as capital in statistical data, and trade of labor increase simultaneously in the absence of changes in the total amount of endowment for society as a whole? Use this model to formalize the argument, proposed by Cheung, Coase, Stigler, and Young, that the size of the ﬁrm is irrelevant; that the size of the ﬁrm may increase or decrease as division of labor evolves, dependent upon whether division of labor is developed via the labor market or via the goods market. 12 M. Liu, 1999: Consider the model in this chapter. Assume that each individual prefers being a boss over being an employee who must do whatever he is told to do. Hence, the utility function becomes u = ( y + ky d )E β where β ≥ 1 is a taste parameter for relative position, E = γ > 1 if an individual chooses an employer conﬁguration, E = ρ < 1 if she chooses an employee conﬁguration, and E = 1 if she chooses a conﬁguration involving no asymmetric relationship between an

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employer and an employee. Solve for the general equilibrium and its inframarginal comparative statics. The solution is the same as in example 8.1 if β = 0. Analyze the implications of the parameter of pursuit of relative position β ≥ 1 for the equilibrium level of division of labor and the equilibrium structure of residual rights. Use this model to explain the effect of a strong labor union and regulations governing the welfare of workers, on the equilibrium level of division of labor, the relative number of employers and employees, and economic development.

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ENDOGENOUS TRANSACTION COSTS, CONTRACTS, AND ECONOMIC DEVELOPMENT

9

9.1 ENDOGENOUS TRANSACTION COSTS AND ECONOMIC DEVELOPMENT In the previous chapters we have seen the importance of transaction costs for the evolution of division of labor and economic development. However, Barzel (1985) has raised the question, “Is transaction cost just cost?” This question draws to our attention the difference between endogenous and exogenous transaction costs. O. Williamson (1985) clearly distinguishes between endogenous transaction costs caused by opportunistic behavior (holding up, cheating, and noncredible commitment) and tangible exogenous transaction costs. North and Thomas (1970) also note the difference between endogenous transaction costs caused by moral hazard, adverse selection, and other types of opportunism and exogenous transaction costs. Exogenous transaction costs are incurred directly or indirectly in the transacting process, and not caused by distortions as a result of decision-makers’ conﬂicts of interest. In the previous chapter we saw that the cost coefﬁcient for each unit of goods purchased is an exogenous transaction cost, since it can be seen before individuals make their decisions and it is not associated with any distortions generated by interest conﬂicts between self-interested decisions. Resources used in the transportation of goods are direct exogenous transaction costs. Resources used to produce transportation, communication, and transacting facilities (computers, automobiles, plastic banking cards) used in the transacting process are indirect exogenous transaction costs. Endogenous transaction costs comprise two subcategories: general and speciﬁc. General endogenous transaction costs are deﬁned as costs incurred in transactions that can be identiﬁed only after all players have made their decisions. In other words, endogenous transaction costs are the consequence of interactions between individuals’ self-interested decisions. Total transaction costs for each individual, and for society as a whole in the preceding chapters, are endogenous, since they are determined by the number of transactions, which is endogenous in the models of endogenous specialization and endogenous number of goods. Since the deﬁnition of indirect exogenous transaction costs, such as expenses on automobiles, overlaps the deﬁnition of general endogenous transaction costs, we use a narrower deﬁnition of endogenous transaction costs in this text. Speciﬁc endogenous transaction costs are deﬁned as those costs associated with a departure of equilibrium from the Pareto optimum. In this text, we use the term “endogenous transaction costs” to denote speciﬁc endogenous transaction costs unless indicated otherwise.

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Endogenous transaction costs are caused by a particular human behavior. For the purposes of our argument, there are three types of human behavior. The ﬁrst, called nonstrategic selfinterested behavior, has the feature that decision-makers do not react directly to others’ decisions, but only to prices. The behavior we examined in chapters 3, 4, 7, and 8 was nonstrategic behavior. The consumer’s price-taking behavior in chapters 5 and 6 is nonstrategic, too. The second type of behavior, called strategic behavior, has the feature that decision-makers directly react to others’ decisions. It can be classiﬁed into two subcategories: non-opportunistic and opportunistic behavior. Non-opportunistic strategic behavior is distinguished by the characteristic that a player’s interests are not pursued at the cost of other players’ interests. The self-interested behavior in the Nash bargaining game in this chapter is non-opportunistic strategic behavior. Opportunistic behavior is that form of strategic behavior in which a player’s interests are pursued at the cost of other players’ interests. Endogenous transaction costs are caused by opportunistic behavior in competing for a greater share of the gains from division of labor between players. The implications of endogenous transaction costs for the equilibrium network size of division of labor and economic development are more important than those of exogenous transaction costs, since endogenous transaction costs are determined by individuals’ decisions and their choice of institutional and contractual arrangements. For example, the Industrial Revolution, which featured rapid evolution of division of labor, took place in Britain partly because the Statute of Monopolies (1624) made it the ﬁrst country to have patent laws, signiﬁcantly reducing the theft (a type of opportunistic behavior) of intellectual property that incurs endogenous transaction costs. As shown by North and Weingast (1989), the most important driving force for the successful industrialization of Britain was the evolution of that country’s institutions in the seventeenth century and subsequent credible governmental constitutional commitments. This signiﬁcantly reduced state opportunism, rent seeking, and related endogenous transaction costs. According to Olson (1996), a typical Haitian immigrant’s productivity and real income under the institution of the US was about ﬁve times higher than her productivity and real income under the institution in her home country in 1980. He compared per capita income between a new German immigrant and a new Haitian immigrant and attributed the difference to the difference in human capital and culture between the two groups of immigrants. After the deduction of the effects of this difference, he showed that the major part of the remaining difference in per capita real income between a Haitian and a US Haitian immigrant cannot be explained by the differences in physical capital, resource endowment, human capital, access to technology, population density, and cultural background between the two countries. The difference was mainly due to the endogenous transaction costs caused by the Haitian government’s opportunistic behavior under deﬁcient institutions. As shown in the 1997 World Development Report of the World Bank, the major obstacle to economic development is endogenous transaction costs caused by governmental opportunistic behavior, including the following. In some less-developed countries, government behavior is predatory and expropriative. Government ofﬁcers use the coercive power of governmental apparatus and taxation to steal citizens’ property. A typical example is the Duvalier government’s behavior in Haiti during the 1950s and 1960s. According to the World Bank (1997, p. 149), the economic pillars of Haiti’s predatory state were expropriation, extortion, tax inﬂation, and corruption. Signiﬁcant resources were devoted to protecting Duvalier himself, totaling 30 percent of total government expenditure during the ﬁrst half of the 1960s. Agriculture, particularly coffee, was heavily taxed. Some sources estimate that Duvalier transferred more than US$7 million a year out of Haiti for personal purposes. Large-scale bribing also took place, through deals with foreign investors on projects that often never materialized. Extortion under the veil of “voluntary” donations was politically institutionalized.

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According to Summer (1992), in some sub-Saharan African countries the government pursued a patronage recruitment policy of government employment and favoritism in issuing trade licenses. Then it distorted exchange rates and prices in favor of relatives’ trade businesses. In China during the 1960s and 1970s, the government used its monopoly in the banking sector, the distribution network, urban real estate sector, and other important sectors to pursue tangible and intangible rents. The approval system for setting up private ﬁrms, the strict licensing system for setting up ﬁrms for foreign trade, and the monopolized job assignment system were used by the government to discriminate against the private businesses. The government used a procurement system that compelled peasants to sell underpriced agricultural goods to government agents, and a residential registration system that restricted rural residents’ mobility, to pursue the interest of urban residents, including the government elite, at the cost of rural residents. (See Yang, Wang, and Wills 1992). In this process, industrialization and economic development became hostages of state opportunism. Sen (1977), Chang and Wen (1998), and Lin and D. Yang (1998) show that the Chinese government’s pursuit of the interests of urban residents at the expense of rural residents was the main cause of the most devastating famines, involving the loss of up to 30 million lives in China. State opportunism not only causes direct endogenous transaction costs, but it also indirectly encourages citizens’ opportunistic behavior. In the worst case, it causes political instability and war. According to the empirical evidence we looked at in chapter 2, geographical conditions (i.e., bad transportation conditions and tropical ecological conditions) are important factors not only because they directly affect economic performance, but they also created historical conditions for evolution of government behavior. In a relatively well-developed market economy, information asymmetry may result in opportunistic behavior that causes so-called adverse selection and associated endogenous transaction costs. Measuring and monitoring the cost of working effort may result in so-called moral hazard and related endogenous transaction costs. There are several ways to investigate endogenous transaction costs. According to our deﬁnition of endogenous transaction costs, the distortion caused by value taxes, monopoly power, externality, and public goods is endogenous transaction cost. In many neoclassical models, monopoly power, information asymmetry, public goods, and externality are all exogenously given. A more realistic approach is to endogenize the degree of monopoly power and externality by specifying some trade-offs. The degree of monopoly can be determined in the market as a consequence of interactions between conﬂicting self-interested decisions. The Dixit–Stiglitz model (example 5.1) is such an example. In the DS model, the efﬁcient trade-off between global economies of scale and distortions caused by monopoly power determines the equilibrium degree of monopoly and competition. In chapter 10, the trade-offs between economies of division of labor, reliability of the related market network, and transaction costs are speciﬁed in order to endogenize the degrees of competition and externality. The second way to study endogenous transaction costs is to specify unobservable or unveriﬁable effort that affects the risk of a bad outcome (hidden actions), or to specify information asymmetry (hidden information), then to investigate endogenous transaction costs caused by moral hazard and information asymmetry. We shall study this approach in sections 9.2 and 9.5, respectively. The third way to study endogenous transaction costs is to use game models to investigate direct interactions between strategic behaviors. The Ricardian model with a tariff game in chapter 3 is used to investigate endogenous transaction costs caused by government strategic behavior. In section 9.3, we will use various game models to study opportunistic behavior and endogenous transaction costs. A dynamic game model with information asymmetry is used to show that endogenous transaction costs may not be as great as predicted by static models with information asymmetry if interactions between strategies and information are considered. In section 9.5, we shall show that dynamic game models can be used to investigate opportunistic behavior and related endogenous transaction costs in the absence of moral hazard and information

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asymmetry. Our examples illustrate that game theory is a powerful instrument in analyzing complicated strategic interactions that cause endogenous transaction costs. In this chapter, we emphasize that general equilibrium models of endogenous transaction costs are much more appropriate than partial equilibrium models of endogenous transaction costs for studies of interdependence between network size of division of labor, related productivity, and endogenous transaction costs. It is important for appreciating the development implication of endogenous transaction costs to investigate the interdependence. Also, models of endogenous specialization are essential. In section 9.2, we study moral hazard and the role of contracts in reducing endogenous transaction costs caused by moral hazard. The Stiglitz model of sharecropping is used as an example of application of the moral hazard model to development economics. In addition, the Holmstrom and Milgrom model is used to investigate the trade-off between moral hazard and monitoring costs, which endogenously determines the degree of externality of the efﬁcient contract. In section 9.3, we introduce basic concepts in game theory and major game models, and use the tool to analyze endogenous transaction costs. In particular, a dynamic game model with interactions between strategies and information (a sequential equilibrium model) is used to study endogenous transaction costs in the credit market with information asymmetry. In section 9.4, we study endogenous transaction costs caused by adverse selection and holding-up behavior, and the role of reputation in reducing these costs. In section 9.5, we use the Grossman–Hart– Moore model to study endogenous transaction costs caused by opportunism and an incomplete contract. Finally, we use the Dewatripont and Maskin model (1995) to investigate commitment problems and soft-budget constraints that might cause endogenous transaction costs.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n n n n n n n n n n n

What are the differences between endogenous and exogenous transaction costs? What is moral hazard and how does it cause endogenous transaction costs? How does the trade-off between incentive provision, risk sharing, and monitoring cost determine the efﬁcient degree of externality? What are the functions of contracts in reducing endogenous transaction costs caused by moral hazard? What are the effects on economic development of endogenous transaction costs caused by opportunistic behavior? Why will information asymmetry generate endogenous transaction costs? What is the function of Nash bargaining in avoiding trade conﬂict and in promoting economic development? What are the effects on economic development of endogenous transaction costs caused by competition to get a greater share of the gains from the division of labor? What is the role of reputation in reducing endogenous transaction costs? How do interactions between dynamic strategies and information asymmetry generate endogenous transaction costs in the credit market? How do noncredible commitment and soft budget constraints generate endogenous transaction costs?

9.2 ENDOGENOUS TRANSACTION COSTS CAUSED BY MORAL HAZARD Moral hazard is the departure of equilibrium from the Pareto optimum caused by a special type of information asymmetry. In a model with moral hazard, the effort of one of two trade

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partners affects the risk of a bad outcome for the business, but the other partner cannot observe the effort level. This implies, for example, that a labor contract to pay a player according to her effort level is impossible; such a labor contract involves a prohibitively high exogenous transaction cost in measuring working effort. It is assumed that the direct effect of effort on the utility of the player choosing that effort is negative, so that if a pure or noncontingent single price is paid for the good or service provided, or if there is no contract, then the lowest effort level will be chosen. Thus, contingent contracted prices of goods or services become essential for reducing such endogenous transaction costs caused by moral hazard. Usually, there are three periods in a model of moral hazard. In period 1, the outcome of the business is yet to be realized, but probabilities for bad and good outcomes, and the relationships between those probabilities and one party’s effort levels, are common knowledge to all players. Two parties sign a contract in period 1 that determines the terms of the deal after the realization of an outcome. In period 2, players choose effort levels for the given contractual terms. In period 3, Nature chooses an outcome according to the probabilities and players’ effort levels. Then contractual terms are implemented and gains from the business are divided. Here, the assumption that the effort level is unobservable and must be chosen before the realization of an outcome is essential to the story. This implies that the player who chooses her effort level has an incentive to cheat. Even though her real effort level may be low, and a bad outcome may be partly attributable to this, she may claim that her effort level is high, and that the bad outcome is just a result of bad luck that is out of her control. The driving force of the story of moral hazard is a trade-off between efﬁcient incentive provision and efﬁcient risk sharing. The two players should somehow share the risk of a bad outcome. But if one player cannot see the other player’s effort levels, which affect the risk, then the effect of the low effort level on the risk cannot be distinguished from bad luck. Hence, there is a conﬂict between incentive provision and risk sharing. If a bad outcome occurs, the player who chooses the effort level should be penalized as far as incentive provision is concerned. But she should not be penalized too severely as far as risk sharing is concerned. So a contract is used to minimize endogenous transaction cost by efﬁciently trading-off risk sharing against incentive provision. In working out the contractual terms, each player should prepare for the worst that could result from the players’ opportunistic behavior. This will ensure that both behave decently ex post. If a player behaves like a decent gentleman ex ante, without taking account of possible opportunistic behavior on each side, then he will behave very opportunistically ex post, so that a bad outcome is more likely to occur. Since effort level is not an uncertain variable for the player who chooses the effort, information asymmetry in a model of moral hazard is different from that which we will study in sections 9.3 and 9.4. Information asymmetry is referred to as hidden action in a model of moral hazard, and as hidden information in the model of adverse selection studied in sections 9.3 and 9.4. Distortions caused by hidden information are referred to as endogenous transaction costs caused by adverse selection. In this section we ﬁrst study three neoclassical principal–agent models. We then study a principal–agent model with endogenous specialization and moral hazard. We shall explore the role of contingent contract in reducing endogenous transaction costs and in raising productivity. Before specifying the models, we need to learn some important concepts: expected utility function, risk aversion, and certainty equivalent. Consider a random variable x ~ N(S, σx), where S = E(x) = ∑s∈S p(s)x(s) is the expected value of x and σx = Var(x) = E[(x − S)2] = ∑s∈S p(s)(x(s) − S)2 is the variance of x. The theory of expected utility establishes conditions under which a decision-maker will rank risky prospects according to their associated expected utilities. Let u be a function that assigns to each monetary outcome x a utility u(x). Then, representing prospects by random variables, the expected utility of prospect x is E[u(x)].

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f (x) f (x2) f (S) af (x2) + (1 − a)f (x2) f (x1)

0

x1

S

x2

x

Figure 9.1 Risk aversion and a strictly concave utility function

For simplicity of presentation, suppose that there are only two contingent states of an event, x1 and x2. An individual’s utility function f (x) is strictly concave, so that: f (αx1 + (1 − α)x2) > αf (x1) + (1 − α)f (x2)

(9.1)

where α ∈(0, 1) and x1 and x2 are two different consumption bundles (vectors). If we interpret α as the probability for state x1 and 1 − α as the probability for state x2, then the weighted average S = αx1 + (1 − α)x2 is equivalent to an event with no uncertainty, or a consumption bundle that can be received through an insurance program which, by pooling risk, guarantees that the insured can receive the weighted average. Hence, (9.1) implies that a person prefers the weighted average of the two contingent states, which does not involve risk, over the contingent event. And hence, we say that the person is risk averse. This implies that a person is risk averse iff her utility function is strictly concave in contingent variables. The person is risk loving if the inequality in (9.1) is reversed. The person is risk neutral if the inequality in (9.1) is made an equality. (9.1) is referred to as Jesen inequality (see ﬁgure 9.1). A twice continuously differentiable function with two independent variables is strictly concave if and only if ∂2f/∂x i2 < 0 and (∂2f/∂x 12)(∂2f/∂x 22) − (∂2f/∂x1∂x2) > 0. The concept of certain equivalent wealth is often used in the theory of contracts. Let’s deﬁne this concept. Compare the expected utility of prospect x, E[u(x)], with a certain prospect that yields the payment V with probability 1. The certain prospect will be indifferent for the decision-maker from the risky prospect x if u(V) = E[u(x)]. V is then called the certain equivalent of the prospect x. Suppose that u is three times continuously differentiable and that u′(.) > 0. Then, approximately, the certain equivalent is V ≈ S − 0.5r(S)Var(x)

(9.2)

where r(S) = −u″(S)/u′(S), which is called the degree of risk aversion, at S. We can use Taylor’s theorem to prove this. Var(x) is the variance of x. According to this theorem, for any z, u(z) = u(S) + (z − S)u′(S) + 0.5(z − S)2u″(S) + R(z), where R(z) = u′′′(X)(z − S)2/6 for some X ∈[S, z] which is negligible. Hence, u(z) ≈ u(S) + (z − S)u′(S) + 0.5(z − S)2u″(S). Substituting x for z in this equation and computing the expectation, we ﬁnd E[u(x)] ≈ u(S) + E[x − S]u′(S) + 0.5E[(x − S)2]u″(S), where E[x − S] = 0. Therefore, we have: E[u(x)] ≈ u(S) + 0.5E[(x − S)2]u″(S)

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Applying Taylor’s theorem again to u(V), where V is close to S, yields u(V) = u(S) + (V − S)u′(S) + Q(V), where Q(V) = 0.5[(V − S)2]u″(X), which is negligible for some X ∈[S, V]. Hence, we have: u(V) = u(S) + (V − S)u′(S) For a certain equivalent, we have u(V) = E[u(x)]. So, combining the above two equations, we have: (V − S)u′(S) ≈ 0.5E[(x − S)2]u″(S) Rearrangement of this equation yields (9.2). On the basis of our deﬁnitions of expected utility, risk aversion, and certainty equivalent, we can now study models of moral hazard. Example 9.1: A neoclassical principal–agent model (Diamond, lecture notes, 1983). There are two players in the model: principal and agent. The principal cannot take care of his own business and must hire the agent to do the job. The agent cannot have her own business and must work for others. The agent is risk averse and her utility function is ua = M − e , where M is the payment she receives from the job. Her effort level can be e = 1 or e = 0. If e = 1, the revenue of the project is: ⎧16 with probability 3/4 R=⎨ 1 ⎩4 with probability /4

If e = 0, then:

⎧16 with probability 1/4 R=⎨ 3 ⎩4 with probability /4 The principal’s utility is up = R − M, which is linear in the contingent variable R. Thus the principal is risk neutral. Suppose the principal can observe the agent’s effort level. He can calculate his expected utility for different levels of effort. Assume that the agent can get utility 1 if she works elsewhere. Then the principal can see that if he pays her M = 4, she will be willing to choose e = 1 and to work for him because ua = M − e = 1 if M = 4 and e = 1. If e = 1 and he pays her M = 4, his expected utility is: Eup = 3/4 (16 − M) + 1/4 (4 − M) = 3/4 (16 − 4) + 1/4 (4 − 4) = 9 If e = 0, the principal can pay the agent M = 1 to get her working for him, since her utility is ua = M − e = 1 if e = 0 and M = 1. Then, the principal’s expected utility for e = 0 and M = 1 is: Eup = 1/4 (16 − 1) + 3/4 (4 − 1) = 6 Certainly, the principal’s expected utility is higher for e = 1 and M = 4 than that for e = 0 and M = 1 (9 > 6). Hence, the principal will pay M = 4 and get the agent to work for him with effort level e = 1.

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But suppose the principal cannot observe the agent’s effort level, or cannot verify this in court if litigation should arise from a dispute about her effort level and corresponding pay. Then the principal must choose a contingent contract to facilitate an efﬁcient trade-off between risk sharing and incentive provision. If pay is not contingent on outcome, it is easy to see that the agent will always choose effort e = 0, since her utility M − e is always larger for e = 0 than for e = 1 for a noncontingent M. Suppose the principal pays M H if the outcome is good or if R = 16 and pays M L if the outcome is bad or if R = 4, where M H > M L. Then the contingent contract will get the agent working for the principal with effort level e = 1 if the following two conditions hold. The ﬁrst condition is to ensure that the agent is not worse off than if she were working elsewhere; that is, her expected utility when she chooses effort level e = 1 should not be lower than her reservation pay 1:

/4 ( M H − 1) + 1/4 ( M L − 1) ≥ 1

3

This is referred to as the participation constraint. The second condition is to ensure that the agent is not worse off when she chooses e = 1 than when she chooses e = 0; that is, her expected utility with effort e = 1 and M H should not be lower than her expected utility with effort e = 0 and M L. That is,

/4 ( M H − 1) + 1/4 ( M L − 1) ≥ 1/4 ( M H − 0) + 3/4 ( M L − 0)

3

This condition is referred to as the incentive compatibility condition. Since the principal’s purpose is to maximize his expected utility, which is a decreasing function of M, he will choose M H and M L from the equalities in the two conditions. The two equations with two unknowns yield the efﬁcient contingent contractual terms: M H = 6.25,

M L = 0.25

It is easy to compute that the principal’s expected utility under the second-best contingent contract is: Eup = 3/4 (16 − 6.25) + 1/4 (4 − 0.25) = 8.25, which is smaller than what can be obtained from the ﬁrst-best labor contract when he can observe the agent’s effort level, which is 9. The difference is endogenous transaction cost caused by moral hazard. In the ﬁrst-best labor contract (pay M = 4 for effort e = 1 and pay M = 1 for effort e = 0), the principal takes all the risk and the agent receives her wage without risk. This contract yields efﬁcient risk sharing in the sense that the risk-neutral principal takes all the risk and the risk-averse agent takes none. You may also interpret this as a trade contract in risk, through which the agent sells all risk to the principal, or the agent is completely insured by the principal. The ﬁrst-best labor contract also provides the right incentive for the agent to choose the right level of effort. This implies that if the principal can see the agent’s effort level, there is no trade-off between efﬁcient risk sharing and efﬁcient incentive provision. But when the principal cannot observe the agent’s effort level, there is a trade-off between risk sharing and incentive provision. If the principal takes all the risk and pays a noncontingent M, which is equivalent to providing the agent with complete insurance, then the agent would not choose the right effort level. But if the principal rewards or penalizes the agent exactly according to the contingent outcome, they would not have efﬁcient risk sharing. The pay to the

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agent will be greater or the principal’s proﬁt lower, because the risk is too high for the agent to take the job if the pay is not that high. Hence, the second-best contingent contract efﬁciently trades off risk sharing against incentive provision to achieve a compromise. Though the efﬁcient trade-off has not achieved the ﬁrst best, and therefore is not Pareto optimal, it nonetheless maximizes the gains from trade net of the unavoidable endogenous transaction costs caused by moral hazard. When moral hazard exists, the ﬁrst best is an unachievable utopia. The second best is a realistically efﬁcient contract. Hence, we call the contingent contract the efﬁcient contract despite its Pareto inefﬁciency. It is important to note, as Hart (1995) points out, that the contingent contract in the principal–agent model is not a labor contract. The contingent contract prices output rather than effort input, because the exact rationale for the contingent contract is that a labor contract for effort input is infeasible. Hence, it is misleading to call the principal–agent model a model of the ﬁrm. The principal–agent model cannot explain why and how ﬁrms emerge, or why we need asymmetric residual returns and residual control. The asymmetric relationship between employers and employees is not endogenized in the principal–agent model. Although the principal looks like an employer, we can show that he does not claim all residual returns, the agent claiming part of these through contingent pricing of outcome. For instance, if outcome R = 16 is realized, the agent gets 6.25 − 1 > 1 where the prevailing market reservation pay is 1. Furthermore, in the principal–agent model, the principal has no residual control rights over the agent’s effort level. What the agent can do (which level of effort she chooses) is completely up to her. But as shown in chapter 8, in a labor contract, what the employee does is up to the employer: the employee must do whatever she is told to do. The two main features of the institution of the ﬁrm and the related labor contract, namely, the asymmetric distribution of residual returns and residual control rights, are absent in the principal–agent model. The model of moral hazard can be applied to analyze many development problems. The sharecropping model is one of these applications. Example 9.2 (Stiglitz, 1974): A trade-off between incentive provision and insurance provision in sharecropping. Sharecropping was considered inefﬁcient by economists, since it gave the tenant only part of his marginal product and thereby did not provide full incentive. But as economists have recognized the possible endogenous transaction costs caused by moral hazard, the function of sharecropping in trading off risk sharing against incentive provision can be appreciated. (See Singh, 1989 for a survey of theories of sharecropping and formal models.) We consider a simple sharecropping model where the landlord is the principal and the tenant is the agent. The production function is y = θALa where L is the tenant’s input of labor in production, y is output level, θ is a random variable and its value is θL with probability ρ and θH with probability 1 − ρ, where θH > θL, and a ∈ (0, 1) is the elasticity parameter of output with respect to labor input. We assume that the amount of land used in production is ﬁxed, so that it is included in parameter A. The tenant receives the share α of realized output and his expected utility is u = αEy + C − bL, where C is a side-payment from the landlord to the tenant and b is a disutility coefﬁcient of working. The tenant’s reservation utility is u0. The landlord cannot observe or verify the labor input level of the tenant, so that a pure wage will generate an unacceptable moral hazard. Hence, the landlord’s optimum contract with the tenant is given by his following decision problem. Max: (1 − α)Ey − C with respect to α and C subject to the tenant’s participation constraint: u = αEy + C − bL ≥ u0 and the ﬁrst-order condition for the tenant’s utility maximization decision: du/dL = 0; where C can be interpreted as land rental if α = 0. The maximization of the landlord’s payoff implies that the equality in the tenant’s participation constraint holds. This, together with the tenant’s ﬁrst-order condition, can be used to express the optimum share α as a function of the optimum side-payment C.

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α = (u0 − C)/(1 − ab)]1−aa a−1/A[θH (1 − ρ) + θL ρ],

263

(9.3)

where ρ can be considered as the degree of risk of a low output level. Inserting this into the landlord’s objective function, the ﬁrst-order condition for maximizing it with respect to C yields the optimum side-payment C* = u0 − {a a−1−1/(1−a)(1 − a)/(1 − ab)[θH (1 − ρ) + θL ρ]}1/a.

(9.4)

It is straightforward that the optimum side-payment is 0 if u0 is too small or if the degree of risk ρ is too great and that dC*/du0 > 0 and dC*/dρ < 0. This, together with the differentiation of (9.3), yields that dα*/dρ = (∂α/∂ρ) + (∂α/∂C)(dC*/dρ) > 0, where ∂α/∂C < 0. If C is 0, the contract is called a pure sharecropping contract; if α = 0, then the contract is called a pure land rental contract with the rental rate of C. Hence, this model predicts that if the risk in production is sufﬁciently great, the optimum contract is pure sharecropping; if the risk is sufﬁciently small, the optimum contract is land renting. If the risk is neither too great nor too trivial, the optimum contract is sharecropping with side-payment. The sharecropping model shows that if moral hazard is considered, a sharecropping contract may be an efﬁcient compromise between an incentive provision and risk sharing. But this result is based on the assumption that no insurance market is available. If the markets for insurance, labor, and capital are well developed, sharecropping may not be the most efﬁcient institution. We now use the Holmstrom and Milgrom model (1994) to show the function of the contract in achieving an efﬁcient trade-off between endogenous transaction costs caused by moral hazard and monitoring cost in reducing moral hazard. Example 9.3: The Holmstrom–Milgrom model (1994). The principal pays the agent a linear compensation w = α + β(z + γy), where z = e + x is the observed outcome of the agent’s effort e, x ~ N(S, σx) is a random variable representing the ﬁrm-speciﬁc uncertainty, y ~ N( T, σy) is a random variable representing industrywide or nationwide uncertainty, the covariance between x and y is σxy = cov(x, y) = E[(x − S)( y − T)] = ∑s∈S p(s)[x(s) − S][ y(s) − T], e is the agent’s effort level that affects proﬁt of the principal’s business but cannot be observed or veriﬁed by the principal, α is a ﬁxed wage, and β is the intensity coefﬁcient of the contingent incentive payment. N(S, σx) is a normal probability distribution. σy = var( y) = E[( y − T)2] = ∑s∈S p(s)[ y(s) − T]2. For simplicity, we assume that S = T = 0. The agent’s certain equivalent wealth (CEW, see (9.2)) is CEWe = α + βe − C(e) − 0.5rβ2V, where C(e) is disutility of effort and C′(e) > 0 and C″(e) > 0, r is the degree of absolute risk aversion, and V ≡ Var(x + γ y) = σx + γ 2σy + 2γ σxy. The agent maximizes this with her effort level e. The ﬁrst-order condition yields β = C′(e). This is the incentive constraint. The principal is risk-neutral, and her payoff and its certain equivalent is CEWr = P(e) − (α + βe), where P(e) is gross proﬁt and α + βe is the expected wage payment.

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Assume that wealth distribution has no effect on productivity (a very strong assumption that abstracts the analysis from effects of transaction costs on productivity, which has been the focus in all Smithian models in this text). Then the efﬁcient contract is determined by maximizing the total certain equivalent wealth of the principal and agent, which is CEW = P(e) − C(e) − 0.5rβ2V. Maximizing this with respect to e, β, and γ, subject to the incentive constraint, yields the ﬁrstorder condition for the efﬁcient contingent incentive contract: P ′(e) = C′(e)[1 + rVC″(e)],

β = C′(e),

γ = −σxy/σy.

Suppose that P(e) = ae, C(e) = ce2. Then P ′(e) = a, C′(e) = 2ce, and C″(e) = 2c. For these speciﬁc functional forms, the efﬁcient contract is γ = −σxy /σy,

e = a/2c(2crV + 1),

β = 2ce = a/(2crV + 1).

Comparative statics of the efﬁcient contract are de/da > 0,

de/dc < 0,

dβ/da > 0,

dβ/dc < 0.

This result indicates that as the beneﬁt coefﬁcient of effort a increases or as the disutility coefﬁcient of effort c decreases, the efﬁcient incentive intensity β increases so that the efﬁcient contract induces a higher level of effort, e. If the unobservable x and observable y are positively correlated, (σxy > 0), the efﬁcient γ is negative, since a good outcome is more likely due to nationwide contingence rather than ﬁrm-speciﬁc contingence. But if σxy < 0, the efﬁcient γ is positive. This story shows that the trade-off between risk sharing and incentive provision implies that too great an incentive intensity may not be efﬁcient. If we introduce the trade-off between monitoring cost and incentive provision into the model, this point becomes more obvious. Suppose Var(x + γ y) = V is a decision variable. Assume that the monitoring cost M(V ) is an increasing function of V, or M′(V ) > 0. Also, we assume that M″(V ) > 0. The new total certain equivalent is now CEW = P(e) − C(e) − 0.5rβ2V + M(V ). The optimum contract is given by maximizing this CEW with respect to e, V, and β, subject to the incentive constraint. The degree of measurement inaccuracy (V ) can be considered as positively relating to the degree of externality. This model formalizes the ideas of Barzel (1985) and Cheung (1970, 1983) on the endogenous degree of externality. In exercise 5 of chapter 10, Holmstrom and Milgrom introduce into the model in this section the trade-off between balanced incentives for two activities that the employee undertakes and strong incentive for each activity. They have shown that the institution of the ﬁrm can more efﬁciently balance the trade-off by imposing some job restrictions and by providing weaker and more balanced incentives than in the market without ﬁrms. This kind of model shows that a realistic analysis of an efﬁcient contract involves many trade-offs, which are much more complicated than the simple trade-off between incentive provision and risk sharing in example 9.1. Most of this kind of model are decision or partial equilibrium models that cannot be used to ﬁgure out the mechanisms that simultaneously determine the network size of division of labor,

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the extent of the market, the number of transactions, total endogenous and exogenous transaction costs, and productivity. The above three neoclassical principal–agent models are not general equilibrium models. The principal–agent relationship is not endogenized, and reservation pay is exogenously given. The principal cannot take care of his own business and must ask the agent to do the job, while the agent cannot have her own business and must work for others. Hence, the relationship between the emergence and development of principal–agent relationships, productivity progress, and the evolution in division of labor cannot be investigated. We next consider a Smithian principal–agent model which enables us to explore these issues. We ﬁrst outline the story behind the model. The Smithian model of the endogenous principal–agent relationship with two consumer goods is similar to the model in chapter 4, except that there is a risk of low transaction efﬁciency in exchanging goods x and y, which is affected by an x-specialist’s effort in avoiding the transaction risk. The effort is not observable, so that moral hazard may arise. There are several trade-offs among economies of division of labor, exogenous transaction costs, endogenous transaction costs caused by moral hazard, the beneﬁts of a high effort level in avoiding transaction risk, and the costs of that high effort level. If an exogenous transaction cost coefﬁcient is large, then autarky is equilibrium where no principal–agent relationship and market exist. If the exogenous transaction cost coefﬁcient is small, then reciprocal principal– agent relationships emerge from the division of labor. For an equilibrium with division of labor, if the cost of a high effort level in avoiding risk is signiﬁcant compared to the resulting gain from a lower transaction risk, then in a general equilibrium environment, an x-specialist will be better off choosing the low effort level, so that a single price contract is enough for coordinating the division of labor. Contingent contracts are not needed. If the cost of effort level is not signiﬁcant, the avoidance of moral hazard becomes worthwhile. Hence, contingent contracts become essential for reducing moral hazard. In a general equilibrium environment with endogenous specialization and an endogenous relative price of all goods, contingent contracts may eliminate endogenous transaction costs caused by moral hazard. Yang and Yeh (2002, see exercise 16 below) show in a model with endogenous specialization and moral hazard for a pair of players who cannot choose between potential partners that within a certain parameter space a man works harder for others in the presence of moral hazard than he works for himself in the absence of moral hazard. Also, as transport conditions are improved, endogenous transaction costs and productivity may increase side by side. This is of course due to the trade-off between economies of division of labor and endogenous and exogenous transaction costs. A sufﬁcient improvement of transport conditions may enlarge the scope for trading-off one conﬂicting force against others, and thereby it is more likely positive network effects of a larger network of division of labor outweigh increasing endogenous and exogenous transaction costs. Welfare and endogenous transaction costs increase side by side. Example 9.4: A principal–agent model of endogenous specialization. Consider a model with a continuun of ex ante identical consumer-producers of mass M, and with two consumption goods x and y. Each person’s utility function is speciﬁed as follows. u = ln[(x + kx x d )( y + ky y d )]

(9.5a)

where x and y are the respective quantities of the two goods self-provided, and x d and y d are the respective quantities of the two goods purchased from the market. The transaction efﬁciency coefﬁcient ky is a parameter, but kx is a random variable, given by the following condition:

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if s ≥ β,

⎧k with probability ρ then kx = ⎨ ⎩t with probability 1 − ρ

if s < β,

then kx = t

(9.5b)

where s is the effort level of a producer of x in avoiding the transaction risk and β is a parameter between 0 and 1. It is assumed that ρ ∈(0, 1) and 1 > k > t and that ky = k. kx x d and ky y d are the respective quantities of the two goods that are received from the purchases of them. This strictly concave utility function represents a preference with risk aversion. Each person is equipped with the same production functions for the two goods. x + x s = Max{0, Lx − a}

(9.6)

y + y s = Max{0, Ly − a}

where y s and x s are respective quantities of the two goods sold, and Li is an individual’s level of specialization in producing good i. The production function displays economies of specialization. Each individual is endowed with one unit of time that can be allocated between production and avoiding transaction risk, so that the endowment constraint for each person is Lx + Ly + s = 1,

(9.7)

where s is the time allocated for avoiding transaction risk. Finally, we assume Li ∈[0, 1], s, x, x s, x d, y, y s, y d ≥ 0. Each individual’s self-interested behavior is represented by a nonlinear programming problem that maximizes her expected utility with respect to Li, s, x, x s, x d, y, y s, y d, subject to the production functions, endowment constraint, and nonnegative constraint. Applying the Wen theorem to the model, we can show that a person never simultaneously buys and sells the same good, never simultaneously buys and self-provides the same good, and never sells more than one good. Taking account of the possibilities for pure and contingent pricing of goods, we can identify 10 conﬁgurations and 6 structures that need to be considered. We assume a Walrasian regime, where a representative pair of consumer-producers sort out their terms of trade and sign a contract in period 1. Then they decide on their quantities of goods to consume, to produce, and to trade, and Nature chooses a realization of kx according to the players’ decisions and prior probabilities in period 2. Trade and consumption take place and the contract is implemented in period 3. In this regime, each person can observe kx, but not the effort level s, of the other. We ﬁrst identify all structures that need to be considered. Then all corner equilibria in the structures will be solved. 1) There is an autarky conﬁguration, A, where there is no market or principal–agent relationship, and each individual self-provides all goods consumed. Structure A consists of M individuals choosing conﬁguration A, which implies a proﬁle of decision variables with Lx, Ly , x, y > 0; s = x s = x d = y s = y d = 0. The decision problem for a person choosing conﬁguration A is Max: U ≡ Eu = E(ln x + ln y) s.t.

x = Max{0, Lx − a}, Lx + Ly = 1

(utility function) y = Max{0, Ly − a}

(production functions) (endowment constraint)

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Table 9.1 Corner solutions in seven conﬁgurations Conﬁguration

Self-provided quantities

Demand and supply

Expected indirect utility

A

x = y = 0.5 − a

(x/y)HD

s = β, x = (1 − a − β)/2

x s = (1 − a − β)/2 y d = px s

ln( pk) + 2[ln(1 − a − β) − ln 2]

(y/x)HD

y = (1 − a)/2

x d = y s/p y s = (1 − a)/2

ρ ln k + (1 − ρ) ln t − ln p + 2[ln(1 − a) − ln 2]

(x/y)LD

s=0 x = (1 − a)/2

x s = (1 − a)/2 y d = px s

ln( pk) + 2[ln(1 − a) − ln 2]

(y/x)LD

y = (1 − a)/2

x d = y s/p y s = (1 − a)/2

ln(t/p) + 2[ln(1 − a) − ln 2]

(x/y) C

s = β, x = (1 − a − β)/2

x s = (1 − a − β)/2 y d = px s

ln k + ρ ln pH + (1 − ρ)ln pL + 2[ln(1 − a − β) − ln 2]

(y/x) C

y = (1 − a)/2

xd = xs ys = p

ρ ln(k/pH) + (1 − ρ)ln(t/pL) + 2[ln(1 − a) − ln 2]

2 ln(0.5 − a)

where E denotes expectation, and Li, x, y are decision variables. The optimum solution for this problem and the maximum expected utility for this conﬁguration are listed in table 9.1. Note that there is no transaction and related transaction risk in autarky. 2) There are two market structures with the division of labor and unique relative price of the two goods. Structure DL is a division of population between conﬁgurations (x/y) DL and (y/x) DL. Conﬁguration (x/y) DL implies that x, x s, y d > 0, s = Ly = x d = y = y s = 0, and an individual choosing this conﬁguration specializes in producing x, chooses a low level of effort in avoiding transaction risk, and accepts only a single relative price of the two goods. Conﬁguration (y/x) DL implies that Ly, y, y s, x d > 0, s = Lx = y d = x = x s = 0, and an individual choosing this conﬁguration specializes in producing y, and accepts only a single relative price of the two goods. Structure DH is a division of population between conﬁgurations (x/y) DH and (y/x) DH. Conﬁguration (x/y) DH is the same as conﬁguration (x/y) DL , except that an individual choosing this conﬁguration chooses a high level of effort in avoiding transaction risk. Conﬁguration (y/x) DH is the same as conﬁguration (y/x) DL , except that her transaction efﬁciency coefﬁcient k is determined by a high effort level of the specialist producer of x. Let us ﬁrst consider individuals’ decision problems in structure DL. In this structure, the decision problem for a person choosing conﬁguration (x/y) DL is Max: Ux ≡ Eux = E[ln(ky d ) + ln x] s.t.

y d = px s

(budget constraint)

x + x = Max{0, Lx − a},

(production function)

Lx = 1

(endowment constraint)

s

where Lx, x s, y d are decision variables and p ≡ px/py is the price of good x in terms of good y. Note that s = 0 for this conﬁguration. The optimum decision for this conﬁguration and the expected indirect utility function are listed in table 9.1.

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Table 9.2 Corner equilibria in four structures Structure

Corner equilibrium-relative price

Expected real income 2[ln(1 − 2a) − ln 2]

A DL

p = (t/k)0.5

2[ln(1 − a) − ln 2] + 0.5(ln t + ln k)

DH

p = [(1 − a)/(1 − a − β)](t/k)0.5(1−ρ)

0.5[(1 + ρ)ln k + (1 − ρ)ln t] + ln(1 − a) + ln(1 − a − β) − 2 ln 2

C

pL = (t/k)0.5(1−ρ)[(1 − a − β)/(1 − a)], pH = pL[(1 − a)/(1 − a − β)]2/ρ

0.5[(1 + ρ)ln k + (1 − ρ)ln t] + ln(1 − a) + ln(1 − a − β) − 2 ln 2

The decision problem for conﬁguration (y/x) DL is Max: Uy ≡ Euy = E[ln y + ln(kx x d )] s.t.

y s = px d

(budget constraint)

kx = t

(transaction condition)

y + y = Max{0, Ly − a}

(production function)

Ly = 1

(endowment constraint)

s

where Ly, x d, y s are decision variables. The optimum decision for this conﬁguration and the expected indirect utility function are listed in table 9.1. The terms of trade in period 1 will be determined by the expected utility equalization condition: Ux = Uy since individuals would keep changing their occupation in period 1 if this condition were not satisﬁed. The market clearing condition My y s = Mx y d or Mx x s = My x d, together with the population equation Mx + My = M, then determines the numbers of individuals choosing the two conﬁgurations. Plugging the corner equilibrium-relative price into the utility function yields the corner equilibrium expected real income in structure DL. All of the information on this corner equilibrium is in table 9.2. Assume that a single equilibrium-relative price prevails. From table 9.1, it is clear that when pH = pL = p, an x-specialist’s expected utility is ln(pk) + 2[ln(1 − a) − ln 2] if she chooses a low effort level, and is 2[ln(1 − a − β) − ln 2] + ln(kp) if she chooses a high effort level. A comparison between the two indirect utility functions implies that for a single relative price, an x-specialist always chooses the low level of effort in avoiding transaction risk. Hence, structure DH never occurs in equilibrium. 3) Market structure C is associated with the division of labor and with two contingent relative prices. This structure comprises a division of M individuals between conﬁgurations (x/y)C and (y/x)C. Conﬁguration (x/y)C is the same as (x/y) DH, just as conﬁguration (y/x)C is the same as (y/x) DH, except that an individual choosing this conﬁguration accepts the relative price pH when kx is k, and the relative price pL if kx is t. The procedure for solving for this corner equilibrium is the same as that for structure DL, except that the incentive compatibility condition is used, together with the utility equalization condition, to determine the two corner equilibrium-relative prices. Assume that in structure C, the relative price is pH when kx is k and that it is pL when kx is t. Assume that p in conﬁguration (x/y)DL is pL. Letting the expected utility of the specialist choosing (x/y)C , given in table 9.1, equal the expected utility for (x/y) DL , the incentive compatibility condition for C can be derived as follows.

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Table 9.3 General equilibrium and its inframarginal comparative statics k/t > [(1 − a)/(1 − a − β)]a/ρ

k/t < [(1 − a)/(1 − a − β)]a/ρ kt < [(1 − 2a)/(1 − a)]4

kt > [(1 − 2a)/(1 − a)]4

k1+ρt1−ρ < B

k1+ρt1−ρ > B

A

DL

A

C

ln(pH/pL) > 2[ln(1 − a) − ln(1 − a − β)]/ρ.

(9.8)

This condition, together with the expected utility equalization condition between conﬁgurations (x/y)C and (y/x)C , yields the corner equilibrium dual contingent relative prices in structure C. Plugging the corner equilibrium prices back into the indirect utility function of either (x/y)C or (y/x)C then yields expected per capita real income (corner equilibrium utility) in structure C. All information on the four corner equilibria is summarized in table 9.2. Individuals will not choose a single noncontingent relative price in DL if (9.8) is not satisﬁed because of moral hazard. Hence, (9.8) sets up a dividing line between structures DL and C. General equilibrium satisﬁes the following conditions. (i) Each individual maximizes her expected utility with respect to conﬁgurations and quantities of each good produced, consumed, and traded for a given set of relative prices of traded goods; (ii) The set of relative prices of traded goods are determined by Nash bargaining. Numbers of individuals choosing different conﬁgurations clears the markets for those goods. Since all individuals are ex ante identical, the relative prices will equalize the expected utility for all individuals selling different goods. Following inframarginal analysis in chapters 3, 4, and 6, we can solve a corner equilibrium for each structure. We can identify the conditions under which each individual has no incentive to deviate from her conﬁguration under the corner equilibrium prices in this structure. Alternatively, we can follow the procedure to prove the Yao theorem in chapter 4 to show that the general equilibrium is the corner equilibrium with the greatest expected per capita real income subject to the incentive compatibility condition. Hence, solving for the general equilibrium becomes a matter of identifying the corner equilibrium with the highest expected real income, subject to the incentive compatibility condition (9.8). A comparison between per capita real incomes in structures A, DL, and C yields the inframarginal comparative statics of general equilibrium, summarized in table 9.3, where B ≡ [(1 − 2a)2/(1 − a)(1 − a − β)]2. The bottom line in table 9.3 gives the equilibrium structure for each particular parameter subspace. The table illustrates that as transaction efﬁciency is improved, the general equilibrium discontinuously jumps from autarky, where there is neither market nor principal–agent relationship, to a structure with the division of labor, where the reciprocal principal–agent relationships emerge from the division of labor and market. It can be seen that the emergence of the principal–agent relationship will involve two contingent relative prices if the beneﬁts k/t of effort in reducing transaction risk are great compared to its cost in terms of reduced production time, that is, β. Otherwise, the emergence of the principal–agent relationship will involve a unique relative price of the two goods (DL). Since the production condition in this model can be represented by the graph in ﬁgure 7.1, a comparison between comparative statics of general equilibrium in table 9.3 and ﬁgure 7.1 suggests that as transaction conditions are improved, the equilibrium production schedule will discontinuously jump from the low line FG to the aggregate production possibility frontier MCAKBJL in the ﬁgure. This explains why contingent contracts can be used to promote economic development.

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Although this model can predict the function of contingent contracts in avoiding moral hazard, the general equilibrium is always Pareto optimal. Hence, in this Smithian general equilibrium model, complete contingent contracts can eliminate endogenous transaction costs. The example in exercise 16 (see Yang and Yeh, 2001) illustrates how endogenous transaction costs are caused by moral hazard when each of the two players cannot choose their trade partner. The implications of moral hazard for the equilibrium network size of division of labor and economic development will be more signiﬁcant if the number of goods is more than 2. The number of conﬁgurations and corner equilibria will increase more than proportionally as the number of goods in the model increases.

9.3 GAME MODELS AND ENDOGENOUS TRANSACTION COSTS 9.3.1 Game models The Walrasian equilibrium model belongs to a special class of game models. In this class of models, it is a game rule that all players are price takers, that is, they do not directly pay attention to what other players are doing since they believe that all information about this is reﬂected in prices. Each player chooses the optimum quantities of goods and factors that are produced and used for given prices. The interactions between individuals’ self-interested decisions therefore take place indirectly, through prices, rather than directly. In this process, any player’s attempt to manipulate prices is nulliﬁed by free entry and the ability of many other players to do the same. Therefore, there are no direct strategic interactions between self-interested decisions. But for many economic games, the game rules are more general or more complicated than the price taking rule. In this section, we study game models with more general game rules. A game is deﬁned by game rules, players, their strategies, outcomes, and players’ payoff functions on outcomes. The game rules specify who moves when, what they know when they move, what they can do, and when the game ends. The players consist of all the decision-makers involved in the game, and Nature, who randomly chooses whatever the other players cannot choose when there are uncertainties in the game. A player’s strategies are the actions she can take when it is her turn to move. A proﬁle of each and every players’ chosen strategies generates an outcome of the game that affects players’ well-being. Players’ objective functions deﬁned on outcomes of the game are called payoff functions. In the next subsection, we use an example to illustrate all of these concepts.

9.3.2 Nash equilibrium An example of Nash equilibrium can be found in example 3.2 in chapter 3. There, the government in each country maximizes a home resident’s utility with respect to the home tariff rate, given the other country’s tariff rate. If Nash bargaining is not allowed, the Nash equilibrium in that model entails a positive tariff if exogenous transaction conditions are not bad (autarky does not occur in equilibrium). The positive tariff makes an equilibrium departure from the Pareto optimum, thereby generating endogenous transaction costs. If exogenous transaction conditions are neither very good nor very bad, then the coexistence of unilateral protectionist tariffs and unilateral laissez fairism generates endogenous transaction costs that cannot be avoided even if tariff negotiation is allowed. If exogenous transaction conditions are sufﬁciently good, the endogenous transaction costs caused by bilateral protectionist tariffs in structure C will offset all mutually beneﬁcial gains from trade compared to structures Ba or Bb.

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Table 9.4a The strategic form of the Nash tariff game in structure Ba Country 2

Country 1

t2 = 0

t2 > 0

t1 = 0

U1(L), U2(H)

U1(L), U2(M)

t1 = t *1

U1(H), U2(M)

U1(L), U2(L)

Table 9.4b The strategic form of the Nash tariff game in structure C Country 2

Country 1

t2 = 0

t2 = t *2

t1 = 0

U1(M), U2(M)

U1(L), U2(H)

t1 = t *1

U1(H), U2(L)

U1(L), U2(L)

Such endogenous transaction costs are incurred by competition for a greater share of the gains from division of labor. Let us use the strategic form to describe that Nash tariff game. Example 9.5: The strategic form of the Nash tariff game in the Ricardian model. We ﬁrst consider structure Ba, in which country 1 produces two goods and exchanges good x for good y with country 2 (see ﬁgure 3.2 and table 3.3 in chapter 3). Country i ’s strategy is tariff rate ti. Table 9.4a summarizes the strategies, payoffs, and outcomes of this game. In table 9.4a, the ﬁrst term in each entry is the utility of an individual in country 1 and the second is that of an individual in country 2. Ui (H) > Ui (M) > Ui (L) can be found in table 3.3. The outcome t1 = t2 = 0 is the result of bilateral laissez fairism, which allocates all gains from trade to country 2. The outcome t1 = t *, 1 t2 = 0 implies that country 1 imposes tariff rate t* 1 such that an individual’s utility in country 2 is the same as in autarky. Hence, country 1 obtains most of gains from trade. The outcome t1 = 0, t2 > 0 implies that country 1 carries out a laissez faire policy while country 2 imposes a protectionist tariff. The outcome t1 = t *, 1 t2 > 0 implies that both countries impose protectionist tariffs. We ﬁrst prove that the outcome t1 = t2 = 0 (bilateral laissez fairism) is not a Nash equilibrium. For t2 = 0, country 1’s utility can be increased from U1(L) to U2(H) by a shift from t1 = 0 to t1 = t *. 1 Hence, country 1 has an incentive to unilaterally deviate from the outcome t1 = t2 = 0. Similarly, country 2 has an incentive to unilaterally deviate away from the outcome t1 = 0, t2 > 0 or the outcome t1 = t *, 1 t2 > 0. For the outcome t1 = t *, 1 t2 = 0, any unilateral deviation reduces the deviator’s utility. Hence, it is the Nash equilibrium in structure Ba. The Nash equilibrium in structure Bb is symmetric with this. Next we consider structure C, in which each country completely specializes. With reference to table 9.4b, Ui (H) > Ui (M) > Ui (L) is apparent from table 3.3. As shown in example 3.2 in chapter 3, each country imposes t *i as high as possible, provided individuals in the other country stay in structure C. Following the same reasoning for the strategic form in table 9.4a, we can show that the outcome t1 = t *, 1 t2 = t * 2 is the unique Nash equilibrium where all net gains from the complete division of labor, compared to alternative structures, are offset by the endogenous transaction costs caused by the tariff war. A mutual laissez faire regime cannot be a Nash equilibrium, despite the fact that it is mutually beneﬁcial. This is called coordination failure due to all players’ rational decisions. The type of game is sometimes called the prisoners’ dilemma – a situation in which, while two players could be better off by cooperating, their rational behavior prevents them from choosing cooperation.

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More generally, a strategy proﬁle s = (s1, s2, . . . , sN) of N players constitutes a Nash equilibrium if for every i = 1, . . . , N, ui (si, s−i ) ≥ ui (s i′, s−i ) for all si′ that player i can choose, where ui (.) is player i’s utility function and s−i is a strategy vector of all players except player i. In many Nash games, there are multiple Nash equilibria. The Murphy–Shleifer–Vishny model (1989) in example 5.3 is an example where there are Pareto rankable multiple Nash equilibria. In order to enhance the predictive power of the theory, we can use various ways to narrow down the set of candidates for the game solution by reﬁning the concept of equilibrium. One way is to allow players to choose a pure strategy with a probability. That is, players can choose mixed strategies. We will examine this kind of mixed strategy game in exercise 1 and in example 9.13. In the next subsection, we introduce the concept of subgame perfect equilibrium to reﬁne the concept of Nash equilibrium.

9.3.3 Subgame perfect equilibrium A shortcoming of the Nash game model is that it does not involve the time dimension. Time is important for strategic interactions. In particular, if we want to investigate endogenous transaction costs caused by an alternating-offer bargaining process, we need a dynamic game model. We use the following example to illustrate the technical substance of a type of dynamic game model called a subgame perfect equilibrium model. Example 9.6: The Rubinstein alternating-offer bargaining model. The game is to divide a pie between two players. Nature randomly chooses a player as the ﬁrst mover (male) who makes an offer in period 1. Player 2 (female) can accept the offer in period 1. This terminates the game, and the pie is divided according to his offer. But she may also reject his offer in period 1 and make a counteroffer in period 2. He can then choose between acceptance and rejection of her counteroffer in the next round of bargaining. The game can go on to an inﬁnite horizon. But the value of time provides players with an incentive to conclude the deal as soon as possible. The value of time also creates the possibility of exploiting the opponent’s impatience, and ensures that a deﬁnite outcome emerges as the equilibrium. Assume that the value of time for a player can be represented by a subjective discount rate ρ ∈ [0, 1]. This may also be taken to be the interest rate. Since $1 principal at t = 0 can generate principal plus interest of $(1 + ρ) at t = 1, $1 at t = 1 is worth only $1/(1 + ρ) at t = 0. In other words, the future value of A dollars at t = 0 is B = (1 + ρ)A, or the present value of B dollars at t = 1, is A = B/(1 + ρ). δ ≡ 1/(1 + ρ) is called the discount factor, which is between 0 and 1. The value of time, or a player’s degree of impatience, increases as the discount factor δ tends to 0 or as the discount rate ρ tends to inﬁnity. We now use the extensive form to describe the dynamic bargaining game. (See ﬁgure 9.2.) At the root of the inverse tree graph, player 1 makes an offer. He can ask for a large share of the pie, denoted by x 1H, or a small share x 1L, or any share in between. x1 represents the share that player 1 asks for at period 1. At the nodes of the second layer, player 2 can choose A (acceptance) for any offer that player 1 made in period 1. This terminates the game according to the terms of player 1. If she does not choose A, then she rejects the offer that player 1 made in period 1. She must then make a counteroffer, x 2H, x 2L, or anything in between, where x2 represents the share that player 2 offers to player 1 in period 2 (player 1 gets x2 and player 2 gets 1 − x2). The dashed circles denote that each player has perfect information about the node at which he is located when it is his turn to move. That is, this is a sequential move game.

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x H1

x H2

x H3

A x L3

x L2

x H3

A

273

x L1

A

A x L3

x H2

x L2

x H3

A

x L3

A

Figure 9.2 The extensive form of the alternating-offer bargaining game

For each node, there is a branch of the tree, called a span, which represents a subgame below that node. If all players’ dynamic strategies are Nash optimal, then in each subgame at any node, the players’ strategies constitute a Nash equilibrium. That is, each player’s sequence of moves must be dynamically optimal for a given opponent’s dynamic optimal strategy. We now consider player 1’s optimum dynamic decision. Suppose he asks for x1 ∈[0, 1] in period 1. His principle for choosing x1 is: (i) x1 must be acceptable to player 2, since delay makes no sense in the model with no information asymmetry and with a discount factor between 0 and 1; (ii) x1 should be as large as possible, provided player 2 accepts it. Condition (i) can be achieved only if player 2’s discounted payoff from rejecting the offer is not more than her payoff from the offer. She receives 1 − x1 if she takes the offer right away. If she rejects x1, then she can make a counteroffer x2 in period 2, which yields a discounted value to her δ(1 − x2). Hence, (i) requires 1 − x1 ≥ δ(1 − x2). Condition (ii) requires that x1 be as large as possible or the lefthand side of the semi-inequality be as small as possible, that is, 1 − x1 = δ(1 − x2). For the same reason, player 2 will choose x2 such that x2 = δx 3 where x3 is player 1’s countercounteroffer in period 3. Considering the symmetry between bargaining situations in different rounds, we can see that in a steady equilibrium, x1 = x3 = x5 . . . and x2 = x4 = x6 . . . Hence, the two players’ optimum decisions in the ﬁrst round summarize the information in all rounds of bargains. Player 1 knows that player 2’s optimum decision in period 2 is dependent on his optimum decision in period 1 because of x2 = δx1 if x1 = x3. He will put himself in her shoes to calculate her optimum decision in period 2 according to the equation, then plug this equation back into the equation 1 − x1 = δ(1 − x2) that gives his optimum decision in period 1, given her optimum decision in period 2. This backward deduction based on sequential rationality, which is called dynamic programming, thus yields the subgame perfect equilibrium. In other words, the following system of equations gives the solution. 1 − x1 = δ(1 − x2),

x2 = δx1.

(9.9a)

x*2 = δ/(1 + δ).

(9.9b)

The solution is x*1 = 1/(1 + δ),

Player 1 offers x *1 and player 2 accepts this in period 1; player 2’s threatening counteroffer is x*2 if player 1’s offer is not as good as x*. 1 The counteroffer threat is essential to restrain player 1’s greed.

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You can easily verify that x*1 > 1 − x*, 1 which means that the ﬁrst mover has an advantage since he can hold up his opponent until period 2 to squeeze her, using her impatience. The ﬁrst mover’s advantage increases as the discount factor is reduced, or as a player’s degree of impatience increases. Exercise 11 shows that if the discount factor differs from player to player, then a more patient player has an advantage, too. The ﬁrst mover advantage may be offset by his greater degree of impatience than the second mover, if the advantage of the second mover’s patience outweighs the ﬁrst mover advantage.

9.3.4 Bayes equilibrium We now consider information asymmetry in a static simultaneous-move Nash game. Again, we have not attempted comprehensive coverage of this ﬁeld of game theory. Instead, we use an example to illustrate the main concepts and this analytical approach to game models as one tool in our toolkit. Example 9.7: A Bayes equilibrium model. Consider the Nash game in a Cournot oligopoly model. The inverse demand function for a good is p = a − bx, where x = x1 + x2, and xi is the amount of the good produced by ﬁrm i which has the cost function Ci = ci xi. We assume that ﬁrm 1’s marginal cost c1 is known to both ﬁrms, but ﬁrm 2’s marginal cost c2 has two possible states: a large value θh with probability ρ and a small value θl with probability 1 − ρ. This twopoint distribution function of potential values of c2 is common knowledge for the two ﬁrms. The actual, or realized, value of c2 is chosen by the third player, Nature. After Nature has chosen a state of c2 according to the distribution function, player 2 is informed of the choice, but player 1 is not. Firm 2, then, has complete information about the realized value of c2 and ﬁrm 1 has incomplete information about c2. This is referred to as information asymmetry about the realized value of c2 between the two ﬁrms. A Bayes equilibrium is a Nash equilibrium in a simultaneous-move game with information asymmetry, where the player with incomplete information maximizes his expected payoff function for given uncertainties of his opponent types. Here, types of the informed player are associated with states of marginal cost about which the other player does not have complete information. Firm 2 has two reaction functions for two different states of c2: x2(θh) = (a − θh − bx1)/2b if c2 = θh

and

x2(θl) = (a − θl − bx1)/2b if c2 = θl.

(9.10a)

Firm 1’s decision problem is Max: Eπ1 = ρ{a − c1 − b[x1 + x2(θh)]}x1 + (1 − ρ){a − c1 − b[x1 + x2(θl)]}x1 x1

where E denotes expectation. The expected proﬁt is a weighted average of two proﬁt levels. The weights are the respective probabilities of the two proﬁt levels. The reaction function of ﬁrm 1 is given by the ﬁrst-order condition for the decision problem as follows. x1 = [a − c1 − ρbx2(θh) − (1 − ρ)bx2(θl)]/2b. (9.10) yields the Bayes equilibrium: x *1 = [a − 2c1 + ρθh + (1 − ρ)θl]/3b, x *(θ 2 h) = [2(a + c1) − (3 + ρ)θh − (1 − ρ)θl]/6b, x *(θ 2 l) = [2(a + c1) − ρθh − (4 − ρ)θl]/6b.

(9.10b)

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This game model with information asymmetry involves interesting interactions between strategies and information.

9.3.5 Sequential equilibrium Example 9.8: A sequential equilibrium model of the credit market. If we introduce information asymmetry into a dynamic game or introduce a time dimension into a Bayes game with information asymmetry, we will have an interesting kind of game – a dynamic game with information asymmetry – which can generate signiﬁcantly higher explainatory power than the Walrasian equilibrium model. The solution of this kind of game is referred to as sequential equilibrium or a perfect Bayes equilibrium. For most dynamic game models with information asymmetry, perfect Bayes equilibrium, which is an extension of Bayes equilibrium to dynamic games, is equivalent to sequential equilibrium, which is an extension of the notion of subgame perfect equilibrium to games with information asymmetry. We use an example to illustrate the concept of sequential equilibrium in a dynamic game with information asymmetry, and its implication for the analysis of credit markets. This is a game between many entrepreneurs and an investor in a credit market. There are two types of entrepreneurs, capable and incapable, denoted by subscripts c and n respectively. For a type c entrepreneur, the proﬁt she can make, the net of repayment of the investment, when the investor makes an investment in her business is 20, which will be equally divided between her and the investor. The capable entrepreneur’s utility function is uc = (3 × 0.5θcαi − pi)αi when she receives a half of the proﬁt θc = 20 that she makes, and consumes a car with quality αi at price pi. Here, subscript i denotes the brand i of car. There are three brands of cars. Brand 1 is BMW, with quality α1 = 4 and price p1 = 70. Brand 2 is Volvo, with quality α2 = 3 and price p2 = 11. Brand 3 is Toyota, with quality α3 = 2 and price p3 = 6. For a type n entrepreneur, the proﬁt he can make when an investor invests in his business is 8, which will be equally divided between him and this investor. His utility function is un = (0.5θn αi − pi)αi when he receives a half of the proﬁt θn = 8 that he makes, and consumes a car with quality αi at price pi. For simplicity, we assume that a car can be used for two periods and the discount factor is 1 (or the discount rate is 0). It is assumed that utility must be non-negative, or the subsistence level of utility is non-negative. The investor has incomplete prior information about the type of entrepreneur she meets. She knows in period 1 that, on average, type c occurs with probability ρ and type n occurs with probability 1 − ρ, where ρ ∈(0, 1) is the ratio of the capable entrepreneurs to the total population of entrepreneurs. The investor’s utility function is v = (θi /2) − 5, where θi is the proﬁt made by the type i entrepreneur who gets the funding, of which the investor gets half. θc = 20 when the capable entrepreneur gets the funding and θn = 8 when the incapable entrepreneur gets the funding. For simplicity, we assume that an investor’s utility is 0 in period 1. In period 1, the two types of entrepreneurs choose the brands of cars they want to drive, then in period 2 the investor infers the entrepreneurs’ types from the brands of cars they drive and decides with whom to deal. This story is interesting because of the complicated interactions between information and dynamic strategies. The investor can infer that a capable entrepreneur will drive a Volvo, since uc(α2, p2) > uc(α1, p1), uc(α3, p3) and an incapable entrepreneur will drive a Toyota, since un(α3, p3) > un(α2, p2) and un(α1, p1) < 0. In other words, an incapable entrepreneur will drive a cheaper car and a capable entrepreneur will drive a more expensive Volvo. Then from the brands of cars the entrepreneurs drive, the investor can get complete information about their types, so that she would invest in the business of the entrepreneur who drives a Volvo and refuse to do business with an entrepreneur driving a Toyota.

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But a rational entrepreneur will drive a Volvo even if he is incapable (check that un(α2, p2) > 0, that is, incapable entrepreneurs can afford a Volvo, despite the fact that this is not a myopic utility maximizing choice), since if he drove a Toyota, he would get no business, so that his income would be 0 and he could not afford even a Toyota. But if all entrepreneurs drive Volvos, the investor cannot tell their competence from their cars. They will not believe any entrepreneur claiming to be capable. Accordingly, if a capable entrepreneur wants to distinguish herself from an incapable one, she can drive a BMW, which an incapable entrepreneur cannot afford (check un(α1, p1) < 0). In other words, what the investor knows about an entrepreneur’s type is dependent on which strategy the entrepreneur chooses. But the strategy that the entrepreneur sees as optimal is, in turn, dependent on the information known to the investor, which affects the investor’s strategies. In a manner analogous to the interdependencies and feedback loops between quantities and prices in a Walrasian equilibrium model, there are inﬁnite interactions and feedback loops between the investor’s information and her dynamic strategies, and between different players’ dynamic strategies. A sequential equilibrium is the outcome of all of the interactions between information and all players’ dynamic strategies. Denoting the brand of car that an entrepreneur chooses in period 1 by s, then in period 2, from observing s, from the perspective of the investor, the posterior probability that an entrepreneur will be type c is μ(s). This updated information may be different from the prior probability, ρ. Hence, a sequential equilibrium is deﬁned by the following two conditions. (i) All players use dynamic programming (backward deduction) to solve for their optimum dynamic strategies for given information which they know; (ii) Each player’s information in each period is updated according to the observed strategies of other players on the basis of the Bayes updating rule. The Bayes updating rule is illustrated in the following solution to the sequential equilibrium. Let us now consider the investor’s decision problem. Her utility is 0 in period 1. In period 2, she has seen the brand s of cars driven by entrepreneurs and has the updated information μ(s). Hence, she can compute her expected utility as Ev = μ(s)[(20/2) − 5] + [1 − μ(s)][(8/2) − 5] = 6μ(s) − 1, which is greater than 0 iff μ(s) > 1/6. Based on this solution, we can work out a pooling equilibrium by assuming μ(s) = ρ > 1/6. A pooling equilibrium takes place when the investor’s prior and posterior information is the same or when μ(s) = ρ and ρ > 1/6. In the pooling equilibrium, all entrepreneurs drive Volvos in period 1, the investor cannot tell the capable entrepreneurs from the incapable ones, and she therefore does business with any entrepreneur in period 2. We ﬁrst check if the investor’s decision to do business with any entrepreneur is optimal for her updated information. Since in a pooling equilibrium μ(s) = ρ, and we have assumed that ρ > 1/6, her expected utility is greater than 0. Therefore, her decision to do business with any entrepreneur is optimal. Though she has an incentive to have more information, we can show that, provided the investor chooses to do business with any entrepreneur, a capable entrepreneur has no incentive to distinguish herself from an incapable entrepreneur, and that an incapable entrepreneur has an incentive to pretend to be a capable entrepreneur by driving a Volvo. You can verify that a type n entrepreneur can afford a Volvo, that his myopic utility maximizing choice is a Toyota car, and that he will lose business if he drives a Toyota. A c type entrepreneur’s total utility in the two periods is −p2α2 + 3 × 0.5θcα 22 = (3 × 0.5θcα2 − p2)α2 = 231, which is greater than that for driving a BMW, which can distinguish her from an incapable entrepreneur. Note that in period 1, the entrepreneur receives no income and pays for a Volvo, and in period 2 she receives a half share of proﬁt and uses the car without further payment. An n type entrepreneur’s total utility in the two periods is −p2α2 + 0.5θl α 22 = (0.5θ lα2 − p2)α2 = 3, which is greater than the zero that occurs when there is no business. Hence, all dynamic strategies are optimal for the updated information, and the information that is updated according to observed strategies is consistent with all players’ dynamic strategies.

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This veriﬁes that for ρ > 1/6, the pooling sequential equilibrium takes place. That is, if the likelihood for an entrepreneur to be capable is high (or capable entrepreneurs sufﬁciently outnumber the incapable ones), the investor will do business with any entrepreneur even if she cannot tell the capable from the incapable ones. Hence, the capable one has no incentive to distinguish herself from the incapable one, so that the incapable can cheat by pretending to be capable. The confused investor cannot get more information when the capable does not choose to distinguish herself from the incapable. Suppose ρ ≤ 1/6. We can show that there exists a screening or separating sequential equilibrium, in which all capable entrepreneurs drive BMWs and all incapable entrepreneurs cannot get any business. For this case, the investor’s expected utility is nonpositive if she cannot tell the capable from the incapable, so that she will not do any business unless she is convinced that an entrepreneur is capable. Hence, a capable entrepreneur has an incentive to distinguish herself from the incapable by driving a BMW, which an incapable entrepreneur cannot afford. Therefore the investor can tell the capable from the incapable, so that she invests only in the business of an entrepreneur who drives BMWs. Her posterior information is μ(s) = 1 when she has seen an entrepreneur driving a BMW and is μ(s) = 0 if she has seen an entrepreneur who is not driving a BMW. In other words, if incapable entrepreneurs sufﬁciently outnumber capable ones, the investor expects a nonpositive utility from doing business with any entrepreneur when she cannot tell which is which. Hence, she will not do any business unless she can establish who is who. This gives the capable entrepreneurs an incentive to convince the investor by driving BMWs, which the incapable entrepreneurs cannot afford. Therefore, screening equilibrium results from complicated interactions between information and all players’ dynamic strategies. Let us now consider the endogenous transaction costs caused by information asymmetry in the credit market. There are two types of endogenous transaction cost in the sequential equilibrium model. Type A endogenous transaction cost is associated with the information distortion in the pooling equilibrium, where the incapable entrepreneur successfully cheats the investor by pretending to be capable. Type B endogenous transaction cost is a “convincing cost,” incurred in the screening equilibrium in a situation in which the investor may not believe the capable entrepreneur even if she tells the truth. The capable entrepreneur must sacriﬁce utility by driving a BMW in order to convince the investor. The convincing cost would not be necessary if the incapable entrepreneur did not cheat, that is, if information asymmetry were absent. The concepts of perfect Bayes equilibrium and sequential equilibrium are useful vehicles for the analysis of endogenous transaction costs because information asymmetry creates the scope for cheating and other opportunistic behaviors that cause endogenous transaction costs. This model can be interpreted in various ways to suit speciﬁc applications. For instance, brands of cars can be interpreted as different levels of expenditure on the advertising that can be used by a producer to signal private information about his ﬁnancial and production capacity, while the investor can be interpreted as a potential buyer of his products. Hence, this model can be used to explain why advertising expenditure is much higher than the level adequate to transmit information about goods to potential buyers. According to the model, if advertising expenditure is not high enough, then capable and incapable producers all can afford to advertise – leaving potential buyers unable to tell the capable from the incapable by observing the advertisement. Again, the high advertising expenditure is a convincing cost. Like the sharecropping model, this model of the credit market shows that the function of the market is much more sophisticated than conventional textbooks predict. This model predicts that if interactions between strategies and information are considered, a shortage of capable entrepreneurs may make cheating less likely to occur in equilibrium. Hence, the shortage of capable entrepreneurs, which is common in less-developed countries, is not a serious problem for economic development. But government monopoly in the capital market, the stiff licensing system for private banking business, restrictions on the trade of land and free migration

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between urban and rural areas, the government’s infringement of private ownership of land are detrimental for economic development. According to North (1981, pp. 158–68), medieval regulations, including usury laws and restrictions on the mobility of capital and labor, were detrimental to economic development in Britain. Their removal was essential for the Industrial Revolution.

9.4

THE ROLE OF NASH BARGAINING GAMES IN REDUCING ENDOGENOUS TRANSACTION COSTS CAUSED BY TRADE CONFLICT

Individual-speciﬁc prices and pricing through bargaining existed long before the emergence of developed markets with impersonal market prices and related pricing mechanisms. In lessdeveloped economies, including Soviet-style ones, pricing is typically determined by bargains between trade partners. In order to understand how impersonal common market prices emerge from prices that are different from player to player, and under what conditions trade negotiation is essential for reducing endogenous transaction costs, we must study bargaining. The concept of games is particularly useful in studying the bargaining process, since bargaining is characterized by direct interactions between players’ self-interested decisions. In this section, we ﬁrst present a Nash bargaining model with endogenous specialization, then compare the Nash bargaining solution to the Walrasian equilibrium. We shall then consider the function of Nash bargaining in reducing endogenous transaction costs caused by a small number of players in the Walrasian model of endogenous specialization. Example 9.9: A Nash bargaining game with endogenous specialization. Consider a Nash bargaining game with two players who have complete information about their opponents’ production and utility functions, transportation conditions, endowment constraint, and the threat point at which they will refuse to participate in the division of labor. Assume that the production and utility functions, endowment constraint, and transportation conditions for two ex ante identical consumer-producers are the same as in chapter 4. But the players try to sort out terms of trade through bargaining. Each player knows that choosing specialization in producing x generates utility ux = (1− x s)ky d, choosing specialization in producing y generates utility uy = (1 − y s )kx d, and choosing autarky generates utility uA = 2−2a. There are two threat points or disagreement points at which each player refuses to participate in trade. The ﬁrst is the bottom line given by real income in autarky uA. A player will refuse to participate in the division of labor if trade generates a lower utility than autarky. Second, a player may use the utility for the occupation conﬁguration in producing y as the threat point when choosing the occupation conﬁguration of x, since she can always change occupation if one occupation generates more utility than the other. Because of the budget constraint, the terms of trade are py/px = x s/y d = x d/y s, where the ﬁrst equality is given by the budget constraint for the specialist of x, px x s = py y d, and the second by the budget constraint for the specialist of y, px x d = py y s. Since market clearing is a constraint for the deal, we have x s = x d and y s = y d. For simplicity of notation, we use X and Y to represent equal quantities demanded and supplied for the two goods. The net gain that an x-specialist can receive from the division of labor is Vx = (1 − X )kY − uA and that for a specialist of y is Vy = (1 − Y )kX − uA. The x-specialist wants the relative price py /px = X/Y to be as high as possible. But he has a trade-off. If Y/X is large, his net gain Vx is great, but his opponent’s net gain Vy is small, so that his opponent has little incentive to get involved in the division of labor. Accordingly, the probability of realizing the large value of Vx is small if the bargaining process is subject to any stochastic disturbance. The disturbance

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could be caused, for example, by a quarrel that the opponent had with her husband at home before coming to the bargaining meeting. In her resulting bad mood, the smallness of her net gain from the deal may cause her to refuse to participate in the division of labor. If we consider Vy as the probability that the x-specialist can realize Vx , then the x-specialist’s expected net payoff from the division of labor is V = Vx Vy + 0 × (1 − Vy ) = VxVy where 1 − Vy is the probability that the net payoff cannot be realized, or that the net payoff is 0. Nash has proved that in a noncooperative bargaining game with marginal stochastic disturbance, the Nash product V will be maximized by self-interested strategies. Hence, the Nash bargaining equilibrium is given by the following maximization problem: Max: V = Vx Vy = [(1 − X)kY − uA][(1 − Y)kX − uA]. X ,Y

(9.11)

In a symmetric model with ex ante identical consumer-producers and symmetric tastes and production and transaction conditions, the Nash bargaining equilibrium deﬁned in (9.11) is equivalent to the one deﬁned by (9.12). If utility in an alternative occupation conﬁguration is considered as a threat point, while utility in autarky is just a bottom line, the Nash product becomes V = (ux − uy)(uy − ux) = −(ux − uy)2

(9.12)

where ux is the utility for specialization in x and uy is the utility for specialization in y. In a Nash bargaining game, the x-specialist threatens to choose specialization in producing y, while the specialist of y threatens to choose specialization in producing x if the terms of trade are unfair. Maximization of the Nash product, of course, implies the minimization of (ux − uy)2, which requires ux = uy. Hence, Nash bargaining will establish the utility equalization condition. The maximization of V with respect to X and Y subject to utility equalization generates the Nash bargaining equilibrium. The ﬁrst-order condition for the constrained maximization problem yields the equilibrium terms of trade,

1 X =Y = , 2

ux = uy =

k , 4

which coincides with the Walrasian equilibrium with endogenous numbers of different specialists. The ﬁrst-order conditions for the problem in (9.11), ∂V/∂X = ∂V/∂Y = 0 or Y = 1 − X and (1 − 2X)[X(1 − X)k − uA] = 0, generate the same solution. However, if the consumption, production, and transportation conditions are asymmetric between the two goods, the solution for the maximization problem (9.11) differs from that for maximizing (9.12). For the case of asymmetric tastes and production and transaction conditions, but ex ante identical consumerproducers, the Nash bargaining equilibrium may be different from the Walrasian equilibrium, although both types of Nash bargaining equilibrium, as well as the Walrasian equilibrium, are Pareto optimal. Example 9.10: The function of Nash bargaining in reducing endogenous transaction costs caused by the Walrasian equilibrium in a Smithian model with a ﬁnite set of consumer-producers. Consider the model in example 9.9. There are only two players (the set of players is not a continuum), but the utility function is u = (x + kx d )1/3( y + ky d )2/3. Hence, per capita real income in autarky is

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(22/3/3)a and the utility functions for conﬁgurations (x/y) and (y/x) are ux = (1 − x s )1/3(ky d)2/3 and uy = (kx d )1/3(1 − y s)2/3, respectively. Walrasian supply and demand functions for the two occupations are x s = 2/3, y d = 2p/3, y s = 1/3, x d = 1/3p, where p is the price of x in terms of y. The indirect utility functions for the two occupations are ux = (2kp)2/3/3 and uy = 22/3(k/p)1/3/3, respectively. The market clearing condition for x or y yields p = 1/2. But this relative price cannot be the equilibrium one, since the two players will choose conﬁguration (y/x) and nobody chooses (x/y) under this relative price. This implies that the market cannot clear (there is supply for y, but no demand for y). Hence, the Walrasain corner equilibrium for the division of labor does not exist, or the Walrasian general equilibrium is always autarky for any k ∈[0, 1] and a > 1. But it is easy to show that the Nash bargaining equilibrium is the division of labor and generates higher per capita real income than in autarky for sufﬁciently large values of k and a. For instance, suppose k = 1. Then the Nash bargaining corner equilibrium for the division of labor is given by the following maximization problem: Max: [(1 − X)1/3Y 2/3 − uA][(1 − Y )2/3X 1/3 − uA], X ,Y

where X = x s = x d and Y = y s = y d are quantities demanded as well as supplied, and uA = (22/3/3)a is per capita real income in autarky. The solution of the bargaining equilibrium is Y = X = 1/2. This Nash bargaining corner equilibrium generates per capita real income 1/2, which is greater than in autarky iff a > ln 2/(ln 3 − 2 ln 2/3) ≈ 1.09. Hence, for a large value of a and k = 1, a coordination failure occurs in the Walrasian regime and the Nash bargaining can successfully coordinate the division of labor. Since maximization of the Nash product is equivalent to the maximization of a social welfare function, it is straightforward that the Nash bargaining equilibrium is always Pareto optimal. This implies that the Nash bargaining equilibrium will not cause endogenous transaction costs. In the model with endogenous specialization, the Nash bargaining outcome not only achieves the Pareto efﬁcient resource allocation for a given level of division of labor, but also ensures the Pareto optimum level of division of labor. Our example shows that for a small number of consumer-producers in an asymmetric Smithian model, the Walrasian equilibrium generates endogenous transaction costs that are caused by a coordination failure of division of labor. In our example, asymmetric tastes for goods x and y imply that specialization in y receives more utility than specialization in x under the Walrasian regime, so that nobody is willing to specialize in x. In other words, the unfair distribution of gains from the division of labor between occupations might cause a coordination failure of division of labor in the Walrasian regime with a ﬁnite number of consumer-producers. In example 3.2 of chapter 3, we have shown that even if the set of ex ante different players is a continuum, the Walrasian equilibrium may generate a very unequal distribution of gains from the division of labor. This will generate incentives for those players who receive few gains to take collective action for rent seeking. For instance, the government in a less-developed country may have an incentive to impose an import tariff to manipulate terms of trade if all gains from the division of labor go to a developed country. It is interesting to note that there might be a trade-off between the reduction of endogenous transaction costs through Nash bargaining and exogenous transaction costs caused by that bargaining. The Pareto optimality of the Nash bargaining solution is based on the assumption that all players know their opponents’ utility and production functions and endowments, which is essential for each player to ﬁgure out the Nash bargaining solution. But the Walrasian equilibrium can be reached even if each player has no information about other players’ utility and production functions and endowments. If the collection of all the information is very expensive, then there is a trade-off between endogenous transaction costs caused by trade

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conﬂict in the Walrasian regime with a ﬁnite set of consumer-producers and exogenous cost in collecting information in the Nash bargaining game. As will be shown in example 9.11, if players do not have complete information about their opponents’ utility and production functions, endowment, and transaction conditions, Nash bargaining may generate endogenous transaction costs too. Therefore, there is a trade-off between endogenous transaction costs, caused by unfair distribution of the gains from the division of labor in the Walrasian regime with a ﬁnite number of consumer-producers, and endogenous transaction costs related to the information problem in the Nash bargaining game. The Nash bargaining game model in this section is a well-closed general equilibrium game model where Walras’s law holds. This feature can be used to endogenize the level of division of labor and to explore the effects of bargaining on the equilibrium size of the network of division of labor and economic development. It can be shown that the Nash bargaining equilibrium is the division of labor iff the Pareto optimum is the division of labor. Also, if the exogenous transaction cost coefﬁcient 1 − k is sufﬁciently large, the equilibrium is autarky; otherwise, it is the division of labor. The shortcoming of the Nash bargaining model is that it does not spell out uncertainties and a time dimension. In the next two sections, the implications of information asymmetry and the time dimension will be examined.

9.5 ENDOGENOUS TRANSACTION COSTS CAUSED BY INFORMATION ASYMMETRY AND HOLDING UP If there is information asymmetry in a bargaining game, it will create scope for cheating (a form of opportunistic behavior). Because of possible cheating, players do not trust each other even if they tell the truth. This causes endogenous transaction costs that prevent the realization of a mutually beneﬁcial division of labor. For the division of labor, a specialist producer of a good certainly knows more about the production of that good than does the buyer, who is specialized in producing other goods. This information asymmetry is a driving force of economies of specialization, as well as a source of endogenous transaction costs. In sub-section 9.5.1, we use a Nash bargaining model with information asymmetry to illustrate endogenous transaction costs caused by adverse selection. Then we introduce alternating-offer bargaining into a model of endogenous specialization in subsection 9.5.2. The subgame perfect equilibrium model is then extended to investigate endogenous transaction costs caused by holding-up behavior in the absence of moral hazard and adverse selection in subsection 9.5.3. Finally, in subsection 9.5.4 we shall address the question of how a reputation mechanism can eliminate endogenous transaction costs and promote economic development using a repeated game model.

9.5.1 Economic development and endogenous transaction costs caused by adverse selection Example 9.11: A Nash bargaining game with information asymmetry. Assume that in the bargaining model in example 9.9, y is a simple housecleaning service which involves no information asymmetry between seller and buyer, so that a specialist producer does not know much more than a buyer about the production of y. Therefore, a y-specialist’s output level y + y s = 1 is common knowledge to everybody. But suppose that good x is a sophisticated manufactured good whose production involves signiﬁcant economies of specialized information, so that a specialist producer of x has more information about its production conditions than a novice buyer. Suppose that an x-specialist’s output level θ is 1.5 at probability 0.5, and is 0.5 with probability 0.5. Nature randomly chooses a value of θ and informs the x-specialist about the

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realized value of θ. The y-specialist has only common knowledge about the distribution function of θ. Assume that a change of profession involves a prohibitively high cost, so that it is not a choice when specialized information is generated by the division of labor. This implies that utility for the alternative profession is not a threat point. Inserting the data into the model in example 9.9, we have the Nash product V = Vx Vy = [(θ − X)kY − uA][(1 − Y )kX − uA], where utility in autarky uA = 2−2a is the threat point. Suppose the specialist of x (male) tells the y-specialist (female) the realized value of θ, and that she trusts what he says. The Nash bargaining equilibrium for the complete information case is X = θ/2,

Y = 0.5,

ux = (θ − X )kY = θk/4,

px /py = Y/X = 1/θ, uy = (1 − Y )kX = θk/4.

(9.13)

This implies that the price of x in terms of y decreases as the output level θ increases. Suppose that the realized value of θ is 1.5, but the specialist of x claims that θ = 0.5 and the specialist of y trusts him. Then the equilibrium terms of trade are X = θ/2 = 1/4, Y = 0.5, px /py = Y/X = 1/θ = 2. But the realized utility of the specialist of x is ux = (θ − X )kY = (1.5 − 0.25)k × 0.5 = 5k/8, which is greater than his realized utility when he tells the truth, θk/4 = 1.5k/4 = 3k/8. Therefore, the x-specialist has an incentive to understate his output level if the y-specialist has incomplete information about it. Since she is aware of the possibility of cheating, she will not trust him when he says θ = 0.5 even if he is telling the truth. If the y-specialist asks for the price that maximizes the expected Nash product based on her incomplete information, then the following problem generates a Nash bargaining solution. Max: EV = 1/2 [( 3/2 − X)kY − uA][(1 − Y )kX − uA] + 1/2 [( 1/2 − X)kY − uA][(1 − Y )kX − uA] X ,Y (9.14)

The solution is X = Y = 0.5, ux = (θ − 0.5)k × 0.5, uy = k/4. But for θ = 0.5, the x-specialist’s utility is nonpositive at the terms of trade. Hence, the deal can be done only if θ = 1.5. The two players’ perfect rationality implies that the Nash bargaining equilibrium terms of trade are given by (9.13), and the division of labor is chosen for θ = 1.5 and ux = uy = θk/4 = 3k/8 > uA = 2−2a. The Nash bargaining equilibrium is autarky if θ = 0.5 for any value of k. Hence, for θ = 0.5 and k > 23−2a, the Nash bargaining equilibrium in the game with information asymmetry generates the Pareto inefﬁcient level of division of labor. Inserting θ = 0.5 into (9.13) yields the Nash bargaining equilibrium for the game with no information asymmetry, which is X = 1/4, Y = 0.5 and ux = uy = θk/4 = 3k/8 > uA = 2−2a for k > 23−2a. That is, the division of labor is chosen for θ = 0.5 and k > 23−2a, if all players have complete information. But with information asymmetry, possible cheating makes players distrust each other, so that autarky is chosen for θ = 0.5 and k > 23−2a. In other words, opportunistic behavior (cheating) causes endogenous transaction costs that prevent the realization of mutually beneﬁcial division of labor. In textbooks, this kind of endogenous transaction cost caused by information asymmetry is commonly referred to as adverse selection. The early model of adverse selection, often referred to as the “lemon model,” was developed by Akerlof (1970). His story is similar to the one in this section. When buyers of second-hand cars do not have complete information about the quality of the cars, they can only accept the average price based on average quality. But the seller of high-quality cars will ask for a price higher than the average. Hence, it is the

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high-quality second-hand cars that cannot be sold. This generates adverse selection in the sense that only low-quality cars are sold in the market. Example 9.7 shows that reality is much more sophisticated than predicted by the adverse selection model if individuals take into account interactions between information and strategies. Adverse selection is caused not only by information asymmetry, but also by the assumption that players are so naive that they do not infer opponents’ private information from observed strategies. Hence, if this model is extended to a sequential equilibrium model with explicit interactions between strategies and information, then it can be shown that adverse selection will not occur if players are not so naive. The algebra of such a model is cumbersome and can be found in Yang and Zhao (1998).

9.5.2 An alternating-offer bargaining game in a model of endogenous specialization Example 9.12 (Yang and Zhao, 1998): An alternating-offer bargaining model of endogenous specialization. Let’s now introduce alternating-offer bargaining into the model in example 4.1 to study the implication of sequential bargaining for the size of the network of division of labor and economic development. Each consumer-producer can choose between specialization in x or y and autarky, so that utility in autarky is a threat point. Because of symmetry, there are two subgame perfect equilibria: one with the x-specialist as the ﬁrst mover and the other with the y-specialist as the ﬁrst mover. The two equilibria in which the ﬁrst mover has the advantage are symmetric. Without loss of generality, we assume that the x-specialist is the ﬁrst mover (referred to as player 1 or he) and the y-specialist is the second mover (referred to as player 2 or she). The two players have the same discount factor δ. We use subscripts to denote the period. Suppose that player 1 offers X1 in exchange for Y1 in period 1. This implies that he offers the terms of trade px /py = Y1/X1 because of the market clearing conditions x s = x d = X and y s = y d = Y, and the budget constraint px /py = Y/X. Player 1’s decision rule is the same as in example 9.5. First, he must ensure that she will take the offer. Second, he maximizes his utility subject to the acceptance constraint. Hence, his offer is given by the following problem. Max: u1x = (1 − X1)kY1, X1 ,Y1

s.t.

u1y ≡ (1 −Y1)kX1 = δ(1 − Y2)kX2 ≡ δu2y

(9.15a)

where u1x is the x-specialist’s utility under the terms of trade in period 1, u1y is the y-specialist’s utility under the terms of trade in period 1, and u2y is the y-specialist’s utility generated by her counteroffer in period 2. Similarly, the y-specialist’s counteroffer in period 2 is given by Max: u2y = kX2(1 − Y2) X 2 ,Y2

s.t.

(1 − X2)kY2 = δ (1 − X1)kY1

(9.15b)

where we have used the fact that in a steady equilibrium X1 = X3 = X5 . . . , Y1 = Y3 = Y5 . . . , X2 = X4 = X6 . . . , and Y2 = Y4 = Y6 . . . Player 1 can then use backward deduction to solve for problem (9.15b) ﬁrst, and then plug the solution back into problem (9.15a). In other words, his sequential rationality implies that he knows that player 2’s optimum decision in period 2 is dependent on his decision in period 1, which is in turn dependent on her decision in period 2. He will fully use this interdependence to pursue his self-interest. (9.15b) yields

X2 = 1 − Y2 ,

Y2 = δ (1 − X1 )Y1 .

(9.16a)

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Inserting this into (10.15a) and then maximizing u1x with respect to X1 and Y1, we obtain the subgame perfect equilibrium terms of trade

X1 = δ /(1 + δ ),

Y1 = 1 − X1 = 1/(1 + δ ).

(9.16b)

Player 1 offers this term and player 2 accepts in period 1. Plugging this back into (9.16a) yields player 2’s threatening counteroffer in period 2: X2 = 1/(1 + δ ),

Y2 = δ /(1 + δ ).

(9.16c)

In this deduction, each player maximizes her utility for a given utility level of the opponent. Hence, the ﬁrst-order conditions for the subgame perfect equilibrium are the same as those for a benevolent dictator’s constrained maximization problem for the Pareto optimum. Hence, dynamic bargaining with complete information will not generate endogenous transaction costs. However, it does generate an unequal distribution of gains to trade. Inserting (9.16b) into the two players’ utility functions yields the equilibrium real incomes ux = k/(1 + δ )2 > uy = δk/(1 + δ )2 for δ ∈(0, 1)

ux = uy for δ = 1

px /py = Y/X = 1/ δ if δ ∈(0, 1);

px /py = 1 if δ = 1.

(9.17a) (9.17b)

The equilibrium real incomes and relative price indicate that the ﬁrst mover’s advantage is greater as the discount factor falls (or as the degree of impatience increases). As the discount factor tends to 1 or as the time lag between offer and counteroffer declines, the two players’ real incomes converge to the same level and the equilibrium terms of trade converge to the level of the impersonal market. But the above deduction is relevant only if the gains from the division of labor, net of transaction costs, are great, since the threat to choose autarky is not credible in this case. Suppose δ ∈ (0, 1). If k ≤ k1 ≡ 2−2 a (1 + δ )2 /δ, then uy ≤ uA in the equilibrium given by (9.16). Player 2’s threat to choose autarky is therefore credible. But so long as k1 > k > k0 ≡ 22(1−a), the division of labor is still mutually beneﬁcial. For this interval of parameter values, the subgame perfect equilibrium can be solved as follows. We ﬁrst solve for X2 and Y2 as functions of X1 and Y1 from (9.15b), then insert the solution into (9.15a) and replace the constraint in (9.15a) with u1y = (1 − Y1)kX1 = uA = 2−2a. We can thus solve for the equilibrium values of X1 and Y1 from (9.15a). The equilibrium values of X2 and Y2 can be solved using the equilibrium values of X1 and Y1. The subgame perfect equilibrium for k ≤ k1 is summarized as follows:

X1 = 1/2a k ,

Y1 = 1 − (1/2a δ ),

Y2 = 1 − (1/2a k ),

X2 = 1/2a k

ux = k[1 − (1/2a k )]2 ,

(9.18)

uy = 2−2 a

If k < k0 ≡ 22(1−a), the solution in (10.18) implies ux < uA = 2−2a. Hence, the subgame perfect equilibrium is autarky for k < k0. It is given by (9.18) for k ∈(k0, k1) and is given by (9.15) for k ∈(k1, 1). It is straightforward that the subgame perfect equilibrium is the division of labor iff the Nash bargaining equilibrium is the division of labor. That is, the alternating-offer bargaining generates not only efﬁcient resource allocation, but also the efﬁcient level of division of labor.

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Table 9.5 The strategic form of the game to compete for ﬁrst mover advantage Player 2

Player 1

T

S

T

uA, uA

uH, uL

S

uL, uH

uD, uD

The shortcoming of the dynamic bargaining model is that it cannot explain who is the ﬁrst mover. All players know that the ﬁrst mover has the advantage, so that they will compete for that position. The competition implies that the solution we have just obtained cannot be an equilibrium. In the next section, we shall show that such competition for a greater share of gains from division of labor will generate endogenous transaction costs.

9.5.3 Economic development and endogenous transaction costs caused by holding up Example 9.13: An alternating-offer bargaining model with endogenous transaction costs. We now allow players to compete for the ﬁrst mover position. We add period 0 to the dynamic game in example 9.12. After period 0, the structure of the new game is the same as in example 9.12. Hence, the game in example 9.12 is a subgame within the new game. In period 0, the two players sort out who is the ﬁrst mover. Consider the case k ∈(k1, 1), which implies that the Nash bargaining equilibrium is the division of labor. Because of backward deduction, the subgame equilibrium from period 1 on is still given by (9.16) and (9.17). Assume that each player has two strategies: tough (T ) and soft (S) in period 0. The tough strategy implies that a player insists on being the ﬁrst mover, and will not accept any terms that give a lower utility than that which the ﬁrst mover receives. The soft strategy implies that a player accepts the second mover’s position if the opponent is tough, and agrees to fair terms, as given by the Nash bargaining solution, if the opponent is soft too. The game in period 0 for a given subgame equilibrium in period 1 is described in table 9.5. In table 9.5, the ﬁrst term in an entry represents player 1’s payoff (utility) and the second represents that for player 2. uA = 2−2a is the real income (utility) in autarky, uD = k/4 is the real income for the division of labor given by a Nash bargaining solution. uH = k/(1 + δ )2 is the ﬁrst mover’s real income in the subgame equilibrium in period 1, and uL = δk/(1 + δ )2 is the second mover’s real income in the subgame equilibrium. It is easy to see that uH > uD > uL > uA for k > k1 > k0 and δ ∈ (0, 1). From table 9.5, we can see that the two players receive real income in autarky if both of them choose a tough strategy, which means that no agreement can be achieved for the terms of trade. They receive real income for the division of labor outcome given by the Nash bargaining solution, and the gains from the division of labor are equally divided between them if both of them are soft. If one player is tough and the other is soft, then the tough one gets the greater gains; nevertheless, mutually beneﬁcial gains from the division of labor are realized, despite the unequal distribution of income. The game in period 0, for a given subgame perfect equilibrium in period 1, is a typical Nash game with two pure strategy Nash equilibria. We ﬁrst prove that outcomes TT and SS are not pure strategy Nash equilibria. We argue by negation. Suppose TT is a Nash equilibrium, so that we consider the upper-left entry in table 9.5. Assume that player 1’s tough strategy is given. It is then clear that player 2 can increase her utility by deviating from T, which gives her uA, to S, which shifts the outcome from TT to

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TS and brings uL (> uA) to her. This implies that she has an incentive to deviate unilaterally from outcome TT. This implies, by the deﬁnition of a Nash equilibrium, that TT cannot be a Nash equilibrium. Using similar reasoning, we can show that SS is not a Nash equilibrium either. It can be seen that no player has an incentive to deviate unilaterally from an asymmetric equilibrium ST or TS. For the Nash pure strategy game, the theory cannot predict which of the two Nash equilibria will take place. But if each player is allowed to choose a probability distribution for each and every strategy, we will have a unique mixed strategy Nash equilibrium. The probability distribution of pure strategies is called a mixed strategy. Mixed strategy is a way to make sure that the game is fair and that all players still participate even if any pure strategy outcome must be unfair to some player. When family members have a disagreement about which TV channel should be on, a fair solution is to ﬂip a coin and let the stochastic process sort out the conﬂict of interests. Suppose player i chooses the soft strategy with probability qi and chooses the tough strategy with probability 1 − qi. Since the purpose of a player’s mixed strategy is to confuse his opponent, player 1 will choose q1 such that player 2 feels indifferent between her choices of T and S. For a given q1, player 2’s expected utility for her choice of T is (1 − q1)uA + q1uH and that for strategy S is (1− q1)uL + q1uD. The two utility levels are indifferent iff q = (uL − uA )/(uH − uD + uL − uA) where uA = 2−2a, uD = k/4, uL = δk/(1 +

(9.19a)

δ )2, and uH = k/(1 +

δ )2.

(9.19b)

Using the symmetry of the model, we can show that the mixed strategy of player 2, q2, that makes player 1 feel indifferent between his choices of T and S is the same as (9.19a). It can be shown that q → 1/2 as δ → 1;

q → 0 as δ → 0;

and ∂q/∂δ > 0.

(9.20)

where 1 − δ can be considered as the exogenous bargaining cost, which is 0 for δ = 1, and takes on its maximum value for δ = 0. The fair Nash bargaining solution takes place with probability q2 and the probability that the mutually beneﬁcial gains from the division of labor cannot be realized is (1 − q)2. Hence, (1 − q)2 represents endogenous transaction costs. (9.20) indicates that in the competition for a greater share of the gains from the division of labor, endogenous transaction costs are not 0 even if exogenous transaction cost tends to 0, though the endogenous transaction cost falls as the exogenous transaction decreases. We now consider the interval k ∈(k0, k1). For this case, since player 2 receives utility in autarky uA, and her threat to opt for autarky thus becomes credible, we must replace uL in table 9.5 with uA. Also, uH in table 9.5 is now given by (9.18) instead by (9.16). Using this information, we can ﬁnd player 1’s expected utility: q1q2uD + (1 − q1)q2uH + (1 − q2)q1uA + (1 − q1)(1 − q2)uA = q1q2uD + (1 − q1)q2uH + (1 − q2)uA, which monotonically decreases with q1 for a given q2. Hence, the optimum value of q1 is 0. Because of the symmetry, the optimum value of q2 is also 0. This implies that for k < k1 the equilibrium is autarky. Since k1 ≡ 2−2 a (1 + δ )2 /δ > k0 ≡ 22 (1− a ) , the subgame perfect equilibrium in the game to compete a greater share of gains from the division of labor is autarky, while the Nash bargaining equilibrium, which is Pareto optimal, is the division of labor for k ∈(k0, k1). In addition, the subgame perfect equilibrium is autarky with probability (1 − q)2 for

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k > k1, while the Nash bargaining equilibrium is the division of labor for certain. Therefore, the competition for a greater share of the gains from the division of labor generates endogenous transaction costs that may preclude the realization of mutually beneﬁcial division of labor. Compared to neoclassical game models that generate endogenous transaction costs, in the bargaining model of endogenous specialization the endogenous transaction costs cause not only inefﬁcient resource allocation, but also an inefﬁcient level of division of labor and inefﬁcient productivity. If you compare the result in this example to ﬁgure 4.1, the development implications of endogenous transaction costs will be clear. For k > k0, production takes place on the PPF in the absence of endogenous transaction costs; it takes place under PPF if the endogenous transaction cost is present.

9.5.4

How can endogenous transaction costs be eliminated by consideration of reputation?

Example 9.14: A model of endogenous specialization in a repeated game. If the pure strategy game in table 9.5 can be repeatedly played, then endogenous transaction costs may be eliminated due to the consideration of reputation. Assume there are inﬁnite periods t = 1, 2, . . . There is a stage game in each period, which is the same as the pure strategy game in table 9.5. Then in all periods there is a super game. In the super game, each player chooses a series of pure strategies to maximize her total discounted utility. It can be shown that in the repeated game, there is at least a Nash equilibrium that makes a cooperative outcome emerge from noncooperative behavior, or that eliminates endogenous transaction costs. We ﬁrst consider a proﬁle of two players’ series of strategies. Player 1 announces that he always chooses a soft strategy as long as player 2 does so, but he will choose a tough strategy forever if player 2 chooses a tough strategy in the previous period. Player 2 can ﬁnd that for this strategy of player 1 her total discounted utility for a soft strategy series is

uD S = uD (1 + δ + δ 2 + . . . . + δT ) =

1 − δT + 1 uD 1−δ

(9.21a)

where S can be solved from S − δS = (1 − δ)S = 1 − δT+1. This total discounted utility converges to uD/(1 − δ) as T tends to inﬁnity. If player 2 chooses a tough strategy in a period, her immediate utility is uH = δk/(1 + δ )2 > k/4. But her utility afterwards is always uA, because player 1 will refuse to cooperate. Hence, the total discounted utility for player 2 is uH + δ(1 + δ + δ2 + . . . + δt−1)uA = uH + δuA /(1 − δ).

(9.21b)

It is easy to see that (10.21a) is greater than (10.21b) iff uD > (1 − δ)uH + δuA

(9.22)

where uD = k/4 > uA = 2−2a for k > k0. Also uH = k/(1 + δ )2 > uD. It can be shown that if δ > 0.5, or if the discount rate is smaller than 100 percent, (10.22) becomes

k(4 2 + 2) > k0 (3 + 2 2 ) which holds for k > k0 because 4 2 + 2 > 3 + 2 2 .

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We may thus conclude that, provided players are not very impatient, the consideration of reputation can eliminate endogenous transaction costs, thereby making cooperation emerge from noncooperative strategic behavior. Here, long-run punishment for deviation from cooperation is the key to the result. The Folk theorem in game theory shows that there are many other Nash equilibria in the super game that can generate the same results, but with limited time for punishment of deviation. For instance, when a player chooses a tough strategy in the previous period, her opponent chooses a tough strategy for three periods and then comes back to a soft strategy afterwards. There are many institutional conditions that are essential for the reputation mechanism to work in eliminating endogenous transaction costs. Society must have a consensus about the moral code, and the legal regime must provide the appropriate enforcement for punishment of deviant behavior. For instance, if in an ancient tribe the “taking” of another’s possession was not considered punishable as stealing (or if Iraq’s invasion of Kuwait was not considered punishable), then the punishment for stealing (or invasion) could not be enforced. In a Sovietstyle economic system, private rights to residual returns and control of ﬁrms are not protected by law, so nobody will care about reputation, which generates residual returns. Again, if laws protecting business names, copyrights, and brands cannot be reasonably enforced, the reputation mechanism will not work either. Our model of repeated games shows that the consideration of reputation can reduce endogenous transaction costs caused by competition for a larger share of gains from division of labor, thereby increasing the equilibrium network size of division of labor and promoting economic development.

9.6 THE GROSSMAN–HART–MOORE INCOMPLETE CONTRACT MODEL Example 9.15: The GHM model of endogenous transaction costs caused by an incomplete contract and two-sided moral hazard. Consider a business venture between two players whose sales revenue may be high, R = 40, or low, R = 10, and whose operating costs may be high, C = 30, or low, C = 10. Player 1’s effort level x determines the probability of realizing the high level of sale revenue. Assume for simplicity that x ∈[0, 1], and that the probability equals x. The probability of the low level of revenue, R = 10, is then 1 − x. Player 2’s effort level y determines the probability of the business achieving the low level of operating costs, where y ∈[0, 1], and we assume that this probability equals y. The probability of the high level of costs, C = 30, is then 1 − y. Player 1 may be considered the salesman and player 2 the producer of goods, so that the proﬁt of their business is jointly determined by the two players’ effort levels. There are four potential outcomes for the business. Their probabilities are presented in table 9.6.

Table 9.6 Probabilities for four contingent states R

C

V

Joint probability

40 40 20 20

10 30 10 30

30 10 10 −10

xy x(1 − y) (1 − x)y (1 − x)(1 − y)

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Suppose, for simplicity, that a state of low revenue and high costs causes bankruptcy that yields zero proﬁt. Then the expected proﬁt of this joint venture is V = y(40 − 10) + x(1 − y)(40 − 30) + (1 − x)y(20 − 10) + (1 − x)(1 − y)0 = 10(xy + x + y) In order to illuminate the incentive problem and the related moral hazard, we assume that player 1’s utility is V1 − αx2, where V1 is the part of the proﬁt that he receives. Player 2’s utility is V2 − 5x2, where V2 is the part of the proﬁt that she receives. In this model, there are three periods. In period 1, two players sign a contract. In period 2, players choose their effort levels. In period 3, Nature chooses a state of outcome according to the prior distribution function of the states and the players’ effort levels. Then realized proﬁt is divided according to the contractual terms. If each player can see the other’s effort level so that there is no moral hazard, then they can work out their optimum effort levels from the following maximization problem and specify a contract that requires such effort levels in period 1: Max: W = V − αx 2 − 5y 2 = 10(xy + x + y) − αx 2 − 5y 2 s.t.

x, y ∈[0, 1]

where W is the two players’ total expected utility. Since ∂W/∂y = 10(1 + x − y) > 0 for all x, y ∈(0, 1), the optimum value of y is 1 according to the Kuhn–Tucker condition. The Kuhn– Tucker condition for maximizing W with respect to x then yields the optimum contractual terms, which are Pareto optimal, in the absence of moral hazard: y* = 1,

for α ≤ 10 ⎧1 x* = ⎨ / 10 α for α > 10, ⎩

Then, the Pareto optimum total utility generated by the business can be computed as follows: ⎧25 − α if α ≤ 10 ⎪ W * = ⎨100 + 5 if α > 10 ⎪ ⎩ α

For this case, the structure of ownership and residual rights makes no difference. Player 1 can claim all proﬁt and then pay player 2 according to her effort level; or player 2 can claim all proﬁt and then pay player 1 according to his effort level; or they can jointly claim the proﬁt and then divide this according to their effort levels. All three structures of ownership of proﬁt will generate the same outcome in the absence of moral hazard. We assume now that each player cannot see the other’s effort level, or cannot verify this in court when a dispute occurs. Hence, a two-sided moral hazard exists. In addition, complete contingent pricing of the four outcome states is prohibitively expensive, so that an incomplete contract is used to get the business going. An incomplete contract speciﬁes the ownership structure of the business and it broadens the scope for renegotiation, in which a difference in structure of ownership generates a difference in disagreement point, which affects the ex post bargaining power of players. We ﬁrst consider a symmetric structure of ownership, D. In this structure the two players are partners. They sort out the contractual terms through ex post Nash bargaining in period 3. The contractual terms between them provide for splitting the proﬁt. For the given terms, each

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player maximizes her expected utility (which is her share of proﬁt net of the disutility of her effort) in period 1, with respect to her effort level for a given effort level of the other party. Player 1’s expected utility is Eu1 = (V/2) − αx2 = 5(xy + x + y) − αx2 and his optimum effort level, for the given effort level of player 2, is x = 5( y + 1)/2α. Player 2’s decision problem in period 2 in anticipating the terms determined in ex post bargaining is Max: Eu2 = (V/2) − 5y2 = 5(xy + x + y) − 5y2 and her optimum effort level for the given effort level of player 1 is y = (x + 1)/2. The equilibrium is determined by the two optimum decisions. Considering possible corner solutions, the equilibrium is x = 0, y = 0

if α ∈(0, 5/4)

x=y=1

if α ∈(5/4, 5)

x = 15/(4α − 5), y = (2α + 5)/(4α − 5)

if α > 5

The total expected utility of the two players in structure D is WD = V − αx2 − 5y2 = 0

for α ∈(0, 5/4)

WD = 25 − α

for α ∈(5/4, 5)

WD = 10(xy + x + y) − ax2 − 5y2

for α > 5

which is lower than the Pareto optimum level of total expected utility W * if α ∈(0, 5/4) or α > 5, and is the same as the Pareto optimum if α ∈(5/4, 5). The difference represents the endogenous transaction costs caused by moral hazard and an incomplete contract. There are two asymmetric structures of ownership and residual rights. In structure A, player 1 is the owner of the business and claims its residual returns via his ex post bargaining power. Player 2 receives a reservation pay, which is exogenously given in the partial equilibrium model. For simplicity, we assume that the reservation pay is 0, so that player 2 will choose y = 0. The owner’s decision problem is Max: Eu1 = V − αx2 = 10x − αx2 The solution is x* = 5/α. The total utility of the two players is WA = 25/α which is smaller than in the Pareto optimum. Since only player 1 is accountable for the effect of his effort on outcome, residual control rights are considered asymmetric in this structure. Similarly, we can solve for the corner equilibrium in the asymmetric structure B, where player 1 receives the reservation pay and player 2 is the owner of the business. The solution is x = 0,

y = 1,

and WB = 5,

which again is smaller than in the Pareto optimum. Hence, each of the three structures of ownership and residual rights generates endogenous transaction costs. In structure D, the two players partly free-ride on their opponents’ efforts, so that a two-sided moral hazard causes

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Table 9.7 The equilibrium structure of ownership and inframarginal comparative statics

Equilibrium Structure

α ∈(0, 5/4)

α ∈(5/4, 43.2)

α > 43.2

A

D

B

endogenous transaction costs. These endogenous transaction costs are attributable to the moral hazard of player 2 in structure A, and of player 1 in structure B. Considering all possible outcomes, two players can always use some side-payment to choose the corner equilibrium with the highest total utility in period 1. An inframarginal analysis shows that for α ∈(0, 5/4), WA > WB > WD; for α ∈( 5/4 , 5), WD > WA > WB; for α ∈(5, 43.2), WD > WB, WA; and for α > 43.1, WB > WD > WA. Hence, the equilibrium and its inframarginal comparative statics can be summarized in table 9.7. Since player 2’s disutility coefﬁcient of effort is ﬁxed at 5, the disutility parameter of player 1’s effort α represents the relative disutility of effort of the two players. Hence, table 9.7 implies that the relative disutility of effort between the two players determines which structure of ownership is the equilibrium. If player 1’s disutility of effort is relatively small, then he will be the owner of the business (structure A) in the equilibrium. If player 1’s disutility of effort is relatively large, then player 2 will be the owner of the business (structure B). If the disutilities of two players’ efforts are close, then they will choose a symmetric relationship between partners (structure D). If the revenue and cost coefﬁcients are parameterized too, it can be shown that the player whose effort has the more signiﬁcant effects on proﬁt and who has the relatively lower disutility will be the owner of the business. If the effects of the two players’ efforts on proﬁt and disutility are close, then a symmetric structure of ownership and residual rights will occur in the equilibrium. Hence, this model veriﬁes the second part of the Coase theorem, that contracts in the market will maximize the gains from trade net of endogenous transaction costs if those costs are unavoidable.

9.7 NONCREDIBLE COMMITMENT AND SOFT BUDGET CONSTRAINT In this section, we consider the simplest version of the Dewatripont and Maskin model (1995) of the commitment game and the soft budget constraint. Example 9.16: The Dewatripont and Maskin model (1995). Consider a game with two regimes. In one of them, there is only a banker who is endowed with two units of capital. She considers making a loan to a project proposed by an entrepreneur. We call this the centralized case. In the other regime, there are two bankers, each with one unit of capital. We call this the decentralized case. There is uncertainty about the project, which could be good or bad. In addition, information is asymmetric: only the entrepreneur knows if his project is good or bad. A banker knows this only after the investment is made. There are two periods. If the project is good one, it is completed within one period and the banker receives a gross payoff R > 1 or a net payoff R − 1 > 0 when she invests one unit of capital in period 1. If the project is a bad one, it cannot be completed within one period and the banker must consider whether she should reﬁnance this project. If reﬁnancing takes place, the banker’s gross payoff is r with probability p, and 0 with 1 − p, where p is a function of the banker’s cost for monitoring the entrepreneur: C = bp2, where C is the total monitoring cost in period 1 and b is a coefﬁcient. We assume

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b ∈(r 2/8, r 2/4)

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(9.23)

The entrepreneur always receives payoff A if the project is completed; he receives payoff E if the project is not completed, regardless of whether the project is good or bad. It is assumed that A > 0 > E which implies that the entrepreneur always has an incentive to get a loan and complete the project. We ﬁrst consider the case of a good project which is completed in period 1 and generates net payoff R − 1 to the banker and A to the entrepreneur regardless of the regime. For a bad project, we can see that under a centralized system the banker has an incentive to reﬁnance the project if (9.23) holds. If she does not reﬁnance in period 1 after one unit of the loan has been made, her net payoff is −1. If she reﬁnances this project in period 2, she can maximize the expected net payoff pr − C − 2 with respect to p subject to C = bp2. The optimum expected net payoff is thus (r 2/4b) − 2, which is greater than −1 if (9.23) holds. But if (9.23) holds, the bad project generates a negative proﬁt, or (r 2/4b) − 2 < 0. It is inefﬁcient to undertake this project at all. This illustrates that due to information asymmetry and a centralized system, the commitment not to reﬁnance the bad project is not credible. Therefore, the soft budget constraint (reﬁnance) associated with this noncredible commitment generates endogenous transaction cost caused by reﬁnancing the bad project. Now we consider the case of two bankers, each with one unit of capital. Suppose that the project is bad, so that the ﬁrst banker cannot reﬁnance the project in period 2. In period 1, the ﬁrst banker maximizes αpr − C − 1 with respect to p subject to C = bp2. Here, α ∈(0, 1) is the fraction of gross payoff generated by the completion of the project that the ﬁrst banker receives, or 1 − α is the fraction of gross payoff received by the second banker, who reﬁnances this project. The optimum p is p* = αr/2b. Here, we assume that the second banker cannot observe the ﬁrst banker’s monitoring intensity. The second banker will not reﬁnance this project if her expected net payoff (1 − α)pr − C − 1 < 0, where p = αr/2b, or if (2 − 3α)αr 2 < 4b. Hence, if α > 2/3 , reﬁnancing will not take place. The entrepreneur who has the bad project will anticipate this, with his sequential rationality. Therefore, he will not ask for a loan from the outset. In other words, in a decentralized system, the commitment not to reﬁnance the bad project is credible, and thereby the budget constraint is hard. Hence, the bad project will not occur in equilibrium for α > 2/3. The model of soft budget constraint is widely applied to studies of transition economies. We will consider the applications in chapter 19. The entrepreneur, from her sequential rationality, knows the bank’s commitment not to reﬁnance is noncredible. She will push through the project. The literature of endogenous transaction costs is one of the most rapidly developing ﬁelds of economics. It includes the study of moral hazard, incomplete information, various game models with endogenous transaction costs (the sequential equilibrium model, models of commitment games, and so on), mechanism design, and models of incomplete contracts and residual rights. In addition to formal models, this literature includes many insights that have yet to be formalized, such as North’s ideas on the development implications of the institution and transaction costs, Barzel’s economics of the state (Barzel, 1997), Hayek’s thoughts on spontaneous order (Hayek, 1944), and Buchanan’s constitutional economics (Buchanan, 1991). We speculate that the formalization of these ideas will require game models that can predict the evolution of game rules (institutions). But so far, evolutionary game models can only predict the evolution of strategies and outcomes (see, for instance, Mailath, 1998 and Weibull, 1995). For instance, so far we do not understand how the institution that penalizes theft, which is essential for economic development, emerged. Much more formal analysis is needed for understanding the development implications of institutions and endogenous transaction costs caused by state opportunism and deﬁcient institutions.

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Key Terms and Review • • • • • • • • • • • • • • • •

Endogenous vs. exogenous transaction costs Moral hazard and related endogenous transaction costs The difference between moral hazard and adverse selection Risk-averse, risk-loving, and risk-neutral preferences Jesen inequality Certainty equivalence Incentive compatibility and participation constraint Functions of the contract, ownership, and residual rights Games, game rules, players, strategies, outcomes, payoff functions The strategic form and extensive form of a game Nash equilibrium, subgame perfect equilibrium, Bayes equilibrium, and sequential equilibrium Super games and stage games Effects of endogenous transaction costs on economic development The conditions under which reputation can be used to reduce endogenous transaction costs Residual returns, residual controls, two-sided moral hazard, and incomplete contracts How noncredible commitment and soft budget constraint cause endogenous transaction costs

Further Reading Surveys on principal–agent models: Arrow (1985), Hart and Holmstrom (1987), Prendergast (forthcoming), Holmstrom and Roberts (1998), Bolton and Scharfstein (1998), Gibbons (1998), and references there; The sharecropping model: Singh (1989) and Stiglitz (1974); The incomplete contract model and ownership structure: Hart (1995), Hart and Moore (1990, 1999), Grossman and Hart (1986), Holmstrom and Roberts (1998), Maskin and Tirole (1999), Tirole (1999), Segal (1999), Yang (2000b); Models of endogenous specialization and moral hazard: Yang and Yeh (2001), Lio and Yang (1997), Yang (2000); Models of moral hazard and adverse selection: Mas-Colell, Whinston, and Green (1995, chs. 6, 13, 14), Varian (1993, ch. 8); Literature of transaction costs economics and economics of property rights without formal models: Williamson (1975, 1985), Barzel (1982, 1985, 1989), Furubotn and Pejovich (1974), Cheung (1970, 1983), North (1990); New political economy models with endogenous stealing: Marcouiller and Young (1995), Skaperdas (1992); General equilibrium models of moral hazard: Helpman and Laffont (1975), Legros and Newman (1996), Kihlstrom and Laffont (1979); Two-sided moral hazard: Bhattacharyya and Lafontaine (1995), Cooper and Ross (1985), Eswaran and Kotwal (1985), Romano (1994); Models with endogenous specialization and endogenous transaction costs caused by information asymmetry: Laffont and Tirole (1986), Lewis and Sappington (1991); The Coase theorem: Coase (1960), Cooter (1989); Implications of endogenous transaction costs and institutions for economic development: North and Weingast (1989), North (1970, 1981), Macfarlane (1988), Mokyr (1990, 1993), Sachs (1997), Rosenberg and Birdzell (1986), World Bank (1997); A good general text and references on formal models of endogenous transaction costs: Milgrom and Roberts (1992). A good introduction to game theory: Dixit and Nalebuff (1991, pp. 7–84); Nash games and Nash equilibrium: Kreps (1990, p. 328), Fudenberg and Tirole (1991, p. 14); Nash equilibrium with mixed strategies: Fudenberg and Tirole (1991, pp. 18–19), Kreps (1990, ch. 11), Fudenberg and Tirole (1991, ch. 2), Tirole (1989, ch. 11); Nash’s axiomatic game model: Osborne and Rubinstein (1990). Bayesian games: Dixit and Nalebuff (1991, ch. 2); intermediate texts can be found in Tirole (1989, ch. 11) and Kreps (1990, ch. 13), Fudenberg and Tirole (1991, ch. 6); Subgame perfect equilibrium, or perfect equilibrium: Dixit and Nalebuff

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(1991, chs. 6 and 11), Tirole (1989, ch. 11) and Kreps (1990, secs. 12.7 and 15.3), Fudenberg and Tirole (1991, ch. 4); Test: Duplicate the algebra in Kreps (1990, p. 556) or Tirole (1989, pp. 430–1), Fudenberg and Tirole (1991, ch. 2); Nash bargaining games: Nash (1950), Osborne and Rubinstein (1994), Gibbons, R. (1992), Fudenberg and Tirole (1991), Kreps (1990), Tirole (1989), Dixit and Nalebuff (1991); Alternatingoffer bargaining games: Rubinstein (1982, 1985), Kreps (1990), Fudenberg and Tirole (1983, 1991), Osborne and Rubinstein (1990), Binmore, Osborne, and Rubinstein (1990), Stahl (1972); The function of price: Gale (1986), North (1987), Hayek (1945), S. Grossman (1989); Information efﬁciency of Walrasian equilibrium: Hurwitz (1973); Endogenous transaction costs caused by trade conﬂict: Cheng, Sachs, and Yang (2000); Super games (repeated games): Fudenberg and Tirole (1991, sec. 4.3), Tirole (1989, sec. 6.3, pp. 247–51) and Kreps (1990, sec. 14.2, pp. 509–12); Sequential equilibrium and perfect Bayes equilibrium: Laffont and Tirole (1986), Lewis and Sappington (1991), Qian (1994), Kreps and Wilson (1982), Tirole (1989, pp. 436– 44), Kreps (1990, secs. 12.7 and 13.2), Fudenberg and Tirole (1991, ch. 8), Farrell and Maskin (1989), Fudenberg and Tirole (1983); Commitment games and soft budget constraints: Dewatripont and Maskin (1995), Maskin (forthcoming), Qian (1994), Maskin and Xu (1999), Roland (2000).

QUESTIONS 1 According to the economics of property rights, the most important thing for economic development is not to win a game, but rather to choose game rules that determine who is the winner. If you try to design a dynamic game with information asymmetry to predict the evolution of game rules, what results (dynamics and comparative dynamics) will you expect from this kind of model? 2 According to North (1981), Macfarlane (1988), Sachs, Huang (1991), and Mokyr (1990, 1993), the following conditions were essential for the Industrial Revolution in Britain, 1750–1830. The transportation conditions were good enough for the development of division of labor. Geographical conditions ensured that Britain could avoid war with other countries at low defense expenses, while ensuring the country had a transportation advantage for trade. A constitutional monarchy and parliamentary democracy provided long-run political stability. The pursuit of riches was legitimated under the prevailing ideology, so that talents were diverted from military, religious, and bureaucratic careers to business activities. Political variety among countries in Europe and decentralized political power in Britain encouraged experiments with new ideas, institutions, and technologies. Secured property rights, including the rights to intellectual property, encouraged invention and innovation. A stable and nonpredatory tax system and the government’s laissez faire policy encouraged business activities. The liberation of civil society with respect to the state and the separation of the Crown’s coffer from the Bank of England enriched the creativity of society and restrained rent seeking. Equity Law made Common Law very adaptive to changing economic and social conditions in the presence of justice. Free association (i.e., the setting up of private ﬁrms needed no approval and license from the government) provided a favorable environment for free enterprise. Analyze which of these economic conditions are essential for a developing country in the twenty-ﬁrst century. Use a speciﬁc country case to illustrate your point. Analyze which of the conditions have yet to emerge in this country, and what can be done to encourage them. 3 Why can rational behavior generate coordination failure? Why can a coordination failure between two players in a Nash game be a coordination success for society as a whole? Why can the Nash equilibrium in a noncooperative game converge to a

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5

6

7 8 9

10

295

Walrasian equilibrium if the number of players tends to inﬁnity and free entry is allowed? According to Baechler (1976), a variety of polities and rivalry between hostile sovereigns in the region was the critical condition for industrialization to take place ﬁrst in Europe. But as Baechler observes, all power tends toward the absolute. Use the model of the prisoners’ dilemma to analyze why the princes in Europe could not coordinate with each other to establish a political monopoly. Baechler believes that the well-developed feudal system, the Church, and geopolitical diversity provided checks and balances on state powers and were responsible for the political fragmentation of Europe. Can you use a game model to formalize his conjecture? According to Mokyr (1990, 1993), the Chinese Emperor’s political monopoly and the cultural monopoly of Confucianism in east Asia prior to the nineteenth century were detrimental for the economic development of that region. Analyze why such a monopoly could prevail during that period. Cheung (1969) argues that sharecropping is a way to efﬁciently share risk if there are transaction costs in measuring work effort. Cheung has even found empirical evidence that land reforms are detrimental to economic development. Show that in example 9.2, if there is no moral hazard, risk sharing itself does not necessitate sharecropping. In example 9.2, we implicitly assume that the market for insurance is not available. If a well-developed market for insurance, labor, and capital is available, is sharecropping still the second best? What is the trade-off between the generality of game rules and the generality of other aspects of a model in specifying an equilibrium model? Why do economists sometimes specify ad hoc demand functions and use misleading partial equilibrium analysis in game models? Why can the perfect Bayes equilibrium model and sequential equilibrium have signiﬁcantly higher explainatory power than the Walrasian equilibrium model? What are the differences and connections between interactions of quantities and prices in a Walrasian equilibrium model, and interactions of information and dynamic strategies in a sequential equilibrium model? Consider the ownership structure in the equipment rental market. TV sets, video cameras, diggers, buckets, and other machines and equipment can be owned by their users or rented from owners. Apply the theory of optimum ownership structure based on the GHM model to analyze the endogenous and exogenous transaction costs associated with the two structures of ownership. Identify the conditions under which each of the two structures is the general equilibrium. Use the example to illustrate why the theory of optimum ownership may have nothing to do with the institution of the ﬁrm. Holmstrom and Roberts (1998, p. 85) indicate that in the incomplete contract model in example 9.15, the institution of the ﬁrm is not well deﬁned. They use BskyB, a satellite broadcasting system in Rupert Murdoch’s media empire, as an example to illustrate the shortcomings of the GHM model. BskyB is a highly successful organization that has created its wealth not by owning physical assets, but by crafting ingenious contracts that have given it inﬂuence over an effective network of media players. Satellite broadcasting requires a variety of highly complementary activities, including acquisition and development of programming, provision of the distribution system (satellites, transmitters, and home receivers) and development of encryption devices (to limit reception to those who pay), all of which must occur

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13

14

15

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before the service can be offered. Other similarly complex and innovative systems of complements, like electric lighting systems or early computer systems, were largely developed within a single ﬁrm. BskyB instead relies on alliances with other ﬁrms. Topsy Tail is even more of a “virtual company.” It employs three people, but has sales of personal appearance accessories (combs, hair clips, and such) approaching $100 million. Topsy Tail conceives of new products, but essentially everything involved in developing, manufacturing, and distributing them is handled through an extensive contractual network. Benetton and Nike, to take some bigger and more conventional ﬁrms, also extensively rely on outsourcing and a small asset base. The critical asset in these cases is of course control of the brand name, which gives them enormous power to dictate how relationships among the various players are to be organized. Use these cases to discuss the difference between the theory of the ﬁrm in chapter 8 and the incomplete contract theory in example 9.15. Why, for the sake of her own self-interest, must an individual ensure that her opponent receives a sufﬁciently large share of the gains from the division of labor? Some economists claim that the Nash bargaining game is a cooperative game that does not capture the noncooperative nature of the bargaining process. Comment on this claim in relation to Nash’s view about the connection between the nature of a Nash bargaining game and marginal disturbance. Hurwicz (1973) shows that the Walrasian regime involves the lowest exogenous cost in collecting and transmitting information. But as we have shown in example 9.11, the Walrasian regime in the new classical framework with a ﬁnite set of consumerproducers may generate trade conﬂict that result in endogenous transaction costs. Use the trade-off between endogenous transaction costs caused by trade conﬂict in the Walrasian equilibrium, and endogenous and exogenous information costs in a Nash bargaining game, to explain the phenomenon that impersonal pricing in the Walrasian regime becomes increasingly more important than individual speciﬁc pricing in bargaining as the network size of division of labor becomes increasingly large. Relate your discussion to North’s point that impersonal pricing is essential for reducing transaction costs and promoting division of labor. Why does the Walrasian equilibrium model involve more information asymmetry than the sequential equilibrium model? Analyze the function of the invisible hand in promoting information asymmetry that generates economies of division of labor and in restricting endogenous transaction costs caused by information asymmetry in a Walrasian equilibrium model with endogenous specialization. Friedman uses a story about the manufacturing of pencils to illustrate how the price system transmits information in such a way as to keep individuals away from what they need not know. When the price of timber increases, the manufacturer of pencils doesn’t need to know if the rise is caused by a devastating forest ﬁre, by a change of consumers’ tastes for furniture, or by some technical change in the other sector. If the level of division of labor is very high, exogenous transaction costs in collecting information about utility and production functions of trade partners, which is essential for bargaining, as described in examples 9.8 and 9.9, will be enormous. But impersonal pricing in the Walrasian regime can avoid all of these exogenous transaction costs. Use the example to illustrate how the invisible hand promotes information asymmetry and the related economies of division of labor while restraining the costs of information transmission.

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18 19

20

21

22

297

Draw a distinction between fair pricing in the Nash bargaining game and equal income distribution, and discuss the implications of the distinction for the debate about “trade-offs between efﬁciency and equity.” Analyze the signiﬁcance of a legal system that protects the residual rights of the owners of the ﬁrm, and of laws protecting brands, copyrights, and business names, in enabling the mechanism of reputation to play its role in reducing endogenous transaction costs. Why does Hart claim that the principal–agent model is not part of the formal theory of the institution of the ﬁrm? John is considering establishing a business with his Russian partner to publish a Directory of American Businesses in Russian. He hopes the business will make money by including advertisements from American companies in the book and from sales revenue net of printing costs in Russia. Suppose John approaches you to seek advice about which of the following three structures of ownership he should choose: (a) He hires the Russian partner to do the job in Russia and he himself takes care of the job in the US. (b) He enters a joint venture with the partner. (c) He asks for a salary from his Russian partner to pay for the job that he takes care of, which must be done in the US. Outline your advice, which is of course dependent on speciﬁc business conditions about which you may make assumptions. For instance, if the Russian legal framework and enforcement of laws are not good, then the Russian partner’s special personal connections to government ofﬁcials and his related efforts may be important for reducing the risk, so that a joint adventure is more likely to be a better choice than an arrangement in which John hires the Russian partner. According to Weber (1961, pp. 251–2) and North (1981, pp. 158–67), a variety of institutions and business formats dating back to medieval times, such as the annuity bond, the stock certiﬁcate, the bill of exchange, the private commercial company, the private bank, the mortgage, security of registration with the deed of trust, was essential for the industrialization of Europe in the nineteenth century. Use the models in this chapter to explain why the institutions were essential for economic development. According to Mokyr (1993, p. 41), the gentriﬁcation of the commercial and industrial class in Britain in the eighteenth and nineteenth centuries had a positive effect on early economic development, but was blamed for the decline of Britain’s leadership in the Victorian age. Also, industrial standardization, developed on the European continent and in the US, swept over Britain in the second wave of industrialization. This implies that the rivalry between Britain and other European countries was a competition between different game rules which provide the elite with incentives to contribute to the inﬂuence and power of their home country in the international arena. “Inﬂuence” and “power” are based on economic development performance. Design a game model to explore the implications of this kind of game for economic development in Europe and the North Atlantic in the nineteenth century. Many institutions reduce endogenous transaction costs of one type while increasing endogenous transaction costs of another type, as suggested by Milgrom and Roberts’ model of entry deterrence (see exercise 4), where an increase in endogenous transaction costs caused by information asymmetry is associated with a decrease in endogenous transaction costs caused by monopoly. Also, patent laws reduce transaction costs in specifying and enforcing rights to intellectual property, while increasing endogenous transaction costs caused by monopoly. The institution of the ﬁrm,

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together with business secrecy, can protect entrepreneurial ideas in the absence of patent laws. But the protection is not as effective as that which patent laws can provide (Mokyr, 1993). Analyze the trade-offs between different transaction costs associated with different institutions. Use the historical documentation about the beneﬁts and costs of patent laws and the institution of the ﬁrm provided by North (1981, p. 165), Rosenberg and Birdzell (1986, pp. 144–64), and Mokyr (1990, pp. 248–54, 1993, pp. 40–6, 58–70) for your analysis. North (1958, 1986) has found empirical evidence of a negative correlation between freight rates and economic development, and of concurrent evolution of the income share of the transaction sector and per capita real income. However, this empirical evidence is relevant only to exogenous transaction costs. Endogenous transaction costs are much more difﬁcult to measure. Can you ﬁnd a way to test the theories of endogenous transaction costs developed in this chapter against empirical observations?

EXERCISES 1 The battle of the sexes: in a game, two players wish to go to an event together, but disagree about whether to go to football or a ballet. Each player gets a utility of 2 if both go to his or her preferred event, a utility of 1 if both go to the other’s preferred event, and 0 if the two are unable to agree and stay home or go out individually. Suppose the two players agree to randomize their choices to make sure it is fair for both players to participate in the game. So he chooses the football game with probability p1 such that her expected utility is indifferent between the choices of football game and ballet, and she chooses the ballet with probability p2, such that his expected utility is indifferent between the two choices. Show that there are two pure strategy Nash equilibria and solve for the mixed strategy Nash equilibrium. Nash uses a ﬁxed point argument to prove that for any mixed strategy Nash game, there exists a Nash equilibrium. 2 Suppose in the Nash (Cournot) equilibrium model of oligopoly in example 9.6, the inverse demand function p = a − bx involves uncertainties. With probability ρ, a = θh and with probability 1 − ρ, a = θl. Firm 2 has private information about the realized value of a after Nature has chosen this. But ﬁrm 1 has only common knowledge about a. Solve for the Bayes equilibrium. If it is b instead of a that involves uncertainty, what is your answer? 3 Consider the Bayes game model in example 9.6 again. Assume that information asymmetry is symmetric between the two ﬁrms: ci involves uncertainties for i = 1, 2 and ﬁrm i has complete information about ci but has incomplete information about cj. The distribution function for c1 and c2 is the same as that speciﬁed in example 9.6. Use the symmetry of information asymmetry to solve for the Bayes equilibrium. 4 The entry deterrence game, Milgrom and Roberts, 1982: In a dynamic game with information asymmetry, there are two players. Player 1 is an incumbent ﬁrm producing a good, called the insider. Player 2 is a potential entrant into the business, called the outsider. The inverse demand function of the good is p = 9 − x. The insider’s cost function is θx + 2.25, where θ = 3 with probability ρ and θ = 1 with probability 1 − ρ. The insider knows the realization of θ, but the outsider

C HAPTER 9: E NDOGENOUS T RANSACTION C OSTS

5

6

7

8

does not. The outsider’s cost function 3x + 2.25 is common knowledge to all players. In period 1, the insider chooses an output level that will give the outsider some signal about the type of the insider, which will in turn affect the outsider’s decision concerning entry in period 2. The outsider maximizes her expected proﬁt in period 2 with respect to the quantity to produce, and decides whether to enter the sector for given information updated from the observation of the insider’s output in period 1. The insider maximizes total proﬁt over the two periods with respect to his output levels in those periods. He is the monopolist in period 1, and again in period 2 if the outsider does not get into the business then. The two ﬁrms have a Cournot equilibrium in period 2 if the outsider gets into the business in period 2. Find the two ﬁrms’ output levels in the two periods, the posterior probability μ(p1) for θ = 3 when the outsider has seen the market price in period 1, p1, the market prices over the two periods in the pooling equilibrium and screening equilibrium for the relevant interval of values of ρ. What is the outsider’s decision concerning entry upon observation of the insider’s output level in period 1? Suppose that the cost function and demand function in a Bentrand model are the same as in the Cournot model, but the two ﬁrms’ strategies are to choose prices rather than quantities. Solve for the Nash equilibrium and prove that it is Pareto optimal. Consider the model in example 9.1. Assume that the probability for R = 16 is θ > 0.5 and that for R = 4 is 1 − θ when effort level is high. The probability for R = 4 is θ and that for R = 16 is 1 − θ when effort level is low. The agent’s utility function is ln w − ln e. Solve for the efﬁcient contract. Consider the model in example 9.3. Assume that the transaction efﬁciency coefﬁcient of good y is k1 for M1 individuals of type 1 and is k2 for M2 individuals of type 2. M1 + M2 = M. Apply inframarginal analysis to solve comparative statics of equilibrium. Note that the utility equalization condition no longer holds between the two different types of individual and more structures with incomplete division of labor are possible. Consider the two-sided moral hazard model in example 9.15. Assume that the parameters are modiﬁed as follows. R

C

V

Joint probability

20

5

15

xy

20

10

10

x(1 − y)

10

5

5

(1 − x)y

10

10

0

(1 − x)(1 − y)

Solve for the general equilibrium and its inframarginal comparative statics. 9 Consider the model in example 9.11. Assume that good x is a producer good, and that utility equals the amount of good y consumed. The production function of y is y + y s = (x + kx d )0.5Ly and the production function of x is x + x s = Lx − a. Solve for the Nash bargaining equilibrium and its inframarginal comparative statics. 10 Assume that player i’s endowment of labor is ai in the model in the preceding exercise. Solve for the Nash bargaining equilibrium and analyze the effects of the relative values of threat points on the relative bargaining power of a player.

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Assume that player i’s discount factor is δi in the model in example 9.5. Solve for the subgame perfect equilibrium in the alternating-offer bargaining game. Analyze the effects of relative degree of impatience (the relative value of δ1 and δ2) and ﬁrst mover’s advantage on the relative bargaining power of a player. In the following bargaining models, what are the determinants of the relative bargaining power of a player? (a) The bargaining model in exercise 10; (b) The bargaining model with information asymmetry in example 9.12; (c) The alternatingoffer bargaining game in exercise 11. Consider the model in example 3.2. Assume that the two governments are allowed to choose between two trade regimes: Nash tariff bargaining and free trade. Suppose there is a cost coefﬁcient c in terms of utility loss caused by the collection of information that is essential for sorting out the Nash bargaining solution. Work out the critical value of c below which the Nash bargaining solution is the general equilibrium. Consider the strategic form of the Nash game in the prisoners’ dilemma model. Each of two criminals can choose the strategy “confess” or “not confess” when caught by police. Their payoffs for four possible outcomes of the game are listed as follows: Prisoner 2 Not confess

Confess Prisoner 1: Confess Not confess

15

16

−5

−5

1

−10

−10

1

0

0

where the ﬁrst ﬁgure in each entry is the payoff to prisoner 1. Identify the Nash equilibrium. Yang, 2000b: Introduce two-sided moral hazard into the model in example 8.1. Assume that transaction efﬁciency coefﬁcients are random variables, dependent on buyers’ efforts in reducing transaction risk. The coefﬁcients are structure speciﬁc since monitoring efﬁciency differs between goods and labor. In structure D (see ﬁgure 8.1), the transaction efﬁciency coefﬁcient of good i, ki = θi with probability si sj and ki = 0 with probability 1 − si sj where si is the effort level of a buyer of good i = x, y. In structure E, the transaction efﬁciency coefﬁcient of good y, ky = θy with probability rx sy and ky = 0 with probability 1 − rx sy where ri is the effort level of a buyer of labor used to produce good i in avoiding transaction risk. The transaction efﬁciency coefﬁcient of labor used to produce good x is tx = μx with probability rx sy and tx = 0 with probability 1 − rx sy. In structure F, ky = θy with probability ry sy and ky = 0 with probability 1 − ry sy. The transaction efﬁciency coefﬁcient of labor used to produce good y, ty = μy with probability ry sy and tx = 0 with probability 1 − ry sy. θi and μi are parameters for good i and for labor used to produce good i, respectively. Solve for the inframarginal comparative statics of equilibrium. Yang and Yeh, 2002: Consider a model with two ex ante identical consumerproducers. Each of them can produce a ﬁnal good y and an intermediate good x. Each person’s utility function is: U = ln[( y + ky d )s] where y and y d are the quantities of the ﬁnal good self-provided and purchased, respectively. k is the trading efﬁciency coefﬁcient. The production functions for the ﬁnal and intermediate goods are y p ≡ y + y s = (x + kx d )Ly

C HAPTER 9: E NDOGENOUS T RANSACTION C OSTS

if Lx = βH,

then

⎧θ H with probability ρH x p ≡ x + xs = ⎨ ⎩θL with probability 1 − ρH

if Lx = βL,

then

⎧θ H with probability ρL x p ≡ x + xs = ⎨ ⎩θL with probability 1 − ρL

where superscript s stands for the amount sold and x and x d are the quantities of the intermediate good self-provided and purchased, respectively, Li is the amount of labor allocated to produce good i = x, y. It is assumed that L > βH > βL > 0, θH > θL > 0, 1 > ρH > ρL > 0. Each individual is endowed with L units of time that can be allocated between working and leisure, so that the endowment constraint for each person is Lx + Ly + s = L, where s is time allocated for leisure. Solve for inframarginal comparative statics of general equilibrium. (Hint: the algebra is cumbersome and the answer can be found in Yang and Yeh, 2002.)

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TRANSACTION RISK, PROPERTY RIGHTS, INSURANCE, AND ECONOMIC DEVELOPMENT

10

10.1 UNCERTAINTIES IN TRANSACTIONS AND THE ECONOMICS OF PROPERTY RIGHTS Mokyr (1993, pp. 40–58, 158–62,) provides historical evidence that one of the major conditions for the British Industrial Revolution in the years 1760–1830 was well speciﬁed and enforced private property rights. He summarizes (pp. 56–8): “The speciﬁc form of government that had emerged in Britain created an environment that was more conducive to economic development than elsewhere. Most important, the right to own and manage property was truly sacrosanct, contrasting sharply with the conﬁscations and conscriptions on the Continent during the French Revolution and Napoleonic era. Personal freedom – with some exceptions – was widely accepted in Britain . . . Nowhere in the world was property perceived to be more secure than in Britain.” North (1981, pp. 158–62) comments: “It was better speciﬁed property rights (not the same thing as laissez faire) which improved factor and product markets . . . The resultant increasing market size induced greater specialization and division of labor, which increased transaction costs. Organizational changes were devised to reduce these transaction costs and had the consequence of radically lowering the cost of innovating at the same time that the increasing market size and better speciﬁed property rights over inventions were raising the rate of returns on innovating. It was this set of developments which paved the way for the real revolution in technology.” Mokyr (1993, p. 44) concurs with him: “Property rights in innovation (patents and trademarks), better courts and police protection, and the absence of conﬁscatory taxation are examples of how the same phenomenon could raise the rate of innovative activity and capital accumulation.” North and Weingast (1989) survey the institutional changes that occurred in Britain in the wake of the Glorious Revolution of 1688, in which wealth holders increased their grip on power, and the government was put on a sound ﬁscal footing and committed itself to respect the existing distribution of property rights. They point to secure contracting and property rights as a precondition for specialization and impersonal exchange. Mokyr (1993, p. 45) also indicates: “By taxing according to prespeciﬁed and well-understood rules, and by gradually abandoning the

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Tudors’ and Stuarts’ reliance on monopoly rights as a source of crown revenues, the post-1689 regime continued a trend that had begun long before and was certainly well established by the Restoration of 1660.” On the other hand, Mokyr regards conﬁscatory taxation in France as an obstacle to economic development (1993, p. 44). Similarly, he (1990, p. 238), Fairbank (1992), and Baechler (1976, p. 82) consider the violation of private entrepreneurs’ property rights under the Ming and Qing dynasties as crucially detrimental for China’s economic development. Yang, Wang, and Wills have also found empirical evidence for the relationship between economic development, evolution of division of labor, and better speciﬁed and enforced property rights. In this chapter, we use Smithian models of endogenous network size of division of labor to study the intimate relationship between economic development, enforcement of property rights, and insurance. In section 10.2, we introduce a transaction risk into each transaction in a model of endogenous specialization. This will generate a trade-off between economies of division of labor and the reliability of the larger network of transactions required by the ﬁner division of labor. Since aggregate transaction risk is an exponential function of the number of transactions, the transaction risk that can be caused by unsecured property rights is a much more important brake to economic development than tangible transportation costs. The problem of coordination reliability of division of labor is important in our daily decisionmaking processes. Because of this problem many individuals do not want to specialize in a particular activity. As an individual increases her level of specialization, she becomes more dependent on other specialists whose products are essential for her consumption and production. Since the division of labor is associated with an input–output network which involves a series connection of many individual specialists, the whole network may fail to work if one of the links in the series connection fails to work. Therefore, the aggregate risk of coordination failure of the network of division of labor increases more than proportionally as the levels of specialization and division of labor increase. In the Soviet-style centrally planned economy of China, a ﬁrm was reluctant to specialize in an activity and tried to self-provide many services, such as setting up its own kindergarten, primary school, cafeterias, and many intermediate goods and services. This reﬂected the high risk of coordination failure resulting from restrictions on free trade. In 1994, one of the 115 automobile companies in China assembled less than 100,000 cars annually and self-provided 80–90 percent of their intermediate goods (see Lardy, 1998a). In the relatively free market system of the US, in contrast, there are only 4 automobile companies assembling cars. Each of them produces more than a million cars annually and less than 40 percent of the necessary intermediate goods (Webster et al., 1990). Recent economic development in the US is associated with the boom in franchise networks, which features a ﬁner division of labor between specialized production of entrepreneurial ideas by franchisers and specialized production of tangible services by franchisees. This feature of economic development in the US is based on more reliable enforcement and protection of rights to intangible entrepreneurial knowledge, such as those included in operations manuals and reputations. The trade-off between economies of division of labor and coordination reliability implies that taking a higher aggregate risk of coordination failure may be efﬁcient so long as the economies of division of labor that can be exploited outweigh the increased aggregate risk. If an improvement in the transportation conditions enlarges the scope for trading-off economies of division of labor against the aggregate transaction risk, the efﬁcient aggregate transaction risk and productivity may increase side by side. Such a higher efﬁcient aggregate risk for coordination failure may be associated with an episode such as the Great Depression in 1930 and the Asian ﬁnancial crisis in 1997. In the 1920s, as a result of successful industrialization in western Europe and the US, a large network of domestic and international division of labor was developed. While on the one hand this high level of division of labor raised productivity and

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created historically unprecedented prosperity, on the other hand it signiﬁcantly increased the risk of coordination failure of the network of division of labor. In that network, many very specialized sectors are connected in a series, so that it might fail to work when one of the professional sectors, such as the banking sector, fails to work; resulting, for example, in the Great Depression and mass unemployment. In other words, the greater risk of an economic crisis caused by the higher risk of coordination failure is endogenously and efﬁciently chosen by individuals, just as we choose a higher risk of being killed when we decide to drive on the freeway by efﬁciently trading-off the cost of doing so against the beneﬁt. Hence, the relationship among economic development, coordination reliability, and property rights is much more sophisticated than the statement that better enforced property rights are conducive to economic development, might lead us to believe. In particular, if the risk of coordination failure for each transaction can be reduced by inputting resources, that risk then becomes an endogenous decision variable. The risk of coordination failure of division of labor can be reduced by allocating resources to the speciﬁcation and enforcement of contractual terms at the cost of rising exogenous transaction costs in specifying and enforcing property rights. We can consider the welfare losses caused by the risk of coordination failure as anticipated endogenous transaction costs caused by the opportunistic behavior examined in chapter 9. Thus, we have a trade-off between the exogenous transaction costs of specifying and enforcing property rights and endogenous transaction costs. We can then see that the efﬁcient trade-off between endogenous and exogenous transaction costs in the marketplace may involve imperfect speciﬁcation and enforcement of property rights. A monthly ticket for a train or bus is an example that illustrates the implications of this trade-off. A monthly ticket does not precisely specify the correspondence between the riding fee and the amount of transport services (number and distance of rides) provided, and it may encourage inefﬁcient travel that generates endogenous transaction costs. However, it involves much lower exogenous transaction costs in collecting payment for each ride than many singleride tickets. Another example might be the arrangements for ﬁnancing construction of a bridge. There are different ways to ﬁnance a bridge. One is for the government to use tax revenue to ﬁnance it. Under this arrangement, individuals who never use the bridge are compelled to pay the tax while others pay no more for frequent use of it. This will generate distortions, which are endogenous transaction costs, so that, relative to the Pareto optimum, the output of the former type of individual is too little compared to that of the latter type. However, this arrangement does not involve many exogenous transaction costs in collecting fees from the users of the bridge. The other way is to allow a private company to construct the bridge and to collect fees from users. This method avoids endogenous transaction costs at the expense of the exogenous transaction costs of collecting fees. The most efﬁcient method is the one with the minimum sum of the two types of transaction costs. If the exogenous transaction costs saved by ﬁnancing the bridge through government taxes outweigh the endogenous transaction costs generated by the tax arrangement in comparison to the arrangement without the tax, then government ﬁnance can be used to promote division of labor and economic development, or to play a role in rectifying “market failure.” Otherwise, the government tax may generate “government failure” and restrict the market from fulﬁlling its function. In many less-developed countries, the government does not know how to use public ﬁnance to develop an infrastructure that promotes evolution of division of labor and related urbanization and economic development. On the other hand, in Soviet-style centrally planned economies, governments extend public ﬁnance to the degree that the market cannot play its role in the development process. The two extreme cases illustrate that it is not easy to ﬁnd the efﬁcient trade-off between endogenous and exogenous transaction costs.

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One more example of the trade-off between endogenous and exogenous transaction costs in relation to coordination reliability is provided by a comparison of a piece-rate wage system with an hourly wage. If the quantity and quality of the job to be done can be precisely measured, the piece-rate wage can be used to precisely specify and enforce contractual terms and thereby reduce the risk of coordination failure of the network of division of labor. However, precise measurement of the quantity and quality of the job may involve prohibitively high exogenous transaction costs. If these costs are taken into account, an hourly wage with more vague contractual terms and with low exogenous transaction costs may be more efﬁcient than a piece-rate wage, despite the fact that the former generates much higher endogenous transaction costs than the latter. The trade-off between exogenous and endogenous transaction costs is referred to by Milgrom and Roberts (1992, pp. 277, 377) as the trade-off between inﬂuencing cost and distortions caused by rigid rules intended to reduce employees’ ability to inﬂuence the decisions of their manager. We will consider the relationship between this interesting trade-off and economic development in section 10.3. In that section we will also consider one of the market mechanisms that can reduce the risk of coordination failure of a large network of division of labor. This mechanism employs competition between peer specialist suppliers to provide so-called parallel connections to the incumbent supplier that can signiﬁcantly reduce the risk of coordination failure. But it involves cost for a buyer to keep in touch with many potential peer suppliers, so there is a trade-off between the costs in deepening the incumbent trade relationship and the costs in broadening potential trade relationships, in addition to the trade-off between economies of division of labor and all kinds of transaction costs. We shall consider the implications of this trade-off for economic development. Another institution that can be used to expand the network of division of labor is insurance. In section 10.4 we use a model of endogenous specialization to show why insurance can promote division of labor and economic development. Then the trade-off between risk sharing and incentive provision is speciﬁed in section 10.5, which also investigates the function of incomplete insurance in reducing endogenous transaction costs caused by moral hazard and in promoting economic development. Since incentive provision is associated with precisely enforced property rights, we have a trade-off between the positive effect of insurance on the reliability of the network of division of labor and the negative effect of insurance on the precise enforcement of property rights. This trade-off implies that the development implications of property rights are much more complicated than many economists have realized. The disappointing development performance of Russia and eastern Europe in the early 1990s illustrates the point. The Soviet Union mimicked the pattern of industrialization in the capitalist economies by developing a high level of division of labor through a central planning system. Each state or republic in the Soviet Union, or in the communist block of eastern Europe, was required to specialize in a particular sector. For instance, the Ukraine specialized in producing grain, Czechoslovakia specialized in producing locomotives, and Bulgaria specialized in producing fruit and vegetables. On the one hand, this high level of division of labor generated quite impressive development performance in the 1930s and 1950s. But on the other hand, it also signiﬁcantly reduced the coordination reliability of the noncommercialized network of division of labor. A system of complete insurance was developed to reduce coordination failure of the large network of division of labor, while generating pervasive moral hazard. In a Soviet-style economic system there is complete insurance for each employee in a state enterprise. She can obtain complete medical insurance, she will never lose her job (a complete unemployment insurance), and she will receive a pension no matter what happens to her job, to her health, or to the enterprise that hired her (a complete insurance for pension payment). Also, each state enterprise is insured by the government through soft budget constraint against all kinds of risk in business operation. In China, such complete insurance is referred to as the

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“iron rice bowl.” It generates a great deal of endogenous transaction costs associated with moral hazard on the one hand, and provides complete insurance that can maintain a reasonable coordination reliability of the network of division of labor on the other. In Russia’s reforms in the early 1990s, this form of complete insurance was abolished when an alternative insurance system had not yet been developed in the market. Hence, breakdown of an enterprise, sector, or link between two states generated spectacular coordination failure of the whole network of division of labor, resulting in the disappointing development performance of the Russian economy in the 1990s. The trade-off between the positive and negative effects of insurance relates to the trade-off between economic reforms requested by the IMF and the insurance mechanism associated with IMF ﬁnancial assistance which was requested by South Korea and other Asian countries during the 1997 ﬁnancial crisis. According to Radelet and Sachs (1998), a harsh push for reforms may exacerbate panic and crisis. Because of the trade-off between economies of division of labor and coordination reliability, no reforms can completely eliminate the risk of such a ﬁnancial crisis. A certain insurance mechanism is essential for mitigating the damage caused by an unavoidable crisis. Then again, moral hazard caused by complete government insurance of the banking system was one of its causes. Terms of insurance and related ﬁnancial assistance which are too soft are not efﬁcient either. It is not easy to ﬁnd the efﬁcient balance of the trade-off. The trade-offs between risk sharing and incentive provision, and between endogenous transaction costs caused by imprecise enforcement of property rights and exogenous transaction costs in enforcing property rights, relate to public policies in handling so-called externality and public goods. In the conventional literature on the subject, represented by Pigou (1940), externality and non-exclusivity of public goods are exogenously given and the role of the government in rectifying market failure is the focus of the analysis. In the literature on the economics of property rights and endogenous externality – represented by Barzel (1989), Cheung (1983), Coase (1960), Hart (1995), Milgrom and Roberts (1992), and O. Williamson (1985) – the above trade-offs are used to endogenize the degree of externality, while the role of a variety of institutions, ownership structures, and contractual arrangements in sorting out the efﬁcient trade-offs is the focus of the analysis. In this chapter we use Smithian general equilibrium models with transaction risk to formalize the notion of endogenous externality and to explore its implications for economic development.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n n n n n

n n n

What is the trade-off between endogenous and exogenous transaction costs? What is the trade-off between transaction costs in deepening incumbent relationships and transaction costs in expanding potential relationships? What are the implications of the trade-off between positive network effects of division of labor and reliability for economic development? Why can competition in the market substitute for precise speciﬁcation and enforcement of property rights in promoting economic development? How does the market sort out the efﬁcient degree of competition, the efﬁcient degree of vagueness in specifying and enforcing property rights, and the efﬁcient level of division of labor? What are the effects of transaction risk and the degree of risk aversion on the equilibrium network size of division of labor and economic development? Why can insurance promote division of labor and economic development? Why will complete insurance and moral hazard generate endogenous transaction costs?

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10.2 ECONOMIC DEVELOPMENT AND THE TRADE-OFF BETWEEN ECONOMIES OF DIVISION OF LABOR AND COORDINATION RELIABILITY We use an extended version of the model in example 7.1 to formalize North’s idea about the intimate relationship between economic development and secured property rights. The model is exactly the same as in example 7.1, except there is risk in each transaction. The story behind the algebra runs as follows. In each transaction there is a risk of delivery failure, which can be considered as a risk of losing property rights. A Cobb–Douglas utility function implies that utility is zero if the amount of any goods consumed is zero. Hence, if an individual purchases n − 1 goods and the risk of delivery failure of each good is 1 − r, then the total risk for her to receive 0 utility is (1 − r)n−1. As transportation efﬁciency is improved, the scope for trading-off economies of division of labor against transportation costs and transaction risk is enlarged, so that the equilibrium network of division of labor and the related extent of the market expand, productivity increases, and the efﬁcient aggregate risk of coordination failure increases. If the risk of coordination failure for each transaction is reduced due, for example, to more secure property rights, the extent of the market, the network size of division of labor, and productivity will rise too. However, if the direct positive effect of the higher reliability of each transaction on the aggregate reliability of the network of division of labor is outweighed by its indirect negative effects through increasing the number of transactions, the aggregate reliability decreases. Otherwise, the equilibrium and efﬁcient aggregate reliability of network of division of labor will increase. Example 10.1: A simpliﬁed version of the Yang–Wills model (1990). Consider an economy with M ex ante identical consumer-producers. The decision problem for a person selling good i is: Max: Vi ≡ Eui = ui P + 0(1 − P) s.t.

(expected utility)

ui = xi(kx ) x

(utility function)

P = r n−1

(reliability of n − 1 transactions)

xi + x = Max{li − α, 0}, xj = Max{lj − α, 0}

(production function)

li + (m − n)lj = 1

(endowment constraint of time)

pi x is = (n − 1)pr x rd

(budget constraint)

d n−1 m−n r j

s i

(10.1)

where xi, xj, x is , x id, li, lj, n, P are decision variables, r and k are parameters, pi is the price of good i. V = Eui is the expected utility, which is a weighted average of ui and 0, where the weights are P and 1 − P respectively. Let us examine the difference in speciﬁcation between this model and the model in example 7.1. The Cobb–Douglas utility function ui is the same as in example 7.1. We have used the symmetry of that model; that is, tastes and production and transaction conditions are the same for all goods. Hence, the amounts of goods purchased, xrd, are the same for all r, the amounts of self-provided goods, xj , and the amounts of labor allocated to the production of nontraded goods, lj , are the same for all j. However, coordination reliability of division of labor P, which is the probability that all goods purchased are received, is new. 1 − r is the probability that the individual fails to receive a good from a purchase contract. We assume that the failure of a seller to deliver the good to

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the buyer is an event that is independent of the failure of any of the other goods. The risk of coordination failure may be caused by trafﬁc accidents or other stochastic events. That risk may also be caused by opportunistic behavior, as discussed in chapter 9. For this case 1 − r can be interpreted as the anticipated risk of coordination failure caused by opportunism. In the alternating-offer bargaining game of example 9.13, where players compete for the advantage of the ﬁrst mover, there is a probability at which mutually beneﬁcial gains to trade cannot be realized. The risk of coordination failure 1 − r in this chapter can be interpreted as that probability as well. Therefore, r is the probability that the buyer receives the good and P = r n−1 is the probability that she receives all n − 1 goods purchased. 1 − P is the probability that she fails to receive at least one of all goods that she buys. Since for the Cobb–Douglas utility function an individual’s utility is zero if the quantity of any good consumed is zero, a consumer-producer will receive 0 utility at probability 1 − P and receives ui at probability P. The production functions in (10.1) are the same as in example 7.1. α is a ﬁxed learning cost in each activity, li and lj are respectively the levels of specialization in producing the traded good i and the nontraded goods j. The budget constraint in (10.1) is also the same as in example 7.1. Assume that prices are sorted out through a Nash bargaining mechanism, which generates the same utility between ex ante identical individuals who have the same disagreement point. As shown in chapter 9, this establishes the utility equalization conditions which, together with the market clearing conditions, will generate the same equilibrium as in a Walrasian regime. The equilibrium has equal prices of all traded goods and an equal number of sellers for each traded good, N = M/n, because of symmetry. With these results, the equilibrium values of decision variables can be solved as follows. For any i = 1, 2, . . . n xi = x rd = xj = [1 − α(m − n + 1)]/m

∀r ∈R, j ∈J

x = (n −1)[1 − α(m − n + 1)]/m s i

li = α + (n/m)[1 − α(m − n + 1)]

(10.2)

P = r n−1 V ≡ Eui = {1 − α(m − n + 1)/m}m(kr)n−1 n = m + 1 − (1/α) − [m/(ln k + ln r)] The inframarginal comparative statics of the general equilibrium are: dn/dr > 0,

dn/dk > 0,

(10.3a)

dP/dr = (∂P/∂r) + (∂P/∂n)(dn/dr) < 0, if and only if (∂P/∂r) < |(∂P/∂n)(dn/dr)|

(10.3b)

dP/dk = (dP/dn)(dn/dk) < 0

(10.3c)

dV/dr = ∂V/∂r > 0,

(10.3d)

dV/dk = ∂V/∂k > 0.

dli/dr = (dli/dn)(dn/dr) > 0,

dli/dk = (dli/dn)(dn/dk) > 0,

(10.3e)

dx is/dr = (dx is/dn)(dn/dr) > 0,

dx is/dk = (dx is/dn)(dn/dk) > 0

(10.3f )

dN/dr = (dN/dn)(dn/dr) < 0,

dN/dk = (dN/dn)(dn/dk) < 0

(10.3g)

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(10.3a) implies that the equilibrium level of division of labor increases as the reliability of each transaction increases, or as the anticipated risk of coordination failure of each transaction caused by endogenous transaction costs falls. (10.3b) implies that as the reliability of each transaction rises, total reliability P would fall if the negative effect of the increase in r, (∂P/∂n)(dn/dr), outweighs its positive effect, ∂P/∂r. Otherwise, total reliability rises. Here, (∂P/∂n) < 0 and (dn/dr) > 0. Since 1 − P can be considered as aggregate risk of coordination failure caused by anticipated endogenous transaction costs, (10.3b) can be interpreted in another way. It means that total endogenous transaction costs in terms of the aggregate risk increase as the endogenous transaction cost, 1 − r, for each transaction falls, if the positive effect of the fall on the total endogenous transaction costs through its impact on the number of transactions outweigh its direct negative effect on total endogenous transaction costs. Otherwise, total endogenous transaction costs decrease with the endogenous transaction cost for each transaction. Because of the connection between total endogenous transaction costs and the degree of softness of the budget constraint, this result implies that the budget constraint may become increasingly soft as the endogenous transaction cost for each transaction falls. (10.3c) implies that as the exogenous transaction cost coefﬁcient, 1 − k, is reduced, or as transaction efﬁciency k rises, total anticipated endogenous transaction costs 1 − P, or the aggregate risk of coordination failure, increase (or aggregate reliability P falls). This is because as exogenous transaction efﬁciency is improved, the beneﬁt of increasing division of labor rises in comparison to increasing endogenous and exogenous transaction costs, so that total endogenous transaction costs may increase to the degree that the increased endogenous transaction costs are outweighed by the increased economies of division of labor that are exploited. (10.3d) means that as the endogenous transaction cost for each transaction falls (or as the coordination reliability for each transaction rises), or as exogenous transaction efﬁciency is improved, expected real income V goes up. We have used the envelope theorem to get this result. (10.3e) and (10.3f ) imply that as the reliability of each transaction r rises, or as exogenous transaction efﬁciency k is improved, each individual’s level of specialization and per capita trade volume go up. Because of economies of specialization, the result implies that the labor productivity of each traded good goes up and the degree of self-sufﬁciency falls. (10.3g) implies that as the reliability of each transaction r goes up (or as the anticipated endogenous transaction cost for each transaction falls), or as exogenous transaction efﬁciency is improved, the number of sellers of each traded good, which represents the degree of competition, goes down. This results in a fall of aggregate reliability and a rise in total anticipated endogenous transaction costs. Since an increase in r can be caused by more secure property rights, this model formalizes North’s conjecture (1981) about the implications of secure property rights for economic development, evolution of division of labor, and expansion of the market. If transaction risk is introduced into the model with the CES utility function in example 7.2, then North’s idea about the intimate relationship between the extent of the market, secured property rights, and emergence of new goods can be formalized. However, our formal model predicts the possible increase in total endogenous transaction cost and aggregate risk of coordination failure as a result of improved transportation conditions (k or r is increased). This prediction invalidates the belief that more secure property rights and improved transaction conditions will always reduce the aggregate risk of coordination failure that results in economic crises like the Great Depression in 1930 and the Asian ﬁnancial crisis in 1997. A high risk of coordination failure can be interpreted as a risk of mass unemployment, as all individuals will be forced to choose autarky when coordination of the division of labor breaks down. Hence, it is possible that secure property rights promote economic development on the one hand, and increase the aggregate risk of economic crisis on the other. The devastating consequences of

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the Great Depression were a major reason that communism spread in many countries after the Second World War. But in the long run, the striking development performance difference between the capitalist systems and the Soviet-style systems shows that the costs of economic development caused by the greater risk of coordination failure associated with a large network of division of labor may be worth paying. From the experience of the recent Asian ﬁnancial crisis we may better appreciate the trade-off between the positive effect of evolution of division of labor on economic development and its effect on the risk of coordination failure. A more general version of the model with endogenous r can be found in Yang and Wills (1990) or in Yang and Ng (1993, ch. 9). The endogenization of r is a feature of the economic literature on the trade-off between economies of division of labor and coordination reliability which distinguishes it from the engineering literature on reliability.

10.3 ENDOGENIZATION OF COORDINATION RELIABILITY IN EACH TRANSACTION AND SUBSTITUTION BETWEEN COMPETITION AND BETTER ENFORCED PROPERTY RIGHTS If probability for coordination failure in each transaction can be reduced by inputting resources into speciﬁcation and enforcement of contractual terms and property rights, then there is a trade-off between endogenous transaction costs caused by imprecise enforcement of property rights and exogenous transaction costs incurred in enforcement. In addition, there are two ways to reduce risk of coordination failure or to reduce the endogenous transaction costs in each transaction. The ﬁrst is to allocate more resources to reducing the risk of coordination failure of each incumbent transaction. The second is to allocate more resources to cultivating more potential relationships, which are in parallel connection with an incumbent relationship. This will increase the number of parallel connections for each incumbent transaction and reduce the risk of coordination failure of the transaction. In other words, extensive connections with many potential partners yield competitive pressure on the incumbent partner, so that the individual can turn to one of the potential partners when the incumbent one fails to deliver what is needed. Mathematically, the total risk of coordination failure of each transaction is (1 − r)N when there are N potential trade partners and each of their deliveries is realized with probability r. Then total reliability of each transaction P = 1 − (1 − r)N can be raised either by reducing the risk of coordination failure with the incumbent partner, 1 − r, or by increasing the number of potential partners, N. Note that r is between 0 and 1 and P increases as r or N increases. For a nontrivial transaction cost in keeping a potential relationship, there is a trade-off between costs in deepening incumbent relationships and costs in broadening potential trade connections. Hence, each buyer’s efﬁcient number of potential sellers of a good with whom she keeps in touch may be smaller than the number of all sellers of the good in the market. This section uses a Smithian model to formalize this trade-off in addition to the trade-off between economies of division of labor and all kinds of transaction costs. The story behind the algebra runs as follows. In an economy, there are many ex ante identical consumer-producers who can choose their levels of specialization. In addition to the trade-off between economies of specialization and transportation costs, there are trade-offs between economies of specialization, transaction risk, and transaction costs in reducing such risk, and between transaction costs in deepening incumbent trade relationships and transaction costs in broadening potential trade connections. If an individual pays higher exogenous transaction costs in specifying and enforcing property rights and related contractual terms, the welfare loss caused by the risk of coordination failure 1 − r of each transaction can be reduced. Hence, 1 − r becomes an individual’s decision variable.

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From our experience of litigation (did you ever have such an experience?), an increase in legal service fees paid to lawyers, a form of exogenous transaction costs, can raise the probability that our property rights are well protected. The damage caused by infringement of property rights can be considered a form of endogenous transaction costs. There is a trade-off between exogenous and endogenous transaction costs. The question of how the efﬁcient trade-off between the two kinds of transaction costs can be achieved is central to the economics of property rights and institutional economics. For instance, in a Soviet-style economy, the exogenous transaction costs associated with legal service fees are trivial. The income share of lawyers’ earnings is very low. But endogenous transaction costs are extremely high, because property rights are not well speciﬁed and enforced, individuals have no incentive to work hard, and the patterns of division of labor and resource allocation are distorted. Such endogenous transaction costs are not easy to measure directly. They can be indirectly measured from long-run development performance. In the US, the opposite situation prevails: exogenous transaction costs and the national income share of lawyers’ earnings are high, whereas endogenous transaction costs are low because of much better speciﬁed and enforced property rights. Individuals are more willing to work hard because of the much lower distortions in information transmission. The inframarginal comparative statics of general equilibrium generate the following interesting results. As the parameter that represents efﬁciency in specifying and enforcing property rights is increased, the equilibrium level of division of labor and per capita real income go up. But two types of changes in transaction reliability may take place in response to improvement in speciﬁcation and enforcement efﬁciency. Individuals can either divert resources from speciﬁcation and enforcement to raising the level of division of labor in production, or allocate the resources that are saved by the more effective speciﬁcation and enforcement of rights to raising the degree of precision of the speciﬁcation and enforcement of property rights in each transaction. These two responses are to some extent substitutes in raising per capita real income. If the ﬁrst generates a greater net beneﬁt than the second, an improvement in speciﬁcation and enforcement efﬁciency will generate a lower reliability of each transaction and thereby a higher aggregate risk of coordination failure when it promotes division of labor and economic development. If the second method is better, then an improvement in speciﬁcation and enforcement efﬁciency will raise the level of division of labor and the reliability of each transaction, meanwhile generating a higher or a lower aggregate risk of coordinate failure. Its effect on the aggregate risk of coordination failure is parameter value dependent, since the positive effect of an increase in the number of transactions on the aggregate risk may or may not outweigh the negative effect of an increase in the reliability of each transaction. For a large value of the cost coefﬁcient for deepening the incumbent relation relative to the cost coefﬁcient for widening potential relations, “classical contracts” with many potential trading partners (similar to perfect competition) may occur at equilibrium. For a small value of the deepening cost coefﬁcient, “relational contracts” without potentially alternative trading partners may occur at equilibrium. As shown in Yang and Wills (1990), in the model with endogenous risk of coordination failure of each transaction, if the transportation efﬁciency coefﬁcient (which differs from the exogenous transaction efﬁciency coefﬁcient in specifying and enforcing each contract) is increased, the equilibrium levels of division of labor, productivity, and per capita real income all rise, while the equilibrium degree of reliability of each transaction and the degree of competition decrease. The inframarginal comparative statics of the general equilibrium explore very complicated relationships among the endogenous transaction costs of each transaction, exogenous transaction costs in specifying and enforcing property rights, exogenous transportation costs, aggregate endogenous transaction costs, and the level of division of labor. These sophisticated relationships imply that it is not efﬁcient to entirely eliminate the aggregate endogenous transaction costs

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that relate to distortions. The idea of eliminating all endogenous transaction costs is too naive to be realistic because it cannot explain why an hourly wage, which has a lower degree of precision in specifying and enforcing property rights than a piece-rate wage, becomes more common than the piece-rate wage as division of labor (commercialization) evolves. It is impossible for the government to identify the efﬁcient trade-offs among so many conﬂicting forces. It requires a laissez faire regime, which allows individuals to choose freely among various structures of division of labor, institutions, and contractual arrangements to sort out the efﬁcient trade-offs. The restriction of free choices among occupations and institutional conﬁgurations and interference with free pricing will paralyze the functioning of the market in sorting out the efﬁcient trade-offs. Mokyr (1993, pp. 47–8) indicates that one of the main conditions for the Industrial Revolution in Britain in 1760–1830 was the British government’s de facto laissez faire policy. He writes: Compared with Prussia, Spain, or the Hapsburg Empire, Britain’s government generally left its businessmen in peace to pursue their affairs subject to certain restraints and rarely ventured itself into commercial and industrial enterprises. Seventeenth-century mercantilism had placed obstacles in the path of all enterprising individuals, but British obstacles were less formidable than those in France. More regions were exempt, and enforcement mechanisms were feeble or absent. One such enforcement mechanism, widely used on the Continent, was the craft guild, yet by the time of the Glorious Revolution of 1688, the craft guild in Britain had declined into insigniﬁcance . . . During the heyday of the Industrial Revolution, even social-overhead projects that in most other societies were considered to have enough public advantages to warrant direct intervention of the state were in Britain left to private enterprise. Turnpikes, canals, and railroads were built in Britain without direct state support; schools and universities were private. Even the less invasive forms of state support, like the policies of William I of Orange in the Low Countries or the Saint-Simonians in France during the Second Empire, were notably absent in Britain. Until the end of the nineteenth century, the British government clearly was reluctant to invade what it considered to be the realm of free enterprise. The general consensus among historians today is that the regulations and rules, most of them relics from Tudor and Stuart times, were rarely enforced. The central government was left to control foreign trade, but most other internal administration was left to local authorities. Internal trade, the regulation of markets in labor and land, justice, police, county road maintenance, and poor relief were all administered by local magistrates. Although in principle these authorities could exercise considerable power, they usually elected not to. By ignoring and evading rather than altogether abolishing regulations, Britain moved slowly, almost imperceptibly toward a free-market society.

According to Coase (1960), even lighthouses, which are usually used in textbooks as a typical example of public goods, were built by the private sector in Britain. Example 10.2: An equilibrium model with a trade-off between deepening the incumbent relationship and broadening potential relationships. The model is the same as in example 7.1 except that there are only two consumption goods and each buyer has a risk of failing to receive the good she buys. The risk may be caused by a transportation accident when the good is delivered, or by some anticipated opportunistic behavior. If each of M ex ante identical consumer-producers chooses autarky, then there is no risk of coordination failure. An individual’s decision problem in autarky is Max: U = xy s.t.

(utility function)

x = Max{0, lx − α}

(production function of x)

y = Max{0, ly − α}

(production function of y)

lx + ly = 1

(endowment constraint of time)

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where x, y, lx, and ly are decision variables. The per capita real income in this structure is UA = [(1 − 2α)/2]2. The decision problem for a specialist producer of good x is Max: Ux = xy dP s.t.

(utility function)

x + x = Max(0, lx − α)

(production function)

px x = py y

(budget constraint)

s

s

d

lc = cN

(labor cost of public relationship)

ls = sr

(labor cost for each incumbent relation)

lx + lc + ls = 1

(endowment constraint of time)

P = 1 − (1 − r) N

(total coordination reliability)

where x, y d, x s, lx , lc , ls , N, r, P are decision variables. c is the cost coefﬁcient for the specialist producer of x to keep in touch with a seller of y. This may be interpreted as a cost of making a phonecall to a potential seller to inquire about prices and availability of goods, or as a cost of cultivating a relationship with the seller. A restriction on the free choice of trade partners, such as those institutional arrangements in a Soviet-style economic system which prohibit individuals from trading land and capital goods, will increase c to a very large value, so that the optimum choice of N will be at its minimum, 1. Hence, N represents the endogenous degree of competition and lc is the total labor cost of broadening potential trade connections. s is the cost coefﬁcient for the specialist producer of x to increase by 1 percent the degree of reliability of the incumbent relationship. This can be interpreted as the cost of specifying and enforcing contractual terms with the incumbent partner. Hence, ls is the total labor cost in deepening the incumbent relationship. Uncertainties in trade may make the number of suppliers of a good an important determinant of the risk of coordination failure from the complex exchange interdependencies associated with the division of labor. To reduce such risk, a buyer of a good may maintain relationships with many suppliers, or alternatively she may increase the precision of the terms stipulated in a contract with the incumbent supplier. The former method of reducing a risk of coordination failure relates to transaction costs in delimiting rights to contracting, or lc, and the latter relates to transaction costs in specifying and enforcing the terms of a contract, or ls. If we draw the distinction between rights speciﬁed in a contract and rights to contracting, we may specify a trade-off between the two kinds of transaction costs and the substitution between increasing competition, which relates to lc , and increasing accuracy in specifying and enforcing the terms of a contract, which relates to ls. An example is the decision problem faced by an assistant professor who holds a tenure-track position. For her given ability and effort and the quality of the match with her incumbent employer, it is uncertain whether the employer will grant tenure to the employee even if she is qualiﬁed, and whether the employee will meet the terms of the contract even if the employer treats her fairly. To reduce the risk of being treated unfairly, the employee may spend time negotiating and enforcing the terms of the contract. Alternatively, she may spend time keeping in touch with potential alternative employers in order to reduce the risk of losing her job. Similarly, the employer may hire several tenure-track employees for one tenured position, or spend resources specifying and enforcing the terms of a contract. The question is: what is the efﬁcient balance of the trade-off between the two alternative uses of resources to reduce the total risk of coordination failure? The efﬁcient balance is crucial for the determination of the

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efﬁcient level of division of labor that balances, in turn, the trade-off between economies of specialization and various transaction costs. The trade-off between the two kinds of transaction costs relates to the trade-off, described by Williamson, between relational costs incurred in mitigating the hazards of opportunism and transaction costs incurred in stipulating detailed contingent contracts (O. Williamson, 1985). The public relations cost function, and the speciﬁcation and enforcement cost function of each incumbent relationship in this section, formalize Williamson’s idea. It will be clear later that for a small value of the relation cost coefﬁcient, “classical contracts” with many potential trade partners (similar to perfect competition) may occur at equilibrium. For a large value of the relation cost coefﬁcient, “relational contracts” without potentially alternative trade partners may occur at equilibrium. Also, the trade-off between the two kinds of transaction costs relates to the trade-off between the distortions caused by imprecise contractual terms and bargaining costs in sorting out precise contractual terms, investigated by Milgrom and Roberts (1992, ch. 7). Milgrom and Roberts use this trade-off to explain why the piece-rate wage is replaced by the monthly wage and why some promotion rules according to seniority can restrain excessive bargaining and “inﬂuencing activities” at the cost of incentive provision. Each buyer of good y receives y d that she orders from a seller of y. She keeps in touch with N sellers of y and can turn to one of them if the incumbent seller fails to deliver the good according to the timing and quality that she requires. The reliability of each seller is r, or each seller has a risk of coordination failure 1 − r. Hence, the total risk of the buyer failing to receive good y when she keeps in touch with N incumbent and potential sellers is (1 − r)N, or her aggregate reliability to receive y d is P = 1 − (1 − r)N. You may interpret P as the probability that the transaction efﬁciency coefﬁcient is 1 and 1 − P = (1 − r)N as the probability that the transaction efﬁciency coefﬁcient is 0. The solution of the decision problem yields not only demand and supply functions for x and y, but also the optimum number of potential partners, N, with whom a buyer should keep in touch, the optimum risk of coordination failure of each relationship 1 − r, and the optimum aggregate coordination reliability P or optimum aggregate risk of coordination failure 1 − P. The decision problem for a specialist producer of y is symmetric to that for a specialist producer of x. Max: Uy = yxdP s.t.

(utility function)

y + y s = Max{0, ly − α}

(production function of y)

py y = px x

(budget constraint)

s

d

lc = cN

(labor cost of public relationship)

ls = sr

(labor cost of each incumbent relation)

ly + lc + ls = 1 P = 1 − (1 − r)

(endowment constraint of time) N

(aggregate coordination reliability)

where y, x d, y s, ly , lc , ls , N, r, P are decision variables. Structure D is a division of M individuals between the two professions. Using the symmetry of the model, we can show that the corner equilibrium-relative price of two goods px /py = 1 and the corner equilibrium numbers of two types of specialists are Mx = My = M/2 in structure D. Also, in the corner equilibrium, the number of trade partners with whom each individual keeps in touch, N, the reliability of the incumbent relationship, r, and the labor allocation between broadening potential relationships and deepening the incumbent relationship are all the same

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Table 10.1 Equilibrium reliability and degree of competition C

s

α

r

N

P

≤ 0.05

0.1

1

1

1

0.01

0.1

0.1

0.69

4

0.991

≥ 0.02

0.1

0.1

1

1

1

0.01

0.2

0.1

0.43

6

0.966

≥ 0.02

0.2

0.1

1

1

1

0.01

0.3

0.1

0.33

8

0.959

0.02

0.3

0.1

0.46

5

0.954

0.03

0.3

0.1

0.57

4

0.966

0.04

0.3

0.1

0.69

3

0.97

0.3

0.1

1

1

1

≥ 0.4

0.1

1

r

≥ 0.05

for the two types of specialists. The corner equilibrium N and r are determined by the ﬁrstorder conditions 2c[1 − (1 − r)N ] = −(1 − cN − sr − α) (1 − r)N ln(1 − r)

(10.4a)

N = −s(1 − r) ln(1 − r)/c

(10.4b)

There are multiple solutions of (10.4). Also, (10.4) does not apply to the several possible corner solutions of r and N. Hence, an analytical solution of comparative statics of the corner equilibrium cannot be obtained. Table 10.1 reports part of the computer simulation results of comparative statics of the corner equilibrium reliability of each transaction, r, the number of trade partners with whom each person keeps in touch (degree of competition), N, and aggregate reliability P in structure D. It shows that if s is sufﬁciently small, then the corner equilibrium value of r is 1, its maximum, so that the equilibrium values of N and P are 1 too; if c is too large, the corner equilibrium value of N is 1, its minimum; as s increases relatively to c, the corner equilibrium value of r falls and the corner equilibrium value of N increases. This implies that as the cost of deepening the incumbent relationship increases in comparison to that in broadening potential relationships, the equilibrium degree of competition, N, increases and the equilibrium degree of reliability for the incumbent relationship, which relates to the degree of precision of contractual terms, decreases. A decrease in the transaction cost coefﬁcient in broadening potential relationships, c, has the opposite effects, decreasing the equilibrium degree of competition and increasing the reliability of the incumbent relationship. The per capita real income in the structure with the division of labor is UD = [(1 − α − lc − ls)/2]2 [1 − (1 − r)N ]

(10.5)

where r = ls /s and N = lc /c are given by the labor cost functions in deepening the incumbent relationship and in broadening potential relationships, respectively. ls and lc are each individual’s decision variables. Applying the envelope theorem to (10.5), we can show that dUD /ds = ∂UD /∂s < 0

and

dUD /dc = ∂UD /∂c < 0.

(10.6)

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1

2

1

E NDOGENOUS T RANSACTION C OSTS

1

1

1

A

2 (a) Autarky

1

1 2

1

1

1

2

2

1

1

2

1

2

2

2

A 2

A

AND

1

1 2

2

2 (b) Division of labor with N = 1

1

2 2 2 (c) Division of labor with N = 2

Figure 10.1 Different degrees of competition in equilibrium

Since per capita real income in autarky is independent of s and c, (10.6) implies that as s or c falls, it is more likely that the corner equilibrium in structure D will be Pareto superior to that in autarky. According to the Yao theorem in chapter 4, this implies that as s and/or c falls, the general equilibrium will jump from autarky to the division of labor. Figure 10.1, where population size M = 4, gives an intuitive illustration of different patterns of equilibrium market structure. In panel (a), large transaction cost coefﬁcients for deepening the incumbent relationship and for broadening potential relationships generate autarky as the general equilibrium. In panels (b) and (c), falling transaction cost coefﬁcients make the division of labor the general equilibrium. But in panel (b), a large transaction cost coefﬁcient for broadening potential relationships, c, relative to the transaction cost coefﬁcient for deepening the incumbent relationship, s, generates the equilibrium N = 1 in an economy with 4 individuals, so that the economy is fragmented into two separate local communities. There is division of labor and transactions within each of the local communities, but no interactions between the communities. In panel (c), a small transaction cost coefﬁcient for broadening potential relationships relative to the transaction cost coefﬁcient for deepening the incumbent relationship generates the equilibrium N = 2, so that each individual has one incumbent trade partner and keeps in touch with another potential partner to put pressure on the incumbent one. The economy is integrated as one market, though this degree of integration is not necessary for all incumbent trade relationships. Dashed lines denote possible trade between potential trade partners when the incumbent suppliers fail to deliver goods. This model shows that there are two functions of the market. One is to execute exchanges. The other is to keep the pressure of competition on individuals in order to reduce the risk of coordination failure in exchanges. The second function may require a local market size that is larger than required to complete all realized exchanges, because each individual may keep in touch with some potential trade partners in order to put pressure on the incumbent trade partners, thereby reducing the risk of coordination failure. If the number of goods is m rather than 2, and population size is greater than 4, then the following point will be clearer. The size of the market network that relates to potential trade partners may be greater than the network size of realized trade connections. For instance, in the model with many goods and large population size, if the equilibrium number of traded goods is 3 due to a low transaction efﬁciency, then three individuals can constitute a local community where each of them sells one good to and buys one good from each of the other individuals. But each individual may keep in touch with half of the population in the economy in order to put pressure on each of her incumbent trade partners to reduce the risk of coordination failure. The empirical work of Barro (1997), Sachs and Warner (1995, 1997), and Frye and Shleifer (1997) cited in chapter 7 provides strong support for the theory developed in this chapter. Yang, Wang, and Wills (1992) have tested this theory against the data set of rural China in 1979–87. The empirical studies show that the reforms in rural China during this period signiﬁcantly

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improved transaction efﬁciency in specifying and enforcing peasants’ rights to use, to transfer, and to appropriate earnings from goods, labor, land, and other assets. The institutional changes raised the level of division of labor, measured by the degree of commercialization in an extensive household survey, and per capita real income. The results of the model in this section differ from the conventional wisdom of market failure, which does not explain why markets do not exist for some commodities, for example, clean air and intangible entrepreneurial ideas. Our model formalizes Cheung’s argument (1970, 1983) that the determination of contractual forms is a matter of the degree of vagueness in specifying and enforcing property rights, or, in less illuminating words, the degree of externality. In particular, if there are many goods, and transaction conditions differ across goods, it can be shown that markets exist only for those goods with better transaction conditions in specifying and enforcing property rights. Eliminating all externalities is not efﬁcient because of the costs of specifying and enforcing exclusive rights to property. The efﬁcient extent of externality will balance the trade-off between the welfare loss caused by the absence of markets and the costs of specifying and enforcing the property rights required for markets. Hence, the absence of the market for some goods is a consequence of the efﬁcient trade-off between economies of division of labor and various transaction costs. Externality caused by the absence of the market is efﬁciently and endogenously determined in the market. The difference between the externalities in buying a pound of oranges and buying clean air is a difference of degree rather than a difference of substance. When people buy oranges, there are externalities resulting from vagueness in weighing oranges and in estimating their quality (Barzel, 1982). However, the equilibrium degree of vagueness in specifying and enforcing property rights is much lower for oranges than for clean air because there is much greater efﬁciency in specifying and enforcing property rights to oranges than to clean air. Since the degree of market competition (related to N) is endogenized in our model, the degree of involvement of a particular exchange in the market is endogenized. Hence, for those goods associated with a small equilibrium value of the number of potential trade partners, N, we may say that the exchange relationship has a low degree of marketization. This implies that our models can be used to explain why some nonmarket exchange relationships exist in a society when transaction costs in keeping extensive connections with potential trade partners are very high. As shown by Mauss (1925), individuals in a primitive society rely on such nonmarket and individual-speciﬁc exchange relationships to develop division of labor. Trade in such a primitive society is conducted via individual-speciﬁc exchanges of gifts. Such nonmarket exchanges are very common in many developing countries, where efﬁciency in keeping extensive market connections is very low. Efﬁciency in specifying and enforcing property rights is determined by both the legal system and technical conditions. For example, low efﬁciency in specifying and enforcing property rights in pre-reform Russia and China can be attributed to a legal system that restrained free trade in labor, land, and capital; while, in general, low efﬁciency in specifying and enforcing property rights to clean air is due to the high cost of the technology used to measure pollution. The following examples provide the intuition behind the models in sections 10.2 and 10.3. Example 10.3: A trade-off related to the institutions of the library and the university. The institution of the university can be used to improve efﬁciency in specifying and enforcing rights to knowledge. Faculty members’ rights to the knowledge that is sold to students is speciﬁed and enforced via wage contracts between a university and the staff members and by student tuition payments. Transaction efﬁciency is lower when teachers collect payment from students individually than when teachers receive payment from students through the university. The improvement in efﬁciency in specifying and enforcing the right to knowledge that is associated with the emergence of a university will promote division of labor between the producers

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of knowledge (faculty members) and future producers of other goods (students), and between different specialist teachers. However, monthly wage contracts are more common between universities and their teaching staff than between students and private tutors who usually charge an hourly fee. If property rights are more vaguely speciﬁed and enforced in a monthly wage contract than in an hourly fee contract, the above example implies that an increase in the division of labor caused by a lower exogenous transaction costs of the institution of the university is associated with a more vague speciﬁcation and enforcement of property rights, as long as the beneﬁts from the higher level of division of labor outweigh the cost caused by the higher level of vagueness of contracts. Further, the emergence of the institution of the university promotes division of labor between the professional management of books (libraries) and the users of books (teachers and students). The emergence of libraries increases the difﬁculty in framing and enforcing rights to the knowledge generated by books. Before professional libraries were established, an individual had to buy a book if she wanted to utilize the knowledge in it, since it was not easy to borrow many different books from other individuals. She could more easily borrow a book without any payment to its author once libraries emerged. Even if students’ tuition includes a payment for using a university library, the payment is not proportional to the frequency of book use, and the payment does not go to the authors of the books. This implies that rights to authors’ knowledge are more vaguely speciﬁed and enforced in a library system than in a book market without the institution of the library. However, the system with libraries will be the equilibrium as long as the beneﬁts generated by division of labor between professional libraries and other sectors outweigh the utility loss generated by the higher level of vagueness in specifying and enforcing the rights to intellectual property. Nevertheless, a new institutional arrangement that charges for each use of a book in a library could be combined with copyright laws to increase the level of division of labor and decrease the level of vagueness in specifying and enforcing rights to intellectual property at the same time, if magnetic cards and a computer system were effectively employed to monitor and collect the required payments. Such arrangements emerged in some northern European countries in the 1980s. Intuitively, it would seem that the slight improvement in transaction efﬁciency due to the emergence of professional libraries increases both the equilibrium level of division of labor and the equilibrium degree of vagueness in specifying and enforcing property rights, because this slight improvement is insufﬁcient to allow both an increase in the level of division of labor and a decrease in vagueness at the same time. By contrast, the emergence of a system that charges for each use of a book, together with copyright laws, magnetic cards, and the computer system, will signiﬁcantly improve transaction efﬁciency in specifying and enforcing authors’ rights to knowledge in books, so that the level of division of labor increases and the degree of vagueness in specifying and enforcing property rights decreases, resulting in a signiﬁcant increase in productivity and welfare. Here, the distinction should be drawn between non-exclusivity and nonrivalry of goods when we analyze endogenous externality. Nonrivalry is a technical characteristic. It implies that use of a good by a person does not prevent another person from using the same good. In other words, a good is nonrival if its production and/or consumption involves only ﬁxed costs and no variable costs. A TV program is a nonrival good, since the cost of its production and consumption does not increase with the number of its viewers: there is only the ﬁxed production cost of the TV program. Hence, nonrivalry implies signiﬁcant increasing returns. This does not necessarily imply non-exclusivity, which is determined endogenously by institutions. If transaction efﬁciency in specifying and enforcing property rights to a good with nonrivalry is very high, then in equilibrium, individuals will choose to fully specify and enforce property rights, so that nonrivalry does not cause externality. The following example illustrates the point.

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Example 10.4: Nonrivalry and non-exclusivity of TV programs. A TV program is a nonrival commodity. When a person watches a program at her home, it does not prevent others from watching the same program at their homes. The number of viewers of the same program can be very large. If the owners of the copyright of the TV program had very low costs for monitoring the consumption of the TV program at each person’s home, they could extract a fee for each viewing of the program by each person. If somebody refused to pay, they could take legal action against her. But in reality, we never see such institutional arrangements, not because it is impossible, but because the monitoring costs are prohibitively high. Hence, the efﬁcient trade-off between the transaction costs in specifying and enforcing property rights and the distortions caused by imprecise speciﬁcation and enforcement will result in free TV programs. This implies that TV programs are endogenously chosen as non-exclusive commodities. The non-exclusivity implies externality and related distortions. However, the degree of externality is endogenously chosen by individuals and the invisible hand (interactions between selfinterested behaviors). The functioning of the market in handling distortions caused by externalities is much more sophisticated than described by neoclassical marginal analysis. For the case of the TV program, there is multilateral trade among three parties: the owner of the copyright of the program, the viewers of the program who are buyers of other tangible goods, and the sellers of the tangible goods. A one-way trading chain may reduce the distortions caused by the non-exclusivity of the TV program. Sellers of the tangible goods make money by selling to TV viewers. The producer of the program makes money from selling advertising time to the sellers of tangible goods, while the viewers obtain utility from freely viewing the program. This one-way trade triangle generates distortions by forcing viewers to watch advertisements that they may not want to see. But it saves on the exogenous transaction costs which the producer of the TV program would incur in collecting payment from the viewers, thereby reducing the externalities caused by the non-exclusivity of the TV program. Compared to cable TV, the open TV system generates more distortions because of the inaccurate correspondence between the amount of payment by viewers and the quantity of TV programs consumed by them, and by forcing viewers to see something that they do not like. The cable TV system causes much less endogenous transaction cost of this kind. But the open TV system saves on exogenous transaction costs caused by deploying cable and collecting fees. As discussed in chapter 10, the market will efﬁciently trade-off economies of division of labor against endogenous and exogenous transaction costs to determine the efﬁcient degree of externality. If the total endogenous and exogenous transaction cost is nearly the same between the open TV system and the cable TV system, they may coexist in a competitive market.

10.4 WHY CAN INSURANCE PROMOTE ECONOMIC DEVELOPMENT? In chapter 9, we learned the concepts of risk aversion and moral hazard. Let us review these concepts before developing new models utilizing them. In the presence of uncertainty, a decisionmaker maximizes expected utility. The institution of insurance can be used to pool risk. Hence, in an economy with a very large population, each individual can receive utility at the weighted average of contingent states. If the decision-maker’s utility function is strictly concave, she prefers the value of the utility function at the weighted average of contingent states, which can be provided by insurance that pools risk, to the weighted average of utility values at contingent states. Therefore, a strictly concave utility function implies that an individual prefers an outcome with insurance to outcomes with uncertainty. In other words, she is risk-averse. If individuals have different degrees of risk aversion, they can all gain from trading in risk. An individual who is more risk-averse than another can sell risk to the latter and both of them

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can be better off. This can be considered as the former buying insurance from the latter. The neoclassical principal–agent model in example 9.1 can be regarded as a model with insurance in which the agent buys insurance from the principal. The principal plays the role of an insurance company. That model shows that complete insurance will generate moral hazard if the principal cannot detect the agent’s effort devoted to reducing risk. The efﬁcient contract between the principal and agent entails incomplete insurance. That is, the payment to the agent is contingent: it is higher when the outcome is good than when the outcome is not good. In sections 10.4 and 10.5 we investigate further the relationship between insurance, division of labor, and endogenous and exogenous transaction costs. The story in this section runs as follows. Assume that there are risks in transactions in the model in example 7.1. In each transaction, transaction efﬁciency k takes on a great value at probability θ and a small value at probability 1 − θ. The transaction risk may be caused by trafﬁc accidents or by opportunistic behavior that takes place with a probability as shown in example 9.13 of chapter 9. Moreover, we assume that all consumer-producers are risk-averse to the same degree, or they have ex ante identical strictly concave utility functions. In the model, there is a trade-off between economies of division of labor and coordination reliability, in addition to a trade-off between economies of division of labor and exogenous transaction costs. If an insurance company collects a premium from each individual and compensates her in the event of low transaction efﬁciency, each individual will have the weighted average of the two levels of transaction efﬁciency for certain by pooling risk. Such an insurance institution will certainly promote division of labor and productivity progress if all individuals are riskaverse. It will promote many other structural changes associated with evolution in division of labor, which we have discussed in chapters 4, 7, and 8. More interestingly, the improved transaction conditions enlarge the scope for trading off economies of division of labor against transaction risk, so that the equilibrium and efﬁcient aggregate risk of coordination failure increases. Also, a decrease in the risk of coordination failure for each transaction may increase the efﬁcient aggregate risk of coordination failure for the same reason. This story is formalized in the following example. Example 10.5: The Lio model (1998). The structure of the model is similar to the one in example 7.1 except that transaction efﬁciency k is a random variable. The decision problem for each consumer-producer selling good i is speciﬁed as follows: 1/ρ

⎫⎪ ⎧⎪ Max: Eui = E ⎨x i ∏ (k r x rd ) ∏ xj ⎬ ⎪⎭ ⎪⎩ r ∈R j ∈J s.t.

xi + x is = Max{0, li − α},

(expected utility) xj = Max{0, lj − α}

(production functions)

li + (m − n)lj = 1

(endowment constraint)

pi x is = (n − 1)pr x rd

(budget constraint)

(10.7)

where xi is the amount of good i self-provided, x rd is the amount of good r purchased, kr is the transaction efﬁciency coefﬁcient for good r, R is the set of n − 1 goods purchased, J is the set of m − n nontraded goods, n is the number of traded goods, xj is the self-provided amount of nontraded good j, x is is the amount of good i sold, li and lj are respective levels of specialization in producing goods i and j, and pi and pr are respective prices of good i and r. It is assumed that each individual is endowed with one unit of nonleisure time. α is the ﬁxed learning cost in each production activity. We will see later that parameter ρ > 1 relates to the degree of risk aversion.

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The larger the value of ρ, the more risk-averse is the individual, since a larger value of ρ implies a more concave utility function. The endowment constraint and the budget constraint in (10.7) are obtained using the symmetry. The difference between this decision problem and the one in example 7.1 is characterized by the transaction efﬁciency coefﬁcient: ⎧ kH with θ kr = ⎨ ⎩kL with 1 − θ

(10.8)

where θ ∈(0, 1) is the probability that transaction efﬁciency is high, kH > kL, r ∈R. That is, there is transaction risk. It is not difﬁcult to see that a special case of the Lio model for ρ = 1, kL = 0 is the model in example 10.1. θ here is equivalent to r in example 10.1. Inserting all constraints into the utility function, the constrained maximization problem in (10.7) can be converted to a nonconstrained maximization problem:

⎛ ⎞ P ≡ E ⎜ ∏ kr ⎟ ⎝ r ∈R ⎠

Max: Eui = WP,

1/ρ

(10.9a)

where x is, li, and n are decision variables, P can be interpreted as the aggregate reliability, or 1 − P can be interpreted as the aggregate transaction risk, and W ≡ {(li − α − x is )[x is/(n − 1)] n−1[(1 − li)/(m − n) − α] m−n}1/ρ.

(10.9b)

Also, it can be shown, using symmetry, that pi/pr = 1 in equilibrium. The procedure to solve for x is and li is the same as in chapter 7. But the procedure to solve for n differs, since the solution of equilibrium n relates to the aggregate transaction risk E(∏ r kr)1/ρ. Let us have a close look at this term. The number of kr is n − 1. Suppose that s of them take on value kH and n − 1 − s of them take on value kL, while s can take on value from 1 to n − 1. Here, kH takes place with probability θ and kL takes place with probability 1 − θ. Therefore, the n − 1 of kr follows a binomial distribution. The probability for n − s of kr to take on value kH and for s − 1 of kr to take on value kL is

Ps = Cns−−11 θn −s (1 − θ) s−1

(10.10)

where Cns−−11 is s − 1 combinations of n − 1 elements. Following a binomial formula, it can be shown that

⎛ ⎞ P = E⎜ ∏ k r ⎟ ⎝ r ∈R ⎠

1/ρ

n−1

= ∑ Ps (k Hn− s k Ls−1 ) 1/ρ s −1

n−1 (n−1)/ρ n −1 = C 0n−1θn−1k H(n−1)/ρ + C 1n−1θn−2(1 − θ)k (n−2)/ρ k 1/ρ kL ] H L + . . . + [C n −1 (1 − θ)

= [θk

1/ρ H

+ (1 − θ)k

(10.11)

1/ρ n−1 L

]

where Ps is given by (10.10) and the ﬁnal equality in (10.11) is given by the binomial formula. Having inserted (10.11) into (10.9), we can express Eui as a function of li , x is, and n. Letting the derivatives of Eui with respect to the three variables equal 0 yields the solutions for the corner equilibrium values of all endogenous variables when insurance is absent.

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li = [n + α(n2 − mn + m − n)]/m lj = [1 + α(n − 1)]/m xi = x rd = xj = [1 − α(1 + m − n)]/m,

xis = (n − 1)xi/n

(10.12)

n = (1 − 1/α) + m{1 − 1/ln[θk H1/ρ + (1 − θ)k 1/ρ L ]} Eu = {[1 − α (1 + m − n)]/m}m/ρ[θk H1/ρ + (1 − θ)k H1/ρ] n−1 1/ρ n−1 P = [θk 1/ρ H + (1 − θ)k L ]

Differentiation of the corner equilibrium values of the endogenous variables with respect to parameters ks(s = H, L), θ, ρ yields comparative statics of the corner equilibrium with no insurance. dn/dks > 0, dli/dks > 0,

dn/dθ > 0,

dn/dρ < 0

dli/dθ > 0,

dli/dρ < 0

d[M(n − 1)x ]/dks > 0, d r

dEu/dks > 0,

(10.13a) (10.13b)

d[M(n − 1)x ]/dθ > 0 d

dEu/dθ > 0

dP/dks = (∂P/∂ks) + (∂P/∂n)(dn/dks) < 0, dP/dθ = (∂P/∂θ) + (∂P/∂n)(dn/dθ) < 0

d[M(n − 1)x ]/dρ < 0, d r

(10.13c) (10.13d)

and (10.13e)

where (n − 1)x dr = x rs is each individual’s aggregate purchase volume and M(n − 1)x rd = Mxsr is the aggregate demand for all goods in the market, which is the extent of the market. As in (10.4d), we have used the envelope theorem to obtain (10.13d). To obtain (10.13e), we have used the solution of n, given in (10.12), and the fact that αm < 1 if the solution of l j, given in (10.12), is between 0 and 1. Comparative statics imply that as transaction efﬁciency kH or kL rises, or as the probability of a high transaction efﬁciency, θ, increases (or as the risk of a low transaction efﬁciency decreases), or as the degree of risk aversion ρ falls, the following phenomena concur. The level of division of labor, n, increases. This implies increases in the number of markets for different goods, in diversity of structure, in market integration, and in production concentration. Aggregate coordination reliability of the network of division of labor, P, decreases, or aggregate risk for coordination failure of the network of division of labor increases. This is quite counterintuitive: an increase in the coordination reliability of each transaction or a decrease in the transaction risk of each transaction will increase aggregate transaction risk! The logic behind this result is that as transaction conditions for each transaction, ks , are improved, or as the risk of coordination failure of each transaction 1 − θ decreases, the scope for trading off economies of division of labor against transaction risk is enlarged, so that individuals can expand the network of division of labor to exploit more economies of division of labor, so that they can afford more aggregate risk of coordination failure of the network of division of labor. Each individual’s level of specialization increases. This implies increases in productivity, in the extent of the market, in the extent of endogenous comparative advantage, in aggregate demand, and in per capita real income. An interesting interpretation of an increase in k is a decrease in tax rate. Also, an increase in θ can be interpreted as a more stable tax rate. Mokyr (1993, pp. 46–58) provides historical evidence that a stable and nonpredatory tax system is essential for economic development. Sachs and Warner (1995a, 1997) provide empirical evidence that economic development performance negatively relates to the transaction risk caused by institutional deﬁciency. They use an institution quality index to measure this.

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Now, we assume that there is an insurance company from which individuals can buy an insurance contract. No matter what the level of transaction efﬁciency, an individual buying insurance must pay a premium π. If transaction efﬁciency is low, or is kL, the insurance company pays the individual c. Hence, the individual’s expected utility is Eui = W [θ(kH − π)1/ρ + (1 − θ)(kL − π + c)1/ρ]n−1

(10.14)

where the nonrandom variable W is given in (10.9b). If the insurance is complete and the market for insurance is competitive, the insurance company’s expected proﬁt must be 0. The company receives premium π at probability 1 from the individual and pays the individual c at probability (1 − θ). Therefore, the complete insurance and zero-proﬁt condition require π = (1 − θ)c

(10.15)

Inserting this expression into (10.14) and letting the derivative of Eui with respect to c equal 0 yields each individual’s optimum insurance policy c = kH − kL. Plugging the optimum policy c into (10.15) yields the optimum premium. π* = (1 − θ)(kH − kL)

(10.16)

Inserting the optimum premium and policy back into (10.14) gives the expected utility in the presence of insurance. Eui = W [θkH + (1 − θ)kL](n−1)/ρ

(10.17)

It says that no matter what the level of transaction efﬁciency, an insured person always gets the utility level at the weighted average of the high and low transaction efﬁciencies θkH + (1 − θ)kL. That is, the insured individual avoids all risk. Such insurance is called complete insurance. We now consider function f (k) = k1/ρ, which is the part of the utility function that involves uncertainty. The function is concave in the random variable k iff ρ > 1. A comparison between Eu in (10.12) and Eu in (10.17) indicates that an individual gets f (Ek) = [θkH + (1 − θ)kL]1/ρ if she is insured, and she gets Ef (k) = θk H1/ρ + (1 − θ)k 1/ρ L if she is not. Since for a strictly concave function f (k), the value of the function at the weighted average of two contingent transaction efﬁciencies is greater than the weighted average of the values of the function at the two contingent transaction efﬁciencies, (10.17) is certainly greater than the expected utility in the absence of insurance. (Recall the Jesen inequality and discussion of this in section 9.2 of chapter 9.) The ﬁrst-order conditions for maximizing (10.17) are exactly the same as those for maximizing (10.9), except for the ﬁrst-order condition for the equilibrium n. These conditions yield the corner equilibrium with insurance. l i′ = [n′ + α(n′ 2 − mn′ + m − n′)]/m l j′ = [1 + α(n′ − 1)]/m x i′ = x rd′ = x j′ = [1 − α(1 + m − n′)]/m,

x is′ = (n′ − 1)xi′/n′

(10.18)

n′ = (1 − 1/α) + m{1 − 1/ln[θkH + (1 − θ)kL ]} Eu′ = {[1 − α(1 + m − n′)]/m}m/ρ[θkH + (1 − θ)kL ](n′−1)/ρ P′ = [θkH + (1 − θ)kL ]n−1/ρ Primes of the variables denote corner equilibrium values with insurance. The differentiation of the corner equilibrium values of the endogenous variables with respect to parameters k, θ, ρ

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indicates that comparative statics in (10.13) hold for the case with insurance. A comparison between the corner equilibrium in (10.12) and that in (10.18) indicates n′ > n,

li′ > li,

dn′/dks > 0, dP′/dks < 0,

P ′ > P,

dn′/dθ > 0, dP′/dθ < 0.

Eu′ > Eu,

Mxis′ > Mxis

dEu′/dks > 0,

(10.19a)

dEu′/dθ < 0

(10.19b)

This implies that the expected utility with insurance is greater than that with no insurance. Applying the Yao theorem, it can be shown that all individuals will choose insurance in a general equilibrium. The corner equilibrium with no insurance is not a general equilibrium. (10.19) implies also that the level of division of labor for society, individuals’ levels of specialization, productivity, aggregate coordination reliability of the network of division of labor, and the extent of the market are all greater in the corner equilibrium with insurance than that in the corner equilibrium with no insurance. The complete insurance in this model is equivalent to the complete insurance in a Sovietstyle economy. But in this model, it is assumed that the risk of low transaction efﬁciency is exogenously given, independent of the effort devoted to reducing such risk. Hence, complete insurance does not generate the endogenous transaction costs that are associated with moral hazard. But we know that complete insurance in a Soviet-style economy indeed generates tremendous endogenous transaction costs and moral hazard problems. In the next section, we will endogenize the risk of a low transaction efﬁciency and investigate the relationships between the level of division of labor, incomplete insurance, and complete insurance that generate moral hazard and endogenous transaction costs.

10.5 ECONOMIC DEVELOPMENT AND ENDOGENOUS TRANSACTION COSTS CAUSED BY MORAL HAZARD Example 10.6: A simpliﬁed version of the Lio model (1996) with endogenous transaction costs caused by complete insurance. The difference between the two Lio models in this section and in the preceding section relates to the probabilities of different levels of transaction efﬁciency. Those probabilities are exogenously given in the last section, whereas here they are endogenously determined by an individual’s effort devoted to reducing the risk of low transaction efﬁciency. It is also assumed that this effort level is not observable to others or not veriﬁable in court when a dispute occurs, so that moral hazard may arise. Since the model with endogenous specialization and with moral hazard is much more difﬁcult to manage than a model with endogenous specialization alone or with moral hazard alone, we assume that there are only two goods in this section. Hence, each ex ante identical consumer-producer’s decision problem is Max: Eu = E[ln(x + kxd ) + ln( y + kyd )] s.t.

x + x = Max{0, lx − α}, s

(expected utility function)

y + y = Max{0, ly − α} s

(production functions)

lx + ly + e = 1

(endowment constraint)

k = kH with probability 2/3 ⎫ ⎬ if e = 1/3 k = kL with probability 1/3 ⎭

(effect of effort on transaction risk)

k = kH with probability 0⎫ ⎬ if e = 0, i = x, y k = kL with probability 1 ⎭

px x s + py y s = px x d + py y d

(budget constraint) (10.20)

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where it is assumed that kH > kL. Variable e is the level of effort devoted to reducing the risk of a low transaction efﬁciency. It can be considered as effort devoted to transporting goods carefully or to protecting the goods from being stolen. For simplicity, we assume that there are only two levels of such effort. The high level of effort e = 1/3 generates a low probability of low transaction efﬁciency (k = kL) and the low level of effort e = 0 causes low transaction efﬁciency for sure. Hence, the risk of low transaction efﬁciency is determined by the level of effort devoted to reducing transaction risk. Since the utility function is strictly concave in the quantities of the two goods consumed, all individuals are risk-averse to the same degree. Also, an increase in the effort level devoted to reducing transaction risk will reduce the amount of labor allocated to the production of goods and thereby reduce income and utility. Hence, each individual has an incentive to choose the low level of effort in reducing transaction risk if complete insurance is available. This implies that complete insurance will generate moral hazard if the division of labor is chosen. From the point of view of an insured, the insurance company cannot observe her effort level if she is completely insured. Her optimum decision is thus to choose the lowest level of effort. The insurance company will go bankrupt if every one of the insured behaves similarly. Hence, the insurance company will provide an incomplete insurance to restrain moral hazard. Suppose that each consumer-producer chooses premium π for a given policy of the insurance company, c. Then, the insurance company chooses the policy for a given π according to the incentive compatibility condition. The second step to sort out the insurance contract terms is equivalent to choosing a parameter β for a given π. The deﬁnition of β is given as follows. β = ( 2/3 )π/( 1/3 )(c − π),

(10.21)

where 1/3 is the probability of a low transaction efﬁciency and 2/3 is the probability of a high transaction efﬁciency, the denominator is the insurance company’s expected net payout in the event of a low transaction efﬁciency and the numerator is its expected premium earnings in the event of a high transaction efﬁciency. Since β is uniquely determined by c for any given π, choosing π for a given c is equivalent to choosing β for a given c. If β = 1, then the expected payout net of premium is the same as the expected premium, so that insurance is complete. If β > 1, the expected net payout is smaller than the expected premium, so that insurance is incomplete and the insured must take part of transaction risks. Hence, parameter β describes the incompleteness of the insurance contract for each transaction. Using the deﬁnition of β, we can express the insurance company’s payout net of premium in the event of low transaction efﬁciency as a function of β and π as well. We thus have c − π = 2π/β

(10.22)

Applying the Wen theorem to the model, there are 6 structures that we must consider. The ﬁrst is autarky, denoted as A. In this structure, there is no trade or transaction risk, so that it is easy to solve for the corner equilibrium in this structure. The second class of structures features division of labor, but with no insurance, denoted as Bi, i = L, M, H. There are three structures in this class. In structure BL, there are two types of specialist producer of the two goods and they choose the low level of effort in reducing transaction risk, that is e = 0. In structure BM, the specialist producers of one good choose the high effort level e = 1/3 and the specialist producers of the other good choose e = 0. Because of symmetry, the outcome is unaffected by which specialist producers choose e = 0 and which choose e = 1/3 . In structure BH , both specialist producers of the two goods choose e = 1/3 . The third class of structures features division of labor with insurance, denoted Ci, i = L, M, H. Structure CL features complete insurance and e = 0. Since it is assumed in (10.20) that the

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probability of the low transaction efﬁciency is 1 if e = 0, the uncertainty disappears for this case, so that the insurance company cannot survive. This implies that the corner equilibrium for this structure does not exist. In structure CM with the division of labor and insurance, one type of specialist producers chooses e = 1/3 and the other type of specialist producers chooses e = 0. Structure CH features division of labor, incomplete insurance, and e = 1/3 chosen by all individuals. Let us ﬁrst consider structure CH. In this structure, the decision problem for a specialist producer of good x is: Max: Eux = ln x + ln y d + 2/3 ln(kH − π) + 1/3 ln(kL + c − π) s.t.

x + x s = Max{0, 1 − α − e}, px x = py y s

d

e = 1/3

(production condition)

(10.23)

(budget constraint)

We can use (10.21) and (10.22) to eliminate c, then solve for the optimum x, x s, y d. Inserting the solution back into (10.23) yields Max: Eux = ln( px/py) + 2 ln[(2 − 3α)/6] + 2/3 ln(kH − π) + 1/3 ln[kL + (2π/β)]

(10.24)

Each specialist in x chooses premium π to maximize Eux for a given β. The optimum premium is π = 1/3 (kH − βkL)

(10.25)

Inserting (10.25) back into (10.24) yields the expected indirect utility function for a specialist in x: Eux = ln( px /py) + 2 ln(2 − 3α) + ln(2kH + βkL) − 3 ln 3 − (ln β/3) − 2 ln 2.

(10.26a)

Following the same procedure, we can solve for the expected indirect utility function for a specialist in y: Euy = ln( py /px) + 2 ln(2 − 3α) + ln(2kH + βkL) − 3 ln 3 − (ln β/3) − 2 ln 2

(10.26b)

The expected utility equalization condition Eux = Euy determines the corner equilibriumrelative price of the two traded goods in structure CH, that is, px /py = 1. The market clearing condition Mx x s = My x d and the population equation Mx + My = M, together with the corner equilibrium-relative price, determine the corner equilibrium numbers of the two types of specialists Mx = My = M/2. An insurance company will choose β according to the incentive compatibility condition. This condition implies that the insured has a higher expected utility when she chooses e = 1/3 than when she chooses e = 0. Following the approach to calculating the expected indirect utility function, we can work out the expected indirect utility function for a specialist in x to choose e = 0. For this case, k = kL will occur for sure, so that the effect on the utility of the expected payout net of premium is ln(kL + c − π). After elimination of c − π using (10.23), the expected indirect utility function for a specialist in x who chooses e = 0 is: Eux = ln( px /py) + 2 ln[(1 − α)/2] + ln(2kH + βkL) − ln 3 − ln β

(10.27)

Incentive compatibility implies that (10.26a) is not smaller than (10.27), that is, the expected utility for a high effort level in reducing transaction risks is not lower than that for a low effort level. This inequality sets up a constraint for β.

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Table 10.2 Expected real incomes in seven structures Equilibrium structure

Expected corner equilibrium per capita real income

A

2 ln[(1 − 2α)/2]

BL

2 ln[(1 − α)/2] + ln kL

BM

ln(2 − 3α) + ln(1 − α) − 2 ln 2 + (ln kH/3) + 2/3 ln kL − ln 3

BH

2 ln(2 − 3α) − 2 ln 6 + 2/3 ln kH + (ln kL/3)

CL

No corner equilibrium exists

CM

ln[(2 − 3α)/3] + ln(1 − α) − 2 ln 2 + 0.5{ln kL − (ln β/3) + ln[(2kH/3) + (βkH/3)]}

CH

2 ln(2 − 3α) − 2 ln 6 + ln[(2kH /3) + (kLβ/3)] − (ln β/3)

β > [3(1 − α)/(2 − 3α)]3

(10.28)

Further, a positive π implies kH > kH − π = (2kH/3) + (βkL/3), where we have used (10.25). This sets up another constraint on β: β < kH /kL

(10.29)

The two constraints on β imply that structure CH with insurance is equilibrium only if kH /kL > [3(1 − α)/(2 − 3α)]3.

(10.30)

If this condition does not hold, the set of candidates for the equilibrium structure comprises only A, BL, and BH. If this condition is satisﬁed, the set comprises A, BL, BH, and CH. Following the procedure used in solving for the corner equilibrium in structure CH, we can solve for all corner equilibria in the seven structures, which are summarized in table 10.2. Using the table, it can be shown that Eu(BM) < Eu(BL), if Eu(BM) > Eu(BH). This implies that either Eu(BM) < Eu(BH) or Eu(BM) < Eu(BL). According to the Yao theorem 5.1, it follows that structure BM cannot be an equilibrium structure. Similarly, we can prove that BH can be an equilibrium structure only if 2

2

⎛ 1 − 2α ⎞ ⎛ 1 − 2α ⎞ −2 3 2/3 ⎜ 1 − α ⎟ > kL > 3 β ⎜ 2 − 3α ⎟ kH ⎝ ⎠ ⎝ ⎠

(10.31)

which holds only if k 2H [(2 − 3α)/3(1 − α)]2 > 3β2/3 where β > 1. It is obvious that this inequality does not hold for α ∈(0, 1). Therefore, BH cannot be an equilibrium structure. Following a similar line of reasoning, it can be shown that BL cannot be an equilibrium structure if kH/kL > [3(1 − α)/(2 − 3α)]3. Taking into account all of the relevant information, comparisons of expected real incomes in all structures yield the general equilibrium and its inframarginal comparative statics, as summarized in table 10.3, where γ ≡ 33[1 − 2a)/(2 − 3a)]2β1/3, A is the autarky structure, BL is the structure with the division of labor and with no insurance, where individuals choose the low effort level in reducing transaction risks, CH is the structure with the division of labor and incomplete insurance where individuals choose the high effort level.

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General equilibrium and its inframarginal comparative statics

kH /kL < [3(1 − α)/(2 − 3α)]3

kH /kL > [3(1 − α)/(2 − 3α)]3

kL < [(1 − 2α)/(1 − α)]2

kL > [(1 − 2α)/(1 − α)]2

2kH + βkL < γ

2kH + βkL > γ

A

BL

A

CH

We need an additional assumption to determine the equilibrium terms of insurance or the equilibrium degree of incompleteness of insurance. Suppose that the market for insurance is competitive and the management cost for an insurance contract is b; then the expected proﬁt for each insurance contract is π − (c/3) − b = 0. Free entry and competition will drive the proﬁt down to 0. Hence, the equilibrium insurance contractual terms can be determined by the zeroproﬁt condition and equations (10.21), (10.22), (10.25). After manipulation of the equations, it can be shown that the equilibrium contractual terms are given by the following equations: β is given by f (β, b, kH, kL) ≡ 2(β − 1)(kH − βkL) − 9b = 0, c = 3b(2 + β)/2(β − 1),

π = (c/3) + b.

Then the equilibrium level of division of labor, endogenous transaction costs, and productivity are explained by the insurance management cost coefﬁcient b. In this model, the efﬁcient balance point (or efﬁcient degree of incompleteness of insurance, β) of the trade-off between incentive provision and risk sharing is determined by the insurance management cost coefﬁcient, b, the degree of risk that relates to 1 − θ, kH/kL, and ρ. Because of the connection between the degree of insurance completeness and the degree of softness of the budget constraint, the trade-off between risk sharing and incentive provision is equivalent to the trade-off between risk sharing and the softness of the budget constraint. This trade-off has many more general implications for the analysis of the relationship between economic development and institutions. From the experience of the Asian ﬁnancial crisis in 1997, we can see that it is not easy to identify the efﬁcient balance point of the trade-off. When the IMF emphasized the reforms of the ﬁnancial market as a precondition for ﬁnancial assistance for alleviating the damage of the crisis, it paid more attention to incentive provision in reducing the risk of a bad outcome. When the Korean and Indonesian governments asked for prompt ﬁnancial assistance from the IMF, they emphasized risk sharing. The bargaining between the two sides was to ﬁnd the efﬁcient balance of the trade-off between incentive provision and risk sharing. Table 10.3 implies that if the two values of transaction efﬁciency are sufﬁciently small, the general equilibrium is autarky where there is no market or transaction risk. As kH and kL increase, the general equilibrium jumps to the division of labor with transaction risks. When the ratio kH /kL is not great, or the gains from a high effort in reducing risk of a low transaction efﬁciency are not great, insurance cannot survive moral hazard. Hence, the division of labor is not associated with insurance and individuals choose the low effort level in reducing transaction risk (structure BL ). When the gains are signiﬁcant, insurance emerges from the division of labor and individuals choose the high effort level in reducing transaction risk (structure CH ). Next, we show that for kH/kL > [3(1 − α)/(2 − 3α)]3, insurance can promote division of labor and productivity progress. Comparisons between corner equilibrium expected real incomes in structures A, BH, and CH, given in table 10.2 yield the following results: Eu(BH) > u(A) iff μ1 ≡ k H2/3k L1/3 > μ0 ≡ [3(1 − 2α)/(2 − 3α)]2 Eu(CH) > u(A) iff μ2 ≡ (2kH + βkL)/3β1/3 > μ0

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A close examination of μ1 and μ2 yields μ2|β→k

H /kL

= μ1

and

∂μ2/∂β < 0 if β < kH/kL

(10.32a) and

∂μ2/∂β > 0 if β > kH/kL

(10.32b)

(10.32b) implies that μ2 reaches its minimum at β = kH/kL. This, together with (10.32a), implies that μ2 > μ1. This implies that Eu(BH) < u(A) and Eu(CH) > u(A) if μ0 ∈(μ1, μ2). In other words, structure CH with insurance is better than autarky, which is in turn better than structure BH with no insurance if μ0 ∈(μ1, μ2). This establishes the proposition that incomplete insurance in CH may promote division of labor and productivity progress. Next, we show that such incomplete insurance cannot eliminate the endogenous transaction costs caused by moral hazard, though it does reduce such endogenous transaction costs. To substantiate this claim, it sufﬁces to prove that the corner equilibrium in structure CH is not locally Pareto optimal. It is easy to show that the corner equilibrium expected real income in CH increases as β tends to 1. Indeed, the local Pareto optimum for the division of labor can be calculated as the corner equilibrium in CH with β = 1. The locally Pareto optimum real income for the division of labor is V = 2 ln(2 − 3α) − 2 ln 6 − ln 3 + ln(2kH + βkL) − [(ln β)/3] and V > u(A) iff μ3 ≡ (2kH + kL)/3 > μ0.

(10.33)

A comparison between μ3 and μ2 indicates that μ3 > μ2. This implies that V is always greater than u(A) whenever Eu(CH) is greater than u(A). But for μ 0 ∈(μ2, μ3), V > u(A) > Eu(CH). Hence, if the effort level in reducing transaction risks is observable, complete insurance can be given only to those who choose the high effort level, so that moral hazard is eliminated and the expected real income is higher than that in structure CH, which is associated with β > 1. In other words, the corner equilibrium in structure CH is not locally Pareto optimal. However, the Pareto optimum is not a feasible utopia when CH is the general equilibrium structure. It is interesting to note three different cases of endogenous transaction costs caused by moral hazard. 1) Suppose kH /kL > [3(1 − α)/(2 − 3α)]3 and μ0 ∈(μ2, μ3), which imply that the general equilibrium structure is A and the Pareto optimum is the division of labor with complete insurance and with no moral hazard. Hence, the division of labor and related welfare gains cannot be realized because of the positive equilibrium endogenous transaction costs. This kind of endogenous transaction cost is called type I endogenous transaction cost, which are associated with the Pareto inefﬁcient equilibrium levels of division of labor and productivity and number of transactions. 2) Suppose kH /kL > [3(1 − α)/(2 − 3α)]3 and μ2 > μ0, which implies that the general equilibrium structure is CH and is not Pareto optimal. Hence, the equilibrium resource allocation is not efﬁcient (i.e., the relative quantity and relative price of the two goods are not efﬁcient) because of the endogenous transaction costs caused by moral hazard, despite the efﬁcient equilibrium level of division of labor. This kind of transaction cost is called type II endogenous transaction cost. 3) Suppose kH/kL < [3(1 − α)/(2 − 3α)]3 and kL > [(1 − 2α)/(1 − α)]2, which imply that the equilibrium structure is BL, is not Pareto optimal, and has a low effort level in avoiding transaction risk. Hence, moral hazard generates endogenous transaction costs that are associated with a low effort level in avoiding transaction risk, despite the Pareto efﬁcient level of division of labor. This is referred to as type III endogenous transaction cost. 4) Suppose kH /kL > [3(1 − α)/(2 − 3α)]3 and μ0 > μ3 > μ2, which imply that the equilibrium structure is A and is Pareto optimal. Assume now that transaction efﬁciency is improved such

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that μ 0 ∈(μ2, μ3). This implies that the general equilibrium jumps from structure A to structure CH and the equilibrium endogenous transaction costs increase from 0 to a positive level. In other words, concurrent increases in endogenous transaction costs, in productivity, and in the level of division of labor may take place as a result of reduced exogenous transaction costs (improved transaction efﬁciency). We call the kind of endogenous transaction cost that emerges from improved exogenous transaction costs and increased productivity type IV endogenous transaction cost. Type I and III transactions are similar to X-inefﬁciency, which causes a low productivity or a low effort level. But type I transaction cost causes organizational inefﬁciency (Pareto inefﬁcient level of division of labor) while type II and type III endogenous transaction costs result in allocative inefﬁciency. Type IV endogenous transaction cost is due both to a higher productivity, which can be used to afford increased endogenous transaction costs, and to moral hazard. These results on endogenous transaction costs substantiate Coase’s conjecture (1960) that if there exist endogenous transaction costs, the interactions between self-interested individuals will sort out the contractual arrangements that maximize economies of division of labor net of endogenous and exogenous transaction cost, rather than minimize a particular type of transaction cost. If the trade-off between measuring the cost of effort level and moral hazard is introduced into the model with the trade-off between incentive provision and risk sharing, the story will be much more realistic and complicated. Milgrom and Roberts (1992, p. 336) survey several models that have the two types of trade-off. In one of the models, promotion according to seniority can reduce inﬂuencing (rent-seeking) cost in a ﬁrm, encourage continuous accumulation of ﬁrmspeciﬁc human capital, and provide risk sharing between the employee and the employer. But it will cause the endogenous transaction costs associated with inaccurate measurement of effort levels and prevent the realization of productivity-enhancing labor mobility. The effects of a promotion scheme according to performance are the opposite. Hence, the efﬁcient promotion criteria must efﬁciently trade-off one against others among incentive provision, risk sharing, employment stability (or its reciprocal, labor mobility), and measurement costs. Example 10.7: Application of the models in examples 10.5 and 10.6 to the analysis of the Asian ﬁnancial crisis in 1997. There are two opposite views of the Asian ﬁnancial crisis in 1997. According to one of them, the ﬁnancial crisis was caused by moral hazard associated with cronyism, and complete insurance of loans provided by the government. The other view (Radelet and Sachs, 1998a, and Stiglitz, 1998) holds that as the network of trade expands, aggregate risk of coordination failure inevitably increases, even if moral hazard is not that serious. Hence, policy missteps and hasty reactions by governments and international organizations may miss the efﬁcient balance of the trade-off between insurance and incentive provision. For instance, overemphasis on ﬁnancial reform programs which reduce moral hazard when insurance should receive more attention, added to the virulence of the banking panics. We can apply the models in examples 10.5 and 10.6 to assess this view. According to (10.13e) and (10.19b), it is obvious that even if moral hazard is absent, the aggregate risk of coordination failure 1 − P increases as transaction conditions are improved or as the risk of coordination failure for each transaction decreases. This is because as the risk of coordination failure for each transaction reduces, the scope for trading off economies of division of labor against aggregate risk is enlarged, so that individuals can afford a higher aggregate risk. Hence, choosing a higher aggregate risk of coordination failure is associated with economic development generated by evolution of division of labor, and it is efﬁcient. This explains why a more successful developed economy has a higher risk of having an episode like the Great Depression than a less-developed economy. And this is why Radelet and Sachs call the 1997 Asian ﬁnancial crisis a “crisis of success.” The higher risk is efﬁciently chosen, just like choosing the higher risk of being killed by driving on a freeway.

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This implies that moral hazard is not the whole story; and is why more moral hazard generated by complete insurance in China and in the Soviet Union does not necessarily imply more risk of ﬁnancial crisis. The model in example 10.6 indicates that the efﬁcient way to handle the Asian ﬁnancial crisis is to balance the trade-off between incentive provision in reducing the risk and risk sharing, rather than paying too much attention to one of them. If the time lag between ﬁnancial decisions and market price signals is considered, we may have another trade-off between the strong incentive created by sensitive feedback of ﬁnancial decisions to market shocks and the stability of the ﬁnancial market. Financial reforms may increase the sensitivity of the feedback mechanism. But feedback that is too sensitive may make overshot more likely, and sometimes it may generate overreactions that create a ﬁnancial crisis. Aghion, Bacchetta, and Banerjee (1998) develop such a cobweb model. See also example 19.5 for a Smithian model with such a trade-off. In policy-making, the trick is to identify the efﬁcient balance of the trade-offs between insurance provision and moral hazard and between strong incentive and stability.

Key Terms and Review • Trade-off between endogenous and exogenous transaction costs • Trade-off between exogenous transaction costs in deepening the incumbent relationships and exogenous transaction costs in expanding potential relationships • Implications of the trade-off between economies of division of labor and various transaction costs, in addition to the above two trade-offs, for economic development • Externality; public goods • Differences between nonrivalry, non-exclusivity, and public goods • The difference between Pigou’s marginal analysis of the distortions caused by externalities and public goods, and inframarginal analysis of endogenous transaction costs and endogenous externality • Substitution between competition in the market and precise speciﬁcation and enforcement of property rights • Why perfect competition and perfectly speciﬁed and enforced property rights may not be efﬁcient if the trade-offs among various endogenous and exogenous transaction costs and economies of division of labor are taken into account • The connection between softness of budget constraint and vagueness in specifying and enforcing property rights • The market mechanism that sorts out the efﬁcient degree of competition, the efﬁcient degree of vagueness in specifying and enforcing property rights, and the efﬁcient level of division of labor • The relationship between risk aversion and a strictly concave utility functions • Degree of risk aversion • Effects of transaction risk and the degree of risk aversion on the equilibrium network size of division of labor and economic development • The effect of insurance on the equilibrium network size of division of labor and economic development • Complete insurance, moral hazard, incomplete insurance, and endogenous transaction costs • What are the features of a Soviet-style economic system with complete insurance? Why does it generate extremely high endogenous transaction costs? Why would productivity decline sharply if the complete insurance system was abolished before a developed market for insurance was available?

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Further Reading Trading off different kinds of transaction costs: Cheung (1969, 1970, 1983), Milgrom and Roberts (1992), Yang and Y.-K. Ng (1993, chs. 10, 11), Yang and Wills (1990), Yang, Wang, and Wills (1992), Williamson (1975, 1985), Monteverde and Teece (1982); Economics of property rights: Barzel (1989), Demsetz (1967, 1988), Demsetz and Lehn (1985), Furubotn and Pejovich (1974), Manne (1975), North (1981), North and Weingast (1989); New political economy models with endogenous stealing: Marcouiller and Young (1995), Skaperdas (1992); Soft budget constraint: Kornai (1980, 1991), Qian (1994); Theory of reliability: Shooman (1968), Sah and Stiglitz (1986, 1988, 1991), Sah (1991), Bazovsky (1961), Lange (1970), Blanchard and Kremer (1997), Kremer (1993). Historical evidence about the relationship between property rights and economic development: Macfarlane (1988), Baechler, Hall, and Mann (1997), Pipe (1999), Jones (1981), Baechler (1976), Rosenberg and Birdzell (1986), and Mokyr (1990, 1993), Landes (1998); Empirical evidence for the relationship between better enforced property rights and economic development: Barro (1997), Sachs and Warner (1995, 1997), Yang, Wang, and Wills (1992), Frye and Shleifer (1997); Insurance and economic development: Lio (1996, 1998), Dixit (1987, 1989); Risk and insurance: Mas-Collell, Whinston, and Green (1995, chs. 6, 13, 14), Varian (1993, ch. 8), Milgrom and Roberts (1992); General equilibrium models of moral hazard: Legros and Newman (1996), Laffont and Tirole (1986), Helpman and Laffont (1975), Kihlstrom and Laffont (1979); Economic crisis and development: Sachs (1986d, 1987, 1989), Radelet and Sachs (1998a).

QUESTIONS 1 The automatic trafﬁc-light system can be used to save on costs of hiring trafﬁc policemen for manual control of trafﬁc lights, but it causes endogenous transaction costs as well. The automatic system is not as ﬂexible as a manually controled system, so that it quite often wastes drivers’ time in waiting for a green light. Technically, an ultrasound system for monitoring trafﬁc conditions at each intersection can be used to reduce such endogenous transaction costs at the exogenous transaction costs of buying the ultrasound system. Discuss under what conditions (for instance, the salary of a policeman is low in a developing country, or technical progress could signiﬁcantly reduce the price of the ultrasound system) acceptance of the endogenous transaction costs caused by the automatic trafﬁc-light system is efﬁcient. Why is the term “externality” misleading for addressing endogenous transaction costs? 2 Before patent laws were ﬁrst introduced in Britain (the Statute of Monopolies, 1624), the invention of new technology involved substantial endogenous transaction costs in trading intellectual property. The patent laws signiﬁcantly reduced such endogenous transaction costs at the cost of increasing the distortions caused by monopoly. A discussion on beneﬁts and costs of the patent laws for the Industrial Revolution can be found in Mokyr, 1993, pp. 40–8. Why are the terms “externality” and “spread-over effect” which are used to describe such endogenous transaction costs misleading? 3 In the earliest postal system in Britain, postal fees were accurately calculated according to the weight and distance traveled of the mail in order to reduce the endogenous transaction costs caused by an inaccurate correspondence between fee and service provided. Analyze why that postal system was replaced with an inaccurate measurement of the correspondence between fee and service based on postage stamps and mailboxes. Why is the term “externality” misleading for describing the various transaction costs involved in the postal system? 4 Holmstrom and Roberts (1998, pp. 80–1) examine the difference between contractual arrangements in the US and Japan. In the US: When products were outsourced, the

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design was typically done by the automaker, with the drawings being provided to the suppliers. This pattern is what Williamson’s hold-up stories would predict, for the investment in design is highly speciﬁc and probably cannot be protected fully by contracts; thus, external suppliers will not make such relationship-speciﬁc investments for fear that they will be held up by buyers after their investments are in place. In stark contrast, it is normal practice for Japanese auto ﬁrms to rely on their suppliers to do the actual design of the products supplied. The design costs are then to be recovered through the sale price of the part, with the understanding that this price will be adjusted in light of realized volumes. A second contrast: the traditional US practice has been that physical assets speciﬁc to an automaker’s needs are owned by the automaker. This clearly applies in the case of internally procured items, but it also holds in cases where the assets are used by the external supplier in its own factory. In Japan, in contrast, these speciﬁc investments are made by the supplier, who retains ownership of the dies. This would seem to present the automaker with temptations to appropriate the returns on these assets, once the supplier has made the relationship-speciﬁc investment. Moreover, because the Japanese auto manufacturers typically have a very small number of suppliers of any part, component or system, the supplier would also seem to be in a position to attempt opportunistic renegotiation by threatening to withhold supply for which there are few good, timely substitutes. The Japanese pattern is directly at odds with transaction cost theory. Meanwhile, the divergence in ownership of the dies between the two countries presents problems for Hart, Grossman, and Moore’s attempts to explain ownership allocation solely in terms of providing incentives for investments. Use the model in example 10.2 to explain the difference between contractual arrangements in Japan and the US in connection with Williamson’s theory of asset speciﬁcity and Hart’s theory of incomplete contracts (example 9.15). 5 Cheung, 1970; Barzel, 1982: Oranges can be grouped in a very ﬁne or a rough way. One of the two extremes is to price each orange precisely according to its quality (taste, color, and size). The other is to set up the same price for all oranges of different qualities. In reality, grouping and pricing of oranges is in-between the two extremes. Apply the models in this chapter to analyze how the efﬁcient degree of precision in measuring oranges is determined in the marketplace. Why is the existence of externality caused by the imprecise measurement of the quality of oranges efﬁcient in the free market system? 6 Use the model of endogenous “externality” to formalize Coase’s and Cheung’s criticisms of Pigou’s welfare analysis of externality and public goods. According to Cheung (1970, 1983) and Coase (1960), so-called externality is endogenously chosen by individuals in efﬁciently trading off between endogenous and exogenous transaction costs, and if exogenous transaction costs in specifying and enforcing property rights are counted, keeping a certain degree of “externality” may be efﬁcient. Also, inframarginal analysis across different structures of property rights is more appropriate than Pigou’s marginal analysis of quantities and prices for a given economic structure. In other words, discontinuous jumps between corner solutions should be taken into account for a general equilibrium analysis of the trade-off between the beneﬁts of trade and all kinds of transaction costs. 7 Marshall (1890, p. 241) described the relationship between the network of division of labor, transaction conditions, and the development of new machinery as follows. “The development of the organism, whether social or physical, involves an increasing subdivision of functions between its separate parts on the one hand, and on the

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other a more intimate connection between them. Each part gets to be less and less self-sufﬁcient, to depend for its well-being more and more on other parts, so that any disorder in any part of a highly developed organism will affect other parts also. This increased subdivision of functions, or ‘differentiation,’ as it is called, manifests itself with regard to industry in such forms as the division of labour, and the development of specialized skill, knowledge and machinery; while ‘integration,’ that is, a growing intimacy and ﬁrmness of the connections between the separate parts of the industrial organism, shows itself in such forms as the increase of security of commercial credit, and of the means and habits of communication by sea and by road, by railway and telegraph, by post and printing-press.” Interpret the models in this chapter in connection with this description. 8 Mokyr (1990, p. 267) writes: “Small ﬁrms do not guarantee competitiveness. If ﬁrms are catering to a small enough market (that is, if transport costs are sufﬁciently high), even a single artisan could be a monopolist. Moreover, competitive industries can devise cushioning mechanisms that mitigate the sharp edges of competition and eventually make the industry behave as a monopolist in some respects. The guild system, although not set up for that purpose, clearly carried out that task in Europe for many centuries.” Use the models in this chapter to substantiate the conjecture on the relationship between the degree of competition and transaction efﬁciency. 9 If the capital market is not developed, a government postal system can be used to develop the market for postal services. Why may the government postal system generate greater endogenous transaction costs than the market for private postal services if the capital market is developed? Some economists use the notion of network externality to justify a government monopoly in the market for postal services. Why may this notion be misleading? 10 Comparative statics of the equilibrium model in example 10.2 can be used to identify the impact of the improvements in two kinds of transaction efﬁciency: efﬁciency in delimiting rights to contracting and efﬁciency in specifying and enforcing contractual terms. For instance, an improvement in transaction efﬁciency in delimiting rights to contracting may increase buyers’ dependence on competition between peer suppliers of a good, and reduce the equilibrium degree of precision in specifying and enforcing contractual terms. An improvement in efﬁciency in stipulating and enforcing a contract may have contrary effects, so that a buyer of a good will increase the precision of a contract rather than maintaining contact with many potential suppliers of the good. Meanwhile, improvements in efﬁciency of either kind may enhance the equilibrium level of division of labor, trade dependence, and productivity. This model can also be used to analyze the structure of property rights in a Sovietstyle economy. Socialist and comparative system economists are now realizing that equivocation in delimiting property rights under a state ownership system is a much more serious problem than distorted prices in a socialist economy. Many Chinese economists believe that more precisely delimited property rights are better. Use the distinction between efﬁciency in delimiting rights to contracting and efﬁciency in specifying and enforcing the terms of a contract to comment on that view. 11 Restrictions that exist on the trading of labor, land, and capital in a Soviet-style economy will substantially reduce transaction efﬁciency in delimiting rights to contracting, thereby restricting institutional development and economic growth. Under such restraints, the scope for people to balance the two types of transaction cost is very limited. Use the model in example 10.4 to analyze the difference between

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a state-run enterprise in a socialist country and a government owned ﬁrm in a free enterprise system, and the difference between a state-run enterprise in a socialist country and a private ﬁrm in a free market. The Chinese and Taiwanese governments use state revenue to develop the freeway system, while in Malaysia the major freeway system is developed by the private sector. Use the models in this chapter to analyze the relative advantages of the two ways of developing infrastructure. Use the models in this chapter to analyze the ﬁnancial crisis in East Asia in 1997. Yang, Wang, and Wills use meticulous documentation of institutional changes in China to estimate sub-indices of transaction efﬁciencies in specifying and enforcing rights to use, transfer, and appropriate earnings from land, goods, labor, and ﬁnancial assets. Then the 12 sub-indices are used to estimate a comprehensive transaction efﬁciency index over 9 years. A regression of the per capita real income on the degree of commercialization (a measure of the level of division of labor) and the transaction efﬁciency index, and a regression of the degree of commercialization on the index, show a signiﬁcant positive relationship between per capita real income, the level of division of labor, and transaction efﬁciency in specifying and enforcing property rights. Derive more empirical implications, and ﬁnd more empirical evidence for the theories developed in this chapter. Use the models in this chapter to analyze the function of the stock market in providing incomplete insurance for entrepreneurial activities and its development implications. In many less-developed societies, individuals allocate a lot of resources to the deepening of personal trade relationships to increase the reliability of exchanges. They do not rely on broad, impersonal market connections to secure transactions (see for instance Mauss, 1925). Use the model in example 10.2 to explain this phenomenon. North (1970) argues that the development of impersonal exchanges is essential for reducing transaction costs and for economic development. Use the models in this chapter to analyze the conditions for the development of impersonal exchanges. Analyze the functions of unemployment insurance, medical insurance, and other insurance in increasing the network size of division of labor and productivity. The Soviet-style economic system provides complete insurance for those specializing in different professions in the state sector. That insurance generates tremendous endogenous transaction costs because of moral hazard, but is an essential condition for the operation of a large network size of division of labor. Explain, using the models in this chapter, why the Russian economy drastically declined in the 1990s after the complete insurance system had been abolished. Analyze why the framework of consumer-producers and the notion of the positive network effect of division of labor on aggregate productivity are essential for exploring the productivity implications of insurance. Use the models of insurance in this chapter to explain the impact of the development of the insurance sector on the success of British commerce and the wealth of the nation in the eighteenth century. Use empirical data to test the concurrent evolution of division of labor and the income share of insurance, which are used to accommodate the increasing risk of coordination failure of a larger network of division of labor. A survey in the Economist (Sept. 5–11, 1998, pp. 4–7) found that the probability of a motorist getting in a trafﬁc jam is higher in a city the faster the upgrading of its transportation infrastructure. Use the theory in this chapter about the trade-off

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24 25

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between the beneﬁt of expanding the network and the reliability of the network to explain why aggregate reliability declines as transaction conditions are improved. The model in example 10.6 shows that in a Smithian model of endogenous specialization, moral hazard, division of labor, and productivity may increase side by side as transaction conditions are improved. Hence, the distortions caused by moral hazard in a developed country might be greater than those in a less-developed country, despite higher productivity in the former. Use this result and other models in this chapter to comment on the claim made by some development economists that mainstream economics is not applicable to developing countries, because the non-existence of many markets in the developing countries creates many more distortions than in the developed countries. Use the models in this chapter to analyze division of labor in producing books and related ideas; and the role of copyright laws and their enforcement in promoting the division of labor. Endogenous transaction costs caused by interest conﬂicts in economic development, investigated in chapters 10 and 11, are treated in conventional development economics under the rubrics of “public goods,” “externality,” “market failure,” and “inequality of income distribution.” Assess the differences between these two approaches to studying obstacles to economic development.

EXERCISES

1 Yang and Wills, 1990: Assume that q in the model of example 10.1 is endogenously determined by labor effort in reducing transaction risk. Solve for general equilibrium and its inframarginal comparative statics. 2 Mokyr (1993, p. 56) describes the trade-off between the negative effect of taxation and its beneﬁt to economic development via developing infrastructure that improves transaction conditions. In the eighteenth and ninteteenth centuries, the British were more heavily taxed than the French, but a stable and pre-speciﬁed tax rule was never allowed to become as arbitrary and conﬁscatory as in France. Tax revenue was used to develop the institutional and transportation infrastructure and signiﬁcantly improved transaction conditions. Hence, in 1788, British GNP per capita was about 30 percent higher than in France. Specify a tax rate on each dollar from sale of goods in the model in example 10.1. Assume that transaction reliability r is an increasing function of tax revenue. Use the extended model to explain Mokyr’s historical facts. Note that because of the trade-off between the positive and negative effects of taxation, there is an optimum tax rate which maximizes per capita real income. 3 Assume that q in the model of example 10.1 differs from good to good, and m = 3. Solve for the general equilibrium and its inframarginal comparative statics. Use your results to analyze why a property that has the same consumption and production conditions as other properties, but involves more restrictions on its trading or has a greater transaction risk q, will have a lower market price if it is traded, and will be more likely not to be traded if only a subset of goods are traded in equilibrium. Apply the analysis to explore the welfare implications of a

C HAPTER 10: T RANSACTION R ISK , P ROPERTY R IGHTS , I NSURANCE

4

5

6

7

public housing program. Use the model to explain why, in many developing countries, government institutions, including government funded universities, are reluctant to buy all kinds of services from the market. They tend to have their own guesthouses instead of buying professional hotel services for their guests, to have their own lawyers instead of buying professional law services from independent law ﬁrms, and so on. Analyze the implications of such a tendency to self-sufﬁciency for the equilibrium network size of division of labor and economic development. Suppose good x in the model in example 10.4 is a producer good that is essential for the production of the consumption good y. Each consumer-producer’s utility is a function of the consumption amount of good y. There is no transaction uncertainty for good y. Solve for the general equilibrium and its inframarginal comparative statics. (Yang and Ng, 1993, ch. 11.) Holmstrom and Milgrom, 1991: The employer hires the employee to undertake two activities to generate proﬁt. The employer’s certain equivalent (see section 9.2 of chapter 9 for the deﬁnition of this concept) is P(e1, e2) − (α + β1e1 + β2e2), where ei is the employee’s effort level in activity i, βi is the incentive intensity coefﬁcient for activity i, P(e1, e2) is the expected gross proﬁt, and α + β1e1 + β2e2 is the expected wage payment. Contingent wage payment is w = α + β1(e1 + x1) + β2(e2 + x2), where xi ~ N(0, σ) is a white noise in activity i and x1 and x2 are independent. The employee’s certain equivalent wealth is α + β1e1 + β2e2 − C(e1 + e2) − 0.5rvar(β1x1 + β2x2), where C(e1 + e2) is the disutility of total effort, r is the employee’s coefﬁcient of absolute risk aversion, and var(β1x1 + β2x2) = (β 12 + β 22)σ. Find the optimum incentive intensity in each activity βi by maximizing the employer’s and employee’s total certain equivalent wealth subject to the ﬁrst-order condition for maximizing the employee’s certain equivalent wealth. Show that the trade-off between balanced incentives for the two activities and the beneﬁt of strong incentives for each activity generates the optimum incentive payment structure that entails much weaker incentives than in the conventional principal–agent model. Holmstrom and Milgrom use this model to show that the institution of the ﬁrm can use such a weak but balanced incentive contract to get a particular activity going, whereas the activity may not occur in the market without the ﬁrm. Discuss the difference between this model and the models in examples 8.1, 9.15, and 10.2. Li, 2001: Introduce stealing into the models in this chapter and assume that an individual can spend time stealing the goods of trade partners in transactions. Also, each individual can spend time protecting herself from theft. Specify a stealing function, of which the right-hand side is time spent stealing and the left-hand side is goods that can be obtained without pay. Then you may specify a protection function on the negative relationship between the degree of theft and the effort spent protecting her property. Use such a model to explore the implications of endogenous stealing for the equilibrium network size of division of labor and economic development. Criminal laws penalize stealing much more than direct economic cost caused by stealing. For instance, according to criminal laws, theft can get a jail sentence of several years, in addition to the ﬁne that covers direct economic damage caused by the theft. Also, the moral code requires responsible individuals to do more than that which is suggested by a cold economic calculation of the cost and beneﬁt of theft. What are the development implications of criminal laws which protect and a moral code respecting private property? Assume that in the model in example 10.5, m = 3 and α1 > α2 > α3. Solve for the corner equilibria with and without insurance, and for the inframarginal comparative statics. Analyze the development implications of insurance.

337

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8 Assume that in the model of example 10.5, m = 3 and kH and kL differ from good to good. Solve for the corner equilibria with and without insurance, and for the inframarginal comparative statics. Analyze the implications for the trade pattern of the difference in transaction risk across goods. 9 Assume that in the model of example 10.6 the utility function is u = [(x + kx x d )( y + ky y d )1/2 10

11

12

13

Solve for the inframarginal comparative statics. Develop a general equilibrium model, on the basis of example 10.6, to endogenize the emergence of professional insurance agents from the evolution of division of labor. You may specify the economies of specialization in estimating transaction risk. Discuss the possible implications of the economies of specialization, which might be used to get results that are contrary to some insurance models, which predict that the insured knows more about risk than the professional insurance company (adverse selection). Kremer, 1993: The production function for a neoclassical ﬁrm is y = kαqnnB, where y is the expected output level, k is the input level of capital, α ∈(0, 1), q is the probability that a worker does a job meeting a quality requirement, or 1 − q is the probability that this worker’s job does not meet a quality requirement, n is the number of jobs that are essential for production, and B is a contribution parameter of each qualiﬁed job to output. Market wage is a function of q, which is positively related to the quality of workers hired. Hence, w = w(q). The interest rate is r. Suppose that good y is the numeraire. Specify the ﬁrst-order conditions for maximizing proﬁt with respect to k and q and identify the market relationship between the wage rate and the quality of workers w(q). (Hint: insert the expression of the optimum k into the ﬁrst-order condition for the optimum q, then solve for the differential equation dw/dq = f (q).) Sah and Stiglitz, 1988: Consider two patterns of the decision-making process in which a project is assessed by two decision-makers. In pattern A (series connection), person 1 assesses a proposed project ﬁrst. She accepts a proposal with probability p and rejects it with probability 1 − p. A proposal that has been accepted by person 1 is then assessed by person 2, who accepts a proposal with p ∈(0, 1). In pattern B (parallel connection), each person assesses each proposal independently of the other’s assessment. Assume that 50 percent of the proposals are good and the others should be rejected. What is the probability that a good proposal is rejected (type I error) under each of the decision patterns? What is the probability that a bad proposal is accepted (type II error) under each of the decision patterns? In example 10.2, assume that reliability for each transaction r is a decreasing function of the number of potential partners, N (because the incumbent partner’s loyalty decreases as a person keeps in touch with many potential substitutes for the incumbent). Solve for the inframarginal comparative statics again. Use your result to analyze why many franchise contracts include a clause that imposes a high cost if the franchisee breaks free of the incumbent franchiser.

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PART III Urbanization and Industrialization

C HAPTER 11: U RBANIZATION 341

URBANIZATION, STRUCTURAL DUALITY BETWEEN URBAN AND RURAL AREAS, AND ECONOMIC DEVELOPMENT

11

11.1 WHY AND HOW CITIES EMERGE FROM THE DIVISION OF LABOR Xenophon (see Gordon, 1975, p. 41), William Petty (1683, p. 947), Adam Smith (1776, chs. 2, 3, book I), and Alfred Marshall (1890, chs. 9–10, book IV) recognized the intrinsic connection between division of labor and the emergence of cities. However, no general equilibrium analysis was developed to explain the emergence of cities from the evolution of division of labor until the 1990s. There are two ways to explore the relationship between urbanization and division of labor. One is proposed by Yang (1991) and Yang and Rice (1994), with the accentuation of the endogenization of individuals’ levels of specialization and degree of market integration. The other is proposed by Fujita and Krugman (1995), with the emphasis on the endogenization of the number of goods and economies of scale. Yang’s model (1991) predicts that if all individuals reside together within a small area to form a city, then transaction efﬁciency can be improved by reducing the distance between each pair of trade partners, so that the level of division of labor and productivity can be raised. But since the logic of that model suggests that all individuals should reside together, it cannot predict the emergence of a structural duality between rural and urban areas. The story behind the Fujita–Krugman model runs as follows. There are trade-offs between global economies of scale, the utility beneﬁt of the consumption variety of manufactured goods, and transaction costs. Farming is land intensive, so farmers must have dispersed residences in rural areas. Manufactured goods are not land intensive, so manufacturers can reside together in the city. In addition, as the residences of manufacturers are concentrated in a city, there is a trade-off between the reduction of transaction costs between urban residents and the increase in transaction costs between rural farmers and urban manufacturers. An increase in population size or in transaction efﬁciency will enlarge the scope for individuals to trade-off among these conﬂicting forces, thereby increasing productivity, per capita real income, and consumption variety. The increase in the number of manufactured goods, an aspect of division of labor, will

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move the efﬁcient balance of the trade-offs toward a more concentrated residential pattern of manufacturers, making a city more likely to emerge. The beneﬁt of concentrated manufacturers’ residences is called type I economies of agglomeration. As comparative statics of the general equilibrium model predict, a decrease in the unit transaction cost coefﬁcient of agricultural goods or a larger population size will make a city more likely to emerge from a greater number of manufactured goods. But concurrent increases in the urban–rural land price differential, decreases in relative per capita consumption of land by urban and rural residents, the population size of urban residents as a share of total population, and increases of individuals’ levels of specialization cannot be predicted by the model. We shall study this model in section 11.2. Yang and Rice’s model (1994) of endogenous specialization predicts the emergence of cities, and of the dichotomy between urban and rural areas, as consequences of the evolution of division of labor and individual specialization. The story behind the model may be outlined as follows. Suppose the production of food is land intensive. The production of many manufactured goods is not land intensive. There are economies of specialization in producing each good, and trade generates transaction costs. Hence, there is a trade-off between economies of specialization and transaction costs. If transaction efﬁciency is low, individuals will choose autarky where no market and city exist. As transaction efﬁciency is slightly improved, the division of labor between partially specialized farmers and partially specialized cloth makers emerges as a consequence of the efﬁcient trade-off between economies of specialization and transaction costs. Since farming is land intensive and cloth making is not, farmers will have dispersed residences while each cloth maker will reside near a farm to reduce the transaction costs caused by division of labor. Hence, the low level of division of labor between farming and cloth making does not generate cities. As transaction efﬁciency is further improved, the division of labor between cloth makers, house builders, and furniture makers emerges in addition to the division of labor between farmers and manufacturers. The manufacturers can have dispersed residences or reside together in a city since their production is not land intensive. In order to save on the transaction costs caused by the division of labor and related transactions among manufacturers, they will reside in a city. Hence, a city and a dichotomy between urban and rural sectors emerge from a high level of division of labor between specialist manufacturers and between professional manufacturers and farmers. In this story, if different specialist manufacturers reside in the city, the transaction cost coefﬁcient for trade between manufacturers (urban residents) is much smaller than that for trade between farmers (rural residents) and urban residents. This transaction efﬁciency differential, due to the different degrees of land intensity in agricultural and industrial production, is a driving force behind the emergence of the city from the division of labor. In the development of urbanization and division of labor, urban residents’ levels of specialization and productivity increase more quickly than rural residents’, since the short distance between each pair of urban residents ensures higher transaction efﬁciency in the urban area than in the rural area. The dual structure, in terms of differences in productivity and in commercialized income between the urban and rural areas, takes place in the transitional phase as the economy moves from a low to a high level of division of labor. However, free migration between areas and between occupations will equalize the per capita real incomes of urban and rural residents, despite the inequality of their per capita commercialized incomes. As transaction efﬁciency is continuously improved, the economy will evolve to a state of complete division of labor. Then the dual structure will disappear and productivity, the degree of commercialization, and commercialized incomes will be equalized between the two areas. Section 11.3 uses a simpliﬁed version of the Yang–Rice model (1994) to formalize the story. Similar to the Fujita– Krugman model, the driving force of the story is type I economies of agglomeration, which look like externality of urbanization.

C HAPTER 11: U RBANIZATION 343

There is another way to explain the relationship between urbanization and the evolution of division of labor in the absence of a differential of transaction efﬁciency between agricultural and industrial goods. This explains urbanization by exploring the general equilibrium implications of interactions between the positive network effects of the division of labor and the geographical concentration of transactions that are required by a particular network of division of labor. Because of the positive network effect of the division of labor, the geographical concentration of transactions required by a particular network of division of labor can save on transaction costs by reducing total traveling distance for each individual. Hence, urbanization can promote division of labor by concentrating a large network of transactions in a city to reduce transaction costs. The beneﬁt of a geographical concentration of transactions is referred to as type II economies of agglomeration, which differs from the beneﬁt of geographical concentration of manufacturers’ residences. Type II economies of agglomeration imply that individuals may come to the city to conduct their transactions even if they do not reside in the city, while type I economies of agglomeration can be realized only if individuals reside in the city. It is interesting to note the interdependence among equilibrium transaction efﬁciency, equilibrium level of division of labor, and the equilibrium geographical pattern of transactions in this story. The concept of general equilibrium is a powerful vehicle in investigating the simultaneous determination of the interdependent variables. Section 11.4 will formalize the story of general equilibrium. In section 11.5, we extend this story to simultaneously endogenize the land price differential between the rural and urban areas, the level of division of labor, and the population density in the urban area. This is done by introducing the consumption level of land into the utility function. In addition to the trade-off between economies of division of labor and transaction costs, there is a trade-off between high transaction efﬁciency for urban residents and congestion in the city. Equilibrium is associated with an efﬁcient trade-off that generates the following phenomenon. As transaction efﬁciency is improved, division of labor evolves. This generates increasingly signiﬁcant economies of agglomeration (transaction efﬁciency increasing with the degree of geographical concentration of transactions), so that more individuals are willing to reside in the city. This bids up the land price of the urban area, resulting in a fall in the per capita consumption of land by urban residents compared to rural residents. The potential for the rise of land prices in the urban area is determined by the potential for the evolution of division of labor.

QUESTIONS TO ASK YOURSELF WHEN READING THIS CHAPTER n What is the relationship between the emergence and development of cities, the level of division of labor, and transaction efﬁciency? n Why do the different land requirements of agricultural and industrial production generate a dual structure between urban areas with a high population density and rural areas with a low population density? n What are the effects of free migration and the absence of free migration on urbanization, evolution in division of labor, and economic development? n Why are transaction efﬁciency, the geographical pattern of transactions, and the level of division of labor interdependent? How are they simultaneously determined in the marketplace? n Why is the price of land in the urban area higher than in the rural area? What are the main economic determinants of the potential for the increase in urban land prices in the development process?

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11.2 THE FUJITA–KRUGMAN MODEL OF URBANIZATION BASED ON A TRADE-OFF BETWEEN ECONOMIES OF SCALE AND TRANSACTION COSTS Example 11.1: A simpliﬁed version of the Fujita–Krugman model (1995). Consider an economy with N identical consumers, an agricultural good, and n manufactured goods, where n is endogenous. It is assumed that the manufacturing activity needs no land. Hence, the central point of the geographic area is a city where all NM manufacturers reside. Suppose that NA = N − NM farmers’ residences are evenly located around the city. The area of land that is employed is endogenously determined in this model. Each rural resident has the following decision problem. Max: uA = z Aα [n(kxA)ρ](1−α)/ρ s.t.

pzA + nqxA = wA

(utility function) (budget constraint)

(11.1a)

where p is the price of the agricultural good, q is the price of the manufactured goods, zA is the quantity of the agricultural good consumed by a rural resident, n is the number of manufactured goods, and xA is the amount of a manufactured good consumed by the rural resident. Each consumer is endowed with one unit of labor, so that the income of a rural resident equals the rural wage rate wA. k ∈ (0, 1) is the transaction efﬁciency coefﬁcient for the manufactured goods. We assume that there is no transaction cost for a rural resident to buy the agricultural good from the local rural market; transaction costs are incurred only in buying the manufactured goods. Note that we have used symmetry to justify equal prices and equal quantities of all manufactured goods consumed. Each urban resident has the following decision problem: Max: uB = (tzB)α [nxBρ ](1− α)/ρ s.t.

pzB + nqxB = wB

(utility function) (budget constraint)

(11.1b)

where subscript B stands for variables for an urban resident and t ∈ (0, 1) is the transaction efﬁciency coefﬁcient for the agricultural good. If we assume that labor at the city is the numeraire, then wB = 1. We assume that there is no transaction cost for an urban resident to buy manufactured goods from the local urban market. Hence, the urban resident incurs transaction costs only in buying the agricultural good. The demand functions and indirect utility function and own price elasticity of demand for a consumer of type i = A, B are: zi = αwi /p,

E = −(n − ρ)/(1 − ρ)n

xi = (1 − α)wi /qn, uA = αα(1 − α)1−αn(1−α)(1−ρ)/ρk(1−α)wA /pαq1−α

(11.2)

uB = αα(1 − α)1−αn(1−α)(1−ρ)/ρt αwB /pαq1−α where the own price elasticity of demand E is calculated using the Yang–Heijdra formula (see expression 5.4 in chapter 5). The simple Leontief production function is assumed for the agricultural sector. So a units of labor and one unit of land are required to produce one unit of z. The zero-proﬁt condition in the agricultural sector yields p = awA.

(11.3)

C HAPTER 11: U RBANIZATION 345

Here, it is assumed that each farmer owns land used for her production of food. Hence, rental income from land and land expenses in the budget constraint cancel out each other. Free migration between the urban and rural areas will establish utility equalization between the two areas. The condition uA = uB, together with (11.3), yields wA = tα/k1− α,

wB = 1.

(11.4)

A linear production function with a ﬁxed cost is assumed for manufacturing a non-agricultural good. Hence, the amount of labor to produce output Q i is f + bQ i. A monopolistically competitive regime prevails in the market for any manufactured good. With the Yang–Heijdra formula for own price elasticity (see (5.4) in chapter 5), the conditions that marginal revenue equals marginal cost and zero proﬁt yield nq(1 − ρ) = (n − ρ)(q − b),

(1 − α)(q − b)(NA wA + N − NA ) = fnq,

(11.5)

where NA is the number of farmers, NB = N − NA is the number of urban residents, and the equilibrium value of wA is given in (11.4). (11.4) and (11.5), together with the market clearing condition for labor or for the manufactured goods, can then be used to determine NA, q, wA, and n. The equilibrium total output level of the agricultural good, Z = zN, can be obtained by plugging the equilibrium price into the demand function, zi = αwi /p, where wi is given in (11.4). Therefore, the demand for labor from the agricultural sector is NA = aZ = a[(αNA/a) + (α(N − NA)/awA)] or NA = αk1−αN/[(1 − α)t α + αk1−α ],

(11.6)

where wA = t α/k1−α is given in (11.4). Inserting (11.6) into (11.5) yields the equilibrium value of the number of manufactured goods, which can be considered as the degree of industrialization. n = ρ + (1 − α)(1 − ρ)t αN/[(1 − α)t α + αk1−α] f.

(11.7)

Differentiation of (11.6) and (11.7) yields dn/dN > 0, dn/dt > 0,

and

d(NB /N )/dt > 0.

dn/dk < 0,

and

d(NB /N )/dk < 0.

(11.8)

This implies that as the population size and/or the transaction efﬁciency for the agricultural good increase, the number of manufactured goods increases, or industrialization develops. Also, comparative statics predict that as the transaction condition for the agricultural good is improved, the population share of urban residents increases, or urbanization develops. But the transaction efﬁciency for the manufactured goods has the opposite effects. The equilibrium land area employed for agricultural production is the same as the output level of the agricultural good z, which increases as the population size rises, as the transaction efﬁciency for the manufactured goods increases, or as the transaction efﬁciency for the agricultural good declines. Fujita and Krugman’s original model is slightly more complicated than this simpliﬁed version. They assume that transaction cost is an increasing function of the distance from the city, which is the middle point of a segment line. All farmers reside on the segment on the two sides of the city. Also, they have discussed the condition for more than one city to emerge from the evolution of the number of manufactured goods. According to Baumgardner (1988b), physicians in large cities are much more specialized than those in small towns. This empirical evidence is consistent with the conjectures of classical

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economists. But the Fujita and Krugman model cannot predict this phenomenon, since individuals’ levels of specialization are not there endogenized. In the next section we consider a model with endogenous specialization and an endogenous emergence of cities from evolution of division of labor.

11.3 EMERGENCE OF A STRUCTURAL DUALITY OF URBAN AND RURAL AREAS FROM THE DIVISION OF LABOR Example 11.2: A simpliﬁed version of the Yang–Rice model (1994). We consider a simpliﬁed version of this model which has been worked out by Monchi Lio. The model is similar to those in chapters 4 and 7. There are three goods, cloth (good 1), furniture (good 2), and food (good 3). Goods 1 and 2 are industrial goods requiring little land in production. Hence, the residences of producers of these two goods can either be dispersed over a large area or concentrated in a small area. The production of good 3, food, is land intensive. The residences of the farmers must be dispersed over a large area. Though all M consumer-producers are ex ante identical, they can choose to specialize in producing different goods and choose their residence location pattern (far away from or close to neighbors). We call those individuals who choose to produce only industrial goods C-type persons, and those who choose to produce agricultural goods R-type persons. The transaction cost coefﬁcient for a unit of goods purchased is 1 − K, or the transaction efﬁciency coefﬁcient is K. But K differs between different types of persons and is dependent on individuals’ decisions concerning the geographic pattern of their residences. If C-type persons reside together within a small area, the transaction efﬁciency coefﬁcient K = k between a pair of C-type persons. The transaction efﬁciency coefﬁcient K = r between a pair of R-type persons and K = s between a C-type person and an R-type person. We assume that k > s > r. The ﬁrst inequality is easy to understand, since the average distance between a pair of C-type persons who reside together is shorter than the average distance between an R-type person, who must occupy a quite large area of land, and a C-type person. Suppose an R-type person resides at the center of her farm, which has the shape of a circle with radius 1. Since a C-type person can minimize transaction costs by residing on the boundary of the farm if she trades with the farmer, the minimum distance between the R-type and C-type persons is 1. But the distance between two R-type persons who reside at the respective centers of their farms with radius 1 is 2. This is why transaction efﬁciency is higher between an R-type person and a C-type person than between a pair of R-type persons, or why s > r. As in the previous chapters, each consumer-producer’s utility function is u = (x1 + Kx 1d )(x2 + Kx 2d )(x3 + Kx 3d ).

(11.9)

Each consumer-producer has the following production functions and endowment constraint for working time: xi + x is = Max{li − α, 0}, α ∈ (0, 1),

li ∈ [0, 1],

l1 + l2 + l3 = 1, i = 1, 2, 3.

(11.10)

α is a ﬁxed learning or training cost in producing a good, li is an individual’s level of specialization in producing good i, subscript i stands for good i, superscript s stands for the quantity sold (supplied), and superscript d stands for the quantity purchased (demanded). According to the Wen theorem, there are three types of conﬁgurations: Autarky (denoted A), shown in ﬁgure 11.1(a), consisting of selling good i and buying good j, denoted (i/j), and selling

C HAPTER 11: U RBANIZATION 347 3 A

1

3 A

2

1

1

1

2

1/3 2

3/1 3

2

1

1

2

1/23

2/13 2

3

3 3 3 A

1

3 A

1

2 2 (a) Autarky, no city, no market

1

1 1/3

3/1

1

2

3 2 3 (b) Partial division of labor, structure P2, no city

3/12

2

3 (c) Complete division of labor, structure D with cities

Figure 11.1 Emergence of cities from evolution of division of labor

Table 11.1 Eight corner solutions Conﬁguration

Self-provided quantity

Level of specialization

Supply

Demand

Indirect utility function

A

xi = (1 − 3α)/3

li = 1/3

(1/2)

x1 = x3 = (1 − 2α)/3

l1 = (2 − α)/3

x1s = (1 − 2α)/3

x 2d = p1x1s /p2

[(1 − 2α)/3]3rp1/p2

(2/1)

x2 = x3 = (1 − 2α)/3

l2 = (2 − α)/3

x2s = (1 − 2α)/3

x 1d = p2 x2s /p1

[(1 − 2α)/3]3rp2/p1

(1/3)

x1 = x2 = (1 − 2α)/3

l1 = (2 − α)/3

x = (1 − 2α)/3

x = p x /p3

[(1 − 2α)/3]3sp1/p3

(3/1)

x3 = x2 = (1 − α)/3

l3 = (2 − α)/3

x3s = (1 − 2α)/3

x 1d = p3 x3s /p1

[(1 − 2α)/3]3sp3/p1

(1/13)

x1 = (1 − α)/3

l1 = 1

x 1s = 2(1 − α)/3

x di = p1(1 − α)/3pi

[(1 − α)/3]3ksp21/p2 p3

(2/13)

x2 = (1 − α)/3

l2 = 1

x = 2(1 − α)/3

x = p2(1 − α)/3pi

[(1 − α)/3]3ksp22/p1 p3

(3/12)

x3 = (1 − α)/3

l3 = 1

x3s = 2(1 − α)/3

x di = p3(1 − α)/3pi

[(1 − α)/3]3s2p23/p2 p1

[(1 − 3α)/3]3

s 1

s 2

d 3

s 1 1

d i

good i and buying goods j and t, denoted (i/jt). There are six of the second type of conﬁguration: (1/2), (2/1), (1/3), (3/1), (2/3), and (3/1), as shown in ﬁgure 11.1(b). There are three of the third type of conﬁguration: (1/23), (2/13), and (3/12), as shown in ﬁgure 11.1(c). Combinations of these conﬁgurations yield four structures. M individuals choosing conﬁguration A constitute an autarky structure A. A division of M individuals between conﬁgurations (1/2) and (2/1) constitutes a partial division of labor structure P1. A division of the population between conﬁgurations (1/3) and (3/1) constitutes structure P2, as shown in ﬁgure 11.1(b). Since a structure based on conﬁgurations (2/3) and (3/2) is symmetric to structure P2, and yields the same per capita real income as P2, we omit it. A division of individuals between the other conﬁgurations (1/23), (2/13), and (3/12) constitutes the complete division of labor structure D, as shown in ﬁgure 11.1(c). Following the inframarginal analysis developed in the previous chapters, we can solve for the corner solutions in the eight conﬁgurations, as shown in table 11.1. From the utility equalization and market clearing conditions, we can solve for the corner equilibria in the four structures, as shown in table 11.2. Comparisons of per capita real incomes in the four corner equilibria, together with the Yao theorem, yield the results shown in table 11.3, regarding the general equilibrium and its inframarginal comparative statics.

348 P ART III: U RBANIZATION Table 11.2 Structure

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Corner equilibria in four structures Relative price

Number of individuals selling different goods

Per capita real income [(1 − 3α)/3]3

A P1

p1/p2 = 1

M1 = M2 = M/2

[(1 − 2α)/3]3r

P2

p1/p3 = 1

M1 = M3 = M/2

[(1 − 2α)/3]3s

D

p2/p1 = 1, p3/p1 = (k/s)1/3

M1 = M2 = M/[2 + (s/k)1/3] M3 = (s/k)1/3M/[2 + (s/k)1/3]

[(1 − α)/3]3(s4/k2)1/3

Table 11.3 General equilibrium and its inframarginal comparative statics > k0

k

< k0

s

< s0

∈(s0, s1)

> s1

< s2

> s2

Equilibrium structure

A

P2

D

A

D

where s0 ≡ [(1 − 3α)/(1 − 2α)]3 < s1 ≡ [(1 − 2α)/(1 − α)]9/k2 iff k < k0 ≡ [(1 − 2α)4/(1 − α)3(1 − 3α)]1.5, and s2 ≡ [(1 − 3α)/(1 − α)]9/4/k0.5.

A comparison between structures P1 and P2 indicates that structure P2 always yields greater per capita real income than does P1. That is, under partial division of labor, it is impossible that two types of individuals exchange industrial goods and self-provide agricultural goods, since in this pattern of partial division of labor all individuals are of R-type (producing food), who have a larger transaction cost coefﬁcient than between the R-type person and the C-type person in structure P2. But structures P1 and P2 can exploit the same economies of division of labor (due to the symmetry of the model). Note that transaction efﬁciency between two R-type persons, r, is lower than that between a C-type person and an R-type person by assumption. Hence, the set of candidates for the equilibrium structure consists of A, P2, and D. Comparisons of per capita real incomes across structures A, P2, and D indicate that P2 is better than A iff s > s0, D is better than P2 iff s > s1. A comparison between s1 and s0 indicates that s1 > s0 iff k < k0. This implies that for k < k 0 the general equilibrium structure is A if s < s0, is P2 if s is between s0 and s1, and is D if s > s1. For k > k0, structure P2 is inferior to either A or D. Hence, A occurs in equilibrium if s < s2 and D occurs in equilibrium if s > s0. Note that in structure P2, no individual selling an industrial good produces the agricultural good, so that she can either reside far away from her trade partner/farmer or reside on the boundary of the farmer. She will choose the latter geographical pattern of residence to save on transaction costs. This implies that each partially specialized seller of an industrial good will reside next to a partially specialized farmer. Therefore, there is no city in structure P2, despite the division of labor between farmers and manufacturers of industrial goods. This establishes the statement that the division of labor is necessary, but not sufﬁcient, for the emergence of cities. For structure D, the division of labor between completely specialized manufacturers of industrial goods 1 and 2 can be organized in such a way as to save on transaction costs by all specialist manufacturers residing in cities. If two manufacturers reside in a city, transaction efﬁciency is k between them. If they have dispersed residences, transaction efﬁciency is s, which is smaller than k.

C HAPTER 11: U RBANIZATION 349

As transaction efﬁciency increases from a low to a high level, the general equilibrium evolves from autarky (A) to the partial division of labor between farmers and manufacturers of industrial goods (P2) where no cities exist, followed by the complete division of labor between specialist manufacturers of industrial goods and between professional farmers and the manufacturers (D). Cities emerge from this high level of division of labor between manufacturers of industrial goods and between farmers and the manufacturers. Hence, a sufﬁcient condition for the emergence of cities from the division of labor is a sufﬁciently high level of division of labor in producing industrial goods which are not land-intensive. Figure 11.1 gives an intuitive illustration of the story based on the formal model. Panel (a) is autarky where there are no transactions or cities, panel (b) is the partial division of labor without cities (P2), and panel (c) is the complete division of labor with cities, where two specialist manufacturers reside in a city denoted by the dashed circle. The geographical distance between the residences of the two manufacturers is much shorter than that between a manufacturer and a farmer. In panel (c) only a local community is used to illustrate structure D. In structure D, there are M/[2 + (s/k)1/3] such local communities, M1 + M2 urban residents who are specialist manufacturers, and M3 professional farmers, where the equilibrium values of Mi are given in table 12.2. In each of the local communities, 2 manufacturers reside in a city and (s/k)1/3 farmers reside in the countryside. In order to save on transaction costs, individuals will trade with those closest. Hence, there is no trade between different local communities. In structure D there are M/[2 + (s/k)1/3] cities. If we introduce many goods into the model, it is not difﬁcult to show that the number of local communities and the number of cities decreases and the size of each city increases as continuous improvement in transaction efﬁciency raises the equilibrium level of division of labor. Yang and Rice (1994) extend the simple model in this section to the case with 4 goods and nonlinear production functions. They draw the distinction between an urban and rural structural duality in terms of the differential of population density, and an urban and rural structural duality in terms of the differential of level of specialization and productivity between the two sectors. They show that as transaction efﬁciency is improved, there will be a transitional stage of unbalanced division of labor as the economy evolves from a low level to a high level of balanced division of labor. During that stage, urban residents have higher levels of specialization and productivity, and higher levels of per capita commercialized income and commercialization. This is because in the transitional stage, the levels of specialization cannot be the same between rural and urban residents, while a higher level of specialization for urban residents generates a higher per capita real income than a higher level of specialization for rural residents because of the higher transaction efﬁciency for urban residents. However, free migration will ensure that per capita real incomes become the same between urban and rural residents despite their unequal commercialized incomes. As transaction efﬁciency is further improved, such a dual structure in terms of a differential in productivity and level of specialization will disappear as it is replaced by complete and balanced division of labor, where levels of specialization and productivity in the two sectors converge.

11.4 WHY CAN THE GEOGRAPHICAL CONCENTRATION OF TRANSACTIONS IMPROVE TRANSACTION EFFICIENCY? The method to explain the emergence of cities from the evolution of division of labor in the preceding section relates to type I economies of agglomeration, which occur as manufacturers’ residences are concentrated, given farmers’ dispersed residences. The other way to explain the emergence of cities from the evolution of division of labor relates to type II economies of

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agglomeration that are associated with the network effects of division of labor and a concentrated location pattern of transactions. If the geographical pattern of individuals’ residences is ﬁxed and each pair of trade partners trade in the geographical midpoint of their residences, total travel distance and related cost will increase more than proportionally as the network of transactions required by a particular level of division of labor is enlarged. If all individuals conduct their transactions at a central place, the large network of transactions can be geographically shrunk and can be concentrated in that central place to signiﬁcantly reduce the total travel distance of all individuals. The economies of agglomeration differ from economies of scale. Some economists call them positive externalities of cities. Indeed, they are generated by interactions between the positive network effects of division of labor and the effects of the geographical concentration of transactions. In other words, not only do the equilibrium topological properties (whether a person has a trade connection with another person) of economic organisms depend on the pattern of resource allocation (quantities of ﬂows of goods and factors which are nontopological properties of economic organisms), but they also depend on the geographical properties of economic organisms (which are also nontopological properties of those organisms). One of the implications of the interplay between the topological and nontopological properties of economic organisms relates to the potential for a rise in land prices in the urban area. If we do not understand this implication, we will not be able to explain why the price of land in Hong Kong, Tokyo, and Taipei has increased by more than 40 times since the Second World War! The most important determinant of the land price of a city is the size of the network of division of labor that is associated with the city as its center of transactions. While that size is determined by transaction efﬁciency, this itself depends on the geographical pattern of transactions. The effect of the geographic pattern of transactions on transaction efﬁciency is in turn determined by the level of division of labor. Hence, transaction efﬁciency, the geographical pattern of transactions, and level of division of labor are interdependent and should be simultaneously determined in general equilibrium. The notion of general equilibrium is a powerful vehicle to explore a mechanism that simultaneously determines all of the variables. We ﬁrst use a simple example to illustrate why the geographical concentration of transactions can improve transaction efﬁciency through the network effects of division of labor. Example 11.3: A general equilibrium model endogenizing the geographical pattern of transactions, transaction efﬁciency, and the network size of division of labor. Let us look at the case where n = 7 in ﬁgure 11.2. Panel (a) or (b) represents a local community with 7 traded goods in a symmetric model in chapter 7. Seven ex ante identical consumer-producers reside at 7 vertices of a grid of triangles with equal sides, which are represented by 7 points. The distance between each pair of neighbors is assumed to be 1. Due to symmetry, each individual sells a good to, and buys a good from, each of the other six individuals in equilibrium. In panel (a), each pair of individuals trades at the geographical middle-point of their residences, which is represented by a small circle. In panel (b), all individuals go to the center of the local community, represented by the small circle, which is the residence of an individual, to trade with each other. Suppose that exogenous transaction costs are proportional to the travel distance of individuals in conducting the transactions required by the division of labor. This assumption implies that there are increasing returns in transactions. Transaction costs are independent of the quantity of goods traded. Imagine that within a certain quantity range of the goods you purchase, transportation cost is proportional to the quantity of gas that you use for your car, which is proportional to the driving distance but independent of the quantity that you buy. That is, your car is large enough to generate increasing returns in transportation. In the next section, this assumption is relaxed and variable transaction costs are speciﬁed as an increasing function of the quantity of goods traded. The relaxation will not change the essence of our result as long as increasing

C HAPTER 11: U RBANIZATION 351 n=2

n=3

(i)

(ii)

n=4

n=5

n=6

n=7

(a) Dispersed location of transactions

(b) Concentrated location of transactions

Figure 11.2 Dispersed and concentrated location patterns of transactions

returns in transactions are sufﬁciently signiﬁcant. Moreover, we assume that one unit of travel distance costs $1. Let us now calculate total transaction cost for the two geographical patterns of transactions. In panel (a), each of the six individuals residing at the periphery of the community has a most distant trade partner. She travels to the center, which is the middle-point between them, to trade with that partner. She can trade with the person at the center by way of the trip. The travel distance for the return trip costs $2. She has two other neighboring trade partners. It costs her $1 to trade with each of them. The distance between her and each of the other two trade partners is 3; a return trip to the middle-point between her and each of them is thus 3. Hence, it costs her $2 3 to trade with the two partners. Her transaction costs with

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six trade partners then total $(2 + 2 + 2 3 ) = $7.46. For the person at the center, transaction costs are zero, since all other individuals will trade with her at the center as they stop by there to trade with their farthest partners. In the geographical pattern in panel (b), all individuals not residing at the center bring their goods there to trade. Total transaction cost for each of them is $2. A comparison of transaction costs between panels (a) and (b) indicates that the geographical concentration of transactions can save on transaction costs if the size of the network of division of labor is sufﬁciently large. O. Williamson refers to the pattern of transactions in panel (b) as the wheel pattern, and that in panel (a) as the pattern of all channels. If the purpose of traveling is to obtain information about products, prices, and partners, then increasing returns to the geographical concentration of transactions will be more signiﬁcant. However, if the geographical concentration of transactions (or exchanges) generates congestion problems for vehicles, and if new computer technology can signiﬁcantly improve the transmission cost of information, then economies of geographical concentration of information exchange may generate such a concentration, as occurs in the case of the information superhighway, rather than a geographical concentration of the physical appearance of individuals and vehicles associated with the relevant exchanges.1 If the ﬁxed construction cost of highways is considered, the increasing returns in transactions will be more plausible. We can deﬁne a central marketplace as a geographical location where many trade partners conduct transactions. This deﬁnition implies a corresponding geographical concentration of transactions. Geographically dispersed bilateral transactions are not associated with the market according to this deﬁnition. It can be shown that the market is not needed if the level of division of labor is low. Consider, for instance, a symmetric model in which there are two traded goods and a community of seven individuals. It can be shown that if the geographical pattern of transactions is such that each pair of trade partners trades at the midpoint between their residences, as shown in the case where n = 2 in ﬁgure 11.2, the transaction cost to each of them is only $1. But if all individuals go to the central marketplace to trade, as shown in ﬁgure 11.2, panel (b), for the case with n = 7, then each individual’s transaction cost is $2. This illustrates that for a low level of division of labor, geographically concentrated transactions will generate unnecessary transaction costs. Thus, the capacity of a geographically concentrated pattern of transactions to save on transaction costs depends on the level of division of labor. In other words, transaction efﬁciency is dependent not only on the geographical pattern of transactions, but also on the level of division of labor. But, as shown in the previous chapters, the level of division of labor is itself determined by transaction efﬁciency. This interdependence among the level of division of labor, the geographical pattern of transactions, and transaction efﬁciency implies that the three variables are simultaneously determined in a general equilibrium environment. It is analogous to the interdependence between the prices and quantities of goods that are consumed and produced in the neoclassical general equilibrium model, where the optimum quantities of goods consumed and produced are dependent on prices, while the equilibrium prices are themselves determined by individual agents’ decisions on the optimum quantities. Now we introduce the geographical pattern of transactions into the Smithian model in section 7.2 of chapter 7 to illustrate how the level of division of labor, transaction efﬁciency, and geographical pattern of transactions are simultaneously determined in general equilibrium. From (7.14) in chapter 7, we can see that the level of division of labor, n, is a function of transaction efﬁciency k, that is n = m + 1 − (1/A) − (m/ln k)

(11.11)

where m is the number of all consumer goods and A is the ﬁxed learning cost in each production activity. Assume now that

C HAPTER 11: U RBANIZATION 353

k = β/d

(11.12)

where β is a parameter that reﬂects transportation conditions and d is the average traveling distance for each individual to trade with a trade partner, which obviously is related to the geographical pattern of transactions. For simplicity, we consider only the cases where n = 1, 2, 3, 4, 5, 6, 7. We ﬁrst assume a given value of n, then for the given n, compare values of d for different geographical patterns of transactions as shown in ﬁgure 11.2. According to the Yao theorem, it can be shown that in equilibrium, individuals will choose a geographical pattern of transactions that has the lowest value of d in order to minimize transaction costs for any given n. Thus, we can use (11.3) and (11.4) to calculate the critical value of β that ensures that values of the level of division of labor, n, transaction efﬁciency, k, and geographical pattern of transactions, reﬂected by d, are consistent with each other in equilibrium. Let us start with n = 2 to use the iterative approach to solving for general equilibrium. As we have mentioned previously, and indicated in ﬁgure 11.2, where n = 2 each individual’s traveling distance d is 1 and transactions are dispersed at the midpoints between each pair of trade partners. Other geographical patterns generate longer traveling distances and higher transaction costs for this level of division of labor. For society as a whole with this level of division of labor, there are M/2 local business communities. If we deﬁne an urban area as a place where many transactions take place among many individuals at the residences of some of them, then there is no city associated with this pattern of transactions, since all transactions are dispersed at many middle-points of many pairs of trade partners. Here, the deﬁnition of an urban area overlaps with the deﬁnition of a central marketplace, but the distinction between them is that an urban area relates to the residences of some of the trade partners, while the deﬁnition of market is independent of individuals’ residences. Inserting d = 1 into (11.12), then inserting (11.12) into (11.11), we can solve for the critical value of β for n = 2, which is β2 = e−mA/[1−(m−1)A], where A is the ﬁxed learning cost in each production activity, m is the number of all consumption goods, and e ≅ 2.718 is the base of the natural logarithm. The level of division of labor n is at least 2 if β ≥ β2. In order to solve for the critical values of other levels of division of labor, let us look at ﬁgure 11.2. The graphs in the left column represent those geographical patterns of transactions in which transactions take place at the middle-points of each pair of trade partners, whereas the graphs in the right column represent those geographical patterns of transactions in which transactions take place at the center of all trade partners. The solid dots denote consumer-producers and the circles denote the locations where transactions take place. Here, we follow that assumptions that all individuals reside at the vertices of a grid of triangles with equal sides, and that the distance between each pair of neighbors is 1. Hence, the values of d for the different patterns of transactions that correspond to various levels of division of labor can be calculated from ﬁgure 11.2. All of the values of d, which are of course dependent on the geographical pattern of transactions as well as on the level of division of labor, are listed in table 11.4. In ﬁgure 11.2, it is evident that the best geographical pattern of transactions for n = 2 is at the midpoints between each pair of trade partners, so that d = 1 for n = 2. For n = 3, there are two geographical patterns of transactions to choose from. In one of them, each pair of partners trades at the geographical midpoint of their residences, so that all transactions in the economy take place at M places. In the other, all partners in a local community where each person trades with each of the other two go to the geographical center of their residences to conduct all transactions between them, so that all transactions in the economy are implemented at M/3 places. For the latter pattern, it is not difﬁcult to use basic geometry to show that d = 0.5 3 < 1, whereas for the former d = 1. For the different geographical patterns of transactions that are associated with different values of d but with the same value of n, there are several corresponding corner equilibria. According to the Yao theorem, individuals will choose

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Table 11.4 Interactions between geographical patterns of transactions, transaction efﬁciency, and level of division of labor Level of division of labor

d for dispersed transactions

d for concentrated transactions

Transaction efﬁciency k

Critical value of βn for a given n

n=2

1

1

β

emA/[(m−1)A−1]

n=3

2/(n − 1)

2β/ 3 6β ÷ (1 + 3 ) 2β

( 3/2)e mA/[(m−2)A−1] (1 + 3 )e mA/[(m−3)A−1]/6

2

5β/2

2

2

β/3

1

n=4

(5 + 3 ) ÷ 2(n − 1)

(2 3 ) ÷ 2(n − 1) (1 + 3 ) ÷ 2(n − 1)

n=5

>2

2 ÷ (n − 1)

n=6

>2

n=7

>2

Table 11.5 Transaction condition β Equilibrium structure n

1

/2 e mA/[(m−4)A−1] /5 e mA/[(m−5)A−1]

/3 e mA/[(m−6)A−1]

General equilibrium and its inframarginal comparative statics < β2

∈(β2, β3)

∈(β3, β4)

∈(β4, β5)

∈(β5, β6)

∈(β6, β7)

β > β7

1

2

3

4

5

6

7

the corner equilibrium with the greatest per capita real income that is associated with the smallest value of d for a given n. Hence, the concentrated pattern of transactions with d = 0.5 3 will be chosen if the equilibrium value of n is 3. There is no city, despite the existence of a marketplace in this structure. Following the same procedure, it can be shown that those concentrated patterns of transactions in the right column of ﬁgure 11.2 yield the smallest value of d for a given n > 2, and that the minimum value of d for any given n > 4 is 2. Inserting the minimum value of d for a given n back into (11.12) yields the values of transaction efﬁciency k for a given n, which are listed in column 4 of table 11.4. Plugging these values of k back into (11.11), we can work out the critical values of β for n = 2, 3, 4, 5, 6, 7, which are listed in column 5. In fact, table 11.4 has already given us the general equilibrium and its inframarginal comparative statics, as summarized in table 11.5. The table shows that the general equilibrium is autarky if β < β2. If β ∈(β2 , β3) the general equilibrium is partial division of labor with n = 2, with the geographical pattern as shown in the left column of ﬁgure 11.2, and with the transaction efﬁciency k as shown by the entry of row n = 2 and column 4 in table 11.4. If β ∈(β3, β4) the equilibrium is the division of labor with n = 3, with the geographic pattern as shown in the right column of ﬁgure 11.2, and with the transaction efﬁciency k as shown in the entry of row n = 3 and column 4 in table 11.4. If β ∈(β4, β5), the general equilibrium is the division of labor with n = 4, with the geographic pattern as shown in the right column of ﬁgure 11.2, and with the transaction efﬁciency k as shown in the entry of row n = 4 and column 4 in table 11.4. If β ∈(β5, β6 ), the general equilibrium is the division of labor with n = 5, with the geographic pattern as shown in the right column of ﬁgure 11.2 for n = 5, and with the transaction efﬁciency k as shown in the entry of row n = 5 and column 4 in table 11.4. If β ∈(β6, β7), the equilibrium is the division of labor with n = 6, with the geographic pattern as shown in the right column of ﬁgure 11.2 for n = 6, and with the transaction efﬁciency k as shown in the entry of row n = 6 and column 4 in table 11.4. If β > β7, the equilibrium is the division of labor with n = 7, with the geographic pattern as shown in the right column of ﬁgure 11.2 for n = 7, and with the transaction

C HAPTER 11: U RBANIZATION 355

efﬁciency k as shown in the entry of row n = 7 and column 4 in table 11.4. Here, cities emerge from the division of labor with n = 5, 6, 7 and the number of cities is M/n. Marketplaces coincide with locations of the cities, and the number of marketplaces is the same as that of cities. There is no market nor any cities in autarky. For n = 2, there are M/n = M/2 marketplaces with two trade partners for each, and no cities. For n = 3, 4, there are M/n marketplaces with n trade partners for each, and no cities exist. The inframarginal comparative statics of general equilibrium suggest again that the division of labor is a necessary but insufﬁcient condition for the emergence of cities. For n = 2, 3, 4, there is division of labor and related marketplaces, but no cities. It is easy to see that the volume of trade that is executed in a marketplace or in a city increases with the equilibrium level of division of labor, which is determined by the transaction condition parameter β.

11.5 SIMULTANEOUS ENDOGENIZATION OF LEVEL OF DIVISION OF LABOR, LOCATION PATTERN OF RESIDENCES, GEOGRAPHICAL PATTERN OF TRANSACTIONS, AND LAND PRICES Although the equilibrium model in the previous section simultaneously endogenizes the level of division of labor, transaction efﬁciency, and the geographical pattern of transactions, it has not endogenized the location pattern of individuals’ residences and the differential of land price between urban and rural areas, since we implicitly assume that d is the same for urban and rural residents. But the average traveling distance for necessary transactions d is much shorter for an urban resident than for a rural resident, since an urban resident can get all transactions done in the city where she resides without traveling around when all necessary transactions are concentrated in the city. In this section, we take into account the difference between traveling distances of urban and rural residents to develop a general equilibrium model with the endogenous geographical pattern of all individuals’ residences and the land price differential between the urban and rural areas. Example 11.4: A Smithian equilibrium model with endogenous residences of individuals and endogenous land prices (Sun and Yang, 1998). Consider a Smithian model similar to that in example 7.1 of chapter 7. We assume that production, consumption, and transaction conditions are the same as in that example, except for the following two new features. Each consumer-producer’s utility is a function of the amount of land consumed by her and of whether the city as a center of transactions emerges from the division of labor. When a dual urban–rural structure occurs in equilibrium, the transaction efﬁciency coefﬁcient is kA for those who reside in the city and k for those who reside in the rural area. The emergence of cities from a sufﬁciently high level of division of labor generates a transaction cost advantage for urban residents whose transaction cost coefﬁcient is much smaller than that for rural residents. For simplicity, we assume that the relative transaction efﬁciency coefﬁcient of urban and rural residents is a constant greater than one, kA/k = λ > 1.

(11.13)

If free migration between urban and rural areas is assumed, then the residential pattern must be endogenously determined rather than exogenously given. Free migration, together with the transaction cost advantage for urban residents and the positive contribution of land consumption to utility, generates a trade-off between type II economies of agglomeration and per capita consumption of land in the urban area, which will be reduced by the competitive bidding up of

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urban land prices. The balance of this trade-off in the market will generate equilibrium location patterns of individuals’ residences and of transactions, while the efﬁcient trade-off between economies of specialization and transaction costs will determine the equilibrium network size of division of labor. Here, the location pattern of residences, the location pattern of transactions, the consumption pattern of land, the relative urban and rural land prices, and the network size of division of labor are interdependent. Therefore, the concept of general equilibrium is a powerful vehicle for ﬁguring out a mechanism that simultaneously determines all the interdependent variables. It will be shown later that for n ≤ 2, the equilibrium location patterns of residences and transactions are trivial, that is, all individuals reside at vertices of the grid of triangles with equal sides, transactions take place at the midpoints between the residences of each pair of trade partners, and no cities exist. Hence, we ﬁrst focus on the case with n > 2, where cities emerge from the division of labor. Later, it will be shown that the equilibrium value of n is greater than 2 if and only if transaction efﬁciency k is sufﬁciently large. Denote the traded goods produced in the urban (or rural) area A-type goods (or B-type goods). Producers of A-type goods (B-type goods) have an incentive to reside in the urban (rural) area to save on commuting costs between their residences and their work places. Therefore, for each consumer-producer, the decision on residence location and occupation choice becomes independent: they choose to reside in the urban (rural) area if and only if they choose to produce A-type (B-type) goods. Thus, we can use symmetry to simplify the algebra signiﬁcantly. Since all individuals’ choices of nA, nB, and n determine the network size of division of labor and the location patterns of residences and transactions, their optimum values must be obtained from inframarginal analysis. A value proﬁle of nA, nB, and n is a structure. First, all individuals’ utility maximizing decisions are solved for the given values of nA, nB, and n. Then the market clearing conditions and utility equalization conditions are used to solve for a corner equilibrium for a given structure. For different value proﬁles of nA, nB, and n there are many corner equilibria. The general equilibrium is the corner equilibrium with the highest per capita real income. The symmetry of the model implies that we need to consider only two types of decision problems. For an urban resident selling an A-type good, the decision problem is: m−n · RA Max: uA = (xA)(kAx dA)n −1(kx Bd)n x jA A

s.t.

B

xA + xAs = Max{0, lA − α}

(production function for a good sold)

xjA = Max{0, liA − α}

(production function for a nontraded good)

lA + (m − nA)ljA = 1

(endowment constraint for working time)

pA x Ad (nA − 1) + pB nB xBd + rA RA = pA xAs + EA

(11.14)

(budget constraint)

where nA (nB) is the number of traded goods produced by the urban (rural) residents; n ≡ nA + nB is the number of all traded goods; xA is the quantity of the A-type good that she self-provides; x As is the amount of the A-type good that she sells to the market; lA is her level of specialization in producing this good; x Ad is the amount of the A-type good that she purchases from the market; xBd is the amount of the B-type good that she purchases from the market; xjA is the amount of a nontraded good that she produces and consumes; and ljA is the quantity of labor that she allocates to the production of a nontraded good. Symmetry implies that xAd is the same for nA − 1 of A-type goods purchased, x Bd is the same for nB of B-type goods purchased, and ljA is the same for m − n nontraded goods. pA and pB are respectively the prices of A-type and B-type goods. rA and rB are respectively the prices of land in the urban and rural areas. RA is the

C HAPTER 11: U RBANIZATION 357

lot size of each urban resident’s house. EA = rA A/MA is the land rental, equally distributed to each urban resident, MA (MB ) is the number of urban (rural) residents. The decision variables are xA, xAs, lA, xjA, ljA, xAd, x Bd , RA , nA , and n. The choice of nA and n, which determines nB, determines how many goods an individual has to buy from the market and how many goods she self-provides. The solution of the decision problem for the given values of nA, nB, and n in (11.14) is an individual’s resource allocation for a given organizational pattern. Standard marginal analysis is applicable to such resource allocation problems. It yields the demand and supply functions and indirect utility function as follows: xAs = {npA [1 − (m − n + 1)α] − (m − n + 1)EA}/pA(m + 1)

(11.15a)

lA = [ pA(1 + nα) + EA]/pA (m + 1), xAd = {pA [1 − (m − n + 1)α] + EA}/pA (m + 1)

(11.15b)

xBd = {pA [1 − (m − n + 1)α] + EA}/pB (m + 1)

(11.15c)

RA = {pA [1 − (m − n + 1)α] + EA}/rA(m + 1) uA =

(11.15d) m +1

nB

kAn−1 ⎛ pA ⎞ ⎧ EA + pA [1 − (m − n + 1) α ⎫ ⎬ ⎜ ⎟ ⎨ rA pAm ⎝ pB ⎠ ⎩ m +1 ⎭

(11.15e)

.

The optimum decision for a rural resident is symmetric to (11.15), that is, it can be obtained by exchanging subscripts A and B in (11.15). A corner equilibrium is determined by the market clearing conditions for land and goods, the utility equalization condition between urban and rural residents, and individuals’ optimum decisions for given values of nA, nB, and n. The land market clearing conditions are MARA = A,

MB RB = B.

(11.16)

where A (B) is the exogenously given parameter of land area which can be used for urban (rural) development. The market clearing condition for A-type goods (the traded goods produced in the urban area) yields

npA [1 − (m − n + 1)α] − (m − n + 1)EA MA ⋅ (m + 1) pA nA p [1 − (m − n + 1)α] + EA MA p [1 − (m − n + 1)α] + EB ⋅ MB ⋅ = A (nA − 1) + B nA (m + 1) pA (m + 1) pA

(11.17)

The market clearing condition for B-type goods is not independent of (11.16) and (11.17) because of Walras’s law. The utility equalization condition yields

⎛ kA ⎞ ⎜ ⎟ ⎝ k⎠

n −1

m+1

⎧ EA + pA [1 − (m − n + 1)α] ⎫ ⎨ ⎬ ⎩ EB + pB [1 − (m − n + 1)α] ⎭

=

rA ⎛ pA ⎞ ⎜ ⎟ rB ⎝ pB ⎠

m −n

.

(11.18)

(11.16) to (11.18), the population equation MA + MB = M, and the deﬁnitions EA ≡ rA A/MA and EB ≡ rBB/MB yield a corner equilibrium for a given structure deﬁned by nA, nB , and n.

358 P ART III: U RBANIZATION

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I NDUSTRIALIZATION

1/n

⎧ Bθ ⎫ (1−n )/n p p≡ A =⎨ , ⎬ λ pB ⎩ A(1 − θ) ⎭

l A = lB =

rA =

1 + (n − 1)α m

[1 − (m − n + 1)α]θM [1 − (m − n + 1)α](1 − θ) M p, rB = , mA mB

(11.19)

n M MB = B = (1 − θ)M, n

n M MA = A = θM, n

RA AMB A(1 − θ) = = , RB BMA Bθ k n −1 (1 + f ) ⎛ θ ⎞ uA = A (1− θ)n +1 ⎜ ⎟ Mf ⎝1 − θ⎠

(1−θ) n

m

⎧ [1 − (m − n + 1)α] ⎫ ⎨ ⎬ m ⎩ ⎭

1/( n +1)

n ⎡A ⎛ θ ⎞ ⎤ n −1 ⋅ ⎢ ⋅ where f ≡ , θ ≡ nA/n, and a B-type good is assumed to be the numeraire. λ ⎜ ⎟ ⎥ ⎢B ⎝1 − θ⎠ ⎥ ⎣ ⎦ A general equilibrium has two components. The ﬁrst consists of a set of relative prices of traded goods and two types of land, and a set of numbers of individuals choosing different conﬁgurations of occupation and residence, a pattern of individuals’ residences, and a location pattern of transactions that satisﬁes the market clearing and utility equalization conditions. The second component consists of each individual’s choice of nA and n, or n and θ, and each individual’s resource allocation that maximizes the decision-maker’s utility. Following a similar procedure to that used to prove the Yao theorem in chapter 4, we can prove that the Yao theorem holds for the model in this section. Let us outline the proof. Because of the equal distribution of urban (rural) land among urban (rural) residents, we know that RA = A/MA and RB = A/MB. This implies that rj Rj = Ej for j = A, B. Hence, the decision problem in (11.6) can be rewritten by deleting rA RA and EA in the budget constraint and letting RA in the utility function equal a constant A/MA. The indirect utility function generated by the equivalent decision problem is nB

m

⎛ p ⎞ ⎧[1 − (m − n + 1)α] ⎫ A uA ( p, N ) = kAn−1 ⎜ A ⎟ ⎨ , ⎬ m ⎝ pB ⎠ ⎩ ⎭ MA where p ≡ pA/pB is the price of an A-type good in terms of a B-type good, N ≡ (n, nA, β) is a vector of decision variables. n and nA determine a person’s number and structure of traded goods and her network of trade partners and transactions. β relates to her choice of location of residence and transactions. The value of k is affected by β. Exchanging subscripts A and B, we can obtain a B-type person’s indirect utility function uB( p, N ). Note that ∂uA/∂p > 0

and

∂uB/∂p < 0.

(11.20)

Now, assume that N′ and p′ are the Pareto optimum corner equilibrium values of N and p respectively, and that N″ and p″ are Pareto inefﬁcient corner equilibrium values of N and p respectively. To prove that a Pareto inefﬁcient corner equilibrium is not a general equilibrium,

C HAPTER 11: U RBANIZATION 359

we need to establish that at the relative price p″ either urban or rural residents have an incentive to deviate from N″ to N′. Or at least one of the following inequalities must hold: uA( p″, N′) > uA( p″, N″)

and

uB( p″, N′) > uB (p″, N″).

(11.21a)

Since N′ at p′ is Pareto superior to N″ at p″ and utility equalization holds in each corner equilibrium, we have uA( p′, N′ ) > uA( p″, N″)

and

uB( p′, N′) > uB( p″, N″ ).

(11.21b)

(11.21a) and (11.21b) together imply that at least one of the two inequalities in (11.21a) holds if at least one of the following two inequalities holds. uA( p″, N′) > uA( p′, N′) uB( p″, N′ ) > uB( p′, N′).

and

(11.22a) (11.22b)

Because the functional forms on the two sides of each inequality in (11.22) are the same, and because of (11.20), (11.22) is equivalent to p″ > p′ 1/p″ > 1/p′.

and

(11.23a) (11.23b)

It is obvious that one of the two inequalities in (11.23) must hold. Hence, at least one of the two inequalities in (11.21a) must hold, that is, either urban or rural residents have an incentive to deviate from the Pareto inefﬁcient corner equilibrium network of division of labor (N″ ) under the Pareto inefﬁcient corner equilibrium-relative prices. Therefore, any Pareto inefﬁcient corner equilibrium is not a general equilibrium. The Yao theorem is pivotal to the results in this chapter, since it establishes the claim that a decentralized market can fully utilize the economies of agglomeration (which look like externalities) and the network effects of division of labor by choosing the Pareto efﬁcient pattern of individuals’ residences, the efﬁcient location pattern of transactions, and the efﬁcient network size of division of labor. This theorem also rules out multiple equilibria with different per capita real incomes, and shows that there is no coordination difﬁculty in a static general equilibrium model with network effects of division of labor and location patterns.2 The very function of the market is to coordinate individuals’ decisions in choosing the pattern and size of the network of division of labor and in choosing the location patterns of residences and transactions in order to fully utilize the network effects and the economies of agglomeration. The maximization of uA in (11.7e) with respect to n for a given nB and the maximization of uB, which is symmetric with uA, with respect to n for a given nA, together with the market clearing and utility equalization conditions, will generate a corner equilibrium that is not the Pareto optimum corner equilibrium. This corner equilibrium is based on individuals’ Nash strategies in choosing trade patterns (an A-type individual’s choice of n is dependent on a B-type person’s choice of nB). According to the Yao theorem, that Pareto inefﬁcient corner equilibrium partly based on Nash strategies is not a Walrasian general equilibrium. Using the Yao theorem, we can prove the following proposition. Proposition 11.1: In a symmetric model, the economy is divided into M/n separate business communities. For n ≤ 2, all individuals’ residences are evenly located and all transactions (if any) are evenly dispersed. For n > 2 traded goods, all trade partners within a business

360 P ART III: U RBANIZATION

AND

I NDUSTRIALIZATION

community will choose to execute all transactions that are essential for the division of labor among them in the central marketplace of the community, even if some of them do not reside in the central marketplace. Proof : It is trivial to prove the ﬁrst statement since each person needs only n − 1 trade partners and will incur unnecessary transaction costs to trade with other n − 1 partners in the symmetric model. Hence, n trade partners will form a local business community that does not trade with other local business communities. We now check whether residences are evenly located when the equilibrium value of n is not greater than 2, and whether the dual urban–rural structure emerges from n > 2. Because all individuals are ex ante identical and have the same preferences for consumption of land, in equilibrium each person must consume the same amount of land in autarky, and the price of land must be the same everywhere, which means residences must be evenly located. For n = 2, it is not difﬁcult to show that residences are evenly located too, because the ex ante identical individuals have the same tastes for land consumption. There are two possible location patterns of transactions. The pattern in ﬁgure 11.2(a) involves trade at the midpoint between two trade partners’ residences, and pattern 11.2(b) involves trade at one person’s residence (city). For the latter case, the land price in the city is high enough to offset the transaction cost advantage of residing in the city. Hence, patterns (a) and (b) are equivalent. Let us assume that unequal land prices between the urban and rural areas generate inﬁnitesimally small disutility for urban residents. Then (a) is Pareto superior to (b). According to the Yao theorem (a) instead of (b) will occur in equilibrium for n = 2. For n = 3, simple arithmetic shows that a location pattern (ii) of transactions, with one person’s residence as a central marketplace, generates a lower total transaction cost than in (i) of panel (b), which generates a lower total transaction cost than in panel (a) of ﬁgure 11.2. Hence, a central marketplace will emerge from n = 3, which implies in turn that the transaction cost advantage of residing at the central marketplace will generate a land price differential, which implies that per capita land consumption is unequal between urban and rural residents and their residences cannot be evenly located in equilibrium. For n = 4 in a symmetric model, the location pattern in (i) of panel (b) is better than that in (a). But in (ii), two persons who reside more closely to the central marketplace certainly have a transaction cost advantage, so that the land price cannot be the same for all residential lots. This implies that the initial, even location of residences cannot be sustained in equilibrium, since that even pattern occurs only if the land price is the same for all localities. This implies that evenly dispersed residences cannot occur in equilibrium, so that the dual urban–rural structure, such as in (ii) where two persons reside in a city and the other two reside in the rural area with higher per capita consumption of land, may occur at equilibrium for n = 4. Following the same reasoning, we can show that the dual urban–rural structure occurs in equilibrium if and only if n > 2. Q.E.D. With the Yao theorem and proposition 11.1, we can solve for the general equilibrium by maximizing the corner equilibrium per capita real income given in (11.19) with respect to nA and nB. Since nA + nB = n, this is equivalent to maximizing per capita real income in (11.19) with respect to n and θ ≡ nA/n. The ﬁrst-order conditions for this problem yield: −1

⎧1 − θ ⎡ A(1 − θ)λn −1 ⎤1/(n +1)⎫⎪ ⎡ A(1 − θ)λn −1 ⎤ 1 −2 ⎪ ln ⎢ θ + = +⎢ ⎨ ⎬ . ⎥ θ ⎥ Bθ θ Bθ ⎣ ⎦ ⎣ ⎦ ⎩⎪ ⎭⎪ mα ln k + = −θ ln λ 1 − (m − n + 1)α

(11.24a) (11.24b)

C HAPTER 11: U RBANIZATION 361

(11.24a) determines the general equilibrium values of n and θ as functions of k, λ, α, m, A, B, which characterize the size and pattern of the network of division of labor and the location pattern of individuals’ residences and transactions. Note that the left-hand side of (11.16a) is an increasing function, while the right-hand side is a decreasing function of λn−1A(1 − θ)/Bθ, so that (11.24a) holds if and only if

λn −1 =

θ B ⋅ . A 1− θ

(11.25)

Differentiation of (11.25) yields

⎡ 1 ⎤ [ln λ ]dn = ⎢ ⎥ dθ ⎣ θ(1 − θ) ⎦

(11.26)

(11.26) implies that θ ≡ nA/n increases with n, or the number of traded goods produced in the urban area increases more than proportionally as the network size of division of labor n increases. Using (11.17) and (11.19), we can also show that the general equilibrium-relative price p = 1.

(11.27)

It can be shown that the ﬁrst-order conditions in (11.24), together with the second-order condition that requires a negative deﬁnite Hessian matrix (D 2u (n, θ) < 0), leads to: −1

⎫ dn ⎧ mα 2 =⎨ − θ(1 − θ)(ln λ)2 ⎬ > 0. 2 dk ⎩ [1 − (m − n + 1)α] ⎭

(11.28)

The second-order condition can be worked out as follows. Inserting (11.25) and (11.27) into the second-order derivative of u* in (11.19) with respect to n and θ yields ∂2u n(n + 2) 1 ⋅ =− ∂θ2 (n + 1)2 θ(1 − θ)

(11.29a)

∂2u n(n + 2) ⋅ ln λ = ∂θ ∂n (n + 1)2

(11.29b)

mα 2 ∂2u θ(1 − θ)(ln λ)2 = − + [1 − (m − n + 1)α]2 (n + 1)2 ∂n2

(11.29c)

The negative deﬁniteness of the Hessian matrix D2u(n, θ) < 0 requires that (11.29a) and (11.29c) be negative and 2

∂2u ∂2u ⎛ ∂2u ⎞ ⋅ > 0. − ∂θ2 ∂n2 ⎜⎝ ∂θ ∂n ⎟⎠

(11.29d)

362 P ART III: U RBANIZATION

AND

I NDUSTRIALIZATION

(11.29a) and (11.29c) are negative and (11.29d) holds if mα 2 > θ(1 − θ)(ln λ)2 . [1 − (m − n + 1)α]2

(11.30)

Since (11.30) holds if and only if (11.28) holds, (11.28) holds if the second-order conditions for maximizing u* with respect to n and θ are satisﬁed. Since kA = λk where λ > 1 is a constant, (11.28) also implies

dn >0 dkA

(11.31)

This implies that the number of traded goods for each individual, as well as for society as a whole, increases with transaction efﬁciency. (11.26), (11.28), and (11.31) imply dθ dθ , >0 dkA dk

(11.32)

where θ ≡ nA/n. This implies that the number of traded goods produced in the urban area increases more than proportionally as improvements in transaction conditions enlarge the equilibrium network of division of labor, n. (11.28), (11.31), and (11.32) summarize comparative statics of the general equilibrium network size of division of labor and the equilibrium location patterns of residences and transactions because of the correspondence between choices of residences and occupations. Since all endogenous variables are determined by n and θ, comparative statics of the general equilibrium values of other endogenous variables can be worked out by using (11.28), (11.31), and (11.32). Differentiation of all corner equilibrium values of the endogenous variables in (11.19), together with (11.28), (11.31), and (11.32), yields comparative statics of general equilibrium. nA/nB = MA/MB = θ/(1 − θ) increases with transaction efﬁciency k rA = [1 − (m − n + 1)α]θM/mA increases with transaction efﬁciency k rA /rB = Bθ/A(1 − θ) increases with transaction efﬁciency k n increases with transaction efﬁciency k nA = θn increases with transaction efﬁciency k

(11.33)

RA/RB decreases with transaction efﬁciency k li (an individual’s level of specialization in producing the good sold) increases with transaction efﬁciency k u* (per capita real income) increases with transaction efﬁciency k. To identify the positive effect of k on u* in (11.33), we have used the envelope theorem to u* in (11.19). Adapting the analysis of chapter 7, we can also show that the following concurrent phenomena are different aspects of the evolution in division of labor driven by exogenous improvements in transaction conditions. The degree of diversity of economic structure (which is deﬁned by the number of different occupations), the differences between different occupations,

C HAPTER 11: U RBANIZATION 363

and the number of markets for different goods, all increase. The number of transactions for each individual, trade dependence (which is deﬁned by the ratio of trade volume to real income), interdependence among individuals of different occupations, the extent of the market (which is deﬁned by per capita aggregate demand for all traded goods), and the degree of commercialization (which is deﬁned by the ratio of the income from the market to total real income), all increase. The extent of endogenous comparative advantage (which is deﬁned as the difference in productivity between sellers and buyers of traded goods) increases. The degree of market integration (which is deﬁned by the reciprocal of the number of separate communities) increases as more separate local communities merge into fewer, increasingly integrated larger communities. The number of separate communities is also the number of cities in this model. Production concentration (which is deﬁned as the reciprocal of the number of producers of each traded good) increases as per capita real income and productivity of each good increase. Now we consider the location patterns of residences and transactions that are associated with the general equilibrium values of division of labor, n = 1 and n = 2, respectively. If transaction efﬁciency k is sufﬁciently low, the transaction costs caused by a large network size of division of labor outweigh the positive network effects of the division of labor generated by the ﬁxed learning cost in each activity, so that the general equilibrium level of division of labor n = 1. This implies that each individual’s number of goods purchased is n − 1 = 0, or autarky is chosen. According to proposition 11.2, all individuals’ residences are evenly located. Each individual self-provides m consumption goods, and no market or cities exist, as shown in ﬁgure 11.3(a). Only four of M self-sufﬁcient consumer-producers are represented by four circles. Only four of m self-provided goods are represented by four lines. As transaction efﬁciency k is slightly improved, the equilibrium value of n increases to 2. Each pair of individuals will establish a local business community in which each trader sells one good to and buys one good from the other. In order to save on transaction costs, according to proposition 11.1, two trade partners meet at the midpoint between their residences to exchange goods 1 and 2. In order to maximize utility with respect to consumption of land, all individuals will reside at vertices of the grid of triangles with equal sides, so that the equilibrium price of land is equal for each residence. Hence, many local markets emerge from the low level of division of labor, but there is no central marketplace or city. All transactions are evenly dispersed at M/2 places, as shown in panel (b), where there is no division between the urban and rural areas. Only four of m goods are represented by lines and only four of M individuals are represented by four circles in (b). As transaction efﬁciency is further improved such that n > 2, then the central marketplace generates economies of agglomeration, according to proposition 11.2. In the symmetric model, each individual needs only n − 1 trade partners. In order to save on transaction costs, n individuals will form a local business community where each person sells her produce to, and buys one good from, each of n − 1 other individuals. The good that she sells is different from the one sold by each of the other n − 1 members of the community. All of the n members of the local community go to the central marketplace to trade with each other. As shown in ﬁgure 11.3(c), nA of the n individuals reside at the central marketplace which is a city, and nB of the n individuals reside in the countryside. The population size of each local community is then n, and the number of such local communities is thus M/n. The urban land size of each local community is An/M and the rural land size of each local community is Bn/M because of the assumption of ﬁxed respective total sizes of urban and rural areas. In panel (c) M/n separate local business communities are represented by 4 medium squares and cities are denoted by small squares. All transactions in a community are executed at the city. The graph under (c) illustrates the network of transactions of all n urban and rural residents that are executed at the city when n = m = 4 and M = 16.

364 P ART III: U RBANIZATION (a) Autarky without market and cities 1

1

3

3

A

4 3

2

A 3

3

2 2

1

1 2

1

1

4

3

1 4

2

A

4

I NDUSTRIALIZATION

(b) Low level of division with market and without cities

1 2

A

4

AND

4

2 2

4 An/M nA

3

2

1

1

(c) Division of labor with market and M/n = 4 cities

nB

4

An/M nA

Bn/M

Bn/M

nB

3

2 An/M nA

An/M nA nB

Bn/M

Bn/M

nB

1 An/M nA nB

Bn/M

1

An/M nA nB

2 1 2 3 4

4 1

Bn/M 4 4

2 3 2

2 41 3

3 3

An/M nA nB (e) Very high level of division of labor with an integrated market and a city, M/n = 1

Bn/M

(d) High level of division of labor with M/n = 2 cities and 2 separate communities

Figure 11.3 Evolution of division of labor and location pattern of residences and transactions

Panel (e) represents a general equilibrium with a very high level of division of labor (n = M), where there is an integrated market and a single city. Big arrows denote the direction of the evolution of division of labor and the location patterns of residences and transactions caused by improvements of transaction efﬁciency. Note that if m < M, then the structure in (e), with a single city, cannot occur since n ≤ m. In other words, the number of occupations (number of traded goods), n, cannot be greater than the number of all goods, m, so that a single city for the integrated market does not occur in equilibrium if the population size M is much greater than m, which implies that the maximum value of the number of cities M/m > 1 in the symmetric model. As division of labor evolves (i.e., n increases) due to improved transaction conditions, the number of separate local communities (which is also the number of cities) decreases, the area size of each community as well as its urban or rural area increases, the land price in the urban area increases absolutely as well as relatively to that in the rural area. Relative per capita land consumption between the urban and rural areas declines.3 The degree of concentration of residential location increases not only because the relative population size of urban and rural residents increases, but also because the average population size of cities and the population density of the urban area increase as division of labor evolves.

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In summary, we have Proposition 11.2: Improvements in transaction conditions will generate the following concurrent phenomena. The ratio of urban to rural land prices increases, the network of division of labor is enlarged, the number of traded goods for each individual as well as for society as a whole increases, the number of traded goods produced in the urban area increases absolutely as well as relatively to that in the rural area, the population ratio of urban to rural residents increases, each individual’s level of specialization increases, the number of markets increases, the diversity of economic structure increases, the number of transactions for each individual, trade dependence, and interdependence among individuals of different occupations all increase, the extent of the market and the extent of endogenous comparative advantage increase, the degree of market integration and production concentration increase, and per capita real income and productivity of each good increase. A distinguishing feature of the type II economies of agglomeration in this model is that even if which nB out of n traded goods to be produced in the rural area is indeterminate in equilibrium, a high level of division of labor will make the concentration of urban residences and all transactions in the urban area emerge from ex ante identical individuals with identical production conditions of all goods. The assumption made by Yang and Rice (1994, see example 11.2) and Fujita and Krugman (1995, see example 11.1) that land-intensive agricultural production must be dispersed in the rural area, is not necessary for the existence of type II economies of agglomeration. Also, a variety of manufactured goods that are not land intensive may be produced in the rural area because of the trade-off between economies of agglomeration and the high land prices in the city. This has a ﬂavor of the theory of complexity: some phenomena that do not exist for each individual element of a system emerge from a complex structure of a collection of numerous identical individual elements. This is just like different DNA structures of the same molecules generating many species of animals. In this chapter, we have shown that one of the most important functions of the invisible hand (interactions between self-interested behaviors) is to sort out simultaneously the efﬁcient location patterns of transactions and individuals’ residences, the related network size of division of labor, and transaction efﬁciency. Our models predict that the potential for increases of land price in the large cities is determined by the potential for evolution of division of labor. As a large city becomes the central marketplace for an increasingly more integrated large network of division of labor, land prices in the city can go up to a degree far beyond that which the marginal analysis of demand and supply may predict. Baumgardner (1988b) ﬁnds empirical evidence for the positive relationship between urbanization and individuals’ levels of specialization. Colwell and Munneke (1997) provide empirical evidence for the negative relationship between land price and distance from the city (and per capita consumption of land). Simon and Nardinelli (1996) ﬁnd empirical evidence from a data set of English cities in the period 1861–1961 for a positive relationship between transaction conditions and city size, which is predicted by the Yang and Rice and Sun and Yang models in this chapter. They have also found empirical evidence against the positive relationship between the size of ﬁrms and city size, which is predicted by the Krugman and Fujita model in this chapter. They argue that the evidence suggests that external economies, rather than internal economies of scale, are a driving force of urbanization. Here, their notion of external economies of scale, from Marshall (1890), should be interpreted as the positive network effects of division of labor, since their data set shows a positive relationship between the evolution of occupation diversity and urbanization. Also, their data set suggests a positive relationship between urbanization and evolution of the employment share of the transaction sector. More empirical works are needed for establishing the positive relationship between the land price differential of cities

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and rural areas, the degree of commercialization (level of division of labor), urbanization, and transaction efﬁciency. Y. Zhang (2000) has found empirical evidence that rejects a positive correlation between the degree of urbanization and average size of ﬁrms in urban areas: this positive correlation is referred to as type III scale effect. The theory of indirect pricing in chapter 8, together with the Smithian models of urbanization in this chapter, imply that increases in urbanization and in the level of division of labor and a decrease in the average size of ﬁrms concur if division of labor evolves between ﬁrms as a result of improved trading efﬁciency of goods relative to that of labor. If division of labor evolves within ﬁrms, a type III scale effect may occur as a phenomenon based on comparative statics of general equilibrium.

Key Terms and Review • The conditions essential for cities to emerge from division of labor • The relationship between urbanization, network size of division of labor, and transaction efﬁciency • The relationship between the difference of land intensity in producing agricultural and industrial goods, and the function of urbanization in promoting division of labor • The general equilibrium mechanism that simultaneously determines network size of division of labor, location pattern of transactions, and transaction efﬁciency • The general equilibrium mechanism that simultaneously determines the network size of division of labor, the location pattern of individuals’ residences, and the land price differential between urban and rural areas • Type I and type II economies of agglomeration • The relationship between the potential for rises of urban land prices and evolution of division of labor • The role of free migration, free choice of occupation conﬁguration, and free pricing in enabling the market to simultaneously sort out the efﬁcient location pattern of transactions, the location pattern of individuals’ residences, the network size of division of labor, and transaction efﬁciency

Further Reading Classical theory of the city: Petty (1683), von Thünen (1826), Wartenberg (1966); Division of labor and cities: Scott (1988), Marshall (1890, ch. 11), Smith (1776, chs. 2, 3), Petty (1683, pp. 471–2); Models of city and economies of scale: Ben-Akiva, de Palma, and Thisse (1989), Fujita, Krugman, and Venables (1999), Krugman (1991, 1993, 1994), Fujita and Krugman (1994, 1995), Tabuchi (1998), Fujita (1988, 1989), Fujita and Mori (1997), Fujita and Thisse (1996), Quigley (1998), Page (1999), Kendrick (1978); Hierarchical structure of cities: Yang and Hogbin (1990), Yang and Ng (1993, ch. 13), Fujita and Krugman (1994); Smithian models of cities and economies of specialization: Yang (1991), Yang and Rice (1994), Yang and Ng (1993, ch. 6), Sun and Yang (1998); Neoclassical models with constant returns to scale, transaction costs, cities: Kelley and Williamson (1984), Hahn (1971), Karman (1981), Kurz (1974), Mills and Hamilton (1984), Schweizer (1986), Henderson (1996); Urban biased development: Lipton (1977, 1984), Brown (1978), Sah and Stiglitz (1984), Sen (1977, 1981), Lin and Yang (1998); Economies of agglomeration, externality of cities, and size of cities: Abdel-Rahman (1988), Arnott (1979), Fujita (1989), Henderson (1974), Mills (1967), Kanemoto (1980); Dual economy: Murphy, Shleifer, and Vishny (1989a,b), Yang and Rice (1994); Land price of cities: Colwell and Munneke (1997); Empirical evidence: Simon and Nardinelli (1996), Baumgardner (1989), Y. Zhang (2000).

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QUESTIONS 1 North (1981, pp. 158–62) ﬁnds historical evidence for the following fact. “An urban world is a development that has occurred during the last hundred years and is associated not so much with the industrial city as with a dramatic decline in the costs of transportation, the increase in agricultural productivity, and the agglomerative beneﬁts of central places for economic activity.” Use the model in this chapter to explain this assertion. 2 Consider an extended version of the model in example 11.3. In the extended model, the equilibrium number of traded goods might be as large as 49. Consider the following hierarchical structures of cities. M consumer-producers are divided among M/49 local communities. In each of them, each person sells one good to and buys one good from each of the other 48 individuals. Each local community has one large central marketplace and 6 smaller central marketplaces. Each individual trades with her 6 neighboring trade partners through a small marketplace and goes to the large central marketplace to trade with the other 42 individuals. In other words, there is a hierarchical structure of cities. The large city is the central marketplace for the local community with 49 members, as well as the trade center for 7 individuals who reside near the large city. Each of the 6 small cities is a trade center among 7 individuals, similar to the one in ﬁgure 11.2(b). Another location pattern of transactions is that all 49 individuals go to the center of the community to trade with each other. The third pattern is that each pair of trade partners can trade at the middle-point between them. The fourth pattern is similar to that in ﬁgure 11.2(b), that is, M individuals are divided as M/7 separate local communities. Discuss under what conditions each of the four patterns occurs at general equilibrium. Analyze the difference in trade volume between the large and small cities in the ﬁrst pattern. 3 Discuss the implications of a blend between the model in question 2 and the model in example 11.4 for a hierarchical structure of land prices between cities of different ranks. Use this model to predict the potential for increases of land prices in the large cities. Braudel (1984, II, ch. 2) provides historical evidence for the role of cities as the centers of transactions. Use the evidence in connection with your casual observation of the features of the cities you have seen in the real world to discuss the relevance of the models in this chapter. 4 Analyze the role of free migration, free choice of occupation conﬁguration, and free trade and pricing of land in enabling the market to sort out the efﬁcient pattern of urbanization and the efﬁcient geographical pattern of transactions. 5 Baumgardner (1988b) ﬁnds empirical evidence for the positive relationship between urbanization and individuals’ levels of specialization. Design a method to test the concurrent evolution of division of labor and the degree of urbanization against empirical observations. Find a way to test the theories developed in examples 11.2, 11.3, and 11.4 against empirical observations. 6 Discuss the differences between the models in example 11.1 and in examples 11.2, 11.3, and 11.4. Simon and Nardinelli (1996) ﬁnd empirical evidence, from a data set of English cities over the years 1861–1961, for a positive relationship between transaction conditions and city size, which is predicted by the Yang and Rice and Sun and Yang models in this chapter. They and Y. Zhang (2000) have also found empirical

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evidence against a positive relationship between the size of ﬁrms and city size, which is predicted by the Krugman and Fujita model in this chapter. Find more empirical observations that can be used to test these models against each other. Why does the Fujita–Krugman model predict a decline in the degree of urbanization as a result of improved transaction conditions of manufactured goods? 7 Fei and Ranis (1964) claim that agricultural development and a surplus of agricultural products are essential for industrialization and urbanization. But Jacobs (1969, pp. 6–9) claims that urbanization is a driving force of agricultural development rather than vice versa: “If we wait for the emergence of agricultural surplus without cities, such surplus never takes place. Industrialization and urbanization are the driving force of agricultural surplus rather than the surplus being the necessary condition for industrialization and urban development.” Use the concept of general equilibrium to comment on these views.

EXERCISES 1 Assume that in example 11.1., the agricultural good is the sole consumption good and all manufactured goods are employed to produce the agricultural good. Use the model to explain the structural changes caused by industrialization. Compare your explanation to the conventional theory of labor surplus and structural changes (Lewis, 1955, and Fei and Renis, 1964). 2 M. Lio: Extend the model in example 11.2 to a case with three industrial goods and one agricultural good. Solve for general equilibrium and its inframarginal comparative statics. Show that a dual economy, featuring an asymmetric structure of division of labor (i.e., urban residents have a higher level of specialization than rural residents), may occur during the transitional period from a low level (urban and rural residents have the same level of specialization and productivity) to a high level of balanced division of labor. 3 Yang and Rice, 1994: Assume that in the model in exercise 2, the production functions are x i + x is = l ia , a > 1. Solve for the general equilibrium and its inframarginal comparative statics. 4 Extend the model in example 11.3 to the case with the number of traded goods n ∈ [1, 49]. Analyze the possible equilibrium hierarchical location pattern of transactions, in which individuals trade with neighbors through a local marketplace, similar to that in ﬁgure 11.2(b), with n = 7, and trade with non-neighbors through a larger central marketplace, which may emerge from a large network size of division of labor with n = 49. The central marketplace looks like a large city that channels more transactions than each smaller marketplace. Discuss the possible evolution of the number of layers of the hierarchical system of cities if the level of division of labor is allowed to be [1, m]. 5 Assume that in the model in example 11.4, total land area is a ﬁxed constant, but urban and rural land areas are endogenous variables. Solve for comparative statics of the general equilibrium. Analyze the effects of the evolution of division of labor on the relative areas of cities and countryside.

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Notes 1 Quigley (1998) considers beneﬁts from intracity informational spillovers. Tabuchi (1998), by combining the methods of Henderson (1974) and Krugman (1991), considers the trade-off between type I economies of agglomeration and the cost of intracity congestion. 2 But because of indeterminancy about who specializes in which activity, which n out of m goods are traded, and which nA out n traded goods are produced in the urban area in equilibrium, we have multiple equilibria that generate the same per capita real income. 3 The result that the number of cities decreases as division of labor evolves can be changed either by endogenizing population size or by endogenizing the number of layers of city hierarchy, as discussed in section 11.5.

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INDUSTRIALIZATION, STRUCTURAL CHANGES, ECONOMIC DEVELOPMENT, AND DIVISION OF LABOR IN ROUNDABOUT PRODUCTION

12

12.1 THE FEATURES OF INDUSTRIALIZATION The purpose of this chapter is twofold. First, we shall use the Smithian models to predict the emergence of new producer goods and related new technology from the evolution of division of labor. Second, a Smithian model of endogenous specialization with an endogenous number of links in a roundabout production chain will be developed to investigate industrialization. From as far back as Smith (1776, pp. 14, 105), Joseph Harris (1757), Josiah Tucker (1756, 1774), and Hegel (1821, p. 129), to Marshall (1890, p. 256) and Walker (1874, pp. 36–7), many economists have recognized that the emergence of new tools and machines, and the related invention of new technologies, are dependent on the development of division of labor. This classical mainstream view of invention and technology substantially differs from neoclassical saving and technology fundamentalism.1 According to the neoclassical view, innovation is a matter of investment in research and development (R&D), regardless of the levels of specialization for individuals and the level of division of labor for society (see chapter 15). In contrast, according to the classical mainstream, the invention of new machines and technology is a matter of the size of the network of division of labor and the related extent of the market. If the network of division of labor is not sufﬁciently developed, not only can new technology not be invented, but even if it were invented, it would be commercially nonviable. That is why the invention of paper, the compass, printing technology, and metallurgical technology by the Chinese in the twelfth century did not generate industrialization, whereas the commercialization of these technologies through the development in division of labor in Europe promoted other inventions that led to the Industrial Revolution in 1750–1830 (Elvin, 1973). However, all Smithian models of endogenous specialization developed so far in the previous chapters cannot predict the emergence of new producer goods from the evolution in division of labor.

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In order to formalize the classical ideas about the emergence of new producer goods from the evolution in division of labor, we shall extend the model with an endogenous number of consumption goods and endogenous specialization in example 7.2 to endogenize the number of producer goods. If we specify the CES production function in the model of endogenous specialization in chapter 2, the classical ideas about the intimate relationship between invention of new technology, the size of the network of division of labor, and the institution of the ﬁrm can be formalized. According to Mokyr (1990, 1993), Huang (1991), Rosenberg and Birdzell (1986, pp. 145 –84), North (1981), Macfarlane (1988), Baechler (1976), and Sachs (1998), the driving mechanism for the Industrial Revolution worked as follows. A variety of polities and rivalries between hostile sovereignties in the same culture in Europe encouraged many different institutional experiments. As a consequence of the range of institutional experimentation and internal and external political pluralism, a particular set of institutions emerged in Britain prior to the Industrial Revolution.2 This set of institutions, featuring great adaptability and social learning capacity of institutional arrangements, signiﬁcantly improved transaction conditions. Prior to and during the Industrial Revolution, extensive international trade, due to improved transportation conditions, stimulated evolution of division of labor.3 Constitutional monarchy and parliamentary democracy provided long-run political stability. Patent laws and evolving common law secured property rights. The securing of residual rights to ﬁrms reduced transaction costs in setting up ﬁrms and encouraged specialized entrepreneurial activities, while secured rights to intellectual property directly improved transaction conditions for technology and encouraged specialized invention of new technology. When patent laws were not enough to protect entrepreneurial ideas and rights to inventions, the institution of the ﬁrm was used to protect intellectual property rights via the residual rights of the ﬁrm and trade secrets. As the sources cited in chapters 1 and 10 suggest, a stable, nonpredatory tax system and government laissez-faire policy encouraged business activities and the evolution of division of labor. Free association (i.e., where setting up private ﬁrms need no approval or license from the government) improved transaction conditions for the evolution of the institution of the ﬁrm. Hence, the endogenous and exogenous transaction costs for each transaction were signiﬁcantly reduced, the level of division of labor in invention and other activities increased, and new producer goods and related new technology emerged. We will use two Smith–Young models of endogenous specialization to formalize this mechanism for economic development and technical progress. The earliest theories of industrialization were proposed by Smith (1776) and Young (1928). Smith conjectured that a decrease of the income share of the agricultural sector is caused by the relative difference in the beneﬁts of specialization, compared to the seasonal adjustment cost caused by specialization between the industrial and agricultural sectors. An extension of this hypothesis implies that a decline in the income share of the agricultural sector occurs not because of a change in tastes, in income, or in exogenous technical conditions, but because the agricultural sector has a higher coordination cost of division of labor compared to the beneﬁts derived from the division of labor, and it can improve productivity only by importing an increasingly number of industrial goods. These goods are produced by a high level of division of labor in the manufacturing sector, where transaction costs are more likely to be outweighed by economies of division of labor. Young considered industrialization as a process that involves evolution of division of labor in the roundabout production process, which enlarges the market network and increases productivity. There are at least three other types of models of industrialization. The ﬁrst is the model with a labor surplus and dual economy (Lewis, 1955, Fei and Ranis, 1964). In the model with a labor surplus, the expansion of the industrial sector is explained by a labor surplus in the agricultural sector and exogenous technical progress or capital accumulation in the industrial sector. As

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exogenous technical progress takes place, or as investment is used to raise the capital–labor ratio in the industrial sector, the marginal productivity of labor increases, so that demand for labor increases. Because of the existence of a labor surplus, increasing demand does not raise the wage rate and the cost of the expansion of the industrial sector. Hence, the industrial sector can be developed at a zero or low cost to the agricultural sector. Labor surplus in this model is caused by an ad hoc assumption that the price of labor is higher than the equilibrium level for some unspeciﬁed institutional reason. Since there is no trade-off between exploitation of exogenous comparative advantage and transaction costs in the model of labor surplus, this model cannot explain productivity progress in the absence of disequilibrium in the labor market. As shown in chapter 3, if we abandon the neoclassical dichotomy between pure consumers and ﬁrms, it is possible to specify the trade-off between the exploitation of exogenous comparative advantage and transaction costs in a model with constant returns to scale technology. The trade-off can be used to explain economic development by transaction efﬁciency in the absence of disequilibrium in the labor market. The second type of theory of industrialization, what Krugman (1995) calls “high-development economics,” was developed by Rosenstein-Rodan (1943), Nurkse (1952), Fleming (1955), and Hirschman (1958). Those authors did not use general equilibrium models to formalize their vague ideas, which there are two ways to interpret. According to Krugman (1995), economies of scale are an important factor for industrialization. He argues that the theory of labor surplus was more popular than high-development economics because the former was easier to formulate in the context of a model with constant returns to scale, while economists did not know the right way to formalize the latter idea using the general equilibrium model with economies of scale. Hence, the models of monopolistic competition which we have seen in chapter 5, provide technical vehicles for substantiating high-development economics and the theory of industrialization. However, most high-development economists do not mention economies of scale. They talk about interdependencies of proﬁtability in different industrial sectors, balanced and unbalanced industrialization, circular causation in the industrialization process, and pecuniary external economies of the industrial linkage network. All these notions are not difﬁcult to formalize in a general equilibrium model. Circular causation is, of course, a notion of general equilibrium. In a standard neoclassical general equilibrium model, each individual’s decision in choosing her quantities demanded and supplied is dependent on prices, while general equilibrium prices are determined by all individuals’ decisions in choosing their quantities. This circular causation implies that all interdependent endogenous variables must be simultaneously determined by a general equilibrium mechanism (or a ﬁxed point). Comparative statics of general equilibrium are a powerful technical vehicle to substantiate the mechanism. Thus, high-development economics relates to the notion of general equilibrium. When economists were unfamiliar with the technical substance of general equilibrium models, they could only use vague words to address general equilibrium phenomena, such as circular causation, interdependent decisions in different industries, pecuniary externality of industrial linkages (external economies that can be exploited via the market price system), and so on. (See questions 7–9 in chapter 5 and questions 16 and 17 in this chapter for more detail of high-development economics.) However, there are three types of general equilibrium model. In a neoclassical general equilibrium model with constant returns to scale, circular causation happens between quantities and prices and between individuals’ decisions in different sectors. In a general equilibrium model with economies of scale and an endogenous number of goods, the sort of model we saw in chapter 5, circular causation occurs among quantities, prices, productivity, per capita real income, and the number of goods, in addition to interdependencies among different markets and different individuals’ decisions. In the Smithian general equilibrium model we looked at in chapters 4, 6, and 7, there are interdependencies of the network

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size of division of labor, the extent of the market, productivity, trade dependence, the diversity of economic structures, the number of goods, the degree of market integration, and the degree of endogenous comparative advantage, in addition to interdependencies among quantities, prices, different individuals’ decisions, and different markets. It seems to us that high-development economists’ discussion about pecuniary externality based on the industrial linkage network, circular causation, and balanced and unbalanced industrialization relates more closely to the positive network effect of division of labor in a long roundabout production chain than to economies of scale. The essence of Rosenstein-Rodan’s idea (1943) about big-push industrialization is to advocate state-led industrialization because of coordination failure in exploiting the network effects of division of labor in a decentralized market. Hirschman’s idea (1958) about the pecuniary externality of industrial linkages relates more or less to market-led industrialization, since the network effects of division of labor are pecuniary (and can be exploited by the price system). The phrase “balanced and unbalanced industrialization” may be misleading. Unbalanced industrialization strategy may be associated with specialization of a country in a particular sector and with the international division of labor between countries. Hence, from the point of view of the world market, such a strategy is a balanced industrialization strategy, although it is not balanced within a single country (Sheahan, 1958). High-development economics and the related theory of industrialization have been formalized by the general equilibriu