Time Zones, Communications Networks, and International Trade

Time Zones, Communications Networks, and International Trade Advances in digital technology have driven large decrease...

Author: Toru Kikuchi

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Time Zones, Communications Networks, and International Trade

Advances in digital technology have driven large decreases in the costs of data transfer and telecommunications. There is a consequent increase in many kinds of international trade. One of the fastest-growing parts of this industry is “remote maintenance” whereby Indian companies debug software for companies in other parts of the world, often taking advantage of time zone differences to offer overnight service. In the existing literature on trade theory, however, relatively few attempts have been made to address the theme of communications networks and the role of time zones. The main purpose of this book is to illustrate, with simple models of international trade, how the introduction of communication networks and the utilization of time zone differences can affect both the structure of international trade and world welfare. Other technological aspects of recent international trade (e.g., competition between international standards, the impact of switching costs on imported products’ introduction) are also examined. Although a focus on theoretical trade models, the book will appeal to scholars, policy makers and business units who wish to learn from the recent changes in communications networks and its impact on the global economy. It provides information and suggestions for better policy formulation in the fast-changing world economy. Toru Kikuchi is Professor of Economics at the Graduate School of Economics, Kobe University, Kobe, Japan. He began his study of economics at Otaru Â�University of Commerce, Japan. After earning a Ph.D. in Economics from Kobe University, he began teaching at Kobe University in 1995 and was promoted to full Professor in 2009. He regularly teaches in both undergraduate and graduate courses in international economics. His main research field is the theory of international trade under increasing returns and imperfect competition. Recently, his research has focused on the Â�relationship between communications networks and time zone differences. His research papers have appeared in scholarly journals such as Canadian Journal of Economics, Economic Modelling, Japanese Economic Review, Journal of Â�Economics, Manchester School, Open Economies Review, Review of Development Economics, and Review of International Economics.

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90 Time Zones, Communications Networks, and International Trade Toru Kikuchi

Time Zones, Communications Networks, and International Trade Toru Kikuchi

First published 2011 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Simultaneously published in the USA and Canada by Routledge 711 Third Avenue, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2011.

To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. © 2011 Toru Kikuchi The right of Toru Kikuchi to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Kikuchi, Toru, 1968– â•…Time zones, communication networks and international trade / Toru Kikuchi. p. cm. Includes bibliographical references and index. 1. Communication in international trade. 2. Time and economic reactions. 3. International trade. 4. Business logistics. 5. Business enterprises– Communication systems. I. Title. HF1379.K55 2011 382.01–dc22 2010040854 ISBN 0-203-82802-X Master e-book ISBN

ISBN: 978-0-415-59312-0 (hbk) ISBN: 978-0-203-82802-1 (ebk)

Contents

Preface

â•‡ 1 Introduction

xiii 1

PART I

Preliminaries â•‡ 2 Basic models of international trade I

13

â•‡ 3 Basic models of international trade II

26

â•‡ 4 A decomposition of the home market effect

34

â•‡ 5 Monopolistic competition and distribution of trade gains

39

PART II

Communications networks and time zones â•‡ 6 Country specificity of communications networks

49

â•‡ 7 Interconnectivity of communications networks

59

â•‡ 8 Interconnected communications networks and home market effects

70

â•‡ 9 Time zones as a source of comparative advantage

81

10 Service trade with time zone differences

90

11 Growth with time zone differences

97

xiiâ•‡â•‡ Contents PART III

Network effects and switching costs 12 Direct network effects

107

13 Indirect network effects

117

14 Switching costs

126

15 Foreign brand penetration

132

PART IV

Cost heterogeneity and trade 16 Increasing costs in product diversification

145

17 Efficiency gaps and Heckscher–Ohlin trade patterns

157

18 Chamberlinian-Ricardian trade patterns

168

19 Strategic export policies

176

20 Concluding remarks

185

188 202 216

Notes Bibliography Index

Preface

Over the past two decades, communications networks have come to play a crucial role in economic activities in the world economy. Due to communications revolutions, we can transmit voice, graphics, and large volumes of digitized data instantly and at close to zero marginal cost to large populations around the world. Yet relatively little attention has been paid to the relationship between communications networks and international trade. This volume, a collection of essays that represents my work on international trade and communications Â�networks over the past 15 years, intends to fill this gap. I am indebted to my teachers in Otaru University of Commerce, Kobe Â�University, and Simon Fraser University for kindling my interest in the subject matter of economics. Masao Satake, Hideki Funatsu, Jun-Ichi Itaya, the late Kiyoshi Ikemoto, Kazuhiro Igawa, Masayuki Hara, Seiichi Katayama, the late Koji Shimomura, Junichi Goto, Fumio Dei, Hiroshi Ohta, Tetsuya Kishimoto, Takeshi Nakatani, Noritsugu Nakanishi, John Chant, Richard Harris, Steve Easton, Nicolas Schmitt, and James Atsu Amegashie have been instrumental to my early and continuing interest in the discipline. Quite a few of the chapters in this volume are drawn from joint contributions I made with several of my teachers and friends. I would like to thank Ngo Van Long, Kazumichi Iwasa, Sugata Marjit, the late Koji Shimomura, and Dao-Zhi Zeng for their kindness. I would also like to thank David Anderson for editing almost every manuscript included in this book. To communicate with overseas teachers and friends via communications networks (with some time zone differences) is one crucial driving force for my research. Over the years, interactions with many people have benefited me immensely in clarifying my concepts. Notable among them are Kenzo Abe, David Anderson, Mitsuyo Ando, Koji Aoki, Kosuke Aoki, Eric Bond, Kwan Choi, Ichiro Daitoh, Colin Davis, Junko Doi, Masahiro Endoh, Wilfred Ethier, Kenji Fujiwara, Marcelo Fukushima, Taiji Furusawa, Koichi Hamada, Tetsugen Haruyama, Kenichi Â�Hashimoto, Masayuki Hayashibara, Yunfang Hu, Makoto Ikema, Jota Ishikawa, Takatoshi Ito, Takekazu Iwamoto, Naoto Jinji, Ronald Jones, Jiandong Ju, Takashi Kamihigashi, Murray Kemp, Fukunari Kimura, the late Kazuharu Kiyono, Kozo Kiyota, the late Kiyoshi Kojima, Kenji Kondoh, Hiroshi Kurata, Sajal Lahiri, Edwin Lai, Chia-Hui Lu, Mutsumi Matsumoto, Naoki Mitani, Eiichi Miyagawa,

xivâ•‡â•‡ Preface Tomoya Mori, Hiroshi Mukunoki, Sei-il Mun, Takumi Naito, Kenshiro Ninomiya, Masao Oda, Masao Ogaki, Takao Ohkawa, Michihiro Ohyama, Hisayuki Okamoto, Masayuki Okawa, Toshihiro Okubo, Ray Riezman, Nobuhito Suga, Katsuhiko Suzuki, Takatoshi Tabuchi, Takaaki Takahashi, Fumiko Takeda, Shumpei Takemori, Makoto Tawada, Nobuo Teramachi, Eiichi Tomiura, Ryuhei Wakasugi, Kar-Yiu Wong, Mitoshi Yamaguchi, Kazuhiro Yamamoto, Akihiko Yanase, Makoto Yano, Morihiro Yomogida, Zhihao Yu, and Lex Zhao. In addition, helpful comments from journal editors and referees are gratefully acknowledged. This volume would not have been possible without the generous support of numerous institutions. Notable among them are the Graduate School of Â�Economics, Kobe University; Simon Fraser University; McGill University; and Yale University. I am particularly grateful to Koichi Hamada for funding my research visit to Yale University. I acknowledge the Ministry of Education, Culture, Sports, Science and Technology of Japan for financial support via grant 22243024. I am also grateful for able assistance from Yuji Matsuoka. Teaching international trade theory to both graduate and undergraduate Â�students at Kobe University provided me with quite interesting opportunities. Some of the ideas for the chapters in this book came from casual conversations with my Â�students. I would like to say thank you to my colleagues and my students. The organization of this volume would not have been possible without the able assistance of Yong-Ling Lam, the Associate Editor for Routledge. Comments from anonymous referees were most helpful. I am also indebted to Routledge for their interest and encouragement. Finally, I am grateful to my wife Chiharu for all of her help, guidance and support. She also teaches Industrial Organization. Her suggestions on several topics in this book have been quite helpful. I appreciate the comments from my mother and my mother-in-law, Noriko and Chieko, who have checked almost every chapter in this book. I am also grateful to my son Takatoshi who always provides me with inspiration. I thank them all.

1 Introduction

1.1Â€Â€Communications networks and international trade Over the past two decades, communications networks have come to play a crucial role in economic activities in the world economy. Communications networks are the infrastructure through which different parties communicate with each other. Traditional examples include postal and telecommunications systems; more recent examples of communications networks are the Internet and related networks, Â�satellite communications systems, mobile telephone networks, etc., which have raised international business transactions to a new level. Innovations in communications technologies enable us to transmit voice, graphics, and large volumes of digitized data instantly, and at close to zero marginal cost, to large populations around the world. Motivated by these changes, the role of new types of Â�communications networks in the world economy has been widely discussed. What are the major implications of these new types of communications networks for world trade? Rapid technological change in communications networks has a dual impact on the economics of world trade: it affects both trade in goods and trade in services. The following subsections explain each point briefly. Communications networks affecting trade in goods Changes in communications networks can increase the quality and speed of coordination activities between two agents. For example, improved communications networks make communications with a central office or with customers more efficient. These improvements facilitate the cross-border fragmentation of production processes. To put it another way, as communication links improve, the incentives for specialization and outsourcing expand.1 In this context, services provided by communications networks are at the very core of the internationalization of Â�economic activities, providing connections and allowing the coordination of Â�geographically separated production processes.2 Several articles have been devoted to the study of various aspects of fragmentation. In their seminal contribution, Jones and Kierzkowski (1990) argued that fragmented technology requires service links, which are mainly provided by information and communications networks, to connect separated production

2â•‡â•‡ Introduction blocks. Deardorff (2001a) argued that liberalizing trade in services facilitates fragmentation, which, in turn, stimulates trade in goods. The link between services and fragmentation of production processes is further explored by Long, Riezman, and Soubeyran (2005).3 Communications networks affecting trade in services Service transactions are often characterized by the requirement that there be a double coincidence in both time and space of the proximity of the buyer and the seller. In other words, production and consumption of a service must generally take place simultaneously.4 This non-storable nature of services implies that production and consumption tend to occur at the same time and in the same location. However, the new types of communications networks, at reasonably low cost, break the necessity for the buyer and the seller to be in the same location, even though the coincidence in time may not be broken. In a series of articles, Harris provides insightful findings on this aspect.5 In particular, Harris (1998, p. 146) suggests that the improved communications networks create a form of “virtual mobility” of services and thus enhance the international trade of these services, which was not previously possible.6 In other words, technological advancement in communications technologies tends to increase the tradability of services to the extent that they make it easier to unbundle the production and consumption of information-intensive service activities: research and development, software development, data entry, inventory management, quality control, accounting, personnel, secretarial, marketing, advertising, distribution and legal services. Grossman and Rossi-Hansberg (2008) called these situations trade in tasks. The above point may be summarized by a classification of service transactions that uses the physical proximity of consumers and providers as a reference point (see Figure 1.1).7 Most international transactions in services require either the Â�consumer to move to the location of the producer (e.g., tourism) or the factors of production to move to the place of consumption (e.g., the provision of certain business services). In Figure 1.1, the former is classified as Type 2 and the latter as Type 3. As has already been pointed out, however, there are services that can be traded internationally in a similar fashion to goods via cross-border supply (Type 1 in Figure 1.1); neither consumers nor providers move. The improved communications technologies change Type 2/Type 3 service transactions into

Provider does not move

Provider moves

User does not move

Type 1

Type 3

User moves

Type 2

Figure 1.1Â€Â€

Introductionâ•‡â•‡ 3 Type 1 transactions. The rise of distance education is one of the major examples (Type 2 to Type 1), and the rise in overseas call and help centers is another (Type 3 to Type 1).8 Due to communications revolutions, will all service transactions become Type 1 in the near future? Related to this point, Leamer and Storper (2001) emphasize that while the new types of communications networks (e.g., the Internet) transmit simple codifiable messages with ease, it is not so with complex uncodifiable (context-Â� dependent) messages, by which “close relationships” are made.9 They also review the impact of innovation in transacting technologies and argue that previous rounds of infrastructure improvement always have had a double effect: (1) permitting dispersion of certain routine activities, but also (2) increasing the complexity and time dependence of productive activity, and thus making agglomeration more important.10 The coordination of new and innovative activities depends on the successful transfer of complex uncodifiable messages, requiring a kind of closeness between the sender and receiver that the Internet does not allow. Based on their argument, we can predict that, while many service transactions are moving from Type 2/ Type 3 to Type 1, more new service transactions are entering as Type 2/Type 3, or are only provided domestically. Not all service transactions become tradable. Somewhat ironically, as more and more service transactions do become tradable, the value of being close and making “face-to-face” contact becomes higher. The above argument also suggests that even Type 1 service transactions are not automatically made possible by the introduction of new types of communications networks. Leamer and Storper (2001, p. 660) list the limited number of “faraway” countries that have overcome the force of gravity (i.e., distance): the older Anglo-Saxon countries (New Zealand and Australia), and more recently Taiwan, Singapore, and, increasingly, Ireland. The experiences of these countries strongly suggest that there is a long and difficult (though not impossible) process of creating the relational networks necessary to become part of the world core.11 Although interaction via communications networks may help to create and Â�maintain these relational networks, it cannot be a substitute for the relational Â�networks themselves.12 This might be especially true for the higher order activities of invention, innovation, and management. Related to this, Jones and Marjit (2001) argue that the role of young generations (who are familiar with new types of communications technologies) in developing countries has become more important as a determinant of those countries’ development process. Until now, we have discussed the impact of new types of communications networks on trade in services. Based on the above discussion, one factor emerges as a key driver of world trade: time zone differences between countries. The Â�following subsection describes this as an important aspect of new types of Â�communications networks. Time zone differences as a determinant of service trade Usually, time zone differences bear significant costs of doing business across countries and have a negative impact on world trade flows. With reference to this

4â•‡â•‡ Introduction point, Stein and Daude (2007) consider time differences in the context of the location of foreign direct investment. They found that transaction costs associated with time zone differences are important for frequent real-time communications between corporate headquarters and their affiliates. However, for some kinds of service transactions, the utilization of different time zones enables more efficient production. In a recent contribution, Marjit (2007) argues for the inclusion of time zone differences as a determinant of trade patterns.13 Here, we would like to indicate two possible sources of service trade with time zone differences.14 Continuity effect: By operating around the clock (i.e., by passing a project electronically from a country whose workday has ended to a country whose workday is just beginning), it becomes possible to take advantage of the full twenty-four hours of the world’s workday. This kind of continuity effect increases firms’ productivity. â•… One of the major examples is the “remote maintenance” whereby Indian companies debug software for companies in other parts of the world, often taking advantage of time zone differences to offer overnight service. Another example is the use of the design teams in New Zealand, India, Ireland, and Canada to work on the same project and to “pass it on” westward during the day, a practice that is being used by some software and engineering firms to cut down on development cycle times.15 2 Synchronization effect: Another important source of trade with time zone differences is related to the “coincidence in time” aspect of service transactions. Trade with different time zones is gainful when fulfilling nighttime demand in one country by utilizing daytime supply in the other country. In general, nighttime wage rates are higher than daytime wage rates. Thus, utilizing communications devices makes it possible to take advantage not only of the international wage rate differences but also daytime/nighttime wage rate differences. 1

It is important to note that these kinds of service trade may be interpreted as new versions of periodic intra-industry trade.16 Traditionally, trade in (perishable) agricultural products, electricity, and similar goods is based on predictable, periodic fluctuations in countries’ production of, or demand for, these commodities. As for agricultural products, for example, the cycle is seasonal, based on the Â�differences in climatic zones. This book emphasizes that, due to communications revolutions, similar kinds of trade based on the differences in time zones emerge. It is also important to note that this type of trade is crucially dependent on the degree of codifiability of service transactions. These new types of trade in services, made possible by modern communications networks, have drawn a great deal of media attention. However, many economists are quite skeptical about the role of these types of trade. In all likelihood the new types of service trade play a relatively limited role in total world trade. Furthermore, it seems clear that differences in time zones are not the sole

Introductionâ•‡â•‡ 5 determinant of services trade. The complementary/substitutional effects on building relational networks must be clarified. However, the possibility that trade reducing factors can become trade enhancing via technological changes needs further investigation. Although there are several restrictions, due to the communications revolution, utilization of both communications networks and time differences may become a primary driving force behind world trade. In the existing literature on trade theory, however, relatively few attempts have been made to address the theme of communications networks and the role of time zones. One of the main purposes of this book is to explain, with simple trade theory, how the new types of communications networks can affect the nature of world trade. For this purpose, several types of international trade models are built. I also pay special attention to the role of time zone differences as a key driver of new types of world trade (mainly trade in services). Other technological aspects of recent international trade (e.g., competition between international standards, the impact of switching costs on imported products’ introduction) are also examined. I hope that the analyses of these trade models will help the understanding of the world economy with rapidly improving communications technologies.

1.2Â€Â€The book’s structure Part I: Preliminaries Part I lays some groundwork for the analysis. It begins with a restatement of the conventional Ricardian trade model (Chapter 2). It then describes the basic “new trade theory” model of monopolistic competition, which has been popularized by a series of works by Paul Krugman (Chapter 3). I also pay special attention to the model of monopolistic competition with iceberg trade costs (Chapters 4 and 5). The reason is twofold. For one thing reductions in marginal trade costs (e.g., transport costs and tariffs) and related “Home market effect” are real issues. At the same time, in order to capture the aspects of utilization of time zone differences, the model of monopolistic competition with iceberg transport costs will be useful as a benchmark. Part II: Communications networks and time zones Based on preliminary groundwork in Part I, Part II develops approaches to trade with special emphasis on communications networks and time zone differences. The first three chapters (Chapters 6–8) concentrate on the role of communi cations networks as a determinant of comparative advantage. The next three chapters (Chapters 9–11) turn to the role of time zone differences as a source of comparative advantage. In the first three chapters I emphasize two aspects of communications networks: (1) country specificity of communications networks, and (2) interconnectivity of communications networks.

6â•‡â•‡ Introduction Country specificity of communications networks: Country specificity reflects the fact that communications services are often provided by national Â�(government-owned) monopolies. In other words, most countries pursue policies of one kind of another that restrict the access of foreign communications service providers to the domestic market. In such a situation, the quality and scale of the communications infrastructure within a country, and the number and sophistication of people using that infrastructure, become ever more crucial factors in determining the performance of the country’s economy. Related to this, Roller and Waverman (2001) argue that both developing and developed economies require a healthy, dynamic telecommunications sector if they are to prosper in an increasingly global economy.17 2 Interconnectivity of communications networks: Interconnectivity allows network users in one country to communicate with users in another country.18 If a network located in one country is purely country-specific and is not connected to the internationally interconnected networks, users of the former will be at a disadvantage. â•… The concept of interconnectivity is also related to Leamer and Storper’s “relational networks” as reviewed in the previous section. If cultural, relational, and linguistic barriers continue to hinder the full interconnection of communications networks, then one of the first effects of trade liberalization will be an increase in inequality among nations.19 Differences in interÂ� connectivity among countries reflect the difficulty of creating relational Â�networks among countries. 1

Based on these two aspects, Part II examines the relationship between communications networks and world trade. The contents are as follows. Chapter 6 develops a basic model of monopolistic competition that captures the role of country-specific communications networks in determining the comparative advantages of countries. A communications network is characterized by: (1) the existence of a large fixed cost for its construction; and (2) a public monopoly that employs average cost pricing. It is demonstrated that the size of a country, measured by the size of the country’s endowment of factors of production, Â�determines its comparative advantage. Next, in Chapter 7, a multi-country model of trade is developed that captures the role of country-specific communications network interconnectivity, which enhances trade in intermediate business services. The number of countries Â�connected to internationally interconnected networks is found to determine the structure of comparative advantage. That is, countries with interconnected Â�networks have a comparative advantage in the product that requires business services provided via networks. In connected countries, producers of that product benefit from the efficient transmission of business services. This chapter also demonstrates that countries whose country-specific networks are not connected to the interconnected networks may become worse off as the result of trade. In Chapter 8, I develop a model of trade that highlights the effects of the interconnection of country-specific communications networks as a driving force

Introductionâ•‡â•‡ 7 behind trade in high-tech products with positive transport costs. By constructing a two-country model of monopolistic competition with two production factors, it is shown that the locational decisions of firms may magnify the influence of interconnected networks. In a reversal of the standard home market effects, the abundance of unskilled labor in the developing countries can attract high-tech firms from the developed countries. Chapter 9 proposes a three-country model of monopolistic competition that captures the role of time zones in the division of labor. The connectivity of business service sectors via communications networks (e.g., the Internet, satellite communications systems) is found to determine the structure of comparative advantage. In other words, two countries with connected service sectors have a comparative advantage in the good that requires business services. Chapter 10 proposes a two-country model of service trade that captures the role of time zone differences as a determinant of trade patterns. It is shown that the utilization of communications networks induces dramatic change in industrial structure due to firms taking advantage of time zone differences. Finally, in Chapter 11, I propose a two-country growth model of intermediate business services trade that captures the role of time zone differences. It is shown that a time-saving improvement in intermediate business services trade involving production in different time zones can have a permanent impact on productivity. Part III: Network effects and switching costs Networks are often characterized by the existence of strong network effects: the more people who use them, the more useful they are to any individual user. Network effects are direct when direct connection between users matters (e.g., telecommunications networks and speakers of a language). On the other hand, a similar network effect, an indirect network effect, may arise when individuals consume a system that consists of a “hardware” good and complementary software products.20 Part III develops new types of trade models with direct/indirect network effects. It also examines other technological aspects of recent interÂ� national trade (e.g., competition between international standards, the impact of switching costs on imported products’ introduction), which are crucially related to communications networks. Chapter 12 examines how the direct network effects of communications activities and trading opportunities interact to determine the structure of comparative advantage. These interactions are examined by constructing a two-country, three-sector model of trade involving a country-specific communications network sector. The role of the connectivity of network providers, which allows users of a network to communicate with users of another network, is also explored. Next, in Chapter 13, I examine how trade liberalization affects production Â�structure in the presence of indirect network effects (hardware/software systems). For these purposes I construct a simple two-country model of trade with two

8â•‡â•‡ Introduction incompatible hardware technologies. It is shown that, given that both types of hardware exist before trade liberalization, liberalization and increased intra-industry trade in software products may reduce the variety of hardware technology via intensified indirect network effects. In Chapter 14, I consider a two-period model of market entry with homogeneous products and switching costs. It is shown that the pro-competitive effect of a foreign firm’s entry (i.e., unilateral trade liberalization) emerges before the entry. In addition, conditions which are conducive to a competitive environment in the second period are shown to yield a less competitive outcome in the first period. In other words, when the marginal cost of the foreign entrant is relatively low, the first-period output of a domestic monopolist is relatively low as well. The main purpose of Chapter 15 is to illustrate, with a simple monopolistic competition trade model, how trade liberalization (i.e., a decline in trade costs) can affect domestic entrepreneurs’ decision between providing domestic or foreign brands, and thus the degree of foreign brand penetration. It is shown that, as trade costs decrease, more entrepreneurs choose to provide foreign brands. Furthermore, the shift to foreign brands is shown to magnify the negative impact of trade liberalization on the profits of firms selling domestic brands. Part IV: Cost heterogeneity and trade Finally, Part IV turns to the basic theory of international trade, with special reference to the role of cost heterogeneity among/within countries. Although these chapters do not perfectly fit with the “new-new-trade-theory” literature à la Melitz (2003), They aim to provide some complementary view on the role of technological heterogeneity. In Chapter 16, I extend a monopolistically competitive trade model with symmetric costs (reviewed in Chapter 3) to one with asymmetric costs in product diversification. Both the trade pattern and the effects of the opening of trade on welfare are examined. It is shown that: (1) the larger country will be a net importer of differentiated products, which contradicts the result of Krugman (1980); (2) the greater the size of the country, the smaller the share of the intraindustry trade; and (3) the larger the trading partner of a country, the larger the gains from trade of the country. Chapter 17 presents an extended version of monopolistic competition model with asymmetric costs (Chapter 16). In this chapter I develop a two-factor, three-sector model of international trade in which the monopolistically compeÂ� titive firms are characterized by different fixed production costs. It is shown that, depending on the pattern of the international distribution of factor endowments, the trade pattern is determined not only by relative factor endowments as suggested by Heckscher and Ohlin, but also by absolute factor endowments via a mechanism of competitive selection in the monopolistically competitive sector. Chapter 18 provides a simple, many-industry model of trade which emphasizes the interaction between cross-country technical heterogeneity (i.e., a Ricardian

Introductionâ•‡â•‡ 9 aspect) and monopolistic competition among producers of differentiated products (i.e., a Chamberlinian aspect) as determinants of trade patterns. It is shown that the emergence of intra-industry trade is crucially dependent on the shape of the technology index schedule, which is obtained as a step-function. The purpose of Chapter 19 is to further explore how optimal export policies are affected by the nature of oligopolistic competition and the structure of demand. It is shown that (1) the more cost competitive the home firm is, the higher the optimal level of export intervention becomes; (2) as the goods become better complements, the optimal level of export intervention increases; and (3) the nature of the effects of strategic export policies on foreign firms depends on both the mode of competition and the structure of demand. Chapter 20 presents a summary and conclusion.

Part I

Preliminaries

2 Basic models of international trade I

2.1Â€Â€Introduction As Jones (1995, p. 237) emphasizes, one of the most distinguishing characteristics of international trade is the “co-existence of markets with overlapping domains.” In other words, while goods are supposed to be traded on international markets, factors are not allowed to move across borders. The latter reflects an important point that the movement of production factors (e.g., labor and capital) is often subject to controls at the border and is generally much less free than the movement of goods. Owing to this special characteristic, links and feedbacks between markets with overlapping domains are major concern in international trade theory. In order to understand these links and feedbacks, let us begin with the analysis of international trade using the classic Ricardian model, which has two goods and one factor (labor). One of the main purposes of this chapter is to explain the impact of international trade opening on national labor markets. To do so, we propose a convincing graphical exposition that emphasizes the role of labor markets. The following section presents the basic Ricardian model. In section 2.3, Â�utilizing a diagram of the labor market, we propose a new graphical method of decomposing Ricardian trade gains. A Ricardian model with external economies of scale is presented in section 2.4. A new graphical decomposition method is also applied for the model with external economies of scale in section 2.5. Section 2.6 concludes the chapter.

2.2Â€Â€Ricardian model Suppose that there are two countries in the world, Home and Foreign.1 There is only one factor of production, labor, and the size of each country is measured in terms of labor force size: the total labor force at Home is L and Foreign is L*.2 In each country, two goods (good 1 and good 2) are produced under constant returns to scale technologies. Denote by ai the amount of labor needed to produce one unit of good i, and by yi the output level of good i, respectively. Then the Home production possibility frontier (PPF) is represented by

14â•‡â•‡ Preliminaries a1 y1 + a2 y2 = L.

(2.1)

Figure 2.1(a) depicts a linear PPF, VP. The slope of the PPF is a1/a2. Both goods are produced at Home only if the wages earned in the two sectors are the same. Denote pi the price of good i, wage rate in i-th sector is pi/ai. Then, wage rates are equalized across sectors if and only if p1 ___

p2 ___ aâ•‰â•¯ 1â•¯â•‰â•¯= aâ•‰â•¯ 2â•¯â•‰â•¯.

(2.2)

In other words, in autarky (i.e., no international trade), the relative price of good 1 is determined by its opportunity cost: a __ â•‰â•¯pâ•›1â•¯â•¯â•‰ __1 A

pâ•›

A 2

= â•‰â•¯a â•¯â•‰â•¯,

(2.3)

2

where superscript A represents the autarky equilibrium. In Figure 2.1(a), the autarky equilibrium might occur at point A. Panel (b) depicts Foreign PPF, P*V* and the autarky equilibrium at A*. Suppose that Home has a comparative advantage in producing good 1, meaning that a1 __

a* â•‰â•¯ â•¯â•‰â•¯< ___ â•‰â•¯ 1â•¯â•¯â•‰.â•¯ a2 a*2

Combining this with (2.3) and its Foreign counterpart, the Home autarky relative price of good is lower than Foreign: pâ•›A p1*A â•‰â•¯__1Aâ•¯â•¯â•‰ < ____ â•‰â•¯ â•¯â•‰.â•¯â•¯ pâ•›2 p2*A (a)

(b)

Good 2

Good 2 P*

V

C

C*

A*

A

(a1/a2)

Figure 2.1Â€Â€

P Good 1

(a1*/a2*)

V* Good 1

Basic models of international trade Iâ•‡â•‡ 15 It is important to note that technological differences across countries are translated into differences in autarky relative prices. Now let us suppose that the two countries open their goods markets. To obtain the trading equilibrium relative price p1T/pT2 at which world demand equals world supply, let us use the world relative supply and demand curves, as illustrated in Figure 2.2. Let us begin with the derivation of the world relative supply curve, which has a step with flat sections linked by a vertical section. To derive this supply curve, let us consider the following three cases. (a) If the relative price is lower than the Home autarky relative price T pA ____ p *A ___ â•‰â•¯ â•¯â•‰â•¯â•¯â•›<â•› â•‰â•¯ 1â•¯â•‰â•¯â•¯â•›<â•› â•‰â•¯ 1 â•¯â•‰,â•¯â•¯ pT2 p2A p2*A

p1 ___

both countries are fully specialized in good 1, so the world relative supply of good 1 is zero. (b) If the relative price is in between the autarky relative prices A pT ____ p *A ___ â•‰â•¯ A â•¯â•‰â•¯â•¯â•›<â•› â•‰â•¯ T1â•¯â•‰â•¯â•¯â•›<â•› â•‰â•¯ *A1 â•¯â•‰,â•¯â•¯ p2 p2 p2

p1 ___

Home is fully specialized in good 1, while Foreign is fully specialized in good 2. In this case, the world relative supply is (L/a1)/(L*/a *2 ). (p1/p2)

(a1*/a2* )

(pT1/pT2 )

T

(a1/a2)

(L /a1) (L*/a2* )

Figure 2.2Â€Â€

16â•‡â•‡ Preliminaries (c) If the relative price is higher than the Foreign autarky relative price p p p ____ ___ ___ â•‰â•¯ A1â•¯â•‰â•¯â•¯â•›<â•› â•‰â•¯ *A1 â•¯â•‰â•¯â•¯â•›<â•› â•‰â•¯ T1â•¯â•‰,â•¯â•¯ A

p2

*A

p2

T

p2

both countries are specialized in good 1. From (a), (b), and (c), the world relative supply curve becomes a stair-step shape function. According to the world relative demand function, let us suppose that tastes are identical and homothetic. We can illustrate a downward-sloping world relative demand function. Let us take the case in which the world relative supply curve and the world relative demand curve intersect at point T. Now let us look back to each country’s PPF (Figure 2.1). Since p p ___ ___ â•‰â•¯ A1â•¯â•‰â•¯â•¯â•›<â•› â•‰â•¯ T1â•¯â•‰â•¯, A

p2

T

p2

Home is fully specialized in good 1 at point P, then trades at the relative price pT1/pT2 to obtain the consumption point C. Similarly, Foreign is fully specialized in good 2 at point P*, then trades at the relative price pT1/pT2 to obtain the consumption point C*. Clearly, each country can consume both goods at a point above its PPF, which implies that trade gains are mutual in this case. It is important to note that Home exports good 1, which is in keeping with Home’s comparative advantage in producing good 1: a __ a* __ â•‰â•¯ 1â•¯â•‰â•¯< â•‰â•¯ *1â•¯â•‰â•¯. a2 a2 Now we can restate a deep insight from the classic Ricardian model. Proposition 2.1 (Ricardo): Trade patterns are determined by comparative advantage. Note that this trade pattern occurs even if Foreign has an absolute disadvantage in both goods:3 a1 < a*1, a2 < a*2. In other words, even if Home has an absolute advantage in both goods, via wage adjustments, it is still possible for Foreign to export good 2. Before closing this section it may be worth pointing out, in passing, that the relative price in trading equilibrium does not always in between autarky relative prices. For example, if L becomes sufficiently large, the relative supply curve is shifted as a dotted line, as represented by Figure 2.3. Then the relative demand intersect at point T’: the relative price equals the Home autarky relative price. When Home is sufficiently large, it does not gain from trade. In other words, in this kind of perfectly competitive setting, the distribution of trade gains is unequal

Basic models of international trade Iâ•‡â•‡ 17 (p1/p2)

T

(pT1/pT2 )

T'

Figure 2.3Â€Â€

in the sense that the terms-of-trade improvements are unequal: the smaller country gains more than the larger country. This is known as “Mill’s Paradox.”4 We will return to the distribution of trade gains between countries in Chapter 5.

2.3Â€Â€Decomposition of Ricardian trade gains In this section, we concentrate on what happens in the Home labor market.5 To Â�simplify the argument, we treat world prices as given. Figure 2.4(a) reproduces Home PPF in Figure 2.1(a). Now let us add one more panel for a better understanding: Figure 2.4(b) depicts labor allocation between sectors. The horizontal axis Â�represents the total labor force, L. The quantity of workers employed in sector 1 (resp. sector 2) is measured from the left (resp. right). The left (resp. right) vertical axis shows the wage rate in the sector 1 (resp. sector 2). Initially, in the autarky equilibrium, wage rates are equalized between sectors [see (2.2)] and O1L workers are hired in sector 1, while LO2 workers are hired in sector 2. The total income (in terms of the numeraire, good 2) is shown by the shaded rectangle. Now let us move to the trading situation with fixed terms of trade (Figure 2.5). If the terms of trade are given by the slope of the line DP, Home specializes in

18â•‡â•‡ Preliminaries (a)

(b)

Good 2

V

(p2A/a2)

(p1A/a1) A

Good 1

P

O1

L Sector 1 employment

O2 Sector 2 employment

Figure 2.4Â€Â€

(a)

(b) New equilibrium

Good 2 (p /a1) T 1

D V'

(p1A/a1)

V A

C

Initial equilibrium

P B

Good 1 O1

L Sector 1 employment

O2 Sector 2 employment

Figure 2.5Â€Â€

good 1 at point P. Assume that consumption occurs at point C located on the consumption possibility frontier DP, so that CBP is the trade triangle (the country exports BP units of good 1 and imports BC units of good 2). Now we can decompose the movement toward the trading equilibrium into two steps, which is in line with the traditional separation of trade gains into

Basic models of international trade Iâ•‡â•‡ 19 Â� consumption and production gains. First, suppose that in the short run labor allocation is fixed, and thus Home is staying at the autarky production point, A, while it is able to trade at the terms of trade (pT1/pT2 â•›). Then, the consumption possibility frontier expands from VAP to V’AP as in Figure 2.5(a). In Figure 2.5(b), this change may be illustrated as an increase in the wage rate for the workers employed in sector 1 (i.e., from p 1A/a1 to pT1/a1). Their total increase in wage income is shown by the dotted rectangle in Panel (b), which is shown as V’V in Panel (a). Next, let us consider the (long-run) labor movement between sectors. Since sector 1 offers the higher wage rate, workers will gradually move from sector 2 to sector 1 (shown by the arrows in Figure 2.5). It should be noted that this process of labor movement (i.e., the process of specialization according to comparative advantage) may seem unfair to the comparative disadvantage sector.7 Home firms in sector 2 lose market share even though they have an absolute advantage in producing good 2: 6

a2 < a*2. One of the deepest insights from the Ricardian model is that even if a firm is more productive than its counterpart abroad, it may still lose market share because domestic firms in other sectors have a higher productivity advantage Â�relative to foreign firms. Let us now return to the labor market diagram. In Figure 2.5(b), the eventual distribution of labor force will be one with O1O2 workers in sector 1, which Â�corresponds to the production point P in Panel (a). The effect of this labor movement among sectors is shown as the expansion of the consumption possibility frontier from V'AP to DP in Panel (a), reflected by the horizontally shaded area in Panel (b). In terms of the numeraire, trade gains are measured by VD in Panel (a), and the sum of the dotted rectangle and the horizontally shaded Â�rectangle in Panel (b).

2.4Â€Â€External economies of scale Until now, we have concentrated on the case of constant returns to scale (CRS) technologies. Under this setting, “Ricardian” comparative advantage – differences in technologies across countries – is a major cause of trade. In other words, countries trade in order to take advantage of their differences. Although Ricardian comparative advantage is the major reason for the existence of international trade, it is not the only possible explanation of international trade. Trade economists have recognized that there is another one: increasing returns to scale (IRS). Given the existence of economies of scale, countries also trade because there are inherent advantages to specialization.8 Increasing returns to scale generated by external economies have become a main feature of many economic models that deal with trade gains, endogenous growth, multiplicity of equilibria, and indeterminacy in dynamic models of

20â•‡â•‡ Preliminaries growth.9 The simplest route to understanding a basic mechanism in these models is the one-sector Ricardian trade model with IRS. Yet this model lacks a compelling graphical representation.10 The purpose of this and following sections is to offer such a representation. Our experience indicates that this graphical approach helps the reader to gain, almost effortlessly, a clear understanding of the effect of IRS on trade gains. As with section 2.3, we concentrate on what happens in the Home labor market. To simplify the argument we treat world prices as given. Home produces two goods (good 1 and good 2) with one factor of production: labor.11 Let Yi and Li denote respectively output and employment levels of sector i. Good 1 is produced in a competitive industry under external economies of scale. The output of the representative firm (employing ℓ1 units of labor) is given by y1 = (L1)γ ℓ1, γ â•›≥ 0,

(2.4)

where the firm takes (L1)γ as exogenous. The firm perceives that its marginal product of labor is (L1)γ which it takes as a constant. Aggregating over all the firms in industry 1, we get Y1 = (L1)γ L1 = L11+γ ≡ L1ε,Â€Â€Â€Â€Â€Â€Â€Â€ε ≡ 1 + γ.

(2.5)

Therefore, at the industry level, the marginal product of labor is εLγ1â•›â•›>â•›Lγ1 if γ >â•›0. We call εâ•›L1γ the marginal social product of labor in sector 1, and Lγ1 the marginal private product of labor, as perceived by the firms. Here ε is the degree of external economies of scale: ε = 1 corresponds to the case without external economies of scale. Let aLi denote the amount of labor needed to produce one unit of good i. In sector 1, aL1 is defined as follows: L __ –γ a1 (L1) ≡ â•‰â•¯ 1â•¯â•‰â•¯= (L1)–γ = (Y 1/ε 1 ) . Y1

(2.6)

Thus a greater employment level L1 results in a lower value of a1. Good 2 is the numeraire good. It is produced by a competitive industry under constant returns to scale technology, so that a2 is a constant. Thus the Home PPF is represented by a1Y1 + a2Y2 = (Y1)1/ε + a2Y2 = L,

(2.7)

where L is the total amount of labor. With ε >â•›1, the marginal social cost of good 1 in terms of good 2 falls as Y1 increases; this gives rise to a convex PPF, VP, depicted at Figure 2.6(a).12 In addition, the marginal social cost of good 1 in terms of good 2 is lower than its private counterpart.13 Let µ be the expenditure share on good 1. In autarky, the relative price of good 1 is obtained as follows. First, from the definition of µ, and using the facts that in the Ricardian model national income equals the wage bill, wL, and that the price equals labor cost per unit of output, so that w = p2/a2, we can write

Basic models of international trade Iâ•‡â•‡ 21 (a)

(b) (p2 /a2)

(p1 /a1)

Good 2

∼ w (L1, p1T ) [p1A /a1(L1)] V A Good 1

P

O1

L1 Sector 1 employment

O2 Sector 2 employment

Figure 2.6Â€Â€

p2 __ p1Y1 = µ(p1Y1 + p2Y2) = µwL = µLâ•›â•‰â•¯a â•¯â•‰â•¯. 2

(2.8)

Thus at the autarkic equilibrium p2 ____ Y1 = â•‰â•¯p aâ•¯â•¯â•‰â•¯ (µL) 1 2

(2.9)

the equalization of the price ratio to the labor cost ratio gives A a1(L1A ) __ 1 1 ____ â•‰â•¯1–ε __ εâ•¯â•‰â•¯ –γ â•‰â•¯p1â•¯â•‰â•¯â•¯ â•‰â•› = â•‰â•¯______ â•‰ __ â•¯= â•‰â•¯a â•¯â•¯â•‰â•¯â•›(Y 1/ε 1 ) = â•‰â•¯a â•¯â•¯â•‰â•¯Y 1 a â•¯â•‰â•¯ p

   2

2

2

2

(2.10)

or p1a2 ____

1–ε p2 ____ 1–ε ____ ____ â•‰â•¯ p â•¯â•‰â•¯= â•‰ â•‰â•¯p aâ•¯â•¯â•‰â•¯â•¯â•‰â•›â•‰â•¯ εâ•¯â•‰â•¯(µL)â•‰â•¯ εâ•¯â•‰â•¯ 2 1 2

(2.11)

1–ε ____ p a2 __1εâ•¯â•‰â•¯ â•‰ ____ â•‰â•¯ p1 â•¯â•‰â•¯ â•¯â•‰â•‰â•¯ = (µL)â•‰â•¯ εâ•¯â•‰â•¯.

(2.12)

  

   2

Finally, we obtain a1(L1A ) ______ (µL)1–ε p A ______ â•‰ __ â•‰â•¯p1â•¯â•‰â•¯â•¯ â•‰ = â•‰â•¯ a â•¯â•‰â•¯ â•¯= â•‰â•¯ a â•¯â•‰â•¯ ,â•¯

   2

2

2

(2.13)

where the superscript A represents the autarkic equilibrium. The autarkic price ratio is obtained as line VA.

22â•‡â•‡ Preliminaries Now let us add one more panel for a better understanding: Figure 2.6(b) depicts labor allocation between sectors. The horizontal axis represents the total labor force, L. The quantity of workers employed in sector 1 (resp. sector 2) is measured from the left (resp. right). The left (resp. right) vertical axis shows the wage rate in sector 1 (resp. sector 2). Initially, in the autarkic equilibrium, wage rates are equalized between sectors and O1L1 workers are hired in sector 1, while L1O2 workers are hired in sector 2. The total income (in terms of the numeraire, good 2) is shown by the shaded rectangle. For later use, we add a curve that represents the relationship between the wage rate (value of average product of labor) in sector 1 and the hypothetical employment level in that sector, L1, for a given price p1. This hypothetical curve is denoted by w ˜ 1(L1; p1): p _____ = p1L1ε –1. w ˜ 1(L1; p1) ≡ â•‰â•¯ 1â•¯ â•¯â•‰â•¯ a1(L1)

(2.14)

The dotted increasing curve in Figure 2.6(b) depicts w ˜ 1(L1, p 1A ). Since economies of scale are external to firms (and workers), this curve is not perceived by them.14 Note that as ε approaches unity this curve approaches a horizontal line.

2.5Â€Â€Decomposition of trade gains Now let us move to the trading situation with a fixed free trade price ratio (p1T/pT2) (Figure 2.7).15 If the terms of trade are given by the slope of the line DP (i.e., the free trade relative price of good 1 is higher than the autarkic price ratio), the economy specializes in good 1 at point P. Assume that consumption occurs at point C located on the consumption possibility frontier DP, so that CBP is the (a) D

(b)

Good 2

New equilibrium [p1T /a1(L)]

∼ w (L1, pT1 )

[p1T /a1(L1)] [p1A/a1(L1)]

V'

C

V Initial equilibrium

A P C

Good 1 O1

L1 Sector 1 employment

Figure 2.7Â€Â€

O2 Sector 2 employment

Basic models of international trade Iâ•‡â•‡ 23 trade triangle (the country exports BP units of good 1 and imports BC units of good 2). Now we can decompose the movement toward the trading equilibrium into two steps, which is in line with the traditional separation of trade gains into consumption and production gains.16 First, suppose that in the short run labor allocation is fixed, and thus Home is staying at the autarky production point, A, while it is able to trade at the terms of trade ( pT1/pT2 ). Superscript T denotes the trading equilibrium. Then, the consumption possibility frontier expands from VAP to V'AP as in Figure 2.7(a).17 In Figure 2.7(b), this change may be illustrated as an increase in the wage rate for the workers employed in sector 1 (i.e., from p1A/a1(L1A) to p1T/a1(L1A ). Their total increase in wage income is represented by the dotted rectangle in Panel (b), which is shown as V'V in Panel (a). It is also important to note that, as the result of moving from autarkic price to the free trade price, the curve of hypothetical wage in sector 1, w ˜ 1(L1, p1), shifts up from w ˜ 1(L1, p1A) to w ˜ 1(L1, p 1T). Second, let us consider the (long-run) labor movement between sectors. Since sector 1 offers a higher wage rate, workers will gradually move from sector 2 to sector 1 (as shown by the arrows in Figure 2.7). Due to external economies of scale, each unit of labor moved from sector 2 to sector 1 generates a larger output increase than the previous unit, which implies a higher wage rate (i.e., a movement along the w ˜ 1(L1, p T1 ) curve. In Panel (b), the eventual distribution of the labor force will be one of complete specialization (with O1O2 workers in sector 1), which corresponds to the production point P in Panel (a). The effect of this labor movement among sectors is shown as the expansion of the consumption possibility frontier from V'AP to DP in Panel (a), reflected by the sum of the horizontally shaded area and the vertically shaded area in Panel (b). It is important to note that, by utilizing a labor market graph, the gains from labor movement can be decomposed into (1) direct gains from labor movement (the horizontally shaded area) and (2) indirect gains via external economies of scale (the vertically shaded area). Note that the direct gains from labor movement also exist under constant returns-to-scale technology. Note also that, the higher the numerical value of ε, the bigger the indirect gains. In terms of the numeraire, trade gains are measured by VD in Panel (a), and by the sum of the dotted rectangle, the horizontally shaded rectangle, and the vertically shaded rectangle in Panel (b). We must now find out what happens when p 1T is lower than p1A (Figure 2.8). In this case the curve of hypothetical wage in sector 1, w ˜ 1(L1, p1), shifts down from w ˜ 1(L1, p1A ) to w ˜ 1(L1, p1T ). The wage rate in sector 1 becomes lower and workers will gradually moves from sector 1 to sector 2 (shown by the arrows in Figure 2.8). The eventual distribution of labor force will be one with O1O2 workers in sector 2, which corresponds to the production point V in Panel (a). The total income (in terms of the numeraire, good 2) is shown by the sum of the shaded area and the horizontally shaded rectangle, which is the same as the total income under the autarky equilibrium. Since the price of good 1 becomes lower in terms of the numeraire, this implies an increase in total real income.

24â•‡â•‡ Preliminaries (a)

(b)

Good 2 New equilibrium [p1T /a1(L)] [p1A/a1(L1)] (p2A/a2) V B

[p1T /a1(L1)]

Initial equilibrium

C A P

Good 1 O1

L1 Sector 1 employment

O2 Sector 2 employment

Figure 2.8Â€Â€

Now we can restate Ethier’s (1982a) interesting result on trade gains under external economies of scale. Proposition 2.2 (Ethier): A small country entering into international trade will be driven to specialize in that commodity with the lower autarkic relative price. Regardless of which commodity that is, the small country will gain from free trade relative to autarky. Figure 2.8 also illustrates the possibility of multiple equilibria that can be Paretoranked. Although when p1T is lower than p1A the economy gains relative to its autarky welfare level (at A) by specializing in good 2, it can obtain a larger gain by economy specializing in good 1 if the following condition holds: pT __ w ˜ 1(L; p1T ) > â•‰â•¯a22â•¯â•¯â•‰â•›.

(2.15)

Recall that by normalization, pT2 = p 2A = 1. By shifting the labor force toward sector 1 instead of sector 2, the economy can obtain the indirect gain via external economies of scale. When the above inequality holds, the national income in terms of good 2 when the country produces at point P is w ˜ 1(L; pT1 )L, which is greater than when it produces at point V. In Figure 2.8(b) the extra gains from specializing in good 1 are depicted by the vertically shaded rectangle. When there are multiple equilibria, in general it is not clear which one is likely to prevail, though some sort of stability argument may help in the equilibrium selection.18 Myerson (2009, p. 1111) points out that the existence of multiple

Basic models of international trade Iâ•‡â•‡ 25 equilibria is “a pervasive fact of life that needs be appreciated and understood, not ignored by economists.”19

2.6Â€Â€Concluding remarks In this chapter we have briefly reviewed two types of Ricardian model: a model with constant returns-to-scale technologies and a model with increasing returnsto-scale technologies (i.e., a model with external economies of scale). In order to gain a better understanding, we have extensively utilized a new graphical exposition that emphasizes the role of labor markets. We recognize that there are many alternative ways to understand Ricardian trade gains and that what works well for someone may not be attractive to others. However, we believe that the way presented here, which emphasizes the links between the international goods markets and the national labor market, provides a helpful tool for understanding Ricardian trade models.

3 Basic models of international trade II

3.1Â€Â€Introduction Among several competing trade models, the model of monopolistic competition à la Dixit–Stiglitz–Krugman (Krugman 1979, 1980, 1981; Dixit and Norman 1980; Helpman and Krugman 1985) provides an elegant account of intra-industry trade and plays a major role in the recent literature.1 In his influential survey, Matsuyama (1995, p. 701) provides the following definition of monopolistic competition: 1 2 3

The products are differentiated. Each firm, as the sole producer of its own brand, is aware of its monopoly power and sets the price of its product. The number of firms (and products) is so large that each firm ignores its Â�strategic interactions with other firms; its action is negligible in the aggregate economy. Entry is unrestricted and takes place until the profits of incumbent firms are driven down to zero.

This model is also attractive because increasing returns are internal to the firms, so the problem of multiple equilibria does not arise (as it did in the models of external economies reviewed in Chapter 2). Furthermore, as Matsuyama has pointed out, by assuming that firms are very small, we don’t have to worry about strategic interactions between firms that make any general treatment of oligopolies impossible. Although this type of model relies heavily on specific functional forms (e.g., CES utility), it remains appropriate to model global phenomena using the monopolistic competition model.2 In this chapter, we present the now standard Dixit–Stiglitz–Krugman trade model of monopolistic competition. Furthermore, we propose a convincing graphical exposition that emphasizes the firms’ entry–exit process, which will be used in later chapters. The following section presents the basic model. The nature of the trading equilibrium is considered in section 3.3. The effects of factor mobility are briefly reviewed in section 3.4, followed by concluding remarks in section 3.5.

Basic models of international trade IIâ•‡â•‡ 27

3.2Â€Â€The model Suppose that there are two countries: Home and Foreign. Home (resp. Foreign) is endowed with L (L*) units of labor, which is the only primary factor of production. The countries have identical tastes and technologies. Each country produces two consumption goods, good X and good Y. Good Y is sold in a perfectly competitive market, while Good X is sold in a monopolistically competitive market. Good Y is produced under constant returns using only labor; units are chosen such that one unit of labor produces one unit of output. Wage rates are normalized to unity. In each country, agents have the following utility function: u = X µY 1 – µ, 0 < µ < 1,

(3.1)

where Y is the consumption level of good Y and X is a good X aggregate, given by

    n

1/ρ



X = â•‰ â•‰ â•¯ â•‰â•⁄â•‰â•¯ â•‰(ci)ρ  â•‰ , 0 < ρ < 1, i =â•›1

(3.2)

where consumption of each variety is given by ci, n is the number of product varieties produced at Home, and σ ≡ 1/(1 – ρ) >â•›1 is the elasticity of substitution between every pair of good X varieties, respectively. A lower value of σ implies that consumers value product diversity more. The consumer’s utility maximization problem may be solved in two steps.3 First, for a given allocation of spending across goods, maximize X subject to total spending on the differentiated products, EX. Second, determine spending on good X and good Y. For the first step, one can check that the demand function for variety i may be written as4 p –σ ci = ______ â•‰â•¯ i 1–σ   â•‰â•¯ EX (PX)

(3.3)

     

p –σ EX = â•‰ ___ â•‰â•¯ iâ•¯â•‰â•¯â•¯â•‰ â•‰ ___ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰, PX PX where PX is the price index of good X, which is dual to X:5

   n



(ρ–1)/ρ

PX = â•‰ â•‰ â•¯ â•‰â•⁄â•‰ â•‰â•¯ (pi)ρ/(ρ–1)â•¯ â•‰ i =â•›1

   n

1/(1–σ)



= â•‰â•‰ â•¯ â•‰â•⁄â•‰ â•‰â•¯(pi)1–σ  â•‰ i =â•›1

.

(3.4)

Now we turn to the problem of finding the optimal spending on good X, EX. EX may be obtained by solving the following problem: max u = X µ Y 1–µ, s.t. PX X + Y = E,

28â•‡â•‡ Preliminaries where E represents national income. Then, one can obtain EX = µE.

(3.5)

Substituting this back into (3.3), one can obtain the demand function: p –σ ______ ci = â•‰â•¯ i 1–σ   â•‰â•¯ µE. (PX)

(3.6)

It is important to note that the demand function perceived by the typical firm is not (3.6) but rather:6 c = ϕ p–σ, ϕ = µE(PX )σâ•›–1,

(3.7)

with the intercept ϕ assumed to be taken as given by the firm.7 Figure 3.1(a) shows the constant elasticity demand curve described by equation (3.7). Note also that we can express maximized utility as a function of income and the price index for good X, giving the indirect utility function: E E _____ __ V = µ µ (1 – µ)1–µ â•‰â•¯ â•¯µ â•¯ â•‰= µ µ (1 – µ)1 – µ â•‰â•¯ â•¯â•‰. (PX) P

(3.8)

The term P ≡ (PX ) µ is the cost-of-living index at Home.8 Now turn to the production of each variety. Each product is supplied by a mono polistically competitive firm. Before starting production, α units of labor are required as a fixed cost of production. Then, β units of labor are required as a marginal cost of production. Thus, the toal cost function of the typical firm becomes9: TC = α + βx,

(3.9)

where x is the output level. This implies a horizontal marginal cost (MC) curve at the level β, and an average cost (AC) curve which is a rectangular hyperbola with respect to the vertical axis and the marginal cost curve. These curves are also illustrated in Figure 3.1(a). Given a Dixit–Stiglitz specification with constant elasticity σ, each firm sets its price as σ _____ p = â•‰â•¯   â•¯â•‰â•¯β. σ –â•›1

(3.10)

With free entry and exit, the level of output that generates zero profits is given by α –x = __ â•‰â•¯  â•‰â•¯(σ – 1). β

(3.11)

Basic models of international trade IIâ•‡â•‡ 29 (a)

(b)

p

c C' C D AC

Z

A'

x A

MC x

Z

C'

C n

A

n

Figure 3.1Â€Â€

It is important to note that the (long-run) equilibrium output of each firm is constant. Now let us add one more panel for a better understanding. Figure 3.1(b) depicts the relationship between the total number of varieties, n, and the demand level for each variety, c. In the present setting the total expenditure for Good X is constant:10 npc = µE = µL.

(3.12)

Substituting the pricing rule (3.10) into this and rearranging, one can obtain the following relationship: µL 1 (σ –â•›1) ___ â•‰â•¯   â•¯ â•‰â•¯â•‰â•¯  â•‰â•¯. c = __ â•‰â•¯ â•¯â•‰______ n σ β

(3.13)

This demand condition (i.e., budget constraint) is depicted as hyperbola CC in panel (b). On the other hand, the zero-profit condition implies that each firm must sell at least –x in the long run. This is depicted as the horizontal line ZZ. In equilibirum, then, the following condition must hold for each variety: c = –x .

(3.14)

By combining these conditions, the equilibrium number of varieties is obtained: µL ___ n A = â•‰â•¯ â•¯ â•‰, ασ

(3.15)

30â•‡â•‡ Preliminaries where the superscript A represents the autarky (i.e., no international trade) equilibrium value. Thus the autarky equilibrium value of the cost-of-living index becomes: µ/(1 – σ)

PA = â•‰  nAâ•¯â•‰

 

µL µ/(1 – σ) _____ σβ µ p = â•‰ ___ â•‰â•¯ â•¯ â•‰â•¯â•¯â•‰ â•‰ â•‰â•¯  â•¯â•‰â•¯â•¯â•‰ , ασ σ –â•›1

  



(3.16)

     

L dPA µ –â•›â•‰ ___ â•‰â•¯ Aâ•¯â•¯â•‰â•¯â•¯ â•‰â•‰ ____ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰= _____ â•‰â•¯   â•¯â•‰â•¯ . P dL σ –â•›1 It is important to note that the cost-of-living index is a decreasing function of the labor endowment: the larger country can support a greater number of vari eties of differentiated products than can the smaller country.11 Note also that as the share of good X, µ, becomes larger and/or product differentiation matters more (i.e., σ is smaller), the impact of a change in labor endowment on the price index becomes larger. In panel (b), the autarky equilibrium is obtained as the intersection of curve CC and curve ZZ, point A. This graphical exposition provides an easier understanding of comparative statics analysis. Let us consider, for example, an increase in the labor endowment, L. In this case, the hyperbola CC moves upward to C'C'. – : each Then, in the short run, each firm can sell more than the zero-profit output xâ•› firm earns positive profits. This situation is depicted as point A'. However, responding to positive profits, new firms enter the good X sector. Since consumers spread their income among all varieties, demand for each variety becomes lower. This change is shown by the arrow in panel (b). In the long run, each firm sells –x again: changes in the level of the labor endowment L lead to adjustments in industry output via changes in the number of firms only.12

3.3Â€Â€Trading equilibrium Suppose that the two countries open their goods markets: the effect will be the same as if each country had experienced an increase in its labor force.13 The product market equilibrium requires that the demand for each product is equal to the zero-profit output level: c + c* = –x ,

(3.17)

where c* represents the demand for a Home product in Foreign. Adding (3.13) and its Foreign counterpart, the LHS of (3.17) may be obtained as follows: µ(L + L*) c + c* = â•‰â•¯________ â•¯â•¯ â•‰. (n + n*)p

(3.18)

Substituting this and (3.10) into (3.17), one can obtain the total number of varieties in the trading equilibrium, which is the sum of the number of varieties in the autarky equilibrium,

Basic models of international trade IIâ•‡â•‡ 31 µ(L + L*) N T ≡ n T + n*T = ________ â•‰â•¯ â•¯   â•¯ â•‰= n A + n*A, ασ

(3.19)

where superscript T indicates a trading equilibrium value. Opening trade may be interpreted as an expansion of market size. Now we can show the impact of trade liberalization in Figure 3.2. Let us take the case of Lâ•›=â•›L*. Panel (b) shows the relationship between N and c, while panel (a) is its Foreign counterpart. As in the case of autarky, the demand condition (i.e., budget constraint) is depicted by hyperbolas CC and C*C*. The production equilibrium in each country is depicted by point A and point A*, respectively. Suppose that the opening of trade does not affect the production structure. On the other hand, since consumers now face twice as many product varieties (from nA to NT = 2nA), demand for each product becomes halved (the increase from –x to –x/2). Because each country specializes in a different range of differentiated Â�products, intra-industry trade in good X occurs. Home consumers’ consumption point moves from point A to point B. Thus, the total import volume of Foreign varieties is shown by the shaded rectangle. Although the (wage) income level in terms of the numeraire remains unchanged, an increase in the number of product varieties implies that the cost-of-living index becomes lower: PT = (PXT ) µ = (N T) µ/(1–σ) p µ < (nA)µ/(1–σ) pµ = (P XA ) µ = P A.

(3.20)

Note that an increasing availability of differentiated products leads to a lower cost of obtaining each unit of utility, u, although the price of each product remains constant.14

c*

(b)

c

C*

(a)

C x

B*

C*

A

A*

Z

Z

B

x/2

C

n*

n N � 2n T

Figure 3.2Â€Â€

A

n*

A

n

A

N � 2n T

A

32â•‡â•‡ Preliminaries

3.4Â€Â€Factor mobility Now suppose that there are impediments to trade in goods, but economic integ ration makes it possible for some workers to migrate across countries.15 Workers migrate toward the country where the equilibrium real wage is higher. Using (3.16), one can define the real wage rate in one country:

 

1 µL µ/(σ – 1) _____ σ –â•›1 µ â•‰â•¯__â•¯â•¯â•‰= â•‰ ___ â•‰â•¯ â•¯ â•‰â•¯â•¯â•‰ â•‰ â•‰â•¯   â•¯ â•‰â•¯ â•‰ . P ασ σβ

  



(3.21)

That is, in the presence of internal scale economies, a larger country offers a greater number of differentiated products and thus the real wage rate becomes higher than in the smaller country. In this setting, workers migrate from the smaller country to the larger country. Thus, the size of the larger country will expand, while the size of the smaller country will shrink. The point is that there will be a cumulative process in which the wide range of differentiated products attracts workers, and immigration will enhance further expansion of the range of differentiated products. Figure 3.3 illustrates the allocation of labor between countries. The horizontal axis represents the total labor force in the world economy, L + L*. The quantity of labor employed in Home (resp. Foreign) is measured from the left (resp. right). The left (resp. right) vertical axis shows the real wage rate (3.21) in Home (resp. Foreign). Initially, in the autarkic equilibrium with identical labor endowments (L = L*), wage rates are equalized between countries. The relationship in Home between the total labor force and the real wage rate is depicted with the curve ω:

 

1 µL µ/(σ – 1) _____ σ –â•›1 µ ω(L) ≡ â•‰â•¯__â•¯â•‰= â•‰ ___ â•‰â•¯ â•¯ â•‰â•¯â•¯â•‰ â•‰ â•‰â•¯   â•¯ â•‰â•¯ â•‰ . P ασ σβ

  



(3.22)

v

v*

v*

L

Figure 3.3Â€Â€

v

L*

Basic models of international trade IIâ•‡â•‡ 33 Likewise, the relationship in Foreign is depicted with the curve ω*. Now let us describe the process of labor movement. If some workers move from Foreign to Home, it raises the real wage rate in Home, while lowering the real wage rate in Foreign. This wage gap further stimulates labor movement from Foreign to Home. Note that this movement hurts those left behind in Foreign (i.e., the smaller country). While the Home wage rate increases along the ω curve, the Foreign counterpart decreases along the ω* curve. This provides a striking contrast with the case of trade in goods, in which all workers gain and those in the small country gain the most.16 Until now, we have concentrated on the case with identical technologies between countries. Now let us briefly review what happens if both fixed and variable costs are higher in one country.17 In this case it is clearly desirable that all worker should move to the other country, but if the inferior country starts with a large enough share of the labor endowment, migration may move in the wrong direction.18 As in the case of external economies, the world economy may be trapped into a Pareto inferior situation.19

3.5Â€Â€Concluding remarks In this chapter, we have briefly reviewed the now standard Dixit–Stiglitz–Â� Krugman trade model of monopolistic competition. In particular, we have Â�proposed a convincing graphical exposition that emphasizes firms’ entry–exit process, which facilitates the understanding of several topics such as determinants of equilibrium and existence of intra-industry trade. Although this tractable model of monopolistic competition relies heavily on specific functional forms, it will remain as one of the key ingredients of trade models for internal scale Â�economies.20 Note that, since this model is quite special, one should view it as a complement to rather than a substitute for the other models of trade (e.g., trade models for external economies).

4 A decomposition of the home market effect

4.1Â€Â€Introduction The monopolistic competition model, characterized by increasing returns and differentiated products, is a major workhorse of the “New Trade Theory.” Â�Originally conceived by Joan Robinson and Edward Chamberlin in the 1930s, it became highly useful after the mathematical formulation by Dixit and Stiglitz (1977). In their seminal contributions, Krugman (1980) and Helpman and Krugman (1985, ch. 10.4) demonstrate that under monopolistic competition, country size determines the net trade flows in differentiated products when trade is subject to trade costs. The key idea is what is called the home market effect: if two countries differ only in size, in the presence of trade costs, the larger country will end up with a more-than-proportional share of the production of differentiated products.1 The home market effect has become one of the most important concepts in both trade theory and the new economic geography.2 However, it lacks a compelling graphical representation. The purpose of this chapter is to offer such a representation. Our experience indicates that this graphical approach helps the reader to gain, almost effortlessly, a clear understanding of the home market effect. The following section presents the basic model. The nature of the trading equilibrium is considered in section 4.3, followed by concluding remarks in section 4.4.

4.2Â€Â€The model Suppose that there are two countries: Home and Foreign. Home (resp. Foreign) is endowed with L (L*) units of labor, which is the only primary factor of Â�production. The countries have identical technologies. Each country produces two consumption goods, good X (differentiated products) and good Y (homogeneous goods). Good Y is sold in a perfectly competitive market, while good X is sold in a monopolistically competitive market. Good Y is produced under constant returns using only labor; units are chosen such that one unit of labor produces one unit of output. Wage rates are normalized to unity. International trade of good X incurs “iceberg” transport costs,

Decomposition of the home market effectâ•‡â•‡ 35 meaning that for every τ units of good X shipped from abroad only one unit arrives. This raises the price to consumers of an imported variety from p* to τp*, where p* is the mill price and τ >â•›1 is the transport cost factor. In each country, agents have the following utility function: u = X µY 1–µ, 0 < µ < 1,

(4.1)

where Y is the consumption of good Y and X is an aggregator of the consumption of the differentiated products,

   n

  

1/ρ

n*

X = â•‰ â•‰ â•¯ â•‰â•⁄â•‰â•¯â•‰(ci)ρ + â•‰ â•¯â•⁄â•‰â•¯â•‰â•‰(c*iâ•¯)ρ  â•‰ , 0 < ρ < 1. iâ•›=1

(4.2)

iâ•›=1

Consumption of each variety is given by ci and σ ≡ 1/(1 – ρ) < 1 is the elasticity of substitution between every pair of good X varieties. The price index for good X (which is dual to the aggregator X) is represented by PX =

  â•‰â•‰â•¯

n â•‰ â•‰ â•¯ â•⁄â•‰(pi)ρ/(ρ-1) iâ•›=1

  n*



(ρ-1)/ρ

+ â•‰ â•¯â•⁄â•‰â•¯â•‰â•‰(τp*i )ρ/(ρ–1)â•¯ â•‰â•› iâ•›=1

.

(4.3)

Home consumers’ demand for a Home product is c = p–σ (PX)σ–1 µL.

(4.4)

Similarly, the derived demand (i.e., including units lost by iceberg transport costs) for a Foreign product from Home consumers is ˜c = τ(τp*)–σ (PX)σâ•›–1µL.

(4.5)

The production of a differentiated product involves a constant marginal cost β and α units of labor as a fixed cost. With the total number of products available to consumers being very large, each producer sets its price by applying a constant mark-up factor on marginal cost σβ p = p* = â•‰â•¯_____ â•¯â•‰. â•¯ σ –â•›1

(4.6)

Free entry ensures that profit is zero in the long run, hence the long-run equilibrium output of each variety, x, is a constant, independent of the level of trade costs: α __ x = â•‰â•¯  â•¯â•‰â•›(σ – 1). β

(4.7)

Before moving to the trade equilibrium, it is important to note the entry–exit process. If, in the short-run, the demand for a differentiated product exceeds the long-run equilibrium output, x, there are positive profits, which creates an incentive

36â•‡â•‡ Preliminaries for new firms to enter the industry. Conversely, if the short-run demand is smaller than x, some firms will exit. This entry–exit process plays an important role in determining the degree of the home market effect.

4.3Â€Â€Trade equilibrium Turning to the trade equilibrium with positive trade costs, the product market equilibrium requires that supply equals demand for each Home product: x = c + ˜c* ≡ C.

(4.8)

By substituting (4.4) for c, the Foreign counterpart of (4.5) for ˜c*, into equation (4.8) and denoting ϕ ≡ τ 1–σ < 1 we obtain the following aggregate demand for a Home product (C) and its Foreign counterpart (C *):

 



 



µ _______ L L* __ _________ C = â•‰â•¯ â•¯ â•‰â•‰ â•‰â•¯ â•¯ *â•¯â•‰â•¯ + â•‰â•¯ â•¯ â•¯â•‰â•¯â•¯ â•‰, p n + ϕn n + (n*/ϕ)

(4.9)

µ _________ L L* __ _______ C* = â•‰â•¯ â•¯ â•‰â•‰ â•‰â•¯ â•¯ *â•¯â•‰â•¯ + â•‰â•¯ â•¯ â•¯â•‰â•¯â•¯ â•‰. p (n/ϕ) + n ϕn + n*

(4.10)

Figure 4.1 depicts the relationship between the number of varieties in each country, n and n*, and the level of demand for each variety, C and C*. Aggregate demands are depicted as the curve CC in panel (a) (i.e., the space n, C), and curve C *C * in panel (b) (i.e., the space n*, C *), respectively. The long-run equilibrium output level x is represented as the intersection of the horizontal line ZZ with the vertical axis. The initial equilibria are depicted by points E and E *. Along the curve CC (resp. C *C *), we treat n* (resp. n) as an exogenous variable:

(b)

C*

C*

(a)

C C'

C ''

C

c*'

Z

E* E *'

n*

C* C *' C *''

Figure 4.1Â€Â€

E' E ''

E *''

Z

E

C '' C' C n

Decomposition of the home market effectâ•‡â•‡ 37

  p  (n + ϕ n )

∂C L ϕL µ ___ â•‰â•¯ â•¯â•¯â•‰= – â•‰â•¯__â•¯ â•‰â•‰_________ â•‰â•¯ â•¯* 2â•¯â•‰â•¯ + â•‰â•¯_________ â•¯ â•‰< 0, * 2â•¯â•‰â•¯â•¯ ∂n

 (n + ϕn )

2 *

(ϕn + n )



∂C µϕ L L ___ â•‰â•¯ *â•¯â•¯â•‰â•¯= – â•‰â•¯___â•¯  â•‰â•¯â•‰_________ â•‰â•¯ â•¯ * 2â•¯â•‰â•¯ + â•‰â•¯_________ â•¯* 2â•¯â•‰â•¯â•¯ â•‰< 0. ∂n

p

*

(ϕn + n )



(4.11)

(4.12)

Equation (4.11) implies that the curve CC is decreasing in n, while (4.12) indicates that the curve CC is shifted downward when there is an increase in n*. Now suppose that an exogenous labor movement from Foreign to Home occurs: in Home, the labor force becomes Lâ•›+â•›∆ L, while in Foreign, the labor force becomes L*â•›–â•›â•›∆L. We can decompose the movement toward the new Â�equilibrium into two steps. Step 1: First, suppose that in the short run, the number of varieties in each country is fixed. The increase in L, combined with the decrease in L*, shifts the curve CC upward (dotted C´C´) because ϕn* < n*/ϕ, while the curve C*C* is shifted downward (dotted Câ•›*´Câ•›*´). The new short-run equilibrium is obtained as point E´ (resp. E *´). Thus each Home (resp. Foreign) firm experiences an increase (resp. decrease) in βσ demand relative to its long-run output level x. Since the price stays put at _____ â•‰â•¯  â•¯â•¯â•‰ σ–1 while average fixed cost falls in Home, profit rises for each home firm. Similarly, profit falls for each foreign firm. These changes trigger the entry of new firms in Home, while exits begin to occur in Foreign, which are shown as arrows in each panel. (If exits did not occur in Foreign, the new equilibrium number of home firms would be indicated by the intersection of the dotted C´C´ curve and the line ZZ.) Step 2: The above entry–exit process gives rise to a second round of curve shifting, and thus a second round of entries and exits. C´C´ is shifted further up by a reduction in n* (to C´´C´´), while C *´C *´ is shifted further down by an increase in n (to C *´´C *´´). Thus the new long-run equilibrium is obtained as the point E´´ (for Home) and E *´´ (for Foreign). It is important to note that the second round constitutes the main source of the home market effect. Expenditure shifting between countries triggers an entry–exit process in each country, which reinforces the first entry–exit process. This demonstrates that a change in the relative size of a country’s market has a magnified effect on the relative size of its good X sector. Proposition 4.1 (Krugman): If two countries differ only in terms of size, the larger country will end up with a more-than-proportional share of world output of differentiated products. Finally, we can point to the “home market magnification.” Freer trade magnifies the degree of relocation that comes from a given shift in population. In other words, industry becomes more footloose, not less footloose, as trade gets freer.

38â•‡â•‡ Preliminaries

4.4Â€Â€Concluding remarks In this chapter, we have decomposed the home market effect into two steps: a short-run response to population shift, creating entry-stimulating excess profits (in the short run) for firms in the country that experiences a population gain, and a further round of entries into the monopolistic sector of the expanding country induced by exits in foreign industry. Our diagrammatic representation illustrates the process in an intuitive way. A similar diagrammatic approach may be used to show how freer trade magnifies the home market effect.

5 Monopolistic competition and distribution of trade gains

5.1Â€Â€Introduction In Chapter 2 we have shown that, given two countries of different sizes with open trade in a perfectly competitive Ricardian setting, the distribution of trade gains is unequal in the sense that the terms-of-trade improvements are unequal: the smaller country gains more than the larger country.1 It is also well known that country size does not matter in determining trade patterns under perfectly competitive, constant returns to scale setting. On the other hand, as we have reviewed in Chapter 4, under a monopolistically competitive setting with increasing returns and differentiated products, country size determines net trade flows when trade is subject to trade costs. The key idea is what is called the home market effect: if two countries differ only in size, the larger country will end up with a more-than-proportional share of the production of differentiated products. This idea seems to indicate that, from a welfare point of view, the larger country gains more than the smaller country.2 However, relatively little is known about the relationship between relative country size and the welfare consequences of trade in monopolistically competitive settings. The purpose of this chapter is to explore this relationship a little further. To achieve this, I use the Helpman and Krugman (1985, ch. 10.4) two-country model of trade, which has already been examined in Chapter 4. I precisely define the trade-costs-saving effect and the variety-of-imports effect. The division of trade gains is determined by the tension between these two effects. I will show that, given that both countries produce differentiated products in trading equilibrium, the rate of welfare changes brought about by opening trade will be equalized across the countries. The following section sets out the model. The role of trade costs and relative country size in determining the distribution of trade gains is examined in section 5.3. Section 5.4 presents some conclusions.

5.2Â€Â€The model Suppose that there are two countries in the world, Home and Foreign, and that they are similar in regard to consumers’ preferences and production technologies

40â•‡â•‡ Preliminaries but not necessarily in their sizes.3 There is only one factor of production, namely labor, and relative country size is measured by labor force size. Let L denote the size of the world’s total labor force, and let γL (0â•›<â•›γ <â•›1) denote the Home country size. There are two sectors: a monopolistically competitive sector producing a large variety of differentiated products and a perfectly competitive sector producing a homogeneous good. The latter serves as the numeraire, and units are chosen such that one unit of labor produces one unit of output. The central assumption is that there are positive (but not prohibitive) trade costs even after opening trade. International shipments of differentiated products incur the “iceberg” effect of trade costs: for every τ (τ >â•›1) units shipped, only one unit arrives. Thus, the price of an imported differentiated product to the home consumers will be τ p*, where p* is the producer’s price for Foreign product. On the other hand, the numeraire is assumed to be costlessly tradable, and both countries produce it after trade; thus, the wage rates faced by producers are common in both countries.4 We assume constant expenditure shares between the differentiated products and the numeraire, and that the sub-utility for the former takes the Dixit–Stiglitz form. The price index for the differentiated products that is dual to the sub-utility is represented by

   n

  n*



(ρ–1)/ρ

PX = â•‰ â•‰ â•¯ â•¯â•⁄â•‰â•¯â•‰â•‰(pi)ρ/(ρ–1) + â•‰ â•¯â•¯â•⁄â•‰â•¯â•‰â•‰(τ p*i )ρ/(ρ–1)â•¯ â•‰ iâ•›=1

iâ•›=1

(5.1)

where n (n*) is the number of products available from Home (Foreign) and σ is the elasticity of substitution. Home consumers’ demand for a Home product is c = p–σ(PX)σ –1µγL,

(5.2)

where µ is the share of spending devoted to the differentiated products and γ L is Home’s national income. Similarly, the derived demand for a Foreign product from Home consumers is ˜c = τ(τ p*)–σ(PX)σ–1µγL.

(5.3)

A producer of a differentiated product has to commit α units of labor as a fixed cost and has constant marginal input β. With the total number of products available to consumers being very large, each producer chooses its constant mark-up price as σβ _____ p = p* = â•‰â•¯ â•¯â•¯â•‰. â•¯ σ –â•›1

(5.4)

Free entry ensures that profit is zero in the long run; hence the long-run equilibrium output of each variety, –x, is a constant, independent of the level of trade costs: α –x = â•‰â•¯__ â•¯â•‰(σ – 1). β

(5.5)

Competition and trade gains distributionâ•‡â•‡ 41 In autarky (i.e., the case of prohibitive trade costs), the number of differentiated products in each country is given by µγL ____ â•‰, nA = â•‰â•¯ â•¯â•¯ ασ µ(1-γ)L _______ n*A = â•‰â•¯ â•¯ â•¯ â•‰, â•¯ ασ where superscript A represents the value in autarky equilibrium. Units are chosen so that one country’s autarky number of varieties equals its relative size; i.e., by setting (µL/ασ) = 1, we obtain nA = γ, n*A = 1 – γ.

(5.6)

Turning to the trade equilibrium with positive (but not prohibitive) trade costs, the product market equilibrium requires that supply equals demand for each Home product: –x = c + ˜c. By substituting (5.2), Foreign counterpart of (5.3), and (5.5) into this equation and denoting ϕ ≡ τ 1–σ (0 < ϕ < 1) yields the following equilibrium condition for a Home product and its Foreign counterpart: γ ϕ(1â•›–â•›γ ) ______ _______ 1 = â•‰â•¯ â•¯ *â•¯ â•¯â•‰+ â•‰â•¯ â•¯â•‰â•¯ , nâ•›+â•›ϕ n ϕnâ•›+â•›n*

(5.7)

ϕγ 1â•›–â•›γ _______ ______ 1 = â•‰â•¯ â•¯ â•¯ â•¯â•‰+ â•‰â•¯ â•¯â•¯â•‰. â•¯ n + ϕn* ϕnâ•›+â•›n*

(5.8)

Using (5.7) and (5.8), the equilibrium number of varieties may be obtained: γ – ϕ(1 – γ) __________ â•¯ â•¯ â•‰, nT = â•‰â•¯ â•¯ 1–ϕ

(5.9)

(1 – γ) – ϕγ __________ n*T = â•‰â•¯ â•¯ â•¯ â•‰, â•¯ 1–ϕ

(5.10)

where superscript T represents the trading equilibrium. Using (5.6), (5.9), and (5.10), the changes in the production structure brought about by trade liberalization can be shown as ϕ _____ nT – nA = â•‰â•¯ â•¯ â•¯â•‰(2γ â•¯ – 1). 1–ϕ

(5.11)

If Home is the larger one (i.e., if γ â•›>â•›1/2), it will attract more producers of differentiated products by opening trade. This outcome implies that producers prefer producing in the larger country, since they would face trade costs on a smaller

42â•‡â•‡ Preliminaries share of their output. This is the home market effect, which was reviewed in Chapter 4. Figure 5.1 helps to illustrate this effect. The 45-degree line and the dotted line show the relationship between country size and the number of products in autarky and in trading equilibrium, respectively (ignore the heavy line at this stage). The latter is steeper than the former, indicating that the larger country has a more-than-proportional number of firms in trading equilibrium. Note that both countries will produce differentiated products only if γ lies in the range ϕ _____

1 _____ â•‰. â•‰â•¯ â•¯ â•¯â•‰â•¯< γ < â•‰â•¯ â•¯ â•¯â•¯ 1+ϕ 1+ϕ In what follows, the analysis is restricted to this case, where both countries produce the differentiated products.

5.3Â€Â€Distribution of trade gains In this section I will investigate the welfare consequences of opening trade. Before turning to the analysis, some terminology needs to be clarified. Trade

1

Number of varieties

c b

a

ab (a*b*): trade costs saving effect

c*

bc (b*c*): variety of imports effect

a*

b* 45° 0

Figure 5.1Â€Â€

1��

�

1 Relative country size

Competition and trade gains distributionâ•‡â•‡ 43 gains are measured in terms of the rate of changes in the welfare level achieved by opening trade. Thus, I will compare these rates in order to investigate the distribution of trade gains. In this model, the national income, which equals the wage income, does not change when trade opens. Therefore, to see the welfare changes, the price indices of the differentiated products must be checked: it implies minimum expenditure to obtain one unit of sub-utility. Furthermore, owing to constant mark-up pricing (see (5.4)), changes in the price indices reflect changes in the number of available varieties. Thus I will concentrate on the changes in the number of available varieties. Let us first consider the changes in the price indices. From (5.1) and (5.6), the price indices in autarky are

  

σ –1

PA ___ â•‰ â•‰â•¯ Xâ•¯â•‰â•¯â•¯ â•‰ p

1 __ 1 __ = â•‰â•¯ Aâ•¯â•¯â•‰â•¯= â•‰â•¯ â•¯â•‰â•›â•›, n γ

  

P *A σ –1 ___ 1 _____ 1 ___ â•‰ â•‰â•¯ Xâ•¯ â•¯â•‰â•¯â•¯ â•‰ = â•‰â•¯ *Aâ•¯ â•¯â•‰â•¯= â•‰â•¯ â•¯ â•¯â•¯ â•‰. p n 1–γ

(5.12) (5.13)

Next, using (5.1), (5.9), and (5.10), the price indices in the trading equilibrium become P T σ –1 ________ 1 1 ___ ________ â•‰ â•‰â•¯ Xâ•¯â•‰â•¯â•¯ â•‰ = â•‰â•¯ T â•¯ *Tâ•¯â•¯ , â•‰= â•‰â•¯ â•¯ â•¯â•‰â•›â•¯ p n + ϕn γ (1 + ϕ)

  

(5.14)

  

(5.15)

P *T σ –1 ________ 1 1 ___ ____________ â•‰ â•‰â•¯ Xâ•¯ â•¯â•‰â•¯ â•‰ = â•‰â•¯ T â•¯ *Tâ•¯â•‰â•¯ = â•‰â•¯ â•¯â•¯â•¯â•¯â•‰â•›. p ϕn + n (1 – γ )(1 + ϕ)

From (5.12) to (5.15), changes in the price indices for each country may be obtained as follows:

  

1 P T σ –1 _______ γ ___ _____ â•‰ â•‰â•¯ AXâ•¯â•‰â•¯â•¯â•‰ = â•‰â•¯ â•¯â•‰= â•‰â•¯ â•¯ â•¯â•¯ â•‰â•›, â•¯ â•¯ PX γ (1 + ϕ) 1 + ϕ

(5.16)

P â•‰â•¯ â•¯â•¯â•‰â•¯â•‰ â•‰  ___ P

(5.17)

*T σ –1 X *A X

1 1–γ ___________ _____ = â•‰â•¯ â•¯â•¯ â•¯ â•¯â•‰= â•‰â•¯ â•¯ â•¯â•‰. â•¯ (1 – γ)(1 + ϕ) 1 + ϕ

Equations (5.16) and (5.17) imply the surprising feature of the Helpman–Krugman model. Proposition 5.1: Given that both countries produce differentiated products in trading equilibrium, the rate of welfare changes will be equalized. Figure 5.1 illustrates the implications of this proposition. The heavy line shows the number of available products after opening trade.5 Note that the contribution of imported varieties to welfare changes is weighted by ϕ (0 < ϕ < 1). Because

44â•‡â•‡ Preliminaries of trade costs, the contribution of imported varieties is less than that of domestic varieties. For the present, it may be useful to fix Home’s autarky situation at point a. As mentioned__above, trade gains may be measured as the increase in the number of varieties, â•‰acâ•‰â•¯. These gains may be divided into two effects, which I call the trade-costs-saving effect and the variety-of-imports effect. __ The trade-costs-saving effect is shown by abâ•‰ â•‰ â•¯. This corresponds to the home market effect in that, if Home were the larger one, it would have more domestic varieties and pay less in trade costs by opening trade (see (5.11)). Thus, the larger country must benefit from a positive trade-costs-saving effect. __ The variety-of-imports effect is shown by bcâ•‰ â•‰ .â•¯ This reflects the contribution of imported varieties to welfare changes. Since the number of imported varieties is small in the larger country, that country will have a smaller variety-of-Â� imports effect. This outcome corresponds to the fact that the larger country has a relatively small terms-of-trade improvement in a perfectly competitive setting. ____ By the same procedure, trade gains for the smaller country, â•‰a*c*â•¯ â•‰, may be divided into two components. I fix the initial situation as point a*, which corresponds to a____ country size of 1â•›–â•›γ. Now the trade-costs-saving effect, represented by aâ•‰ *b*â•¯ â•‰, will be negative, indicating that the smaller country will lose some of its domestic firms by opening trade. ____On the other hand, the relative Â�magnitude of the variety-of-imports effect, â•‰ b*c*â•¯ â•‰, will be larger than that of the __ larger country, â•‰bcâ•‰â•¯. This outcome implies that the smaller country will import a relatively large number of varieties after opening trade. Again, this corresponds to the fact that the smaller country gains more in a perfectly competitive setting. Now the rate of increase in the number____ of available ________ varieties may be repre__ ___ sented as acâ•‰â•› â•‰ â•¯/â•›â•‰γaâ•‰â•¯for the larger country and aâ•‰ *c*â•¯ â•‰â•›/â•›â•‰(1 – γ )a*â•¯ â•‰for the smaller country. It is clear from the above illustration that the two effects offset each other and that both the larger and the smaller countries experience the same rate of welfare changes (see (5.16) and (5.17)). This point sharply contrasts with the conventional argument that there is an unequal distribution of trade gains in a perfectly competitive setting.

5.4Â€Â€Concluding remarks In this chapter, we have investigated the welfare consequences of opening trade in the Helpman and Krugman (1985, ch.10.4) two-country model of trade with increasing returns and trade costs. Of course, the Helpman–Krugman model depends on several restrictive assumptions, and the analysis in this chapter is obviously suggestive rather than conclusive. Nonetheless, two features derived here should not be overlooked. One corresponds to the consequences of the existence of both increasing returns and trade costs (the trade-costs-saving effect), and the other corresponds to the traditional argument for trade gains (the variety-of-imports effect). The important point is that the distribution of trade gains is determined by the tension

Competition and trade gains distributionâ•‡â•‡ 45 between these two effects. Under some conditions, these two effects offset each other and the division of trade gains is equalized. I would like to stress that the Helpman–Krugman model has important implications not only in the positive sense (e.g., the emergence of the home market effect) but also in the normative sense (e.g., the equalization of the rate of welfare changes).

Part II

Communications networks and time zones

6 Country specificity of communications networks

6.1Â€Â€Introduction1 Over the past decade, communications networks have come to play a crucial role in economic activities in the world economy. Communications networks are the facilities through which different parties communicate with each other. Traditional examples include postal and telecommunications systems; more recent examples of communications networks are the Internet and related networks, satellite communications systems, mobile telephone networks, etc., which have raised international business transactions to a new level. As technology progresses, the quality and scale of the communications infrastructure within a country, and the number and sophistication of people using that infrastructure, become ever more crucial factors determining the performance of the country’s economy.2 Moreover, differences between countries in these characteristics of quality, scale, participation, and sophistication seem to influence the structure of the countries’ comparative advantages. Evidence of this includes the strong showing of the US economy, which is currently equipped with the most sophisticated communications networks in the world. Despite these facts, in the existing literature on international trade there has not been a model that captures the role of country-specific communications Â�networks in determining the comparative advantages of countries. This study develops such a model. Harris (1995) was perhaps the first to investigate the role of a communications network in international trade.3 However, his focus was on the case in which all manufacturers of traded goods in the world used services provided by a single communications network industry that was not country-Â� specific, but conducted its business in all the countries. This chapter, in contrast, focuses on the role of country-specific communications networks and examines their influence on the determination of comparative advantage. For this purpose, the chapter builds a two-country model of monopolistic competition with a single production factor. The model has two types of good. The first type is a homogeneous good, the production of which does not require communications network services. The homogeneous good, which I call the Â�non-network good, is supplied competitively. The other type consists of differentiated products that are supplied by monopolistically competitive firms. I call

50â•‡â•‡ Communications networks and time zones these network goods. Each country has its own communications network industry. A country-specific communications network is available to all firms in the network goods sector and its construction requires a large fixed cost. Following Harris’s treatment, I assume that average cost pricing is adopted in the communications network industry. On the basis of the model outlined above, this study demonstrates that the size of a country, measured by the size of its endowment of the factors of production, determines its comparative advantage; that is, the larger country has a comparative advantage in the network goods. This is because the average cost of network construction can be reduced by an increase in the endowment of a country’s factors of production. The study also demonstrates that technological progress in the communications network industry stimulates international trade. This result is similar to what Harris observes in his model. However, Harris’s model is not suitable for the determination of comparative advantage. The main result of this chapter, which captures the relationship between a country’s size and the structure of its comparative advantage, has not appeared in the existing literature. The structure of this chapter is as follows. The following section presents the basic model. Trade patterns are considered in section 6.3. Section 6.4 deals with the question of trade gains, and concluding remarks are presented in section 6.5.

6.2Â€Â€The model Consider an economy that has two categories of goods: a homogeneous good, which is produced with constant-returns-to-scale technology, and differentiated products, which are produced with increasing-returns-to-scale technology. I refer to the former as the non-network good and to the latter as the network goods. It is assumed that a single factor of production, say, labor, exists and that L units of labor are endowed. I let the non-network good be the numeraire and choose units such that one unit of labor produces one unit of output. The representative consumer has a Cobb–Douglas utility function: U = X sY 1–s, 0 < s < 1, where Y is the amount of consumption of the non-network good, and X is the index for the consumption of the network goods. The index takes the form

    n

1/θ

X = â•‰ â•‰ â•¯â•¯â•‰â•⁄â•‰ â•‰â•¯c θi â•¯ â•‰ , 0 < θ < 1, iâ•›=1

where ci is the amount of consumption of the i-th product and n is the number of network-reliant firms, each producing a differentiated product. The aggregate price index for the network goods that is dual to X may be obtained as:

   n



–(1–θ)/θ

P = â•‰ â•‰ â•¯â•¯â•‰â•⁄â•‰â•¯ â•‰pi–θ/(1–θ)â•¯ â•‰ iâ•›=1

,

(6.1)

Specificity of communications networksâ•‡â•‡ 51 where pi is the price of the i-th differentiated product. Solving the utility maximization problem yields the following demand functions: ci = p–1/(1–θ) Pθ/(1–θ)sI, i = 1, …, n, i

(6.2)

where I is the national income. The central assumption is that production of the network goods requires communications. A single communications network is available to all firms in the network goods sector. The communications network may be thought of as being provided by a public monopoly, which I call a network services provider, that employs average cost pricing.4 To get on the network requires the payment of a fixed fee, γ. Note that a key assumption is that γ is fixed. Once each firm gets on the communications network, it must commit α as a fixed production cost, in addition to a constant marginal cost of β. These assumptions are summarized in the i-th firm’s total cost function TCi, given by TCi = α + βxi + γ, i = 1, …, n, where xi is the output level of the i-th firm. In this study the main stress falls on γ, which will be referred to as the network cost.5 The network cost is paid to the network services provider to cover its total costs. For tractability, I assume a simple cost function for the provider: K(n) = F + gn, where F and g are fixed and marginal costs respectively and n is the number of users (i.e., the number of firms). This assumption emphasizes the public good, fixed-cost nature of a communications network. Because of average cost pricing, the level of the network cost is determined as follows: K(n) __ F γ (n) = ____ â•‰â•¯ â•¯ â•¯ â•¯â•‰= â•‰â•¯ â•¯â•‰â•¯+ g, γ´ < 0. n n

(6.3)

This implies that the network cost per firm falls as the number of firms in the network goods sector increases, allowing more users to share the common cost of constructing the network, F. This cost-sharing effect is a natural consequence of the existence of a large fixed cost for the construction of the communications network. With the number of products being very large, the producer of the i-th product chooses the profit-maximizing price, β __ pi = p = â•‰â•¯  â•‰â•›â•¯, i = 1, …, n. θ With n firms, the profit of each firm, π, is given as: π = px – (α + βx + γ ).

(6.4)

52â•‡â•‡ Communications networks and time zones Thus, the level of output that generates zero profits with n firms is given by: [α + γ (n)]θ x(n) = __________ â•‰â•¯ â•¯ â•¯â•‰  , x´ < 0. β(1 – θ)

(6.5)

Substituting (6.4) into (6.2), the relationship between the number of differentiated products and the demand for a product is obtained as: θsI ___ c(n) = â•‰â•¯ â•¯â•‰. â•¯ bn

(6.6)

Equating (6.5) and (6.6) yields the equilibrium number of products,6 (1 – θ)sL – F nA = ___________ â•‰â•¯ â•¯â•¯ â•¯ â•¯ â•‰, α+g

(6.7)

where A refers to the equilibrium value in autarky. If there is an increase in the labor force, the number of varieties increases and the level of output per firm decreases.

6.3Â€Â€Trade patterns Suppose that two countries (home and foreign) open their goods markets and have a trade relationship. The two countries are assumed to be identical except for the size of their labor forces. Without loss of generality, the foreign country is assumed to be larger than the home country. Throughout this chapter, the communications network industry is assumed to be country-specific. First, consider the demand condition of the network goods in the trading world. Since homothetic preferences are assumed, both countries’ demands for a product when all products are sold at price β/θ may be aggregated into the world demand, which is given by θ s(I + I *) C(n,n*) = â•‰â•¯________ â•¯â•‰â•¯ , β(n + n*)

(6.8)

where the asterisk refers to the foreign country. Given the number of firms, every firm can sell the demand quantity C(n,n*) units of a network good. While each firm can sell this amount, the zero-profit quantity at which each firm earns zero profits, xdnT, is dependent on the network cost (see (6.5)). If the demand quantity exceeds the zero-profit quantity, each firm earns positive profits. Figure 6.1 illustrates this case.7 Assume that each firm has the following demand function: ∂D ∂D ∂D D = D(p,n,n*), ___ â•‰â•¯ â•¯â•¯â•‰< 0, â•‰â•¯___â•¯â•¯â•‰< 0, â•‰â•¯___*â•¯â•¯â•‰< 0. ∂p ∂n ∂n As shown in section 6.2, the MR and the MC are equated at price β/θ when the wage rate is unity. This implies that the demand curve passes through point [C(n,n*), β/θ] and that the MR curve intersects the MC curve at C(n,n*). Thus,

Specificity of communications networksâ•‡â•‡ 53 C(n,n*) = D(β/θ, n,n*). The analysis in section 6.2 showed that the AC decreases as output x or the number of products n increases. The AC curve is downward-sloping and passes through point (x/n, β/θ) in Figure 6.1. If free entry and exit occur in response to profits or losses, the difference between the demand quantity and the zero-profit quantity plays an important role in the entry–exit process and determines trade patterns, which is a prominent feature of the model examined below. Turning now to the equilibrium condition, each value of n determines the zero-profit quantity x(n), as indicated in (6.5). There is some value n* which will equate the demand quantity in (6.8) to the home zero-profit quantity. Following Ethier (1979, 1982a), I call this relation between n and n* the home allocation curve.8 Setting x(n) = C(n,n*) in (6.5) and (6.8) gives the implicit formula for the home allocation curve: α + γ (n) ________ s(L + L ) ________ â•‰â•¯ â•¯ . â•¯   â•¯ â•‰= â•‰â•¯ *â•¯â•‰â•¯ *

(6.9)

n+n

1–θ

Similarly, the foreign allocation curve may be obtained as α + γ (n ) ________ s(L + L ) ________ â•‰â•¯ â•¯ . â•¯   â•¯ â•‰= â•‰â•¯ *â•¯â•‰â•¯ *

1–θ

*

(6.10)

n+n

The graphs (6.9) and (6.10) may be drawn as OAC and OAB in Figure 6.2(a). Using curve OAC, we consider the entry–exit process of home firms. Begin with point A, for example, on the home allocation curve OAC. At point A, x(n) = C(n,n*), which implies that the demand curve is tangent to the AC curve at price β/θ in Figure 6.1. Therefore profits are zero. Now consider the implications of vertical movements up or down, starting from point A on Figure 6.2(a). The AC curve is unchanged because n is fixed. With movement down, a decrease in n* shifts the demand curve to the right. As long as some non-network goods are produced and the wage rate is equal to unity, the price is set at a level of β/θ. Firms expect positive profits, and entry will occur. With movement up, it is clear that exit will occur. That is, home firms will enter below the home allocation curve and exit above the home allocation curve.9 The allocation curves may be truncated because labor endowments limit the number of network goods. Consider the case in which the home country completely specializes in the network goods. Let N be the maximal number of network goods under complete specialization. Once N is determined, the corresponding AC curve may be drawn in Figure 6.1. This curve passes through point (x(N), β/θ). If a firm sets its price at β/θ, the firm’s zero-profit quantity x(N) may be read from the AC curve. The quantity x(N) is determined by the equality between the AC and price β/θ, which implies that

  

β F + (α + g)N + βx(N)N = â•‰ __ â•‰â•¯  â•¯â•‰â•¯ â•‰x(N)N. θ The full employment condition may be written as

p

b/u Demand curve

AC MC

b MR

0

[ (n )

C (n,n*)

Quantity

Figure 6.1Â€Â€

(a)

(b) I

n* N*

n* F

B

I

B J

D

N*

G

F

D J A

A

0

Figure 6.2Â€Â€

E

CN

n

0

H

N

E

C

n

Specificity of communications networksâ•‡â•‡ 55 F + (α + g)N + βx(N)N = L. The above equations may be solved for the maximal number of network goods:10 (1 – θ )L – F N = ___________ â•‰â•¯ â•¯ â•¯ â•¯ â•‰. α+g

(6.11)

The equation (1 – θ)L* – F ___________ â•¯ N * = â•‰â•¯ â•¯ â•¯ â•‰ α+g

(6.12)

may be obtained for the foreign country in the same way. Consider the entry–exit process when the allocation curve is truncated at N. With a move from point H toward point N in Figure 6.2(b), n* decreases, and the demand curve shifts upward. Since the supply is fixed at x(N), the price becomes higher than β/θ, and profits become positive. This implies that home firms enter below the home allocation curve and exit above the home allocation curve, even in the case in which n is fixed at N. Thus, the full home (foreign) allocation curve consists of N*O plus OAC (NO plus OAB) in Figure 6.2(a), and N*O plus OAHN (NO plus OAGN*) in Figure 6.2(b).11 These curves intersect in three places: at A, B, and C in Figure 6.2(a), and at A, N, and N* in Figure 6.2(b).12 At such intersections, the zero-profit quantity of an individual product in each country is equal to a common world demand quantity, so the world is in the free-trade equilibrium.13 By taking into account the above-mentioned entry–exit process in which firms enter if profits are positive and exit if they are negative, it is clear that the equilibrium at A is unstable, while the other two equilibria are stable. To examine specialization patterns, it is necessary to know where the autarky equilibrium is located on the nâ•›–â•›n* plane. By allowing L*/L to vary while keeping __ * Lâ•›+â•›L constant at â•‰Lâ•‰â•¯, all pre-trade situations can be depicted. This is shown by the dotted line DE in Figure 6.2. If two countries are identical in size, the autarky equilibrium is located at A.14 As the relative size of the foreign country increases, the point that represents the autarky situation moves along the segment DA toward D.15 If the world enters free trade from autarky, the actual trading equilibrium will be point B (diversification by the foreign country) in Figure 6.2(a) and point N* (complete specialization by both countries) in Figure 6.2(b). The foreign country will export the network goods, while the home country will export the non-network good. It may thus be concluded that a comparative advantage in the network goods is held by the larger country. Proposition 6.1: If the two countries commence free trade from autarky, the larger country completely or incompletely specializes in the network goods and the smaller country completely specializes in the non-network good.

56â•‡â•‡ Communications networks and time zones Proposition 6.1 describes the end result of a dynamic process. The opening of trade provides an opportunity for entry into the foreign country’s network goods sector because, with expanded cost-sharing, the level of the network cost per firm is lower. On the other hand, the home firms will not be able to cover their higher network cost and will be pushed out of the market. Thus, the scale of the home communications network will contract, while the foreign one will expand. The differences in the network costs will be reinforced with this entry–exit process. That is, there will be a cumulative process in which the export of the network goods brings an opportunity for entry, and the entry promotes exports. This process will continue until the home country’s communications network disappears. The effect of advances in communications technology on international trade is worth a mention in passing. A fall in the cost of network construction (i.e., a reduction in F) increases the number of varieties in the trading equilibrium. This implies that the export of the network goods is stimulated by technological progress in the communications network industry. This result corresponds to that of Harris (1995).

6.4Â€Â€Gains and losses from trade Now turn to the normative issue of whether individual countries will gain from trade. Consider, first, the larger (foreign) country. By Proposition 6.1, this country will be driven to increase its production of the network goods, possibly with complete specialization, by opening international trade. If the larger country does not specialize (as represented by point B in Figure 6.2(a)), it will produce some of the non-network goods and the price of each network good will not change (see (6.4)). Since the price remains constant and the number of products increases, the larger country necessarily gains from trade. If free trade induces complete specialization (as represented by point N * in Figure 6.2(b)), the price of each foreign network good, p*T, will be βsL _________ p*T = â•‰â•¯ â•¯ â•¯â•‰â•¯ , θ (1 – s)L* where T refers to the equilibrium value in free trade.16 For both countries to specialize, Figure 6.2(b) reveals that sL > (1 – s)L* is necessary,17 and that βsL β _________ __ p*T = â•‰â•¯ â•¯ â•¯â•‰â•¯ > â•‰â•¯  â•‰â•¯= p*A. θ (1 – s)L* θ

(6.13)

The larger country gains from trade in this case also: there are gains both from the availability of a greater variety of products and from an improvement in the terms of trade. Proposition 6.2: The larger country will gain from trade in the equilibrium that is attained as a result of a movement from autarky to free trade.

Specificity of communications networksâ•‡â•‡ 57 Now turn to the smaller (home) country. The smaller country exports the nonnetwork good and in fact specializes in it. If the larger country does not completely specialize, then the price of each network good will not change and the number of products will be increased. Therefore the smaller country will gain. Consider, then, an equilibrium in which both countries specialize. Since the non-network good is the numeraire, (6.13) shows that the terms of trade for the smaller country will deteriorate. However, it cannot be concluded that the smaller country loses from trade without taking into account the change in the number of products. In the free trade equilibrium with both countries specializing, the number of products will be N* (see (6.12)). Now the price index for the network goods, P (see (6.1)), may be used.18 It is easy to verify that the smaller country will become worse off from trade if and only if –(1 – θ)/θ

â•‰  nAâ•¯â•‰

–(1–θ)/θ

p A < â•‰ N *Tâ•¯â•‰

p*T.

(6.14)

By substituting (6.4), (6.7), (6.12), and (6.13) into the above condition and taking the natural logarithm of each side, the following expression may be obtained: â•‰â•¯

 

 

(1 – θ)sL – F sL ___________ ________     â•‰â•¯ln â•‰â•‰â•¯ â•¯â•¯â•¯â•‰â•¯ â•‰+ ln â•‰â•‰â•¯ â•¯ â•¯â•‰â•¯â•¯ â•‰> 0. (1 – θ)L* – F (1 – s)L*

1–θ _____ θ





(6.15)

The first term represents the variety effect, which comes from the increase in the number of product varieties. Since the smaller country will benefit from the greater variety of products, the first term will be negative. The second term Â�represents the terms-of-trade effect. If two countries completely specialize, the second term on the left-hand side of condition (6.14) has a positive sign. Â�Evidently there are some cases where two countries completely specialize and condition (6.14) does not hold. In these cases the gains from increased product diversity outweigh the conventional terms-of-trade effect, and the smaller country gains from trade. Proposition 6.3: If condition (6.14) holds, the smaller country will become worse off from trade. Note that the normative implication of this is quite different from the one in the usual models of monopolistic competition. In popular analyses, sufficiently small differences in countries’ sizes or factor contents imply that every country will gain from trade.19 In this model, given that condition (6.14) holds, the closer in size the two countries become, the more the smaller country will lose from trade. If two countries are quite similar in size, the worldwide number of products will not increase so much by opening trade. This is because the number of missing products in the smaller country is relatively large. In contrast to the popular assertion of trade gains between similar countries, a distribution of trade gains remains a matter of debate if the case of country-specific networks in those countries is considered.

58â•‡â•‡ Communications networks and time zones

6.5Â€Â€Concluding remarks The Internet, satellite communications systems, and mobile phone systems are communications networks that have raised international business transactions to a new level. All share one characteristic: the bigger they are, the better they work. In this chapter, I have presented a model of monopolistic competition that includes the features of country-specific communications networks. A communications network is characterized by (1) the existence of a large fixed cost for its construction, and (2) a public monopoly that employs average cost pricing. This model is used to analyse the nature of the trading equilibrium. It should be emphasized that differences in infrastructure among country-specific communications networks determine the comparative advantages of countries. That is, a comparative advantage in the network goods is held by the larger country. Furthermore, the current analysis reveals the possibility that the smaller country will be harmed by trade as a consequence of losing its communications network. This result may also provide an alternative explanation for the distribution of trade gains between countries. The current analysis must be regarded as very preliminary. Hopefully it provides a useful paradigm for considering how communications networks affect the structure of international trade. There are some directions in which the model could be extended. One extension would be to model realistically the network technology, which is subject to congestion effects and network externalities. Moreover, strategic aspects between networks may become more important as world markets are further integrated. It therefore seems important to consider the industrial organization of the communications network industry in order to address such aspects properly.

7 Interconnectivity of communications networks

7.1Â€Â€Introduction1 In the past decade the role of communications networks such as the Internet, mobile telephone networks, and satellite communications systems in the world economy has been widely discussed. It is increasingly recognized that the growing connectivity of individuals and organizations is achieved through improved communications networks and a consequent increase in the flow of business services across borders. Related to this, Cairncross (1997, pp. 214–215) issued the following statement: More dramatic than the effect of falling transport prices on tangible goods will be the effect of falling communications costs on those intangible processes and products that can be distributed on-line … The effects will come first in trade between businesses, such as data processing and business software. As Cairncross suggested, intermediate business services such as consulting, engineering, software development, and so forth have been playing major roles in today’s world trade.2 In a relatively recent contribution, Harris (1998) explores an important aspect of communications networks – their ability to remove the barriers to mobility of business services. He suggests that the improved networks create “virtual mobility” of business services and thus enhance trade of these services, which was not previously possible. There is one other thing that is important in the relationship between networks and trade in business services: interconnectivity, which allows network users in one country to communicate with users in another country.3 If a network located in one country is purely country-specific and is not connected to the internationally interconnected networks, users of the former will be at a disadvantage. The Economist, for example, reports that the capacity of Internet links between Latin America and the rest of the world has quintupled over the past year, while the worst-connected region is Africa (3 November 2001, p. 106). Clearly, lack of interconnectivity might work as a trade barrier for business services, and it might be a determinant of the structure of comparative advantage.4 This seems to suggest

60â•‡â•‡ Communications networks and time zones that the focus on the “virtual mobility” nature of intermediate business services should be accompanied by a focus on interconnectivity. The main purpose of this chapter is to illustrate, with simple trade theory, how the interconnectivity of country-specific networks can affect the nature of trading equilibrium. Following Harris (1998), I assume that the production of intermediate business services requires communication through a network. Harris studied the impact of networks on factor markets. He assumed a small open economy and paid scant attention to the structure of comparative advantages. In contrast, in this chapter I focus on the impact of interconnected networks and examine their influence on the determination of comparative advantages. For these purposes, a multi-country model of monopolistic competition with a single production factor is built. The model has two goods. The first is a homogeneous good, good Y, the production of which does not require communications network services. The production of the other good, good X, consists of assembling intermediate business services. The business services sector is characterized by (1) monopolistically competitive service firms; (2) production and distribution that require communications through a country-specific network; and (3) network services provided by an average-cost-pricing natural monopoly supplier (this specification follows that of Harris 1995). On the basis of the model outlined above, this study demonstrates that the number of countries which are connected through communications networks determines the nature of the trading equilibrium. That is, countries with interconnected networks have a comparative advantage in good X. This is because, in these countries, the good X sector works efficiently through the expansion of the range of available business services. It is also demonstrated that countries which are not connected and thus cannot utilize other countries’ business services may become worse off as the result of trade. Gains from increased efficiency through utilizing networks are similar to what Harris (1998) observed in his model. However, Harris’s model is not suitable for the determination of comparative advantage. Note also that our model is a modified version of the models of the previous chapter (Kikuchi 2002), and Kikuchi and Ichikawa (2002), which consider the effects of country-specific communications networks on comparative advantages. In particular, Kikuchi and Ichikawa (2002) analyse a network in which congestion may occur and show that country size and the prevalence of congestion determine comparative advantages in goods that require communications. In this chapter, however, I assume away both congestion and the size differences among countries and concentrate on the role of interconnectivity in determining comparative advantages. The main result of this chapter, which captures the relationship between the interconnectivity of countryspecific networks and the structure of comparative advantage, has not appeared in the existing literature. The structure of this chapter is as follows. In the following section I present the basic model. The nature of the trading equilibrium is considered in section 7.3, followed by concluding remarks presented in section 7.4.

Interconnectivity of communications networksâ•‡â•‡ 61

7.2Â€Â€The model Consider a world economy consisting of a large number of identical, small countries. Each country is endowed with L units of labor, which is the only primary factor of production. There are two consumption goods, good X and good Y. Both goods are sold in perfectly competitive markets. Good Y is produced under constant returns using only labor. Let good Y be the numeraire; units are chosen such that one unit of labour produces one unit of output. Good X is produced under constant returns using only differentiated business services as inputs. The production and the unit cost functions for good X are, respectively,

    n

1/ρ

â•‰â•¯  ρiâ•¯â•‰â•¯   â•‰ , 0 < ρ < 1, X = â•‰ â•‰ â•¯â•¯â•‰xâ•‰ i=1

 

C = â•‰  â•‰ â•¯ â•¯â•‰â•‰â•¯â•‰piρ/(ρ-1)â•¯â•‰ n

i=1

(ρ–1)/ρ

,

(7.1) (7.2)

where n is the number of available intermediate business services, xi and pi are the quantity and price of service i, respectively, and σ ≡ 1/(1 – ρ) > 1 is the elasticity of substitution between every pair of services.5 Equation (7.1) has the property that, as input differentiation increases, productivity rises. Intermediate business services are supplied by monopolistically competitive firms, hereafter referred to as service firms. The central assumption is that both the production and the distribution of business services require communications through a country-specific network, which is provided by a natural monopolist. It is implicit in (7.1) that service firms can interact and thus have positive demand only if they can communicate with other service firms.6 To connect to the network, each service firm has to pay a fixed fee, α. This assumption implies (a) that there are aggregate constant returns in providing communications services, and (b) that the pricing of communications services is done on an average-cost basis.7 Once each service firm connects to the network, it must pay a constant marginal cost β. Thus, to produce x units of service, βx units of labor are required.8 Given a Dixit–Stiglitz specification with constant elasticity σ, and a labor wage rate w, each service firm sets its price as p __

βσ â•‰â•¯ â•¯â•¯â•‰= _____ â•‰â•¯  â•¯â•‰â•¯ . w σ–1

By choice of units, one can set β = (σ – 1)/σ, to have p = w

(7.3)

With free entry and exit, the level of output that generates zero profits is given by x = ασ.

(7.4)

62â•‡â•‡ Communications networks and time zones Consider the situation in which there is no trade in goods or business services. In this case, each country must produce all of the goods and services, which means that P, the price of good X, must be equal to cost:9 P = C = n1/(1–σ) = (ασ)1/σX –1/σ.

(7.5)

The curve SS, showing the above condition, is depicted in Figure 7.1. Note that this curve is truncated _ because _ labor endowments limit the number of business services. The terms X and C represent the maximal amount of good X and its corresponding cost:

_ _

X = Lσ/(σ–1)(ασ)1/(1–σ), C = (L/ασ)1/(1–σ).

P,C

S D

PA

A

S

C

D

0

Figure 7.1Â€Â€

XA

X

X

Interconnectivity of communications networksâ•‡â•‡ 63 On the demand side, it is assumed that the representative consumer has CobbDouglas preferences over good X and good Y, with share coefficients µ and 1 – µ. Thus, the following relationship must be satisfied: PX = µL.

(7.6)

The curve DD, satisfying the above condition, is also depicted in Figure 7.1. Clearly the autarky equilibrium occurs at point A. The autarky number of service firms becomes µL ___ n A = â•‰â•¯ â•¯ â•¯â•‰â•›, ασ where A refers to the autarky value. Thus, the autarky price and quantity are as follows: PA = (µL/ασ)1/(1–σ ),

(7.7)

XA = (µL)σ /(σ –1)(ασ)1/(1–σ ).

(7.8)

7.3Â€Â€Trading equilibrium Suppose that M identical small countries open their goods markets and have a trade relationship. Also assume that m (mâ•›<â•›M ) countries’ country-specific networks can be interconnected. Thus, business services are traded virtually through these interconnected networks, while M – m countries cannot be connected with these networks.10 Let us call the former “connected countries” and the latter “unconnected countries.”11 Figure 7.2 demonstrates how the interconnection of networks affects the Â�production structure of the world. Figure 7.2(a) shows the situation before the interconnection takes place, while 7.2(b) shows the situation afterwards. The effect of interconnection is shown by the change in the supply curve. The extended curve SS in Figure 7.2(b) reflects the increased connectivity within the m connected Â�countries, while the curves for the unconnected countries remain unchanged. We should notice that the curve SS implies that there are gains from increased Â�specialization, and that resource constraints are relaxed. First, in the connected countries, the good X sector purchases services from all of the business service firms located in the connected countries. Thus, in aggregate, the number of business services provided rises from n to mn and the unit cost of good X falls. In other words, the productivity benefits of interconnection are the gains from trade that accrue from increased specialization in the provision of intermediate business services. Second, interconnection effectively offers the integration of business services and good X sectors internationally. Thus, the resource constraints of business services are relaxed within the connected countries.

S

A

PA C

S

XA

MX

X

Figure 7.2(a )Â€Â€

S'

S

T'

P T' P

A

PT

T S

XT

Figure 7.2(b)Â€Â€

X T'

Interconnectivity of communications networksâ•‡â•‡ 65 By taking into account a simple entry–exit process, the connected counties will specialize in both good X and business services: Proposition 7.1: A comparative advantage in good X is held by the connected countries. Let us consider this proposition more precisely. In the connected countries, there are opportunities for entry into the business services sector because, with the increased connectivity of service firms, the average cost of good X becomes lower and the export of good X will be enhanced.12 Thus, the size of connected network users will expand, while the size of unconnected network users will shrink. The point is that there will be a cumulative process in which the increased connectivity will enhance exports, and exports will enhance further expansion in the size of the users of interconnected networks. Depending on the relation between µ and m/M, two cases may emerge as the trading equilibrium.13 In the following subsections each case is discussed in detail. Case A: Non-specialization equilibrium Suppose that the following condition holds: m __ µ ≤ â•‰â•¯ â•¯â•‰â•›â•¯. M

(7.9)

This implies that µ, the expenditure share for good X, is relatively small and/or the number of connected countries is relatively large. In this case, the equilibrium point is located on the curve SS (e.g., at point T) and the equilibrium price and quantity become, respectively: P T = (µmL/ασ)1/(1–σ ) < PA,

(7.10)

X T = ( µmL)σ /(σ–1)(ασ)1/(1–σ ).

(7.11)

It is notable that both connected and unconnected countries produce good Y, and the wage rates are equalized among them. In this case, every country will gain from trade regardless of its interconnectivity. Proposition 7.2: If the expenditure share for good X is relatively small and/ or the number of connected countries is relatively large, every country in the world will gain from trade. Case B: Complete specialization equilibrium Next, suppose that the following condition holds: m __ µ > â•‰â•¯ â•¯â•¯â•‰â•›. M

(7.12)

66â•‡â•‡ Communications networks and time zones This implies that the expenditure share for good X is relatively large and/or the number of connected countries is relatively small. Under the assumption of a simple entry–exit process, the connected countries completely specialize in both good X and business services, while the unconnected countries are driven to increase the production of good Y, possibly with complete specialization. In what follows, the analysis is restricted to the case of complete specialization.14 In this case, the equilibrium point is located somewhere on the vertical segment of the supply curve (SS), as exemplified by point T'. In this complete specialization equilibrium, countries’ wage rates will diverge. The wage rate in the connected countries, wc, is determined by the following balance-of-payments condition: wC (1 – µ)mL = (M – m)µL.

(7.13)

Thus, the equilibrium price and quantity become, respectively: (M – m)µ PT = (mL/ασ)1/(1–σ )wC = (mL/ασ)1/(1–σ ) ________ â•‰â•¯ â•¯â•‰  , â•¯ m(1 – µ)

(7.14)

Xâ•›T = (mL)σ /(σ–1)(ασ)1/(1–σ ).

(7.15)

In this case, trade gains are asymmetrical between connected and unconnected countries. On the one hand, the connected countries always gain; there are gains both from the increased connectivity of service firms and from improvement in the terms of trade. On the other hand, the unconnected countries might lose from trade. Because the income in terms of good Y remains constant, they will be harmed if PT > PA holds. By substituting (7.7) and (7.14) into this, the following condition may be obtained:

 

µ σ /(σ –1) ______ M–m __  â•‰â•¯â•¯â•‰> 1. â•‰ â•‰â•¯  â•¯â•‰â•¯ â•‰ â•‰ â•‰â•¯ m 1–µ

  



(7.16)

We should note that this condition is not exactly the same as the standard ones for increasing returns economies. Two points deserve explicit emphasis. First, this condition holds when the expenditure share for good X, µ, is relatively large: if the connected countries are to specialize in good X, the world must have a sufficient liking for that good to allow a competitive equilibrium with the resultant large output. Second, this condition does not hold (i.e., both connected and unconnected countries gain) when the substitutability between services, σ, is relatively small. If σ decreases, the number of services produced in the connected countries increases, which provides larger gains from increased specialization. Then the consideration is the large cost reduction from concentrating good X production in the connected countries. This corresponds to the “knife-edge” phenomenon emphasized by Ethier (1982a): the existence of increasing returns introduces the possibility of distinct features, but these are less likely, the greater the degree of increasing returns.15

Interconnectivity of communications networksâ•‡â•‡ 67 Proposition 7.3: If condition (7.16) holds, the unconnected countries become worse off from trade. A comparison between the above two cases highlights the importance of network interconnectivity. If the non-specialized equilibrium is attained, the lack of interconnectivity does not matter. On the other hand, if the complete specialization equilibrium is attained, interconnectivity brings worthwhile gains through both the increased connectivity and the consequential improvement in the terms of trade. Enlarged networks We are now ready to consider the impact of an exogenous increase in the number of connected countries. Let us suppose that, given that the complete specialization equilibrium is attained, one of the unconnected countries’ networks joins the interconnected networks.16 This country will be driven to increase its production of business services and will experience an increase in the level of its national income. What will happen to the connected countries? Let us consider the real income, ω C ≡ w C/(P T ) µ. The total differential of the real income is: d ln ω C M µ ______ _____ â•‰â•¯______â•¯â•¯ â•‰= –(1 – µ)â•›â•‰â•¯ â•¯ â•¯â•‰â•¯ + â•‰â•¯   â•¯â•‰. â•¯ d ln m M–m σ–1

(7.17)

The first term represents the negative effect from a deterioration in the terms of trade.17 The second term represents the positive effect from the increased productivity of good X. Evidently, there are some cases in which the former dominates the latter: the connected countries may become worse off by accepting a newcomer.18 Hence, the successful development of one country, while a Paretoimproving move from that country’s viewpoint, may not be Pareto improving from the viewpoint of the world economy (see similar discussion in Matsuyama 1996). The last proposition summarizes this interesting result: Proposition 7.4: If one of the unconnected countries is able to connect to the interconnected networks, it will gain from this change. On the other hand, the connected countries may become worse off from this change. Discussion In this subsection I describe three directions in which the model could be extended. First, consider the existence of rival networks, which will be supported by language, culture, and legal system differences. For illustrative purposes, assume that the world is divided into two types of “connected countries,” which are different in size. In this case, one might expect that the connected countries with larger populations would specialize in good X. However, this result may not

68â•‡â•‡ Communications networks and time zones always hold. If the relatively small connected countries reached there first, the larger connected countries might not produce good X. As is well documented in the new trade theory literature, there is potentially an important role for historical accident in determining trade patterns (see, e.g., Helpman and Krugman 1985, ch. 3). This may allow established patterns of specialization to persist even when they run counter to comparative advantage. Thus there is room for further investigation.19 Second, let us consider the relationship between our model and the new economic geography. The models of economic geography always incorporate the “centripetal” forces that produce agglomerations. In the basic core–periphery model, this force is represented by the interaction of scale economies, market size, and marginal trade costs (see, e.g., Fujita, Krugman, and Venables 1999, ch. 5). In the current model, however, there are no marginal trade costs, which provides a geography, and then the agglomeration force is represented by the interaction of scale economies and interconnectivity of communications networks. As a first step to incorporate interconnectivity, I have concentrated on this interaction and downplayed the role of marginal trade costs. If there are marginal trade costs, this model adheres more closely to the basic core–periphery model. In order to analyze the interaction of interconnectivity and economic geography, this kind of extension needs further consideration. Third, let us consider the relationship between the current model and our previous models (Kikuchi 2002; Kikuchi and Ichikawa 2002). As mentioned before, I assumed away congestion and size differences among countries, which were key factors in the previous studies. Given that there is no congestion, the connected countries will have an automatic advantage through increased connectivity between service firms. If there are congestion effects, however, the interconnected networks will work inefficiently because of congestion. Then, the connected countries may be divided into subgroups and some may end up specializing in good Y.20 This example suggests that a more complicated but important extension of the current model would be to have both congestion and size differences among countries.

7.4Â€Â€Concluding remarks In this chapter I highlight the role of network interconnectivity as a driving force behind trade in intermediate business services. It is shown that a comparative advantage in the good that uses business services is held by the connected countries. There is also some possibility that the unconnected countries will be harmed by trade. Although these results are derived under the assumption that there are no marginal trade costs, it appears that something similar to this will occur in the more general setting considered here. In addition, it should be noted that if business services are virtually mobile via the interconnected networks, the scale disadvantage of a small country in providing services will be eliminated. What really matters is the interconnectivity rather than the size of countries.

Interconnectivity of communications networksâ•‡â•‡ 69 These results have some importance for economic policy. If cultural, technological, and linguistic barriers continue to hinder the interconnection of communications networks (i.e., the virtual movements of business services), then one of the first effects of trade liberalization will be an increase in the inequality of nations. Further research should focus on these policy implications. The model could be enriched with the inclusion of marginal trade costs in order to analyse the role of interconnected communications networks in the process of gradual trade liberalization. In Chapter 8, I will examine a variant of the model with marginal trade costs.

8 Interconnected communications networks and home market effects

8.1Â€Â€Introduction1 Two of the most important trends in the global economy in recent decades have been (1) the dramatic increase in the role of information-intensive inputs in Â�economic activities, and (2) the decline in transaction costs such as transport and communications costs. Advances in digital technology have driven particularly large decreases in the costs of data transfer and telecommunications. Lower costs have incurred a growing connectivity of individuals and organizations achieved through improved communications networks (e.g., the Internet and satellite communications networks) and a consequent increase in the flow of information across borders. In the context of development, one result of these trends has been the interconnection of country-specific networks. Network users in one country are increasingly able to share a common communications infrastructure with users in another country. Because communications networks involve a high fixed cost of provision, interconnection facilitates cost sharing among users. For example, the formation of corporations through interconnection agreements and the creation of the Internet Exchange Point (IXP) have become more important among Internet Service Providers (ISPs) in developing countries. A group of ISPs in Kenya built the Kenyan IXP in November 2000 to improve the quality of their services and reduce connectivity costs; it reduced the price of a leased line for Internet connectivity (a 512kbit/s circuit) from US$9546 to US$650 (OECD 2002). As a barrier to cost sharing, unconnectedness emerges as a source of inefficiency and it may be a determinant of comparative advantage. This suggests that an examination of communications networks and falling communications costs should be accompanied by a focus on the effect of interconnection on trade patterns. The purpose of this chapter is to illustrate, with a simple two-country (North/ South), two-good (homogeneous good/differentiated high-tech products), two-Â� factor (skilled/unskilled labor) model, how the interconnection of country-specific networks can affect the nature of the trading equilibrium. To sharpen the analysis, I assume that product development activities are subject to fixed communications costs while trading activities are subject to variable (per-unit) transport costs.2 This chapter establishes a causal link between the interconnection of country-Â�specific

Interconnected networks and HM effectsâ•‡â•‡ 71 networks and the location of firms. Without interconnection, the skilled laborabundant country (North) is assumed to produce a more than proportional share of high-tech products, a result of the national income differential due to the higher endowment of skilled labor in the North. Interconnection of networks and a consequent decrease in communications costs through better cost sharing will lead to a reduction in the North–South income gap. If the magnitude of change is great enough, some high-tech products developed in the North will be produced in the South: as the North’s abundance of skilled labor in terms of factor income matters less, the relative importance of the larger unskilled labor base of the South will be heightened. These effects imply that the repercussions of inter connected networks are magnified by firms’ locational decisions. The analysis of interconnection is still in its infancy. Cremer, Rey, and Tirole (2000), for example, considered the impact of the connection of Internet Service Providers (ISPs). Their focus, however, was on the strategic aspects of interconnection in a closed economy. In the global context, Kikuchi (2003) investigated the impact of the interconnection of networks in a model of multi-country trade without transport costs. The main result of the present study, which establishes a link between the interconnection of networks and firms’ locational decisions, has not yet appeared in the existing literature.3 The following section presents the basic model without network interconnection. The effects of interconnection are considered in section 8.3, and concluding remarks are presented in section 8.4.

8.2Â€Â€The model Consider a world with two countries (North and South), each with two factors (skilled labour, H, and unskilled labour, L) and two types of goods (a homogeneous good and a large variety of differentiated high-tech products). The countries have similar technologies, but differ with respect to their absolute factor endowments. Introducing scale parameters γ, δ, and allowing “*” to denote variables for the South, we can summarize the factor endowment conditions as follows: H = γ H *, γ ≥ 1; L* = δL, δ ≥ 1.

(8.1)

I refer to the North as a “skilled labor-abundant country” and the South as an “unskilled labor-abundant country.” Consumers have Cobb-Douglas preferences over both categories and spend a fraction of their income on high-tech products. The price index for high-tech products is represented by the Dixit Stiglitz form: 1/(1–σ)

Pâ•›= â•‰ n(p)1–σ + n*(tp*)1–σ â•‰

, σ â•›>â•›1,

(8.2)

where σ is the degree of substitution between every product, p and p* are the producer prices of high-tech products in the North and South, and n and n* are the number of varieties produced in the North and South, respectively. Transport

72â•‡â•‡ Communications networks and time zones costs t (t >â•›1) for the high-tech products are in the form of “iceberg costs.” Thus, the demands of consumers in the North for a northern variety and a southern variety are c = p–σPσâ•›–1αI,

(8.3)

c´ = tp*–σPσâ•›–1αI,

(8.4)

where I is the national income of the North. The homogeneous good is produced with constant returns, using only unskilled labor as an input. Units are chosen so that one unit of unskilled labor produces one unit of output. As usual in new geography models, no transport costs exist for the homogeneous good, which serves to tie down the wage rate. Assume also that the parameters of the model are such that both countries produce the homogeneous good; thus constant, identical wages for unskilled labor hold (hereafter set to unity). The production of each variety of high-tech product requires a design that is developed by skilled labor. As in Martin and Ottaviano (1999), one of the central assumptions is that the design is firm-specific, but it need not be developed in the country where production actually takes place, because there is free trade in designs. For example, if a variety developed by northern skilled labor is produced in the South, the operating profits are repatriated to the North. To produce one unit of a product, β units of unskilled labor are required. Given a Dixit Stiglitz specification with constant elasticity σ, each firm sets its price as p = (βσ )/(σ – 1). By choice of units, one can set β = (σ – 1)/σ to have p = p* = 1.

(8.5)

Given that a design is required to start production, the payment for each design, r (r* ), must satisfy x r = px – β x = __ â•‰â•¯ â•¯ â•‰,â•¯ r* = px* – βx* = x*/σ, σ

(8.6)

where x (x*) is the output of a northern (southern) representative firm. When trade in designs is unrestricted, the world price for designs will prevail, which implies that r = r* and thus x = x*. Now turn to product development activities. The development of each new design requires one unit of skilled labor. The central assumption is that product development activities also require communication through a country-specific network. In other words, communication is treated as an input in product development activities along with skilled labor. This implies that product development activities directly depend only on these two inputs, not on the presence of agglomeration externalities, which are usually associated with product development activities. This is a rather extreme assumption. Normally, agglomeration externalities play an important role in product development. To highlight the information-intensive

Interconnected networks and HM effectsâ•‡â•‡ 73 aspect of product development activities, however, here I concentrate on the role of connection and downplay the role of agglomeration externalities.4 Communications services are provided by a public monopoly employing average-cost pricing. For network connection, each skilled labor must pay a fixed communications cost of g(H) (g < 1) units of skilled labor. Once each skilled labor connects to the network, 1 – g(H) units of labor remain for product development activities. Given that one unit of skilled labor is required for the development of a new design, the total number of designs developed within each country, K(K *), becomes K = H[1 – g(H)], K * = H *[1 – g(H *)].

(8.7)

Again note that K is the number of designs developed by northern skilled labor while n is the number of firms operating in the North. Now consider the cost structure of the network service provision. One of the main assumptions is that the provision of a network involves only a fixed cost: F units of skilled labor. Throughout this chapter I will assume that F is exogenously given and simply use it as an index of communications technology. Because of average-cost pricing, communications costs per skilled labor are simply F F __ ___ g(H) = â•‰â•¯ â•¯â•¯â•‰â•›, g(H *) = â•‰â•¯ *â•¯â•¯â•‰â•¯. H H

(8.8)

This implies that communications costs per skilled labor fall as the total quantity of skilled labor increases, allowing more users to share the common cost of providing the network, F. The joint assumptions on factor supply (8.7) and communications costs (8.8) are summarized in the total number of designs within each country, given by5 K = H[1 – g(H)] = γH * – F, K * = H *[1 – g(H *)] = H * – F.

(8.9)

These equations imply that the skilled labor-abundant country (the North) can develop new products relatively more efficiently [(K/H) > (K */H *)]. Through better cost sharing, each user of the northern network can provide more resources for product development activities. In contrast to firms, households are immobile, so that their incomes are geographically fixed even though firms are not. Since factor income for skilled labor is equal to payments for designs, the national income of each country can be obtained as follows (see (8.1)): I = L + rK = L + r(γ H * – F), I * = L* + rK * = δL + r (H * – F).

(8.10)

Now consider the location of firms. The product market equilibrium requires that supply equals demand for each variety produced in the North: x = c + tc*. Substituting (8.3), the southern counterpart to (8.4), and (8.10) into this condition yields the following equilibrium condition for a northern product and its southern counterpart:

74â•‡â•‡ Communications networks and time zones α(L + rK) ___________ τα(L* + rK *) x = _________ â•‰â•¯ â•¯ â•¯ + â•‰â•¯ â•¯â•‰â•¯ â•¯ , *â•¯â•‰ n + τn τn + n*

(8.11)

τα (L + rK) __________ α(L* + rK *) x* = â•‰â•¯__________ â•¯ + â•‰â•¯ â•¯â•‰â•¯ ,â•¯ *â•¯â•‰â•¯ n + τn τn + n*

(8.12)

where τ ≡ t1–σ (τ ≤ 1) measures the freedom of trade. The total number of varieties, N, is fixed by the number of designs (K + K *). Thus by using (8.9), N = n + n* = K + K * = (γ + 1)H * – 2F.

(8.13)

In equilibrium, the world labor market must be cleared. A constant fraction of world income must be paid for the designs. Hence, at the world level, this implies that α (I + I *)/σ = r(K + K *).

(8.14)

Substituting national income (8.10) into (8.14) yields the equilibrium payment for a design:6 α (1 + δ )L ____________ r = â•‰ _____ â•‰â•¯    â•¯ â•¯â•¯ â•¯â•¯â•‰. â•‰â•¯ â•‰â•‰â•¯ σ – α  (γ + 1)H* – 2F

(8.15)

The skilled labor income differential between countries is α (1 + δ )L(γ – 1) _____ ______________ â•¯â•¯ â•¯â•¯ r(K – K *) = â•‰  â•‰â•¯    â•¯ â•‰â•¯ â•‰â•‰â•¯ â•¯â•‰. σ – α  γ + 1 – (2F/H *)

(8.16)

Assume that this skilled labor income differential is substantial and that northern income is larger than southern income (I >â•›I * ). Using (8.10), this implies that r(K – K *) > (δ –â•›1)L. It follows that a difference in skilled labor income must exceed that in unskilled labor income: the North’s advantage in skilled labor abundance outweighs the South’s advantage in unskilled labor abundance. If we use (8.10) and (8.15), the proportion of firms located in the North becomes n __

1 – τ (I * â•‰â•¯ â•¯â•¯â•‰= ________________ â•¯â•¯â•¯â•¯â•¯â•‰â•›. â•‰â•¯ N I)/(1 – τ)[1 + (I */I)]

(8.17)

When the national income of the North is greater than that of the South (i.e., (I*/I) <â•›1), the above condition implies that (n/N) > (1/2) holds, which means that the location with the highest national income will house the majority of firms. While intra-industry trade occurs, the North becomes a net exporter of high-tech products. This result is the standard “home market effects” analyzed by Helpman and Krugman (1985, ch. 10).

Interconnected networks and HM effectsâ•‡â•‡ 75

8.3Â€Â€Interconnection and home market effects From now on I consider the following scenario: given that the initial equilibrium in which each country utilizes its own network has been attained, two countries’ country-specific networks can be interconnected. Skilled labor in each country can connect to the interconnected networks and utilize the common infrastructure. The service provider of the interconnected networks is assumed to continue to employ average-cost pricing.7 Now consider the impact of interconnection on factor supply. The interconnection of networks has two effects on skilled labor. First, it reduces the total cost of network provision. Through the efficient utilization of the common infrastructure, the total cost of network provision decreases from 2F to F.8 Second, and more important, it changes the distribution of designs within the world economy. As there is more skilled labor in the North, most network provision costs are covered by payments from northern skilled workers. In other words, each user in the small southern network gains extra cost savings from connecting to the large northern network. For each southern skilled labor, communications costs fall from g(H *) = F/H * to g(H + H *) = F/(H + H *). The second effect works in favor of southern skilled labor. These two effects are summarized in the following specification for the designs: KC = γ H * – [γ/(γ + 1)]F, K *C = H * – [1/(γ + 1)]F,

(8.18)

where superscript C denotes network connection. Now the total number of designs becomes NC = nC + n*C = KC + K*C = (γ + 1)H* – F. Solving the world skilled labor market condition (8.14) yields the equilibrium payment for a design: α (1 + δ )L ____________ r = â•‰  _____ â•‰â•¯    â•¯ â•¯â•¯ â•¯â•¯â•‰ â•‰â•¯ â•‰â•‰â•¯ σ – α  (γ +â•›1)H * – F *

(8.19)

Now the skilled labor income differential becomes α (1 + δ )L(γ – 1) r C (K C – K *C ) = â•‰ _____ â•‰â•¯    â•‰â•¯â•¯ â•‰_____________ â•‰â•¯ â•¯â•¯ â•¯ â•¯â•‰ . σ – α γ+1

(8.20)

When we compare (8.6) and (8.20), it is clearly seen that the income differential will decrease, owing to the interconnection of networks. The change in skilled labor income differentials is defined as the following function: φ(γâ•›; F) ≡ r(K – K *) – rC (K C – K *Câ•›)

 

α(1 + δ )L ___________________ (γ – 1)(2F/H*) = â•‰ _________ â•‰â•¯ â•¯ â•¯â•¯ â•¯â•¯â•¯â•‰.   â•¯ â•‰â•¯ â•‰â•‰â•¯ σ–α (γ +â•›1)[γ +â•›1 – (2F/H *)]



(8.21) (8.22)

The signs of (d φ/d γ) depends on the level of γ. Taking the total derivative of ϕ with respect to γ reveals sign (dlnφ/dlnγâ•›â•›) = sign [–γâ•›â•›2â•›+â•›2γ +â•›3â•›–â•›(4F/H*)]. This

76â•‡â•‡ Communications networks and time zones implies that, __given that the difference in skilled labor endowment is not so large (i.e., 1 ≤ γ â•›≤ γâ•› â•‰ â•‰â•¯≡ 1 + 2[1 – (F/H*)](1/2)), increases with respect to γ (see_Appendix A for a proof). In the following analysis, γ is assumed to be smaller than γâ•‰ â•‰ .â•¯ Lemma: (1) As the difference in skilled labor endowments becomes larger, the difference in skilled labor income differentials becomes smaller, owing _ to interconnection. Given that 1 ≤ γâ•› ≤ γâ•‰ â•‰ ,â•¯ φ increases with γ. (2) As the total cost of network provision increases, the difference in skilled labor income differentials also becomes smaller owing to interconnection: ϕ increases with F. Figure 8.1 summarizes these relationships. The horizontal axis is the difference in the endowment of skilled labor, γ. The vertical axis is the change in skilled labor income differential due to interconnection. The two curves correspond to equation (8.21) with different values of F. This figure emphasizes that the change in skilled labor income differentials becomes smaller due to interconnection as (1) the North is endowed with more skilled labor and/or (2) the total cost of network construction grows. Owing to improved cost sharing over a broader population, the share of southern designs in the world economy increases from Change in the skilled-labor income differential due to interconnection

High F

Low F

g 1

Figure 8.1Â€Â€

Interconnected networks and HM effectsâ•‡â•‡ 77 K /(K + K ) to K /(K + K ), which results in a smaller skilled labor income differential. Although this result depends on the values of certain parameters, it captures the impact of interconnection on factor income distribution, which plays an important role in determining firms’ location decisions. Now turn to the location of firms. Interconnection implies that the total amount of resources devoted to product development activities increases. Furthermore, this cost-sharing effect works in favor of southern skilled labor: southern skilled labor can supply more resources as a result of better cost sharing over a broader population. Through these factor market effects, the North–South income gap decreases. In some cases southern national income becomes larger than northern national income:9 *

*

*C

C

(I *C/I C ) > (1/2) > (I */I).

*C

(8.23)

That is, the skilled labor income differential becomes smaller owing to interconnection, and will be outweighed by the unskilled labor income differential. If there is a discrete change, owing to the interconnection of networks, the income differential will be reversed and firms’ locations will be drastically altered. Some of the varieties developed in the North will be produced in the South, which now has the highest expenditure level owing to its relatively large amount of unskilled labor. This implies that the North exports both designs and the homogeneous good, while the South becomes a net exporter of high-tech products.10 These effects are attributable to a combination of asymmetries in factor endowments and the presence of transport costs. Figure 8.2 illustrates this relationship. On the horizontal axis is the southern relative income (Iâ•›*/I). On the vertical axis is the proportion of firms that are located in the North (n/N). Lines ll and l´l´ correspond to (8.17), with different values of t.11 Point 1 shows the initial situation with unconnected networks while point 2 is the situation after interconnection has taken place. From this figure, it is clear that the level of transport costs, as represented by t, determines the magnitude of the production shift. Line l´l´ depicts the case with relatively free trade (i.e., smaller t). When transport costs become lower, the sensitivity of location decisions to market size differentials increases, because it is easier for firms to locate in the larger country and then export to the other, smaller country.12 Looking at this figure, we can compare the impact of the interconnection of networks (i.e., a decline in communications costs g) to that of a decline in transport costs (t). Two notable features emerge. First, if there is a decrease in transport costs while communications networks remain unconnected, industrial concentration in the North (from point 1 to point 1´) occurs. Second, if there are falling communications costs owing to the interconnection of networks and there is a consequent change in relative income levels such that the southern national income exceeds that of the North as in (8.22), in contrast, a more substantial production shift (from point 1´ to point 2´) or industrial diversion occurs. In other words, home market effects work in reverse, owing to the drastic expenditure shifting (see Appendix B for a proof).

78â•‡â•‡ Communications networks and time zones 1 1'

l'

1': a decline in transport costs 2': interconnection of networks

n /N 1'

l

1

1/2 2

l

2'

l' I */I

1

I *c/I c

I */I

Figure 8.2Â€Â€

Proposition 8.1: (1) Falling transport costs without network interconnection result in industrial concentration in high-tech products. (2) Falling communications costs owing to interconnection result in a drastic industrial diversion of high-tech products. These results have important policy implications for developing countries. If a southern government introduces an economic policy to lower transport costs (e.g., by subsidization to transport infrastructure), it may end up weakening its domestic industrial base for high-tech products. On the other hand, an economic policy in favor of connected networks improves the productivity of southern skilled labor. Furthermore, by using network interconnection as leverage, the South can attract more high-tech firms; it may even convert northern centers for the export of high-tech products into southern centers. Note the welfare aspects of the interconnection of networks. Since the prices of high-tech products remain constant (see (8.5)), it is relevant to check changes in national income and the share of firms. Clearly, southerners gain through both an increase in national income (due to falling communications costs) and a discrete

Interconnected networks and HM effectsâ•‡â•‡ 79 increase in domestic production (due to the production shift). In particular, the latter means a saving of transport costs. It is important to note that there is a link between factor market effects and production market effects. From the viewpoint of the South, interconnection implies an increased factor base for product development activities, which is further reinforced by expenditure shifting through factor market interactions. On the other hand, northerners may lose out from this change. There are gains from an increase in the total number of available brands, while the number of domestic brands decreases and northerners have to import more products from the South and pay higher total transport costs. This raises another important point: the threat of not connecting to the network can be very valuable for the North. It is well known that the threat of non-connection increases the larger network’s bargaining power (see, e.g., Cremer, Rey, and Tirole 2000). The results of the present study imply that it is important to analyze the strategic aspects of interconnection in the global context. Before closing this section, I will describe two directions in which the model could be extended. First, consider the importance of cost savings from interconnection. So far in this analysis, I have considered the case in which the total provision cost is halved by interconnection (2F → F).13 Now assume that two existing national networks open up. In this case there is no saving in terms of resources but only a common average cost, owing to the fact that the two countries now share an international network composed of two national networks. The average cost falls in the South while rising in the North: (F/H) < [2F/(H + H *)] < (F/H * ). While southern skilled labor can supply more resources for product development and can earn more income, skilled labor supply for product development will decrease in the North. As in the analysis, the North–South income gap will be reduced by interconnection, which further causes industrial diversion of high-tech products. This suggests that changes in the distribution of designs due to interconnection are more important than changes in the provision costs themselves.14 Second, consider the strategic interaction between country-specific service providers. So far I have assumed that two country-specific providers are combined into one provider and continue to employ average cost pricing. If I relax the assumption of non-strategic behavior, each provider would then change its pricing strategy as a result of interconnection. In this case, one might expect that a pro-competitive effect will emerge, which will constitute another source of gains. This kind of extension needs further consideration.

8.4Â€Â€Concluding remarks This study highlights the effects of the interconnection of country-specific communications networks and the consequent decrease in communications costs as driving forces behind trade in differentiated high-tech products with positive transport costs. Through better cost sharing over a broader population, interconnection works in favor of the unskilled labor-abundant country. Each user of the southern

80â•‡â•‡ Communications networks and time zones network gains much from connecting to the northern network. Furthermore, it is shown that the impact of interconnection may be magnified by firms’ locational decisions. Owing to the “reversed” home market effect, products developed in the North begin to be produced in the South. That is, the industrial structure will be drastically changed by the interconnection of networks. These results have important policy implications for developing countries. Through the utilization of interconnected networks, developing countries can attract high-tech firms from developed countries and themselves become major exporting centers. Further research should focus on these policy implications.

8.5Â€Â€Appendix A: Proof of Lemma Taking the total derivative of ϕ with respect to γ reveals d ln φ _____

2[γ + 1 – (2F/H *)] – (γ – 1)(γ + 1) ____________________________  â•‰  = â•‰â•¯ â•¯â•‰. â•‰â•¯ â•¯ â•¯â•¯â•¯ â•¯â•¯â•¯ d ln γ (γ – 1)(γ + 1)[γ + 1 – (2F/H *)]

(8.24)

Since the denominator of the RHS is positive, the following condition may be obtained: sign (d ln φ/d ln γ ) = sign [–γ 2 + 2γ_ + 3 – (2F/H *)]. The term [–γ 2 + 2γ + 3 – (2F/H *)] = 0 has one positive_ root: γâ•‰ â•‰ â•¯ = 1 + [4 – (2F/H*)](1/2). It is also assumed that γ ≥ 1. Thus, if 1 ≤ γ ≤ γâ•‰ â•‰ â•¯, then φ increases with γ. Similarly, taking the total derivative of φ with respect to F reveals d ln φ _____

1 _________________ 2 __ â•¯â•‰â•¯ = â•‰â•¯ â•¯â•‰+ â•‰â•¯ â•‰â•¯   â•¯â•¯â•¯â•¯â•‰> 0. d ln F F H * [γ + 1 – (2F/H *)]

(8.25)

8.6Â€Â€Appendix B: Proof of proposition 1

From (8.17), one can obtain the following expression: ∂(n/N) ________________ (I /I)[(I/I ) –1] ______   â•¯ â•‰â•¯â•‰â•¯ â•¯â•‰. â•‰â•¯ â•¯â•¯ â•¯â•¯ 2 * *

∂τ

2

*

(1 – τ) [1 + (I /I)]

This expression is positive as long as (I/I * ) >1: the proportion of firms located in the North will increase with lower transport costs (a higher τ). From (8.17), n/N is a decreasing function of I */I. Thus, if there is an increase in I */I due to interconnection, n/N will decrease (see Figure 8.2).

9 Time zones as a source of comparative advantage

9.1Â€Â€Introduction1 Two of the most important trends in the global economy in recent decades have been (1) the dramatic increase in the role of information-intensive inputs in Â�economic activities, and (2) the decline in transaction costs such as transport and communication costs. In particular, advances in digital technology have driven large decreases in the costs of data transfer and telecommunications. To put it plainly, globalization is closely related to the increased connectivity of individuals and organizations achieved through improved communications networks such as the Internet. There is a consequent increase in many kinds of international trade, particularly in business service sectors such as banking, engineering, and software development, which do not require physical shipments of products. The rise of the Indian software industry provides a prime example. One of the fastest-growing parts of this industry is “remote maintenance” whereby Indian companies debug software for companies in other parts of the world, often taking advantage of the time difference to offer an overnight service. For instance, the programming Â�problems of some U.S. corporations are e-mailed to India at the end of the U.S. workday. Indian software engineers work on them during their regular office hours and provide solutions. By the time the offices reopen in the U.S., the solutions have already arrived, mainly as e-mail attachments. This type of trade in business services requires two basic conditions: a difference in time zones between the trading partners and good connections via communications networks (e.g., the development of the Internet and satellite communications systems).2 Related to these phenomena, Cairncross (2001) wrote: In some parts of the world, communications offer a new competitive advantage: time zones. It becomes possible to take advantage not only of geography but of the full twenty-four hours of the world’s working day.â•›.â•›.â•›. that means more efficient use of global resource. (Cairncross 2001, p. 202) In other words, due to the communications revolution, time differences may become a primary driving force behind business services trade.

82â•‡â•‡ Communications networks and time zones In the existing literature on trade theory, however, relatively few attempts have been made to address the theme of communications networks and the role of time zones. In a seminal contribution, Marjit (2007) examined the role of international time differences in a vertically integrated Ricardian framework. He suggested that countries located in opposite time zones can save time and costs if they produce various stages of a commodity. However, the role of communications networks is downplayed in the analyses. Related to the role of communications networks, Harris (1998) used the term virtual economic integration to refer to situations in which communications networks make trade possible in business services. Along this line, this note focuses on another important practice: the utilization of time differences via communications networks which allows business service producers in one country to collaborate with (or outsource to) those in another country efficiently. The utilization of time differences plays a crucial role in economic activities in the world economy: if producers in one country fail to exploit differences in time zones, they may be excluded from the internationally connected network that is essential to certain types of trade. In other words, the neglect of time differences might work as a trade barrier for business services. The main purpose of this note is to illustrate, with a simple three-country model of monopolistic competition, how the utilization of time differences can affect the structure of comparative advantage. For this purpose, this chapter builds a three-country model of monopolistic competition with a single production factor (i.e., labor). The model has two final goods. The first is a homogeneous good (good Y ), the production of which does not require communications network services. The production of the other good (good X ) consists of assembling business services. The business services sector is characterized by monopolistically competitive firms. The central assumption is that one unit of a business service requires production in two stages, each of which requires one working day: the utilization of time differences (i.e., the outsourcing of one of the stages to another country) reduces total production costs. On the basis of the model outlined above, this chapter demonstrates how the differences in time zones determine the nature of the trading equilibrium. Two countries that are virtually integrated via the communications network acquire a comparative advantage in the business service intensive good, good X. This is because, in these countries, the good X sector works efficiently through the expansion of the range of available business services. Section 9.2 presents the basic model. The nature of the trading equilibrium is considered in section 9.3, followed by concluding remarks in section 9.4.

9.2Â€Â€The model In this model there are three countries: Country 1, Country 2, and Country 3. Each country is endowed with L units of labor, which is the only primary factor of production. The countries have identical technologies and the only differences are in time zones. There is no overlap in working hours: when Country 1’s workday ends, Country 2’s workday begins, and so on (See Figure 9.1). Each

Time zones as comparative advantageâ•‡â•‡ 83

Country 3’s workday

Country 1’s workday 24

16

8

Country 2’s workday

Figure 9.1Â€Â€Working hours.

country produces two consumption goods, good X and good Y, and one intermediate business services good, good Z. Good X and good Y are tradable. Good Z comes in n differentiated varieties and it is assumed that each unit of variety requires production in two stages. None of the variety is tradable, even though the production of the second part of each variety may be outsourced. Goods X and Y are sold in perfectly competitive markets. Good Y is produced under constant returns using only labor; units are chosen such that one unit of labor produces one unit of output. Wage rates are normalized to unity. Good X is produced under constant returns using only differentiated business services as inputs. The production and unit-cost functions for good X are respectively:

 

1/ρ

X = â•‰  â•‰ â•¯â•¯â•‰â•¯â•‰â•‰zâ•‰ ρiâ•¯â•‰â•¯  â•‰ , 0 < ρ < 1, n

i=1

 

â•‰ , C = â•‰  â•‰ â•¯â•¯â•‰â•¯â•‰â•‰piρ/(ρ–1)â•¯(ρ–1)/ρ n

i=1

(9.1) (9.2)

84â•‡â•‡ Communications networks and time zones where n is the number of available business services, zi (pi ) is the quantity (price) of service i, and σ ≡ 1/(1 – ρ) > 1 is the elasticity of substitution between every pair of services. This production function has the property that as input differentiation increases, the unit production cost falls. In fact, a large number of existing studies are based on similar assumptions. These studies include Ethier (1982b), Markusen (1989), Harris (1998), Kikuchi (2003), and Long, Riezman, and Soubeyran (2005). Differentiated business services (good Z ) are supplied by monopolistically competitive service firms. Before starting production, α units of labor are required as a fixed cost of production. The central assumption is that each unit of a business service requires production in two stages: the second stage must start after the first stage has been completed. Each stage requires one unit of labor. If production occurs within a country, there is no need for a communications network: communications networks are needed only when the international outsourcing of a production process occurs. Thus, the cost function of the i-th service firm becomes CA TCâ•‰â•¯ iâ•¯ â•‰â•¯â•¯= w(α + 2zi), i = 1, …, n,

(9.3)

where w is the wage rate and superscript CA denotes the case of a “communications autarky” (i.e., no outsourcing). Given a Dixit–Stiglitz specification with constant elasticity σ, each service firm sets its price as pCA = 2σ w/(σ – 1).

(9.4)

With free entry and exit, the level of output that generates zero profits is given by zCA = (α/2)(σ – 1).

(9.5)

Alternatively, each firm may “outsource” the second stage to the next country. By doing so, a firm can complete its production earlier and reduce its working hours. It is assumed that 1 + β (β < 1) units of labor are required for one unit of service. This captures the idea that specialization to take advantage of time differences reduces marginal production costs.3 Although I do not explicitly model the time aspect of production, this seems to be a reasonable assumption.4 Another important assumption is that outsourcing requires communications between the outsourcing country and the insourcing country via a communications network: each service firm has to both send and receive its intermediate good via a network. To get on to the network, each service firm has to pay a fixed fee (γ ). It may be natural to assume that the connection fee is a function of factors such as the number of users, market structure, and so forth.5 In this study, to make the model tractable, the assumptions about network technology are drastically simplified. These assumptions are summarized in the following cost function: TCâ•‰Oâ•¯iâ•¯â•¯â•‰â•¯= w[α + γ + (1 + βâ•›)zi], i =â•›1, …, n,

(9.6)

Time zones as comparative advantageâ•‡â•‡ 85 where superscript O denotes the case of “outsourcing.” The costs of communicating across national borders may be offset by a lower marginal production cost.6 With outsourcing, each service firm sets its price as pO = [(2 – δ )σ w]/(σ – 1),

(9.7)

where δ ≡ (1 – β ) represents the reduction in marginal cost. With free entry and exit, the level of output that generates zero profits is given by zO = [(α + γâ•›)/(2 – δâ•›)](σ – 1).

(9.8)

Now consider the supply function of good X. Making use of (9.2), in a communications autarky, this supply function becomes7 CCA = n1/(1–σ ) pCA = [â•›pCA (zCA)1/σâ•›]â•›X –1/σ.

(9.9)

The supply curve SS, showing the above condition, is depicted in Figure 9.2(a). It is important to note that, since there are productivity gains from increased specialization, the supply curve has a convex shape. Note also that this curve is truncated because labor endowments limit the number of business services. Alternatively, with international outsourcing, the supply function becomes C O = n1/(1–σ ) pO = [â•›pO (zO )1/σâ•›â•›]X –1/σ.

(9.10)

Comparing (9.9) and (9.10), one can obtain the relative cost of good X:

 

O 2 – δ (σ –1)/σ _____ α + γ 1/σ â•‰â•¯ CAâ•¯â•¯â•‰â•¯= â•‰ _____ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰ â•‰ â•‰â•¯     â•¯â•‰â•¯ â•‰ . C 2 α

C ____



 



(9.11)

This index captures important aspects of the utilization of time differences. While the reduced prices of services due to outsourcing have a positive effect, the reduced range of services due to additional fixed connection costs have a negative effect. The overall effects are determined by the tension between these two countervailing effects. Note also that the degree of substitution between business services (σ) determines the relative impact of these effects: as input differentiation matters less (i.e., σ grows), the effect of a reduced price due to outsourcing becomes more important. Using (9.11), one can obtain the important condition for international outsourcing as follows: σ /(σ –1)

â•¯â•¯â•‰â•¯â•¯â•‰ â•‰  â•‰â•¯____ C  CO

CA

 

1/(σ –1)

2 – δ _____ α+γ = â•‰ _____ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰â•‰ â•‰â•¯     â•¯ â•‰â•¯ â•‰ 2 α

 



< 1.

(9.12)

Proposition 9.1: If condition (9.12) holds, it is more profitable to outsource than to maintain a communications autarky.

(a)

P

S

D

A

PA

D

S

XA (b)

S' P T'

PT

T S'

XT

Figure 9.2Â€Â€Outsourcing and industrial structure.

Time zones as comparative advantageâ•‡â•‡ 87 Before turning to the trading equilibrium, consider the situation in which there is no trade in goods or business services (i.e., no outsourcing). In this case, each country must produce all of the goods and services it will use, which means that the price of good X (P) must be equal to the cost C CA: P = C CA = [ pCA (zCA)1/σâ•›â•›]X –1/σ.

(9.13)

On the demand side, it is assumed that the representative consumer has CobbDouglas preferences: U = X µY 1–µ. Thus, PX = µL must be satisfied. The curve DD showing this condition is also depicted in Figure 9.2(a). Clearly the autarky equilibrium without outsourcing occurs at point A. The autarky number of service firms becomes8 nCA = µL/ασ. Thus, the autarky price and quantity of good X are as follows: PCA = (µL/ασ)1/(1–σ ) [2σ/(σ – 1)],

(9.14)

Xâ•›CA = (â•›µL/σ)σ/(σ –1) α 1/(1–σ ) [(σ – 1)/2].

(9.15)

9.3Â€Â€A trading equilibrium with outsourcing In this section, three countries are assumed to open their goods markets. In addition, assume that every country continues to produce Good Y.9 Furthermore, the business service sectors in Country 1 and Country 2 are assumed to be connected via communications networks while Country 3 is not connected. Let us call the former two “connected countries.” Between the connected countries, the middle processes of business services are traded virtually through the network: utilization of the network implies the virtual integration of two countries’ business service sector. These connected countries can take advantage of time differences: if Country 1 specializes in the first stage, it becomes efficient to outsource the second stage to Country 2, not Country 3. Assume also that CO < CCA (i.e., condition (9.12)) holds. Figure 9.2 demonstrates how outsourcing affects the production structure of the world economy. Figure 9.2(a) shows the situation before outsourcing takes place, while Figure 9.2(b) shows the situation afterwards. The effect of using time differences is shown by the change in the supply curve. The extended curve S´S´ in Figure 9.2(b) reflects the enhanced division of labor between connected countries, while the curve for Country 3 remains unchanged. This figure shows that there are two sources of gains. First, in the connected countries, the good X sector purchases services from all service firms located in the connected countries and

88â•‡â•‡ Communications networks and time zones the number of available business services increases. Second, due to the efficient utilization of time differences, each service firm within the connected countries can supply its service at a lower cost, pO, which also reduces the production cost of good X. By taking into account a simple entry–exit process, connected counties will specialize in both good X and business service Z. Proposition 9.2: A comparative advantage in good X is acquired by connected countries that can take advantage of time differences. Let us consider this more closely. In connected countries, the network provides opportunities for entry into the service sector because, with the increased division of labor due to outsourcing, the average cost of good X becomes lower and the export of good X is enhanced.10 Thus, the size of connected countries’ business service sectors will expand, while the size of the third country’s service sector will shrink. The point is that there will be a cumulative process in which the increased connectivity via a network will enhance exports, and exports will enhance further specialization in the business service sector. Now turn to the welfare effects of trade. The equilibrium point is located on the curve S´S´ (e.g., at point T ): the trading equilibrium number of service firms becomes nT = 3µL/(α + γâ•›)σ, where superscript T denotes the trading equilibrium. Note that nT firms located in Country 1 specialize in the first stage and the second part of each variety is outsourced to Country 2. The equilibrium price and quantity for good X become, respectively:11 PT = [3µL/(α + γ )σ]1/(1–σ)[(2 – δ )σ/(σ – 1)],

(9.16)

Xâ•›T = (3µL)/σ σ/(σ –1)(α + γ )1/(1–σ)[(σ – 1)/(2 – δ )].

(9.17)

Making use of (9.14) and (9.16), we can show that the price of good X decreases if the following condition holds:

 

1/(1–σ )

3α _____ â•‰â•¯ â•‰ â•‰ â•‰â•¯   â•¯ α+γ



 

  

1/(σ –1)

2–δ 2 – δ _____ α+γ _____ _____ â•‰â•¯ â•‰ â•‰ â•‰â•¯ â•¯â•‰â•¯  â•¯ â•‰= â•‰ â•‰â•¯ â•¯â•‰â•¯  â•¯ â•‰â•‰ â•‰â•¯     â•¯ 2 2 α

  



1/(σ –1)

  

1 __ â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰ 3

<â•›1.

(9.18)

It is notable that, given that each country continues to produce good Y and condition (9.12) holds, condition (9.18) also holds and each country will gain from trade (i.e., the utilization of time differences) regardless of its connectivity and location. Proposition 9.3: If the expenditure share for good X is sufficiently small and condition (9.12) holds, each country in the world will gain from trade. Before closing this section, it is worthwhile to note the potential for multiple equilibria. To simplify the argument we have assumed that Country 1 (when

Time zones as comparative advantageâ•‡â•‡ 89 completing the first stage of production) and Country 2 (when completing the second stage) are exogenously connected via a network and specialize in good X. However, it should be clear by now that Country 2 (first stage) and Country 3 (second stage) may specialize in good X. The case of Country 3 (first stage) and Country 1 (second stage) is also possible. Thus, there are multiple equilibria. An important conclusion that may be drawn from our analysis is that the countries should not complete both of the stages on their own.12 Therefore, a natural extension would be to include the endogenous formation of the network connection, which needs further consideration.

9.4Â€Â€Concluding remarks This chapter highlights the role of time zones as a driving force behind trade. It is shown that a comparative advantage in the good provided using business services is held by the countries that utilize time differences and outsource (or insource) their production processes. Even more noteworthy is the finding that there is a circular causation between increased connectivity via a network and trade creation. Although these results are derived under the specific assumptions that there is only one factor of production and the type of connection is exogenously given, it appears that a more general setting would yield similar results.

10 Service trade with time zone differences

10.1Â€Â€Introduction A tremendous change is taking place in the world economy: globalization, caused both by the communications revolution and by the deterioration of barriers to international trade. Many kinds of trade, particularly in service sectors such as banking, engineering, retailing, and software development, do not require physical shipments of products.1 The rise of the Indian software industry provides a prime example. The programming problems of some U.S. corporations are e-mailed to India at the end of the U.S. workday. Indian software engineers work on them during their regular office hours and provide solutions. By the time the offices reopen in the U.S., the solutions have already arrived, mainly as e-mail attachments.2 Ireland, pitching to host Europe’s main international call centers, offers another example. Cairncross (1997, p. 219) emphasized the rise of the call center service industry in Ireland, which is taking geographical advantage of being in between the U.S. and Europe. These types of service trade require two basic conditions. First, there must be a difference in time zones between the trading partners. Second, there must be good connections via communications networks (e.g., the Internet) which enable the services to be “transported” quickly with little cost. In other words, thanks to the communications revolution, time zone differences can become a primary driving force behind service trade. This seems to suggest that the focus on “market proximity” as an advantage in service provision should be accompanied by focus on a time zone (or remoteness) advantage. In the existing literature on trade theory, however, relatively few attempts have been made to address the role of time zones. In a seminal contribution, Marjit (2007) examined the role of international time zone differences in a vertically Â�integrated Ricardian framework. He showed that time difference emerges as an independent driving force of international trade besides taste, technology, and endowment.3 According to this line, we propose a two-country monopolistic competition model of service trade that captures the role of time zone differences.4 Â�Following Marjit (2007), we assume that two countries are located in different time zones. Marjit studied the role of time zones in perfectly competitive markets with constant returns technology. In contrast, in this study we examine their role in

Trade with time zone differencesâ•‡â•‡ 91 monopolistically competitive markets with increasing returns technology, which enables us to include service firms’ location decisions explicitly. Furthermore, by introducing differentiated services, we will analyze the interaction between the degree of product differentiation and time zone differences as determinants of trade patterns. The key assumption is that domestic service production requires one workday and that products are ready for sale after one workday: domestic delivery bears significant costs. In contrast to this, the utilization of communications networks allows production in a foreign country where non-overlapping work hours and service trade via networks enable a quick delivery and low shipping costs; in other words, imported services whose production benefits from time zone differences realize higher value than domestically produced services. Although this assumption is at odds with that of the standard monopolistic competition model with trade costs (e.g., Krugman, 1980),5 it captures the idea that consumers would like to have services sooner rather than later. On the basis of the model outlined above, we will show that the utilization of communications networks induces dramatic change in industrial structure due to firm relocation to take advantage of time zone differences. In section 10.2 we present the basic model. In section 10.3 we deal with the issue of trade patterns. Section 10.4 concludes the chapter.

10.2Â€Â€The model Suppose there are two countries, Home and Foreign, and that they are identical in regard to tastes and technology.6 There is only one factor of production, namely labor, and relative country size is measured by labor force size. Let L denote the size of the world’s total labor force, and λL (0 < λ < 1) denote Home’s labor force size. The two countries are located in different time zones and there is no overlap in working hours: when Home’s workday ends, Foreign’s workday begins (see Figure 10.1). There are two sectors: a monopolistically competitive sector producing a large variety of differentiated services and a perfectly competitive sector producing a homogeneous good. The latter serves as the numeraire, and units are chosen such that one unit of labor produces one unit of output. The production of the numeraire is instantaneous in the sense that one unit of output can be produced within one workday. The central assumption is that there are positive time costs for the delivery of differentiated services. We assume that the production of each service requires one workday. Then, one unit of service which is produced in Home is ready for sale after one workday. In order to capture this point, we assume that domestic shipments of differentiated services incur the “iceberg” effect of delivery costs: for every t (t >â•›1) units shipped, only one unit arrives. Thus, the price of a Home service to Home consumers will be tp, where p is the producer’s price for the service. In other words, we can interpret (t –â•›1)/t as a rate of discount. Another important assumption is that, if the utilization of communications networks becomes possible, a country can import differentiated services more

92â•‡â•‡ Communications networks and time zones

Foreign’s workday

Home’s workday

Figure 10.1Â€Â€Working hours.

cheaply. For every t´ units shipped, one unit arrives. The key assumption is the following condition: t > t´ > 1.

(10.1)

Note that this effect comes not from lower production costs in Foreign, but from faster delivery. This assumption captures the idea that production taking advantage of time zone differences increases the value of each service. We assume constant expenditure shares between the differentiated services and the numeraire, and that the sub-utility for the former takes the Dixit and Stiglitz (1977) form:

  

  n*

n

σ /(σ – 1)



*

D = â•‰ â•‰ â•¯â•¯â•‰â•‰(d â•‰â•¯ i)(σ – 1)/σ + â•‰ â•¯â•¯â•‰â•⁄â•‰â•¯ â•‰(d j )(σ – 1)/σâ•¯ â•‰ i

j

, σ â•›> 1.

where di (d *j ) is the consumption level of the Home (Foreign) services, σ is the elasticity of substitution between differentiated services, and n (n* ) is the number of products available from Home (Foreign). It is important to note that the larger the value of σ becomes, the less the degree of product differentiation between services matters. The price index for the differentiated services that is dual to the sub-utility D is represented by

   n

  n*

1/(1 – σ)



P = â•‰ â•‰ â•¯â•¯â•‰â•‰(tp â•‰â•¯ i)1 – σ + â•‰ â•¯â•¯â•‰â•⁄â•‰â•¯ â•‰(t´p*j )1 – σâ•¯ â•‰ i

j

.

(10.2)

Note that P measures the minimum cost to obtain one unit of D: welfare gains are measured by a reduction in P. The Home consumers’ derived demand for a Home service is

Trade with time zone differencesâ•‡â•‡ 93 c = td = t(tp)–σP σ – 1µλL,

(10.3)

where µ is the share of spending devoted to differentiated services. Similarly, the derived demand for a Foreign service from Home consumers is c*´ = t´*d *j = t´(t´p* )–σP σ – 1µλL.

(10.4)

A producer of a differentiated service has to commit α units of labor as a fixed cost and has constant marginal input β. With the total number of services available to consumers being very large, each producer chooses its constant mark-up price as p = p* = (σβ )/(σ – 1).

(10.5)

It is important to note that, as the degree of differentiation rises (i.e., the smaller σ is), producers are able to charge higher prices. Free entry ensures that the equilibrium output per service, x, is constant, common across countries, and independent of the level of delivery costs: x = [α (σ – 1)]/β.

(10.6)

Before turning to the trading equilibrium, we must draw attention to the autarky equilibrium (i.e., the equilibrium when t´ is prohibitively high due to the lack of communications networks). In autarky, the number of differentiated services in each country is given by n A = (µλL)/ασ ,Â€Â€Â€Â€Â€Â€Â€Â€n*A = [µ(1 – λ)L]/ασ ,

(10.7)

where A refers to the value in autarky equilibrium. Autarky equilibrium levels of price indices become P A = [(nA)t1 – σ p1 – σ ]1/(1 – σ), P*A = [(n*A)t1 – σp*1 – σ ]1/(1 – σ).

10.3Â€Â€Service trade via communications networks Let us turn to the case of service trade via communications networks. In this case, the service market equilibrium requires that supply equal demand for each Home service: x = c + c´. Substituting Eq. (10.3), the Foreign counterpart of Eq. (10.4) and Eq. (10.6) into this equation and denoting τ ≡ t 1–σ and τ´ ≡ t´1–σ yields the following equilibrium conditions for a Home product and its Foreign counterpart: ασ ________ τ´ (1 – λ) τλ ___ ________ â•‰â•¯ â•¯â•¯â•‰= â•‰â•¯ â•¯ *â•¯â•‰â•¯ + â•‰â•¯ * â•¯â•‰â•›â•›â•¯ , µL

τn + τ´n

τn + τ´n

(10.8)

94â•‡â•‡ Communications networks and time zones τ(1 – λ) τ´λ ασ ___ â•‰â•¯ â•¯â•¯â•‰= â•‰â•¯________ â•¯*â•¯â•‰â•¯ + â•‰â•¯________ â•¯ â•¯â•‰. â•¯ * µL

τn + τ´n

(10.9)

τn + τ´n

Using Eqs (10.8) and (10.9), the equilibrium number of varieties may be obtained:

 

 

   

   

(1 – λ)τ´ – λτ ___ µL λτ´ – (1 – λ)τ ___ µL ____________ ____________ â•¯â•¯ â•¯â•¯ n = â•‰ â•‰â•¯ â•¯ â•¯ â•‰â•¯ â•‰â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯â•¯â•‰,Â€Â€Â€Â€Â€Â€Â€Â€n* = â•‰ â•‰â•¯ â•¯ â•¯ â•‰â•¯ â•‰â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯â•¯â•‰. τ´ – τ ασ τ´ – τ ασ

(10.10)

Using Eqs (10.7) and (10.10), the changes in Foreign production structure brought about by utilizing time zone differences may be shown as

 

  

τ´ µL ___ n* – n*A = â•‰ â•‰â•¯_____ â•¯ â•¯ â•¯â•‰â•¯ â•‰â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯â•¯â•‰(2λ – 1). τ´ – τ ασ

(10.11)

If Foreign is the smaller country (i.e., λ > ½), it will attract more service firms by utilizing communications networks. This outcome implies that producers prefer producing in the country next to the larger country in order to take advantage of time zone differences. This effect may be interpreted as a variant of the home market effect, which is emphasized in the trade literature. Figure 10.2 helps to illustrate this effect. The 45º line and the downward sloping curve show the relationship between relative country size and the relative number of products in autarky and in trading equilibrium, respectively. The latter indicates that a relatively small country will have a more than proportional number of service firms in the trading equilibrium (see the upward arrow in

n*/n The 45° line

1 n* t � t(1 � L)/L � n t'(1 � L)/L� t

O

Figure 10.2Â€Â€

t/t'

1

t'/t

(1 � L)/L

Trade with time zone differencesâ•‡â•‡ 95 Figure 10.2). Although this result depends critically on the assumption of delivery costs (see eq. (10.1)), it demonstrates the idea that the utilization of communications networks induces dramatic change in service trade as firms take advantage of time zone differences, which has not appeared in the existing literature. Several remarks are in order. First, let us consider what happens if both countries are located in the same time zone (i.e., t = t´). In this case, the number of services does not change with the opening of trade. However, since each country produces a different range of services, intra-industry trade in services occurs. Note that, as is well documented in the new trade theory literature, this type of intra-industry trade in services is driven by the combination of product differentiation and increasing returns technology. Next, let us consider the interaction between the degree of product differentiation and time zone differences. From eq. (10.11), it is clear that the larger the degree of product differentiation becomes (i.e., the smaller σ is), the bigger the change in production structure that results from opening trade (i.e., the larger n* – n*A becomes). This implies that, as services become more differentiated, more firms take advantage of time zone differences and Home’s service imports increase. The reason for this may be explained by the fact that more firms choose to locate in Foreign, which reduces the demand for each service produced there due to intensified competition. A higher degree of differentiation allows firms to charge higher prices (see eq. (10.5)) and, therefore, weakens this negative effect: more firms choose to locate in Foreign taking advantage of time zone differences. Specialization patterns are determined by the interaction between product differentiation and time zone differences. According to this point, assuming that there is no product differentiation, Marjit (2007) showed that each country completely specializes in a different stage of production. Thus, there is a strong connection between Marjit’s insightful analysis and our case with differentiated services. Before closing this section, it is worthwhile noting Home’s welfare gain from service trade liberalization, which can be measured by the change in the price index (see eq. (10.2)). Before trade, the number of Home varieties is n A, while it becomes n + n* with trade. Home’s price index in the trading equilibrium becomes 1/1 – σ

P = [(nt1 – σ + n*t´1 – σ )p1 – σ ]

.

Thus, the welfare gain due to opening trade is PA – P (i.e., a reduction in the price index), which becomes larger as the reduction in the delivery costs becomes larger (i.e., as t´ becomes smaller).

10.4Â€Â€Concluding remarks Both deeper market integration and advances in digital technology have driven a particularly large decrease in the cost of service provision. In this chapter, we propose a two-country monopolistic competition model of service trade that Â�captures the role of time zone differences. We have shown that the utilization of

96â•‡â•‡ Communications networks and time zones communications networks induces dramatic change in industrial structure due to firms taking advantage of time zone differences: service firms move away from larger countries in favor of small countries. Although these results are derived under the specific assumption that the delivery costs of imported services are lower than for domestically provided services, it appears that something similar to this will occur for the more general setting we consider here. The current analysis must be regarded as tentative. Hopefully it provides a useful paradigm for considering how time zone differences affect both the structure of service provision and international trade patterns. The model could be enriched with the inclusion of both FDI and outsourcing aspects in order to analyze the organization of firms.7

11 Growth with time zone differences

11.1Â€Â€Introduction In recent decades, trade in many kinds of intermediate goods and services has increased between developed and developing countries. In particular, the offshoring of business services such as engineering, consulting, and software development, which do not require physical shipments of products, plays a major role in today’s world trade.1 The availability of the global high-bandwidth network infrastructure has increased the feasibility of reducing costs by going offshore. These changes have invited new types of business services trade which take advantage of time zone differences between countries. The semiconductor industry provides a prime example. According to Brown and Linden (2009, p. 87): Some chip companies with foreign design subsidiaries value the opportunity to design on a 24-hour cycle because of the enormous pressure to reach the market ahead of, or no later than competitors. One established U.S. chip company adopted a rolling cycle between design centers in the United States, Europe, and India. In other words, due to the communications revolution, time zone differences may become a primary driving force behind business services trade.2 It is increasingly recognized that the rapid growth of India is attributable to this kind of business service trade utilizing time zone differences.3 Related to these phenomena, Marjit (2007) examined the role of international time zone differences in a vertically integrated Ricardian framework. It has been shown that time zone differences emerge as an independent driving force of international trade besides taste, technology, and resource endowment.4 Yet to be determined is the dynamic effect of this kind of intermediate business services trade utilizing time zone differences. Based on casual empiricism, we believe that time-saving technological improvements (e.g., the utilization of communications networks such as the Internet) can trigger a series of events that leads to a permanent increase in productivity. In the existing literature on growth and trade, however, relatively few attempts have been made to address the effect of time zones on growth. This seems to suggest that the focus on trade involving

98â•‡â•‡ Communications networks and time zones different time zones should be accompanied by a focus on its effect on growth. The main purpose of this study is to illustrate, with simple growth theory, how a time-saving improvement in business services trade benefiting from different time zones can have a lasting impact on productivity. For these purposes, following Acemoglu and Ventura (2002), we propose a simple two-country AK model of intermediate services trade that captures the role of time zone differences.5 Two countries (Home and Foreign) are assumed to be located in different time zones and there is no overlap in daily working hours. The key assumption is that domestic business services production requires one workday and that products are ready for sale after one workday: the delivery of domestic business services involves significant costs in terms of delay. In contrast to this, the utilization of communications networks allows for production in a foreign country where non-overlapping work hours and business services trade via networks enable a quick delivery and low shipping costs. For these reasons, imported services whose production benefits from time zone differences provide higher value than domestically produced services. Although this assumption is at odds with that of the standard model with trade costs, it captures the idea that final good producers would like to have services sooner rather than later.6 Based on the model outlined above, this study shows that an acceleration in intermediate business services trade using different time zones can have a permanent impact on productivity. The structure of this chapter is as follows. In section 11.2 we present the basic model. The impact of a time-saving technological improvement on growth is considered in section 11.3, followed by concluding remarks in section 11.4.

11.2Â€Â€The model There are two countries, Home and Foreign. They are located in different time zones and there is no overlap in daily working hours: when Home’s daytime working hours end, Foreign daytime working hours begin (Figure 11.1). In Home, the final good, Y, and the intermediate business services, X, are both produced under perfect competition. The final good is produced with capital, K, Home intermediate good, X�, and Foreign-produced intermediate good, X� according to7 (1 – α) (1 – α) ______ _____ â•¯ Y = Kα(Xâ•›) â•‰â•¯ 2â•¯ â•¯â•‰â•¯ (X� )â•‰â•¯ 2â•¯â•‰â•¯

(11.1)

There is trade in intermediate business services and no trade in the final good or capital. Home intermediate business services are produced with the final good one for one. The key assumption is that there are positive time costs for the delivery of intermediates. In order to capture this point, we assume that shipments of intermediates incur the “iceberg” effect of delivery costs: to sell one unit of Foreign intermediates in the Home market t � units must be shipped, with t � >1. Thus, the price of Foreign intermediates becomes t � times higher than its original price.

Growth with time zone differencesâ•‡â•‡ 99

Foreign’s workday

Home’s workday

Home Business services production Daytime Foreign

Final good production Nighttime

Daytime

Business services production

Services trade via networks

Figure 11.1Â€Â€

One can interpret t � as a measure of the inverse of the “delivery timeliness” of Foreign intermediate business services in the Home market: a lower value of t � implies a quicker delivery. As mentioned above, domestic intermediates are ready for sale after one workday, whereas imported intermediates whose production benefits from time zone differences are available sooner (see Figure 11.1). To parametarize the timing of delivery, we treat the utilization of communications networks (i.e., technological improvement) as a reduction in the delivery time of imported intermediates (i.e., a decrease in t )� . Let us denote the Foreign intermediates’ delivery timeliness before technological change as t 1� and that after change as t 2� . Then the following condition holds: t �1 > t > t 2� .

(11.2)

Note that this effect comes not from lower production costs in Foreign but from faster delivery. Let the final good, Y, be the numeraire. Then the unit price of good Y is equal to one, and this is also the unit cost of producing the Home intermediates. Since markets are perfectly competitive, the price of Home intermediates, X, is equal to its unit cost; thus it is also equal to one. In contrast to this, the price of Foreign intermediate business service is given by p.� Given these assumptions, the demand for intermediate business services is determined by profit maximization in the final goods sector; that is, the optimal X and X� maximize final sector profits: Kα (Xâ•›)â•‰â•¯ 2â•¯ â•¯â•‰â•¯(X � )â•‰â•¯ 2â•¯ â•¯â•‰â•¯– X – t p� X� � . (1 – α) _____

(1 – α) _____

The first-order conditions for this problem are:

100â•‡â•‡ Communications networks and time zones

 

1–α X = â•‰ _____ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰Y. 2



 

1–α _____ t p� X� â•¯â•‰Y. � = â•‰ â•‰â•¯ 2â•¯â•‰â•¯ 



Substituting back into equation (11.1) we obtain: – αâ•›) (1 – α) â•‰â•¯(1_____   â•‰â•¯ _____ α  â•‰â•¯1 – â•¯â•‰â•¯ â•¯â•‰ α K. Y = (t p� )� –â•›â•‰â•¯ 2α  â•¯â•‰â•‰ _____ 2

(11.3)

So even though the production function (11.1) has a diminishing marginal product of capital, we still have an AK model, with Y = AK, where the marginal product of capital, A, is given by _____ â•‰â•¯(1 –  α)â•¯â•‰â•¯ 1–α α â•‰â•‰ _____ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰ . 2

 

A = (t �p)� â•‰â•¯



(1 – α) – _____ â•¯ â•› 2α  â•¯

(11.4)

Note that A depends negatively on the relative price of Foreign intermediate business services.8 Now, let us assume a constant saving rate so that we can obtain the capital accumulation equation, namely . K = sY – δK Thus, Home’s growth rate depends positively on its saving rate according to . K

/K = sA – δ.

Next let us consider Foreign. Foreign’s production function for the final good is given by â•‰â•¯ 2  â•‰â•¯â•¯ Yf = Kf (Xf)â•‰â•¯ 2  â•‰â•¯(X�f) . (1 – α) _____

(1 – α) _____

α

(11.5)

Suppose that t f� measures the inverse of the “delivery timeliness” of Home intermediates in the Foreign market: to sell one unit of Home intermediates in the Foreign market, t f� units must be shipped from Home. As with Home, Foreign will import the amount t f� X�f of the Home’s intermediates, where t f� X�f is given by

 

1–α â•‰â•¯ â•¯â•‰tf� X�f = â•‰ _____ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰Yf. p� 2

1 __



(11.6)

By analogy to (11.3) we have _____ â•‰â•¯(1α– α)â•‰â•¯ (1 – α) (1 – α) 1 – α _____ _____ _____ Yf = (t f� )â•‰â•¯ 2α  â•¯â•‰â•¯(â•›p)� â•‰â•¯ 2α  â•¯â•‰â•‰ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰ Kf . 2

 



(11.7)

Growth with time zone differencesâ•‡â•‡ 101 As with Home, Foreign’s production function becomes Yf = Af Kf, where the marginal product of capital, Af, is given by _____ â•‰â•¯(1 –  α)â•¯â•‰â•¯ (1 – α) 1–α α _____ â•‰â•¯ â•‰ â•‰â•¯ â•¯â•‰ _____ 2α  â•¯ 2α â•¯ Af = (t f� ) ( p)� â•¯â•‰ . â•‰ â•‰â•¯ â•¯â•‰â•¯  2

 

(1 – α) _____



(11.8)

From (11.6) and (11.7): __ 1 1 – α â•‰â•¯αâ•¯ â•¯â•‰ 1–α (1 – α) ____ _____ â•‰â•¯ â•‰ â•¯ â•‰â•¯ 2â•¯   â•¯â•‰ Kf. t f� X�f = (t �f ) ( p)� â•‰â•‰ â•‰â•¯ â•¯â•‰â•¯  2

 

–â•›_____ â•¯ 2α  â•¯



(11.9)

From the Home export’s value condition (t p� X� � ), we have __ 1 1 – α â•‰â•¯αâ•¯ â•‰â•¯ â•‰â•¯(1 – α) â•‰ _____ t �pX� â•¯â•‰ K. â•‰ â•‰â•¯ â•¯â•‰â•¯  � = (t �p)� 2

 



–â•›_____ 2α  â•¯

(11.10)

Trade balance implies that t �p�X� = t f� X�f holds.9 Then, by equating the right-hand sides of (11.9) and (11.10), we can solve for the equilibrium relative price of Foreign intermediates: 1–α ____ â•¯ 2â•¯  â•‰â•¯

 t � 

t �f p� = â•‰ __ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰â•‰

Kα,

(11.11)

K where k is the relative capital stock: k ≡ /Kf. Now let us consider the steady state. From Home’s growth equation, we have _____ â•‰â•¯(1 – α)â•‰â•¯ (1 – α) _____ 1–α α /K = s(t �p)� –â•›â•‰â•¯ 2α  â•¯â•‰â•¯â•‰ _____ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰â•› – δ 2

. K.

 



(11.12)

â•‰â•¯ α  â•‰â•¯ (1 – α2) (1 – α)2 1–α ____ ______ ____ â•¯ â•¯ (t f� ) – â•‰â•¯4α  â•‰â•¯ k – â•‰â•¯ 2â•¯  â•‰â•¯â•›â•›– δ. (t �)– â•‰â•¯4α  â•‰ â•¯ (1 – α) _____

 

1–α _____ â•¯â•‰ Â€Â€Â€Â€Â€= sâ•›â•‰ â•‰â•¯ â•¯â•‰â•¯  2



From the analogous Foreign growth equation, we have . Kf

_____ â•‰â•¯ 2α  â•¯â•‰â•¯ â•‰â•¯(1 – α)â•‰â•¯â•¯ 1–α α _____ /Kf = sfâ•›â•‰ â•›â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰ â•‰ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰ – δ t f� 2 (1 – α) _____

     p� __



(11.13)

2 2 1 – α â•‰â•¯ α  â•¯â•‰â•¯ –â•›____ 1–α â•‰â•¯(1 – αâ•›  )â•¯â•‰â•¯ –â•›_____ â•‰â•¯(1 – α)  â•¯â•¯â•‰ ____ _____ â•¯â•‰ (t f� ) 4α (t �) 4a â•›k â•‰â•¯ 2â•¯  â•‰â•¯ – δ. Â€Â€Â€Â€Â€Â€= sf â•‰ â•‰â•¯ â•¯â•‰â•¯  2

 

(1 – α) _____



It follows that the growth rate of the relative capital stock, k, is just the differen. . tial growth rate K/K – Kf/Kf . Equations (11.12) and (11.13) imply

102â•‡â•‡ Communications networks and time zones â•‰â•¯ a  â•‰â•¯ 2 2 2 (1 – αâ•›2) 1–α 1–α – ____ – â•‰â•¯____ â•‰â•¯(1 – αâ•›  )â•¯â•‰â•¯ – _____ â•‰â•¯(1 – α)  â•¯â•¯â•‰ ____   â•¯ â•‰â•¯ – _____ â•‰â•¯(1 – α)  â•¯â•¯â•‰ ____ â•‰ s(t �) â•› 4α (t f� ) 4a k – â•‰â•¯ 2â•¯  â•‰â•¯– sf (t f� ) â•› 4α (t �) â•› 4a kâ•›â•‰â•¯ 2â•¯  â•¯â•‰â•¯â•‰. (1 – α) _____

 

1–α _____ / = â•‰ â•‰â•¯ â•¯â•‰â•¯  â•¯â•‰

. k k

2



(11.14)

This is a stable ordinary, differential equation with the unique steady state __ â•‰â•¯1â•¯â•‰â•¯ α â•‰â•¯____ â•¯ t �f 2 1 – â•¯α â•‰ __ k* = â•‰ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰ â•‰ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰ , sf t�

      s __

(11.15)

where an asterisk is used to denote the steady-state value of a variable. Substituting this back into (11.11), one can obtain the steady-state relative price of foreign intermediates: __ â•‰â•¯1â•¯â•‰â•¯ α s ____ t f� 2 1 – α â•‰ __ â•¯   â•¯ __ p� = â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰â•‰ â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰ .

*

 s   t �  f

(11.16)

Substituting (11.15) and (11.16) into (11.4) and (11.8), one can obtain the steady state marginal productivity of capital: 1–α sf _â•¯12â•¯â•¯â•‰ â•›____ __ A* = â•‰ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰â•‰ (t �t f� )– â•‰â•¯4α  â•‰â•¯, s

  

(11.17)

  

(11.18)

1–α s __12â•¯â•‰â•¯ â•›____ __ Af* = â•‰ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰â•‰â•¯ â•¯ (t �t f�)– â•‰â•¯4α  â•‰â•¯ , sf

11.3Â€Â€The impact of a technological advance in communications networks Now let us consider the impact of a time-saving technological advance in communications technologies, which is captured by a reduction in one country’s delivery cost. Suppose that the value of t � decreases from t 1� to t 2� (see (11.2)), while t �f remains unchanged. This implies that the final good producers in Home could utilize imported intermediates X� more quickly. From (11.17) and (11.18) it may be shown that, in the new steady state, both countries experience an increase in the marginal productivity of capital at the same rate. Proposition 11.1: A decrease in one country’s delivery cost for imported intermediates increases both countries’ marginal product of capital. Let us consider this proposition more precisely. From (11.4), other things being equal, a lower t � will tend to cause faster capital stock growth in Home. Since Home final good producers can use imported Foreign intermediates more quickly, the demand for them rises. On the contrary, the Foreign demand for Home intermediates, X�f, will not grow as fast as the Home demand for Foreign intermediates. Thus, the relative price of Foreign intermediates p� must increase

Growth with time zone differencesâ•‡â•‡ 103 so as to preserve the trade balance. This “terms-of-trade effect” will tend to bring Home’s growth rate down (Acemoglu and Ventura 2002). In Foreign, this “terms-of-trade improvement” triggers faster capital stock growth: via changes in the terms-of-trade, the effect of one country’s technological improvement will be transmitted to the other country. This effect works to stabilize world growth: growth rates of K and Kf will approach each other. Our result suggests that one country’s time-saving technological improvement, which induces firms to take advantage of time zone differences, will also boost the other country’s permanent growth. Let us suppose that Home is a developed country, while Foreign is a developing country. Our result suggests that time-saving technological improvement in the developed country, which then requires more intermediates made with the benefit of time zone differences, triggers faster growth in the developing country via improved terms of trade.

11.4Â€Â€Concluding remarks This chapter highlights the role of business services trade benefiting from time zone differentials as a driving force behind growth. It is shown that an acceleration in intermediate business services trade involving production in two time zones can have a permanent impact on productivity. Even more noteworthy is the finding that, via terms-of-trade improvements, the country without technology improvement will also attain faster economic growth. Although these results are derived under the specific assumptions that markets are perfectly competitive and the range of intermediate business services is exogenously given, it appears that a more general setting would yield similar results.

Part III

Network effects and switching costs

12 Direct network effects

12.1Â€Â€Introduction1 The rapidly growing connectivity of individuals and organizations achieved through improved communications networks (e.g., the Internet, mobile telephone networks, and satellite communications systems) has allowed a consequent increase in the flow of business transactions. These physical networks are often characterized by the existence of strong direct network effects: the more people who use them, the more useful they are to any individual user.2,3 Accordingly, sophisticated and well-connected country-specific networks have become recognized as the “competitive weapons” with which battles for comparative advantage are won. In his recent bestselling book The World Is Flat, Thomas Friedman argues as follows: Information technologies are important not only because they are big global businesses in and of themselves, but also because they are critical to advancing productivity and innovation.â•›.â•›.â•›. The more you connect an educated Â�population to the flat world platform in an easy and affordable way, the more things they can automate, and therefore the more time and energy they have to innovate. (Friedman, 2006, p. 350) Friedman also highlights the importance of producers in knowledge-based, hightech industries, such as the consulting, financial services, software, and marketing industries. The seminal contribution on the role of network effects is by Katz and Shapiro (1985), who analyzed oligopolistic competition between providers of network services.4 However, as their model is based on a closed market for a consumption good, the role of direct network effects as a determinant of trade patterns is downplayed in the analysis. Since such effects are often observed in the world economy, it seems important to explore the relationship between direct network effects and trading opportunities in the open economy setting. As its primary contribution, this chapter examines how the direct network effects of communications activities and trading opportunities interact to determine

108â•‡â•‡ Network effects and switching costs the trade patterns between countries. I also emphasize an important concept related to direct network effects – Interconnectivity – which allows users of a network to communicate with users of other networks.5 For these purposes I construct a twocountry, three-sector model of trade with country-specific communications networks. It will be shown that the good which requires network services is exported by the country with interconnected networks. The main result of this chapter, which captures the importance of interconnectivity of networks as a determinant of comparative advantage, has not appeared in the existing literature on trade theory under increasing returns, which only emphasizes the size of countries. The structure of this chapter is as follows: In section 12.2 I present the basic model. The nature of the trading equilibrium is considered in section 12.3. Section 12.4 explores several directions in which the model could be extended and section 12.5 offers concluding remarks.

12.2Â€Â€The model Consider a world economy consisting of two countries, Home and Foreign. There are two goods: a primary commodity which is produced only by labor and a knowledge-based, high-tech product which is produced with both human capital and communications services. Communications services are assumed to be provided by country-specific network service providers. The n identical Â�providers in each country are Cournot competitors. Providers are indexed by label i (i = 1, …, n). Let xi denote the size of the i-th provider (i.e., the number of subscribers), yi denote the size of the network with which the i-th provider is n associated, and z denote (z = â•‰ â•⁄ â•¯â•‰iâ•›â•‰â•¯=1 xi) the total number of network users. For example, when provider 1 and provider 2 are interconnected,

 

y1 = y2 = x1 + x2. Let the high-tech product be the numeraire and p indicate the relative price of the primary good. The primary good is produced under constant returns technology; units are chosen such that its unit input coefficient is unity. Each country is populated by a continuum of workers with population L. Each worker is endowed with one unit of labor and some level of human capital for the production of the high-tech product, which is measured by index r. The values of r are uniformly distributed over the interval [0, L]. Each worker’s Â�productivity is also affected by the level of direct network effects, vy ei, where v (v ≤ 1) is a valuation parameter and y ei is the worker’s expectation of the size of the (i-th) network. The v term captures gains through increased information flow between individuals: if more workers join the network, each worker can collect information more efficiently. It is simply assumed that a type-r worker can produce r + vy ie units of the high-tech product. Workers have the choice of either supplying labor for the production of the primary good or becoming suppliers of the high-tech product, and workers will become the latter only if they connect to a communications network. To connect

Direct network effectsâ•‡â•‡ 109 to the i-th provider’s network, each worker must pay a connection fee, fi , in exchange for unlimited access up to the maximum throughput of their particular connection. In other words, fi may be interpreted as the price of the i-th provider’s services. A type-r worker chooses to connect to the network for which r + vy ei – ( fi + p)

(12.1)

is the largest. This may be interpreted as follows. If r + vy ei – fi ≥ p holds for a particular worker, that worker pays the connection fee and starts to produce the high-tech product. However, if r + vy ie – fi < p holds, that worker chooses not to connect to the network and produces the primary good instead. As p rises, more workers choose not to connect to the network. Thus, one can interpret fi + p as a connection fee including the outside option. In equilibrium, providers i and j will both have a positive number of subscribers only if ( fi + p) – vy ei = ( fj + p) – vy ej ,

(12.2)

where ( fi + p) – vy ei is the connection cost adjusted for network size.6 Let Φ denote the common value of this cost. For a given value of Φ, only those workers for whom r > Φ become producers of the network good. Given the uniform distribution of r, there are L – Φ workers who choose to connect to the networks. Thus, if the total number of network users is z, z = L – Φ holds. Then, by substituting Φ = ( fi + p) – vy ei into this, we obtain the condition for the connection fee: fi = L – p + vy ei – z.

(12.3)

To simplify the analysis, I assume that the production cost for each provider is equal to zero. Thus, the i-th provider’s profits are π i = xi fi = xi (L – p + vy ei – z).

(12.4)

Each provider chooses its optimal number of subscribers by differentiating Â�equation (12.4) with respect to xi.

110â•‡â•‡ Network effects and switching costs Before turning to providers’ behavior, let us consider the equilibrium supply level of the high-tech product. By equations (12.1) and (12.3) a type-r worker can produce r + z + f + p – L units of product. Furthermore, only those workers for whom r is greater than L – z join the network, while the others choose to produce the primary good. Integrating all workers who do connect to the Â�networks, we can obtain the total output of the high-tech product:

 

  

L z2 __ S(z) = â•‰ â•¯ â•‰â•‰â•¯ (ρ + z + f + p – L)d ρ = â•‰ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰+ (f + p)z. L–z 2

(12.5)

We can interpret this as the supply function of the high-tech product. This function is represented by OS in Figure 12.1(b). As the total number of network users becomes larger, the average productivity of each high-tech product supplier rises: [S(z)/z]' > 0. This is shown as lines OA and OA' in Figure 12.1(b). Each country thus has a supply function that exhibits increasing returns to the size of the networks. There are two sources of these gains: (1) as more workers join the networks and the total number of subscribers increases, each infra-marginal worker can attain higher productivity through intensified network effects; and (2) through these network externalities, each service provider chooses to set a lower connection fee, which further attracts more workers. More noteworthy is that, in terms of income inequality between sectors, as the size of the networks becomes larger, income inequality between sectors increases.7 Depending on the interconnectivity between providers, several cases can emerge as the production equilibrium. The following subsections discuss two special cases: fully interconnected networks and unconnected networks. The case of interconnected networks Let us assume that n providers are fully interconnected.8 A user who connects to one network can communicate with users of other networks. Interconnectivity expands the size of each network to the total membership of all providers. This raises the productivity gains enjoyed by a worker who subscribes to only one provider’s network because network effects depend on the total size of the network (i.e., z = x1 + … + xn). Equation (12.4) becomes π i = xi fi = xi (L – p + vy ei – z). Maximizing this with respect to xi, we obtain xi = L – p + vz e – z. Imposing the requirement that in equilibrium workers’ expectations are fulfilled (fulfilled expectations equilibrium), ze = z = nx holds. Then we obtain the Â�equilibrium number of subscribers for each provider:

Direct network effectsâ•‡â•‡ 111 L � p � vy, [(n � 1)z]/n (a) N

L � p � vz L � p � v (z /n)

L�p

Total number of users O

z1

zU Output level

(b) S � (z ^2/2) � (f � p)z

A' A Total number of users O

zU

z1

Figure 12.1Â€Â€Industry equilibrium.

L–p x = _________ â•‰â•¯ â•¯â•¯â•‰. â•¯ n + 1 – nv

(12.6)

By summing equation (12.6) over all providers, we obtain the total network size as a function of the relative price of the high-tech product (1/p).

  

1 n(L – p) I´ __ _________ â•¯ â•¯â•¯ â•‰, z > 0, z I â•‰ â•‰â•¯ â•¯â•‰â•¯ â•‰= â•‰â•¯ p n + 1 – nv

(12.7)

112â•‡â•‡ Network effects and switching costs where superscript I denotes the fulfilled expectations equilibrium value when the networks are fully interconnected. The equilibrium is depicted in Figure 12.1(a). The horizontal axis shows the total size of the network, z, while the vertical axis shows the values of L – p + vz and [(n + 1)z]/n. Equilibrium is obtained at an intersection of two curves: line ON represents [(n + 1)z]/n while the other curve represents L – p + vz. As p becomes smaller, the curve will shift upward, which results in a larger total size of the network. The case of unconnected networks Next, let us consider the case in which n providers are not connected to each other. Subscribers on one network cannot communicate with those on the other networks. In this case, yi = xi holds. If there exists a symmetric equilibrium, x = z/n holds. Thus, instead of (12.7) we obtain

  

1 n(L – p) U´ zU â•‰ __ â•‰â•¯ â•¯â•‰â•¯ â•‰= â•‰â•¯________â•¯ â•¯â•¯ â•‰, z > 0, p n+1–v

(12.8)

with superscript U denoting the equilibrium value of the unconnected networks. This case is represented by the dotted curve in Figure 12.1(a). Since network externalities are smaller than in the case of interconnection, the equilibrium total size of the network, zU, also becomes smaller than z I. With these figures we obtain the supply curves of the high-tech product (Figure 12.2). The supply curve of the country with interconnected networks is located to the right of the country with unconnected networks.9

12.3Â€Â€The impact of trade liberalization Suppose that the only difference between two countries is the interconnectivity of the country-specific communications networks. Without loss of generality, Home is assumed to have interconnected networks while Foreign has unconnected networks. In addition, let each country have the same demand function for the high-tech product, D(1/p) (D' < 0) which is shown as a downward sloping curve in Figure 12.2.10 Note that z I > z U (S > S *) holds.11 Let us define the export supply functions of the high-tech product:

        

  

1 1 1 E â•‰ __ â•‰â•¯ â•¯â•‰â•¯ â•‰≡ S â•‰zI â•‰ __ â•‰â•¯ â•¯â•‰â•¯ â•‰â•¯ â•‰– D â•‰ __ â•‰â•¯ â•¯â•‰â•¯ â•‰, p p p

  

     

  

1 1 1 E * â•‰ __ â•‰â•¯ â•¯â•‰â•¯ â•‰≡ S * â•‰z U â•‰ __ â•‰â•¯ â•¯â•‰â•¯ â•‰â•¯ â•‰– D â•‰ __ â•‰â•¯ â•¯â•‰â•¯ â•‰. p p p

(12.9) (12.10)

Autarky equilibrium requires that E = E * = 0. Thus, from (12.9) and (12.10), Home has the lower autarky price for the high-tech product: 1 __ 1 __ â•‰â•¯ â•¯â•‰< â•‰â•¯ *â•¯â•¯â•‰â•›â•¯. p p

Direct network effectsâ•‡â•‡ 113 Relative price of the high-tech product (1/p) Supply curve with unconnected networks

(1/pU ) (1/pT )

Supply curve with interconnected networks

(1/p1 )

Demand curve [D (l /p)]

O

Demand/supply levels of the high-tech product (S )

Figure 12.2Â€Â€Impact of trade integration.

Now suppose that Home and Foreign open their goods markets and have a trading relationship. The opening of trade provides an opportunity for entry into Home’s high-tech product sector because, with the expanded network size, the average productivity of Home workers is much higher than that of Foreign workers. Furthermore, as trade opens and 1/p rises, more Home workers choose to subscribe to the networks. From their viewpoint, producing the primary good becomes less attractive.12 At the same time, as 1/p* falls, producing the high-tech product becomes less attractive in Foreign. Thus, the scale of Home (interconnected) networks will expand while Foreign (unconnected) networks will contract. The differences in the network sizes will be reinforced by this entry–exit process. In Home, additional entry of new workers enhances exports of the hightech product: E' (1/p) > 0. Through these mechanisms, the circular relationship between network expansion and trade creation continues. That is, there will be a cumulative process in which the opportunity for trade (i.e., an increase in price) brings about the opportunity for larger networks, and the increased sizes of the networks promote (through intensified network effects) exports. This process

114â•‡â•‡ Network effects and switching costs will continue until the price differential between countries disappears. From (12.9) and (12.10), the trading equilibrium price (1/pT ) is determined by the following condition:

  

  

1 1 __ __ E â•‰ â•‰â•¯ Tâ•¯â•¯â•‰â•¯ â•‰– E* â•‰ â•‰â•¯ Tâ•¯â•¯â•‰â•¯ â•‰= 0. p p

(12.11)

Proposition 12.1: A comparative advantage in the high-tech product is held by a country with interconnected networks. If the two countries commence free trade from autarky, the country with interconnected networks incompletely specializes in the high-tech product and the country with unconnected networks incompletely specializes in the primary good. Note the impact of trade on income inequality between sectors within each country. Since productivity in the primary good sector remains constant (i.e., one unit of labor produces one unit of the primary good), we only have to concentrate on the productivity in the high-tech product sector. As I have shown in the previous section, the size of the networks positively affects productivity. Since (1/p) < (1/pT ) < (1/p* ) holds, the size of the Home network expands [z(1/pT ) > z(1/p)] while the Foreign one contracts [z*(1/pT ) < z* (1/p*)]. This change raises the Home high-tech sector’s productivity, so we can say that Home’s income inequality between sectors becomes greater with the opening of trade. Similarly, we can say that Foreign’s income inequality between sectors becomes smaller as the result of trade. Proposition 12.2: International trade increases inequality in the country that exports the high-tech product and reduces inequality in the country that exports the primary good.

12.4Â€Â€Discussion In this section I describe two directions in which the model could be extended. First, rather than trade between a country with fully interconnected networks and a country with unconnected networks, consider trade between two countries in which the networks are partially interconnected. Analyses in previous subsections reveal that the total size of the network under autarky determines comparative advantage. For illustrative purposes, assume that Foreign networks remain unconnected. Even if only provider 1 and provider 2 in Home are fully interconnected (i.e., y1 = y2 = x1 + x2) and the remaining n – 2 providers are unconnected, the size of Home’s network is larger than that of Foreign’s due to intensified network effects between provider 1 and provider 2. As in the previous section, Home becomes a net exporter of the high-tech product. Since there are various types of partial interconnection, formal modeling of trade under partially connected networks is beyond the scope of this chapter. Thus, there is room for further investigation.

Direct network effectsâ•‡â•‡ 115 Second, let us consider the endogenous formation of interconnected networks. In analyzing this, I will look at each provider’s change in profits, ∆π ≡ π I – π U, where π I (resp. π U) represents each provider’s profits in the case of interconnected (resp. unconnected) networks. In addition, I assume that there is a fixed cost for interconnection, f, which each provider must pay before interconnection. Substituting equilibrium output levels into the profit function (12.4), we can calculate each provider’s equilibrium profits as L–p 2 _________ â•¯â•¯â•‰â•¯â•¯ â•‰ , π I = â•‰ â•‰â•¯ n + 1 – nv

 



L–p 2 ________ â•‰â•¯ â•‰ . π U = â•‰ â•‰â•¯ â•¯â•¯â•¯ n+1–v

 



Thus, the change in profits becomes ∆π = (L – p)2 [(n + 1 – nv)–2 – (n + 1 – v)–2] > 0. Note that both the population size (L) and the magnitude of network effects (v) positively affect this change, while the number of providers (n) negatively affects it. Incentives for interconnection depend on the relationship between π and f. If π > f holds, each provider chooses to connect and interconnected networks emerge. If π < f holds, however, networks remain unconnected. This result has important policy implications. Through subsidization of the fixed cost of interconnection, one country may acquire a comparative advantage in high-tech products.13 Further research should focus on these policy implications.

12.5Â€Â€Concluding remarks This chapter highlights the role of direct network effects as a driving force behind trade in knowledge-based, high-tech products. It should be emphasized that differences in connectivity among country-specific communications networks determine the comparative advantages of countries. When two countries are endowed with equal amounts of labor, the country with connected networks can attain higher productivity with its superior information-handling capabilities. This outcome differs from results obtained from trade models with increasing returns and imperfect competition. In those models, a country with either a larger factor endowment or a larger domestic market acquires a comparative advantage in the good that is produced under increasing returnsto-scale technology.14 The current model suggests, however, that even a

116â•‡â•‡ Network effects and switching costs smaller country can acquire a comparative advantage in a high-tech product via the utilization of interconnected networks. What really matters is interconnectivity rather than country size. More noteworthy is that there is a circular process between network expansion and trade creation which further affects income inequality within each country.

13 Indirect network effects

13.1Â€Â€Introduction1 The proliferation of trade liberalization through both economic integration (e.g., the European Union) and preferential trade agreements (e.g., NAFTA) has spawned a vast literature on the implications of trade liberalization. Since liberalization often provides an opportunity to acquire varieties of products not available from domestic producers, welfare gains via increased product diversification are emphasized in the literature.2 As yet, however, the cases of “hardware/Â� software” systems (i.e., hardware devices and the varieties of complementary software products) are downplayed in the trade literature. In other words, little attention has been paid to the implications of trade liberalization in the presence of products with indirect network effects. Indirect network effects exist when the utility of consumers is increasing in the variety of complementary products available for an electronic hardware device. Examples of such devices include personal computers, video cassette recorders, and consumer electronics products. In systems that pair hardware with software, an indirect network effect arises because increases in the number of users of hardware increase the demand for compatible software and hence the supply of software varieties. Since larger and more integrated markets often provide greater product variation, these characteristics affect the degree to which indirect network effects work. Despite the fact that many industries have indirect network effects that are supported by trade liberalization, the literature on indirect network effects is almost exclusively focused on a closed economy.3 Because the role of indirect network effects is amplified in the globalized world, it seems important to explore the impact of trade liberalization in the presence of products with indirect network effects.4 As our primary contribution, we examine how trade liberalization affects production structure in the presence of indirect network effects. For these purposes we construct a simple, two-country model of trade with two incompatible hardware technologies which is an extension of Church and Gandal’s (1992) closed economy model. We modify their approach to include aspects of trading economies such as intra-industry trade flow of complementary software products and gains/losses from trade. It is shown that, given that two incompatible hardware

118â•‡â•‡ Network effects and switching costs devices exist before trade liberalization, trade liberalization may reduce the variety of hardware devices. It is also shown that, if the variety of hardware devices is reduced by trade liberalization, some consumers are made worse off by trade. The current analysis intends to explain the recent situations where increased intra-industry trade of software products and intensified competition among incompatible systems (e.g., Blu-Ray Discs and HD DVD) may leave some early adopters stranded with abandoned incompatible equipment.5 It is important to note that the result that some consumers are made worse off by trade is not new in trade literature, as Heckscher–Ohlin and other competitive models show.6 However, our results are derived from a non-competitive and increased intra-industry trade setting, which usually emphasizes mutual gains via intra-industry trade. It is also important to note that we are using a Nash equilibrium concept, in which equilibrium outcomes are typically Pareto inefficient: this point is emphasized in duopoly trade models.7 However, this point is also downplayed in an intra-indutry trade setting. The main result of the current study, which illustrates the possibility of loss from trade via increased intra-Â� industry trade, has not appeared in the existing trade literature. This chapter is organized as follows. Section 13.2 describes both consumer preferences and technologies. Section 13.3 describes the basic model and derives an autarky equilibrium. Section 13.4 considers the impact of trade liberalization. Section 13.5 offers concluding remarks.

13.2Â€Â€Consumer preferences and technology Suppose that there are two countries, Home and Foreign, and that they are identical with regard to tastes, size, and technology.8 In each country there are three types of goods: hardware, a large variety of software products, and the outside good. We assume that there are two hardware technologies in both countries: Hardware 0 and Hardware 1. We also assume that the hardware technologies are incompatible: software written for one hardware will not work with the other’s. The characterization of the two hardware technologies is exogenous: each is located at the end-point of the unit line: let Hardware 0’s technology be at the left end point and Hardware 1’s technology be at the right end point. We denote the marginal cost of each hardware production by c. We further assume that the hardware technologies are non-proprietary and that they will be offered at marginal cost. In this and following sections, we consider the Home autarky situation. Following Church and Gandal (1992), consumer preferences over the combination of hardware and software are modeled as a Dixit–Stiglitz (1977) CES utility function. We assume that the distribution of the tastes of Home (Foreign) consumers is uniform along a line of unit length t ∈[0,1]. We normalize the total number of consumers in each country to 1. The preferences of a consumer of type t for system h are:

   nh



(1/θ)

U(t) = â•‰â•‰ â•¯â•⁄â•‰â•¯â•‰ â•‰(x hi )θ   â•‰ â•¯

iâ•›=1

+ ϕ – k | t – h |, 1/2 < θ < 1,

(13.1)

Indirect network effectsâ•‡â•‡ 119 where nh is the number of software products written for Hardware h (h = 0,1), x hi is the level of consumption of software product i written for Hardware h, σ ≡ 1/ (1 – θ) > 2 is the elasticity of substitution between every pair of software products, and we assume that ϕ > k. k is a measure of the degree of product differentiation between the hardware technologies: the greater k, the greater the degree of differentiation. The representative consumer who purchases Hardware h will maximize (13.1) n subject to the following budget constraint: â•‰ â•¯ â•‰â•‰â•‰â•¯i phix hi = e – c, where p hi is the price of software variety i for Hardware h, e is the total expenditure allocated to hardware and software, and c is the price (i.e., cost) of a unit of Hardware h. The solution to this problem consists of the following demand functions:

 

h

  nh

x hi = (e – c)( p hi)–σ/[â•‰ â•¯â•¯â•⁄â•‰â•¯â•‰ â•‰(p hj)1–σ ]. j=1

(13.2)

The indirect utility of a type-t consumer who purchases a system h is V(t) = nh1/(σ–1)(e – c)/ph + ϕ – k |t – h|.

(13.3)

The indirect utility function is concave in nh. The technology for the production of software is characterized by increasing returns to scale, since software creation typically involves fixed costs. We denote the constant marginal cost of software production for every product by b, and the software development cost by f. We assume that software firms are monopolistic competitors, and thus each product is priced at a mark-up over marginal cost b:9 p = bσ/(σ – 1).

(13.4)

13.3Â€Â€The model In this section, we specify a simple game in which the strategy of each software firm in a decision to provide software for either hardware, 0 or 1. The timing of the game is as follows.10 In the first stage software firms enter the industry. There is free entry into the software industry and software firms have rational expectations. Although there may be more than one equilibrium software configuration, we show that the free-entry number of software firms, N = n0 + n1, is unique, where nh is the number of firms providing software for Hardware h. In the second stage, software firms choose simultaneously which platform to provide software for. In the final stage, each consumer purchases either a Hardware 0 or a Hardware 1 system and some of the compatible software. We solve this problem backward. To obtain a better understanding of the model, we make extensive use of a new graphical exposition for equilibrium configuration. Let us begin with the final stage. Since we assume that the marginal costs (prices) of hardware and software are equal for both systems, consumers determine

120â•‡â•‡ Network effects and switching costs which hardware to purchase considering only their tastes and the amount of software available for each system. From (13.3), a consumer located at t purchases Hardware 0 if the following inequality holds: n01/(σ – 1) (e – c)/p + ϕ – kt > (N – n0)1/(σ – 1) (e – c)/p + ϕ – k(1 – t),

(13.5)

where use has been made of the equation n0 + n1 = N. Therefore, the location of the marginal consumer who purchases Hardware 0 is given by a function of n0, that is, – 1) – (N – n0)1/(σ – 1)](e – c)(σ – 1)/2kbσ + 1/2. t(n0) = [n1/(σ 0

(13.6)

And the first derivative of t(n0) is positive: dt(n ) _______________________________ [n (2 – σ)/(σ – 1) + (N – n0)(2 – σ)/(σ – 1)](e – c) _____   t´ (n0) ≡ â•‰â•¯ 0â•¯â•‰â•¯ â•¯= â•‰â•¯ 0 â•¯â•¯â•¯ â•¯â•¯â•‰> 0. dn0 2kbσ

(13.7)

This means that the share of Hardware 0 is increasing in the amount of software for it. It may also be shown that t(0) ≥ 0 and t(N) ≤ 1 ⇔ N 1/(σ-1) ≤ kbσ/[(e – c)(σ – 1)]

(13.8)

t´(N/2) ≥ 1/N ⇔ N 1/(σ –1) ≥ 21/(σ –1) kbσ/2(e – c).

(13.9)

and

Based on the above, we can draw the function t(n0) as shown in Figure 13.1,11 where curves A, B, and C correspond to the graph of t(n0) under each of the Â�following three cases: in case A, N1/(σ–1) ≤ kbσ/[(e – c)(σ – 1)]; in case B, kbσ/[(e – c)(σ – 1)] < N 1/(σ–1) < 21/(σ–1) kbσ/2(e – c); and in case C, N 1/(σ–1) ≥ 21/(σ–1)kbσ/2(e – c).12 Note that in cases B and C, t(n0) can reach 0 or 1, even if there are still two types of software. Since the market is of unit length (that is, 0 ≤ t ≤ 1), there exists a critical number of software firms for each type of hardware such that if the number of software firms for one technology exceeds the critical number, then all consumers purchase the dominant hardware. On the other hand, in case A, there are two types of consumers unless one hardware is standardized; no software for the other hardware exists.13 Now, let us turn to the second stage, where software firms simultaneously select the network for which to supply software. Given the marginal consumer, t, and the number of competing software firms (n0 or n1), the profit of a software firm writing software for Hardware 0 is π 0(t, n0) = t(p – b)x0 – f = t(e – c)/n0σ – f,

(13.10)

Indirect network effectsâ•‡â•‡ 121 t

C

B

1 A

1 2

O

N 2

N

Figure 13.1â•‡ The number of software and the marginal consumer.

and that for Hardware 1 is π 1(t, n1) = (1 – t)( p – b)x1 – f = (1 – t)(e – c)/n1σ – f,

(13.11)

where x1 = (e – c)/n1p. From these equations, it is easily derived that n > > __ __ __ π 0(t, n0) â•‰â•¯ â•¯â•¯â•‰π 1(t, n1) ⇔ t â•‰â•¯ â•¯â•‰â•¯ â•‰â•¯ 0â•¯â•¯â•‰. < < N

(13.12)

Based on the latter inequality, each firm considers whether t(n0) is greater than n0/N or not, and then chooses the network to supply. Next, turn to the first stage. At any equilibrium where two networks coexist, π 0(t, n0) = π 1(t, n1) must be satisfied. Therefore, t = n0 /N holds at the equilibrium and π 0 = π 1 = (e – c)/Nσ – f.

(13.13)

On the other hand, if all software firms provide software for one network at equilibrium, then (t, n0) = (1, N) or (t, n1) = (0, N) hold and π 0 = (e – c)/Nσ – f or π 1 = (e – c)/Nσ – f.

(12.14)

122â•‡â•‡ Network effects and switching costs Thus, the profit of each firm is independent of equilibrium software configurations, and the free-entry number of firms, N, is uniquely given by N = (e – c)/fσ from the zero-profit condition. Based on the foregoing argument, we may conclude that π 0 = π 1 = 0 holds for any pair (t, n0) on the dotted line in Figure 13.1, π 0 = 0 at (1, N), and π 1 = 0 at (0, 0), while π 0 (π 1) is positive (negative) at any pair above the line and vice versa. Based on the foregoing argument, we obtain the Nash equilibrium configurations as follows. In order for a configuration to be a Nash equilibrium, it must be impossible for a software firm to switch networks and increase its profit. In case A, the graph of t(n0) is drawn as curve A in Figure 13.1. So, there are three equilibrium candidates: (n0 = n1 = N/2), (n0 = N, n1 = 0), and (n0 = 0, n1 = N). Since

{

t(n0) > n0 /N â•…â•… if n0 < N/2,(167) < n0 /N â•…â•…â•… if n0 > N/2,

(13.15)

we may conclude that only symmetric equilibrium (n0 = n1 = N/2) is stable in the sense of a Nash equilibrium. On the other hand, in case C, the graph is drawn as curve C and

{

t(n0) < n0 /N â•…â•… if n0 < N/2,(169) > n0 /N â•…â•…â•… if n0 > N/2.

(13.16)

Therefore, only two equilibria, (n0 = N, n1 = 0) and (n0 = 0, n1 = N), are stable.14 Finally, in case B, the graph of t(n) is drawn as curve B and it is apparent from the discussion above that all three of the equilibria, (n0 = n1 = N/2), (n0 = N, n1 = 0), and (n0 = 0, n1 = N), are stable. So, we have the following lemma: Lemma 13.1: Depending on the parameter values, the following three cases emerge: Case A: If N1/(σ-1) ≤ kbσ/[(e – c)(σ – 1)], a unique symmetric equilibrium exists, (n0 = n1 = N/2). Case B: If kbσ/[(e – c)(σ – 1)] < N1/(σ-1) < 21/(σ-1) kbσ/2(e – c), three equilibria, (n0 = n1 = N/2), (n0 = N, n1 = 0), and (n0 = 0, n1 = N), exist. Case C: If N1/(σ-1) ≥ 21/(σ-1) kbσ/2(e – c), only two equilibria, (n0 = N, n1 = 0) and (n0 = 0, n1 = N), exist. Although the present result is the same as that stated in Church and Gandal’s (1992) closed economy model, we believe that our graphic exposition provides a better understanding of the equilibrium configuration. In addition, one major advantage of our graphic exposition is that it makes it easier to extend the analysis to the case of unequal preference distribution.

Indirect network effectsâ•‡â•‡ 123

13.4Â€Â€The impact of trade liberalization Now let us turn to the impact of trade liberalization. Trade liberalization between two identical countries implies one basic change: the total number of consumers becomes 2. This implies that the integrated market can support a larger number of software products: the total number of complementary software products changes from N to 2N. Since we have assumed away Ricardian comparative advantage, there is no incentive for inter-industry trade. Still, since each software firm specializes in a different range of products, an incentive for two-way trade of software products remains. Since consumers prefer to consume a wide variety of software products, trade liberalization may result in gains from product diversification. However, we have to check the changes in the variety of hardware. Depending on parameter values, several possible cases emerge. In order to highlight the interaction between indirect network effects and trade liberalization, let us examine the following two representative cases (these cases are summarized in Figure 13.2). The case of hardware differentiation First, let us assume that the following condition is satisfied: (2N)1/(σ–1) ≤ kbσ/[(e – c)(σ – 1)].

(13.17)

Note that this condition holds when the degree of hardware differentiation (k) is relatively large (or the degree to which indirect network effects exist is relatively low). Note also that this case arises when the absolute number of software products is relatively small. In this case, two types of hardware exist both before and after trade liberalization. Thus, no consumer changes his or her hardware and A

B

C

Differentiation

Standardization

N 1/(s � 1)

N 1/(s � 1)

(2N)1/(s � 1) kbs (e � c)(s � 1)

Figure 13.2â•‡ Equilibrium configurations.

(2N)1/(s � 1) 21/(s � 1)kbs 2(e � c)

124â•‡â•‡ Network effects and switching costs trade liberalization induces twice as many software varieties for each type of hardware: n0 becomes 2n0 and n1 becomes 2n1. From (13.3), this clearly increases every consumer’s utility. Proposition 13.1: Given that condition (13.17) holds, both types of hardware remain in the equilibrium and both countries gain from trade liberalization. Note that these gains correspond to those obtained from the “love-of-variety” approach to trade gains (e.g., Krugman 1979). Through trade liberalization, consumers in each country can obtain a wider variety of products, which results in mutual gains. The case of hardware standardization Next, let us assume that the following condition is satisfied:15 kbσ/[2(e – c)] ≤ N 1/(σ–1) ≤ kbσ/[(e – c)(σ – 1)].

(13.18)

In this case, while both types of hardware exist before trade liberalization, only one type of hardware remains after liberalization. In other words, intensified indirect network effects result in a reduced number of hardware varieties (2 rather than 1). For simplicity, let us suppose that only Hardware 1 remains after trade liberalization. In this case, some consumers have to switch from Hardware 0 to Hardware 1. While there are gains from the increased diversity of software available, there are losses from switching to the other network. The change in the indirect utility of a type-t consumer who switches to the other network is:16 ∆V(t) = [(41/(σ–1) – 1)(N/2)1/(σ–1)(e – c)(σ – 1)]/(bσ) – k(1 – 2t).

(13.19)

Note that the first term on the RHS represents the gains from software diversification while the second term on the RHS represents costs from increased disutility. Let us define a type-˜t consumer who is indifferent to switching hardware as follows: ˜t = (1/2) – [(41/(σ–1) – 1)(N/2)1/(σ–1)(e – c)(σ – 1)]/2kbσ.

(13.20)

Let us define the solution of 21/(σ–1) – 41/(σ–1) + 1 = 0 as σ ˜ . Then we can show that ˜t > 0 holds when σ > σ ˜: ˜t ≥ (1/2) – (41/(σ–1) – 1)/21+1/(σ–1)

{

= (21/(σ–1) – 41/(σ–1) + 1)/2σ/(σ–1) < 0 â•… if 2 < σ < σ˜ (175) > 0 â•…â•…â•‡ if σ > σ˜ Now we can state the possibility of losses from trade.

Indirect network effectsâ•‡â•‡ 125 Proposition 13.2: If condition (13.18) and σ˜ ≤ σ ≤ 3 are satisfied and Hardware 1 (resp. 0) dominates the integrated market, both countries’ consumers located at t ∈ [0,˜t ] (resp. t ∈ [1 – ˜t , 1]) are made worse off by trade liberalization. This implies that trade liberalization leads some consumers to “switch” to an other-dominated brand, thereby increasing disutility. Note that this case is highly contrasted with the cases of universal gains from intra-industry trade, which are emphasized in the literature on non-competitive trade.17

13.5Â€Â€Conclusions In this chapter, we examine how trade liberalization affects production structure in the presence of indirect network effects. For these purposes we construct a simple, two-country model of trade with incompatible hardware technologies. It is shown that, given that both hardware devices remain after liberalization, every consumer gains from trade (Proposition 13.1). It is also shown that, if the number of hardware varieties is reduced by trade liberalization, some consumers may be made worse off by trade (Proposition 13.2). It should be noted that competition in the integrated market is likely to lead to standardization on a single hardware/software system. The current analysis should be regarded as tentative. Hopefully it provides a useful paradigm for considering how indirect network effects (or hardware/ software systems) affect both the structure of production and the gains or losses from trade.

14 Switching costs

14.1Â€Â€Introduction1 In the literature on trade theory, many sources of trade gains under imperfectly competitive markets are widely discussed. In particular, in a single-period setting, pro-competitive gains from trade due to foreign firms’ entry into the domestic market have been studied extensively.2 It is well known that the entry of a costcompetitive (i.e., low-marginal-cost) foreign firm yields a highly competitive outcome. As yet, however, little attention has been paid to the implications of trade liberalization in the context of products with switching costs. In a model with switching costs, it is more costly for consumers (or wholeÂ� salers) to buy from one producer in one period and from another producer in the next.3 In the context of trade liberalization, switching costs include transaction and information costs for import wholesalers.4 Important transaction costs result from differences in languages and customs. If a wholesaler has been buying a good (e.g., steel) from a domestic firm and decides instead to buy it from a foreign firm, then the wholesaler must hire new personnel who are familiar with that country’s language and customs. Another transaction cost is that of negotiating a contract or agreement with the new supplier. Contracting costs with a new foreign supplier are usually higher than contracting costs with a domestic supplier. Switching costs are thus an important factor in any industry in which the product passes through a wholesaler’s hands.5 Although the vitality of industries characterized by switching costs is closely related to trade liberalization, the literature on trade liberalization is almost exclusively focused on products without switching costs. Since the role of switching costs is amplified in the globalized world, it seems important to explore the impact of liberalization in the trade of products with switching costs. As its primary contribution, this chapter examines how trade liberalization (i.e., the entry of a foreign firm into the domestic market) affects the behavior of a domestic monopolist in the presence of switching costs. For this purpose I construct a simple two-period market-entrance model with switching costs. It will be shown that, for the home country, there are always gains from a foreign firm’s entry. It will also be shown that a competitive environment in the second period

Switching costsâ•‡â•‡ 127 caused by the foreign entrant’s relatively low marginal costs is associated with a less competitive outcome in the first period because the domestic monopolist produces less. The latter result differs from one obtained in standard single-Â� period models of trade liberalization in that the inclusion of switching costs Â�drastically changes the impact of trade liberalization.

14.2Â€Â€The model Consider a two-period market-entrance game with homogeneous products and switching costs. A home firm is present in the domestic market in both periods, and producing output xt in each period t. A foreign entrant observes the home firm’s first-period output and enters the market in the second period with output y2. The firms’ products are functionally identical, i.e., we assume that they are undifferentiated except by switching costs. Demand in period t is ft (q), to be interpreted as the q-th consumer having reservation price ft (q) for one unit of either firm’s product in period t, net of any switching costs. Each consumer has a “switching cost” s, which we take as given, of buying either firm’s product for the first time. Products cannot be stored between periods. We assume no discounting. We assume Cournot equilibrium in the second period leading to market prices p2 and p *2 for the home firm’s and the foreign firm’s products respectively. Thus in the second period p *2 = f2 (x2 + y2) – s, p2 = f2 (x2 + y2), ifx2 ≤ x1, p2 = f2 (x2 + y2) – s, ifx2 > x1. In what follows, to simplify the argument, we assume a linear demand curve: ft (q) = a – bq. Firms have no fixed costs and have constant marginal costs. The home firm’s marginal costs are normalized to zero, while c* represents the foreign firm’s Â�marginal costs. Before moving to the trading equilibrium, let us briefly examine the equilibrium without the foreign firm’s entry. In this case, the home firm’s profit is represented by __ __ Πâ•‰ â•‰ â•¯= Πâ•‰ â•‰ â•¯1

__

+ Πâ•‰ â•‰ â•¯2 = (a – bx1 – s)x1 + (a – bx2)x2,

where Πt represents profits in period t. We can obtain the equilibrium output as _ _ 2a – s _____ â•‰xâ•‰1â•¯ = xâ•‰ â•‰ 2â•¯ = â•‰â•¯ â•¯ â•¯ â•¯ â•‰, 4b

(14.1)

128â•‡â•‡ Network effects and switching costs where an overbar indicates value without the foreign firm’s ___ the ___equilibrium ___ entry. Consumer surplus CSâ•‰ â•‰ â•¯= â•‰CSâ•‰â•¯1 + â•‰CSâ•‰â•¯2, total profits and welfare are given as follows: ___ ___ ___ (2a – s)2 _______ â•¯ â•¯ â•‰, CSâ•‰ â•‰ â•¯= CSâ•‰ â•‰ 1â•¯ + CSâ•‰ â•‰ 2â•¯ = â•‰â•¯ â•¯

(14.2)

__ __ â•‰ â•¯= Πâ•‰ Πâ•‰ â•‰ â•¯1

(14.3)

16b

__ (2a – s)2 _______ â•¯ â•¯ â•‰, + Πâ•‰ â•‰ â•¯2 = â•‰â•¯ â•¯ 8b

___ __ 3(2a – s)2 ________ â•‰ â•¯= â•‰CSâ•‰â•¯+ Πâ•‰ â•¯ â•¯ â•‰. â•¯ Wâ•‰ â•‰ â•¯= â•‰â•¯ 16b __

(14.4)

Now, let us move to the case with the foreign firm’s entry. In this case, the analysis is simplified by considering the firm’s second-period reaction curves. We write R( y2) for the home firm’s reaction curve if consumers have no switching costs, and R´(y2) and R*(x2) when consumers have a switching cost s. The emboldened line in Figure 14.1 is the home firm’s reaction curve given x1 > 0.

y2

R

R'

E

R*

y'

x1

Figure 14.1â•‡ Reaction curves.

x2

Switching costsâ•‡â•‡ 129 To derive it, we first recall that, for x2 ≤ x1 the home firm’s residual demand is f2(x2 + y2), whereas for x2 > x1 the residual demand is f2(x2 + y2) – s, as if all its consumers had to pay a switching cost s. The second-period Cournot–Nash equilibrium is at the intersection E. In this case, a small increase in x1 increases the home firm’s second-period output and decreases the foreign firm’s second-period output, i.e., dx2 ___

dy ___ â•‰â•¯ â•¯â•‰â•¯> 0, â•‰â•¯ 2â•¯â•‰â•¯< 0. dx1 dx1

Decreasing y2 raises the home firm’s second-period residual demand everywhere and so increases the home firm’s second-period profits. Therefore, the home firm chooses x1 at a higher level than if it simply maximized its long-run profits ignoring the effect of x1 on y2. In other words, the home firm can create a customer base x1 strategically in order to affect the second-period equilibrium. Considering Figure 14.1, the second-period equilibrium outputs become a – bx1 – c* – s ____________ â•¯ â•¯â•¯ â•‰. â•¯ x2 = x1, y2 = â•‰â•¯ 2b

(14.5)

The home firm’s total profits are Π = Π1 + Π2 = (a – bx1 – s)x1 + [a – b(x2 + y2)]x2.

(14.6)

Substituting (14.5) into (14.6) and maximizing yields the equilibrium output 3a + c* – s _________ â•¯ â•¯ â•‰, ˜x2 = ˜x1 = â•‰â•¯ â•¯ 6b

(14.7)

3a – 7c* – 5s ___________ ˜y2 = â•‰â•¯ â•¯ â•‰, â•¯ â•¯ 12b

(14.8)

where a tilde indicates the equilibrium value with the foreign firm’s entry. Consumer surplus and total profits are as follows: CS = CS1 + CS2 (9a – 5c* – 7s)2 (3a + c* – s)2 _____________ ___________ â•¯ â•‰â•¯ + â•‰â•¯ â•¯ â•‰ = â•‰â•¯ â•¯ â•¯â•¯ â•¯ 72b 288b 4(3a + c* – s)2 + (9a – 5c* – 7s)2 __________________________ = â•‰â•¯ â•¯ â•¯â•¯â•¯ â•¯â•¯â•‰, 288b (3a – c* + s)2 ˜ =Π ˜ 1 +Π ˜ 2 = ___________ Π â•‰â•¯ â•¯ â•¯ â•‰. â•¯ 24b

(14.9) (14.10)

130â•‡â•‡ Network effects and switching costs Since the welfare of the home country is equal to the sum of the consumer surplus and the profits of the home firm, welfare under the foreign firm’s entry may be shown to be 4(3a + c* – s)2 + (9a – 5c* – 7s)2 __________________________ â•¯ W˜ = â•‰â•¯ â•¯â•¯â•¯ â•¯â•¯â•‰. 288b

(14.11)

Using (14.1) and (14.7), one can obtain the change of the home firm’s output level by the announcement of the foreign firm’s entry: _ 2c* + s ______ ˜x1 – xâ•‰ â•¯ â•¯ â•‰> 0. â•‰ â•¯1 = â•‰â•¯ â•¯ 12b

(14.12)

It is important to note that anticipation of the foreign firm’s entry in the second period increases the home firm’s equilibrium output in both periods. Note that this result occurs because the home firm has a strategic incentive to create the customer base in order to affect the second-period equilibrium. Proposition 14.1: Anticipation of the foreign firm’s entry in the second period increases the home firm’s first-period output level. In other words, given that there are switching costs, the pro-competitive effect of the foreign firm’s entry (i.e., unilateral trade liberalization) emerges before the entry. This result seems to reinforce the argument for pro-competitive gains from trade liberalization, which was emphasized by both Brander (1981) and Markusen (1981). To see this point precisely, let us consider welfare changes by the foreign firm’s entry. Suppose that c* = 0 holds initially. In this case, welfare changes may be calculated as follows: __ 1 s 2 _____ __ ˜ c* = 0 – Wâ•‰ â•‰â•‰ 9â•‰  a – â•‰â•¯ â•¯â•¯â•‰â•¯â•¯â•‰ + 10s2â•¯â•‰> 0. W â•‰ â•¯= â•‰â•¯ â•¯ â•¯â•¯ 288b   3

(14.13)

˜ with respect to c*, one can obtain In addition, by differentiating W ˜ _____________ dW 6a + 82c* + 38s ___ â•¯â•¯â•¯ â•¯ â•‰> 0. â•‰â•¯ *â•¯â•‰â•¯= â•‰â•¯ dc 288b

(14.14)

Combining these two conditions, one can state the following proposition on welfare gains from the foreign firm’s entry: Proposition 14.2: Given that c* > 0 holds, there are always gains from the foreign firm’s entry. Before closing this section, it is worthwhile to note the impact of changes in the foreign firm’s marginal costs. Equation (14.7) implies the interesting impact of trade liberalization in the presence of switching costs.

Switching costsâ•‡â•‡ 131 Proposition 14.3: As the foreign entrant’s marginal costs increase, the home firm’s first-period output becomes larger. In other words, the more cost-competitive the foreign entrant, the lower the incentive to capture consumers in the first period (i.e., d˜x1/dc* > 0). This result differs from those obtained in trade models without switching costs. In those models, trade with cost-competitive foreign firms makes the market more competitive. In this model with switching costs, however, the promise of competitive market conditions in the future period makes the current period less competitive. The principle involved is that, since the motivation to capture consumers in the first period is to shift profits away from the foreign entrant in the second period, a less competitive domestic firm (which has a lower incentive to shift profits) will choose a lower output level in the first period.6

14.3Â€Â€Concluding remarks In a two-period market-entrance model with switching costs, it has been shown that the anticipation of the foreign firm’s entry increases the home country’s welfare. In addition, it has been shown that conditions which cause a more competitive environment in the second period (i.e., relatively low marginal costs for a foreign entrant) yield a less competitive outcome in the first period.7 The interaction between trade liberalization and firm behavior in the presence of switching costs is crucial: if the magnitude of switching costs is substantial, some of the pro-competitive gains from trade liberalization in the future period must be offset by a less competitive outcome in the current period. Throughout this chapter, we have concentrated on the case of unilateral trade liberalization: only the foreign firm’s entry into the home market was considered. The model could be enriched with the inclusion of multilateral trade liberalization: the home firm’s entry into the foreign market. Further research should focus on the comparison of these two cases.8

15 Foreign brand penetration

15.1Â€Â€Introduction The proliferation of trade liberalization through both economic integration (e.g., the European Union) and trade agreements (e.g., the WTO) has made foreign brand penetration a significant issue in many countries.1 Accordingly, many studies have examined the impact of trade liberalization on foreign brand penetration, typically using trade models of monopolistic competition which assume the existence of differentiated brands. The simplest models of monopolistic competition are built on the assumption that, due to trade liberalization, every foreign firm increases its exports. This implies that both the number of imported brands and the number of domestic brands remain unchanged by trade liberalization itself.2 In other words, the situation of gradual foreign brand penetration (i.e., a steady increase in the number of foreign brands) cannot be addressed. The past literature ignores one important aspect of real life: foreign producers and domestic sellers are often different entities. For example, cars are most often sold abroad by dealers who are nationals of the country where the cars are sold. In the Japanese apparel industry, companies such as C. Itoh and Mitsui have concentrated on licensing high-quality European and U.S. brands. In Â�particular, there was a large increase in the number of imported brands during the 1980s and 1990s. Related to this, Porter, Takeuchi, and Sakakibara (2000, p. 88) state:3 The more agreements the Japanese rivals signed, frequently with licensors based in the same countries, especially Italy, the more similar they became. As a flood of imported brands hit the Japanese market, their appeal waned. In addition, the unprecedented boom in licensed imports coincided with the peak of the bubble economy. The result: the race to sign licensing agreements ultimately destroyed industry profitability. Related to these phenomena, in a recent influential survey, Rauch (2001) argues that the difficulty of doing business across borders implies the importance of importers (i.e., trading intermediaries such as Japan’s sogo shosha), particularly for the trade of differentiated products.

Foreign brand penetrationâ•‡â•‡ 133 These examples seem to suggest that the focus on increased foreign brand penetration should be accompanied by a focus on domestic importers’ behavior. In other words, on the basis of trade costs, entrepreneurs often switch from providing domestic brands to providing foreign brands. The present study is designed to capture this aspect of global commerce. The main purpose of this chapter is to illustrate, with a simple trade model of monopolistic competition, how trade liberalization (i.e., a decline in trade costs) can affect domestic entrepreneurs’ decision of whether to provide domestic brands or foreign brands, and thus the degree of foreign brand penetration. Following Matsuyama (1995), I assume that there are two groups of differentiated brands, domestic brands and imported brands, each of which must be established and managed by entrepreneurs. Matsuyama assumed a closed economy and paid scant attention to the role of trade liberalization. In contrast, in this study I focus on the case of trade and examine the interaction between trade liberalization and entrepreneurs’ decision making. It is shown that, as trade costs decrease, more entrepreneurs choose to provide foreign brands. Furthermore, entrepreneurs’ switching behavior from domestic brands to foreign brands is shown to magnify the negative impact of trade liberalization on the profits of firms selling domestic brands. The main result of this chapter, which captures the relationship between the gradual shift of domestic entrepreneurs to foreign brands and foreign brand penetration, has not appeared in the existing literature. This chapter is closely related to the recent studies on foreign brand penetration. One of the important modes of foreign brand penetration is “brand name collaboration,” which entails domestic sellers using foreign competitors’ brand names to increase demand. In their seminal paper, Marjit, Beladi, and Kabiraj (2007) analyze this concept. They find that such an agreement is likely to occur between firms which are not “too far apart” in terms of brand reputation. Although the current model does not incorporate the aspects of brand name collaboration, it does shed light on foreign brand penetration from a different perspective. In addition, this study is related to the literature which emphasizes the role of fixed export costs (e.g., Romer 1994; Melitz 2003). From the viewpoint of exporters, the penetration of foreign markets involves significant fixed costs (e.g., the cost of advertising, setting service, and distribution networks). This chapter provides a complementary view from the standpoint of domestic importers. The structure of this chapter is as follows. In section 15.2 I present a basic trade model of monopolistic competition. In section 15.3, the impact of trade liberalization is considered. Concluding remarks are presented in section 15.4.

15.2Â€Â€The model Suppose that there are two countries, Home and Foreign. This discussion will concentrate on what happens in the Home (domestic) market. In Home, there are E individuals, each owning one unit of labor and N/E units of entrepreneurship. This implies that there are N entrepreneurs in Home.4 All individuals in Home have the same utility function over differentiated brands and a numeraire, good

134â•‡â•‡ Network effects and switching costs Y. Good Y is competitively produced under constant-returns-to-scale technology. Assume that the utility function is u = log C + y,

(15.1)

where C and y denote the sub-utility function for differentiated brands and the consumption of good Y, respectively. Suppose that there are two groups of differentiated brands: domestically produced brands with an aggregator denoted by h, and imported brands with an aggregator denoted by f. The sub-utility function and the corresponding price index for differentiated brands are: ____ ____ ε–1 ε – 1 ____   â•¯   â•¯â•‰ ε â•¯â•¯ C =  â•‰αh Châ•‰â•¯ ε â•¯â•‰+ αf Cfâ•‰â•¯ ε â•¯â•¯â•‰â•¯â•‰ε – 1 â•‰, ____ 1

P = [αâ•›hε P1h – ε + αâ•›fε P1f – εâ•›]â•‰â•¯1 –â•¯ε â•¯â•‰,

(15.2) (15.3)

where ε > 1 is the elasticity of substitution between groups, and Ci and Pi are the quantity and price indices for group i (i = h, fâ•›â•›). Note that αfâ•›/αh measures the relative preference for imported brands.5 Although the current model assumes horizontal product differentiation among brands, this parameter (αf/αh) captures brand differentiation across countries.6 Let e denote a Home consumer’s total expenditure on differentiated brands. Equation (16.1) may be written as u = log e – log P + y. Maximizing this with the budget constraint e + y ≤ I, where I denotes the individual’s income (which is the sum of her labor income and the income from her entrepreneurship), we obtain e = 1. That is, each individual spends e = 1 on differentiated brands. Thus, Home’s aggregate expenditure on differentiated brands is equal to the number of individuals, E. The quantity index for group i takes the Dixit–Stiglitz (1977) form ni σ–1 ____ â•‰â•¯σ – 1â•¯â•‰â•¯ Ci = â•‰â•‰ â•¯â•‰â•‰â•‰â•¯ ci ( j )â•‰â•¯ σ  â•¯â•‰â•¯d jâ•¯ â•‰â•› , i = h, f,

  



0

σ ____

(15.4)

where σ > 1 is the elasticity of substitution between brands within a group, ci ( j) is the amount of consumption of brand j, in group i, and [0, ni] represents the range of brands available in the marketplace. The corresponding price index for group i is:

 

ni

Pi = â•‰ â•‰ â•¯0â•‰â•‰â•‰â•¯ â•›pi ( j)

â•‰â•¯1 –â•¯σ â•¯â•‰ d jâ•¯â•‰ , i = h, f, 1 ____

1–σ

(15.5)

where pi(â•›â•›j) is the price of brand j in group i. The demand function for each brand j in group i satisfies7

 

(â•›â•›j) –σ p____ ci (â•›â•›j) = â•‰â•‰â•¯ i â•¯ â•¯â•‰â•¯ â•‰ Ci, i = h, f, Pi



(15.6)

Foreign brand penetrationâ•‡â•‡ 135

 α   P 

C α P ___ â•‰â•¯ hâ•¯â•¯â•‰= â•‰ ___ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰ â•‰ ___ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰ . ε

Cf

f

–ε

(15.7)

f

Equation (15.7) implies that the relative demand for group-h brands is positively related to the preference parameter (αh/αf) and negatively related to its relative price index (Ph/Pf). It is important to note that an increase in the number of imported brands (i.e., a reduction in the price index of group f ) triggers an increase in the relative demand for imported brands. In each group, differentiated brands are produced by monopolistically competitive firms. One of the central assumptions is that each firm must be established and managed by an entrepreneur. Each entrepreneur has to decide what type of brand to provide. There are two options: (1) to set up a domestic firm by hiring Home labor at wage rate wh and provide a domestic brand; or (2) to set up an intermediary and import a Foreign brand for Home consumers.8 In the second case, Foreign brands are assumed to be produced by hiring Foreign labor at a wage rate of wf.9 It is important to note that with the numeraire, good Y, being traded costlessly, its price must be the same in both countries. This ties down the relative wage rate: w ahy ___ â•‰â•¯ hâ•¯â•¯â•‰= ___ â•‰â•¯ â•¯â•¯â•‰, wf

afy

where aiy (i = h, f) is a unit labor requirement for good Y in country i. We can treat the wage rates in both countries as exogenous. In order to simplify the analysis, to produce one unit of any brand, one unit of labor is required. Given a Dixit–Stiglitz specification with constant elasticity σ and a wage rate wi, each firm in group i sets its mill price ρi as σâ•›w ρi = _____ â•‰â•¯ iâ•¯â•¯â•‰â•¯ , i = h, f. σ–1

(15.8)

Further assume that cross-border shipments of Foreign brands incur trade costs via the “iceberg” effect: for every t (t > 1) units shipped, only one unit arrives. Thus, the price of an imported brand for Home consumers will be pf = tρf.

(15.9)

Now we can obtain the profit level for the firm in group i: 1 πi = ___ â•‰â•¯ â•¯  â•‰â•¯PiCi, i = h, f. niσ

(15.10)

The relative profit is

     

     

nh ___ Pf ___ Cf nh ___ αf ε ___ Pf 1 – ε __ __ â•‰â•¯ â•¯â•¯â•‰= â•‰â•¯ â•¯â•¯â•‰â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰â•‰ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰= â•‰â•¯ â•¯â•¯â•‰â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰ â•‰ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰ πh nf Ph Ch nf αh Ph

πf __

(15.11)

136â•‡â•‡ Network effects and switching costs ε–σ αf ε nf ____ wh ε – 1 = â•‰ ___ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰ â•‰ __ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰â•‰â•¯σ – 1 â•¯â•‰â•¯â•‰ ___ â•‰â•¯ â•¯â•¯â•¯â•‰â•¯ â•‰ . αh nh wf t

        

(15.12)

Assume σ > ε (i.e., substitutability within a group is greater than that between groups). The ratio of profit is thus inversely proportional to the ratio of the number of brands.10 Suppose that becoming importers bears additional moving cost to Home entrepreneurs.11 This means that, even in the long run, profits are not equalized between groups. To parametarize the degree of these additional moving costs, I assume that when an entrepreneur moves form group h to group f it would earn only 1/(1 + δ) fraction of the profit in the new sector. δâ•›/(1 + δ) fraction of the profit is lost (due to moving costs). A smaller δ represents a more flexible entrepreneur’s market. δ = 0 represents the usual monopolistic competition model (see Matsuyama 1995). To offset these moving costs, profits of group-f firm must be higher a fraction of δ (δ ≥ 0) compared to group-h firm. Thus, in the long run, the following Â�condition must hold: (1 + δ)πh̃ = π̃f,

(15.13)

where “tilde” indicates the long-run equilibrium value. In the long run, the number of firms is determined by the movement of entrepreneurs such that eq. (15.12) holds. Figure 15.1 shows the determination of the relative number of service firms in the long run. The horizontal axis shows the relative number of group-f firms (nfâ•›â•›/nh), while the vertical axis shows the relative profit level (πf/πh). Given that σ > ε, (15.11) is shown as a downward-sloping curve. Suppose that the initial position is at point I, then the entrepreneurs will move from group h to group f. In the long run, the equilibrium is obtained as the intersection of this curve and (1 + δâ•›)π̃h = π̃ f line, point E. The long-run relative size of imported brands (measured in terms of number of varieties) is

  

      

σ-1 ___

ñ N – ñh 1 α ε wh e – 1 â•‰â•¯σ-ε â•¯â•‰ â•‰â•¯__fâ•¯â•‰â•¯= ______ â•‰â•¯ â•¯ â•¯ â•‰â•¯= â•‰â•‰ _____ â•‰â•¯ â•¯  â•‰â•¯â•¯â•‰â•‰ ___ â•‰â•¯ fâ•¯â•‰â•¯â•¯ â•‰ â•‰ ___ â•‰â•¯ â•¯â•¯â•¯â•‰â•¯ â•‰ â•¯ â•‰ . ñh ñh 1 + δ αh wfâ•›t



(15.14)

Proposition 15.1: In the long run, the relative number of imported brands is positively related to its relative attractiveness (αfâ•›â•›/αâ•›h) and negatively related to both its relative costs (inclusive of trade costs t) and additional costs of movement δ. This implies that the low rate of foreign brand penetration results from both strong preference in favor of domestically provided brands and the existence of additional costs of trade.

Foreign brand penetrationâ•‡â•‡ 137 pf /ph

I

pf � ph

1

E

nf /nh

Figure 15.1Â€Â€

15.3Â€Â€Trade liberalization Suppose that there is a reduction in trade costs for imported brands: a decrease in t. From (15.5), (15.8), and (15.9), Ph = (nh)â•‰â•¯1 –â•¯σ â•‰â•¯ρh,

(15.15)

Pf = (nf)â•‰â•¯1 –â•¯σ â•‰â•¯tρf.

(15.16)

1 ____

1 ____

Thus, the relative price level becomes â•¯ wh 1 – σ â•‰ n ____ â•‰â•¯ â•¯â•¯â•‰= â•‰ __ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰â•¯â•‰ â•¯ â•‰ ___ â•‰â•¯ â•¯â•‰â•¯â•¯ â•‰. Pf nf twf

Ph ___

      1

(15.17)

A reduction in t increases the relative price level, Ph/Pf, and

  

     

P 1 n w â•‰ ___ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰= – _____ â•‰â•¯ â•¯ â•¯â•‰â•¯â•‰ __ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰+ â•‰ ___ â•‰â•¯ hâ•¯â•‰â•¯â•¯ â•‰, Pf σ – 1 nf twf where “hat” indicates a percentage change.

(15.18)

138â•‡â•‡ Network effects and switching costs In order to examine the impact of trade liberalization, it is useful to check the profit level of each firm (πh and πf). Rewriting (15.10), the profit levels for firms are

 

   

1 1 P ___ ___ ___ πh = â•‰â•¯ â•¯  â•‰â•¯PhCh = â•‰â•¯ â•¯  â•‰â•¯â•‰1 – µf â•‰ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰â•¯ â•‰E, nhσ nhσ Pf

  

1 P 1 ___ ___ ___ πf = â•‰â•¯ â•¯ â•¯ â•‰Pfâ•›â•›Cf = â•‰â•¯ â•¯ â•¯ â•‰µf â•‰ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰E, nfâ•›σ nfâ•›â•›σ Pf

(15.19)

(15.20)

where µf (Phâ•›/Pf) is the relative expenditure share for group-f brands:

  

(15.21)

  

(15.22)

Ph αâ•›fâ•›â•›εP1–ε α εf f ___ _____________ _______________ µf â•‰ â•‰â•¯ â•¯â•¯â•‰â•¯ â•‰≡ â•‰â•¯ ε 1–ε â•¯â•¯   â•¯ â•¯â•¯â•¯â•‰, ε 1–ε â•‰= â•‰â•¯ ε Pf αâ•›hâ•›Ph + αâ•›fâ•›â•›Pf α h (Ph/Pf)1–ε + α εf (ε –â•›1)α hε α εf (Ph Pf)–ε P ___ ________________ µ f â•‰ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰= â•‰â•¯ ε   â•¯â•¯â•¯â•‰  > 0. Pf [α h(Ph/Pf)1–ε + α εf ]2

Given that ni is constant in the short run, changes in profit levels come only from changes in the relative expenditure share: ∂πf µf _______ ___ â•‰â•¯ = â•‰â•¯ â•¯â•¯ â•‰E > 0, â•¯ â•¯â•‰â•¯ ∂(Ph/Pf) nfâ•›σ µf = – ___ â•‰â•¯ â•¯ â•¯â•‰E < 0. â•¯ â•¯â•‰â•¯ â•‰â•¯ ∂(Ph/Pf) nhσ

∂πh _______

Via expenditure shifting from domestic toward imported brands, a reduction in trade costs increases the profit levels of firms in group f, while reducing the profit levels of group-h firms. In Figure 15.2, this change is shown as the upward shift of the downward-sloping curve (i.e., from point E to point I´). Proposition 15.2: In the short run, given that nf < nh, the change in each group-f firm’s profit due to trade liberalization is larger (in absolute value) than the change in each group-h firm’s profit:

     

∂π ∂π ____ ____ â•‰ â•‰â•¯ â•¯fâ•›â•›â•¯â•‰â•¯ â•‰> â•‰ â•‰â•¯ hâ•›â•›â•¯ â•¯â•‰â•¯ â•‰. ∂t ∂t This result has important implications. From (15.13) and Proposition 15.1, the relative number of imported brands tends to be smaller, which may occur due to the trade costs. In such a case, the short-run impact of trade liberalization is a relative increase in profits for imported brands.

Foreign brand penetrationâ•‡â•‡ 139 In the long run, entrepreneurs begin to move from group h to group f. These movements tend to reduce the profit of each group-f firm. However, there is an additional effect of these movements: further reduction in the price index Pf. Since the variety of imported brands has been widened, it becomes more preferable for Home consumers to purchase imported brands. From (15.14) and (15.15), this increases the relative price levels of group h and mitigates the negative effect of an increasing number of brands in group f. As the inter-group substitution ε increases, this effect becomes larger. By combining Propositions 15.1 and 15.2, one can examine the impact of gradual trade liberalization. Suppose that trade costs decline from t to t´ first, then from t´ to t´´, and so on. As the share of imported brands increases due to trade liberalization (Proposition 15.1), the impact of trade liberalization itself becomes smaller (Proposition 15.2). This implies that, as trade is liberalized more, the incentive for entrepreneurs to provide imported brands becomes smaller. Figure 15.2 summarizes the above results. With increasing trade liberalization, the downward sloping curve moves upward. The short-run equilibrium moves from E to I´. Then, the entrepreneurs’ switching occurs and the condition (15.12) holds again: the new long-run equilibrium is obtained at E´. As

pf /ph

I I'

1

pf � ph E

E'

nf /nh

Figure 15.2Â€Â€

140â•‡â•‡ Network effects and switching costs the share of imported brands increases, the upward shift of the curve becomes smaller. Now let us consider the change in the long-run profit levels. From (15.10), one may obtain ñhπ̃h + ñfâ•›π̃ f = E.

(15.23)

Given that (1 + δ )πh̃ = π̃f holds in the long run, we can obtain the level of profit for group-h firms as follows: E ∂π̃ ____________ ___ â•¯â•¯â•¯â•¯â•‰, â•‰â•¯ hâ•¯â•‰â•¯> 0. πh̃ = â•‰â•¯ (1 + δâ•›)N – δñh ∂ñh

(15.24)

This implies that the long-run profit levels of group-h firms are increasing in the level of trade costs. As t decreases, it is more profitable to become a group-f firm, then some group-h entrepreneurs begin to switch to become foreign brands’ importers. Since group-f firms earn higher profits in the long-run equilibrium, these switchings tends to reduce profit levels of (remaining) group-h firms. Proposition 15.3: In the long run, from group-h firm’s viewpoint, the effect of trade liberalization is magnified via entrepreneurs’ switching from domestic brands toward imported brands. Let us consider this proposition more precisely. In the short run, a reduction in trade costs increases the profit levels of firms in group f, while reducing the profit levels of group-h firms. Thus there are opportunities for entry (i.e., switching) to group f. Thus the size of group f expands, while the size of group h shrinks. This change works to reduce the profit of each group-f firm, which also reduces an incentive to switch to group f: as a flood of imported brands hits the domestic market, their appeal wanes. At the same time, however, competitive pressure from imported brands, which earn a relatively higher profit, reduces profit levels of domestic brands. The point is that, in the long run, the impact of trade liberalization on domestic firms’ profits will be magnified via entrepreneurs’ switching behavior. It is important to note that this pro-competitive effect from entrepreneurs’ switching behavior has not appeared in previous studies. This seems to suggest that incorporating domestic entrepreneurs is important to analyze the impact of trade liberalization.

15.4Â€Â€Concluding remarks In this chapter, by constructing a simple monopolistic competition trade model, I highlight the role of domestic entrepreneurs’ decision as a driving force behind a gradual foreign (imported) brand penetration. It has been shown that, as trade costs become lower, more entrepreneurs choose to provide foreign brands. However, the impact of trade liberalization (in terms of changes in profit levels)

Foreign brand penetrationâ•‡â•‡ 141 becomes smaller as more entrepreneurs switch to foreign brands (propositions 15.1 and 15.2). In addition, it should be noted, from the remaining domestic brand providers’ perspectives, the negative effect of trade liberalization is magnified via entrepreneurs’ switching from domestic brands toward imported brands (Proposition 15.3). Although these results are derived under the assumption that brands are horizontally differentiated, it appears that something similar to this will occur in the more general setting considered here. This analysis should be regarded as very tentative. Hopefully it provides a useful paradigm for considering how trade liberalization affects the degree of foreign brand penetration. There are some directions in which the morel could be extended. As a first step to incorporate foreign brand penetration, I have concentrated on the case of horizontal brand differentiation and downplayed the role of vertical brand differentiation. If there are heterogeneous marginal costs with quality levels, this model adheres more closely to the model of vertical brand differentiation.12 In order to analyze the interaction of foreign brand penetration and quality levels, this kind of extension needs further consideration. In addition, strategic interaction between domestic brand providers and foreign service providers should be analyzed.13 Furthermore, the model could be enriched with the inclusion of both FDI and outsourcing aspects in order to analyze the organization of firms.14

15.5Â€Â€Appendix Derivations of the demand functions (equations 15.6 and 15.7). Expenditure for differentiated brands E being given, the consumption of each group of brands (i.e., Ch and Cf) is obtained by maximizing C under the constraint PhCh + Pfâ•›â•›Cf ≤ E. The Lagrangian of this problem is L = C + η(E – PhCh – Pfâ•›Cf), and the first order conditions are ∂C ___ ___ â•‰â•¯∂Lâ•¯â•‰â•¯ = â•‰â•¯ â•¯â•¯â•‰ – ηPh = 0,

(15.25)

∂C ___ ___ â•‰â•¯∂Lâ•¯â•‰â•¯= â•‰â•¯ â•¯â•¯â•‰ – ηPf = 0,

(15.26)

∂L ___ â•‰â•¯ â•¯ â•‰= E – PhCh – Pfâ•›â•›Cf = 0.

(15.27)

∂C h ∂C f

∂C h

∂C f

∂η

Using equations (15.21) and (15.22), one can obtain equation (15.7): Ch ___

     

α ε ___ P –ε ___ â•‰â•¯ â•¯â•¯â•‰â•¯= â•‰ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰ â•‰ â•‰â•¯ hâ•¯â•¯â•‰â•¯ â•‰ . Cf αf Pf

Note that the price index Pi, measures the minimum cost to obtain one unit of Ci.

142â•‡â•‡ Network effects and switching costs Thus, by differentiating Pi with respect to pi(j), one can have the demand function to obtain one unit of Ci (i.e., Roy’s identity):

 

â•›p (â•›â•›j) –σ _____ = â•‰â•‰â•¯ i â•¯ â•¯ â•‰â•¯ â•¯â•¯â•‰â•¯ â•¯ â•‰â•¯ â•‰ . ∂pi (â•›â•›j) Pi

∂Pi ______



Then, multiplying equation (15.24) by Ci, one can obtain equation (15.6):

 

p (â•›â•›j) –σ _____ â•¯ â•‰â•¯ â•‰ Ci. ci (â•›â•›j) = â•‰â•‰â•¯ i â•¯ â•¯ Pi



(15.28)

Part IV

Cost heterogeneity and trade

16 Increasing costs in product diversification

16.1Â€Â€Introduction1 The observation of two-way trade in similar goods among advanced countries has led to the construction of theoretical models based on increasing returns to scale, product differentiation, and imperfect competition. In particular, trade models under monopolistic competition have been investigated intensively.2 In previous studies of monopolistically competitive trade models, it has been assumed that every firm has the same level of fixed costs. Spence (1976) pointed out that differences in fixed costs played the crucial role in determining market equilibrium. However, little attention has been given to the role of differences in fixed costs in monopolistically competitive trade models. In one-factor trade models with symmetric cost functions, there have been some ambiguities about the process of entry and exit (which firm enters the market and which one exits) and the direction of trade (which country produces which goods).3 The intention of this chapter is, first, to extend monopolistically competitive trade models to incorporate asymmetric fixed costs in product diversification. Here the term “fixed cost” is not used in the sense that the cost is sunk but in the sense that the cost is independent of the level of output. We consider the case where the later a firm enters the market, the higher its fixed cost, since a newcomer needs more inputs in order to differentiate its products from those already in the market.4 Second, both the pattern of trade and the effects of opening trade on welfare are examined. Contrary to the results of the symmetric costs model of Krugman (1980), we conclude that the larger country will be a net importer of differentiated goods. For an intuitive explanation of the model, we develop two simple geometrical tools: the “variety demand curve” and the “variety supply curve”. With these tools, we can easily show the determination of both the autarky and the trading equilibria and the difference between our results and previous ones. In section 16.2, we present a basic model and examine the autarky equilibrium. In section 16.3, we examine the effects of opening trade on welfare. Finally, in section 16.4, we summarize results derived from our analysis.

146â•‡â•‡ Cost heterogeneity and trade

16.2Â€Â€The model Consider an economy which produces goods in two sectors, X, Y: using the only one mobile factor of production L, which is referred to as “labour”. The first sector, industry X, consists of n firms, each producing only one variant of product X and enjoying some degree of market power. The second sector, industry Y, produces homogeneous goods under constant returns to scale, and they are sold in a perfectly competitive market. We choose the homogeneous good as numeraire. A representative consumer is characterized by the following utility function:

 

n

s/θ

U = Y 1–s â•‰ â•‰ â•¯â•‰â•‰â•‰â•¯ xθi diâ•¯â•‰ , 0 < θ, s <1, i ∈ [0, n], 0

(16.1)

where xi is the amount of consumption of the i-th product in a continuum of potential differentiated products, and Y is the amount of consumption of the numeraire goods. The representative consumer maximizes (16.1) subject to the budget constraint:

 

n

Y + â•‰ â•¯â•‰â•‰â•‰â•¯ pixidi = I, 0

(16.2)

where the price of numeraire is equal to unity, and pi and I are the price of the i-th differentiated product and the income in terms of the numeraire, respectively. Then we have the following demand functions: Y = (1 – s)I,

(16.3)

pi–1/(1–θ) xi = â•‰â•¯__________ â•¯â•¯ â•¯â•‰, i ∈ [0, n]. â•‰  â•‰â•⁄ â•¯â•‰â•‰pâ•‰â•¯ i–θ/(1–θ) djâ•¯â•‰

(16.4)

 

Here it is assumed that the consumer evaluates differentiated products symmetrically. Then, if their prices are the same, (16.4) will be reduced to sI ___ x = â•‰â•¯npâ•¯â•¯â•‰. â•¯

(16.5)

Production of the numeraire is characterized by a cost function that exhibits constant returns to scale, and we choose units in such a way that one unit of labor produces one unit of the numeraire. On the other hand, production of the i-th differentiated product is characterized by the following cost function: TCi = α(i) + βxi, α'(·) > 0, α"(·) = 0, i ∈ [0, n],

(16.6)

where TCi and xi are the total cost and output level of the i-th firm, respectively. Each firm has to commit α(·) units of labor as fixed cost, and has constant

Costs in product diversificationâ•‡â•‡ 147 Â� marginal cost β. Firms are indexed according to the level of fixed costs in such a way that a firm with a greater number i corresponds to a higher fixed cost. This means that a firm which enters the market later has to pay a relatively higher fixed cost than existing ones (i.e., α'(·) > 0).5 Furthermore, the rate of increase of the fixed cost is assumed to be constant (i.e., α(·) = 0). The producer of the i-th product chooses its price to realize its maximized profit. Equation (16.4) implies that each firm faces its own demand curve with elasticity of 1/(1 – θ), and thus we obtain the following profit-maximizing price: pi = θ –l p, i ∈ [0, n].

(16.7)

Since both θ and β are the same for all firms, prices must be the same for all products and we can adopt the shorthand pi = p for all i. However, levels of outputs which attain zero profit are different among firms since each firm’s fixed cost is not the same. The “zero-profit output” (but not the profit-maximizing level) for i is given by α(i)θ xi = _______ â•‰â•¯  â•¯â•‰â•›â•¯ , i ∈ [0, n]. β(1 – θ)

(16.8)

This implies that a firm which has a relatively low index number can cover its fixed cost by selling relatively small amounts. Equation (16.4) implies that the consumer evaluates each product variety symmetrically. Therefore, if the marginal firm, which is the one that enters latest (indexed by n) and has the highest fixed cost, can sell exactly his zero-profit output xn, other, more efficient firms with lower fixed costs will be able to operate at the same output level. Thus the output of each firm is determined by the marginal firm’s zero-profit output, and more efficient firms have positive profits. The profits depend only on the differences in their fixed costs, and are given by π(i) = α(n) – α(i), i ∈ [0, n].

(16.9)

Now, we assume that these positive profits will be transferred to the consumer. Therefore, the national income I consists of profits as well as factor payments: I = I(n) = L + Π(n),

 

n

(16.10)

where Π = â•‰ â•¯â•‰â•‰â•‰â•¯ πidi. 0 We are now in a position to show the equilibrium number of varieties and the equilibrium level of output. In order to give the equilibrium we develop new geometrical tools. In Figure 16.1 the horizontal axis shows index number of product variety, while the vertical axis shows both output and consumption of each product variety. We can derive a specific relationship between n and x from each firm’s zero-profit condition (16.7). It is shown as increasing straight line zz. The zz line shows each firm’s cost condition and is called the “variety supply curve.”

148â•‡â•‡ Cost heterogeneity and trade x

d

z B

1

xA

2(A)

d z

3 O

n

A

n

Figure 16.1Â€Â€

Another relationship between n and x may be derived from the demand function (16.4). Substituting (16.6) and (16.9) into (16.4) we get θsI(n) _____   â•¯ â•‰. â•¯ x = â•‰â•¯ nβ

(16.11)

The relation between n and x can be represented by a decreasing line dd in Figure 16.1.6 The dd curve shows the consumer’s preference for greater product variety: as product variety increases, the consumer reduces consumption of each product and tries to increase the number of product varieties consumed. We call the dd curve the “variety demand curve.” A unique intersection between the two curves determines the equilibrium number of varieties n A and equilibrium output for each firm x A, where A refers to the autarkic equilibrium value.7 These values are given by8

Costs in product diversificationâ•‡â•‡ 149 s(1 – θ)I(n A) n A = ___________ â•‰â•¯ â•¯ â•¯â•‰â•¯ , α(n A)

(16.12)

α(n A)θ ________   x A = â•‰â•¯ â•¯â•‰. â•¯ β(1 – θ )

(16.13)

The volume of consumption and production of differentiated products are represented by the area of rectangle 0123 in Figure 16.1. Using these tools, we can analyze the effects of labor force growth on the structure of production. In Figure 16.1 the equilibrium before labor force increase is given at point A. From (16.11) and (16.12), we find that an increase in L has no effect on zz and it only shifts dd to the right. The new equilibrium is at B, where both n and x rise. Thus, an increase in L causes a larger demand for differentiated products, and more firms will enter the market. As the new marginal firm has a higher level of output to cover a larger fixed cost, each firm will produce more. Proposition 16.1: Product variety in a larger economy (defined by population size) is greater than in a smaller one. Furthermore, since demand for differentiated products is greater in a large economy, higher cost firms can enter the market and each firm produces a larger amount.

16.3Â€Â€The trading equilibrium Suppose that two countries (Home and Foreign) open their markets and have a trade relationship with zero transportation costs. The equilibrium of each country before the opening of trade is described in section 16.2. Countries are assumed to be identical except for their labor size and the range of available products.9 We assume that the foreign country has a larger labor force, and γ measures the relative size of the two countries: L* γ ≡ __ â•‰â•¯ â•¯â•¯â•‰≥ 1, L where * refers to the foreign country. As γ becomes larger, the size of the foreign country becomes relatively larger. We will use the term “large country” to refer to the foreign country, and use the term “small country” for the home. After the opening of trade, consumers can consume all differentiated products produced in the X sectors of the two countries. Therefore, there will be intra-Â� industry trade in differentiated products. Now consider the trading equilibrium. In our model, the two countries will have the same wage rates and prices in the trade equilibrium. Thus, the number of products in the world can be determined from the worldwide zero-profit condition. We can show this by using the following two figures: Figure 16.2 represents the case where countries are identical (i.e., γ â•›= l), and Figure 16.3 represents the case where the foreign country is larger than the home country (i.e., γ â•›> 1).

150â•‡â•‡ Cost heterogeneity and trade x

x*

d

d

z z

X

d

z* d

z* n

D Z

XT

D

Z

N

n*

nT(�n A)

n*T(�n *A)

(a) Home

NT(�n T� n *T )

(b) Foreign

(c) World

Figure 16.2Â€Â€ x

x*

X

z z

z*

Z D

Z n*

n n A → nT (a) Home

D

z*

N

n*T ← n *A (b) Foreign

N T(�nT� n *T ) (c) World

Figure 16.3Â€Â€

The worldwide supply of varieties will be derived as follows. By adding up each country’s variety supply curve of (17.7), we have the following relation for world variety supply: A(î )θ ________ î ∈ [0, N], X(î) = â•‰â•¯  â•¯â•‰,â•¯ β(1 – θ)

(16.14)

where A'(·) = (1/2)α'(·), A(î) = α(i/2). A(·) and î represent the stream of worldwide fixed costs and worldwide index of product variety.10 This relation is shown in Figures 16.2(c) and 16.3(c) as the ZZ curve. The DD curve, which represents worldwide demand for product varieties, is derived from summing up each country’s variety demand curve. The DD curve is expressed as

Costs in product diversificationâ•‡â•‡ 151 θs[I(n) + I(n*)] X = _____________ â•‰â•¯  â•¯â•¯ â•¯ â•‰, Nβ

(16.15)

where N is the total variety in the world (i.e., N = n + n*) and X is the total amount of consumption of each differentiated product. We are now able to show trading equilibrium values NT and XT, where T refers to the trading equilibrium value, using both DD curve and ZZ curve. Those values are calculated as s(1 – θ)[I(nT ) + I *(n*T )] N T = ___________________ â•‰â•¯ â•¯â•¯ â•¯â•¯, â•¯â•‰ A(N T )

(16.16)

A(N T )θ ________   X T = â•‰â•¯ â•¯â•‰. â•¯ βâ•›(1 – θ )

(16.17)

As it is assumed here that each country’s variety supply curve has the same shape, each country will produce one half of the total variety. Thus the number of products produced in each country will be the same: 1 __ nT = n*T = â•‰â•¯ â•¯â•¯â•‰N T. 2

(16.18)

Note that each country produces a different range of products. By using (16.15) and (16.17), we can calculate the number of each country’s varieties in trade equilibrium. For example, the home country produces s(1 – θ)[I(nT ) + I *(n*T )] nT = ____________________ â•‰â•¯ â•¯â•¯ â•¯â•¯. â•¯â•‰ 2α(nT )

(16.19)

Having observed the number of varieties in trade equilibrium, we can then go on to consider the effect of the opening of trade on product variety. In the γ â•›= 1 case (Figure 16.2), the number of product varieties will be the same before and after trade: nT = n*T = nA = n*Aif γ = 1. Here, each country’s marginal firm has the same level of fixed cost, so no firm has an incentive to enter the market. However, since each country’s consumer will consume all product varieties, each country will export one half of the Â�production of each firm; thus intra-industry trade occurs and welfare rises. We turn to the case of γ â•›> 1 (Figure 16.3). In the autarkic equilibria, relatively inefficient firms that have higher fixed costs exist in the foreign country, while the number of firms is limited by a smaller market demand in the home country. After the opening of trade, however, each firm in the home country faces larger market demand and there appears to be an opportunity for entry. On the other hand, the foreign country’s inefficient firms will not be able to cover their higher fixed costs because of efficient firms’ entry, and will be pushed out of the market. From (16.17) it is obvious that the number of product varieties

152â•‡â•‡ Cost heterogeneity and trade will be equalized in the trading equilibrium. It should be noted that each country’s aggregate profit will also be equalized (i.e., Π(nT ) = Π*(n*T )). From the above analysis, we derive the following relationship between the number of varieties produced and the relative size of the counties. Proposition 16.2: By the opening of trade, the number of firms operating in the differentiated product sector increases in the small country, while it decreases in the large country. Next, we examine the pattern of trade. Balance-of-trade conditions for both home and foreign counties are Y – Y˜ + pnT ˜x * = pn*T ˜x ,

(16.20)

Y* – Y˜ * + pn*T ˜x = pnT ˜x *,

(16.21)

where the tilde refers to the levels of consumption.11 Each country’s consumption of a given product depends on its national income, that is: I(nT )X [L + Π(nT )]X ___________ _______________ ˜x = â•‰â•¯ T â•¯â•¯ â•¯ â•¯â•¯ â•¯â•¯â•¯â•‰, *T â•¯â•‰= â•‰â•¯ I(n ) + I(n ) (1 + γ )L + 2Π(nT ) [γL + Π(n*T )]X I *(n*T )X ___________ _______________ ˜x * = â•‰â•¯ T â•¯â•¯ â•¯â•¯â•‰= â•‰â•¯ â•¯â•¯ â•¯â•¯â•¯â•‰. *T I(n ) + I(n ) (1 + γ )L + 2Π(nT )

(16.22)

Equation (16.22) implies that the total consumption of each differentiated product is larger in the foreign country than that in the home country, because per capita consumption is the same. On the other hand, from (16.17), we find that each country produces the same value of differentiated products (i.e., pnT X = pn*T X). Therefore, trade in differentiated products will be imbalanced. Then, for the balance-of-trade conditions (16.20) and (16.21) to be satisfied, the foreign country has to export homogeneous goods while being a net importer of differentiated products. Therefore, both inter- and intra-industry trade occur. Thus, we obtain the next proposition about the trade pattern. Proposition 16.3: The small country will be a net exporter of the differentiated products, while the large country will be a net exporter of the homogeneous good. Proposition 16.3 gives new implications as to the effect of the relative size of countries. If the partner’s size is larger, new firms can enter the world market in the domestic country at the expense of the partner’s inefficient firms. Therefore, the home country will produce more differentiated products relative to its own consumption. In order to discuss the relationship between the composition of trade (in terms of intra- versus inter-industry trade) and the dispersion of relative country size,

Costs in product diversificationâ•‡â•‡ 153 we will use the standard intra-industry trade index developed by Grubel and Lloyd (1975): (Y˜ – Y ) + pâ•›(nT ˜x * – n*T ˜x ) _____________________ GL = 1 – â•‰â•¯ ˜ â•¯â•¯â•¯â•‰. (Y – Y) + p(nT ˜x * + n*T ˜x )

(16.23)

This index has the property that, if there is only “inter-industry” trade, GL = 0, while if there is only “intra-industry” trade, GL = 1. By substituting (16.20), (16.21), and (16.22) into (16.23), we can obtain the following: L + Π(nT ) ______________ GL = â•‰â•¯ â•¯â•¯ â•¯â•¯â•¯â•‰. (1 + γ )L + Π(nT )

(16.24)

From (16.24), we get another proposition. Proposition 16.4: The greater the size difference of countries, the smaller the share of intra-industry trade. GL indexes are sometimes used to measure “the degree of market protection.” In our analysis, however, the lower GL index itself does not imply that the market is closed. Thus, it may be necessary to take care in the use of these indexes as evidence of a closed market. Let us conclude this section with a discussion about gains from trade. For the home country, we can calculate the ratio of utility after trade to that before trade. We take the situation where only intra-industry trade takes place (i.e., the case of γ â•›= 1). The ratio becomes UT ___ â•‰â•¯ Aâ•¯â•¯â•‰= 2s(1–θ)/θ > 1. U Here the home country will gain, and the gain will come solely through increased (doubled) product diversity. As the problem is perfectly symmetric, the partner country enjoys the same welfare gain. As the trading partner becomes larger (i.e., as Y becomes larger), the home country’s gains will be larger in two ways. First, the difference between the number of products available after trade and the number of products available in autarky grows. Second, by the opening of trade, labour will be reallocated from the Y sector to the X sector, and this structural change increases the profits of the X sector by increasing the marginal firm’s zero-profit output (and thus the output of all firms). And as gamma becomes larger, the larger is the structural change resulting from the opening of trade. Therefore, we obtain the following proposition: Proposition 16.5: The larger the trading partner of a country, the larger are the gains from trade of the country.

154â•‡â•‡ Cost heterogeneity and trade The proposition is the counterpart of the one by Lawrence and Spiller (1983), who assumed symmetric cost. Of course our proposition is based on asymmetric cost. What can we say about the foreign country? The answer is ambiguous. On the one hand, the foreign consumer will benefit from the increasing variety of products. On the other hand, however, the reallocation of labor from the X to the Y sector will reduce the profits in the X sector.

16.4Â€Â€Concluding remarks Krugman (1980) defined a “home market effect,” which is based on the monopolistically competitive model with symmetric costs, and concluded that countries will tend to export those goods for which they have relatively large domestic markets. We have presented another monopolistically competitive model with asymmetric technology. We have shown that if some kind of diminishing returns works at an industry level (although each firm has technologies of increasing returns to scale), the argument will return to the traditional analysis with diminishing returns: strong domestic demand for a good will tend to make it an import rather than an export. Furthermore, it has become clear that the small country will always gain from trade, while it is ambiguous for the large country. The analysis in this chapter has obviously been suggestive rather than conclusive. It relies heavily on the specification of the cost function. Nonetheless, the analysis does seem to confirm the idea that the presence of increasing-returns-toscale technology does not always imply that the large country gains from its large market. We should take care to explore not only the conditions of the costs of product diversification for a firm but also the conditions of the costs for a country (i.e., the shape of variety supply curve).

16.5Â€Â€Appendix We will show that, by specifying the functional form of α(·), the variety demand curve will be decreasing in the neighborhood of the equilibrium. We specify the cost function (16.5) as TC(i) = α(i) + βxi = ai + b + βxi, i ∈ [0, n], a, b > 0.

(16.25)

Using (16.8) and (16.25), each firm’s profit is calculated as pi = a(n – i). Total profits Π(n) will then become

 

n 1 __ Π(n) = â•‰ â•¯â•‰â•‰â•‰â•¯ π i di = â•‰â•¯ â•¯â•‰â•›â•¯an2. 2 0

(16.26)

Substituting (16.26) and (16.9) into (16.10), we obtain the following variety demand:

Costs in product diversificationâ•‡â•‡ 155 1

θs(L + __â•‰â•¯2â•¯â•‰â•›an2) ___ 1 dxd ____ θs __ xd = ___________ â•‰â•¯ â•¯ â•‰â•¯limâ•¯â•‰xd = ∞. â•¯ â•‰,â•¯ â•‰â•¯ â•¯â•¯â•‰= â•‰â•¯ 2â•¯â•¯â•‰â•›â•›â•‰â•¯ â•‰â•¯ â•¯â•¯â•‰â•›an2 – Lâ•¯ â•‰, â•¯â•¯â•¯ βn dn βn 2 x→0

 



(16.27)

This variety demand curve will be shown as the curve dd in Figure 16.4. The variety supply curve can be similarly expressed, using (16.7) and (16.25), as (a + bn)θ ___ dx s xs = â•‰â•¯________â•¯â•‰  â•¯ , â•‰â•¯ â•¯â•¯â•‰> 0. β(1 – θ) dn

(16.28)

We are now ready to consider the intersection of these two curves. For the value of n = (2L/a)1/2, θ 1 θ b x d – x s = â•‰â•¯__ â•¯â•‰(2aL)1/2 â•‰ s – â•‰â•¯_____ â•¯  â•‰â•¯â•¯â•‰– __ â•‰â•¯  â•¯â•‰_____ â•‰â•¯ â•¯  â•¯ â•‰< 0. β 1–θ β 1–θ

 



That is, if n = (2L/a)1/2, xs exceeds xd. Thus we may conclude that the variety supply curve intersects with the variety demand curve at a point where the variety demand curve has a negative slope. Figure 16.4 represents these relationships. x

d

z

d

z

0

Figure 16.4Â€Â€

nA

2L a

n

156â•‡â•‡ Cost heterogeneity and trade The equilibrium number of varieties nA may be obtained by solving the equilibrium condition x s = x d. nA = –b + (b2 – AC )1/2 â•‰â•¯ â•¯ â•¯â•¯ â•‰,â•¯ A

_____________________________

where A ≡ [2a – s(1 – θ)a], C ≡ –2s(1 – θ)L.

17 Efficiency gaps and Heckscher–Ohlin trade patterns

17.1Â€Â€Introduction1 The determination of trade patterns is a central topic in trade theory. A large portion of the literature on trade theory seeks to explain them in terms of international differences in factor endowments, while assuming that preferences and technologies are identical among trading countries. The modern factor endowment theory is apparently divided into two strands. One strand asserts that differences in factor endowment ratios among countries matter, while the other holds that it is mainly differences in country size that determine trade patterns. The standard Heckscher–Ohlin theory and the now classical Helpman–Krugman (1985) monopolistically competitive model belong to the former strand, and Ethier’s (1982a) Ricardian model with increasing returns is a notable member of the latter. However, to our knowledge, there has been no attempt to study both ratio and size in a unified theoretical framework. More specifically, the following question is left unexplored: under what conditions can we identify whether differences in the ratio or size of factor endowments explain the pattern of international trade? To begin to study the problem, we develop a two-factor, three-good model of trade with technical heterogeneity among firms in a monopolistically competitive sector. Following Spence (1976), we introduce efficiency gaps in fixed production costs.2 Countries are identical in every respect except for the distribution of factors. With free entry, efficiency gaps among firms result in the endogenous determination of the industry structure. The cost-efficiency composition in the monopolistically competitive sector is determined within the model. By introducing efficiency gaps into a monopolistically competitive sector, we can emphasize the role of absolute factor endowments. Through a mechanism of competitive selection, inefficient firms in an absolutely factor-abundant country will be pushed out of the market. We show that, contrary to the monopolistically competitive model without efficiency gaps, trade patterns are determined by the interaction between relative factor endowments (i.e., a Heckscher–Ohlin aspect) and absolute factor endowments (i.e., the mechanism of competitive selection).3 In a recent contribution, Montagna (2001) investigated the mechanism of competitive selection in a monopolistically competitive trade model. However,

158â•‡â•‡ Cost heterogeneity and trade her focus was on a case in which there is only one factor, and efficiency gaps existed in variable costs. Her model had a Ricardian aspect and paid scant attention to the Hechscher–Ohlin theory. In contrast, in this study we focus on the interaction between relative factor endowments and competitive selection.4 The main result of the current chapter, which captures the interaction between relative factor endowments and absolute factor endowments, has not appeared in the existing literature. The rest of the chapter is structured as follows. Section 17.2 presents our analytical set-up, which is used in section 17.3 to analyze the trading equilibrium. In section 17.4, the link between relative factor endowment and absolute factor endowment is explored. Section 17.5 presents concluding remarks.

17.2Â€Â€The model Consider a world economy consisting of two countries: Home and Foreign. There are three categories of goods: differentiated products (good X) supplied by monopolistically competitive firms, and two types of homogeneous goods (good Y and good Z ) supplied by competitive firms. It is assumed that L (L*) units of labor and K (K *) units of capital are endowed in Home (Foreign). Assume that the preferences of each agent are identical and homothetic:5 U = X αY βZ 1–α–β,Â€Â€Â€Â€Â€Â€Â€Â€0 < α, β < 1, where X is the quantity index of the differentiated products, and Y and Z are the consumption levels of the homogeneous goods. Assuming a continuum of variÂ� eties, the quantity and price indices for good X are, respectively: 1 n n* /θ X = â•‰ â•‰ â•¯â•‰â•‰â•‰â•¯ (xi)θ di + â•‰ â•¯â•‰â•‰â•‰â•¯ (x*j )θ djâ•¯ â•‰ ,Â€Â€Â€Â€Â€Â€Â€Â€0 < θ < 1

   0

  

n

 



0

 

n*

–(1–θ)/θ



P = â•‰ â•‰ â•¯â•‰â•‰â•‰â•¯ (pi)–θ/(1–θ) di + â•‰ â•¯â•‰â•‰â•‰â•¯ (p*j )–θ/(1–θ) djâ•¯ â•‰ 0

0

,

where n (n*) is the range of Home (Foreign) varieties, and xi (xj) and pi ( pi) are the quantity and price of the variety produced by firm i ( j) in Home (Foreign). Solving the utility maximization problem yields the following inverse demand functions for Home consumers: pi = X 1–θ Px θi –1,Â€Â€Â€Â€Â€Â€Â€Â€i ∈ [0, n],

(17.1)

p*j = X 1–θ Px*j θ –1,Â€Â€Â€Â€Â€Â€Â€Â€j ∈ [0, n*].

(17.2)

Now turn to the supply side. The good Y and good Z sectors are perfectly competitive and produce homogeneous outputs under conditions of constant returns to scale.

Heckscher–Ohlin trade patternsâ•‡â•‡ 159 Assume that it is necessary for each monopolistically competitive firm to employ fixed amounts of labor and capital prior to producing its output. The central assumption is that firms are characterized by asymmetric levels of fixed costs.6,7 In order to capture the efficiency ranking of firms, let the first firm (i = 0 and j = 0) be the most efficient (i.e., having the lowest level of fixed costs) with respect to which all other firms can be ranked. For the sake of simplicity, we also assume a monotonic ranking and an efficiency distribution with only one firm per efficiency level. This implies that, within each country, successive entrants will be less efficient than the incumbents. Except for these fixed costs, technology is described by the standard neoclassical production function which assumes linear homogeneity, and is identical between firms. These assumptions are Â�summarized as the following total cost function for a typical firm i (j):8 TC iX= c X(w, r)(xi + µ i),Â€Â€Â€Â€Â€Â€Â€Â€i ∈ [0, n], TC Xj = c X(w*, r*)(xj + µ*j),Â€Â€Â€Â€Â€Â€Â€Â€j ∈ [0, n*]

(17.3)

where w is the wage rate, r is the capital rental rate, and c X (w, r) [c X (w*, r*)] is an increasing, concave, and linearly homogeneous function of factor prices.9 The parameter µ ( µ*) captures the degree of efficiency gaps between countries. For analytical tractability, we concentrate on a case in which µ = µ* = 1: this implies that the “shape” of the fixed cost distribution is the same for both economies.10 Each monopolistic firm chooses its price to maximize its profit. Given both the cost function (17.3) and the Dixit–Stiglitz preferences (Dixit and Stiglitz 1977), a typical firm-i chooses its price as follows:11 c X(w, r) _______   â•¯ â•‰,Â€Â€Â€Â€Â€Â€Â€Â€i ∈ [0, n], pi = p = â•‰â•¯ â•¯ θ

(17.4)

In the economy, the market structure in the monopolistically competitive sector is determined endogenously via free entry. Note that, given the assumed ranking among firms, the larger the number of firms, the higher the fixed set-up costs of the marginal firm. In equilibrium there should be no new entry and the marginal firm (i = n) should break even. Using Equations (17.3) and (17.4), the zero-profit condition for the marginal firm (i.e., π n = pn xn – TC Xn = 0) determines the output level for the marginal firm: θ _____ â•‰n. xn (n) = â•‰â•¯    â•¯ 1–θ

(17.5)

By Equations (17.1) and (17.5), each firm in Home produces the same level of output: xi (n) = xn (n). For simplicity, we write this supply quantity as x(n). Clearly, x´ (n) > 0 holds: as the less efficient marginal firm (indexed by a larger number) enters a market, the incumbent firms can produce more. Thus, in free-entry equilibrium, only the marginal firm breaks even and more efficient firms earn positive profits.12 Equations (17.4) and (17.5) imply that the profit of a

160â•‡â•‡ Cost heterogeneity and trade firm depends only on the differences in its set-up costs from the marginal firm’s costs, and is given by πi = (n – i)c X(w, r),Â€Â€Â€Â€Â€Â€Â€Â€i ∈ [0, n].

(17.6)

We assume that these positive profits will be transferred to consumers. Note that any other firm can enter the market even if positive profits remain: since potential entrants have to pay higher set-up costs than the marginal firm, they cannot cover those costs. Before turning to the trading equilibrium, we must draw attention to the Home autarky equilibrium (i.e., n* = 0) with given factor prices. Given the Â�symmetric pricing rule (18.4) and n* = 0, the demand for each product becomes θαl αl ________ ___ xd = â•‰â•¯ â•¯â•‰â•¯= â•‰â•¯ X â•¯ â•¯â•‰. â•¯ np nc (w, r)

(17.7)

Here l is the aggregate income given by l = wL + rK + Π,

(17.8)

where Π is total profits in Home. Given factor prices and using (17.6), Π is determined as follows:

 

n

 

n

Πâ•›(n) ≡ â•‰ â•¯â•‰â•‰â•‰â•¯ p i di = â•‰ â•¯â•‰â•‰â•‰â•¯ [(n – i)c X(w, r)] di = (1/2)n2 c X(w, r). 0

0

Substituting this into Equation (17.17), we can write the demand function for each product as follows: θα [wL + rK + Π(n)] __________________ â•¯â•‰ xd (n) ≡ â•‰â•¯ â•¯â•¯ â•¯â•¯. nc X(w, r)

(17.9)

Given factor prices, we can obtain the equilibrium number of firms, nA, by the following equilibrium condition:13 x d(n A) = x(n A), where A refers to the equilibrium value in autarky. Before we proceed to the trading equilibrium, we must also draw attention to the role of country size. Suppose that Foreign is larger than Home in terms of factor endowments. Larger factor endowments imply a larger demand for each differentiated product (see 17.9), and more (inefficient) firms will enter the market. Thus nA < n*A holds before the opening of international trade.

17.3Â€Â€Trading equilibrium Now assume that trade in goods takes place in a context where transportation costs and all other barriers to trade are absent. The opening up of trade leads to

Heckscher–Ohlin trade patternsâ•‡â•‡ 161 larger and fully integrated goods markets. This implies that consumers can purchase any of the products from the differentiated sectors of the two countries. Therefore, there will be intra-industry trade in differentiated products. Furthermore, the opening up of trade changes the competitive environment in which firms operate. Let us consider the mechanism of competitive selection more precisely. Suppose that the two countries incompletely specialize in both good Y and good Z, and that factor prices are equalized. Given this, each firm in the good X sector has the same marginal costs cX and sets the same price (17.4). As a result, the zero-profit output for each firm with the same index number (i.e., i = j) will also be equalized between countries. On the other hand, since homothetic preferences are assumed, both countries’ demands for a product when all products are sold at price cX/θ can be aggregated into the world demand (18.7), given by θαl* θαl _____________ _____________ x d(n + n*) + x*A(n + n* ) = â•‰â•¯ â•¯â•¯â•¯â•‰+ â•‰â•¯ â•¯ â•¯â•¯â•¯â•‰. * Xâ•¯ (n + n )c (w, r) (n + n*)c X(w, r)

(17.10)

Thus the equilibrium condition for the marginal firm in each country is given by x(nT ) = x d (xT + x*T ) + x*d (xT + x*T ),Â€Â€Â€Â€and

(17.11)

x(n*T ) = x d (xT + x*T ) + x*d (x T + x*T ),

(17.12)

where T indicates a trading equilibrium value. Given equalized factor prices (w = w*, r = r*), the RHS of these equations will be equalized. Thus, the LHS of these equations will also be equalized: x(nT ) = x(n*T ) holds under factor price equalization. These equations imply that the integration of the goods markets unifies the competitive conditions within which firms operate. The range of Â�varieties produced in each country will be equalized as well.14 Lemma 17.1: nT = n*T holds in the trading equilibrium with factor price equalization. This is a natural consequence of both equal efficiency distribution between countries and equalized factor prices. A firm’s competitive strength is determined by its relative efficiency with respect to all other firms operating in the unified market and not only to domestic firms. Given the equalized number of differentiated products, the aggregate profits of this sector will also be equalized: Π(nT ) = Π *â•›(n*T), a prominent feature of the model examined below. We should note that, through the mechanism of competitive selection, the industry structure of the good X sector will be determined endogenously. The process is as follows. Suppose that Foreign is larger than Home in terms of factor endowments. The opening of trade provides an opportunity for entry into the Home’s good X sector because the level of fixed costs in Home is lower

162â•‡â•‡ Cost heterogeneity and trade than that in Foreign. On the other hand, Foreign inefficient firms will not be able to cover higher fixed costs because of efficient Home firms’ entry and will be pushed out. Thus nA < nT = n*T < n*A holds. Note also that this competitive selection aspect has been overlooked in the monopolistically competitive models with symmetric technology. By using the integrated equilibrium technique, we can understand the trade __ patterns in this model.15 Let Vâ•‰ â•‰ â•¯be the world endowment, and (V, V*) = [(L, __ __ factor __ * * K), (L , K )] be a partition. Let Vâ•‰â•› â•‰ â•¯(J) = [â•‰Lâ•‰â•¯(J ), Kâ•‰ â•‰ (J â•¯ )] be the integrated equilibrium use of factors in the good J (J = X, Y, Z) sector. The λJ (λ*J) are shares for Home (Foreign) of the integrated equilibrium production of good J. The factor price equalization (FPE) set in this case is

{ |

FPE = V, V

*

λX, λ *X, λ Y, λ *Y, λZ, λ *Z ≥ 0 such that λ X = λ *X = ½,

Σ

__

Σ

__

}

* λY + λ *Y = 1, λ Z + λ *Z = 1, V = â•‰   â•¯ â•‰ λ J Vâ•‰â•› â•‰ â•¯(J), V * = â•‰   â•¯ â•‰ λ J Vâ•‰ â•‰ â•¯(J) . J J

We may summarize this as follows: (1) each country produces a half-range of differentiated products in the world economy (recall Lemma 17.1); (2) the production of the homogeneous goods (good Y and good Z) may be apportioned among countries; and (3) this is consistent with the full employment of factors in each country. This has a simple geometric interpretation (Figure 17.1). For simplicity, assume that good X is the most capital-intensive good.16 Each country must have sufficient factors to produce the integrated equilibrium supply of differentiated products using the integrated equilibrium ____ ____ technique. This is reflected by the vectors OO´[(½)â•‰V(X)â•‰]â•¯ and O*O´*[(½)â•‰V(X)â•‰], â•¯ respectively. The equilibrium techniques used in the production of good Y and good Z give rise to conical factor spaces for the two countries. Any division of the world factor endowment that falls within the parallelogram generated by the intersection of these two cones allows the replication of the integrated equilibrium.

17.4Â€Â€Trade patterns Now we look at the determinants of the __ patterns of intra-industry trade. Let E be the endowment point. Then the line Eâ•‰ â•‰ â•¯E describes the factor income of every country and has the slope w/r. The Home/Foreign factor income ratio OC´/C´O* is equal to the GDP ratio in the absence of profits. Home has a smaller absolute factor endowment. In the current case of equalized profits, however, each country appropriates an equal share of world profits (i.e., Π(nT ) = Π *(n*T )). The distribution of profits is represented by point C", which is the middle point of the diagonal OO*. Since GDP consists of factor income plus profits, point C on the diagonal OO* that corresponds to relative GDP levels is located between C' and C". Point C also represents the factor content of consumption. Hence the vector of the factor content of trade is represented by EC: Home is seen to be a net importer of labor services and a net exporter of capital services.17

Heckscher–Ohlin trade patternsâ•‡â•‡ 163 Based on this setting, let us consider the patterns of intra-industry trade. Since the production patterns of the differentiated products are equalized between countries (p = p*, x = x*, n = n*), the patterns of intra-industry trade depend only on the consumption patterns. By using Equation (17.10), the relative export value of good X is determined by the relative GDP of countries: * n*px d __ I _________________ wL + rK + Π(nT ) _____ â•¯â•‰â•¯ ≡ â•‰â•¯ *dâ•¯â•¯ â•‰â•¯ â•‰= â•‰â•¯ *â•¯â•¯â•‰â•¯= â•‰â•¯ * â•¯â•¯ â•¯â•¯â•¯â•‰, EX(X ) npx I wL + rK * + Π *(n*T)

EX (X) ______

(17.13)

where EX*(X) represents the export value of Foreign varieties, and EX(X) represents that of Home, respectively. Given that both factor prices and monopolistic profits are equalized between countries, this ratio depends only on the level of absolute factor endowments. That is, given the level of factor income, the pattern of intra-industry trade is independent of the relative factor endowments between __ countries. We may interpret Eâ•‰ â•‰ â•¯E as an iso-intra-industry trade volume curve. In Figure 17.1, while each country exports its own varieties, Home (the smaller country in terms of factor income) becomes the net exporter of differentiated products: [EX *(X)/EX(X)] < 1 holds. This is because Home has relatively stronger competitive strength in the differentiated products.18 Despite its smallness in terms O*

V(Z )

O *' B'

V(Y )

E

E

K

E' D C'

C''

C E E

O'

O

Figure 17.1Â€Â€FPE set.

L

164â•‡â•‡ Cost heterogeneity and trade of absolute factor endowments (i.e., factor income), the range of Home varieties is the same as that of Foreign varieties, which is a natural consequence of competitive selection in the integrated market. Proposition 17.1: Given that factor prices are equalized, the country with the smaller factor income becomes a net exporter of the differentiated products. Now turn to the patterns of inter-industry trade. First, we have to show the consumption patterns of both good Y and good Z. Since each country’s demand for good Y(Z) is proportional to its size of GDP, we have to construct a parallelogram between O´ and some point on the diagonal O´O*´. Let us call this point D. Point D must be chosen to meet the condition that the ratio O´D/O´O*´ equals OC/OO* since the relative size of Home is represented by the latter.19 Thus a parallelogram constructed between O´ and D determines the Home consumption patterns of good Y and good Z. Based on the above setting, we examine the effects__ on inter-industry trade patterns as movements along the iso-factor-income line (â•‰Eâ•‰â•¯E). Within the FPE set, the factor content of consumption (the vector O´D for both good Y and good Z) remains unchanged. Thus we only have to concentrate on the production patterns. To examine trade patterns, it is useful to construct parallelograms between O´ and E as well as O´ and D. By comparing these parallelograms __we can understand the patterns of inter-industry trade. We will divide the segment Eâ•‰ â•‰ â•¯E into three parts. 1 2

3

__

Segment Eâ•‰ â•‰ â•¯E´ (e.g., E): in this case, Home is sufficiently capital-rich and __ exports good Y while importing good Z.20 As we move from Eâ•‰ â•‰ â•¯ to E´, Home produces less of good Y and the volume of inter-industry trade decreases. Segment E´E´´ (e.g., C´): in this case, Home exports only good X while importing both good Y and good Z. When we reach C´, each country has the same factor endowment ratio. However, Home is a net exporter of the capitalintensive good X. This pattern remains unchanged even if Home becomes a labor-abundant country. Segment E´´ E: in this case, Home is sufficiently labor-rich and exports good Z while importing good Y. As we move from E´´ to E Home produces more of good Z and the volume of inter-industry trade increases.

While cases (1) and (3) are consistent with Heckscher–Ohlin trade patterns, case (2) (i.e., a labor-rich country exporting mostly capital-intensive goods), which is inconsistent with factor proportion predictions, emerges in this model. This quite unusual trade pattern is due to the existence of the monopolistically competitive sector with efficiency gaps. In this case, Home imports both labor and capital services, and pays for these services with monopolistic profits.21 It is important to note that case (2) emerges as a consequence of unequal size between countries. As the relative size of two countries becomes closer, the relative export value of good X approaches unity and the segment E´E” becomes

Heckscher–Ohlin trade patternsâ•‡â•‡ 165 narrower. When each country has the same level of factor income, intra-industry trade will be balanced (i.e., [EX*(X)/EX(X)] = 1 holds) and case (2) never occurs. Repeating the above procedure for every relative size of two countries, we summarize trade patterns in Figure 17.2. We will divide the FPE set into four areas. As relative size differences become larger, the segment of cases (2) and (2´) becomes larger, while the range of Heckscher–Ohlin cases (i.e., cases (1) and (3)) becomes narrower. Let us consider the relationship between the international distribution of factor endowments and trade patterns more precisely. Consider first if the endowment point is located within area (1) in Figure 17.2.22 In this case, the effect of the difference in relative factor endowments dominates that of the difference in absolute factor endowments. Point A is a good example. Here, the two countries are relatively similar in terms of their absolute factor endowments. In this case, the export values of good X in both countries are not very different from each other (recall (17.13) and Proposition 17.1). Thus the net trade patterns are determined mainly by relative factor endowments – relatively capital-rich Home will export Good Y and import Good Z. Next, assume that the endowment point is located within area (2). While Home is smaller in terms of absolute factor endowments, the difference in factor O*

V(Z )

O *' B'

(b' )

V(Y ) A

(a )

C''

K

(c )

E' E'' (b )

B O'

O

Figure 17.2Â€Â€Trade patterns.

L

166â•‡â•‡ Cost heterogeneity and trade endowment ratios is relatively small.23 Since both countries produce the same amount of good X through the mechanism of competitive selection, the smaller Home becomes a net exporter of good X (recall Lemma 17.1). Given that good X is the most capital intensive, the trade pattern in this area does not always follow the Heckscher–Ohlin theory. If the endowment is at point E”, for example, relatively labor-abundant Home will export capital-intensive good X. In other words, the role of the Heckscher–Ohlin trade pattern will be downplayed within area (2): the effect of differences in absolute factor endowments will dominate that of differences in relative factor endowments. The above two cases highlight the relationship between relative and absolute factor endowments in determining trade patterns. Overall trade patterns are determined by the interaction between relative factor endowments as suggested by Heckscher and Ohlin, and absolute factor endowments via competitive selection in the unified market, as shown in Figure 17.2.24 We summarize the determinants of trade patterns as follows. Proposition 17.2: (1) If two countries are close in size in terms of absolute factor endowments, the Heckscher–Ohlin trade patterns are observed: relative factor endowments determine trade patterns. (2) However, if two countries are different in terms of absolute factor endowments, the role of competitive selection in the monopolistically competitive sector is emphasized. Since the production of differentiated goods is equally distributed between countries, the smaller country will become a net exporter of differentiated products.

17.5Â€Â€Concluding remarks In this chapter, by constructing a monopolistically competitive model with efficiency gaps, we highlight the interaction between relative factor endowments (i.e., a Heckscher–Ohlin aspect) and absolute factor endowments (i.e., the mechanism of competitive selection) as determinants of trade patterns. On the one hand, the pattern of intra-industry trade is determined by absolute factor abundance, since the range of varieties is equalized through a mechanism of competitive selection. On the other hand, the pattern of inter-industry trade is mainly determined by relative factor endowments. It should be emphasized that the overall trade patterns are determined by the tension between these two forces. It should also be noted that the current analysis has empirical as well as theoretical significance. Trefler’s (1995) influential study identifies that factor service trade is much smaller than its factor endowments prediction: in particular, endowment (ratio) similarity is associated with poor predictions. By emphasizing the role of competitive selection as a determinant of the trade pattern, this chapter is intended to provide theoretical background to “the case of the missing trade.” Let us describe two directions in which the model could be extended. First, let us consider the assumption about the efficiency gaps in a monopolistically competitive sector. For simplicity, we have assumed that a ranking of fixed

Heckscher–Ohlin trade patternsâ•‡â•‡ 167 inputs is monotone and that these rankings are identical between two countries (i.e., µ = µ* = 1 in Equation (17.3)). Because of these assumptions, each country produces a half-range of differentiated products in the trading equilibrium (recall Lemma 17.1). Relaxing these assumptions and introducing inter-country technology gaps (i.e., µ ≠ µ*) does not change the qualitative results. Even with intercountry efficiency gaps, the zero-profit output for each marginal firm will be equalized (i.e., x(nT ) = x(n*T )). This implies that both countries’ marginal firms have to have equal fixed costs in the trading equilibirum.25 Hence, given that factor prices are equalized, the equilibrium number of firms is determined by the following condition: µnT = µ*n*T. The important point is that the distribution of firms in the differentiated products sector will be determined through competitive selection in the unified market. Note also that this competitive selection further determines the volume of intra-industry trade.26 Next, let us consider the role of factor intensity rankings. For a graphical exposition, we have assumed that good X is the most capital intensive. However, this capital intensity ranking itself does not alter the results of this chapter. For example, if good X were the most labor-intensive good, we could construct a figure similar to Figure 18.1. Furthermore, the interaction between factor proportions and competitive selection still remains. In summary, the current model may be extended to more general models with inter-country efficiency gaps and Â�different factor intensity rankings.

17.6Â€Â€Appendix: Derivation of the line BB´ On the line BB´ in Figure 17.2, the Home’s supply quantity of Good Y, Ys, must be equated to the Home’s demand quantity, Yd. By using the conditions for the clearing of factor markets we obtain the supply quantity:

/

Z z Y s = [c r (L – δ L) – c w (K – δK)] (c Y c Z – c Z c Y ). w r w r

On the other hand, we obtain the demand quantity as follows: Yd = (β/cY )(wL + rK + Π). Substituting these equations into Y s = Y d, we obtain the condition for the line BB´:

[

/

Y Z K = (c cY –â•›∆βw)

(cY cYZ +â•›∆βr)

where ∆ ≡ c wY c Zy – c Zw cYY.

] [

Y Z Y Z Lâ•›+â•› (c c w δ K –â•›c cY δ L + ∆βΠ )

/

(cY cYZ –â•›∆βr)

]

,

18 Chamberlinian–Ricardian trade patterns

18.1Â€Â€Introduction1 It is well known that the share of intra-industry trade (i.e., two-way trade of similar products) in world trade has increased over the post-Second World War period and today it represents a significant proportion of overall trade. The European Union provides a prime example: Fontagne, Freudenberg, and Peridy (1997) find that the share of intra-industry trade in Europe increased from 55 percent in the early 1980s to 65 percent in 1994. East Asia offers another important case study. As economic integration in this region progresses, trade patterns are displaying an ever-greater complexity: though inter-industry trade is still dominant, its share of overall trade is declining. Meanwhile, intra-industry trade is growing in importance.2 Fukao, Ishido, and Ito (2003) note that the technology transfer via inward FDI played an important role in changing East Asian trade patterns. Chamberlinian monopolistic competition models of trade (Krugman 1979; Helpman and Krugman 1985) provide an elegant account of intra-industry trade and play a major role in the recent literature. Based on the assumption of identical, increasing returns-to-scale technology across countries, both relative country size and factor endowment similarity are emphasized as determinants of the volume of intra-industry trade. For example, Helpman (1987) notes that as countries become more similar in size, the volume of intra-industry trade as a proportion of world GDP should increase. As a result, there has been little investigation of technological differences among countries as a determinant of intra-industry trade. However, the increasing importance of technological aspects as a determinant of trade patterns seems to suggest that existing focus on the “Chamberlinian” nature of intra-industry trade should be accompanied by a new attention to “Ricardian” technical heterogeneity. In this chapter we want to provide a simple trade model which emphasizes the relationship between Ricardian cross-country technological differences and Chamberlinian monopolistic competition. We take the standard one-factor monopolistically competitive model (Krugman 1979) as a point of departure, and extend the analysis to include both (1) a large number of industries, and (2) cross-country technical heterogeneity in both fixed costs and marginal costs.3 We

1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Chamberlinian–Ricardian trade patternsâ•‡â•‡ 169 show that trade patterns are determined by the interaction between cross-country technical heterogeneity (i.e., a Ricardian aspect) and monopolistic competition among producers of differentiated products (i.e., a Chamberlinian aspect). In particular, the emergence of intra-industry trade is crucially dependent on the shape of the technology index schedule, which is obtained as a step-function. We also show that, if technology transfer occurs and the share of similar industries becomes larger between countries, the share of intra-industry trade also rises. This model helps to explain the growing importance of intra-industry trade in the world economy. Section 18.2 develops a Chamberlinian–Ricardian model with many industries. Section 18.3 deals with the determinants of trade patterns. Section 18.4 Â�discusses the relationship between technology transfer and the growth of intraindustry trade. Section 18.5 concludes this chapter.

18.2Â€Â€The model Suppose that there are two countries in the world, Home and Foreign. Each country is endowed with L units of labor and the only source of income is the wage, w. We assume that there are M manufacturing industries. Industry-specific variables will be indexed by industry label i (i = 1, …, M ). Consumers have Cobb–Douglas preferences and purchase equal values of the output of all industries. Each industry is modeled as a Dixit–Stiglitz (1977) monopolistically competitive industry, so the quantity index of industry i takes the form __ â•¯θ1â•¯ â•‰ ni n˜ i θ X i = â•‰ â•‰ â•¯ â•⁄â•‰â•¯â•‰â•‰â•‰ d ki â•¯â•‰ + â•‰ â•¯ â•⁄â•‰â•‰ â•‰â•¯â•‰  d k˜i â•¯â•‰θ  â•‰â•‰ , 0 < θ < 1,

  

 

kâ•›=1

˜ =1 kâ•›



(18.1)

where ni (ñ i) is the number of products produced in industry i in Home (Foreign), ˜ in the Home market, and σ ≡ 1/(1 – θ ) > 1 d ki (dk˜i ) is the quantity of product k (k) is the elasticity of substitution between every pair of products. The price index of industry i may be obtained as:

  

_____ ni n˜ i â•‰â•¯θ θ–â•› 1â•¯â•‰ pi = â•‰ â•‰ â•¯â•‰â•¯â•‰â•⁄â•‰â•‰ pki â•¯â•‰â•¯â•‰   â•¯â•‰â•¯+ â•‰ â•¯â•⁄â•‰â•¯â•‰â•‰â•‰ pk˜i â•¯ â•‰â•¯â•‰   â•¯â•¯â•‰â•¯ â•‰ , θ _____ θ–1

kâ•›=1

 

θ _____ θ–1

˜ =1 kâ•›



(18.2)

where pki ( pki ) is the price of the k (˜k )-th differentiated product produced by industry i in Home (Foreign). Note that the total revenue in Home is wL, which will be disbursed in the same manner in each industry due to the assumption of Cobb–Douglas preferences. Solving the consumers’ maximization problem yields the following demand functions for Home consumers:

 

1 _____ wL _________ ˜ dgi = â•‰ pgi â•¯â•‰â•¯â•‰θ –â•›â•¯1â•¯â•‰â•¯â•‰â•‰â•¯ â•¯ â•¯â•‰â•¯â•¯ â•‰where g = k, k. M(P)θ/(θ – 1)



(18.3)

170â•‡â•‡ Cost heterogeneity and trade Assuming that the products are transported at no cost between countries, the prices of each product in two countries are equal. Therefore, the demand functions for Foreign consumers are

 

˜ 1 _____ w ˜L _________ d˜gi = â•‰ p gi â•¯â•‰â•‰â•¯θ –â•›â•¯1â•¯â•¯â•‰â•‰â•‰â•¯ â•‰where g = k, ˜k. θ â•¯ â•¯â•‰â•¯â•¯ M(P) / (θ – 1)



(18.4)

Differentiated products are supplied by monopolistically competitive firms. There is cross-country technical heterogeneity: each Home (Foreign) firm in industry i has both α i (α˜ i) units of labor as a fixed input and β i ( β˜ i ) units of labor as a variable input. With the number of firms being very large, the elasticity of demand for each product becomes σ. Thus, each product is priced at a mark-up over marginal cost: σβw σβ w ˜ ______ ______ p ki = â•‰â•¯ â•¯â•¯â•‰,â•¯â•›p i = â•‰â•¯ â•¯â•¯â•‰.â•¯ (σ – 1) k (σ – 1) Using these pricing equations, the summation in Equation (18.2) takes the form θ _____ θ _____ θ ni n˜ i _____ ˜ iw θ _____ β iw â•‰â•‰â•¯θ –â•› 1â•¯â•¯ β___ ˜ â•‰â•¯θ –â•› 1â•¯â•‰â•¯ i ____ â•‰ â•¯ â•⁄â•‰â•‰ â•‰â•¯â•‰  p ki â•¯â•‰â•¯â•‰θ –â•› 1â•¯â•¯â•‰+ â•‰ â•¯ â•‰â•⁄â•‰â•‰ â•‰â•¯  pk˜ â•¯â•‰â•‰â•¯θ –â•› 1â•¯â•‰â•¯= niâ•‰ â•‰â•¯   â•¯â•‰â•¯â•¯ â•‰+ ñ i â•‰ â•‰â•¯   â•¯â•‰â•¯ â•‰ . θ θ kâ•›=1 ˜ =1 kâ•›

 

 

  

  

Substituting this into the demand function yields the profit function of each Home firm:4 π i = ( p i – β i w)x – α i w 1–θ i _____ â•‰â•¯β w(d i + d˜ i ) – α iw = â•‰â•¯     θ θ _____

β i w â•‰â•¯θ –â•› 1â•¯â•¯ ____ (1 – θ )â•‰ â•‰â•¯   â•¯â•‰â•¯â•¯ â•‰ ˜ wL + w ˜L â•‰ θ ____________________ ________ â•¯ â•¯ â•‰â•¯– α iw, = â•‰â•¯ â•¯â•¯ â•¯â•¯ θ â•‰ â•‰â•¯ _____ θ _____ M â•¯   â•¯â•‰ â•¯ i i θ –â•› 1 â•¯   â•¯ â•¯ ˜ β w θ –â•›1 βw ˜ â•¯ ni â•‰ ____ â•‰â•¯   â•¯â•‰â•¯ â•‰â•‰ â•‰+ ñ iâ•‰ ____ â•‰â•¯   â•¯â•‰â•¯â•¯ â•‰â•‰ θ θ

  

  

  

(18.5)

where x is the output level of each Home firm. Similarly, the profit function of each Foreign firm is θ _____ ˜ iw ˜ â•‰â•¯θ –â•› 1 â•¯ β____ (1 – θ) â•‰ â•‰â•¯   â•¯â•‰â•¯ â•‰ â•¯ wL + w ˜ L˜ â•‰ θ _____________________ ________ â•¯ â•¯ â•‰â•¯– α˜ iw π˜ i = â•‰â•¯ â•¯â•¯ â•¯â•¯ ˜ , θ â•¯â•‰â•‰ â•‰â•¯ _____ θ _____ M â•‰â•¯   â•¯ i i â•‰â•¯   â•¯ ˜ θ –â•›1 θ –â•›1 β β w w ˜ ____ ____ ni â•‰ â•‰â•¯   â•¯â•¯â•‰â•¯ â•‰ â•¯â•‰+ ñ i â•‰ â•‰â•¯   â•¯â•‰â•¯ â•‰ â•¯ θ θ

        

(18.6)

Consider the specialization pattern of industry i. The trading equilibrium with zero-transport costs requires non-positive profits in industry i of each country,

1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Chamberlinian–Ricardian trade patternsâ•‡â•‡ 171 with profits being equal to zero if production takes place. Thus, by setting profits equal to zero for both countries (π i = π˜ i = 0), we can determine whether the coexistence of both countries’ firms is consistent with equilibrium. First, let us draw attention to the condition that, if both countries’ firms in industry i coexist, profits must be identical for each country’s firms, i.e., π i =â•›π˜ i,

(18.7)

This is the condition that must be satisfied if π i = π˜ i = 0 is to hold. Substituting (18.5) and (18.6) into (18.7), we obtain θ ____ wL +â•›w ˜ L˜ ________ â•‰â•¯ â•¯ â•¯ â•‰(1 – θ )θ â•‰â•¯1â•›–â•› θ â•¯ â•¯ ˜ iw α iw – α â•‰ â•¯ _________________ ˜ M _____________________ â•¯â•‰ = â•‰â•¯ â•¯â•¯ â•¯â•¯ â•¯â•¯ â•¯â•¯ â•‰â•¯ θ θ θ â•¯â•‰. _____ _____ _____ θ _____ â•‰ â•¯   â•¯ â•¯â•‰ â•¯ i i i i θ –â•› 1 θ â•¯   â•¯ ˜ ˜ θ –â•› 1 θ –â•› 1 βw βw ˜ â•‰ β wâ•¯â•‰â•‰â•¯   – â•‰ β w ˜ â•¯â•‰â•‰â•¯ –â•› 1â•¯â•‰â•¯ ni â•‰ ____ â•‰â•¯   â•¯â•¯â•‰â•¯ â•‰â•‰ â•¯â•‰+ ñ i â•‰ ____ â•‰â•¯   â•¯â•‰â•¯â•¯ â•‰â•‰

  θ 

  θ 

(18.8)

Inserting the RHS of (18.8) into the profit function yields θ

_____ (β iw)â•‰â•¯θ –â•› 1â•¯â•‰â•¯(α i w –â•›α˜ i w) ˜ __________________ i π = â•‰â•¯ â•¯â•¯ â•¯â•¯ θ θ â•‰â•¯â•‰– α w, _____ _____ â•¯â•‰ â•¯ â•¯ â•¯ i i ˜ θ –â•› 1 θ –â•› 1 (β w)â•‰â•¯   – (β w ˜ )â•‰â•¯  

i

θ _____

˜ iw   â•‰_________________ β ˜ â•¯â•‰â•‰â•¯θ –â•› 1â•¯â•‰â•¯(α iw – α˜ i w ˜)

π˜ = â•‰â•¯ i

˜ i˜ . â•¯â•¯ θ â•‰â•¯â•‰–â•›â•›α w _____ â•¯â•‰ â•¯ â•¯ i θ –â•› 1 ˜ (β w)â•‰â•¯   – â•‰ β w ˜ â•¯â•‰â•‰â•¯   i

θ _____

θ –â•›1 â•¯

Note that this holds only if π i = π˜ i. It is also important to note that profits are independent of the total number of firms. Before turning to the case of coexistence, note that the equilibrium number of firms for the case in which only one country’s firms exist is ˜ (1 – θ )(wL +â•›w ˜ L) _______________ iT â•¯ n{ñiâ•› â•¯â•¯ â•‰, â•¯ =â•›0} = â•‰â•¯ Mα i w

(18.9)

˜ (1 – θ )(wL +â•›w ˜ L) _______________ iT ñ {niâ•› â•¯ â•‰, â•¯ i â•¯â•¯ =â•›0} = â•‰â•¯ ˜ Mα w ˜

(18.10)

where T denotes a trading equilibrium value. Using these results, we obtain the necessary condition for the coexistence of firms. Let us define a technology index for industry i:

     

˜i θ ˜ i 1–θ β__ α ___ Ai ≡ â•‰ â•‰â•¯ iâ•¯â•¯â•‰â•¯â•¯ â•‰ â•‰ â•‰â•¯ iâ•¯â•¯â•‰â•¯ â•‰ . α β

(18.11)

In the free-trade equilibrium the profit must be zero: π i = π˜ i = 0. Simple calculations show that the equations are satisfied only if the technology index, Ai, is equal to the relative wage rate ω ≡ w/w ˜.

172â•‡â•‡ Cost heterogeneity and trade Proposition 18.1: If Ai > (<)ω, only Home (Foreign) firms produce the differentiated products in industry i. Intra-industry trade in industry i (i.e., the coexistence of both countries’ firms) occurs only if Ai = ω. Proof. Suppose that Ai > ω. In this case, both countries’ firms cannot coexist. To see that in equilibrium only Home firms are active, we must show that if Home firms make zero profits, then the profit of a foreign firm would be negative if it enters. π˜

i {ni=niT,ñi=0}

θ

_____ 1 _____ β iw â•‰â•¯1 –â•› θ â•¯â•‰ i ω 1 – θ â•¯ ____ __ = â•‰ â•‰â•¯˜ i â•¯â•¯â•‰â•¯ â•‰ α w –â•›α˜ iw ˜ = α˜ i w ˜ â•‰â•‰ â•‰â•¯ i â•¯â•‰â•¯ â•‰â•¯â•‰ â•¯  â•‰– 1â•¯ â•‰,

 β w˜ 

  A 



where we have substituted (18.9) into (18.5). This becomes negative if Ai > ω since θ ∈ (0,1). Therefore, Foreign firms have no incentive to enter given that niT Home firms are active.5 On the other hand, the case in which only Foreign firms are active cannot support a free trading equilibrium. This is because θ ____

π

i {ni=0,ñi=ñiT }

  

1 _____ ˜ iw ˜ â•‰â•¯1â•›–â•› θ â•‰â•¯â•› i β____ Ai â•‰â•¯1 –â•¯θ â•‰â•¯ __ i i ˜ â•‰â•¯ â•‰ α w = â•‰ â•‰â•¯ i â•¯â•¯â•¯ ˜ – α w = α w â•‰â•‰ â•‰â•¯  â•¯â•‰â•¯ â•‰ – 1â•¯ â•‰ βw ω

   



is positive, and hence Home firms have an incentive to enter the world market. Therefore, only Home firms produce the differentiated products in industry i in the free trade equilibrium. The case of Ai < ω may be proven analogously.

18.3Â€Â€Trade patterns To obtain the world trading equilibrium, we index industries in the order of their diminishing Home comparative advantages: A1 ≥ … ≥ Ai – 1 ≥ Ai ≥ Ai + 1 ≥ … ≥ AM, where Ai is defined in (18.11). This schedule is drawn in Figure 18.1 as step function AA. Let m denote a hypothetical dividing industry between Home- and Foreignproduced commodities such that industries 1 to (m – 1) are captured by Home, while industries (m + 1) to M are captured by Foreign. In addition, let sm (0 ≤ sm ≤ 1) denote Home’s production share in industry m. Equilibrium in the market for Home products requires that Home labor income, wL, equals world spending on Home-produced products: (m – 1 + sm) __________ ˜ â•¯ â•‰â•¯ (wL +â•›w ˜ L). wL = â•‰â•¯ â•¯ M This schedule is drawn in Figure 18.1 as the upward-sloping locus OB and is obtained by rewriting the equation in the form

1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Chamberlinian–Ricardian trade patternsâ•‡â•‡ 173 v B B'

C C'

Possible intra-industry trade O

1

m�1

A

m

Figure 18.1Â€Â€Intra-industry trade.

˜ (m + sm – 1) L __ ω = _______________ â•‰â•¯ â•¯â•¯ â•¯â•¯â•¯â•‰â•‰â•¯ â•¯â•‰. [M – (m + sm – 1)] L The equilibrium relative wage is obtained as the intersection of schedules AA and OB.6 Two types of trading patterns emerge as possible trading equilibria. First, assume that the intersection is obtained at the flat segment in the AA schedule (e.g., C). Thus, the following condition holds: ω = Am. In this case, from Proposition 18.1, firms within industry m can be located in both countries: intra-industry trade within industry m will occur while inter-Â� industry trade occurs in other industries. Chamberlinian determinants of trade in industry m (i.e., monopolistic competition between producers of differentiated products) is emphasized in this case. Second, assume that the intersection is obtained at the vertical segment of the AA schedule (e.g., C´). Then the following condition holds: Am > ω > Am – 1.

174â•‡â•‡ Cost heterogeneity and trade In this case, firms within industries 1 to (m – 1) are located in Home, while firms within industries m to M are located in Foreign.Then, no intra-industry trade occurs between countries: Ricardian productivity differences are emphasized in this case. The above two scenarios are summarized as follows. Proposition 18.2: If the OB schedule cuts a flat segment of the AA schedule, intra-industry trade occurs between countries. If the OB schedule cuts a vertical segment of the AA schedule, no intra-industry trade occurs between countries. This proposition implies that the size of each industry (i.e., the share of an industry in the total number of industries) plays an important role in determining trade patterns.7 On the one hand, if there is a continuum of industries (Dornbusch, Fischer, and Samuelson 1977), intra-industry trade hardly occurs. On the other hand, if the technology-index step function has relatively wide steps, the possibility of intra-industry trade rises. With regard to the latter point, we explore the impact of technology transfer on trade patterns in the next section.

18.4Â€Â€Technology transfer and intra-industry trade In the literature of technology and trade, it is often assumed that closer economic integration can be achieved by increasing trade in goods or increasing the flow of ideas across borders. This implies that a firm in a given industry acquires technical information from the activities of firms in its own industry operating in other countries. With that in mind, let us consider the impact of technology transfer. Although we do not have an explicit model of technology transfer, we can investigate how trade patterns respond to it. Before technology transfer occurs, cross-country information flow is limited: intra-industry trade occurs only at the marginal sector m (e.g., C´ in Figure 18.2). Then, suppose that for some industries, production technologies have become standardized by the international transfer of the least-cost technology.8 This transfer changes the shape of the technology index schedule: within some range, both α =â•› α˜ and β =â•› β˜ hold, and the value of the technology index Ai becomes 1 for those industries. In other words, step function AA will come to have wider steps as the result of newly standardized industries. This type of technology transfer gives rise to intra-industry trade within those standardized industries. This also suggests that the share of intra-industry trade between countries which share common technology can be large, which is consistent with empirical findings.9

18.5Â€Â€Concluding remarks In this chapter, by constructing a monopolistically competitive model with many industries, we highlight the interaction between cross-country productivity

1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Chamberlinian–Ricardian trade patternsâ•‡â•‡ 175 v B'

C'

1

Possibility of intra-industry trade A' O

Figure 18.2Â€Â€Technology transfer and intra-industry trade.

Â� differences (i.e., a Ricardian aspect) and competition within each monopolistically competitive industry (i.e., a Chamberlinian aspect). Trade patterns are Â�crucially dependent on the shape of the technology index schedule, which is obtained as a step function. In his influential study, Krugman (1979, p. 479) argues that trade need not be a result of cross-country differences in technology. We would like to emphasize that the degree of cross-country technical differentiation among industries plays a more important role as a determinant of trade within each industry. We believe that one benefit of our model is its simplicity: the introduction of Ricardian comparative advantage in the Chamberlinian monopolistic competition model with many industries does not make the exercise intractable. Thus we can use this model, and add to it, in order to answer a number of interesting and relevant questions. For example, we can use it to look at the circular relation between intra-industry trade and technology transfer, as emphasized in recent empirical studies.10

19 Strategic export policies

19.1Â€Â€Introduction The theory of strategic export policy for oligopolies started with an article by Brander and Spencer (1985). In their model, a domestic government first decides upon a linear export subsidy, and then a domestic firm and a foreign firm compete (Cournot fashion) in a third market. Although extensive studies considered strategic export policy,1 two points have been given relatively less attention. One is an extension of this analysis to Bertrand competition. Neary (1994) and de Meza (1986) discovered that, under a Cournot framework, the more costcompetitive the home firm, the higher the magnitude of the optimal export subsidy. However, little is known about the comparable relationship under a Bertrand framework. The other issue is how the degree of product differentiation affects strategic export policies.2 In particular, most studies fail to account for the case of complements.3 The purpose of this chapter is to further explore how optimal export policies are affected by the nature of oligopolistic competition (Cournot or Bertrand) and the structure of demand (substitutes or complements). A model is laid out that synthesizes and extends previous work on strategic export policy in the context of a differentiated duopoly. The chapter defines precisely the strategic effect and the allocation effect, and shows their importance in determining the magnitude of optimal export policies. The findings indicate that Neary’s proposition holds in most modes of duopolistic competition. This chapter also addresses the role of the degree of product differentiation. As the goods become better complements, the optimal level of export intervention is shown to increase. Some of the results in this chapter are not new, and our analysis depends crucially on the assumption of linearity. Nonetheless, the geometric analysis of strategic export policies presented here provides some valuable insights into relevant issues.

19.2Â€Â€The model Consider a third-market model in a differentiated duopoly with linear demand and cost functions.4 Such a model is specific, but with general demand and

Strategic export policiesâ•‡â•‡ 177 cost functions we cannot explicitly examine how optimal export policies are affected by the nature of oligopolistic competition and the degree of product differentiation. Denote the prices of the good produced by the home firm (called the home good) and the good produced by the foreign firm (called the foreign good) in the third country by, respectively, p and q. The inverse demand functions for the home and foreign goods in the third country are, respectively, p = α – β x – γ y,Â€Â€Â€Â€Â€Â€Â€Â€|β | > |γ | ≥ 0 and q = α – βy – γ x,Â€Â€Â€Â€Â€Â€Â€Â€|β | > |γ | ≥ 0. Here, x and y are the quantities of the home and foreign goods in the third country. β is a positive constant, and γ denotes the degree of product differentiation. If 0 < γ < β, the goods are substitutes. On the other hand, if –β < γ < 0 they are complements, and if γ = 0 they are independent. The home firm’s profit with a specific subsidy s offered by the home government is π = ( p – c + s)x = (α – βx – γ y – c + s)x, where c is the home firm’s constant marginal cost. Similarly, the foreign firm’s profit is π* = (q – c*)y = (α – βy + γ x – c*)y. where letters with asterisks denote corresponding magnitudes for the foreign firm. Cournot competition Under the assumption of Cournot behavior, the first-order conditions of profit maximization for the home and foreign firms are, respectively, ∂π ___ â•‰â•¯ â•¯â•¯â•‰= α – 2βx – βγ y – c + s = 0 ∂x

and ∂π* ____ â•‰â•¯ â•¯â•‰â•¯= α – 2βy – γ x – c* = 0. ∂x From these equations the equilibrium quantities of the home and foreign goods in the third country and responses of x and y to a change in s are obtained as follows:

178â•‡â•‡ Cost heterogeneity and trade 2β (α – c + s) – γ (α – c*) ______ ∂xC (s) _______ 2β xC (s) = _____________________ â•‰â•¯ â•¯â•¯, â•‰â•¯ , â•¯â•‰ â•¯ â•¯ â•‰â•¯= â•‰â•¯ 2 â•¯ 2â•¯â•‰â•›â•›â•¯ 2 2â•¯â•¯ (4β – γ ) ∂s 4β – γ

(19.1)

2β (α – c*) – γ (α – c + s) ∂yC(s) _______ γ _____ yC(s) = _____________________ â•‰â•¯ â•¯â•‰ â•¯â•¯,Â€Â€Â€Â€Â€Â€Â€Â€â•‰â•¯ â•¯ â•¯â•‰, â•¯ â•¯ â•‰= â•‰â•¯ 2 â•¯ 2â•¯ 2 2â•¯â•¯ 4β – γ ∂s 4β – γ

(19.2)

and

where superscript C means Cournot competition. Now consider the optimal export subsidy for the home country. The welfare of the home country is represented by W(s) = π – sx = (p – c)x. Differentiating W with respect to s yields dW(s) _____ â•‰â•¯

2β ∂p dy dx 2 _____ ___ xC(s) – â•‰â•¯________ â•¯ â•¯â•‰â•¯ s. â•¯ â•¯ â•‰â•¯= x â•‰â•¯ â•¯â•¯ â•‰– s â•‰â•¯ â•¯â•¯â•‰= γ â•‰â•¯________ 2 â•¯ 2â•¯â•‰â•¯ ds ∂y ds ds 4β 2 – γ 2 4β – γ

An infinitesimal change in the level of the subsidy causes two effects. The (marginal) strategic effect, ∂p dy _______ γ 2 STC(s) = xC(s) â•‰â•¯_____â•¯â•¯ xC(s) â•‰= â•‰â•¯ 2 â•¯ 2â•¯â•‰â•¯ ∂y ds 4β – γ γ 2[2β (α – c + s) – γ (α – c*)] = â•‰â•¯________________________ â•¯â•¯â•¯ â•¯â•‰ â•¯â•¯, (4β 2 – γ 2)2

(19.3)

represents the extra benefits to producers from capturing additional rent. This effect arises from induced changes in the foreign firm’s output. The (marginal) allocation effect, dx 2β ALC(s) = s â•‰â•¯___â•¯â•¯â•‰= _______ â•¯ â•¯â•‰â•¯ s, â•‰â•¯ ds 4β 2 – γ 2

(19.4)

indicates the additional loss from a distorted resource allocation. An increase in s induces expansion of the home firm’s output, and this causes a wider divergence of social marginal revenue and social marginal cost. Clearly, the magnitude of these effects depends on the level of the subsidy. The relationship between the level of the export subsidy and these two effects is summarized graphically in Figure 19.1(a); the greater the value of the subsidy, the greater these two effects become. If the STC exceeds the ALC, it is beneficial to raise the level of the subsidy. At the optimal level, these two effects completely offset each other. The optimal subsidy in the case of Cournot competition (soptC hereafter) is γ 2[2β (α – c) – γ α – c*] ____________________ soptC = â•‰â•¯ â•¯â•¯ â•¯â•¯ â•¯â•‰, 4β (4β 2 – γ 2)

(19.5)

Strategic export policiesâ•‡â•‡ 179 Having done the groundwork, we are now in a position to examine some comparative statics. First, consider the degree of product differentiation.5 An increase in the value of γ from 0 toward β reflects an increase in substitutability between the home good and the foreign good. Similarly, a decrease in the value of γ from 0 toward -β reflects an increase in complementarity between the home good and foreign good. The relationship between the degree of product differentiation and the optimal export policies is summarized in Figure 19.2(a).6 The figure shows that the magnitude of soptC increases as goods become more interdependent. This may be interpreted to mean that there is more room or government intervention if goods become more interdependent and the magnitude of the strategic effect becomes larger. Figure 19.1(b) helps to define the effects of a change in the degree of product differentiation. An increase in the degree of substitutability (resp. complementarity) shifts the STC and ALC schedules upward. Since the shift in STC is larger than that in ALC, the magnitude of the optimal export subsidy increases as the absolute value of γ increases. Next, consider the comparative static effects of the marginal cost. From Eq. (19.1) we see that the lower the marginal cost of the home firm, the more it produces. This enhances the strategic effect (see eq. (19.3)), and may be shown as an upward shift in the STC schedule in Figure 19.1(a). On the other hand, the level of the home firm’s marginal cost does not directly affect the allocation effect. Therefore, the lower the marginal cost of the home firm, the higher the optimal subsidy level. This is consistent with the proposition of Neary (1994, p. 203). Bertrand competition Using procedures analogous to those used in the above subsection, the equilibrium quantities of the home and foreign goods in the third country and responses of x and y to a change in s under Bertrand behavior are found to be β [(2β 2 – γ 2)(α – c + s) – βγ (α – c*)] _______________________________ â•¯â•‰, xB(s) = â•‰â•¯ â•¯â•¯â•¯ â•¯â•¯â•¯ (β 2 – γ 2)(4β 2 – γ 2) ∂x (s) ______ â•‰â•¯

B

â•¯ â•¯ â•‰â•¯= â•‰â•¯

∂s

(19.6)

β(2β – γ ) ________________ â•¯â•¯ 2 2 â•¯â•¯ 2 2 â•¯â•‰, 2

2

(β – γ )(4β – γ )

and β [(2β 2 – γ 2)(α – c*) – βγ (α – c + s)] _______________________________ y B(s) = â•‰â•¯ â•¯â•‰, â•¯â•¯â•¯ â•¯â•¯â•¯ (β 2 – γ 2)(4β 2 – γ 2)

(19.7)

∂y (s) ________________ βγ (α – c) ______ â•‰â•¯ â•¯ â•¯ â•‰â•¯= â•‰â•¯ 2 2 â•¯â•¯ 2â•¯â•¯ 2 â•¯â•‰, C

∂s

(β – γ )(4β – γ )

where superscript B means Bertrand competition.7 Eaton and Grossman (1986) show that the optimal export policy under Bertrand competition is an export tax.

180â•‡â•‡ Cost heterogeneity and trade Therefore, we define t = -s. An increase in the level of the export tax causes two effects which are similar to those in the Cournot case. Let us introduce the Â�following notations: γ 2 βγ 2[(2β 2 – γ 2)(α – c – t) – βγ (α – c*)] _______ ________________________________ STB(t) = â•‰â•¯ 2 â•¯ 2â•¯â•‰â•¯ xB(t) = â•‰â•¯ â•¯â•¯â•¯ â•¯â•¯â•¯ â•¯â•‰. 4β – γ (β 2 – γ 2)(4β 2 – γ 2)2

(19.8)

β (2β 2 – γ 2) dx ________________ ___ ALB(t) = s â•‰â•¯ â•¯â•¯â•‰= â•‰â•¯ 2 â•¯â•¯ â•¯â•¯â•¯â•‰t. ds (β – γ 2)(4β 2 – γ 2)

(19.9)

(a) AL(s )

ST(s )

s s optC

(b)

AL(s )

ST (s )

s s optC

(c) AL (t )

s s optC

Strategic export policiesâ•‡â•‡ 181

(c) AL (t )

ST (t )

t t optB

Figure 19.1Â€Â€

The relationship between the level of the export tax and these two effects is Â�summarized in Figure 19.1(c). At the optimal level of the export tax these two effects must offset each other, and we find the optimal export tax under Bertrand competition (toptB hereafter):8 γ 2[(2β 2 – γ 2)(α – c) – βγ (α – c*)] ____________________________ â•¯â•‰ tâ•›optB = â•‰â•¯ â•¯â•¯â•¯ â•¯â•¯ . 4β 2(2β 2 – γ 2 )

(19.10)

We are now ready to investigate the role of the degree of product differentiation: γ. The relationship between the optimal export tax and the degree of product differentiation is summarized in Figure 19.2(b).9 Let us start with the case of substitutes. As the figure indicates, if the goods approximate perfect substitutes (i.e., γ ≅ β ), the optimal export policy becomes no intervention. To see this, consider that an increase in the degree of the goods’ interdependence (i.e., γ rises toward β ) causes two opposite effects. The first enhances strategic interdependence as in the Cournot case, while the second results from increasing competitive pressure which lowers strategic interdependence. For the case in which γ is close to 0, the former effect will dominate the latter because there is little competitive pressure. As the goods become better substitutes, however, the latter effect will dominate the former. This corresponds to the fact that, under certain conditions, Bertrand competition is viewed as more “competitive” than Cournot competition.10 Therefore, we will find little scope for government intervention when γ is close to β. Let us leave the case of substitutes and turn to the case of complements. In this case, contrary to the former, as the goods become better complements (i.e., γ falls toward -β ), the level of the optimal export tax becomes higher. To see this, let us compare a case of complements with a case of substitutes, both having the same absolute value of γ. It is clear from Eqs (19.8) and (19.9) that, given the

182â•‡â•‡ Cost heterogeneity and trade

soptC

�B

��0

B

(a) Cournot

t optB

�B

��0

B

(b) Bertrand

Figure 19.2Â€Â€

value of the export tax, the magnitude of the strategic effect in the case of complements is bigger than that in the case of substitutes, while the magnitudes of allocation effects are the same in the two cases. Therefore, for the same absolute value of γ, the magnitude of the optimal export tax is higher in the case of complements than in the case of substitutes. This should be said with some emphasis. Next, let us move to the comparative static effects of marginal cost differentials. The lower the marginal cost of the home firm, the higher the home good’s price–cost margin becomes. This enhances the strategic effect of the export tax and may be shown as an upward shift of the STB schedule in Figure 19.1(c). On the other hand, the level of the home firm’s marginal cost does not directly

Strategic export policiesâ•‡â•‡ 183 affect the allocation effect. Therefore, as the marginal cost of the home firm decreases, the optimal level of tax becomes higher. For an explanation of this relationship, we must point to the role of the export tax. In the case of Bertrand competition, the home firm can commit to a higher price by raising marginal cost. Therefore, the role of the export tax is to artificially raise costs. The lower the true marginal cost becomes, the more room there is for raising it artificially. This creates additional rent for the home country.

19.3  Preliminary summary and effects on the foreign firm Let us summarize the main points that have been made in this chapter. We have examined how the levels of optimal export policies are affected by the two exogenous changes in the degree of product differentiation and the firms’ marginal costs. About the degree of product differentiation, it was observed that the magnitudes are crucially dependent on the mode of competition. Furthermore, we concentrated on the magnitude of optimal export policy when the home and foreign goods are complements. Proposition 19.1: For the same absolute value of γ (the degree of product differentiation), the level of optimal export intervention in the case of complements is higher than in the case of substitutes. This proposition suggests that we must draw attention to the strategic export policy in the case of complements. In regard to the firms’ marginal costs, it was observed that the more costcompetitive the home firm becomes, the larger the strategic effect of the export policy. Therefore, the reduction in marginal cost induces a higher optimal level of intervention. Table 19.1 summarizes these results. Therefore, the relationship between the home firm’s cost-competitiveness and the optimal level of government intervention holds, whatever the mode of competition. In relation to changes in the home firm’s marginal cost, we can present the following proposition. Proposition 19.2: Which ever the mode of competition (i.e., Cournot or Bertrand ) and the structure of demand (i.e., substitutes or complements) may be, the lower the home firm’s marginal cost becomes, the higher the optimal level of export intervention. Table 19.1Â€Â€The nature of the effects of the strategic export policies on the foreign firm

Substitutes

Complements

Cournot Bertrand

Profit shifting Profit creation

Profit creation Profit shifting

184â•‡â•‡ Cost heterogeneity and trade Table 19.2Â€Â€The relationship between the marginal costs and the optimal level of intervention (the signs of comparative static effect [∂TsoptC (∂ optB )/∂c?)])

Cournot Cournot Independent Bertrand Bertrand substitutes complements substitutes complements

Home firm’s MC – Foreign firm’s MC +

– –

0 0

– +

– –

We are not dealing with the foreign firm’s profit, but it is interesting to note the effect of strategic export policies on the foreign firm. Using Eqs (19.1), (19.2), (19.6), and (19.7), we obtain the equilibrium profit of the foreign firm, and the effect on profit from a change in s or t.11 There are two kinds of effects on the foreign firm: (1) profit shifting, which shifts the foreign firm’s monopoly rent to the home firm, and (2) profit creation, which brings additional rent to both home and foreign firms. Table 19.2 summarizes the relationship between the nature of strategic effects and the mode of competition. It may be worth pointing out that the signs of the effects on foreign profits are the same for Cournot competition with substitutes and Bertrand competition with complements. The sign is also the same for Cournot competition with complements and Bertrand competition with substitutes.12 Therefore, we cannot identify the effects of strategic export policies on the foreign firm by simply specifying the mode of competition. A great deal of effort has gone into studies of strategic export policies, and most have concluded that the role of these policies is to shift profit under Cournot competition and create profit under Bertrand competition. However, such conclusions crucially depend on the assumption that the relevant goods are substitutes.

20 Concluding remarks

The phenomenon of growing worldwide connectivity among individuals, firms, and organizations via improved communications networks raises myriad questions of economic importance. Foremost is the question of how communications networks influence the patterns of world specialization and trade, and with Â�network-based trade in intangible services becoming increasingly possible, what is the role of time zone differences as a determinant of comparative advantages among countries? This book takes up these challenging questions. Based on monopolistic Â�competition models of trade à la Dixit, Stiglitz, and Krugman, as reviewed in Chapters 3 to 5, I have examined the interaction between communications Â�networks and international trade. In Chapter 6, I emphasize the country specificity of communications networks. I show that the quality and scale of the communications infrastructure within a country, and the number and sophistication of people using that infrastructure, become crucial factors determining the patterns of trade. There will be a cumulative process in which the export of the network goods brings an opportunity for entry, and the entry promotes exports. Then, in Chapter 7, I explain the role of the interconnectivity of communications networks. The number of countries connected to international networks is found to determine the structure of comparative advantage. That is, countries with interconnected networks have a comparative advantage in the product that requires business services provided via networks. In connected countries, producers of that product benefit from the efficient transmission of business services. Based on those arguments, Chapters 9 to 11 discuss the role of time zone Â�differences as a determinant of trade and growth. One basic message is that, combining communications networks and time zone differences, countries can take advantage of their “remoteness” (in terms of longitude) as a source of Â�comparative advantage. These chapters also emphasize the “continuity effect” (i.e., working around the clock) as a key driver of trade in services. The consumption of network-related (or information-intensive) products is crucially related to the existence of both network effects and switching costs. In Part III (Chapters 12 to 15), using foundations from the industrial organization

186â•‡â•‡ Cost heterogeneity and trade literature, I have presented various monopolistic competition trade models with these features. From this we may conclude that, in the globalized world economy, trade patterns are highly dependent upon the degree of those network effects and switching costs. For example, in Chapter 13, it is shown that if the number of hardware varieties is reduced by trade liberalization, some consumers may be made worse off by opening trade. It should be noted that competition in the integrated market is likely to lead to standardization with a single hardware/ software system. Finally, in Part IV (Chapters 16 to 19), I have turned to the basic theory of international trade, with special reference to the role of cost heterogeneity among and within countries. Although these chapters are not directly related to the analysis of either communications networks or time zone differences, they might provide some groundwork for future work on those topics.

20.1Â€Â€Future directions I hope the framework presented in this book will serve the purpose of making the analysis of communications networks and time zone differences part of the core of trade theory rather than a peripheral concern. There are, however, important issues in international trade theory that will require new tools, going beyond what we have developed here. What I would like to do in this concluding section is to point out two problems that I believe are in particular need of further work. The first problem relates to the modeling of the determinants of interconnectivity of communications networks. As pointed out in Chapter 1, communications networks or time zone differences themselves are not the sole determinants of the comparative advantages of countries. The experiences of countries such as New Zealand, Australia, Taiwan, Singapore, and Ireland suggest that there is a long and difficult, though not impossible, process of creating the relational Â�networks necessary to become part of the world core.1 Although interaction via communications networks may help to create and maintain these relational Â�networks, it cannot be a substitute for the relational networks themselves. In addition, the existence of time zone differences might offer a possible source of new types of service transactions. However, without close relationships (involving trust) between agents in different countries, service transactions taking advantage of time zone differences cannot be realized. Such transactions are of particular interest in the presence of continuity effects, as when people in several time zones are working on the same project and “passing it on” westward during the day, a practice that is being used by some software and engineering firms to shorten development cycles. To simplify the analyses, in Chapters 7, 8, 9, and 12 I have assumed the existence of interconnected communications networks. This may be seen only as a first step in understanding the role of communications networks in trade. However, the process of interconnection itself needs further consideration. There is a huge literature on network formation.2 To integrate such an aspect into the present framework seems to be an important task. A trade model with switching

Concluding remarksâ•‡â•‡ 187 costs (Chapter 14) and models of domestic entrepreneurs (Chapter 15) may assist in the completion of such a task. The second problem arises in the modeling of dynamics. Trade based on time zone differences is truly an issue of dynamics: consumers’ preferences to obtain goods and services sooner rather than later depend largely on the rate of time preference. Nevertheless, I have developed many versions of static trade models throughout this book (e.g., the models in Chapters 9 and 10; Chapter 11 is an exception). To some extent the analysis of static trade models may act as proxy for that of dynamic trade models, but I am not satisfied that it does so adequately. Trade and dynamics are not new ideas,3 but to integrate that combination with time zone differences is not a simple task. The framework presented in this book must be regarded as tentative. Hopefully it provides a useful paradigm for considering how communications networks and time zone differences affect both the structure of production and the gains or losses from trade.

Notes

1Â€Â€Introduction 1 Freund and Weinhold (2004) analyze the effect of Internet diffusion on trade and find a significant and increasing impact from 1997 to 1999 (see also Freund and Weinhold 2002, and Fink, Matoo, and Neagu 2005). 2 According to this, it has been argued that the emergence of international production networks has been driven by improved communication links that facilitated the Â�coordination of geographically dispersed production processes (see, e.g., Krugman 1995; Feenstra 1998; Venables 2001). 3 See also Arndt (1997), Chen, Ishikawa, and Yu (2004), Deardorff (2001b, 2001c), Dixit and Grossman (1982), Egger and Falkinger (2003), Ishikawa, Morita, and Mukunoki (2010), Kimura and Ando (2003), Kohler (2004a, 2004b), Long (2005), Marjit (1987), Sanyal (1983), Yi (2003), and Yomogida (2007, 2010). 4 Hill 1977. See also Melvin (1989, 1990). 5 Harris 1993, 1995, 1998, 2001. 6 Related to this, in the literature on international business, the point that advanced communications technologies have made it easier for firms to connect with individuals and other firms remotely and to interact with them at many levels, no matter where they are located, was emphasized. It was also emphasized that such remote electronic access (REA) is particularly feasible in activities that levels of information or digital content (see, e.g., Quinn 1992). 7 See, e.g., Bhagwati (1984) and Sampson and Snape (1985). 8 According to the latter, Krugman and Obstfeld (2006, p. 20) note, “So far, these exotic new forms of trade are still a relatively small part of the overall trade picture, but that may change in the years ahead.” 9 Closely related to these concepts, Levy and Murnane (2004) have distinguished “routine” and “non-routine” tasks. 10 Leamer and Storper (2001, pp. 642–643). 11 See Rauch (2001), Rauch and Trindade (2002, 2003), and Leamer (2007). 12 Gasper and Glaeser (1998) express similar concerns from the perspective of city Â�formation. See also Mun (1993). 13 See also Marjit (2008). Jones (2000, ch. 7), and Jones, Kierkowzki, and Lurong (2005) also emphasize the role of different time zones. 14 The following two terms (“continuity effect” and “synchronization effect’â•›”) are taken from Head, Mayer, and Ries (2009). However, my interpretation of the synchronization effect is slightly different from theirs. 15 Zaheer and Manrakhan (2001, p. 667). 16 Grubel and Lloyd (1975).

Notes 189 17 Related to this, Limao and Venables (2001) construct an index of infrastructure density – including availability of telecommunications – and find that it is a significant determinant of bilateral trade. 18 Here, I use the term “interconnectivity” not in the sense of government regulation but in the universal sense of allowing for the possibility of interconnection (see Chapters 7 and 8). 19 This point will be emphasized in Chapters 7, 8, and 12. 20 Farrell and Klemperer (2007). 2Â€Â€Basic models of international trade I 1 The Ricardian model presented below may be found in standard textbooks on international economics. See, e.g., Caves, Frankel, and Jones (2002, ch. 5), Feenstra (2004, ch. 1), Krugman and Obstfeld (2006, ch. 2), Wong (1995), and Zhang (2008, ch. 2). 2 In what follows, Foreign variables are represented by asterisks. 3 We shall return to this point in the next section. 4 See Chipman (1965) on this point. 5 The following discussion is based on Kikuchi and Long (2010a). 6 See, e.g., Dixit and Norman (1980, pp. 71–72), and Maneschi (1998a, 1998b). 7 See Brakman et al. (2006, pp. 70–71), Krugman (1993, 1998) and Irwin (2009, p. 34) for this point. 8 See, e.g., Krugman (1987, pp. 301–302; 1991a, p. 6). 9 Jones (1968), Herberg and Kemp (1969), Kemp (1969, ch. 8), Kemp and Negishi (1970), Melvin (1969), Negishi (1969, 1972), Panagariya (1981), Tawada (1989), Ethier (1979, 1982a), and Grossman and Rossi-Hansberg (2010) offer key contributions to the IRS literature in the static trade theory. Helpman and Krugman (1985, ch. 3), Chang and Katayama (1995), and Choi and Yu (2002) provide comprehensive surveys. For indeterminacy in models of trade and growth with IRS, see Nishimura and Shimomura (2002). 10 Francois and Nelson (2002) offer a notable exception. They develop a general graphical framework for division of labor models. 11 The model is taken from Ethier (1982a). See also Panagariya (1981). 12 When there are more factors, the shape of the PPF will in general be determined by the tension between: (1) differences in factor intensities which tend to make the PPF concave, and (2) external economies of scale which tend to make the PPF convex. See Herberg and Kemp (1969), Kemp (1969, ch. 8), Melvin (1969), and Markusen and Melvin (1984) for discussion. 13 The marginal social cost of good 1 in terms of good 2 is (1/εa2)Y-γ/ε1 and the marginal private cost of good 1 in terms of good 2 is (1/a2)Y-γ/ε1. Both fall as more of good 1 is produced along the PPF. 14 Alternatively, we may assume that all agents know this relationship but they do not act on it because individually they are atomistic. 15 The following discussion is based on Kikuchi and Long (2010b). 16 See, e.g., Dixit and Norman (1980, pp. 71–72). 17 At the production point A, under free trade consumers will consume more of good 2 than before, because good 2 becomes relatively cheaper than under autarky, pT > pA. 18 Note that Proposition 2.2 implies that when pT1 is lower than pA1 the country will not be “driven” to the (unstable) equilibrium point p, by the usual stability argument, as illustrated by the arrows in Figure 2.8. Only an active industrial policy can lead to this equilibrium (e.g., by coordinating expectations). 19 Multiplicity of equilibria occurs in nature as well. As Gould (1993, p. 28) noted, “places with apparently identical vegetation, moisture, and temperature might harbor shells of maximally different form.”

190 Notes 3Â€Â€Basic models of international trade II 1 See Helpman (1990), Baldwin et al. (2003, ch. 2), Bernhofen (2002), Combes, Mayer, and Thisse (2008, chs 3–4), Feenstra (2004, ch. 5), and Ohyama (1999) for surveys. In a series of articles, Neary (2001, 2004, 2009) provides an excellent overview of the literature. 2 For other types of trade model of monopolistic competition, see Ottaviano, Tabuchi, and Thisse (2002). 3 See, e.g., Helpman and Krugman (1985, ch. 6). 4 Note that this function is log-linear in own price, pi, and total spending on good X, EX, are both deflated by a price index of good X. â•‡ 5 Note that PX is defined in terms of negative exponents (σ > 1). See Neary (2001, p. 537) on this point. 6 Hereafter, the subscript i is dropped for simplicity. 7 Neary (2001, p. 538) and Helpman (2006, p. 593). 8 Fujita, Krugman, and Venables (1999, p. 48). Baldwin et al. (2003, p. 15) call it a “perfect” price index in that real income defined with P is a measure of utility. 9 Note that the wage rate is normalized to unity. 10 Since free entry ensures that profits will be zero in the long run, the national income consists only of wage income. 11 Fujita, Krugman, and Venables (1999, pp. 56–57) call this the price index effect. 12 Neary (2001, p. 539). 13 See Krugman (1979) on this point. 14 For the discussion on the gains from variety, see Broda and Weinstein (2006). 15 Krugman (1979, pp. 477–478), Helpman and Krugman (1985, ch. 11), and Â�Matsuyama (1995, pp. 712–713). 16 Matsuyama (1995, p. 712). 17 Krugman (1979, p. 478). Matsuyama and Takahashi (1998) present a model of two regional economies with similar features. 18 Related to this, in the case of trade in goods, Lancaster (1980, pp. 167–168) notes that a size difference between countries may become a source of “false comparative advantage.” That is, autarky relative prices do not serve as reliable predictors of trade patterns. 19 Note also that this model is similar to the models of standard setting in the industrial organization literature. See, e.g. Chou and Shy (1990, 1993). 20 In his influential contribution, Melitz (2003) has proposed an extension of the Dixit–Stiglitz–Krugman model that makes it possible to work with heterogeneous firms in terms of their marginal labor input requirement. See Helpman (2006) for a survey of the relevant literature. 4Â€Â€A decomposition of the home market effect 1 In a review of the scientific contribution of Paul Krugman, Neary (2009, p. 233) argues that this was to prove perhaps the most innovative of his contributions. 2 See, e.g., Brakman, Garretsen, and van Marrewijk (2009, ch. 1), Combes, Mayer, and Thisse (2008, ch. 4), and Feenstra (2004, ch. 5). Applications of economic geography to open economy macroeconomics include Alesina and Barro (2002). 5Â€Â€Monopolistic competition and distribution of trade gains 1 This is known as “Mill’s Paradox.” See Chipman (1965). See also section 2.2. 2 See, e.g., Davis (1998) for discussion on this point. 3 The following discussion is based on Kikuchi (2001). 4 According to this assumption, see, Davis (1998), Picard and Zeng (2004), Yu (2005), and Zeng and Kikuchi (2009).

Notes 191 5 The flat segments of the heavy line correspond to the cases in which countries are Â�sufficiently unequal in size, and the larger country produces all the differentiated products. I ignore these cases and concentrate on the case of incomplete specialization. 6  Country specificity of communications networks 1 Earlier versions of this chapter were presented at the IEFS Japan meeting in January 1999; the Kobe Conference on International Economics and Finance in March 1997; and the Workshop on International Economics at the Kwansei-Gakuin University Seminar House in 1996. I am grateful to Professors David Anderson, Wilfred Ethier, Taiji Furusawa, Kazuhiro Igawa, Nori Nakanishi, Peter Rosendorff, Katsuhiko Suzuki, and two anonymous referees for their comments on earlier versions of this chapter. Thanks are also extended to the editor, Makoto Yano, and Professor Fumio Dei for their helpful editorial comments on this chapter. Needless to say, I am solely responsible for all the remaining errors and shortcomings. 2 See, e.g., the discussion in Cairncross (1997). 3 Harris suggests that, unlike transport costs, communications networks are characterized by: (1) low marginal and high fixed costs; (2) a supplying industry that displays elements of a natural monopoly and produces goods that are quasi-public in nature; and (3) the presence of significant “network externalities.” 4 As Ishikawa (1992, p. 58) notes, a single provider with average cost pricing has been discussed in the context of contestable markets. In addition, the government may force the monopolistic provider to price at average cost. 5 One may also interpret γ as a quasi-fixed cost. “Quasi-” implies that each firm Â�perceives this as a fixed cost, while the level of it depends on the number of firms. 6 In equilibrium, all firms in the network goods sector and the network services Â�provider earn zero profits. Therefore, the national income equals factor payments, L. 7 Note that prices are set at a constant proportionate mark-up over marginal cost, as indicated in (6.4). 8 Note that Ethier (1979, 1982a) analyses the case of two homogeneous goods. 9 In the figures the directions of motion are shown by arrows. 10 It should be noted that the full employment condition indicates that the supply of each product is fixed at x(N). 11 Figure 6.2(a) corresponds to the case where (1 – s)/s > (L*/L) > s/(1 – s) holds. This implies that the expenditure share for the network goods is relatively small and that diversification occurs. On the other hand, Figure 6.2(b) corresponds to the case where (1 – s)/s < (L*/L) < s/(1 – s) holds. 12 The coordinates of points A, B, C are ([(1 – θ )s(L + L*) – 2F ]/2(α + g),[(1 – θ ) s(L + L*) – 2Fâ•›]/2(α + g)), (0,[(1 – θ )s(L + L*) – F]/(α + g)) and ([(1 – θ )s(L + L*) – Fâ•›]/ (α + g),0), respectively. 13 This corresponds to Proposition 2 in Ethier (1979) and to Proposition 5 in Ethier (1982a). 14 Point A also corresponds to the free trade equilibrium where both countries produce an equal number of products (i.e., n = n* = [(1 – θ )sL̅ â•›– 2F]/2(α + g)). Thus the line D E, which is represented by nA + n*A = [(1 – θ )sL̅ â•›– 2F]/(α + g), passes through point A. 15 At the same time, point F moves along line IJ, which is represented by N + N* = [(1 – θ )â•›L â•› ̅ – 2F ]/(α + g). 16 In the complete specialization equilibrium, countries’ wage rates will diverge. I denote the foreign wage rate in terms of the numeraire, w*. By using the international Â�market-clearing condition for the non-network good [(1 – s)w* L* = sL], w* can be calculated, and then p*T may be obtained by substituting w* into the firm’s pricing rule. 17 See footnote 10.

192 Notes 18 Since the non-network good is the numeraire and the smaller country produces it both before and after trade, the national income of the smaller country, L, does not change. To determine the welfare changes, the price index of the network goods, which indicates the minimum expenditure to obtain one unit of X, must be checked. 19 See, e.g., Krugman (1981). 7  Interconnectivity of communications networks 1 I would like to thank David Anderson, Kunio Kawamata, Kazuharu Kiyono, Michihiro Ohyama, Nic Schmitt, Yoshimasa Shirai, seminar participants at Simon Fraser University, McGill University, and New York University, and two anonymous referees for constructive comments. I also thank the Department of Economics at Simon Fraser University for generous support and hospitality over the period during which this chapter was written. 2 The World Trade Organization (2001, p. 161) reports that between 1990 and 2000 the annual percentage change in world exports of “other commercial services,” which include business services such as legal, accounting, management consulting, and research and development services, was 8 percent, and their share of total commercial services trade in 2000 was 44.6 percent. 3 In this chapter, I will use the term “interconnectivity” not in the sense of government regulation but in the universal sense of possibility for connection. 4 Related to this, MacKie-Mason and Varian (1995, p. 1144) conjectured that a primary factor in determining the industry structure of digital communications networks will be ease of interconnection. There may be several factors that affect interconnectivity. Differences in the quality of communications infrastructure and the sophistication of people who use that infrastructure may be major factors. Differences in languages, trade customs, and industrial standards are among other factors. 5 This specification follows that of Ethier (1982b). See also Markusen (1989). 6 This emphasizes the point that the provision of highly differentiated business services requires a network capable of transferring complex information. 7 It may be natural to assume that this connection fee is a function of a number of factors such as the number of users, market structure, and so forth (see Harris 1995; Kikuchi 2002). In this chapter, to make the model tractable, the assumptions about network technology are dramatically simplified. 8 Hereafter, the subscript i is dropped for simplicity. 9 Note that p = w = 1 holds because good Y is produced domestically. 10 As space is limited, I concentrate on the nature of the trading equilibrium and pay scant attention to the factors that determine interconnectivity. 11 It is natural to assume that there is an additional cost of interconnection for each network. However, to keep matters simple, assume that there are no additional costs. 12 This is shown as a movement along the curve SS in Figure 7.2(b). 13 To derive the trading equilibrium, one can make use of Ethier’s allocation curve method (1982a, 1982b). 14 It is well known that the existence of increasing returns technology results in multiple trading equilibria (see Ethier 1982a). In this chapter the matter is left open and the plausible equilibrium is concentrated on. 15 Note that, given that product differentiation in services doesn’t matter (i.e., σ → ∞), (7.16) coincides with (7.12). In general, however, (7.16) is more strict than (7.12). 16 Assume for simplicity that there are no conversion costs. 17 Note that here m is treated as a continuous variable. 18 One example of parameter values is as follows: σ = 2, µ = 0.6, m/M = 0.5. 19 Furthermore, a natural extension would include the endogenous formation of the interconnected networks. It is also a debatable point. 20 I would like to thank one referee for pointing this out.

Notes 193 8  Interconnected communications networks and home market effects 1 I would like to thank David Anderson, Stephen Easton, Richard Harris, Nicolas Schmitt, and two anonymous referees for their constructive comments. 2 This highlights characteristic differences between these types of transaction costs. Communications costs have a strong fixed-cost nature stemming from network construction, while transport costs are proportionally dependent on the volume of transactions (Harris 1995). 3 Although it is static, the current model is built on the copious literature on North– South knowledge spill-overs and growth. Rivera-Batiz and Romer (1991) considered the impact of increased information flows across borders in the context of endogenous growth. See also Van de Klundert and Smulders (1996). 4 In order to analyze the interaction between connectivity and agglomeration, this kind of extension needs further consideration. 5 For a non-negative number of designs in each country, the RHS of (8.9) needs to be non-negative. Given that F is sufficiently small, this constraint does not bind. For simplicity, it is assumed that H* > 2F. â•‡ 6 Note that σ > 1 > µ > 0. 7 The importance of this assumption will be discussed at the end of this section. 8 It is natural to assume that there is an additional cost of interconnection and that the total provision cost is not halved. However, to keep matters simple, I assume that there are no additional costs. The extension of this assumption will be discussed at the end of this section. 9 In these cases rc (KC – K*C) < (γ –â•›1)L holds. 10 Note that the North develops more varieties as long as γ â•›>â•›1. 11 Note that, from (8.17), [d(n/N)/d(I*/I)] < 0 holds. 12 Note that the term “large” is used here in reference to national income, not factor endowment. 13 Note that this assumption is closely related to the timing of events. 14 I would like to thank an anonymous referee for pointing this out. 9Â€Â€Time zones as a source of comparative advantage 1 I would like to express my gratitude to David Anderson, Koichi Hamada, Jota Ishikawa, Takatoshi Ito, Ronald Jones, Sugata Marjit, Tomoya Mori, Sei-il Mun, Raymond Riezman, Takaaki Takahashi, Morihiro Yomogida, Laixun Zhao, seminar participants at the Midwest International Economics Group meeting at the University of Minnesota and Urban Economics Workshop at Kyoto University, and two anonymous referees for constructive comments. I acknowledge financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan (the Grantin-Aid for the twenty-first-century COE Program “Research and Education Center of the New Japanese Economic Paradigm”). 2 See Marjit (2007) or the less formal account in Friedman (2006). 3 In what follows, I use the terms “outsourcing” and “the utilization of time differences” interchangeably. 4 In an alternative approach, Marjit (2007) incorporated a rate of discount due to delayed product completion. 5 See Harris (1995, 1998). 6 Note that this correponds to Jones and Kierzkowski’s (1990, 2001) concept of “fragmentation.” 7 Note that w = 1 holds because good Y is produced domestically. 8 Note that the wage rate is equal to 1. 9 Technically, I assume that µ is sufficiently small. 10 This is shown as a movement in the direction of the arrow along the curve S´S´ in Figure 9.2(b).

194 Notes 11 Note that, in the trading equilibrium, the expenditure on good X is 3µL. 12 This point corresponds to Marjit’s (2007) argument. 10  Service trade with time zone differences 1 Freund and Weinhold (2002) found that Internet penetration, which is measured by the number of Internet hosts in a country, has a positive and significant effect on service trade. â•‡ 2 In his recent bestselling book The World Is Flat, Friedman (2006, pp. 31–32) also introduced “remote executive assistant service” in India: owing to the time differences between India and the U.S., assistants in India can work on their assignments while U.S. customers sleep and have them back to the U.S. the next morning. 3 Jones et al. (2005, p. 309) also emphasize the role of time zone differences as a determinant of trade patterns. 4 Kikuchi (2006) presents a different type of monopolistic competition trade model with time differences in which services are assumed to be an intermediate input. 5 See also Evans and Harrigan (2005) in which transport time increases with the distance traveled. 6 In this way, we rule out Ricardian comparative advantage. 7 Antras and Helpman (2004), See Helpman (2006), and Antras and Rossi-Hansberg (2009). 11  Growth with time zone differences 1 In what follows, for brevity, we will refer to both information and communication technology (ICT) services and business process outsourcing (BPO) as “business services.” 2 The rise of the Indian software industry provides another prime example. The programming problems of some U.S. corporations are e-mailed to India at the end of the U.S. workday. Indian software engineers work on them during their regular office hours and provide solutions. By the time the offices reopen in the U.S. the solutions have already arrived, mainly as e-mail attachments. A recent empirical study by Head, Mayer, and Ries (2009) found that in OCS (“other commercial services” in the OECD ‘s classification) trade, the continuity effect (the ability to operate around the clock) dominates the synchronization effect (the need to coordinate operations during business hours). According to a recent McKinsey report, India contributed about twothirds of global ICT outsourcing and about half of global BPO offshoring in 2004 (The Economist, June 3–9, 2006). Jones, Kierzkowski, and Lurong (2005) also emphasize the role of time zone differences as a determinant of the efficient worldwide division of labor. Furthermore, the fragmentation of production stages and of service provision has been studied within a static trade-theoretic framework by Jones and Kierzkowski (1990, 2001), Grossman and Helpman (2005), Long, Riezman, and Soubeyran (2005), and Do and Long (2008). Aghion and Howitt (2009) also discussed the implications of a two-country version of the AK model. See also Dasgupta (2005). Based on a model of economic geography, Harrigan and Venables (2006) argue that when the stages of the value chain are physically separated, it takes more time to complete a project. Contrary to that, we argue that it takes less time to complete a project if one utilizes time zone differentials. 3 According to a recent McKinsey report, India contributed about two-thirds of global ICT outsourcing and about half of global BPO offshoring in 2004 (The Economist, June 3–9, 2006). 4 Jones, Kierzkowski, and Lurong (2005) also emphasize the role of time zone differences as a determinant of the efficient worldwide division of labor. Furthermore, the fragmentation of production stages and of service provision has been studied within a

Notes 195 static trade-theoretic framework by Jones and Kierzkowski (1990, 2001), Grossman and Helpman (2005), Long, Riezman, and Soubeyran (2005), and Do and Long (2008). 5 Aghion and Howitt (2009) also discussed the implications of a two-country version of the AK model. See also Dasgupta (2005). 6 Based on a model of economic geography, Harrigan and Venables (2006) argue that when the stages of the value chain are physically separated, it takes more time to complete a project. Contrary to that, we argue that it takes less time to complete a project if one utilizes time zone differentials. 7 It is important to note that labor is absent in the current model. If this is introduced in equation (1) as a part of the Cobb-Douglas production function, the production function will display increasing returns to scale. 8 This implies that A depends positively on Home’s terms of trade: 1/p˜â•›. 9 To simplify the analysis, we assume that a country cannot run a deficit in intermediate goods trade, financed by a surplus in final goods trade. 12  Direct network effects 1 The author is grateful to Kenzo Abe, David Anderson, Fukunari Kimura, Kazuharu Kiyono, Chieko Kobayashi, Kenji Kondoh, Nic Schmitt, Ryuhei Wakasugi, and three anonymous referees for many constructive comments. The author is also grateful to the Ministry of Education, Culture, Sports, Science and Technology of Japan for financial support provided to the Twenty-first-Century Center of Excellence Project. 2 According to this, Farrell and Klemperer (2007, p. 1974) provide the following definition: A good exhibits direct network effects if adoption by different users is complementary, so that each user’s adoption payoff, and his incentive to adopt, increases as more others adopt. Thus users of a communications network or speakers of a language gain directly when others adopt it, because they have more opportunities for (beneficial) interactions with peers. 3 A similar network effect, an indirect network effect, may arise when individuals consume a system that consists of a “hardware” good and complementary software products. We shall return to the implications of indirect network effects in Chapters 13 and 14. 4 See Katz and Shapiro (1994) and Roson (2002) for surveys of the relevant literature. 5 Cremer et al. (2000) explore the role of interconnectivity between Internet service providers in the closed-economy setting. Yano and Dei (2006) explore the impact of the introduction of a new product which is accompanied by network effects. Kikuchi (2003, reprinted as Chapter 7) explores the role of interconnectivity using a monopolistically competitive trade model. However, that article offers little insight into the role of direct network effects as a determinant of comparative advantage, which is the main focus of this note. 6 (12.2) implies that in equilibrium all the existing networks necessarily provide the same “surplus,” which is defined as (12.1). 7 Note that productivity in the primary good remains constant. 8 As space is limited, I concentrate on the nature of the equilibrium and pay scant attention to the factors that determine interconnectivity. The case of endogenous formation of interconnected networks will be discussed in section 12.4. 9 Note also that, since productivity rises as the relative price of the high-tech product rises, the supply curves have concave shapes. 10 Note that we assume away any income effect. 11 In what follows, an asterisk denotes variables for Foreign.

196 Notes 12 Note that r + vz – f = p holds for the marginal worker. 13 Furthermore, a natural extension would consider international policies to coordinate the subsidization of interconnected networks. The benefit of such policies is debatable. 14 See e.g. Helpman and Krugman (1985, chs 3 and 10). See also discussions in Chapters 4 and 5. 13  Indirect network effects 1 I would like to thank David Anderson, Koichi Hamada, Jota Ishikawa, Masao Oda, Eiji Ogawa, Hisayuki Okamoto, Ryuhei Okumura, Makoto Tawada, Dao-Zhi Zeng, Laixun Zhao, and the two anonymous referees for their helpful comments. 2 One of the seminal contributions on the gains from variety is Krugman (1979). 3 The important contributions on the role of a “hardware/software” system are Chou and Shy (1990), Church and Gandal (1992), and Desruelle, Gaudet, and Richelle (1996). See Economides (1996) and Gandal (2002) for surveys of the relevant literature. In the international context, Gandal and Shy (2001) analyze governments’ incentives to recognize foreign standards when there are network effects. See also Kikuchi (2007a) for an analysis of trade liberalization in the presence of network effects. 4 OECD (2006, ch. 2) reports that there has been a huge increase in intra-industry trade of software products in the past ten years. 5 We do not mean to suggest that a reduction in the variety of hardware devices is always socially undesirable. There is a rich industrial organization literature, for example, concerned with the gains from standardization of hardware/software systems. See e.g. Sykes (1995). 6 For example, based on the North–South trade model, Chichilnisky (1981) demonstrates that national welfare decreases after increasing international trade. Another possibility is the losses from trade due to externalities (Chichilnisky 1994). 7 See e.g. Clark and Collie (2003). 8 In this way, we rule out Ricardian comparative advantage. 9 Hereafter, we drop the superscript h. 10 This is taken from Church and Gandal’s (1992) closed economy model. 11 The second derivative of t(n0) is negative (positive) if n0 is smaller (greater) than N/2, (3–2σ )/(σ–1) d 2t(n0) [n___________________________________ – (N – n0)(3–2σ )/(σ–1)](σ – 2)(e – c) 0 since ______ â•‰â•¯ 2â•¯ â•‰ = â•¯ â•¯ – â•‰â•¯ â•¯â•¯â•¯â•¯ â•¯â•¯â•¯ â•¯â•‰, where σ > 2 from the dn0 2kbσ (σ – 1) assumption θ > 1/2. 12 The importance of discrimination between case B and C will appear in the following. 13 Since we assume that hardware only facilitates the consumption of software and Â�provides no stand-alone benefits, in case A, the marginal consumer, t, changes discontinuously to 0 or 1 when n0 is equal to 0 or N. 14 In the interval of n where t(n0) is greater than 1 (smaller than 0), the actual marginal consumer, t, is equal to 1 (0) and is still above (below) the line t = n0/N. 15 Note that σ ≤ 3 is required for this condition. 16 Note that, in the case of hardware standardization, the number of software varieties for Hardware 1 increases from n1 to 4n1 (or from N/2 to 2N). 17 See e.g. Krugman (1979). Related to the present result, Chou and Shy (1991) considered the case where the variety of non-traded domestic products is reduced by trade liberalization. 14  Switching costs 1 I thank Kazumichi Iwasa and the referee for helpful suggestions. 2 See, e.g., Brander (1981) and Markusen (1981). 3 See Klemperer (1987a, 1987b, 1987c).

Notes 197 4 See To (1994) for discussion. 5 See Klemperer (1995) for surveys of the relevant literature. For the strategic export policy context, see To (1994). 6 A related argument may be found in the strategic trade policy literature. See e.g., Collie and de Meza (2003). 7 A similar result is found in the analysis of horizontally differentiated duopoly with switching costs. See Kikuchi (2007b). 8 For example, Collie (1996) analyzes the welfare effects of unilateral trade liberaliÂ� zation under Cournot duopoly. See also Clark and Collie (2003) for unilateral trade liberalization under Bertrand duopoly. 15Â€Â€Foreign brand penetration 1 Another important aspect of foreign penetration is foreign direct investment. Ono (1990) and Richardson (1998) use oligopoly models to deal with this point. 2 See, e.g., Helpman and Krugman (1985) and Helpman (1990). 3 Beyond the apparel industry, they introduce the case of Japanese chocolate manufacturers: after MARS introduced M&Ms to Japan in 1973 through a 100 percent-owned subsidiary, 25 imitation products appeared on the Japanese market within six months, each of which possesses an insignificant market share. 4 In what follows, an “entrepreneur” is synonymous with “one unit of entrepreneurship.” 5 A similar scenario is introduced in Venables (1987) and Roy and Viaene (1998). The larger αf/αh becomes, the more consumers spend on imported brands. 6 For example, “French brands of wine and perfume,” and “Italian brands of apparel” are differentiated from similar brands from other countries. Recent marketing research suggests that this differentiation is indeed a significant determinant of purchasing decisions (e.g., Bilkey and Nes 1982; Knight 1999). 7 See Appendix for derivation. 8 To simplify the argument, I assume that Home entrepreneurs can decide whether to import Foreign brands independently. It is more natural, however, to assume that such a decision requires agreement between Home entrepreneurs and Foreign producers. Marjit, Beladi, and Kabiraj (2007) examine the latter case under a Cournot–Nash framework. 9 Another possible scenario is for domestic workers to be hired for domestic distribution. Still, if we assume that the distribution or sale of imported brands requires relatively more skill, we may assume that wf is different from wh. I would like to thank an anonymous referee for pointing this out. 10 See Matsuyama (1995, p. 714) on this point. 11 These costs include, for example, building service and communications networks. 12 Melitz (2003, p. 1699) provides this kind of interpretation to his model of heterogeneous marginal costs. 13 Along this line, Neven, Norman, and Thisse (1991), and Chiou, Hu, and Lin (2003) provide important analyses of international price competition models with nationbased consumer preferences. They also consider the effect of optimal tariffs and its impact on social welfare. 14 See Helpman (2006) for a survey of the relevant literature. 16  Increasing costs in product diversification 1 I would like to thank Kiyoshi Ikemoto, Kazuhiro Igawa, Katsuhiko Suzuki, Koji Aoki, and Noritsugu Nakanishi for constructive comments. 2 See, e.g., Kierzkowski (1984) and Helpman and Krugman (1985). 3 We will use the term “(a)symmetric cost” to refer to the case where each firm in the industry has the same (different) cost function. It would be more correct to say the “homogeneous (heterogeneous) cost.”

198 Notes 4 Another explanation for asymmetric costs may be as follows: fixed costs can be interpreted as the fixed costs of setting up a service and parts supply network necessary before products can be used in the economy, and the timing of entry affects the level of fixed costs. â•‡ 5 See Introduction and fn. 2. 6 In the Appendix, it is shown that this curve will be decreasing in the neighborhood of the equilibrium. 7 We can apply these tools to explain the model of symmetric costs. Then, the variety supply curve will be shown as a horizontal line (see Chapter 3). 8 These values depend on the functional form of α(·). 9 That is, foreign differentiated products, which are different from home products, do not exist in the home country before the opening of trade. We assume that the index number of home differentiated products belongs to [0, n], whereas the foreign number belongs to [O*, n*]. 10 This index corresponds to the stream of worldwide fixed costs: both countries’ firms are indexed according to a level of fixed costs in such a way that a firm with a greater number i corresponds to a higher fixed cost. Because of the linearity of each country’s variety supply curve, the worldwide variety supply curve will be a linear one and its slope will be half of each country’s curve. 11 In our model, the price of both countries’ homogeneous good is normalized to equal 1. Thus, there are no potential terms-of-trade effects. 17  Efficiency gaps and Heckscher–Ohlin trade patterns 1 We are grateful to David Anderson, Kwan Choi, Fumio Dei, Kenji Fujiwara, Takashi Kamihigashi, Sajal Lahiri, Ngo Van Long, Masao Oda, Masayuki Okawa, Laixun Zhao, and two anonymous referees for helpful comments. We are also grateful to the Ministry of Education, Culture, Sports, Science and Technology of Japan for financial support provided to the twenty-first-century Center of Excellence Project. 2 This assumption implies, for example, that the fixed costs of setting up a service and distribution network are necessary before the product can be used in the country, and the level of these costs also depends on the timing of entry. 3 Based on a two-factor, two-good oligopolistic competition model with increasing returns to scale, Fujiwara and Shimomura (2005) also explored the determinants of trade patterns. 4 Note also that our model is a modified version of Kikuchi (1996), which considered the welfare effect of opening trade in a one-factor model of monopolistic competition with efficiency gaps in the fixed production costs. 5 For tractability, we assume simple Cobb-Douglas preferences. 6 These costs are interpreted as fixed costs for setting up a service and parts supply network necessary before products can be used in the economy. Furthermore, for analytical tractability, it is assumed that these set-up costs do not depend on the firm’s plant size. 7 Romer (1994) also assumed that firms are characterized by different fixed production costs. His focus was, however, on the analysis of the welfare costs of trade restrictions. 8 Employing a more general function such as cX (w, r)xi + cF (w, r)µi, where cF (w, r)µi is firm i´s cost function for fixed inputs, does not change the qualitative results. 9 Both w and r emerge from the general equilibrium and we treat these as exogenous variables in this section. 10 The case of inter-country efficiency gaps (i.e., µ = µ*) will be discussed in section 17.5. 11 In what follows, we concentrate on the equilibrium conditions for the Home firms. 12 Since the demand for each product is symmetric (see 17.1), it is optimal for the inframarginal firms to sell the same amount as the marginal firm: total revenue of each infra-marginal firm is constrained by the number of firms.

Notes 199 13 More precisely, n is given as the positive root of the following quadratic equation: A

[[1 – (1/2)(1 – θ )α]/(1 – θ )] câ•›X n 2 – α (wL + rKâ•›) = 0 14 Note that each country produces differentiated types of products. 15 The technique of integrated equilibrium analysis was first suggested by Samuelson (1949) and developed by Dixit and Norman (1980), Helpman and Krugman (1985), Davis (1995), Lahiri and Ono (1995), and Shimomura (1998). 16 More general cases will be discussed in section 17.5. 17 This approach is closely related to that used in Helpman and Krugman (1985) in the context of a Cournot oligopoly. 18 If two countries are the same size in terms of absolute factor endowments, the value of each country’s exports in the differentiated products will be balanced. 19 We obtain point D as the intersection between the diagonal O´O*´ and the vector that extends from C, which is parallel to the vector OO´. 20 Note that Home is also a net exporter of good X. 21 For the similar discussion, see Helpman and Krugman (1985). 22 The case of area (3) may be analyzed in a similar way. 23 The case of area (2´) may be analyzed in a similar way. 24 Given that the unit cost function of good i is ci(w, r), the line BB´ corresponds to the following condition: K = [(cY c rz – ∆βw)/(cY c rz + ∆βr)] L + [(cY cwZ δK – cY c rz δ L + ∆βΠ )/(cY c rz – ∆βr)],Â€Â€Â€Â€Â€Â€Â€Â€∆ ≡ cwY c rz – c wZ crâ•›â•›Y,

where for convenience we use subscripts to represent partial derivatives with respect to the factor price, and δL and δK represent the factor use in the good X sector. Derivation of this condition is discussed in the Appendix to this chapter. 25 In this case, the output level for the marginal firm is as follows: x(n) = [θ (1 – θ)]µn. 26 Montagna (2001) introduced this type of inter-country efficiency gap, though she concentrated on the case of differences in marginal production costs.

/

18  Chamberlinian–Ricardian trade patterns 1 We are grateful to Eric Bond, Fumio Dei, Wilfred Ethier, Elhanan Helpman, Jota Ishikawa, Nic Schmitt, Makoto Tawada, Makoto Yano, Laixun Zhao, and an anonymous referee for helpful comments. Kikuchi and Shimomura acknowledge the Ministry of Education, Culture, Sports, Science and Technology of Japan for financial support provided to the Twenty-first-century Center of Excellence Project “Research and Education Center of New Japanese Economic Paradigm.” Zeng acknowledges the Ministry of Education, Culture, Sports, Science and Technology of Japan for financial support 18530179, 19203013, and Zhejiang University of China for CRPE joint research support. 2 In the case of technology-intensive products, intra-industry trade among the East Asian countries is very active. In 1999, Japan exported 272.4 billion yen worth of telecommunications equipment and parts to China and Hong Kong and imported 221.8 billion yen worth of the same products from these two economies. For details on this issue, see Fukao, Ishido, and Ito (2003). 3 Venables (1987) explores the influence of technological differences in the monopolistically competitive sector on trade patterns. However, his results are dependent on both the existence of transport costs and asymmetric preferences. See also Suzuki (1991, 1995). 4 Hereafter, the subscript k is dropped for simplicity.

200â•‡â•‡ Notes 5 It is assumed that the entry would not change ñ from 0 to 1: it only changes from 0 to 0+. â•‡ 6 A decrease in L will shift the curve OB up, resulting in a higher equilibrium ω. Since the nominal price of any product is the same in both countries, this means that the smaller country will have higher per capita income. 7 It is also important to note that the technology index is not purely technological: it contains the preference parameter θ. 8 Dornbusch, Fischer, and Samuelson (1977) examine this type of technology transfer which “flattens” the technology schedule. Since there are no product differentiations, specialization between two identical countries becomes inessential in their model, which is contrary to our results. 9 See, e.g., Loertscher and Wolter (1980). 10 See, e.g., Hakura and Jaumotte (1999). 19Â€Â€Strategic export policies 1 For a recent survey and a systematic analysis of strategic trade policy, see Brander (1995). 2 In recent contributions, Clark and Collie (2008) and Fujiwara (2009) consider the impact of the degree of product differentiation in the context of trade liberalization. 3 One exception is Eaton and Grossman (1986); however, so far the study of strategic export policy in the case of complements has been rather superficial. 4 The following analysis is based on Kikuchi (1998). This model is analogous to the model in the recent study by Cheng (1988). However, he assumes the existence of domestic consumption. 5 The sign on the optimal export policy does not depend on whether the goods are substitutes or complements. See Eaton and Grossman (1986, p. 391). 6 By differentiating soptc with respect to γ, we obtain (α – c)[(4βγ – 3γ )â•›+â•›8βγ (2β – γ )] ∂s _____ ____________________________ â•‰â•¯ â•¯ â•¯ â•¯ â•¯â•¯â•¯ â•¯â•‰ â•¯â•¯ > (<)0, for γ > (<)0. â•‰= â•‰â•¯ 2 2 2 optc

∂γ

2

3

[4β(2β – γ )]

To simplify the calculation, assume that c = c*. The values of parameters in Figure 19.2 are as follows: α – c = α – c* = 1, = 10, – 10 < γ < 10. The minimum scale of vertical axis is 0.1. 7 Under the assumption of Bertrand behavior, the first-order conditions of profit maximization for the home and foreign firms are, respectively,

∂π ___

â•‰â•¯ â•¯â•¯â•‰= (α – c + s)β – (2B2 – γ 2)x – βγ y = 0, ∂x

and ∂π ____ *

â•‰â•¯ â•¯â•‰â•¯= (α – c*)β – (2B2 – γ 2)y = βγ x = 0. ∂x

8 See Note 4. 9 Here we again assume that c = c*. By differentiating toptB with respect to γ, we obtain 4β 2γ (α – c)[(4β 2 – 4γ 2 – 3βγ )(2β 2 – γ 2) + 2γ (2β 2 – γ 2 – βγ )] __________________________________________________ â•¯ â•¯â•¯â•¯â•¯â•¯ â•¯â•‰ â•¯â•¯â•¯. â•¯ â•¯ â•‰=â•› â•‰â•¯ ∂γ [4β 2(2β 2 – γ 2)]2

∂t _____ â•‰â•¯

opt B

10 Vives (1985, p. 171) says, “An intuitive reason behind this view is that in Cournot competition each firm expects the other to cut prices in response to price cuts, while

Notesâ•‡â•‡ 201 in Bertrand competition the firm expects the others to maintain their prices; therefore, Cournot penalizes price cutting more.” 11 These values are as follows: β [(2β 2 – γ 2)(α – c*) – βγ (α – c – t)]2 π *c = â•›_______________________________ â•‰â•¯ â•¯â•¯â•¯ â•¯â•‰ â•¯â•¯ (4β 2 – γ 2)2 β [2β (α – c*) – γ (α – c + s)]2 _________________________ â•¯â•¯â•¯ â•¯â•¯ â•¯â•‰. π *B = â•› â•‰â•¯ (β 2 – γ 2)(4β 2 – γ 2)2 12 The fact that these two pairs have a dual relationship was pointed out by Sakai (1990, ch. 2). 20Â€Â€Concluding remarks 1 See Rauch (1996, 1999, 2001) for the theoretical and empirical foundations of the role of relational (business and social) networks. See also Leamer and Storper (2001) and Leamer (2007). 2 See, e.g., Mukunoki and Tachi (2006), Furusawa and Konishi (2005, 2007), and Endoh, Hamada, and Shimomura (2008). 3 See Hamada (1966), Stiglitz (1970), Buiter (1981), Shimomura (1993), Fukao and Hamada (1994), Cremers (2001), Bond, Trask, and Wang (2003), Chen, Nishimura, and Shimomura (2004), Shimomura (1992, 1993), Ju and Wei (2007), Kikuchi and Hamada (2011), Kikuchi and Shimomura (2006a, 2007a), and Hamada, Iwasa and Kikuchi (2010).

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Index

absolute advantage 16 Acemoglu, D. 98, 103 AK model 98 allocation curve 53 Ando, Mitsuyo 188 average cost pricing 51, 73 balance-of-trade conditions 152 Baldwin, Richard 190 Beladi, Hamid 197 Bertrand competition 179 brand differentiation 141 Brander, James 130, 200 Brander and Spencer 176 Business services 194 Cairncross, F. 59, 81, 90 call center service 90 Chamberlinian-Ricardian model 169 Church, J. 117 Collie, David 197, 200 communications networks 49; country specificity of 6, 49; definition of 49; interconnectivity of 6, 59, 108 comparative advantage 14, 65, 88, 114 competitive selection 157 continuity effect 4, 185, 186, 194 cost heterogeneity 8, 186 cost-sharing effect 51 Cournot competition 177 cumulative process 32, 56, 65, 88, 113 Davis, Donald 190, 199 Deardorff, Alan 2 Dei, Fumio 195 delivery timeliness 99 direct network effects 7, 107 Dixit and Norman 189, 199 Dixit and Stiglitz 40, 61, 84, 118, 134, 169 Dixit-Stiglitz-Krugman model 26 Eaton and Grossman 179

Endoh, Masahiro 201 Entrepreneur 135 Ethier, Wilfred J. 24, 53, 66, 84, 157 external economies 19 factor mobility 32 factor price equalization set 162 false comparative advantage 190 Feenstra, Robert 188 foreign brand penetration 132 fragmentation 1, 193, 194–5 Friedman, Thomas 107 fulfilled expectations equilibrium 110 Fujita, Masahisa 68 Fujiwara, Kenji 198, 200 Fukao, Kyoji 168, 201 Furusawa, Taiji 201 Gains from trade 56, 65, 88; pro-competitive 126, 130 Gandal, N. 117 Grossman, Gene M. 2 Grubel-Lloyd index 153 Hamada, Koichi 201 hardware/software system 117 Harris, Richard G. 2, 49, 56, 59, 82, 84, 188 Heckscher-Ohlin theory 157 Helpman, Elhanan 168 Helpman and Krugman 34, 39, 43, 157, 168 home market effect 34, 39, 74, 154 home market magnification 37 indirect network effects 7, 117 industrial concentration 77 industrial diversion 77 integrated equilibrium 162 Internet Exchange Point (IXP) 70 Internet Service Providers (ISPs) 70 intra-industry trade 31, 153, 168, 174 Ishido, Hikari 168 Ishikawa, Jota 188, 190

Indexâ•‡â•‡ 217 Ito, Keiko 168 Iwasa, Kazumichi 201 Jiandong Ju 201 Jones, Ronald W. 3, 13, 188, 189, 194 Katz, M. 107 Katayama, Seiichi 189 Kemp, Murray 189 Kimura, Fukunari 188 Kohler, Wilhelm 188 Krugman, Paul 5, 34, 37, 124, 145, 168, 188 Lahiri, Sajal 199 Lancaster, Kelvin 190 Leamer, Edward 3 Long, Ngo Van 2, 84, 188, 189 love-of-variety approach 124 Marjit, Sugata 3, 82, 90, 95, 97, 188, 193, 197 Markusen, James R. 84, 130 Matsuyama, Kiminori 26, 67, 133, 136, 190 Melitz, Marc 8, 133 Melvin, James 189 Mill’s paradox 17, 190 monopolistic competition 26, 34, 39 Montagna, Catia 157 Morita, Hodaka 188 Mukunoki, Hiroshi 188, 201 multilateral trade liberalization 131 multiple equilibria 24 Mun, Sei-il 188 Myerson, R. 24 Neary, Peter J. 176, 179, 190 Negishi, Takashi 189 network service provider 51, 108 Nishimura, Kazuo 189 Ohyama, Michihiro 190 Ono, Yoshiyasu 197, 199 Ottaviano, J 190 outsourcing 193 periodic intra-industry trade 4 Porter, Michael E. 132 price index effect 190 pro-competitive effect 140 profit creation 184 profit shifting 184 Rauch James 132, 201 reaction curve 128 relational networks 3, 186

remote maintenance 4, 81 remoteness 185 Ricardian model 13 Richardson, Martin 197 Riezman, Raymond 2, 84 Roy, S. 197 Sakakibara, Mariko 132 Samuelson, Paul 199 service links 1–2 service trade 2, 90 Shapiro, M. 107 Shimomura, Koji 189, 198, 199 sogo shosha 132 Spence, M. 145, 157 Strategic export policies 176 Storper, M. 3 Suzuki, Katsuhiko 199 switching costs 126 synchronization effect 4, 194 Tabuchi, Takatoshi 190 Takahashi, Takaaki 190 Takeuchi, Hirotaka 132 Tawada, Makoto 189 technology index 171 technology transfer 174 terms-of-trade effect 57 Thisse, J. 190 time zone difference 3, 82, 90, 97, 98 trade-costs-saving effect 44 trade gains: decomposition of 17, 22 trade in tasks 2 Trefler, D. 166 unilateral trade liberalization 131 variety effect 57 variety-of-import effect 44 Venables, A. 68, 188 Ventura, J. 98, 103 virtual economic integration 82 virtual mobility 2, 59, 60 Wei, S.-J. 201 Wong, Kar-yiu 189 Yano, Makoto 195 Yomogida, Morihiro 188 Yu, Eden 189 Yu, Zhihao 188, 190 Zeng, Dao-Zhi 190 Zhang, W.-B. 189