Marxian Reproduction Schema (Routledge Frontiers of Political Economy)

Marxian Reproduction Schema

In 1878 Karl Marx developed the reproduction schema: his model of how total capital is produced and reproduced. This is thought to be the first two-sector economic model ever constructed. Two key aspects of Marx’s writings are widely agreed to be undeveloped: the role of aggregate demand and the role of money. This book has as its aim the synthesis of various strands of economic thought in an attempt to understand and clarify the structure of the reproduction schema. This synthesis will challenge prevailing orthodoxies. A macro monetary model is constructed which draws on a wide range of economic theories, both within the Marxian economic tradition and further afield in the traditions of Keynes, Kalecki, Domar, Sraffa and Leontief. Marxian economics has been dominated by supply-side thinking, including general equilibrium theory and pronouncements about the shortage of surplus value. Post Keynesians have failed to take seriously the importance of reproduction and the multisectoral structure of capitalism. By locating aggregate demand and the circuit of money in the reproduction schema, the objective of this book is to provide an analytical contribution to both Marxian and Post Keynesian economics. A.B. Trigg is Senior Lecturer in Economics at the Open University, UK.

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Marxian Reproduction Schema Money and aggregate demand in a capitalist economy

Andrew B. Trigg

First published 2006 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Ave, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group © 2006 A.B. Trigg

This edition published in the Taylor & Francis e-Library, 2006. “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.” All rights reserved. No part of this book may be reprinted or reproduced or utilised 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. 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 A catalog record for this book has been requested ISBN 0–415–33669–4 (Print Edition)

Contents

List of illustrations Acknowledgements

xi xii

1

Introduction

1

2

The multiplier

6

Marx’s reproduction schema 7 The Keynesian multiplier 11 Leontief input–output analysis 16 3

The Kalecki principle

21

Kalecki and the reproduction schema 22 Surplus value 26 The Kalecki multiplier 28 The value-form 30 4

The monetary circuit

33

The theory of the monetary circuit 33 A Marxian alternative 39 The macro monetary model 46 5

Money, growth and crisis Capital outlays and sales 50 Domar and balanced reproduction 53 Conditions for economic crisis 57

50

x

Contents

6

Beyond underconsumption

63

Disproportionality 64 Luxemburg and accumulation 68 Luxemburg’s two parallel questions 73 7

The falling rate of profit

76

Grossmann’s law of capitalist breakdown 77 Return of the Kalecki principle 81 Simulation without breakdown 83 The falling rate of profit 85 8

The transformation problem

89

Marx’s transformation solution 90 Marx after Sraffa: the new interpretation 94 Generalization of the macro monetary model 96 Appendices Notes Bibliography Index

102 112 119 127

Illustrations

Figures 7.1 7.2

The rate of profit in the Kalecki simulation Components of the rate of profit in the Kalecki simulation

86 86

Tables 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5 4.6 5.1 5.2 6.1 6.2 6.3 7.1 7.2 8.1a 8.1b 8.1c

Marx’s simple reproduction schema Marx’s expanded reproduction schema Locating the multiplier in Department 1 Expanded reproduction in an input–output table The allocation of surplus value in the two-sector schema Ex ante three-sector reproduction schema Ex post three-sector reproduction schema Kalecki’s interpretation of the three-sector schema An input–output interpretation of the three-sector schema Two-sector Kalecki schema Two-sector Marxian reproduction schema Expanded reproduction in an input–output table Inventories in the reproduction schema Composition of money outlays Money circuits in the current production period Marx’s expanded reproduction schema Rates of growth in Marx’s reproduction schema Simple reproduction schema Simple reproduction in an input–output table Expanded reproduction in an input–output table Grossmann’s reproduction schema Kalecki modified reproduction schema Marx’s calculation of prices (physical categories) Marx’s value calculation Marx’s price calculation

9 11 12 17 22 22 23 23 27 35 40 41 42 43 45 54 56 65 66 67 79 84 90 91 93

Acknowledgements

I would like to express my thanks, and acknowledgement, to the editors and referees of the five journal articles from which material for this book has been drawn (see Appendix 1). For encouragement and help during the formation of my ideas, I am very grateful to Riccardo Bellofiore, Victoria Chick, Giuseppe Fontana, Bruce Philp, Susan Himmelweit, John Rosenthal, Fred Lee and Roberto Simonetti. Members of OPE-L, the online discussion group, have also offered invaluable ideas and discussion; and Rob Langham at Routledge has been an extremely patient and flexible editor. For particular help in reading various chapters of the book, my thanks are extended to Angelo Reati, Jochen Hartwig, John King, Jan Toporowski, Paul Zarembka, Ian Wright and Sheila Watson. I am responsible for any remaining errors.

1

Introduction

It may be hard to imagine that the origins of macroeconomics, as we know it today, came from a German revolutionary, exiled to England and ignored by the economic establishment. In 1878, working for the last time on his great writing project, Capital, Karl Marx developed the reproduction schema: his model of how total capital is produced and reproduced. This is thought to be the first two-sector economic model ever constructed, with two great departments producing means of production and means of consumption. Not only did this model capture the division between consumption and investment that later became the centrepiece of Keynes’s General Theory (1936), it went beyond the short-term focus of Keynes to explore the structure of economic growth. Marx has thus been described as the forerunner of macroeconomic growth theory.1 As with all great works, a common complaint is that they are never properly read in the original. Marx’s Capital is no exception. After the publication of volume 1 in 1867 – the only part which Marx was able to finish – his wife, Jenny, complained: You can believe me that seldom has a book been written under more difficult circumstance, and I could write a secret history that would uncover an infinite amount of worry, trouble and anxiety. If the workers had an inkling of the sacrifice that was necessary to complete the work, written only for them and in their interest, they would perhaps show a bit more interest. (McLellan 1973: 353) Of course, for those who manage to make it through the material, Capital is a work of art: a masterpiece exposing the vagaries of unbridled capitalism. But even leading figures in the labour movement have found this a struggle. On receiving the first volume, a trade union colleague of Marx

2

Introduction

‘felt like a man who had been given an elephant and did not know what to do with it’ (ibid.: 353). Similarly, the British Labour Prime Minister, Harold Wilson, admitted that he had not got past the first page. The reason may have been as identified by Marx’s lifelong collaborator, Friedrich Engels, in his comment that Marx started the volume with the most difficult chapters, continually interrupted the flow with extensive examples and failed to summarize its purpose and direction.2 If the first volume of Capital is difficult to absorb, the reader of the second volume, where the reproduction schemes are located, faces an even greater challenge. Due to the unfinished form of the material, which Engels assembled from Marx’s notes, it is generally agreed that it lacks coherence. Engels viewed the part of the material on the reproduction schema as ‘excellent in content, but fearfully heavy in form, patched together from two treatments of the problems by two different models’ (quoted in Zarembka 2000: 197). Commenting on the unfinished state of the second (and third) volumes of Capital, Joan Robinson warned, ‘The waters are dark and it may be that whoever peers in them sees his own face’ (Robinson 1968: 111). From these murky waters, a host of different models and perspectives have emerged. In the absence of any clear statement of the purpose of the reproduction tables, there is no agreement as to what they are for, how they relate to the rest of Capital, volume 2, and how they relate to Capital as a whole. For Tsuru (1994: 191), ‘Participants in the discussion . . . concretized the original simple tableau of Marx in whatever way most suited for their respective conclusions.’ One of the greatest schisms in political economy, since the early part of the twentieth century, is over the role played by aggregate demand in the reproduction schema. Where, argued the fiery Rosa Luxemburg, does the demand come from for every growing capacity generated by expanded reproduction? ‘In Marx’s diagram,’ she scathingly points out, ‘accumulation, production, realisation and exchange run smoothly with clockwork precision, and no doubt this kind of “accumulation” can continue ad infinitum, just as long, that is to say, as ink and paper do not run out’ (Luxemburg 1951). The first main purpose of this book is to formalize the role of aggregate demand as a constraint on expanded reproduction. I will develop an analytical model which explores the conditions under which profits can be realized in the reproduction schema. This approach is in keeping with the spirit of Dillard’s (1984: 425) statement that ‘Marx’s economics would be strengthened by a more formal treatment of the theory of effective demand.’ For daring to criticize Marx, Luxemburg was labelled a heretic, failing to properly understand the role of the reproduction schema in Marx’s system. In the wake of Stalin’s purges, the importance of demand was overtaken by

Introduction

3

Marx’s falling rate of profit, which he presented in Capital, volume 3. It was argued by Henryk Grossmann that capitalism is vulnerable to breakdown because of the falling rate of profit tendency. This theory of crisis has become the standard canon of the far left; for supply-side Marxists it provides a bulwark against the (reformist) Keynesian aggregate demand approach. Marx’s reproduction tables, though used to illustrate the Grossmann breakdown scenario, have been downplayed as a mere interlinking device between first and third volumes of Capital. In the universities, a mathematical strand of supply-side Marxism has evolved that is closer to mainstream general equilibrium theory. Notably, for Morishima (1973: 105), ‘Marx’s models are very similar to Walras’ in many aspects: Marx’s scheme of simple reproduction, or reproduction on the same scale, corresponds to Walras’ static general equilibrium system of production . . . ’ Aggregate demand has hardly any role to play in this microeconomic approach. Furthermore, a major shortcoming of the supply-side Marxists is their failure to consider the importance of money. In Brody (1974: 9), for example: ‘Theories of money . . . are not discussed, although a parallel mathematical approach to them is much needed and indeed within reach’ (see also Roemer 1978). The problem is that money is essentially neutral in general equilibrium models, a characteristic more appropriate to a barter economy than to capitalism. And in the Grossmann falling rate of profit thesis, money is stripped from the reproduction schema despite its central importance to Capital, volume 2. The second main purpose of this book is to develop an alternative interpretation of the reproduction schema in which money plays a key role. Some degree of formalization is required here with respect to circulation of money, which takes on various often contradictory guises in Marx’s work. As Foley (1973: viii) commented, ‘Marx’s writings on money remain in a “pre-model” stage.’ My objective is to develop a coherent model of how the circulation of money intertwines with the reproduction of commodities. At the heart of this contribution to Marxian economics is an analytical framework for modelling aggregate demand in which a Keynesian multiplier is nested in the schema. Every economics student is taught that each pound of investment has a multiplied effect on total income. Lianos (1979) has shown how the multiplier relationship between income and investment can be modelled in one of Marx’s departments of production. My specific analytical contribution is to generalize this insight to the full multisectoral structure of Marx’s tables, without losing the simplicity of the scalar Keynesian multiplier. The key role of money in the reproduction process is addressed by using some of the insights provided by Michal Kalecki. He was schooled in the

4

Introduction

rich vein of Polish Marxism at the start of the twentieth century – both Luxemburg and Grossmann were Polish – but became famous as the economist who discovered the rudiments of the General Theory before Keynes (or so it is claimed). Like Keynes, Kalecki emphasized the importance of aggregate demand for investment as the driving force of a capitalist economy. In a rudimentary model of the circuit of money, capitalists cast money into circulation as aggregate investment, and this returns back to them as profits. This is the Kalecki principle: that capitalists earn what they spend. A key starting point for considering the relationship between the Marxian and Keynesian traditions is Kalecki’s demonstration of how this macroeconomic principle works in the context of Marx’s reproduction schema. Armed with the multiplier and the Kalecki principle, a potential contribution can also be made to Post Keynesian economics, in which there has been a tendency to take money seriously, but not reproduction. Although Keynes himself developed a two-sector model, he had great problems dealing with user cost – defined as constant capital in Marxian categories.3 How all capital is reproduced under capitalism has become a side issue for Keynesians, often by resorting to a one-sector framework. Similarly, the Franco-Italian circuitist school has focused on the circuit of money without paying any attention to the reproduction of commodities. Flows of money between banks, firms and consumers are modelled without considering the relationship between sectors of production. The money circuit has been given prominence without due attention paid to the circuit of commodities. In addition, the importance of money and aggregate demand can be carried through to the modelling of expanded reproduction over time. It is well known in economic growth theory that the Harrod–Domar model has a close affinity to Marx’s reproduction model. For Kuhn (1979: 40), ‘the Marxian growth model, in the framework of an essentially unstable economy, has anticipated the important conclusions of the Harrod–Domar analysis.’ However, it is not so widely known that money has a key role to play. There is a paradox of borrowing, in which capitalists have to secure credit for expanded reproduction to take place. Coupled with the key role of aggregate demand in the drive for capital accumulation, the Marxian growth model provides a powerful tool for highlighting the stringent conditions required for expanded reproduction. My analytical contribution is to show how the Harrod–Domar model – more specifically, its Domar variant – can be derived from the multisectoral reproduction schema, with the multiplier and the monetary circuit as the key building blocks. These building blocks are defined using Leontief ’s input–output analysis, a model which has its origins in the Marxian economic tradition.

Introduction

5

Finally, this analytical framework is used to cast light on the Marxian theory of crisis. Once money and demand are taken seriously, the reproduction schema provide the basis for Marx’s possibility theory of crisis; his demonstration of the likelihood of economic crises taking place. The analytical precision provided by the Domar interpretation provides a platform for interpreting some of the great controversies of twentiethcentury Marxism – in particular between protagonists such as Hilferding, Bauer, Luxemburg and Grossmann. The book is thus a series of steps, from the multiplier and its role in the reproduction schema in Chapter 2 to the Kalecki principle in Chapter 3 and a detailed consideration of the circuit of money in Chapter 4. Having built up a macro monetary model of the reproduction schema, in which both money and aggregate demand are featured, Chapter 5 derives the Domar growth model from these analytical foundations. The relevance of this growth model to Marxian theories of crisis is explored and further developed in Chapter 6. A subtext of this analysis is an attempt to address some of the limitations of the reproduction schema. Two main limitations of the schema, as modelled in Chapters 2–6, are the absence of free competition, based on the mobility of capital, and the lack of any room for technical progress. Chapter 7 examines the Grossmann model of how technical progress drives the tendency of the falling rate of profit. And in Chapter 8, free competition is considered by turning to Marx’s famous transformation problem; a problem that has dominated discussions in Marxian economics. This analysis draws on a wide range of economic theory, both within the Marxian economic tradition and further a field in the traditions of Keynes, Kalecki, Domar, Sraffa and Leontief. In the same way that Marx was open to the whole corpus of classical economics in the nineteenth century, this book has as its aim the incorporation of various strands of economic thought in an attempt to understand and clarify the structure of the reproduction schema.

2

The multiplier

When first embarking on his study of economics, in 1851, Marx wrote to Engels, ‘I am so far advanced that in five weeks I will be through with the whole economic shit’ (McLellan 1973: 283). As it turned out, he was to spend the next twenty-five years in the British Museum Library, defining a whole school of thought: the school of classical economics. At the end of this journey, the Marx who worked up the second volume of Capital, in the late 1870s, was not the young philosopher engaged in Hegelian metaphysics. Of course, Marx’s philosophical background to some extent explains how his critique of classical economics developed. For Chakravarty (1982: 13), ‘Marx’s early philosophical interest did provide him with the basic insight that any particular socioeconomic formation should not be viewed as an eternal category but a transient arrangement . . . ’ But for Zarembka (2000: 188), ‘Marx’s mature work in political economy is not dependent upon Hegel and dialectics.’ Indeed, for the prominent Hegelian Marxist, Geert Reuten, referring to the passages where Marx develops his reproduction tables, ‘the text is not systematic-dialectical’ (Reuten 1998: 223, original emphasis).1 Even for Reuten, the reproduction schema is best understood as a conventional model, of the kind used in modern economics. The purpose of this chapter is to examine two main aspects of Marx’s reproduction model. The first concerns the way in which sales of commodities are realized in the reproduction and circulation of commodities. Whereas in volume 1 of Capital the focus is on the production of value, on the assumption that each individual good is automatically sold, in volume 2 the market place is introduced. For Mandel (1978: 14), in his introduction to the Penguin edition of volume 2, ‘we have to understand the inner connection between the production of value and its realization.’ Commodities have to be sold, whether wage goods purchased by workers or means of production purchased by other capitalists. Reproduction can only take place if in aggregate

The multiplier

7

the value produced is matched by aggregate demand. Drawing upon some recent Marxian contributions, the role of the Keynesian multiplier can be considered as a way of formalizing the role of aggregate demand. In addition, the production of value is represented in the structure of this multiplier by considering the role of Marx’s value categories. Now economists are very fond of diagrams, and one of the few diagrams Marx ever used was to summarize Quesnay’s Tableau Economique (Marx 1969a). Quesnay was the doyen of the physiocrats, who thought that land was the source of all value; hence the tableau shows the circulation of commodities between farmers and landlords. As shown by Pressman (1994), Marx shaped this model into his reproduction schema: a model of how commodities circulate between capitalists and workers. For Marx (1969a: 344), the tableau ‘was an extremely brilliant conception, incontestably the most brilliant for which political economy had up to then been responsible’. Marx regarded work, after Quesnay, by major figures in classical economics such as Adam Smith, as ‘retrogression’ (Marx 1978: 436). Quesnay was able to model the flow of capital as a whole, including all its elements. Marx’s charge, and one of the key motivations for the reproduction schema, was that Smith only dealt with outlays of capitalists on wages, ignoring capital outlays on machinery and raw materials – what he refers to as constant capital. This is the second aspect of Marx’s model considered in this chapter. Using Leontief’s input–output analysis, the role of constant capital can be formalized using a multisectoral multiplier. Moreover, the unique analytical contribution of this chapter is to derive a scalar Keynesian multiplier from these multisectoral foundations.

Marx’s reproduction schema In chapter 20 of Capital, volume 2, Marx sets out the task of establishing how the total social capital can reproduce itself. A renewal is required of all elements of means of production such as raw materials and machinery that are used up in the production process. In addition, both the working class and the capitalist class have to be maintained such that the required amount of consumption goods is produced each year. Marx writes: The immediate form in which the problem presents itself is this. How is the capital consumed in production replaced in its value out of the annual product, and how is the movement of this replacement intertwined with the consumption of surplus-value by the capitalists and of wages by the workers? (1978: 469)

8

The multiplier

Or in other words, ‘will the level of aggregate demand generated by any level of output be sufficient to purchase the whole of that output?’ (Kenway 1980: 33). This, Kenway argues, is the issue ‘confronted by Marx in the second volume of Capital and in particular, in chapter twenty’ (ibid.: 33). An analysis which focuses mainly on individual commodities, as conducted by Marx in much of Capital, volume 1, would not be worthy of such close attention to the type of commodities produced. It would not matter ‘whether it was machines or corn or mirrors’ (Marx 1978: 470). In a partial analysis of individual commodities, the theorist can concentrate specifically upon the production of value. For each individual commodity, an assumption can be made that it will be sold in the market place and that elements of the commodity used up in production will be replaced. But for Marx, ‘this formal manner of presentation is no longer sufficient once we consider the total social capital and the value of its product’ (ibid.: 470). The reproduction of the total social capital requires a consideration of both the value and the use-value of an individual commodity, the use for which it is required in the economic system. Marx therefore develops a macroeconomic approach to establishing the conditions under which the economic system can reproduce itself; one in which individual commodities are both produced and sold in the market place. To achieve this task, Marx collects industrial activities into two great departments of production. Department 1 produces means of production, capital goods that replace the constant capital (Ci) used up in production. Department 2 produces consumption goods that take the form of variable capital (Vi) consumed by workers, and are also consumed by capitalists out of the surplus value (Si) extracted from the production process. As a starting point for this analysis, Marx assumes that capitalists consume all of their surplus value. Hence, the system does not grow, since none of the surplus is set aside for capital expansion. All available resources are devoted to either consumption or the renewal of constant capital. This is the case of simple reproduction. It may be objected that simple reproduction is ‘an assumption foreign to the capitalist basis’ (ibid.: 470), since real capitalist economies are generally characterized by capital expansion. However, Marx argues that even under capital accumulation ‘simple reproduction still remains a part of this’ (ibid.: 471). The process of renewal that takes place under simple reproduction is an integral part of the more complicated process of expanded reproduction, and allows us to see more clearly its component parts. Table 2.1 shows the first empirical example used by Marx (1978: 473) to illustrate simple reproduction. Department 1 is assumed to produce nondurable outputs that are used up as constant capital during a single period

The multiplier

9

Table 2.1 Marx’s simple reproduction schema

Dept. 1 Dept. 2

Ci

Vi

Si

Wi

4,000 2,000 6,000

1,000 500 1,500

1,000 500 1,500

6,000 3,000 9,000

of production.2 In addition, Marx assumes that prices are equivalent to values. ‘Moreover, we assume not only that products are exchanged at their values, but also that no revolution in values takes place in the components of the productive capital’ (ibid.: 469). It is therefore possible to interpret the units of measurement in either value (abstract labour) or money units, with £1 of output equal to a unit of labour. The analysis that follows, until right at the end of the book, retains this unrealistic assumption of equivalence between prices and values. This is in keeping with Marx’s theoretical approach, in which there is much to be understood about the reproduction schema before introducing additional layers of complexity such as price–value deviations. Marx also assumes the rate of surplus value (the ratio of Si to Vi) is the same in both departments. In Department 1, for example, 1,000 units of variable capital are employed at a rate of surplus value of 100 per cent, which generates 1,000 units of surplus value. Each worker performs an hour of labour for himself and an additional hour for the capitalist. The total amount of living labour performed (2,000) is added to the amount of constant capital (4,000) used up, to give a total value produced in Department 1 (W1) of 6,000. Similarly, Department 2 uses 2,000 units of constant capital, 500 units of variable capital, and extracts 500 units of surplus value to yield a total value (W2) of 3,000. The general formula for calculating total values, Wi  Ci  Vi  Si, is captured in Table 2.1. There are two main ways in which reproduction is made possible. First, the two departments have complementary requirements. Department 2 exchanges 2,000 units of its output of consumption goods for 2,000 units of means of production produced by Department 1. These 2,000 units of consumption goods fulfil the variable capital (1,000) and capitalist consumption (1,000) requirements of Department 1. And the 2,000 units of means of production supplied by Department 1 allow capitalists in Department 2 to replace used-up constant capital. Reproduction is facilitated by mutual exchange between the two departments. Second, the other 4,000 units of means of production, produced in Department 1, are required to replace used-up constant capital in Department 1. In Department 2, the 500 units of variable capital and 500 units of surplus value are also produced and used up in Department 2 by its

10

The multiplier

own workers and capitalists. Here, individual departments reproduce their own requirements of production and consumption. Marx therefore shows how the total output of 9,000 units can be reproduced, 6,000 units as means of production and only a third, 3,000 units, as consumption goods. In contrast to the approach taken by Adam Smith, who does not allow for means of production, a demonstration is provided of how means of production take up a significant part of the national product. Yet Adam Smith put forward this fanciful dogma, which is still believed to this day . . . according to which the entire value of the social product resolves itself into revenue, i.e. into wages plus surplus-value, or as he expresses it, into wages plus profit (interest) plus rent. (ibid.: 510) Another of the great classical economists, Ricardo, is also charged with the same error, the contribution of the schema being to show how total social capital, with constant capital a constituent part, can be reproduced. Whereas Moseley (1998: 160) has argued that the refutation of Adam Smith is the ‘most important immediate purpose of Marx’s reproduction tables’, others, as we have seen, emphasized their importance in addressing the issue of how surplus value is realized. The key role of consumption is illustrated sharply by the scheme of simple reproduction, since all of the surplus value is consumed by capitalists. Simple reproduction is oriented by nature to consumption as its aim. Even though the squeezing out of surplus-value appears as the driving motive of the individual capitalist, this surplus-value – no matter what its proportionate size – can be used here, in the last analysis, only for his individual consumption. (Marx 1978: 487) Although under expanded reproduction surplus value is directed to more productive uses, Marx argues that the underlying role of consumption under simple reproduction is still a key part of the process of expanded reproduction. The most developed expanded reproduction schema is referred to by Marx as ‘schema (B)’ of the ‘First Example’ in section 3 of chapter 21, Capital, volume 2 (ibid.: 586–9). This is shown in Table 2.2, the numbers representing a modification of the simple reproduction table. The same assumptions are maintained as under simple reproduction, apart from relaxation of the restriction that all surplus value be allocated to capitalist consumption.

The multiplier

11

Table 2.2 Marx’s expanded reproduction schema

Dept. 1 Dept. 2

Ci

Vi

Si

Wi

4,000 1,500 5,500

1,000 750 1,750

1,000 750 1,750

6,000 3,000 9,000

The key difference is that Department 1 produces 6,000 units of capital goods, but only 5,500 are required to replace constant capital in the two departments.3 Department 2 now requires 1,500 units of capital goods in order to replace the amount it uses up. But Department 1 continues to produce a surplus of 2,000 units of capital goods (equivalent to 1,000 variable capital plus 1,000 surplus value) over and above the 4,000 it needs to replace constant capital. Therefore, the mutual exchange that took place between the two departments under simple reproduction, where surplus consumption goods were swapped for surplus capital goods, is only partially fulfilled. Marx (1978: 587) explains that in each period of production the surplus of capital goods produced by Department 1 ‘remains to be realized’.4 This additional demand is satisfied by capitalists, from both departments of production, requiring 500 additional units of constant capital in the next period of production. Hence there is an aggregate demand for capital goods that enables surplus value to be realized. Since a key objective of Marx’s reproduction schema is to show how the total social capital can be reproduced, the analysis that follows concentrates specifically upon the aggregate (macroeconomic) interpretation of the schema. The emphasis at this stage is upon highlighting the aggregate categories and main economic relationships that can be established. As the analytical complexity unravels, more attention will be given to the component parts of the system and related structural issues.

The Keynesian multiplier This emphasis on the importance of aggregate demand suggests a multiplier relationship. In Keynesian terms, the aggregate demand for capital goods produced by Department 1 can be defined as investment demand. Since this demand provides for future expansion of means of production, in the current period of production it can reasonably be assumed to be exogenous, not dependent upon any current parameters or constraints. The multiplier provides a possible way of capturing the structural relationship between investment demand and the aggregate income of the economy.

12

The multiplier

In the large body of work that has explored the relationship between the systems of Marx and Keynes,5 there is no established understanding of the role played by the multiplier. This can be illustrated by some of the more recent attempts to interpret the multiplier from a Marxian perspective. Two main topics of concern are (1) the role of the multiplier in the reproduction schema; and (2) the way in which Marx’s category of surplus value relates to the structure of the multiplier. The following brief consideration of this recent literature provides the backdrop to a full critique, in which some of its limitations will be addressed. Lianos (1979) provides an accessible insight into how the multiplier can be located in the reproduction schema. By focusing specifically upon Department 1 he states, ‘it is convenient to assume a one sector economy’ (ibid.: 407). Only information from Department 1 of the example used by Marx (Table 2.2) is included in the Lianos reproduction schema, as shown in Table 2.3. The key modification which enables a translation to Keynesian economic categories is to interpret all value added, variable capital plus surplus value, as net income (Y1) for Department 1. Assuming away for the moment the problems associated with Adam Smith’s dogma, this income is net of constant capital. The net income of the one-good economy is 2,000, consisting of 1,000 units of variable capital and 1,000 units of surplus value. A distinction is also made between the current period of production (period 1) and the subsequent period of production (period 2). The aggregate investment demand of 500 is explicitly shown as relating to the expansion of means of production in period 2. This is net investment, additional to the replacement of means of production used up in period 1. An analytical leap can now be made that provides the cornerstone of the rest of this book. Located in this reproduction schema is a Keynesian multiplier that enables a relationship to be specified between net investment and net income. The intuition runs as follows. Capitalists anticipate that they will expand their constant capital by 500 in the next period of production. There is therefore a net investment demand for 500 units of output to be produced in the current period.6 Workers are hired to produce this

Table 2.3 Locating the multiplier in Department 1 Periods

Constant capital (C1)

Variable capital (V1 )

Surplus value (S1 )

Net income (Y1 )

1 2

4,000

1,000

1,000

2,000

Net investment (I1 ) 500

The multiplier

13

output, and with their wages they purchase further amounts of output, which result in the hiring of more workers, and so on. The initial impact of the 500 units of investment multiplies throughout the economy, creating four times more income than the original injection – a net income of 2,000. The multiplier is easily located, with a value of 4 in Department 1 of Marx’s expanded reproduction schema. Having nested the multiplier in the reproduction schema, some attention can be given to its structure. As a starting point, the Keynesian income multiplier takes the form y

1 I 1b

(2.1)

where y is aggregate net income, I is aggregate investment, and b is the propensity to consume. De Angelis (2000) examines the structure of the multiplier by defining the relationship y  ␲L

(2.2)

where ␲ represents labour productivity (y/L) and L is a measure of total labour in hours of work. It follows that the employment multiplier relationship L

1 I ␲  ␲b

(2.3)

can be derived. De Angelis refers to 1/␲  ␲b as the ‘social multiplier’, with the term ␲b defined as the ‘social wage rate’ and ␲  ␲b the profit per hour. Note that if B is the money value of total consumption we can write ␲b 

yB B  Ly L

(2.4)

The social wage rate is simply a ratio of consumption to labour, the consumption (in money units) per unit of labour power. A number of simplifying assumptions are made in order to relate equation (2.4) to Marxian economic categories. Capitalist consumption is assumed to be empirically negligible, a particularly unrealistic claim which can be relaxed later. In addition, there is assumed to be no exogenous element in worker consumption; and although workers are allowed to save, their savings are not included as part of the social wage rate. The social wage rate captures

14

The multiplier

worker consumption B that is necessary for the reproduction of labour power. De Angelis therefore argues that the social wage rate is a monetary expression for Marx’s value of labour power – it represents the money value of the labour embodied in the commodity bundle required to reproduce each unit of labour power. An inverse relationship between the multiplier and the rate of surplus value is established, thereby providing a penetrating insight into the structure of the multiplier, ‘to show how class relations are represented, in a mystified form, in economic categories’ (ibid.: 85). In this spirit, a further examination of the structure of the propensity to consume can provide an even more incisive insight into the structure of class relations. By simple decomposition, the propensity to consume can be written as LB bB y yL

(2.5)

On this interpretation b represents the labour–output ratio (L/y) multiplied by the consumption per unit of labour ratio (B/L).7 This expression, it can be argued, represents the value of labour power – the labour embodied in the commodity bundle required to reproduce each unit of labour.8 Since the propensity to consume is a pure number (money/money), decomposition makes it possible to show that it is identical to the value of labour power (labour/labour), which is also a pure number. An examination of equation (2.1), therefore, reveals that the value of labour power itself (not its monetary expression) appears as the core component of the Keynesian income multiplier. This represents a more revealing insight into the structure of class relationships, with Marx’s theory of surplus value directly represented in the denominator of the multiplier. Since the component b is the value of labour power, the denominator 1b is the share of surplus value, the proportion of labour time extracted as surplus value. This interpretation of the multiplier penetrates beneath the surface of monetary economic categories as considered by De Angelis, to the Marxian labour categories. Two additional insights are therefore suggested relative to the contribution of De Angelis (2000). First, by applying the new method of decomposition a more direct translation between the multiplier and the Marxian categories is achieved by identifying an expression for the value of labour power itself, instead of its monetary expression, as a core component of the multiplier. Moreover, instead of introducing concepts such as the ‘social multiplier’ and ‘social wage rate’ this translation employs existing and well-established economic categories. Second, instead of restricting this analysis to the employment multiplier, the structure of the income multiplier is also examined.

The multiplier

15

The main problem with this decomposition of the multiplier is that it is restricted to a one-good model. A contribution which relates the Keynesian multiplier to a two-good model, along the lines of Marx’s reproduction schema, has been provided by Hartwig (2004). As a starting point, net income in the two departments is captured by the identities Y1  V1  S1

(2.6)

Y2  V2  S21

(2.7)

and

Following the approach taken by Keynes (1936) in parts of his General Theory, the propensity to consume b is applied to total net income, y  V1  V2  S1  S2, such that the amounts demanded D(·) for the outputs of each department are D(Y1)  (1  b)y D(Y2)  by

(2.8) (2.9)

In equation (2.9) the proportion of income consumed is represented by the amount of consumption goods demanded from Department 2. In (2.8), the amount saved appears as the amount of capital goods demanded from Department 1. In equilibrium, Y1  D(Y1) and Y2  D(Y2), and for reproduction to take place the proportion Y2 b  Y1 1  b

(2.10)

must be established between the two departments. Since in Keynesian notation Y1 can be written as net investment I, and Y2 as consumption B, a ‘structural’ multiplier relationship can be specified that takes the form, B

b I 1b

(2.11)

Capitalists in Department 2 use this multiplier to anticipate how much consumption goods they need to produce in order to respond to the investment decisions of Department 1. Hartwig (2004) provides a particular interpretation of the methodology employed by Keynes, in which entrepreneurs use the multiplier to plan their outputs at the start of each production period. A key advantage of this multiplier, in comparison to a one-good Keynesian model, is that it embodies the requirement of proportionality between departments of production.

16

The multiplier

There is a logical equivalence between this structural multiplier and the more traditional Keynesian variant. By writing (2.11) as B

冢1 1 b  1冣 I

(2.12)

it follows that BI

1 I 1b

(2.13)

Since y  B  I, it follows that the traditional Keynesian multiplier (see equation 2.1) can be derived from (2.13) as y

1 I 1b

(2.14)

This demonstrates that the scalar Keynesian multiplier relationship can in principle be derived from a two-sector model. As it stands, however, since (2.14) is defined using net income, no account is taken of the constituent role of constant capital in the production process.9 In embracing Keynes to model aggregate demand, a Marxian response is required to the charge that the scalar multiplier falls prey to Smith’s dogma.

Leontief input–output analysis In order to consider constant capital explicitly in a formal model of aggregate demand, a possible solution is provided by Leontief input–output analysis. There is a well-established tradition in Marxian economics for interpreting the reproduction schema as an input–output table. It has been argued that Leontief took his lead from Marx. Focusing on his earlier work, Gilibert (1998: 42), for example, states, ‘In his PhD thesis, Leontief had argued in favour of the substitution of the principle of circular flow (the reproducibility viewpoint) for that of homo oeconomicus (the scarcity viewpoint) as the cornerstone of economic theory.’ Similarly, Kurz and Salvadori (2003: 63) argue that Leontief applied his model to ‘an economy in which both capital and consumption goods are produced and reproduced’. Closely related to the Leontief approach is the theoretical legacy of Sraffa’s Production of Commodities by Means of Commodties (1960). De Vivo (2003: 1) has shown that the starting point for Sraffa’s production model has been ‘derived . . . from Marx’s reproduction schemes’. In the

The multiplier

17

ensuing development of the Leontief approach, it will become clear how it can also be characterized as broadly in keeping with a Sraffian perspective. To begin the analysis, Marx’s numerical example of expanded reproduction can be recast as an input–output framework. Table 2.4(a) re-expresses the numerical elements of Table 2.2 as an input–output table. The advantage of this table is that it shows explicitly how Marx assumes capitalists spend their 1,750 units of surplus value: on 500 units of new constant capital (dC), 150 new variable capital (dV) and 1,100 capitalist consumption (u). In this input–output format, elements of Table 2.4 can be read either along the rows as outputs of a particular department, or column-wise as inputs to that department. For example, reading row-wise, Department 2 produces 1,000 units of consumption goods for Department 1’s workers, 750 for itself, 150 for additional variable capital and 1,100 for capitalist consumption. Reading column-wise, Department 2 uses inputs of 1,500 constant capital from Department 1 and 750 of consumption goods from itself. The surplus value element of 750 is viewed as an input of value added to Department 2. For both departments, inputs and outputs are in balance, as shown by the identical column and row sums (6,000 and 3,000). Having set up the expanded reproduction schema in an input–output format, the path is now clear for it to be modelled as a multiplier framework. To achieve this aim, input coefficients aij  Xij/Xj specify the ratio between physical flows of means of production (Xij), from department i to department j, to (physical) gross output (Xj ) of department j. In Marx’s reproduction schema, these input coefficients are applied to Department 1, the only sector producing means of production. For Department 2, different notation is required for our multiplier framework. Ratios to gross output of the total number of labour units employed in each sector (Lj) are represented by labour coefficients lj  Lj /Xj; and consumption coefficients hi  Bi/L are Table 2.4 Expanded reproduction in an input–output table Dept. 1

Dept. 2

dC

(a) Numerical categories Dept. 1 4,000 Dept. 2 1,000 Si 1,000 Wi 6,000

1,500 750 750 3,000

500

(b) Leontief categories Dept. 1 p1a11X1 Dept. 2 p2h2l1X1 S1 p1X1

p1a12X2 p2h2l2X2 S2 p2X2

p1da

dV

u

Wi

150

1,100

6,000 3,000 9,000

p2dh

p2Ck

p1X1 p2X2

18

The multiplier

ratios of total consumption of each physical good (Bi) to the total volume of labour units (L). To express these physical magnitudes in money units, money prices pj are defined for each department j. The elements of Marx’s numerical example are also represented in algebraic terms (Table 2.4b). Consider inputs of constant and variable capital to Department 2. The 1,500 units of constant capital are represented by p1a12X2, the money output of Department 1 required by Department 2. And the 750 units of variable capital are represented by p2h2l2X2, the amount of consumption goods set aside by Department 2 for its own use. Elements representing expansions of capital are defined by conjoining money prices with physical volumes of new means of production (da) and physical quantities of new means of consumption (dh). Similarly the physical quantity of capitalist consumption goods is shown by the term Ck. The first row of Table 2.4(b) is captured by a balancing equation p1a11X1  p1a12X2  p1da  p1X1

(2.15)

and for the second row p2h2l1X1  p2h2l2X2  p2dh  p2Ck  p2X2

(2.16)

Cancelling out p1 in (2.15) and p2 in (2.16), the full quantity system for Marx’s expanded reproduction schema can be specified as X1  a11X1  a12X2  da X2  h2l1X1  h2l2X2  dh  Ck

(2.17) (2.18)

Expressing this quantity system in terms of matrix algebra, an input– output model of Table 2.4b, closed with respect to worker consumption, therefore takes the form

冤XX 冥  冤a0 1 2

11

冥冤XX 冥  冤h0 冥[l

a12 0

1 2

2

1

冤XX 冥  冤dh da C 冥

l2]

1 2

(2.19)

k

On the right-hand side of this expression, elements representing new constant and variable capital, together with capitalist consumption, are collected in a vector representing ‘final demand’ for the goods produced by the two departments – final demand in this closed input–output model does not include income-dependent worker consumption. By specifying X as the column vector of gross outputs for each sector, A the square matrix of interindustry input coefficients, h the column vector of worker consumption

The multiplier

19

coefficients, l the row vector of labour coefficients and F as the column vector representing final demand, the structure of (2.19) is summarized by the expression X  AX  h[lX]  F

(2.20)

With net outputs defined as Q  (I ⫺ A)X it follows that (2.20) can be re-expressed as Q  h[vQ]  F

(2.21)

where v  l(I ⫺ A)⫺1 is Pasinetti’s (1981) row vector of vertically integrated labour coefficients (labour values). Pre-multiplication of (2.21) by the row vector v yields vQ  vh[vQ]  vF

(2.22)

which, by factoring the scalar vQ, allows the derivation of the multiplier form vQ 

1 vF 1  vh

(2.23)

Under Marx’s assumption, in Capital, volume 2, that prices and values are identical, and hence £1 of output is equal to an hour of labour time, this equation captures both an income and multiplier relationship. The equivalence between prices and values is embodied in the identity p  v such that the total employment of labour units (vQ) is equal to total money net income (pQ). Similarly, vF the total number of labour units required to produce final demand, is equal to total money final demand (pF). Hence, the expression 1/1  vh is an income/employment multiplier, in which the scalar vh represents the propensity to consume b, derived from the twodepartment schema.10 We shall refer to this as the Keyensian scalar multiplier, since although it is somewhat unusually defined according to worker consumption it retains the 1/1  b structure that is so common to economics textbooks. The simplicity of the Keynesian multiplier is retained in a two-department setting. This multiplier has a particularly interesting denominator (see Appendix 2 for an equivalent interpretation of the Leontief matrix multiplier). Following the logic of my interpretation of the one-good multiplier, the term vh can be interpreted to represent the value of labour power: the labour embodied (v) in the bundle consumed by workers per unit of labour (h). The

20

The multiplier

denominator can therefore be expressed as e, the corresponding per capita share of surplus value extracted from each unit of labour. It follows that (2.23) can be expressed as a macro income multiplier y  1e f

(2.24)

where, in this special case, net money output is y  vQ  pQ and money final demand f  vF  pF. The role of Marx’s category of surplus value can therefore be identified in a macro scalar multiplier without the restrictive assumption of a onegood model. This scalar multiplier captures the inter-departmental structure of the reproduction schema without constant capital being assumed away. A formal model of aggregate demand in the reproduction schema is developed, which retains the simplicity of the Keynesian multiplier together with Marx’s value categories.

3

The Kalecki principle

The work of Michal Kalecki has been seen as a key bridging point between Marx and Keynes. Although Kalecki was in many ways the equal of Keynes, independently working out some of the same ideas, they came from very different backgrounds. Whereas Keynes had a classical Oxbridge education, moving from Eaton to Cambridge, Kalecki went to Gdansk Polytechnic; and whilst Kalecki was an official in the UK Treasury, revered by the British establishment, Kalecki was schooled in the underworlds of European Marxism.1 From these roots, Kalecki developed an interpretation of the reproduction schema, in which aggregate demand is the main driving force. Under the auspices of the ‘Kalecki principle’, that capitalists earn what they spend, the role of money is brought into focus. The thrust of this principle is expressed by Marx in Capital, volume 2: ‘In point of fact, paradoxical as it may seem at the first glance, the capitalist class itself casts into circulation the money that serves towards the realisation of the surplus-value contained in its commodities’ (Marx 1978: 409). There are two main ways in which Kalecki’s interpretation of the reproduction schema is underdeveloped. First, although Kalecki (1991d: 459) claims that his model is ‘fully in the Marxian spirit’, he did not examine the direct relationship between his approach and Marx’s original text. Sardoni (1989) has provided perhaps the most concerted effort to make this connection, but does not engage directly with Marx’s numerical examples. Second, coming from the other extreme, Reuten (1998) provides a most systematic and detailed exploration of Marx’s original tables, giving special mention to the Kalecki principle, but without providing a direct connection to Kalecki’s analytical model of the reproduction schema. The contribution of this chapter is to provide a detailed assessment of the role of the Kalecki principle in Marx’s reproduction schema. As part of this assessment, the structure of the scalar multiplier framework is further developed, together with the relationship between the Kalecki principle and Marx’s value categories.

22

The Kalecki principle

Kalecki and the reproduction schema A first step in the analysis is to show explicitly how the elements of surplus value are allocated. Marx’s numerical example of expanded reproduction (Table 2.2) can be explored in more detail by distinguishing, for each sector i, between capitalist consumption (ui), incremental changes in constant capital (dCi) and changes in variable capital (dVi). Numerical values for these terms are displayed in Table 3.1. In Department 1, for example, one half of the extracted surplus value of 1,000 is invested in the expansion of capital, with 400 directed to new constant capital and 100 to new variable capital. The remaining 500 units of surplus value are consumed by Department 1 capitalists. Following Kalecki (1991d: 459), the reproduction schema can be further disaggregated by dividing the activity of Department 2, producing consumption goods, into a new Department 2 producing capitalist consumption goods and an additional Department 3 producing wage goods. The numbers in Table 3.2 provide an illustration of how Marx’s table could be looked at from Kalecki’s perspective. Note that with the new Department 2 producing 1,100 units of capitalists’ consumption goods, and Department 3 producing 1,900 of wage goods, the combined total output of 3,000 units is the same as the output of Marx’s Department 2 in the two-sector table. Similarly, Department 1 in the three-sector table produces exactly the same output (6,000 units) as Department 1 in the original table. Table 3.2 can viewed as a decomposition of Marx’s schema to provide a more detailed analysis of the structure of consumption. Table 3.1 The allocation of surplus value in the two-sector schema Ci

Dept. 1 Dept. 2

4,000 1,500 5,500

Vi

1,000 750 1,750

Si

Wi

ui

dCi

dVi

500 600 1,100

400 100 500

100 50 150

6,000 3,000 9,000

Table 3.2 Ex ante three-sector reproduction schema Ci

Dept. 1 Dept. 2 Dept. 3

4,000 550 950 5,500

Vi

1,000 275 475 1,750

Si

Wi

ui

dCi

dVi

500 220 380 1,100

400 36 23 63 13 500

100 18 31 31 23 150

6,000 1,100 1,900 9,000

The Kalecki principle 23 The reproduction schemes shown so far can be characterized as showing the ex ante2 production of year 1 (see Desai 1979: 149; Reuten 1998: 225). At the start of the year, capitalists use 5,500 units of constant capital in total and produce 6,000 units of output of constant capital. There is an ex ante imbalance between these two quantities, and also between quantities of consumption goods produced and consumed. In order to ensure ex post balance, at the end of year 1, the additional units of constant (dCi) and variable (dVi) capital set aside for future production can be grouped together with the ex ante volumes of capital consumed at the start of the period (Table 3.3). Department 1, for example, has constant capital of 4,400 units at the end of the period, made up of the original 4,000 consumed and the additional 400 required for production in the next period. Similarly, variable capital is now 1,100 units, made up of the original 1,000 units and the new 100 inputs of variable capital. The new ex post categories of constant and variable capital are referred to in Table 3.3 as Ci* and V* i respectively. A final rearrangement of the categories in Marx’s numerical table can be achieved by introducing a different way of looking at profits. For Marx, profits in each department are specified as the surplus value left after accounting for ex ante inputs of constant and variable capital (Si  Wi  Ci  Vi). However, for Kalecki, profits in each department ( P* i ) are the total value left after accounting for ex post variable capital ( Pi*  Wi  Vi* ). Kalecki is concerned with gross undistributed profits, a definition of profits that can be applied to the reproduction schema by simply adding the constant capital components of Table 3.3 to the components for capitalists’ consumption. In Department 1, for example, 4,400 units Table 3.3 Ex post three-sector reproduction schema

Dept. 1 Dept. 2 Dept. 3

Ci*

Vi*

ui

Wi

4,400 586 23 1,013 31 6,000

1,100 293 13 506 23 1,900

500 220 380 1,100

6,000 1,100 1,900 9,000

Table 3.4 Kalecki’s interpretation of the three-sector schema

Dept. 1 Dept. 2 Dept. 3

Vi*

Pi*

Wi

1,100 293 13 506 23 1,900

4,900 806 32 1393 13 7,100

6,000 1,100 1,900 9,000

24

The Kalecki principle

of constant capital are added to 500 units of capitalists’ consumption, resulting in 4,900 of gross profits. This result is shown in Table 3.4, which gives a numerical demonstration of Kalecki’s categories of wages (Vi* ) and profits ( Pi* ). (The full algebraic structure of the three-sector schema is laid out in Appendix 3.) Having reformulated Marx’s categories and rearranged the reproduction schema, along the lines suggested by Kalecki, a key result is established. 1 Table 3.4 shows that Department 3 produces a surplus of 1,393 3 wage goods, and these are sold to workers in the other two departments (1,39331  1,100  29313 ). Expressing this identity in algebraic terms: P3*  V1*  V2*

(3.1)

Following Kalecki (1991d: 460), adding P1*  P2* to both sides of equation (3.1) yields P1*  P2*  P3*  P1*  V1*  P2*  V2*

(3.2)

and hence P*  W1  W2

(3.3)

This is an ex post identity between total profits (P*) and the economy’s output of capital goods (W1) and capitalists’ consumption goods (W2). Kalecki poses the key question as to how we should interpret this identity. Are expenditures upon capital goods and capitalists’ consumption goods determined by profits, or are profits determined by these expenditures? He argues that ‘capitalists can decide how much they will invest and consume next year, but they cannot decide how much they shall sell and profit’ (ibid.: 461). It is the money expenditures by capitalists upon consumption and investment that generate the resultant volume of profits. Cartelier (1996: 217) has linked this so-called Kalecki principle, that capitalists earn what they spend, to the circulation of money. ‘As a result of their ability to initiate circulation entrepreneurs, as a whole, more or less have the power to determine their income.’ Moreover, he argues, ‘the Kalecki principle does not contradict the Classical view which makes profit equal to the value of surplus.’ Key passages in Marx’s writings that demonstrate the role of the Kalecki principle in relation to the circulation of money are in chapter 17 of Capital, volume 2 (see Sardoni 1989: 211). Starting with the case of simple reproduction, Marx considers the circulation of money using the example of an individual capitalist. ‘During the first year he advances a money capital of £5,000, let us say, in payment for means of production (£4,000) and for

The Kalecki principle 25 labour-power (£1,000)’ (Marx 1978: 409). At a 100 per cent rate of surplus value it can be assumed that £1,000 of surplus value is appropriated. The problem is that the capitalist advances £5,000, which can be referred to as M, but receives back £6,000, the realized amount M. Focusing upon the difference between the two amounts (MM), Marx poses the question ‘where does this money come from?’ (ibid.: 407). The simple answer to this question is that the extra money is provided by the unproductive personal expenditure of the capitalist. The capitalist consumes the same £1,000 as the volume of surplus value. This ‘£1,000 is converted into money with the money that he threw into circulation not as capitalist, but as consumer, i.e. did not advance, but actually spent’ (ibid.: 410). Moreover, this consumption is financed out of the capitalist’s own money hoard: it ‘means nothing more than that he has to cover his individual consumption for the first year out of his own pocket’ (ibid.: 409). Marx generalizes this key role for unproductive expenditure to the capitalist class as a whole. It was assumed in this case that the sum of money that the capitalist casts into circulation to cover his individual consumption until the first reflux of his capital is exactly equal to the surplus-value that he produces and hence has to convert into money. This is obviously an arbitrary assumption in relation to the individual capitalist. But it must be correct for the capitalist class as a whole, on the assumption of simple reproduction. It simply expresses the same thing as this assumption implies, namely that the entire surplus-value is unproductively consumed.... (ibid.: 410) Since there is no expansion of the capital stock under simple reproduction, all surplus values are directed to unproductive expenditure, but at the same time capitalists enable this mass of surplus value to be realized by casting the money for unproductive expenditure into circulation. The case of expanded reproduction, as considered in Tables 3.1–3.4, ‘does not offer any new problems with respect to money circulation’ (ibid.: 418). The difference is that part of the additional money cast into circulation (MM) now consists of money capital advanced for productive purposes. (The other part consists of the money cast into circulation for purposes of unproductive expenditure by capitalists, as before in the case of simple reproduction.) As far as the additional money capital is concerned, that required for the function of the increased productive capital, this is supplied by the portion of realised surplus-value that is cast into circulation by the capitalists as money capital, instead of as the money form of revenue. (ibid.: 418)

26

The Kalecki principle

Under expanded reproduction, surplus value is clearly realized by capital investment and capitalists’ consumption. Hence for Sardoni (1989: 214), ‘Capitalists’ profits therefore now depend on their consumption and investment expenditure, just as in Kalecki’s analysis.’ There is strong evidence for the Kalecki principle, that capitalists earn what they spend, operating in Marx’s analysis of expanded reproduction.

Surplus value Despite his direct engagement with Marx’s reproduction schema, and the illuminating insights he provided into the determination of profits, Kalecki has been widely characterized as a ‘non-Marxist’ (see Sawyer 1985: 175; Freeman and Carchedi 1996: xii). This can be attributed in part to the treatment that he received during the years of post-war repression orchestrated by the Polish communist party. Of independent disposition, Kalecki was not a person given to toeing the line, resigning from three jobs on separate occasions. This independence is reflected in his engagement with the writings of a previous Polish heretic, Rosa Luxemburg, which would not have endeared him to the party establishment. In theoretical terms, the non-Marxist tag can be largely attributed to a lack of engagement with the labour theory of value. For Sebastiani (1994: 108), Kalecki’s silence on this issue could be interpreted ‘either as a tacit acceptance or as a tacit rejection of Marx’s premises’. Kerr (1997: 23), in her textual analysis of Marx and Kalecki, takes the first position, aiming ‘to make explicit what Kalecki often left as understood in the more abstract presentations of his analysis’. In contrast, Brus (1977: 59) reported that Kalecki felt ‘a strong distaste for the Marxian theory of value, which he considered metaphysical and (if I am not mistaken) never wanted to discuss’. Whichever interpretation is correct, Kalecki’s silence on the labour theory of value leaves open the theoretical possibility that its relevance can be fruitfully explored. To relate Kalecki’s model of reproduction to Marx’s theory, a reconfiguration is required of the definition of profits. The problem, as we have seen, is that Kalecki’s model requires a gross definition of profits that is different from Marx’s category of surplus value. The Kalecki principle has not been precisely demonstrated in the context of Marx’s reproduction schema, in which surplus value is the key category of analysis. To apply the Kalecki principle directly to Marx’s schema, attention can be focused on an important difference between Marx and Kalecki about the way in which investment is specified. Whereas for Kalecki investment is associated specifically with the capital-goods producing department, for

The Kalecki principle 27 Marx investment (accumulation) is directed to goods produced by both departments. As demonstrated by Zarembka (2000: 190), there is a conception which Marx uses throughout most of his work, that accumulation of capital entails increases in both the value of the means of production used in production processes and in the value of expenditure on labour power, i.e. increases in both constant and variable capital (original emphasis). Although Sardoni (1989: 211) mentions these different specifications of investment in his comparison of Marx and Kalecki, he does not highlight their importance. To demonstrate the importance of this difference, the Leontief input–output framework can again be used to model the final demand of each department of production such that investment demand cuts across departments. This Leontief interpretation of the reproduction schema allows Marx’s categories to be retained alongside the Kalecki principle. Table 3.5 is a Leontief representation of the three-sector reproduction scheme considered previously in Tables 3.2–3.4. Following the logic of the input–output approach, elements of this table can be read along the rows as outputs of a particular sector, or column-wise as inputs to that sector. For example, Department 3 produces outputs of 1,000 in wage goods for Department 1, outputs of 275 for Department 2 and 475 for itself. Reading column-wise, Department 3 uses 950 inputs of constant capital from Department 1 and 475 inputs of wage goods from itself. Since investment, redefined as additional constant capital (dC) and variable capital (dV), is now separately defined as part of final demand, profits in each sector are terms representing surplus value (Si). The total personal consumption of capitalists (u) is shown as the final demand for goods produced by Department 2.3 Without losing too much information, Table 3.5 can be translated into the more familiar two-sector schema used by Marx. All that is required is an Table 3.5 An input–output interpretation of the three-sector schema Dept. 1

Dept. 2

Dept. 3

Si dC

Dept. 1 Dept. 2 Dept. 3 Si Wi

4,000

550

950

Wi dV

u

500 1,100

1,000 1,000 6,000

275 275 1,100

475 475 1,900

150

6,000 1,100 1,900 1,750 9,000

28

The Kalecki principle

adding together of the elements of the two rows and two columns relating to sectors 2 and 3. By aggregating Table 3.5, it can be translated into Table 2.4, the two-sector schema displayed earlier in Chapter 2. Following the analysis of Chapter 2 (equations 2.15–2.24), the simple Keynesian multiplier y  1e f

(3.4)

captures the macroeconomic structure of the two-sector schema. To recap, under the working assumption of Capital, volume 2, that prices and values are equivalent, the scalar y represents net money output, f is money final demand and the denominator of the Keynesian multiplier e is the share of surplus value. With total final demand ( f  u  dC  dV ) made up of investment (I  dC  dV ) and capitalist consumption (u), equation (3.4) can be re-expressed as the identity SuI

(3.5)

or Surplus value  capitalist consumption  investment where S  ey represents the total volume of surplus value produced in the economy.4 Equation (3.5) provides an alternative way of representing the Kalecki principle in Marx’s reproduction scheme. Instead of examining the determinants of gross undistributed profits, as in Kalecki’s equation (3.3), an alternative ex post identity based on the input–output model is derived, in which profits (surplus value) are set equal to investment plus capitalist consumption. The Kalecki principle, that capitalists earn what they spend, can be applied to equation (3.5), with capitalist consumption together with investment in constant and variable capital determining the total volume of surplus value. In contrast to the Kalecki formulation there is a clear role for Marx’s theory of surplus value. Capitalists cast money into circulation as aggregate demand on capitalist consumption and investment, which is realized as surplus value.5

The Kalecki multiplier In a more sophisticated model of the determination of profits, Kalecki develops his own multiplier framework. The advantage of this approach is that capitalist consumption is divided into an autonomous part and a part dependent on profits. This Kalecki multiplier can be easily reconciled with

The Kalecki principle 29 the scalar Keynesian multiplier derived from the reproduction schema. The constant part of capitalist consumption (u) is defined as B0, with the remaining part depending upon total profits (in proportion ␭) such that u  B0  ␭P

(3.6)

where P represents total profits. Since P  u  I, P  B0  ␭P  I

(3.7)

and hence P

B0  I 1␭

(3.8)

This final equation represents a multiplier relationship between total profits and the total exogenous expenditure by capitalists (B0  I ), the multiplier being defined as 1/1␭. With this Kalecki multiplier relationship, profits are determined using exogenous investment and capitalist consumption. Since profits consist of total capitalist consumption and investment, (3.8) could be employed as the scalar for final demand f in (3.4). Substituting (3.8) into (3.4), the Keynesian multiplier takes the form y

1 (B  I) e(1  ␭) 0

(3.9)

The Keynesian multiplier has as its constituent elements the Marxian term representing the share of surplus value e and the Kalecki multiplier 1/1␭. It should also be emphasized that this adaptation of the Kalecki system represents an interpretation of the reproduction schema that is consistent with Marx’s system. As Lee (1998) has argued, Kalecki has a restrictive production model in which each department is vertically integrated, producing its own raw materials. In contrast, Marx assumes that raw materials are a part of constant capital, produced in the first department and circulated to other departments. A failure to fully take into account connections between industries leaves the Kalecki system vulnerable to a Sraffian critique. Steedman (1992), for example, has lambasted the Kaleckian price system for the absence of multisectoral relationships. By establishing the Kalecki principle in an input–output context, an interpretation of the reproduction schema is possible in which linkages between industries are taken seriously.

30

The Kalecki principle

An additional advantage of this input–output approach is that it can be generalized to a more complex matrix multiplier framework. Miyazawa (1976) developed such a framework in which both production and income are disaggregated into multiple categories. This has become an established input–output format for modelling the relationship between income and expenditure in a Kalecki system (see Mongiovi 1991; Hewings et al. 1999). A generalization is provided in Trigg (1999) of how the Leontief multiplier considered in Appendix 2, with surplus value as its constituent element, can be related to the Miyazawa multiplier.

The value-form Although the input–output approach may help defend Kalecki’s system against the challenge provided by Sraffian economics, the claim that it can be a vehicle for capturing the macroeconomic role of money is very much against the grain of current thinking in Marxian economics. Input–output analysis is a key part of the Sraffian critique of the labour theory of value, in which it is argued that Marx failed to correctly transform the values of both inputs and outputs into prices.6 In the Sraffian representation of Marx, separate value and price systems are compared, where values are calculated as embodied labour coefficients. Once the correct transformation of values is carried out, the whole raft of results obtained by Marx from the labour theory of value is discredited. Where money is considered, its role in this Sraffian interpretation of Marx is limited. For Saad-Filho (2002: 24), ‘As the analysis is primarily concerned with the relationship between the value and price systems, money has no autonomous role and, when considered at all, it is merely a numeraire.’ A key defence of Marx’s theory, against the Sraffian critique, is to argue that the Srafffians do not take money seriously. An alternative strand of value theory that corrects this mistake is the value-form tradition, which ‘emphasised the importance of money for value analysis, because value only appears in and through price’ (ibid.: 27). As a way of testing the possibility that money can be taken seriously in the input–output approach, it can be explored how the preceding analysis of the Kalecki principle can be reconciled with the value-form approach. At the very start of Capital, volume 1, Marx (1976) defines commodities as having a double existence, as useful objects (use-values) and as exchange-values. The use-value of a commodity is the physical quality it bestows to the user of the commodity. As an example, Marx indicates that the commodity could have use-value ‘directly as a means of subsistence, i.e. an object of consumption, or indirectly as a means of production’ (ibid.: 125). Indeed, it is these two different use-values that are the basis for

The Kalecki principle 31 Marx’s two great departments of production in the reproduction schema. For exchange between such use-values to take place, however, they must also have exchange-value. Exchange-value is defined in quantitative terms, since the exchange of capital goods for consumption goods requires a measuring rod to establish how much of one is exchanged for the other. The measuring rod is provided by labour-time. ‘As exchange-values, all commodities are merely definite quantities of congealed labour-time’ (ibid.: 130). Marx writes, ‘Now we know the substance of value. It is labour. We know the measure of its magnitude. It is labour-time’ (ibid.: 131). What is now required is a definition of the form which value takes as exchange-value. For Marx the value-form is expressed in monetary prices. Labour-time embodied in use-values can only be socially validated as value when as commodities they are sold for money. Money is the form in which commodities appear as exchange-values in the market place. In their exposition of this value-form approach, Reuten and Willams (1989: 53) conclude, ‘In bourgeois society . . . labour and the products of labour are thus socially recognized as useful only by assuming the form of value: money.’ From this perspective the embodied labour coefficients, employed in the Sraffian interpretation of Marx, are based on an ‘exclusive focus on the use-value aspect’ (ibid.: 54). Furthermore, ‘These constructs inhibit the account of a capitalist economy as an essentially monetary system’ (ibid.: 54). As argued by Clarke: Thus the sum of value expressed in a particular commodity cannot be identified with the quantity of labour embodied in it, for the concept of value refers to the socially necessary labour-time embodied, to abstract rather than to concrete labour, and this quantity can only be established when private labours are socially validated through the circulation of commodities and of capital (original emphasis).7 (1994: 133) Although Marx himself specified value in terms of labour embodied, the Sraffian Marxists are charged with calculating labour values without recourse to their validation in the market place as money. It may be that Sraffians have implicitly assumed that what is produced is sold, but the lack of importance attached to monetary questions has left their approach open to the value-form critique. At the other extreme, there is the danger that all mention of value as labour embodied is written out of economic theory. Steedman (1981: 15) has argued that Marxists, in avoiding the use of embodied labour, are in danger of ‘draining it of all content’. The problem is that without labour

32

The Kalecki principle

embodied categories value theory may fail to penetrate beneath the surface of money prices. As a contribution to this debate, it could be argued that the earlier derivation of the Kalecki principle provides a way of conserving both the labour embodied concept and the value-form. This is very straightforward, on the assumption of volumes 1 and 2 of Capital, that prices and values are equivalent. With p the vector of money prices and v the vector of embodied labour values, pv

(3.10)

The embodied labour values represent the total (direct and indirect) labourtime required to produce each unit of physical output. These embodied labour values have to be socially validated in their value-form as money. By setting prices equal to values, the embodied labour magnitude and the money value-form are assumed to be identical. What is more, these equally valid ways of defining value are consistent with a macroeconomic interpretation of the autonomous role of money. Since under the Kalecki principle capitalists earn what they spend, the social validation of the market, led by capitalist investment and consumption, is the starting point for economic activity. Commodities are only produced, labour is only employed, if capitalists cast into circulation the money required for sales to be realized – for labour embodied in commodities to become socially necessary. Since money, with its specific role in a capitalist economy, is so central to the Kalecki principle, a possible synthesis can be suggested with the value-form approach; without, that is, compromising the use of a Leontief/Keynesian multiplier framework together with embodied labour categories.

4

The monetary circuit

In the Anglo-American universities, economics has been held in a vice-like grip by the neoclassical orthodoxy. One of its key limitations is the neutral role played by money in the microeconomic determination of prices. Although the liberal right embraced the term monetarism, its actual meaning is that money has no real impact on economic activity (apart from causing inflation). In the face of this establishment position, mainstream Keynesian economics has fought a timid rearguard action, being forced to accept the tools and assumptions of neoclassical theory. On the European continent, however, a new genre of monetary macroeconomics has emerged, often referred to as the Franco-Italian circuit school; an approach that ‘has its antecedents in the writings of Marx on the circuit of money capital’ (Bellofiore and Seccareccia 1999: 753).1 What sets this circuit approach apart is its institutionally relevant analysis of the relationship between banks, firms and workers. A model of the circuit of money is developed in which prime importance is placed upon the role of banks in financing industrial activities. Central to this approach is an application of the Kalecki principle, that capitalists earn what they spend; the question being how an injection of money can circulate around the economy and return back to the capitalists. Moreover, how is this circuit of money intertwined with the activities of industrial sectors? And how much money is required for the circuit to be complete? Marx’s reproduction schema provides a natural starting point for addressing these questions.

The theory of the monetary circuit It is generally agreed that ‘the most powerful model of the monetary circuit’ (Bellofiore and Realfonzo 1997: 97) is that developed by Graziani (1989). This model has a distinct Marxian flavour. There is a class demarcation between workers and capitalists and, although intersectoral relationships are not fully explored, a distinction is made between consumer and

34

The monetary circuit

capital goods. The key departure from a more traditional Marxian approach, however, is its opposition to a commodity theory of money. In a triangular structure of relationships, banks give credit to firms in order to finance their outlays on workers. ‘Money cannot be a commodity because the purchase of labour power is logically prior to the production of commodities and therefore also to the production of the money commodity itself’ (Bellofiore and Realfonzo 1997: 100). Once the monetary requirements of the economic system are taken into account, alongside modern institutional arrangements, money is defined as a credit instrument – money that has symbolic value and no intrinsic value. A monetary circuit must have a starting point and an end point. The starting point in the Graziani model is the initial amount of money borrowed by firms from banks. Firms then use this money to finance their total wage bill, employing workers to produce commodities. Under the assumption that workers do not save, which is maintained throughout the analysis that follows, wages are spent on consumer goods, all of the money returning back to the firms. At the end of the circuit, firms are accordingly able to pay back their debt to the banks. The money, which was originally borrowed, is destroyed when it returns back to the banks, and the circuit is closed. It should be noted that this model also provides a modification of the standard Marxian representation of the circulation of money, since only wages are advanced. In the standard interpretation of Marx’s system, the total amount of money (M) that firms advance consists of variable and constant capital, which is transformed in the production process to a new volume of money (M) that includes profits made by firms. However, for Graziani: If we consider firms as a whole, their only external purchase is labour force. All other exchanges being internal transactions, no further monetary payment is required. Only at the end of the production process firms buy capital goods to be used in the following period. (1989: 4) In comparison to Marx, therefore, the circuit approach significantly reduces the amount of money that has to be advanced in order for the production process to be initiated. Although the Graziani model distinguishes between consumption and investment goods, a possible criticism is that there is no systematic analysis of the relationship between the sectors that produce these goods. By internalizing transfers between firms in relation to capital goods, there is no consideration of the two-way exchange that takes place between the capital

The monetary circuit 35 Table 4.1 Two-sector Kalecki schema

Dept. 1 Dept. 2

Wages

Profits

Output

V1* V2*

P1* P2*

W1 W2

and consumption goods sectors. In the analysis that follows we explore two alternatives. In the first, the advance of wages is argued to be insufficient to service a complete monetary circuit (Seccareccia 1996). In the second, an alternative extreme is adopted in which only the wage bill advanced in the capital goods sector is considered (Nell 1998, 2004). It has been argued by Nell (1998: 207) that both these interpretations were considered by Marx in his notes on the circulation of money, collected in Capital, volume 2. Consider Table 4.1, where for simplicity capitalist consumption is subsumed under household consumption out of wages, and there is no government sector or external trade. This is a two-sector representation of the Kalecki schema, shown previously in Table 3.4, with gross outputs (Wi), measured in money units, made up of profits (P*i ) and wages (Vi*). The subscript i takes a value of 1 for Department 1, producing capital goods, and 2 for Department 2, producing consumer goods. After allocating goods to support its own workers, the consumption goods sector produces a surplus (P2*) which is used to support workers in the capital goods sector. Workers in the capital goods sector spend their wages (V1*) on these surplus consumption goods and hence P2*  V1*

(4.1)

This two-sector version of equation (3.1), derived previously in Chapter 3, is referred to by Deleplace and Nell (1996: 20) as the ‘Marxian principle’, that the wages of the capital goods sector determine the profits of the consumption goods sector. Seccareccia (1996) uses (4.1) to show that the advance of money in the Graziani model (M) is equal to the output of the consumer goods sector: M  V1*  V2*  P2*  V2*  W2

(4.2)

The total wage bill is equal to the output of the consumer goods sector (W2). However, if this is the case, ‘where do firms in the investment goods sector get the money to reimburse the banks, thus closing the circuit of

36

The monetary circuit

credit?’ (ibid.: 405). A proposed solution is for firms to advance both wages and investment at the start of the circuit (see also Rochon 1999). A larger amount M  W1  W2

(4.3)

is borrowed from banks by firms at the start of the monetary circuit. This is a ‘single swap’ approach in which the ‘gross product swaps in a single exchange for an equivalent sum of money’ (Nell 1998: 207). For Nell, this approach closely resembles the first of Marx’s solutions in Capital, volume 2, to the problem of establishing where the money comes from to service the gap between the amount advanced by capitalists and the amount M they receive as income.2 As we saw in Chapter 3, Marx addresses this issue by positing that capitalists advance the amount MM in addition to M. Under the Kalecki Principle, MM is the amount of money cast into circulation by capitalists in order to realize profits. Ignoring for simplicity the role of capitalist consumption, this amount is required to purchase additional quantities of capital. Hence, capitalists advance the whole of M. ‘On this view, theoretically, it is correct to speak of M becoming M, but in practice there is no initial sum of money, M, followed later by a larger sum, M; there is only M’ (ibid.: 207). In the single swap approach this advance of money is sufficient to fund total income in one run of the monetary circuit. Nell develops a critique of this single swap approach by arguing that there is an exaggeration of the amount of money required in the circulation process. The problem with the single swap approach is that it retains the idea that the total money supply equals the value of total output. This results in a pattern of circulation that appears at times to run counter to economic common sense. If the total wage bill and funds for total investment are both advanced, then the capital goods sector will find itself awash in unnecessary cash. For when the capital goods sector sells investment goods to the consumer sector, it will receive funds equal to its wage bill. Yet it has just borrowed its wage bill! Why does it borrow this money (incurring expenses and interest) when it can earn it? (ibid.: 212–13) There is no allowance in the single swap approach for transactions taking place sequentially, with a given amount of money circulating between households and firms over time.3 The principle being proposed here is that capitalists will earn income from selling outputs to capitalists in other

The monetary circuit 37 sectors of production. A ‘mutual exchange’ model is required that takes into account the mutual benefits to capitalists of sectoral interdependence. Nell (2004) sets up his mutual exchange model of Table 4.1 under the assumption that production is defined in distinct periods. In each production period there is 100 per cent depreciation of capital goods, each item lasting for the duration of that period, before being replaced in the next period. Replacement of capital used up is carried out with capital goods produced in the previous period. The same assumption is applied to households, with consumption goods carried forward from the previous period. At the start of the production period, therefore, inventories of capital and consumption goods are inherited from the previous period of production. As a consequence, production in the current period is geared up for the replacement of items used up by firms and consumers in the current period. The production period is effectively a slice of time, which has a before and after.4 This approach is very different from the Graziani model in which time starts with the advance of credit by banks to initiate production, with all items of production generated subsequent to this process (see Fontana 2002: 156–60). The Nell production period takes as its starting point the outlay on wages by firms in the capital goods sector. In strictly Marxian terms, this is ‘the initial moment of exchange between capital and labour’ (Graziani 1997: 29), under which money takes the form of money capital in the investment goods sector. The starting point could alternatively be in the consumer goods sector, but a choice is required in order to simulate the knock on effects between sectors. A sequence of ‘stages’ of circulation are examined, all of which take place within the period of production. Three of the initial stages in the money circuit can be explained as follows: Stage 1 At the outset firms in the capital goods sector (sector 1) begin to borrow money from banks in order to finance the wage bill of that sector.5 Out of these wages, workers in sector 1 purchase consumption goods from sector 2. Stage 2 In response, by selling consumption goods to sector 1, firms in the consumption goods sector (sector 2) direct these funds to the payment of sector 2 wages. Workers in sector 2 spend their wages on consumption goods that return back to the firms in sector 2. The money re-emerges in sector 2 to be spent on capital goods produced in sector 1. Stage 3 From sales of capital goods to sector 2, firms in sector 1 are able to pay wage advances and use gross profits to purchase their own capital goods. The money circulates between the two sectors until all of the initial money advanced as wages in the capital goods sector is put into circulation.

38

The monetary circuit

The circuit is closed once wages in the capital goods sector (V1*) are equal to profits in the consumption goods sector (P2*), equation (4.1) providing a balancing constraint between the two sectors. As Graziani (1997: 30) has demonstrated, the initial outlay of money as capital, in the hiring of labour, is followed by a phase of money in circulation acting as an ‘intermediary of exchange’. The circulation of money in Nell’s model has some resemblance to Marx’s analysis of mutual exchange between departments of production, as discussed in Capital, volume 2 (Marx 1978: 474–8). Marx provides a similar example in which capitalists in the capital goods sector (Department 1) advance a sum of £1,000 to workers. He writes: The workers use this £1,000 to purchase means of consumption of the same value from the capitalists in department II, and thereby transform half of department II’s constant capital into money. The capitalists in department II, for their part, use this £1,000 to buy means of production to the value of £1,000 from the capitalists in department I. (ibid.: 475) By selling means of production to the consumption goods sector (Department 2), the capitalists of Department 1 are able to effect a reflux of their money outlay on wages: ‘the same amount flows back to the respective capitalists as they themselves advanced for the monetary circulation’ (ibid.: 477). Although Nell (1988a: 94–5) highlights some of the inconsistencies in Marx’s development of this example, he argues that it provides the correct starting point for an analysis of the circulation of money between sectors. Moreover, this process of interaction between sectors in Marx’s example can be interpreted as a multiplier relationship. The impact of the initial £1,000 advanced by capitalists in Department 1 multiplies between the two sectors. Oiled by the circulation of money, workers in Department 1 purchase consumption goods from Department 2, which allows capitalists in Department 2 to purchase means of production from Department 1. The formal model of the multiplier process developed by Nell (2004) can be demonstrated by writing total money output (WT) as WT  V1*  V2*  P1*  P2*  2V1*  V2*  P1*

(4.4)

For the second element in (4.4) a multiplier relationship is specified (see Nell 1998: 563), where w is the wage rate and n2 is the labour coefficient for the consumption goods sector. Wages paid out in the capital goods sector have an initial impact on the wage bill in the consumption goods

The monetary circuit 39 sector of V1*, which in the next round is wn2V1*, in the next (wn2)2V1*, and so on, with the overall impact captured by the multiplier relationship V2* 

1 V* (1  wn2) 1

(4.5)

Nell also assumes two subsectors for the capital goods sector, the first selling capital goods to the consumer goods sector, and the second selling capital goods to other firms in the capital goods sector. Labour coefficients are assumed to be the same in each sector. A multiplier can be constructed that captures the relationship between the subsectors and the consumer goods sector. To start this process the first subsector sells capital goods to the consumer goods sector, receiving proceeds of P2*(  V1*). In order to repay its loans the first subsector withdraws wn1P2*, and an amount (1  wn1)P2* is spent on new and replacement capital goods from the second subsector. The second subsector accordingly spends (1  wn1)(1  wn1)P2* leading to a sequence that has as its sum the multiplier relationship 1 P* P1*  wn 2 1

(4.6)

Substituting into (4.4) the multiplier expressions from equations (4.5) and (4.6) yields an overall multiplier relationship between total income and the initial outlay on wages in the capital goods sector: WT  V1*[2  {1(1  wn2)}  {1wn1}]

(4.7)

In this model the outlay V1*, once circulated between the capital and consumer goods sectors, is sufficient to fund income, including wages and profits, in both sectors. The multiplier effect allows for substantially less monetary advance than in both the Graziani and single swap models, generating the same overall volume of income.

A Marxian alternative Although it has been shown that Nell’s (2004) model of the circulation of money bears some resemblance to Marx’s system, two key issues remain to be resolved. First, in adopting the Kalecki schema of intersectoral flows (Table 4.1), Nell narrowly associates accumulation with the production of means of production (capital goods). There is no mention of the accumulation of consumption goods, which are placed at the centre of Marx’s reproduction schema. Second, the role of Marx’s category of surplus value is obscured in the Kalecki table. As demonstrated in Chapter 3, for the

40

The monetary circuit

three-sector schema, a translation can be made between the Kalecki categories and Marx’s original categories specified in the third part of Capital, volume 2. Let Vi*  Vi  dVi P*i  Ci  dCi

(4.8) (4.9)

where Vi and Ci respectively are Marx’s original terms for variable and constant capital, and dVi and dCi represent new amounts of capital available for productive use in the next period. Using these categories, elements of Table 4.1 can be re-expressed as in Table 4.2. Gross outputs are the same in both reproduction tables but the capital components are shown in terms of Marx’s categories. Following the approach worked out in Chapter 3, Table 4.1 shows that in the Kalecki-type formulation profits in each sector are defined in gross terms, consisting of expenditure on the replacement of existing constant capital and its expansion (Ci  dCi); whereas in Table 4.2 profits (Pi) are defined in net terms (dCi  dVi). The latter definition of profits is consistent with Marx’s interpretation, with the total increment of capital identical to the volume of surplus value, after accounting for the replacement of current inputs of constant and variable capital. As discussed earlier, in relation to the single swap approach, it may also be posited that capitalists advance the amount MM required to purchase the total increment of capital. In addition to funding the production of this capital increment, the monetary advance allows the realization of the volume of surplus value required for its production. Capitalists earn a net volume of profits (surplus value) that is driven by increments dC  dC1  dC2 and dV dV1  dV2 of constant and variable capital respectively. Ignoring for simplicity the role of capitalist consumption, the total volume of surplus value P  dV  dC is driven by capitalist requirements for new constant and variable capital. In contrast to the single swap approach, however, it can also be argued that the money required for additional capital can be advanced without advancing the whole of the economy’s gross income. In Marx’s terminology it may

Table 4.2 Two-sector Marxian reproduction schema Pi

Dept. 1 Dept. 2

C1 C2

V1 V2

Output

dCi

dVi

dC1 dC2

dV1 dV2

W1 W2

The monetary circuit 41 Table 4.3 Expanded reproduction in an input–output table Dept. 1

Dept. 2

dC

(a) Numerical categories Dept. 1 4,000 Dept. 2 1,000 Si 1,000 Wi 6,000

1,500 750 750 3,000

500

(b) Marxian categories Dept. 1 C1 Dept. 2 V1 S1 W1

C2 V2 S2 W2

dC

(c) Leontief categories Dept. 1 p1a11X1 Dept. 2 p2h2l1X1 S1 p1X1

p1a12X2 p2h2l2X2 S2 p2 X2

p1da

dV

u

Wi

150

1,100

6,000 3,000 9,000

dV

u

W1 W2

p2dh

p2Ck

p1X1 p2 X2

be possible to model an advance of money MM without assuming that capitalists advance M. As discussed earlier, Nell (2004), in his mutual exchange approach, is led by his critique of the single swap approach to discount the importance of MM, arguing that a proportion of the variable capital part of M may be sufficient to service the circulation of money. In contrast, an alternative perspective can be developed in which we discount the role played by all initial advances contained in M. This embraces the Kalecki principle, with the amount of money spent by capitalists returning to them as profits; but the money income of the rest of the economy is also generated out of the initial spending of capitalists. This alternative approach can be developed by again interpreting Marx’s reproduction schema as an input–output table. Using the analytical approach developed in Chapter 2, the two-sector schema in Table 4.2 can be translated into Table 4.3(b). All that is required, in addition to switching rows into columns, is a re-introduction of capitalist consumption as an explicit category. Table 4.3(b) shows how the rows of the reproduction scheme of Table 4.2 can be read as column-wise inputs. In addition, Table 4.3(a) displays Marx’s numerical example, with Table 4.3(c) using the input–output notation.6 In the analysis that follows the circuit of money is modelled using both the numerical and algebraic categories. Key to modelling the circulation of money in this Marxian reproduction schema is a consideration of how it intertwines with the circulation of commodities between sectors. A precondition for the circuit of money is the commodity circuit. To explore in more detail how commodities circulate in Marx’s system, the role of inventories has to be considered. Taking his lead

42

The monetary circuit

from Quesnay, Marx is clear in Capital, volume 2, that ‘it is always the previous year’s harvest that forms the starting-point of the production period’ (Marx 1978: 435). Similarly, ‘Just as the current year concludes on the side of department II with a commodity stock for the next, so it began with a commodity stock on the same side left over from the previous year’ (ibid.: 581). Each production period begins with inventories of goods produced in the previous period, and its current output provides inventories for the next period (see also Okishio 1988: 3). Marx argues that the accumulation of these stocks is vital to the continuity of the production process. The ‘capitalist must hold in reserve a certain stock of raw materials, so that the production process can keep going for shorter or longer intervals on the previously determined scale, without depending on the accidents of daily supply on the market’ (ibid.: 200). The role of inventories in the reproduction schema can be illustrated using Marx’s numerical example (Table 4.3a). The elements of this schema can be recast in a tableau representing three periods of production, as shown in Table 4.4. Outputs of the production process are represented for this year and last year. First, the outputs of last year are shown as inputs of production in the current period. For example, the 4,000 units of constant capital used up by Department 1 this year were produced by Department 1 in the previous year. Similarly, the 1,000 units of variable capital (consumption goods) used up by Department 1 this year were produced by Department 2 in the previous year. Second, the outputs of this year replace the inputs used up this year, and allow an expansion of inputs in the next period. Following Lange (1969: 47), these outputs can be interpreted as ‘reproduction flows’. For example, Table 4.4 Inventories in the reproduction schema

Last year This year Next year Surplus value

Dept. 1 Dept. 2 Dept. 1 Dept. 2 Dept. 1 Dept. 2

Last year This year

Next year

1

1

2 1

2

4,000 1,500 1,000 750 4,400 1,600 1,100 800 1,100 1,000

Total

2

Capitalist Total consumption

750

6,000 3,000

Source: Adapted from Stone (1965).

6,000 3,000

9,000

The monetary circuit 43 Table 4.5 Composition of money outlays This year

dC

Dept. 1 Dept. 2 Total outlays

dV

1

2

400

100

400

100

u

Total receipts

1

2

1

2

100 100

50 50

500 500

600 600

500 1,250 1,750

Department 1 produces 4,400 capital goods this year that are used up next year. This sum includes (1) 4,000 units that are required to replace the 4,000 units used up this year; and (2) 400 additional units of constant capital that are used to expand production in the next period. Similarly, Department 2 produces 800 units of consumption goods that are used in the next period, 50 of which represent an expansion of variable capital in Department 2. For simplicity, it can be assumed that capitalist consumption goods are produced and consumed in the current period of production. The starting point for the circulation of money, under the auspices of the Kalecki principle, is the expenditure outlays of the capitalist class. In Table 4.5, the composition of these expenditures is made up of money outlays on capitalist consumption (u) and new constant and variable capital (dC and dV ). Outlays are made by capitalists in each department of production. For example, the capitalists in Department 1 spend 400 units on new constant capital, 100 units on new variable capital and 500 units on capitalist consumption. The outlays on the products of both departments are collected in the final row as total outlays, which sum to 1,750. Depending upon what is purchased, each outlay is also a receipt. Department 1’s purchase of 100 consumer goods from Department 2, for example, is a receipt for Department 2. The final column of Table 4.5 collects these receipts, which make up 1,750. The capitalist class outlays 1,750 in total, which returns to it as 1,750 in receipts. It is clear from this example that the Kalecki principle holds, with the capitalist class earning what it spends. But this is only part of the story: the capitalists may earn the money cast into circulation as their own income, but there is much more income to be generated from this initial injection. Using Table 4.3c, a multiplier process can be examined in which the level of income is expanded in a series of circuits. By again deriving the system of quantity equations from Table 4.3c (see equation 2.19):

冤XX 冥  冤a0 1 2

11

冥冤XX 冥  冤h0 冥[l

a12 0

1 2

2

1

冤XX 冥  冤dh da C 冥

l2]

1 2

k

(4.10)

44

The monetary circuit

Applying this model to the circulation of money requires two steps. First, the input and consumption coefficients are collected together such that

冤XX 冥  冤ha l 1

11

2

21

冥冤XX 冥  冤dh da C 冥

a12 h2l2

1 2

(4.11)

k

or X  A丣X  F

(4.12)

And second, the system can be re-expressed in money units as P ˆ X  Pˆ A丣Pˆ 1Pˆ X  Pˆ F

(4.13)

where P ˆ

冤p0 p0 冥 1

2

is a diagonal matrix of money prices. It follows that the money input–output system takes the form W  A†W  F†

(4.14)

with W  P ˆ X representing a column vector of gross money outputs, F†  P ˆ F a column vector of money final demands and A†  Pˆ A丣Pˆ 1 the matrix of per money unit input coefficients. This system can be solved by writing W  (I  A†)1F†

(4.15)

The overall impact on gross income of advances of capitalist money is captured by the Leontief inverse (I  A†)1. To explore this relationship in more detail the Leontief inverse can be expressed as a series of impacts, (I  A†)1  I  A†  (A†)2  . . . (A†)n

(4.16)

Each impact represents a circuit of money, in which money is advanced and circulates back to the capitalist. In the first circuit the impact on gross income is F†, in the second circuit A†F†, in the third circuit (A†)2F†, and so on. This can be illustrated using Marx’s numerical example, in which the matrix of money coefficients has the structure

冤 冥

a† A†  11 a†21

冤

4000 a†12 6000  a†22 1000 6000

冥冤 冥

1500 2 3000 3  750 1 3000 6

1 2 1 4

(4.17)

The monetary circuit 45 Table 4.6 Money circuits in the current production period This year

1st circuit 1

Dept. 1 Dept. 2 Total outlays

2

400 100 600 650 1,000 750

Sub total

2nd circuit Sub total 1 2

500 333 1,250 83 1,750 416

625 313 938

3rd circuit Sub total 1 2

958 264 396 76 1,354 340

573 182 755

837 . . . 258 . . . 1,095 . . .

Total receipts 6,000 3,000 9,000

These coefficients are derived from Table 4.3a, the input–output formulation of Marx’s reproduction schema. Table 4.6 shows three of the money circuits that can be identified in Marx’s schema. The first circuit (F†) is the initial impact of capitalist outlays, as introduced in Table 4.5. For example, capitalists in Department 1 outlay 1,000 units of money, 400 of which are directed to the purchase of capital goods from itself and 600 from the purchase of consumption goods (for worker and capitalist consumption) from Department 2. In addition to the 400 units that Department 1 sells to itself, another 100 units of capital goods are sold to Department 2. The total receipts from these sales are only 500 in the first circuit, precisely 500 short of the amount it lays out. However, Department 2 gets receipts of 1,250, which is more than its total outlay of 750. Overall, the 1,750 cast into circulation returns back to the capitalist class. As a result of the first circuit, gross output has increased by 500 in Department 1 and 1,250 in Department 2. It is assumed that any sales of inventories to meet the outlays of the two departments are immediately matched by production levels that allow them to be replaced. In the second circuit (A†F†) these increases have secondary impacts upon the outputs of both departments. Since, from equation (4.17), a†12  –12, the increase of 1,250 in Department 2’s output results in a further increase, by –12, in the output of Department 1: Department 1 sells 625 units of capital goods in order to meet (replace) the capital goods requirements of Department 2. In this second circuit we see Department 1 burgeoning with cash, the receipts of 958 this time outstripping outlays of 416. This is the mutual exchange story, identified by Nell in Marx’s writings. The capitalists in Department 1 only have to advance part of their income because of the money that bounces back from exchange with the other department. The main difference with Nell is that in this model the monetary outlay (investment) takes place in both departments of production. Our multiplier process also obviates the need for Nell’s somewhat unwieldy consideration of subsectors in the capital goods sector (see equation 4.6).

46

The monetary circuit

It should be noted that the initial outlay (and receipt) of 1,750 by the capitalist class in the first circuit is all that is required to initiate subsequent circuits. Out of this circulating amount of money, outlays of 1,354 and 1,095 are injected in the second and third circuits, and beyond. Once the circuits have petered out, and the multiplier process has come to an end, the sum of all outlays equals the sum of receipts (9,000). The formulation of 9,000 units of income and output has been oiled by 1,750 units of money.

The macro monetary model Looking at the system as a whole this suggests a macroeconomic interpretation of the circuit of money. By writing the coefficient matrix A丣 from (4.12) in terms of its constituent parts (see equation 2.20): X  AX  h[lX]  F

(4.18)

The system can at this juncture be translated into money units by pre-multiplying throughout by p, the row vector of money prices: pX  pAX  ph[lX]  pF

(4.19)

A simplification is made possible by noting first that ph, the money value of per capita worker consumption, is the scalar wage rate w (under the assumption that workers do not save). And since wlX is the total wage bill, by decomposition if w  wlX/pX is the share of wages in gross income, ph[lX]  wpX

(4.20)

Second, the scalar term representing money constant capital can be re-expressed as pAX  cpX

(4.21)

where c  pAX/pX, the share of total constant capital in money income. By writing x  pX as aggregate gross money output, and f  pF as money final demand, (4.19) can be written as x  cx  wx  f

(4.22)

Hence x

1 f 1cw

(4.23)

The monetary circuit 47 is an aggregate multiplier relationship derived from the two-sector reproduction schema. This provides a very simple model of the monetary circuit. It can be posited at the start of the circuit that capitalists take out credit to finance their outlay on new investment in constant and variable capital, and outlays on capitalist consumption ( f ⫽ dC ⫹ dV ⫹ u). Via the multiplier 1/(1  c  w) this outlay circulates between the consumption and capital goods sectors, leading to a level of gross national income (x) that is greater than the initial monetary outlay.7 Equation (4.23) is comparable to a quantity equation in which 1/(1  c  w) is a term representing the velocity of money. To take an example given by Marx (1969a: 341), say that 1,000 units of money circulate in the economy with a velocity of 3. The total price of commodities, or in the terminology of equation (4.23) the total income, is in this example 3,000. Dividing the income (3,000) by the velocity establishes the amount of money required to circulate (1,000). In our example the initial outlay is 1,750 and the total income is 9,000. Hence the velocity of money (and hence the multiplier) has a value of 5 17. This can be interpreted as an average of the many circuits of money that are reported in Table 4.6. As Marx writes in Capital, volume 1: Given the total number of times all the circulating coins of one denomination turn over, we can arrive at the average number of times a single coin turns over, or, in other words, the average velocity of circulation of money. (1976: 216) In Table 4.6 the first circuit is initiated by an injection of 1,750, some of which is required to fuel the injection of 1,354 in the next circuit, the rest turning over for only one circuit. The scalar velocity of money provides an average amount of time each money unit turns over. As shown by Moore (1984: 126), the velocity is only equal to the multiplier under the assumption that the period of production and the period during which the multiplier is completed are the same as the period during which a given volume of money circulates. Under this assumption, the magnitude of spill-over effects, associated with an initial money outlay on investment through the multiplier process, provides an equilibrium constraint on the size of the velocity.8 This macroeconomic interpretation of the circulation of money provides a direct way of explaining the narrow assumptions implicit in both the Graziani and single swap approaches, in which each production period is restricted to one cycle in the circulation of money. As shown in the first part of this chapter, in the Graziani (single swap) model there is (1) only one

48

The monetary circuit

round of payment of wages (total income) at the start of the production period; and (2) no allowance for spill-over effects between sectors. This implies that the velocity of circulation is equal to 1, with all income, be it simply total wages (Graziani) or the sum of wages and profits (single swap), circulating in one cycle.9 The parallel assumption of the circuit approach is that the multiplier is also equal to 1, meaning that there are no income–expenditure spill-over effects between sectors, with the amount advanced having no multiplied impact upon income. The multiplier relationship in (4.23) can be presented as a general model in which the multiplier/velocity is a parameter that can vary in value. From this perspective, the Graziani and single swap models represent a particularly narrow case in which the value of this parameter is restricted to 1. In contrast to Schmitt (1996), the multiplier in equation (4.23) should not be seen as a barrier to understanding the circulation of money. Schmitt’s main argument against the multiplier is that there is a confusion between actual amounts of income and increments in income. His complaint is that the multiplier process is driven by increments in spending, yet somehow ‘the given level of employment and income has been sustained in the periods preceding the new impulse that initiates the multiplier process . . .’ (ibid.: 123, original emphasis). The problem is that the ‘multiplier analysis unjustifiably treats the two integral parts of total income . . . in two entirely different ways’ (ibid.: 123). Total income is reproduced in the current period but its increment is somehow supposed to initiate a multiplier process.10 However, by locating equation (4.23) in the reproduction schema, the role that the multiplier plays in the reproduction process is explained. Increments in demand, represented by new capital, and financed by the advance of credit money, are the driving force of economic activity. Moreover, this injection of money provides the demand impetus and monetary wherewithal for firms to use up inventories and replace them. Reproduction is oiled by the injection of money demand, the outcome being the replacement of inputs and the expanded reproduction of the system once additional inputs are in place. Income is both sustained and increased in this reproduction process. By focusing on Marx’s reproduction schema, a logical attempt can be made to marry increments in income with the reproduction of income in a multiplier framework. As a way of locating increments of demand in the reproduction process, the multiplier in equation (4.23) has distinct advantages over the mutual exchange multiplier developed by Nell (2004) in his critique of the single swap approach. As both a way of exposing the narrow assumptions of the single swap and Graziani models and a way forward for modelling the circulation of money, this alternative approach is advantaged by its simplicity.

The monetary circuit 49 A comparison with equation (4.7) demonstrates that (4.23) is considerably less complicated than the far from standard approach to modelling the multiplier developed by Nell (2004). A marked degree of clarity and accessibility is therefore offered by this application of the simple Keynesian multiplier to the circulation of money in a macro economy. In addition, Appendix 4 shows that the interindustry foundations of this model are consistent with Marx’s value categories and his definition of investment. As a basis for future research, this macro monetary model is offered as a way of potentially improving communication between the Franco-Italian circuit school and the Marxian and Post Keynesian traditions.

5

Money, growth and crisis

For Marx, the task of establishing how a capitalist economy can reproduce itself is not limited to a particular period of production. The reproduction examples that he carves out in the final part of Capital, volume 2, show how balanced reproduction can take place over an extended number of years. Despite the limitations he faced, with a lack of formal modelling tools, computing power and waning personal health – the reproduction schemes were one of his last contributions to political economy – Marx was able to devise complex numerical examples, in which somehow a 10 per cent rate of growth is sustained in each period of production. It is not for nothing that he has been described as the father of modern growth theory. Of particular importance is the role of money in balanced reproduction. For the balance between aggregate demand and supply to be sustained, circuits of money must continuously open and close in successive periods of production. The key question is not just how much money is required for successive circuits to function, but also where does the money come from. Under expanded reproduction, an increasing amount of money is required to service the growing requirements placed upon a capitalist economy.

Capital outlays and sales A seminal contribution to understanding the role of money in expanded reproduction has been provided by Foley (1986) in chapter 5 of his book, Understanding Capital. This is an extremely detailed model of all the facets of Marx’s system of reproduction, including the complex role of time lags between various activities and the way in which capital is transformed into its different forms. In the analysis that follows a stripped down version of this model is presented. Foley develops a circuit of capital that locates money outlays as the starting point (ibid.: 67). The money capital outlay is represented by C(t), where t is the current period of production. These capital outlays are used to

Money, growth and crisis

51

purchase inventories and partly finished goods that are subsequently turned into finished products. At the end of the current period these finished products are sold, as represented by money sales S(t). Under simple reproduction, the receipts from sales provide sufficient money revenue to meet the capital outlays in the next period: C(t)  S(t  1)

(5.1)

This is made possible by sales consisting of two elements. First, S(t  1) are sales that allow capitalists to recover their costs of production – the amount of money spent on means of production and wages. This match-up is achieved by selling the precise amount of means of production and worker consumption goods. Second, S (t  1) are sales that allow capitalists to recover money outlays on their own personal consumption. A precise volume of luxury goods is required for this match-up to be established. Since S(t  1)  S (t1) S  (t 1)

(5.2)

total sales are sufficient to recover the initial outlays by capitalists on capital goods and luxury consumption. Because of the time delay between sales in one period and capital outlays in the next period capitalists set aside a hoard of money. As mentioned in Chapter 3, when capitalists are ready for new capital outlays money is drawn from the money hoard. De Brunhoff (1973: 38–44) shows how money hoards are essential to the circulation of money and commodities in Marx’s system, enabling a continuous production process. As lucidly stated by Marx (1964: 136), ‘The hoards thus act as channels for the supply or withdrawal of circulating money, so that the amount of money circulating as coin is always just adequate to the immediate requirements of circulation.’ Under simple reproduction, the amount of money required for circulation is constant. Capitalists allocate all of their surplus value to personal consumption, feasting in luxury instead of investing in expansion. Since there is no room for the economy to grow, there is no demand for the money hoard to grow. Output is static, with the same volume of commodities reproduced each year, serviced by the same money hoard. However, under expanded reproduction a much more demanding requirement is placed on the circuit of money. Capitalists increase their capital outlay on new elements of constant and variable capital. If we define dC as new constant capital and dV as new variable capital, there is an extra amount of money (dC  dV) that is required to service expanded

52

Money, growth and crisis

reproduction. Indeed, there is a shortfall in the amount of money that is provided by sales in order to meet these capital outlays: C(t)  S(t  1)  dC  dV

(5.3)

It follows that if capitalists decide to expand their capital outlays this places a drain upon the money hoard, which is not sufficiently replenished by sales. Moreover, as capital expands in each period the shortfall will get bigger: hence the solution of having capitalists start with a money reserve, which worked for simple reproduction, will not work for expanded reproduction. Any finite initial reserve of money would be exhausted at some point on the path of expanded reproduction. (Foley 1986: 87) The conclusion drawn by Foley is that new borrowing is required to meet this shortfall. There is a paradox of borrowing, the borrowing requirement contrasting with the received opinion in Marxist circles that all investment is drawn from an existing pool surplus value.1 With B(t) defined as ‘new capital borrowing’ (ibid.: 89), capital outlays under expanded reproduction are met by setting C(t)  S(t  1)  B(t)

(5.4)

Borrowing in period t is used to supplement the money hoard inherited from sales in period t  1. At the end of period t, capital outlays lead to expanded sales, which enhance the size of the money hoard. Under expanded reproduction, capital outlays are met from a growing hoard of money that is replenished by a combination of borrowing and sales. It can be pointed out that Foley implicitly embraces a single swap approach to the circuit of money. He assumes that capitalists must advance as money capital the total value of output, which once sold earns the precise amount of revenue required to recover the outlay. This is seen most clearly in equation (5.1), where the money capital advance is equal to the total sales of all capital and consumption goods. In Chapter 4 we saw that this approach, associated with Seccareccia (1996), has been heavily criticized by Nell (2004) for overestimating the amount of money required to oil the circuit of money – a serious miscalculation since it is important to know the precise borrowing requirements placed on the financial system. Indeed, a consequence of this miscalculation is that it wipes out any theoretical role for the income–expenditure multiplier in the reproduction

Money, growth and crisis

53

schema. Once it is recognized that the multiplier can expand income beyond the initial capital outlay, a much more realistic model of the circuit of money is possible. The macro monetary model developed in Chapter 4 can be summarized using Foley’s notation as C(t)  B(t)  dC  dV  u

(5.5)

S(t)  mC(t)

(5.6)

In (5.5) borrowing is used to finance all money capital outlays on capitalist consumption (u) and new constant and variable capital (dC  dV ); in (5.6) this outlay has a multiplier effect (in proportion m ) on total sales. As a consequence, the money circuit is viable without the requirement of a money hoard, accumulated from the previous period’s sales. Abolishing the money hoard allows a model of the money circuit that is relevant to contemporary institutional arrangements. In an interpretation of Marx that is in keeping with both Post Keynesian and circuit school perspectives, the central focus of this model is on the provision of loans by a developed banking system. The key insight is that each new loan is both an asset and a liability, allowing banks to finance the bulk of their outlays via deposits in their own balance sheets (see Chick 1997). There is, it should be noted, usually a requirement that banks hold small reserves, of around 3 per cent of deposits; but this is light years away from the assumption made by Marx in Capital, volume 2, that capitalists hoard metallic money (and the assumption by Foley (1986) that all the income from sales is used to replenish a money hoard). As we shall see, however, it is difficult to tap the rich seam of Marx’s writings, in particular when we look at his theories of economic crisis, without returning back to the money hoard.

Domar and balanced reproduction An emphasis on borrowing, with the multiplier firmly located in Marx’s reproduction schema, is provided by the Domar model of economic growth. Instead of providing a snapshot of each period of production, the schema can be developed over an extended number of periods; thereby providing a more complete picture of economic growth over time. The contribution of the following analysis will be to derive the model developed by Domar (1947) from foundations that are consistent with Marx’s multisectoral schema. Domar’s model is particularly suitable for this purpose because it specifies the conditions required for balanced growth. In contrast to Harrod’s variant of the model, in which actual investment is determined by an accelerator mechanism, in Domar’s model ‘the actual level of investment

54

Money, growth and crisis Table 5.1 Marx’s expanded reproduction schema

Year 1 Dept. 1 Dept. 2 Year 2 Dept. 1 Dept. 2 Year 3 Dept. 1 Dept. 2 Year 4 Dept. 1 Dept. 2 Year 5 Dept. 1 Dept. 2

Ci

Vi

Si

Wi

4,000 1,500 5,500

1,000 750 1,750

1,000 750 1,750

6,000 3,000 9,000

4,400 1,600 6,000

1,100 800 1,900

1,100 800 1,900

6,600 3,200 9,800

4,840 1,760 6,600

1,210 880 2,090

1,210 880 2,090

7,260 3,520 10,780

5,324 1,936 7,260

1,331 968 2,299

1,331 968 2,299

7,986 3,872 11,858

5,856 2,129 7,985

1,464 1,065 2,529

1,464 1,065 2,529

8,784 4,259 13,043

is not determined within the confines of the model’ (Jones 1975: 64). Marx had a similar focus on the dynamic conditions for balanced growth, without trying to formulate a model of actual economic growth. Table 5.1 shows the two-department expanded reproduction schema over five years.2 The familiar assumption of a constant rate of surplus value of 100 per cent is maintained, together with a 4:1 ratio of constant to variable capital in Department 1 and a 2:1 ratio in Department 2. Constant capital inputs are non-durable, used up during a single period of production, and £1 of output is assumed equal to a unit of labour. Key to this economy’s capacity to expand is the production of sufficient surplus value to invest in additional units of capital. Marx assumes that a half of surplus value in Department 1 is invested in this way. For year 1 this means that 500 of the total 1,000 units of surplus value produced in Department 1 are directed to 400 units of new constant capital and 100 units of new variable capital. In year 2 constant capital expands from 4,000 to 4,400 units, and variable capital from 1,000 to 1,100 units, maintaining the 4:1 ratio between constant and variable capital. A new position of balance is established by also maintaining Department 2 at its original 2:1 ratio.

Money, growth and crisis

55

Examining the elements of Table 5.1 reveals that from year 3 onwards each department, and hence the economy as a whole, expands at a balanced growth rate of 10 per cent. Total output of 11,858 in year 4, for example, represents a 10 per cent increase on the 10,780 produced in year 3. The conditions required to establish this balanced growth path will now be explored in detail. The starting point for this analysis is the Keynesian multiplier y

1 I e(1  ␭)

(5.7)

which has as its constituent elements the Marxian term representing the share of surplus value (e) and Kalecki’s ratio of capitalist consumption to total profits (␭). This multiplier has been derived, in Chapter 3, from the two-department expanded reproduction schema (see equation 3.9). It captures the relationship between aggregate net income (y) and autonomous investment (I). For simplicity, in the present analysis autonomous capitalist consumption is assumed to be zero. By defining ␭  1 ␭ as the ratio of investment to profits, the multiplier relationship between each increase in income (dy) and investment (dI) is dy  1 dI e␭

(5.8)

Following Domar (1947), the supply side of economic growth can be modelled by letting the economy’s capacity to increase income in proportion to the increase in capital stock (␴) represent the productivity of investment. Given that investment is the same as an increase in the capital stock it follows that ␴

dy I

(5.9)

Domar assumes at the outset that there is full capacity utilization, and moreover that ‘the fraction of labour force employed is a function of the ratio between national income and productive capacity’ (ibid.: 37). Since the supply side models the economy’s capacity to produce output, full employment of the labour force requires that the potential change of output is equal to the change in output demanded via the multiplier. Hence, the full employment balanced rate of growth can be established by setting dI  I␴ ␭e

(5.10)

56

Money, growth and crisis

It follows from multiplying both sides of (5.10) by ␭e, and dividing by I, that dI  ␭e␴ I

(5.11)

Since by assumption income in (5.7) is a constant multiple of investment, it also follows that the rate of change of investment is equal to the rate of change of income: dy dI y  I  ␭e␴

(5.12)

(see ibid.: 41). The balanced growth rate would, in the unlikely event that this could be achieved, be equal to the multiple of ␭ (the ratio of investment to profits), e (the per capita share of surplus value) and ␴ (the productivity of investment). Using the analysis provided in Appendix 5, this balanced growth relationship can also be specified as dy y  ␭r

(5.13)

where r is the money rate of profit, which is calculated by the formula r  s(1  g). The term g is a measure of the money composition of capital, and s is the ratio of profits to wages, which can also be expressed as the ratio e/(1  e).3 Equation (5.13) is the Cambridge equation, also derived by Foley (1986: 76) from his model of the circulation of money. To bring these results alive, they can be nested in the Marx’s numerical examples. Table 5.2 shows the expanded reproduction schema of Table 5.1 in a form that enables some of the parameters to be seen more clearly. First, the ratio of investment to profits can be calculated, for example in year 4, Table 5.2 Rates of growth in Marx’s reproduction schema Year

Constant capital

Variable capital

Profits

Net income

dy/y

I

dI/I

1 2 3 4 5

5,500 6,000 6,600 7,260 7,985

1,750 1,900 2,090 2,299 2,529

1,750 1,900 2,090 2,299 2,529

3,500 3,800 4,180 4,598 5,058

— 0.09 0.1 0.1 0.1

— 650 790 869 955

— — 0.22 0.1 0.1

Money, growth and crisis

57

as ␭  I/P  955/2,299  0.415. Second, e  1/2 is shown by calculating the share of profits in net income for year 4 as the ratio 2,299/4,598. Finally, the productivity of investment in year 4 takes the value ␴  dy/I  418/869  0.481. Hence, the balanced rate of growth is ␭e␴  0.415 0.5 0.481  0.1

(5.14)

Using the alternative Cambridge equation approach, the balanced rate of growth takes the form4 ␭r  0.415 0.2414  0.1

(5.15)

Domar provides the same insight as Foley into the role of money under expanded reproduction. In (5.12), expanding investment (dI  0) is established under balanced growth. It follows that investment in period t must be higher than investment in the previous period (It  It1). Now in equilibrium investment in each period is identical to total savings (Savt), which means that It1  Savt1.5 Hence it can be concluded that It  Savt⫺1. Under expanded reproduction, ‘Investment of today must always exceed savings of yesterday . . . . An injection of new money (or dishoarding) must take place every day’ (Domar 1947: 42). This is the paradox of borrowing, as also shown in Foley’s model of the circulation of money. Notwithstanding the rich complexity of the Foley model in its treatment of time, the main advantage of Domar’s demonstration of the paradox of borrowing is that it embodies the Keynesian multiplier relationship. A much more general model of the circuit of money is suggested, compared to the single swap approach adopted by Foley. Moreover, since our derivation of the Domar result is established from input–output foundations, it is not restricted to Marx’s two-sector schema, but could in principle be generalized to a multisectoral framework.

Conditions for economic crisis By establishing the role of money as a condition for expanded reproduction, a foundation is provided for exploring the circumstances under which there might be economic crisis. This monetary perspective has been largely neglected by official Marxian economics, with the main focus on ‘real’ analysis (see Arnon 1994: 355). For Pollin (1994: 101), ‘Marxian economics had until recently almost completely overlooked monetary and financial phenomena.’ Similarly, Hein (2002: 1) argues that attempts ‘to reconstruct Marx’s theory of money and credit remained without major consequences for Marxian theories of accumulation and crisis’. And for Crotty (1985: 45),

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‘the Marxian crisis theory literature has had very little to say about monetary and financial aspects of capitalist macrodynamics.’ It should also be emphasized that the Domar/Foley paradox of borrowing – that balanced growth requires borrowing – has not been widely recognized. One can search in vain for any mention of this borrowing paradox in the mainstream literature on the economics of growth, and in the Marxian literature other matters have been given much more attention. Foley’s work on the transformation problem, for example, has been far more widely cited than his modelling of the circulation of money. In the analysis that follows, in this and subsequent chapters, an attempt is made to set the paradox of borrowing in the context of Marxian crisis theory. The abstract starting point for Marx’s monetary theory of crisis is provided in chapter 17 of Theories of Surplus Value part 2. Here Marx explores the role of money under simple circulation (M–C–M). Money provides the starting point and end point of the circuit of commodities. Capitalists use money to purchase commodities (M–C) in order to carry out production, and must find an outlet to sell their commodities to a buyer willing to spend the right amount of money (C–M). This separation of purchase from sale is fraught with the possibility of breakdown. The difficulty of converting the commodity into money, of selling it, only arises from the fact that the commodity must be turned into money but the money need not be immediately turned into commodity, and therefore sale and purchase can be separated. (Marx 1969b: 509) Given the myriad transactions that take place, Marx considers it entirely possible that there will not be sufficient co-ordination for all purchases and sales to be in balance. There are three main consequences of this separation of purchase from sale. The first is a critique of Ricardo’s assertion that ‘no man produces but with a view to consume or sell’ (Ricardo 1951: 290; see Kenway 1980: 28). Instead of a separation of purchase from sale, Ricardo assumes each individual is simultaneously a producer and consumer, deciding what to produce and consume in the same breath. This is Say’s Law, that supply creates its own demand. Marx was very scathing about Say’s Law, viewing it as ‘childish babble’ and ‘a cosy description of bourgeois conditions’ (Marx 1969b: 502–3). From a class-based perspective, there is a demarcation between the production decisions of a small number of capitalists and the consumption decisions of the population as a whole. Second, a nascent multiplier process can be identified. Mitchell and Watts (2003: 154) argue that Marx ‘laid the foundations of multiplier

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theory by arguing, in Theories of Surplus Value, that, once this unity of sale and purchase was disturbed, the chain of contractual relationships between suppliers became threatened and overproduction, and then bankruptcies and unemployment, became widespread.’ Marx considers the linkages between demand for the goods produced by capitalists and the consumption of workers employed to make these goods (an embryonic consumption function). For the case of a slump in the market for calico: The stagnation in the market, which is glutted with cotton cloth, hampers the reproduction process of the weaver. This disturbance first affects his workers. Thus they are now to a smaller extent, or not at all, consumers of his commodity – cotton cloth – and of other commodities which entered into their consumption. (Marx 1969b: 522) Stagnation has a multiplier effect on the consumption of workers which feeds back on the ability of producers to sell their wares. Finally, Marx develops the separation between purchase and sale by identifying the specific role of money as a means of payment. Crotty (1985: 57) defines means of payment as ‘money used by a borrower to fulfil a legallybinding contract’. Marx (1969b: 511) uses the example of a weaver purchasing constant capital. The weaver, producing cloth, may purchase raw materials from the spinner by borrowing from the bank. Once the cloth is sold to the merchant, he may receive a bill of exchange that is used to settle with the bank. Further back in the chain the spinner purchases from the flax-grower using a bill of exchange, and the maker of machines purchases from producers of iron, coal and timber. In each transaction money is used to pay for commodities as the final goal (a means of payment), without it being transformed simultaneously into a purchase. Suppose, Marx says, that the merchant doesn’t pay: The flax-grower has drawn on the spinner, the machine manufacturer on the weaver and the spinner. The spinner cannot pay because the weaver cannot pay, neither of them pay the machine manufacturer, and the latter does not pay the iron, timber of coal supplier . . . . Thus the general crisis comes into being. (ibid.: 511) Money as means of payment enhances the possibility of general crisis; a crisis that is less abstract and more of a concrete possibility. Representing money as a means of payment is an important step in developing a mature theory of crisis, one that is relevant to full-blown capitalism. Marx argues that his analysis of means of payment is not

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sufficiently developed to explain the cause of crises; but it is at least a step in the right direction: ‘we can already see the connection between the mutual claims and obligations, the sales and purchases, through which the possibility can develop into actuality’ (ibid.: 511). A further concrete step in the development of a monetary theory of crisis is established by Marx in part 5 of Capital, volume 3. Key to this approach is an understanding of how the credit system develops. In a developed capitalist economy hoards are no longer held by individual capitals; ‘in advanced bourgeois countries they are concentrated in the reservoirs of banks’ (Marx 1964: 137). Hoards are collected in a central pool of credit money, managed by the banks. ‘Small sums which are incapable of functioning as money capital by themselves are combined into great masses and thus form a monetary power’ (Marx 1981: 529). Notwithstanding the lurking presence of a commodity theory of money in this hoarding approach (see Nelson 1999), Marx shows how important the credit system is to an economic expansion. ‘The development of the production process expands credit, while credit in turn leads to an expansion of industrial and commercial operations’ (Marx 1981: 612). Together with the benefits afforded by credit, however, there are also potential fragilities.6 The problem is that credit allows capitalists to ‘pursue the production process past its capitalist barriers: too much trade, too much production, too much credit’ (ibid.: 640). Speculation, and even swindling on the part of those who operate the credit system, helps to fuel an overexpansion of the financial system. In particular, the relative autonomy of the credit system creates a disjunction between production and its realization. Capitalists can obtain finance to expand their production, even if demand is stagnant (see Campbell 2002: 220). Economic crisis is required to bring the economy back to order. When, as eventually it must, confidence collapses, banks increase their hoarding: ‘the country requires twice as much circulation as in ordinary times, because the circulation is hoarded by bankers and others’ (quotation from a banker, Marx 1981: 660). And with the restriction of credit provided by banks, most likely taking the form of a hike in the rate of interest charged on borrowing, investment is restored to a more sustainable growth path. For de Brunhoff (1973: 118), ‘The hoarding in a crisis is only the reverse side of the failure to sell commodities and the cessation of investment which follow an excessive expansion of production and commerce.’ This insight into how financial crises develop can be examined in the light of the Foley/Domar borrowing paradox. To recap, we have established that expanded reproduction requires borrowing on the part of the capitalist class. How then does Marx’s insight, that borrowing can outstrip realization, relate to the expanded reproduction schema? To answer this question

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we will have to delve a little more deeply into the structure of the Domar model. Looking back at equation (5.10), investment (I) is the key economic variable. The problem, as articulated by Domar (1947), is the dual role of investment in this equation. On the left-hand side the increment in investment determines, via the multiplier, the increment of income which the economy demands. On the right-hand side, however, the increment in capacity, which the economy can supply, is determined by the amount of investment – itself representing the required change in the capital stock. Whereas changes in investment are necessary in order to induce increasing aggregate demand, only a particular amount of investment is required to enable a matching increase in supply. For Domar this provides the heart of the problem as to why balanced growth is so difficult to achieve for a capitalist economy. An absolute amount of investment generates an increase in capacity, but an increase in investment is required to realize this capacity in terms of increasing income. This is why even in relatively prosperous periods a certain degree of underemployment has usually been present. Indeed, it is difficult enough to keep investment at some reasonably high level year after year, but the requirement that it always be rising is not likely to be met for any considerable length of time. (ibid.: 47) Overproduction of capacity, relative to aggregate demand, is a persistent tendency inherent in the schemes of expanded reproduction, as formalized in the Domar growth model. Introducing the financial system into this picture leads to severe consequences. Not only must investment continually grow at a particular rate to sustain the required amount of aggregate demand, it must also be financed by borrowing from the financial system. All investment in new capacity, according to the Domar/Foley insight, must be financed by borrowing. In the reproduction schema, therefore, all borrowing is continually in tension with realization, at all rates of positive growth. Since it is very difficult for investment to ever grow enough to satisfy capacity, the credit that makes it possible is always released on shaky grounds. On this interpretation, financial crises are not just applicable to excessive expanded reproduction, when financial speculation ‘takes off on its own’; financial fragility is embedded in expanded reproduction itself. This Domar interpretation can be placed in stark contrast to the argument made by Shoul (2000: 98) that ‘Marx’s reproduction models postulate the operation of Say’s Law’ (see also Robinson 1968: 111). The argument,

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which has a long history in Marxian economics, is that Marx established his model of balanced growth on the assumption that supply creates its own demand. Since the reproduction schemes show the conditions under which supply and demand are in balance, the argument is that Say’s Law must hold. Shoul argues that Marx’s refutation of Say’s Law, in Theories of Surplus Value part 2, where the role of money in capitalism is taken seriously, is analytically separate from the reproduction schema, in which money is an absent guest. Say’s Law has a dual role, on the one hand being refuted where money is considered, and on the other hand implicitly assumed when growth is considered.7 As we have seen, however, the circulation of money also plays a pivotal role in the reproduction schema. Without borrowing from the financial system expanded reproduction is not possible. Investment is exogenous, financed not out of the pockets of capitalists, but by the financial system. Embedded in the tension, established by Domar, between investment as a dual source of capacity and demand, is a fragile network of credit relationships between capitalists and banks. Marx’s reproduction schemes expose the stringent conditions on the finance and realization of investment that are required for balanced growth. Since these conditions are unlikely to be met – supply is unlikely to create its own demand – a refutation of Say’s Law is offered by the reproduction schema.

6

Beyond underconsumption

The early part of the twentieth century was a golden period for Marxian economics. With the dominant German Social Democratic Party at its centre, a rich ferment of discussion took place over the meaning and application of Marx’s Capital; and in particular over the role of the reproduction schema. This golden period came to a brutal end. Rosa Luxemburg was murdered by right-wing terrorists, Hilferding perished at the hands of the Gestapo in France and Bukharin fell victim to Stalin’s show trials. In view of the enormous damage to the Marxian economic tradition inflicted by this age of extremes, it is vital that the ideas developed during this period are salvaged. Two key interpretations of the reproduction schema from this golden age are considered here. First, the disproportionality school, with Tugan Baranovsky and Hilferding as its main proponents, looked at the proportions between Marx’s two great departments of production. For Kuhn (1979: 215), ‘this was the dominant strain in Marxist thought prior to World War I’. Economic crisis is closely identified with a disproportion between departments of production when one of them engages in overproduction relative to the other. This approach was developed as a response to underconsumptionists, such as Sismondi and Malthus, who argued that consumption is the main constraint on capital accumulation. Underconsumption is reduced to a special case, where there is overproduction by the department producing consumption goods. And so long as proportionality is maintained the problem of underconsumption is assumed away. Second, Rosa Luxemburg’s Accumulation of Capital provides an exceptionally detailed examination of Marx’s reproduction schema. Aznar (2004: 253) argues that ‘Luxemburg believed this book to be a continuation of “Capital” book 2, which Marx had left unfinished’. Key to Luxemburg’s interpretation is the role of demand, which she argues is obscured by Marx’s specific focus on the question, ‘Where does the money come from?’ Marx is criticized for assuming that capital can accumulate unimpeded, without identifying how new capacity can be profitably realized.

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For daring to question Marx, Luxemburg has been lambasted for being an underconsumptionist. Sweezy (1942: 171), for example, considered her to be ‘the queen of underconsumptionists’, regarding consumption as the key constraint upon capital accumulation.1 Foley (1986: 151) argues that for Luxemburg ‘there is something strikingly un-Marxist about the premise that the ultimate aim of capitalist production is workers’ consumption’. Similarly, for Howard and King (1989: 113), ‘But she herself is mistaken in imputing to the capitalist system as a whole the goal of expanding human consumption.’ Yet, on a close reading of Accumulation, capitalists are engaged in the pursuit of exchange-value: the pursuit of money profits. In a quotation that has been highlighted by Desai (1979: 155), Luxemburg writes, ‘This means that the starting point of capitalist production is not a given number of workers and their demands, but that these factors themselves are constantly fluctuating, “dependent variables” of the capitalist expectations of profit’ (Luxemburg 1951: 134).2 The purpose of this chapter is to review particular aspects of these two interpretations of the reproduction schema in the light of the macro monetary model developed in previous chapters. How do these interpretations relate to our emphasis in the reproduction schema upon the importance of money, credit and the multiplier? And what is the distinctive contribution of the macro monetary model relative to these golden age interpretations? By re-interpreting these approaches through the lens of our macro monetary model, the objective is to explore in more depth the role of the reproduction schema in Marxian economic theory.

Disproportionality Buried in the murky waters of Capital, volume 2, Marx makes passing reference to the importance of proportionality between departments of production. Under simple reproduction, disproportion would have disastrous consequences: ‘the whole basis of the schema would be destroyed, i.e. reproduction on the same scale, which presupposes complete proportionality between the various systems of production’ (Marx 1978: 530). By assuming balance in the reproduction schema, co-ordination is established between capital and consumption-good producing sectors. For some Marxists, writing at the start of the twentieth century, this provided a seductive insight into how governments might impose order on the economic system. The main proponent of the disproportionality approach was Rudolf Hilferding, who built on the ideas of the Russian Marxists, Tugan Baranovsky and Bulgakov. Key to the occurrence of disproportions is the

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propensity of capitalists to seek exchange-value, the pursuit of individual profits. If capitalists behave as profit-seeking individuals, can they take into account the size of the market as a whole? As stated by Mandel (1962: 366), ‘It follows logically from this idea that if the capitalists were capable of investing “rationally”, i.e. so as to maintain proportions of equilibrium between the two main sectors of production, crises could be avoided.’ Such rational behaviour is unlikely, however. As argued by Harris (1972: 511), there is ‘no guarantee that the system could achieve equilibrium’. To address the problem, the disproportionality school has suggested government intervention to ensure balance between the departments of production. In Hilferding’s Finance Capital, first published in 1910, this approach is married with an analysis of the role of cartels and banks in compounding the inflexibility of the economic system: its inability through competition to remedy any disproportions. Co-ordination can only be achieved by ‘subordinating the whole of production to conscious control’ (Hilferding 1981: 296). The most basic proportions embedded in the reproduction schema are established under simple reproduction. This was touched on in our introduction to the schema in Chapter 2, and in establishing the mutual exchange which takes place between departments of production in the circulation of money (Chapter 4). These proportions can be formally derived, in Table 6.1, by displaying the elements of Marx’s numerical example (Table 2.1) alongside the Marxian algebraic symbols.3 The mutual exchange condition for simple reproduction, established in Table 6.1(a), is that Department 2 exchanges 2,000 units of consumption goods for 2,000 units of means of production produced by Department 1. These 2,000 units of means of production are represented in Table 6.1(b) as used-up constant capital C2. Similarly, the 2,000 units of consumption goods are purchased in Department 1 out of variable capital V1 and surplus value S1. Hence the condition for simple reproduction can be expressed as C2  V1  S1

(6.1)

Table 6.1 Simple reproduction schema Ci (a) Numerical categories Dept. 1 4,000 Dept. 2 2,000 6,000 (b) Marxian categories Dept. 1 C1 Dept. 2 C2

Vi

Si

Wi

1,000 500 1,500

1,000 500 1,500

6,000 3,000 9,000

V1 V2

S1 S2

W1 W2

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Beyond underconsumption Table 6.2 Simple reproduction in an input–output table Dept. 1

Dept. 2

Capitalist consumption (u)

(a) Numerical categories Dept. 1 4,000 2,000 Dept. 2 1,000 500 1,000 500 Si Wi 6,000 3,000

1,500

(b) Marxian categories Dept. 1 C1 Dept. 2 V1 S1 W1

u

C2 V2 S2 W2

Wi

6,000 3,000 9,000 W1 W2

It can now be shown how this result can be derived using an input–output interpretation of the simple reproduction schema. Following the same procedure first introduced in Chapter 2, Table 6.2(a) re-expresses the numerical elements of Table 6.1 as an input–output table. Table 6.2(b) is an algebraic representation, using Marxian categories, of the input–output table for simple reproduction. In comparison with Table 6.1, this provides a clearer and more detailed representation of simple reproduction, since the expenditure of surplus value on capitalist consumption is shown explicitly as u. Moreover, the condition of simple reproduction is embodied in the assumption that total inputs are equal to total outputs (see Sweezy 1942: 162). Writing out these input–output balances explicitly, C1  V1  S1  C1  C2 C2  V2  S2  V1  V2  u

(6.2) (6.3)

The condition for simple reproduction, as shown in (6.1), is easily obtained from (6.2) by cancelling out the element C1 from both sides of the equation. Since u  S1  S2, it is also straightforward to obtain the same condition by cancelling out V2 and S2 from (6.3). Once the input–output approach to balancing Marx’s accounts is adopted, the simple reproduction condition of proportionality between departments is implicitly assumed. This introduction to simple reproduction, from an input–output perspective, paves the way for a consideration of the more relevant and complex case of expanded reproduction. Table 6.3(a) is the numerical input–output representation of the expanded reproduction schema (see Table 2.4). In algebraic terms, the expansion of constant capital is represented by dC and new variable capital by dV. Table 6.3(b) shows the set of input–output accounts using Marxian notation, with the new role for capital accumulation represented alongside the terms previously modelled under simple reproduction.

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Table 6.3 Expanded reproduction in an input–output table Dept. 1

Dept. 2

dC

(a) Numerical categories Dept. 1 4,000 Dept. 2 1,000 Si 1,000 Wi 6,000

1,500 750 750 3,000

500

(b) Marxian categories Dept. 1 C1 Dept. 2 V1 S1 W1

C2 V2 S2 W2

dC

dV

u

Wi

150

1,100

6,000 3,000 9,000

dV

u

W1 W2

Since there is again an assumed balance between row and column sums, it follows that the condition for expanded reproduction can be derived by writing C1  V1  S1  C1  C2  dC C2  V2  S2  V1  V2  dV  u

(6.4) (6.5)

Manipulation of each of these equations4 yields the condition for expanded reproduction C2  dC  V1  S1

(6.6)

Comparing this to the condition for simple reproduction (6.1), the only difference is the element for expansion of constant capital dC. This illustrates Marx’s claim that the condition of simple reproduction lives on as a structural entity under expanded reproduction. It also follows that the proportionality condition for expanded reproduction is implicitly assumed in the input–output accounts. How then can the input–output approach provide an insight into Marxian crisis theory, when the very basis for these accounts is proportionality? As Rosdolsky (1977: 470) has argued, for writers such as Tugan and Bulgakov economic crises are derived ‘solely from the disproportionality between the various branches of industry’. A position of restricted consumption, for example, can be exclusively captured by overproduction of the department producing consumption goods, relative to the capital-goods producing department: the latter failing to provide a sufficient market for consumption goods (see Kuhn 1979: 216). On the assumption of proportionality, how can there be room for any other theories of crisis? A coherent response requires a re-statement of the macroeconomic conditions for balanced growth (Chapter 5). Recall that the Domar conditions

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have been established using a macroeconomic multiplier relationship that is derived from an input–output foundation (equation 5.7). It therefore follows that the Domar balanced growth equation, as we have derived it, assumes proportionality between departments of production. Now using the Domar interpretation of the reproduction schema, balanced reproduction on an expanded scale has two main dimensions. First, the paradox of borrowing, established by Foley and Domar, stipulates that capital accumulation on an expanded scale is only possible if new credit is made available to capitalists. Second, investment has to grow at a particular rate such that the new capacity it generates is balanced by increments in demand. From a macroeconomic perspective, establishing balanced growth requires an analysis of the rate of change of new investment, financed by the required amount of credit. These macroeconomic questions are posed for a model under which proportionality between Departments 1 and 2 is assumed. Consider again (5.10), which exposes the contradiction in the Domar model between absolute amounts of investment, which create new capacity and changes in investment that drive the required amount of aggregate demand. There you see that investment (I) is made up of increments in constant and variable capital, new goods produced by both departments of production. Similarly, the share of surplus value (e) is derived from the value of labour power, which measures the value of inputs (produced in both departments) congealed in worker consumption goods. These macroeconomic terms aggregate across the two departments; they transcend the more micro question of proportionality between the two departments. This does not mean that disproportionality is irrelevant to modelling economic crises. Even the most minor disruption or disjuncture in the economic system would, in all likelihood, be associated with disproportion between the departments of production. The argument, however, is that an exclusive focus on disproportion does not ask the right questions about how the reproduction process functions as a macroeconomic entity. Questions of aggregate demand and the role of credit, it can be argued, are obscured by a focus on proportionality. In the analysis that follows the macroeconomic questions posed by Rosa Luxemburg are considered to be a more incisive challenge for the reproduction schema.

Luxemburg and accumulation Whereas Hilferding, who eventually became the German Minister of Finance, occupied the centre ground of the German Social Democratic Party, its left-wing firebrand was Rosa Luxemburg. For Howard and King (1989: 106), ‘Her treatise The Accumulation of Capital, published in 1913, was a major theoretical work comparable with Hilferding’s Finance Capital

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in its serious purpose and scholastic tone.’ Luxemburg also follows Hilferding in viewing the reproduction schema as the main vehicle for exploring the conditions for capital accumulation, but with radically different conclusions. Far from showing how the proportions between departments of production can be planned, Luxemburg argues that expanded reproduction is impossible. For scholars of Marx, a common complaint is that Marxian economics, as practiced in the universities, fails to reflect the original purpose of Marx’s writings. Models of reproduction, in particular, ignore the importance of money and the way in which Marx uses the schema to expose the perceived dogma of Adam Smith (see Moseley 1998). A close reading of Luxemburg’s Accumulation of Capital, as we shall see, does not disappoint on either of these fronts. The starting point for Luxemburg’s investigation is the reproduction of the total social capital. ‘Karl Marx made a contribution of lasting service to the theory of economics when he drew attention to the problem of the reproduction of the entire social capital’ (Luxemburg 1951: 31). The historically specific cornerstone of capitalist reproduction is that it requires the formation of profits: only those goods are produced which can with certainty be expected to sell, and not merely to sell, but to sell at the customary profit. This profit becomes an end in itself, the decisive factor which determines not only production but also reproduction. (ibid.: 34) Capitalism therefore involves a multitude of individual producers engaged in the pursuit of profit. To conjoin these individual decisions into a reproducing total capital requires circulation and exchange. ‘Capitalist production is primarily production by innumerable private producers without any planned regulation. The only social link between these producers is the act of exchange’ (ibid.: 34). The exchange of commodities between producers is underpinned by Marx’s theory of value. In contrast to Adam Smith, a correct distinction is made by Marx between dead and living labour (see Chapter 2). Constant capital – raw materials, machinery and premises – are produced by past labour, in previous periods of production. Variable capital and surplus value are produced by living labour in the current period of production. For Luxemburg: This specific connection of each past period of production with the period following forms the universal and eternal foundation of the social process of reproduction and consists in the fact that in every

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Beyond underconsumption period parts of the produce are destined to become the means of production for the succeeding period: but this relation remained hidden from Smith’s sight. (ibid.: 73)

The fatal error committed by Smith is to ignore the role of constant capital; a mistake that is attributed to his undeveloped theory of value. For each individual capitalist, therefore, the value of each commodity is made up of constant capital, variable capital and surplus value. Moreover, commodities have value in exchange only when they are sold in their money form. ‘Once the commodity has been produced, it must be realized, it must be converted into a form of pure value; that is, into money’ (ibid.: 38). However, when Luxemburg examines the reproduction of total capital, the use-form of commodities is also important. Whereas it does not make the slightest difference to the individual capitalist whether he produces machinery, sugar, artificial manure or a progressive newspaper – provided only that he can find a buyer for his commodity so that he can get back his capital plus surplus value – it matters infinitely to the ‘total capitalist’ that his total product should have a definite use-form. By that we mean that it must provide three essentials: the means of production to renew the labour process, simple provisions for the maintenance of the workers, and provisions of higher quality and luxury goods for the preservation of the ‘total capitalist’ himself. (ibid.: 81) This emphasis on the importance of the use-form provides a rationale for the reproduction schema, in which separate departments of production are established for consumption goods and means of production. Luxemburg argues for simplicity that one category of consumption goods incorporating goods consumed by workers and capitalists can be considered. In addition, the formula for calculating values (C  V  S) can be applied to both individual and total capitals, but at the aggregate level has to be complemented by the reproduction schema (ibid.: 83). Starting with Marx’s case of simple reproduction, Luxemburg considers two of the key ways in which Marx models the circuit of money in Capital, volume 2. As argued by Bellofiore (2004: 289), Luxemburg’s ‘theory is always framed in terms of some kind of a model of the money circuit’. Again scholars of Marx should not fail to be impressed by the way in which Luxemburg sets out the role of money in the reproductions schema. The circulation of money is examined in the context of Marx’s numerical example of simple reproduction (Table 6.1).

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First, a mutual exchange theory of money is formulated. Money ‘first comes into circulation by the payment of wages’ (Luxemburg 1951: 94). Capitalists in Department 1 advance 1,000 units of money to their workers as variable capital. Capitalists in Department 2 sell consumption goods to Department 1 for this value of 1,000 units. The money, first advanced in Department 1, circulates into the hands of capitalists in Department 2. With the money received from this transaction, Department 2’s capitalists are able to purchase means of production from Department 1 and the money returns into the hands of the Department 1 capitalists. The same type of mutual exchange happens for the 500 units advanced as variable capital in Department 2. Second, the Kalecki principle, that capitalists earn what they spend, can also be identified in Luxemburg’s interpretation of Marx.5 The mutual exchange of money advanced as wages is insufficient to oil all of the exchange between the two sectors. In particular, Department 2 capitalists ‘have not yet renewed the second half of their constant capital’ (ibid.: 95). To fill this void, Luxemburg points out that ‘the needs of the capitalists, as consumers, must be satisfied just as constantly as the needs of the workers’. Capitalists must advance money in order to satisfy their own consumption requirements. There are, of course, 1,000 units of money that are bouncing between the departments from the original advance of wages, but this cannot be used to oil capitalist consumption. Capitalists must consume at the same time as workers consume. For Luxemburg, ‘Both capitalists may each advance 500 units of the money necessary for the exchange, or possibly the two departments will contribute in different proportions’ (ibid.: 96). Luxemburg is uncertain as to how exactly capitalists advance this money, the main criteria being that there is sufficient money for capitalist consumption and constant capital to be purchased in full. Luxemburg therefore identifies the Kalecki principle in Marx’s reproduction schema: ‘if the capitalists themselves have set in motion all the money which circulates in society, they must also advance the money needed for the realization of their own surplus value’ (ibid.: 98). Under simple reproduction, this money is earned from the extraction of surplus value in previous periods, but in the current period of production capitalists clearly earn what they spend (the Kalecki principle). So long as there is sufficient money cast into circulation for capitalist consumption, together with the mechanism of mutual exchange, all goods are sold in the market place. Under simple reproduction, as summarized by Howard and King (1989: 107), ‘There is no deficiency in the demand for either department’s output, and no reason why production should not continue at this level in later periods.’

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Beyond underconsumption

Since all surplus value is consumed by capitalists under simple reproduction, it is very easy to see how profits are realized. Where the problems start are under expanded reproduction. For Luxemburg: The essential difference between enlarged reproduction and simple reproduction consists in the fact that in the latter the capitalist class and its hangers-on consume the entire surplus value, whereas in the former a part of the surplus value is set aside from the personal consumption of its owners, not for the purpose of hoarding, but in order to increase the active capital, i.e. for capitalization. (Luxemburg 1951: 112) Under expanded reproduction, not all of the surplus value is consumed by capitalists. A part of it is now directed to expanding the means of production, and there must be sufficient aggregate demand to purchase these new goods. Luxemburg poses the key question: ‘Where is this continually increasing demand to come from, which in Marx’s diagram forms the basis of reproduction on an ever rising scale?’ (ibid.: 131). Of course, Luxemburg has been widely criticized for arguing that the source of this demand must come from non-capitalist buyers (ibid.: 366); but our focus here is upon how the problem of demand is first established in the reproduction schema.6 As argued by Zarembka (2002: 24), ‘Luxemburg turns to a serious analysis of the role of a non-capitalist environment only after discovering the weakness in Marx’s presentation.’ This demand problem is examined by considering the ‘peculiar’ dominance of Department 1 (ibid.: 120). By applying the rule that capitalists in Department 1 invest a half of their surplus value in new capital, it is assumed that Department 2 is completely passive.7 Once Department 1 has followed this rule to start the production of capital goods, the question is asked: ‘And who requires these additional means of production?’ (ibid.: 132). The answer must be that Department 2 requires these capital goods in order to expand its production of consumption goods. This begs a further question from Luxemburg, ‘Well then, who requires these additional consumer goods?’ (ibid.: 132). This demand must come from Department 1, since it is employing more workers to make the additional capital goods.8 There is, she argues, a serious problem here: We are plainly running in circles. From the capitalist point of view it is absurd to produce more consumer goods merely in order to maintain more workers, and to turn out more means of production merely to keep this surplus of workers occupied. (ibid.: 132)

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More circling is involved in the consideration of money. There is a problem of establishing where the money comes from to back up the aggregate demand. Luxemburg considers Marx’s example of capitalists A, that produce a surplus product of capital goods, and capitalists B, that consume this surplus product. The problem is that to get the money to purchase from the A’s, the B’s must also sell their surplus products. ‘But who could have bought their surplus product? It is obvious that the difficulty is simply shifted from the A’s to B’s without having been mastered’ (ibid.: 143). The money could be found in the transition from simple reproduction to expanded reproduction, when capitalists reduce their own consumption, making money available for accumulation (ibid.: 147). Aside from these very narrow circumstances, however, Luxemburg argues that Marx’s focus on where the money comes from is a major distraction. Marx finds the money for accumulation on the basis of a reduction in consumption, a restriction of demand. For Luxemburg, ‘It is not the source of money that constitutes the problem of accumulation, but the source of the demand for the additional goods produced by the capitalized surplus value’ (ibid.: 147). Kotz has argued that Luxemburg is wrong to differentiate between money and demand. ‘Counterposing “money” and “demand” as two distinct potential problems of accumulation is not a very useful way to view the issue, since the monetary problem appears to be an aspect of the demand problem’ (Kotz 1991: 121). It could, however, be argued, in Luxemburg’s defence, that she is not trying to banish money from the accumulation story. Her main point is that ‘the very exposition of the difficulty’ – the problem of identifying the source of money – obscured the role of demand in Marx’s investigation. The statement by Kotz that ‘the monetary problem appears to be an aspect of the demand problem’ is entirely consistent with the considerable attention given to the circulation of money in Luxemburg’s account. Indeed, Luxemburg identifies the source of money as a distinct part of the problem. Towards the end of chapter 9, which considers the ‘Difficulty as Regards Circulation’, she states: True, if the capitalized surplus value is to be realized at all, money must be forthcoming in adequate quantities for its realization. But it is quite impossible that this money should come from the purse of the capitalist class itself. (ibid.: 165)

Luxemburg’s two parallel questions This reading of Luxemburg throws up two parallel questions: Where does the demand and money come from for capital accumulation? Possible

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answers are offered by our macro monetary model. First, the multiplier framework, as considered in Chapter 4, provides a way of modelling the two aspects of Marx’s circulation of money identified by Luxemburg: the mutual exchange between departments of production and the Kalecki principle (capitalists earn what they spend). As a vehicle for exploring Marx’s circulation of money, this model provides a way of addressing the question, ‘where does the money come from?’ The answer, on this interpretation, is that money is advanced and returns back to capitalists in their expenditures on investment and capitalist consumption, and it multiplies here and to between the departments of production to oil the economy’s total income. This multiplier framework allows both the Kalecki principle and the mutual exchange mechanism to be synthesized into a coherent model of the monetary circuit. Second, the Domar model can address Luxemburg’s question, ‘where does the demand come from?’ In equation (5.10) investment has a dual role. On the one hand increments in capacity are determined by the absolute amount of investment; on the other hand the required demand is determined by increments in investment. For Domar, this provides the heart of the problem as to why balanced growth is so difficult to achieve for a capitalist economy. An absolute amount of investment generates an increase in capacity, but an increase in investment is required to realize this capacity in terms of increasing income. There is a mismatch between the contrasting requirements of demand and supply in the reproduction schema, the main source of the contradiction being the hungry requirements of the demand side of the balanced growth equation. This contradiction bears a close resemblance to Luxemburg’s posing of the question of how new capital goods can be produced in the absence of sufficient demand to satisfy the new capacity. Sufficient demand, to meet the requirements of a balanced growth in capacity, is unlikely to be forthcoming from within the Domar model, from within the reproduction schema. Joan Robinson’s interpretation of Luxemburg has some resonance with the Domar definition of the problem: What motive have the capitalists for enlarging their stock of real capital? How do they know that there will be demand for the increased output of goods which the new capital will produce, so that they can ‘capitalize’ their surplus in a profitable form? (Robinson 1951: 20) For Zarembka (2002: 36), Robinson is able here to ‘explain and appreciate the basic problem Luxemburg raises’: a problem that we argue can be formalized using the Domar model.

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Aside from the problem of how demand meets the new capacity developed by capital goods, there is the additional problem that capitalists must borrow money. Luxemburg recognized the importance of borrowing, in chapter 30 of Accumulation of Capital, when considering the importance of non-capitalist demand (see Foley 1986: 88). She also highlighted the importance of borrowing in Reform and Revolution. ‘When the inner tendency of capitalist production to extend boundlessly strikes against the restricted dimensions of private property, credit appears as a means of surmounting these limits in a particular capitalist manner’ (Luxemburg 1986: 14). Luxemburg’s interpretation of the relationship between credit and crises is close to that developed by Marx in Capital, volume 3. She writes: To begin with, it increases disproportionately the capacity of the extension of production and thus constitutes an inner motive force that is constantly pushing production to exceed the limits of the market. But credit strikes from two sides. After having (as a factor of the process of production) provoked overproduction, credit (as a factor of exchange) destroys, during the crisis, the very productive forces it itself created. (ibid.: 14) Credit has a double role, in which it breaks through the limits of the market, but also exaggerates the extent of the crisis. ‘In short, credit reproduces all the fundamental antagonisms of the capitalist world. It accentuates them. It precipitates their development and thus pushes the capitalist world forward to its own destruction’ (Luxemburg 1986: 15). As shown in Chapter 5, however, the paradox of borrowing gives credit an endemic role in capital accumulation, not just as a way of expanding capacity beyond its usual confines, but as core to capital accumulation itself. The Domar model can therefore be offered as a vehicle for identifying how credit can provide a more fundamental source of fragility, at the heart of capital accumulation, than both Luxemburg and Marx recognized. Not only does the Domar model capture Luxemburg’s emphasis on the importance of demand, as a key contradiction in capital accumulation; it also amplifies the importance of credit as a factor driving capital accumulation and economic crises.

7

The falling rate of profit

Towards the end of the 1920s, in the wake of Rosa Luxemburg’s arguments about the barriers to expanded reproduction, a new theory of crisis was developed by the Polish Marxist, Henryk Grossmann. In opposition to Luxemburg’s emphasis on the importance of aggregate demand, Grossmann modelled Marx’s law of the tendency of the falling rate of profit. This was first seen as an extremely unorthodox position compared to the then popular underconsumption and disproportionality perspectives. As Jacoby (1975: 35) has pointed out, ‘Prior to Grossmann it [the falling rate of profit] received very little attention.’ In more recent years, however, the law of the falling rate of profit has taken centre stage as a theory of crisis. Cullenberg (1998: 163), for example, regards the law as ‘one of the most important and hotly debated issues in Marxian economics’; and for Weeks (1981: 202), ‘the law as such provides the key to unlocking the dynamics of capitalist crises’. The cornerstone of Grossmann’s contribution is his extension of Otto Bauer’s simulation of the reproduction schema. Compared to Bauer’s simulation over four years, Grossmann demonstrates for a 35-year period that the accumulation of capital leads to a scarcity of surplus value and eventual economic breakdown. Howard and King (1989) have surveyed the numerous criticisms that have been made of the Grossmann position, with particular emphasis on the complex relationship between technological change and the rate of profit. A stringent defence has also been provided by Kuhn (1995), drawing upon the recent Marxist literature on the rate of profit. One dimension of Grossmann’s simulation that has received limited attention, however, is the role played by the personal consumption of capitalists. The purpose of this chapter is to take issue with the treatment of capitalist consumption, and the associated role of investment, in the breakdown model. In contrast to Grossmann’s narrow focus on production, we revisit our argument that capitalists cast money into circulation (the Kalecki principle). It can be argued, once the role of money is taken seriously in Marx’s reproduction schema,

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that it is no longer possible for accumulation to swallow up all the available surplus value. It will be shown, by modifying the breakdown simulation to include the Kalecki principle, that the class neutrality assumption of a constant rate of exploitation is accordingly relaxed. Both Bauer and Grossmann regarded this assumption as provisional. And as has been noted by Laibman (1992: 122), ‘a rising rate of exploitation is as much a source of contradiction and an imminent critical tendency in capitalism as is a falling rate of profit’. Moreover, it can be argued that the consequences of a rising rate of exploitation are important to Marx’s exposition of the falling rate of profit thesis in Capital, volume 3.

Grossmann’s law of capitalist breakdown The starting point for Grossmann’s model of accumulation is provided by Otto Bauer’s 1913 adaptation of Marx’s reproduction schema (Bauer 1986). Grossmann’s objective was to directly engage and contend with Bauer’s argument that capital accumulation could be sustained through successive periods of expanded reproduction, without breakdown. The approach taken by Grossmann (1992: 67) is to ‘demonstrate the real facts through Bauer’s reproduction scheme’. Furthermore, ‘Bauer succeeded in constructing a reproduction scheme which, apart from some mistakes, matches all the formal requirements that one could impose on a schematic model of this sort’ (ibid.: 67). Since Grossmann plays such a key role in establishing the credibility of the Bauer model, reaching radically different conclusions to Bauer, we shall also refer to it interchangeably as the Grossmann model. Grossmann (1992: 65) adapts the Bauer model with the explicit aim of forming a theory of crisis from the ‘essence of capitalist production’. Following Marx’s employment of the reproduction schemes, prices are assumed to be identical to values, so that deviations of demand from supply are not considered in Grossmann’s abstract theory of crisis. Similarly, problems associated with credit, that in practice are always present in economic crises, are not considered relevant at this abstract level of analysis. Key to the Bauer model is an assumption that constant capital increases at a higher rate than variable capital – the former increases at 10 per cent per annum and the latter at 5 per cent (ibid.: 67). The result is a continual increase in the organic composition of capital, the ratio of constant to variable capital. The rate of surplus value, the ratio of total surplus value to variable capital, is assumed to remain constant at all times. With variable capital increasing at 5 per cent each year, the same increase in the pool of total surplus value takes place, out of which additional increments of constant and variable capital are funded. Capitalist consumption is treated

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as a residual, funded by the amount of surplus value that remains after the appropriate amount required for capital accumulation has been set aside. Table 7.1 shows Grossmann’s simulation, the numbers being very slightly different from the original after correcting for rounding errors and minor errors of calculation.1 In addition, although Grossmann models the departments of production explicitly, for ease of exposition only economywide totals are considered. At the outset the economy employs 200,000 units of constant capital and 100,000 units of variable capital. With a rate of surplus value of 100 per cent, a consequent 100,000 units of surplus value are produced, resulting in a rate of profit (100,000/100,000200,000) of 33.3 per cent. This pool of surplus value is used for funding a 10 per cent expansion in constant capital of 20,000 and a 5 per cent expansion of variable capital by 5,000. The fourth column of Table 7.1 shows that, after funding this capital expansion, 75,000 units are left as a residual for purposes of capitalist consumption. In this initial year of economic activity, the capitalists retain 75 per cent of their profits for personal consumption (savings of 25 per cent). Year 2 shows a new input of 220,000 units of constant capital incorporating the additional 20,000 units produced in the previous period; and a new 105,000 units of variable capital incorporating the additional 5,000 units of variable capital. With the rate of surplus value remaining the same, a new pool of 105,000 units of surplus value is produced, and disposed of with further increases in constant capital (by 22,000) and variable capital (by 5,250). The residual volume of capitalist consumption, after funding the capital expansion, is 77,750. Note that although there is an increase in capitalist consumption, the proportion of profits consumed by capitalists falls to 74.05 per cent compared to 75.00 per cent in year 1. This reduction in the proportion of profits consumed has important consequences for the economy as the simulation is repeated over subsequent periods. Although Bauer was able to demonstrate that expanded reproduction is sustainable over a four-year period, Grossmann showed that if the simulation is continued for 35 years then this results in economic breakdown. Table 7.1 shows a steady fall in the proportion of profits consumed until, in year 34, only 2.16 per cent are consumed. The stringent demands of capital accumulation are fulfilled, with constant and variable capital increasing by 10 and 5 per cent respectively throughout the 35-year period. The problem, however, is that with variable capital failing to keep pace with constant capital the pool of surplus value extracted from variable capital also fails to keep pace. The portion of surplus value destined for accumulation as additional constant capital . . . increases so rapidly that it devours a progressively larger share of surplus value. It devours the portion reserved for

200,000 220,000 242,000 266,200 292,820 322,102 354,312 389,743 428,718 471,590 518,748 759,500 1,111,983 1,223,182 1,345,500 1,969,947 2,383,635 3,172,619 3,489,880 4,222,755 4,645,031 5,109,534

1 2 3 4 5 6 7 8 9 10 11 15 19 20 21 25 27 30 31 33 34 35

100,000 105,000 110,250 115,763 121,551 127,628 134,010 140,710 147,746 155,133 162,889 197,993 240,662 252,695 265,330 322,510 355,567 411,614 432,194 476,494 500,319 525,335

Variable capital (V) 75,000 77,750 80,538 83,354 86,191 89,037 91,878 94,700 97,486 100,217 102,870 112,144 117,430 117,742 117,513 109,390 99,425 73,771 61,596 30,394 10,800 ␾

Capitalist consumption (u) 20,000 22,000 24,200 26,620 29,282 32,210 35,431 38,974 42,872 47,159 51,875 75,950 111,198 122,318 134,550 196,995 238,364 317,262 348,988 422,276 464,503 510,953

Change in C (dC) 5,000 5,250 5,513 5,788 6,078 6,381 6,700 7,036 7,387 7,757 8,144 9,900 12,033 12,635 13,266 16,125 17,778 20,581 21,610 23,825 25,016 26,267

Change in V (dV)

Note Grossmann uses the symbol ␾ to refer to a negative quantity, which is economically meaningless.

Constant capital (C)

Year

Table 7.1 Grossmann’s reproduction schema

400,000 430,000 462,500 497,725 535,921 577,358 622,331 671,164 724,209 781,855 844,527 1,155,486 1,593,307 1,728,572 1,876,160 2,614,967 3,094,770 3,995,846 4,354,269 5,175,744 5,645,669 6,160,204

Total value (W) 25.00 25.95 26.95 28.00 29.09 30.24 31.44 32.70 34.02 35.40 36.85 43.36 51.21 53.41 55.71 66.08 72.04 82.08 85.75 93.62 97.84 102.26

Proportion of profits saved (%)

33.3 32.3 31.3 30.3 29.3 28.4 27.4 26.5 25.6 24.8 23.9 20.7 17.8 17.1 16.5 14.1 13.0 11.5 11.0 10.1 9.7 9.3

Rate of profit (%)

80

The falling rate of profit capitalist consumption . . . , swallows up a large part of the portion reserved for additional variable capital . . . and is still not sufficient to continue the expansion of constant capital at the postulated rate of 10 per cent a year. (ibid. 1992: 80)

By year 35, a breakdown is reached in which there is insufficient surplus value to fund the capital expansion and personal consumption of capitalists. Grossmann’s lasting contribution to Marxist economics was to explain his breakdown theory in terms of Marx’s law of the tendency of the falling rate of profit. Table 7.1 shows how a continuous increase in the organic composition of capital results in a fall in the rate of profit; with the rate of surplus value constant the economy is constrained by an insufficient pool of total surplus value. The tendency for constant capital to substitute for labour means that labour is more productive, but also that less labour is available, relative to capital as a whole, for the production of surplus value. In contrast to Bauer, Grossmann argues that under Marx’s falling rate of profit thesis the expanded reproduction of capital is not sustainable if a long enough period of expansion is considered. To understand this outcome, a particularly useful analysis of the Bauer model has been provided by Samuelson and Wolfson (1986), the precise details of which are provided in Appendix 7.1. They point out that all bar one of the components which constitute the model are exogenous, independent values that are not allowed to vary. The rate of surplus value is set at 100 per cent, the rates of growth of constant and variable capital are set at 10 and 5 per cent, and the initial stocks of constant and variable capital are 200,000 and 100,000 units respectively. The only component of the model that is variable is the capitalists’ propensity to save out of surplus value. As we have seen, the eighth column of Table 7.1 shows that this propensity steadily increases from an initial value of 25 per cent in the first year, to 35.4 per cent in year 10, and so on until in year 35 all profits are exhausted in the funding of capital expansion. Since all of the other components are exogenously fixed, the one parameter that can change is the capitalists’ propensity to save. With constant capital expanding at a higher rate than variable capital and with a fixed rate of surplus value, something must give, and hence the savings propensity is the component that must increase as part of the process of capital accumulation. The consequence of the way in which this model is set up is that eventually the savings propensity reaches 100 per cent, so that no profits are left to fund capitalist consumption and even the expansion of capital cannot be facilitated. In the next part of this chapter, we question the validity of this treatment of the propensity to save as an endogenous residual.

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Return of the Kalecki principle The Bauer/Grossmann interpretation of Marx’s reproduction schema can be contrasted with our alternative perspective in which the role of money provides the focus of analysis. For Kalecki (1991c: 241), it is capitalist ‘investment and consumption decisions which determine profits, and not vice versa’. In the Grossmann approach, however, capitalist consumption is a residual left over once capitalists have decided their production of surplus value, out of which new constant and variable capital are allocated. The capitalist consumption portion of surplus value is not determined by the amount of money advanced at the start of the production period, but by the portion left once production has been completed. Using Marx’s reproduction schema, Kalecki derives an aggregate relationship between profits and capitalist expenditures.2 As demonstrated in Chapter 3, under the assumption of zero savings on the part of workers, an aggregate identity is established between profits, capitalist consumption and investment, which is shown as PuI

(7.1)

or profits  capitalist consumption  investment This equation shows clearly how the Kalecki principle works, with profits determined by capitalist expenditures. Since capitalists can only choose what they spend, and not what they earn, they ‘as a class determine by their expenditure their profits and in consequence the aggregate production’ (Kalecki 1991a: 25). To explore how the Kalecki principle can be applied to Grossmann’s numerical simulation, we can first show how equation (7.1) relates to Table 7.1. In year 1, total profits of 100,000 consist of 75,000 units of capitalist consumption together with 20,000 constant capital and 5,000 variable capital: 25,000 units of investment in total. Hence the identity 100,000  75,000  25,000

(7.2)

can be established between profits and capitalist outlays on consumption and investment. Kalecki pays particular attention to the structure of capitalist consumption, defining the constant part as B 0 and the part which is dependent on profits according to the proportion ␭. Hence u  B0  ␭P

(7.3)

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In order to activate the expenditure side of the profit equation, we can make use of Kalecki’s working assumptions about the structure of capitalists’ consumption. Kalecki (1990a: 69) argues that capitalists’ consumption is ‘relatively inelastic’, that is a large part does not depend on profits. Only a small proportion of capitalist consumption will change in response to a change in profits. In an empirical exercise, which Kalecki (1990b: 132) argues ‘is confirmed by statistical evidence’, he argues that about 3/4 of capitalists’ consumption is made up of the constant part. Since capitalists’ consumption is so inelastic with respect to profits, only 1/4 part is directly related to profits. These proportions can be used, for purposes of illustration, to explicitly model the structure of capitalists’ consumption in Table 7.1. There we see that in year 1 capitalists consume 75,000 units. Using Kalecki’s assumptions the constant part could constitute 56,250, representing 3/4 of the total volume of capitalists’ consumption. It follows, if the parameter relating capitalist consumption to profits takes a value of 0.1875, then capitalist consumption has the structure 75,000  56,250  (0.1875 100,000)

(7.4)

In year 1 of the Grossmann simulation this provides a different way of viewing the same volume of capitalists’ consumption. Instead of capitalist consumption depending completely upon the amount of profits which remains after capitalists have decided how much to invest, it can instead be argued that such consumption can be modelled in its own right. From either perspective, in year 1 the capitalists extract and realize surplus value representing 100,000 units. As argued in Chapter 3, there is no suggestion here that the using Kalecki’s approach should undermine the critical role of surplus value in the origin of profits. Where this alternative perspective provides different results from Grossmann is when the simulation is continued beyond the first year. Again, following Kalecki, we can assume that the constant part of capitalists’ consumption will increase over time. ‘A secular rise in wealth and income of capitalists tends to raise, with rather a long time-lag, their “standard of living”, i.e. the amount they are apt to consume irrespective of the level of their current income’ (Kalecki 1991b: 184). However, ‘the long-run rise in capital and profits may be associated with the concentration of both’ (ibid.: 184) and this could cause a reduction in the constant part of capitalists’ consumption. In view of these factors it is plausible to assume a slowly increasing constant part of capitalists’ consumption. For our adaptation of Grossmann’s simulation, a rate of growth of 2.5 per cent can be assumed for the constant part of capitalist consumption, half the 5 per cent rate of growth for variable capital.3

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Simulation without breakdown Applying the Kalecki principle and these empirical assumptions to the Grossmann table, a new simulation of expanded reproduction is presented in Table 7.2. As shown in Chapter 3, the Kalecki multiplier relationship (see equation 3.8) can be derived by substituting (7.3) into (7.1): P

B0  I 1␭

(7.5)

This represents a multiplier relationship between total profits (P) and the total exogenous expenditures by capitalists (B0  I ), the multiplier being defined as 1/1  ␭. This multiplier relationship is used to determine profits in Table 7.2 (see Appendix 7.2 for more detail). The Kalecki modified schema retains the key characteristics of the Grossmann model. Constant capital still grows at 10 per cent each year compared to 5 per cent for variable capital, and this requires a steady increase in the proportion of profits saved, from 25 per cent in year 1 to 65.4 per cent in year 35. Also in keeping with the Grossmann model, the rate of profit steadily falls over time, from 33.3 per cent in year 1 to 14.6 per cent in year 35. The difference, however, is that capitalist consumption is not treated as a residual, dependent upon the amount of profits that happen to remain after the prior commitments of capital accumulation. In Table 7.2, capitalist consumption is modelled as an active component in the model, providing an important driver in the generation of profits, as capitalists cast money into circulation. Table 7.2 also shows that after an initial period of stagnation in the first 11 years, the rate of surplus value increases during the 35-year period of expanded reproduction. The role given to capitalist expenditures on investment and consumption, in the determination of profits, serves to increase the rate of surplus value from 1.000 to 1.564 during the course of the simulation. Under Grossmann, surplus value is extracted on a one-to-one basis from each unit of variable capital – at a rate of 100 per cent. Once, however, surplus value is determined by the expenditure decisions of capitalists then this one-to-one extraction of surplus value is relaxed.4 This modification of the model is consistent with the spirit of the original Bauer formulation, which Grossmann adheres to so closely. In developing the reproduction schema, Bauer states, ‘To simplify the investigation we assume for the time being that the rate of surplus value remains unchanged, at 100 per cent’ (Bauer 1986: 93, emphasis added). Although, as Bauer’s translator (J.E. King) points out, the promise to later relax this assumption is not fulfilled, the assumption of a constant rate of surplus value is not regarded as having any particular theoretical significance. Indeed for Grossmann (1992: 128),

Constant capital (C)

200,000 220,000 242,000 266,200 292,820 322,102 354,312 389,743 428,718 471,590 518,748 759,500 1,111,983 1,223,182 1,345,500 1,969,947 2,383,635 3,172,619 3,489,880 4,222,755 4,645,031 5,109,534

Year

1 2 3 4 5 6 7 8 9 10 11 15 19 20 21 25 27 30 31 33 34 35

100,000 105,000 110,250 115,763 121,551 127,628 134,010 140,710 147,746 155,133 162,889 197,993 240,662 252,695 265,330 322,510 355,567 411,614 432,194 476,494 500,319 525,335

Variable capital (V)

Table 7.2 Kalecki modified reproduction schema

100,000 104,500 109,305 114,441 119,937 125,826 132,141 138,921 146,208 154,048 162,491 203,482 259,646 276,772 295,371 387,521 446,810 557,481 601,337 701,614 758,867 821,486

Profits (P) 1.000 0.995 0.991 0.989 0.987 0.986 0.986 0.987 0.990 0.993 0.998 1.028 1.079 1.095 1.113 1.202 1.257 1.354 1.391 1.472 1.517 1.564

Rate of surplus value(s) 75,000 77,250 79,592 82,033 84,578 87,234 90,009 92,911 95,949 99,133 102,472 117,633 136,414 141,819 147,554 174,401 190,668 219,638 230,739 255,514 269,348 284,265

Capitalist consumption (u) 25.00 26.08 27.18 28.32 29.48 30.67 31.88 33.12 34.37 35.65 36.94 42.19 47.46 48.76 50.04 55.00 57.33 60.60 61.63 63.58 64.51 65.40

Proportion of profits saved (%)

33.3 32.2 31.0 30.0 28.9 28.0 27.1 26.2 25.4 24.6 23.8 21.3 19.2 18.8 18.3 16.9 16.3 15.6 15.3 14.9 14.7 14.6

Rate of profit (%)

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85

‘The basic mistake is Bauer’s assumption that the rate of surplus value is constant despite the assumed rising organic composition of capital.’ This rising rate of surplus value is also consistent with Marx’s theory of surplus value. It has been shown that under the Kalecki principle profits are determined by capitalist consumption. Under simple reproduction, profits are identical to capitalist consumption, with investment in new capital included under expanded reproduction. However, whilst capitalists may first cast into circulation the money required for such luxury consumption, the reflux of that money back to the capitalist class is only made possible by the production of surplus value. Although the consumption of luxury goods is unproductive, in comparison to how this surplus value could have been more usefully employed,5 the labour power that produces these goods is productive, since it produces surplus value (see Howard and King 1985: 129). Hence an expansion of demand for luxury goods generates an expansion in the mass of surplus value congealed in the total volume of these goods produced, thereby increasing the rate of surplus value.6 As Yaffe (1972: 24), a follower of Grossmann, argued, ‘It is quite amazing that critics of Marx such as Joan Robinson can say that Marx’s theory rests on the assumption of a constant rate of exploitation.’ For Yaffe the key question is whether the rate of surplus value can rise sufficiently to enable the combination of a sustained fall in the rate of profit and an increasing mass of surplus value. Yaffe (1972: 26) argues that for this combination to be sustained the rate of surplus value must increase at an accelerated rate. Of course, the requirement of an accelerating rate of surplus value is difficult to sustain. Yaffe (1972: 27) refers to the ‘increasing difficulty in raising the rate of exploitation sufficiently to satisfy the self-expansion requirements of capital as capitalism progresses’. However, it is not possible in the Kalecki modified framework to identify a particular year of breakdown after n years of simulation, as in the Grossmann model. In contrast to Grossmann’s Table 7.1, in Table 7.2 capitalist consumption increases steadily throughout the 35-year period, without breakdown. Moreover, the simulation can be extended to a period of 100 years, and beyond, without there being a drying up of surplus value. This 100-year simulation of Table 7.2 is illustrated by the trajectory of the rate of profit in Figure 7.1, with Figure 7.2 showing the accelerating rate of surplus value.

The falling rate of profit In addition to questioning the relationship of the Grossmann breakdown thesis to Marx’s reproduction schema, consideration can also be given to its relevance to Marx’s exposition of the falling rate of profit tendency in

35

Rate of profit (%)

30 25 20 15 10 5 0 1

100 Year

Figure 7.1 The rate of profit in the Kalecki simulation.

250

Organic composition of capital Rate of surplus value

200

150

100

50

0 1

100 Year

Figure 7.2 Components of the rate of profit in the Kalecki simulation.

The falling rate of profit

87

Capital, volume 3. Grossmann’s claim to have faithfully represented Marx’s theory rests on passages in section 3 of chapter 15, ‘Excess Capital and Excess Population’.7 The breakdown scenario, in which the mass of surplus value dries up in year 35 of the Bauer schema, is interpreted by Grossmann (1992: 76) as a case of ‘overaccumulated capital’. Quoting from Marx, ‘there would be a steep and sudden fall in the general rate of profit’ (Marx 1959: 246). Moreover, ‘The fall in the rate of profit would then be accompanied by an absolute decrease in the mass of profit . . . . And the reduced mass of profit would have to be calculated on an increased total capital’ (ibid.: 247). The problem with this interpretation, however, is that in these passages Marx was considering a particular case in which there is a rise in wages and a fall in the rate of surplus value. It is for this reason that there can be overaccumulation for which increases in capital generate no extra profits. To quote Marx in full: there would be a steep and sudden fall in the general rate of profit, but this time due to a change in the composition of capital not caused by the development of productive forces, but rather by a rise in the moneyvalue of the variable capital . . . and the corresponding reduction in the proportion of surplus labour to necessary labour. (ibid.: 247, emphasis added) Here we see some of the words quoted by Grossmann in italics, but put in the context of the rest of the sentence. The overaccumulation scenario that he finds in Marx is associated with the particular case of an increase in wages, a causal factor that has no mention in Grossmann’s interpretation. Indeed, since the falling rate of profit is expounded by Marx in the context of an increasing rate of surplus value, it is difficult to place this overaccumulation scenario at the centre of his theory. A different reading of Capital, volume 3, can be suggested, in which questions of realization are the main focus of analysis (see Rosenthal 1999). Thus far, in applying the Kalecki principle to Marx’s circulation of money, we have assumed that monetary outlays take place, funding the purchase of all capital and consumption requirements. However, as capital expands, the volume of profits accumulates to such an extent that stringent demands are placed upon the economic system in terms of the amount of money that has to be cast into circulation for realization of these profits. Marx places realization problems at the centre of his analysis of the falling rate of profit. With the development of this process as expressed in the fall in the profit rate, the mass of surplus-value thus produced swells to monstrous proportions. Now comes the second act in the process. The

88

The falling rate of profit total mass of commodities, the total product, must be sold, both the portion that replaces constant and variable capital and that which represents surplus-value. If this does not happen, or happens only partly, or only at prices that are less than the price of production, then although the worker is exploited, his exploitation is not realized as such for the capitalist and may even not involve any realization of the surplus-value extracted, or only a partial realization; indeed, it may even mean a partial or complete loss of his capital. (Marx 1981: 352)

Marx is clear, in this key part of his discussion of the falling rate of profit, that the realization of surplus value is not guaranteed. ‘The conditions for immediate exploitation and for the realization of that exploitation are not identical. Not only are they separate in time and space, they are also separate in theory’ (ibid.: 352). Indeed, this provides a key underpinning for Marx’s argument as to why the falling rate of profit, and its associated burgeoning mass of profits, provides such severe problems for capitalism. ‘The means – the unrestricted development of the forces of social production – comes into persistent conflict with the restricted end, the valorization of the existing capital’ (ibid.: 359). By focusing on the realization of the mass of profits, an alternative to Grossmann’s overaccumulation scenario can be suggested that is consistent with Marx’s core thesis of a falling rate of profit with a rising rate of surplus value. As the basis for a theory of crisis, this demand-side perspective does not provide a precise mechanical breakdown of the type developed by Grossmann. Moreover, the development of a complete alternative is beyond the confines of the present study. However, since under the Kalecki modification of the Grossmann model the rate of surplus value accelerates because of the monetary outlays on spending by the capitalist class, the sustainability of this process must depend upon the finance of these monetary outlays. One of the key determinants of these outlays is the role of banks in providing credit to fund such spending activity. In contrast to Grossmann’s relegation of credit to a less abstract level of analysis, the Kalecki modified model points towards the relevance of the financial system to Marx’s falling rate of profit thesis.

8

The transformation problem

After Marx’s death, in 1883, Engels undertook the major task of patching together the second and third volumes of Capital. Whereas volume 2 slipped out into the public domain in 1885 like a battleship leaving port in the middle of the night, volume 3 was launched in the full glare of public scrutiny. In his introduction to volume 2, Engels set a famous essay prize, in which scholars were invited to come up with their own solution to the transformation problem: the problem of how values can be transformed into prices. When volume 3 was finally published in 1894 it became, and still is, the subject of intense controversy. Critics argued that Marx failed to correctly transform capital inputs from values to prices. This claim, that Marx’s transformation solution is inconsistent and wrong, has become the Achilles heel of Marxian economics. Marxists have sought for the last 100 years to defend the labour theory of value against the charge of inconsistency. Marx’s development of the reproduction schema in the second volume of Capital is predicated on an assumption that prices are proportionate to values: In as much as prices diverge from values, this circumstance cannot exert any influence on the movement of the social capital. The same mass of products is exchanged afterwards as before, even though the value relationships in which the individual capitalists are involved are no longer proportionate to their respective advances and the quantities of surplus-value produced by each of them. (Marx 1978: 469) The purpose of this chapter is to consider how our macro monetary interpretation of the reproduction schema can be generalized into a model with price–value deviations. This generalization is attempted by considering the new interpretation of the transformation problem, as developed by Foley (1982).1 In contrast to the perceived Sraffian view of capitalism, as a system producing a physical

90

The transformation problem

surplus, proponents of the new interpretation have focused on the value of money as a way of relating the labour theory of value to the circuit of money. Since the circuit of money is so closely intertwined with the reproduction of capital, the purpose of this chapter is to consider the new interpretation in the light of our macro monetary interpretation of the reproduction schema. A summary is provided of how the analytical components of the macro monetary model can be generalized under deviations of prices from values. An important criticism of Marx’s development of the reproduction schema in Capital, volume 2, is that he fails to consider the importance of competition. For Howard and King (1985: 191), Marx’s reproduction models ‘do not relate to a full competitive capitalist system, in which capital mobility and credit flows operate to equalise profit rates and bring about prices of production which deviate from labour values.’ As a result, Marx may have drawn ‘unwarranted conclusions as to the difficulties involved in achieving fully co-ordinated production in capitalism’ (ibid.: 191). This key limitation of the reproduction schema is addressed here.

Marx’s transformation solution In chapter 9 of Capital, volume 3, Marx developed a procedure for the ‘Transformation of Commodity Values into Prices of Production’ (Marx 1981: 254). Instead of using Marx’s rather complex example of five branches of production, in which fixed capital is employed, we shall explain his procedure using a simplified example for three sectors, borrowed from Howard and King (1985: 99). In this example, all capital is assumed to be of the circulating type, and simple reproduction is assumed, so that there is no expansion of capital over time. Table 8.1(a) shows the physical units required for production. The first department produces steel (means of production), the second corn (wage goods), and the third gold – in Howard and King’s example gold is a luxury Table 8.1(a) Marx’s calculation of prices (physical categories) Inputs

Output

Means of production Dept. 1 Dept. 2 Dept. 3 Total

80 tons steel 10 tons steel 30 tons steel 120

Labour   

40 50 30 120

→ → →

120 tons steel 60 quarters corn 60 ounces gold

The transformation problem

91

good, consumed by capitalists. In the first sector, for example, 80 tons of steel inputs are combined with 40 units of labour to produce an output of 120 tons of steel. These outputs are used to replace the 80 tons used up in Department 1, the 10 tons used in Department 2, and the 30 tons used up in Department 3. Note that this is simple reproduction because the amount produced exactly matches the amount used up as inputs. Now the labour values of each commodity – measuring the direct and indirect labour embodied in each commodity – are conveniently valued at unity for each of the three departments (Howard and King 1999: 100). In the value schema, therefore, inputs of steel (constant capital) used up by each of the three sectors have a (labour) value of 80 for Department 1, 10 for Department 2, and 30 for Department 3. These are shown in Table 8.1(b), together with the components of variable capital, which represent the labour embodied in units of corn consumed by labourers. In this value schema, it is also assumed that there is a uniform rate of surplus value, which is set at 100 per cent. Hence, for example, 20 units of surplus value are extracted in Department 1 from 20 units of variable capital; in total 60 units of surplus value are extracted from 60 units of variable capital. Using the formula Ci  Vi  Si, values can be calculated for each department. In Department 1, for example, the total value of output is 120; in Department 2, the total value is 60. In our previous analysis of Marx’s reproduction schema, based on the second volume of Capital, it was assumed that these values are also the total prices of each department. However, in the third volume Marx focuses on the organic composition of capital, which measures the ratio (Ci /Vi) between constant and variable capital.2 These ratios vary between 4 and 0.4 in this example. And it is this variation that leads Marx to argue that values cannot be sustained as indicators of price for each department of production. The problem is that the rate of profit (Si/Ci  Vi) for each department is calculated as a ratio between total surplus value and total capital. Yet, for each department its own mass of surplus value is calculated from the variable capital employed. Table 8.1(b) Marx’s value calculation

Dept. 1 Dept. 2 Dept. 3 Total

Constant capital (Ci )

Variable capital (Vi )

Surplus value (Si )

Total value (Ci ViSi )

Organic composition (Ci /Vi )

Rate of profit (%) (Si /CiVi )

80 10 30 120

20 25 15 60

20 25 15 60

120 60 60 240

4 0.4 2

20 71.4 33.3

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The transformation problem

Departments with a relatively high proportion of constant capital to variable capital (a high organic composition) will find that this drags down their rate of profit, since the constant capital term appears in the denominator. Departments with a relatively low organic composition of capital have a higher rate of profit. In Table 8.1(b), Department 1 has an organic composition of 4 and a rate of profit of 20 per cent; Department 2 has a rate of profit of 71.4 per cent with a much lower organic composition of 0.4. For Marx, such a disparity of profit rates would be blown apart by capital mobility. Capitalists seek the maximum rate of profit they can obtain; so if a department has higher profitability than others, new capital will move into this department until rates of profit are equalized. Instead of values governing the exchange between departments of production, new prices of production are defined under equal rates of profit. Table 8.1(c) shows Marx’s procedure for calculating prices of production. This is a two-stage procedure. First, the average rate of profit is established for the economy as a whole, so that

兺Si

兺Ci  Vi



60  3313% 120  60

(8.1)

Second, this rate of profit is applied to each department’s costs of production to establish the amount of profit made. In Department 1, for example, profits of 33.3 are made on the total (constant and variable capital) cost price of 100. The price of production for each sector consists of the cost price plus profits: in Department 1 this is 133.3. For this numerical example, prices deviate above value for departments with a high organic composition of capital (13.3 for Department 1) and below for a low organic composition (13.3 for Department 2). Department 3 in the example is neutral, having an average composition of capital. Two invariance postulates are established. First, the deviations of prices from values sum up to zero, which means that total prices (240) are equal to total values (240). Second, total money profits (60) are equal to total surplus value (60). Although for individual departments there are deviations of prices from values, and profits from surplus value, in the economy as a whole value categories are preserved. Marx defends his value theory using a macroeconomic solution, in which profits are determined by surplus value, and all that is required is a redistribution of surplus value between departments of production. Compared to his classical predecessors, who often failed to take into account the deviation of prices from value, it has been generally recognized that Marx’s transformation procedure represented an important step in the development of value theory. However, there is an issue with Marx’s transformation that he himself recognized. The two-stage transformation of

120

Total

60

20 25 15

Variable capital (Vi )

Source: Howard and King (1985: 99).

80 10 30

Dept. 1 Dept. 2 Dept. 3

Constant capital (Ci )

Table 8.1(c) Marx’s price calculation

180

100 35 45

Cost price (Ci  Vi ) 33 3 % 1 33 3 % 1 33 3 %

1

Average rate of profit ( Si/Ci  Vi )

60

33.3 11.7 15

Total profits

240

133.3 46.7 60

Price of production

0

13.3 13.3 0

Price minus value

94

The transformation problem

values to prices is based on an assumption that the inputs of means of production are measured in values, but only the outputs are transformed from values to prices. In Table 8.1(c), for example, notice that the inputs of constant capital to the three departments of production are 80, 10 and 30 – the same in the price calculation as in the value calculation (Table 8.1(b)). Hence Marx (1981: 265) warns that ‘if the cost price of a commodity is equated with the value of the means of production used up in producing it, it is always possible to go wrong. Our present investigation does not require us to go into further detail on this point.’ Marx’s critics, however, have made a great deal of this point of detail. The apparent failure to transform inputs from values to prices is the crux of the transformation problem: the charge that Marx’s solution is inconsistent and wrong. How, in particular, can reproduction be established when producers are buying inputs at one set of prices and selling them at another set of prices? In Table 8.1 (c), after Marx’s transformation procedure has been employed, Department 1 sells its output of capital goods for 133.3, yet the inputs of capital goods used up are still 120: a discrepancy of 13.3. Similarly, for Department 2, wage goods are sold at 46.7 but the amount of wage goods used up is still 60: a discrepancy of 13.3. Hence, for Sweezy (1942: 114), ‘the Marxian method of transformation results in a violation of the equilibrium of Simple Reproduction.’ This is no way to build a reproduction schema in which prices deviate from values.

Marx after Sraffa: the new interpretation The overwhelming response to this transformation problem, for both Marx’s critics and disciples, has been to abandon the definition of value as a quantity of labour embodied in production. Either value is redefined in a way that allows the transformation problem to be solved, or the labour theory of value is abandoned altogether. The latter response has been adopted in the Sraffian critique of Marx. This approach has its roots in the pioneering contribution, in 1907, of von Bortkiewicz, who set up a procedure for transforming both inputs and outputs into prices (Bortkiewicz 1951–2). The result, later generalized by Winternitz (1948) and Seton (1975), is a weakening of the relationship between values and prices. Marx’s invariance postulates, that total profits should equal total surplus value and total prices should equal total value, cannot both be maintained once inputs and outputs are transformed into prices. This weakening of the relationship between value and price is taken further by Steedman (1977) in his Marx after Sraffa. Core to this approach is the Sraffian price equation p  (1  r)(pA  phl)

(8.2)

The transformation problem

95

Here p is a row vector of money prices, A is the matrix of input coefficients, h is a column vector of consumption coefficients and l is a row vector of labour coefficients. In this price equation all inputs are calculated using money prices; the money value of capital good inputs, for example, is represented by the term pA. The equilibrium reproduction condition is therefore easily established since the same price vector is applied to inputs and outputs. In addition, the mark-up of profits is calculated on the basis of the money cost price (pA ⫹ phl). The scalar r is a money rate of profit, in contrast to Marx’s value rate of profit. In a further weakening of the relationship between the price and value domains, Steedman argues that in general the value and money profit rates will differ.3 Furthermore, it follows from (8.2) that the money rate of profit is determined by the ‘physical picture of the economy’ as represented by the technical coefficients and the real wage in the Sraffian price equation. Steedman (1977: 66) argues that ‘value magnitudes are irrelevant to the proximate determination of the profit rate and of production prices,’ and hence the labour theory of value is redundant. During the 25 years or so since the publication of Marx after Sraffa, there has been a concerted effort to salvage the labour theory of value from this powerful critique. The main defence has been to place emphasis on the money value-form of commodities, instead of the labour embodied form. Value-Form Marxism has a number of variants, but the most important contribution is the ‘new interpretation’, as represented here following Foley (1982). The main thrust of the new interpretation is to provide a translation between total money value added (the money value of total net output, pQ) and total direct labour-time (lX). By defining the value of money (␭m) as the ratio of total labour-time to total money value added, lX  ␭mpQ

(8.3)

where ␭m 

lX pQ

Now pQ  V  P: the money value added is made up of money wages (V) and money profits (P). It is therefore possible to express the component parts of value added in Marxian categories. First, the value of labour power (VLP) is defined as VLP  ␭mV

(8.4)

96

The transformation problem

Instead of measuring the value of labour power in the traditional way as the labour embodied in commodities consumed by workers, an attempt is made to measure its value-form: the value-form of total money wages. Second, once wages have been translated into the value of labour power (the paid proportion of total labour-time), it follows that money profits can be translated into surplus value (unpaid labour-time): S  ␭mP

(8.5)

Hence, Foley (1982: 42) argues, ‘the most central of Marx’s claims about the “transformation” of values into prices of production, that profit arises from unpaid labour time, is sustained . . . .’ A direct correspondence is established between surplus value and money profits. This holds regardless of how prices are determined, including the Sraffian price equation (8.2). Moreover, prices can systematically deviate from values without damaging this aggregate relationship. Even if the money price of goods consumed by workers deviates from the labour embodied in these commodities, which Foley argues renders the traditional labour embodied definition of the VLP irrelevant, the value-form definition of VLP is completely operational. Under (8.5), Marx’s invariance postulate between total profits and surplus value is therefore established, with the value of money as the mediating coefficient. And in place of the equality between total value and price, a new invariance postulate is suggested in (8.3) between total labour-time and money value added. A coherent defence of Marx’s labour theory of value is developed by abandoning the second invariance postulate and the labour embodied definition of the value of labour power (see Foley 1982: 43). Furthermore, in the new interpretation money plays a key role in defining the way in which labour power is valued.4 This is contrasted with the labour embodied approach. ‘The usual interpretation, which posits a bundle of subsistence goods whose labour content defines the value of labour power, short-circuits this relation, and makes money disappear as a mediating element in the situation’ (ibid.: 43). Similarly, for Mohun (1994: 405), in his defence of the new interpretation, ‘money becomes in embodied labour accounts of value an irrelevance to theoretical explanation’. In addition to providing a defence of the labour theory of value, the new interpretation offers a way of modelling capitalism as a system in which surplus value is appropriated in its money value-form.

Generalization of the macro monetary model An overarching aim of this book is to develop a formal model which captures the role of both aggregate demand and money in the reproduction schema.

The transformation problem

97

Using the new interpretation, this model is summarized here in its most general form, with prices deviating from values. This provides a summary of how the model contributes both as a vehicle for exploring some key issues in political economy and as a synthesis between various fragments. The macro multiplier Although it is traditional in Marxian frameworks for capitalists to initiate the circulation of money with an advance of constant and variable capital, our previous discussion, in Chapter 4, showed that there are a number of ways in which the circulation of money can be modelled. In the single swap approach all of income is advanced; in the Franco-Italian circuit approach only the wage bill is advanced; in Nell’s mutual exchange approach only wages in the capital goods sector are advanced. Our contribution has been to suggest, under the Kalecki principle (first introduced in Chapter 3), that capitalists advance an amount of money sufficient to realize their profits. This model is predicated on the definition of investment as accumulation of constant and variable capital. Recall from equation (4.23) that a multiplier relationship x

1 f 1cw

(8.6)

is key to modelling the circuit of money. Capitalists advance a sum of money (f  pF), spent on new (constant and variable) capital goods and capitalist consumption, which generates a multiplied effect 1/(1  c  w) on the total level of gross national income (x  pX). This multiplier is also, under certain conditions, equal to the velocity of circulation; and it has been derived from input–output relations between industrial sectors and consumer expenditures. How does this model of the circuit of money relate to the transformation problem? It can be shown how this model can be generalized to a Sraffian interpretation. Since c  pAX/pX and w  wlX/pX it follows from (8.6) that pF  pX  pAX  wlX

(8.7)

Since pF  r(pAX  wlX), it is straightforward to derive (8.7) from the Sraffian price equation.5 The Sraffian price system can be easily made consistent with our macro monetary multiplier. From a Sraffian perspective, however, the gross multiplier and price system do not require any mention of labour values. The parameters of the system are defined in physical and money price terms. However, using

98

The transformation problem

the new interpretation this Sraffian system can be re-shaped using Marxian categories. Since Q  X  AX, (8.7) can be expressed in net terms as pQ  wlX  pF

(8.8)

Now we can write wlX  w lX pQ  w␭my pQ

(8.9)

where ␭mw is per money unit definition of the value of labour power under the new interpretation (see equation 8.4). Substituting (8.9) into (8.8) it follows, with y  pQ, that y  ␭mwy  f

(8.10)

or y

1 f 1 f 1  ␭mw e*

(8.11)

This is the simple Keynesian multiplier relationship between money net output and money final demand, of the type first derived from the reproduction schema in Chapter 2. Cutting through the dense and voluminous material that has been written about Marx’s reproduction schema, this scalar multiplier offers an extremely succinct summary of its macroeconomic structure. Using the new interpretation, (8.11) is derived from multisectoral foundations with a clear role for the new surplus value term e* in the denominator. The denominator of this multiplier is once again a term representing the share of surplus value, but defined according to the (valueform) new interpretation of the value of labour power. The per money unit VLP expression ␭mw is also the propensity to consume derived from multisectoral foundations.6 This simple multiplier is derived without making any restrictive assumptions about the proportionality between prices and values. This multiplier further establishes the consistency between the Kalecki principle, that capitalists earn what they spend, and Marx’s theory of surplus value. Since in (8.11) f  u  I, it follows that S*  u  I or surplus value  capitalist consumption  investment

(8.12)

The transformation problem

99

where total surplus value is redefined in its value-form as S* under the new interpretation.7 As in Chapter 3, capitalists cast money into circulation as aggregate demand that is realized as surplus value. This is achieved here, however, under the more general case of prices deviating from values. Under the assumptions of Capital, volume 2, where prices were identical to values, it was straightforward in Chapter 3 to reconcile the value-form with the labour embodied form of individual commodities. The new interpretation establishes consistency between the value-form of profits and the money cast into circulation at the aggregate level, but not at the level of individual commodities. Following the analysis carried out in Chapter 3, the Keynesian multiplier can also be synthesized with the Kalecki multiplier. By again redefining the share of surplus value as e*, the expression (3.9) can be re-written as8 y

1 (B  I) e*(1  ␭) 0

(8.13)

The scalar 1/1  ␭ is the Kalecki multiplier, which provides an alternative interpretation, in Chapter 7, of Grossman’s model of economic breakdown. This multiplier, together with the Kalecki principle, is applied to the Grossmann model of rising organic composition of capital. From this perspective, in which capitalists cast money into circulation as an endemic part of the reproduction schema, Grossmann’s demonstration of a precise year of economic breakdown is not possible; a demonstration that is consistent, under the new interpretation, with the deviation of prices from values. Moreover, the key contradiction identified by Marx under the falling rate of profit thesis is the problem of how the burgeoning mass of surplus value can be realized. Although this Keynes–Kalecki multiplier provides a succinct way of modelling aggregate demand, our analysis of the circuit of money requires a gross multiplier relationship – in order to fully take into account the circulation of money required by the exchange of capital goods between sectors. It is possible, however, to locate the (new interpretation) value of labour power in the gross multiplier. Consider in (8.6) the expression for the share of wages in gross income, which can be re-expressed as w

wlX pQ lX  w  ␾␭mw pX pX pQ

(8.14)

where ␾  pQ/pX is the ratio of money net output to money gross output. It follows that the gross income multiplier can take the form x

1 f 1  c  ␾␭mw

(8.15)

100

The transformation problem

Using the new interpretation, the value of labour power can be located in our macro model of the circuit of money. It should be noted, however, that our application of the new interpretation does not imply that the traditional labour embodied definition of value should be completely abandoned. Foley (2000: 30) is open to the possibility that there may be a role for both the new and traditional interpretations of the value of labour power. As Appendix 4 shows, the labour embodied definition of the value of labour power is nested in the input–output model of the circulation of money between departments of production, regardless of how prices are defined. The deviation of prices from values does not modify the constituent role of the labour embodied measure in the interindustry monetary circuit. It is only when a macroeconomic aggregation is developed under price–value deviations, and in the derivation of the scalar Keynesian multiplier, that a switch to the value-form definition is required. The Domar growth model Whereas the gross macro multiplier is required for modelling the circuit of money (a snapshot of the reproduction schema), the net multiplier is useful for modelling economic growth (expanded reproduction over time). In Chapter 5, the net multiplier is used to develop the multisectoral foundations of the Domar growth model. Under the more general case, in which prices deviate from values, the Domar model can be reconfigured with the share of surplus value derived from the new interpretation (e*). As we have seen, this is not the same as the share of surplus value (e), which made up the denominator of the Keynesian multiplier used in Chapter 5, under the assumption of proportionality between prices and values. Substituting e* for e in the Domar balanced growth equation, derived in Chapter 5,9 we get dy dI y  I  ␭e*␴

(8.16)

Balanced growth has to be equal to a multiple of ␭ (the ratio of investment to profits), e* (the new per capita share of surplus value) and ␴ (the productivity of investment). In Chapters 5 and 6, two main arguments are made about the contribution of this model to political economy. First, the Domar model exposes the stringent requirements on aggregate demand that are associated with balanced growth. Whereas new capacity is generated by absolute levels of investment, a matching aggregate demand requires investment to increase. Domar identifies the problem of demand at

The transformation problem

101

the heart of capitalist accumulation. This interpretation makes nonsense of the claim that in Marx’s reproduction schema supply automatically creates its own demand (Say’s Law). Domar shows that balanced growth is unlikely to be achieved because the required demand is not automatically forthcoming. Second, Domar shows that there is a paradox of borrowing in expanded reproduction (an insight later provided by Foley). Capitalists cannot borrow from an existing money hoard in order to expand capital accumulation; they must borrow from financial institutions. This places financial fragility at the heart of the reproduction schema, since all capital accumulation is associated with borrowing; and hence, all borrowing is potentially undermined by the problem of demand. This contrasts with Marx’s identification of financial instability with occasions when capital accumulation overstretches itself. These insights provide a way of addressing Rosa Luxemburg’s two-pronged question, ‘Where does the money and demand come from?’ As shown in Chapter 6, the Domar model provides a way of formalizing Luxemburg’s arguments about the stringent requirements for money and demand that are placed on the reproduction schema. In addition, it provides an alternative to the traditional association of demand problems with disproportionality and underconsumption. These contributions of the Domar model can therefore be established for the general case in which prices deviate from values. Using the new interpretation it is possible to extend the macro monetary model to the consideration of expanded reproduction in a fully competitive economy. It should be noted that proponents of the new interpretation do not claim that they have solved the transformation problem as such, which is why they view their approach to be an interpretation rather than a solution. However, what their approach does show is that it is possible, at least in principle, to retain Marxian value categories in a general model of money and aggregate demand in a capitalist economy. There is of course a voluminous literature on the transformation problem, and much discussion of how the value-form approach can be extended beyond the confines of the new interpretation. As a project for future research, there is much to be discovered about how different models of transformation relate to the circuit of money.10 The suite of different models of the circuit model could be compared with the suite of transformation algorithms. A common complaint, however, is that the transformation problem is given far too much attention; and perhaps this is why other areas of Marxian economics such as the study of Marx’s forgotten volume of Capital are so ignored. The preceding pages are an attempt to address this imbalance, showing that Marx’s second volume has much to offer as a vehicle for understanding the importance of money and aggregate demand in a capitalist economy.

Appendices

Appendix 1 Author’s source material The book draws material from the following refereed journal articles: Trigg, A.B. (2002) ‘Marx’s reproduction schema and the multisectoral foundations of the Domar growth model’, History of Economic Ideas, X (2): 83–98. Trigg, A.B. (2002) ‘Surplus value and the Kalecki principle in Marx’s reproduction schema’, History of Economics Review, 35: 104–14. Trigg, A.B. (2002) ‘Surplus value and the Keynesian multiplier’, Review of Radical Political Economics, 34(1): 55–65. Trigg, A.B. (2004) ‘Kalecki and the Grossmann model of economic breakdown’, Science and Society, 68(2): 187–205. Trigg, A.B. (2004) ‘Marx and the theory of the monetary circuit’, Research in Political Economy, 21: 143–60.

Appendix 2 Surplus value and the Leontief inverse The result, obtained in Chapter 2, that Marx’s category of surplus value can be identified as a constituent element of the Keynesian scalar multiplier, can also be derived for the Leontief matrix multiplier. Starting with the input–output identity X  AX  hlX  F

(A2.1)

(see equation 2.20), it follows that (I  A  hl)X  F

(A2.2)

such that X  (I  A  hl)1F

(A2.3)

Appendices 103 The relationship between final demand and gross output is specified according to the output matrix multiplier M  (I  A  hl)1. The structure of this output multiplier matrix can be examined by first considering the scalar employment multiplier. Since vQ  lX, the employment multiplier (2.23) can be written as lX  1e vF

(A2.4)

where e is the scalar representing the share of surplus value. In the input–output literature (1/e)v is a type II employment multiplier, closed with respect to households; v  l(I  A)1 is the type I employment multiplier, open with respect to households (see Bradley and Gander 1969). Hence, e is the ratio of type I to type II employment multipliers. It was Olgin (1992) who first pointed out that this ratio happens to be a scalar representing Marx’s category of surplus value. However, Olgin employed a somewhat unwieldy matrix partition method to locate the surplus value term in the output multiplier matrix. An alternative derivation is suggested by substituting (A2.4) into (A2.1) such that X  AX  1e hvF  F

(A2.5)

Hence X  MF

(A2.6)

where M  (I  A)1(I  1e hv)

(A2.7)

The Leontief output multiplier matrix M can be decomposed with the scalar e (the share of surplus value) as a constituent element.

Appendix 3 Structure of the Kalecki reproduction schema The three-sector reproduction schema, explored in Tables 3.2–3.4, can be displayed algebraically, showing more precisely the way in which Kalecki’s interpretation is derived from Marx’s numerical example. Starting with

104

Appendices

Marx’s ex ante schema, as represented in Table 3.2, there are three balancing equations: C1  V1  u1  dC1  dV1  W1 C2  V2  u2  dC2  dV2  W2 C3  V3  u3  dC3  dV3  W3

(A3.1)

Table 3.3, the ex post schema, involves a simple re-arrangement of the elements of each equation such that (C1  dC1)  (V1  dV1)  u1  W1 (C2  dC2)  (V2  dV2)  u2  W2 (C3  dC3)  (V3  dV3)  u3  W3

(A3.2)

In Kalecki’s interpretation (Table 3.4), the equation terms are then grouped according to categories of wages (V* i ) and profits ( P* i ), so that (V1  dV1)  (C1  dC1  u1)  W1 (V2  dV2)  (C2  dC2  u2)  W2 (V3  dV3)  (C3  dC3  u3)  W3

(A3.3)

where V* i  Vi  dVi and P* i  Ci  dCi  ui.

Appendix 4 Surplus value and the interindustry monetary circuit The purpose of this appendix is to clarify the role of surplus value in the interindustry model of the circuit of money in Chapter 4. The elements of the Leontief inverse in W  (I  A†)1F†

(A4.1)

(see equation 4.15) can be written out explicitly in terms of prices as W  (I  P ˆ A丣Pˆ 1)1F†

(A4.2)

It follows, since in matrix algebra (BC)1  C1B1, that W  (P ˆ Pˆ 1  Pˆ A丣Pˆ 1)1F†  (P ˆ 1  A丣Pˆ 1)1Pˆ 1F† P ˆ (I  A丣)1Pˆ 1F†

(A4.3)

Appendices 105 By now writing the coefficient matrix A丣 in terms of its constituent parts, WP ˆ (I  A  hl)1Pˆ 1F†

(A4.4)

Hence, from the decomposition established in Appendix 2, it follows that WP ˆ (I  A)1(I  1e hv)Pˆ 1F†

(A4.5)

The term representing surplus value (e) is a constituent element of the interindustry model of the circuit of money. Therefore, regardless of how prices are defined, the traditional labour embodied definition of surplus value has a role to play in modelling the interindustry circuit of money. This has important ramifications for the transformation problem, for which value-form theorists have suggested a different definition of surplus value, as discussed in Chapter 8.

Appendix 5 The rate of profit and balanced growth Further decomposition of the balanced growth equation (5.12), considered in Chapter 5, is carried out in two steps. First, the structure of ␴ is considered, followed by an examination of e. The analysis draws heavily from Lianos (1979). The structure of ␴ Define C

n2

兺 p1a1j Xj

(A5.1)

j1

and V

n2

兺 p2h2ljXj

(A5.2)

j1

where C refers to the total money value of constant capital and V is the total money value of variable capital. The composition of capital, measured in units of money, can take the form g

C CV

(A5.3)

106

Appendices

Since C

g V 1g

(A5.4)

it therefore follows that dC 

g dV 1g

(A5.5)

For Marx, investment is made up of increments in constant and variable capital. In money terms, I  dC  dV

(A5.6)

Substituting (A5.5) into (A5.6), and re-arranging, we get I

dV 1g

(A5.7)

Finally, this part of the derivation requires the structure of income to be specified such that yVP

(A5.8)

where P is total money profits and y is total money income. If s  P/V (the rate of surplus value) then y  (l  s)V

(A5.9)

dy 1s

(A5.10)

and dV 

Substituting (A5.10) into (A5.7), dy  (1  g)(1  s) I

(A5.11)

Appendices 107 or ␴  (l  g)(l  s)

(A5.12)

The derivation of e Since e is the share of profits in income ( P/y), from (A5.8) e

P  PV  s P  V PV  1 s  1

(A5.13)

The balanced growth equation From (5.12), dy dI y  I  ␭e␴

(A5.14)

Substituting (A5.12) and (A5.13), dy dI s y  I  ␭1  s(1  g)(1  s)  ␭s(1  g)

(A5.15)

It follows that

冢 V P冢 V C  V冣

C CV  s(1  g)  P V CV CV



P CV

冣 (A5.16)

This shows that the money rate of profit for the economy as a whole has the structure r  s(l  g)

(A5.17)

Hence, from (A5.15), the balanced rate of growth equation can be written as dy y  ␭r

(A5.18)

108

Appendices

The balanced growth rate can be specified as the ratio of investment to profits ( ␭ ) multiplied by the money rate of profit (r).

Appendix 7.1 Structure of the Bauer–Grossmann model Using the analytical framework developed by Samuelson and Wolfson (1986: 69–70), the Bauer–Grossmann model, considered in Chapter 7, can be represented by a series of simple equations.1 The first relationship to be specified is that between net income (yt) and variable capital (Vt), where t represents a time subscript. Income consists of variable capital plus surplus value extracted at the rate s: yt  (1  s)Vt

(A7.1)

An initial volume of variable V1 capital grows in each subsequent year at a given rate ␤ such that2 Vt  V1(1  ␤)t  1

(A7.2)

Substituting (A7.2) into (A7.1) yields yt  (l  s)V1(l  ␤)t  1

(A7.3)

Under the assumption of zero savings on the part of workers, a relationship can also be established between the capitalists’ propensity to save out of total income ( ␭*t ) and their propensity to save out of surplus value ( ␭t). With the total savings of capitalists equal to the latter savings propensity multiplied by total surplus value ( ␭t sVt), and total income represented by (A7.1), it follows (with the Vt term cancelling out) that ␭*t 

␭t s 1s

(A7.4)

The standard equilibrium condition that savings equal investment can also be represented by It  ␭*t yt

(A7.5)

where It represents investment. In addition, constant capital in the Bauer model grows at the rate ␣ from an initial value in year 1 of C1. The value Ct

Appendices 109 taken in each year t is Ct  C1(l  ␣)t  1

(A7.6)

Taking investment to be made up of new constant and variable capital3 we can write, using (A7.2) and (A7.6), It  ␣C1(l  ␣)t  1  ␤V1(1  ␤)t  1

(A7.7)

From (A7.5), the savings-investment identity therefore takes the form ␭*t yt  ␣C1(l  ␣)t  1  ␤V1(1  ␤)t  1

(A7.8)

Substituting (A7.4) into (A7.8): ␭t s y  ␣C1(1  ␣)t1  ␤V1(1  ␤)t1 1s t and therefore ␭t 

␣C1(1  ␣)t1(1  s) ␤V1(1  ␤)t1(1  s)  syt syt

(A7.9)

By then substituting (A7.3) into (A7.9), it follows that ␭t 

␣C1(1  ␣)t1(1  s) ␤V1(1  ␤)t1(1  s)  s(1  s)V1(1  ␤)t1 s(1  s)V1(1  ␤)t1

and cancelling out some of the terms, we get ␭t 

␣C1(1  ␣)t1 sV1(1  ␤)

t1

␤  s

(A7.10)

Equation (A7.10) shows how the savings propensity ( ␭t ) is determined by the other parameters of the model. Initial quantities of constant capital (C1) and variable capital (V1) in year 1 are assumed together with a constant rate of surplus value (s). Key to the eventual outcome of the Grossmann table, however, is the assumption that ␣  ␤, that is the rate of growth of constant capital is greater than the rate of growth of variable capital. (A7.10) shows that this steady increase in the organic composition of capital generates a steady increase in the savings propensity until eventually, as Grossmann suggests, it reaches 100 per cent.

110

Appendices

Appendix 7.2 The Kalecki modified model The model specified in Appendix 7.1 can be modified to allow for the modelling of capitalist consumption along the lines suggested by Kalecki. First, the savings-investment identity (equation A7.8) can be modified to include capitalist consumption alongside investment: ␭*t yt  ␣C1(1  ␣)t1  ␤V1(1  ␤)t1  B0(1  ␥)t1

(A7.11)

where ␥ is the rate of growth of the exogenous part of capitalist consumption (B0). After accounting for the requirements of worker consumption and the endogenous part of capitalist consumption, income is allocated in the form of savings to investment in constant and variable capital and a stipulated amount of exogenous capitalist consumption. Following the same procedure as before (Appendix 7.1), by substituting (A7.4) into (A7.11), we get ␭ts y  ␣C1(1  ␣)t1  ␤V1(1  ␤)t1  B0(1  ␥)t1 1s t (A7.12) and therefore ␭t 

␣C1(1  ␣)t1(1  s) ␤V1(1  ␤)t1(1  s)  syt syt 

B0(1  ␥)t1(1  s) syt

(A7.13)

Again following the same procedure as before, by substituting (A7.3) into (A7.13), ␭t 

␣C1(1  ␣)t1(1  s) s(1  s)V1(1  ␤)t1 



␤V1(1  ␤)t1(1  s) s(1  s)V1(1  ␤)t1

B0(1  ␥)t1(1  s) s(1  s)V1(1  ␤)t1

(A7.14)

Cancelling out some of the terms yields the expression ␭t 

B0(1  ␥)t1 ␣C1(1  ␣)t1 ␤   s sV1(1  ␤)t1 sV1(1  ␤)t1

(A7.15)

Appendices 111 In this equation for the capitalist propensity to save, as compared with equation (A7.10), an additional term for capitalist consumption is included. Moreover, following Kalecki’s approach, in which only the exogenous component of capitalist consumption is allowed to vary, the capitalist propensity to save can be modelled as a fixed constant ␭t  1  ␭

(A7.16)

where ␭ is the capitalist propensity to consume out of profits. Examination of (A7.15) reveals that if the savings propensity is now assumed to be exogenous then one of the other previously exogenous components on the right-hand side must be allowed to be endogenous. A case can be made for keeping the initial quantities of constant capital (C1) and variable capital (V1), so as to have the same starting point as Grossmann. Similarly, in order to model the same increase in the organic composition of capital the same rates of growth of constant and variable capital (␣ and ␤) should be assumed. And since B0(l  ␥)t  1 is the exogenous part of capitalist consumption, the only remaining component that can be allowed to vary endogenously is s, the rate of surplus value. Re-arranging equation (A7.15), and substituting for equation (A7.16), it follows that st 

冤

冥

B0(1  ␥)t1 ␣C1(1  ␣)t1 1 ␤ t1 1  ␭ V1(1  ␤) V1(1  ␤)t1

(A7.17)

In this Kalecki modified model the rate of surplus value st is now an endogenously determined variable, with a time subscript t indicating that it varies from period to period, subject to the impact of the Kalecki multiplier 1/1  ␭ conjoined with the investment and personal consumption expenditures of the capitalist class.

Notes

1 Introduction 1 For Evintsky (1963: 159), ‘Marx may truly be considered the forerunner of contemporary economic model-builders for it was he who first demonstrated diagrammatically the complex relationship between the accumulation process and economic growth.’ Similarly, for Krelle (1971: 123), ‘As a matter of fact, growth theory could have started right from these ideas some 70 years earlier . . . ’; and for Ott (1967: 195), ‘Marx already anticipated the principal finding of post-Keynesian growth-theory – the condition of equilibrium economic growth.’ 2 See Oakley (1983). A more recent and highly accessible biography of Marx is provided by Wheen (1999). 3 For a discussion of the problem of user cost in Keynes see Torr (1992). Tsuru (1942) and Fan-Hung (1968) provide a comparison of user cost and constant capital in Marx and Keynes. 2 The multiplier 1 There is some dispute about whether Marx had a fully worked out plan for Capital, under which the reproduction schema would be fully consistent with his Hegelian inheritance. This argument is developed in The Making of Marx’s Capital (1977), a monumental contribution to understanding Marx’s method, whose author, Roman Rosdolsky, was a survivor of Auschwitz. Against this view Turban (1984: 102), a fellow Ukranian, understands ‘Marx’s economic thought as a struggle between different forms of argument in which the dominance of Hegelian methods and philosophical arguments were displaced increasingly by a modern and exact scientific discourse.’ 2 For reasons of simplicity, this non-durability of capital assumption is maintained throughout the book. For a discussion of the role of fixed capital in simple reproduction, see Carchedi and Haan (1995) and Lyall (1985); for expanded reproduction see Glombowski (1976). 3 Notice also that in Table 2.2 the organic composition of capital (the ratio of constant to variable capital) now varies between the two sectors, taking a value of 4 in Department 1 and a value of 2 in Department 2. Under capital mobility, this disparity would undermine the assumed equivalence between prices and values, an issue that was not considered to be important by Marx in his

Notes

4

5 6 7

8 9

10

113

presentation of the reproduction tables. A treatment of capital mobility will also be delayed here until we consider the transformation problem in Chapter 8. This is consistent with an earlier quote from Marx’s Grundrisse, highlighted by Sardoni (1981: 386): ‘. . . this demand, that production should be expanded simultaneously and at once in the same proportion makes external demands upon capital which in no way arise out of itself’ (Marx 1973: 414). For a detailed survey of the literature on Marx and Keynes see chapter 5 of Howard and King (1992). Assuming that capitalists spend 500 on their own consumption, out of 1,000 units of surplus value there are savings of 500 available to meet investment requirements. Zero worker savings will be assumed throughout the rest of this book, for reasons of simplicity. Hence, B is no longer a proxy for worker consumption, as assumed by De Angelis, but is precisely worker consumption. The propensity to consume b is now precisely the ratio of worker consumption to net income. This argument was first made for the one-good case by Trigg (2002a); see Dixon (1988) for a similar interpretation of a two-good model. Hartwig (2004: 323) modifies his structural multiplier to incorporate constant capital. However, the simplicity of the b/1  b structure is not retained. His modification requires new elements in the numerator and denominator. My objective is to incorporate constant capital in the Keynesian 1/1  b multiplier, without losing its simplicity. Although the main purpose of this analysis is to develop the multisectoral structure of the Keynesian multiplier, by implication a contribution can also be made to generalizing the foundations of its structural counterpart. For the two-department case, v  [v1 v2], p  [p1 p2]

and h

冤h0 冥 2

Hence, vh  v2h2  v2B2/L, where B2 is total consumption of good 2, and L is total employment. Since v2  p2 and L  vQ  pQ  y, where y is total net money income, it follows that vh  p2B2/y  b, the ratio of total money consumption by workers to total net income (the propensity to consume). 3 The Kalecki principle 1 Keynes (1936: 32) commented on how the ‘great puzzle of effective demand’ had previously been confined to the ‘underworlds of Karl Marx, Silvio Gesell or Major Douglas’. 2 The expression ex ante should not be confused here with Kalecki’s (1990c) consideration of capitalists’ investment decisions. In relation to the reproduction schema, ex ante refers specifically to the imbalance between row and column sums at the start of the production period. 3 Each of these terms represents an aggregation of elements across departments, such that dC  dC1  dC2  dC3, dV  dV1  dV2  dV3, and u  u1  u2  u3.

114

Notes

4 In terms of the numerical example e  12 and total net income is equal to y  L  3,500. It follows that the total volume of surplus value (see Table 3.5) is calculated by the equation, S  ey  12 3,500  1,750. 5 This provides an alternative to the argument by Fine and Saad-Filho (2004: 66) that in Keynesian theory ‘there is, in Marx’s terms, no role for the production of surplus value and the conflict over this fundamental economic relation’. 6 See Chapter 8 for a full discussion of the transformation problem. 7 There has been considerable debate in recent years about whether concrete labour can become abstract before it is validated in the market place (see Freeman et al. 2004). 4 The monetary circuit 1 Similarly, for Nell (1998: 206), the circuit approach ‘in its contemporary form appears to owe its origin to Marx’; and for Graziani (1989: 2), ‘elements from the Marxian doctrine are surely present in the debates on the monetary circuit’. 2 Marx also considers the possibility that the additional money is provided by an increase in the production of gold. Sardoni (1989) regards this to be a ‘restrictive assumption’ that Marx makes in order to clarify the role of money in the reproduction schemes. ‘Marx himself pointed out that he did not take account of credit and banks in the schemes only for simplicity’s sake’ (ibid.: 215). 3 Several issues with the single swap approach are discussed by Nell (1998: 208–9), including its failure to deal with how productivity improvements might speed up turnover, and its exaggeration of the expense incurred by firms in terms of interest payments. 4 I am grateful to Victoria Chick for suggesting to me this interpretation of the production period, and its contrast with the circuit approach. Thanks are also due to Giuseppe Fontana, and two excellent anonymous referees for Research in Political Economy, for pressing me on this and other points. 5 Nell (2002: 527) has made it clear that the wage bill ‘gradually accumulates in the hands of the firms of the consumer goods sector. It isn’t spent until the production process in capital goods is complete, at which point the entire wage bill will have been paid out and spent’. 6 This is a reproduction of Table 2.4, Chapter 2. 7 This type of scalar multiplier can also be derived from the two-sector Kaleckian schema, as shown by Nell (1988b: 112), although this latter multiplier was not applied specifically to the circulation of money. A possible advantage of equation (4.23), since it is derived from an input–output model, is that it could be easily generalized to an n sector framework. 8 For Moore (1984), this identity between the velocity and the multiplier is unlikely to hold in a real nonergodic economy, where expectations are continually changing. It should be emphasized, however, that Marx’s reproduction schema provides a limiting extreme in which unlikely conditions such as those associated with balanced growth are assumed to hold. 9 In pure circuit theory, the velocity of circulation can be regarded as too orthodox a concept, partly due to the unrealistic quantity theory assumption that it is a stable parameter. However, in an implicit defence of the velocity concept, Graziani (2003: 12) has denigrated the extreme case of an undefined, infinite velocity as being associated with a quasi-barter economy ‘in which money did not exist’.

Notes

115

10 Schmitt (1996: 123) also argues against the narrow Keynesian specification of the multiplier as a model of impacts ‘between the investment sector and the consumption sector’. This is the approach taken by Nell (2004). Following Marx’s definition of investment as increments in constant and variable capital, the multiplier in equation (4.23) is exempt from this criticism, locating increments in both sectors. 5 Money, growth and crisis 1 The paradox of borrowing also has some resonance with this statement by Marx (1981: 640): ‘The final illusion of the capitalist system, that capital is the offspring of a person’s own work and savings, is thereby demolished.’ 2 The first year of the schema was previously shown in Table 2.2, Chapter 2. 3 From equation A5.13 (Appendix 5), the share of surplus value can be written as e

s s1

and hence s

e 1e

4 The elements of r, in year 1 of Table 5.2, are: 5,500 C   0.75862 C  V 5,500  1,750 0.5 e s   1. 1  e 1  0.5 g

Hence r  s(1  g)  0.2414. 5 For Domar, the first two elements of the balanced growth equation represent the propensity to save, ␦  e ␭. The share of profits out of total income (e) combined with the proportion set aside for investment (␭) make up the proportion of income saved (␦). Hence, from the multiplier relationship y  (1/e␭)It, where there is no exogenous capitalist consumption (see equation 5.7), it follows that It  ␦t yt  Savt. 6 There are similarities here between Marx and Minsky, the prominent Post Keynesian, who emphasized the importance of financial fragilities (see Arnon 1994; Crotty 1986). 7 Shoul’s main motivation is to demonstrate the power of Marx’s tendency of the falling rate of profit, which in her view operates even when Say’s Law is postulated, even when questions of demand are assumed away (see Shoul 2000: 28). Further consideration of this issue is provided in Chapter 7, where it is argued that realization problems are in fact central to Marx’s falling rate of profit thesis.

116

Notes

6 Beyond underconsumption 1 On Bleaney’s definition, underconsumptionism is characterized by ‘a persistent tendency towards insufficiency of demand for consumption goods’ (Bleaney 1976, original emphasis). 2 Similarly, Bleaney (1976: 194) points out that Luxemburg clearly identifies the importance of demand for means of production as part of capital accumulation. It is not just demand for consumption goods that is important to capital accumulation: hence ‘the non-underconsumptionist character of Rosa Luxemburg’s ideas’. 3 Tarbuck (1989: 62) argues that the leading Bolshevik economist Bukharin ‘gave us the first fully algebraic exposition of accumulation in the Marxian tradition’. 4 The condition is established by subtracting C1 from both sides of (6.4); or by adding dC to both sides of (6.5) and noting that S1  S2  dVudC. 5 See Chapter 4 for a detailed discussion on the roles played by mutual exchange and the Kalecki principle in Capital, volume 2. 6 Luxemburg (1951: 339) also shows how the problem of demand is accentuated under a rising organic composition of capital. 7 Naqvi (1960: 22) describes this as the ‘false problem of priority of one department over the other’. In the same vein, Luxemburg also considers Marx’s second numerical example in which accumulation ‘proceeds uniformly’ in both departments (Luxemburg 1951: 124). Although this example is less arbitrary, the same problem arises of how Department 2 will acquire the precise amount of additional capital goods produced by Department 1. 8 In chapter 23 of Accumulation, Luxemburg identifies this problem of demand in her critique of Tugan Baranovsky’s disproportionality approach. See Kalecki (1971) for a discussion of this disagreement. 7 The falling rate of profit 1 For example, the entry for constant capital in year 4 is 266,200 instead of Grossmann’s miscalculation of 266,000 (see Howard and King 1989: 334). The numbers shown here are calculated with the advantage of spreadsheet technology. 2 Following the interpretation of the Kalecki principle in Chapter 3, profits and investment are defined in net terms. This approach is consistent with Marx’s category of surplus value, in contrast to the gross definition of profits adopted by Kalecki. 3 Marx argues that ‘it is at least clear that the consumption of the entire capitalist class and the unproductive persons dependent on it keeps even pace with that of the working class’ (Marx 1978: 407). The simulation that follows will show that by making Kalecki’s empirical assumptions capitalist consumption does roughly keep pace with variable capital. 4 The rate of surplus value is now an endogenous parameter, in contrast to its previous status as an exogenous parameter in the Grossmann model. The previously endogenous parameter for the proportion of profits saved is now an exogenous parameter. 5 Comparison of Tables 7.1 and 7.2 shows that autonomous capitalist consumption, in the latter, leads to a lower productivity of labour (W/SV). For example, in year 31 a unit of labour in the Grossmann schema produces 5.05 units of output, compared to only 4.38 in the Kalecki modified schema. Capitalist consumption provides a drag on labour productivity, since more workers are hired to produce

Notes

117

use-values that are not channelled back into the productive process. More output is produced without any additional increment to constant capital. (I am grateful to Cheol-Soo Park for pressing me on this point.) 6 This relationship between luxury goods and surplus value can be distinguished from Marx’s analysis in Theories of Surplus Value part 3, of productivity in the luxury goods department. As is well known, luxury goods do not enter as means of subsistence for workers, and therefore a change in productivity will not impact upon the value of labour power (the denominator of the rate of surplus value). ‘The cheapening of luxury articles does not enable the workers to live more cheaply. He requires the same amount of labour-time to reproduce his labour power as he did previously’ (Marx 1972: 350). However, under the Kalecki principle, if more luxury goods are consumed by capitalists, the labour congealed in these surplus goods can be posited to represent an increase in the mass of surplus value (the numerator of the rate of surplus value). 7 In considering these passages, the 1959 Lawrence and Wishart issue of Capital is cited in order to be consistent with the interpretation of Grossmann (1992). The more recent Penguin issues of Capital are considered otherwise. 8 The transformation problem 1 This approach, also known as the new solution to the transformation problem, was independently developed by Dumenil (1983). 2 In the reproduction tables of Capital, volume 2, Marx allowed variations in the organic composition of capital between sectors alongside a technically incorrect proportionality between prices and values (see Chapter 2). 3 ‘The implication is clear; (S/C  V) is not a significant rate of profit in a capitalist economy, and it does not equal the actual, money, rate of profit’ (Steedman 1977: 30). 4 The importance of money to the new interpretation is examined in relation to money circuits by Bellofiore et al. (2000). 5 Post-multiplying throughout (8.2) by X: pX  (1  r)(pA  phl)X  pAX  phlX  r(pAX  phlX) Since pF  r(pAX  wlX), and under the assumption of zero worker savings phlX  wlX, it follows that pX  pAX  wlX  pF which can be re-arranged to yield (8.7). 6 Under the zero worker savings assumption, total variable capital represents both the total wage bill and total worker consumption (V). Hence, lXw V ␭mw  y  y is the ratio of worker consumption to net income (the propensity to consume). 7 This derivation replicates (3.4) and (3.5), in Chapter 3, with (8.11) replacing (3.4).

118

Notes

8 This derivation can be achieved by substituting (3.8) into (8.11). 9 The new generalized Domar equation (8.16) can be derived by following the steps from (5.7) to (5.12), with (5.7) replaced at the outset by (8.13) – assuming zero autonomous capitalist consumption (B0  0). See Trigg (2002b) for the complete derivation. 10 Notable alternative transformation algorithms have been provided by Moseley (2000), Kliman and McGlone (1999) and Wolff et al. (1984). Appendices 1 A largely presentational difference between this exposition and that of Samuelson and Wolfson (1986) is that we dispense with natural exponentials for the modelling of cumulative growth. In keeping with Table 7.1, in which the schema starts at t  1, the approach taken by Orzech and Groll (1983: 534) is followed, with constants raised to the power t  1. 2 Inspection of year 2 in Table 7.1, for example, shows that with ␤  0.05 and t  2, variable capital is calculated to be 100,000 (1.05)1  105,000. 3 In contrast, Samuelson and Wolfson (1986) exclude variable capital in their calculation of investment. Examination of Table 7.1 shows their calculation to be incorrect. In year 1, for example, total savings of 25,000 are equal to 20,000 investment in additional constant capital plus 5,000 investment in additional variable capital. This approach to modelling investment in Marx’s reproduction schema has been introduced in Chapter 3.

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Index

The Accumulation of Capital (Luxemburg) 63, 64, 68–9 aggregate demand 2–3, 7, 11; role in drive for capital accumulation 4, 63–4, 72–3; role in investment 4, 61; source of demand for capital accumulation 2, 63–4, 68, 72, 73–5, 101 Aznar, E.A. 63 balanced growth 50; and Domar’s growth model 53–7, 61, 67–8, 74; and rate of profit 105–8; role of money in 50 banks: money hoarding 60; role in financing industrial activities 33, 34, 35–6, 37, 53, 62 Baranovsky, Tugan 63, 64, 67 Bauer, O. 5 Bauer model 76, 77–8, 80, 81, 83, 85, 87; structure 108–9 Bellofiore, R. 33, 34, 70 borrowing paradox 4, 52, 53, 57, 58, 60–1, 68, 75, 101, 115 n.1 Brus, W. 26 Bukharin, Nikolai 63, 116 n.3 Bulgakov, S. 64, 67 Capital (Marx) 1–2, 6, 7, 10, 19, 21, 24, 30, 32, 38, 47, 50, 60, 63, 64, 70, 75, 77, 87, 89, 101, 112 n.1 capital accumulation 4, 63–4; Luxemburg’s 2, 68–73, 116 n.2; source of money and demand for 73–5, 101

capitalist consumption: Grossmann breakdown theory 5, 76, 77–80, 81, 99; Kalecki modified model 83–5, 110–11 capital outlays: and sales 50–3 Cartelier, J. 24 Chakravarty, S. 6 Clarke, S. 31 commodities 30; circulation 4, 6–7, 41–2; exchange between producers 69–70; use-value 30–1 constant capital 4, 7, 16, 34, 69–70, 113 n.9 credit 4, 60, 75 Crotty, J.R. 57–8, 59 Cullenberg, S. 76 De Angelis, M. 13, 14, 113 n.7 De Brunhoff, S. 51, 60 Deleplace, G. 35 Desai, M. 64 De Vivo, G. 17 Dillard, D. 2 disproportionality 63, 64–8, 76, 101; proportionality 15, 67 Domar, E.D. 57 Domar’s growth model 4, 53–7, 61–2, 67–8, 74; multisectoral foundations 4, 100–2; relevance to Marxian crisis theory 5; borrowing paradox 58, 60, 61, 68 Dumenil, G. 95, 117 n.1 economic growth theory 1, 50, 112 n.1; see also balanced growth

128

Index

Engels, Friedrich 2, 6, 89 exchange-value 30–1, 64, 65 expanded reproduction 4; algebraic terms 18–20; input–output format 17–18, 41, 66–7; Marxian numerical examples 10–11, 22, 42, 56; role of Kalecki principle in relation to money circulation 25–6; role of money 50–3, 57; and surplus value 72 falling rate of profit 3, 76, 80, 85, 86–8, 115 n.7; and technical progress 5, 76 Finance Capital (Hilferding) 68 Foley, D.K. 3, 64 Foley’s model of monetary circuit 50–3, 56, 57, 58 Foley’s transformation problem 58, 89–90, 95, 96 free competition 5, 90 Gilibert, G. 16 Graziani, A. 114 n.1, 114 n.9 Graziani model of money circulation 33–5, 37, 47–8 Grossmann, Henryk 3, 4, 5, 76 Grossmann’s law of capitalist breakdown 5, 76, 77–80, 81, 99 Harris, D.J. 65 Harrod’s growth model 4, 53 Hartwig, J. 15, 113 n.9 Hegel, Georg Wilhelm Friedrich 6 Hein, E. 57 Hilferding, R. 5, 63, 64, 68–9 Howard, M.C. 64, 68, 71, 76, 90 input–output analysis 4, 7, 16–18, 27, 30, 41, 44, 66–7, 97, 103 inventories 41–3, 51 investment: difference between Marx and Kalecki 26–8; dual role 61–2, 74; importance of aggregate demand in 4, 61 Jacoby, R. 76 Kalecki, Michal 3–4, 21, 26; silence on labour theory of value 26 Kalecki multiplier 28–30, 83, 99, 111

Kalecki principle 4, 21, 22–4, 71, 74, 76, 77, 81–2, 117 n.6; input–output approach 27–8, 29–30; role in money circulation 24–6, 33, 35, 36, 43, 87, 97; and value-form 30–2, 98 Kenway, P. 8 Kerr, P. 26 Keynes, John Maynard 1, 4, 12, 15, 21 Keynesian multiplier 3, 7, 11–16, 19–20, 28, 29, 49, 55, 57, 98, 99, 113 n.9 King, J.E. 64, 68, 71, 76, 83, 90 Kotz, D.M. 73 Kuhn, R. 76 Kurz, H.D. 16 labour theory of value 89; Kalecki’s silence on 26; new interpretation 94–6; relation to monetary circuit 90; Sraffian critique 30, 31, 94–5 Laibman, D. 77 Lee, F.S. 29 Leontief, Wassily 16, 17, 32, 102 Leontief inverse 44; and surplus value 102–3 Leontief’s input–output analysis see input–output analysis Lianos, T.P. 12 Luxemburg, Rosa 4, 5, 26, 63; and capital accumulation 68–73, 116 n.2; critics 64; critique of Marx 2, 63–4, 68, 72, 101 luxury goods 51, 85, 117 n.6 macro monetary model 5, 46–9, 53, 64, 74; generalization under price-value deviations 89–90, 96–101 Malthus, T.R. 63 Mandel, E. 6, 65 Marx, Karl 1, 6, 21, 29, 30, 50, 89, 112 n.1; Luxemburg’s critique 2, 63–4; refutation of Say’s Law 58, 62 Marxian crisis theory 3, 5, 57–62, 67; relevance of Domar model 5; possibility theory 5, 59 ‘Marxian principle’ 35 Marx’s category of surplus value 39–40, 85; relation to multiplier structure 12, 14, 20 Mitchell, W. 58–9 Miyazawa, K. 30

Index 129 Mohun, S. 96 monetarism 33 monetary circuit 3, 4, 70–3, 97; in expanded reproduction 25–6, 50–3; Franco-Italian circuitist school 4, 33, 49, 97; Graziani model 33–5, 37, 47–8; macro monetary model 5, 46–9, 53; Marxian alternative 39–46; Nell’s mutual exchange model 37–9, 41, 48; role in balanced growth 50; simple reproduction 24–5, 51; single swap approach 36–7, 40, 47–8, 52, 57, 114 n.3 money: as means of payment 59–60; opposition to commodity theory of money 33–4; source of money for capital accumulation 73–5, 101; value-form tradition 30–2 money hoards 25, 51, 53, 60; drain of 52 mutual exchange 9, 11, 37, 38, 41, 45, 48, 65, 71, 74, 97, 116 Moore, B.J. 47, 114 n.8 Morishima, M. 3 Moseley, F. 10 multiplier 3, 5, 11–12, 47, 52, 58, 61, 113 n.9, 114 n.7, 8, 115 n.5, 10; and transformation problem 97–100; see also Kalecki multiplier; Keynesian multiplier Nell, E.J. 35, 45, 114 n.1, 114 n.5, 115 n.10; critique of single swap approach 36–7, 114 n.3 Nell’s mutual exchange model of monetary circuit 37–9, 41, 48, 97 Pollin, R. 57 production: mutual exchange between departments of 38, 45, 65–6, 74; of value 6–7, 8 Quesnay, Francois 7, 42 Realfonzo, R. 33, 34 reproduction schema 1, 2–3, 6, 7–12, 20–4, 28, 33, 41, 53–7, 63, 65–6, 69–71, 76–7, 84–5, 89–90, 94, 96, 103–4 Reuten, Geert 6, 21, 31

Ricardo, D. 10, 58 Robinson, Joan 2, 74, 85 Rosdolsky, R. 67, 112 n.1 Saad-Filho, A. 30, 114 n.5 sales: and capital outlays 50–3 Salvadori, N. 16 Samuelson, L. 80, 108, 118 n.1 Sardoni, C. 21, 27, 114 n.2 Say’s Law 58, 61–2, 101, 115 n.7 Schmitt, B. 48, 115 n.10 Sebastiani, M. 26 Seccareccia, M. 33, 35, 52 Seton, F. 94 Shoul, B. 61, 62, 115 n.7 simple reproduction 8–10, 11; amount of money required for circulation 51; disproportionality 64–6, 67; role of Kalecki principle in relation to money circulation 24–5; and surplus value 71–2 single swap model of monetary circuit 36, 40, 47–8, 52, 57, 97 Sismondi, J.C.L. de 63 Smith, Adam 7, 10, 12, 16, 69, 70 social wage rate 13–14 Sraffa, P. 16–17 Sraffian critique of labour theory of value 30, 94–5 Sraffian price equation 94–5, 96, 97–8 Steedman, I. 29, 31, 94, 95 surplus value 8–9, 69, 70, 78, 80, 115 n.2; and expanded reproduction 72; in interindustry monetary circuit 104–5; and Kalecki principle 26–8, 39–40; and Leontief inverse 102–3; and simple reproduction 71–2 Sweezy, P.M. 94 technical progress: and falling rate of profit 5, 76 theory of crisis, Marxian see Marxian crisis theory transformation problem: Foley’s 58, 89–90, 95, 96; Marx’s 5, 89, 90–4 Tsuru, S. 2 underconsumption 63–4, 76, 101, 116 n.1 use-value 30–1

130

Index

value-form 30–2, 95 variable capital 69, 70, 78, 80 velocity of circulation 47–8, 97, 114 n.9 von Bortkiewicz 94

Williams, M. 31 Wilson, Harold 2 Winternitz, J. 94 Wolfson, M. 80, 108, 118 n.1

Walras, Leon 3 Watts, M. 58 Weeks, J. 76

Yaffe, D.S. 85 Zarembka, P. 6, 72, 74

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