Andrew Trigg-Marxian Reproduction Schema (Routledge Frontiers of Political Economy) (2006)

Marxian Reproduction Schema

In 1878 Karl Marx developed the reproduction schema: his model ofhow total capital is produced and reproduced. This is thought to be the firsttwo-sector economic model ever constructed. Two key aspects of Marx’swritings are widely agreed to be undeveloped: the role of aggregate demandand the role of money. This book has as its aim the synthesis of variousstrands of economic thought in an attempt to understand and clarify thestructure of the reproduction schema. This synthesis will challengeprevailing orthodoxies.

A macro monetary model is constructed which draws on a wide range ofeconomic theories, both within the Marxian economic tradition and furtherafield in the traditions of Keynes, Kalecki, Domar, Sraffa and Leontief.Marxian economics has been dominated by supply-side thinking, includinggeneral equilibrium theory and pronouncements about the shortage ofsurplus value. Post Keynesians have failed to take seriously the importance ofreproduction and the multisectoral structure of capitalism. By locatingaggregate demand and the circuit of money in the reproduction schema, theobjective of this book is to provide an analytical contribution to bothMarxian and Post Keynesian economics.

A.B. Trigg is Senior Lecturer in Economics at the Open University, UK.

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78 Marxian ReproductionSchemaMoney and aggregate demand in a capitalist economyA.B. Trigg

Marxian Reproduction SchemaMoney and aggregate demand in acapitalist economy

Andrew B. Trigg

First published 2006by Routledge2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

Simultaneously published in the USA and Canadaby Routledge270 Madison Ave, New York, NY 10016

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© 2006 A.B. Trigg

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 writingfrom the publishers.

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Contents

List of illustrations xiAcknowledgements xii

1 Introduction 1

2 The multiplier 6

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

3 The Kalecki principle 21

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

4 The monetary circuit 33

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

5 Money, growth and crisis 50

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

6 Beyond underconsumption 63

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

7 The falling rate of profit 76

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

8 The transformation problem 89

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

Appendices 102Notes 112Bibliography 119Index 127

x Contents

Illustrations

Figures

7.1 The rate of profit in the Kalecki simulation 867.2 Components of the rate of profit in the Kalecki simulation 86

Tables

2.1 Marx’s simple reproduction schema 92.2 Marx’s expanded reproduction schema 112.3 Locating the multiplier in Department 1 122.4 Expanded reproduction in an input–output table 173.1 The allocation of surplus value in the two-sector schema 223.2 Ex ante three-sector reproduction schema 223.3 Ex post three-sector reproduction schema 233.4 Kalecki’s interpretation of the three-sector schema 233.5 An input–output interpretation of the three-sector schema 274.1 Two-sector Kalecki schema 354.2 Two-sector Marxian reproduction schema 404.3 Expanded reproduction in an input–output table 414.4 Inventories in the reproduction schema 424.5 Composition of money outlays 434.6 Money circuits in the current production period 455.1 Marx’s expanded reproduction schema 545.2 Rates of growth in Marx’s reproduction schema 566.1 Simple reproduction schema 656.2 Simple reproduction in an input–output table 666.3 Expanded reproduction in an input–output table 677.1 Grossmann’s reproduction schema 797.2 Kalecki modified reproduction schema 848.1a Marx’s calculation of prices (physical categories) 908.1b Marx’s value calculation 918.1c Marx’s price calculation 93

Acknowledgements

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

1 Introduction

It may be hard to imagine that the origins of macroeconomics, as we knowit today, came from a German revolutionary, exiled to England and ignoredby the economic establishment. In 1878, working for the last time on hisgreat writing project, Capital, Karl Marx developed the reproductionschema: his model of how total capital is produced and reproduced. This isthought to be the first two-sector economic model ever constructed, withtwo great departments producing means of production and means ofconsumption. Not only did this model capture the division betweenconsumption and investment that later became the centrepiece of Keynes’sGeneral Theory (1936), it went beyond the short-term focus of Keynes toexplore the structure of economic growth. Marx has thus been described asthe forerunner of macroeconomic growth theory.1

As with all great works, a common complaint is that they are neverproperly read in the original. Marx’s Capital is no exception. After thepublication of volume 1 in 1867 – the only part which Marx was able tofinish – his wife, Jenny, complained:

You can believe me that seldom has a book been written under moredifficult circumstance, and I could write a secret history that woulduncover an infinite amount of worry, trouble and anxiety. If the work-ers had an inkling of the sacrifice that was necessary to complete thework, written only for them and in their interest, they would perhapsshow a bit more interest.

(McLellan 1973: 353)

Of course, for those who manage to make it through the material, Capitalis a work of art: a masterpiece exposing the vagaries of unbridled capital-ism. But even leading figures in the labour movement have found this astruggle. On receiving the first volume, a trade union colleague of Marx

‘felt like a man who had been given an elephant and did not know what todo with it’ (ibid.: 353). Similarly, the British Labour Prime Minister, HaroldWilson, admitted that he had not got past the first page. The reason mayhave been as identified by Marx’s lifelong collaborator, Friedrich Engels, inhis comment that Marx started the volume with the most difficult chapters,continually interrupted the flow with extensive examples and failed tosummarize its purpose and direction.2

If the first volume of Capital is difficult to absorb, the reader of thesecond volume, where the reproduction schemes are located, faces an evengreater challenge. Due to the unfinished form of the material, which Engelsassembled 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 fromtwo treatments of the problems by two different models’ (quoted inZarembka 2000: 197).

Commenting on the unfinished state of the second (and third) volumesof Capital, Joan Robinson warned, ‘The waters are dark and it may be thatwhoever peers in them sees his own face’ (Robinson 1968: 111). From thesemurky waters, a host of different models and perspectives have emerged.In the absence of any clear statement of the purpose of the reproductiontables, there is no agreement as to what they are for, how they relate to therest of Capital, volume 2, and how they relate to Capital as a whole. ForTsuru (1994: 191), ‘Participants in the discussion . . . concretized the origi-nal simple tableau of Marx in whatever way most suited for their respectiveconclusions.’

One of the greatest schisms in political economy, since the early part of thetwentieth century, is over the role played by aggregate demand in the repro-duction schema. Where, argued the fiery Rosa Luxemburg, does the demandcome 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 nodoubt this kind of “accumulation” can continue ad infinitum, just as long, thatis 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 aggregatedemand as a constraint on expanded reproduction. I will develop an analy-tical model which explores the conditions under which profits can be real-ized in the reproduction schema. This approach is in keeping with the spiritof Dillard’s (1984: 425) statement that ‘Marx’s economics would bestrengthened by a more formal treatment of the theory of effective demand.’

For daring to criticize Marx, Luxemburg was labelled a heretic, failing toproperly 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

2 Introduction

Marx’s falling rate of profit, which he presented in Capital, volume 3.It was argued by Henryk Grossmann that capitalism is vulnerable tobreakdown because of the falling rate of profit tendency. This theory ofcrisis has become the standard canon of the far left; for supply-side Marxistsit provides a bulwark against the (reformist) Keynesian aggregate demandapproach. Marx’s reproduction tables, though used to illustrate theGrossmann breakdown scenario, have been downplayed as a mere interlinkingdevice between first and third volumes of Capital.

In the universities, a mathematical strand of supply-side Marxism hasevolved that is closer to mainstream general equilibrium theory. Notably,for Morishima (1973: 105), ‘Marx’s models are very similar to Walras’ inmany aspects: Marx’s scheme of simple reproduction, or reproduction onthe same scale, corresponds to Walras’ static general equilibrium system ofproduction . . . ’ Aggregate demand has hardly any role to play in thismicroeconomic approach.

Furthermore, a major shortcoming of the supply-side Marxists is theirfailure to consider the importance of money. In Brody (1974: 9), for exam-ple: ‘Theories of money . . . are not discussed, although a parallel mathemat-ical approach to them is much needed and indeed within reach’ (see alsoRoemer 1978). The problem is that money is essentially neutral in generalequilibrium models, a characteristic more appropriate to a barter economythan to capitalism. And in the Grossmann falling rate of profit thesis, moneyis stripped from the reproduction schema despite its central importance toCapital, volume 2.

The second main purpose of this book is to develop an alternative inter-pretation of the reproduction schema in which money plays a key role.Some degree of formalization is required here with respect to circulation ofmoney, 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 thecirculation of money intertwines with the reproduction of commodities.

At the heart of this contribution to Marxian economics is an analyticalframework for modelling aggregate demand in which a Keynesian multi-plier is nested in the schema. Every economics student is taught that eachpound of investment has a multiplied effect on total income. Lianos (1979)has shown how the multiplier relationship between income and investmentcan be modelled in one of Marx’s departments of production. My specificanalytical contribution is to generalize this insight to the full multisectoralstructure of Marx’s tables, without losing the simplicity of the scalarKeynesian multiplier.

The key role of money in the reproduction process is addressed by usingsome of the insights provided by Michal Kalecki. He was schooled in the

Introduction 3

rich vein of Polish Marxism at the start of the twentieth century – bothLuxemburg and Grossmann were Polish – but became famous as the econ-omist who discovered the rudiments of the General Theory before Keynes(or so it is claimed). Like Keynes, Kalecki emphasized the importance ofaggregate demand for investment as the driving force of a capitalist econ-omy. In a rudimentary model of the circuit of money, capitalists cast moneyinto circulation as aggregate investment, and this returns back to them asprofits. This is the Kalecki principle: that capitalists earn what they spend.A key starting point for considering the relationship between the Marxian andKeynesian traditions is Kalecki’s demonstration of how this macroeconomicprinciple works in the context of Marx’s reproduction schema.

Armed with the multiplier and the Kalecki principle, a potential contri-bution can also be made to Post Keynesian economics, in which there hasbeen a tendency to take money seriously, but not reproduction. AlthoughKeynes himself developed a two-sector model, he had great problems deal-ing with user cost – defined as constant capital in Marxian categories.3

How all capital is reproduced under capitalism has become a side issue forKeynesians, often by resorting to a one-sector framework. Similarly, theFranco-Italian circuitist school has focused on the circuit of money with-out paying any attention to the reproduction of commodities. Flows ofmoney between banks, firms and consumers are modelled without consid-ering the relationship between sectors of production. The money circuithas been given prominence without due attention paid to the circuit ofcommodities.

In addition, the importance of money and aggregate demand can be car-ried through to the modelling of expanded reproduction over time. It is wellknown in economic growth theory that the Harrod–Domar model has aclose affinity to Marx’s reproduction model. For Kuhn (1979: 40), ‘theMarxian growth model, in the framework of an essentially unstable econ-omy, has anticipated the important conclusions of the Harrod–Domaranalysis.’ However, it is not so widely known that money has a key role toplay. There is a paradox of borrowing, in which capitalists have to securecredit for expanded reproduction to take place. Coupled with the key roleof aggregate demand in the drive for capital accumulation, the Marxiangrowth model provides a powerful tool for highlighting the stringentconditions 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 multisectoralreproduction schema, with the multiplier and the monetary circuit as thekey building blocks. These building blocks are defined using Leontief’sinput–output analysis, a model which has its origins in the Marxianeconomic tradition.

4 Introduction

Finally, this analytical framework is used to cast light on the Marxiantheory of crisis. Once money and demand are taken seriously, the repro-duction schema provide the basis for Marx’s possibility theory of crisis; hisdemonstration of the likelihood of economic crises taking place. Theanalytical precision provided by the Domar interpretation provides aplatform for interpreting some of the great controversies of twentieth-century 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 thereproduction schema in Chapter 2 to the Kalecki principle in Chapter 3 anda detailed consideration of the circuit of money in Chapter 4. Having builtup a macro monetary model of the reproduction schema, in which bothmoney and aggregate demand are featured, Chapter 5 derives the Domargrowth model from these analytical foundations. The relevance of thisgrowth model to Marxian theories of crisis is explored and furtherdeveloped in Chapter 6.

A subtext of this analysis is an attempt to address some of the limitationsof the reproduction schema. Two main limitations of the schema, asmodelled in Chapters 2–6, are the absence of free competition, based onthe mobility of capital, and the lack of any room for technical progress.Chapter 7 examines the Grossmann model of how technical progress drivesthe tendency of the falling rate of profit. And in Chapter 8, free competi-tion is considered by turning to Marx’s famous transformation problem; aproblem that has dominated discussions in Marxian economics.

This analysis draws on a wide range of economic theory, both within theMarxian economic tradition and further a field in the traditions of Keynes,Kalecki, Domar, Sraffa and Leontief. In the same way that Marx was opento the whole corpus of classical economics in the nineteenth century, thisbook has as its aim the incorporation of various strands of economicthought in an attempt to understand and clarify the structure of thereproduction schema.

Introduction 5

2 The multiplier

When first embarking on his study of economics, in 1851, Marx wrote toEngels, ‘I am so far advanced that in five weeks I will be through with thewhole economic shit’ (McLellan 1973: 283). As it turned out, he was tospend the next twenty-five years in the British Museum Library, defining awhole school of thought: the school of classical economics.

At the end of this journey, the Marx who worked up the second volumeof Capital, in the late 1870s, was not the young philosopher engaged inHegelian metaphysics. Of course, Marx’s philosophical background to someextent explains how his critique of classical economics developed. ForChakravarty (1982: 13), ‘Marx’s early philosophical interest did providehim with the basic insight that any particular socioeconomic formationshould not be viewed as an eternal category but a transient arrangement . . . ’But for Zarembka (2000: 188), ‘Marx’s mature work in political economyis not dependent upon Hegel and dialectics.’ Indeed, for the prominentHegelian Marxist, Geert Reuten, referring to the passages where Marxdevelops his reproduction tables, ‘the text is not systematic-dialectical’(Reuten 1998: 223, original emphasis).1 Even for Reuten, the reproductionschema is best understood as a conventional model, of the kind used inmodern economics.

The purpose of this chapter is to examine two main aspects of Marx’sreproduction model. The first concerns the way in which sales ofcommodities 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 volume2 the market place is introduced. For Mandel (1978: 14), in his introductionto the Penguin edition of volume 2, ‘we have to understand the inner connectionbetween the production of value and its realization.’ Commodities have to besold, whether wage goods purchased by workers or means of production pur-chased by other capitalists. Reproduction can only take place if in aggregate

the value produced is matched by aggregate demand. Drawing upon somerecent Marxian contributions, the role of the Keynesian multiplier can beconsidered as a way of formalizing the role of aggregate demand. In addi-tion, the production of value is represented in the structure of this multiplierby considering the role of Marx’s value categories.

Now economists are very fond of diagrams, and one of the few diagramsMarx ever used was to summarize Quesnay’s Tableau Economique (Marx1969a). Quesnay was the doyen of the physiocrats, who thought that landwas the source of all value; hence the tableau shows the circulation of com-modities between farmers and landlords. As shown by Pressman (1994),Marx shaped this model into his reproduction schema: a model of howcommodities circulate between capitalists and workers. For Marx (1969a:344), the tableau ‘was an extremely brilliant conception, incontestably themost brilliant for which political economy had up to then been responsible’.

Marx regarded work, after Quesnay, by major figures in classical eco-nomics such as Adam Smith, as ‘retrogression’ (Marx 1978: 436). Quesnaywas 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 cap-ital outlays on machinery and raw materials – what he refers to as constantcapital. This is the second aspect of Marx’s model considered in this chap-ter. Using Leontief’s input–output analysis, the role of constant capital canbe formalized using a multisectoral multiplier. Moreover, the unique ana-lytical contribution of this chapter is to derive a scalar Keynesian multiplierfrom these multisectoral foundations.

Marx’s reproduction schema

In chapter 20 of Capital, volume 2, Marx sets out the task of establishinghow the total social capital can reproduce itself. A renewal is required of allelements of means of production such as raw materials and machinery thatare used up in the production process. In addition, both the working classand the capitalist class have to be maintained such that the required amountof consumption goods is produced each year. Marx writes:

The immediate form in which the problem presents itself is this. Howis the capital consumed in production replaced in its value out of theannual product, and how is the movement of this replacement inter-twined with the consumption of surplus-value by the capitalists and ofwages by the workers?

(1978: 469)

The multiplier 7

Or in other words, ‘will the level of aggregate demand generated by anylevel of output be sufficient to purchase the whole of that output?’ (Kenway1980: 33). This, Kenway argues, is the issue ‘confronted by Marx in thesecond volume of Capital and in particular, in chapter twenty’ (ibid.: 33).

An analysis which focuses mainly on individual commodities, asconducted by Marx in much of Capital, volume 1, would not be worthy ofsuch close attention to the type of commodities produced. It would notmatter ‘whether it was machines or corn or mirrors’ (Marx 1978: 470). In apartial analysis of individual commodities, the theorist can concentratespecifically upon the production of value. For each individual commodity,an assumption can be made that it will be sold in the market place and thatelements of the commodity used up in production will be replaced. But forMarx, ‘this formal manner of presentation is no longer sufficient once weconsider the total social capital and the value of its product’ (ibid.: 470).The reproduction of the total social capital requires a consideration of boththe value and the use-value of an individual commodity, the use for whichit is required in the economic system.

Marx therefore develops a macroeconomic approach to establishing theconditions under which the economic system can reproduce itself; one inwhich individual commodities are both produced and sold in the marketplace. To achieve this task, Marx collects industrial activities into two greatdepartments 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 variablecapital (Vi) consumed by workers, and are also consumed by capitalists outof the surplus value (Si) extracted from the production process. As a start-ing point for this analysis, Marx assumes that capitalists consume all oftheir surplus value. Hence, the system does not grow, since none of the sur-plus is set aside for capital expansion. All available resources are devotedto either consumption or the renewal of constant capital. This is the case ofsimple reproduction.

It may be objected that simple reproduction is ‘an assumption foreign tothe capitalist basis’ (ibid.: 470), since real capitalist economies are gener-ally characterized by capital expansion. However, Marx argues that evenunder capital accumulation ‘simple reproduction still remains a part ofthis’ (ibid.: 471). The process of renewal that takes place under simplereproduction is an integral part of the more complicated process ofexpanded reproduction, and allows us to see more clearly its componentparts.

Table 2.1 shows the first empirical example used by Marx (1978: 473) toillustrate simple reproduction. Department 1 is assumed to produce non-durable outputs that are used up as constant capital during a single period

8 The multiplier

of production.2 In addition, Marx assumes that prices are equivalent tovalues. ‘Moreover, we assume not only that products are exchanged at theirvalues, but also that no revolution in values takes place in the componentsof the productive capital’ (ibid.: 469). It is therefore possible to interpret theunits 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 rightat the end of the book, retains this unrealistic assumption of equivalencebetween prices and values. This is in keeping with Marx’s theoreticalapproach, in which there is much to be understood about the reproductionschema before introducing additional layers of complexity such asprice–value deviations.

Marx also assumes the rate of surplus value (the ratio of Si to Vi) is thesame in both departments. In Department 1, for example, 1,000 units ofvariable capital are employed at a rate of surplus value of 100 per cent,which generates 1,000 units of surplus value. Each worker performs anhour of labour for himself and an additional hour for the capitalist. The totalamount of living labour performed (2,000) is added to the amount ofconstant capital (4,000) used up, to give a total value produced inDepartment 1 (W1) of 6,000. Similarly, Department 2 uses 2,000 units ofconstant capital, 500 units of variable capital, and extracts 500 units ofsurplus value to yield a total value (W2) of 3,000. The general formula forcalculating 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 2exchanges 2,000 units of its output of consumption goods for 2,000 units ofmeans of production produced by Department 1. These 2,000 units of con-sumption goods fulfil the variable capital (1,000) and capitalist consump-tion (1,000) requirements of Department 1. And the 2,000 units of meansof production supplied by Department 1 allow capitalists in Department 2to replace used-up constant capital. Reproduction is facilitated by mutualexchange between the two departments.

Second, the other 4,000 units of means of production, produced inDepartment 1, are required to replace used-up constant capital inDepartment 1. In Department 2, the 500 units of variable capital and 500units of surplus value are also produced and used up in Department 2 by its

The multiplier 9

Table 2.1 Marx’s simple reproduction schema

Ci Vi Si Wi

Dept. 1 4,000 1,000 1,000 6,000Dept. 2 2,000 500 500 3,000

6,000 1,500 1,500 9,000

own workers and capitalists. Here, individual departments reproduce theirown requirements of production and consumption.

Marx therefore shows how the total output of 9,000 units can be repro-duced, 6,000 units as means of production and only a third, 3,000 units, asconsumption goods. In contrast to the approach taken by Adam Smith, whodoes not allow for means of production, a demonstration is provided of howmeans of production take up a significant part of the national product.

Yet Adam Smith put forward this fanciful dogma, which is stillbelieved to this day . . . according to which the entire value of the socialproduct 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 thesame error, the contribution of the schema being to show how total socialcapital, with constant capital a constituent part, can be reproduced.

Whereas Moseley (1998: 160) has argued that the refutation of AdamSmith is the ‘most important immediate purpose of Marx’s reproductiontables’, others, as we have seen, emphasized their importance in addressingthe issue of how surplus value is realized. The key role of consumption isillustrated sharply by the scheme of simple reproduction, since all of thesurplus 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 drivingmotive of the individual capitalist, this surplus-value – no matter whatits proportionate size – can be used here, in the last analysis, only forhis individual consumption.

(Marx 1978: 487)

Although under expanded reproduction surplus value is directed to moreproductive uses, Marx argues that the underlying role of consumptionunder simple reproduction is still a key part of the process of expandedreproduction.

The most developed expanded reproduction schema is referred to byMarx 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 numbersrepresenting a modification of the simple reproduction table. The sameassumptions are maintained as under simple reproduction, apart fromrelaxation of the restriction that all surplus value be allocated to capitalistconsumption.

10 The multiplier

The key difference is that Department 1 produces 6,000 units of capitalgoods, but only 5,500 are required to replace constant capital in the twodepartments.3 Department 2 now requires 1,500 units of capital goods inorder to replace the amount it uses up. But Department 1 continues to pro-duce a surplus of 2,000 units of capital goods (equivalent to 1,000 variablecapital plus 1,000 surplus value) over and above the 4,000 it needs to replaceconstant capital. Therefore, the mutual exchange that took place between thetwo departments under simple reproduction, where surplus consumptiongoods were swapped for surplus capital goods, is only partially fulfilled.Marx (1978: 587) explains that in each period of production the surplus ofcapital goods produced by Department 1 ‘remains to be realized’.4

This additional demand is satisfied by capitalists, from both departmentsof production, requiring 500 additional units of constant capital in the nextperiod of production. Hence there is an aggregate demand for capital goodsthat enables surplus value to be realized. Since a key objective of Marx’sreproduction schema is to show how the total social capital can be repro-duced, the analysis that follows concentrates specifically upon the aggre-gate (macroeconomic) interpretation of the schema. The emphasis at thisstage is upon highlighting the aggregate categories and main economicrelationships that can be established. As the analytical complexity unravels,more attention will be given to the component parts of the system andrelated structural issues.

The Keynesian multiplier

This emphasis on the importance of aggregate demand suggests amultiplier relationship. In Keynesian terms, the aggregate demand forcapital goods produced by Department 1 can be defined as investmentdemand. Since this demand provides for future expansion of means ofproduction, in the current period of production it can reasonably beassumed to be exogenous, not dependent upon any current parameters orconstraints. The multiplier provides a possible way of capturing thestructural relationship between investment demand and the aggregateincome of the economy.

The multiplier 11

Table 2.2 Marx’s expanded reproduction schema

Ci Vi Si Wi

Dept. 1 4,000 1,000 1,000 6,000Dept. 2 1,500 750 750 3,000

5,500 1,750 1,750 9,000

In the large body of work that has explored the relationship between thesystems of Marx and Keynes,5 there is no established understanding of therole played by the multiplier. This can be illustrated by some of the morerecent attempts to interpret the multiplier from a Marxian perspective. Twomain topics of concern are (1) the role of the multiplier in the reproductionschema; and (2) the way in which Marx’s category of surplus value relatesto the structure of the multiplier. The following brief consideration of thisrecent literature provides the backdrop to a full critique, in which some ofits limitations will be addressed.

Lianos (1979) provides an accessible insight into how the multiplier canbe located in the reproduction schema. By focusing specifically uponDepartment 1 he states, ‘it is convenient to assume a one sector economy’(ibid.: 407). Only information from Department 1 of the example used byMarx (Table 2.2) is included in the Lianos reproduction schema, as shownin Table 2.3. The key modification which enables a translation to Keynesianeconomic categories is to interpret all value added, variable capital plussurplus value, as net income (Y1) for Department 1. Assuming away forthe moment the problems associated with Adam Smith’s dogma, thisincome is net of constant capital. The net income of the one-good economyis 2,000, consisting of 1,000 units of variable capital and 1,000 units ofsurplus value.

A distinction is also made between the current period of production(period 1) and the subsequent period of production (period 2). The aggre-gate investment demand of 500 is explicitly shown as relating to the expan-sion of means of production in period 2. This is net investment, additionalto the replacement of means of production used up in period 1.

An analytical leap can now be made that provides the cornerstone of therest of this book. Located in this reproduction schema is a Keynesianmultiplier that enables a relationship to be specified between net investmentand net income. The intuition runs as follows. Capitalists anticipatethat they will expand their constant capital by 500 in the next period ofproduction. There is therefore a net investment demand for 500 units of out-put to be produced in the current period.6 Workers are hired to produce this

12 The multiplier

Table 2.3 Locating the multiplier in Department 1

Periods Constant Variable Surplus Net Netcapital capital value income investment(C1) (V1 ) (S1 ) (Y1 ) (I1 )

1 4,000 1,000 1,000 2,0002 500

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 ofthe 500 units of investment multiplies throughout the economy, creatingfour 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’sexpanded reproduction schema.

Having nested the multiplier in the reproduction schema, some attentioncan be given to its structure. As a starting point, the Keynesian incomemultiplier takes the form

(2.1)

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

y � �L (2.2)

where � represents labour productivity (y/L) and L is a measure oftotal labour in hours of work. It follows that the employment multiplierrelationship

(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 profitper hour. Note that if B is the money value of total consumption we canwrite

(2.4)

The social wage rate is simply a ratio of consumption to labour, the con-sumption (in money units) per unit of labour power. A number of simplify-ing assumptions are made in order to relate equation (2.4) to Marxianeconomic categories. Capitalist consumption is assumed to be empiricallynegligible, a particularly unrealistic claim which can be relaxed later. Inaddition, there is assumed to be no exogenous element in worker consump-tion; and although workers are allowed to save, their savings are notincluded as part of the social wage rate. The social wage rate captures

�b �yL

By �

BL

L �1

� � �bI

y �1

1 � bI

The multiplier 13

worker consumption B that is necessary for the reproduction of labourpower. De Angelis therefore argues that the social wage rate is a monetaryexpression for Marx’s value of labour power – it represents the money valueof the labour embodied in the commodity bundle required to reproduceeach unit of labour power. An inverse relationship between the multiplierand the rate of surplus value is established, thereby providing a penetratinginsight into the structure of the multiplier, ‘to show how class relations arerepresented, in a mystified form, in economic categories’ (ibid.: 85).

In this spirit, a further examination of the structure of the propensity toconsume can provide an even more incisive insight into the structure ofclass relations. By simple decomposition, the propensity to consume can bewritten as

(2.5)

On this interpretation b represents the labour–output ratio (L/y) multi-plied by the consumption per unit of labour ratio (B/L).7 This expression, itcan be argued, represents the value of labour power – the labour embodiedin the commodity bundle required to reproduce each unit of labour.8 Sincethe propensity to consume is a pure number (money/money), decomposi-tion makes it possible to show that it is identical to the value of labourpower (labour/labour), which is also a pure number. An examination ofequation (2.1), therefore, reveals that the value of labour power itself (notits monetary expression) appears as the core component of the Keynesianincome multiplier. This represents a more revealing insight into the struc-ture of class relationships, with Marx’s theory of surplus value directly rep-resented in the denominator of the multiplier. Since the component b is thevalue of labour power, the denominator 1�b is the share of surplus value,the proportion of labour time extracted as surplus value. This interpretationof the multiplier penetrates beneath the surface of monetary economiccategories as considered by De Angelis, to the Marxian labour categories.

Two additional insights are therefore suggested relative to the contributionof De Angelis (2000). First, by applying the new method of decompositiona more direct translation between the multiplier and the Marxian categoriesis 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 eco-nomic categories. Second, instead of restricting this analysis to the employ-ment multiplier, the structure of the income multiplier is also examined.

b �By �

Ly

BL

14 The multiplier

The main problem with this decomposition of the multiplier is that it isrestricted to a one-good model. A contribution which relates the Keynesianmultiplier to a two-good model, along the lines of Marx’s reproductionschema, has been provided by Hartwig (2004). As a starting point, netincome in the two departments is captured by the identities

Y1 � V1 � S1 (2.6)

and

Y2 � V2 � S21 (2.7)

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

D(Y1) � (1 � b)y (2.8)D(Y2) � by (2.9)

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

(2.10)

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

(2.11)

Capitalists in Department 2 use this multiplier to anticipate how muchconsumption goods they need to produce in order to respond to the invest-ment decisions of Department 1. Hartwig (2004) provides a particular inter-pretation of the methodology employed by Keynes, in which entrepreneursuse the multiplier to plan their outputs at the start of each productionperiod. A key advantage of this multiplier, in comparison to a one-goodKeynesian model, is that it embodies the requirement of proportionalitybetween departments of production.

B �b

1 � bI

Y2

Y1�

b1 � b

The multiplier 15

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

(2.12)

it follows that

(2.13)

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

(2.14)

This demonstrates that the scalar Keynesian multiplier relationship canin 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 theconstituent role of constant capital in the production process.9 In embrac-ing Keynes to model aggregate demand, a Marxian response is required tothe 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 aggre-gate demand, a possible solution is provided by Leontief input–outputanalysis. There is a well-established tradition in Marxian economics forinterpreting the reproduction schema as an input–output table. It has beenargued that Leontief took his lead from Marx. Focusing on his earlier work,Gilibert (1998: 42), for example, states, ‘In his PhD thesis, Leontief hadargued in favour of the substitution of the principle of circular flow (thereproducibility viewpoint) for that of homo oeconomicus (the scarcityviewpoint) as the cornerstone of economic theory.’ Similarly, Kurzand Salvadori (2003: 63) argue that Leontief applied his model to ‘an econ-omy in which both capital and consumption goods are produced andreproduced’.

Closely related to the Leontief approach is the theoretical legacy ofSraffa’s Production of Commodities by Means of Commodties (1960).De Vivo (2003: 1) has shown that the starting point for Sraffa’s productionmodel has been ‘derived . . . from Marx’s reproduction schemes’. In the

y �1

1 � bI

B � I �1

1 � bI

B � � 11 � b

� 1�I

16 The multiplier

ensuing development of the Leontief approach, it will become clear how itcan also be characterized as broadly in keeping with a Sraffian perspective.

To begin the analysis, Marx’s numerical example of expanded reproduc-tion can be recast as an input–output framework. Table 2.4(a) re-expressesthe numerical elements of Table 2.2 as an input–output table. The advantageof this table is that it shows explicitly how Marx assumes capitalists spendtheir 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 eitheralong the rows as outputs of a particular department, or column-wise asinputs to that department. For example, reading row-wise, Department 2produces 1,000 units of consumption goods for Department 1’s workers,750 for itself, 150 for additional variable capital and 1,100 for capitalistconsumption. Reading column-wise, Department 2 uses inputs of 1,500constant capital from Department 1 and 750 of consumption goods fromitself. The surplus value element of 750 is viewed as an input of value addedto 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 for-mat, 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 betweenphysical flows of means of production (Xij), from department i to depart-ment j, to (physical) gross output (Xj) of department j. In Marx’s reproduc-tion schema, these input coefficients are applied to Department 1, the onlysector producing means of production. For Department 2, different notationis required for our multiplier framework. Ratios to gross output of the totalnumber of labour units employed in each sector (Lj) are represented bylabour coefficients lj � Lj /Xj; and consumption coefficients hi � Bi/L are

The multiplier 17

Table 2.4 Expanded reproduction in an input–output table

Dept. 1 Dept. 2 dC dV u Wi

(a) Numerical categoriesDept. 1 4,000 1,500 500 6,000Dept. 2 1,000 750 150 1,100 3,000Si 1,000 750Wi 6,000 3,000 9,000

(b) Leontief categoriesDept. 1 p1a11X1 p1a12X2 p1da p1X1

Dept. 2 p2h2l1X1 p2h2l2X2 p2dh p2Ck p2X2

S1 S2

p1X1 p2X2

18 The multiplier

ratios of total consumption of each physical good (Bi) to the total volumeof 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 alge-braic terms (Table 2.4b). Consider inputs of constant and variable capital toDepartment 2. The 1,500 units of constant capital are represented byp1a12X2, the money output of Department 1 required by Department 2. Andthe 750 units of variable capital are represented by p2h2l2X2, the amount ofconsumption goods set aside by Department 2 for its own use.

Elements representing expansions of capital are defined by conjoiningmoney prices with physical volumes of new means of production (da) andphysical quantities of new means of consumption (dh). Similarly the phys-ical 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 forMarx’s expanded reproduction schema can be specified as

X1 � a11X1 � a12X2 � da (2.17)X2 � h2l1X1 � h2l2X2 � dh � Ck (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

(2.19)

On the right-hand side of this expression, elements representing newconstant and variable capital, together with capitalist consumption, are col-lected in a vector representing ‘final demand’ for the goods produced by thetwo departments – final demand in this closed input–output model does notinclude income-dependent worker consumption. By specifying X as thecolumn vector of gross outputs for each sector, A the square matrix ofinterindustry input coefficients, h the column vector of worker consumption

�X1X2� � �a11

0a120 ��X1

X2� � � 0

h2�[l1 l2]�X1

X2� � � da

dh � Ck�

coefficients, l the row vector of labour coefficients and F as the columnvector representing final demand, the structure of (2.19) is summarized bythe expression

X � AX � h[lX] � F (2.20)

With net outputs defined as Q � (I � A)X it follows that (2.20) can bere-expressed as

Q � h[vQ] � F (2.21)

where v � l(I � A)�1 is Pasinetti’s (1981) row vector of vertically inte-grated 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 multiplierform

(2.23)

Under Marx’s assumption, in Capital, volume 2, that prices and valuesare identical, and hence £1 of output is equal to an hour of labour time, thisequation captures both an income and multiplier relationship. The equiva-lence between prices and values is embodied in the identity p � v such thatthe total employment of labour units (vQ) is equal to total money netincome (pQ). Similarly, vF the total number of labour units required to pro-duce final demand, is equal to total money final demand (pF). Hence, theexpression 1/1 � vh is an income/employment multiplier, in which thescalar vh represents the propensity to consume b, derived from the two-department schema.10 We shall refer to this as the Keyensian scalar multi-plier, since although it is somewhat unusually defined according to workerconsumption it retains the 1/1 � b structure that is so common to econom-ics textbooks. The simplicity of the Keynesian multiplier is retained in atwo-department setting.

This multiplier has a particularly interesting denominator (see Appendix 2for an equivalent interpretation of the Leontief matrix multiplier). Followingthe logic of my interpretation of the one-good multiplier, the term vhcan be interpreted to represent the value of labour power: the labour embod-ied (v) in the bundle consumed by workers per unit of labour (h). The

vQ �1

1 � vhvF

The multiplier 19

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

(2.24)

where, in this special case, net money output is y � vQ � pQ and moneyfinal demand f � vF � pF.

The role of Marx’s category of surplus value can therefore be identifiedin a macro scalar multiplier without the restrictive assumption of a one-good model. This scalar multiplier captures the inter-departmental structureof the reproduction schema without constant capital being assumed away. Aformal model of aggregate demand in the reproduction schema is devel-oped, which retains the simplicity of the Keynesian multiplier together withMarx’s value categories.

y �1e f

20 The multiplier

3 The Kalecki principle

The work of Michal Kalecki has been seen as a key bridging point betweenMarx and Keynes. Although Kalecki was in many ways the equal ofKeynes, independently working out some of the same ideas, they camefrom very different backgrounds. Whereas Keynes had a classical Oxbridgeeducation, moving from Eaton to Cambridge, Kalecki went to GdanskPolytechnic; and whilst Kalecki was an official in the UK Treasury, reveredby the British establishment, Kalecki was schooled in the underworlds ofEuropean Marxism.1 From these roots, Kalecki developed an interpretationof the reproduction schema, in which aggregate demand is the main drivingforce. Under the auspices of the ‘Kalecki principle’, that capitalists earnwhat they spend, the role of money is brought into focus. The thrust of thisprinciple is expressed by Marx in Capital, volume 2: ‘In point of fact, par-adoxical as it may seem at the first glance, the capitalist class itself casts intocirculation the money that serves towards the realisation of the surplus-valuecontained in its commodities’ (Marx 1978: 409).

There are two main ways in which Kalecki’s interpretation of the repro-duction schema is underdeveloped. First, although Kalecki (1991d: 459)claims that his model is ‘fully in the Marxian spirit’, he did not examine thedirect relationship between his approach and Marx’s original text. Sardoni(1989) has provided perhaps the most concerted effort to make this con-nection, but does not engage directly with Marx’s numerical examples.Second, coming from the other extreme, Reuten (1998) provides a mostsystematic and detailed exploration of Marx’s original tables, giving specialmention to the Kalecki principle, but without providing a direct connectionto Kalecki’s analytical model of the reproduction schema. The contributionof this chapter is to provide a detailed assessment of the role of the Kaleckiprinciple in Marx’s reproduction schema.

As part of this assessment, the structure of the scalar multiplier frame-work is further developed, together with the relationship between theKalecki principle and Marx’s value categories.

Kalecki and the reproduction schema

A first step in the analysis is to show explicitly how the elements of surplusvalue 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 aredisplayed in Table 3.1. In Department 1, for example, one half of the extractedsurplus value of 1,000 is invested in the expansion of capital, with 400 directedto new constant capital and 100 to new variable capital. The remaining 500units of surplus value are consumed by Department 1 capitalists.

Following Kalecki (1991d: 459), the reproduction schema can be furtherdisaggregated by dividing the activity of Department 2, producing con-sumption goods, into a new Department 2 producing capitalist consumptiongoods and an additional Department 3 producing wage goods. The numbersin Table 3.2 provide an illustration of how Marx’s table could be looked atfrom Kalecki’s perspective. Note that with the new Department 2 produc-ing 1,100 units of capitalists’ consumption goods, and Department 3 pro-ducing 1,900 of wage goods, the combined total output of 3,000 units is thesame as the output of Marx’s Department 2 in the two-sector table.Similarly, Department 1 in the three-sector table produces exactly the sameoutput (6,000 units) as Department 1 in the original table. Table 3.2 canviewed as a decomposition of Marx’s schema to provide a more detailedanalysis of the structure of consumption.


Table 3.1 The allocation of surplus value in the two-sector schema

Ci Vi Si Wi

ui dCi dVi

Dept. 1 4,000 1,000 500 400 100 6,000Dept. 2 1,500 750 600 100 50 3,000

5,500 1,750 1,100 500 150 9,000

Table 3.2 Ex ante three-sector reproduction schema

Ci Vi Si Wi

ui dCi dVi

Dept. 1 4,000 1,000 500 400 100 6,000Dept. 2 550 275 220 36 18 1,100Dept. 3 950 475 380 63 31 1,900

5,500 1,750 1,100 500 150 9,000

23

13

13

23

The reproduction schemes shown so far can be characterized as showingthe 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 totaland produce 6,000 units of output of constant capital. There is an ex anteimbalance between these two quantities, and also between quantities ofconsumption goods produced and consumed. In order to ensure ex postbalance, at the end of year 1, the additional units of constant (dCi) andvariable (dVi) capital set aside for future production can be groupedtogether with the ex ante volumes of capital consumed at the start of theperiod (Table 3.3). Department 1, for example, has constant capital of 4,400units at the end of the period, made up of the original 4,000 consumed andthe additional 400 required for production in the next period. Similarly, vari-able capital is now 1,100 units, made up of the original 1,000 units and thenew 100 inputs of variable capital. The new ex post categories of constantand variable capital are referred to in Table 3.3 as and respectively.

A final rearrangement of the categories in Marx’s numerical table canbe achieved by introducing a different way of looking at profits. ForMarx, profits in each department are specified as the surplus value leftafter accounting for ex ante inputs of constant and variable capital(Si � Wi � Ci � Vi). However, for Kalecki, profits in each department ( )are the total value left after accounting for ex post variable capital( ). Kalecki is concerned with gross undistributed profits, adefinition of profits that can be applied to the reproduction schema bysimply adding the constant capital components of Table 3.3 to the compo-nents for capitalists’ consumption. In Department 1, for example, 4,400 units

P*i � Wi � V*i

P*i

V*iC*i

The Kalecki principle 23

Table 3.3 Ex post three-sector reproduction schema

ui Wi

Dept. 1 4,400 1,100 500 6,000Dept. 2 586 293 220 1,100Dept. 3 1,013 506 380 1,900

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

23

13

13

23

V*iC*i

Table 3.4 Kalecki’s interpretation of the three-sectorschema

Wi

Dept. 1 1,100 4,900 6,000Dept. 2 293 806 1,100Dept. 3 506 1393 1,900

1,900 7,100 9,000

13

23

23

13

P*iV*i

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( ) and profits ( ). (The full algebraic structure of the three-sectorschema is laid out in Appendix 3.)

Having reformulated Marx’s categories and rearranged the reproductionschema, along the lines suggested by Kalecki, a key result is established.Table 3.4 shows that Department 3 produces a surplus of 1,393 wagegoods, and these are sold to workers in the other two departments (1,393 � 1,100 � 293 ). Expressing this identity in algebraic terms:

(3.1)

Following Kalecki (1991d: 460), adding to both sides of equa-tion (3.1) yields

(3.2)

and hence

P* � W1 � W2 (3.3)

This is an ex post identity between total profits (P*) and the economy’soutput 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 goodsdetermined by profits, or are profits determined by these expenditures? Heargues that ‘capitalists can decide how much they will invest and consumenext year, but they cannot decide how much they shall sell and profit’ (ibid.:461). It is the money expenditures by capitalists upon consumption andinvestment that generate the resultant volume of profits.

Cartelier (1996: 217) has linked this so-called Kalecki principle, thatcapitalists earn what they spend, to the circulation of money. ‘As a result oftheir ability to initiate circulation entrepreneurs, as a whole, more or lesshave the power to determine their income.’ Moreover, he argues, ‘theKalecki principle does not contradict the Classical view which makes profitequal to the value of surplus.’

Key passages in Marx’s writings that demonstrate the role of the Kaleckiprinciple 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 repro-duction, Marx considers the circulation of money using the example of anindividual 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

P*1 � P*2 � P*3 � P*1 � V*1 � P*2 � V*2

P*1 � P*2

P*3 � V*1 � V*2

13

13

13

P*iV*i


labour-power (£1,000)’ (Marx 1978: 409). At a 100 per cent rate of surplusvalue it can be assumed that £1,000 of surplus value is appropriated. Theproblem is that the capitalist advances £5,000, which can be referred to asM, but receives back £6,000, the realized amount M�. Focusing upon thedifference between the two amounts (M��M), 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 bythe unproductive personal expenditure of the capitalist. The capitalistconsumes the same £1,000 as the volume of surplus value. This ‘£1,000 isconverted into money with the money that he threw into circulation not ascapitalist, but as consumer, i.e. did not advance, but actually spent’ (ibid.:410). Moreover, this consumption is financed out of the capitalist’s ownmoney hoard: it ‘means nothing more than that he has to cover his individ-ual consumption for the first year out of his own pocket’ (ibid.: 409).

Marx generalizes this key role for unproductive expenditure to thecapitalist class as a whole.

It was assumed in this case that the sum of money that the capitalist castsinto circulation to cover his individual consumption until the first refluxof his capital is exactly equal to the surplus-value that he produces andhence has to convert into money. This is obviously an arbitrary assump-tion in relation to the individual capitalist. But it must be correct for thecapitalist class as a whole, on the assumption of simple reproduction. Itsimply expresses the same thing as this assumption implies, namely thatthe 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 sametime capitalists enable this mass of surplus value to be realized by castingthe money for unproductive expenditure into circulation.

The case of expanded reproduction, as considered in Tables 3.1–3.4, ‘doesnot offer any new problems with respect to money circulation’ (ibid.: 418). Thedifference is that part of the additional money cast into circulation (M��M)now consists of money capital advanced for productive purposes. (The otherpart consists of the money cast into circulation for purposes of unproductiveexpenditure by capitalists, as before in the case of simple reproduction.)

As far as the additional money capital is concerned, that required forthe function of the increased productive capital, this is supplied by theportion of realised surplus-value that is cast into circulation by thecapitalists as money capital, instead of as the money form of revenue.

(ibid.: 418)


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

Surplus value

Despite his direct engagement with Marx’s reproduction schema, and theilluminating insights he provided into the determination of profits, Kaleckihas been widely characterized as a ‘non-Marxist’ (see Sawyer 1985: 175;Freeman and Carchedi 1996: xii). This can be attributed in part to the treat-ment that he received during the years of post-war repression orchestratedby the Polish communist party. Of independent disposition, Kalecki was nota person given to toeing the line, resigning from three jobs on separateoccasions. This independence is reflected in his engagement with the writ-ings of a previous Polish heretic, Rosa Luxemburg, which would not haveendeared him to the party establishment.

In theoretical terms, the non-Marxist tag can be largely attributed to alack of engagement with the labour theory of value. For Sebastiani (1994:108), Kalecki’s silence on this issue could be interpreted ‘either as a tacitacceptance or as a tacit rejection of Marx’s premises’. Kerr (1997: 23), inher textual analysis of Marx and Kalecki, takes the first position, aiming‘to make explicit what Kalecki often left as understood in the moreabstract presentations of his analysis’. In contrast, Brus (1977: 59)reported that Kalecki felt ‘a strong distaste for the Marxian theory ofvalue, which he considered metaphysical and (if I am not mistaken) neverwanted to discuss’.

Whichever interpretation is correct, Kalecki’s silence on the labourtheory of value leaves open the theoretical possibility that its relevancecan be fruitfully explored. To relate Kalecki’s model of reproduction toMarx’s theory, a reconfiguration is required of the definition of profits.The problem, as we have seen, is that Kalecki’s model requires a grossdefinition of profits that is different from Marx’s category of surplusvalue. The Kalecki principle has not been precisely demonstrated in thecontext of Marx’s reproduction schema, in which surplus value is the keycategory of analysis.

To apply the Kalecki principle directly to Marx’s schema, attention canbe focused on an important difference between Marx and Kalecki about theway in which investment is specified. Whereas for Kalecki investment isassociated specifically with the capital-goods producing department, for


Marx investment (accumulation) is directed to goods produced byboth departments. As demonstrated by Zarembka (2000: 190), there is aconception which

Marx uses throughout most of his work, that accumulation of capitalentails increases in both the value of the means of production used inproduction 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 ofinvestment in his comparison of Marx and Kalecki, he does not highlighttheir importance. To demonstrate the importance of this difference, theLeontief input–output framework can again be used to model the finaldemand of each department of production such that investment demand cutsacross departments. This Leontief interpretation of the reproduction schemaallows Marx’s categories to be retained alongside the Kalecki principle.

Table 3.5 is a Leontief representation of the three-sector reproductionscheme considered previously in Tables 3.2–3.4. Following the logic of theinput–output approach, elements of this table can be read along the rows asoutputs of a particular sector, or column-wise as inputs to that sector. Forexample, Department 3 produces outputs of 1,000 in wage goods forDepartment 1, outputs of 275 for Department 2 and 475 for itself. Readingcolumn-wise, Department 3 uses 950 inputs of constant capital fromDepartment 1 and 475 inputs of wage goods from itself. Since investment,redefined as additional constant capital (dC) and variable capital (dV), isnow separately defined as part of final demand, profits in each sector areterms representing surplus value (Si). The total personal consumption ofcapitalists (u) is shown as the final demand for goods produced byDepartment 2.3

Without losing too much information, Table 3.5 can be translated into themore 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 Wi

dC dV u

Dept. 1 4,000 550 950 500 6,000Dept. 2 1,100 1,100Dept. 3 1,000 275 475 150 1,900

Si 1,000 275 475 1,750

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

adding together of the elements of the two rows and two columns relatingto sectors 2 and 3. By aggregating Table 3.5, it can be translated intoTable 2.4, the two-sector schema displayed earlier in Chapter 2.

Following the analysis of Chapter 2 (equations 2.15–2.24), the simpleKeynesian multiplier

(3.4)

captures the macroeconomic structure of the two-sector schema. To recap,under the working assumption of Capital, volume 2, that prices and valuesare equivalent, the scalar y represents net money output, f is money finaldemand and the denominator of the Keynesian multiplier e is the share ofsurplus 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

S � u � I (3.5)

or

Surplus value � capitalist consumption � investment

where S � ey represents the total volume of surplus value produced in theeconomy.4 Equation (3.5) provides an alternative way of representing theKalecki principle in Marx’s reproduction scheme. Instead of examiningthe determinants of gross undistributed profits, as in Kalecki’s equation(3.3), an alternative ex post identity based on the input–output model isderived, in which profits (surplus value) are set equal to investment pluscapitalist consumption. The Kalecki principle, that capitalists earn whatthey spend, can be applied to equation (3.5), with capitalist consumptiontogether with investment in constant and variable capital determining thetotal volume of surplus value. In contrast to the Kalecki formulation thereis a clear role for Marx’s theory of surplus value. Capitalists cast moneyinto circulation as aggregate demand on capitalist consumption andinvestment, which is realized as surplus value.5

The Kalecki multiplier

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

y �1e f


the scalar Keynesian multiplier derived from the reproduction schema. Theconstant part of capitalist consumption (u) is defined as B0, with theremaining 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

(3.8)

This final equation represents a multiplier relationship between totalprofits and the total exogenous expenditure by capitalists (B0 � I ), the mul-tiplier being defined as 1/1��. With this Kalecki multiplier relationship,profits are determined using exogenous investment and capitalistconsumption.

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

(3.9)

The Keynesian multiplier has as its constituent elements the Marxian termrepresenting the share of surplus value e and the Kalecki multiplier 1/1��.

It should also be emphasized that this adaptation of the Kalecki systemrepresents an interpretation of the reproduction schema that is consistentwith Marx’s system. As Lee (1998) has argued, Kalecki has a restrictiveproduction model in which each department is vertically integrated, pro-ducing its own raw materials. In contrast, Marx assumes that raw materialsare a part of constant capital, produced in the first department and circu-lated to other departments. A failure to fully take into account connectionsbetween industries leaves the Kalecki system vulnerable to a Sraffian cri-tique. Steedman (1992), for example, has lambasted the Kaleckian pricesystem for the absence of multisectoral relationships. By establishing theKalecki principle in an input–output context, an interpretation of the repro-duction schema is possible in which linkages between industries are takenseriously.

y �1

e(1 � �)(B0 � I )

P �B0 � I1 � �


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

The value-form

Although the input–output approach may help defend Kalecki’s systemagainst the challenge provided by Sraffian economics, the claim that it canbe a vehicle for capturing the macroeconomic role of money is very muchagainst the grain of current thinking in Marxian economics. Input–outputanalysis 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 ofboth inputs and outputs into prices.6 In the Sraffian representation of Marx,separate value and price systems are compared, where values are calculatedas embodied labour coefficients. Once the correct transformation of valuesis carried out, the whole raft of results obtained by Marx from the labourtheory of value is discredited.

Where money is considered, its role in this Sraffian interpretation ofMarx is limited. For Saad-Filho (2002: 24), ‘As the analysis is primarilyconcerned with the relationship between the value and price systems,money has no autonomous role and, when considered at all, it is merely anumeraire.’A key defence of Marx’s theory, against the Sraffian critique, isto argue that the Srafffians do not take money seriously. An alternativestrand of value theory that corrects this mistake is the value-form tradition,which ‘emphasised the importance of money for value analysis, becausevalue only appears in and through price’ (ibid.: 27). As a way of testing thepossibility that money can be taken seriously in the input–output approach,it can be explored how the preceding analysis of the Kalecki principle canbe reconciled with the value-form approach.

At the very start of Capital, volume 1, Marx (1976) defines commoditiesas having a double existence, as useful objects (use-values) and asexchange-values. The use-value of a commodity is the physical quality itbestows to the user of the commodity. As an example, Marx indicates thatthe 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


Marx’s two great departments of production in the reproduction schema.For exchange between such use-values to take place, however, they mustalso have exchange-value.

Exchange-value is defined in quantitative terms, since the exchange ofcapital goods for consumption goods requires a measuring rod to establishhow much of one is exchanged for the other. The measuring rod is providedby labour-time. ‘As exchange-values, all commodities are merely definitequantities of congealed labour-time’ (ibid.: 130). Marx writes, ‘Now weknow the substance of value. It is labour. We know the measure of its mag-nitude. It is labour-time’ (ibid.: 131). What is now required is a definitionof the form which value takes as exchange-value.

For Marx the value-form is expressed in monetary prices. Labour-timeembodied in use-values can only be socially validated as value when ascommodities they are sold for money. Money is the form in which com-modities appear as exchange-values in the market place. In their expositionof this value-form approach, Reuten and Willams (1989: 53) conclude, ‘Inbourgeois society . . . labour and the products of labour are thus sociallyrecognized as useful only by assuming the form of value: money.’

From this perspective the embodied labour coefficients, employed in theSraffian interpretation of Marx, are based on an ‘exclusive focus onthe use-value aspect’ (ibid.: 54). Furthermore, ‘These constructs inhibit theaccount 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 beidentified with the quantity of labour embodied in it, for the concept ofvalue refers to the socially necessary labour-time embodied, to abstractrather than to concrete labour, and this quantity can only be establishedwhen private labours are socially validated through the circulation ofcommodities and of capital (original emphasis).7

(1994: 133)

Although Marx himself specified value in terms of labour embodied, theSraffian Marxists are charged with calculating labour values withoutrecourse to their validation in the market place as money. It may be thatSraffians have implicitly assumed that what is produced is sold, but the lackof importance attached to monetary questions has left their approach opento the value-form critique.

At the other extreme, there is the danger that all mention of value aslabour embodied is written out of economic theory. Steedman (1981: 15)has argued that Marxists, in avoiding the use of embodied labour, are indanger of ‘draining it of all content’. The problem is that without labour


embodied categories value theory may fail to penetrate beneath the surfaceof money prices.

As a contribution to this debate, it could be argued that the earlier deri-vation of the Kalecki principle provides a way of conserving both the labourembodied concept and the value-form. This is very straightforward, on theassumption of volumes 1 and 2 of Capital, that prices and values are equiv-alent. With p the vector of money prices and v the vector of embodiedlabour values,

p � v (3.10)

The embodied labour values represent the total (direct and indirect) labour-time required to produce each unit of physical output. These embodiedlabour values have to be socially validated in their value-form as money. Bysetting prices equal to values, the embodied labour magnitude and themoney value-form are assumed to be identical.

What is more, these equally valid ways of defining value are consistentwith a macroeconomic interpretation of the autonomous role of money.Since under the Kalecki principle capitalists earn what they spend, thesocial validation of the market, led by capitalist investment and consump-tion, is the starting point for economic activity. Commodities are only pro-duced, labour is only employed, if capitalists cast into circulation the moneyrequired for sales to be realized – for labour embodied in commodities tobecome socially necessary. Since money, with its specific role in a capital-ist economy, is so central to the Kalecki principle, a possible synthesiscan be suggested with the value-form approach; without, that is, compro-mising the use of a Leontief/Keynesian multiplier framework together withembodied labour categories.


4 The monetary circuit

In the Anglo-American universities, economics has been held in a vice-likegrip by the neoclassical orthodoxy. One of its key limitations is the neutralrole played by money in the microeconomic determination of prices.Although the liberal right embraced the term monetarism, its actualmeaning is that money has no real impact on economic activity (apart fromcausing inflation). In the face of this establishment position, mainstreamKeynesian economics has fought a timid rearguard action, being forced toaccept the tools and assumptions of neoclassical theory. On the Europeancontinent, however, a new genre of monetary macroeconomics hasemerged, often referred to as the Franco-Italian circuit school; an approachthat ‘has its antecedents in the writings of Marx on the circuit of moneycapital’ (Bellofiore and Seccareccia 1999: 753).1

What sets this circuit approach apart is its institutionally relevant analysisof the relationship between banks, firms and workers. A model of thecircuit of money is developed in which prime importance is placed upon therole of banks in financing industrial activities. Central to this approach isan application of the Kalecki principle, that capitalists earn what theyspend; the question being how an injection of money can circulate aroundthe economy and return back to the capitalists. Moreover, how is this circuitof money intertwined with the activities of industrial sectors? And howmuch money is required for the circuit to be complete? Marx’s reproductionschema 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 demarcationbetween workers and capitalists and, although intersectoral relation-ships are not fully explored, a distinction is made between consumer and

capital goods. The key departure from a more traditional Marxianapproach, however, is its opposition to a commodity theory of money. In atriangular structure of relationships, banks give credit to firms in order tofinance their outlays on workers. ‘Money cannot be a commodity becausethe purchase of labour power is logically prior to the production of com-modities and therefore also to the production of the money commodityitself’ (Bellofiore and Realfonzo 1997: 100). Once the monetary require-ments of the economic system are taken into account, alongside moderninstitutional arrangements, money is defined as a credit instrument – moneythat has symbolic value and no intrinsic value.

A monetary circuit must have a starting point and an end point. Thestarting point in the Graziani model is the initial amount of moneyborrowed by firms from banks. Firms then use this money to finance theirtotal wage bill, employing workers to produce commodities. Under theassumption that workers do not save, which is maintained throughoutthe analysis that follows, wages are spent on consumer goods, all of themoney returning back to the firms. At the end of the circuit, firms areaccordingly able to pay back their debt to the banks. The money, which wasoriginally borrowed, is destroyed when it returns back to the banks, and thecircuit is closed.

It should be noted that this model also provides a modification of thestandard Marxian representation of the circulation of money, since onlywages are advanced. In the standard interpretation of Marx’s system, thetotal amount of money (M) that firms advance consists of variable andconstant capital, which is transformed in the production process to a newvolume of money (M�) that includes profits made by firms. However, forGraziani:

If we consider firms as a whole, their only external purchase is labourforce. All other exchanges being internal transactions, no furthermonetary payment is required. Only at the end of the productionprocess firms buy capital goods to be used in the following period.

(1989: 4)

In comparison to Marx, therefore, the circuit approach significantly reducesthe amount of money that has to be advanced in order for the productionprocess to be initiated.

Although the Graziani model distinguishes between consumption andinvestment goods, a possible criticism is that there is no systematic analysisof the relationship between the sectors that produce these goods. By inter-nalizing transfers between firms in relation to capital goods, there is noconsideration of the two-way exchange that takes place between the capital


and consumption goods sectors. In the analysis that follows we explore twoalternatives. In the first, the advance of wages is argued to be insufficientto service a complete monetary circuit (Seccareccia 1996). In the second,an alternative extreme is adopted in which only the wage bill advancedin the capital goods sector is considered (Nell 1998, 2004). It has beenargued by Nell (1998: 207) that both these interpretations were consideredby Marx in his notes on the circulation of money, collected in Capital,volume 2.

Consider Table 4.1, where for simplicity capitalist consumption issubsumed under household consumption out of wages, and there is nogovernment sector or external trade. This is a two-sector representation ofthe Kalecki schema, shown previously in Table 3.4, with gross outputs (Wi),measured in money units, made up of profits and wages . Thesubscript 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 consumptiongoods sector produces a surplus which is used to support workers inthe capital goods sector. Workers in the capital goods sector spend theirwages on these surplus consumption goods and hence

(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 theconsumption goods sector.

Seccareccia (1996) uses (4.1) to show that the advance of money in theGraziani model (M) is equal to the output of the consumer goods sector:

(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 goodssector get the money to reimburse the banks, thus closing the circuit of

M � V*1 � V*2 � P*2 � V*2 � W2

P*2 � V*1

(V*1 )

(P*2 )

(V*i )(P*i )

The monetary circuit 35

Table 4.1 Two-sector Kalecki schema

Wages Profits Output

Dept. 1 W1

Dept. 2 W2P*2V*2

P*1V*1

credit?’ (ibid.: 405). A proposed solution is for firms to advance both wagesand investment at the start of the circuit (see also Rochon 1999). A largeramount

M � W1 � W2 (4.3)

is borrowed from banks by firms at the start of the monetary circuit. This isa ‘single swap’ approach in which the ‘gross product swaps in a singleexchange for an equivalent sum of money’ (Nell 1998: 207).

For Nell, this approach closely resembles the first of Marx’s solutions inCapital, volume 2, to the problem of establishing where the money comesfrom to service the gap between the amount advanced by capitalists and theamount M� they receive as income.2 As we saw in Chapter 3, Marxaddresses this issue by positing that capitalists advance the amount M��Min addition to M. Under the Kalecki Principle, M��M is the amount ofmoney cast into circulation by capitalists in order to realize profits.Ignoring for simplicity the role of capitalist consumption, this amount isrequired to purchase additional quantities of capital. Hence, capitalistsadvance the whole of M�. ‘On this view, theoretically, it is correct to speakof 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 sin-gle swap approach this advance of money is sufficient to fund total incomein one run of the monetary circuit.

Nell develops a critique of this single swap approach by arguing thatthere is an exaggeration of the amount of money required in the circulationprocess. The problem with the single swap approach is that

it retains the idea that the total money supply equals the value of totaloutput. This results in a pattern of circulation that appears at times torun counter to economic common sense. If the total wage bill andfunds for total investment are both advanced, then the capital goodssector will find itself awash in unnecessary cash. For when the capitalgoods sector sells investment goods to the consumer sector, it willreceive funds equal to its wage bill. Yet it has just borrowed its wagebill! 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 takingplace sequentially, with a given amount of money circulating betweenhouseholds and firms over time.3 The principle being proposed here is thatcapitalists will earn income from selling outputs to capitalists in other


sectors of production. A ‘mutual exchange’ model is required that takes intoaccount the mutual benefits to capitalists of sectoral interdependence.

Nell (2004) sets up his mutual exchange model of Table 4.1 under theassumption that production is defined in distinct periods. In each productionperiod there is 100 per cent depreciation of capital goods, each item lastingfor the duration of that period, before being replaced in the next period.Replacement of capital used up is carried out with capital goods produced inthe previous period. The same assumption is applied to households, withconsumption goods carried forward from the previous period. At the start ofthe production period, therefore, inventories of capital and consumptiongoods are inherited from the previous period of production. As a conse-quence, production in the current period is geared up for the replacement ofitems used up by firms and consumers in the current period. The productionperiod is effectively a slice of time, which has a before and after.4 Thisapproach is very different from the Graziani model in which time starts withthe advance of credit by banks to initiate production, with all items ofproduction generated subsequent to this process (see Fontana 2002: 156–60).

The Nell production period takes as its starting point the outlay on wagesby firms in the capital goods sector. In strictly Marxian terms, this is ‘the ini-tial moment of exchange between capital and labour’ (Graziani 1997: 29),under which money takes the form of money capital in the investmentgoods sector. The starting point could alternatively be in the consumergoods sector, but a choice is required in order to simulate the knock oneffects between sectors. A sequence of ‘stages’ of circulation are examined,all of which take place within the period of production. Three of the initialstages in the money circuit can be explained as follows:

Stage 1 At the outset firms in the capital goods sector (sector 1) begin toborrow money from banks in order to finance the wage bill of thatsector.5 Out of these wages, workers in sector 1 purchase consumptiongoods from sector 2.

Stage 2 In response, by selling consumption goods to sector 1, firms in theconsumption goods sector (sector 2) direct these funds to the payment ofsector 2 wages. Workers in sector 2 spend their wages on consumptiongoods that return back to the firms in sector 2. The money re-emerges insector 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 ableto pay wage advances and use gross profits to purchase their own capitalgoods.

The money circulates between the two sectors until all of the initialmoney advanced as wages in the capital goods sector is put into circulation.


The circuit is closed once wages in the capital goods sector are equal toprofits in the consumption goods sector , equation (4.1) providing abalancing constraint between the two sectors. As Graziani (1997: 30) hasdemonstrated, the initial outlay of money as capital, in the hiring of labour, isfollowed by a phase of money in circulation acting as an ‘intermediary ofexchange’.

The circulation of money in Nell’s model has some resemblance toMarx’s analysis of mutual exchange between departments of production, asdiscussed in Capital, volume 2 (Marx 1978: 474–8). Marx provides a similarexample 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 thesame value from the capitalists in department II, and thereby transformhalf of department II’s constant capital into money. The capitalists indepartment II, for their part, use this £1,000 to buy means of productionto 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 oftheir money outlay on wages: ‘the same amount flows back to the respec-tive capitalists as they themselves advanced for the monetary circulation’(ibid.: 477). Although Nell (1988a: 94–5) highlights some of the inconsis-tencies in Marx’s development of this example, he argues that it provides thecorrect starting point for an analysis of the circulation of money betweensectors. Moreover, this process of interaction between sectors in Marx’sexample can be interpreted as a multiplier relationship. The impact of theinitial £1,000 advanced by capitalists in Department 1 multiplies betweenthe two sectors. Oiled by the circulation of money, workers in Department1 purchase consumption goods from Department 2, which allows capitalistsin Department 2 to purchase means of production from Department 1.

The formal model of the multiplier process developed by Nell (2004) canbe demonstrated by writing total money output (WT) as

(4.4)

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

WT � V*1 � V*2 � P*1 � P*2 � 2V*1 � V*2 � P*1

(P*2 )(V*1 )


sector of , which in the next round is , in the next , and soon, with the overall impact captured by the multiplier relationship

(4.5)

Nell also assumes two subsectors for the capital goods sector, the first sellingcapital goods to the consumer goods sector, and the second selling capitalgoods to other firms in the capital goods sector. Labour coefficients areassumed to be the same in each sector. A multiplier can be constructed thatcaptures the relationship between the subsectors and the consumer goodssector. To start this process the first subsector sells capital goods to the con-sumer goods sector, receiving proceeds of . In order to repay itsloans the first subsector withdraws , and an amount isspent on new and replacement capital goods from the second subsector.The second subsector accordingly spends leading toa sequence that has as its sum the multiplier relationship

(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 theinitial outlay on wages in the capital goods sector:

(4.7)

In this model the outlay , once circulated between the capital andconsumer goods sectors, is sufficient to fund income, including wages andprofits, in both sectors. The multiplier effect allows for substantially lessmonetary 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 ofmoney bears some resemblance to Marx’s system, two key issues remain tobe resolved. First, in adopting the Kalecki schema of intersectoral flows(Table 4.1), Nell narrowly associates accumulation with the production ofmeans of production (capital goods). There is no mention of the accumula-tion of consumption goods, which are placed at the centre of Marx’sreproduction schema. Second, the role of Marx’s category of surplus valueis obscured in the Kalecki table. As demonstrated in Chapter 3, for the

V*1

WT � V*1 [2 � {1�(1 � wn2)} � {1�wn1}]

P*1 �1

wn1P*2

(1 � wn1)(1 � wn1)P*2

(1 � wn1)P*2wn1P*2

P*2 ( � V*1 )

V*2 �1

(1 � wn2)V*1

(wn2)2V*1wn2V*1V*1


three-sector schema, a translation can be made between the Kaleckicategories and Marx’s original categories specified in the third part ofCapital, volume 2. Let

(4.8)

(4.9)

where Vi and Ci respectively are Marx’s original terms for variable andconstant capital, and dVi and dCi represent new amounts of capital availablefor productive use in the next period. Using these categories, elements ofTable 4.1 can be re-expressed as in Table 4.2. Gross outputs are the same inboth reproduction tables but the capital components are shown in terms ofMarx’s categories.

Following the approach worked out in Chapter 3, Table 4.1 shows that inthe Kalecki-type formulation profits in each sector are defined in grossterms, consisting of expenditure on the replacement of existing constantcapital and its expansion (Ci � dCi); whereas in Table 4.2 profits (Pi) aredefined in net terms (dCi � dVi). The latter definition of profits is consis-tent with Marx’s interpretation, with the total increment of capital identicalto the volume of surplus value, after accounting for the replacement ofcurrent inputs of constant and variable capital.

As discussed earlier, in relation to the single swap approach, it may alsobe posited that capitalists advance the amount M��M required to purchasethe total increment of capital. In addition to funding the production of thiscapital increment, the monetary advance allows the realization of the volumeof surplus value required for its production. Capitalists earn a net volumeof profits (surplus value) that is driven by increments dC � dC1 � dC2 anddV �dV1 � dV2 of constant and variable capital respectively. Ignoring forsimplicity the role of capitalist consumption, the total volume of surplusvalue P � dV � dC is driven by capitalist requirements for new constantand variable capital.

In contrast to the single swap approach, however, it can also be argued thatthe money required for additional capital can be advanced without advanc-ing the whole of the economy’s gross income. In Marx’s terminology it may

P*i � Ci � dCi

V*i � Vi � dVi


Table 4.2 Two-sector Marxian reproduction schema

Pi Output

dCi dVi

Dept. 1 C1 V1 dC1 dV1 W1

Dept. 2 C2 V2 dC2 dV2 W2

be possible to model an advance of money M��M without assuming thatcapitalists advance M. As discussed earlier, Nell (2004), in his mutualexchange approach, is led by his critique of the single swap approach to dis-count the importance of M��M, arguing that a proportion of the variablecapital part of M may be sufficient to service the circulation of money. Incontrast, an alternative perspective can be developed in which we discountthe role played by all initial advances contained in M. This embraces theKalecki principle, with the amount of money spent by capitalists returningto them as profits; but the money income of the rest of the economy is alsogenerated out of the initial spending of capitalists.

This alternative approach can be developed by again interpreting Marx’sreproduction schema as an input–output table. Using the analyticalapproach developed in Chapter 2, the two-sector schema in Table 4.2 can betranslated into Table 4.3(b). All that is required, in addition to switchingrows into columns, is a re-introduction of capitalist consumption as anexplicit category. Table 4.3(b) shows how the rows of the reproductionscheme 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 theinput–output notation.6 In the analysis that follows the circuit of money ismodelled using both the numerical and algebraic categories.

Key to modelling the circulation of money in this Marxian reproductionschema is a consideration of how it intertwines with the circulation of com-modities between sectors. A precondition for the circuit of money is thecommodity circuit. To explore in more detail how commodities circulate inMarx’s system, the role of inventories has to be considered. Taking his lead





(b) Marxian categoriesDept. 1 C1 C2 dC W1

Dept. 2 V1 V2 dV u W2

S1 S2

W1 W2

(c) Leontief categoriesDept. 1 p1a11X1 p1a12X2 p1da p1X1

Dept. 2 p2h2l1X1 p2h2l2X2 p2dh p2Ck p2X2

S1 S2

p1X1 p2X2

from Quesnay, Marx is clear in Capital, volume 2, that ‘it is always theprevious year’s harvest that forms the starting-point of the productionperiod’ (Marx 1978: 435). Similarly, ‘Just as the current year concludes onthe side of department II with a commodity stock for the next, so it beganwith a commodity stock on the same side left over from the previous year’(ibid.: 581). Each production period begins with inventories of goodsproduced in the previous period, and its current output provides inventoriesfor the next period (see also Okishio 1988: 3). Marx argues that theaccumulation of these stocks is vital to the continuity of the productionprocess. The ‘capitalist must hold in reserve a certain stock of raw materials,so that the production process can keep going for shorter or longer intervalson the previously determined scale, without depending on the accidents ofdaily supply on the market’ (ibid.: 200).

The role of inventories in the reproduction schema can be illustratedusing Marx’s numerical example (Table 4.3a). The elements of this schemacan be recast in a tableau representing three periods of production, asshown in Table 4.4. Outputs of the production process are represented forthis year and last year. First, the outputs of last year are shown as inputs ofproduction in the current period. For example, the 4,000 units of constantcapital used up by Department 1 this year were produced by Department 1in the previous year. Similarly, the 1,000 units of variable capital (con-sumption goods) used up by Department 1 this year were produced byDepartment 2 in the previous year.

Second, the outputs of this year replace the inputs used up this year, andallow 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 Capitalist Total

1 2 1 2 1 2consumption

Last Dept. 1 4,000 1,500year Dept. 2 1,000 750

This Dept. 1 4,400 1,600 6,000year Dept. 2 1,100 800 1,100 3,000

Next Dept. 1year Dept. 2

Surplus 1,000 750value

Total 6,000 3,000 9,000

Source: Adapted from Stone (1965).

Department 1 produces 4,400 capital goods this year that are used up nextyear. This sum includes (1) 4,000 units that are required to replace the 4,000units used up this year; and (2) 400 additional units of constant capital thatare used to expand production in the next period. Similarly, Department 2produces 800 units of consumption goods that are used in the next period,50 of which represent an expansion of variable capital in Department 2. Forsimplicity, it can be assumed that capitalist consumption goods areproduced and consumed in the current period of production.

The starting point for the circulation of money, under the auspices of theKalecki principle, is the expenditure outlays of the capitalist class. InTable 4.5, the composition of these expenditures is made up of moneyoutlays on capitalist consumption (u) and new constant and variable capital(dC and dV ). Outlays are made by capitalists in each department of produc-tion. For example, the capitalists in Department 1 spend 400 units on newconstant capital, 100 units on new variable capital and 500 units on capital-ist consumption. The outlays on the products of both departments are col-lected in the final row as total outlays, which sum to 1,750. Dependingupon what is purchased, each outlay is also a receipt. Department 1’s pur-chase of 100 consumer goods from Department 2, for example, is a receiptfor 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, whichreturns to it as 1,750 in receipts.

It is clear from this example that the Kalecki principle holds, with thecapitalist class earning what it spends. But this is only part of the story: thecapitalists 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 levelof income is expanded in a series of circuits.

By again deriving the system of quantity equations from Table 4.3c(see equation 2.19):

(4.10)�X1X2� � �a11

0a120 ��X1

X2� � � 0

h2�[l1 l2]�X1

X2� � � da

dh � Ck�


Table 4.5 Composition of money outlays

This year dC dV u Total

1 2 1 2 1 2receipts

Dept. 1 400 100 500Dept. 2 100 50 500 600 1,250

Total outlays 400 100 100 50 500 600 1,750

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

(4.11)

or

A� (4.12)

And second, the system can be re-expressed in money units as

A� (4.13)

where

is a diagonal matrix of money prices. It follows that the money input–outputsystem takes the form

W � A†W � F† (4.14)

with W � X representing a column vector of gross money outputs,F† � F a column vector of money final demands and A� thematrix 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 iscaptured by the Leontief inverse (I � A†)�1. To explore this relationship inmore 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 andcirculates back to the capitalist. In the first circuit the impact on grossincome is F†, in the second circuit A†F†, in the third circuit (A†)2F†, and soon. This can be illustrated using Marx’s numerical example, in which thematrix of money coefficients has the structure

(4.17)A† � �a†11

a†21

a†12

a†22� � �

4000600010006000

150030007503000

� � �2316

1214�

P̂�1A† � P̂P̂P̂

P̂ � �p10

0p2�

P̂�1P̂X � P̂FP̂X � P̂

X � FX �

�X1X2� � �a11

h2l1

a12h2l2��X1

X2� � � da

dh � Ck�


These coefficients are derived from Table 4.3a, the input–output formulationof Marx’s reproduction schema.

Table 4.6 shows three of the money circuits that can be identified inMarx’s schema. The first circuit (F†) is the initial impact of capitalistoutlays, as introduced in Table 4.5. For example, capitalists in Department1 outlay 1,000 units of money, 400 of which are directed to the purchase ofcapital goods from itself and 600 from the purchase of consumption goods(for worker and capitalist consumption) from Department 2. In addition tothe 400 units that Department 1 sells to itself, another 100 units of capitalgoods are sold to Department 2. The total receipts from these sales are only500 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 totaloutlay of 750. Overall, the 1,750 cast into circulation returns back to thecapitalist class.

As a result of the first circuit, gross output has increased by 500 inDepartment 1 and 1,250 in Department 2. It is assumed that any sales ofinventories to meet the outlays of the two departments are immediatelymatched by production levels that allow them to be replaced. In the secondcircuit (A†F†) these increases have secondary impacts upon the outputs ofboth departments. Since, from equation (4.17), � 1–

2, the increase of

1,250 in Department 2’s output results in a further increase, by 1–2, in the

output of Department 1: Department 1 sells 625 units of capital goodsin order to meet (replace) the capital goods requirements of Department 2.In this second circuit we see Department 1 burgeoning with cash, thereceipts of 958 this time outstripping outlays of 416. This is the mutualexchange story, identified by Nell in Marx’s writings. The capitalists inDepartment 1 only have to advance part of their income because of themoney 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 multiplierprocess also obviates the need for Nell’s somewhat unwieldy considerationof subsectors in the capital goods sector (see equation 4.6).

a†12


Table 4.6 Money circuits in the current production period

This year 1st circuit Sub 2nd circuit Sub 3rd circuit Sub Total

1 2total

1 2total

1 2total receipts

Dept. 1 400 100 500 333 625 958 264 573 837 . . . 6,000Dept. 2 600 650 1,250 83 313 396 76 182 258 . . . 3,000

Total outlays 1,000 750 1,750 416 938 1,354 340 755 1,095 . . . 9,000

It should be noted that the initial outlay (and receipt) of 1,750 by thecapitalist class in the first circuit is all that is required to initiate subsequentcircuits. Out of this circulating amount of money, outlays of 1,354 and 1,095are injected in the second and third circuits, and beyond. Once the circuitshave petered out, and the multiplier process has come to an end, the sum ofall outlays equals the sum of receipts (9,000). The formulation of 9,000 unitsof 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 interpre-tation of the circuit of money. By writing the coefficient matrix A�

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 bypre-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 moneyvalue of per capita worker consumption, is the scalar wage rate w (under theassumption that workers do not save). And since wlX is the total wage bill,by decomposition if � wlX/pX is the share of wages in gross income,

ph[lX] � pX (4.20)

Second, the scalar term representing money constant capital can bere-expressed as

pAX � pX (4.21)

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

x � x � � f (4.22)

Hence

(4.23)x �1

1 � c � wf

wxc

c

c

w

w


is an aggregate multiplier relationship derived from the two-sectorreproduction schema. This provides a very simple model of the monetarycircuit. It can be posited at the start of the circuit that capitalists take outcredit to finance their outlay on new investment in constant and variablecapital, and outlays on capitalist consumption ( f � dC � dV � u). Via themultiplier 1/(1 � � ) this outlay circulates between the consumptionand 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 � � ) is a term representing the velocity of money. To take anexample given by Marx (1969a: 341), say that 1,000 units of money circu-late in the economy with a velocity of 3. The total price of commodities, orin the terminology of equation (4.23) the total income, is in this example3,000. Dividing the income (3,000) by the velocity establishes the amountof 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 .This can be interpreted as an average of the many circuits of money that arereported in Table 4.6. As Marx writes in Capital, volume 1:

Given the total number of times all the circulating coins of one denom-ination turn over, we can arrive at the average number of times a singlecoin turns over, or, in other words, the average velocity of circulationof money.

(1976: 216)

In Table 4.6 the first circuit is initiated by an injection of 1,750, some ofwhich is required to fuel the injection of 1,354 in the next circuit, the restturning over for only one circuit. The scalar velocity of money provides anaverage amount of time each money unit turns over.

As shown by Moore (1984: 126), the velocity is only equal to the multi-plier under the assumption that the period of production and the periodduring which the multiplier is completed are the same as the period duringwhich a given volume of money circulates. Under this assumption, themagnitude of spill-over effects, associated with an initial money outlay oninvestment through the multiplier process, provides an equilibriumconstraint on the size of the velocity.8

This macroeconomic interpretation of the circulation of money providesa direct way of explaining the narrow assumptions implicit in both theGraziani and single swap approaches, in which each production period isrestricted to one cycle in the circulation of money. As shown in the first partof this chapter, in the Graziani (single swap) model there is (1) only one

17

wc

wc


round of payment of wages (total income) at the start of the productionperiod; and (2) no allowance for spill-over effects between sectors. Thisimplies that the velocity of circulation is equal to 1, with all income, be itsimply total wages (Graziani) or the sum of wages and profits (singleswap), circulating in one cycle.9

The parallel assumption of the circuit approach is that the multiplier isalso equal to 1, meaning that there are no income–expenditure spill-overeffects between sectors, with the amount advanced having no multipliedimpact upon income. The multiplier relationship in (4.23) can be presentedas a general model in which the multiplier/velocity is a parameter that canvary in value. From this perspective, the Graziani and single swap modelsrepresent a particularly narrow case in which the value of this parameter isrestricted to 1.

In contrast to Schmitt (1996), the multiplier in equation (4.23) should notbe seen as a barrier to understanding the circulation of money. Schmitt’smain argument against the multiplier is that there is a confusion betweenactual amounts of income and increments in income. His complaint is thatthe multiplier process is driven by increments in spending, yet somehow ‘thegiven level of employment and income has been sustained in the periods pre-ceding the new impulse that initiates the multiplier process . . .’ (ibid.: 123,original emphasis). The problem is that the ‘multiplier analysis unjustifiablytreats the two integral parts of total income. . . in two entirely different ways’(ibid.: 123). Total income is reproduced in the current period but itsincrement is somehow supposed to initiate a multiplier process.10

However, by locating equation (4.23) in the reproduction schema, therole that the multiplier plays in the reproduction process is explained.Increments in demand, represented by new capital, and financed by theadvance of credit money, are the driving force of economic activity.Moreover, this injection of money provides the demand impetus andmonetary wherewithal for firms to use up inventories and replace them.Reproduction is oiled by the injection of money demand, the outcome beingthe replacement of inputs and the expanded reproduction of the systemonce additional inputs are in place. Income is both sustained and increasedin this reproduction process. By focusing on Marx’s reproduction schema,a logical attempt can be made to marry increments in income with thereproduction 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 mutualexchange multiplier developed by Nell (2004) in his critique of the singleswap approach. As both a way of exposing the narrow assumptions of thesingle swap and Graziani models and a way forward for modelling the cir-culation of money, this alternative approach is advantaged by its simplicity.


A comparison with equation (4.7) demonstrates that (4.23) is considerablyless complicated than the far from standard approach to modelling themultiplier developed by Nell (2004).

A marked degree of clarity and accessibility is therefore offered by thisapplication of the simple Keynesian multiplier to the circulation of moneyin a macro economy. In addition, Appendix 4 shows that the interindustryfoundations of this model are consistent with Marx’s value categories andhis definition of investment. As a basis for future research, this macromonetary model is offered as a way of potentially improving communica-tion between the Franco-Italian circuit school and the Marxian and PostKeynesian traditions.


5 Money, growth and crisis

For Marx, the task of establishing how a capitalist economy can reproduceitself is not limited to a particular period of production. The reproductionexamples that he carves out in the final part of Capital, volume 2, showhow balanced reproduction can take place over an extended number ofyears. Despite the limitations he faced, with a lack of formal modellingtools, computing power and waning personal health – the reproductionschemes were one of his last contributions to political economy – Marx wasable to devise complex numerical examples, in which somehow a 10 per centrate of growth is sustained in each period of production. It is not for nothingthat 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, cir-cuits of money must continuously open and close in successive periods ofproduction. The key question is not just how much money is required forsuccessive circuits to function, but also where does the money come from.Under expanded reproduction, an increasing amount of money is requiredto service the growing requirements placed upon a capitalist economy.

Capital outlays and sales

A seminal contribution to understanding the role of money in expandedreproduction has been provided by Foley (1986) in chapter 5 of his book,Understanding Capital. This is an extremely detailed model of all the facetsof Marx’s system of reproduction, including the complex role of time lagsbetween various activities and the way in which capital is transformed intoits different forms. In the analysis that follows a stripped down version ofthis model is presented.

Foley develops a circuit of capital that locates money outlays as the start-ing point (ibid.: 67). The money capital outlay is represented by C(t), wheret is the current period of production. These capital outlays are used to

purchase inventories and partly finished goods that are subsequently turnedinto finished products. At the end of the current period these finished productsare sold, as represented by money sales S(t).

Under simple reproduction, the receipts from sales provide sufficientmoney 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 – theamount of money spent on means of production and wages. This match-upis achieved by selling the precise amount of means of production andworker consumption goods. Second, S�� (t � 1) are sales that allow capital-ists to recover money outlays on their own personal consumption. A precisevolume of luxury goods is required for this match-up to be established.Since

S(t � 1) � S� (t�1) �S � (t� 1) (5.2)

total sales are sufficient to recover the initial outlays by capitalists on capitalgoods and luxury consumption.

Because of the time delay between sales in one period and capital outlaysin the next period capitalists set aside a hoard of money. As mentioned inChapter 3, when capitalists are ready for new capital outlays money isdrawn from the money hoard. De Brunhoff (1973: 38–44) shows howmoney hoards are essential to the circulation of money and commodities inMarx’s system, enabling a continuous production process. As lucidly statedby Marx (1964: 136), ‘The hoards thus act as channels for the supply orwithdrawal of circulating money, so that the amount of money circulat-ing as coin is always just adequate to the immediate requirements ofcirculation.’

Under simple reproduction, the amount of money required for circulationis constant. Capitalists allocate all of their surplus value to personal con-sumption, feasting in luxury instead of investing in expansion. Since thereis no room for the economy to grow, there is no demand for the moneyhoard to grow. Output is static, with the same volume of commoditiesreproduced each year, serviced by the same money hoard.

However, under expanded reproduction a much more demandingrequirement is placed on the circuit of money. Capitalists increase theircapital outlay on new elements of constant and variable capital. If we definedC as new constant capital and dV as new variable capital, there is anextra amount of money (dC � dV) that is required to service expanded

Money, growth and crisis 51

reproduction. Indeed, there is a shortfall in the amount of money that isprovided 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 placesa drain upon the money hoard, which is not sufficiently replenished bysales. Moreover, as capital expands in each period the shortfall will getbigger:

hence the solution of having capitalists start with a money reserve,which worked for simple reproduction, will not work for expandedreproduction. Any finite initial reserve of money would be exhaustedat some point on the path of expanded reproduction.

(Foley 1986: 87)

The conclusion drawn by Foley is that new borrowing is required to meetthis shortfall. There is a paradox of borrowing, the borrowing requirementcontrasting with the received opinion in Marxist circles that all investmentis drawn from an existing pool surplus value.1 With B(t) defined as ‘newcapital borrowing’ (ibid.: 89), capital outlays under expanded reproductionare met by setting

C(t) � S(t � 1) � B(t) (5.4)

Borrowing in period t is used to supplement the money hoard inheritedfrom sales in period t � 1. At the end of period t, capital outlays lead toexpanded sales, which enhance the size of the money hoard. Underexpanded reproduction, capital outlays are met from a growing hoard ofmoney that is replenished by a combination of borrowing and sales.

It can be pointed out that Foley implicitly embraces a single swapapproach to the circuit of money. He assumes that capitalists must advanceas money capital the total value of output, which once sold earns the pre-cise amount of revenue required to recover the outlay. This is seen mostclearly in equation (5.1), where the money capital advance is equal to thetotal sales of all capital and consumption goods. In Chapter 4 we saw thatthis approach, associated with Seccareccia (1996), has been heavily criti-cized by Nell (2004) for overestimating the amount of money required tooil the circuit of money – a serious miscalculation since it is important toknow the precise borrowing requirements placed on the financial system.

Indeed, a consequence of this miscalculation is that it wipes out any the-oretical role for the income–expenditure multiplier in the reproduction


schema. Once it is recognized that the multiplier can expand incomebeyond the initial capital outlay, a much more realistic model of the circuitof money is possible. The macro monetary model developed in Chapter 4can 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 capitalistconsumption (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 aconsequence, the money circuit is viable without the requirement ofa money hoard, accumulated from the previous period’s sales.

Abolishing the money hoard allows a model of the money circuit that isrelevant to contemporary institutional arrangements. In an interpretation ofMarx that is in keeping with both Post Keynesian and circuit school per-spectives, the central focus of this model is on the provision of loans by adeveloped banking system. The key insight is that each new loan is both anasset and a liability, allowing banks to finance the bulk of their outlaysvia deposits in their own balance sheets (see Chick 1997). There is, itshould be noted, usually a requirement that banks hold small reserves, ofaround 3 per cent of deposits; but this is light years away from the assump-tion made by Marx in Capital, volume 2, that capitalists hoard metallicmoney (and the assumption by Foley (1986) that all the income from salesis used to replenish a money hoard). As we shall see, however, it is difficultto tap the rich seam of Marx’s writings, in particular when we look at histheories 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’sreproduction schema, is provided by the Domar model of economic growth.Instead of providing a snapshot of each period of production, the schemacan be developed over an extended number of periods; thereby providing amore complete picture of economic growth over time. The contribution ofthe following analysis will be to derive the model developed by Domar(1947) from foundations that are consistent with Marx’s multisectoralschema. Domar’s model is particularly suitable for this purpose because itspecifies the conditions required for balanced growth. In contrast toHarrod’s variant of the model, in which actual investment is determined byan accelerator mechanism, in Domar’s model ‘the actual level of investment


is not determined within the confines of the model’ (Jones 1975: 64). Marxhad a similar focus on the dynamic conditions for balanced growth, withouttrying to formulate a model of actual economic growth.

Table 5.1 shows the two-department expanded reproduction schema overfive years.2 The familiar assumption of a constant rate of surplus value of100 per cent is maintained, together with a 4:1 ratio of constant to variablecapital in Department 1 and a 2:1 ratio in Department 2. Constant capitalinputs 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 sufficientsurplus value to invest in additional units of capital. Marx assumes thata half of surplus value in Department 1 is invested in this way. For year 1this means that 500 of the total 1,000 units of surplus value producedin Department 1 are directed to 400 units of new constant capital and100 units of new variable capital. In year 2 constant capital expands from4,000 to 4,400 units, and variable capital from 1,000 to 1,100 units, main-taining the 4:1 ratio between constant and variable capital. A new positionof balance is established by also maintaining Department 2 at its original2:1 ratio.


Table 5.1 Marx’s expanded reproduction schema

Ci Vi Si Wi

Year 1Dept. 1 4,000 1,000 1,000 6,000Dept. 2 1,500 750 750 3,000

5,500 1,750 1,750 9,000

Year 2Dept. 1 4,400 1,100 1,100 6,600Dept. 2 1,600 800 800 3,200

6,000 1,900 1,900 9,800

Year 3Dept. 1 4,840 1,210 1,210 7,260Dept. 2 1,760 880 880 3,520

6,600 2,090 2,090 10,780

Year 4Dept. 1 5,324 1,331 1,331 7,986Dept. 2 1,936 968 968 3,872

7,260 2,299 2,299 11,858

Year 5Dept. 1 5,856 1,464 1,464 8,784Dept. 2 2,129 1,065 1,065 4,259

7,985 2,529 2,529 13,043

Examining the elements of Table 5.1 reveals that from year 3 onwardseach department, and hence the economy as a whole, expands at a balancedgrowth 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 con-ditions required to establish this balanced growth path will now be exploredin detail.

The starting point for this analysis is the Keynesian multiplier

(5.7)

which has as its constituent elements the Marxian term representing theshare of surplus value (e) and Kalecki’s ratio of capitalist consumption tototal profits (�). This multiplier has been derived, in Chapter 3, from thetwo-department expanded reproduction schema (see equation 3.9). It cap-tures the relationship between aggregate net income (y) and autonomousinvestment (I ). For simplicity, in the present analysis autonomous capitalistconsumption is assumed to be zero.

By defining � 1 �� as the ratio of investment to profits, the multiplierrelationship between each increase in income (dy) and investment (dI) is

(5.8)

Following Domar (1947), the supply side of economic growth can be mod-elled by letting the economy’s capacity to increase income in proportion tothe increase in capital stock (�) represent the productivity of investment.Given that investment is the same as an increase in the capital stock itfollows that

(5.9)

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

(5.10)dI�e

� I�

� �dyI

dy �1

e�dI

�

y �1

e(1 � �)I


It follows from multiplying both sides of (5.10) by e, and dividingby I, that

(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 ofchange of income:

(5.12)

(see ibid.: 41). The balanced growth rate would, in the unlikely event thatthis could be achieved, be equal to the multiple of (the ratio of investmentto profits), e (the per capita share of surplus value) and � (the productivityof investment).

Using the analysis provided in Appendix 5, this balanced growthrelationship can also be specified as

(5.13)

where r is the money rate of profit, which is calculated by the formular � 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 theratio e/(1 � e).3 Equation (5.13) is the Cambridge equation, also derived byFoley (1986: 76) from his model of the circulation of money.

To bring these results alive, they can be nested in the Marx’s numericalexamples. Table 5.2 shows the expanded reproduction schema of Table 5.1in 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,

dyy � �r

�

dyy �

dII

� �e�

dII

� �e�

�


Table 5.2 Rates of growth in Marx’s reproduction schema

Year Constant Variable Profits Net dy/y I dI/Icapital capital income

1 5,500 1,750 1,750 3,500 — — —2 6,000 1,900 1,900 3,800 0.09 650 —3 6,600 2,090 2,090 4,180 0.1 790 0.224 7,260 2,299 2,299 4,598 0.1 869 0.15 7,985 2,529 2,529 5,058 0.1 955 0.1

as . Second, e � 1/2 is shown by calculatingthe 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

. Hence, the balanced rate of growth is

(5.14)

Using the alternative Cambridge equation approach, the balanced rate ofgrowth takes the form4

(5.15)

Domar provides the same insight as Foley into the role of money underexpanded reproduction. In (5.12), expanding investment (dI � 0) is estab-lished under balanced growth. It follows that investment in period t must behigher than investment in the previous period (It � It�1). Now in equilibriuminvestment in each period is identical to total savings (Savt), which meansthat It�1 � Savt�1.5 Hence it can be concluded that It � Savt�1. Underexpanded reproduction, ‘Investment of today must always exceed savingsof yesterday . . . . An injection of new money (or dishoarding) must takeplace every day’ (Domar 1947: 42). This is the paradox of borrowing, asalso shown in Foley’s model of the circulation of money.

Notwithstanding the rich complexity of the Foley model in its treatmentof time, the main advantage of Domar’s demonstration of the paradox ofborrowing is that it embodies the Keynesian multiplier relationship. Amuch more general model of the circuit of money is suggested, comparedto the single swap approach adopted by Foley. Moreover, since our deriva-tion of the Domar result is established from input–output foundations, itis not restricted to Marx’s two-sector schema, but could in principle begeneralized 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 theremight be economic crisis. This monetary perspective has been largely neg-lected by official Marxian economics, with the main focus on ‘real’ analy-sis (see Arnon 1994: 355). For Pollin (1994: 101), ‘Marxian economics haduntil recently almost completely overlooked monetary and financial phe-nomena.’ Similarly, Hein (2002: 1) argues that attempts ‘to reconstructMarx’s theory of money and credit remained without major consequencesfor Marxian theories of accumulation and crisis’. And for Crotty (1985: 45),

�r � 0.4150.2414 � 0.1

�e� � 0.4150.50.481 � 0.1

� � dy/I � 418/869 � 0.481

� � I/P � 955/2,299 � 0.415


‘the Marxian crisis theory literature has had very little to say about monetaryand 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 themainstream literature on the economics of growth, and in the Marxian lit-erature other matters have been given much more attention. Foley’s work onthe transformation problem, for example, has been far more widely citedthan 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 ofborrowing in the context of Marxian crisis theory.

The abstract starting point for Marx’s monetary theory of crisis is providedin chapter 17 of Theories of Surplus Value part 2. Here Marx explores therole of money under simple circulation (M–C–M). Money provides thestarting point and end point of the circuit of commodities. Capitalists usemoney 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 spendthe right amount of money (C–M). This separation of purchase from sale isfraught 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 intomoney 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 entirelypossible that there will not be sufficient co-ordination for all purchases andsales to be in balance.

There are three main consequences of this separation of purchase fromsale. The first is a critique of Ricardo’s assertion that ‘no man produces butwith a view to consume or sell’ (Ricardo 1951: 290; see Kenway 1980: 28).Instead of a separation of purchase from sale, Ricardo assumes each indi-vidual is simultaneously a producer and consumer, deciding what to pro-duce and consume in the same breath. This is Say’s Law, that supply createsits own demand. Marx was very scathing about Say’s Law, viewing it as‘childish babble’ and ‘a cosy description of bourgeois conditions’ (Marx1969b: 502–3). From a class-based perspective, there is a demarcationbetween the production decisions of a small number of capitalists and theconsumption decisions of the population as a whole.

Second, a nascent multiplier process can be identified. Mitchell andWatts (2003: 154) argue that Marx ‘laid the foundations of multiplier


theory by arguing, in Theories of Surplus Value, that, once this unity of saleand purchase was disturbed, the chain of contractual relationships betweensuppliers became threatened and overproduction, and then bankruptciesand unemployment, became widespread.’ Marx considers the linkagesbetween demand for the goods produced by capitalists and the consumptionof workers employed to make these goods (an embryonic consumptionfunction). For the case of a slump in the market for calico:

The stagnation in the market, which is glutted with cotton cloth, hampersthe reproduction process of the weaver. This disturbance first affectshis workers. Thus they are now to a smaller extent, or not at all, con-sumers of his commodity – cotton cloth – and of other commoditieswhich entered into their consumption.

(Marx 1969b: 522)

Stagnation has a multiplier effect on the consumption of workers whichfeeds back on the ability of producers to sell their wares.

Finally, Marx develops the separation between purchase and sale by identi-fying 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 legally-binding contract’. Marx (1969b: 511) uses the example of a weaver purchasingconstant capital. The weaver, producing cloth, may purchase raw materialsfrom the spinner by borrowing from the bank. Once the cloth is sold to themerchant, 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 abill 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 asthe final goal (a means of payment), without it being transformed simultane-ously into a purchase. Suppose, Marx says, that the merchant doesn’t pay:

The flax-grower has drawn on the spinner, the machine manufactureron the weaver and the spinner. The spinner cannot pay because theweaver cannot pay, neither of them pay the machine manufacturer, andthe latter does not pay the iron, timber of coal supplier . . . . Thus thegeneral crisis comes into being.

(ibid.: 511)

Money as means of payment enhances the possibility of general crisis; acrisis that is less abstract and more of a concrete possibility.

Representing money as a means of payment is an important step indeveloping a mature theory of crisis, one that is relevant to full-blowncapitalism. Marx argues that his analysis of means of payment is not


sufficiently developed to explain the cause of crises; but it is at least a stepin the right direction: ‘we can already see the connection between themutual claims and obligations, the sales and purchases, through which thepossibility can develop into actuality’ (ibid.: 511).

A further concrete step in the development of a monetary theory of crisisis established by Marx in part 5 of Capital, volume 3. Key to this approachis an understanding of how the credit system develops. In a developedcapitalist economy hoards are no longer held by individual capitals; ‘inadvanced bourgeois countries they are concentrated in the reservoirs ofbanks’ (Marx 1964: 137). Hoards are collected in a central pool of creditmoney, managed by the banks. ‘Small sums which are incapable of func-tioning as money capital by themselves are combined into great masses andthus form a monetary power’ (Marx 1981: 529). Notwithstanding the lurk-ing presence of a commodity theory of money in this hoarding approach(see Nelson 1999), Marx shows how important the credit system is to aneconomic expansion. ‘The development of the production process expandscredit, while credit in turn leads to an expansion of industrial and commercialoperations’ (Marx 1981: 612).

Together with the benefits afforded by credit, however, there are alsopotential fragilities.6 The problem is that credit allows capitalists to ‘pursuethe production process past its capitalist barriers: too much trade, too muchproduction, too much credit’ (ibid.: 640). Speculation, and even swindlingon the part of those who operate the credit system, helps to fuel an over-expansion of the financial system. In particular, the relative autonomy ofthe credit system creates a disjunction between production and its realization.Capitalists can obtain finance to expand their production, even if demand isstagnant (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 abanker, Marx 1981: 660). And with the restriction of credit provided bybanks, most likely taking the form of a hike in the rate of interest chargedon borrowing, investment is restored to a more sustainable growth path. Forde Brunhoff (1973: 118), ‘The hoarding in a crisis is only the reverse sideof the failure to sell commodities and the cessation of investment whichfollow an excessive expansion of production and commerce.’

This insight into how financial crises develop can be examined in thelight of the Foley/Domar borrowing paradox. To recap, we have establishedthat expanded reproduction requires borrowing on the part of the capitalistclass. How then does Marx’s insight, that borrowing can outstrip realiza-tion, relate to the expanded reproduction schema? To answer this question


we will have to delve a little more deeply into the structure of the Domarmodel.

Looking back at equation (5.10), investment (I ) is the key economicvariable. The problem, as articulated by Domar (1947), is the dual role ofinvestment in this equation. On the left-hand side the increment in invest-ment determines, via the multiplier, the increment of income which theeconomy demands. On the right-hand side, however, the increment incapacity, which the economy can supply, is determined by the amount ofinvestment – itself representing the required change in the capital stock.Whereas changes in investment are necessary in order to induce increasingaggregate demand, only a particular amount of investment is required toenable a matching increase in supply. For Domar this provides the heartof the problem as to why balanced growth is so difficult to achieve for acapitalist economy. An absolute amount of investment generates an increasein capacity, but an increase in investment is required to realize this capacityin terms of increasing income. This is why

even in relatively prosperous periods a certain degree of underemploy-ment has usually been present. Indeed, it is difficult enough to keepinvestment at some reasonably high level year after year, but therequirement that it always be rising is not likely to be met for anyconsiderable length of time.

(ibid.: 47)

Overproduction of capacity, relative to aggregate demand, is a persistenttendency inherent in the schemes of expanded reproduction, as formalizedin the Domar growth model.

Introducing the financial system into this picture leads to severeconsequences. Not only must investment continually grow at a particularrate to sustain the required amount of aggregate demand, it must also befinanced by borrowing from the financial system. All investment in newcapacity, according to the Domar/Foley insight, must be financed by bor-rowing. In the reproduction schema, therefore, all borrowing is continuallyin tension with realization, at all rates of positive growth. Since it is verydifficult for investment to ever grow enough to satisfy capacity, the creditthat makes it possible is always released on shaky grounds. On this inter-pretation, financial crises are not just applicable to excessive expandedreproduction, when financial speculation ‘takes off on its own’; financialfragility is embedded in expanded reproduction itself.

This Domar interpretation can be placed in stark contrast to the argumentmade by Shoul (2000: 98) that ‘Marx’s reproduction models postulate theoperation of Say’s Law’ (see also Robinson 1968: 111). The argument,


which has a long history in Marxian economics, is that Marx established hismodel of balanced growth on the assumption that supply creates its owndemand. Since the reproduction schemes show the conditions under whichsupply and demand are in balance, the argument is that Say’s Law musthold. Shoul argues that Marx’s refutation of Say’s Law, in Theories ofSurplus Value part 2, where the role of money in capitalism is taken seri-ously, is analytically separate from the reproduction schema, in whichmoney is an absent guest. Say’s Law has a dual role, on the one hand beingrefuted where money is considered, and on the other hand implicitlyassumed when growth is considered.7

As we have seen, however, the circulation of money also plays a pivotalrole in the reproduction schema. Without borrowing from the financialsystem 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 adual source of capacity and demand, is a fragile network of credit relation-ships between capitalists and banks. Marx’s reproduction schemes exposethe stringent conditions on the finance and realization of investment that arerequired for balanced growth. Since these conditions are unlikely to bemet – supply is unlikely to create its own demand – a refutation of Say’s Lawis offered by the reproduction schema.


6 Beyond underconsumption

The early part of the twentieth century was a golden period for Marxianeconomics. With the dominant German Social Democratic Party at its centre,a rich ferment of discussion took place over the meaning and application ofMarx’s Capital; and in particular over the role of the reproduction schema.This golden period came to a brutal end. Rosa Luxemburg was murdered byright-wing terrorists, Hilferding perished at the hands of the Gestapo inFrance and Bukharin fell victim to Stalin’s show trials. In view of the enor-mous damage to the Marxian economic tradition inflicted by this age ofextremes, it is vital that the ideas developed during this period are salvaged.

Two key interpretations of the reproduction schema from this golden ageare considered here. First, the disproportionality school, with TuganBaranovsky and Hilferding as its main proponents, looked at the proportionsbetween 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 depart-ments of production when one of them engages in overproduction relative tothe other. This approach was developed as a response to underconsumption-ists, such as Sismondi and Malthus, who argued that consumption is themain constraint on capital accumulation. Underconsumption is reduced toa special case, where there is overproduction by the department producingconsumption goods. And so long as proportionality is maintained theproblem of underconsumption is assumed away.

Second, Rosa Luxemburg’s Accumulation of Capital provides anexceptionally detailed examination of Marx’s reproduction schema. Aznar(2004: 253) argues that ‘Luxemburg believed this book to be a continuationof “Capital” book 2, which Marx had left unfinished’. Key to Luxemburg’sinterpretation is the role of demand, which she argues is obscured by Marx’sspecific focus on the question, ‘Where does the money come from?’ Marxis criticized for assuming that capital can accumulate unimpeded, withoutidentifying how new capacity can be profitably realized.

For daring to question Marx, Luxemburg has been lambasted for beingan underconsumptionist. Sweezy (1942: 171), for example, considered herto be ‘the queen of underconsumptionists’, regarding consumption as thekey constraint upon capital accumulation.1 Foley (1986: 151) argues thatfor Luxemburg ‘there is something strikingly un-Marxist about the premisethat the ultimate aim of capitalist production is workers’ consumption’.Similarly, for Howard and King (1989: 113), ‘But she herself is mistaken inimputing to the capitalist system as a whole the goal of expanding humanconsumption.’

Yet, on a close reading of Accumulation, capitalists are engaged in thepursuit of exchange-value: the pursuit of money profits. In a quotation thathas been highlighted by Desai (1979: 155), Luxemburg writes, ‘This meansthat the starting point of capitalist production is not a given number ofworkers and their demands, but that these factors themselves are constantlyfluctuating, “dependent variables” of the capitalist expectations of profit’(Luxemburg 1951: 134).2

The purpose of this chapter is to review particular aspects of these twointerpretations of the reproduction schema in the light of the macro mone-tary model developed in previous chapters. How do these interpretationsrelate to our emphasis in the reproduction schema upon the importance ofmoney, credit and the multiplier? And what is the distinctive contribution ofthe macro monetary model relative to these golden age interpretations? Byre-interpreting these approaches through the lens of our macro monetarymodel, the objective is to explore in more depth the role of the reproductionschema in Marxian economic theory.

Disproportionality

Buried in the murky waters of Capital, volume 2, Marx makes passingreference to the importance of proportionality between departments of pro-duction. Under simple reproduction, disproportion would have disastrousconsequences: ‘the whole basis of the schema would be destroyed, i.e.reproduction on the same scale, which presupposes complete proportional-ity between the various systems of production’ (Marx 1978: 530). Byassuming balance in the reproduction schema, co-ordination is establishedbetween capital and consumption-good producing sectors. For someMarxists, writing at the start of the twentieth century, this provided a seduc-tive insight into how governments might impose order on the economicsystem.

The main proponent of the disproportionality approach was RudolfHilferding, who built on the ideas of the Russian Marxists, TuganBaranovsky and Bulgakov. Key to the occurrence of disproportions is the


propensity of capitalists to seek exchange-value, the pursuit of individualprofits. If capitalists behave as profit-seeking individuals, can they take intoaccount 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 ofinvesting “rationally”, i.e. so as to maintain proportions of equilibriumbetween 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 govern-ment intervention to ensure balance between the departments of production. InHilferding’s Finance Capital, first published in 1910, this approach is marriedwith an analysis of the role of cartels and banks in compounding the inflexi-bility of the economic system: its inability through competition to remedy anydisproportions. Co-ordination can only be achieved by ‘subordinating thewhole of production to conscious control’ (Hilferding 1981: 296).

The most basic proportions embedded in the reproduction schema areestablished under simple reproduction. This was touched on in our intro-duction to the schema in Chapter 2, and in establishing the mutual exchangewhich takes place between departments of production in the circulation ofmoney (Chapter 4). These proportions can be formally derived, in Table 6.1,by displaying the elements of Marx’s numerical example (Table 2.1) along-side the Marxian algebraic symbols.3

The mutual exchange condition for simple reproduction, established inTable 6.1(a), is that Department 2 exchanges 2,000 units of consumptiongoods 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) asused-up constant capital C2. Similarly, the 2,000 units of consumptiongoods are purchased in Department 1 out of variable capital V1 and surplusvalue S1. Hence the condition for simple reproduction can be expressed as

C2 � V1 � S1 (6.1)

Beyond underconsumption 65

Table 6.1 Simple reproduction schema

Ci Vi Si Wi

(a) Numerical categoriesDept. 1 4,000 1,000 1,000 6,000Dept. 2 2,000 500 500 3,000

6,000 1,500 1,500 9,000

(b) Marxian categoriesDept. 1 C1 V1 S1 W1

Dept. 2 C2 V2 S2 W2

It can now be shown how this result can be derived using an input–outputinterpretation of the simple reproduction schema. Following the same pro-cedure first introduced in Chapter 2, Table 6.2(a) re-expresses the numericalelements of Table 6.1 as an input–output table.

Table 6.2(b) is an algebraic representation, using Marxian categories, ofthe input–output table for simple reproduction. In comparison withTable 6.1, this provides a clearer and more detailed representation of simplereproduction, since the expenditure of surplus value on capitalist consump-tion is shown explicitly as u. Moreover, the condition of simple reproductionis embodied in the assumption that total inputs are equal to total outputs (seeSweezy 1942: 162). Writing out these input–output balances explicitly,

C1 � V1 � S1 � C1 � C2 (6.2)C2 � V2 � S2 � V1 � V2 � u (6.3)

The condition for simple reproduction, as shown in (6.1), is easily obtainedfrom (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 bycancelling out V2 and S2 from (6.3). Once the input–output approach tobalancing Marx’s accounts is adopted, the simple reproduction conditionof 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 ofexpanded reproduction. Table 6.3(a) is the numerical input–output representa-tion of the expanded reproduction schema (see Table 2.4). In algebraic terms,the expansion of constant capital is represented by dC and new variable capi-tal by dV. Table 6.3(b) shows the set of input–output accounts using Marxiannotation, with the new role for capital accumulation represented alongside theterms previously modelled under simple reproduction.


Table 6.2 Simple reproduction in an input–output table

Dept. 1 Dept. 2 Capitalist Wi

consumption (u)

(a) Numerical categoriesDept. 1 4,000 2,000 6,000Dept. 2 1,000 500 1,500 3,000Si 1,000 500Wi 6,000 3,000 9,000

(b) Marxian categoriesDept. 1 C1 C2 W1

Dept. 2 V1 V2 u W2

S1 S2

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 bywriting

C1 � V1 � S1 � C1 � C2 � dC (6.4)C2 � V2 � S2 � V1 � V2 � dV � u (6.5)

Manipulation of each of these equations4 yields the condition for expandedreproduction

C2 � dC � V1 � S1 (6.6)

Comparing this to the condition for simple reproduction (6.1), the onlydifference is the element for expansion of constant capital dC. This illus-trates Marx’s claim that the condition of simple reproduction lives on as astructural entity under expanded reproduction. It also follows that the pro-portionality condition for expanded reproduction is implicitly assumed inthe input–output accounts.

How then can the input–output approach provide an insight into Marxiancrisis theory, when the very basis for these accounts is proportionality? AsRosdolsky (1977: 470) has argued, for writers such as Tugan andBulgakov economic crises are derived ‘solely from the disproportionalitybetween the various branches of industry’. A position of restricted con-sumption, for example, can be exclusively captured by overproduction ofthe department producing consumption goods, relative to the capital-goodsproducing department: the latter failing to provide a sufficient marketfor consumption goods (see Kuhn 1979: 216). On the assumption ofproportionality, how can there be room for any other theories of crisis?

A coherent response requires a re-statement of the macroeconomicconditions for balanced growth (Chapter 5). Recall that the Domar conditions





(b) Marxian categoriesDept. 1 C1 C2 dC W1

Dept. 2 V1 V2 dV u W2

S1 S2

W1 W2

have been established using a macroeconomic multiplier relationship that isderived from an input–output foundation (equation 5.7). It therefore followsthat the Domar balanced growth equation, as we have derived it, assumes pro-portionality between departments of production. Now using the Domar inter-pretation of the reproduction schema, balanced reproduction on an expandedscale has two main dimensions. First, the paradox of borrowing, established byFoley and Domar, stipulates that capital accumulation on an expanded scaleis only possible if new credit is made available to capitalists. Second, invest-ment has to grow at a particular rate such that the new capacity it generatesis balanced by increments in demand. From a macroeconomic perspective,establishing balanced growth requires an analysis of the rate of change of newinvestment, financed by the required amount of credit.

These macroeconomic questions are posed for a model under whichproportionality between Departments 1 and 2 is assumed. Consider again(5.10), which exposes the contradiction in the Domar model betweenabsolute amounts of investment, which create new capacity and changes ininvestment that drive the required amount of aggregate demand. There yousee that investment (I ) is made up of increments in constant and variablecapital, 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) con-gealed in worker consumption goods. These macroeconomic terms aggre-gate across the two departments; they transcend the more micro question ofproportionality between the two departments.

This does not mean that disproportionality is irrelevant to modellingeconomic crises. Even the most minor disruption or disjuncture in the eco-nomic system would, in all likelihood, be associated with disproportionbetween the departments of production. The argument, however, is that anexclusive focus on disproportion does not ask the right questions about howthe reproduction process functions as a macroeconomic entity. Questions ofaggregate demand and the role of credit, it can be argued, are obscured bya focus on proportionality. In the analysis that follows the macroeconomicquestions posed by Rosa Luxemburg are considered to be a more incisivechallenge for the reproduction schema.

Luxemburg and accumulation

Whereas Hilferding, who eventually became the German Minister ofFinance, occupied the centre ground of the German Social DemocraticParty, 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


in its serious purpose and scholastic tone.’ Luxemburg also followsHilferding in viewing the reproduction schema as the main vehicle forexploring the conditions for capital accumulation, but with radically differ-ent conclusions. Far from showing how the proportions between depart-ments of production can be planned, Luxemburg argues that expandedreproduction is impossible.

For scholars of Marx, a common complaint is that Marxian economics,as practiced in the universities, fails to reflect the original purpose ofMarx’s writings. Models of reproduction, in particular, ignore the impor-tance of money and the way in which Marx uses the schema to expose theperceived dogma of Adam Smith (see Moseley 1998). A close reading ofLuxemburg’s Accumulation of Capital, as we shall see, does not disappointon either of these fronts.

The starting point for Luxemburg’s investigation is the reproduction ofthe total social capital. ‘Karl Marx made a contribution of lasting service tothe theory of economics when he drew attention to the problem of thereproduction of the entire social capital’ (Luxemburg 1951: 31). The his-torically specific cornerstone of capitalist reproduction is that it requires theformation of profits:

only those goods are produced which can with certainty be expected tosell, and not merely to sell, but to sell at the customary profit. Thisprofit becomes an end in itself, the decisive factor which determinesnot only production but also reproduction.

(ibid.: 34)

Capitalism therefore involves a multitude of individual producers engagedin the pursuit of profit. To conjoin these individual decisions into a repro-ducing total capital requires circulation and exchange. ‘Capitalist produc-tion is primarily production by innumerable private producers without anyplanned regulation. The only social link between these producers is the actof exchange’ (ibid.: 34).

The exchange of commodities between producers is underpinned byMarx’s theory of value. In contrast to Adam Smith, a correct distinction ismade by Marx between dead and living labour (see Chapter 2). Constantcapital – raw materials, machinery and premises – are produced by pastlabour, in previous periods of production. Variable capital and surplus valueare produced by living labour in the current period of production. ForLuxemburg:

This specific connection of each past period of production with theperiod following forms the universal and eternal foundation of thesocial process of reproduction and consists in the fact that in every


period parts of the produce are destined to become the means ofproduction for the succeeding period: but this relation remained hiddenfrom 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 ismade up of constant capital, variable capital and surplus value. Moreover,commodities have value in exchange only when they are sold in their moneyform. ‘Once the commodity has been produced, it must be realized, it mustbe converted into a form of pure value; that is, into money’ (ibid.: 38).However, when Luxemburg examines the reproduction of total capital, theuse-form of commodities is also important.

Whereas it does not make the slightest difference to the individualcapitalist whether he produces machinery, sugar, artificial manure or aprogressive newspaper – provided only that he can find a buyer for hiscommodity so that he can get back his capital plus surplus value – it mat-ters infinitely to the ‘total capitalist’ that his total product should have adefinite use-form. By that we mean that it must provide three essentials:the means of production to renew the labour process, simple provisionsfor the maintenance of the workers, and provisions of higher quality andluxury goods for the preservation of the ‘total capitalist’ himself.

(ibid.: 81)

This emphasis on the importance of the use-form provides a rationale forthe reproduction schema, in which separate departments of production areestablished for consumption goods and means of production. Luxemburgargues for simplicity that one category of consumption goods incorporatinggoods consumed by workers and capitalists can be considered. In addition,the formula for calculating values (C � V � S) can be applied to both indi-vidual and total capitals, but at the aggregate level has to be complementedby the reproduction schema (ibid.: 83).

Starting with Marx’s case of simple reproduction, Luxemburg considerstwo 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 isalways 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 whichLuxemburg sets out the role of money in the reproductions schema. Thecirculation of money is examined in the context of Marx’s numericalexample of simple reproduction (Table 6.1).


First, a mutual exchange theory of money is formulated. Money ‘firstcomes into circulation by the payment of wages’ (Luxemburg 1951: 94).Capitalists in Department 1 advance 1,000 units of money to their workersas variable capital. Capitalists in Department 2 sell consumption goods toDepartment 1 for this value of 1,000 units. The money, first advanced inDepartment 1, circulates into the hands of capitalists in Department 2. Withthe money received from this transaction, Department 2’s capitalists areable to purchase means of production from Department 1 and the moneyreturns into the hands of the Department 1 capitalists. The same type ofmutual exchange happens for the 500 units advanced as variable capital inDepartment 2.

Second, the Kalecki principle, that capitalists earn what they spend, canalso be identified in Luxemburg’s interpretation of Marx.5 The mutualexchange of money advanced as wages is insufficient to oil all of theexchange 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 theworkers’. Capitalists must advance money in order to satisfy their ownconsumption requirements. There are, of course, 1,000 units of money thatare bouncing between the departments from the original advance of wages,but this cannot be used to oil capitalist consumption. Capitalists mustconsume at the same time as workers consume. For Luxemburg, ‘Bothcapitalists may each advance 500 units of the money necessary for theexchange, or possibly the two departments will contribute in differentproportions’ (ibid.: 96). Luxemburg is uncertain as to how exactly capital-ists advance this money, the main criteria being that there is sufficientmoney for capitalist consumption and constant capital to be purchasedin full.

Luxemburg therefore identifies the Kalecki principle in Marx’sreproduction schema: ‘if the capitalists themselves have set in motion allthe money which circulates in society, they must also advance the moneyneeded for the realization of their own surplus value’ (ibid.: 98). Under sim-ple reproduction, this money is earned from the extraction of surplus valuein previous periods, but in the current period of production capitalistsclearly earn what they spend (the Kalecki principle). So long as there is suf-ficient money cast into circulation for capitalist consumption, together withthe 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 laterperiods.’


Since all surplus value is consumed by capitalists under simplereproduction, it is very easy to see how profits are realized. Where theproblems start are under expanded reproduction. For Luxemburg:

The essential difference between enlarged reproduction and simplereproduction consists in the fact that in the latter the capitalist class andits hangers-on consume the entire surplus value, whereas in the formera part of the surplus value is set aside from the personal consumptionof its owners, not for the purpose of hoarding, but in order to increasethe active capital, i.e. for capitalization.

(Luxemburg 1951: 112)

Under expanded reproduction, not all of the surplus value is consumedby capitalists. A part of it is now directed to expanding the means of pro-duction, and there must be sufficient aggregate demand to purchase thesenew goods. Luxemburg poses the key question: ‘Where is this continuallyincreasing demand to come from, which in Marx’s diagram forms the basisof reproduction on an ever rising scale?’ (ibid.: 131). Of course, Luxemburghas been widely criticized for arguing that the source of this demand mustcome from non-capitalist buyers (ibid.: 366); but our focus here is uponhow the problem of demand is first established in the reproduction schema.6

As argued by Zarembka (2002: 24), ‘Luxemburg turns to a serious analysisof the role of a non-capitalist environment only after discovering the weaknessin Marx’s presentation.’

This demand problem is examined by considering the ‘peculiar’ domi-nance of Department 1 (ibid.: 120). By applying the rule that capitalists inDepartment 1 invest a half of their surplus value in new capital, it is assumedthat Department 2 is completely passive.7 Once Department 1 has followedthis rule to start the production of capital goods, the question is asked:‘And who requires these additional means of production?’ (ibid.: 132). Theanswer must be that Department 2 requires these capital goods in order toexpand its production of consumption goods. This begs a further questionfrom Luxemburg, ‘Well then, who requires these additional consumergoods?’ (ibid.: 132). This demand must come from Department 1, since itis 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 isabsurd to produce more consumer goods merely in order to maintainmore workers, and to turn out more means of production merely tokeep this surplus of workers occupied.

(ibid.: 132)


More circling is involved in the consideration of money. There is a problemof establishing where the money comes from to back up the aggregatedemand. Luxemburg considers Marx’s example of capitalists A, that pro-duce a surplus product of capital goods, and capitalists B, that consume thissurplus product. The problem is that to get the money to purchase from theA’s, the B’s must also sell their surplus products. ‘But who could havebought their surplus product? It is obvious that the difficulty is simplyshifted from the A’s to B’s without having been mastered’ (ibid.: 143).

The money could be found in the transition from simple reproduction toexpanded reproduction, when capitalists reduce their own consumption,making money available for accumulation (ibid.: 147). Aside from thesevery narrow circumstances, however, Luxemburg argues that Marx’s focuson where the money comes from is a major distraction. Marx finds themoney for accumulation on the basis of a reduction in consumption, arestriction of demand. For Luxemburg, ‘It is not the source of money thatconstitutes the problem of accumulation, but the source of the demand forthe additional goods produced by the capitalized surplus value’ (ibid.: 147).

Kotz has argued that Luxemburg is wrong to differentiate betweenmoney and demand. ‘Counterposing “money” and “demand” as two distinctpotential problems of accumulation is not a very useful way to view theissue, since the monetary problem appears to be an aspect of the demandproblem’ (Kotz 1991: 121). It could, however, be argued, in Luxemburg’sdefence, that she is not trying to banish money from the accumulationstory. Her main point is that ‘the very exposition of the difficulty’ – theproblem of identifying the source of money – obscured the role of demandin Marx’s investigation. The statement by Kotz that ‘the monetary problemappears to be an aspect of the demand problem’ is entirely consistent withthe considerable attention given to the circulation of money in Luxemburg’saccount. Indeed, Luxemburg identifies the source of money as a distinctpart 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, moneymust be forthcoming in adequate quantities for its realization. But it isquite impossible that this money should come from the purse of thecapitalist class itself.

(ibid.: 165)

Luxemburg’s two parallel questions

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


answers are offered by our macro monetary model. First, the multiplierframework, as considered in Chapter 4, provides a way of modelling the twoaspects of Marx’s circulation of money identified by Luxemburg: themutual exchange between departments of production and the Kalecki prin-ciple (capitalists earn what they spend). As a vehicle for exploring Marx’scirculation of money, this model provides a way of addressing the question,‘where does the money come from?’ The answer, on this interpretation, isthat money is advanced and returns back to capitalists in their expenditureson investment and capitalist consumption, and it multiplies here and tobetween the departments of production to oil the economy’s total income.This multiplier framework allows both the Kalecki principle and themutual exchange mechanism to be synthesized into a coherent model of themonetary circuit.

Second, the Domar model can address Luxemburg’s question, ‘wheredoes the demand come from?’ In equation (5.10) investment has a dual role.On the one hand increments in capacity are determined by the absoluteamount of investment; on the other hand the required demand is determinedby increments in investment. For Domar, this provides the heart of the prob-lem as to why balanced growth is so difficult to achieve for a capitalisteconomy. An absolute amount of investment generates an increase in capac-ity, but an increase in investment is required to realize this capacity in termsof increasing income. There is a mismatch between the contrasting require-ments of demand and supply in the reproduction schema, the main sourceof the contradiction being the hungry requirements of the demand side ofthe balanced growth equation.

This contradiction bears a close resemblance to Luxemburg’s posing ofthe question of how new capital goods can be produced in the absence ofsufficient demand to satisfy the new capacity. Sufficient demand, to meetthe requirements of a balanced growth in capacity, is unlikely to be forth-coming from within the Domar model, from within the reproductionschema. Joan Robinson’s interpretation of Luxemburg has some resonancewith 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 outputof 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 appreciatethe basic problem Luxemburg raises’: a problem that we argue can beformalized using the Domar model.


Aside from the problem of how demand meets the new capacity developedby capital goods, there is the additional problem that capitalists mustborrow money. Luxemburg recognized the importance of borrowing, inchapter 30 of Accumulation of Capital, when considering the importance ofnon-capitalist demand (see Foley 1986: 88). She also highlighted theimportance of borrowing in Reform and Revolution. ‘When the inner ten-dency of capitalist production to extend boundlessly strikes against therestricted dimensions of private property, credit appears as a means of sur-mounting these limits in a particular capitalist manner’ (Luxemburg 1986: 14).

Luxemburg’s interpretation of the relationship between credit and crisesis close to that developed by Marx in Capital, volume 3. She writes:

To begin with, it increases disproportionately the capacity of theextension of production and thus constitutes an inner motive force thatis constantly pushing production to exceed the limits of the market. Butcredit strikes from two sides. After having (as a factor of the process ofproduction) 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 themarket, but also exaggerates the extent of the crisis. ‘In short, credit repro-duces all the fundamental antagonisms of the capitalist world. It accentu-ates them. It precipitates their development and thus pushes the capitalistworld forward to its own destruction’ (Luxemburg 1986: 15).

As shown in Chapter 5, however, the paradox of borrowing gives credit anendemic role in capital accumulation, not just as a way of expanding capacitybeyond its usual confines, but as core to capital accumulation itself. TheDomar model can therefore be offered as a vehicle for identifying how creditcan provide a more fundamental source of fragility, at the heart of capital accu-mulation, than both Luxemburg and Marx recognized. Not only does theDomar model capture Luxemburg’s emphasis on the importance of demand,as a key contradiction in capital accumulation; it also amplifies the importanceof 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 argumentsabout the barriers to expanded reproduction, a new theory of crisis wasdeveloped by the Polish Marxist, Henryk Grossmann. In opposition toLuxemburg’s emphasis on the importance of aggregate demand, Grossmannmodelled Marx’s law of the tendency of the falling rate of profit. This wasfirst seen as an extremely unorthodox position compared to the thenpopular 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 thefalling 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 andhotly debated issues in Marxian economics’; and for Weeks (1981: 202), ‘thelaw as such provides the key to unlocking the dynamics of capitalist crises’.

The cornerstone of Grossmann’s contribution is his extension of OttoBauer’s simulation of the reproduction schema. Compared to Bauer’s sim-ulation over four years, Grossmann demonstrates for a 35-year period thatthe accumulation of capital leads to a scarcity of surplus value and eventualeconomic breakdown.

Howard and King (1989) have surveyed the numerous criticisms thathave been made of the Grossmann position, with particular emphasis on thecomplex relationship between technological change and the rate of profit.A stringent defence has also been provided by Kuhn (1995), drawing uponthe recent Marxist literature on the rate of profit. One dimension ofGrossmann’s simulation that has received limited attention, however, is therole played by the personal consumption of capitalists. The purpose of thischapter is to take issue with the treatment of capitalist consumption, andthe associated role of investment, in the breakdown model. In contrast toGrossmann’s narrow focus on production, we revisit our argument that cap-italists cast money into circulation (the Kalecki principle). It can be argued,once the role of money is taken seriously in Marx’s reproduction schema,

that it is no longer possible for accumulation to swallow up all the availablesurplus value.

It will be shown, by modifying the breakdown simulation to include theKalecki principle, that the class neutrality assumption of a constant rate ofexploitation is accordingly relaxed. Both Bauer and Grossmann regardedthis assumption as provisional. And as has been noted by Laibman (1992:122), ‘a rising rate of exploitation is as much a source of contradiction andan imminent critical tendency in capitalism as is a falling rate of profit’.Moreover, it can be argued that the consequences of a rising rate ofexploitation are important to Marx’s exposition of the falling rate of profitthesis in Capital, volume 3.

Grossmann’s law of capitalist breakdown

The starting point for Grossmann’s model of accumulation is provided byOtto Bauer’s 1913 adaptation of Marx’s reproduction schema (Bauer 1986).Grossmann’s objective was to directly engage and contend with Bauer’sargument that capital accumulation could be sustained through successiveperiods of expanded reproduction, without breakdown. The approach takenby Grossmann (1992: 67) is to ‘demonstrate the real facts through Bauer’sreproduction scheme’. Furthermore, ‘Bauer succeeded in constructing areproduction scheme which, apart from some mistakes, matches all theformal requirements that one could impose on a schematic model of thissort’ (ibid.: 67). Since Grossmann plays such a key role in establishing thecredibility of the Bauer model, reaching radically different conclusions toBauer, we shall also refer to it interchangeably as the Grossmann model.

Grossmann (1992: 65) adapts the Bauer model with the explicit aim offorming a theory of crisis from the ‘essence of capitalist production’.Following Marx’s employment of the reproduction schemes, prices areassumed to be identical to values, so that deviations of demand from sup-ply are not considered in Grossmann’s abstract theory of crisis. Similarly,problems associated with credit, that in practice are always present in eco-nomic crises, are not considered relevant at this abstract level of analysis.

Key to the Bauer model is an assumption that constant capital increasesat a higher rate than variable capital – the former increases at 10 per centper annum and the latter at 5 per cent (ibid.: 67). The result is a continualincrease in the organic composition of capital, the ratio of constant to vari-able capital. The rate of surplus value, the ratio of total surplus value tovariable capital, is assumed to remain constant at all times. With variablecapital increasing at 5 per cent each year, the same increase in the pool oftotal surplus value takes place, out of which additional increments ofconstant and variable capital are funded. Capitalist consumption is treated

The falling rate of profit 77

as a residual, funded by the amount of surplus value that remains after theappropriate amount required for capital accumulation has been set aside.

Table 7.1 shows Grossmann’s simulation, the numbers being veryslightly different from the original after correcting for rounding errors andminor errors of calculation.1 In addition, although Grossmann models thedepartments of production explicitly, for ease of exposition only economy-wide totals are considered.

At the outset the economy employs 200,000 units of constant capital and100,000 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 rateof profit (100,000/100,000�200,000) of 33.3 per cent. This pool of surplusvalue is used for funding a 10 per cent expansion in constant capitalof 20,000 and a 5 per cent expansion of variable capital by 5,000. Thefourth 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. Inthis initial year of economic activity, the capitalists retain 75 per cent oftheir profits for personal consumption (savings of 25 per cent).

Year 2 shows a new input of 220,000 units of constant capital incorpo-rating the additional 20,000 units produced in the previous period; and anew 105,000 units of variable capital incorporating the additional 5,000units 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 ofwith further increases in constant capital (by 22,000) and variable capital(by 5,250). The residual volume of capitalist consumption, after funding thecapital expansion, is 77,750. Note that although there is an increase in cap-italist consumption, the proportion of profits consumed by capitalists fallsto 74.05 per cent compared to 75.00 per cent in year 1.

This reduction in the proportion of profits consumed has importantconsequences for the economy as the simulation is repeated over subse-quent periods. Although Bauer was able to demonstrate that expandedreproduction is sustainable over a four-year period, Grossmann showed thatif the simulation is continued for 35 years then this results in economicbreakdown. Table 7.1 shows a steady fall in the proportion of profits con-sumed until, in year 34, only 2.16 per cent are consumed. The stringentdemands of capital accumulation are fulfilled, with constant and variablecapital increasing by 10 and 5 per cent respectively throughout the 35-yearperiod. The problem, however, is that with variable capital failing to keeppace with constant capital the pool of surplus value extracted from variablecapital also fails to keep pace.

The portion of surplus value destined for accumulation as additionalconstant capital . . . increases so rapidly that it devours a progressivelylarger share of surplus value. It devours the portion reserved for


Tabl

e 7.

1G

ross

man

n’s

repr

oduc

tion

sch

ema

Year

Con

stan

tVa

riab

leC

apit

alis

tC

hang

eC

hang

eTo

tal

Pro

port

ion

Rat

e of

capi

tal

capi

tal

cons

umpt

ion

in C

inV

valu

eof

pro

fits

prof

it(C

)(V

)(u

)(d

C)

(dV

)(W

)sa

ved

(%)

(%)

120

0,00

010

0,00

075

,000

20,0

005,

000

400,

000

25.0

033

.32

220,

000

105,

000

77,7

5022

,000

5,25

043

0,00

025

.95

32.3

324

2,00

011

0,25

080

,538

24,2

005,

513

462,

500

26.9

531

.34

266,

200

115,

763

83,3

5426

,620

5,78

849

7,72

528

.00

30.3

529

2,82

012

1,55

186

,191

29,2

826,

078

535,

921

29.0

929

.36

322,

102

127,

628

89,0

3732

,210

6,38

157

7,35

830

.24

28.4

735

4,31

213

4,01

091

,878

35,4

316,

700

622,

331

31.4

427

.48

389,

743

140,

710

94,7

0038

,974

7,03

667

1,16

432

.70

26.5

942

8,71

814

7,74

697

,486

42,8

727,

387

724,

209

34.0

225

.610

471,

590

155,

133

100,

217

47,1

597,

757

781,

855

35.4

024

.811

518,

748

162,

889

102,

870

51,8

758,

144

844,

527

36.8

523

.915

759,

500

197,

993

112,

144

75,9

509,

900

1,15

5,48

643

.36

20.7

191,

111,

983

240,

662

117,

430

111,

198

12,0

331,

593,

307

51.2

117

.820

1,22

3,18

225

2,69

511

7,74

212

2,31

812

,635

1,72

8,57

253

.41

17.1

211,

345,

500

265,

330

117,

513

134,

550

13,2

661,

876,

160

55.7

116

.525

1,96

9,94

732

2,51

010

9,39

019

6,99

516

,125

2,61

4,96

766

.08

14.1

272,

383,

635

355,

567

99,4

2523

8,36

417

,778

3,09

4,77

072

.04

13.0

303,

172,

619

411,

614

73,7

7131

7,26

220

,581

3,99

5,84

682

.08

11.5

313,

489,

880

432,

194

61,5

9634

8,98

821

,610

4,35

4,26

985

.75

11.0

334,

222,

755

476,

494

30,3

9442

2,27

623

,825

5,17

5,74

493

.62

10.1

344,

645,

031

500,

319

10,8

0046

4,50

325

,016

5,64

5,66

997

.84

9.7

355,

109,

534

525,

335

�51

0,95

326

,267

6,16

0,20

410

2.26

9.3

Not

eG

ross

man

n us

es t

he s

ymbo

l �

to r

efer

to

a ne

gativ

e qu

anti

ty, w

hich

is

econ

omic

ally

mea

ning

less

.

capitalist consumption . . . , swallows up a large part of the portionreserved for additional variable capital . . . and is still not sufficient tocontinue the expansion of constant capital at the postulated rate of10 per cent a year.

(ibid. 1992: 80)

By year 35, a breakdown is reached in which there is insufficient surplusvalue to fund the capital expansion and personal consumption of capitalists.

Grossmann’s lasting contribution to Marxist economics was to explainhis breakdown theory in terms of Marx’s law of the tendency of the fallingrate of profit. Table 7.1 shows how a continuous increase in the organiccomposition of capital results in a fall in the rate of profit; with the rate ofsurplus value constant the economy is constrained by an insufficient poolof total surplus value. The tendency for constant capital to substitute forlabour means that labour is more productive, but also that less labour isavailable, relative to capital as a whole, for the production of surplus value.In contrast to Bauer, Grossmann argues that under Marx’s falling rate ofprofit thesis the expanded reproduction of capital is not sustainable if a longenough period of expansion is considered.

To understand this outcome, a particularly useful analysis of the Bauermodel has been provided by Samuelson and Wolfson (1986), the precisedetails of which are provided in Appendix 7.1. They point out that all barone of the components which constitute the model are exogenous, inde-pendent values that are not allowed to vary. The rate of surplus value is setat 100 per cent, the rates of growth of constant and variable capital are set at10 and 5 per cent, and the initial stocks of constant and variable capital are200,000 and 100,000 units respectively. The only component of the modelthat is variable is the capitalists’ propensity to save out of surplus value. Aswe have seen, the eighth column of Table 7.1 shows that this propensitysteadily increases from an initial value of 25 per cent in the first year, to35.4 per cent in year 10, and so on until in year 35 all profits are exhaustedin the funding of capital expansion. Since all of the other components areexogenously fixed, the one parameter that can change is the capitalists’propensity to save. With constant capital expanding at a higher rate thanvariable capital and with a fixed rate of surplus value, something must give,and hence the savings propensity is the component that must increase aspart of the process of capital accumulation. The consequence of the way inwhich this model is set up is that eventually the savings propensity reaches100 per cent, so that no profits are left to fund capitalist consumption andeven the expansion of capital cannot be facilitated. In the next part of thischapter, we question the validity of this treatment of the propensity to save asan endogenous residual.


Return of the Kalecki principle

The Bauer/Grossmann interpretation of Marx’s reproduction schema can becontrasted with our alternative perspective in which the role of money pro-vides the focus of analysis. For Kalecki (1991c: 241), it is capitalist ‘invest-ment and consumption decisions which determine profits, and not viceversa’. In the Grossmann approach, however, capitalist consumption is aresidual left over once capitalists have decided their production of surplusvalue, out of which new constant and variable capital are allocated. Thecapitalist consumption portion of surplus value is not determined bythe amount of money advanced at the start of the production period, butby the portion left once production has been completed.

Using Marx’s reproduction schema, Kalecki derives an aggregaterelationship between profits and capitalist expenditures.2 As demonstratedin Chapter 3, under the assumption of zero savings on the part of workers,an aggregate identity is established between profits, capitalist consumptionand investment, which is shown as

P � u � I (7.1)

or

profits � capitalist consumption � investment

This equation shows clearly how the Kalecki principle works, with prof-its determined by capitalist expenditures. Since capitalists can only choosewhat they spend, and not what they earn, they ‘as a class determine by theirexpenditure their profits and in consequence the aggregate production’(Kalecki 1991a: 25).

To explore how the Kalecki principle can be applied to Grossmann’snumerical simulation, we can first show how equation (7.1) relates toTable 7.1. In year 1, total profits of 100,000 consist of 75,000 units of cap-italist consumption together with 20,000 constant capital and 5,000 variablecapital: 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 consumptionand investment.

Kalecki pays particular attention to the structure of capitalist consump-tion, defining the constant part as B0 and the part which is dependent onprofits according to the proportion �. Hence

u � B0 � �P (7.3)


In order to activate the expenditure side of the profit equation, we can makeuse 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 asmall proportion of capitalist consumption will change in response to achange in profits. In an empirical exercise, which Kalecki (1990b: 132)argues ‘is confirmed by statistical evidence’, he argues that about 3/4 ofcapitalists’ consumption is made up of the constant part. Since capitalists’consumption is so inelastic with respect to profits, only 1/4 part is directlyrelated 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’sassumptions the constant part could constitute 56,250, representing 3/4 ofthe total volume of capitalists’ consumption. It follows, if the parameterrelating capitalist consumption to profits takes a value of 0.1875, thencapitalist 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 ofviewing the same volume of capitalists’ consumption. Instead of capitalistconsumption depending completely upon the amount of profits whichremains after capitalists have decided how much to invest, it can instead beargued that such consumption can be modelled in its own right. From eitherperspective, in year 1 the capitalists extract and realize surplus value repre-senting 100,000 units. As argued in Chapter 3, there is no suggestionhere that the using Kalecki’s approach should undermine the critical role ofsurplus value in the origin of profits.

Where this alternative perspective provides different results fromGrossmann is when the simulation is continued beyond the first year.Again, following Kalecki, we can assume that the constant part of capital-ists’ consumption will increase over time. ‘A secular rise in wealth andincome of capitalists tends to raise, with rather a long time-lag, their “stan-dard of living”, i.e. the amount they are apt to consume irrespective of thelevel of their current income’ (Kalecki 1991b: 184). However, ‘the long-runrise 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 capital-ists’ consumption. In view of these factors it is plausible to assume a slowlyincreasing constant part of capitalists’ consumption. For our adaptation ofGrossmann’s simulation, a rate of growth of 2.5 per cent can be assumed forthe constant part of capitalist consumption, half the 5 per cent rate of growthfor variable capital.3


Simulation without breakdown

Applying the Kalecki principle and these empirical assumptions to theGrossmann table, a new simulation of expanded reproduction is presentedin 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):

(7.5)

This represents a multiplier relationship between total profits (P) and thetotal exogenous expenditures by capitalists (B0 � I ), the multiplier beingdefined as 1/1 � �. This multiplier relationship is used to determine profitsin Table 7.2 (see Appendix 7.2 for more detail).

The Kalecki modified schema retains the key characteristics of theGrossmann model. Constant capital still grows at 10 per cent each yearcompared to 5 per cent for variable capital, and this requires a steadyincrease in the proportion of profits saved, from 25 per cent in year 1 to65.4 per cent in year 35. Also in keeping with the Grossmann model, therate of profit steadily falls over time, from 33.3 per cent in year 1 to 14.6per cent in year 35. The difference, however, is that capitalist consumptionis not treated as a residual, dependent upon the amount of profits that hap-pen to remain after the prior commitments of capital accumulation. InTable 7.2, capitalist consumption is modelled as an active component in themodel, providing an important driver in the generation of profits, as capitalistscast money into circulation.

Table 7.2 also shows that after an initial period of stagnation in the first11 years, the rate of surplus value increases during the 35-year period ofexpanded reproduction. The role given to capitalist expenditures on invest-ment and consumption, in the determination of profits, serves to increase therate of surplus value from 1.000 to 1.564 during the course of the simula-tion. Under Grossmann, surplus value is extracted on a one-to-one basisfrom each unit of variable capital – at a rate of 100 per cent. Once, however,surplus value is determined by the expenditure decisions of capitalists thenthis one-to-one extraction of surplus value is relaxed.4 This modification ofthe model is consistent with the spirit of the original Bauer formulation,which Grossmann adheres to so closely. In developing the reproductionschema, Bauer states, ‘To simplify the investigation we assume for the timebeing 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, theassumption of a constant rate of surplus value is not regarded as having anyparticular theoretical significance. Indeed for Grossmann (1992: 128),

P �B0 � I1 � �


Tabl

e 7.

2K

alec

ki m

odif

ied

repr

oduc

tion

sch

ema

Year

Con

stan

tVa

riab

leP

rofi

tsR

ate

ofC

apit

alis

tP

ropo

rtio

nR

ate

ofca

pita

lca

pita

l(P

)su

rplu

sco

nsum

ptio

nof

pro

fits

prof

it(C

)(V

)va

lue(

s)(u

)sa

ved

(%)

(%)

120

0,00

010

0,00

010

0,00

01.

000

75,0

0025

.00

33.3

222

0,00

010

5,00

010

4,50

00.

995

77,2

5026

.08

32.2

324

2,00

011

0,25

010

9,30

50.

991

79,5

9227

.18

31.0

426

6,20

011

5,76

311

4,44

10.

989

82,0

3328

.32

30.0

529

2,82

012

1,55

111

9,93

70.

987

84,5

7829

.48

28.9

632

2,10

212

7,62

812

5,82

60.

986

87,2

3430

.67

28.0

735

4,31

213

4,01

013

2,14

10.

986

90,0

0931

.88

27.1

838

9,74

314

0,71

013

8,92

10.

987

92,9

1133

.12

26.2

942

8,71

814

7,74

614

6,20

80.

990

95,9

4934

.37

25.4

1047

1,59

015

5,13

315

4,04

80.

993

99,1

3335

.65

24.6

1151

8,74

816

2,88

916

2,49

10.

998

102,

472

36.9

423

.815

759,

500

197,

993

203,

482

1.02

811

7,63

342

.19

21.3

191,

111,

983

240,

662

259,

646

1.07

913

6,41

447

.46

19.2

201,

223,

182

252,

695

276,

772

1.09

514

1,81

948

.76

18.8

211,

345,

500

265,

330

295,

371

1.11

314

7,55

450

.04

18.3

251,

969,

947

322,

510

387,

521

1.20

217

4,40

155

.00

16.9

272,

383,

635

355,

567

446,

810

1.25

719

0,66

857

.33

16.3

303,

172,

619

411,

614

557,

481

1.35

421

9,63

860

.60

15.6

313,

489,

880

432,

194

601,

337

1.39

123

0,73

961

.63

15.3

334,

222,

755

476,

494

701,

614

1.47

225

5,51

463

.58

14.9

344,

645,

031

500,

319

758,

867

1.51

726

9,34

864

.51

14.7

355,

109,

534

525,

335

821,

486

1.56

428

4,26

565

.40

14.6

‘The basic mistake is Bauer’s assumption that the rate of surplus value isconstant despite the assumed rising organic composition of capital.’

This rising rate of surplus value is also consistent with Marx’s theory ofsurplus value. It has been shown that under the Kalecki principle profits aredetermined by capitalist consumption. Under simple reproduction, profitsare identical to capitalist consumption, with investment in new capitalincluded under expanded reproduction. However, whilst capitalists mayfirst cast into circulation the money required for such luxury consumption,the reflux of that money back to the capitalist class is only made possibleby the production of surplus value. Although the consumption of luxurygoods is unproductive, in comparison to how this surplus value could havebeen more usefully employed,5 the labour power that produces these goodsis productive, since it produces surplus value (see Howard and King 1985:129). Hence an expansion of demand for luxury goods generates an expan-sion in the mass of surplus value congealed in the total volume of thesegoods produced, thereby increasing the rate of surplus value.6

As Yaffe (1972: 24), a follower of Grossmann, argued, ‘It is quiteamazing that critics of Marx such as Joan Robinson can say that Marx’s the-ory rests on the assumption of a constant rate of exploitation.’ For Yaffe thekey question is whether the rate of surplus value can rise sufficiently toenable the combination of a sustained fall in the rate of profit and anincreasing mass of surplus value. Yaffe (1972: 26) argues that for thiscombination to be sustained the rate of surplus value must increase at anaccelerated rate.

Of course, the requirement of an accelerating rate of surplus value isdifficult to sustain. Yaffe (1972: 27) refers to the ‘increasing difficulty inraising the rate of exploitation sufficiently to satisfy the self-expansionrequirements of capital as capitalism progresses’. However, it is not possiblein the Kalecki modified framework to identify a particular year of break-down after n years of simulation, as in the Grossmann model. In contrast toGrossmann’s Table 7.1, in Table 7.2 capitalist consumption increases steadilythroughout the 35-year period, without breakdown. Moreover, the simulationcan be extended to a period of 100 years, and beyond, without there being adrying up of surplus value. This 100-year simulation of Table 7.2 is illus-trated by the trajectory of the rate of profit in Figure 7.1, with Figure 7.2showing the accelerating rate of surplus value.

The falling rate of profit

In addition to questioning the relationship of the Grossmann breakdownthesis to Marx’s reproduction schema, consideration can also be given to itsrelevance to Marx’s exposition of the falling rate of profit tendency in


0

5

10

15

20

25

30

35

1 100Year

Rat

e of

pro

fit (

%)

Figure 7.1 The rate of profit in the Kalecki simulation.

0

50

100

150

200

250

1 100Year

Organic composition of capitalRate of surplus value

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

Capital, volume 3. Grossmann’s claim to have faithfully represented Marx’stheory rests on passages in section 3 of chapter 15, ‘Excess Capital andExcess Population’.7 The breakdown scenario, in which the mass of surplusvalue dries up in year 35 of the Bauer schema, is interpreted by Grossmann(1992: 76) as a case of ‘overaccumulated capital’. Quoting from Marx, ‘therewould 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 byan absolute decrease in the mass of profit . . . . And the reduced mass of profitwould have to be calculated on an increased total capital’ (ibid.: 247).

The problem with this interpretation, however, is that in these passagesMarx was considering a particular case in which there is a rise in wages anda fall in the rate of surplus value. It is for this reason that there can beoveraccumulation 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, butthis time due to a change in the composition of capital not caused bythe development of productive forces, but rather by a rise in the money-value of the variable capital . . . and the corresponding reduction in theproportion of surplus labour to necessary labour.

(ibid.: 247, emphasis added)

Here we see some of the words quoted by Grossmann in italics, but put inthe context of the rest of the sentence. The overaccumulation scenario thathe finds in Marx is associated with the particular case of an increase inwages, a causal factor that has no mention in Grossmann’s interpretation.Indeed, since the falling rate of profit is expounded by Marx in thecontext of an increasing rate of surplus value, it is difficult to place thisoveraccumulation scenario at the centre of his theory.

A different reading of Capital, volume 3, can be suggested, in whichquestions 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 ofall capital and consumption requirements. However, as capital expands, thevolume of profits accumulates to such an extent that stringent demands areplaced upon the economic system in terms of the amount of money that hasto be cast into circulation for realization of these profits. Marx placesrealization 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 theprofit rate, the mass of surplus-value thus produced swells tomonstrous proportions. Now comes the second act in the process. The


total mass of commodities, the total product, must be sold, both theportion that replaces constant and variable capital and that which rep-resents surplus-value. If this does not happen, or happens only partly,or only at prices that are less than the price of production, thenalthough the worker is exploited, his exploitation is not realized as suchfor the capitalist and may even not involve any realization of the sur-plus-value extracted, or only a partial realization; indeed, it may evenmean 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 forimmediate exploitation and for the realization of that exploitation are notidentical. Not only are they separate in time and space, they are also sepa-rate in theory’ (ibid.: 352). Indeed, this provides a key underpinning forMarx’s argument as to why the falling rate of profit, and its associated bur-geoning mass of profits, provides such severe problems for capitalism. ‘Themeans – the unrestricted development of the forces of social production –comes into persistent conflict with the restricted end, the valorization of theexisting capital’ (ibid.: 359). By focusing on the realization of the mass ofprofits, an alternative to Grossmann’s overaccumulation scenario can besuggested that is consistent with Marx’s core thesis of a falling rate of profitwith a rising rate of surplus value.

As the basis for a theory of crisis, this demand-side perspective does notprovide a precise mechanical breakdown of the type developed byGrossmann. Moreover, the development of a complete alternative is beyondthe confines of the present study. However, since under the Kalecki modi-fication of the Grossmann model the rate of surplus value acceleratesbecause of the monetary outlays on spending by the capitalist class, the sus-tainability of this process must depend upon the finance of these monetaryoutlays. One of the key determinants of these outlays is the role of banks inproviding credit to fund such spending activity. In contrast to Grossmann’srelegation of credit to a less abstract level of analysis, the Kalecki modifiedmodel points towards the relevance of the financial system to Marx’s fallingrate of profit thesis.


8 The transformation problem

After Marx’s death, in 1883, Engels undertook the major task of patchingtogether the second and third volumes of Capital. Whereas volume 2slipped out into the public domain in 1885 like a battleship leaving port inthe middle of the night, volume 3 was launched in the full glare of publicscrutiny. 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 thetransformation problem: the problem of how values can be transformed intoprices. When volume 3 was finally published in 1894 it became, and still is,the subject of intense controversy. Critics argued that Marx failed to cor-rectly transform capital inputs from values to prices. This claim, that Marx’stransformation solution is inconsistent and wrong, has become the Achillesheel of Marxian economics. Marxists have sought for the last 100 years todefend the labour theory of value against the charge of inconsistency.

Marx’s development of the reproduction schema in the second volume ofCapital is predicated on an assumption that prices are proportionate to values:

In as much as prices diverge from values, this circumstance cannotexert any influence on the movement of the social capital. The samemass of products is exchanged afterwards as before, even though thevalue relationships in which the individual capitalists are involved areno longer proportionate to their respective advances and the quantitiesof surplus-value produced by each of them.

(Marx 1978: 469)

The purpose of this chapter is to consider how our macro monetaryinterpretation of the reproduction schema can be generalized into a modelwith price–value deviations.

This generalization is attempted by considering the new interpretation ofthe transformation problem, as developed by Foley (1982).1 In contrast tothe perceived Sraffian view of capitalism, as a system producing a physical

surplus, proponents of the new interpretation have focused on the value ofmoney as a way of relating the labour theory of value to the circuit ofmoney. Since the circuit of money is so closely intertwined with the repro-duction of capital, the purpose of this chapter is to consider the new inter-pretation in the light of our macro monetary interpretation of thereproduction schema. A summary is provided of how the analytical com-ponents of the macro monetary model can be generalized under deviationsof prices from values.

An important criticism of Marx’s development of the reproductionschema in Capital, volume 2, is that he fails to consider the importance ofcompetition. For Howard and King (1985: 191), Marx’s reproduction mod-els ‘do not relate to a full competitive capitalist system, in which capitalmobility and credit flows operate to equalise profit rates and bring aboutprices of production which deviate from labour values.’ As a result, Marxmay have drawn ‘unwarranted conclusions as to the difficulties involved inachieving fully co-ordinated production in capitalism’ (ibid.: 191). This keylimitation 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’ (Marx1981: 254). Instead of using Marx’s rather complex example of fivebranches of production, in which fixed capital is employed, we shall explainhis procedure using a simplified example for three sectors, borrowed fromHoward and King (1985: 99). In this example, all capital is assumed to beof the circulating type, and simple reproduction is assumed, so that there isno expansion of capital over time.

Table 8.1(a) shows the physical units required for production. The firstdepartment produces steel (means of production), the second corn (wagegoods), 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 Labourproduction

Dept. 1 80 tons steel � 40 → 120 tons steelDept. 2 10 tons steel � 50 → 60 quarters cornDept. 3 30 tons steel � 30 → 60 ounces gold

Total 120 120

good, consumed by capitalists. In the first sector, for example, 80 tons ofsteel inputs are combined with 40 units of labour to produce an output of120 tons of steel. These outputs are used to replace the 80 tons used up inDepartment 1, the 10 tons used in Department 2, and the 30 tons used upin Department 3. Note that this is simple reproduction because the amountproduced exactly matches the amount used up as inputs.

Now the labour values of each commodity – measuring the direct andindirect labour embodied in each commodity – are conveniently valued atunity for each of the three departments (Howard and King 1999: 100). Inthe value schema, therefore, inputs of steel (constant capital) used up byeach of the three sectors have a (labour) value of 80 for Department 1, 10for Department 2, and 30 for Department 3. These are shown inTable 8.1(b), together with the components of variable capital, whichrepresent the labour embodied in units of corn consumed by labourers.

In this value schema, it is also assumed that there is a uniform rate ofsurplus value, which is set at 100 per cent. Hence, for example, 20 units of sur-plus value are extracted in Department 1 from 20 units of variable capital; intotal 60 units of surplus value are extracted from 60 units of variable capital.

Using the formula Ci � Vi � Si, values can be calculated for eachdepartment. 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’sreproduction schema, based on the second volume of Capital, it wasassumed that these values are also the total prices of each department.However, in the third volume Marx focuses on the organic compositionof capital, which measures the ratio (Ci/Vi) between constant and variablecapital.2 These ratios vary between 4 and 0.4 in this example. And it is thisvariation that leads Marx to argue that values cannot be sustained as indi-cators of price for each department of production. The problem is that therate of profit (Si/Ci � Vi) for each department is calculated as a ratiobetween total surplus value and total capital. Yet, for each department itsown mass of surplus value is calculated from the variable capital employed.

The transformation problem 91

Table 8.1(b) Marx’s value calculation

Constant Variable Surplus Total Organic Rate ofcapital capital value value composition profit(Ci) (Vi ) (Si ) (Ci�Vi�Si) (Ci /Vi ) (%)

(Si /Ci�Vi)

Dept. 1 80 20 20 120 4 20Dept. 2 10 25 25 60 0.4 71.4Dept. 3 30 15 15 60 2 33.3

Total 120 60 60 240

Departments with a relatively high proportion of constant capital to variablecapital (a high organic composition) will find that this drags down their rateof profit, since the constant capital term appears in the denominator.Departments with a relatively low organic composition of capital have ahigher rate of profit. In Table 8.1(b), Department 1 has an organic compo-sition of 4 and a rate of profit of 20 per cent; Department 2 has a rate ofprofit 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 capi-tal mobility. Capitalists seek the maximum rate of profit they can obtain; soif a department has higher profitability than others, new capital will moveinto this department until rates of profit are equalized. Instead of valuesgoverning the exchange between departments of production, new prices ofproduction 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 establishedfor the economy as a whole, so that

(8.1)

Second, this rate of profit is applied to each department’s costs ofproduction to establish the amount of profit made. In Department 1, forexample, 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 thecost price plus profits: in Department 1 this is 133.3. For this numericalexample, prices deviate above value for departments with a high organiccomposition of capital (�13.3 for Department 1) and below for a loworganic composition (�13.3 for Department 2). Department 3 in the exampleis neutral, having an average composition of capital.

Two invariance postulates are established. First, the deviations of pricesfrom values sum up to zero, which means that total prices (240) are equalto total values (240). Second, total money profits (60) are equal to total sur-plus value (60). Although for individual departments there are deviations ofprices from values, and profits from surplus value, in the economy as awhole value categories are preserved. Marx defends his value theory usinga macroeconomic solution, in which profits are determined by surplusvalue, and all that is required is a redistribution of surplus value betweendepartments of production.

Compared to his classical predecessors, who often failed to take intoaccount the deviation of prices from value, it has been generally recognizedthat Marx’s transformation procedure represented an important step inthe development of value theory. However, there is an issue with Marx’stransformation that he himself recognized. The two-stage transformation of

�Si

�Ci � Vi

�60

120 � 60� 331

3%


Tabl

e 8.

1(c)

Mar

x’s

pric

e ca

lcul

atio

n

Con

stan

tVa

riab

leC

ost

Ave

rage

Tota

lP

rice

of

Pri

ce m

inus

capi

tal

capi

tal

pric

era

te o

f pr

ofit

prof

its

prod

ucti

onva

lue

(Ci)

(Vi)

(Ci�

Vi)

(S i

/Ci�

Vi)

Dep

t. 1

8020

100

33%

33.3

133.

3�

13.3

Dep

t. 2

1025

3533

%11

.746

.7�

13.3

Dep

t. 3

3015

4533

%15

600

Tota

l12

060

180

6024

00

Sou

rce:

How

ard

and

Kin

g (1

985:

99)

.

1 31 31 3

values to prices is based on an assumption that the inputs of means ofproduction are measured in values, but only the outputs are transformedfrom values to prices. In Table 8.1(c), for example, notice that the inputs ofconstant 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 isequated 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 requireus 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 ofthe transformation problem: the charge that Marx’s solution is inconsistentand wrong. How, in particular, can reproduction be established when pro-ducers are buying inputs at one set of prices and selling them at another setof prices? In Table 8.1 (c), after Marx’s transformation procedure has beenemployed, Department 1 sells its output of capital goods for 133.3, yet theinputs 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 ofwage goods used up is still 60: a discrepancy of 13.3. Hence, for Sweezy(1942: 114), ‘the Marxian method of transformation results in a violationof the equilibrium of Simple Reproduction.’ This is no way to build areproduction schema in which prices deviate from values.

Marx after Sraffa: the new interpretation

The overwhelming response to this transformation problem, for bothMarx’s critics and disciples, has been to abandon the definition of value asa quantity of labour embodied in production. Either value is redefined in away that allows the transformation problem to be solved, or the labour theoryof value is abandoned altogether.

The latter response has been adopted in the Sraffian critique of Marx. Thisapproach has its roots in the pioneering contribution, in 1907, of vonBortkiewicz, who set up a procedure for transforming both inputs and outputsinto prices (Bortkiewicz 1951–2). The result, later generalized by Winternitz(1948) and Seton (1975), is a weakening of the relationship between valuesand prices. Marx’s invariance postulates, that total profits should equaltotal surplus value and total prices should equal total value, cannot both bemaintained once inputs and outputs are transformed into prices.

This weakening of the relationship between value and price is takenfurther by Steedman (1977) in his Marx after Sraffa. Core to this approachis the Sraffian price equation

p � (1 � r)(pA � phl) (8.2)


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 oflabour coefficients. In this price equation all inputs are calculated usingmoney prices; the money value of capital good inputs, for example, is rep-resented by the term pA. The equilibrium reproduction condition is there-fore easily established since the same price vector is applied to inputs andoutputs.

In addition, the mark-up of profits is calculated on the basis of the moneycost price (pA � phl). The scalar r is a money rate of profit, in contrast toMarx’s value rate of profit. In a further weakening of the relationshipbetween the price and value domains, Steedman argues that in general thevalue and money profit rates will differ.3

Furthermore, it follows from (8.2) that the money rate of profit isdetermined by the ‘physical picture of the economy’ as represented by thetechnical coefficients and the real wage in the Sraffian price equation.Steedman (1977: 66) argues that ‘value magnitudes are irrelevant to theproximate determination of the profit rate and of production prices,’ andhence the labour theory of value is redundant.

During the 25 years or so since the publication of Marx after Sraffa, therehas been a concerted effort to salvage the labour theory of value from thispowerful critique. The main defence has been to place emphasis on the moneyvalue-form of commodities, instead of the labour embodied form. Value-FormMarxism 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 translationbetween 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) asthe ratio of total labour-time to total money value added,

lX � �mpQ (8.3)

where

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 componentparts of value added in Marxian categories. First, the value of labour power(VLP) is defined as

VLP � �mV (8.4)

�m �lXpQ


Instead of measuring the value of labour power in the traditional way as thelabour embodied in commodities consumed by workers, an attempt is madeto 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 canbe translated into surplus value (unpaid labour-time):

S � �mP (8.5)

Hence, Foley (1982: 42) argues, ‘the most central of Marx’s claims aboutthe “transformation” of values into prices of production, that profit arisesfrom unpaid labour time, is sustained . . . .’A direct correspondence is estab-lished between surplus value and money profits. This holds regardless ofhow prices are determined, including the Sraffian price equation (8.2).Moreover, prices can systematically deviate from values without damagingthis aggregate relationship. Even if the money price of goods consumed byworkers deviates from the labour embodied in these commodities, whichFoley argues renders the traditional labour embodied definition of the VLPirrelevant, the value-form definition of VLP is completely operational.

Under (8.5), Marx’s invariance postulate between total profits and surplusvalue is therefore established, with the value of money as the mediating coef-ficient. And in place of the equality between total value and price, a newinvariance postulate is suggested in (8.3) between total labour-time andmoney value added. A coherent defence of Marx’s labour theory of value isdeveloped by abandoning the second invariance postulate and the labourembodied definition of the value of labour power (see Foley 1982: 43).

Furthermore, in the new interpretation money plays a key role indefining the way in which labour power is valued.4 This is contrasted withthe labour embodied approach. ‘The usual interpretation, which posits abundle of subsistence goods whose labour content defines the value oflabour power, short-circuits this relation, and makes money disappear as amediating element in the situation’ (ibid.: 43). Similarly, for Mohun (1994:405), in his defence of the new interpretation, ‘money becomes in embod-ied labour accounts of value an irrelevance to theoretical explanation’.In addition to providing a defence of the labour theory of value, the newinterpretation offers a way of modelling capitalism as a system in whichsurplus 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 capturesthe role of both aggregate demand and money in the reproduction schema.


Using the new interpretation, this model is summarized here in its mostgeneral form, with prices deviating from values. This provides a summaryof how the model contributes both as a vehicle for exploring some keyissues in political economy and as a synthesis between various fragments.

The macro multiplier

Although it is traditional in Marxian frameworks for capitalists to initiatethe circulation of money with an advance of constant and variable capital,our previous discussion, in Chapter 4, showed that there are a number ofways in which the circulation of money can be modelled. In the single swapapproach all of income is advanced; in the Franco-Italian circuit approachonly the wage bill is advanced; in Nell’s mutual exchange approach onlywages in the capital goods sector are advanced. Our contribution has beento suggest, under the Kalecki principle (first introduced in Chapter 3), thatcapitalists advance an amount of money sufficient to realize their profits.This model is predicated on the definition of investment as accumulation ofconstant and variable capital.

Recall from equation (4.23) that a multiplier relationship

(8.6)

is key to modelling the circuit of money. Capitalists advance a sum ofmoney (f � pF), spent on new (constant and variable) capital goods andcapitalist consumption, which generates a multiplied effect 1/(1 � )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 beenderived from input–output relations between industrial sectors and consumerexpenditures.

How does this model of the circuit of money relate to the transformationproblem? It can be shown how this model can be generalized to a Sraffianinterpretation. Since � pAX/pX and � 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 theSraffian price equation.5 The Sraffian price system can be easily madeconsistent with our macro monetary multiplier.

From a Sraffian perspective, however, the gross multiplier and pricesystem do not require any mention of labour values. The parameters of thesystem are defined in physical and money price terms. However, using

wc

c � w

x �1

1 � c � wf


the new interpretation this Sraffian system can be re-shaped using Marxiancategories. Since Q � X � AX, (8.7) can be expressed in net terms as

pQ � wlX � pF (8.8)

Now we can write

(8.9)

where �mw is per money unit definition of the value of labour power underthe new interpretation (see equation 8.4). Substituting (8.9) into (8.8) it fol-lows, with y � pQ, that

y � �mwy � f (8.10)

or

(8.11)

This is the simple Keynesian multiplier relationship between money netoutput and money final demand, of the type first derived from the repro-duction schema in Chapter 2. Cutting through the dense and voluminousmaterial that has been written about Marx’s reproduction schema, thisscalar multiplier offers an extremely succinct summary of its macroeco-nomic structure. Using the new interpretation, (8.11) is derived from mul-tisectoral foundations with a clear role for the new surplus value term e* inthe denominator. The denominator of this multiplier is once again a termrepresenting the share of surplus value, but defined according to the (value-form) new interpretation of the value of labour power. The per money unitVLP expression �mw is also the propensity to consume derived from multi-sectoral foundations.6 This simple multiplier is derived without making anyrestrictive assumptions about the proportionality between prices and values.

This multiplier further establishes the consistency between the Kaleckiprinciple, that capitalists earn what they spend, and Marx’s theory ofsurplus value. Since in (8.11) f � u � I, it follows that

S* � u � I (8.12)

or

surplus value � capitalist consumption � investment

y �1

1 � �mwf �

1e*

f

wlX � w lXpQ

pQ � w�my


where total surplus value is redefined in its value-form as S* under the newinterpretation.7 As in Chapter 3, capitalists cast money into circulation asaggregate demand that is realized as surplus value. This is achieved here, how-ever, under the more general case of prices deviating from values. Under theassumptions of Capital, volume 2, where prices were identical to values, it wasstraightforward in Chapter 3 to reconcile the value-form with the labourembodied form of individual commodities. The new interpretation establishesconsistency between the value-form of profits and the money cast into circu-lation at the aggregate level, but not at the level of individual commodities.

Following the analysis carried out in Chapter 3, the Keynesian multipliercan also be synthesized with the Kalecki multiplier. By again redefining theshare of surplus value as e*, the expression (3.9) can be re-written as8

(8.13)

The scalar 1/1 � � is the Kalecki multiplier, which provides an alternativeinterpretation, in Chapter 7, of Grossman’s model of economic breakdown.This multiplier, together with the Kalecki principle, is applied to theGrossmann model of rising organic composition of capital. From this per-spective, in which capitalists cast money into circulation as an endemic part ofthe reproduction schema, Grossmann’s demonstration of a precise year of eco-nomic breakdown is not possible; a demonstration that is consistent, under thenew interpretation, with the deviation of prices from values. Moreover, the keycontradiction identified by Marx under the falling rate of profit thesis is theproblem of how the burgeoning mass of surplus value can be realized.

Although this Keynes–Kalecki multiplier provides a succinct way ofmodelling aggregate demand, our analysis of the circuit of money requiresa gross multiplier relationship – in order to fully take into account the cir-culation of money required by the exchange of capital goods between sec-tors. It is possible, however, to locate the (new interpretation) value oflabour power in the gross multiplier. Consider in (8.6) the expression for theshare of wages in gross income, which can be re-expressed as

(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

(8.15)x �1

1 � c � ��mwf

w �wlXpX

�pQpX

lXpQ

w � ��mw

y �1

e*(1 � �)(B0 � I)


Using the new interpretation, the value of labour power can be located inour macro model of the circuit of money.

It should be noted, however, that our application of the new interpretationdoes not imply that the traditional labour embodied definition of valueshould be completely abandoned. Foley (2000: 30) is open to the possibil-ity that there may be a role for both the new and traditional interpretationsof the value of labour power. As Appendix 4 shows, the labour embodieddefinition of the value of labour power is nested in the input–output modelof the circulation of money between departments of production, regardlessof how prices are defined. The deviation of prices from values does notmodify the constituent role of the labour embodied measure in theinterindustry monetary circuit. It is only when a macroeconomic aggrega-tion is developed under price–value deviations, and in the derivation of thescalar Keynesian multiplier, that a switch to the value-form definition isrequired.

The Domar growth model

Whereas the gross macro multiplier is required for modelling the circuit ofmoney (a snapshot of the reproduction schema), the net multiplier is usefulfor modelling economic growth (expanded reproduction over time). InChapter 5, the net multiplier is used to develop the multisectoral founda-tions of the Domar growth model. Under the more general case, in whichprices deviate from values, the Domar model can be reconfigured with theshare of surplus value derived from the new interpretation (e*). As we haveseen, this is not the same as the share of surplus value (e), which made upthe denominator of the Keynesian multiplier used in Chapter 5, under theassumption of proportionality between prices and values.

Substituting e* for e in the Domar balanced growth equation, derived inChapter 5,9 we get

(8.16)

Balanced growth has to be equal to a multiple of (the ratio of invest-ment to profits), e* (the new per capita share of surplus value) and � (theproductivity of investment). In Chapters 5 and 6, two main arguments aremade about the contribution of this model to political economy.

First, the Domar model exposes the stringent requirements on aggregatedemand that are associated with balanced growth. Whereas new capacity isgenerated by absolute levels of investment, a matching aggregate demandrequires investment to increase. Domar identifies the problem of demand at

�

dyy �

dII

� �e*�


the heart of capitalist accumulation. This interpretation makes nonsense ofthe claim that in Marx’s reproduction schema supply automatically createsits own demand (Say’s Law). Domar shows that balanced growth is unlikelyto be achieved because the required demand is not automatically forthcoming.

Second, Domar shows that there is a paradox of borrowing in expandedreproduction (an insight later provided by Foley). Capitalists cannot borrowfrom an existing money hoard in order to expand capital accumulation; theymust borrow from financial institutions. This places financial fragility at theheart of the reproduction schema, since all capital accumulation is associatedwith borrowing; and hence, all borrowing is potentially undermined by theproblem of demand. This contrasts with Marx’s identification of financialinstability with occasions when capital accumulation overstretches itself.

These insights provide a way of addressing Rosa Luxemburg’s two-prongedquestion, ‘Where does the money and demand come from?’ As shown inChapter 6, the Domar model provides a way of formalizing Luxemburg’sarguments about the stringent requirements for money and demand that areplaced on the reproduction schema. In addition, it provides an alternative tothe traditional association of demand problems with disproportionality andunderconsumption.

These contributions of the Domar model can therefore be establishedfor the general case in which prices deviate from values. Using the newinterpretation it is possible to extend the macro monetary model to theconsideration of expanded reproduction in a fully competitive economy.

It should be noted that proponents of the new interpretation do not claimthat they have solved the transformation problem as such, which is whythey view their approach to be an interpretation rather than a solution.However, what their approach does show is that it is possible, at least inprinciple, to retain Marxian value categories in a general model of moneyand aggregate demand in a capitalist economy.

There is of course a voluminous literature on the transformation prob-lem, and much discussion of how the value-form approach can be extendedbeyond the confines of the new interpretation. As a project for futureresearch, there is much to be discovered about how different models oftransformation relate to the circuit of money.10 The suite of different mod-els of the circuit model could be compared with the suite of transformationalgorithms. A common complaint, however, is that the transformation prob-lem is given far too much attention; and perhaps this is why other areas ofMarxian economics such as the study of Marx’s forgotten volume ofCapital are so ignored. The preceding pages are an attempt to address thisimbalance, showing that Marx’s second volume has much to offer as a vehi-cle for understanding the importance of money and aggregate demand in acapitalist 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 multisectoralfoundations 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’sreproduction schema’, History of Economics Review, 35: 104–14.

Trigg, A.B. (2002) ‘Surplus value and the Keynesian multiplier’, Review ofRadical Political Economics, 34(1): 55–65.

Trigg, A.B. (2004) ‘Kalecki and the Grossmann model of economic break-down’, Science and Society, 68(2): 187–205.

Trigg, A.B. (2004) ‘Marx and the theory of the monetary circuit’, Researchin 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 canbe identified as a constituent element of the Keynesian scalar multiplier,can also be derived for the Leontief matrix multiplier. Starting with theinput–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)

The relationship between final demand and gross output is specifiedaccording to the output matrix multiplier M � (I � A � hl)�1. The structureof this output multiplier matrix can be examined by first considering thescalar employment multiplier. Since vQ � lX, the employment multiplier(2.23) can be written as

(A2.4)

where e is the scalar representing the share of surplus value. In theinput–output literature (1/e)v is a type II employment multiplier, closedwith respect to households; v � l(I � A)�1 is the type I employment mul-tiplier, open with respect to households (see Bradley and Gander 1969).Hence, e is the ratio of type I to type II employment multipliers. It wasOlgin (1992) who first pointed out that this ratio happens to be a scalar rep-resenting Marx’s category of surplus value.

However, Olgin employed a somewhat unwieldy matrix partition methodto locate the surplus value term in the output multiplier matrix. An alternativederivation is suggested by substituting (A2.4) into (A2.1) such that

(A2.5)

Hence

X � MF (A2.6)

where

(A2.7)

The Leontief output multiplier matrix M can be decomposed with thescalar 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 bedisplayed algebraically, showing more precisely the way in which Kalecki’sinterpretation is derived from Marx’s numerical example. Starting with

M � (I � A)�1(I �1ehv)

X � AX �1ehvF � F

lX �1evF

Appendices 103

Marx’s ex ante schema, as represented in Table 3.2, there are three balancingequations:

C1 � V1 � u1 � dC1 � dV1 � W1

C2 � V2 � u2 � dC2 � dV2 � W2 (A3.1)C3 � V3 � u3 � dC3 � dV3 � W3

Table 3.3, the ex post schema, involves a simple re-arrangement of theelements of each equation such that

(C1 � dC1) � (V1 � dV1) � u1 � W1

(C2 � dC2) � (V2 � dV2) � u2 � W2 (A3.2)(C3 � dC3) � (V3 � dV3) � u3 � W3

In Kalecki’s interpretation (Table 3.4), the equation terms are then groupedaccording to categories of wages ( ) and profits ( ), so that

(V1 � dV1) � (C1 � dC1 � u1) � W1

(V2 � dV2) � (C2 � dC2 � u2) � W2 (A3.3)(V3 � dV3) � (C3 � dC3 � u3) � W3

where and .

Appendix 4 Surplus value and the interindustrymonetary circuit

The purpose of this appendix is to clarify the role of surplus value in theinterindustry model of the circuit of money in Chapter 4. The elements ofthe Leontief inverse in

W � (I � A†)�1F† (A4.1)

(see equation 4.15) can be written out explicitly in terms of prices as

A� (A4.2)

It follows, since in matrix algebra (BC)�1 � C�1B�1, that

A�

A�

A�) (A4.3)�1P̂�1F†� P̂(I �

P̂�1)�1P̂�1F†� (P̂�1 �

P̂�1)�1F†W � (P̂P̂�1 � P̂

P̂�1)�1F†W � (I � P̂

P*i � Ci � dCi � uiV*i � Vi � dVi

P*iV*i

104 Appendices

By now writing the coefficient matrix A� in terms of its constituent parts,

(A4.4)

Hence, from the decomposition established in Appendix 2, it follows that

(A4.5)

The term representing surplus value (e) is a constituent element of theinterindustry model of the circuit of money. Therefore, regardless of howprices are defined, the traditional labour embodied definition of surplusvalue has a role to play in modelling the interindustry circuit of money. Thishas important ramifications for the transformation problem, for whichvalue-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), consideredin Chapter 5, is carried out in two steps. First, the structure of � is considered,followed by an examination of e. The analysis draws heavily fromLianos (1979).

The structure of �

Define

(A5.1)

and

(A5.2)

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

(A5.3)g �C

C � V

V � �n�2

j�1p2h2ljXj

C � �n�2

j�1p1a1j Xj

W � P̂(I � A)�1(I �1ehv)P̂�1F†

W � P̂(I � A � hl)�1P̂�1F†

Appendices 105

Since

(A5.4)

it therefore follows that

(A5.5)

For Marx, investment is made up of increments in constant and variablecapital. In money terms,

I � dC � dV (A5.6)

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

(A5.7)

Finally, this part of the derivation requires the structure of income to bespecified such that

y � V � P (A5.8)

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

y � (l � s)V (A5.9)

and

(A5.10)

Substituting (A5.10) into (A5.7),

(A5.11)dyI

� (1 � g)(1 � s)

dV �dy

1 � s

I �dV

1 � g

dC �g

1 � gdV

C �g

1 � gV

106 Appendices

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)

(A5.13)

The balanced growth equation

From (5.12),

(A5.14)

Substituting (A5.12) and (A5.13),

(A5.15)

It follows that

(A5.16)

This shows that the money rate of profit for the economy as a whole has thestructure

r � s(l � g) (A5.17)

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

(A5.18)dyy � �r

�P

C � V

�PV � V

C � V�

s(1 � g) �PV�C � V

C � V�

CC � V�

� �s(1 � g)

dyy �

dII

� �s

1 � s(1 � g)(1 � s)

dyy �

dII

� �e�

e �P

P � V�

P�VP�V � 1

�s

s � 1

Appendices 107

The balanced growth rate can be specified as the ratio of investment toprofits ( ) 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, canbe represented by a series of simple equations.1 The first relationship to bespecified is that between net income (yt) and variable capital (Vt), where trepresents a time subscript. Income consists of variable capital plus surplusvalue extracted at the rate s:

yt � (1 � s)Vt (A7.1)

An initial volume of variable V1 capital grows in each subsequent year at agiven 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 relationshipcan also be established between the capitalists’ propensity to save out oftotal income ( ) and their propensity to save out of surplus value ( ).With the total savings of capitalists equal to the latter savings propensitymultiplied by total surplus value ( sVt), and total income represented by(A7.1), it follows (with the Vt term cancelling out) that

(A7.4)

The standard equilibrium condition that savings equal investment canalso be represented by

(A7.5)

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

It � �*t yt

�*t ��t s

1 � s

�t

�t�*t

�

108 Appendices

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 wecan 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):

and therefore

(A7.9)

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

and cancelling out some of the terms, we get

(A7.10)

Equation (A7.10) shows how the savings propensity ( ) is determinedby the other parameters of the model. Initial quantities of constant capital(C1) and variable capital (V1) in year 1 are assumed together with a constantrate of surplus value (s). Key to the eventual outcome of the Grossmanntable, however, is the assumption that � , that is the rate of growth ofconstant capital is greater than the rate of growth of variable capital.(A7.10) shows that this steady increase in the organic composition ofcapital generates a steady increase in the savings propensity untileventually, as Grossmann suggests, it reaches 100 per cent.

�t

�t �C1(1 � )t�1

sV1(1 � )t�1�

s

�t �C1(1 � )t�1(1 � s)

s(1 � s)V1(1 � )t�1�

V1(1 � )t�1(1 � s)

s(1 � s)V1(1 � )t�1

V1(1 � )t�1(1 � s)syt

�t �C1(1 � )t�1(1 � s)

syt�

�t s1 � s

yt � C1(1 � )t�1 � V1(1 � )t�1

Appendices 109

Appendix 7.2 The Kalecki modified model

The model specified in Appendix 7.1 can be modified to allow for themodelling of capitalist consumption along the lines suggested by Kalecki.First, the savings-investment identity (equation A7.8) can be modified toinclude capitalist consumption alongside investment:

(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 theendogenous part of capitalist consumption, income is allocated in the formof savings to investment in constant and variable capital and a stipulatedamount of exogenous capitalist consumption.

Following the same procedure as before (Appendix 7.1), by substituting(A7.4) into (A7.11), we get

(A7.12)

and therefore

(A7.13)

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

(A7.14)

Cancelling out some of the terms yields the expression

(A7.15)�t �C1(1 � )t�1

sV1(1 � )t�1�

s �

B0(1 � �)t�1

sV1(1 � )t�1

�B0(1 � �)t�1(1 � s)

s(1 � s)V1(1 � )t�1

�t �C1(1 � )t�1(1 � s)

s(1 � s)V1(1 � )t�1�

V1(1 � )t�1(1 � s)

s(1 � s)V1(1 � )t�1

�B0(1 � �)t�1(1 � s)

syt

�t �C1(1 � )t�1(1 � s)

syt�

V1(1 � )t�1(1 � s)syt

�ts1 � s

yt � C1(1 � )t�1 � V1(1 � )t�1 � B0(1 � �)t�1

�*t yt � C1(1 � )t�1 � V1(1 � )t�1 � B0(1 � �)t�1

110 Appendices

In this equation for the capitalist propensity to save, as compared withequation (A7.10), an additional term for capitalist consumption is included.Moreover, following Kalecki’s approach, in which only the exogenouscomponent of capitalist consumption is allowed to vary, the capitalistpropensity to save can be modelled as a fixed constant

(A7.16)

where � is the capitalist propensity to consume out of profits. Examinationof (A7.15) reveals that if the savings propensity is now assumed to beexogenous then one of the other previously exogenous components on theright-hand side must be allowed to be endogenous. A case can be made forkeeping the initial quantities of constant capital (C1) and variable capital(V1), so as to have the same starting point as Grossmann. Similarly, in orderto model the same increase in the organic composition of capital the samerates of growth of constant and variable capital ( and ) should beassumed. And since B0(l � �)t � 1 is the exogenous part of capitalistconsumption, the only remaining component that can be allowed to varyendogenously is s, the rate of surplus value. Re-arranging equation (A7.15),and substituting for equation (A7.16), it follows that

(A7.17)

In this Kalecki modified model the rate of surplus value st is now anendogenously determined variable, with a time subscript t indicating thatit varies from period to period, subject to the impact of the Kaleckimultiplier 1/1 � � conjoined with the investment and personal consumptionexpenditures of the capitalist class.

st �1

1 � ��C1(1 � )t�1

V1(1 � )t�1� �

B0(1 � �)t�1

V1(1 � )t�1�

�t � 1 � �

Appendices 111

Notes

1 Introduction

1 For Evintsky (1963: 159), ‘Marx may truly be considered the forerunner ofcontemporary economic model-builders for it was he who first demonstrateddiagrammatically the complex relationship between the accumulation processand 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 principalfinding of post-Keynesian growth-theory – the condition of equilibriumeconomic growth.’

2 See Oakley (1983). A more recent and highly accessible biography of Marx isprovided 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 constantcapital in Marx and Keynes.

2 The multiplier

1 There is some dispute about whether Marx had a fully worked out plan forCapital, under which the reproduction schema would be fully consistent with hisHegelian inheritance. This argument is developed in The Making of Marx’sCapital (1977), a monumental contribution to understanding Marx’s method,whose author, Roman Rosdolsky, was a survivor of Auschwitz. Against thisview Turban (1984: 102), a fellow Ukranian, understands ‘Marx’s economicthought as a struggle between different forms of argument in which the domi-nance of Hegelian methods and philosophical arguments were displacedincreasingly by a modern and exact scientific discourse.’

2 For reasons of simplicity, this non-durability of capital assumption is maintainedthroughout the book. For a discussion of the role of fixed capital in simplereproduction, see Carchedi and Haan (1995) and Lyall (1985); for expandedreproduction see Glombowski (1976).

3 Notice also that in Table 2.2 the organic composition of capital (the ratio ofconstant to variable capital) now varies between the two sectors, taking a valueof 4 in Department 1 and a value of 2 in Department 2. Under capital mobility,this disparity would undermine the assumed equivalence between prices andvalues, an issue that was not considered to be important by Marx in his

presentation of the reproduction tables. A treatment of capital mobility will alsobe delayed here until we consider the transformation problem in Chapter 8.

4 This is consistent with an earlier quote from Marx’s Grundrisse, highlighted bySardoni (1981: 386): ‘. . . this demand, that production should be expandedsimultaneously and at once in the same proportion makes external demandsupon capital which in no way arise out of itself’ (Marx 1973: 414).

5 For a detailed survey of the literature on Marx and Keynes see chapter 5 ofHoward and King (1992).

6 Assuming that capitalists spend 500 on their own consumption, out of 1,000units of surplus value there are savings of 500 available to meet investmentrequirements.

7 Zero worker savings will be assumed throughout the rest of this book, forreasons of simplicity. Hence, B is no longer a proxy for worker consumption, asassumed by De Angelis, but is precisely worker consumption. The propensity toconsume b is now precisely the ratio of worker consumption to net income.

8 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.

9 Hartwig (2004: 323) modifies his structural multiplier to incorporate constantcapital. However, the simplicity of the b/1�b structure is not retained. Hismodification requires new elements in the numerator and denominator. Myobjective is to incorporate constant capital in the Keynesian 1/1 � b multiplier,without losing its simplicity. Although the main purpose of this analysis is todevelop the multisectoral structure of the Keynesian multiplier, by implication acontribution can also be made to generalizing the foundations of its structuralcounterpart.

10 For the two-department case,

and

Hence, , where B2 is total consumption of good 2, and L istotal employment. Since v2 � p2 and L � vQ � pQ � y, where y is total netmoney income, it follows that the ratio of total moneyconsumption by workers to total net income (the propensity to consume).


1 Keynes (1936: 32) commented on how the ‘great puzzle of effective demand’had previously been confined to the ‘underworlds of Karl Marx, Silvio Gesellor Major Douglas’.

2 The expression ex ante should not be confused here with Kalecki’s (1990c) con-sideration of capitalists’ investment decisions. In relation to the reproductionschema, ex ante refers specifically to the imbalance between row and columnsums 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.

vh � p2B2/y � b,

vh � v2h2 � v2B2/L

h � � 0h2�

v � [v1 v2], p � [p1 p2]

Notes 113

4 In terms of the numerical example e � and total net income is equal toy � L � 3,500. It follows that the total volume of surplus value (see Table 3.5)is calculated by the equation, S � ey � 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 ofsurplus 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 (seeFreeman et al. 2004).


1 Similarly, for Nell (1998: 206), the circuit approach ‘in its contemporary formappears to owe its origin to Marx’; and for Graziani (1989: 2), ‘elements fromthe 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 anincrease in the production of gold. Sardoni (1989) regards this to be a ‘restric-tive assumption’ that Marx makes in order to clarify the role of money in thereproduction schemes. ‘Marx himself pointed out that he did not take accountof 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 mightspeed up turnover, and its exaggeration of the expense incurred by firms interms of interest payments.

4 I am grateful to Victoria Chick for suggesting to me this interpretation of theproduction period, and its contrast with the circuit approach. Thanks are also dueto Giuseppe Fontana, and two excellent anonymous referees for Research inPolitical Economy, for pressing me on this and other points.

5 Nell (2002: 527) has made it clear that the wage bill ‘gradually accumulates inthe hands of the firms of the consumer goods sector. It isn’t spent until theproduction process in capital goods is complete, at which point the entire wagebill 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 notapplied specifically to the circulation of money. A possible advantage of equa-tion (4.23), since it is derived from an input–output model, is that it could beeasily generalized to an n sector framework.

8 For Moore (1984), this identity between the velocity and the multiplier isunlikely to hold in a real nonergodic economy, where expectations are continuallychanging. It should be emphasized, however, that Marx’s reproduction schemaprovides a limiting extreme in which unlikely conditions such as those associatedwith balanced growth are assumed to hold.

9 In pure circuit theory, the velocity of circulation can be regarded as too orthodoxa concept, partly due to the unrealistic quantity theory assumption that it is astable parameter. However, in an implicit defence of the velocity concept,Graziani (2003: 12) has denigrated the extreme case of an undefined, infinitevelocity as being associated with a quasi-barter economy ‘in which money didnot exist’.

12

12

114 Notes

10 Schmitt (1996: 123) also argues against the narrow Keynesian specification ofthe multiplier as a model of impacts ‘between the investment sector and the con-sumption sector’. This is the approach taken by Nell (2004). Following Marx’sdefinition of investment as increments in constant and variable capital, themultiplier in equation (4.23) is exempt from this criticism, locating incrementsin both sectors.


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 theoffspring 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

and hence

4 The elements of r, in year 1 of Table 5.2, are:

.

Hence

r � s(1 � g) � 0.2414.

5 For Domar, the first two elements of the balanced growth equation represent thepropensity to save, � � e . The share of profits out of total income (e) combinedwith the proportion set aside for investment ( ) make up the proportion ofincome saved (�). Hence, from the multiplier relationship y � (1/e )It, where thereis no exogenous capitalist consumption (see equation 5.7), it follows thatIt � �t yt � Savt.

6 There are similarities here between Marx and Minsky, the prominent PostKeynesian, who emphasized the importance of financial fragilities (see Arnon1994; Crotty 1986).

7 Shoul’s main motivation is to demonstrate the power of Marx’s tendency ofthe falling rate of profit, which in her view operates even when Say’s Law ispostulated, 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 arguedthat realization problems are in fact central to Marx’s falling rate of profit thesis.

��

�

s �e

1 � e�

0.51 � 0.5

� 1

g �C

C � V�

5,5005,500 � 1,750

� 0.75862

s �e

1 � e

e �s

s � 1

Notes 115


1 On Bleaney’s definition, underconsumptionism is characterized by ‘a persistenttendency towards insufficiency of demand for consumption goods’ (Bleaney1976, original emphasis).

2 Similarly, Bleaney (1976: 194) points out that Luxemburg clearly identifies theimportance of demand for means of production as part of capital accumulation.It is not just demand for consumption goods that is important to capital accu-mulation: hence ‘the non-underconsumptionist character of Rosa Luxemburg’sideas’.

3 Tarbuck (1989: 62) argues that the leading Bolshevik economist Bukharin ‘gaveus 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 byadding dC to both sides of (6.5) and noting that S1 � S2 � dV�u�dC.

5 See Chapter 4 for a detailed discussion on the roles played by mutual exchangeand the Kalecki principle in Capital, volume 2.

6 Luxemburg (1951: 339) also shows how the problem of demand is accentuatedunder a rising organic composition of capital.

7 Naqvi (1960: 22) describes this as the ‘false problem of priority of one depart-ment over the other’. In the same vein, Luxemburg also considers Marx’s sec-ond numerical example in which accumulation ‘proceeds uniformly’ in bothdepartments (Luxemburg 1951: 124). Although this example is less arbitrary,the same problem arises of how Department 2 will acquire the precise amountof additional capital goods produced by Department 1.

8 In chapter 23 of Accumulation, Luxemburg identifies this problem of demand inher critique of Tugan Baranovsky’s disproportionality approach. See Kalecki(1971) for a discussion of this disagreement.


1 For example, the entry for constant capital in year 4 is 266,200 instead ofGrossmann’s miscalculation of 266,000 (see Howard and King 1989: 334). Thenumbers shown here are calculated with the advantage of spreadsheet technology.

2 Following the interpretation of the Kalecki principle in Chapter 3, profits andinvestment are defined in net terms. This approach is consistent with Marx’scategory of surplus value, in contrast to the gross definition of profits adoptedby Kalecki.

3 Marx argues that ‘it is at least clear that the consumption of the entire capitalistclass and the unproductive persons dependent on it keeps even pace with that ofthe working class’ (Marx 1978: 407). The simulation that follows will show thatby making Kalecki’s empirical assumptions capitalist consumption does roughlykeep pace with variable capital.

4 The rate of surplus value is now an endogenous parameter, in contrast to itsprevious status as an exogenous parameter in the Grossmann model. Thepreviously endogenous parameter for the proportion of profits saved is now anexogenous 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/S�V). For example, inyear 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 consumptionprovides a drag on labour productivity, since more workers are hired to produce

116 Notes

use-values that are not channelled back into the productive process. More outputis produced without any additional increment to constant capital. (I am gratefulto Cheol-Soo Park for pressing me on this point.)

6 This relationship between luxury goods and surplus value can be distinguishedfrom Marx’s analysis in Theories of Surplus Value part 3, of productivity in theluxury goods department. As is well known, luxury goods do not enter as meansof subsistence for workers, and therefore a change in productivity will notimpact upon the value of labour power (the denominator of the rate of surplusvalue). ‘The cheapening of luxury articles does not enable the workers to livemore cheaply. He requires the same amount of labour-time to reproduce hislabour power as he did previously’ (Marx 1972: 350). However, under theKalecki principle, if more luxury goods are consumed by capitalists, the labourcongealed in these surplus goods can be posited to represent an increase in themass of surplus value (the numerator of the rate of surplus value).

7 In considering these passages, the 1959 Lawrence and Wishart issue of Capitalis cited in order to be consistent with the interpretation of Grossmann (1992).The more recent Penguin issues of Capital are considered otherwise.


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 theorganic composition of capital between sectors alongside a technically incorrectproportionality between prices and values (see Chapter 2).

3 ‘The implication is clear; (S/C � V) is not a significant rate of profit in acapitalist 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 tomoney 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 savingsphlX � 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,

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).

�mw �lXw

y �Vy

Notes 117

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) – assumingzero autonomous capitalist consumption (B0 � 0). See Trigg (2002b) for thecomplete 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 ofSamuelson and Wolfson (1986) is that we dispense with natural exponentials forthe modelling of cumulative growth. In keeping with Table 7.1, in which theschema starts at t � 1, the approach taken by Orzech and Groll (1983: 534) isfollowed, with constants raised to the power t � 1.

2 Inspection of year 2 in Table 7.1, for example, shows that with � 0.05 andt � 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 cal-culation of investment. Examination of Table 7.1 shows their calculation to beincorrect. In year 1, for example, total savings of 25,000 are equal to 20,000investment in additional constant capital plus 5,000 investment in additionalvariable capital. This approach to modelling investment in Marx’s reproductionschema has been introduced in Chapter 3.

118 Notes

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126 Bibliography

Index

The Accumulation of Capital(Luxemburg) 63, 64, 68–9

aggregate demand 2–3, 7, 11; role indrive for capital accumulation 4,63–4, 72–3; role in investment 4,61; source of demand for capitalaccumulation 2, 63–4, 68, 72,73–5, 101

Aznar, E.A. 63

balanced growth 50; and Domar’sgrowth model 53–7, 61, 67–8, 74;and rate of profit 105–8; role ofmoney in 50

banks: money hoarding 60; role infinancing industrial activities 33,34, 35–6, 37, 53, 62

Baranovsky, Tugan 63, 64, 67Bauer, O. 5Bauer model 76, 77–8, 80, 81, 83, 85,

87; structure 108–9Bellofiore, R. 33, 34, 70borrowing paradox 4, 52, 53, 57, 58,

60–1, 68, 75, 101, 115 n.1Brus, W. 26Bukharin, Nikolai 63, 116 n.3Bulgakov, 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 for73–5, 101

capitalist consumption: Grossmannbreakdown theory 5, 76, 77–80,81, 99; Kalecki modified model83–5, 110–11

capital outlays: and sales 50–3Cartelier, J. 24Chakravarty, S. 6Clarke, S. 31commodities 30; circulation 4, 6–7,

41–2; exchange between producers69–70; use-value 30–1

constant capital 4, 7, 16, 34, 69–70,113 n.9

credit 4, 60, 75Crotty, J.R. 57–8, 59Cullenberg, S. 76

De Angelis, M. 13, 14, 113 n.7De Brunhoff, S. 51, 60Deleplace, G. 35Desai, M. 64De Vivo, G. 17Dillard, D. 2disproportionality 63, 64–8, 76, 101;

proportionality 15, 67Domar, E.D. 57Domar’s growth model 4, 53–7, 61–2,

67–8, 74; multisectoral foundations4, 100–2; relevance to Marxian crisistheory 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

Engels, Friedrich 2, 6, 89exchange-value 30–1, 64, 65expanded reproduction 4; algebraic

terms 18–20; input–output format17–18, 41, 66–7; Marxian numericalexamples 10–11, 22, 42, 56; role ofKalecki principle in relation to moneycirculation 25–6; role of money50–3, 57; and surplus value 72

falling rate of profit 3, 76, 80, 85,86–8, 115 n.7; and technicalprogress 5, 76

Finance Capital (Hilferding) 68Foley, D.K. 3, 64Foley’s model of monetary circuit

50–3, 56, 57, 58Foley’s transformation problem 58,

89–90, 95, 96free competition 5, 90

Gilibert, G. 16Graziani, A. 114 n.1, 114 n.9Graziani model of money circulation

33–5, 37, 47–8Grossmann, Henryk 3, 4, 5, 76Grossmann’s law of capitalist

breakdown 5, 76, 77–80, 81, 99

Harris, D.J. 65Harrod’s growth model 4, 53Hartwig, J. 15, 113 n.9Hegel, Georg Wilhelm Friedrich 6Hein, E. 57Hilferding, R. 5, 63, 64, 68–9Howard, 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, 51investment: difference between Marx

and Kalecki 26–8; dual role 61–2,74; importance of aggregate demandin 4, 61

Jacoby, R. 76

Kalecki, Michal 3–4, 21, 26; silenceon 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–outputapproach 27–8, 29–30; role inmoney circulation 24–6, 33, 35, 36,43, 87, 97; and value-form 30–2, 98

Kenway, P. 8Kerr, P. 26Keynes, John Maynard 1, 4, 12, 15, 21Keynesian multiplier 3, 7, 11–16, 19–20,

28, 29, 49, 55, 57, 98, 99, 113 n.9King, J.E. 64, 68, 71, 76, 83, 90Kotz, D.M. 73Kuhn, R. 76Kurz, H.D. 16

labour theory of value 89; Kalecki’ssilence on 26; new interpretation94–6; relation to monetary circuit90; Sraffian critique 30, 31, 94–5

Laibman, D. 77Lee, F.S. 29Leontief, Wassily 16, 17, 32, 102Leontief inverse 44; and surplus value

102–3Leontief’s input–output analysis see

input–output analysisLianos, T.P. 12Luxemburg, Rosa 4, 5, 26, 63; and

capital accumulation 68–73, 116 n.2; critics 64; critique of Marx2, 63–4, 68, 72, 101

luxury goods 51, 85, 117 n.6

macro monetary model 5, 46–9, 53, 64,74; generalization under price-valuedeviations 89–90, 96–101

Malthus, T.R. 63Mandel, E. 6, 65Marx, 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’ 35Marx’s category of surplus value

39–40, 85; relation to multiplierstructure 12, 14, 20

Mitchell, W. 58–9Miyazawa, K. 30

128 Index

Mohun, S. 96monetarism 33monetary 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 alternative39–46; Nell’s mutual exchangemodel 37–9, 41, 48; role in balancedgrowth 50; simple reproduction24–5, 51; single swap approach36–7, 40, 47–8, 52, 57, 114 n.3

money: as means of payment 59–60;opposition to commodity theory ofmoney 33–4; source of money forcapital 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.8Morishima, M. 3Moseley, F. 10multiplier 3, 5, 11–12, 47, 52, 58, 61,

113 n.9, 114 n.7, 8, 115 n.5, 10; andtransformation 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 swapapproach 36–7, 114 n.3

Nell’s mutual exchange model ofmonetary circuit 37–9, 41, 48, 97

Pollin, R. 57production: mutual exchange between

departments of 38, 45, 65–6, 74; ofvalue 6–7, 8

Quesnay, Francois 7, 42

Realfonzo, R. 33, 34reproduction 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, 58Robinson, Joan 2, 74, 85Rosdolsky, R. 67, 112 n.1

Saad-Filho, A. 30, 114 n.5sales: and capital outlays 50–3Salvadori, N. 16Samuelson, L. 80, 108, 118 n.1Sardoni, C. 21, 27, 114 n.2Say’s Law 58, 61–2, 101, 115 n.7Schmitt, B. 48, 115 n.10Sebastiani, M. 26Seccareccia, M. 33, 35, 52Seton, F. 94Shoul, B. 61, 62, 115 n.7simple reproduction 8–10, 11; amount

of money required for circulation51; disproportionality 64–6, 67;role of Kalecki principle in relationto money circulation 24–5; andsurplus value 71–2

single swap model of monetary circuit36, 40, 47–8, 52, 57, 97

Sismondi, J.C.L. de 63Smith, Adam 7, 10, 12, 16, 69, 70social wage rate 13–14Sraffa, P. 16–17Sraffian critique of labour theory of

value 30, 94–5Sraffian price equation 94–5, 96, 97–8Steedman, I. 29, 31, 94, 95surplus value 8–9, 69, 70, 78, 80,

115 n.2; and expanded reproduction72; in interindustry monetary circuit104–5; 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 ofprofit 5, 76

theory of crisis, Marxian see Marxiancrisis 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

Index 129

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

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

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

Yaffe, D.S. 85

Zarembka, P. 6, 72, 74

130 Index

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Andrew Trigg-Marxian Reproduction Schema (Routledge Frontiers of Political Economy) (2006)

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