The Keynesian Multiplier (Routledge Frontiers of Political Economy)

The Keynesian Multiplier

The multiplier is a central concept in Keynesian and post-Keynesian economics. It is largely what justifies activist full-employment fiscal policy: an increase in fiscal expenditures contributing to multiple rounds of spending, thereby financing itself. Yet, while a copingstone of post-Keynesian theory, it is not universally accepted by all post-Keynesians, for reasons vastly different than the mainstream. This book explores both the pros and cons of the multiplier from a strictly post-Keynesian – and Kaleckian – approach. Anchored within the tradition of endogenous money, this book offers a lively discussion from a number of wellknown post-Keynesians from a variety of perspectives: history of thought, theory and economic policy. The book is divided into three sections. Part I, titled ‘Some Views on the Multiplier’, contains three chapters that explore and review the notion of the multiplier in the annals of history of thought. The second part is titled ‘Critical Insights on the Multiplier’, and the contributors to this section take a critical view and explore the limits of the multiplier. The final three chapters, composing the third part of this book, ‘Toward a Re-Interpretation of the Multiplier’, offer some interesting new views. They represent a bridge between the critics and advocates of multiplier analysis and are all rooted in endogenous money. They argue that endogenous money and multiplier analysis are compatible, but it depends on some conditions. Debating all aspects of the Keynesian multiplier, this book is highly relevant to all students of economic theory and philosophy, macroeconomics and political economics. Louis-Philippe Rochon is Associate Professor of Economics at Laurentian University, Ontario, Canada. Claude Gnos is Associate Professor and Director of the Centre for Monetary and Financial Studies at the University of Burgundy, Dijon, in France.

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The Keynesian Multiplier

Edited by Claude Gnos and Louis-Philippe Rochon

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Contents

List of illustrations List of contributors The Keynesian multiplier: an introduction

xiv xv 1

Claude Gnos and Louis-Philippe Rochon

Structure of the book  3 Part I

Some views on the multiplier

7

1 Three views of the multiplier

9

Jochen Hartwig

Introduction  9 The traditional interpretation of the multiplier  9 Problems of the traditional interpretation of the multiplier  13 The principle of effective demand and the multiplier  15 A third view of the multiplier  18 A short remark on the dynamical aspects of the ‘third view’ of the multiplier  24 Tracing back the third view of the multiplier to Keynes’s works  24 Conclusion  26

2 John Maurice Clark’s contribution to the genesis of the multiplier analysis: a note with some related unpublished correspondence Luca Fiorito

32

xii  Contents

3 The multiplier relation as the pure theory of output and employment in a monetary production economy 

58

Heinrich Bortis

Introduction  58 A remark on method  62 Some historical remarks   63 Kaldor’s two multipliers  66 The multiplier and inherent instability (Harrod and Domar)   69 Institutions and the system: the supermultiplier trend  72 Behaviour and its coordination by the system: the business cycle  75 The role of autonomous variables in the medium-term and long-term cycles  76 Two further types of the multiplier  78 Part II

Some critical insights on the multiplier

85

4 The investment multiplier and income saving 

87

Xavier Bradley

The search for a finite value of the multiplier  87 The I = S relationship and the funding of stocks  90 The I = S relationship and the multiplication process  95

5 The intertemporal transmission of money in the endogenous monetary economy: a blessing from the past or a curiosity?

106

Alain Parguez

The multiplier versus the circuit approach: the debate  106 The Keynesian and post-Keynesian multipliers do not exist  109

6 The demise of the Keynesian multiplier revisited 

120

Basil J. Moore

7 Consumption, investment and the investment multiplier Jean-Luc Bailly

Introduction   127 Logical multiplier versus dynamic multiplier   128 The producers of consumption goods have anticipated ∆I  133 The producers of consumption goods failed to foresee ∆I   138 Conclusion   147

127

Contents  xiii Part III

Toward a re-interpretation of the multiplier 

151

8 Kalecki and the multiplier

153

Malcolm Sawyer

Introduction  153 Some simple multipliers in Kalecki’s analysis  155 ‘External markets’  159 Financing and funding   160 Savings and investment: the causal links  163 Crowding out and all that  165 Conclusions  166

9 The Keynesian multiplier: the monetary pre-conditions and the role of banks as defended by Richard Kahn’s 1931 paper – a horizontalist re-interpretation

168

Louis-Philippe Rochon

Introduction  168 Post-Keynesian criticism of the multiplier analysis  169 The theory of the monetary circuit   172 The role of banks and Keynesian multiplier analysis  174 Conclusion   177

10 The multiplier, the principle of effective demand and the finance motive: a single coherent framework

181

Claude Gnos

Introduction  181 Is the multiplier theory rebutted by I–S identity?  181 I–S identity at variance with the supposed multiplier expansion path  184 Keynes’s own statement of the I–S identity   186 Keynes’s ‘logical theory of the multiplier’ and its critique  187 The coherence of Keynes’s theory of employment  189 Conclusion  191

Index

193

Illustrations

Figures 1.1 Marx–Keynes reproduction scheme – completely successful reproduction 6.1 The Keynesian multiplier

19 122

Tables 5.1 Keynesian and post-Keynesian multiplier processes 5.2 The structural factors of the transmission process

108 118

Contributors

Jean-Luc Bailly is Associate Professor of Economics at the University of Burgundy in Dijon, France. He is a member of the Center for Monetary and Financial Studies in Dijon, and of the Research Laboratory of Monetary Economics at the Centre for Banking Studies in Lugano, Switzerland. Among his publications are ‘La pensée économique de Keynes’, in Montoussé (ed.), Histoire de la pensée economique (Bréal, 2000); ‘On the Macroeconomic Foundations of the Wage–Price Relationship’, in Rochon and Rossi (eds), Modern Theories of Money (Edward Elgar, 2003); ‘Definition et intégration de la monnaie: l’apport de la thèse de l’endogénéité’ with C. Gnos, in Piégay and Rochon (eds), Théories monétaires post Keynésiennes (Economica, 2003). Heinrich Bortis has been Professor of Political Economy, History of Economic Theory, and Economic History at the University of Fribourg, Switzerland, since 1980. His major publications are Institutions, Behaviour and Economic Theory: A Contribution to Classical-Keynesian Political Economy (Cambridge University Press, 1997) and ‘Keynes and the Classics: Notes on the Monetary Theory of Production’, in Rochon and Rossi (eds), Modern Theories of Money: The Nature and Role of Money in Capitalist Economies (Edward Elgar, 2003). Xavier Bradley is an associate professor at the University of Burgundy in Dijon, France. He is a member of the Center for Monetary and Financial Studies Centres at the University of Burgundy and a member of the Research Laboratory of Monetary Economics at the Centre for Banking Studies in Lugano, Switzerland. His publications include ‘Involuntary Unemployment and Investment’, in Rochon and Rossi (eds), Modern Theories of Money: The Nature and Role of Money in Capitalist Economies (Edward Elgar, 2003) and ‘Taux d’intérêt et «propriétés fondamentales» de la monnaie’, in Piégay and Rochon (eds), Théories monétaires post Keynésiennes (Economica, 2003). Luca Fiorito is an associate professor in the Faculty of Political Science, University of Palermo, Italy. He received his B.A. from the University of Siena and his Ph.D. in Economics from the New School for Social Research in New York. He is the author of several articles on the history of American economics during the two world wars with special reference to the evolution of American institutionalism. He has also edited unpublished works and correspondence by Wesley C. Mitchell, Edwin R. Seligman, and Frank Knight.

xvi  Contributors Claude Gnos is Associate Professor of Economics at the University of Burgundy and Director of the Center for Monetary and Financial Studies in Dijon, France. He is the author of L’Euro (Management et Société, 1998) and Les grands auteurs en économie (Management et Société, 2000), and co-editor of Post Keynesian Principles of Economic Policy (Elgar, 2006, with L.-P. Rochon). He has also published a number of articles on monetary economics, circuit theory, and the history of economic thought, which have appeared in books and refereed journals, including Journal of Post Keynesian Economics, Review of Political Economy, International Journal of Political Economy, Economie Appliquée, Revue d’Economie Politique, and Economies et Sociétés. Jochen Hartwig is a senior researcher at KOF Swiss Economic Institute in Zurich. He also lectures in economic policy at ETH Zurich. His research interests cover diverse fields such as international business cycles, productivity and growth, national accounting, health economics, and post-Keynesian theory. His recent publications include papers in Journal of Health Economics, Review of Social Economy, and European Journal of the History of Economic Thought. Basil Moore is currently Professor Extraordinaire of Economics at the University of Stellenbosch, South Africa. Before that, he was for many years a professor at Wesleyan University in the United States. He has published numerous articles on monetary theory and policy, and his book Verticalists and Horizontalists: The Macroeconomics of Credit Money (Cambridge University Press, 1988) remains a classic work in post-Keynesian economics. His latest book is Shaking the Invisible Hand: Complexity, Endogenous Money and Exogenous Interest Rates (Palgrave, 2006). Alain Parguez, Professor of Economics at the University of Besançon, France, has been closely associated with many international universities, where he has lectured and held seminars, in particular the University of Ottawa, the University of Missouri at Kansas City, the University of Texas at Austin, and the University of Massachusetts in Boston. He has worked and published extensively on monetary theory, macroeconomics, economic policy, international economics, and the history of economic thought in French, Spanish, and English. He is now involved in research programmes with the European Investment Bank (Luxembourg) and is working on the book Money Creation, Employment and Economic Stability. Malcolm Sawyer is Professor of Economics, University of Leeds, in the United Kingdom, and Pro-Dean for Learning and Teaching for the Faculty of Business. He is the managing editor of International Review of Applied Economics and the editor of the series New Directions in Modern Economics, published by Edward Elgar. He is the author of 11 books and has edited 18 books, published over 70 papers in refereed journals, and contributed chapters to nearly 100 books. His research interests are in macroeconomics, fiscal and monetary policy, the political economy of the European Monetary Union, the nature of money, causes and concepts of unemployment, and the economics of Michal Kalecki. Louis-Philippe Rochon is Associate Professor of Economics at Laurentian University, Canada. He has authored over 70 journal and book articles, and has written or edited numerous books, including Credit, Money and Production

Contributors  xvii (Edward Elgar, 2005), Modern Theories of Money: The Nature and Role of Money in Capitalist Economies (Edward Elgar, 2003, co-edited with Sergio Rossi), Monetary and Exchange Rate Systems: A Global View of Financial Crises (Edward Elgar, 2006, co-edited with Sergio Rossi), Credit, Money and Macroeconomic Policy (Edward Elgar, 2008, with Claude Gnos; forthcoming) and Employment, Growth and Development (Edward Elgar, 2008, with Claude Gnos; forthcoming). His papers have appeared in, among other journals, Review of Political Economy, International Journal of Political Economy, Metroeconomica, Journal of Economic Issues, Economie Appliquée, and Journal of Post Keynesian Economics. His research covers macroeconomic and monetary theory and policy, and post-Keynesian economics.

The Keynesian multiplier An introduction Claude Gnos and Louis-Philippe Rochon

Multiplier analysis is a central focus of Keynesian – and Kaleckian – macroeconomics. It is the basis upon which much of Keynesian and post-Keynesian theory of employment and aggregate demand is based. It is, in particular, what gives strong validity to activist fiscal policies, the aim of which is to reduce unemployment and increase economic growth. Of course, the post-Keynesian multiplier tradition is inherited from Keynes, whose General Theory remains, flaws and all, a central focus of post-Keynesian macroeconomics. In the General Theory, Keynes broke two cardinal rules of ‘classical’ economics: first, ‘classical’ economics, as Keynes labelled what we would otherwise call neoclassical theory today, argues that savings create investment, and that investment can be financed only through ex ante saving. Second, saving and investment are brought into equality through variations in the rate of interest: in a situation of excess saving, a reduction in the rate of interest would decrease saving, but increase investment, thereby bringing the two into equality. In the General Theory and after, therefore, Keynes abandoned these notions. First, set in historical time, investment, financed by bank credit, created saving: investment logically preceded saving. In other words, investment is not financed by saving, and a lack of saving can therefore never constrain investment: ‘The investment market can become congested through the shortage of cash. It can never become congested through the shortage of saving’ (1973, p. 222; see Rochon, 1997, for a discussion of Keynes’s finance motive and the specific role of banks). Second, Keynes also rejected the notion of the natural rate of interest, that is the existence of a rate that would equilibrate saving and investment. But with Say’s law clearly discarded, Keynes needed the means to bring investment and saving into equality, and restore equilibrium. Inspired by Richard Kahn’s earlier (1931) paper,1 Keynes introduced the multiplier as the mechanism by which saving was brought into equality with investment: while investment created saving, changes in income were required to increase saving to the desired level. Keynes therefore relied on the multiplier process. As he tells us, ‘The multiplier tells us by how much their employment has to be increased to yield an increase in real income sufficient to induce them to do the necessary extra saving, and is a function of

2  Gnos and Rochon their psychological propensities. . . [It is a] logical theory of the multiplier, which holds good continuously, without time-lag, at all moments of time’ (1936/1973, pp. 117 and 122). Of course, many economists have come to question the validity of the multiplier process altogether. This criticism goes back to Keynes’s contemporaries. For instance, Pigou (1933/1968, 1941), Robertson (1936), Hawtrey (1950, 1952), among others, were critical of the multiplier process. Of course, the tradition of doubting the multiplier process extends beyond Keynes’s contemporaries, and even among his most faithful followers. Indeed, some heterodox economists have also been critical of the multiplier. For instance, Asimakopulos (1986) and Moore (1988) have perhaps been its most vocal critics. For Asimakopulos, the issue was one of the time dimension: if Keynes’s General Theory is purported to be a theory of the short run, how can this be reconciled with a multiplier process that must take time to fulfil itself? Indeed, in discussing the issue of short-term and longterm financing of investment, Asimakopulos (1986, p. 83) argues that there is an important sequential process involved. After an initial investment, the increased saving . . . is only available after the full multiplier effect is achieved. This increase in desired saving does not occur simultaneously with the expenditure of the newly acquired increase in investment finance, even though ex post investment and ex post saving are always equal by definition. It takes place only when the full multiplier effects of an increase in investment have worked themselves out. Hence, there is a need for ‘the passage of time.’ Hence, if output increases thereby allowing saving to adjust to investment, the subsequent rounds of spending need time to occur: Keynes’s treatment of the multiplier is thus incomplete. It is always necessary to keep in mind that the passage of time is not dealt with in comparative static analysis, and this time element must be introduced in any application of the analysis that is concerned with the effects of changes. Keynes’s language in referring to the multiplier sometimes gives the impression that he is dealing with changes, but his treatment of it is confined to comparative statics. (Asimakopulos, 1991, p. 68) As for Moore (1988), his criticism rested on the necessary accounting equality between investment and saving, and the rejection of equilibrium analysis. As such, saving and investment need not be brought into equality. Hence, as Moore (ibid., p.  309) argues, the accounting identity between saving and investment, which is tied directly to the endogeneity of money, refutes ‘the Keynesian notion that the level of income adjust to bring planned saving and planned investment . . . into equality by a “multiplier” process’. Hence, ‘income does not adjust to equate planned investment with planned saving. What then is left of Keynes’s income–expenditure multiplier analysis of the equilibrium level of income? The

Introduction  3 answer must be – nothing’ (ibid., p. 314). As a result, ‘All increases in investment spending, whether financed internally or externally, from non-banks or banks, are thus accompanied by equal increases in saving in the same period . . . The Keynesian multiplier analysis is thus flawed’ (ibid., p.  312). Moore returns to ‘the demise of the Keynesian multiplier’ in his recent book, Shaking the Invisible Hand (2006). His conclusion is that multiplier analysis is fundamentally contradictory to endogenous money. Not surprisingly, Moore’s attack on the Keynesian ‘holy grail’ was not well received. Indeed, a number of post-Keynesians took offence at his rejection of the multiplier. For instance, in a powerful article, Cottrell (1994) objects to Moore’s definitions of saving, claiming that Moore fails to differentiate between planned and realized savings (see Gnos, this volume, for a discussion of this debate). According to Cottrell (1994, p.  114), Moore fails to distinguish between ‘actual’ investment and saving that ‘are indeed identically equal’ and ‘planned’ or ‘intended’ investment and saving that ‘are not identical and must be brought into equality by means of some mechanism or other.’ Hence, ‘The actual mechanism whereby Y changes in response to I is typically explicated in terms of inventory accumulation or dissimulation. So long as planned investment exceeds planned saving, sales will exceed production and producers experience an unplanned fall in inventory levels. They react by employing more workers and producing more’ (ibid., p. 111). Despite some fierce criticism, the multiplier remains very much entrenched in post-Keynesian analysis. Indeed, Moore’s arguments have proven to be too radical for most post-Keynesians. If there is no multiplier, what then could be the purpose of fiscal policy and its effectiveness for unemployment and growth? Moore’s argument seems to question the very foundation of activist fiscal policy.

Structure of the book The purpose of this book is to explore some of the issues related to the multiplier. It stems from a number of discussions between the two editors over the years, which then became two sessions at the Eastern Economic Association. At those sessions, some further discussion ensued with a number of our colleagues and the idea of editing a book on the Keynesian multiplier was born. It is the result of a long gestational period that resulted in high-quality research. In this book, we offer a number of articles that address various aspects of the multiplier and its controversy within post-Keynesian circles. While some articles are critical of the multiplier, others attempt to offer a solution that, the authors hope, bridge the gap between the more extreme Moorian position and other postKeynesian views. The book is divided into three parts. Part I, ‘Some Views on the Multiplier’, contains three chapters that explore and review the notion of the multiplier in the annals of the history of thought. Jochen Hartwig argues that there are three different definitions of the multiplier in Keynes, although only one of them is consistent with the notion of effective demand.

4  Gnos and Rochon In his contribution, Luca Fiorito explores carefully the existence of the multiplier in the work of John Maurice Clark, even proclaiming for him the ‘independent discovery of the multiplier principle.’ In Chapter 3, Heinrich Bortis argues that the multiplier principle in its various shapes constitutes a most powerful theoretical tool (in Marshall’s sense) for explaining employment levels in the short, medium and long term as well as system-caused involuntary unemployment, and provides a solid conceptual basis for the formulation of employment policies. In the second part, ‘Critical insights on the multiplier’, Xavier Bradley explores the limits of the multiplier by exploring in great detail the consistency of the definitions of investment and saving used by Keynes. In Chapter 5, Alain Parguez takes to task the issue of the multiplier and argues, quite controversially, that ‘rejecting the multiplier is the sine qua non of a genuine full-employment policy.’ In Chapter 6, Basil Moore returns to his criticism of the multiplier. He defends his rejection of the multiplier and offers post-Keynesians some thoughtful insights on endogenous money, investment financing, endogenous money and complexity. In Chapter 7, Jean-Luc Bailly looks at whether the structural relationship between consumption and investment, quantified by using Keynes’s logical multiplier, can be logically transposed to the causal plane so as to construct a dynamic theory of the way national income is determined. He investigates the causal connection between the formation of additional income in the capital goods sector and its spending on the purchase of consumption goods. He asks whether it is possible to trigger an income multiplication process by spending such income on consumption. The final three chapters, constituting the third part of this book, ‘Toward a reinterpretation of the multiplier’, offer some interesting new views. They represent a bridge between the critics and advocates of multiplier analysis. All are rooted in endogenous money. Yet contrary to Moore, they argue that endogenous money and multiplier analysis are compatible, dependent on some conditions. In his contribution in Chapter 8, Malcolm Sawyer argues that Kalecki’s macroeconomics can be seen as consistent with a multiplier story, although he finds that the multiplier process does not play a central role in Kalecki’s work. Like Louis-Philippe Rochon, Sawyer concludes that the multiplier process depends on the banking system. Indeed, Rochon bases his arguments on a careful re-reading of Kahn’s original paper on the multiplier. In Chapter 9, he argues that in a monetary economy of production, the multiplier is not automatic but depends on the generosity of the banking system in renewing credit. Finally, in Chapter 10, Claude Gnos argues that the multiplier expansion path, as depicted by the standard Keynesian literature, is undoubtedly at variance with the features of bank money, which cannot finance (on demand) any investment by firms without simultaneously generating an equivalent saving by income recipients. Whatever the distinction between planned and actual magnitudes, then, every investment ties up the corresponding savings, which therefore cannot be spent on consumption goods and generate new incomes. What then is left of the

Introduction  5 multiplier theory? Gnos argues that Keynes’s conception of the multiplier cannot be reduced to the standard version of it and so deserves a full reappraisal within the framework of his actual theory of employment as characterized by the principle of effective demand and the finance motive. We hope that the articles in this book will generate some thoughtful and much needed discussion of the nature of monetary economies of production and the mechanisms behind the multiplier process. Indeed, this may help us to carefully re-evaluate the role of banks and monetary and fiscal policies.

Notes 1 In an interesting recent paper, Kent (2007) argues, in fact, that Keynes had developed a version of the multiplier as early as 1929, and was thereby himself a ‘predecessor’ to Kahn.

Bibliography Asimakopulos, A. (1986), ‘Finance, Liquidity, Saving, and Investment’, Journal of Post Keynesian Economics, 9 (1), pp. 79–90. Asimakopulos, A. (1991), Keynes’s General Theory and Accumulation, Cambridge: Cambridge University Press. Cottrell, A. (1994) ‘Post-Keynesian Monetary Theory’, Cambridge Journal of Economics, 18 (6), pp. 587–605. Hawtrey, R. G. (1950), Currency and Credit, 4th ed. London: Longmans, Green. Hawtrey, R. G. (1952), Capital and Employment, 2nd ed. London: Longmans, Green. Kahn, R. (1931), ‘The Relation of Home Investment to Unemployment’, Economic Journal, June, pp. 173–98. Kent, R. (2007), ‘A 1929 Application of Multiplier Analysis by Keynes’, History of Political Economy, 39 (Fall), 529–43. Keynes, J. M. (1936/1973), The Collected Writings of John Maynard Keynes. Vol. 7: The General Theory of Employment, Money and Interest, D. Moggridge (ed.), London: Macmillan and St Martin’s Press. Keynes, J. M. (1937/1973), The Collected Writings of John Maynard Keynes. Vol. 14: The General Theory and After, Defence and Development, D. Moggridge (ed.), London: Macmillan and Cambridge University Press. Lavoie, M. (1992), Foundations of Post-Keynesian Economic Analysis, Aldershot: Edward Elgar. Moore, B. (1988), Horizontalists and Verticalists: The Macroeconomics of Credit Money, Cambridge: Cambridge University Press. Moore, B. (2006), Shaking the Invisible Hand: Complexity, Endogenous Money and Exogenous Interest Rates. London: Palgrave. Pigou, A. C. (1933/1968), The Theory of Unemployment, New York: Augustus M. Kelley. Pigou, A. C. (1941/1979), Employment and Equilibrium, Westport, CT: Greenwood. Robertson, D. H. (1936), ‘Some Notes on Mr. Keynes’ General Theory of Employment’, Quarterly Journal of Economics, 51 (November), pp. 168–91. Rochon, L.-P. (1997), ‘Keynes’s Finance Motive: A Reassessment. Credit, Liquidity Preference and the Rate of Interest’, Review of Political Economy, 9 (3), pp. 277–93. Rochon, L.-P. (1999), Credit, Money and Production: an alternative post-Keynesian approach, Cheltenham: Edward Elgar.

Part I

Some views on the multiplier

1 Three views of the multiplier Jochen Hartwig1

Introduction This chapter endeavours to re-interpret one of the most fundamental concepts of macroeconomics: the Keynesian investment multiplier. It is demonstrated that there are three different views of the multiplier in Keynes’s own works, and that only one of them is in line with the principle of effective demand as exposed in chapter 3 of The General Theory. The chapter is organised as follows. First, what I call the ‘traditional interpretation of the multiplier’ is restated. This traditional view is then criticised for its lack of logical coherence and ‘realisticness’.2 It is argued that the multiplier and Keynes’s principle of effective demand constitute an analytical unity; therefore it is necessary to restate the principle of effective demand. This is done somewhat differently than in the existing (post-Keynesian) literature on effective demand. The subsequent section elaborates on what is here called Keynes’s ‘third view’ of the multiplier – the one that is held to be compatible with the principle of effective demand. This ‘third view’ envisages the multiplier as an equilibrium condition that prescribes the proportionality between the two ‘departments’ of the economy – the consumption- and the investment goods sectors – necessary for what is here called ‘completely successful reproduction’. The Marxian concept of reproduction schemes is combined with Keynes’s ‘fundamental psychological law’ (which states that the marginal propensity to consume is ‘positive and less than unity’; Keynes, 1973a, p. 96) to derive this result. Some dynamic aspects of the ‘third view’ of the multiplier are briefly discussed. The final section traces back the ‘third view’ of the multiplier – which seems to have escaped the attention of a wider audience so far – to Keynes’s own writings. The last section offers some conclusions.

The traditional interpretation of the multiplier The issue of the multiplier seems to be settled. Everybody knows what it is. Textbooks usually present the familiar relation for a closed economy without state activity:

10  Hartwig Y = C + I ⇒ Y = c · Y + I ⇒ Y – c · Y  = I ⇒ (1 – c) · Y = I ⇒ =  [1/(1 – c)] · I

(1.1)3

where Y = income, C = consumption, I = investment and c = marginal propensity to consume. This calculation starts from the ‘expenditure perspective’ on national income. National income is at disposal either for consumption or for investment. But in the second step the perspective switches, so to speak, to the production account: if (an additional) income is somehow generated, some part of it will be consumed. After several simple mathematical manipulations a relation between investment and national income emerges which is known as the ‘multiplier relation’. Keynes gave prominence to investment as the ‘prime mover’ in the process of income generation,4 because the multiplier relation ‘proves’ that every increase in investment increases national income multiplicatively by [1/(1 – c)], and that every decrease in investment decreases income by a much larger amount than the value of investment itself. But how can a certain investment demand increase national income by a factor greater than 1? The pure existence of a mathematical or logical relation does not yet provide an answer to this question. Besides the multiplier relation there must be some multiplier process. The traditional view of this multiplier process has been cogently stated by James Meade: Suppose . . . that we start with a given level of the flow of investment expenditures. This is sensible because investment is in fact influenced primarily by outside or ‘exogenous’ influences such as the confidence and expectations of businessmen in the case of private investment and governmental decisions in the case of public investment. These investment expenditures will generate the payment of wages, rents, interest, profits etc. to those engaged in the production of these capital equipment in question. Those engaged in the production of these capital goods will save some of the incomes so earned but will spend the rest on consumption goods. The producers of these consumption goods will thus earn incomes, part of which they will save but part of which they will in turn spend on other consumption goods, thus generating still other incomes which will be partly saved and partly spent on consumption, and so on. This process will generate a conver­ging series of ever diminishing waves of expenditures which will result in a finite level of demand for goods and services to meet both the original investment demand and the subsequent induced demands for consumption goods. The level of economic activity so generated may or may not be sufficient to provide full employment for the available productive resources in the community. (1975, p. 84) In the beginning, before production has taken place, there is an investment demand which is then satisfied by production. Due to this production activity in the investment goods sector, income is generated which induces a demand for

Three views of the multiplier  11 consumption goods. In an infinite process of demand–production–income generation–demand, the final outcome will be the one given by the multiplier relation. As is well known to post-Keynesians, ‘Keynesianism’ has often misinterpreted Keynes – but not in this case! Keynes described the multiplier process in the same way as Meade: There is nothing fanciful or fine-spun about the proposition that the construction of roads entails a demand for road materials, which entails a demand for labour and also for other commodities, which, in their turn, entail a demand for labour . . . Generally speaking, the indirect employment which schemes of capital expenditure would entail is far larger than the direct employment . . . But the fact that the indirect employment would be spread far and wide does not mean that it is in the least doubtful or illusory. On the contrary, it is calculable within fairly precise limits. (Keynes and Henderson, 1972, p. 105, fn.) Keynes expands on this view in ‘The Means to Prosperity’ (1972). Here, he distinguishes between ‘primary expenditure (employment)’ in the production of investment goods and ‘secondary expenditure (employment)’ in the consumption goods sector. The multiplier process as it is presented by Meade and Keynes supports two policy prescriptions which are closely associated with the name of Keynes. First, whenever the volume of private investment expenditure is insufficient to ‘generate’ full employment, the government can and should fill that gap. Public investment, or, to be more specific, any public expenditure which creates income for somebody, has the same multiplicative effects as private investment expenditures. Unlike monetary policy, fiscal policy offers the theoretical possibility to create full employment under all circumstances. The second policy prescription concerns the role of saving. Whereas for a neoclassical economist high saving (and perhaps also a high interest rate which encourages high saving) is welcome because the non-consumption of resources is believed to be the supply-side requirement for high investment, high saving has a detrimental role for Keynes. It is obvious that the investment multiplier [1/(1 – c)] increases if the marginal propensity to consume (c) converges to unity. For this reason, Keynes considers high saving as disadvantageous: it appears to be a ‘leakage’ out of the income-generating multiplier process. To quote Meade again: Investment expenditure could be regarded as an injection from outside of a flow of purchasing power into an income-generating system; saving could be regarded as a leakage of purchasing power out of this income-generating system. Given an initial injection of investment demand into the system, incomes would be generated by a succession of waves of induced demand for consumption goods until the resulting leakage out (saving) was equal to the original injection in (investment). The greater the level of investment and the

12  Hartwig lower the proportion of their income which people decide to save, the higher would be the level of the resulting effective demand for goods and services and so the demand for output and for the employment of labour. (Meade, 1975, p. 84) Keynes’s proposition that saving always equals investment (1973a, p. 84) implies more than just an accounting identity. The identity of saving and investment is the result of a process in which part of the ‘induced income’ is saved in every ‘round’. At the end of this income-generating process the sum of the savings must be equal to the initial investment expenditure. Although, according to Keynes, high saving cannot be encouraged, it is important that something is saved, because if nothing was saved at all, the incomegenerating process would not converge to a point of rest. That is why Keynes sometimes presents his ‘fundamental psychological law’, which states that the marginal propensity to consume is ‘positive and less than unity’ (ibid., p. 96) as a stability condition: My theory itself does not require my so-called psychological law as a premise. What the theory shows is that if the psychological law is not fulfilled, then we have a condition of complete instability. If, when incomes increase, expenditure increases by more than the whole of the increase in income, there is no point of equilibrium. Or, in the limiting case, where expenditure increases by exactly 100 per cent of any increase in income, then we have neutral equilibrium, with no particular preference for one position over another.5 (Keynes, 1973d, p. 276) To conclude this section, I restate the first two views of the multiplier in Keynes’s works – those two views that should be well known to economists familiar with the Keynesian literature. According to the first view, the multiplier is a functional relation between a conceivable level of investment expenditure and of income. The multiplier relation implies stability. To grasp this, we can compare the relation between investment expenditure and income at two hypothetical points in (logical) time.6 If the stability condition – the marginal propensity to consume must be smaller than one – is violated, the logical multiplier relation is also invalidated. According to the second view, the multiplier is a dynamic process (probably in historical time – the literature is not outspoken on this point) that guarantees an increase in national income, caused by an investment ‘injection’. The additional income is greater than the initial investment injection. Two quotes from The General Theory support these two views: •

View 1 (the multiplier is a logical relation between investment and income that implies stability):

Three views of the multiplier  13 The multiplier tells us by how much their (the public’s) employment has to be increased to yield an increase in real income sufficient to induce them to do the necessary extra saving. (Keynes 1973a, p. 117; my emphasis) •

View 2 (the multiplier is a dynamic process): Let us call k the investment multiplier. It tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment. (ibid., p. 115; my emphasis on ‘will’)

We can perhaps synthesise the two views of the multiplier presented so far – the combination of which constitutes what I call the ‘traditional interpretation of the multiplier’ – by saying that the income-generating process would not converge to a point of rest if the marginal propensity to consume was not smaller than one, and in this case the logical multiplier relation could not be maintained. So we might say that Keynes’s ‘fundamental psychological law’ is the connecting link between the two views of the multiplier.

Problems of the traditional interpretation of the multiplier In this section it will be argued that the traditional interpretation of the multiplier presented above is (a) contradictory in terms, (b) a false abstraction from reality and (c) incompatible with the principle of effective demand as presented in chapter 3 of The General Theory. The contradictory nature of the multiplier concept can easily be assessed. How can a dynamic process that consists of an infinite series of induced expenditure streams ever reach a final level of national income? In other words: the logical relation between different levels of investment expenditure and income established by the first view of the multiplier mentioned above will only be reached by the multiplier process (view 2) in the limit. It is also noteworthy that, whereas the first view of the multiplier implies that saving and investment are identical, the second view implies that they are different: as long as the multiplier process goes on (and it goes on forever) the sum of savings will be smaller than the initial investment expenditure. Of course, we face here a central problem of the economics of Keynes: the problem of reconciling dynamic analysis (which proceeds in historical time) with comparative-static analysis (which proceeds in logical time). It was noted long ago that Keynes’s inability to solve this problem eventually led him to turn to comparative statics: It was realized straightaway that Keynes had changed his methodology when he moved from A Treatise on Money to The General Theory. He abandoned dynamic period analysis in which disequilibrium analysis was possible and

14  Hartwig adopted comparative statics.  .  .  In terms of comparative statics, different hypothetical rates of new investment and different marginal propensities to consume (multipliers) can be assumed, giving different temporary equilibrium states, different levels of employment. These temporary equilibria are snapshot photographs. As Shackle puts it so well, ‘At each curtain rise the General Theory shows us, not the dramatic moment of inevitable action but a tableau of posed figures. It is only after the curtain has descended again that we hear the clatter of violent sceneshifting’ . . . It is quite clear from The Collected Writings of Keynes that he made the change to statics after long consideration and for good reasons at the time. Keynes wrote to Professor Ohlin regarding ex post and ex ante method, . . . ‘My reason for giving it up was owing to my failure to establish any definite unit of time and I found that that made very artificial any attempt to state the theory precisely. So, after writing out many chapters along what was evidently Swedish lines, I scrapped the lot and felt that my new treatment was much safer and sounder from the logical point of view. I used to speak of the period between expectation and the result as ‘funnels of process’, but the fact that the funnels are all of different length and overlap one another meant that at any given time there was no aggregate realized result capable of being compared with some aggregate expectation at some earlier date. (Gilbert, 1982, p. 209, fn.) However well considered this change of methodology might have been, it is not totally convincing. As was mentioned earlier: the fact that a mathematical or logical relation between economic variables exists does not answer the question how this relation is brought into being. The ‘clatter of .  .  . sceneshifting’, the dynamic process, must be elucidated. And Keynes acknowledged this by not abandoning the dynamic view of the multiplier in the General Theory. But in what has been referred to so far, he has not been able to reconcile the two views of the multiplier. But this is not my main criticism of the traditional interpretation of the multiplier. What seems to be more damaging to the presentation of the multiplier process à la Meade or Keynes is that it seems to constitute a grossly false abstraction from economic reality. A theoretical concept must be regarded as ‘unrealistic’ if it ‘does not refer to anything actual’ (Mäki, 1998, p.  410). Almost thirty years ago, the German socio-economist Werner Hofmann levelled the critique that the view of the multiplier process presented above would establish a ‘disjunction and independence of aspects of the economic process which belong together’ (Hofmann 1979, p.  185; my translation). He accused Keynes of having ‘disrupted the connection between the markets for consumption goods and the markets for means of production’ (ibid., p. 189; my translation). I think this criticism is justified. Is it really plausible to assert that, in the first place, there is only a ‘primary’ or ‘direct’ employment in the investment goods sector, and that the employment in the consumption goods sector is only ‘indirect’ and, so to speak, ‘induced’ by this primary employment by the demand of those occupied in the investment

Three views of the multiplier  15 goods sector? Imagine the following scenario: at first the plants of the (for example) machine manufacturers work at full speed while the plants of the (for example) tinned food industry stand still. Then, after all machines that had been ordered have been produced, the workers in the machine manufacturing industry want to eat and demand tinned food. This is when the tinned food industry starts its production. Meanwhile, the plants of the machine manufacturers stand still. Then, something happens that nobody has expected: the workers of the tinned food industry also want to eat! So, a second wave of production is induced and a second wave of income is generated which (surprise!) leads to a third wave of demand and so on to the end of all times. This is absurd – but it seems to be a fairly accurate description of the traditional view of the multiplier process which I believe to be responsible for that ‘peculiar reversal of the connection, in which prior spending leads to subsequent production and income, and in which investment – unconcerned with its purpose – leads to the demand that has been the reason and the justification for that investment in the first place’ (Hofmann 1979, p. 221; my translation). In reality, of course, production of investment goods and of consumption goods takes place simultaneously at each moment in time; and in both departments income is generated. Note also that this interpretation of the multiplier process seems to be mainly responsible for some influential misinterpretations of Keynes’s theory which still defend their place in textbooks. For example, there is the conclusion drawn from the income–expenditure (45°) model maintaining that Keynes has simply shifted the equilibrating role (between supply and demand) from prices to quantities – in other words the notion of ‘fast quantities’ but ‘slow prices’ in Keynes (originating with Leijonhufvud,7 who later recanted (1974); but still alive in the so-called New Keynesian school); and the notion that Keynes has simply turned Say’s law upside down: not every supply creates its own demand but every demand creates its own supply. These ideas are attributed to Keynes, but – as will be argued in the next section – they are not compatible with his principle of effective demand.

The principle of effective demand and the multiplier Arestis, Dunn and Sawyer (1999, p. 46) claim that the principle of effective demand is the ‘unifying agenda’ for post-Keynesian economics. Therefore, it is of paramount importance for post-Keynesians and economists more generally to have a correct understanding of that principle. The essence of the principle of effective demand is often purported to be a quantity reaction of real income which brings about ‘equilibrium’ (equality of saving and investment),8 and which could be labelled ‘multiplier process’. But this is certainly not the way Keynes presents the principle of effective demand in chapter 3 of The General Theory. His presentation will now be restated briefly.9 To understand the principle of effective demand, it is highly important to visualise the economic process as a sequence of production periods (Chick, 1983, pp. 16–21). The production period is mainly an analytical concept. But in order not to be a false abstraction, it has to have some grounding in reality. I think it has.

16  Hartwig Entrepreneurs do plan for certain periods of the (uncertain) future. The production period is characterised by the length of time that an entrepreneur is bound by his employment decisions taken at the beginning of that period. The term of the wage contract and the period of notice for work contracts seem to be important elements that influence the length of the production period of an individual firm. Keynes turned to comparative statics because he realised that the production periods of individual firms ‘are all of different length and overlap one another’ (see above), a property that seemed to be inconsistent with the idea of a macroeconomic production period. But I think he overstated the difficulties inherent in the concept of production period. The rules of collective bargaining and legal regulations concerning the beginning and the end of the accounting year tend to bring the production periods of individual firms into line.10 Another solution to the problem of establishing a macroeconomic production period is to make it very short so that the individual firms’ periods won’t overlap any more, and Keynes considered this possibility in The General Theory.11 Now, entrepreneurs decide at the beginning of the production period how much to produce during that period, and they deduce from this decision how much employment to offer. From the definition of the production period follows that they are not able to revise these decisions during the production period. It is the principle of effective demand that guides their decision how much to produce. Their cost conditions together with the aim to maximise profits are reflected in their supply function (Z). The price component inherent in the Z-function is not the market price level an entrepreneur expects (as in the bulk of the post-Keynesian literature on Z), but the proceeds he must have for the last unit of output at each level of employment to satisfy the profit maximising condition. This unit supply price will grow with employment under conditions of decreasing marginal returns to labour.12 The supply functions of individual firms can be aggregated straightforwardly (cf. Davidson, 1987), which yields the aggregate supply function of the economy: Z = φ(N). The Z-function will be strictly convex (in the aggregate employment/ aggregate proceeds quadrant) if, with rising employment, the profit share in aggregate proceeds grows relative to the wage share.13 Because of fundamental uncertainty in a monetary production economy, Say’s law does not hold good (Keynes, 1973c). Therefore, each entrepreneur is forced to form expectations about how much he might be able to sell. This leads to (to quote Vickers, 1987) ‘the producer’s expected demand curve’. Contrary to Vickers (1987, p. 98), the price level implicit in the expected demand curve need not be equal to the price level implicit in the supply curve at the same level of employment. The price level implicit in the supply curve shifts with employment. The price level implicit in the expected demand curve, however – the proceeds each individual entrepreneur thinks he will be able to receive for a unit of output – is independent of the level of employment he offers. Each entrepreneur has to form an expectation about the price that can be enforced for his product in the (at least to some degree) competitive markets that characterise contemporary capitalism. Contrary to the supply curves, the individual demand curves cannot be ag-

Three views of the multiplier  17 gregated straightforwardly. To repeat: since no single producer expects his own proceeds to be negatively influenced if he cuts back employment, the producer’s expected demand curve should be a horizontal line in a graph with his own offers of employment as abscissa and his own expected proceeds as ordinate (Parinello, 1980, pp. 68–70). But although it is true that no entrepreneur will expect to sell more just because he employs more people, each entrepreneur will expect to sell more if he expects aggregate employment to be higher in the next production period, because each entrepreneur knows that in this case aggregate demand will be higher. If we interpret the employment quantity with regard to the individual entrepreneur’s D-curve as the share of expected aggregate employment for an individual firm, then the D-curve of every single firm (as well as the aggregate Dcurve) will be strictly concave. There is a range of conceivable total employment levels along with the specific share of an individual firm. The expected proceeds of each firm grow with this share, but due to decreasing marginal returns to labour, (real) income and also sales proceeds are expected to grow with a decreasing slope.14 So we have two cases: if entrepreneurs have some macroeconomic insights, the aggregate demand curve D = f(N) (which is expectation-dependent15) will be strictly concave. If they have no such insights, it will be a horizontal line.16 Each entrepreneur fixes his labour demand at the point where his D- and Zcurve intersect, ‘for it is at this point that the entrepreneurs’ expectation of profits will be maximised’ (Keynes, 1973a, p. 25). Note that, although the concepts of price and employment are different for both curves (supply price level as a thought experiment, in which profit-maximising strategies in response to possible levels of demand are considered (and which is dependent on costs) versus demand price level as the aggregation of the prices entrepreneurs think their respective markets will accept; employment level of the firm versus employment level as the firm’s share of expected total employment), they are all mutually consistent at this point of intersection. The supply price equals the demand price, and the firm’s de facto employment equals the entrepreneur’s expectation as to how much of total employment is attributable to that firm. If the above-mentioned qualifications are taken into consideration, the individual D- and Z-curves can be aggregated, which yields the point of effective demand for the economy as a whole. This point contains all information about price, output, and employment levels for the next production period. One might conceive of this point as an equilibrium, but it is not some kind of ‘market equilibrium’. It is a point at which the entrepreneurs’ expectations and aspirations concerning different things, such as prices, costs, profits, demand and so on, are mutually consistent. Understood this way, the principle of effective demand has fatal consequences for certain interpretations of Keynes’s theory. Consider the familiar ‘quantity reactions’. They are simply impossible. The entrepreneurs decide at the beginning of the production period how much to produce and how many people to employ. They use the D- and Z-curves to find out which level of employment will be profit-maximising, given what they know and what they expect. If their

18  Hartwig expectations turn out to be wrong, for example if they have underestimated demand, they are not able to correct their decisions ad hoc. They are bound by them until the end of the production period. Victoria Chick was right to point out that ‘[e]ffective demand is an unfortunate term, for it really refers to the output that will be supplied; in general there is no assurance that it will also be demanded’ (1983, p. 65). It is not the de facto demand, but the ex ante expected demand, that is decisive (together with the Z-function) for output and employment during each production period. If the entrepreneurs have (ex ante) over- or underestimated the period’s de facto demand they cannot produce more or less ad hoc – as in the 45° model. The definition of the production period given above (the length of time that an entrepreneur is bound by his employment decisions) implies that corrections could only affect next period’s supply.17 If we try, in the light of these insights, to assess the relationship between the principle of effective demand and the multiplier, we are forced to admit that the dynamic view of the multiplier (as a process in the course of which ever diminishing waves of expenditures induce ‘indirect’ demand and employment) is as incompatible with the principle of effective demand as is the ‘quantity reaction’ interpretation of Keynes’s theory. There is no room for such a process in an economy in which output and employment quantities are fixed at the beginning and for the duration of the production period at a point that must be interpreted as the producers’ ‘expectations equilibrium’. What about the ‘first view’, which envisages the multiplier as a logical relation between investment and income? It is not at all clear why this logical relation should necessarily hold good in an economy in which the expectation-dependent production decisions of the producers of consumption goods are independent of those of the producers of investment goods. As this remark indicates, I find it convenient – if not necessary – to reinterpret Keynes’s theory in a scheme with two sectors; and this task will be taken up in the next section.

A third view of the multiplier In this section, I draw heavily on Marx’s reproduction schemes (Marx, 1973, chapters 20 and 21) as well as on associated concepts, such as value and surplus value, that are not totally alien to Keynes.18 Readers might be inclined to ask immediately whether any Marxian concept can sit comfortably with Keynes – given the indisputable (not only theoretical) differences between the two economists. The exposition in this section draws to a certain extent on the work of Amit Bhaduri, who has forcefully argued in favour of the compatibility of Marxian reproduction schemes and Keynes’s principle of effective demand (Bhaduri, 1986, chapter 2).19 In Marx’s reproduction schemes there are two ‘departments’: department I produces investment goods, and department II produces consumption goods. Social reproduction is effected by each department, consuming part of its own output and exchanging the remaining part with the other department. Reproduction will be called ‘completely successful’ if the whole output of both departments is sold for

Three views of the multiplier  19 its value during a production period and if (at the same time) all ex ante plans have been fulfilled at the end of the period. The people attached to each department are either capitalists (entrepreneurs) or workers. The reproduction scheme presented below in Figure 1.1 differs significantly from those in the second volume of Kapital. Though I adopt the division of the value of output into variable capital and surplus value, I drop the constant capital part. Constant capital is absent from the scheme (in other words: the net value added instead of the gross value added of the two departments is dealt with) to account for Keynes’s treatment of the transfer of the value of constant capital onto the output. National accounts distinguish between gross and net income. Keynes’s ‘indubitable [proposition] . . . that the income derived in the aggregate by all elements in the community concerned in a productive activity has a value exactly equal to the value of the output’ (Keynes, 1973a, p. 20) is correct for gross income, but it is only net ‘national income’ that households have at their disposal for consumption or saving and that is relevant for the reproduction scheme (as well as for the D-curve). In other words, the value of constant capital transferred onto the output during a production period has to be paid for by the purchasers and constitutes gross income for the entrepreneurs, but the marginal propensity to save with regard to this part of gross income is unity (cf. ibid., pp. 57–8). So, if we are applying Keynes’s ‘fundamental psychological law’, which states that the marginal propensities both to consume and to save are ‘positive and less than unity’ (ibid., p. 96), it is convenient to concentrate on those parts of gross income for which this ‘law’ can possibly hold – and these constitute net income respectively net value added (cf. also Bhaduri 1986, chapters 1 and 2).20 The incorporation of Keynes’s ‘fundamental psychological law’ constitutes the second difference between the reproduction scheme shown in Figure 1.1 and that of Marx. On page 121 of The General Theory, Keynes estimates the marginal propensity to consume as about 0.8, and that is the value I am going to use. In the reproduction scheme of Figure 1.1 it is assumed that the rate of surplus value is unity in both departments. This implies that the amount of variable capital S(W1) = 50

department I:

250v

S(E1) = 50 +

250s =

500

C(W1) = 200 S(W2) = 200 department II:

1000v

S(E1) = 200

C(E1) = 200

+

2000

1000s =

C(E2) = 800 C(W2) = 800

Figure 1.1  Marx–Keynes reproduction scheme – completely successful reproduction.

20  Hartwig (v) and of surplus value (s) are equal in each department. What the entrepreneurs (E) spend as variable capital, constitutes income for the workers (W). The rest of the value added, the surplus value, belongs to the entrepreneurs and constitutes their income. Of course, the income of the entrepreneurs has to be realised in the process of reproduction by selling their products to other entrepreneurs and to the workers. In the General Theory, Keynes does not distinguish between workers and entrepreneurs as far as the disposal of their income is concerned. As ‘households’ they dispose of their income according to the ‘fundamental psychological law’. That is why the marginal propensities to consume are assumed to be the same for workers and entrepreneurs in Figure 1.1. Nevertheless, assuming different marginal propensities to consume for different classes of the population has a tradition in both Kaleckian and post-Keynesian economics. This will be allowed for below. The workers of department I want to consume the equivalent of 80% of their income of $250, which gives a value of desired consumption of $200 (indicated by the arrow annotated by C(W1) = 200). The entrepreneurs of department I also want to spend $200 on consumption whereas both the workers and the entrepreneurs of department II want to consume the equivalent of $800. All consumption plans add up to $2000, which happens to be the value added of department II. In the same way the savings sum up to the value added of department I.21 The whole output has been sold for its value; the reproduction has been ‘completely successful’. But there is a central precondition for completely successful reproduction. There has to be a certain proportionality between the two departments. In the example presented above, every proportion other than 1:4 would lead to a divergence between the demand for consumption goods and the value of the output of department II (and also between saving and the value of the output of department I). An equalisation of supply and demand during the production period concerned could then only be achieved by price variations. One department would have to sell above value, the other below value. Suppose department II is twice as big as in Figure 1.1, whereas department I is the same. In this case the value of the output of department II would be $4000, but the aggregate consumption demand would add up to only $1600C(W2) + $1600C(E2) + $200C(W1) + $200C(E1) = $3600. The output of department II could only be sold for $400 below its value. On the other hand, the nominal demand for the output of department I would be much higher than the value of its output. An alternative to price cuts in department II would be building up inventories. But regardless of what the entrepreneurs do, the condition for a completely successful reproduction is violated. The output cannot be sold for its value, and not all plans are realised. In neoclassical economics (of Marshallian provenance), it is the interest rate mechanism that equalises saving and investment and that ensures completely successful reproduction. If the interest rate mechanism were to do that job here, then the excess supply of saving of $400 would have to lower the interest rate to an extent that the marginal propensity to consume would rise from 0.8 to 0.89 (as the reader can easily check). Of course, according to Keynes, ‘the short-period

Three views of the multiplier  21 influence of the rate of interest on individual spending out of a given income is secondary and relatively unimportant, except, perhaps, where unusually large changes are in question’ (Keynes, 1973a, p. 94). Proposition 1 As a general rule, the precondition for a completely successful reproduction in a scheme with two departments and validity of Keynes’s ‘fundamental psychological law’ is that the two departments keep the proportion department I : department II as 1:[c/(1 – c)]. I will call this proportion the ‘equilibrium proportion of departments’.22 It is invariant to changes in the profit rate in one of the departments or both. But it only holds good if the marginal propensity to consume is the same for workers and entrepreneurs. Proof Let: vaI = value added of department I: vaI = vI + sI vaII = value added of department II: vaII = vII + sII D(vaI) = demand for the value added of department I: D(vaI) = (1 – c) · (vI+vII+sI+sII) D(vaII) = demand for the value added of department II: D(vaII) = c · (vI+vII+sI+sII) The equilibrium conditions are: vaI = D(vaI) ∧ vaII = D(vaII) In equilibrium we have: vaI = (1 – c) · (vI + vII + sI + sII) ⇔ (vI + vII + sI + sII) = [vaI/(1 – c)] ∧ vaII = c · (vI + vII + sI + sII) ⇔ (vI + vII + sI + sII) = [vaII/c] Equalisation of the right-hand sides gives: [vaI/(1 – c)] = [vaII/c] ⇔ vaI :vaII = [(1 – c)/c] = 1:[c/(1 – c)] The reader may notice some similarities between this model and that of Kregel (1973, chapter 4). It was perhaps Kregel’s insistence on different marginal

22  Hartwig propensities to consume between workers and entrepreneurs that prevented him from setting up a formula for the equilibrium proportion of departments. In the most general case, the marginal propensities to consume are different for workers and entrepreneurs, and the share of the surplus value in the value added (let us call it h) is also different between the two departments. Proposition 2 If the marginal propensities to consume between workers and entrepreneurs are not identical, the equilibrium proportion of departments (for a closed economy) is: Department I : department II as 1:(cEhI + cW – cWhI)/(1 – cEhII – cW + cWhII) Proof We can calculate the equilibrium proportion of departments from either one of the two equilibrium conditions mentioned above. If we choose the second one we get: vaII = cE · (hI · vaI + hIIvaII) + cW[(1 – hI) · vaI + (1 – hII) · vaII] If we solve this equation for vaII we obtain proposition 2. What are the consequences of these law-like propositions for the multiplier? The multiplier provides an instrument for the entrepreneurs of department II to calculate ex ante how much more they should produce, if they expect an increment in the production of department I at the beginning of a production period. Keynes’s statement: ‘There is nothing fanciful or fine-spun about the proposition that the construction of roads entails a demand for road materials, which entails a demand for labour and also for other commodities, which, in their turn, entail a demand for labour’ (Keynes and Henderson, 1972, p. 105) seems to be indisputable. The entrepreneurs of the consumption goods department can exploit the information that an additional income in department I will create an additional demand for consumption goods, and that the production in department II will also generate income and further demand for consumption goods. This results in: ∆C = lim( c ⋅ ∆I + c ⋅ ( c ⋅ ∆I ) + c ⋅ ( c 2 ⋅ ∆I ) + ... + c 2 ⋅ ∆I ) ⇒ n→∞

∆C = lim ∆I ⋅ (1 + c + c 2 + ... + c n ) − ∆I ⇒ n→∞

∆C = ∆I ⋅ ( ∆C =

1 − 1) ⇒ 1− c

c ⋅ ∆I 1− c



(1.2)

Three views of the multiplier  23 Of course, this calculation utilises Keynes’s ‘fundamental psychological law’ (0  <  c  <  1) and the formula for adding up a convergent geometric series. But we should not take this as a description of a ‘converging series of ever diminishing waves of expenditures’ (Meade) in logical (or even historical) time. The entrepreneurs of department II can use this formula to estimate ex ante the total ‘emanation’ (in value terms) of an expected additional investment expenditure into the consumption goods department.23 This ‘emanation’ will include the total additional consumption demand of those producing the additional consumption goods. As in the reproduction scheme above, there is only one addition to the value of department II that is equal to the total additional demand for consumption goods, and this value added can be calculated ex ante as given above. The economically important variable is not so much the investment multiplier [1/(1 – c)], but the multiplier [c/(1 – c)]. It designates the proportion of department II relative to department I that is necessary for completely successful reproduction and that must be sustained in an expanding economy to ensure the identity between saving and investment. The multiplier is here not interpreted as a dynamic process (or quantity reaction of output) nor as a logical relation (or ratio) between income and investment expenditure, but as an equilibrium condition which prescribes the proportionality between the two departments necessary for completely successful reproduction.24 As compared to the traditional view, this ‘third view’ of the multiplier allows us to incorporate expectations into the analysis and to interpret the multiplier as the guideline for the entrepreneurs of department II on how to form these expectations. As I mentioned before, there are similarities between the analysis presented so far and Bhaduri (1986, chapter 2). Bhaduri also presents the multiplier as an equilibrium relation between the consumption- and the investment goods departments, and his ‘macroeconomic balance equation’25 is in fact a special case of the formula presented above (in Proposition 2). There are fundamental differences between his analysis and mine, though. Bhaduri does not visualise the economic process as a succession of production periods (as defined above). Therefore, he does not link his multiplier analysis to expectation-building of entrepreneurs at the beginning of each production period. Consequently, he does not reject the view that the multiplier describes a ‘quantity adjustment [that] can take place in successive rounds’ (Bhaduri, 1986, p. 42). This makes it difficult for him to disentangle price reactions and quantity reactions during the multiplier ‘process’. Even though he correctly acknowledges the possibility of a ‘multiplier theory based on price adjustment’ (ibid., p. 45), to which I will come below, he restricts price reactions to situations of full employment in the consumption goods department. Something similar can be said about the differences between my exposition and that of Edward J. Nell, with whom I agree on the importance of reproduction schemes. Nell presents the ‘multiplier sequence’ as a converging series of induced demands for consumption goods (i.e. quantity reactions with fixed prices) (1998, pp. 560–4). This is an interpretation I am opposing. Nell, on the other hand, would most probably not approve of my reconstruction of the principle of effective demand (cf. ibid., pp. 618–21). Additional differences stem from the fact that Nell

24  Hartwig (unlike myself) most of the time applies the ‘classical savings hypothesis’. He therefore denies the significance of ‘psychological propensities of households’ in the context of multiplier analysis (ibid., p. 563).

A short remark on the dynamical aspects of the ‘third view’ of the multiplier The ‘third view’ of the multiplier has implications for the business cycle and for structural change. If the two departments are out of balance, as in the example given above, this will most likely have consequences for the next production period. It can be expected that the disappointed entrepreneurs of department II will cut back employment, perhaps even too much to establish the equilibrium proportion of departments. In other words, a disproportion of the two departments might be a cause for fluctuations in economic activity. Here, Hicks’s distinction between ‘single-period theory’ and ‘continuation theory’ comes into play (cf. Hicks, 1982, 1985; Fontana, 2004). ‘Single-period theory’ is concerned with the equilibrium position of the economy within the production period; that is, in Keynes’s terms, the point of effective demand. ‘Continuation theory’ traces out the succession of those periods. Changes in the equilibrium position from period to period are prompted by disequilibria in the previous period which lead to changes in entrepreneurs’ expectations and to adaptations of their decisions. Not much can be said in general about those changes within the confines of the historical time theory that Keynes (1973a, p. 293) and Kregel (1976) have called the theory (or model) of ‘shifting equilibrium’ because, as Hicks (1985, pp. 87–8) points out, ‘The ‘equilibrium’ forces are (relatively) dependable; the ‘disequilibrium’ forces are much less dependable’. If a change is considered to be permanent by the entrepreneurs as a whole, then that change must be called structural. The adapted multiplier formula tells us that minimal variations in the marginal propensity to consume (if they are considered to be permanent) require huge shifts in the composition of the productive resources. A (permanent) fall in the marginal propensity to consume from, say, 0.8 to 0.79 would change the equilibrium proportion of departments from 1:4 to 1:3.76.

Tracing back the third view of the multiplier to Keynes’s works To conclude this chapter, I would like to draw the reader’s attention to instances where Keynes himself displayed the ‘third view’ of the multiplier. In The General Theory this view can be found in the fourth paragraph of chapter 10, where Keynes writes: The discussion has been carried on, so far, on the basis of a change in aggregate investment which has been foreseen sufficiently in advance for the consumption industries to advance pari passu with the capital-goods indus-

Three views of the multiplier  25 tries without more disturbance to the price of consumption-goods than consequential, in conditions of decreasing returns, on an increase in the quantity which is produced. (Keynes, 1973a, p. 122) Keynes adopts a scheme with two departments and states the multiplier in terms of ex ante expectations. But he does not make clear what it means that ‘the consumption industries advance pari passu with the capital-goods industries’. It means, of course, that they expand in the proportion [c/(1 – c)]:1. Keynes’s remark about prices is also illuminating. It has been pointed out above that the price component inherent in the Z-function is the price level that covers marginal cost. This price has to grow with employment under conditions of decreasing returns (as long as the wage unit does not change). These are the ‘normal’ disturbances to the price.26 But there can be ‘more disturbance to the price’ consequential upon the possibility of a non-equilibrium proportion of departments. In the remainder of the fourth paragraph of chapter 10 Keynes points out that the entrepreneurs of department II are often unable to anticipate the expansion of department I correctly. In my interpretation, such incorrect anticipations imply that the proportion of the two departments is not given by 1:[c/(1 – c)]; and this would cause a disparity between saving and investment. In my interpretation, the marginal propensity to consume is not affected by this disparity; it remains stable at the value given by the ‘fundamental psychological law’. Although the marginal propensity to consume need not be constant forever, it is a ‘psychological’ magnitude that varies only gradually with employment or real income. It is not exposed to violent changes (cf. also Keynes, 1973a, p. 120). But in the fourth paragraph of chapter 10, Keynes gives a totally different account of the character of the marginal propensity to consume. He considers that an expansion in department I may not be foreseen at all by the entrepreneurs of department II, so that the additional demand for consumption goods of those attached to department I subsequently leads to a depletion of stocks and to a rise in prices for consumption goods.27 But for the ‘logical view’ of the multiplier to be upheld ‘at all moments of time’ this would necessitate the marginal propensity to consume to drop to zero initially.28 This interpretation seems quite artificial to me, because, even though it is uncontroversial that the newly employed workers of department I cannot consume if there is (initially) absolutely no additional supply of consumption goods, the marginal propensity to consume of the whole society would not drop to zero. One would have to operate with different marginal propensities to consume to ‘rescue’ the logical multiplier relation. In my interpretation of the multiplier as an equilibrium condition (that can be violated), this is not necessary. Keynes’s clearest statement of the ‘third view of the multiplier’ appears in his famous 1937 article The General Theory of Employment. There he writes: Incomes are created partly by entrepreneurs producing for investment and partly by their producing for consumption. The amount that is consumed depends on the amount of income thus made up. Hence the amount of

26  Hartwig consumption-goods which it will pay entrepreneurs to produce depends on the amount of investment-goods which they are producing. If, for example, the public are in the habit of spending nine-tenths of their income on consumption-goods, it follows that, if entrepreneurs were to produce consumptiongoods at a cost more than nine times the cost of the investment-goods they are producing, some part of their output could not be sold at a price which would cover its cost of production. For the consumption-goods on the market would have cost more than nine-tenths of the aggregate income of the public and would therefore be in excess of the demand for consumption-goods, which by hypothesis is only nine-tenths . . . [T]here is always a formula, more or less of this kind, relating the output of consumption-goods which it pays to produce to the output of investment-goods; and I have given attention to it in my book under the name of the multiplier . . . The conclusion appears to me to be quite beyond dispute. Yet the consequences which follow from it are at the same time unfamiliar and of the greatest possible importance. (1973c, pp. 120–1) Although Keynes should not have identified total cost with aggregate income – he should have distinguished between the cost and the profit part in income – this quote is important. If the marginal propensity to consume is 0.9, the equilibrium proportion of departments is 1:9 or 1:[0.9/(1 – 0.9)]. But Keynes errs when he says that he has given attention to this in The General Theory under the name of the multiplier, because in that book he did not use the structural multiplier [c/ (1 – c)], but only the so-called investment multiplier [1/(1 – c)].

Conclusion In this chapter it has been argued that the view expressed by Patinkin – that the multiplier is logically equivalent to the theory of effective demand29 – can be maintained only if the multiplier is interpreted as an equilibrium proportion of two departments within a reproduction scheme. Two other views of the multiplier can be found in the literature. One takes the multiplier for a logical relation between investment expenditure and income that ‘holds good continuously, without time-lag, at all moments of time’ (Keynes, 1973a, p.  122), the other one for a dynamic process that ‘generate[s] a converging series of ever diminishing waves of expenditures’ (Meade, 1975, p. 84). I have argued that both these (traditional) views rest on unrealistic assumptions. To defend the ‘logical view’ it is necessary to introduce an extreme volatility in the marginal propensity to consume. But this contradicts the very concept of the marginal propensity to consume as it is normally presented by Keynes. The ‘dynamic view’ of the multiplier has been rejected because it cannot claim to refer to anything real. Furthermore, it is incompatible with the principle of effective demand as presented in chapter 3 of Keynes’s General Theory. To sum up, the principle of effective demand expresses the aggregate result of a thought experiment of each entrepreneur aiming to estimate ex ante which

Three views of the multiplier  27 output and employment level will realise his maximum profit. The result of this thought experiment implies an expectation of macroeconomic balance between the two departments of the economy; and the multiplier is an expression of this balanced structure.

Notes 1 This chapter shares a common progenitor with Hartwig (2004). 2 Cf. Mäki (1998) for the methodological content of this term. 3 To keep things simple, I assume throughout that there is no ‘autonomous consumption’ and no non-linearity in the consumption function. In this case the marginal propensity to consume equals the average rate of consumption. 4 For example, he wrote in 1931: ‘I feel, then, no serious doubt or hesitation whatever as to the causes of the world slump. I trace it wholly to the breakdown of investment throughout the world’ (Keynes, 1973b, p. 358). 5 This quote seems to indicate a change of mind on the part of Keynes, because two years earlier he had written: ‘This psychological law was of the utmost importance in the development of my own thought, and it is, I think, absolutely fundamental to the theory of effective demand as set forth in my book’ (Keynes, 1973c, p. 120). 6 Economic models in logical time can be solved back and forth without making a difference to the model’s position at each specific point in time. This is to be contrasted with historical-time models in which ‘events occur in a uni-directional sequence’ (Setterfield, 1995, p. 3). Cf. also Robinson (1973, p. 256). 7 ‘In the Keynesian macrosystem the Marshallian ranking of price- and quantityadjustment speeds is reversed: In the shortest period flow quantities are freely variable, but one or more prices are given, and the admissible range of variation for the rest of the prices is thereby limited. The “revolutionary” element of The General Theory can perhaps not be stated in simpler terms’ (Leijonhufvud, 1968, p. 52; emphasis in original). 8 Milgate, for example, writes: ‘The formal proposition is that saving and investment are brought into equality by variations in the level of income (output). This is the principle of effective demand’ (1982, p. 78). 9 I concentrate on those aspects of the principle of effective demand that are important for what follows. It is not possible, though, to give a full account of this principle, which has been interpreted differently by different (post-) Keynesians. I broadly conform to the interpretation of Vickers (1987). 10 It should be noted that Hicks (1982, 1985) and Lindahl (1939) also envisaged the economic process as a succession of production periods. As Fontana (2004, p.  79) points out: ‘Besides, as he [Hicks] explains, when agents make decisions they have in mind a stage-by-stage temporal frame. It was not only for theoretical convenience but also for the realism [better: realisticness – J. H.] of the study that period analysis had to be considered superior to continuous analysis.’ 11 ‘Daily here stands for the shortest interval after which the firm is free to revise its decision as to how much employment to offer. It is, so to speak, the minimum effective unit of economic time’ (Keynes, 1973a, p. 47, fn. 1). 12 Under the assumption that labour is the only variable input in the production process, the supply price is given by: PS = w · (dN/dY), with w = nominal wage rate, N = employment and Y = output. Cf. Chick (1983, p. 66). 13 If the profit share does not grow, the Z-curve is a straight line. In this case the ratio average product of labour–marginal product of labour remains constant, too, when employment rises (as in, for example, Y = αNβ); cf. Davidson (1994, pp. 173–4, fn. 8). For a formal derivation, see Vickers (1987, p. 93). 14 Few scholars have so far considered this solution. It is implied in Koenig (1980,

28  Hartwig

15

16

17 18 19 20

21

22

pp. 437, 454) and explicit in Wells (1978, p. 319). But Casarosa (1981, p. 192) believes it to be ‘completely incompatible with the theory of the firm operating in an atomistic (let alone perfectly competitive) market’, and claims that ‘the notion that the expected demand function is the producers’ estimate of the expenditure function is clearly a theoretical aberration which has strangely survived’ (ibid.). Casarosa is right that the notion of firms forming ex ante expectations about their market share is incompatible with the microeconomic theory of the small firm operating under perfect competition; cf. also Asimakopulos (1991, pp. 43–4.). But I do not think that Keynes – who was concerned with the real world – had such firms in mind. In his theory firms are not ‘atomistic’ but are also not powerful enough to dictate the price. They have to form expectations about the price that they can enforce for their products and about the market share that might be attributable to them. Sometimes, Keynes uses the term ‘aggregate demand’ or even ‘aggregate effective demand’ to describe the aggregate demand that has been realised ex post (cf. Keynes, 1973a, p.  259). Contrary to this practice, one has to distinguish carefully between ‘effective demand’ (the point of intersection of the D- and Z-curve), ‘aggregate demand curve’ (the D-curve in expectations terms) and ‘aggregate demand’ as realised ex post. As to the shapes of D and Z the following should be noted: Z may be a linear function of N even under decreasing marginal returns (cf. note 13, above). It will be a straight line under constant returns, with the slope given by the wage rate. In this case, the Dcurve, too, will be a linear function of N, with the slope given by the marginal propensity to consume multiplied by the demand price level and by the (constant) marginal product of labour. The slopes of D and Z depend crucially on the assumptions made about the ‘production function’ – in other words: about the marginal product of labour. Note also that the case of increasing returns cannot be handled with the D/Z-model, because then the Z-curve becomes concave, the D-curve becomes convex, the two curves do not intersect and there is no point of effective demand. Inventories can be and are used as buffers. Depletion and accumulation of inventories are the only forms of ‘quantity reactions’ during a production period that are possible under the theory of effective demand. Wray (1999) argues that Keynes could have easily adopted a labour theory of value because it was consistent with the purpose of The General Theory. Readers are referred to this piece of literature for a further elaboration on this point. Differences between my approach and Bhaduri’s are pointed out below. What I call ‘the value of constant capital transferred onto the output’ (or total depreciation) equals (in terms of chapter 6 of The General Theory) the sum of user cost and supplementary cost minus what modern production accounts (not Keynes) call ‘intermediate consumption’. A remark is apposite about workers’ savings. In the reproduction scheme it looks as if their savings would constitute a direct demand for investment goods. Of course, this is not the case. The transfer of workers’ savings to the entrepreneurs is effected by what Keynes has called the ‘financial machine’ (Keynes, 1973b, p. 352). It is assumed here that no part of workers’ savings is hoarded. (Indeed, this is a precondition for ‘completely successful reproduction’; cf. also Rochon, 1999, p. 35.) If workers save part of their income (and do not hoard) they are, in effect, granting loans to the entrepreneurs. Then they can participate in the distribution of the surplus value (which is divided between profit and interest on debt). It follows that it is an oversimplification not to distinguish between functional and personal income distribution in the scheme. On the other hand, that won’t be harmful as long as the marginal propensities to consume are assumed to be identical. I should emphasise that this equilibrium proportion need not imply full employment of labour.

Three views of the multiplier  29 23 For that it is also necessary that they estimate the marginal propensity to consume (which is here equal to the fraction of income that is consumed). 24 Moore (1988, p. 312) has criticised the dynamic view of the multiplier by claiming that ‘the equality of planned investment and saving does not occur through the adjustment of income, as the Keynesian income-multiplier approach asserts’ (I agree) and that ‘the Keynesian multiplier analysis is thus fundamentally flawed’. Notwithstanding the fact that the soundness of his critique (which rests on Moore’s theory of endogenous money – and thus on a plane that cannot be discussed here) has been disputed (cf. Cottrell, 1994; Dalziel, 1996; Moore, 1994), I believe the interpretation of the multiplier offered in this chapter to be much less open to Moore’s critique than the dynamic view thereof. 25 Bhaduri (1986, p. 40, equation 2.17). 26 Note that, in the absence of productivity growth and cuts in the wage unit, entrepreneurs will only expand employment in reaction to a higher (expected) aggregate demand if they expect that the higher marginal cost can be covered by a higher demand price per unit of output. We can conclude that the D-curve can only shift to the top if there is a shift in the price component inherent in it. Keynes seems to have believed that the higher supply price necessary to accommodate higher marginal cost would always be enforceable if the economy was to expand. He wrote: ‘there cannot be rising output without rising prices’ (Keynes, 1965, p. 33). 27 This conforms to my interpretation that quantity reactions (other than accumulation or depletion of inventories) are not possible within the production period – or ‘single period’ in Hicks’s terms. Alternatively, as Bhaduri (1986, p. 45) has correctly stated, we can have something like ‘a multiplier theory based on price adjustment’. But, contrary to Bhaduri, these price adjustments can take place whenever expectations have been incorrect. They are not restricted to situations of full employment. 28 Keynes writes that ‘the logical theory of the multiplier . . . holds good continuously, without time-lag, at all moments of time’ (Keynes, 1973a, p. 122). In our example, this ‘logic’ could only work if the marginal propensity to consume were to drop to zero initially. In this case, the logical multiplier relation continues to hold, because we have: ∆Y = ∆I = [1/(1 – 0)] · ∆I. Note that this reasoning also offers a possibility to defend Keynes’s proposition (ibid, p. 84) that saving and investment are perpetually identical. 29 Patinkin (1976, p. 71).

References Arestis, P., Dunn, S. P., Sawyer, M. (1999), ‘Post-Keynesian Economics and Its Critics’, Journal of Post Keynesian Economics, 21 (4), pp. 527–49. Asimakopulos, A. (1991), Keynes’s General Theory and Accumulation, Cambridge: Cambridge University Press. Bhaduri, A. (1986), Macroeconomics. The Dynamics of Commodity Production, Houndsmills: Macmillan Education. Casarosa, C. (1981), ‘The Microfoundations of Keynes’s Aggregate Supply and Expected Demand Analysis’, Economic Journal, 91 (1), pp. 188–94. Chick, V. (1983), Macroeconomics after Keynes. A Reconsideration of the General Theory, Oxford: Philip Allan. Cottrell, A. (1994), ‘Endogenous Money and the Multiplier’, Journal of Post Keynesian Economics, 17 (1), pp. 111–20. Dalziel, P. (1996), ‘The Keynesian Multiplier, Liquidity Preference, and Endogenous Money’, Journal of Post Keynesian Economics, 18 (3), pp. 311–31.

30  Hartwig Davidson, P. (1987), ‘Aggregate Supply Function’, in The New Palgrave: A Dictionary of Economics, Vol. 1, London: Palgrave Macmillan, pp. 50–2. Davidson, P. (1994), Post-Keynesian Macroeconomic Theory. A Foundation for Successful Economic Policies in the Twenty-First Century, Aldershot: Edward Elgar. Fontana, G. (2004), ‘Hicks on Monetary Theory and History: Money as Endogenous Money’, Cambridge Journal of Economics, 28 (1), pp. 73–88. Gilbert, J. C. (1982), Keynes’s Impact on Monetary Economics, London: Butterworths. Hartwig, J. (2004), ‘Keynes’s Multiplier in a Two-Sectoral Framework’, Review of Political Economy, 16 (3), pp. 309–34. Hicks, J. R. (1982), ‘Methods of Dynamic Analysis’, in J. Hicks (ed.), Money, Interest and Wages. Collected Essays on Economic Theory, Vol. 2, Oxford: Basil Blackwell, pp. 217–35. Hicks, J. R. (1985), Methods of Dynamic Economics, Oxford: Clarendon Press. Hofmann, W. (1979), Theorien der Wirtschaftsentwicklung. Vom Merkantilismus bis zur Gegenwart. Sozialökonomische Studientexte, Vol. 3, 3rd ed., Berlin: Duncker and Humbolt. Keynes, J. M. (1965), ‘An Open Letter (to President Roosevelt)’, in A. Smithers and J. K. Butters (eds), Readings in Fiscal Policy, 3rd ed., London: Allen and Unwin, pp. 31–7. Keynes, J. M. (1972), ‘The Means to Prosperity’, in The Collected Writings of John Maynard Keynes, Vol. 9: Essays in Persuasion, London: Cambridge University Press, pp. 335–66. Keynes, J. M. (1973a), The General Theory of Employment, Interest, and Money, reprint, London: Macmillan. Keynes, J. M. (1973b), ‘An Economic Analysis of Unemployment’, in The Collected Writings of John Maynard Keynes, Vol. 13: The General Theory and After. Part I – Preparation, London: Cambridge University Press, pp. 343–67. Keynes, J. M. (1973c), The General Theory of Employment, in The Collected Writings of John Maynard Keynes, Vol. 14: The General Theory and After. Part II – Defence and Development, London: Macmillan and St Martin’s Press, pp. 109–23. Keynes, J. M. (1973d), ‘Letter to Elisabeth Gilboy (1 February 1939)’, in The Collected Writings of John Maynard Keynes, Vol. 14: The General Theory and After. Part II – Defence and Development, London: Macmillan and St Martin’s Press, pp. 273–7. Keynes, J. M., and Henderson, H. (1972), ‘Can Lloyd George Do It?’ in The Collected Writings of John Maynard Keynes, Vol. 9: Essays in Persuasion, London: Macmillan and St Martin’s Press, pp. 86–125. Koenig, G. (1980), ‘Les fondements microéconomiques du principe de la demande effective’, Revue Economique, 31 (3), pp. 430–64. Kregel, J. (1973), The Reconstruction of Political Economy: An Introduction to PostKeynesian Economics, London: Macmillan. Kregel, J. (1976), ‘Economic Methodology in the Face of Uncertainty: The Modelling Methods of Keynes and the Post-Keynesians’, Economic Journal, 86 (2), pp. 209–25. Leijonhufvud, A. (1968), On Keynesian Economics and the Economics of Keynes. A Study in Monetary Theory, New York: Oxford University Press. Leijonhufvud, A. (1974), ‘Keynes’ Employment Function’, History of Political Economy, 6 (1), pp. 164–70. Lindahl, E. (1939), ‘The Dynamic Approach to Economic Theory, Part 1’, in E. Lindahl (ed.), Studies in the Theory of Money and Capital, London: Allen and Unwin. Mäki, U. (1998), ‘Realisticness’, in J. B. Davis, D.  W. Hands and U. Mäki (eds), The Handbook of Economic Methodology, Cheltenham: Edward Elgar, pp. 409–13.

Three views of the multiplier  31 Marx, K. (1973), Das Kapital. Kritik der Politischen Ökonomie, Vol. 2, 2nd ed., Berlin: Dietz. Meade, J. (1975), ‘The Keynesian Revolution’, in M. Keynes (ed.), Essays on John Maynard Keynes, Cambridge: Cambridge University Press, pp. 82–8. Milgate, M. (1982), Capital and Employment. A Study of Keynes’s Economics, London: Academic Press. Moore, B. (1988), Horizontalists and Verticalists: The Macroeconomics of Credit Money, Cambridge: Cambridge University Press. Moore, B. (1994), ‘The Demise of the Keynesian Multiplier: A Reply to Cottrell’, Journal of Post Keynesian Economics, 17 (1), pp. 121–33. Nell, E. J. (1998), The General Theory of Transformational Growth. Keynes after Sraffa, Cambridge: Cambridge University Press. Parinello, S. (1980), ‘The Price Level Implicit in Keynes’ Effective Demand’, Journal of Post Keynesian Economics, 3 (1), pp. 63–78. Patinkin, D. (1976), Keynes’ Monetary Thought: A Study of Its Development, Durham, NC: Duke University Press. Robinson, J. (1973), ‘A Lecture Delivered at Oxford by a Cambridge Economist’, in J. Robinson (ed.), Collected Economic Papers of Joan Robinson, Vol. 4, Oxford: Basil Blackwell, pp. 254–64. Rochon, L.-P. (1999), Credit, Money and Production: An Alternative Post-Keynesian Approach, Cheltenham: Edward Elgar. Setterfield, M. (1995), ‘Historical Time and Economic Theory’, Review of Political Economy, 7 (1), pp. 1–27. Vickers, D. (1987), ‘Aggregate Supply and the Producer’s Expected Demand Curve: Performance and Change in the Macroeconomy’, Journal of Post Keynesian Economics, 10 (1), pp. 84–104. Wells, P. (1978), ‘In Review of Keynes’, Cambridge Journal of Economics, 2 (3), pp. 315–25. Wray, L. R. (1999), ‘Theories of Value and the Monetary Theory of Production’, Working Paper No. 261, Annandale-on-Hudson, NY: Jerome Levy Economics Institute.

2 John Maurice Clark’s contribution to the genesis of the multiplier analysis A note with some related unpublished correspondence Luca Fiorito1 Scientific theories are like children in that they have a life of their own. But, unlike children, they may have more than one father. (Samuelson, 1959, p. 183)

For the historian of economic thought, John Maurice Clark stands as an intriguing intellectual puzzle. On the one hand, he was among the most active promoters of American institutionalism during the interwar years. Together with Walton H. Hamilton, Clark participated in the 1918 AEA conference, which marked the formal public launching of the movement in the United States under that title. On that occasion he presented the paper ‘Economic Theory in an Era of Social Readjustment’, calling for an economic science both ‘actively relevant to the issues of its time’ and able to furnish the student ‘with tools of thought rather than with the finished product; with knowledge of the general features of the institutions he is studying; and with principles of a widely varying sort, embodying many ways in which business affects human desires, directly and indirectly’ (Clark, 1919, p. 290). On the other hand, John Maurice Clark never fully rejected John Bates Clark’s theoretical contribution. He denied any discontinuity between his father’s two major works, The Philosophy of Wealth and The Distribution of Wealth,2 and saw himself as attempting to continue his efforts to develop a dynamic theory.3 As he once put it in a letter to Professor Maurice Roche-Agussoll in 1918, he was aiming at developing a ‘dynamic social or institutional economics or realistic economics’. This to him was the third division of the field of economics. The first two, which composed ‘value economics’, were ‘1) Static value – or price – economics’ and ‘2) dynamic value – or price – economics.’4 This ambivalent nature of John Maurice Clark’s thought has been remarked upon by many commentators. Joseph Dorfman, for instance, speaks of Clark’s economics in terms of a ‘constructive synthesis of tradition and new dynamics’ (Dorfman, 1946–59, Vol.  5, p.  438), whereas, in a more critical vein, Baldwin Ramson describes it as a ‘middle way’, which ‘does not accept orthodox theory as adequate, but neither does it accept the need for a new theoretical domain’ (Ramson, 1977, p. 467).

John Maurice Clark’s contribution  33 This note focuses on a specific aspect of Clark’s work, which epitomizes his attempt to combine the rigor of traditional economic analysis with his ‘institutionalized’ attitude, namely his contribution to the multiplier principle. First we will discuss Clark’s independent discovery of the multiplier principle – by which is meant the familiar notion that an initial increase (or decrease) in expenditures has a multiple effect on total expenditures – also providing in the appendix some unpublished evidence that seems to confirm that Clark arrived at it before reading Kahn’s celebrated 1931 article, ‘The Relation of Home Investment to Unemployment.’ Then we will delve into some more analytical aspects of Clark’s treatment of the multiplier, focusing, in particular, on his attempt to reconcile the traditional ‘Kahn–Keynes’ approach with the so-called ‘velocity of circulation’ approach. While John Maurice Clark is commonly recognized as one the fathers, together with Thomas Nixon Carver, Albert Aftalion, Ralph Hawtrey and Charles Bickerdicke, of the so-called ‘accelerator principle’ (Junankar, 1987) and as an anticipator of the ‘multiplier-accelerator’ model (Shackle, 1967, pp. 264–5), his contribution to the development of the multiplier analysis is often neglected. Hints at Clark’s studies on the multiplier analysis are to be found in Joseph Dorfman’s encyclopedic enterprise The Economic Mind in American Civilization and in two more recent works by Laurence Shute (1994, 1997). Both authors insist on the fact that Clark arrived at the idea of the multiplier while unaware of Kahn’s and Keynes’s formulations of the principle. In Dorfman’s own words: ‘Clark was one of several students who, working independently at about the same time, began a quantitative formulation of this idea (the multiplier). While the exact formal statement of the principle became associated . . . with R. F. Kahn and J. M. Keynes, Clark in typical fashion felt that the multiplier was useful chiefly as a model’ (Dorfman, 1946–59, Vol. 5, p. 762; see also Dorfman, 1970). A more detailed and insightful assessment of the role played by Clark in the development of the multiplier is provided by Ronnie Davis in The New Economics and the Old Economists. Davis deals with Clark’s treatment of the expansionary effects of public spending in order to support his claim that most American economists favored countercyclical fiscal policy before the publication of Keynes’s General Theory, and that they based this advice on an understanding of income–expenditure theory. Quite curiously, the lengthy discussion by Davis neglects Clark’s monograph on public works (Clark, 1935b), just concentrating on a single paragraph in Strategic Factors in Business Cycles (Clark, 1935c) on how reduction in savings can result in a dwindling series of contractions in income and spending, which sum to a finite value, and on the accompanying footnote stating that Clark wrote the paragraph before reading Kahn (1933). Like Dorfman and Shute, Davis observes: ‘It is interesting to note that Clark’s recognition and use of the multiplier principle was anterior to his seeing Kahn’s publication of “Public Works and Inflation” ’ (Davis, 1971, p. 6). Davis’s contention about American economists as anticipators of Keynesian deficit-financed fiscal expansion has been challenged by Robert W. Dimand. In this connection, Dimand argues that even the only two American economists with

34  Fiorito a grasp of the multiplier theory, Paul Douglas of Chicago and John Maurice Clark of Columbia, had explicitly derived their analysis from articles by Richard Kahn and J. M. Keynes, with Clark explicitly naming the multiplier ‘the Kahn–Keynes approach’. Dimand phrases his critique of Davis as follows: Davis does not mention that Clark devoted a paper to ‘The Cumulative Effects of Changes in Aggregate Spending as Illustrated by Public Works’ in the American Economic Review [1935a], reprinted under a shortened title in his Preface to Social Economics [1936], expanded as Chapter IX of his report on Economics of Planning Public Works [1935b], and presented to the American Economic Association in December 1934. Clark’s presentation of the multiplier theory in his paper is striking both for its clarity and for its name: he called it ‘the Kahn–Keynes approach.’ Clark attributed the multiplier theory to Keynes’ pamphlet The Means to Prosperity [1933/1972] and to two papers by Richard Kahn [1931, 1933], and concluded that it had only limited validity, as just one of the forces affecting the velocity of circulation of money. (Dimand, 1990, p. 45; see also Dimand, 1988) Evidence from our archival research seems to refute Dimand’s critique and confirm the thesis of Clark’s independent discovery of the multiplier principle. Clark’s correspondence is particularly illuminating on this regard. Clark insisted on the fact that his recognition and use of the multiplier principle preceded his reading of Kahn (1933) both in a correspondence with Paul Samuelson dated 1953 (the exchange is reproduced in this chapter’s appendix) and in a long letter sent three years later to his friend and colleague at Columbia, Joseph Dorfman. In both letters, however, Clark generously admitted that Kahn is the one who deserves priority: When I worked out my asymptotic form of the multiplier, published in ‘Economics of Planning Public Works’, I noted that it furnished another kind of mechanism whereby the increase in total income resulting from an increase in investment might tend to taper off . . . I dreamed up this asymptotic multiplier in 1930, when R F. Kahn was well along with his essentially similar concept, so he has priority.5 Interestingly, in the same letter Clark also denied any influence from Nicholas Johannsen’s early writings on the ‘multiplying principle’: ‘Johannsen’s work I don’t think I ever grappled with; I recall only vague & general ideas about it — so when about 1924 or 1925, he wrote asking me for some public recognition of work, I was embarrassed, and I didn’t feel competent to appraise it.’6 Furthermore, it is worth pointing out that Clark’s first formulation of the multiplier principle – although less rigorous in its mathematical formulation – did not appear in Clark (1935a), but in The Costs of the World War to the American People, published in 1931 (Clark, 1931/1970). In that work, in discussing the United States’s productivity in 1916, Clark made clear his view that the volume

John Maurice Clark’s contribution  35 of production may vary more widely than economists had generally conceived, as a result of changes in aggregate demand. From the letter he wrote to Dorfman we learn that the book was recognized by Nicolas Kaldor as an anticipation of Keynes’s ideas: ‘As to multipliers, in my “Cost of the World War” discussing the neutrality-boom of 1916, I evolved a rough foreign-trade multiplier. Kaldor found some bits of that book to be anticipations of Keynesism.’7 A final word of caution should be added about the historiographic significance of the statements Clark made in his correspondence with Samuelson and Dorfman. They were made by Clark two decades later after the significance of the multiplier was very well known and therefore they should by no means be considered as equivalent to primary sources from the 1930s. Nevertheless, they provide interesting evidence of Clark’s later recollections and tend to confirm what Clark had already affirmed, although only in a footnote, in 1935. Let us now turn our attention to more specific aspects of Clark’s treatment of the multiplier. According to The New Palgrave: A Dictionary of Economics, the theory of the multiplier ‘in its pure (or static) form’ can be described as follows: In a capitalistic economy investment can always be realized in real terms. The necessary saving will be made available by means of corresponding variations of the level of income, given the propensity to save. With generally underutilized capacity and labour and fixed prices – the most common hypothesis – real income will take whatever value generates a flaw of saving equal to planned investment. Alternatively, in the presence of supply constraints, the level of prices will adjust and deflate consumption expenditure so as to make available the real resources required for investment. (Medio, 1987, p. 565) Although the argument as a whole is familiar to modern readers, there are certain features of Clark’s discussion that deserve notice. First of all, it is worth emphasizing that at the time Clark first formulated his version of the multiplier theory, he was chiefly concerned, not with the framing of a general theory à la Keynes, but rather with a realistic analysis of the upswing of a business cycle. As he explicitly admitted in his later recollections: ‘My own first consideration of this theory [the multiplier] was as an explanation of the expansion phase of a normal business cycle’ (Clark, 1939, p. 201). As a consequence of this, the American economist did not follow Kahn in assuming a given level of wage rates and perfect supply elasticity, and spoke of the successive spending as inflationary throughout his analysis.8 Also Clark’s treatment of ‘leakages’ shows a fundamental difference from that of Kahn and Keynes (1933/1972). To our knowledge, Clark was among the first writers who accentuated that savings, which are regarded as ‘leakages,’ do not remain idle. According to Clark, the term leakage refers to ‘a sum of funds which does not increase production beyond what has been accounted for in the formula’ (1935b, p. 89). Clearly, this definition does not imply idleness of funds. For Clark, the leakages that are responsible for

36  Fiorito the failure of the multiplier to go on expanding indefinitely represent themselves deflationary uses of income generated from the public spending, and these tend to offset the inflationary effect of the public borrowings: ‘They (the leakages) may not all come directly into the banks as loanable funds, but if they do not do that, they strengthen someone’s credit position and thereby are likely to reduce the need of borrowing from the banks in the future’ (1939, p. 202). Starting from these premises, Clark was therefore justified in opposing the inflationary effect of public borrowing to the deflationary effect of leakages. This point will be taken up below. Second, Clark (1935a,b) individuated two possible approaches to the multiplier analysis: ‘one via successive cycles of income and spending by ultimate recipients of income’ – which he termed the ‘Kahn–Keynes’ approach – ‘the other via the volume of money and its velocity of circulation.’ As to the latter approach, Clark (1935a, p. 383) affirmed that ‘it has, so far as I am aware, not found its way into print.’ A clear and early statement of the view held by the exponents of the ‘velocity’ approach is provided by a letter that Alvin Hansen sent to Clark in 1934 (dated August 8; see also full text of the letter in the appendix to this chapter). Clark had asked Hansen for some comments on an early draft of chapter 9 of his Economics of Planning Public Works. In his reply the Harvard economist dismissed Clark’s reasoning on the ground that it ‘still follows too much along the Keynes lines’ which, at that time, he considered ‘definitely wrong.’9 For Hansen the explanation of how an initial change in the rate of spending will induce further increments in the level of total income was essentially a question of (a) the volume of means of payment and (b) the income velocity of money: Public works may affect either one of these two or both. It is quite correct, as Keynes said, that the public works expenditures may not enlarge the volume of “money.” In this event, the effect presumably is to transfer money from idle hands to active hands. In other words, the income velocity increases. Or there may actually be injected into the market new ‘money,’ and the income velocity might conceivably remain on the average as before. Or there may be a combination of these two tendencies. Also the Keynesian concept of ‘leakages’, that is, those portions of a given stream of spending that are not re-spent within the period considered, become devoid of any specific content once the ‘circulation’ approach is adopted: Keynes’ ‘leakages,’ I think, are also dangerous. The most important ‘leakage’ is his saving “leakage” and this when analyzed amounts to nothing more or less than our old friend, a change in income velocity. If all of us hold idle a half of our income which we formerly spent, – save it without investing it, in other words – the income velocity has been cut in two. Thus the total income of society in the next succeeding period has been reduced to one-half by this process of ‘savings running to waste’.

John Maurice Clark’s contribution  37 As a consequence of this, there will be no secondary effects unless the primary expenditure results in an increase in the quantity of money, its velocity, or – as it seems more probable – both: All that public expenditures do is to throw new funds into the market, and thereby increase the income, which action, since it is certainly not likely to reduce the income velocity of ‘money’ is very likely to increase the total ‘money’ income of society by more than the amount of ‘money’ injected. It is, therefore, correct to say that public expenditures are likely to have an effect on income in excess of the expenditures. This is all there is to it, it seems to me.10 Clark did not share Hansen’s criticisms and viewed a possible merging of the two competing approaches. In order to better understand Clark’s argument, two concepts should be introduced. The first one is the concept of income propagation period, by which is usually understood the time lag between successive waves of expenditure of the additional net income deriving from the primary investment expenditure.11 Clark estimated this period at 2 months, which corresponds to six cycles of secondary effects per year, in consideration of the large amount that wage payments normally constitute of the deficit spending.12 The second concept is the more familiar ‘circuit’ (or ‘income’) velocity of money, defined by Clark as ‘the ratio between the total amount of circulating media in the country and the total net volume of production, or the total national income, which those media of exchange serve to finance’ (Clark, 1935b, p. 96). Drawing upon Angell’s (1933) monetary studies, Clark estimated an average rate of circuit velocity of money of 1.6 per year which, in turn, corresponds to an average cycle of 7½ months for money to flow from a consumer through all the exchanges involved in producing the goods he buys and to get back to an ultimate consumer again.13 This velocity, however, does not remain constant at 1.6 per year. Clark provided convincing evidence showing that it varies in harmony with the business cycle, increasing with industrial revival and falling with industrial depression. Throughout his discussion Clark warned the reader that the ‘income propagation period’ and the circuit velocity of circulation should not be confused. As he put it, ‘the 6 cycles per year do not represent the velocity of circulation of anything, but rather the speed with which an increased velocity is transmitted through the economic system’ (1935b, p. 88).14 Third, in assuming an income propagation period of two months, whereas the average circuit velocity of money, reckoned at 1.6 per year, implies a period of 7½ months, Clark was implicitly assuming ‘that the volume of business increases faster than could be accounted for by the existing volume of purchasing media and their existing circuit velocity.’ Therefore, he argued, in order to finance a permanent increase in investment expenditure, either the circuit velocity of money must increase or business must acquire more circulating media through an expansion of credit, or both. Part of the task could be accomplished by the increased flow of

38  Fiorito savings injected into the system through the multiplier and which ‘may take effect in increased credit used by business in financing this expansion without bringing any increase in the volume of business beyond what the formula already calls for.’ But even if all the leakages were taken and ‘used’ by business, a problem would still emerge. In fact: ‘During approximately the first year and a half . . . the total amount of otherwise idle funds resulting from the leakages would not be sufficient to finance the indicated expansion of business at the existing rate of the circuit velocity of funds, and so an increase in the circuit velocity will be called for’ (ibid., p. 95).15 On this basis, Clark observed that the conditions described by Kahn and Keynes would themselves furnish a sufficient cause of increased circuit velocity of money, ‘simply because they cause an increased volume of business without a proportionate increase in volume of means of payment’ (ibid., p. 101). For Clark, also the analysis of the agents’ behaviour shows that the nature of the process can be seen to tend towards increasing circuit velocity. The actual mechanism whereby income changes in response to investment is explicated in terms of inventory accumulation or decumulation. As a consequence of the increase in effective demand caused by the new investments, sales will exceed production and producers experience an unplanned fall in inventory levels. They react by employing more workers and producing more. All of these activities, he writes, call for payments: If business has sufficient funds to make these payments it will joyfully make them. In a depression, the ratio of cash balances to volume of business becomes larger than normal . . . These balances are kept, not employed to normal capacity, because nothing better offers. When something does offer, they will be promptly used and an increase in rapidity of circulation will naturally result. If a particular business does not have sufficient funds, it will try to borrow them, and in that case will call into active use some of the otherwise idle funds which have been designated as leakages in the Keynes approach to the problem. Or if a business has sufficient funds to make the payments, but not sufficient to make them without drawing down its balances lower than seems desirable, then, again, it will try to borrow, but even if it fails it will not cease to do the increased volume of business . . . Most of the funds will circulate within the business community, using them faster will not exhaust them, and business as a whole will always have funds available to make. (ibid.) In summation, Clark argued that an increase in circuit velocity is required both to provide funds to finance an increase in investment, and to meet the higher transactions demand resulting from the consequent increase in economic activity. Furthermore, he continued, this leads to an interesting conclusion: ‘that there is no absolute necessity at any stage of the process for government outlays to take the form of an increase in the supply of purchasing media. If the attitude here taken toward changes in velocity is correct – and of that the writer has no doubt – this necessity disappears’ (ibid., p. 102).

John Maurice Clark’s contribution  39 Clark, then, concluded the whole discussion affirming that since the velocity approach implies a multiplier value equal to unity, the two methods should give similar results only if they are applied to a short length of time and if proper assumptions are made – among which, as we will see below, he included a decreasing rate of leakages in the Kahn–Keynes approach. Fourth, Clark’s attempt to find a merging of the two approaches to the multiplier was welcomed with ‘mixed feelings.’ To our knowledge the first reference to Clark’s discussion of the multiplier is to be found as early as in 1936 in a note by H. Neisser commenting on Kahn (1931). In a brief and rather vague passage, the German economist informed the reader that ‘in a paper . . . published after the finishing of this article, J. M. Clark distinguishes the ‘Kahn–Keynes approach’ and the approach via money and its circuit velocity.’ According to Neisser, the latter approach ‘is identical with the method chosen in the text above and already developed in the year 1931 by various German authors, Lautenbach, Colm, Marschak, and the present writer. The discussion overlooked however, that the scheme suggested would work only if the crisis and depressions were of a specific type’ (Neisser, 1936, p. 26). From the institutionalist camp, Sumner H. Slichter, who reviewed Economics of Planning Public Works for the American Economic Review in the following year, found it to be ‘the best book available on the economics of public works.’ The chapter on the cumulative effects of public expenditures, he continued, ‘contain an excellent analysis and comparison of the Kahn–Keynes successive-spending approach and the approach by volume and velocity of circulating medium’ In particular, Slichter agreed with Clark’s treatment of ‘leakages’ as funds which play an active role in the multiplier process: Incidentally, the expression ‘leakage’ is in a way unfortunate, because it suggests that incomes that are not employed immediately to increase production do no good. As a matter of fact the expenditures represented by ‘leakages’ may be the most useful of all. To a considerable extent they go to build up cash reserves or to reduce indebtedness. In the midst of depression many enterprises and individuals will not materially increase their purchase of commodities until they have built up their holdings of cash or reduced their debts. (Slichter, 1937, p. 187) A different opinion from Slichter’s is the one presented by Paul Samuelson four years later. In a lengthy contribution appearing in the Quarterly Journal of Economics, the Harvard economist polemically referred to those writers who have attempted a reconciliation of the multiplier and the velocity approach. ‘Unfortunately,’ he wrote, ‘their reconciliations have been trivial, as one-sided as an agreement between a totalitarian state and one of its puppet creations, or else have been founded upon error’ (Samuelson, 1942, p. 602). However, in dealing with Clark’s contribution, Samuelson phrased his critique in a rather conciliatory vein:

40  Fiorito In his path-breaking Economics of Public Works, J. M. Clark, almost as an afterthought, attempted such a reconciliation. By refusing to push the analysis beyond a year’s time, and by taking advantage of the fact that a convexly growing time shape of income can in a finite range be approximated by a straight line, the two hypotheses are given a semblance of compatibility, which will, I fear, please neither camp. If the analysis had been continued in time, Professor Clark would have found it necessary to introduce a sudden, arbitrary, unexplained and unexplainable collapse in velocity, in order to maintain consistence with the multiplier time sequence. (ibid., p. 603; emphasis added) The point raised by Samuelson is pertinent and appropriate. However, a textual scrutiny of chapter 9 of Clark’s Economics of Planning Public Works reveals that the Columbia economist had realized himself that if the analysis of the multiplier effects had been continued over time (and assuming a constant marginal propensity to consume), ‘the conditions would be reversed’, that is, that there would be an excess of savings which would call for a sudden decrease in the velocity of circulation. Nevertheless, Clark pointed out, this would mean to carry the multiplier analysis over its proper limits of time, because ‘by the time this happened, the total volume of business expansion would have passed under the control of factors not accounted for in these mathematical formulas’ (Clark, 1935b, p. 95). Also in 1941, Henry H. Villard dedicated a whole chapter of his Deficit Spending and the National Income to an appraisal of Clark (1935b). Specifically, Villard turned his attention on Clark’s distinction between the rate of transmission of an impulse through the system – what we termed the income propagation period – and the circuit velocity of money. ‘There are two ways,’ he argued, ‘in which output could increase in less than 7½ months in the example given by Professor Clark: either the circulation of the existing output can increase or the new output can have a circulation more rapid than 7½ months.’ Since Clark seems to assume that the new investment will bring no change in the circuit velocity of the existing purchasing media, Villard continues, then it is not clear why the new money should pass through the system at a more rapid rate than similar existing money: we do not know definitely whether the different rate will be faster or slower, and in any case there seems to be no reason for believing that the income that is generated by the subsequent spending of the primary government expenditure will be generated any more rapidly than income generated by the spending of the similar portion of existing incomes. (1941, p. 152; emphasis in original) Therefore, he argued, ‘it seems correct to conclude that it is V and not the ‘rate of transmission of an impulse’ that is important unless there is a change in the V of the existing M’ (ibid.). A more recent assessment of Clark’s treatment of the multiplier is provided by Hugo Hegeland. According to Hegeland, ‘Clark’s analysis appears to be the first

John Maurice Clark’s contribution  41 comparative study between these two approaches [the multiplier and the rate of circulation of money], but he did not succeed in convincing the reader about the possibility of such a convergence’ (Hegeland, 1966, pp. 45–6). More specifically, Hegeland observes, albeit without providing any evidence to support his claim, that in his treatment of the multiplier Clark does not seem to have recognized the so-called Kahn–Meade relation, namely, the equality between the initial spending and the ensuing amount of leakages. Our opinion differs from Hegeland’s. In fact, as it appears from the above discussion, Clark’s concern is not with a theory of equilibrium in terms of comparative statics. The novelty of Clark’s contribution lies in its pointing out that, even if the ex post equality of the new streams of expenditure and the new streams of saving can be demonstrated, their distribution over time differs substantially, with savings being insufficient, at the outset, to finance the higher level of investment in each period. This, in turn, would necessarily imply an increase in the circuit velocity of money, provided that ‘there is no literal inflation of the amount of money sufficient to handle the increase in business without an increase in velocity’ (Clark, 1935a, p. 388). This is not the place to quarrel with the empirical validity of Clark’s assumption about the behaviour of velocity of circulation of money, debatable as it may be. What is relevant here is that to Clark the discussion of the so-called ‘velocity approach’ mainly served to arrive at an estimate of the time dimension of the multiplier effects, an aspect which, as he stated in his 1934 address, ‘has not been worked out, as far as I am aware’ (ibid., p. 385). After the publication of the General Theory, several economists, including its author, followed Clark in exploring in greater detail the dynamic implications of the multiplier, especially in relation to the so-called ‘finance motive.’ In 1939, just to cite one of the most significant examples, Nicholas Kaldor further developed Clark’s argument – albeit without mentioning the name of the American economist – showing that, if the multiplier is not instantaneous, the Kahn–Meade relation does not hold and arguing that a low propensity to save increases the size of the additional funds needed to finance a permanent increase in investment. All this leads us to our final point, namely Clark’s awareness of the intrinsic limitations of the multiplier analysis. Clark was in fact very sceptical towards any attempt to compute the exact numerical value of the multiplier, for: ‘Beside the elements acting on the factors in the formula, other outside elements are important, chiefly bearing on the effect of such a program on private business’ (Clark, 1935a, p. 387). Among these ‘outside elements,’ Clark mentioned (a) the possible ‘crowding out’ of private investments by public spending programs, maintaining that ‘when one considers the condition that the funds borrowed by Government must be funds which would not otherwise be used by private industry, it becomes rather irrelevant to project the estimate of future stimulative effects beyond, let us say, the next industrial revival, which may come in two or three years’ (1935b, p. 84)16; (b) the impairment of business confidence by ‘unlimited deficit financing’ (ibid., p.  86); and (c) the possibility of a fall in private capital investment due to the expectation that growth of demand will cease after deficit spending disappears.17 To these it should be also added (d) Clark’s scepticism towards the

42  Fiorito idea of a constant marginal propensity to consume. To Clark, this idea was based on the rather unjustified assumption that the same propensity to consume can be presumed for each subsequent stage of income generation. ‘Actually,’ he wrote, ‘there is . . . the probability that the percentage of leakage will decrease as industrial conditions grow better, as individuals have less urgent need to get out of pressing debt, and as those with available savings find more opportunity to invest them in such ways that they will actually be spent for productive equipment’ (ibid., p. 9). For these reasons, Clark concluded, ‘estimates of stimulative effects, based on such an approach as the Kahn–Keynes formula, are hardly worth carrying beyond, let us say, one year, even as rough approximations’ (1935a, p. 387). In conclusion, Clark’s treatment of the multiplier emblematically represents the tension in his thought between the search for a theoretical system which would complement his father’s work, and the ‘institutionalist’ awareness of the limitations that any mechanical formula necessarily imply. It was his eagerness to arrive at a ‘dynamic economics’ which led Clark to the discovery of the multiplier, a theory which, as he stated in 1939, contains a ‘significant truth,’ although ‘some formulations need considerable qualification’ (Clark, 1939, p.  200). Certainly, Clark’s discussion of the ‘income-flow’ analysis never reached the originality and completeness of Keynes’s General Theory and this in part may explain why, in the late 1930s, many young institutionalists found in Keynesianism a more valid and fascinating alternative to orthodox economics. We may also add that, as remarked by Villard as early as 1941, Clark’s discussion of the multiplier presented a fundamental shortcoming: namely, it did not explain adequately how an increase in circuit velocity of money is transmitted throughout the system once a primary investment has taken place. Nevertheless, Clark’s contribution to the multiplier deserves our attention. Not only, in fact, did Clark arrive at the formulation of the principle independently from Kahn and Keynes – as the archival evidence presented in the appendix to this chapter seems to confirm – but he was among the first writers who explicitly pointed out that the secondary effects do not do not occur simultaneously and to attempt an analysis of the ‘time dimension’ of the multiplier. As he wrote in a later reappraisal of his 1935 monograph: ‘The reader may note that my assumptions as to time are different from those which appear to underlie Keynes’s form of this theory. The kind of adjustment I have in mind does not appear to be one that can take place instantaneously’ (Clark, 1941a, p. 47; emphasis added). On the other hand, as we have pointed out, Clark considered the multiplier just as a ‘rough approximation’ – a formula which would work only under ideal conditions. On more than one occasion he did not hesitate to warn his colleagues against the risks of ‘blind dogmatism,’ caused by an unqualified application of what – after the 1960s – has come to be known as ‘hydraulic Keynesianism.’18 It is the same Columbia economist who candidly admitted his peculiar ‘middle way’ position in a memorable passage of his letter of 24 July 1941 to John Maynard Keynes: It has seemed to me that what I call the ‘income-flow analysis,’ of which yours is the most noted presentation, has done something which has not been

John Maurice Clark’s contribution  43 done in comparable degree since Ricardo and Marx: namely, constructed a coherent logical theoretical system or formula having the quality of a mechanism, growing directly out of current conditions and problems which are of paramount importance and furnishing a key for working out definite answers in terms of policy. On this a ‘school’ has grown up. All that has tremendous power; and is also exposed to the dangers of too-indiscrimating application, from which ‘classical’ economics suffered, and of which I think the Gilbert– Humphrey attitude is one illustration. I am myself enough of an ‘institutionalist’ (whatever that may mean) to have more than a lurking distrust of formulas and equations! But not enough of an institutionalist to ignore their importance: merely to want to think all round them and reckon with the imponderables that modify their action: and the other factors which no single formula can comprehend – for instance, the long-run incidence of continue large deficit-spending [emphasis added].19

Notes 1 Writing this chapter has been facilitated through correspondence and conversation with Pier Francesco Asso, Augusto Graziani, Warren J. Samuels, and Ernesto Screpanti who, as usual, are not in any way implicated in the final outcome. 2 See J. M. Clark’s remarks on his father’s contribution to economic theory in the letter to G. S. Hauge reproduced in the appendix to this chapter. 3 See Morgan and Rutherford (1998, p. 3). 4 J. M. Clark to Maurice Roche-Agussol: 14 September 1918, Joseph Dorfman Papers, Rare Book and Manuscript Library, Columbia University. The letter is reproduced in the appendix to this chapter. 5 Clark to Dorfman, 12 May 1956. Emphasis has been added. Joseph Dorfman Papers, Rare Book and Manuscript Library, Columbia University. The letter is included in the Appendix to this chapter. 6 Ibid. Johannsen not only coined the expression ‘multiplying principle’, but also was the first economist who attempted to calculate numerically the secondary effects of an initial reduction of total expenditures out of a given income. See Hagemann and Rühl (1990). 7 Ibid. It should be noted that Dimand (1990, p.  45) acknowledges ‘the less formal but still suggestive multiplier analysis’ of Clark (1931/1970), but doesn’t attach great relevance to it. 8 See Hegeland (1966). 9 On Hansen’s early appraisal of Keynes’ work, see Asso (1990, pp. 62–70). 10 Hansen to Clark, August 8, 1934. Joseph Dorfman Papers, Rare Book and Manuscript Library, Columbia University. 11 The term was introduced by Machlup (1939). 12 ‘As to the period of circulation, it may be assumed that wages are spent, for the most part, within a week, and begin to result in increased wage payments to other workers in a fairly short period. Interest and dividend payments may be received on the average, about two months after they are earned, but are slower in being spent. On this basis it would seem that an average cycle of two months would be a conservative estimate’ (Clark, 1935b, p. 87). 13 As Hansen remarked in his letter to Clark, this figure includes time deposits as part of circulating money but, if they are excluded, the rate of circulation is increased to 3 per year: ‘I am exceedingly sceptical of Angell’s 1.6 income velocity, Pigou arrives at the figure of 3.0, which seems to me about right in normal times. I do not see how it could

44  Fiorito

14

15 16

17

18

19

possibly be as low as 1.6 unless one assumes, as Angell may do, that savings deposits are part of the means of payment. This view I should challenge.’ Clark illustrated the difference between the two concepts by a physical analogy: ‘suppose the production of a commodity divided into 15 stages, each requiring 3 days, while 12 days’ reserve supply of materials or intermediate products is on hand at each stage in addition to goods in process. Then there will be 7½ months’ supply on reserve or in process in the whole system, and the average series velocity will be 1.6 per year. But it would take only 45 days for a unit of material to move through the series if it were not kept waiting in the reserve stocks. And, what is to the present purpose, if there were a sudden increase of demand for the final product, (and if there were spare plant capacity at each stage) the speeding out of output could be transmitted back from stage to stage through the whole series, not in 7½ months but very possibly in 7½ days; indeed there is no physical impossibility in its happening in 7½ hours’ (Clark, 1935b, p. 88). Note that this is true under Clark’s assumption discussed above. Clark (1935b) also reminded the reader that the expansion of public works may defeat its purpose by raising the cost of private construction. To support this claim he asserted that in 1934 governmental demand helped to maintain wages and prices of materials at levels which discouraged private buildings. On these issues see also Wiles (1971). ‘Moreover, if an increase of business is known to be due to a public deficit-spending, which presumably must come to an end before long, business may for that reason fail to respond with increased expenditures on its durable productive equipment, such as it would make if the same increase in business came from purely private sources’ (Clark, 1935b, p. 86). For instance, as he explicitly put it in 1942, ‘Keynes offers a reversed Ricardianism, of similar power and exposed to similar dangers, including that of undue dogmatism on the part of disciples’ (Clark, 1942, p. 9, quoted in Dorfman, 1970). See also Clark (1941b). J. M. Clark to J. M. Keynes, 24 July 1941, quoted in Dorfman (1970, p. 13).

References Angell J. W. (1933), ‘Money, prices and production: Some fundamental concepts,’ Quarterly Journal of Economics, 48 (1), pp. 39–76. Asso P. F. (1990), The Economist behind the Model: The Keynesian Revolution in Historical Perspective. Roma: Ente per gli Studi Monetari e Finanziari Luigi Einaudi. Clark J. M. (1919), ‘Economic theory in an era of social readjustment’ and ‘Rejoinder,’ American Economic Review, 9 (supplement), pp. 280–90 and 323–24. Clark J. M. (1935a), ‘Cumulative effects in aggregate spending as illustrated by public works,’ American Economic Review, 25, pp. 14–20. Clark J. M. (1935b), Strategic Factors in Business Cycles. New York: National Bureau of Economic Research and Committee on Recent Economic Changes. Clark J. M. (1935c), Economics of Planning Public Works. A Study Made for the National Planning Board of the Federal Emergency Administration of Public Works. Washington, DC: US Government Printing Office. Clark J. M. (1936), Preface to Social Economics: Essays on Economic Theory and Social Problems. Moses Abramovitz and Eli Ginzberg (eds), New York: Farrar and Rinehart. Clark J. M. (1939), ‘An appraisal of the workability of compensatory devices,’ American Economic Review, 29 (supplement), pp. 194–208. Clark J. M. (1941a), ‘Investment in relation to business activity and employment,’ Stud-

John Maurice Clark’s contribution  45 ies in Economics and Industrial Relations, University of Pennsylvania Bicentennial Conference. Philadelphia: University of Pennsylvania Press, pp. 37–51. Clark J. M. (1941b), ‘Further Remarks on Defense Financing and Inflation,’ Review of Economic and Statistics, 21, pp. 107–12. Clark J. M. (1942), ‘Economic Adjustment after the War: The Theoretical Issues,’ American Economic Review, 32 (supplement), pp. 1–12. Clark J. M. (1931/1970), The Costs of the World War to the American People. New Haven, CT: Yale University Press. Reprinted with an introductory essay by Joseph Dorfman, New York: Augustus M. Kelley Publishers. Davis R. (1971), The New Economics and the Old Economists, Ames: Iowa University Press. Dimand R. W. (1988), The Origins of the Keynesian Revolution. London: Elgar. Dimand R. W. (1990), ‘The New Economics and American economists in the 1930s reconsidered,’ Atlantic Economic Journal, 18, pp. 42–7. Dorfman J. (1946–1959), The Economic Mind in American Civilization, 5 vols, New York: Viking Press. Dorfman J. (1970), ‘Some Documentary Notes on the Relations among J. M. Clark, N.A.L.J. Johannsen and J. M. Keynes.’ Introduction to reprint of J. M. Clark, The Costs of the World War to the American People, New York: Augustus M. Kelley Publishers. Hagemann H. and C. Rühl. (1990), ‘Nicholas Johannsen and Keynes’ “Finance Motive,” ’ Journal of Institutional and Theoretical Economics, 146, pp. 445–69. Hegeland H. (1966), The Multiplier Theory. New York: Augustus M. Kelley. Junankar P. N. (1987), ‘Acceleration principle,’ in The New Palgrave: A Dictionary of Economics, J. Eatwell, M. Milgate, and P. Newman (eds), London: Macmillan, pp. 10–11. Kahn R. F. (1931), ‘The Relation of Home Investment to Unemployment,’ Economic Journal, 41, 173–98. Kahn R. F. (1933), ‘Public Works and Inflation,’ Journal of the American Statistical Association, 23 (supplement), pp. 168–73. Kaldor N. (1939), ‘Speculation and economic stability,’ Review of Economic Studies, 7, pp. 1–27. Keynes J. M. (1936), The General Theory of Employment, Interest and Money, London: Macmillan. Keynes J. M. (1933/1972), ‘The Means to Prosperity’, in The Collected Writings of John Maynard Keynes, Vol. 9: Essays in Persuasion, London: Macmillan and Cambridge University Press for the Royal Economic Society. Machlup F. (1939), ‘Period Analysis and Multiplier Theory,’ Quarterly Journal of Economics, 54 (1), pp. 1–27. Medio A. (1987), ‘Multiplier–Accelerator Interaction,’ in The New Palgrave: A Dictionary of Economics, J. Eatwell, M. Milgate, and P. Newman (eds), London: Macmillan, pp. 564–6. Morgan M. and M. Rutherford (1998), ‘American Economics: The Character of the Transformation, ‘ in M. Morgan and M. Rutherford (eds), From Interwar Pluralism to Postwar Institutionalism, Durham, NC: Duke University Press, pp. 1–26. Neisser H. (1936), ‘Secondary Employment: Some Comments on R. F. Kahn’s formula,’ Review of Economic Statistics, 18, pp. 24–30. Ramson B. (1977), ‘The Alternative Paths to Theory of Clark and Ayres,’ Journal of Economic Issues, 11, pp. 461–7. Samuelson P. (1942), ‘Fiscal Policy and Income Determination,’ Quarterly Journal of Economics, 56 (4). pp. 570–605.

46  Fiorito Samuelson P. (1959), ‘Alvin Hansen and the Interactions between the Multiplier Analysis and the Principle Of Acceleration,’ Review of Economics and Statistics, 41, pp. 183–4. Shackle G. L. S. (1967), The Years of High Theory: Invention and Tradition in Economic Thought, 1926–1939. Cambridge: Cambridge University Press. Shute L. (1994), ‘John Maurice Clark (1884–1953),’ in G. M. Hodgson, W. J. Samuels, and M. Tool (eds), The Elgar Companion to Institutional and Evolutionary Economics, 2 vols, London: Elgar, pp. 50–4. Shute L. (1997), John Maurice Clark: A Social Economics for the Twenty-First Century. New York: St. Martin’s Press. Slichter S. H. (1937), ‘Review of Economics of Planning Public Works: A Study Made for the National Planning Board of the Federal Emergency Administration of Public Works by John Maurice Clark,’ American Economic Review, 27, pp. 186–90. Villard H. H. (1941), Deficit Spending and the National Income, New York: Farrar and Rinehart. Wiles R. C. (1971), ‘The Macroeconomics of John Maurice Clark,’ Review of Social Economy, 29, pp. 164–79.

Appendix Clark’s correspondence is published here with the permission of the Rare Books and Manuscript Library of Columbia University. The relevant material was found among the Joseph Dorfman papers, Box 11, Folder F. I am indebted to Pier Francesco Asso for encouraging publication and to Bernard Crystal, the assistant librarian, for much friendly cooperation during my research. John Maurice Clark to Maurice Roche-Agussol, 14 September 1918 My dear Professor Roche-Agussol: I am staying here with my father, and he has been prevented from replying immediately to your letter by the fact that he was off on a motor trip. I have made a list of the articles by him which appeared in the New Englander and tabulated the chapters in the “Philosophy of Wealth” to which they correspond. An article entitled “The Philosophy of Value” appeared in 1881, and is practically identical with chapter V of the “Philosophy of Wealth.” My father will verify other bibliographical matter and let you have the whole. As far as the material about myself, I was born in 1884, studied at Amherst College 1901–1905 and Columbia University 1905–1908, Instructor in Economics and Sociology, Colorado College, Associate Professor of “Political Economy,” University of Chicago, 1915– . I have published a doctor’s dissertation entitled “Standards of Reasonableness in Local Freight Discrimination,” Columbia University Studies, 1910. (I would handle the theory quite differently if I were writing now). I collaborated with my father in the second edition of his “Control of Trusts” and am collaborating with W. H. Hamilton of Amherst and H. G. Moulton of Chicago in a book of readings in “The Economics of War.” Also I have published articles on topics so varied as to indicate a deplorable lack of specialization. It happens

John Maurice Clark’s contribution  47 that I recently published two articles in the Journal of Political Economy, January and February, 1918, on the subject of Economics and Psychology. These are an abbreviated version of some manuscript which is not ready for publication in more extended form. These articles indicate in a general way the type of study that is needed in order to develop the economic aspects of modern psychology; and in order to take into account those sides of human nature that are left out of existing theory though they are very relevant to modern economic issues. Another thing on the same subject is a paper by Carleton Parker, read at the meeting of the American Economic Association last Christmas. (American Economic Review Supplement, March, 1918.) I think this is significant, and not because of the particular headings chosen under which to catalogue the instincts, but because of the method of treating economic problems which is suggested: e. g. the study of labor troubles as results of balked dispositions. The results of such study might be important. Rationalism says: “To satisfy a man, give him what he demands.” The theory of Professor Parker says: “To satisfy a man, study him to see if his demand (perhaps in itself impracticable to gratify) is not the expression of an underlying discontent due to causes which the man itself does not know and could not formulate in words.” Professor Parker and myself, working independently, have treated two complementary aspects of human nature: he the innate qualities, I the modifying elements of the environment. You doubtless know also Prof. W.  C. Mitchell’s papers and articles bearing on the subject of psychology and economics: American Economic Review Supplement, March 1916, and Journal of Political Economy, vol. 29, pp. 1–47; also American Economic Review, vol. 2, p. 269. Also Walton H. Hamilton’s articles, Journal of Political Economy March & April, 1918. My article in the American Economic Review, December 1917, on the basis of “War-Time Collectivism” (also much abbreviated from the original manuscript) has some treatment, I think, of the weakening of individualism and the enlarged scope for collective activity which result from facts of human nature which the marginal-utility theory has left out of account. In attempting to say anything further as to the present position of psychoeconomics, I am in a delicate position, as you will appreciate, but I want to explain my views frankly. I have been trying (1) to carry on my father’s projects of study, (2) to reach an independent position as to the criticisms of his work. I have come to disagree somewhat with my father as to the nature of dynamic theory and its relation to static. I divide economics broadly into three divisions: By “value economics” I mean any system in which exchange value, or the choices of individuals as expressed in exchanges, are taken as the final measure of economic qualities, so far as the system of theory is concerned. Such system may be part of a man’s thinking, but subordinated or combined somehow to other less narrowly limited standards of judgment. “Value theory” includes all the marginal equilibrium theory, including Fetter’s and Davenports. Both trends are found in the work of the great men, including Adam Smith, J. S.

48  Fiorito A

B

Value Theory

(1) (2) (3)

Static value — or price — economics Dynamic value — or price — economics. (This includes or presupposes (1) probably.) Dynamic social or institutional economics, or ‘realistic’ economics.

Mill, Sidgwick, Marshall, etc. etc. (see Hamilton’s articles). Germs of both are found in the “Philosophy of Wealth,” and the standard set for economics to work toward is of the broadest kind. I accept this standard, but in working toward it I find the effect on the static theory to be “rather chemical than mechanical.” (Philosophy of Wealth p. 34). My father regards the marginalutility view of human nature as partial only (Philosophy of Wealth, p. 36 last half) and he has constructed a tentative system on this partial basis after setting a standard that demands a fully and realistic “anthropology.” And he also holds that a system based on imperfect anthropology cannot be completed by “making allowances for disturbing factors.” (pp. 32–35). Frankly, I think the term “psychological school,” as used by Fetter, is an incorrect description. If we ever get a real psychological school we still have no more left to give it. The view of human nature which this school employs is either (a) Rationalistic or hedonistic: “man satisfies his wants in order of their intensity” and price measures marginal intensity of desire. (Philosophy of Wealth, Chapter V); (b) static: “Man has a fixed order in satisfying his wants” (Böhm-Bawerk) or (c) Agnostic. (Davenport, Fetter and others whose theory takes “human wants for granted” and does not go behind them). Neither (a) (b) nor (c) represents real psychology or is based on the positive results of psychological science. I think the line of development for this type of theory is to be merged in theories based on broader premises. For these broader theories, it will be good to go through a period of “casting around” in whatever direction seems promising, guided by the varied insights of different students. Economics studies the efficiency of our system of production to attain social ends. If it is time to break away from “marginal utility” and price as final measures of such efficiency (final, that is, for the purposes of economic theory) we are forced to study social ends directly — rally study the purposes that dominate nations and other social groups, larger and smaller. The system best suited to attain the ends of an aggressively utilitaristic nation is different from that best suited to a pacific democracy, safe from invasion, as the United States has been in the past. The study of social purpose is sociology and the economist should use whatever results the sociologists may have established, just as he should use whatever result the psychologists have established as to human nature. He should put his work in proper relation to whatever is known about social purposes. The Marginal Productivity analysis is a different story. Here we have more to do with finance and industrial technique and less with psychology. Here there are some important lines of development open. (1) Study of the lack of

John Maurice Clark’s contribution  49 correspondence between marginal contribution to the profits of the employer and marginal contribution to social product. J.  S. Mill, Sidgwick, Landry, Pigou, Hobson, Veblen, etc., have hardly exhausted this topic. (2) Study of imputation on a more realistic basis. Static theory assumes that producers get the “best combination of factors” in the existing “state of the arts.” But the very fact that the state of the arts is imperfect means that producers do not have the best combination. They are using a customary combination, improved by the method of trial and error or (if not improved) growing more and more obsolete. This destroys the exactness of imputation and thereby gives scope for much latitude of economic policy, even in a competitive society. These policies are governed by principles of some sort, which become a part of dynamic economic theory. E.G. wages aiming to stimulate efficiency for the future rather than to reward exactly the efficiency attained in the past. In a word I am largely interested in seeing economic theory (a) to become independent of the exchange value of goods as a measure of social wealth, and (b) show the relation between individual choices and underlying social institutions in its true perspective. I do not want to appear or to be quoted as engaged in critical attacks on the validity of the general system my father has developed. A full statement of my position includes a discussion of what validity means in economic theory. Stated in skeleton form, my idea is: (1) Absolute truth is impossible in general economic theory: it must be erroneous to the extent that it must be artificially simplified. The idea that much simplified results are still true pictures of a real part of the real world, is delusion in most cases if not in all. It is certainly so in the matter of human nature (Philosophy of Wealth, pp. 33–34), will explain more fully what I mean. Simplified theories are hypotheses whose resemblance to facts may be close enough to make their useful in certain situation and for certain purposes. (2) Such more or less erroneous pictures of parts of the world may be useful to help meet particular sets of issues. E. G. if the individual is a less incompetent judge of his own interest than anyone else, a theory, based on marginal utility and picturing the serviceability of individualism, is useful. But if science advances so that so that it becomes practicable (it must also be politically practicable, of course!) to judge the individual’s interest for him better than he can judge them himself, such a theory comes to be an obstacle to getting the possible gains from the new achievements of science. We may say that the theory was formerly pragmatically valid, but that it has become pragmatically invalid. (3)  More likely the situation is not so clean-cut and the theory remains “true” with reference to certain issues and “false” with reference to others. In other words, it is usefully relevant to some issues and not to others. The truth of theories is relative to particular issues to which they may be applied. (4) A particular issue is usually a conflict of principles: individualistic, socialistic, syndicalistic, feudal, cooperative, regulatory or what not. A purely individualistic economics can be usefully relevant only to those issues where the individualistic principle is right and the others are wrong. It needs to contain all the other principles expressing the good in all

50  Fiorito the other methods in order to be capable of furnishing a “description” of society that remains useful in a variety of circumstances. So much for the general principles indicating what I mean by “validity.” As to marginal utility, it has had and still has a great deal of pragmatic validity, but it is not actively relevant to most modern issues of social reform. The effect is passive, negative, toward such questions. This may be useful in combating crude forms of social revolution, mercantilism, etc. but there are more scientific measure of social reform, and the principles underlying them need to be developed to a rank coordinate with that given to marginal utility, and not treated as subordinate things, exceptions, allowances, or simply as separate “practical” problems without any theoretical bearing whatever. I hope the outline I have given is not too condensed to make my meaning clear. Yours very sincerely, J. M. Clark Alvin H. Hansen to John Maurice Clark, 8 August 1934 Dear Clark: Thanks very much for sending me your chapter nine dealing particularly with the cumulative effects of public expenditures. I regret that I have not had time to read it closely, and the comments I am making below are subject to the qualification that I have not given the chapter as close study as I hope to do later. I wonder if you happen to have noted the long footnote to my chapter in the report of the Columbia Commission on pages 211–212? This footnote is, of course, too brief to really clarify the matter and there are some points I would now phrase differently even from this brief treatment. In general, I have the impression that your analysis still follows too much along the Keynes lines. Keynes’ analysis I regard as definitely wrong, and I hoped that I would be able to make a brief article clarifying the issue, but have not ad time to do so. It is, of course, possible that once I get thoroughly into it I will find that I am wrong and he is right. It must be clearly be kept in mind, I think, that Keynes’ multiplier is really a transactions velocity of money concept. In his Means to Prosperity, he shows this clearly by giving the fallacious argument advanced by all the Fisher script money supporters that if a city put out stamp money to its unemployed, the income of the city would be increased per annum by the number of times this stamp money circulated. Keynes swallows this whole, and argues that the only thing wrong with this line of reasoning is that it overlooks the “leakage.” Keynes’ receipts in each transfer, in short, are not “income” but “gross income.” I have the impression that there is, on this point, some confusion in your page 155.

John Maurice Clark’s contribution  51 The first thing, it seems to me, absolutely necessary is to eliminate wholly the conception of transaction velocity from this whole discussion. So long as this concept is included, confusion results. The whole thing, it seems to me, is a question of (1) the volume of means of payment, or “money” and (2) the income velocity of “money.” Public works may affect either one of these two or both. It is quite correct, as Keynes said, that the public works expenditures may not enlarge the volume of “money.” In this event, the effect presumably is to transfer money from idle hands to active hands. In other words, the income velocity increases. Or there may actually be injected into the market new “money,” and the income velocity might conceivably remain on the average as before. Or there may be a combination of these two tendencies. Keynes’ “leakages,” I think, are also dangerous. The most important “leakage” is his saving “leakage” and this when analyzed amounts to nothing more or less than our old friend, a change in income velocity. If all of us hold idle a half of our income which we formerly spent, — save it without investing it, in other words — the income velocity has been cut in two. Thus the total income of society in the next succeeding period has been reduced to one-half by this process of “savings running to waste”. These “leakages” in short, apply not only to governmental expenditures, but to all incomes in deflationary periods. This leads me to remark that it does not seems to me that you have rightly stated the position of what you call the “income velocity group.” It is certainly not my view that governmental expenditures will result in a continuos inflation as you infer on page 171a and 176a and in various other places. For example, there might be merely an increase in “money” as a result of the funds thrown into the market by public expenditures. The total income would be increased correspondingly in the next succeeding period and thereafter would remain constant unless there were a further change either in the volume of “money” or in the income velocity of “money.” You are, I think, quite right in emphasizing the point that one can lay down no mechanical rule (as Keynes does) of a progressively declining rate, one-half, one-fourth, one-eighth, etc. it is always Keynes’ defect to be far too mechanical. It is quite impossible to appraise the effect of public expenditures in any such mechanical matter. Therefore, I think the whole approach is fallacious. All that public expenditures do is to throw new funds into the market, and thereby increase the income, which action, since it is certainly not likely to reduce the income velocity of “money” is very likely to increase the total “money” income of society by more than the amount of “money” injected. It is, therefore, correct to say that public expenditures are likely to have an effect on income in excess of the expenditures. This is all there is to it, it seems to me. But the precise effect upon the volume of “money” and upon the income velocity of “money” will vary enormously from one phase of the cycle to another, and in different centuries, and at different times, and therefore no formula can be laid down indicating what the results will be. If,

52  Fiorito however, one knows at the bottom of the depression what the income velocity of “money” is, it seems that one must be at least safe in assuming that public expenditures would increase the “money” income by the new “money” injected multiplied by the then prevailing velocity of “money.” I am exceedingly skeptical of Angell’s 1.6 income velocity, Pigou arrives at the figure of 3.0, which seems to me about right in normal times. I do not see how it could possibly be as low as 1.6 unless one assumes, as Angell may do, that savings deposits are part of the means of payment. This view I should challenge. I have stated the points as you will note far more dogmatically than I have any right to, for as I have said, I have not thoroughly canvassed the matter, but for your purpose this dogmatism will surely do not harm. Very sincerely yours, Alvin H. Hansen J. M. Clark to G. S. Haug, 16 December 1937 Dear Mr. Hauge: Your inquiry raises the question of a change in my father’s attitude from the abandonment of competition in his “Philosophy if Wealth” to a defense of it as a morally justifiable system, in the “Distribution of Wealth.” I do not think my father was conscious of any change in his basic attitude. And I do not recall the earlier book as an “abandonment” of competition — rather as a recognition of evils and a plea for moral elements, with hopes of developing cooperative institutions which should themselves make their way by the competitive route; competing with competitive business, if I recall correctly. What happened was in the first instance largely the direct and indirect consequences of the method he adopted for breaking up the manifold problem of economics and attacking it systematically, step by step. The “Philosophy of wealth” was his first reaction to the economic system as a whole; the distribution was a first step, and avowedly only that, in a more systematic analysis: in which he isolated the economic forces corresponding to the force of gravity, by the device of a static equilibrium, implying perfect markets, perfect competition and perfect fluidity. Thus the second book is not supposed to be a realistic picture of existing society, nor concerned with the grindings of the actual and imperfect market mechanism. In the “Philosophy” he contemplated the latter. Labor could be exploited by the use of bargaining advantages and a “good” bargain is morally a bad one. (Nobody could get a better bargain than anyone else in the “static state” described in the “Distribution.”) On one point you can find both the first and second stages of thinking in the earlier book; namely, on the matter of the economic conception of human

John Maurice Clark’s contribution  53 nature. He demands a more realistic “anthropology,” which cannot be had from the asking; and in the meantime proposes a first approximation. This turns out to be his form of marginal utility theory, which is essentially a static abstraction in the field of human nature (as I tried to show in my article on Economics and Modern Psychology, Jour. Of Pol. Econ., 1918). The third stage of the process was to have been dynamics, conceived as putting in what statics left out. In the mean time, several things had happened. He had grown older. The time spent in developing the static abstraction presumably influenced his later perspective, tending to make him feel that his first approximation (the static state) was nearer to a representative picture than he might have thought when writing the articles which later became “The Philosophy of Wealth.” It has been said by critics that static elements clung to his later dynamics. I could explain my own views on this, but hesitate to do so, for the same reasons which have made me avoid this issue in print. You may find implications bearing on this in my contribution to my father Festschrift; also in my “Social Control” volume. Another major thing that happened was external. In the period leading up to the “Essentials” competition was threatened, not by a benevolent cooperation, but to exploitive monopoly, typified in the Standard Oil and Tobacco “Trusts” — also in restrictive labor union policies. One is influenced by the evils one reacts against! And my father had a faculty of simplifying a complex situation by picking out the element which seems to him to deserve paramount weight. In this case the need of defending competition against monopoly appears to have been that element. Even here there is continuity of attitude with the “Philosophy of Wealth,” the continuing factor being the emphasis on the need of moralizing competition by developing and enforcing standards of fair competition. It is interesting to be invited to review and formulate my ideas on this matter. Sincerely yours, J. M. Clark Paul A. Samuelson to John M. Clark, 16 April 1953 Dear Professor Clark: The Millikan volume Income Stabilization for Developing Democracy has finally come out and I am enclosing a reprint of my own contribution. Perhaps you remember reading it at an earlier stage and giving me the benefit of your criticisms. I felt that I benefited immensely from them and any remaining inadequacies must naturally be blamed on me alone. I read in the New York Times of your going over to emeritus status. At the time I felt the urge to drop you a note telling you how much I think you have added to American economics. But as so often with these impulses, it passed

54  Fiorito off before I had gotten around to doing anything about it. May I take this occasion to reiterate these sentiments and wish you pleasant years ahead. I greatly enjoyed your chapter in the Spiegel volumn and also your remarks in the Impact of the Union dealing with your father’s role in this history of economic doctrines. At the time of the American University meeting, you may remember mentioning that at some future date I might write asking you about the psychological genesis of the theory of the accelerator principle in your mind. I have always been interested in the process by which our ideas come to us — such extra-logical considerations as were involved in Henri Poincaré’s perceiving a complete mathematical theory at the moment he stepped on a street car. There is no reason why at this late date you should remember how this idea first came to you. But if you do and if it is the sort of things that merits communication, I should find the information exceedingly interesting. Thank you again for your help. Sincerely yours, Paul A. Samuelson John M. Clark to Paul A. Samuelson, 21 April 1953 Dear Samuelson: I appreciate your letter, with its good wishes, very much, also the reprint which I look forward to examining. I have reason to regret that I have not had enough foresight to ask in advance for the kind of reprint of things I have contributed recently to collaborative volumes. I could have made good use of such reprints if I had them. About the genesis of the “accelerator principle” I am afraid I have no definite picture of the precise process. It grew out of my reading of Wesley Mitchell’s original volume of business cycles, in which he emphasized monetary or financial factors, and it seemed to me that there was a physical or technical factor implied in his description of the cumulative processes (or if that is too strong a term, at least implicit in the process) and that it might usefully be separated out for purposes of analysis. Of course, the distinction between the two sectors of demand for capital — replacements and net additions — was well understood, so the separating out of the element of net addition and putting it into a simplified theoretical model was a pretty natural step. I had it in mind when I came across Mr. Leigh’s railroad figures, and they seemed very pertinent. I did not think I realized at the time that this was a peculiarly available selection of figures, because it involved a sector of demand for capital which responded to a demand for the proximate end product — namely, freight transportation — which registered the general state of economic activity, while the item of capital demand involved was sufficiently limited so that by the reverse impact of capital demand on flow of purchasing and demand for ultimate products — Or not too much confused?

John Maurice Clark’s contribution  55 Your question reminds me of a couple of other instances: the proposition about the sum of the marginally-imputed products absorbing the total product, and the conditions necessary to this, and the working out of a rough form of the R. F. Kahn-type multiplier. I remember where I got the answer to the first: namely in a hotel room where my father and I had gone to meet David Kinley. I had been wrestling with the problem, and figured out a geometrical solution. Later, I talked it over with my friend, Charley Cobb, and he converted it into a case of Euler’s theorem. Before trying to publish it, I did some investigating, and discovered Wicksteed’s monograph, and Flux’s review, which converted Wicksteed’s demonstration into a case of Euler’s theorem. So that had clearly been anticipated. As to the multiplier, I got that idea as one answer to the problem why an expansion, with its cumulative effects which were well recognized, should turn into a contraction. And it occurred to me that if the expansionary effects of an increasing capital investment returned in cumulative fashion, but diminished by “leakages”, that could produce a series of the type, the sum of which to infinity is a finite quantity, and also that the time-profile of that series would be an asymptotic curve, concave downward, increasing at a diminishing rate. Combine this with the accelerator principle, with time lags, and you could get a model that would convert the expansion into a contraction; as you showed in your article in equating the accelerator principle with the multiplier. I always wished that you had made more deviations from mathematical “elegance”, and explained, in language that a non-mathematician could assimilate, how or “why” the various results that you showed in that article came from the various combinations of factors worked out. I did not do anything at the time with this idea, being very busy with other work, and in any case, R.F. Kahn must have been well along with his multiplier study (which was published, I think, maybe a couple of months after I got the notion) so that he properly had priority. I am afraid that none of these recollections give you the precise psychological point you are fishing for. I may not have taken note of that sort of thing at the time and at any rate I do not remember it now. With best wishes, Sincerely yours, J. M. Clark John M. Clark to Joseph Dorfman: May 12, 1956 Dear Joe: Your draft of a chapter or section on my economics gives me a lot to think about. Your appraisal is generous — maybe overgenerous — but I won’t quarrel on that score. You have — necessarily — had to resort to oversimplified characterizations, under pressure for brevity; and some of

56  Fiorito these are bound to make the subject squirm a bit. My squirmings, as recorded in this letter, aren’t intended to interfere with your right to your exercise of judgment; merely to indicate my reaction, for what it may be worth, along with other evidence. And where I have put in bibliographical details which you wouldn’t have any business to include in your chapter, they’re merely intended as background material. There’s one would-be contribution I tried to make that has been completely ignored by everybody; namely, my revision of the Dublin & Lotka method of estimating costs of death and disability, in the “Cost of the World War.” I hold no brief for the accuracy of my tables in the appendix but the guesswork there is a tiny matter compared to the major exaggeration and distortion of the Dublin and Lotka method. Dublin once told me of course I was right, but he’s never done anything about it. Key points on pp. 214–222, and Appendix B, pp. 298 ff. Now to go through your manuscript. Page 1: Johannsen’s work don’t think I ever grappled with; I recall only vague and general ideas about it — So when about 1924 or 25, he wrote asking me for some public recognition of his work, I was embarrassed, and didn’t feel competent to appraise it . . . Page 1, line 9: “fuse orthodoxy and heterodoxy:” from my standpoint it wouldn’t be orthodox of the J.B.C. (John Bates Clark) sort to accept his “statics” as final truth; it would be “orthodox” in that sense to try to put in as much as possible of what “statics” leaves out: including what seemed to be elements of truth underlying criticisms by people like Veblen and Davenport but not their specific methods or results. Hence “fuse” seems not the most accurate word. But I am handicapped by not knowing how you have defined “orthodoxy” an “heterodoxy.” . . .  Page 2: . . . Reverting to formative impacts, there’s a problem of order of presentation, relative to order of teaching positions held and relative to times when the resulting studies were made. Overhead Costs came first, 1905-1923, nest in time I’d put the working out of a position relative to Veblen’s and Davenport’s criticisms of J.B.C. centering on “Social Productivity Vs. Private Acquisition.” This pointed to examination of premises but Patten and Bagebot didn’t resolve all questions. All this in the Amherst period. Criticisms of the psychological assumptions of utility theory remained a challenge, and led to the two 1918 articles on psychology with W. James’ psychology the most obvious source: Cooley’s “Human Nature and Social Organization” next, perhaps. Carleton Parker came later, I think, as did Cooley’s “Social Process.” “Inappropriables” formed a natural key concept, and Ely’s “Property and Contract” (1934) put content into it, followed by Roscoe Pound and Ernst Freund. Meanwhile Pigou’s “Wealth and Welfare” (1912) and Hobson’s “Work and Wealth” (1914) put Welfare Economics on the map, relative to “social productivity vs. private acquisition.” Mitchell’s “Business Cycles” led to the “acceleration” article, as you indicate. I thought I’d found a technical factor underlying the financial quantities on which Mitchell tended to concentrate his attention. . .

John Maurice Clark’s contribution  57 Page 12, line 12: None of the previous statements explain how the “acceleration” principle bears on this timing feature; because none of them bring out the feature responsible for the name “acceleration;” namely, a relationship in which the absolute amount of one variable (e.g. monthly output of certain machines) is a function (in significant part) of the rate of change of another variable (e.g. total installed capacity of such machines) which in turn responds – with a lag ordinarily – to rate of change in demand for the products these machines make. So if the increase in total installed capacity slows down, output of machines is likely to decline absolutely, while total installed capacity is still increasing; i.e. before it reaches its peak. Your preceding statements all deal with intensified amplitude of derived fluctuations, but leave out this timing factor. Taken in connection with the Investment-multiplier effect on demand for consumer goods, this would explain (in a simplified model) a cycle four times the length of the time-lag between an impulse from the demand side and the full response of the capitalbuilding industries. E.G. if it takes 18 months for a peak of rate of growth of consumer demand to generate a derived peak in production of means of production, and for the resulting incomes in the industries producing means of production to get distributed and spent, then when the derived peak is reached, consumer demand might stop growing and production of means of production might shrink to a replacement basis — perhaps with the same 18 month lag. And so on. In a simplified model, this could explain a 3 year cycle, neglecting asymmetries which would be likely to occur at the bottom because the timing of working-off of excess equipment isn’t likely to be the same as the timing of new additions to capital equipment. When I worked out my asymptotic form of the multiplier, published in “Economics of Planning Public Works,” I noted that it furnished another kind of mechanism whereby the increase in total income resulting from an increase in investment might tend to taper off. Then, the increase coming to an end, the investment flow might shrink toward a replacement basis, causing total income to shrink instead of merely ceasing to expand. I can’t remember if I ever put this feature on paper. It might not have seemed germane to a public works report. I dreamed up this asymptotic multiplier in 1930, when R. F. Kahn was well along with his essentially similar concept, so he has priority. As to multipliers, in “My Costs of the World War,” discussing the neutrality-boom of 1916, I evolved a rough foreign-trade multiplier. Kaldor found some bits of that book to be anticipations of Keynesism . . . I may have not told you that I’ve let myself in for a book on competition (with dynamic emphasis as indicated in my recent papers) for Brookings: and also (in order to get those Kazanjian lectures into commercial circulation) a collections of papers on borderline matters – Welfare and such – for Knopf. Sincerely yours, J. M. Clark

3 The multiplier relation as the pure theory of output and employment in a monetary production economy Heinrich Bortis

Introduction The multiplier relation represents the pure theory of output and employment in a monetary production economy. This relation states how the scale of economic activity, that is, aggregate output and employment, is, in principle, determined by effective demand, which, significantly, is a monetary magnitude. Effective demand always enters the scene as autonomous and derived demand, with the former being, in principle, independent of income and output and with the latter dependent upon these magnitudes. In the multiplier formula the multiplier coefficient links, via derived or secondary demand, autonomous demand to equilibrium output and employment. This coefficient is directly associated with the leakages out of total income, that is, the secondary incomes created by the primary incomes which, in turn, equal autonomous expenditures. The crucial point is that the multiplier relation is, as a rule, associated with a level of employment below the full employment level, whereby, in principle, all the sectors of production and all the kinds of labour are affected in the same way. Involuntary unemployment may permanently exist, and there is no self-regulating mechanism to bring about full employment. These propositions hold for the short term, but also for the medium and long run (see, for example, Bortis, 1997, chapter 4; and Bortis, 2003a, pp. 461 ff.). An equilibrium involving involuntary unemployment can occur only in a monetary production economy where structural rigidities dominate: Keynes recognised that the industrial system was inflexible; to him this was a reason for switching economic analysis (based upon adjustment through substitution) to the analysis of shocks (upon a technical-institutional system where complementarities prevail) (see Skidelsky, 1992, p. 370). Technical rigidities prevail in the social and circular process of production, represented by the constant, but not invariable, Sraffa–Leontief–Pasinetti production coefficients. Normal (long-period) private and state expenditures are governed by institutions (consumption habits, legal dispositions relating to taxes and government expenditures). Institutions, though they are as a rule slowly evolving, are also associated with rigidities. This incidentally implies that saving becomes a pure residual: with the propensity to consume institutionally determined through consumption habits and with taxes and expenditures legally fixed, saving adjusts to investment through variations in output and

The multiplier relation  59 employment. In such a system there is inherent price rigidity once money wages are given, and quantity adjustments dominate, except in the course of the business cycle where quantities vary together with prices and profits. Since in a monetary production economy goods are always exchanged against money – there are flows of money and of goods in opposite directions in the processes of production and circulation – the problem of demand in money terms inevitably arises, as is immediately evident from the Marxian scheme of production and circulation (Marx, 1867–94/1973–74, Vol. 2, p. 31): M – C – P – C´ – M´

(3.1)

In the first stage, producers dispose of money and finance, M (G in original), and buy means of production, that is, commodities and labour force, C (W in original). These are transformed into final products, C´ (W´), in the vertically integrated labour view of the social process of production, P, which implies the horizontal land aspect of production (on the labour and land aspects of production, see Bortis, 2003a). The final goods, C´, are transformed into money, M´ (G´). At this second stage of circulation, M´ governs C´, the amount of final goods that may be exchanged against money. It is here that the effective demand problem arises and the multiplier, potentially implying equilibrium with involuntary unemployment, enters the scene. This is the central theme of Keynes’s General Theory, which (starting with the Treatise in 1930) ‘evolved into what is primarily a study of the forces which determine changes in the scale of output and employment as a whole [and] it is found that money enters into the economic scheme in an essential and peculiar manner . . . A monetary economy . . . is essentially one in which changing views about the future are capable of influencing the quantity of employment and not merely its direction’ (Keynes, 1936/1973, p. xxii). It is the scale of economic activity which is at stake, not proportions at a given scale (Bortis, 1997, chapter 4; and Bortis, 2003a). This implies that multiplier analysis is essentially of a macroeconomic nature since all the sectors of production, whatever their number, are affected by the size of effective demand. All this is in striking contrast to the neoclassical exchange model in which the level of output and employment is given, and in which full employment prevails if market conditions are competitive. In the neoclassical model, with productive resources and consumers’ tastes given, the optimal allocation of the given resources, regulated by the principle of substitution combined with maximising behaviour under constraints, moves to the fore. Money is, in principle, unimportant in the neoclassical scheme, although Marshall had established a monetary theory of exchange according to which in the markets for factors of production and for final goods commodities are exchanged against money (Bortis, 2003b); in fact, in the neoclassical scheme, money and credit appear as disturbing factors if monetary magnitudes are not in line with real magnitudes. For example, if the quantity of money grows faster than real output, inflation sets in. The working of the principle of substitution appears with particular clarity in an underemployment situation: The price of labour, that is, the money and

60  Bortis the real wage, is supposed to decline as profit and interest rates increase, as a first step. As a consequence, labour, having become cheaper relative to capital, is substituted for capital which raises employment. Simultaneously, due to the initial rise of the rate of profits and of interest, the volumes of investment and saving increase, thus creating additional work places. These processes come to an end when full employment is reached. Hence in the neoclassical exchange-based framework the optimising behaviour of economic agents is associated with the allocation problem. This problem is solved once given quantities and prices stand in definite relations to each other, that is, once equilibrium structures are established. Thus, while there may be voluntary or frictional unemployment, there does not exist any problem of involuntary or systemic unemployment in neoclassical analysis since the optimum allocation of given resources, including labour, is considered. Therefore, with the scale of economic activity already determined, there can be no multiplier either. To establish the principle of effective demand and hence the theory of the multiplier it must be shown that neoclassical theory is, in principle, not able to come to grips with the great problems of a monetary production economy, specifically the problem of output and employment. The critique of neoclassical theory is, on the one hand, theoretical and, on the other, historical,. The theoretical critique, in turn, goes on in two directions: monetary and real. These two routes to effective demand, a monetary and a real route, are suggested in Garegnani (1983). The monetary critique is Keynes’s (1936/1973): money is not only a means of transaction, but also a store of value. The rate of interest does not bring into line saving and investment, but the supply and the demand for liquidity (money). In macroeconomic equilibrium, (planned) investment equals planned saving. Investment (I) is autonomous, governed by long-period expectations; saving depends upon aggregate income (S = sY), where s is the marginal and average propensity to save. This immediately leads to the simplest possible form of the multiplier relation: Y = (1/s)I

(3.2)

Keynes’s monetary critique was absorbed by orthodox real – supply and demand – theory by means of the IS–LM diagram (Hicks, 1937/1982). To establish the principle of effective demand, and hence the multiplier, a critique of the neoclassical real model, the supply and demand mechanism, is required. This critique – Garegnani’s real route to effective demand – is represented by the capital theory debate which followed the publication of Sraffa (1960). With production being a social and circular process and capital being a produced factor of production, depending upon the conditions of production and upon income distribution, capital cannot be measured in physical terms and there are, in principle, no ‘well-behaved’ relationships between the rate of profits (or interest) and the quantity of capital: more capital cannot always be associated with lower rates of profit and interest, and vice versa. These and other results of the capital theory debate are comprehensively set forth in Harcourt (1972). Most importantly, with no well-behaved associations between factor prices and factor quantities existing

The multiplier relation  61 in principle, falling real wages may be linked with lower employment levels. The price mechanism, or the supply-and-demand mechanism, is, in principle, unable to produce a tendency towards full employment if the process of production is of a social nature. This does not exclude that in specific real-world situations such a tendency may exist temporarily. The empirical–historical side of the critique of neoclassical theory in general and of neoclassical employment theory in particular is provided by the employment situation that prevailed during the great depressions, particularly in the deep depressions of the last quarter of the nineteenth century and of the 1930s. These socioeconomic catastrophes in terms of involuntary unemployment shattered belief in the normal functioning of capitalist economies; in fact, the belief in ‘the myth of the market economy’ (Lazonick, 1991) broke down. The fact that real wages rose together with unemployment does not mean that the rigidity of money wages was a fundamental cause of the crisis. The high real wages were not a cause but a result of unemployment: the breakdown of effective demand, specifically investment demand, combined with overcapacities, resulted in a sharp decline of output and employment volumes – due to multiplier effects! – and of prices, with the latter resulting in a rise of the real wage rate. The deep crisis of the capitalist system worked as a strong incentive for alternatives. Since the socialist alternative was not attractive to Keynes, he opted for a middle way (Fitzgibbons, 1988; Mini, 1991; O’Donnell, 1989). Keynes’s endeavours to work out a third-way alternative to liberalism and socialism culminated in his General Theory. The results produced by the critique of exchange-based neoclassical theory in general and of the neoclassical theory of employment in particular, on the basis of theoretical principles and historical events, clears the way for the multiplier principle, which is intimately connected with the determination of the scale of output and employment in a monetary production economy. The purpose of these notes is to present some important variants of the multiplier principle, to bring into the open the immense fruitfulness of this principle. We begin with a remark on method, which is followed by some very sketchy historical reflections. The central sections deal with different types of the multiplier relation. First, Kaldor’s two multipliers, based upon Keynes’s Treatise on Money and General Theory, respectively, are sketched. Subsequently, Harrod’s and Domar’s association of the multiplier with the inherent instability of the investment and output path is presented; this path is in fact a behavioural knife-edge equilibrium. This contrasts, in the third section, with the fundamental stability of the system equilibrium associated with the supermultiplier equation set forth in Bortis (1997, chapter 4). Fourth, the multiplier in the business cycle is alluded to. The crucial role of autonomous variables in shaping the trend and the cycle is sketched in the fifth section. The following section presents two further types of the multiplier relation: the saving/investment multiplier associated with the internal employment mechanism and the foreign trade multiplier linked up with the external employment mechanism (Bortis, 1997, pp. 190–8). This is followed by some concluding remarks.

62  Bortis

A remark on method In these notes we deal uniquely with the pure theory of the multiplier, the multiplier principle or ‘the logical theory of the multiplier, which holds good, without time-lag, at all moments of time’ (Keynes, 1936/1973, p. 122). Hence we consider how the causal forces involved work in principle, independently of historical realisations. If there is involuntary unemployment, autonomous expenditures bring about a multiple of secondary expenditures and thus of output and employment. In contradistinction to the logical theory of the multiplier, there is the applied theory of the multiplier consisting of applications of the multiplier principle to some concrete situation set in historical time, picturing, for example, ‘the consequences of an expansion in the capital goods industries which take gradual effect, subject to time-lag and only after an interval’ (ibid.). The meaning of the two multiplier concepts can be seen most clearly by taking the extreme case where the expansion of employment in the capital-goods industries is so entirely unforeseen that in the first instance there is no increase whatever in the output of consumption goods. In this event the efforts of those newly employed in the capital-goods industries to consume a proportion of their increased incomes will raise the prices of consumption-goods until a temporary equilibrium between demand and supply has been brought about partly by the high prices causing a postponement of consumption, partly by a redistribution of income in favour of the saving classes as an effect of the increased profits resulting from the higher prices, and partly by the higher prices causing a depletion of stocks. So far as the balance is restored by a postponement of consumption there is a temporary reduction of the marginal propensity to consume, i.e. the multiplier itself, and in so far as there is a depletion of stocks, aggregate investment increases for the time being by less than the increment of investment in the capital-goods industries. . . As time goes on, however, the consumption goods industries adjust themselves to the new demand, so that when the deferred consumption is enjoyed, the marginal propensity to consume rises temporarily above its normal level, to compensate for the extent to which it previously fell below it, and eventually returns to its normal level; whilst the restoration of stocks to their previous figure causes the increment of aggregate investment to be temporarily greater than the increment of investment in the capital-goods industries. (ibid., pp. 123–4; emphasis added) Two features emerge from this passage. First, behavioural outcomes fluctuate around institutionalised normal levels of consumption and investment. This way of looking at things is grounded in Marshall’s Principles of Economics (1920/1930). Indeed, Book V, on normal demand and supply – hence on normal prices and quantities – represents the core of the Principles, implying that longperiod prices and quantities, which underlie medium- and short-period prices and quantities, are located in the present; in a way, ‘the long run is always there’, as

The multiplier relation  63 Pasinetti suggests (1981, p. 127, fn. 1). This is also the treatment of the long run contained in Bortis (1997, specifically pp. 204–20). Second, the applied theory of the multiplier, reflecting multiplier processes set in historical time, is necessarily very complex, whilst the logical or the pure theory of the multiplier, picturing how the relevant causal forces work in principle, is of striking simplicity. In the following, the logical theory of the multiplier is dealt with. Different aspects of employment reality are considered, such that various types of the logical multiplier, that is, of the multiplier principle, enter the scene. As has been suggested already, the pure theory of the multiplier is about how the relevant forces governing output and employment in a monetary production economy work in principle. This implies that the multiplier principle is independent of historical realisations of this relation. In general, principles are not reflections or even copies of real world situations. As such, principles are not theoretical explanations, starting from given premises, of economic phenomena, eventually leading to testable propositions. A set of principles represents the essential and fundamental elements constituting a phenomenon, with all the accidental elements left aside, and is, as such, a reconstruction or a re-creation of aspects of the real world – for example, the determination of employment levels in the case of the multiplier – by means of reason interacting with intuition, which, in the social and political sciences, is related to a vision of man and of society. In this way, principles illuminate phenomena from inside and contribute to the understanding of how, for example, the socioeconomic system essentially functions; moreover, principles represent a framework and a starting point for the elaboratation of scientific theories (on the significance of principles see also Bortis 2003a, pp. 411–15). Hence the pure theory of the multiplier states how levels of output and employment are governed, in principle, according to the Keynesian, post-Keynesian and classical-Keynesian visions, and represents, as such, an approach for coming to grips with the phenomenon of employment and involuntary or system-caused unemployment. 

Some historical remarks  The first representation of the multiplier principle was by François Quesnay in his fundamental zigzag tableau (le grand tableau ou tableau fondamental), set forth and commented on in Oncken (1902, pp. 386–402). From Quesnay’s grand tableau it beautifully emerges how the autonomous expenditures – consisting of land rents – of the landlords (the nobility and the king), amounting to two million pounds, set economic activity into motion, resulting in a social product of seven million pounds, five million being the value in money terms of agricultural products and two million of manufactures. Quesnay worries very much about the fact that the landlords might not spend the whole of the rent since this would disrupt the socioeconomic system because cumulative contractive processes would set in: output and rents would be reduced, the reduction of rent would cause a further decline of output and so on. System-caused or involuntary unemployment would result. Quesnay sees autonomous expenditures as a kind of engine which initiates

64  Bortis economic activity and where the social product is a multiple of rent expenditures. Besides setting up a simple and a very robust theory of output and employment, Quesnay deals, explicitly or implicitly, with other great problems of political economy. Production is conceived as a social and circular process, with commodities and money circulating in opposite directions. Implied in the grand tableau is a sociological, even a political, theory of distribution based upon the surplus principle. Fundamental prices are determined within production, and Quesnay explicitly mentions that these fundamental prices are known before goods come to the market, and that market prices deviate, as a rule, from the fundamental prices of production. Given this, François Quesnay may be considered the founder of political economy, which deals with the functioning of the socioeconomic – that is, institutional – system, in contradistinction to economics that considers behaviour of economic agents and its coordination by the institutional system or by the market (on political economy and economics, see Bortis, 1997, pp.  76–8, and Bortis, 1999). Indeed, Quesnay’s grand tableau and its implications already synthesise classical and Keynesian-type elements of analysis, which is the hallmark of various postKeynesian and classical Keynesian developments in political economy (see, for example, Arestis, 1992; Bortis, 1997 and 2003a; Lavoie 1992; and Lee, 1998). It is not surprising, therefore, that Piero Sraffa based his Production of Commodities by Means of Commodities upon Quesnay’s social and circular conception of the process of production (1960, p. 93). And Karl Marx termed Quesnay’s tableau the only stroke of genius produced by classical political economy (1905–10/1973, p. 319). While the multiplier principle is implicit in Quesnay’s grand tableau, explicit formulations of the multiplier principle were elaborated at the end of the nineteenth and at the beginning of the twentieth centuries mainly within the framework of the analysis of business cycles by Knut Wicksell, Alfred Aftalion, Irving Fisher, N. Johannsen and others, with Robert Malthus and Karl Marx as important predecessors (Schneider, 1965, pp. 178–8 and 199). Of particular interest is N. Johannsen, who elaborated the multiplier principle already in 1903 and took it up in a book published ten years later: Die Steuer der Zukunft. This book contains two sections explicitly related to the multiplier: ‘Das multiplizierende Prinzip’ (p. 232 ff.) and ‘Tragweite [Significance] des multiplizierenden Prinzips’ (p. 259 ff.) (cf. Schneider, 1965, p. 179). The theme of the multiplier was taken up definitively and systematically at the outset of the Great Depression in Richard Kahn’s ‘The Relation of Home Investment to Unemployment’, published in the Economic Journal (1931). This is the starting point of the fascinating – and perilous – story of the investment multiplier as it finally appeared in Keynes’s General Theory (Skidelsky, 1992, pp. 449–52): Kahn’s multiplier article . . . was an attempt to answer the three main objections to loan-financed public works as a remedy for unemployment: the mea-

The multiplier relation  65 greness of the employment produced; the budgetary burden entailed; and the crowding out of private borrowing. The inability of Keynes and Henderson to meet these objections . . . turned the balance of the argument against largescale public works under the Labour government and led to their cessation in the aftermath of the fiscal crisis of 1931. Hubert Henderson abandoned Keynes and sided with the Treasury. (ibid., p. 449) Kahn started work on the multiplier theory . . . in August 1930. [His] starting point was the Keynes–Henderson assertion . . . that a public works programme would provide primary employment (on the job and making materials for the job) and also secondary employment resulting from the newly employed spending their wages, but that these secondary effects were incalculable. As Kahn later said, ‘there was no obvious reason why the multiplier was not infinite’. (ibid.) Kahn eventually achieved his finite number by making two deductions (alleviations) from the enlarged expenditure stream: saving on the dole (that is, what the unemployed were already spending) and spending on imports.  .  . James Meade generalised the calculation by allowing the increased spending to be divided between raising output and raising the price of output. This would create a third leakage – ‘unspent profits minus any diminution in rate of saving due to rise in prices’. (ibid., p. 450) But the personal-saving or consumption function first came into the multiplier literature with an article by the Danish statistician Jens Warming in the Economic Journal of June 1932. . . Keynes probably saw Warming’s article when it was first submitted to the Economic Journal, of which he was a co-editor. [In fact,] he started to make use of a consumption function in the spring of 1932. So the theoretical influence may have run more directly form Warming to Keynes than from Kahn to Keynes at this point. Kahn, influenced in turn by Warming, presented a multiplier derived from marginal propensities to save and import in a paper on ‘Public Works and Inflation’ to the American Statistical Association in Cincinnati in December 1932; Keynes’ ‘The Means to Prosperity’, published three months later, presented this revised version of Kahn’s theory. (ibid., pp. 451–2) The Keynesian multiplier was born. In the light of this historical sketch based on Schneider and Skidelsky, is it fair and right to speak of the Keynesian multiplier? In fact, from the point of view of

66  Bortis the history of economic theory, the Keynesian multiplier is nothing new. Modern multiplier theory is, in fact, a reinvention, bearing in mind that the multiplier principle is implied in Quesnay’s grand tableau and was explicitly developed by N. Johannsen (cf. Schneider, 1965, pp. 179–81). Moreover, there exist countless empirical descriptions of multiplier processes; for example, in the mercantilist literature the cumulative effects of export surpluses on economic activity are put to the fore. It is also very likely that the rulers of the ancient empires in Egypt, Mesopotamia and Persia, as well as the rulers of Rome, were already clear about the very favourable effects of large-scale public works on economic life (handicrafts and trade) as well on the stabilising social effects, since entire societies were given gigantic social peace-time aims, as was the case, for example, with pyramid building – a point Keynes explicitly insists upon (1936/1973, pp. 130–1). Association of the multiplier relation with the name of Keynes is justified by the fact that this principle is part of a general theory of employment, interest and money. As such, the multiplier expresses the principle of effective demand, which can, in turn, easily be associated with classical elements of economic theory related to value and distribution based upon the surplus principle of distribution and the labour principle of value. In this way the multiplier becomes part of a wider framework of classical-Keynesian political economy encompassing a monetary theory of production (Bortis, 1997, 2003a), providing thus the starting point for erecting a classical-Keynesian alternative to the exchange-based neoclassical (Walrasian–Marshallian–Austrian) framework of analysis. In a way, a lot has been said about the multiplier before Keynes, but Keynes was the only one who integrated this principle into a comprehensive and coherent theoretical scheme capable of further elaboration and of integration into wider frameworks of analysis.

Kaldor’s two multipliers In his article on alternative theories of distribution, Nicholas Kaldor distinguishes between two different applications of the multiplier: ‘The principle of the Multiplier . . . could be alternatively applied to a determination of the relation between prices and wages, if the level of output and employment is taken as given, or the determination of the level of employment, if distribution (i.e. the relation between prices and wages) is taken as given’ (Kaldor, 1955–56/1980, p.  227; emphasis added). Kaldor goes on to say that ‘the reason why multiplier-analysis has not been developed as a distribution theory is precisely because it was invented for the purpose of an employment theory’ (ibid., pp. 227–8). And ‘yet these two uses of the multiplier principle are not as incompatible as would appear at first sight: the Keynesian technique, as I hope to show, can be used for both purposes, provided the one is conceived as a short-run theory and the other as a long-run theory – or rather, the one is used in the framework of a static model, and the other in the framework of a dynamic growth model’ (ibid., p. 228). Hence Kaldor conceives of the short-period multiplier theory as a ‘fixed price’ theory in which profit margins are fixed at normal capacity utilisation. The mar-

The multiplier relation  67 ginal propensity to consume and, as a consequence, the multiplier are assumed to be given. Moreover, capacities are underutilised in all sectors of production. As a consequence a macroeconomic equilibrium with planned saving equalling planned investment is reached through quantity adjustments. This appears from the conventional textbook presentation of the macroeconomic S = I equilibrium condition: I = S = –a + sY and Y = (1/s) (a + I)

(3.3)

In principle, if planned saving exceeds planned investment, the demand of households for consumption goods falls short of the supply of consumption goods by producers. Stocks pile up, i.e. involuntary investment occurs, to make investment instantaneously identical to saving. Given this, producers will offer less. Income and saving will decline until condition (3.3) is satisfied, and vice versa, if planned saving falls short of planned investment. With Kaldor’s long-period multiplier, however, employment is given and the long-period equilibrium between saving and investment in an economy growing at the natural rate of growth is secured through changes in income distribution (ibid., pp. 229–32). The macroeconomic equilibrium condition: I = S = sPP + sWW = sP P + sW (Y – P) = (sP – sW)P + sWY implies the double-sided relationship between investment and profits. On the one hand, with investment, output and employment given, saving adjusts to investment through changes in income distribution, that is, changes in the share of profits in income: (I/Y) = (sP – sW) P/Y) + sW

(3.4)

The inverse of the right-hand side of this relation represents the (flexible) longperiod investment multiplier linking investment to output growing at the natural rate of growth (the rate of growth of technical progress and of population). As will be suggested below, this flexible multiplier is also of crucial importance for picturing cyclical movements, in the course of which output (Y), investment (I) and the profit share (P/Y) are continuously changing due to the interaction of the income and of the capacity effect of investment (see Bortis, 1997, pp. 204–20). In fact, Kaldor’s long-period multiplier should be more appropriately conceived of as a medium-term multiplier which brings saving into line with investment in the course of the business cycle. On the other hand, income distribution – the profit share in income – is governed by the investment–output ratio and the propensities to save out of wages and profits: P/Y = [1/(sP – sW)] · (I/sP) – [sW/(sP – sW)]

(3.5)

68  Bortis The economic system is stable if the propensity to save from profits exceeds the propensity to save out of wages. Indeed, if saving falls short of investment – that is, if aggregate demand exceeds aggregate supply – prices and profits will rise relative to money wages to bring about the equilibrium depicted by relation (3.4), and, vice versa, with saving exceeding investment. However, with sP < sW, there would be persisting inflation: with saving falling short of investment, prices and profits would rise, the wages share of income would decline, and, consequently, the gap between saving and investment would widen, since the propensity to save out of wages is larger than that out of profits; contrariwise, with saving exceeding investment, there would be continuous deflation. In the limiting case where sW = 0, the amount of profits is equal to the sum of investment and capitalist consumption, i.e.: P = (1/sP)I

(3.5a)

This is the assumption implicit in Keynes’ parable about the widow’s curse – where a rise in entrepreneurial consumption raises their total profits by an identical amount – and of Mr. Kalecki’s theory of profits which can be paraphrased by saying that ‘capitalists earn what they spend, and workers spend what they earn.’ (Kaldor, 1955–56/1980, p. 230) From this it emerges that Kaldor’s short-period employment multiplier is the multiplier in the General Theory, and that his long-period ‘distribution multiplier’ is derived from Keynes’s Treatise on Money. The critical assumption is that the investment–output ratio is an independent variable. Following Harrod, we can describe the determinants of the investment–output ratio in terms of the rate of growth of output capacity (g [G in original]) and the capital–output ratio, v [a given technical coefficient]: I/Y = gv

(3.6)

In a state of continuous full employment [g] must be equal to the rate of growth of the ‘full employment ceiling’, i.e. the sum of the rate of technical progress and the growth in working population (Harrod’s ‘natural rate of growth’ [g´]). (ibid., p. 231) Since I/Y = s = S/Y, it emerges from relations (3.4) and (3.6) that saving adjusts to the investment required to bring about the warranted rate of growth (g) through changes in income distribution. ‘Hence the “warranted” [g] and the “natural” [g´] rates of growth are not independent from each other; if profit margins are flexible, the former will adjust to the latter through a consequential change in P/Y’

The multiplier relation  69 (ibid., p. 232). As a consequence, if restrictions on minimum wages and profits are satisfied (ibid., p.  233), ‘there will be an inherent tendency to growth and an inherent tendency to full employment. Indeed the two are closely linked to each other’ (ibid., p. 235). This optimistic conclusion was a reflection of the unprecedented upswing of the 1950s and 1960s, which was, presumably, due the presence of some important autonomous variables: the reconstruction after World War II, resource flows from developed to underdeveloped countries, armaments expenditures due to the Cold War, and the development and introduction of new technologies. Kaldor’s optimism on employment implied abandoning the General Theory to return to the Treatise on Money. However, from the early 1970s onwards Kaldor attempted to build a growth model that would imply that involuntary unemployment would adjust to the new employment situation following up the oil-price shock (Targetti, 1992, pp. 193–205).

The multiplier and inherent instability (Harrod and Domar)  The interplay of the income and the capacity effect of investment lies at the root of the instability of a capitalist economy evolving in historical time. Indeed, on the one hand, when factory buildings are erected and machines are constructed, primary and secondary incomes are created through the multiplier mechanism (relation 3.2), implying that the demand for consumption goods increases. On the other hand, while the process of producing the capital goods in question is going on, no additional supply is yet forthcoming. However, when the factories stand and the machines are put to productive use, supply increases but effective demand declines because fewer workers are required in the investment goods sectors once the construction of the capital goods referred to is terminated. Investment must increase so as to bring about additional effective demand through the multiplier mechanism. This is the basic idea implied in the so-called Harrod–Domar growth model (Harrod, 1939/1970; Domar, 1946/1973). Domar’s emphasis was on the conditions of the dynamic growth equilibrium, Harrod’s on the instability of this equilibrium. With Domar (1946/1973), the starting point is the equilibrium between macroeconomic supply Q and macroeconomic demand Y in some period of time 0, governed by the income effect of investment, exhibited by the multiplier relation: Q0 = Y0 = (1/s)I0

(3.7)

In period 1 output increases because of the capacity effect of investment: ∆Q = Q1 – Q0 = (1/v*)I0

(3.8)

where 1/v* is the technically given output–capital ratio (Q/K), the inverse of the capital–output ratio put to use in the preceding section.

70  Bortis Effective demand based upon the multiplier effect only increases if investment rises: ∆Y = Y1 – Y0 = (1/s)∆I*

(3.9)

where (∆I* = I1 – I0). Combining relations (3.8) and (3.9) yields Domar’s condition for the dynamic growth equilibrium: g* = ∆I*/I0 = s/v*

(3.10)

where g* is Domar’s equilibrium growth rate (Harrod’s warranted rate of growth) of investment, output and capital. Domar’s growth equilibrium exhibited by condition (3.10) is inherently unstable. Indeed, if ∆I < ∆I*, then the realised growth rate g falls below the warranted rate g*. From (3.8) and (3.9) it emerges that now ∆Q  >  ∆Y, that is, additional effective demand (∆Y) is not high enough to absorb the additional output (∆Q). The reason is that entrepreneurs have not invested enough (relation 3.9) to create the effective demand required to absorb the additional output (relation 3.8). This leads to what has been dubbed the Harrod Paradox: if the realised rate of growth (g): g = ∆I/I0 = s/v

(3.10a)

falls short of the warranted (equilibrium) rate of growth (g*) as exhibited by relation (3.10), entrepreneurs have, paradoxically, not invested enough to create sufficient effective demand. This paradox has been derived by Harrod (1939/1973) in a slightly different way. Harrod starts from the Keynesian macroeconomic equilibrium condition of saving (S = sQ) equalling investment (I* = v*∆Q): I* = v*∆Q = sQ = S

(3.11)

To recap, v* is the technically given marginal capital–output ratio. As a consequence, the warranted (equilibrium) rate of growth of output (g*) is given by: g* = ∆Q/Q = s/v*

(3.12)

If entrepreneurs invest too little (I < I*), the realised rate of growth of output falls short of the warranted rate (g < g*). However, entrepreneurs think they have invested too much since (1/s)I  <  Q, i.e. effective demand, (1/s)I, falls short of output produced (Q). A provisional equilibrium will be restored through v rising above v*: g = s/v

(3.12a)

The multiplier relation  71 The realised capital–output ratio v now exceeds the technically required capital–output ratio v*, because stocks pile up due to a lack of effective demand. Given this, entrepreneurs will reduce investment, which means that the gap between g* and g widens even more. On the other hand, if g > g* we have v < v*, i.e. stocks are run down because entrepreneurs have invested too much and have, as a consequence, created too much effective demand [(1/s)I > Q]. Paradoxically, however, they think, that they have not invested enough and now invest even more. Again the gap between g and g* widens. Hence the equilibrium defined by relations (3.11) and (3.12) is an equilibrium on the ‘razor’s edge’ – the economic system is completely unstable. This is due to the fact that there are macroeconomic laws (the paradox of thrift) that stand in contradiction to the rationality of individuals. As a consequence the rational behaviour of the individuals is coordinated in an inappropriate way by the system. The ‘rationality’ of the system is different from the ‘rationality’ of individual producers. Subsequently, Harrod has shown that the instability of the system is reduced if there are autonomous investments. Some outlays of capital have no direct relation to the current increase of output. They may be related to a prospective long-period increase of activity, and be but slightly influenced, if at all, by the current increase in trade. Or they may be induced by new inventions calculated to cheapen production or change consumers’ modes of spending their income, so that they are not related to increments of output, but are designed to revolutionise the methods for producing some portion of already existing output or to substitute one line of goods for another in the consumers’ budget. (Harrod, 1939/1970, p. 57) If the income share of autonomous expenditures of some kind, including export surpluses, is denoted by a, Harrod’s S = I condition (relation (3.11)) and his equation for the warranted rate of growth (relation (3.12)) becomes: I = aQ + v*∆Q = sQ

(3.11a)

and g* = ∆Q*/Q = (s – a)/v*

(3.13)

It must be noticed that [v* and v] now stand not for the total increase of capital [desired and actual, respectively] per unit increment of output, but only for the net increase of capital after the capital represented by [a] has been subtracted. (ibid., p. 58) Relation (3.13) corresponds to the modified Domar growth formula:

72  Bortis g* = ∆I*/I0 = (s – a)/v*

(3.10b)

The modified growth relations (3.10b) and (3.13) show that the warranted rate of growth (g*) is reduced once autonomous expenditures are introduced, implying that the economic system becomes more stable. Less investment and output growth is required to set an economy – temporarily – on a cumulative growth path in the direction of full employment. The Harrod–Domar model of the long-period instability of capitalism has subsequently given rise to developing a host of multiplier–accelerator models. This development has culminated in Hicks’s theory of the trade cycle (Hicks, 1950).

Institutions and the system: the supermultiplier trend Since the capital stock is given in the short run, the short-period multiplier is about capacity utilisation. If capacities are sufficiently large, full employment may eventually be reached through the income effect of investment (relations 3.2 and 3.3 above). However, the problem of providing that new capital investment shall always outrun capital-disinvestment sufficiently to fill the gap between net income and consumption presents a problem which is increasingly difficult as capital increases. New capital investment can only take place in excess of current capital-disinvestment if future expenditure on consumption is expected to increase. Each time we secure today’s equilibrium by increased investment we are aggravating the difficulty of securing equilibrium tomorrow. A diminished propensity to consume today can only be accommodated to the public advantage if an increased propensity to consume today is expected to exist some day. (Keynes 1936/1973, p. 105) This passage raises the problem of the relationship between capacity and income in the medium and in the long term, which is intimately related to the issues of the trend and of the cycle. The present section deals with the multiplier in a long-term context (the trend); the next will be devoted to the medium term (the cycle). The relationship between trend and cycle has been dealt with extensively by Michal Kalecki (1971, specifically pp. 165–83). He remarks on this issue: The contemporary theory of growth of capitalist economies tends to consider this problem in terms of a moving equilibrium rather than adopting an approach similar to that of applied in the theory of business cycles.  .  . I do not see why this approach should be abolished in the face of the problem of long-run growth. In fact, the long-run trend is but a slowly changing component of a chain of short-period situations; it has no independent entity, and the [basic theoretical relations regarding effective demand and investment]

The multiplier relation  73 should be formulated in such a way as to yield the trend cum business-cycle phenomenon. (ibid., p. 165) This is not the way we want to take, however. We would agree with Garegani that ‘we must [attempt to] explain why an economy may [fluctuate] around [a trend implying 5 per cent of permanent – long-period – unemployment] rather than [a trend implying 20 per cent of permanent unemployment], i.e. we must aim at a long-period theory of aggregate output’ (1983, p. 78). The trend having been explained, a theory of cyclical fluctuations must be elaborated and combined with trend theory. There is, however, a problem here:  The situation is that, on the one hand, the macro-economic models which provide a cyclical interpretation of economic activity cannot give any explanation of economic growth and, on the other hand, those theories which define, or rely on the conditions for a dynamic equilibrium to be reached and maintained cannot give an explanation of business cycles. From a theoretical point of view, the situation would not be so unsatisfactory if the two phenomena – which yet are so obviously interconnected in their real manifestations could be explained by two different theoretical models to be combined and integrated. (Pasinetti, 1960/1974, p. 69) In our view, this is what has to be done. The long-period trend model must be different from the model picturing cycles. The trend model pictures uniquely the functioning of the system, i.e. the interplay of institutions, and is associated with fully adjusted situations; the [cycle model] deals with aggregate behavioural outcomes, e.g. aggregate investment and consumption behaviour, co-ordinated by parts of the system, i.e. the law of effective demand. The two models thus deal with different aspects of socioeconomic reality; they are complementary and can thus be combined and integrated. (Bortis, 1997, p. 136) This is, however, possible on the level of principles only; in the real world, the institutional trend and cyclical fluctuations interact; for example, gross investment, associated with fluctuations, gradually modifies the fully adjusted capital stock associated with the trend. Trend or long-period output Q* and employment N* are determined by effective demand components, all of which are governed by institutions and technology, that is, the economic basis upon which sociopolitical and cultural institutions may be erected (Bortis, 1997, chapters 3 and 4). Institutions and technology represent the constant or slowly evolving factors the classical political economists had in mind when they attempted to understand the nature of economic phenomena.

74  Bortis The autonomous variables, government expenditures (G) and exports (X), set economic activity into motion giving rise to derived demand, that is, consumption and investment, with part of the income leaking abroad through imports. The autonomous variables are linked with equilibrium output and employment through the supermultiplier (Bortis, 1997, pp. 142–54, and Bortis, 2003a, pp. 461–7). Q* =

G+ X zs 1 − (1 / k )  + π ( b1 + b2 ) − ( g + d )v



(3.14)

where zs = 1 – cs = ss + ts

(3.14a)

The normal prices and quantities associated with trend output and employment represent a hidden system equilibrium which cannot be directly observed. In fact, the system equilibrium is superseded by cyclical movements and by the vagaries of the market (Bortis, 1997, pp. 81–9 and 103–17).  Q* is trend or long-period gross domestic product; the star indicates that all the magnitudes on the right-hand side represent effective demand components associated with institutions and with the conditions of production (ibid., pp. 199–204). For example, normal government expenditures (G) are determined by legal prescriptions, exports (X) depend, among other factors, on the quality of the education system, research and development activity leading to the production of new products and high-quality standards for existing products, and the ‘exportmindedness’ of the entrepreneurs. The trend rate of growth of output and employment (g) is determined by the rate of growth of the autonomous variables; d is the replacement coefficient and v the capital–output ratio; hence (g + d)v represents the gross-investment–output ratio. The trend or long-period investment volume [I* = (g + d)vQ*] is thus derived demand, depending upon the long-period growth of output. The terms of trade are �; b1 is the fraction of output required to buy the imports necessary in the social process of production, and b2 the fraction of income spent upon non-necessary goods associated with consumption. 1 – (1/k) is the share of property income – in fact, the social surplus – comprising profits, land rents and labour rents associated with special abilities and with privileges of some kind. Finally, zs is the leakage out of property income (definition 3.14a), hence zs[1 – (1/k)] is the leakage out of domestic income which is negatively associated with output and employment. The leakage out of income increases when income distribution becomes more unequal, that is, if the property share 1 – (1/k) increases and if property income is itself unequally distributed. The latter implies that the leakage out of property income (zs = 1 – cs = ss + ts) is large because more is saved if property income is unequally distributed. The negative association between unequal distribution and the level of output and employment is the crucial feature of the supermultiplier relation. The leakage coefficient zs (3.14a) indicates the fraction of the surplus over ordinary wages which is not consumed, the fraction consumed being cs. Consequently,

The multiplier relation  75 the leakage coefficient is the sum of the fractions of the surplus paid for taxes (ts) and saved (ss). Since the long-period consumption coefficient (cs) and the longperiod tax coefficient (ts) are both determined by institutions – consumption habits and tax laws – ‘the long-period saving propensity ss is a pure residual varying with the normal or trend level of output and employment’ (Bortis, 1997, pp. 166–8). This is analogous to Keynes’s short-period theory of output determination. Saving being a pure residual means that the process of adjustment to the longperiod equilibrium is, in principle, based upon quantity adjustments; moreover, the economic system is stable (see on this Bortis, 1998, pp. 25–9). This can be seen immediately from the supermultiplier relation: if long-period output is below Q* the realised rate of profits (r), the mark-up (k) and the property share [1 – (1/k)] all exceed their institutionalised normal levels. Given this, investment, output and employment will, in principle, rise until the trend level is reached, and vice versa if output and employment are above the trend level. The stable system equilibrium pictured by the supermultiplier implies that output capacities have adjusted to long-period effective demand. The system equilibrium is stable because of the institutionally governed autonomous demand components, normal government expenditures (G) and normal exports (X), which are, in principle, independent of the level of economic activity and set the economic system into motion; output and employment increase until macroeconomic equilibrium (S = I) is achieved. In this process saving is entirely passive and adjusts with changes in the level of output and employment (Bortis, 1997, pp. 166–8). Harrod’s knife-edge equilibrium, however, is entirely unstable because the autonomous variable initiating income and output creation, such as investment, is a potentially highly volatile magnitude depending upon the behaviour of investors. Moreover, since the average and marginal propensity to saving is fixed and the income effect of investment is much stronger than the capacity effect, there is no mechanism to bring into line planned saving and planned investment. Hence in the long term only the capacity effect of investment is relevant, with capacities adjusting to long-period effective demand. However, in the short term only the income effect of investment is relevant, since capacities are given. We now turn to the medium term, where the income and the capacity effect of investment interact.

Behaviour and its coordination by the system: the business cycle The supermultiplier can also be used to picture cyclical movements around the long-period trend whereby the mechanism of the cycle rests upon an interaction between the income and the capacity effect of investment (Bortis, 1997, pp. 204–20). Cyclical movements occur because an economy is never in a system equilibrium as is pictured by relation (3.14) above. Entrepreneurs, when investing in the past, could not know what the normal prices and quantities would be in the present. Formally, the supermultiplier relation remains the same if all the variables are governed by the behaviour of the various actors (on the relation between systemgoverned and behaviourally determined magnitudes, see ibid., pp. 81–9):

76  Bortis Q=

G+ X  zs 1 − (1 / k )  + π ( b1 + b2 ) − ( g + d )v

(3.15)

However, all the independent variables on the right hand of relation (3.15) now – temporarily – deviate from the institutionally governed variables and parameters of relation (3.14). In particular, this is true of the investment–output ratio [(g + d) v] and of the property share [1 – (1/k)], and hence of prices and profits. This gives rise to the double-sided relationship between profits and investment or between the rate of profits and the rate of growth put to the fore by the post-Keynesians (for example Kaldor, 1955–56/1980; Robinson, 1962, p. 48), and classical-Keynesians like Kalecki (1971). The mutual relationship between investment and profits represents the income effect of investment which interacts with the capacity effect of investment to produce the business cycle (see, for example, Bortis, 1997, pp. 207–14). Indeed, if appropriately interpreted, the Kaldorian relation (3.4) above could be used in place of the supermultiplier relation (3.15) above.  On the basis of relations (3.14) and (3.15) the mechanism of the cycle can be broadly sketched: if the behaviourally determined realised output (Q) is below the trend output (Q*), then the realised rate of profits (r) and the realised property share [1 – (1/k)] will rise above their respective system-governed trend or normal levels. As a consequence, the realised rate of growth (g) and the realised level of investment (I) will rise above the corresponding trend levels (g* and I*). Expanding investment levels and growth rates will, in turn, lead to higher profit rates and larger investment volumes. With high investment volumes the capacity effect of investment will gradually work out ever stronger. Realised output (Q) will increase fast and rise above trend output (Q*). With real output growing faster than trend effective demand, the capacity effect of investment will gradually exert a pressure on realised profits and hence the property share, as is evident from relation (3.15). This downward pressure on profits will become stronger with rapidly increasing productive capacities and output and employment levels and will compensate gradually for the upward pressure on profits exerted by rising growth rates and investment levels on the basis of the income effect of investment. Once realised profits fall below desired profits a downward movement sets in. The growth rate and the volume of investment recede. This will induce a decline of profit due to the income effect. However, the pressure exercised on profits due to the fact that capacity output is now well above trend effective demand will be much stronger. There are now overcapacities and, consequently, unused capacities will appear; profits now diminish rapidly, and investment and output will grow at a rate below the trend growth rate or will even decline. Hence, in the course of the cycle, the supermultiplier (3.15) combines Kaldor’s two multipliers. Indeed, relation (3.15) simultaneously captures quantity changes at a given distribution and changes in distribution with given quantities.

The multiplier relation  77

The role of autonomous variables in the medium-term and long-term cycles Temporary deviations of autonomous variables from their institutionally governed long-period levels will modify the course of the medium-term cycle sketched above. For example, due to exceptional circumstances, a natural calamity say, government expenditures (G) in relation (3.15) may temporarily exceed the institutionally governed (G*) of relation (3.14). It is likely that prices and quantities and, consequently, profits will increase, widening thus the amplitude of the cycle. The position of the long-period trend may be modified if important additions to the autonomous variables G and X occur for longer periods of time, for example socially necessary autonomous expenditures (B) in relation (3.16) below. Infrastructure projects, substantial improvements in the social security system or spurts in research and development expenditures, or permanent expenditures for cultural purposes, such as sports, might be cases in point:   Q* =

B+G+ X    zs 1 − (1 / k )  + π ( b1 + b2 ) − ( g + d )v

(3.16)

Contrary to productive trend investment – I* = (g + d)vQ* in this relation – the capacity effect of autonomous investment is nil or negligible. However, there will be a considerable income effect. The additional autonomous expenditure (B*) will give rise to derived demand. Consumption demand will increase, whereby the rise in demand will be stronger if the property share – 1 – (1/k) in relation (3.16) – is relatively low and property incomes equally distributed. The latter implies that zS  =  1  –  cS will be low due to a larger propensity to consume out of property income. Investment demand [(g + d)vQ in (3.16)] will increase for two reasons. First, there will be an increase in trend investment because of the shift of the trend caused by B and because of an eventually higher trend rate of growth (g). B may also grow for some time; both will raise net investment. Second, investment will increase because, on the traverse to a higher trend, the growth rate and the corresponding investment volume will rise above the corresponding trend magnitudes. This may initiate and modify medium-term cycles based upon the interaction between profits and investment, that is, the income effect of investment. On account of the capacity effect of investment output may rise well above trend output. This gradually depresses profits. The pressure on profits will intensify once B gradually peters out. The downswing now ensuing will be the more violent the larger are the overcapacities that have been built up in the upswing – that is, the more that realised output Q has risen above trend output Q*. This very rough theoretical sketch might be used to illustrate the fruitfulness of the multiplier principle in providing tentative starting points to explain events of economic history. The above sketch might, for example, be taken as a provisional starting point to explain the extraordinary upswing that took place in

78  Bortis Western Europe between the late 1840s and the early 1870s (Hobsbawm, 1975) due to the massive extension of the railway network, and the great depression that followed from the early 1870s to the mid-1890s. The temporary increase in autonomous expenditures – B in relation (3.16) above – would stand for the massive temporary increase in autonomous demand occasioned by the building up of the railway structure. The impact on economic activity is likely to be very strong because there is an income effect of investment only, and the capacity effect is negligible. Railways and roads do not result in much direct output but provide the foundations – the infrastructure – for increased production. The impact on economic activity of autonomous expenditures is strong because the income effect is much more important than its eventual capacity effect. As such autonomous expenditures stand in direct opposition to productive investment which is directed towards increasing output through the capacity effect. Keynes is very explicit on the difference between various kinds of autonomous expenditures – railways may enhance production in the long run, monuments of some kind lead to expenditures only – and productive investment: Since the value of a house depends upon its utility, every house which is built serves to diminish the prospective rents obtainable from further housebuilding and therefore lessens the attraction of further similar investment. But the fruits of gold-mining do not suffer from this disadvantage. Ancient Egypt was doubly fortunate . . . in that it possessed two activities, namely, pyramid-building as well as the search for the precious metals, the fruits of which, since they could not serve the needs of man by being consumed, did not stale with abundance. The Middle Ages built cathedrals and sang dirges. Two pyramids, two masses for the dead, are twice as good as one; but not so two railways from London to York [and even less two additional textile factories]. (Keynes, 1936/1973, pp. 130–1) And among cynics it is well known that – in the short-term at least – wars are most efficient in employment creation. War expenditures do not result in consumable output but, on the contrary, occasion destruction which, in turn, requires expenditures devoted to reconstruction.

Two further types of the multiplier The supermultiplier – equations (3.14) and (3.15) above – contains two basically different variants of the multiplier relation. The first is based upon the equality of saving and investment which represents the fundamental (internal) macroeconomic equilibrium condition; the second emerges from the foreign balance, that is, the balance on current account, which is associated with external equilibrium. Both variants of the multiplier principle are associated with a particular mechanism of employment determination: the internal and the external mechanism respectively.

The multiplier relation  79 Each mechanism represents an alternative way of determining, in principle, longperiod employment and output (see Bortis, 1997, pp. 190–8). Again, the two multipliers considered here are Nicholas Kaldor’s (1989). The long-period ‘internal’ multiplier is analogous to the Keynesian multiplier, the simplest form of which is given by relation (3.2) above (pp. 90–1). With the second variant of the multiplier, that is the ‘foreign trade multiplier’[,] exogenously given exports . . . together with the propensity to import which is assumed to be a simple function of income . . . determine the equilibrium level of output at the point at which exports and imports are equal . . . which can be expressed, in terms analogous to the Keynesian model as [equilibrium output equals the inverse of the propensity to import times exports]. This is more likely to provide the critical constraint when we consider the problem, not in the context of a short-period static equilibrium, but of the equilibrium of an economy in a steady state of growth . . . Under these conditions investment must be treated as an endogenous [our emphasis; this postulate necessarily underlies the whole of long-period supermultiplier analysis] factor, depending on the rate of change of demand (on the so-called ‘accelerator’ principle). (ibid., pp. 91–2) From the supermultiplier relation (equation (3.14) above) we can directly derive the ‘internal’ multiplier based upon the macroeconomic equilibrium condition ‘saving equals investment’ (Bortis, 1997, p. 190) by postulating an equilibrium in the foreign balance: Qi* =

G zs 1 − (1 / k )  − ( g + d )v



(3.17)

Let us recall here that the first term in the denominator of this relation stands for the leakage out of total income (z = 1 – c = s + t), where, in long-period analysis, the propensity to consume and the tax rate (t) are both institutionally determined, with the saving ratio being a pure residual. Since, in macroeconomic equilibrium, s equals the investment–output ratio [(g + d)v], the multiplier in (3.17) equals (1/t). Hence, investment being derived demand in the long run, output and employment depend, in principle, upon the relation between government expenditures (G) and leakage (z). The latter is, in turn, dependent upon income distribution: in a postKeynesian vein, s increases if the distribution of income becomes more unequal. Again, the negative association between unequal distribution and employment constitutes the crucial feature of the long-period ‘saving equals investment’ or ‘internal’ multiplier. The ‘foreign trade multiplier’ picturing the ‘external’ employment mechanism obtains from the foreign balance equilibrium contained in the supermultiplier relation (3.14):

80  Bortis Qe* =

X  π ( b1 + b2 )

(3.18)

In principle, output and employment are larger the higher the export volume, the lower the import dependence exhibited by the import coefficients and the more favourable the terms of trade are (a low π indicates favourable terms of trade). The effect of foreign trade upon output and employment will be particularly strong if exports mainly consist of labour-intensive high-quality manufactures and imports of land-intensive primary products and standard manufactured goods in the main. Cases in point are Germany, Japan, Switzerland and Taiwan. For example: Japan’s exceptionally high growth rate [in the time period 1953–76] was due both to her exceptional success as an exporter, with her export volume rising at 16 percent a year, and her exceptionally low income elasticity of demand for imports (which was no doubt assisted by various forms of ‘invisible restraints’ on the import of manufactures). (Kaldor, 1989, p. 93, fn. 6) The internal employment mechanism is extremely difficult to handle from a political point of view. In the first place, each society must find an appropriate balance between state activity, the non-profit sector and the private sector. Given this, long-period employment policy primarily becomes distribution or incomes policy: a more equal distribution is, in principle, associated with higher output and employment levels. This is perhaps the basic tenet of Keynes’s General Theory. It is well known that incomes policies are difficult to handle. Moreover, a stimulation of domestic demand may lead to difficulties regarding the foreign balance in that import surpluses may occur.  Given this, most countries seem to rely at present upon the external employment mechanism. To become or remain a successful exporter, each country or region attempts to attract firms which produce on its territory and export most of the production. This implies offering favourable conditions to such firms, such as a well-trained labour force, but not very high wages; a good infrastructure and a high-level education system, but not high taxes; a performing social security system with only modest contributions to social security institutions; and certainly no incomes policy and not too much protection of the natural environment. Most importantly, state expenditures and the general level of taxation are to be reduced through privatisation. For these reasons, state activity, including expenditures for social security, has presumable stagnated in the last twenty years or so or even diminished at the world level, and income distribution has, according to all statistics, become more unequal. Since world economic activity is governed by the internal mechanism (relation (3.17) above), this is likely to restrain world economic activity, as the ultimate sources of world effective demand – private and public consumption – have stagnated or, perhaps, even declined in recent years. This is bound to result in very high levels of involuntary unemployment and underemployment worldwide, which does now affect about 30 per cent of the world la-

The multiplier relation  81 bour force, according to eminent international organisations. This does not mean, however, that all countries in the world are in a bad socioeconomic situation. The successful exporters – above all, those who manage to export high-quality, labour-intensive manufactured goods and services with a large value added and to import land-intensive primary products (agricultural goods, raw materials, goods related to energy, such as oil) and standard manufactures – will enjoy a favourable employment situation, and vice versa. The employment situation is likely to become particularly dramatic if foreign exchange shortages occur because of capital flights and high levels of debt service. There is thus an inherent contradiction between the internal and the external employment mechanism on the world level. It would seem that this contradiction is, partly at least, at the origin of the deteriorating employment situation worldwide, accompanied by growing inequalities between countries, regions, social groups and individuals. This is perhaps the main tenet that emerges from Nicholas Kaldor’s later work, specifically Kaldor (1985), which led to increasing emphasis on cumulative destabilising processes due to increasing returns to scale and upon the interaction of the domestic and the foreign trade multiplier on a world level, as just pictured.

Conclusions The multiplier in its various shapes, some of which have been mentioned in these notes, is the natural theory of employment in a monetary production economy. Here, only the pure theory of the multiplier, the multiplier principle, has been sketched. This means picturing the relevant causal forces in their pure form, independently of historical realisations. In a few illuminating pages, Keynes brought into the open the basic difference between the logical (pure) and the applied theory of the multiplier (Keynes 1936/1973, pp.  122–5). In the real world the working of the multiplier may be most tortuous: there may be temporary bottlenecks or temporary increases of leakages; the appropriate labour force may not be available; with persistent unemployment it is the weaker and the less qualified who are squeezed out of the production system; on the other hand, many work places are occupied by overqualified or not appropriately qualified people. All this may hamper the smooth functioning of the applied multiplier. However, these real world difficulties are not a relevant critique of the pure theory of the multiplier – they represent very complex problems which arise in any case, and which one must attempt to solve approximately if the employment situation is to be improved. First and fundamentally, the discussion must take place on the level of principles. As a consequence, the counterpart to the multiplier principle is the (pure) neoclassical employment theory, that is, the labour market model, in a partial or general equilibrium setting. It has been suggested above that for theoretical and empirical-historical reasons, the multiplier model, that is, the Keynesian, post-Keynesian and classical-Keynesian theories of employment and involuntary unemployment, is probably – in the sense of Keynes (1921/1973) – superior to the neoclassical theory of employment and output, including the output and employment model proposed by the neoclassical synthesis, that is, the IS–LM diagram. It

82  Bortis would indeed seem that the post-Keynesian elaboration of Keynes in the direction of a synthesis between Keynes and the classical economists is far more efficient at coming to grips with real world phenomena than is the market equilibrium setting of neoclassical, neo-Keynesian and IS–LM models (Arestis, 1992; Bortis, 1997, 2003a, Lavoie 1992; Lee, 1998). The classical-Keynesian approach in political economy also allows us to establish links with modern industrial and managerial economics where the social process of production, technical change, cooperation and business organisation are put to the fore, while the market plays a secondary role. William Lazonick’s (1991) Business Organization and the Myth of the Market Economy is highly revealing in this respect. Finally, in Bortis (1997) it has been suggested that classical-Keynesian political economy may easily be linked to other social sciences (sociology, law, politics), including social philosophy and social ethics. The multiplier principle in its various shapes constitutes a most powerful theoretical tool (in Marshall’s sense) for explaining employment levels in the short, medium and long term as well as system-caused involuntary unemployment, and provides a solid conceptual basis on which to formulate employment policies. The multiplier, embodying the principle of effective demand, emerges, then, as the natural tool for dealing with employment and involuntary unemployment in a monetary production economy where we have circuits of goods and of money. In dealing with the scale aspect of classical-Keynesian political economy (Bortis, 2003a, p. 461 ff.), the multiplier governs, in principle, the breadth of the flow of money and goods.

Acknowledgement I am greatly indebted to Claude Gnos, Geoffrey Harcourt, Louis-Philippe Rochon and Sergio Rossi for very helpful comments, with all responsibility remaining mine.

References Arestis, P. (1992), The Post Keynesian Approach to Economics, Aldershot: Edward Elgar. Bortis, H. (1997), Institutions, Behaviour and Economic Theory – A Contribution to Classical-Keynesian Political Economy, Cambridge: Cambridge University Press. Bortis, H. (1998), ‘A Note on Keynesian Long-Period Theory’, History of Economic Ideas, 6 (3), pp. 8–33. Bortis, H. (1999), ‘Political Economy, Economics, and Social Science’, in Shri Bhagwan Dahiya (ed.), The Current State of Economic Science, Vol. 1, Rohtak: Spellbound Publications, pp. 17–42 Bortis, H. (2003a), ‘Keynes and the Classics – Notes on the Monetary Theory of Production’, in L.-P. Rochon and S. Rossi (eds), Modern Theories of Money, Cheltenham: Edward Elgar. Bortis, H. (2003b), ‘Marshall, the Keynesian Revolution, and Sraffa’s Significance: A Review of 50 Years a Keynesian and Other Essays and Selected Essays on Economic Policy’, Journal of Economic Studies, 30 (1), pp. 77–97.

The multiplier relation  83 Domar, E. (1946/1973), ‘Capital Expansion, Rate of Growth and Employment’, Econometrica, 14, pp. 137–47. Reprinted in A. Sen (ed.), Growth Economics, Harmondsworth: Penguin, pp. 65–77. Fitzgibbons, A. (1988), Keynes’s Vision: A New Political Economy, Oxford: Clarendon Press. Garegnani, P. (1983), ‘Two Routes to Effective Demand: Comment on Kregel’, in J. Kregel (ed.), Distribution, Effective Demand and International Economic Relations, London: Macmillan. Harcourt, G. C. (1972), Some Cambridge Controversies in the Theory of Capital, Cambridge: Cambridge University Press. Harrod, R. F. (1939/1970), ‘An Essay in Dynamic Theory’, Economic Journal, 49, pp. 43–64. Reprinted in A. Sen (ed.), Growth Economics, Harmondsworth: Penguin, pp. 43–64. Hicks, J. R. (1937/1982), ‘Mr. Keynes and the ‘Classics’: A Suggested Interpretation’, Econometrica, 5, pp. 147–59. Reprinted in J. R. Hicks (ed.), Money, Interest and Wages: Collected Essays on Economic Theory, Vol. 2, Oxford: Basil Blackwell, pp. 100–15. Hicks, J. R. (1950), A Contribution to the Theory of the Trade Cycle. Oxford: Oxford University Press. Hobsbawm, E. (1975), The Age of Capital, London: Weidenfeld & Nicolson. Johannsen, N. (1913), Die Steuer der Zukunft und ihre Einwirkung auf geschäftliche Depressionen und volkswirtschaftliche Verhältnisse, Berlin: Puttkammer & Mühlbrecht. Kahn, R. (1931), ‘The Relation of Home Investment to Unemployment’, Economic Journal, June, 41, pp. 173–98. Kaldor, N. (1955–56/1980), ‘Alternative Theories of Distribution’, in N. Kaldor, Essays on Value and Distribution, 2nd edition, London: Duckworth. Originally published in 1955–56. Kaldor, N. (1985), Economics without Equilibrium, Armonk, NY: M. E. Sharpe. Kaldor, N. (1989), ‘The Role of Effective Demand in the Short Run and the Long Run’, in F. Targetti and A. P. Thirlwall (eds), Collected Economic Essays, Vol. 9: Further Essays on Economic Theory and Policy, London: Duckworth, pp. 90–9. Kalecki, M. (1971), Selected Essays on the Dynamics of the Capitalist Economy, Cambridge: Cambridge University Press. Keynes, J. M. (1921/1973), A Treatise on Probability, London: Macmillan. Keynes, J. M. (1930/1971), A Treatise on Money; Vol. I: The Pure Theory of Money, and Vol. II: The Applied Theory of Money, London: Macmillan. Keynes, Maynard (1936/1973), The General Theory of Employment, Interest and Money, London: Macmillan. Lavoie, M. (1992), Foundations of Post Keynesian Economic Analysis, Aldershot: Edward Elgar. Lazonick, W. (1991), Business Organization and the Myth of the Market Economy, Cambridge: Cambridge University Press. Lee, F. (1998), Post Keynesian Price Theory, Cambridge: Cambridge University Press. Marshall, A. (1920/1930), Principles of Economics, 8th edition, London: Macmillan. Marx, K. (1867–94/1973–74), Das Kapital, 3 vols, Berlin: Dietz. Marx, K. (1905–10/1973), Theorien über den Mehrwert, Erster Teil (Band 26.1 der Marx/ Engels–Werke), Berlin: Dietz. Mini, P. (1991), Keynes, Bloomsbury and the General Theory, London: Macmillan. O’Donnell, R.M. (1989), Keynes: Philosophy, Economics and Politics – The Philosophical Foundations of Keynes’s Thought and Their Influence on his Economics and Politics, London: Macmillan.

84  Bortis Oncken, A. (1902), Geschichte der Nationalökonomie, Vol. I, Leipzig: Hirschfeld. Pasinetti, L. L. (1960), ‘Cyclical Fluctuations and Economic Growth’, Oxford Economic Papers, new series, Vol. 12, pp. 215–41. Reprinted in: Growth and Income Distribution – Essays in Economic Theory. Cambridge: Cambridge University Press, 1974, pp. 54–85. Robinson, J. (1962), Essays in the Theory of Economic Growth. London: Macmillan. Schneider, E. (1965), Einführung in die Wirtschaftstheorie, Band III: Geld, Kredit, Volkseinkommen und Beschäftigung, Tübingen: J.C.B. Mohr (Paul Siebeck). Skidelsky, R. (1992), John Maynard Keynes, Volume Two: The Economist As Saviour – 1920–1937. London: Macmillan. Sraffa, P. (1960), Production of Commodities by Means of Commodities, Cambridge: Cambridge University Press. Targetti, F. (1992), Nicholas Kaldor – the Economics and Politics of Capitalism as a Dynamic System. Oxford: Clarendon Press.

Part II

Some critical insights on the multiplier

4 The investment multiplier and income saving Xavier Bradley

During the period of formalisation of the multiplier, the notion of multiplication was never called into question. The main problem was rather to prove that the final amount of income was a finite quantity1 because the inability to establish the existence of a finite limit to the multiplication process would have ipso facto revealed a flaw in the analysis. After some hesitation, the limiting condition of the multiplication process was found in saving. But, in the General Theory, the compatibility of this limited multiplying mechanism with the equality, at all times, between saving and investment was founded on a dissymmetry in the relationship, with investment being the driving force. However, this construction raises doubts about the consistency of the definitions used by Keynes and requires a clarification concerning the formation and use of incomes. It appears, finally, that the notion of a multiplication of incomes beyond the initial impulse is based on the confusion, in the same operation, of the formation and the spending of incomes. Restored in all its analytical relevance, the I = S relationship limits the multiplication to the initial creation of incomes. But precisely this allows a focus on the symmetrical operations of creation and destruction of incomes.

The search for a finite value of the multiplier The multiplier theory was elaborated to justify public expenditure programs; its aim was to establish a precise evaluation of the multiplying effect of these expenditures on national income and employment. Originally the multiplier was considered to be a relationship between the jobs created by the initial impulse and the induced employment. In his first writings on the subject2 Keynes proposed various evaluations of the effect, but he believed that a precise figure could not be worked out (see Keynes, 1929, p. 106). In the argumentation developed at that time, J.  M. Keynes insisted on the distinction between direct and indirect employment. In the 1929 pamphlet ‘Can Lloyd George Do It?’, indirect employment corresponds to the various intermediate activities needed before obtaining a commodity in its final form; in this

88  Bradley respect, Keynes gave the example of the fabric used in the manufacture of a suit. This approach had the advantage of founding the evaluation of the multiplier on the technical links between productions: given the manufacturing conditions in a specific activity, it is possible to measure with tolerable precision the total volume of employment involved in the whole chain leading to the finished product. However, in his 1931 paper on ‘home investment,’ R. Kahn abandoned the approach based on the technical relationship between direct and indirect employment; for him, employment will be multiplied because, when spent, incomes from a given activity will stimulate other activities. Indirect employment should therefore be included in primary employment.3 This perspective was adopted by J. M. Keynes in 19334 in ‘The Means to Prosperity’ and incorporated into the core analysis of the General Theory (see Keynes, 1936, p.  113). Under this new approach, the multiplier should not be confused with the necessity of public services (for example education, health care and so on) for an efficient working of the productive system because, in a sense, these public services belong to the indirect activities needed to obtain consumption goods. While reflecting much later on the development of the multiplier concept, R. Kahn (1984, p. 92) explained that it was indeed logical to exclude ‘indirect’ employment from induced employment because it does belong to the manufacturing process of the original activity. If the initial bank credit is sufficient both to pay the employees of the firm and to order intermediate goods, the incomes will not be multiplied beyond the primitive payment: it is as if the firm had directly employed all the employees involved in the whole process. On the other hand, if the primitive payment covers the incomes of only a limited part of the activities implicated in the manufacture of a finished good, it will not be possible to use simultaneously the same bank credit to purchase goods from other firms. The argumentation developed by R. Kahn tried to formalise the perspective outlined by Keynes in ‘Can Lloyd George Do It?’: the multiplication process will release its own funding.5 The induced activity is then subjected to a limit determined by the following relation (Kahn, 1931, pp. 189, 191): Cost of investment = saving on the dole + increase in imports + increase in unspent profits . . . This relation can be deducted in an a priori kind of way by considering that money paid out by the Government to the builders of roads continues to be passed on from hand to hand until it reaches one of the culs-de-sac indicated by the various terms on the right-hand side of the equation. By utilising it as a basis, it should be possible to deduce a formula for the ratio of secondary to primary employment that is applicable whatever may be the elasticity of supply of consumption-goods. The cul-de-sac expression used by Kahn means clearly that all the income destinations corresponding to the right-hand side of the equation prevent the transmission of the incomes to other economic agents: this has to do with leakages6 block-

The investment multiplier and income saving  89 ing the multiplication process. However, in the article of June 1931, the analysis is not yet presented in its generalised form. It was in fact Jens Warming who clarified the nature of the leaks. In his article of June 1932, Warming emphasised that only part of the increase in income will result in an increase in consumption, the remainder being saved. In September 1932,7 Kahn denied that he had neglected saving because his 1931 article did mention unspent profits and money saved on spared unemployment benefits. However, Kahn later recognised that Warming had indeed clearly identified the halting condition of the process (1984, p. 101): However, Warming made an extremely important linguistic breakthrough. He pointed out that it is the extra saving made out of increased income which is ‘the real source of investment’; ‘the secondary employment must continue until the total created income causes so much saving that the original investment can be paid’. Kahn’s employment multiplier was elaborated within the analytical framework of J.  M. Keynes’s Treatise on Money; it was based on the possibility of a difference arising between investment (I) and saving (S). But the interpretation of saving as both the halting condition of the multiplication and the final funding of the initial investment marked the passage to the perspective of the General Theory. From that time on, the analysis would be based on the I = S relationship (Kahn, 1984, p. 101): Warming was NOT using the word ‘saving’ in the sense used by Keynes in the Treatise (so as to exclude ‘abnormal profits’) but, I pointed out, ‘in the ordinary sense of the aggregate of the excess of individuals’ receipts over their expenditure on consumption. But in this simple-minded sense of the term, savings are always and necessarily equal to investment . . . Whatever the level of investment, funds are always available to pay for it. In the General Theory, Keynes focused on the multiplication of incomes. As in Warming’s analysis, the mechanism is founded on a psychological law, the division between consumption and saving being the determining factor of the national income (Keynes, 1936, p. 97). The formalisation of the multiplier is presented in his chapter 10 (p. 115): Let us define, then, dCw/dYw as the marginal propensity to consume. This quantity is of considerable importance, because it tells us how the next increment of output will have to be divided between consumption and investment. For ∆Yw = ∆Cw + ∆Iw, where ∆Cw and ∆Iw are the increments of consumption and investment; so that we can write ∆Yw = k∆Iw, where 1 – 1/k is equal to the marginal propensity to consume. Let us call k the investment multiplier. It tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment.

90  Bradley Kahn’s employment multiplier was only obtained through a process, whereas the General Theory explicitly referred to two8 different types of multiplier. Initially, Keynes (1936, p. 112) emphasised the existence of an adjustment mechanism, but he added the following detail: I have found, however, in discussion that this obvious fact often gives rise to some confusion between the logical theory of the multiplier, which holds good continuously, without time-lag, at all moments of time, and the consequences of an expansion in the capital-goods industries which take gradual effect, subject to time-lag and only after an interval. However, the process of adjustment between activities rests on the fact that the initial investment causes a progressive accumulation of savings, which will eventually reach an amount equivalent to that of investment (Keynes, 1936, pp. 64, 82, 117). The analysis leads thus to the following paradox: ‘Although S equals I by definition, Keynes holds, at the same time, that the multiplier makes them equal’ (Lutz, 1938, p. 151). Is it then possible to reconcile the immediate equality of saving and investment with the existence of a process of adjustment ensuring the multiplication of the incomes? To answer this question, it is first necessary to clarify the meaning of the equality, verified at all times, of saving and investment. Secondly, we have to study the compatibility of this relationship with the existence of a multiplication process.

The I = S relationship and the funding of stocks Investment was conceived of by Keynes as the operation that increases the stock of capital, including liquid capital.9 This implied that goods are invested as soon as their production is completed because, if not instantaneously consumed, the goods are necessarily stored. Symmetrically, the incomes paid to the factors of production are immediately saved. Saving is therefore immediately equal to investment (Lutz, 1938, p. 153): The reason why saving is always equal to investment is that in every moment of time an amount of new money corresponding to the new net investment is somewhere in the cash holdings of the system, and has to be counted as saving according to Keynes’ definition of this term. However, in the General Theory, Keynes proposed a justification for the necessary equality between investment and saving that went far beyond the simple consequence of his definitions. According to this argument, the amount of savings cannot differ from that of investment because no one can save without purchasing either an existing or a new asset.10 In the first case, the operation is neutral because the seller consumes in place of the saver but, in the second case, there is a net increase in both

The investment multiplier and income saving  91 investment and saving. This conception would have placed net investment and saving on the same footing but would have required an extensive analysis of the operation of income spending. Instead of elaborating on this approach, Keynes did choose to develop a completely different point of view and introduced the idea of a dissymmetry in the relationship between saving and investment. This dissymmetry constituted the foundation for the Keynesian multiplier: saving by individuals cannot generate supplementary investments11; on the other hand, investment generates savings of the same amount through an increase in incomes.12 As mentioned earlier, Keynes acknowledged two different kinds of multiplier: the ‘logical’ multiplier and the dynamic multiplier. The ‘logical’ multiplier was described as follows (Keynes, 1936, p. 123): But in every interval of time the theory of the multiplier holds good in the sense that the increment of aggregate demand is equal to the product of the increment of aggregate investment and the multiplier as determined by the marginal propensity to consume. This relationship concerns realised magnitudes: the amount of investment and the marginal propensity to consume observed at a given moment in time. Although the ‘logical’ multiplier is not at the centre of Keynes’s analysis, it is interesting to remark that, in this case, the use of the word multiplier13 is clearly based on the confusion between causality and proportionality. It is true that at every moment investment will represent a fraction of the global income but this cannot be taken as evidence that the global income is generated by this investment. Instead of placing emphasis on a multiplication, an accurate description of the relationship should use the expression divisor. Let us keep in mind this problem of inverted causality as we proceed to the main versions of the multiplier. Although, apart from the ‘logical’ multiplier, Keynes explicitly considered only one unique version, there are indeed two foremost interpretations of the multiplier. It may be considered either as a manifestation of the effective demand principle or as a process of adjustment between variables through time,14 the latter version being itself subdivided in two varieties.15 For the moment let us concentrate on the ‘effective demand variant’. In each period, the firms have decisions to make concerning their level of production; in this respect, it could be that the anticipation of a change in the level of activity in one branch leads to expect an increase in demand for firms of other branches. According to Chick (1983, p. 253), ‘The comparative-static analysis should ask how much investment is needed to sustain a new level of income.’ Here we meet again the opposition between the multiplier and the divisor. It would seem that the effective demand principle starts from a global level of demand which is then divided between various activities. This is precisely the direction that Keynes seemed to point to each time he insisted that the main problem concerning unemployment has to do with the global level of activity and not with the distribution of employment between branches.16 But again Keynes backtracked by focusing on the effective demand being the sum of the demands for

92  Bradley consumption goods (D1) and for investment goods (D2). If the effective demand is indeed determined by the addition of D1 and D2 instead of being first determined as a global quantity and then divided amongst sectors, it does not make sense to try to separate the ‘global’ perspective for unemployment and the distribution of labour resources among branches. In other words, there would be no specific macro determination but only a sum of micro determinations (by Keynes’s own definition the branch level must be incorporated in micro-analysis). Nevertheless, the ‘effective demand’ multiplier does depend on D1 and D2 being two types of demand that follow completely different systems of relations. D1, or demand for consumption goods, is a utilisation of incomes. Consequently, the firms in this sector must compare their outlays to what may be expected as receipts. But here, through saving, the psychological laws are held responsible for causing a leakage amongst distributed incomes. This means that production in the consumption sector cannot be organised unless the expected leakage can be compensated by consumption spending from some other source. D2, on the other hand, is supposed to be an autonomous expenditure independent of any pre-existing income. Should we accept this composition of global demand as well as the characteristics of D1 and D2, we would have to conclude that investment, that is, D2, is the ultimate determinant of the global level of activity. In this perspective, the amount of investment would give us the amount of leakage that the consumption sector can afford and therefore the amount of production that may be safely carried out in this sector. Consequently, the global level of activity would indeed appear as a multiple of the activity in the investment sector. Still, before accepting this line of thought, we must be aware that it is the result of a particular interpretation of the working of the economic system based on two supporting pillars: saving is supposed to cause a leakage preventing incomes from being spent and investment is identified with a free injection of new incomes. These elements must therefore be examined in their own right. First of all, is it legitimate to maintain the term investment to designate the creation of incomes? In other words, is there any ground to consider that producing equipment is a particular activity that conditions the rest of the economic system? Assume a credit granted by a bank to a firm. If the firm buys goods already present on the markets, this credit constitutes a loan of existing incomes. However, in keeping with Keynes’s definitions, there is no additional saving in the economy as a whole; by the same token, a part of the existing capital takes a different form without any increase in the global stock (liquid capital is transformed into fixed assets). Selling the goods therefore does not create new incomes; it only enables compensation for the debts incurred by the supplying firm to carry out its production. Of course the profits of the seller have to be accounted for but this has to do with transfer mechanisms and not with the formation of net additional incomes. Now suppose that the firm devotes the credit from the bank to pay its factors of production to produce new goods; in this case, new incomes are paid to households. Such a payment cannot however constitute a purchase of goods since these

The investment multiplier and income saving  93 do not pre-exist in the property of the factors of production. Consequently, the formation of the new incomes is not the effect of an expenditure of pre-existing incomes. One cannot then identify this operation with an investment, that is, with the spending to accumulate capital. It appears therefore that the operation of investment (in the sense of building up a stock) can take place only after the production has been completed: investment is a utilisation and not a creation of a product. This means that it is not possible to ‘predetermine’ the destination of the commodities. Although it is clear that equipment should normally be acquired by firms in view of capital accumulation, nevertheless the investment will not be confirmed17 until the equipment is effectively sold to a firm. If the stock of equipment is left unsold, then the manufacturing firm will incur losses and this will amount to a consumption forced on the owners and financers of the firm. Now let us examine the second component of the ‘effective demand multiplier’. Is saving really a preservation of income? Let us consider this interpretation by contrasting it with saving as a form of income spending (following Keynes’s argument as presented earlier). The former conception corresponds to the analysis of liquidity preference defended by Keynes, who considered it similar to a propensity to hoard (Keynes 1936, p. 174). The objective of Keynes is to steer away from the ‘pre-Keynesian’ conception of interest rates as the result of a confrontation between I and S. For Keynes, the rate of interest is the price of the renunciation of liquidity; in contrast to the traditional view of interest as being direct remuneration for saving, interest, according to Keynes, rewards an additional operation, that of spending to invest savings. The link with the rate of interest seems a priori to imply that the distinction between liquid and invested savings is primarily based on the existence of remuneration for the funds. However this criterion is obviously inadequate because it would be purely institutional; indeed it would only depend on banking regulations. It is however undeniable that Keynes did waver over the definition of money, especially concerning the frontier between money and ‘debts’ (Keynes, 1936, p. 167, fn. 1). Nevertheless, for ‘a causal analysis which ought to be exact’ (Keynes, 1936, p. 39), it is essential to adopt a logical distinction. Under the liquidity preference perspective, the only criterion available is that of distinguishing savings formed by the simple conservation of incomes (liquid savings) from savings formed by an effective expenditure (placed savings). Unfortunately this distinction presents the serious disadvantage of establishing two different versions of the I  =  S relationship. One corresponds to a funding relationship: saving provides the firms with the means of accumulating equipment, that is, of investing. The other relationship does not establish any economic relation between the incomes that are saved and the accumulated liquid capital; we have a numerical equality but it is not justified by any link between saving incomes (which by assumption are preserved) and investing the production. In this case, saving is not used for any funding while investment is carried out without mobilising any financial resource.

94  Bradley Can we build a more coherent analysis by developing the logical consequences of the definition initially suggested by Keynes? According to this interpretation, saving consists in buying an asset. This approach does not present any difficulty when saving corresponds to a deposit on a savings account or the purchase of securities by income holders; in both cases, the incomes are therefore spent by their initial holders. On the other hand, a more detailed examination is required for the situation between the perception of the incomes and the transaction for a voluntary placement. If we leave aside the payment of incomes in bank notes and coins, the perception of incomes will immediately lead to an entry on a bank deposit. The incomes are thus immediately deposited in the banking system; consequently, as soon as the incomes are received, the factors of production automatically buy liquid assets. We have therefore expenditure and not a conservation of the incomes. But then what is the nature of the link with the build-up of stocks? Let us consider the situation of the banking system. It is at the same time indebted to the depositors and in a creditor position towards the firm. Consequently, through the banking system, the firm is in fact committed to the holders of the bank deposits, to supply on demand the goods in stock. The debt of the firm is the consequence of the formation of the stock, which therefore is financed by the loan of the incomes. From that starting point, it is coherent to identify incomes with the value of the goods because, by being stored, all the goods are acquired by a provisional purchaser. This analysis gives indeed an economic meaning to the I = S relationship. The incomes are first created then saved – that is, spent – to finance the building up of the stock. By the same token, as soon as they are completed in the firm, the goods are ‘invested’ – that is, stored. Finally there is no dissymmetry between I and S. Those two variables are simultaneously determined because they come into being at the same stage of the operations, the use of the incomes (S) corresponding to that of the products (I). This conclusion is not affected by the fact that the firms’ payment of wages is usually backed up by a pre-existing reserve. In fact, these funds correspond to profits or to a contribution from financers; they are therefore savings that originated either from the formation of a stock or from a loan to consumers. The payment of incomes will therefore carry out two operations simultaneously: on the one hand, there is indeed a creation of new incomes in relation to the new production, on the other hand, there is an exchange between the firm which gives up its financial rights and the holders of the new incomes who give up their rights to the stock of the new goods. At this stage of the analysis, it does not seem that there is ground to accept the peculiar conception of investment and saving necessary to envisage the ‘effective demand’ multiplier. However, we need to go on into our enquiry to examine the working of the dynamic process. The first reason is that, even in the effective demand perspective, this dynamic process is implicit. The second reason is that we have focused on the relationship between investment and saving at the stage

The investment multiplier and income saving  95 immediately following the production but this is only a temporary situation; it is therefore necessary to check whether a multiplication may ensue at later stages.

The I = S relationship and the multiplication process The equality of saving and investment being realised as soon as the incomes are paid, at this stage the multiplier remains equal to 1. In other words, the increase in incomes is positive but limited to the remunerations paid in the activity at the origin of the process.18 For the continuation of the operations, two possibilities could be envisaged: 1 The funds spent by the consumers circulate from one economic agent to another allowing, at each stage, the formation of additional incomes for the incipient. Here, the multiplier can take a value higher than unity because spending the incomes formed in the initial activity will generate supplementary productions.19 2 The receipts of the sellers always compensate for debts incurred in the formation of stocks. Even if the beneficiaries of new incomes do purchase existing goods from other firms, they indeed enable the sellers to repay their debts.20 These firms avoid losses by passing on to customers goods which they had been temporarily forced to acquire through the borrowing of incomes. In addition, the savers, who indirectly had a claim on this old stock just cleared, are now empowered to buy the stock of newly produced goods. Let us examine the logical consequences of each of these possibilities. The interpretation in terms of a circulation of incomes from one agent to another implies the existence of two distinct modes of income formation. Regarding the initial operation, the incomes are formed by a creation: they are new for those who receive them but they do not originate from any pre-existing reserve. On the other hand, in case of consumption, the incomes result from a transmission since, following Becher’s principle,21 the incomes received by the producers are the very same incomes spent by the purchasers. The existence of a multiplying effect greater than one is indeed conditioned by the existence of a transmission of incomes through spending. As a matter of fact, the value of the dynamic multiplier k is based on the marginal propensity to consume c and corresponds to the limit of the sum 1 + c + c2 + . . . + cn. The global increase of income is equal to the sum of all the incomes supposed to be generated by the initial expenditure; it is therefore the concept of circulation22 of incomes which must prevail if k is to be larger than one unit. The existence of a limit to the multiplication process depends on c being smaller than 1. From the point of view of mathematics, it means that the sum will tend towards a finite value; from the point of view of economics, this means that only a fraction of every income will generate new incomes. However, this condition can be considered on two different levels:

96  Bradley • •

As a permissive condition: an income will not generate other incomes because it is stored in a deposit. As a strict condition: an income will not generate other incomes because once deposited it is definitively unavailable for this type of operation.

We are already satisfied that liquid saving cannot be identified with a simple conservation of income if we take into account the economic justification of the I = S relationship; that is, the financing of storage. However, should we not conceive deposits as a reserve from which it could be possible to draw to carry out expenditures that will circulate the incomes? Before jumping to conclusions, we need to interpret more precisely the expenditure of incomes that have been saved. Is the ‘second’ expenditure free to finance any activity or is it only and necessarily available to clear (in Keynes parlance, to disinvest) the stocks that were financed by the first expenditure? The assumption of a freedom in spending saved incomes must be rejected because it would lead to an unlimited multiplication. If incomes circulate, then they are transmitted through expenditures; saving would therefore limit circulation only temporarily (see Schmitt, 1971, p. 40. Cf . also pp. 40–3): The difficulty comes from the fact that hoarding does not destroy incomes. To identify leakages with hoarding introduces in the working of the multiplier a contradiction of which it was initially devoid. The consequence is that instead of obtaining a stable finite value, as it should be, we are faced with an equilibrium value that increases indefinitely. This result is without any doubt the sign of a flaw in the analysis. Sooner or later the deposited incomes will circulate again so that there is no real ending to the chain of transmission. The expression culs-de-sac was clearly used by Kahn (1931, p. 191) to mean that the incomes do not circulate anymore; however, this also implied that the incomes are not destroyed: they remain available (kept at the bottom of the ‘sac’) to be spent later. But would it not be sufficient to take account of the time dimension23 of the variables to avoid this negative conclusion? The absurdity of an unending multiplication provides us with a criterion of judgement: if the analysis leads inevitably to an infinite multiplier, then it must be flawed somewhere. If c < 1, the sum k = 1 + c + c2 + . . . + cn will tend towards a finite limit. Once this condition is fulfilled, the length of the period is of no consequence: k does increase with n but by a decreasing amount. Now, if saving only postpones the free spending of the incomes, we have to conclude that, by enlarging the period of observation, we will necessarily reach the moment when the incomes are spent. The larger the period, the closer c will be from the value of 1 and k will tend to grow without any limit. Here, an arbitrary definition of the period24 becomes the only way to obtain a finite value for the multiplier whereas the halting condition of the multiplication should obey a law internal to the process.

The investment multiplier and income saving  97 It is of interest to remark that the multiplication of incomes beyond the initial creation met with a certain degree of scepticism at the time of the publication of The General Theory.25 Nevertheless we owe the solution of this problem to Schmitt (1971, 1972): the multiplier cannot differ from unity26 because of the inner nature of the circuit of incomes or, in other words, because of the conditions of the integration of money into the economic system.27 This is precisely the perspective involved in the strict condition: deposited incomes are definitively unavailable to finance other activities. At first sight, however, we seem to be confronted with a dilemma. Apparently saving does preserve the incomes since the saver will be able to spend later, but conservation leads to an unending multiplication. On the other hand, a final definitive unavailability of the incomes would ensure a finite limit to the multiplication, but this seems invalidated by the fact that saved incomes are undoubtedly to be spent again later. This dilemma is only apparent. Savings result indeed from expenditure, thus incomes are not kept unspent; however this expenditure is only a temporary destruction: the incomes are recreated later on to be spent again in an operation that will definitively destroy them. We saw that liquid saving is formed by the expenditure that finances the formation of stocks. Through saving, the depositors become indirectly the owners of the stored goods. However, as Keynes emphasised, the goods ‘invested’ in stock are sooner or later ‘disinvested’.28 Consequently, the sale of the goods in store determines a disinvestment, that is, consumption, while the final spending of the incomes determines dis-saving. This sale of the goods is only the repetition of the initial spending of the incomes: the depositors obtain in kind the goods which had been made indirectly their property; at the same time, the firm is released from its liability. The deposited incomes are not available for any expenditure other than clearing stocks financed by savings. This rule is satisfied even though the savers have indeed complete freedom to buy any commodity available. By buying goods that they did not produce themselves, the consumers take the place of the producers in carrying out the final expenditure of the incomes; in exchange for this, the present consumers must become producers of goods in the future and accept that they will be substituted in their consuming capacity by today’s producers. Consequently, the deposited incomes are indeed definitively destroyed in the clearing of the production from which they originated; on the other hand, the identity of the users of the incomes can be modified by exchange operations. If saved incomes were completely free to use, there would not be any true ‘organic’ bond between savings and stocks: stocking the goods (investing) would not be really financed. Precisely the failure to take this into account explains the strange appeal to Keynes of sumptuary wasting (the building of pyramids) or of absurd activities (the digging of fields planted with bottles filled with bank notes) (Keynes, 1936, p. 129). Keynes even went on to praise activities generating products for which there are no apparent purchasers on the grounds that they

98  Bradley would induce the strongest multiplying effect. But economic consumption should not be confused with physical consumption; to observe that no one spontaneously purchases the goods does not prove that the goods are not effectively paid for and, even more, it does not prove that they need not be sold. In reality, the building up of a stock of goods is financed by borrowing the incomes as soon as the incomes are paid. It is therefore imperative for the firm to sell the goods – that is, to clear the stock – to households or other firms in order to repay the debt. This rule applies to any production, whatever the future destination of the goods. If the firms do not manage to find enough customers, several possibilities can be envisaged. The owners or those who financed the firm can decide to go on with the activity; then they can either keep the stock of old goods in the hope of selling it in the future or sell immediately at a discounted price or finally destroy the stock physically. It is also possible to fold up and decide not to engage in any new production. In all cases, the firm will incur a loss corresponding to a (possibly partial) sale of the goods forced onto the owners or financers of the firm.29 The same pattern must be applied to the production of equipment. In the usual case, the producers (that is, the employees) will spend the wages to buy consumable goods. The production of equipment will therefore be profitable only on condition that, in the whole of the economy, there are enough captured (profits) or voluntarily placed incomes to finance an accumulation of equipment. The problem is therefore to secure the initial stocking of equipment so as to give it a permanent character and allow the manufacturer to repay his debts. This repayment thus characterises all the situations in which goods are sold (in the event of profits, there is simply a transfer of savings). However, the repayment of debts imposes a multiplier equal to unity: each expenditure destroys as much income as it needs to be carried out. Keynes’s presentation leaves the impression that the initial activity will condition the whole process by inducing the realisation of other activities. But, if the necessity to clear stocks, whatever the nature of the products, is taken into account, it could also be argued that these others activities determine the initial one. A strange feature of the multiplication beyond the initial activity is that it could not take place should the income-holders directly buy the goods they have produced. Should we not be suspicious with the conclusion that a swift and complete stock clearing appears to be detrimental to the economic activity whereas unsold commodities are heralded as a source of prosperity? If this were true, mismanagement and wasting of resources should be recognised as public virtues worthy of all praise. As mentioned earlier, the Kahn–Keynes multiplier has nothing to do with technical relations between productions. This means that the problem of useless waste should not be confused with the question of public services necessary for an efficient productive system. But then should we not accept that the process of adjustment could be based on the distinction between voluntary and involuntary saving? A variant of this approach would rather insist on I and S being always equal ex post but differing if we consider intended or planned magnitudes.30

The investment multiplier and income saving  99 Keynes did emphasise this idea in the General Theory although he had already used it in his Treatise on Money (1930b): according to this argument, there could be a mismatch between the structure of production (the respective proportions of production devoted to investment goods and consumption goods, i.e. C/I) and the proportion of the global income that economic agents want to affect to consumption and saving. In other words, although the observed proportion C/S is necessarily equal to the observed proportion C/I at any time, it could nevertheless differ from the proportion desired or planned by economic agents. Through the spending of their incomes, the economic agents could then provoke an increase in the production of consumption goods until the observed proportion finally reaches the desired level. In fact, this analysis is dependent on the determination of the economic nature of the products at the stage of production. If we do have a certain level of investment already determined by the production of investment goods and if the proportion between investment and consumption does not yet correspond to what the economic agents are supposed to desire, then there should be a process that increases the production of consumption goods and that raises net voluntary savings to the level of investment. The problem with this argument is that it is based on confusion between the physical characteristics of the commodities and their economic nature; the latter cannot be determined at the stage of production but only when the commodities are sold either to (voluntary or forced) consumers or to investing firms. If equipment cannot be sold, then the losses of the manufacturing firm mean that the equipment is sold by force to the owners (forced consumption implies a transfer of property between households) and they finally become consumption goods instead of investment goods. The dynamic process only seems to be inevitable because investment is supposed to be determined irrevocably at the early stage of production; this is in fact the real basis for the dissymmetry in the relationship between investment and saving. Once we take forced consumption into account, we plainly see that there is no inevitability and we also see that the idea of a predetermined C/I proportion does not stand up to scrutiny. Let us now consider the problem from the point of view of the evolution of savings. Initially these are entirely formed as deposits on current accounts; then savers will usually transfer these liquid savings to time deposits or will purchase securities or commodities. Consequently, with the passing of time, there is indeed a modification in the amount and in the forms of savings. However this should not lead us to conclude at once that the transformation of liquid savings into durable savings is accompanied by an increase in the amount of income.31 The transfer to time deposits and the purchase of securities shift the question of the use of incomes to those economic agents who receive the payment; we need therefore to consider what may happen with them. The effective spending of the funds that are saved can only be devoted to purchasing commodities available in the economic system. Consequently, this expenditure cannot cause the production of these goods. There would be a direct causal relationship only if the expenditure of the incomes were in itself an operation that forms incomes but it is only the

100  Bradley decision to produce that is the direct cause of formation of the new incomes. When an income-holder devotes his income to the purchase of existing goods that he has not contributed to manufacture, the operation only amounts to an exchange of incomes and goods without any new creation. Moreover, if the savings are used to compensate for losses, then we no longer have net saving inasmuch as eventually we do not have investment but only forced consumption. But then should not the multiplier be salvaged in the situation in which an income-holder wants to buy something that is not available? Is it not obvious that, by placing an order, the prospective customer really generates a new activity and therefore new incomes? This is an interesting case, but what is the exact nature of the relationship between the incomes involved? In fact, it is not the spending of incomes that generates the new activity, precisely because it is not possible to spend as long as the new products are not yet available. Consequently, the relationship concerns the placing of the order, that is, a demand, and the reaction of the manufacturer. The whole process boils down only to a way of revealing a demand that was not accurately expected. In this respect, it is interesting to remark that Keynes had to relax his own assumption of accurate expectations by firms to allow for the dynamic process.32 To avoid confusing the issues it is much preferable to retain the accuracy assumptions. Let us compare the situations at the beginning and at the end of the process. The problem raised by Keynes was that of the availability of labour resources that cannot be employed because of an insufficient profitability of investment projects. Of course, as argued earlier, even this presentation can be criticised on the grounds that saving cannot in itself prevent the transformation of the willingness to work at market conditions into effective demand; however, for the sake of argument, let us accept Keynes’s way of reasoning. In the multiplier procedure, the production of equipment is first realised and then it becomes possible to employ those willing to work. But apart from the fact that the production of equipment is forced onto the system, the main problem is still pending at the end of the process. The question of the sale of the equipment is completely neglected although, as mentioned earlier, until the effective sale of the equipment, we cannot tell whether we shall eventually have an investment or a (forced) consumption. If the economy suffers from a lack of investment, the ‘autonomous expenditure’ cannot guarantee that we shall have an effective increase in the level of investment. Moreover, the profitability problem has mysteriously disappeared from the picture.32 From the Keynesian perspective, involuntary unemployment is the result of the impossibility of translating a supply of labour into a profit-making demand on the production system. The dynamic movement conceals the transfer of emphasis from this question to that of revealing the potential demand for consumption goods. In direct contradiction to the Keynesian assumption on short-term expectations, the latter approach reduces the whole question of involuntary unemployment to the need of improving the decision-making process. If lack of profitability

The investment multiplier and income saving  101 is a real structural problem that has to be addressed, then the multiplier theory fails to provide an answer to it.

Conclusion The analysis of the multiplier presented by Kahn and Keynes did focus in some degree on the creation of incomes; however, likening this operation to investment led to confusion between payments creating new incomes associated with production and expenditures for the final acquisition of products. This confusion hindered any clear understanding of saving precisely because savings exist in the intermediate period between these two operations. Moreover the destruction of incomes, the complementary operation of creation, was overlooked by Keynesian analysis, and this led directly to a multiplier larger than unity. In fact, saving does not preserve incomes; it is an expenditure which temporarily destroys incomes. This characteristic, which is specific to monetary economies, enables exchanges of savings. Moreover, contrary to Keynes’s interpretation, consumption is not a transmission but a definitive destruction of incomes albeit with or without exchanges of savings and with or without transfers of incomes: there is no circulation of incomes.

Notes 1 ‘In particular, the puzzle was why the process did not continue indefinitely, i.e. why the additional spending generated by employing one additional worker would not lead to a sequence of additional spending by the other workers, which would continue until the last of the unemployed had found work’ (Patinkin, 1976, p. 70). Richard Kahn has confirmed this interpretation: ‘When I was aged about 8, my father explained to me the cumulative effect of providing one extra man with employment. What he did not explain to me – and what I was too young to ask – is why the multiplier is not infinite’ (Kahn, 1984, p. 101). 2 ‘Can Lloyd George Do It?’ (1929) and ‘The Great Slump of 1930’ (1930a). 3 ‘The increased employment that is required in connection actually with the increased investment will be described as the “primary” employment. It includes the “direct” employment, and also, of course, the ‘indirect’ employment that is set up in the production and transport of the raw materials required for making the new investment. To meet the increased expenditure of wages and profits that is associated with the primary employment, the production of consumption goods is increased. Here again wages and profits are increased, and the effect will be passed on, though with diminished intensity. And so on ad infinitum. The total employment that is set up in this way in the production of consumption goods will be termed the “secondary” employment’ (Kahn, 1931, pp. 175–6). 4 In spite of persistent allusions to intermediate consumption, for example Keynes (1933, p. 339). 5 ‘Something will be provided by the very prosperity which the new policy will foster . . . It is precisely with our unemployed productive resources that we shall make the new investments’ (Keynes, 1929, p. 120). 6 According to Patinkin, the term leakage was used by Kahn for the first time only in 1933. See Patinkin (1982, p. 198). 7 The chronology of the development of the multiplier may not be perfectly clear, especially if we try to take into account James Meade’s contribution. If we follow Meade

102  Bradley

8 9

10

11

12 13

14

15



16

(1993), then it was Meade who focused on the importance of saving as the limiting condition. However, according to Dimand (1994), it could be that this formalisation of the multiplier occurred later than the exchange between Kahn and Warming. It can be argued that there are more than two types of multiplier. We shall come back to this point later. On this see Chick (1983, p. 256). ‘Thus, assuming that income in the popular sense corresponds to my net income, aggregate investment in the popular sense coincides with my definition of net investment, namely the net addition to all kinds of capital equipment . . . Investment, thus defined, includes, therefore, the increment of capital equipment, whether it consists of fixed capital, working capital or liquid capital; and the significant differences of definition (apart from the distinction between investment and net investment) are due to the exclusion from investment of one or more of these categories’ (Keynes, 1936, p. 75). ‘But no one can save without acquiring an asset, whether it be cash or a debt or capital goods; and no one can acquire an asset which he did not previously possess unless either an asset of equal value is newly produced or someone else parts with an asset of that value which he previously had. In the first alternative there is a corresponding new investment: in the second alternative someone else must be dis-saving an equal sum’ (Keynes, 1936, pp. 81–2). ‘It is true, that, when an individual saves he increases his own wealth. But the conclusion that he also increases aggregate wealth fails to allow for the possibility that an act of individual saving may react on someone else’s savings and hence on someone else’s wealth. . . Every such attempt to save more by reducing consumption will so affect incomes that the attempt necessarily defeats itself. It is, of course, just as impossible for the community as a whole to save less than the amount of current investment, since the attempt to do so will necessarily raise incomes to a level at which the sums which individuals choose to save add up to a figure exactly equal to the amount of investment’ (Keynes, 1936, pp. 83–4). ‘The act of investment in itself cannot help causing the residual or margin, which we call saving, to increase by a corresponding amount’ (Keynes, 1936, p. 64). ‘The “logical theory” is not a theory at all but a description of a necessary ex post relationship. It applies to disequilibrium situations, while the multiplier applies only to equilibrium situations’ (Chick, 1983, p. 267, fn. 2). Even in this interpretation, the judgement that the ‘logical’ multiplier describes disequilibrium situations is entirely dependent on proving that the multiplier is a correct interpretation of equilibrium situations. See V. Chick (1983, p. 254): ‘As a description of what will occur if autonomous expenditure changes, the multiplier has the character of a process. It is dynamic. The alternative is to view the multiplier as a statement of the necessary condition for expansion of income to some predetermined new level or maintenance of income at any particular level.’ Moreover, ‘the process analysis asks: for a given change in investment, how much change in income will we get’ (ibid., p. 253). ‘According to one interpretation, there is a rise in investment in the first period; subsequently this elevated level is not sustained and investment falls back to its previous level. The ‘change in income’ represents the cumulative sum of differences of the new income levels each period over what income would have been had the autonomous change in I and its consequences not occurred. Call this dynamic multiplier DM1. ‘On the other interpretation (DM2), the elevated level of I is sustained indefinitely and the new level of Y becomes, in the limit, permanently established. These are dramatically different stories to be represented by the same mathematics, yet a perusal of textbooks suggests that their coexistence appears to cause no great discomfort’ (Chick, 1983, p. 256). ‘To put the point concretely, I see no reason to suppose that the existing system seriously misemploys the factors of production which are in use. There are, of course,

The investment multiplier and income saving  103

17 18

19

20

21 22 23

errors of foresight; but these would not be avoided by centralising decisions. When 9,000,000 men are employed out of 10,000,000 willing and able to work, there is no evidence that the labour of these 9,000,000 men is misdirected. The complaint against the present system is not that these 9,000,000 men ought to be employed on different tasks, but that the tasks should be available for the remaining 1,000,000 men. It is in determining the volume, not the direction, of actual employment that the existing system has broken down’ (Keynes, 1936, p.  379). Earlier in the book, Keynes had explained that there is a need for a specific macro-analysis which is monetary by nature: ‘The division of economics between the theory of value and distribution on the one hand and the theory of money on the other hand is, I think, a false division. The right dichotomy is, I suggest, between the theory of the individual industry or firm and of the rewards and the distribution between different uses of a given quantity of resources on the one hand, and the theory of output and employment as a whole on the other hand. So long as we limit ourselves to the study of the individual industry or firm on the assumption that the aggregate quantity of employed resources is constant, and, provisionally, that the conditions of other industries or firms are unchanged, it is true that we are not concerned with the significant characteristics of money. But as soon as we pass to the problem of what determines output and employment as a whole, we require the complete theory of a monetary economy’ (ibid., p. 293). If, as noted by Moore (1994, p. 125), investment can only be measured ex post, then the notion of a dissymmetry between I and S becomes untenable. ‘Let us try to make up a little story of a money flow that is started by an outlay of “new money”, say, for building a road. At the moment when that increase in investment takes place and the outlay of the new money is made, a money income of exactly the same amount is received by somebody, to wit, by the workers employed on the investment project. We assume . . . that nothing else has changed. Thus there is at the moment (or short interval) an increase in income which equals the increase in investment; that is, the instantaneous Multiplier is one’ (Machlup, 1939, p. 210). ‘The dealer re-stocks with little delay. The money goes to a wholesaler and from him, via a collecting agency, to a factory which increases its production in order to fill the increased orders. New workers are employed by the factory, and they receive the money as their net income. The money spent by our first income recipients, the road workers, has now reached second income recipients, the factory workers. . . The total increase in the flow of income above its size before the increase in investment exceeds the investment of the moment (or short interval) by the income of the second income recipients; the Multiplier at the particular moment is, therefore, greater than one’ (Machlup , 1939, pp. 210–11). ‘The recipients of the income thus created . . . are likely to turn around and spend the greatest part of the income for their consumption. In our story they take advantage of a cheap sale . . . This expenditure implies, of course, the receipt of the money by the dealer. It happens, however, that the latter . . . regards no part of the proceeds as his net income. Strictly speaking, such a liquidation of inventory should be called a disinvestment’ (Machlup, 1939, pp. 210–11). When presenting this principle in his History of Economic Analysis, Schumpeter (1954, pp. 283–4) did refer explicitly to Keynes’s analysis. On the comparison of the circuit and circulation concepts, see Gnos and Rasera (1985). ‘With the Multiplier equal to infinity the “final” rate of income would be reached only after a time lag of infinite length. . . This case . . . is hardly a possible one, because the duration of fixed propensities (to consume, to save, to invest, to be liquid, etc.) will be shorter than the adjustment period: the propensities that would make for the infinite increase in income are likely to change after a finite time interval’ (Machlup, 1939, p. 216).

104  Bradley 24 ‘[T]he chronological time duration of the Keynesian multiplier process remains completely undefined’ (Moore, 1994, p. 128; emphasis in original). 25 See for example Haberler (1936) and Robertson (1940). 26 Machlup insisted that the multiplier is equal to 1 when the incomes are devoted to the repayment of a debt but he was considering only the case of repayment by the holders of income; however, in this case, a repayment only transfers the incomes to other economic agents. On the other hand, from the point of view of the firm which sells the goods, consumption does condition the repayment of its debts; it is not a question of alternative uses of the incomes. See Machlup (1939, p. 216). 27 For a detailed analysis of the integration of money, see Schmitt (1984, pp. 75–175). 28 Keynes, 1936, p. 105. We shall not deal here with the study of the characteristics of fixed capital. 29 It is the relationship to the new production which determines the emergence of losses. The argument also applies to the governmental activities initially financed by a loan. The final spending is carried out when the state finds the resources allowing refunding of the initial loan. If the state refuses to clear its debt, the final financing will be supported by the creditors. 30 A. Cottrell, for example, explains that this has become the standard resolution of the apparent contradiction between the adjustment process and the equality of I and S observed at all times (see Cottrell, 1994, pp. 113–14). See also the presentation of the multiplier by Dalziel (1996, pp. 311–28). 31 ‘An increase in investment cannot occur without an increase in aggregate income as determined by the multiplier, not, as Keynes says, because otherwise the public will not be prepared to provide the necessary savings but because we have assumed that it cannot occur otherwise’ (Haberler, 1936, p. 200). Haberler added these details in a footnote: ‘If there is an additional investment this is in itself, by Keynes [sic] own definition, savings and nobody is called upon to provide savings.’ 32 ‘In general, however, we have to take account of the case where the initiative comes from an increase in the output of the capital goods industries which was not fully foreseen’ (Keynes, 1936, p. 122). 33 Transferring the responsibility of the investment programme to the state makes it more difficult to analyse the questions of the sale of the equipment and the profitability of these projects. If the manufacturers of equipment were private contractors, we would clearly and directly identify the victims of the forced investment policy, whereas with a state programme the problem, being diluted within the whole community, is much less conspicuous, at least for some time.

References Chick V. (1983), Macroeconomics after Keynes, Oxford: Phillip Allan. Cottrell A. (1994), ‘Endogenous Money and the Multiplier’, Journal of Post Keynesian Economics, Fall, Vol. 17, No. 1, pp. 111–20. Dalziel P. (1996), ‘The Keynesian Multiplier, Liquidity Preference, and Endogenous Money’, Journal of Post Keynesian Economics, Spring 1996, Vol. 18, No. 3, pp. 311–31. Dimand R.W. (1994), ‘Mr Meade’s Relation, Kahn’s Multiplier and the Chronology of the General Theory’, The Economic Journal, September, pp. 1139–42. Gnos C. and Rasera J.-B. (1985), ‘Circuit et circulation: une fausse analogie’, in Production et Monnaie, Cahier de la revue d’Économie Politique. Haberler G. (1936), ‘Mr. Keynes’s Theory of the ‘Multiplier’: A Methodological Criticism’, Zeitschrift für Nationalökonomie, Vol.  7, pp.  299–305. Reprint in Haberler (1944), Readings in Business Cycle Theory, Philadelphia/Toronto: American Economic Association, Blackiston Company, pp. 193–202.

The investment multiplier and income saving  105 Kahn R. (1931), ‘The Relation of Home Investment to Unemployment’, Economic Journal, June, pp. 173–98. Reprint in Hansen A. and Clemence, R. V. (1953), Readings in Business Cycles, London, George Allen & Unwin. Kahn R. (1932), ‘The Financing of Public Works: A Note’, Economic Journal, September, pp. 492–5. Kahn R. (1984), The Making of Keynes’ General Theory, London, Cambridge University Press. Keynes J. M. (1929), ‘Can Lloyd George Do It’?, in (1973) The Collected Writings of John Maynard Keynes, Vol. 9, Cambridge, MacMillan. Keynes J. M. (1930), ‘The Great Slump of 1930’, in (1973) The Collected Writings of John Maynard Keynes, Vol. 9, Cambridge, MacMillan. Keynes J. M. (1930), A Treatise on Money, in (1971) The Collected Writings of John Maynard Keynes, Vols 5 & 6, Cambridge, MacMillan. Keynes J. M. (1933), ‘The Means to Prosperity’, in (1973) The Collected Writings of John Maynard Keynes, Vol. 9, Cambridge, MacMillan. Keynes J. M. (1936), The General Theory of Employment Interest and Money in (1973) The Collected Writings of John Maynard Keynes, Vol. 7, Cambridge, MacMillan. Meade J. (1993), ‘The Relation of Mr Meade’s Relation to Kahn’s Multiplier’, The Economic Journal, May 1993, pp. 664–5. Lutz F. (1938), ‘The Outcome of the Saving–Investment Discussion’, Quarterly Journal of Economics, Vol. 52, August, pp. 588–614 Reprint in Haberler (1944), Readings in Business Cycle Theory, Philadelphia, American Economic Association, Blackiston Company, pp. 131–57. Machlup F. (1939), ‘Period Analysis and Multiplier Theory’, Quarterly Journal of Economics, Vol. 54, November, pp. 1–27. Reprint in Haberler (1944), Readings in Business Cycle Theory, Philadelphia, American Economic Association, Blackiston Company, pp. 203–34. Moore B. (1994), ‘The Demise of the Keynesian Multiplier: A Reply to Cottrell’, Journal of Post Keynesian Economics, Fall, Vol. 17, No. 1, pp. 121–33. Patinkin D. (1976), Keynes’ Monetary Thought: A Study of Its Development, Durham, NC: Duke University Press. Patinkin D. (1982), Anticipations of the General Theory, Oxford, Basil Blackwell. Robertson D. H. (1940) ‘Mr. Keynes and the Rate of Interest’, in Fellner, W. and Haley, B. F. (1950), Readings in the Theory of Income Distribution, London, George Allen & Unwin. Schmitt B. (1971), L’analyse macro-économique des revenus, Paris, Dalloz. Schmitt B. (1972), Macroeconomic Theory: A Fundamental Revision, Albeuve, Castella. Schmitt B. (1984), Inflation, chômage et malformations du capital, Albeuve/Paris, Castella/Economica. Schumpeter J. A. (1954), History of Economic Analysis, London, Allen & Unwin. Warming J. (1932), ‘International Difficulties Arising out of the Financing of Public Works during Depression’, Economic Journal, June, pp. 211–24.

5 The intertemporal transmission of money in the endogenous monetary economy A blessing from the past or a curiosity? Alain Parguez The multiplier versus the circuit approach: the debate For a long time, many post-Keynesians have criticized the theory of the monetary circuit because it ignores the multiplier. They argue that what is in question is the very nature of money, because when the multiplier is denied money becomes ‘ephemeral’, vanishing as soon as it is created, an idea at odds with the concept of the non-neutrality of money which underlies the post-Keynesian monetary research project. The post-Keynesian defence of the multiplier1 is rooted in three propositions: 1 A necessary existence condition of non-neutral money is that it can be transmitted over time; as such, it has a time dimension. 2 In the circuit approach, the multiplier is bereft of this temporal dimension since all of the money created in one period is destroyed in the same period. Ephemerality of money is therefore absolute; it is as if money never truly existed. 3 The Keynesian multiplier is the sole process of intertemporal transmission of money. It is therefore the existence condition of non-neutral money. According to the third proposition, the multiplier stems from the fact that the largest share of the money created in one period by banks for firms is automatically transmitted to the following period. The ‘leakage factor’ is the desired increase in the stocks of hoarded deposits accounting for the so-called demand for money.2 Assuming a constant leakage factor, starting from some given increase in the stock of money in time 1, the quantity of transmitted money decreases over time until the economy reaches a new equilibrium state in which all of the initial increase is absorbed by desired hoarding. In any period firms need new money to only meet the discrepancy between their desired expenditures and transmitted money. The weaker the leakage factor, the greater is the amount of transmitted money, which is tantamount to the fundamental proposition that:

Transmission of money  107 The time dimension of money reflects the share of aggregate income devoted to hoarding. As the rate of hoarding falls, money is granted some permanence, and money creation by banks is determined only by acceleration in the desired growth of income.3 The rate of hoarding cannot become nil because then equilibrium would not exist and there would be no multiplier; hence the multiplier acts as both a transmission process and a monetary equilibrium theory. The multiplier cannot exist without equilibrium between the available supply of deposits and their desired stocks. In the likes of the old Keynesian multiplier, the dynamic adjustment process over time stems from a static equilibrium condition, as shown by Table 5.1. The Keynesian multiplier is rooted in the old equilibrium conditions that impose the equality of desired saving and investment, while its new version depends on the neoclassical equilibrium conditions that impose the equality of the supply of deposits and their desired stock as a component of wealth. Post-Keynesians do not reject the Keynesian multiplier – at least most of them don’t. Both adjustments must therefore lead to the same final state T, so that the following condition holds: A(1/s) = ∆M (1/l) = ∆Y (l/s) = (∆M/A) 0 ∆M

(5.1)

A = ∆St = ∆F + ∆L = ∆F + ∆M

(5.2)

which we can write as A – ∆F = ∆M

(5.3)

Equations (5.1) and (5.2) are equilibrium conditions generating the intertemporal transmission process. Aggregate saving has two components: non-hoarded saving, which provides funds for the finance of initial injection A, and hoarded savings, which is the sole source of the leakage of money. Non-hoarded saving encompasses both acquisition of bonds (or stocks) and firms’ saving of profits, which explains why, as long as equation (5.2) holds, the problem of ‘the finance of investment’ is irrelevant. Ultimately, the initial increase in the money supply must be equal to the excess of ‘investment’ over the induced generation of long-term finance by saving. Post-Keynesians just need to add that the circuit approach ignores the multiplier because of the postulate of a leakage factor equal to zero. Equations (5.1) and (5.3) only hold if both l and s are positive. Herein lies the crucial proposition that

1 A s

t =1

t =T

∑ ∆St = A

Existence condition  0 < l < 1

t =T 1 ∆Y = ∑ ∆Yt = ∆M l t =1

t =1

t =T

∆L = ∑ ∆Lt = ∆M

Note: s = aggregate saving rate (average propensity to save); l = propensity to hoard; St = aggregate saving in t; ∆F = increase in available finance for expenditures; ∆M = aggregate increase in hoard of stock of money (or hoarded savings); A = initial injection of money or initial expenditures

Existence condition  0 < s < 1

t =1

∆Y = ∑ ∆Yt =

t =T

Equilibrium condition in state T  ∆S = ∆S =

Increase in banks’ supply of deposits, ∆M ∆Y1 = M Induced increase in supply of deposits, ∆Mt = ∆Mt–1(1 – l)  = Yt

Initial injections in t = 1  in expenditures A Initial increase in income  ∆Y1 = A Transmission factor  induced expenditures ∆Yt = ∆Yt–1 (1 – s) Leakage factor  induced increase in saving ∆St = s∆Yt ∆LtL = ∆Mt = ∆t–1(1 – l) Induced hoarding  ∆Lt = l∆Y

Post-Keynesian multiplier

Keynesian multiplier

Table 5.1  Keynesian and post-Keynesian multiplier processes

Transmission of money  109 ‘closes the system’ in the multiplier theory: the existence condition of a positive saving rate – as a support to the income or expenditures transmission process – is hoarding. Denying hoarding is to deny the very possibility of any kind of dynamic transmission process. Post-Keynesians also argue that circuitists derive the temporality of money from their crude assumptions that firms borrowing money from banks in one period have to repay bank loans in full in the same period4 (see Rochon, this volume, for an excellent presentation of the critical role of banks in the multiplier process). Post-Keynesians should therefore build on the logical equivalence of the proposition that the transmission of money is forbidden by a strong reimbursement constraint and the assumption that the multiplier does not exist when there is a zero propensity to hoard. This logical equivalence helps to avoid the conclusion that a zero propensity to hoard would bestow eternal life on banks’ money, which would generate an endless transmission of money, bereft of a final anchor state, because it implies that a zero rate of hoarding is logically identical to the hard reimbursement rule. This logical equivalence is the underlying rationale of the General Theory of the multiplier. One could be puzzled by its absence (at least in explicit terms) from the post-Keynesian literature.5

The Keynesian and post-Keynesian multipliers do not exist The proof of this must be spelled out using the same assumptions used by the multiplier theory (however unrealistic they may be): there is no state, deposits are the sole form of money, and bank loans to firms are the sole source of money. No more specific assumptions are required; the multiplier does not exist because it contradicts the very nature of money. The multiplier ignores the reimbursement constraint According to the logical equivalence theorem, in any period loan reimbursement is equal to the increase in hoarding. Loan reimbursement is therefore determined by portfolio choices of individual wealth-holders for whom it reflects the subjective preference for liquidity. Banks are deprived of control on their balance sheet, to which they must be indifferent. They never impose creditworthiness conditions on their debtors; they are passive suppliers of money to firms, which implies that they are neutral agents, like some automatic device existing to close the system. The idea of bank neutrality fits in with that of the non-existence of a reimbursement constraint on firms, which owe nothing to banks. Identifying reimbursement with addition to hoarding is nothing but a logical disguise for the assumption of the sheer absence of firms’ liabilities to banks. Bank money without liabilities cannot exist, loans without counterparts in the form of debts are not loans at all, and instead of a genuine endogenous expenditures-determined bank money, in such an approach the quantity of money would be entirely determined by portfolio choices. Such a money would obviously be independent from credit. The

110  Parguez multiplier relies on a logical equivalence theorem, which itself engenders a paradox contradicting the existence of money. This paradox explains the makeshift financial structure6 resulting from equations (5.2) and (5.3): initial injection, the increase in ‘investment’, would be financed in part by non-liquid new savings that cannot be raised when A is undertaken since they are the outcome of the adjustment process initiated by A. This temporal paradox unravels the irrelevance of money and therefore of finance in the multiplier economy. It must be removed by the restoration of a reimbursement constraint that is independent from hoarding. The sole sensible reimbursement constraint is the strong one spelled out by the circuit approach It follows from our assumptions that money exists only to provide firms with the value of output that generates their desired accumulation of wealth. This essentiality of money (Parguez, 2001) is tantamount to the proposition that money exists because it has a value and this value is the value of output resulting from the creation of money; money must therefore disappear or be destroyed when the value of output has been fully realized, granting firms their wealth accumulation. The structure of bank balance sheets reflects the law of value of the capitalist economy. Money is the outcome of twin debt relationships involving firms and banks. As soon as banks endorse firms’ target of wealth, they must provide society as a whole with enough money to realize the required value of output. Banks’ commitment materializes on the liability side of their balance sheet in the form of deposits; firms give back those deposits to banks as soon as the value of output has been realized. Firms’ debt is payable in the future at the end of the production process; it materializes on the asset side of banks’ balance sheets. Banks’ liabilities and assets being equal, when firms give back deposits there is a simultaneous destruction of assets and liabilities on bank balance sheets. Deposits being banks’ liabilities and the sole form of money, as soon as deposits are back in a firm’s account there is an equal destruction of money, whether the channel through which firms recoup deposits is the sale of output or the sale of debt titles to savers. Aggregate saving being equal to the share of deposits that is not recouped by the sale of output, firms are always able to recoup all the deposits. All of the money created to undertake a production process is always destroyed at the end when firms take in their accumulated wealth, which is tantamount to the proposition that: Because of its very nature under the assumptions of the multiplier theory, not the least amount of money can be transmitted into the future. Essential money is ephemeral money. Herein is the proof that no multiplier exists in a genuine monetary economy. This proposition holds no matter what the legal or accounting practice of banks. It has sometimes been argued that banks can roll over loans, allowing firms to recycle deposits ad infinitum. Were this argument true, new money would be just

Transmission of money  111 equal to the increase in firms’ expenditures. This argument is absurd because what destroys deposits is the sale reflux of those deposits into firms’ accounts independently of the practical nature of the contract between banks and firms (reflux occurs when firms recoup money initially invested in expenditures through the sale of their output). Rolling over debts just implies that a new debt agreement is only needed to finance the rise in expenditures; it cannot mean that old money has survived from the past reflux. Hoarding money is impossible The preference for liquidity cannot be denied as long as income-earners want to secure the value of their assets against the impact of both future drops in profits that lead to a fall in stocks prices and future interest rate hikes that depreciate bonds. This is reflected by the share of savings or new financial capital which materializes in the form of hoarded deposits. These account for a net increase in banks’ liabilities, to which the counterpart is firms’ unpaid debt to banks in banks’ assets. As banks’ liabilities, hoarded deposits are a loan of income to banks, which balance them with new long-term loans to firms. Firms are therefore recouping in their accounts an equal amount of deposits, which is reflected by an equal destruction of money. Herein lies the proof of the impossibility of hoarding money in the Keynesian and post-Keynesian sense. Instead of transmitting money to the future, liquidity preference allows the ultimate destruction of money Hoarded deposits have lost the nature of money, as they have been transformed into financial capital. A subsidiary proof is that banks usually pay interest on liquid capital to savers when the banks do not need it. The central bank requests interest on hoarded deposits because as soon as they are hoarded, the deposits become deprived of value. If savers wanted to recycle their liquid capital into future expenditures, they would oblige banks to create an equal amount of money to be added to the money already created to realize the value of output. Dis-hoarding would therefore add valueless money to real money endowed with a value. The impact of dis-hoarding is pure inflation, generating an unexpected rise in the unit price level of output. The central bank is therefore keen to encourage banks to pay interest on hoarded deposits, to deter hoarders from converting their liquid capital into money. Ultimately the impossibility of transmitting money over time by the multiplier emphasizes the fundamental distinction between money and liquidity, which is a part of the stock of assets.7 Firms cannot accumulate free profits in money The multiplier relies on both the ability of firms to gain free profits in money and firms’ passivity. They should recoup an amount of money equal to their receipts

112  Parguez minus their income costs, which would account for their profits in money. They should recycle all of those profits into future expenditures, which implies that there must not be leakage factors constraining firms’ expenditures out of their monetary profits: such an assumption is the twin of the logical equivalence theorem explaining leakage in terms of the portfolio choices of non-firm individuals. Even under our stringent assumptions, firms earn profits in money, which are equal to the excess of the value of output over their income costs encompassing wages and interest payments to their creditors, including banks. One can doubt the very existence of profits without imposing excruciating assumptions. Doubts arose from the initial assumption that firms only borrow to pay wages and can only recoup those wages in full when wage-earners do not save. This assumption is a straitjacket, which does not fit the nature of money. According to the law of value of the capitalist mode of production, money creation must encompass all firms’ expenditures leading to the creation of value, costs and investment. Costs include interest payments, which are advanced by banks to firms that have to reimburse them in the reflux stage. Firms hence exact profits in money because profits are always equal to aggregate monetary receipts over costs paid previously in money. Profits materialize when the value of output has been fully realized: they are equal to the excess of investment over aggregate saving or leakage by wage-earners and renters, so that saving leakage includes banks profit. Profits reflect firms’ accumulation of net wealth since they are the discrepancy between the rise in their assets or gross wealth (investment) and their liabilities (saving). There are no free profits because profits are instantaneously spent to repay an equal share of the initial debt incurred to finance investment, which leads to their destruction in terms of money. What remains is firms’ real net wealth, which is the share of the increase in the stock of equipment not bearing a debt. Such an instantaneous transformation of profits fits the fundamental law of value, according to which all deposits recouped by firms are instantaneously destroyed. It is therefore impossible for firms to retain profits in their monetary form under the initial assumptions of the multiplier theory. The non-existence of retained profits is the twin of the non-existence of hoarding. Here is the ultimate foundation of the demise of the multiplier: neither firms nor savers can foil the law of value, which enshrines the ephemeral nature of money. The state deficit and income-earners’ net indebtedness can generate retained profits but the transmission process is very weak and shortlived In a genuine monetary economy firms’ debt is not the sole source of money. The state exists, and it enjoys the power to create money for its expenditures while a share of the creation of money by banks is backed by income-earners’ net debt. Under strong assumptions firms can therefore retain profits available for future expenditures.

Transmission of money  113 The state deficit as a source of retained profits State expenditures generate an equal creation of money, which materializes as an increase in the liabilities of the banking branch of the state, the central bank. Since it exists to ensure the perfect convertibility of bank money into state money, the central bank has the same balance sheet as banks, which explains why state money appears on the liability side and the asset side accounts for tax liabilities and money, such as the payment of private debt to banks. Unlike banks, the state imposes the amount of tax liabilities; they can be greater or lower than the amount of money initially created by state outlays. In the first case (fiscal surplus), taxes destroy more money than the amount initially injected; in the second case, they destroy less than what has been initially injected (fiscal deficit). This deficit is reflected by the net increase in the quantity of state money, which, assuming a total conversion in banks’ money, is equal to the net in banks’ reserves. The state deficit generates an equal surplus in the private sector, which materializes as supplementary profits, because it is a contribution to firms’ receipts from the sale of equipment goods to the state and consumption goods to recipients of salaries and social incomes paid by the state. With high levels of deficit, it becomes greater than the private saving leakage. Theoretically, it could occur that firms achieve free profits they are able to retain. Since liquidity preference always exists, firms carry debts to banks, which have been forced on them by past liquid saving. As soon as firms recoup deposits out of profits generated by the deficit, there is an equal destruction of money and liabilities. Profits in their monetary aspect can only survive if they are greater than the stock of liquid capital held in deposits. Such a situation is not impossible, but it requires an exceptionally high deficit for sensible levels of the preference for liquidity. What would remain would be a very small, if not insignificant, part of the state deficit. To protect banks’ accumulation of wealth the state sells them bonds, which leads to the destruction of unwanted reserves. Ultimately, on banks’ balance sheets, retained profits materialize as the excess of assets held in bonds over liabilities generated by liquid capital. Firms are then entitled to recycle their retained profits into the future production process by spending them to finance a share of new investment. Let us assume that the state is no longer running a deficit, and that investment is exogenous relative to short-term factors, which explains why there is no change in the level of investment. There is no reason to assume a change in the rate of interest while the long-term targeted rate of profit cannot be affected by the small amount of retained profits. Firms pay the same amount of wages but their interest payments to banks fall by an amount equal to the reimbursement of past debt induced by hoarding plus the share of new investment financed by retained profits. State payment of interest on bonds replaces firms’ payment of interest, which automatically cuts the leakage factor. New profits are now just equal to the excess of current investment over the new saving leakage, while the debt resulting from investment is just equal to the excess of current investment over retained profits. Let G0, I, S0, L0, π0R, S1 and

114  Parguez π1R be, respectively, the state deficit in state 0, investment, saving leakage in state 0, outstanding stock of liquid capital in state 0, retained profits in state 0, saving leakage in state 1 and retained profits in state 1. We can thus write π0R = (G0 + L0) – (S0 + L0)

(5.4)

π1R = (I – S1) – (I – π0R) = π0R – S1

(5.5)

St < S0 

(5.6)

Let us rely on the strong assumption that thanks to the fall in rentiers’ saving leakage in equation (5.6), π1R is still positive. Firms recycle π1R in investment undertaken in state 2 but rentiers’ saving cannot fall any more, which prevents any new drop in the drain of return profits because there is no reason to assume either a change in the rate of interest or a change in the long-term targeted rate of profit, which cannot be affected the small amount of retained profit. The state deficit can trigger a transmission process of money over time but it is very short-lived and its magnitude very weak because it requires deficits high enough to match the outstanding payable debt of firms. The greater the liquidity preference of savers has been in the past, the lower is the probability of deficit-induced retained profits. Income-earners’ indebtness as a source of retained profits In contemporary capitalism, income-earners accept a debt toward banks to finance acquisition of commodities or firms’ debt titles. It is sensible to assume that only wage-earners are indebted to banks and that their current indebtedness is greater than their gross savings, which accounts for a net indebtedness or a negative saving rate. Bank loans for consumption (including spending for housing) increase simultaneously wage-earners’ available money and their liability to banks. Since they do not recoup money from sales for commodities, they have to meet their commitments out of their future income, which must include both reimbursement and interest paid to banks. As soon as they run into debt, firms get supplementary profits which can generate free profits if they are greater than rentiers’ savings. As in the case of state deficit, it is not enough to create retained profits, because firms run a debt which becomes payable as soon as they achieve free profits; it is the debt induced by past liquidity preference. The existence condition of retained profits is therefore that wage-earners’ debt must be greater that the sum of rentiers’ saving and the outstanding stock of liquid capital held in deposits. It is a very strong condition but it can be met easily because wage-earners always strive to run into debt to compensate for the discrepancy between their desired expenditures and their income imposed by firms. Firms automatically recycle their retained profits in the next production process to finance a share of new investment. Let us again assume an exogenous constant

Transmission of money  115 investment, a constant rate of interest and an unchanged desired rate of profit. Wages do not change, but let us also assume that wage-earners are not increasing their debt any further. Firms’ new debt falls relative to the past to the past by an amount equal to retained profits. Profits are now just equal to the excess of investment over aggregate leakage out of income paid by firms, encompassing rentiers’ saving and wage-earners’ reimbursement of a share of their debt. Rentiers’ saving cannot fall because their income is the same as in the past period because firms’ debt has been replaced in their assets by wage-earners’ debt. Interest payments by wage-earners are just substituted for interest payments by firms. Ultimately, all interest income generates a leakage, in contrast to the case of state-induced profits. Whatever the share of reimbursement imposed by banks, aggregate leakage must be greater than in the initial period. Let D0, SR0, SR1 and b be, respectively, the wage-earners’ debt in state 0, rentiers’ saving in state 0, rentiers’ saving in state 1 and the share of reimbursement of debt. Retained profits in 0 and 1 are π0R = D0 – (SR0 + L)

(5.7)

π1R = π0R – (SR1 + bD0)

(5.8)

π1R = D0(1 – b) – (L + 2SR0)

(5.9)

because SR1 = SR0

(5.10)

The magnitude of the transmission process is much smaller than in the case of state-induced retained profits. π1R must be zero or negative, but for exceptionally high levels of wage-earners’ debt that could be deemed unsustainable even by wage-earners keen to compensate for their lack of income. Banks also create more and more money to finance the acquisition of stocks by wage-earners directly or through the intermediation of various financial institutions; herein is the so-called ‘financial markets restoration’ which is nothing but a roundaboutness of the monetary structure of the capitalist economy. Let us now assume that firms thrive so much on such a structure that they finance their whole investment by the sale of stocks to wage-earners. They borrow to banks just an amount of money equal to their income costs, while wage-earners get an amount of money equal to their acquisition of stocks. Profits are therefore equal to investment minus rentiers’ saving leakage and all profits are free profits since firms have not incurred a debt to banks to undertake their investment. As always, retained profits are equal to the excess of free profits over liquid capital. Their existence condition is that firms’ ‘animal spirits’ have been thriving so greatly on monetary roundaboutness that they imposed an exceptionally high level of investment. Their buoyant spirits reflect the miracle of the ‘financial trick of capitalism’.8 While

116  Parguez profits are balanced by an increase in firms’ indebtedness, which should mean that firms do not really increase their net wealth, all profits are now transformed into net wealth. This is indeed a pure ‘financial trick’ hiding wealth and therefore inflation. In the next period wage-earners do not want new stocks and banks just recover interest on their debt. Using stocks as the collateral of loans they postpone reimbursement to prevent the sale of stocks by debtors that would induce a fall in their prices. Firms finance a share of the constant level of investment by recycling their retained profits. Profits are equal to investment minus rentiers’ savings which must be the same because, for a given rate of interest, wage-earners’ debt has just been substituted for firms’ debt in their assets. Because of banks’ optimism relative to their collateral, the possibility of new retained profits, although very low, is greater than in the case in which loans finance consumption. Let D0 be wage-earners’ debt in a state financing the acquisition of stocks: π0R = D0 – (SR0 + L)

(5.11)

π1R = π0R – SR1 = D0 – (L + 2SR0)

(5.12)

with b=0 SR1 = SR2 As long as banks maintain a zero-rate reimbursement to protect the value of their collateral, the impact of the transmission process can be greater than in the previous case. As soon as their own ‘animal spirits’ lead banks to a more pessimistic view of the future, they impose a positive net rate of reimbursement. It determines a collapse of the previous dynamic process because retained profits vanish and become negative. Retained profits are a curiosity meaning little for economic policy It has been fully proven that the post-Keynesian critical assessment of the circuit approach does not hold because it is rooted into the multiplier theory, which is false. It contradicts the very nature of money. As long as firms’ expenditures are the sole source of money, money cannot survive the realization of value, which means that retained profits do not exist. The non-existence of retained profits reflects the absolutely ephemeral nature of money. Such a nature does not mean that money does not matter; to the contrary, it is the mark of its essentiality as the existence condition of the capitalist mode of production. Once and for all, we must reject the Keynesian multiplier and stop trying to reconcile it with endogenous money. Three conditions must be met in order for retained profits to exist:

Transmission of money  117 1 There must be either a state deficit or a net indebtedness of wage-earners for consumption or acquisition of stock motives. Both conditions lead to a creation of money which is debt-free for firms. 2 This deficit or indebtedness must be high enough to generate profits greater than rentiers’ saving leakage. 3 Those free profits must be greater than the stock of liquid capital held in deposits. As soon as they appear, retained profits generate a transmission process over time. It vanishes very soon, except in the case of an extremely high initial level of state deficit or wage-earners’ debt, because of the strength of leakage factors resulting from rentiers’ saving and wage-earners’ commitments to banks. As shown by Table 5.2 (which compares the three possible cases), the transmission process does not depend on any kind of equilibrium condition in the manner of adjustment of saving to investment or of the demand for money to its supply. Usually, retained profits should be greater in A, but in contemporary capitalism states are increasingly imposing fiscal thrift upon themselves, which explains why retained profits must be greater in B and C. When wage-earners take strong bets on future prices of stocks, they do not take care of future incomes, which makes them impervious to constraints on their ability to borrow. Banks share those speculative bets, thereby ignoring restraint in their loans. Initial retained profits must be greater in C than in B, whereas future leakage is lower in C than in B until banks change their mind. The impact of the transmission process is greater in C than in B and could match the impact of A. Table 5.2 proves that even in some exceptional states only a very small share of firms’ expenditures can be financed by money from the past. Abstracting from this abnormal state, we can say that free profits are always less than the stock of liquid capital. Ultimately it seems that post-Keynesians wish to defend the multiplier because, like Keynes, they believe that it is the underlying rationale of a full-employment policy. This is a misleading belief, because rejecting the multiplier is the sine qua non of a genuine full-employment policy. It should henceforth be impossible for policy-makers to give themselves over to the dangerous gamble allowed by the belief in the automatic transmission over time of expenditures and therefore of value and employment.

Exogenous decision of the state

None but self-imposed

G0 – (S0 + L) Aggregate future savings

Initial factors

Constraints

Retained profits Leakage factors

A – State deficit

Table 5.2  The structural factors of the transmission process

Desire to compensate for income rationing Banks’ will to comply Expectations about future incomes D0 –  (SR0 + L) Rentiers’ saving and reimbursement

B – Wage-earners’ debt for consumption

D0 –  (SR0 + L) Rentiers’ saving as long as b = 0

Expectations about on the rise in the value of stocks Banks’ will to comply

C – Wage-earners’ debt for acquisition of stocks

Transmission of money  119

Notes 1 Chick (2000) is the best assessment of the post-Keynesian side of the debate, displaying a genuine attempt to understand the circuitist side. 2 Whatever the motives, the demand for money is identical to desired hoarding. The distinction between active and passive balances is irrelevant. 3 As shown by Parguez and Seccareccia (2000), post-Keynesians seem to agree on the proposition that the creation of new money is needed only to finance growth. 4 For instance, Chick (2000). 5 An explanation lies in their reluctance to reject the entire legacy of the General Theory, particularly the multiplier and the liquidity preference. Thereby they are led to explain the very existence of money by reference to the fundamental uncertainty of the future. 6 Statements such as ‘Investment generates its own finance’ are obviously logically absurd. Keynes himself used to rely on such a temporal paradox when, for instance, in his writings on the finance motive he emphasized the existence of a ‘revolving fund’ and the role of consumption as a source of finance-matching investment. The existence of a finance motive for accumulating deposits does not eliminate the paradox. 7 The logical consequence is that there cannot be a shortage of liquidity; desired hoarding generates an equal increase in the stock of liquid capital. 8 The concept of ‘financial trick’ was first spelled out by Kalecki (1991) in his analysis of the ‘crucial reform’ of capitalism.

Bibliography Chick, V. (2000), ‘Money and Effective Demand’ in John Smithin (ed.), What Is Money, London: Routledge. Kalecki, M. (1991), ‘Observation of the Crucial Reform,’ in Collected Works of Michael Kalecki, Vol. 21, Oxford: Clarendon Press. Parguez, A. (2001), ‘Victoria Chick and the Theory of the Monetary Circuit: An Enlightening Debate’ in Philip Arestis, Meghmad Desai and Sheila Dow (eds), Money, Macroeconomics and Keynes: Essays in Honour of Victoria Chick, Vol. I, London: Routledge. Parguez, A., and Seccarecia, M. (2000), ‘A Credit Theory of Money’, in John Smithin (ed.), What Is Money, London: Routledge. Rochon, L.-P. (1999), Credit, Money and Production: An Alternative Post-Keynesian Approach, Cheltenham: Edward Elgar.

6 The demise of the Keynesian multiplier revisited Basil J. Moore

Keynes believed that, unlike consumption expenditure, investment spending was not a function of current disposable income. Investment is forward-looking, and concerns the prospective yield relative to the current supply price. Since the future is unknowable, changes in investment spending are determined by changes in investor expectations about prospective yields. This in turn depends on expected future receipts and the present and future cost of finance. In order to emphasize the evanescent, unquantifiable and unknowable nature of investor long-term expectations, Keynes in a felicitous phrase termed them ‘animal spirits.’ In his vision changes in ‘animal spirits’ behind investment spending were the driver of cyclical changes in AD and AS (see Keynes, 1936, chapters 11 and 12). Keynes was correct that changes in ‘effective demand,’ (what is now termed ‘aggregate demand’ (AD) and includes all consumption, investment and government spending on current final goods) cause an identical change in AS in the same period on a one-for-one basis: ∆ADt0 = ∆Yt0 (see Keynes, 1936, chapter 3). This can now be demonstrated more clearly by following Kalecki and distinguishing two separate sectors: the flex-price sector and the fix-price sector. In the fix-price sector, which in developed economies constitutes more than 95 per cent of GDP, most firms have market power and are price-setters and quantity-takers in imperfectly competitive markets. The AS relationship can be viewed as a horizontal line in inflation-output space, where the core inflation rate is determined by the change in unit costs. The change in unit cost is the excess of the average rate of increase in money wages over the average rate of labour productivity growth. In developed economies GDP is always demand-constrained, since AD is characteristically less than the economy’s full employment capacity output (Moore, 2006, chapter 14). But in Book III of The General Theory, ‘The Propensity to Consume,’ Keynes went on to argue that, because the marginal propensity to consume could be assumed, a stable function of current income there would be a ratio of income to investment, called the ‘multiplier.’ An increase in investment spending would result in a multiple increase in aggregate income and output.1 Keynes’s ‘multiplier’ analysis was comparative-static equilibrium analysis. Given an initial equilibrium position where AD was equal to AS, it attempted to trace out, ceteris paribus, the effects of a once-and-for-all change in autonomous investment on the level

The demise of the Keynesian multiplier revisited  121 of GDP until a new position was reached at which the economy was again in equilibrium. But if economies are complex systems, change is continual, and economies have no tendency to approach any future position of ‘equilibrium’ or balance where all change ceases. Complex systems have special characteristics, like emergent properties, sensitive dependence on initial conditions and phase transitions, and can only be modeled with non-linear systems. Non-linear systems have no closed-form solution and can be simulated but never solved (Moore, 2006, part 1). In order to analyse the dynamic process of change in complex systems, all variables must be dated. Once this is done, Keynes’s ‘multiplier’ analysis about the multiple effect of current investment on future income may be shown to be mistaken. In the complex real world, expectations about the future and autonomous investment spending change continually over time. For complex systems, it is illegitimate to consider the effects of a change in autonomous investment on income in an initial time period, and then assume ceteris paribus that autonomous spending will remain constant throughout the adjustment period until all effects of the initial change in investment on income and consumption have worked their way through the system. Yet this is exactly what the Keynesian multiplier process logically requires. Once the multiplier process is not assumed to be instantaneous, but is recognized as occurring over calendar time, in each ‘period’ of the multiplier process expectations and autonomous investment will change. Unless expectations are ‘frozen,’ and held constant under the ceteris paribus clause, the system will never reach a new stationary position of ‘equilibrium’ where income has increased by some determinate ‘multiple’ of the initial change in autonomous spending. The change in consumption in any period is not determined solely by the current change in disposable income. A multitude of other forces impact consumption spending: current, lagged and expected future changes in income; wealth; capital gains; tastes; fashion etc. But the level of consumption next period is superficially well explained by the level of current income and current consumption in the current period, since such series have unit roots. Since both consumption and income have unit roots, current changes have permanent effects, and all trends found in such series will be time-dependent. Since income is defined as consumption plus saving, consumption and income are co-integrated. First differences in consumption are not well explained by concurrent first differences in income, since both series broadly follow a random walk. In complex systems ‘equilibrium,’ whether defined as a position of balance where all adjustments have ceased or as a position of general market clearing where all expectations are realized, never occurs (Moore, 2006, part 1). The above is very old-hat. It is simply a roundabout way of stating that the marginal propensity of consumption does not remain absolutely constant over real calendar time. But what has not been widely emphasized is that if a complex system has no tendency to move towards some determinate future ‘equilibrium’ position, there can be no Keynesian ‘multiplier’ process.

122  Moore The Keynesian multiplier (M) is derived from the national income identity plus a behavioural consumption relationship: Y ≡ C + I

(6.1)

C = c0 + cY

(6.2)

Substituting (2) into (1) and solving for Y, Y = (c0 + I) · [1/(1 – c)] ≡ (c0 + I)M 

(6.3)

where M ≡ 1/(1 – c) and c ≡ ∆C/∆Y. The nature of the multiplier identity is shown in Figure 6.1, the familiar C + I + G diagram, with the government and the foreign sector omitted. The Keynesian multiplier is the ratio of the change in income to the change in autonomous investment spending (m ≡ ∆Y/∆I). In the simplest case the multiplier may be rewritten as m ≡ 1/(1 – c), where c is the marginal propensity to consume. In Figure 6.1 the value of the multiplier expression may easily be derived geometrically, using comparative-static equilibrium analysis: ∆Y ≡ ∆C + ∆I 

(6.4)

Rearranging (6.4) and substituting ∆I ≡ ∆Y – ∆C into the definition of the multiplier (6.3), we get: m ≡ ∆Y/∆I ≡ ∆Y/(∆Y – ∆C)

(6.5)

AD

45º C + I´

E(t + n) ∆I(t0) ∆I(t0)

E(t0)

C+I

∆C(t + n) ∆Y(t + n) YEt

YE(t0)

Figure 6.1  The Keynesian multiplier.

∆Y(t + n)

YE(t + n)

AS

The demise of the Keynesian multiplier revisited  123 Dividing the numerator and denominator of equation (6.5) by ∆Y yields: m ≡ 1/(1 – [∆C/∆Y])

(6.6)

m ≡ 1/(1 – c), where c ≡ ∆C/∆Y

(6.7)

or

As professors of macroeconomics love to show on the blackboard, the essence of the multiplier process is that given an initial equilibrium position YE(t0), an increase in autonomous spending of ∆Ito will yield a new equilibrium position ∆YE(t + n), where the change in income is a multiple of the change in investment spending. YE(to) and YE(t  +  n) are shown to be ‘equilibrium’ positions since AD is equal to AS, and there is no unintended change in inventories. So planned investment is equal to planned saving and business managers have no incentive to change investment spending. But the (implied) comparative-static assumption that the Keynesian ‘multiplier’ is ‘instantaneous’ is analytically bankrupt and highly misleading. It is simply a non-transparent way of getting rid of time, and with time the complex events of the transition process, in order to pursue comparative-static equilibrium analysis. If the income-adjustment process evolves over chronological time, as is necessary if the theory is to shed light on real world behaviour, all variables must be dated. In complex systems it is not possible to assume that ‘animal spirits’ undergo a once-and-for-all change in the initial period and are then ‘frozen’ and held unchanged over the time it takes for the multiplier to work itself out. This is what must be assumed if a quantitative value of the multiplier is to be derived. The change in investment (∆It0) is assumed to remain constant over the adjustment period (t + n) since only consumption (Ct + n) and income (Yt + n) are permitted to change. But as a complex system production, income, investment, consumption and output change continuously over time. Keynes’s comparative-static equilibrium procedure assumes an initial exogenous change in ‘animal spirits’ and investment spending, and then in effect waves a magic wand and traces out the consequences of this exogenous change in investment for the accompanying changes in income and consumption in the system in logical time, while holding investment constant over the adjustment period. At the beginning of the second ‘period,’ income will increase by the change in exogenous spending to Yt + 1. But however this initial period is defined, once it is admitted to take place in chronological time, expectations of the future and animal spirits must be allowed to change, as well as the level of income, consumption and investment (Yt + 1, C t + 1 and It + 1). At any intermediate time period in the adjustment process, the situation is analogous to the situation at the beginning of the process. Flux is continuous and autonomous investment spending changes continuously over time. There is no determinate ‘multiplier’ relationship between investment and income. In any short-run single period (Yt + 1) there is no ‘multiplier effect.’ The change in income is simply equal to the change in investment (It  +  1) and consumption (Ct + 1) in the period.

124  Moore As shown in Figure 6.1, if all variables in the multiplier process are dated, as is necessary for process analysis, the logical inconsistency of the analysis is clearly revealed. In the final ‘equilibrium’ position, consumption and income have been allowed to change (∆Ct + n, ∆Yt + n), but investment has been held at its initial period value (∆It0). Yet in the real world of chronological time, during each ‘period’ of the transition process, expectations of future events are continually changing. It must still be shown how bank-financed deficit-spending is accompanied by increases in the money supply which enables AD to grow over time. The kernel of truth in the Keynesian multiplier story is that although spending on current output has identical, one-for-one effects on AD, irrespective of whether it is for investment or consumption goods, investment and consumption spending differ in the manner in which they are financed. Capital goods have by definition an expected future lifetime that extends beyond one year. Capital budgeting considerations dictate that only their current consumption (‘depreciation’) must be currently expensed and paid for in the current period. As a result, a much larger proportion of investment expenditures are externally financed by newly created money compared with consumption expenditures. The consequence is that investment spending is financed to a much greater degree than consumption by deficit spending financed by bank borrowing. Deficit-spending financed by bank credit will be shown to be the key to AD growth in market economies (see Rochon, 2005, for a discussion on the existence of profits along the arguments presented here). Future events are continually changing, and with them ‘autonomous’ spending is also changing. Unless future expectations are ‘frozen’ it is impossible to determine the future effects of current exogenous changes in investment. Spending changes continuously over time and the system never approaches a new ‘equilibrium’ position. What would be logically required to demonstrate a determinate ‘multiplier’ is the following counterfactual experiment: Assume the existence of two hypothetical ‘identical’ economies at a point in calendar time. Let an exogenous change occur in one economy, and then observe how both economies change over future chronological time. The multiplier could be directly calculated ex post as the difference in income and output between the two previously identical economies at different future dates. But there is no reason whatsoever to expect that such a ‘multiplier’ would remain stable over different periods in historical time. A separate criticism of the Keynesian multiplier is that it does not address how an increase in exogenous investment is financed. It implicitly assumes that excess money balances (‘hoards’) are available to internally finance any desire to deficit-spend, and the result is a rise in income velocity. But if such ‘hoards’ do not exist the finance for the deficit-spending must be raised by borrowing. When the borrowing is from the banking system, the money supply will increase. In the real world a high proportion of investment spending is externally financed by borrowing for working capital from the banking system. In contrast a high proportion of consumption spending is financed internally out of current income. This provides an alternative insight by which the differential effects of investment and consumption spending on AD can be explained.

The demise of the Keynesian multiplier revisited  125 The Quantity Theory of Money, like the multiplier. is another identity: Yt ≡ MtVt

(6.8)

where Y = income, M = money supply and V = velocity (Y/M). But the variables in the above identity are incommensurate, since income (Yt) is a flow variable whereas the money supply (Mt) is a stock variable. This dimensional incommensurateness is resolved by defining velocity (Vt) as the ratio of the flow of income to the stock of money, i.e. the average number of times money circulates as money income in one period (Y/M). As such its value depends on the length of the period over which income is defined. Vt ≡ Yt/M t or Yt ≡ MtVt

(6.9)

The level of income over any period may be expressed as the product of the money supply at the beginning of the period times the average income velocity of money over the period. The Quantity Theory as an identity is true at every instant of time and over every period of time. The quantity equation can be totally differentiated with respect to time: the change in income is equal to the change in the money supply in the next period times the current income velocity of money, plus the change in the income velocity of money in the next period times the current supply of money. ∆Yt ≡ ∆Mt + 1Vt + ∆Vt + 1Mt

(6.10)

Like other macro-variables, velocity has a unit root and approximates a random walk. The velocity of money is continually changing. But since it has a unit root, the best estimate of next period’s velocity is the current period’s velocity, so the expected change in velocity is zero (∆Vet + 1 = 0) (see Nelson and Plosser, 1982). This radically simplifies the analysis but at the same time radically reduces its explanatory power. Since the expected change in velocity is zero, the expected change in income over the next period is the expected change in the money supply in the next period times current income velocity. ∆Yet + 1 = ∆Met + 1 · Vt

(6.11)

Suppose the following two strong but not absurd assumptions are made: 1 Changes in investment spending are totally financed by bank lending (∆It + 1 ≡ ∆Lt + 1) 2 Bank lending finances only investment expenditures (∆Lt + 1 ≡ ∆Mt + 1) The change in investment is then equal to the change in the money supply: ∆It+1 ≡ ∆Mt+1. Substituting the change in investment for the change in the money supply in equation (11), the expected change in income in the following period is

126  Moore equal to the change in investment in the following period times the current income velocity of money: ∆Yet + 1 = ∆It + 1 · Vt

(6.12)

In each individual time period the value of the Keynesian multiplier – the ratio of the increase in income to the increase in autonomous spending (m = ∆Y/∆I) – is then the income velocity of money (V = ∆Y/∆M).2 In each period the Keynesian multiplier is the income velocity of money! Both the Keynesian multiplier and velocity are identities, true over every period and every instant of time. There is, however, one problem. The length of the multiplier period over which income adjusts to a change in investment, and the velocity period over which income adjusts to a change in the money supply, are not identical. Velocity is arbitrarily defined for an income period of one year. But the time period of the multiplier remains undefined. The period (t + 1) representing the change in income associated with a change in the money supply (6.11) is not identical to the period (t + 1) representing the change in income associated with a change in investment spending (6.12).3

Notes 1 Keynes took the concept of the multiplier from an article by R. F. Kahn, ‘The Relation of Home Investment to Unemployment’ (see Kahn, 1931). 2 This was the paradox put forward in Horizontalists and Verticalists by B. J. Moore (1988). 3 Formally each (t + 1) represents a different time period, so the equality is apparent.

References Kahn, R. (1931), ‘The Relation of Home Investment to Unemployment’, Economic Journal, 41, June, pp. 173–87. Keynes, J. M. (1936), The General Theory of Employment, Interest and Money, London: Macmillan. Moore, B. J. (1988), Horizontalists and Verticalists, The Macroeconomics of Credit Money, London: Cambridge University Press. Moore, B. J. (2006), Shaking the Invisible Hand, Complexity, Endogenous Money and Exogenous Interest Rates, London: Palgrave. Nelson, C. R., and Plosser, C. I. (1982), ‘Trends and Random Walks in Macroeconomic Time Series’, Journal of Monetary Economics, 10, pp. 139–62. Rochon, L.-P. (2005), ‘The Existence of Monetary Profits within the Monetary Circuit: An Essay in Honour of Augusto Graziani’, in G. Fontana and R. Bellofiore (eds), The Monetary Theory of Production: Tradition and Perspectives, London: Macmillan, pp. 125–38.

7 Consumption, investment and the investment multiplier Jean-Luc Bailly

Introduction Most of the many reviews of Keynes’s theory of the multiplier concentrate on the issue of savings being equal to investment and on the distinction between ex ante and ex post equilibrium. Very few of them consider the chain of events that supposedly gives rise to an income multiplication process. However, Keynes develops his theory of the multiplier on the basis of an ambiguity in his use of the central concept of the marginal propensity to consume. The fact of the matter is that Keynes attributes two separate functions to this concept. First of all, within the framework of his logical theory of the multiplier, the marginal propensity to consume has a structural function. It expresses the stable quantitative relationship between consumption and income. As such it describes a state of the behaviour of households with regard to consumption and appears initially as a determinant of the structure of the national product but not of the size of that product or of changes in it. In his dynamic version, the multiplier theory considers the marginal propensity to consume as a factor that increases income. The theory is based on the idea that the multiplier mechanism supposedly engages when a fraction of the new income derived from additional wages paid in the capital goods sector is spent on the purchase of consumption goods. Such spending allegedly gives rise to new income in the consumption goods sector. And so the dynamic part of the theory is based on the idea that the spending of the extra income (or its equivalent) distributed in the capital goods sector as purchase of consumer goods starts up a mechanical process of income multiplication. In this scheme, the income formed in the investment goods sector not only expresses how households divide their income between consumption and saving but also generates income in the consumption goods sector. The question we propose to study here is whether the structural relationship between consumption and investment, quantified by using the logical multiplier, can be logically transposed to the causal plane so as to construct a dynamic theory of the way national income is determined. We will investigate any causal connection between the formation of additional income in the capital goods sector and its spending on the purchase of consumption goods. More specifically, we focus

128  Bailly on whether it is possible to trigger an income multiplication process by spending such income on consumption. This remainder of this chapter is divided into three parts. In the following section, after situating the issue in the theoretical context of the fundamental definitions of the General Theory, we raise two cases in which a multiplier process might be triggered. In the next part we consider the first of these case: we assume that the entrepreneurs who produce consumer goods have anticipated the payment of additional wages in the capital goods sector. In the last part we take on the other case: we assume that the producers of consumption goods have not anticipated the payment of extra wages in the investment goods sector. We then check whether in both instances the holders of additional income formed in the investment goods sector exert any net purchasing power over consumption goods. It is concluded that no income multiplication process can be observed when income is spent.

Logical multiplier versus dynamic multiplier In the General Theory, Keynes (1936, p. 122) makes a distinction between ‘the logical theory of the multiplier’ and what may be termed the theory of the income multiplication process through spending: I have found, however, in discussion that this obvious fact often gives rise to some confusion between the logical theory of the multiplier, which holds good continuously, without time-lag, at all moments of time, and the consequences of an expansion in the capital goods industries which take gradual effect, subject to time-lag and only after an interval. The consistency of the General Theory of employment requires, however, that both conceptions of the multiplier comply with the framework of general definitions laid down in chapter 6 of The General Theory. Consider the following: Income = value of output = consumption + investment Saving = income – consumption Saving = investment (ibid., p. 63) The first equation is generally written as Y = C + I and takes the form of a true structural definition in which the respective shares of the production of consumption goods and of investment goods are determined by entrepreneurs’ expectations as to outlets for their products. It shows that: Incomes are created partly by entrepreneurs producing for investment and partly by their producing for consumption. The amount that is consumed depends on the amount of income thus made up. (Keynes, 1937a, p. 120)

Consumption, investment and the investment multiplier  129 The division of income between consumption and investment does not actually come about until households and entrepreneurs have purchased products on the various markets: That there should be such a thing as market value for output is, at the same time, a necessary condition for money-income to process a definite value and a sufficient condition for the aggregate amount which saving individuals decide to save to be equal to the aggregate amount which investing individuals decide to invest. (Keynes, 1936, p. 64) It is therefore logically inconceivable that the amount of income spent should differ from the amount of income formed. Savings equals investment not because the wants or simple expectations of economic agents coincide but rather because of their action in the different markets; Y, C and I are determined by the dual movement of the formation and the spending of income. Income is formed when production factors employed in both sectors are paid and its component parts are ultimately determined when it is spent on consumption and investment, respectively: ‘It follows that total realized demand can only be known simultaneously with realized income’ (Schmitt, 1972, p. 64). Therefore the equation Y=C+I is an identity that holds true at all times and not an equilibrium relationship resulting from adjustment of its two terms. At no time can Y be different from C + I since C and I are its component parts in respect to both its formation and its expenditure. This would seem to be the very principle behind effective demand. Income is created by the value in excess of user cost which the producer obtains for the output he has sold; but the whole of this output must obviously have been sold either to a consumer or to another entrepreneur. The decisions to consume and the decisions to invest between them determine incomes. (Keynes, 1936, p. 64) Thus, with c being the marginal propensity to consume, we can write C = cY, which allows us to express the equation for disposal of income as Y  =  cY  +  I, where cY is the effective spending of households on consumption goods and I is the spending of entrepreneurs in purchasing capital goods. As I is the current investment by all entrepreneurs, which by definition is ‘equal to the value of that part of current output which is not consumed’ (ibid., p. 63), we may write: I = (1 – c)Y. Which means that Y = cY + (1 – c)Y characterizes both the identity of the income formed (Y to the left of the equals sign) and of the income spent (Y to the right of the equals sign) and the identity of saving and investment in (1 – c)Y.

130  Bailly The logical version of the multiplier It is possible to derive from the equation Y = cY + I a stable quantitative equation for investment and aggregate income, namely Y = [1/(1 – c)] I. For in given circumstances a definite ratio, to be called the multiplier, can be established between income and investment . . . (Keynes, 1936, p. 113) When expressed as the equation 1/(1 – c) = k, in its logical formulation, the multiplier defines the terms of the structural composition of current income between consumption and investment. It indicates that in any period, 1 – c being the marginal propensity to save, consumption stands to investment in the same proportion as is found in the division of income between consumption and saving. This means that as investment equals savings at any moment in time, this is not equilibrium, or, in other words, it is not the outcome of some adjustment over time between magnitudes expected by firms and magnitudes actually achieved (Schmitt, 1971). In short, the logical multiplier principle is based on the law that saving equals investment. The equivalence between the quantity of saving and the quantity of investment emerges from the bilateral character of the transactions between the producer on the one hand and, on the other hand, the consumer or the purchaser of capital equipment. (Keynes, 1936, p. 63) In its logical form, which is usually termed its ‘static form’, the multiplier cannot therefore be interpreted as a theory of adjustment of magnitudes making up national income. It is a theory of ‘the order of events’ in that it makes a distinction in macroeconomics between the expenditure that forms and the expenditure that disposes of national income. The formation of income is dependent on the expectations of entrepreneurs about how their output will find outlets either with households or with other firms. However, not all of the income formed in the investment goods sector is saved and not all of the income formed in the consumption goods sector is consumed. The workers who produce investment goods consume and those who produce consumption goods save. This means that aggregate income is ultimately and actually determined when it is spent in the various markets for goods and securities. The logical multiplier reflects the precise point at which incomes formed in the two sectors are not spent directly on purchasing the products to which they correspond, but that nonetheless the spending structure is congruent with the income-formation structure. The amount equivalent to the income formed in the consumption sector is spent in purchasing consumption goods, while the amount equivalent to the income formed in the capital goods sector is spent in purchasing capital goods. Understood in the context of the law that saving equals investment, ‘the multiplier is ultimately just a factor of proportionality’ (Schmitt, 1971, p.  96) that

Consumption, investment and the investment multiplier  131 makes it possible to calculate the respective shares of national income made over to consumption (and therefore saving) and investment. It marks the objective connection between entrepreneurs’ production decisions and spending by households and firms in product markets. In other words, the logical multiplier is the proportional rule serving as the quantitative relation which, in view of the behaviour of income-holders with regard to consumption, develops between the volume of output of goods intended for investment and the volume of output of goods intended for consumption. It indicates, while being reversed in a sense as it expresses expenditure in product markets, that production for consumption must give rise to income in an amount that is a determined multiple of the amount of income formed in the production of capital goods. In his 1937 paper The General Theory of Employment, Keynes sets out the following point which he terms ‘very greatly illuminating’ from his correspondence with D. H. Robertson (cf. Keynes, 1973, p. 90). If, for example, the public are in the habit of spending nine-tenths of their income on consumption goods, it follows that if entrepreneurs were to produce consumption goods at a cost more than nine times the cost of the investment goods they are producing, some part of their output could not be sold at a price which would cover its cost of production. For the consumption goods on the market would have cost more than nine-tenths of the aggregate income of the public and would therefore be in excess of the demand for consumption goods, which by hypothesis is only nine-tenths. Thus entrepreneurs will make a loss until they contract their output consumption down to an amount at which it no longer exceeds nine times their current output of investment goods. (Keynes, 1937a, p. 120) As it is presented here, the multiplier rule does not define any order of cause and effect in the ordering of incomes in spending. There is no ground for asserting that the income formed in producing investment goods fuels the income distributed in the consumer goods sector. Keynes did indeed assert that the amount entrepreneurs spent on producing consumption goods depended on the amount produced in the capital goods sector: The theory can be summed up by saying that, given the psychology of the public, the level of output and employment as a whole depends on the amount of investment. (ibid., p. 121) However, the dependency in question here is not expressed in terms of a process whereby the income distributed in the consumer goods sector is formed from the income created in the capital goods sector. Admittedly, Keynes says that investment drives the economy but investment comes into play in accordance with the (given) structuring function of the propensity to consume. The numerical

132  Bailly example with which Keynes illustrates his analysis in The General Theory of Employment suggests that the equivalent to income formed in each of the two sectors is spent in each sector in accordance with the marginal propensity to consume that prevails in the period under consideration. It is noticeable that the surplus output of the consumption goods sector obviously cannot find an outlet by virtue of the income distributed in the capital goods sector. Keynes writes that if the volume of consumption goods produced is greater than the propensity to consume the aggregate income, which he hypothesizes to be 9/10, then ‘entrepreneurs will make a loss until they contract their output of consumption goods to an amount at which it no longer exceeds nine times their current output of investment goods’ (ibid., p. 120). Although the production of investment goods is presented as decisive for increasing the aggregate output and employment in both sectors, it would be wrong to assert that in its logical version, the multiplier expresses the idea that income from the investment goods sector is the basis from which income distributed in the consumption sector is formed. The multiplier conceived of as a process When he likens his concept of the multiplier to that of the employment multiplier described by R. F. Kahn (1931), Keynes attempts to bring out a causal connection between the amount of income formed in the investment goods sector and the aggregate income through consumer spending. The former is described as primary income of a sort, which, because it is spent on consumption, gives rise to the secondary income, and so on. Thus, proceeding by analogy with the process that Kahn describes, Keynes attributes to the coefficient k the power to give rise to income in the consumption goods sector from consumption spending of income initially created in the capital goods sector. In so doing, he transposes the structural definition of aggregate income to the level of causal relations and constructs another theory designed to describe a mechanism whereby income is multiplied by the chain of events in spending income. Many Keynesians advance the idea, as the basis of the multiplication process, that one person’s spending forms another person’s income. Thus Robinson (1948, p. 14) writes: But income is the product of spending as well as the source of spending. People acquire income by meeting their mutual demand. One person’s spending is the sum (source) of other people’s income and one person’s income stems from the spending of others. (emphasis in original) The usual interpretation of the equation ∆Y  =  k∆I is that ∆Y arises because the incomes formed in the capital goods sector, but not yet spent in purchasing these same goods, are spent on consumption and accordingly gives rise to extra income in this sector. For the multiplication process to kick in, it is necessary but not sufficient for additional new wages ∆I to be paid out. For the mechanism to be triggered those who hold additional income formed in producing capital goods

Consumption, investment and the investment multiplier  133 must spend some of it in purchasing consumption goods. It is this expenditure of income from one sector (investment) in the other sector (consumption) that supposedly brings about a more than proportional rise in national income, which, ‘in the long run’, allows sufficient saving to provide an outlet for the investment goods initially produced. This means that if there were such a mechanism it would challenge the law that saving equals investment, since the two would not be equal at all times. Accordingly it seems necessary to enquire into the possibility that the amount equivalent to income formed in producing investment goods might be spent in the consumer goods sector. Following Keynes in this, we shall look in turn at two separate hypotheses: 1 Knowing the amount of expenditure in the investment goods sector, the consumption goods sector adapts its output in response to the law of the marginal propensity to consume. 2 The producers of consumer goods have failed to anticipate the increased output of the investment goods sector.

The producers of consumption goods have anticipated ∆I With Y = C + I as the definition of income for a given period of time, any variation in income recorded between two periods may be written as Y + ∆Y = C + ∆C + I + ∆I. A priori there is no adjustment process between the two terms of the equation. Reasoning in terms of variations does not require any new definitions of the magnitudes nor of their relationships. Like I and C, ∆I and ∆C represent both the output and the sale of consumption and investment goods. It follows that ∆Y = ∆C + ∆I is also a structural definition or, in other words, an identity assuming no causal connection between its terms other than that stating that variation in income results from combined variations in consumption and investment. The way in which households distribute their increased income between consumption and saving is not dependent on the amount of the variation in investment but on their behaviour in respect to consumption. On this point Keynes very clearly states that it is the marginal propensity to consume that indicates ‘how the next increment of output will have to be divided between consumption and investment’ (Keynes, 1936, p.  115). The marginal propensity to consume expresses nothing other than the normal relationship between current spending on consumption and the current amount of income. In other words, the increased income is divided between consumption and saving in the same proportion as before the increase occurred. k as a factor of proportionality The question of the ordering of events and of the multiplication of income over time involves the issue of whether income distributed in the capital goods sector or its equivalent may ultimately be spent in purchasing consumption goods, while the firms producing the consumer goods determine the volume of their output by anticipating the payment of ∆I.

134  Bailly The discussion has been carried on, so far, on the basis of a change in aggregate investment which has been foreseen sufficiently in advance for the consumption industries to advance pari passu with the capital goods industries without more disturbance to the price of consumption goods than is consequential, in conditions of decreasing returns, on an increase in the quantity which is produced. (Keynes, 1936, p. 122) As the division of the increased income between consumption (saving) and investment is given by the marginal propensity to consume, it is certain that the amount of saving cannot be the result of entrepreneurs’ choices about the production of goods to be capitalized. In addition, as it is the inverse of the marginal propensity to save, the multiplier coefficient k contains no concept of adjustment between saving and investment. The equation ∆Y = [1/(1 – c)] ∆I cannot be written without the principle of identity between variation in saving and variation in investment, and is actually another way of saying the identity between saving and investment, ∆S = ∆I. It is itself an identity that is observed from one period to another (Chick, 1983; Moore, 1994). In the expression ∆Y = k∆I, ∆I represents the formation of new income arising from the payment made to factors employed in the capital goods sector. These wages do not arise from any income or any wealth formed beforehand, but they are created directly with the production of the new output: income  =  value of output. As Moore (1988, 1994) points out, in the General Theory Keynes fails to show how the increased spending in the investment goods sector is financed. However, it may be considered, as Graziani (1985, 1988) argues, that the 1937 papers (Keynes 1937b,c) on the ‘finance motive’ provide an answer to this question. It is difficult to say today that ‘the fatal flaw in the textbook treatment of the multiplier is that it never addresses how an autonomous increase in investment spending is financed’ (Moore, 1994, p. 127; emphasis in original). Having earned ∆I in the capital goods sector, the production factors supposedly spend part of this new income on consumption goods that have been newly produced in expectation of the increased employment in the investment goods sector. The marginal propensity to consume, c, means that households having received ∆I spend c∆I on the purchase of consumption goods. There are decreasing returns in the consumption goods sector because the industries in question do not purchase extra equipment, ∆I, before engaging in their new production and increasing their output. So as to meet the expected new demand, firms producing consumption goods will take on and pay new workers additional wages for an amount of ∆C.1 The overall variation in income may then be expressed as ∆Y  =  ∆C  +  ∆I, where ∆Y = [1/(1 – c)] ∆I. Clearly, the producers of consumption goods are themselves going to consume some of their own output, namely c∆C. Thus it may be thought that to meet the new demand for consumption goods, and knowing beforehand the amount of additional employment in the investment goods sector and assuming that the marginal propensity to consume is stable, firms in the consumer goods sector will

Consumption, investment and the investment multiplier  135 decide their new level of output making allowance for the new wages paid in both sectors. This means that the increased output in the consumption goods sector will be not c∆I but: ∆C = c∆C + c∆I or ∆C = [c/(1 – c)] ∆I It is indisputable that the variation in national income is a multiple of the variation in wages paid in producing capital goods on the basis of ∆Y = [1/(1 –c)] ∆I. However, it is not at all certain that ∆Y results from the multiplication of wage units paid in the capital goods sector. k is not a factor of multiplication of wage units In the case under examination, because it has been assumed that entrepreneurs in the consumption goods sector have anticipated the increased employment in the investment goods sector, it is logically certain that the wages ∆C paid out in anticipation as from the first period do not arise from the sale of consumption goods. The immediate inference is that the wages paid in the investment goods sector do not provide the income formed in the production of consumption goods. The dynamics of multiplication, leading to a more than proportional increase in national income, cannot therefore arise from them being passed on through spending them. The national income is equal to the amount of new wages created and paid in both sectors. This means that the increased income of the current period, ∆Y, arises from the formation of both ∆I on the one hand and of ∆C on the other. The equation ∆Y = ∆C + ∆I is no more informative than the equation Y = C + I; there is no causal connection between the spending of ∆I and the formation of ∆C. This means that ∆Y = ∆C + ∆I is the structural definition of the variation in income and not the expression of a process of equilibrium adjustment. ∆Y = [1/(1 – c)]∆I is a proportionality equation that is identical in all respects to the equation of the logical multiplier: Y = [1/(1 – c)]I Of course, the holders of income formed in the investment goods-sector do not save all of their income, but neither do all of the new wage-earners employed in the consumption goods sector consume all of their wages. Let us assume that both comply with ‘the prevailing psychological law’ of the propensity to consume. A priori there is no reason to think that the marginal propensity to consume income formed in the consumption goods sector differs from that of income formed in the investment goods sector, and it can be inferred that wages paid in the consumption goods sector are saved in the same proportions as wages formed in the investment goods sector. According to the theory of the multiplier, there is an arithmetical relation between the level of consumption and the level of net investment, so that

136  Bailly other things equal . . .  consumption and net investment rise and fall in the same proportion. (Keynes, 1973, p. 155) Given that c∆C + c∆I = ∆C, and that ∆C = c∆C + (1 – c)∆C, it can be deduced that: c∆I = (1 – c)∆C

(7.1)

Moreover: c∆I + (1 – c)∆I = ∆I

(7.2)

Combining (7.1) and (7.2) gives: ∆I = (1 – c)∆C + (1 – c)∆I

(7.3)

as variation in aggregate saving is: ∆S = (1 – c)∆C + (1 – c)∆I

(7.4)

It follows immediately from this that: ∆S = ∆I

(7.5)

The consequence of this is that no ‘disequilibrium’ is found between saving and investment to warrant any adjustment process whatsoever. The part of ∆I that is consumed is immediately counterbalanced by the part of ∆C that is saved. This means that the increased output of the investment goods sector is immediately offset by the increased aggregate saving. There is an exchange of sorts between the producers of consumption goods and the producers of investment goods. Whereas the latter have the power to purchase the goods they have produced, they do not exercise it over these same goods, but, in proportion to c∆I, over the purchase of consumption goods. Neither do the producers of consumption goods, for their part, spend all of their income on consumption, but save some of it and in so doing contribute to making up the aggregate saving required to provide an outlet for investment goods. The law that saving equals investment holds true. Having established that overall the variation in saving equals the variation in investment, it can be inferred that the equivalent amount to the wages formed in the investment goods sector is not consumed and that, from this, the marginal propensity to consume ∆I is zero. The income corresponding to ∆I cannot then contribute to the formation of additional income in the consumption goods sector. Thus, in each period, the wage units formed in the output of investment goods are multiplied by a coefficient k = 1/(1 – 0) = 1.

Consumption, investment and the investment multiplier  137 The equation ∆Y = [1/(1 – c)]∆I cannot then be interpreted in terms of a causal process of the formation of incomes, the one from the other. Income formed in the consumption goods sector does not arise from the spending of income distributed in the investment goods sector. ∆Y = k∆I must be read solely as an expression of the respective proportions of consumption and investment within the current aggregate income. There is no difference in kind between this situation where the output of investment goods increases and that where investment is renewed as before. In both cases the producers of consumption goods define the amount of their output by anticipating the amount of output of the capital goods sector by virtue of their knowledge of the behaviour of households with regard to consumption and therefore of the multiplier Y = [1/(1 – c)]I. But in every interval of time the theory of the multiplier holds good in the sense that the increment of aggregate demand is equal to the product of the increment of aggregate investment and the multiplier as determined by the marginal propensity to consume. (Keynes, 1936, p. 123) It will be remembered that we begin from the hypothesis that the producers of consumer goods anticipate the increased employment in the investment goods sector. This means that they decide to increase their own output even before the income distributed in the investment goods sector can be spent. It is therefore impossible for ∆C to arise from the spending of income formed in the production of investment goods. The increase in national income arises, from period to period, from the simultaneous increase in income distributed in the consumption goods sector and in the investment goods sector: ∆Y = ∆C + ∆I. This equation is strictly of the same kind as the equation in the definition Y = C + I and the fundamental relations between the values are not changed in any way by reasoning in terms of variation. The increased aggregate income, ∆Y, is indeed a multiple of the increase in employment in the investment goods sector, ∆I, but it is so precisely because the fundamental identities characterizing the proportions of consumption and investment in income are unchanged. In other words, ∆Y is a multiple of ∆I just as Y is a multiple of I. Given that ∆C is not supplied by c∆I, the arithmetic relation that may be established between consumption and investment is not based on the multiplication of wage units paid in the investment goods sector. The additional wages formed in the latter sector cannot therefore be analysed as the ‘income base’ from which other income would be created by multiplication of their constituent wage units. The fact that each income-holder individually may spend his or her wage in purchasing consumption goods does not mean that on aggregate the equivalent amount of the wages formed in the production of investment goods may be spent in purchasing consumption goods. In the case just examined, the spending of additional income formed in the production of investment goods on purchasing consumption goods does not provide the new additional income formed in the

138  Bailly consumption goods sector. The incomes distributed in both sectors are the result of firms’ anticipation of outlets for their products and of the spending of previously formed income. The fact that some firms anticipate the increased income distributed in other firms and decide to increase the employment they offer is not to be confused with a process of multiplication of income through spending. Even when variations are considered, it holds true that income created in producing both capital goods and consumption goods is spent in each sector respectively in the same proportions as it was created. This is what the logical version of Keynes’s multiplier expresses at its most fundamental.

The producers of consumption goods failed to foresee ∆I In general, however, we have to take account of the case where the initiative comes from an increase in the output of capital goods industries which was not fully foreseen. It is obvious that an initiative of this description only produces its full effect on employment over a period of time. . .  The explanation of these . . . sets of facts can be seen most clearly by taking the extreme case where the expansion of employment in the capital goods industries is so entirely unforeseen that in the first instance there is no increase whatever in the output of consumption goods. (Keynes, 1936, pp. 122–3) This ‘second’ formulation of the multiplier, which is generally considered the more fundamental one, seeks to explain that national income increases in a series of waves as a result of the time lag between the production of investment goods and the production of consumption goods. As investment is for Keynes ‘that factor which is most prone to sudden and wide fluctuation’ (Keynes, 1937a), it can be described as the driving force behind the process. Let us call k the investment multiplier. It tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment. (Keynes, 1936, p. 115) Here the causal process is supposed to unfold over time. Taking the initiative in increasing their production, the firms producing capital goods, because of the distribution of additional income, will cause an increase in demand for consumption goods to which firms producing consumption goods will have to respond sooner or later. These firms are then supposed to derive the necessary resources for financing an increase in their production from the expenditure of wage-earners in the first sector. As a corollary, given that some of the income formed in producing capital goods is spent on consumption, a transitory situation occurs during which savings does not equal investment. In addition, this conception of the multiplier is based by implication on the idea that the marginal propensity to consume has a

Consumption, investment and the investment multiplier  139 ‘dynamiting’ effect since the effect of passing on income by spending it supposedly varies with the amount involved. The hypothesis that incomes are ordered by spending them As the formation of national income is now analysed from the perspective of a time-based process by which ‘incomes generate spending and spending generates incomes’ (Hawtrey, 1967, p. 32), the equation ∆Y = ∆C + ∆I must be read as the expression of a mechanism whereby the increase in incomes formed in the production of capital goods, ∆I, brings about an increase in spending on consumption, which spending drives the increase in incomes formed in the consumption goods sector, ∆C. The consequence of this ordering of incomes by expenditure is supposedly that the aggregate income varies by an amount that is more than proportional to the initial injection, ∆I. Thus, the formation of wage units in the consumption goods production sector supposedly does not obey the same law as applies in the investment goods sector. In the latter sector, wages are said to be formed out of zero, whereas in the consumption sector, they are supposedly formed through the spending of pre-existing income. The wages corresponding to increased output in the capital goods sector therefore form in some sense the base2 of the income which goes to form the wages distributed in the consumption goods sector. However, because income-holders do not consume all of their income immediately, the multiplication mechanism is supposed to act over a certain period of time: the time it takes for individuals to build up additional saving equal to that of the initial additional investment. Keynes summarized the working of the multiplication process thus: An increment of investment in terms of wage-units cannot occur unless the public are prepared to increase their savings in terms of wage-units. Ordinarily speaking, the public will not do this unless their aggregate income in terms of wage-units is increasing. Thus their effort to consume a part of their increased incomes will stimulate output until the new level (and distribution) of incomes provides a margin of saving sufficient to correspond to the increased investment. (Keynes, 1936, p. 117) Under the first proposition it is saving that ultimately finances investment and investment only really occurs in proportion to saving by the public. This means that making an investment requires two separate but complementary operations, namely (1) the production of investment goods, and (2) the purchase of these same goods through savings formed from increased income. The second proposition combines the two sectors. The increased saving required to finance the increased investment stems from both the increased output of investment goods and the increased output of consumer goods; the latter increase appears as a response to the former in accordance with a mechanical effect. The third proposition contains in substance the essential features foreshadowing

140  Bailly the transposition of the identities established in chapter 6 of The General Theory in terms of causal relations of equilibrium. The propensity to consume (the public’s efforts) becomes a factor of increased output and therefore of the formation of additional income in the consumption goods sector. It is because the holders of ∆I spend some of their income on purchasing consumption goods that, to meet this new demand, the producers of consumption goods increase their output and therefore the income distributed. The aggregate increase in production appears therefore to be dependent on the level of the marginal propensity to consume, which is now no longer presented as a state of consumption behaviour by income-holders but as a factor determining variations in aggregate income. Thus, in the exposition of the multiplication process, the marginal propensity to consume expresses both the spending of part of the income formed in the production of investment goods on the purchase of consumption goods and the increase in income formed in the consumption goods sector (Asimakopulos, 1991, p. 66). It is on the basis of this interpretation of the marginal propensity to consume as a factor of income formation that Dalziel presents the initial phase of the process thus: In the first round of the process, the factors of production that received the income arising out of the investment expenditures spend some proportion of that income on consumption goods and services .  .  . The consumption expenditure creates further income (and the beginning of the multiplier effect). (1996, p. 316) To summarize we might say that the increase in investment, now assimilated to the production of investment goods alone, ∆I, is the first operation but that the multiplier process kicks in because households spend some of their additional income on purchasing consumption goods and that this spending mechanically generates new income in the consumption goods sector.3 The chronology of the process further supposes that the increase in investment precedes the increase in saving, which, through the increase in aggregate income, will adjust to the amount of additional capital goods produced. The Keynesian multiplier concerns the process by which saving and investment are equilibrated in a monetary production economy. (Moore, 1994, p. 121) Clearly there is no longer any question of identity between saving and investment, as the multiplier process is supposed to occur for so long as ∆S < ∆I and, because of the variation in income, until ∆S = ∆I. Although it is inferred from the definition Y = kI, the equation ∆Y = k∆I is no longer a definition but an equilibrium between two separate values whose variations adjust over time. By the very fact that it is variations that are being considered, what was a structural definition of the distribution of the aggregate output between consumption and investment has become a causal process of adjustment. It is the

Consumption, investment and the investment multiplier  141 increase in investment, ∆I, and the increase alone rather than the total investment, I + ∆I, that supposedly creates the necessary conditions for multiplication of the wage units initially issued in the production of capital goods. In the equation Y + ∆Y = C + ∆C + I + ∆I, ∆I is seemingly not of quite the same nature as I. In the equation defining income Y = C + I, I represents the production and purchase of investment goods. In the equation ∆Y = ∆C + ∆I, ∆I represents the production of investment goods but not their purchase. The proof of this is that the income multiplication mechanism is assumed to unfold for so long as ∆S < ∆I, that is, throughout the time when the economy is still without the financial resources for purchasing the investment goods produced. To illustrate this we may refer to the developments on ‘wasteful loan expenditures’ that may enrich the community although no one purchases the useless products (Keynes, 1936, pp. 128–9). The process cannot be engaged immediately The multiplication process supposedly kicks in when some part of ∆I is spent on purchasing consumption goods, that is, when current saving varies by less than the variation in expenditure on the production of investment goods. This also means that, as increased output in the investment goods sector is likened to the variation in investment, the actual investment generates additional purchasing power over consumption goods. An assertion of this kind seems to contradict the following passage from the General Theory: Assuming that the decisions to invest become effective, they must in doing so either curtail consumption or expand income. Thus the act of investment in itself cannot help causing the residual or margin, which we call saving, to increase by a corresponding amount. (Keynes, 1936, p. 64) This leads us to query whether the approach highlighting a multiplier process has any sound basis either in logic or in fact. The central issue is still whether or not the terms of the definition of income Y = C + I can be transposed to the level of causal connections ∆I  ∆C  ∆Y = k∆I. In order to answer this question we have to enquire whether the part of current aggregate income corresponding to ∆I, or more specifically to the fraction c∆I of ∆I, really can be spent on purchasing anything other than investment goods.4 As firms in the consumption goods sector have not anticipated any increase in income in the investment goods sector, they have not increased employment and do not offer more products on the markets. The initial stage of the process is supposedly characterized by the situation where ∆C = 0 in its formation. Current income in this initial stage can then be expressed by the equation Y + ∆Y = C + I + ∆I. Under these circumstances, like Keynes we are entitled to think that additional demand for consumption goods generated by the increased wages distributed in the capital goods sector will bring about an increase in consumption prices.

142  Bailly In this event the efforts of those newly employed in the capital goods industries to consume a proportion of their increased incomes will raise the prices of consumption goods until a temporary equilibrium between demand and supply has been brought about partly by the high prices causing a postponement of consumption, partly by a redistribution of income in favour of the saving classes as an effect of the increased profits resulting from the higher prices, and partly by the higher prices causing a depletion of stocks. (ibid., pp. 123–4) The prices of consumer goods increase because the new workers employed in producing capital goods naturally exercise demand for consumption goods for an amount c∆I. By spending c∆I the producers of investment goods obtain consumption goods. But as output of consumption goods has not increased, ∆C = 0, that same amount of goods will not be available for the holders of income formed in the next round of production of consumption goods, C, and investment goods, I, which also undergo a price rise. The increase in the prices of consumer goods undoubtedly affects the distribution of income and in particular brings about an increase in the profits of firms producing consumer goods. Even if they were fully redistributed, profits, or their equivalent, cannot be spent on purchasing consumption goods. They are necessarily saved because they result from the fact that firms in the consumption sector cannot immediately provide enough goods to satisfy the demand from incomeholders. Consequently, because the volume of consumption goods available has not increased in proportion to the wages paid out in the production of investment goods, the amount of additional saving – whether in the form of profits, cash bank deposits (liquidity preference) or financial placements – is strictly equal to ∆I (Schmitt, 1996). At the first stage, the equivalent of additional new wages paid in the investment goods sector is saved. This is not the choice of economic agents, as Barrère (1990, p. 151) seems to believe, but a factual constraint. Because no consumption goods are available, additional income cannot be consumed – it can only be saved. That is tantamount to saying that for the equivalent of ∆I, income-holders have strictly no purchasing power over consumption goods.5 In other words, the propensity to consume the equivalent of ∆I is strictly zero. As a consequence there is a fall in the mean propensity to consume because consumption remains constant while income increases: C/(Y + ∆Y) < C/Y. Only in the event of the community maintaining their consumption unchanged in spite of the increase in employment and hence in real income, will the increase of employment be restricted to the primary employment provided by the public works. (Keynes, 1936, p. 117)

Consumption, investment and the investment multiplier  143 Keynes saw in this a special case of a type of behaviour by income holders, whereas it is in fact a general principle. That the marginal propensity to consume the equivalent of ∆I is zero is not dependent on the income holders but on the fact that there are no consumption goods on which to spend their income. Thus consumption does not increase, in other words, from the standpoint of income expenditure ∆C = 0. It is hardly surprising under these circumstances that there is at least a transient fall in marginal propensity to consume of all income holders (Cottrell, 1994). But it is not this fall that has a decisive effect on the multiplier. What matters here is the amount of the marginal propensity to consume the equivalent of the income distributed in the investment goods sector, ∆I. It is certain that in the equation ∆Y = [1/(1 – c)]∆I, c represents the marginal propensity to consume the additional income formed in the investment goods sector. It is this propensity, and not the general marginal propensity to consume, that gives the multiplier coefficient k its ‘multiplying force’. Now, given that c applied to ∆I is zero, it follows that k = 1/(1 – c) = 1. In other words, the multiplier of income formed in the capital goods sector being equal to unity, no income multiplication process can engage. The upshot of that is that the total increase in aggregate income is strictly equal to the amount that is paid in producing capital goods, ∆Y = ∆I. The injection of ∆I cannot directly and immediately generate an increase in income greater than ∆I. Conversely, new saving ∆S, equal to the purchasing power required to acquire the additional capital goods produced, ∆I, is observed. At this first stage ∆I = ∆S. In view of the fact that the multiplier effect of increased income in the production-goods sector does not necessarily have any direct and immediate effect, we may share Keynes’s view that the action of the mechanism may be deferred. The hypothesis of deferred consumption Considering that the income-holders have not consumed today the equivalent of ∆I and have saved this same amount, Keynes asserts that they will be able to spend this saving later on purchasing consumption goods when the firms in the sector have increased their output. As time goes on, however, the consumption goods industries adjust themselves to the new demand, so that when the deferred consumption is enjoyed, the marginal propensity to consume rises temporarily above its normal level, to compensate for the extent to which it previously fell below it, and eventually returns to its normal level. (Keynes, 1936, p. 124) What makes up the new demand to which the producers of consumption goods adapt? In the case in point, it is the demand from the initial injection of income and not that generated by the repetition of ∆I from one period to another. The problem raised, remember, is how is the multiplier process triggered by the issue

144  Bailly of ∆I that was not anticipated by the producers of consumption goods and by the spending of c∆I in purchasing consumption goods? Let us consider the problem on the basis of Hansen’s presentation of the multiplier process: Imagine a society with a normal marginal propensity to consume of 2/3. Assume we start with a stable income flow. We then inject on a sustained basis an additional 100 units of investment per year. By reason of expenditure lag, consumption would not rise at all in the first period when the new injection is made. Let ∆C1 = 0, and ∆Y1 = 100. Then ∆C1/∆Y1 = 0. In the second period, ∆C2 = 67 and ∆Y2 (measured from the initial stable base) is 167; or ∆C2/∆Y2  =  67/167. In the third period, ∆C3  =  111.5 and ∆Y3  =  211.6; thus ∆C3/∆Y3 = 111.5/211.5. (Hansen, 1953, p. 78) Hansen’s reasoning is ambiguous to say the least and may be interpreted in either of two ways. 1 We may accept that the increase in income in the second period, ∆Y2, is 167 because investment increased by 100 each year: ∆I1 = 100, ∆I2 = 100, etc. In this case, it must be accepted that because of the expenditure lag the marginal propensity to consume ∆I  =  100 is equal to 0 each year, hence c∆I1  =  0, c∆I2  =  0, etc. From one period to another then there is no increase in the marginal propensity to consume. 2 If we consider, as the brackets seem to indicate, that the injection of an initial investment of 100 in the first year is renewed year after year, we cannot say that aggregate investment is growing in the second period, in the third period, etc.; it only grows in the first period. If we write ∆I1 = 100, conversely we cannot logically write ∆I2 = 100, but should write ∆I2 = 0 instead. It follows that if we were to accept that ∆C2 = 67, ∆Y2 would not be 167 but 67, that is, the amount of ‘dis-saving’. Yet this hypothesis itself is clearly unjustified. It fails to allow for the fact that for households to consume an additional 67, the consumption goods sector must increase its output and therefore employment to meet the new demand. It would also imply that the firms producing consumption goods would simply follow the variations in the capital goods production sector with a time-lag, giving ∆I  ∆S  ∆C. Let us work through the reasoning again. The ‘new demand’ made on firms producing consumer goods corresponds to the postponement of consumption produced by the rise in prices (Keynes, 1936, p. 142), which Keynes argues is reflected by the constitution of saving6 for ‘deferred consumption’. This additional demand for consumption goods that income-holders were unable to satisfy, not because of Hansen’s ‘expenditure lag’ but simply because there were no consumption goods on which to spend the income, is purportedly expressed by dis-saving of the equivalent of c∆I.

Consumption, investment and the investment multiplier  145 The holders of the income saved cannot purchase any new consumption goods until the industries in the consumption goods sector have increased their output. In addition, for the multiplier mechanism to come into play, it must be supposed that ‘dis-saving’ does not affect the purchase of products previously stockpiled7 but consumption goods produced in the ensuing periods, which we can group under the term ‘the second stage’. Let us pursue Keynes’s reasoning and assume that the consumption goods production sector increases its output to meet this additional demand of deferred consumption. Indisputably, to increase its output the consumption goods sector must increase employment, which is reflected by the formation of additional income the amount of which may be expressed by ∆C.8 Because of the law of propensity to consume, the holders of new income will acquire consumption goods for an amount c∆C. This means that for there to be any ‘deferred consumption’, measured in currentwage units, firms in the consumption goods sector must increase their output by more than the expected amount of ‘dis-saving’. It may then be thought that the multiplier mechanism is triggered and that ∆C, in part at least, is supplied by the expenditure of income generated previously by capital goods producers. Wray is quite clear about this point: On the surface, it may appear that releases of money hoards can also generate growth. A release of hoards may represent the purchase of paper issued by those who want to deficit spend. However, hoards represent the surpluses received as others used deficit spending in the past, and so represent debts that have not been retired. Thus, intermediation of released hoards cannot be the source of sustained growth. (Wray, 1991, p. 961) Obviously ‘dis-savers’ are going to purchase those consumption goods that are not bought by the holders of ∆C;9 in other words they will buy at most for an amount of (1  –  c)∆C. It can then be observed that the variation in current spending, formed on additional income distributed in the production of consumption goods, is strictly equal to the amount of dis-saving. It can be inferred that the amount of income spent on purchasing consumption goods is no higher (nor any lower) than the amount of income formed in the production of consumption goods. It follows that no part of the equivalent of wages formed previously in the production of capital goods is spent on purchasing consumption goods. On aggregate the marginal propensity to consume does not vary. In effect, the saving formed previously is fully reconstituted through the exchange made between the new producers of consumption goods and the ‘dis-savers’. One person’s saving leaves scope for another person’s consumption. But no one can save without acquiring an asset, whether it be cash or a debt or capital goods; and no one can acquire an asset which he did not previously possess, unless either an asset of equal value is newly produced or someone else parts with an asset of that value which he previously had. . .  It follows

146  Bailly that the aggregate saving of the first individual and of others taken together must necessarily be equal to the amount of current new investment. (Keynes, 1936, pp. 81–2) From this point of view, dis-saving is not net for the whole economy and so it contributes nothing to the formation of the new current income. The saving formed in the first round for an amount ∆I is still not spent on purchasing consumption goods. At no time can any deviation whatsoever be found between ∆S and ∆I. This is because, as the logic multiplier indicates, expenditure of an amount equivalent to the income formed in the production of investment goods cannot occur in the consumption goods sector, even if deferred. If it were otherwise, the producers of investment goods could not find outlets for their products for want of purchasing power in the economy; the investment would fail. If it were accepted that, at the second stage, the income or a part of the income formed in the capital goods sector was finally spent on consumption, that would imply first of all that the producers of capital goods had still not sold their products and not recovered their production costs. The formation of a new income constitutes a ‘semi-transaction’ which is only viable as a whole when the complementary semi-transaction is adjoined too it; simply put: the income created in the production of a commodity must later be spent in purchasing it; if the corresponding final expenditure is lacking, a given income creation brings no additional purchasing power to the economy as a whole, thus placing the improved level of employment in immediate jeopardy. (Schmitt, 1996, p. 125; emphasis in original) Thus, rather than explaining how income is multiplied, it is actually shown that the saving required to finance investment would finally be lacking and that far from an increase in aggregate income being observed, it would tend instead to contract. Being unable to find outlets for their products, the firms producing capital goods would not readily renew the production of ∆I and so would reduce their activity, and thereby employment and the income distributed in the following periods. By the same token, if there could be any saving that was ‘lost for investment’ because it was spent on consumption,10 the very existence of the logical multiplier, Y = [1/(1 – c)]I, would be challenged and through it the concept of the propensity to consume and the law that saving equals investment. In truth, at the second stage, the new income distributed by the producers of consumption goods is not fuelled by net dis-saving because, even before selling their products, they must distribute new income for an amount greater than the new additional demand c∆I. Accordingly, we find ourselves back at the first case examined above where firms are aware of the change in output of other sectors. The only difference here lies in the lag between the time at which some firms decide to produce more and the time at which others take account of this by increasing their output. The time to be taken into account is only the time it takes

Consumption, investment and the investment multiplier  147 to physically implement the additional production of consumption goods, and in no event the time required for the adjustment of saving and investment through income, which, for the period under consideration, does not vary. Even if there is a lag between the various entrepreneurs deciding to increase their output, I and S are not adjusted over time, and ∆I does not generate any income multiplier mechanism as it (or its equivalent) cannot be spent in purchasing consumption goods. The increase in national income appears as a multiple of the increase in the amount of wages distributed in the investment goods sector, solely because of the proportionality equation Y = [1/(1 – c)]I and not because the income formed in the consumption goods sector derives from the income formed in the capital goods sector. As a consequence, no process can be observed whereby the income of one period is determined further to the multiplication of wage units issued in a specific sector of the economy. All income spent in final consumption has its equivalent in the income formed in the production of consumption goods and all saving has as its equivalent the income formed in the production of capital goods (Bradley, 1994, p. 100). This conclusion, which is consistent with the logical multiplier principle, challenges the idea that there can be an ordering mechanism of income and spending, for the basic reason that the expenditure that supposedly provides the wages in the consumption goods sector cannot be made until the same sector has increased its own output and by the same token distributed additional income. The fact that the equivalent of income formed in the capital goods sector cannot be sold in purchasing consumption goods shows that it is impossible to trigger a time-based income multiplication process.

Conclusion The two formulations of the multiplier do not strictly derive from the same conceptual framework, and the structural definitions underlying the logical multiplier theory cannot logically be transposed to the realm of cause and effect. In other words, expenditures on consumption derived from the income formed in the investment goods sector is not the source of supply of income distributed in the consumption goods sector. If the increase in income in the capital goods sector can ultimately be reflected by an increase in the income formed in the consumption sector, it is not because of any transmission of purchasing power but because the firms in the latter sector decide to increase their output. It is the principle of effective demand that prevails and the passage of time does not contradict it; today’s income is not formed from yesterday’s income. Aggregate income does not increase because of inter-sector spending of additional income formed in either sector, but because firms, anticipating outlets for their products, have decided to increase their output, and therefore to increase employment and the corresponding wages. In macroeconomics, since incomes are determined in the dual movement of their formation and their spending, they cannot form an uninterrupted chain over time. One person’s spending does not form another person’s income because, in

148  Bailly our monetary production economy, all income originates from production and all spending by some on purchasing the output of others involves an exchange wherein the income of those who spend is destroyed. For the exchange to occur, all involved must have generated new outputs and therefore contributed to the formation of aggregate income for strictly the same amount as the value of their output, that is, of their own income. From this, it is impossible to demonstrate any multiplication process whereby the wage units issued in one sector could supply the wages distributed in another. Generally, there is no dynamic multiplier of a value other than unity, and it follows that no income dynamics can be constructed logically by the spending of income on the different markets.

Notes 1 Which in turn are funded by finance (Graziani, 1985, 1988). 2 Just as in the framework of the credit multiplier theory, we speak of the monetary base. 3 This is the standard textbook presentation of things. 4 Which would be in contradiction with Keynes’s own definition of investment, namely ‘that part of current output which is not consumed’ (Keynes, 1936, p. 63). 5 Thus, contrary to what A. Cottrell (1994) seems to argue, monetary creation alone cannot trigger a multiplier mechanism. 6 Which may be liquid: liquidity preference. J. Kregel (1985) shows the indissociable connection between the dynamic multiplier and liquidity preference. 7 It is therefore not a dis-investment. 8 Whether this income is distributed from profits constituted previously when prices rose or is formed from monetary creation does not fundamentally change matters here. 9 Here we do not consider the holders of ∆I so as not to complicate the argument. 10 An idea that Keynes himself contests: cf. Keynes (1936, p. 81).

References Asimakopulos A. (1991) Keynes’s General Theory and Accumulation, Cambridge: Cambridge University Press. Barrère A. (1990) Macroéconomie Keynésienne: Le projet économique de John Maynard Keynes, Paris: Dunod. Bradley X. (1994) ‘Le multiplicateur d’investissement et l’épargne des revenus’, Recherches Economiques de Louvain, Vol. 60, No. 1, pp. 87–104. Chick V. (1983) Macroeconomics after Keynes, Deddington, UK: Philip Allan. Cottrell A. (1994) ‘Endogenous Money and the Multiplier’, Journal of Post Keynesian Economics, Vol. 17, No. 1, Fall, pp. 111–20. Dalziel P. (1996) ‘The Keynesian Multiplier, Liquidity Preference, and Endogenous Money’, Journal of Post Keynesian Economics, Vol. 18, No. 3, Spring, pp. 311–31. Graziani A. (1985) ‘Le débat sur le ‘motif de financement’ de J. M. Keynes’, Economie Appliquée, Vol. 38, No. 1, pp. 159–75. Graziani A. (1988) ‘Le financement de l’économie dans la pensée de J. M. Keynes’, Cahiers d’Economie Politique. La théorie de John Maynard Keynes: un cinquantenaire, Paris: L’harmattan, pp. 151–66. Hawtrey R. (1967) Incomes and Money, London: Longanes.

Consumption, investment and the investment multiplier  149 Hansen A. H. (1953) A Guide to Keynes, New York: McGraw-Hill. Kahn R. (1931) ‘The Relation of Home Investment to Unemployment’, Economic Journal, June, pp. 173–98. Keynes J. M. (1936) The General Theory of Employment, Interest and Money. London: Macmillan. Reprinted in The Collected Writings of John Maynard Keynes, Vol. 7, London: Macmillan, 1973. Keynes J. M. (1937a) ‘The General Theory of Employment’, Quarterly Journal of Economics, February. Reprinted in The Collected Writings of John Maynard Keynes, Vol. 14, London: Macmillan, 1973, pp. 109–23. Keynes J. M. (1937b) ‘Alternative Theories of the Rate of Interest’, Economic Journal, June. Reprinted in The Collected Writings of John Maynard Keynes, Vol. 14, London: Macmillan, 1973, pp. 201–15. Keynes J. M. (1937c) ‘The ‘Ex Ante’ Theory of the Rate of Interest’, Economic Journal, December. Reprinted in The Collected Writings of John Maynard Keynes, Vol. 14, London: Macmillan, 1973, pp. 215–23. Keynes J. M. (1973) ‘Harrod: “The Trade Cycle”: Lecture Notes’, in The Collected Writings of John Maynard Keynes, Vol. 14, London: Macmillan, pp. 151–62. Kregel J. (1985) ‘Le multiplicateur et la préférence pour la liquidité: deux aspects de la théorie de la demande effective’, in Keynes Aujourd’hui: Théories et Politiques, Paris: Economica, pp. 223–39. Moore B. J., (1988) Horizontalists and Verticalists. The Macroeconomics of Credit Money. Cambridge: Cambridge University Press. Moore B. J. (1994) ‘The Demise of the Keynesian Multiplier: A Reply to Cottrell’, Journal of Post Keynesian Economics, Vol. 17, No. 1, Fall, pp. 121–33. Robinson J. (1948) ‘Introduction à la théorie de l’emploi’, Etudes et Documents de l’I.N.S.E.E., Paris: Presses universitaires de France. Schmitt B. (1971) L’analyse Macro-économique des Revenus, Paris: Dalloz. Schmitt B. (1972) Macroeconomic Theory. A Fundamental Revision, Albeuve, Switzerland: Castella. Schmitt B. (1996) ‘A New Paradigm for the Determination of Money Prices’, in G. Deleplace and E. Nell (eds), Money in Motion: The Post Keynesian and Circulation Approaches, New York: Macmillan, pp. 104–38. Wray L. R. (1991) ‘Saving, Profits, and Speculation in Capitalist Economies’, Journal of Economic Issues, Vol. 25, No. 4, December, pp. 951–75.

Part III

Toward a re-interpretation of the multiplier

8 Kalecki and the multiplier Malcolm Sawyer

Introduction The terminology of the ‘multiplier’ did not feature heavily in Kalecki’s writings. In his review of Keynes’s General Theory (Kalecki, 1990, pp. 223–2) and in a paper published shortly afterwards in 1937 using very similar material (ibid., pp. 529–571), Kalecki did discuss ‘the Keynesian multiplier’. In some of his early work, Kalecki presented formulae which (as will be seen below) could readily be given a multiplier-type interpretation though Kalecki himself did not do so at the time. But, as will also be seen below, Kalecki did discuss the effects of an expansion of investment on output and other sectors of the economy in ways which are consistent with a ‘multiplier view’. That means there are direct and indirect effects of an expansion of investment on output and employment in the economy. In this chapter we seek to discuss Kalecki’s ideas as they relate to the ‘multiplier’, which we interpret as the general idea that investment (and other forms of autonomous expenditure) generates changes in output and income of the same sign as the change in investment, and is generally larger in magnitude. In considering the significance of his writings for the multiplier, the following points should be borne in mind. First, Kalecki gave attention to the determinants of the decisions on investment, and then portrayed those decisions being carried through in a subsequent period (or spread over a number of periods). Investment decisions were carried through in full which implied that there is sufficient capacity in the investment goods industry to meet the demand: ‘We wish now to state that the present investment .  .  . is the result not of present but of former investment decisions, for, as we shall see immediately, a certain, relatively long, time is needed to complete the investment projects. This fact is of fundamental importance for the dynamics of an economic system’ (ibid., p. 534). Second, the investment expenditure can only proceed if it is financed, and Kalecki made the working assumption in the development of his business cycle model that bank credit would be readily available to finance the proposed investment. ‘We assume – as is actually the case – that increased investment is carried out by means of creation of purchasing power rather than at the expense of capitalist consumption’ (ibid., p. 165, fn.). In the event that banks did not provide the

154  Sawyer required credit the investment would not proceed, and banks did have it within their power to cut off an intended increase in investment. The financing of additional investment is affected by the so-called creation of purchasing power. The demand for bank credits increases and these are granted by the banks. The financial means used by entrepreneurs for the construction of new investments reach the investment goods industries. This additional demand makes for setting to work idle equipment and unemployed labour. The increased employment is a source of additional demand for consumer goods and thus results in turn in higher employment in the respective industries. Finally, the additional investment outlay finds its way directly and through the workers’ spending, into the pockets of capitalists (we assume that workers do not save). The additional profits flow back as deposits to the banks. Bank credits increase by the amount additionally invested and deposits by the amount of the additional profits. The entrepreneurs who engage in additional investment are ‘propelling’ into the pockets of other capitalists profits which are equal to their investment, and they are becoming indebted to these capitalists to the same extent via banks. (ibid., p. 190) Third, Kalecki used (at least) two modes of analysis where investment and economic activity were concerned, and these can be found, for example, in his early writings (in the first half of the 1930s). One mode of analysis as seen used a (short-period) equilibrium, from which it would be possible (though Kalecki rarely did) to derive a ‘multiplier’ between the difference in income (or more often in Kalecki’s analysis, profits) and the difference in investment expenditure. The other mode of analysis, for which Kalecki is better known, was the development of a model of the business cycle from the two-way interactions between investment and economic activity. On the one hand, investment decisions (and thereby future investment expenditure) depend on factors such as profitability which are linked with the level of economic activity. On the other hand, investment expenditure helps to determine the level of economic activity and profitability. In this mode of analysis there is a two-way relationship between investment and economic activity, and it is then difficult to ask the ‘multiplier’ question – that is how much different would economic activity be for a given difference in investment expenditure. This chapter proceeds by first considering the multipliers which do appear in Kalecki’s writings and the status and meaning of those multipliers. These multipliers are restricted to the relationship between investment and economic activity, and the next section briefly broadens this discussion by considering Kalecki’s views on the role of ‘external markets’, that is, export surpluses and budget deficits. Decisions to undertake expenditure have to be financed if they are to come to fruition, and this leads to the role of finance, which is the topic of the fourth

Kalecki and the multiplier  155 section. The general thrust of this approach is that investment causes savings, the issue explored next. The final section provides a brief review of the arguments on ‘crowding out’, where it is argued that (with one exception) Kalecki effectively dismissed those arguments.

Some simple multipliers in Kalecki’s analysis In one of his earliest papers,2 Kalecki (1990, p. 69) derived the following simple relationship: Where P is profits, B0 is the constant part of capitalists’ consumption, A is gross accumulation (‘all goods which are used in the reproduction and expansion of fixed capital as well as the increase in inventories’) and λ is marginal propensity to consume out of profits (where Kalecki assumed that all wages were consumed): P = (B0 + A)/(1 – λ)

(8.1)

This equation, in turn, was derived from two simple equations, namely P = C + A and a capitalists’ consumption function, C = B0 + λP. At this stage in the development of his approach, Kalecki did not postulate any relationship between profits and income (his development of the ‘degree of monopoly’ as that which governs the distribution of income between wages and profits came later in a paper published in 1938), though he did in later presentations as seen below. In this equation, it is clear that Kalecki saw causality as running from right to left, and (at the aggregate level) capitalists’ expenditure as determining profits. As Kalecki was to later write, ‘capitalists as a class gain exactly as much as they invest or consume, and if – in a closed system – they ceased to construct and consume they could not make any money at all’ (Kalecki, 1990, p. 79). The assumption that wages are spent and the view that capitalists’ expenditure determines their income was reflected in an aphorism ascribed by Joan Robinson to Kalecki that ‘the workers spend what they get, and capitalists get what they spend’ (Robinson, 1966, p.  341), though these words cannot be found in the writings of Kalecki. It would have been a simple step from this relationship to derive a multiplier result for the effects of a change in A (and indeed B0) on profits. A further assumption, such as a constant distribution of income between wages and profits, would then have been required to derive a multiplier in terms of income and A. Kalecki followed the derivation of the equation quoted above by discussing investment decisions and model investment (relative to the capital stock K) as a function of the rate of profit (P/K) and the rate of interest (i), written as I/K = f(P/K, i). He then substituted for P/K from the equivalent of equation (8.1) above, and assumed that the rate of interest moved with the rate of profit, to reach: I/K = ψ(B0 + A/K)

156  Sawyer which ‘holds as long as there is no intervention of the central bank and no crisis of confidence’ (see equation 9 in Kalecki, 1990, p. 74). In other words, the intervention of the central bank could break the relationship between rate of profit and rate of interest and could place limits on credit creation. A crisis of confidence would exert an impact on investment decisions. He then linearized the equation, which was used to help generate the mechanism of the business cycle (ibid., pp. 76 ff.). In terms of ‘the multiplier’, the significance of equation (8.1) is twofold. First, Kalecki could have given the equation a multiplier-type interpretation, but he did not do so. His interest (in this paper) appears to have been the interaction of profits and investment in the generation of the business cycle, rather than in the relationship between investment expenditure and income. However, his discussion later in the paper drew out what are in effect multiplier-type conclusions: [W]hen production of investment goods rises, aggregate production increases directly pro tanto, but in addition there is an increase due to the demand for consumer goods on the part of the workers newly engaged in the investment goods industries. The consequent increase in employment in the consumer goods industries leads to a further rise in the demand for consumer goods. Since at the same time prices rise, new demand is met only in part by new production, and in part at the expense of incomes of the earlier employed workers whose real wages now decline. (ibid., p. 79) Second, Kalecki presented equation (8.1) as a relationship which held at each point in time. He treated investment decisions as being fully carried out. It can also be seen from above that no lag between profits and consumption was assumed, and hence no lag between savings and profits. Kalecki was dealing here with an equilibrium position, though he did not use that term. However, as can be seen from the account given below, the relationship of equation (8.1) held continuously such that the substitution for profits can be made in the investment function. Later in the paper, he asserted that ‘the aggregate production and prices will ultimately rise to such an extent as to assure an increment in real profits equal to that of production of investment goods and capitalist consumption’ (ibid., p. 79; emphasis added). The causal nature of investment and savings (out of profits) in Kalecki’s approach can be clearly seen in the following: We have shown that the spending of the capitalists ‘forces’ a capitalist income which is equal to this spending. As the spending of the capitalists consists of their consumption and investment, and the income of the capitalists of their consumption and saving, it can also be said that the investment ‘forces’ saving to an amount which is equal to the amount of their investment.’ (ibid., p. 532; emphasis added). Investment was viewed as ‘forcing’ savings of an equal amount in the period in which the investment occurred. This would correspond to the national accounts

Kalecki and the multiplier  157 identity between investment and savings, and portrays investment as being carried out as planned and savings having to follow. But, further, as can be seen from above, Kalecki generally viewed ‘the multiplier’ as an instantaneous relationship in the sense that it held at each point in time. In his approach to the business cycle, the relationship between profits and investment in equation (1), which could be seen as an equilibrium relationship, was also one which held such that the level (and rate) of profits from this equation could be substituted in the subsequent equations. When Kalecki discussed the ‘Keynesian multiplier’, he argued that, with I being investment and Y being income: we can write, therefore, without making a considerable mistake: Y = f(I) f is here an increasing function and its shape is defined by the given capital equipment, capitalist propensity to consume, and the tastes of capitalists and workers. The derivative of this function: dY/dI = f´(I) is the Keynesian multiplier. If investment changes from the given level I to a given level I + ΔI – where ΔI is a small increment – then income will change from level Y to Y + ΔI.f ´(I). This is the only question the multiplier answers and no other service can be required from it. (1990, pp. 533–4) The equation above was described as ‘the short-period equilibrium’. Prior to the use of this equation, Kalecki wrote that ‘we see now that the spending of the capitalists determines a position of marginal value-added curves such that the sum of the hatched areas, i.e. the incomes of the capitalists, is equal to the amount they spend. In this way the level of spending of the capitalists (expressed in wage units) is the chief determinant of the short-period equilibrium and particularly of employment and income’ (ibid., p. 532). ‘For with a given propensity to consume there corresponds to I [total investment per unit of time expressed in wage units] definite capitalist consumption C, and thus we have the total spending of the capitalists C + I and its distribution between consumption and investment. To determine the short-period equilibrium in full detail we need, in addition to this, some knowledge of the kind of investments and the tastes of both capitalists and workers’ (ibid., p. 533). There is an implied adjustment process to reach equilibrium: ‘if capitalist consumption is, say, lower that the level C corresponding to the amount I of saving, then the capitalists will consume more; in this way they will push their income to the level C + I at which the proportion between consumption C and saving I is in accordance with their propensity to consume’ (ibid.). Kalecki often discussed the lags between investment decisions and investment, and as noted above he assumed that decisions were fully implemented albeit with

158  Sawyer lags. But Kalecki did not pay attention to the lags between the investment expenditure taking place and the subsequent effects on profits, savings and output. In a number of cases, he wrote as though the effects of investment on profits involved an equilibrium relationship (e.g. as in equation (1) above) and then as though the equilibrium relationship held continuously. One discussion of lags came in a chapter of his Theory of Economic Dynamics in 1954,3 in which he portrayed capitalist consumption as depending on lagged profits (and again assumed that wages are all immediately consumed) with the following equation (Kalecki, 1991, p. 246): Ct = qPt – a + A In the initial exposition foreign trade and government budget are taken as balanced. Hence: P=I+C Pt = It + qPt – a + A Kalecki considered q to be relatively small such that the series q, q2, q3 was ‘quickly decreasing’. Profits at time t are determined by current investment and profits at time t – a, and those profits in turn were determined by investment at that time and profits at time t – 2a. Hence: roughly speaking, profits follow investment with a time-lag. We can thus write as an approximate equation: Pt = f(It – ω) where ω is the time-lag involved.

(1991, p. 247)

This equation stands in comparison with the equation without lags, such as equation (8.1) above. A multiplier-type relationship involving time lags can be readily derived for the case where the level of investment is constant. This is: Pt = (It – ω + A)/(1 – q) In Kalecki’s words: The significance of [this] equation is that it reduces the number of determinants of profits from 2 to 1 as a result of taking into consideration the dependence of capitalist consumption on past profits . . . Profits according to [this] equation are fully determined by investment, with a certain time-lag involved. Moreover, investment depends on investment decisions still farther

Kalecki and the multiplier  159 back in time. It follows that profits are determined by past investment decisions (1990, p. 248). Kalecki then modifies this by including workers’ savings, foreign trade and government budget position. With the sum of private investment, export surplus and budget deficit denoted by I´, and workers’ savings by s, the equation becomes: Pt = (I´t – ω – st – ω + A)/(1 – q) This equation indicates the equivalence, so far as the determination of profits was concerned, between private investment, export surplus and budget deficit. It also illustrates the notion that investment (and these other components) determine the level of profits (and thereby the level of economic activity). It is intended though as an approximate equation (as noted above). In this approach Kalecki allowed for the time lags in terms of the response of capitalists’ expenditure to their income (profits). Production was (implicitly) assumed to respond to demand. In addition to the focus on profits (rather than income), Kalecki’s approach here differed from the standard multiplier approach in that he relates the level of profits now to the level of investment ω periods before, where the length of ω represents the average lag. The standard textbook multiplier would relate the level of income in equilibrium with the level of investment, whereas Kalecki was seeking to reflect the impact of past investment in current profits.

‘External markets’ The discussion so far has focused on investment, and this follows the balance of discussion in Kalecki’s own work. However, he was always aware of the roles of foreign trade and budget deficit in the determination of the level of economic activity and of the volume of profits. He described these as ‘external markets’. These are markets outside of the domestic private sector for the firms in that sector. He argued that: In order to stimulate the upswing by means of foreign trade, the balance of trade component of profits must increase, i.e. new surplus of exports over imports must be achieved. This surplus, like a boom in investment activity, leads to such a general increase in production and in the profit per unit of output that aggregate profits rise by an amount equal to the increment of the balance of trade. (1990, p. 165) He described the determination of profits as follows: profits are equal to investment plus export surplus budget deficit minus workers savings plus capitalist consumption. It follows directly that an increase in export surplus will raise profits pro tanto if other components remain

160  Sawyer unchanged. . . The value of an increment in the production of the export sector will be accounted for by the increase in profits and wages of that sector. The wages, however, will be spent on consumer goods. Thus production of consumer goods for workers will be expanded up to the point where profits out of this production will increase by the amount of additional wages in the export sector. (1991, p. 245) He further argued that: A budget deficit has an effect similar to that of an export surplus. It also permits profits to increase above the level determined by private investment and capitalist consumption.  .  . In the case of the export surplus, a country receives more from its exports than it pays for its imports. In the case of the budget deficit, the private sector of the economy receives more from government expenditure than it pays in taxes. The counterpart of the export surplus is an increase in the indebtedness of the foreign countries towards the country considered. The counterpart of the budget deficit is an increase in the indebtedness of the government towards the private sector. (1991, pp. 245–6) The consideration of these ‘external markets’ do not raise any further issues in relation to ‘the multiplier’ and serve to indicate the equivalence of investment, export surplus and budget deficit for the determination of profits.

Financing and funding The role of investment (and more generally of ‘autonomous expenditure’) in the determination of the level of economic activity raises two questions related to the issue of ‘where does the money come from’? This can be divided into two separate issues which we label here that of financing and that of funding. Financing refers to the question of how investment expenditure is financed, recognizing that in a monetary economy, planned expenditure can only be made effective by the possession of money. Funding refers to the ‘sources and uses of funds’ by firms. We will use this terminology, though Kalecki in places used the term financing (as in ‘development finance’) where we use the term funding. Kalecki indicated how the flow of money between capitalists arising from investment expenditure would limit the requirements for money to fund investment. He argued that: If we abstract from the ‘technical’ elements of the money market, we may say that capitalists as a whole do not need money in order to achieve this [finding the means to increase the production of investment goods or their personal consumption] since . . . the expenditure of some capitalists is converted into profits for others; the outlay on construction of a fixed asset is by no means

Kalecki and the multiplier  161 frozen . . . but it is already returned in the course of construction in the form of profits accruing to the firms whose sales .  .  . are directly or indirectly connected with this construction. If during a particular period more money is spent, e.g. out of bank deposits, then pro tanto more money flows back into the banks in the form of realized profits so that the sum of deposits remains unchanged. (1990, p. 80) However, what Kalecki termed ‘credit inflation’ – that is, increase in credit and money (and not signifying any causal link from credit to price inflation) – arose for two reasons. First, there is what may be termed as a mismatch between investment orders and the production of capital goods. There is, in effect, what Keynes later labelled the ‘finance motive’ for holding money in operation: When placing investment orders businessmen ensure for themselves corresponding sums of money, with the help of which they subsequently finance deliveries of the ordered investment goods. These funds we shall call investment reserves. At any given moment the accounts of investment reserves increase (per unit of time) by the value of the placed investment orders, and at the same time they are reduced by the sums spent on the newly produced capital goods A. (ibid., p. 80) Second, there is an increased demand for money in circulation arising from the increased level of production (cf. ibid., p. 81). As he had earlier noted, ‘the demand for money will certainly increase on account of an increase in output and prices, but not necessarily by as much as the sum spent’ (ibid., p. 148). Kalecki argued that ‘business fluctuations are strictly connected with credit inflation’ (ibid.). He answered the question as to what is inflation by saying that ‘inflation in the broadest sense of the term is the creation of purchasing power not based on a contribution to current social income’ (ibid.; emphasis in original). In this paper (published in 19324), he first envisaged that ‘someone has a chest of gold and at a certain moment begins to spend it for the construction of some factory’ (ibid.). He then argued that ‘exactly the same effects . . . will come from spending hoarded banknotes or funds received from a foreign loan. A similar type of inflation is the financing of investments from bank deposits, a process usually not classified as inflation but one which perhaps has the greatest importance in the inflationary financing of investments during an upswing in the business cycle’ (ibid., p. 149). ‘The entrepreneur spent his gold, made use of a foreign loan, borrowed bank deposits from their owner, raised credits in the central bank or in a private bank’ (ibid., p. 151) to enable investments to be undertaken. Kalecki asks ‘whether the inflationary mechanism . . . can be more a passive instrument in the hands of the entrepreneur, and can become an active factor encouraging him to make use of its services’ and answers in the ‘affirmative, though with some serious reservations’

162  Sawyer (ibid.): in effect the impact of lowering interest rates on investment is likely to be small. He used the working assumption that ‘the financing of additional investment is affected by the so-called creation of purchasing power. The demand for bank credit increases, and these are granted by the banks’ (ibid., p. 190). However, he argued that credit was generally available at the relevant prevailing rate of interest, though noting that banks could respond to an increased demand for loans by raising the corresponding rate of interest. [T]he possibility of stimulating the business upswing is based on the assumption that the banking system, especially the central bank, will be able to expand credits without such a considerable increase in the rate of interest. If the banking system reacted so inflexibly to every increase in the demand for credit, then no boom would be possible on account of a new invention, nor any automatic upswing in the business cycle. . . Investments would cease to be the channel through which additional purchasing power, unquestionably the primus movens of the business upswing, flows into the economy. (ibid., p. 489) In a similar vein, he argued that if this rate [of interest] were to increase sufficiently fast for the influence of the increase in gross profitability to be fully offset, an upswing would prove impossible. There is thus a close connection between the phenomenon of the business cycle and the response of the banking system to the increase in demand for money in circulation, at a rate of interest which is not prohibitive to the rise in investment. (ibid., p. 473) Kalecki (1933 and 1990; especially 1990, pp. 94–6) drew the distinction between ‘unattached’ deposits (‘deposits without a specific designation’), investment reserves (‘funds used for the immediate financing of the production of capital goods’) and money in circulation. The financing of investment may occur through the shifting of money from ‘unattached’ deposits to investment reserves through borrowing by the intending investors. But, in reality, the increased demand for investment reserves and money in circulation is met not only by a change of unattached deposits to deposits of specific designation but also by an expansion of the credit operations of banks, i.e. by credit inflation in the strict sense, when the assets and liabilities of banks increase. In other words, the increase of credits is matched on the side of assets by an increase in investment reserves, and on the side of liabilities by an increase of money in circulation. (1990, p. 95)

Kalecki and the multiplier  163 The issue of funding comes out more clearly in Kalecki’s discussion on budget deficit, where, of course, the issue of ‘where the money comes from’ has always been raised against the use of budget deficits. Kalecki pushed aside these concerns when he wrote that ‘although it has been repeatedly stated in recent discussions that the budget deficit always finances itself – that is to say, its rise always causes such an increase in incomes and changes in their distribution that there accrue just enough savings to finance it – the matter is still frequently misunderstood’ (ibid., p. 358, emphasis added). This was based on the equality (in a closed economy) of savings with budget deficit plus investment, for ‘whatever the general economic situation, whatever the level of prices, wages, or the rate of interest, any level of private investment and budget deficit will always produce an equal amount of savings to finance these two items’ (ibid., p. 360). The answers that Kalecki gave to the questions of financing and funding are straightforward. The financing of investment (and indeed any form of expenditure) requires credit creation to enable the investment to proceed, and this is generally undertaken by banks. The funding of investment or of a budget deficit comes from the pool of savings that are generated as a consequence of the investment expenditure or the budget deficit.

Savings and investment: the causal links It is argued here that there are no simple causal linkages between savings and investment and that two different approaches to the question of causality should be distinguished. The first approach arises from a thought experiment of the form: compare two otherwise identical time periods (or sets of time periods) where the only difference is the intended level of investment (or of savings); the difference in the intended level can then be said to cause something or other to happen. This approach arises from (though it is not limited to) comparative-static exercises and for that reason uses the concept of logical time (Robinson, 1974). The second approach relates to a historical process whereby investment expenditure at one time influences future savings which in turn influence investment expenditure in the subsequent time period. Further, in some cases saving and investment decisions are taken by the same economic agent (usually the enterprise) whereas in other cases those decisions are separated. In the first approach it is possible to answer the question about the causality involved, whereas in the second approach it is not. The creation of money through loans clearly permits investment expenditure to proceed ahead of the corresponding savings being generated (with actual investment leading to actual savings). In Kalecki’s work on the casual links between investment and savings there are two perhaps contrasting aspects to be investigated.5 The first is that the causal link runs from investment to savings. However, the causal link is based on a thought experiment: suppose that planned investment expenditure rises, then what happens? The general view on the direction of

164  Sawyer causation is well summarized by Kalecki in his review of Keynes (1936) when he wrote that: For the time being we must stress that, following the previous reasoning, saving does not determine investment but, on the contrary, it is precisely investment which creates savings. The equilibrium between the demand for capital and the supply of capital always exists, whatever the rate of interest, because investment always forces savings of the same amount. (1990, p. 228; emphasis added) The use here and elsewhere of the word ‘forces’ clearly indicates the causal nature of the investment–savings link. But Kalecki also uses the term ‘equilibrium’ where ‘equality’ would seem more appropriate. He is, though, (implicitly) contrasting the loanable funds view that savings and investment are equalized through changes in the interest rate (which suggests an equilibrium adjustment process) and the view that there is some other adjustment process (such as changes in the level of economic activity) which brings about the equality between savings and investment. But the savings are viewed as being ‘forced’ by investment rather than as arising from voluntary decisions. It is also notable that this is a causal relationship which holds at the aggregate level (and does not, in general, hold at the microeconomic or firm level). The second view on the question of causality comes from Kalecki’s analysis of the trade cycle. Since the trade cycle is a continuous process through time with no beginning and no end, it is impossible to talk of causation in the sense of an initial cause (unless that is the creation of the universe). It is also the case that the analysis of the trade cycle could be viewed as firmly based in historical time (in the sense of recognizing that time is irreversible). There is a well-known two-way relationship between profits and investment in the analysis of Kalecki, as seen above: at the level of the enterprise, profits influence investment decisions, and at the aggregate level, investment expenditure generates profits. Since profits and savings are closely linked in Kalecki’s work, there is also a two-way relationship between savings and investment. In some versions of his trade cycle analysis, Kalecki included a ‘re-investment’ factor in the investment equation which reflects the degree to which savings in one period influence investment in a subsequent period (at the level of enterprise). The firm’s financial resources are based on its current savings, and additional savings generate some additional investment but on a less than one-for-one basis: Investment decisions are closely related to ‘internal’ accumulation of capital, that is, to the gross savings of firms. There will be a tendency to use these savings for investment, and, in addition, investment may be financed by new outside funds on the strength of the accumulation of entrepreneurial capital. The gross savings of firms thus extends the boundaries set to investment plans by the limited capital market and the factor of increasing risk. (1991, p. 282)

Kalecki and the multiplier  165 Moreover: It follows from the above that the expansion of the firm depends on its accumulation of capital out of current profits. This will enable the firm to undertake new investment without encountering the obstacles of the limited capital market or ‘increasing risk’. Not only can savings out of current profits be directly invested in the business, but this increase in the firm’s capital will make it possible to contract new loans. (ibid., p. 278) The relationships between investment and profits (and thereby between investment and savings) arise at two levels. At the level of the firm, a higher level of profits and of savings may lead the firm to decide on a higher level of investment which is then carried through. In one sense it could be said that a higher level of profits and savings have caused, or at least influenced, a higher level of investment. If an economic agent is portrayed as striving for an optimizing decision subject to the constraints which she faces, then a change in the constraint can be portrayed as leading to a change in the decision variable, and in that way causing the change in the decision variable. But in the way in which Kalecki viewed matters the firm has a choice as to how to deploy the profits gained. There is nothing ‘forcing’ higher savings to lead to higher investment, but there can be, in Kalecki’s words, a ‘tendency to use these savings for investment’. In Kalecki’s writings, the relationship between investment and savings is not a simple one. But there is a clear aggregate causal chain from investment decisions to investment expenditure to savings: investment ‘forces’ savings. At the level of the firm, however, greater profits and savings enable more investment to take place through direct provision of finance and the enhanced ability to borrow.

Crowding out and all that Any multiplier-type formula holds sway only for the comparison between one equilibrium position and another provided that ceteris paribus conditions hold. The multiplier-type relationship envisaged by Kalecki, Keynes and others is a relationship between a difference in the real level of investment expenditure and a difference in the real level of output. The crowding out argument is that the difference in the real level of output arising from a difference in the level of investment predicted from the multiplier relationship cannot be fully realized, notably when higher levels of investment and output are involved. (It is worth noting that crowding-out arguments are usually applied to the case of an increase in government expenditure rather than to an increase in investment or export surplus). It has been argued that there would be crowding out of other forms of expenditure resulting from a rise in the rate of interest. From the section above on financing and funding it is clear that Kalecki dismissed this idea. Investment expenditure and government expenditure generate savings (by reason of the national accounts identity) to fund those expenditures without any pressure on interest rates. Thus,

166  Sawyer crowding out as a result of higher interest rates (which would reduce investment) would simply not occur, in the view of Kalecki. Another set of arguments suggesting crowding out arises from supply-side reasoning such as the claim that the ‘natural rate of unemployment’ constrains the level of output. Kalecki’s argument on this point was simple: It may be objected that government expenditure financed by borrowing will cause inflation. To this it may be replied that the effective demand created by government acts like any other increase in demand. If labour, plants and foreign raw material are in ample supply, the increase in demand will be met by an increase in production. . . It follows that if the government intervention aims at achieving full employment but stops short of increasing effective demand over the full employment mark, there is no need to be afraid of inflation. (1990, p. 348) Thus crowding out would only arise if output were already at full capacity, and where unit costs rose rapidly. If output is in this above capacity range, then since unit costs are rising, prices will also rise relative to wages, and hence real wages will decline. In general Kalecki saw capitalist economies as ‘demand constrained’ rather than ‘supply constrained’, and therefore containing considerable underutilized capacity. Hence an expansion in demand would bring forth increased supply. But in circumstances of capital shortage, supply would not be able to increase to match increased demand, and some form of crowding out would result.

Conclusions According to Kalecki’s approach, it is clear that higher levels of investment generate higher levels of savings and profits (and income). At the system level the causation runs from investment to savings, though there is the caveat that at the level of the firm, higher profits and savings encourage higher future investment. Investment decisions are viewed as being carried out with a lag, with credit generally provided by banks to enable those decisions to be implemented: again a caveat has to be registered that banks could cut off any expansion through a refusal to create credit. The ‘multiplier’ as such does not play a central role in Kalecki’s writings, and where it does so it is derived in an instantaneous equilibrium manner. Kalecki paid little attention to the lags involved in the workings of the multiplier. In general, output would respond to an increase in demand, and in Kalecki’s work the only instance in which output would not respond to demand would be the relatively unusual case of firms working at or above capacity.

Notes 1 First published as ‘A Theory of the Business Cycle’, Review of Economic Studies, Vol. 4, February 1937.

Kalecki and the multiplier  167 2 First published in English in Essays in Business Cycle Theory (1933) as ‘Outline of a General Theory’. Originally published in Polish as Próba teorii koniunktury, by OSBCP, Warsaw. 3 Reprinted in Kalecki (1991, pp. 205–348). 4 ‘Koniunktura a inflacja’, Polska Gospodarcza, 13/48, pp. 1411–15. 5 For discussion on the causal links between investment and savings see, for example, Asimakopulos (1983) and Kregel (1995).

References Asimakopulos, A. (1983), ‘Kalecki and Keynes on Finance, Investment and Saving’, Cambridge Journal of Economics, Vol. 7, pp. 221–33. Kalecki, M. (1954), Theory of Economic Dynamics, London: George Allen and Unwin. Kalecki, M. (1990), Collected Works of Michal Kalecki, Vol. 1, edited by J. Osiatynski, Oxford: Clarendon Press. Kalecki, M. (1991), Collected Works of Michal Kalecki, Vol. 2, edited by J. Osiatynski, Oxford: Clarendon Press. Keynes, J. M. (1936), The General Theory of Employment, Interest and Money, London: Macmillan. Kregel, J. (1995), ‘Causality and Real Time in Asimakopulos’s Approach to Saving and Investment in the Theory of Distribution’ in G. Harcourt, A. Roncaglia and R. Rowley (eds), Income and Employment in Theory and Practice, London: Macmillan. Robinson, J. (1966), ‘Kalecki and Keynes’ in Economic Dynamics and Planning: Essays in Honour of Michal Kalecki, Oxford: Pergamon. Robinson, J. (1974), ‘History versus Equilibrium’, Thames Papers in Political Economy, Autumn, pp. 335–41.

9 The Keynesian multiplier The monetary pre-conditions and the role of banks as defended by Richard Kahn’s 1931 paper – a horizontalist re-interpretation Louis-Philippe Rochon Introduction The Keynesian multiplier and the theory of effective demand are no doubt among the most revolutionary aspects of the General Theory. Since Keynes, the multiplier has been at the core of Keynesian and post-Keynesian economic theories, which rely on its existence to justify activist or expansionary government fiscal policies aimed at regulating business cycles and reducing unemployment. Post-Keynesians have generally accepted the multiplier. Those who reject or undermine its importance are generally mainstream economists who introduce crowding-out effects to show the irrelevance of multiplier effects. In some cases, it is argued even that fiscal policy can have negative effects on output. Criticism originally came from outside post-Keynesian circles. This changed when Moore, in his seminal book Horizontalists and Verticalists (1988), attacked the relevance of multiplier analysis, thereby distancing himself from many of his post-Keynesian contemporaries. In his criticism, Moore argued that the multiplier was necessarily equal to unity – a position also defended by a number of circuitists (see Parguez, 1975, p. 278). To be sure, Moore’s criticism was quickly attacked. For instance, Cottrell (1994) gave a spirited defence of the multiplier and dismissed Moore’s objections as outdated and smacking of monetarism. This chapter will examine the concept of the multiplier and will propose the conditions under which it operates. In a sense, it seeks to build a bridge between Moore and other post-Keynesian critics of the multiplier and those, such as Cottrell and others, who defend the validity of the multiplier. Contrary to the standard post-Keynesian interpretation, however, I will argue that the multiplier is not an automatic phenomenon – its existence depends on characteristics inherent to a monetary economy of production. My position is therefore simple: within a single period of production, the multiplier is indeed necessarily equal to unity. However, its value may increase over the course of several periods of production, depending precisely on the role of the banking system in renewing existing credit or granting new credit. This is an important distinction: since endogenous money and the banking system are key elements of post-Keynesian theory, they seem to have been excluded from any serious discussion of the multiplier.

The Keynesian multiplier  169 Hence, inspired by the principles of the theory of the monetary circuit, this chapter seeks to integrate the theory of the multiplier within a theory of endogenous money where banks play a role in granting credit. Contrary to Moore, in this respect, endogenous money does not ‘knock out’ the multiplier. Rather, I argue that it is only within the confines of endogenous money combined with the theory of the reflux that the multiplier has any credibility. In this sense, I agree with Gnos’s assessment (see Chapter 10) that although ‘Moore’s criticism of the multiplier is well grounded . . . it is not the end of the multiplier story.’ This argument is not original, although it has been overlooked. The purpose of this chapter is to bring these arguments back into the post-Keynesian story, since they carry important policy implications and, I believe, give a proper theoretical context to the use of fiscal policy. There is some support for this position from rather obvious sources. Richard Kahn himself defended this position in his original multiplier paper, according to which the existence of the multiplier rests on the ‘co-operation of the banking system’ (1931, p. 174). The same argument was made by Trevithick (1994, p. 78), who claims that ‘a policy of monetary accommodation is, in general, a prerequisite for the multiplier process to become airborne.’ This argument is also consistent with Sawyer’s analysis of Kalecki (see Chapter 8), in which he argues that ‘In the event that banks did not provide the required credit the investment would not proceed, and banks did have it within their power to cut off an intended increase in investment.’ Hence without the extension of bank credit by the banking system, the multiplier, in Kahn’s own words, is ‘rendered nugatory’ (1931, p. 175). The following section quickly sketches Moore’s arguments in undermining the multiplier. The next section presents some of the key elements of the theory of the monetary circuit. The fourth section builds on the insights of the previous section and develops a theory of the multiplier that relies on the existence of banks and bank credit. It will be argued, following Lavoie (1987, p. 88) that ‘the multiplier effect is not automatic’. Hence the value of the multiplier depends on the behaviour of banks. Before proceeding, let me be clear on one thing: this chapter does not seek to discuss the size of the multiplier, but rather the conditions under which it exists.

Post-Keynesian criticism of the multiplier analysis In the General Theory, Keynes rejected the notion that the demand and supply of savings determined the rate of interest. For Keynes, the interest rate was a monetary phenomenon determined by the demand and supply of money. The equality between saving and investment was guaranteed by the principle of effective demand. Rejecting the orthodox causality between saving and investment, Keynes and post-Keynesians have argued that investment creates saving. But this argument is not sufficient to explain their equality. Since investment and saving are undertaken by different agents, they must somehow become equal through some process. Moore’s criticism rests primarily on two notions. First, in a non-ergodic world

170  Rochon with changing expectations of the future, a proper position of rest cannot be defined. Since the multiplier is essentially an equilibrium mechanism, it must be rejected and the Keynesian multiplier is hence ‘fundamentally flawed’ (Moore, 1988, p. 312). Second, since saving and investment are equal at all times, they are a mere accounting reflection of one another, the notion that changes in income are needed to bring them into equality is rejected. Expanding on the first criticism, Moore (1994, p.  133) has argued that ‘the Keynesian multiplier falls because it is intrinsically tied to the paradigm of macroeconomic equilibrium analysis. If, in a non-ergodic world, macroeconomic equilibrium must be discarded, so too must the Keynesian multiplier.’ According to most accounts of the multiplier, an initial increase in expenditures will increase savings to the points where planned investment and planned savings converge to a final position of rest, i.e. equilibrium. Amadeo (1987, p. 567), among others, has defended this conventional position: ‘Thus, through the multiplier mechanism, a change in the level of investment gives rise to an equal level of saving. The multiplier is essentially an equilibrating mechanism.’ For instance, in using the IS–LM diagram, an initial increase in investment or government expenditures will shift the IS curve out and to the right. The vertical change measures the change in expenditures, ∆A, while the horizontal distance measures the multiplier effect, that is ∆Y = α∆A, where α is the multiplier. The story, however, is how one moves from one position of equilibrium to another. Of course, the crowding-out story matters little in the sense that it only determines the final resting position of the system, that is, whether we have more or less output. Moreover, adopting a horizontal LM curve solves nothing in this case: we simply have the full multiplier effect. In static equilibrium analysis, therefore, once there is an increase in expenditures, we move from one position of equilibrium to another. The criticism initially raised by Moore is directed precisely at the notion of equilibrium. Moore (1988, 1994) was one of the first to alert us to the contradiction between the pervasive nature of uncertainty and the multiplier. The issue is that in a non-ergodic world, a final position of rest is inconceivable. With investment depending on ‘animal spirits,’ changing long-term expectations will affect investment plans. As more or less investment is realized, this position of equilibrium is affected. Hence, according to Moore (1994, p. 127): Whenever expectations change, so does the macroeconomic equilibrium position. But in a nonergodic world, our expectations of the unknown future change continuously. As a result, in a nonergodic world it is impossible even to conceive of any stable macroeconomic equilibrium configuration towards which the system is tending. Ergo, there can be no Keynesian income multiplier.1 The second criticism is closely related to the first. If Moore and others reject the notion of the multiplier as an equilibrating mechanism between saving and investment, by what other way are they equalized?

The Keynesian multiplier  171 Traditionally, post-Keynesians have argued that the equality between investment and saving is explained by increases in aggregate demand and income, initiated by an initial increase in expenditures (investment) (see Davidson, 1990, 1994). Hence the theory of the multiplier is simple: increases in exogenous expenditures, say investment, increase overall spending, through multiple rounds of consumption, by an amount greater than the initial injection. Convergence is assured by a marginal propensity to consume of less than unity. Hence, an initial increase in government expenditures or investment will increase consumption repeatedly until the incremental increases in savings equal the initial increase in expenditures. Investment and saving are equal ex post. For post-Keynesians, therefore, investment and saving are not equal ex ante and ‘must be brought into equality by means of some mechanism or other’ (Cottrell, 1994, p. 114). For Moore, however, this cannot be correct. Rather, saving and investment are always equal to one another. Saving by definition is the mere accounting equivalent of investment given the principle of double-entry accounting. This approach may take two separate routes. According to Moore (1998), the notion that saving equals investment is an accounting identity, which means that it holds at all times, irrespective of the time unit or period being considered. If investment is volatile, then so is saving, since there does not exist an independent behavioural saving function. Moore’s argument is that saving is not a behavioural phenomenon (as is assumed in Keynes, 1973a, p. 64), but rather an identity that mimics the behaviour investment. Hence Moore does not see saving as ‘consumption forgone’, but rather as net addition to net wealth. Another possible argument to bolster the claim that investment always equals saving is to address the narrow definition of saving associated with household behaviour. In his General Theory, Keynes identified the act of saving with the behaviour of households only. By defining saving as income that is not consumed, Keynes ignored the saving done by firms in the production process. Keynes (1973a, p. 61) defines saving as the ‘excess of income over expenditures on consumption. . . Expenditures on consumption during any period must mean the value of goods sold to consumers during that period.’ The discussion of saving is thus wrapped around the behaviour of the consumer, thereby ignoring firms. The problem of course is that firms also are part of national accounts, and are active players in the dynamics of saving. Firms spend and collect revenues, and their ‘excess of income over expenditures’ must also be counted within the definition of saving. Keynes, however, specifically excludes the consumption and saving behaviour of firms. A possible reason for Keynes’s omission of profits in total saving is because he sees the behaviours of firms and households as independent acts. Thus, the two cannot be conflated. For firms, saving is identified with the undistributed profits. In this case, by the end of the day, there is a residual amount of saving that is equal to the saving of households and of firms. Either way, the equality of investment and saving holds irrespective of the distinction between actual and planned saving and investment (see Gnos, this volume). Despite this argument, as I will argue below, the necessary equality

172  Rochon between saving and investment does not invalidate per se the multiplier process. For me, the multiplier is not a story of bringing investment and saving together, as they are always, by definition, equal to one another. Rather, it is a theory of how an initial spending, such as by the state, can create additional spending, and of the mechanisms that allow this process to take place. As we will see, the banking system is a key element in this story.

The theory of the monetary circuit The theory of the monetary circuit has received considerable attention in the last few years, with some of the clearest developments appearing in Deleplace and Nell (1996) and, more recently, in Rochon and Rossi (2003). While differences exist between circuit and post-Keynesian approaches to credit and money, there also exist a number of important similarities. For instance, both approaches share the causal role of credit and banks in the production process, the endogenous nature of money and the exogenous nature of the interest rate. They each believe in the importance of effective demand and demand-constrained economies, uncertainty (although with different emphasis), and the importance of institutions. I have elsewhere discussed the theory of the monetary circuit (Rochon, 1999) and will not undertake here a complete overview (see also Lavoie, 1992). I will, however, offer a discussion of what I consider are its relevant arguments – relevant in so far as the multiplier is concerned. The theory of the monetary circuit emphasizes the irreversibility of actions and events – both in goods and in money markets – and the hierarchical relationship between different macro groups. The sequential analysis of the monetary circuit – which stands in contrast to those theories where everything is determined simultaneously – is linked, in fact, to the hierarchy inherent in production. Production cannot begin before firms have access to finance with which they employ workers and purchase other inputs of production; banks cannot lend without a prior demand for bank credit; workers cannot spend without first receiving an income (thus the necessary ex post nature of savings); and the central bank must first set the rate of interest at which it agrees to supply the needed reserves.2 Each agent3 has a specific role to play in the greater sphere of the production process. This sequence begins with the production and investment decisions of entrepreneurial firms in either the consumption goods or investment goods sector. Since saving is a residual (it is created by investment), firms must first borrow from banks to cover the costs of production. In other words, for investment plans to be realized and wages to be paid, firms must obtain some initial finance, which is usually provided by banks.4 When banks agree to meet the demand for loans,5 they credit the bank account of firms, or extend to them a line of credit. Money as bank deposits is thus created either when the bank accounts are instantly credited, or when firms draw down their lines of credit in order to cover the costs of inputs. Money is therefore endogenously created through the debt activities of private agents in their attempt to begin production. The ‘money supply,’ in more con-

The Keynesian multiplier  173 ventional terms, expands and contracts with the debt needs of the economy. The endogeneity of money has little to do with uncertainty, but rather is a direct result of its very nature as debt.6 Capitalist economies, therefore, are not barter economies, and they are more than mere money economies: they are debt economies. The difference between money and debt economies should be obvious: debt, not money per se, is central to the discussion of capitalist economies and production. The notion of debt is therefore at the heart of the production process. This logic applies to firms in all sectors of the economy: consumption goods and investment goods firms. The demand for bank credit is in direct relationship with the level of wages, the level of employment and capacity utilization, and the growth of the production capacity of firms through capital. The money thus created endogenously responds to the needs of the economy to reproduce itself and grow. The creation of money is also simultaneously the creation of income. As Godley and Cripps (1983, p.  82) argue, ‘The act of money creation is also an act of expenditure and (therefore) of income creation.’ Firms demand credit for the creation of income in the consumption goods sector (as wages to workers) and in the capital goods sector as well (the purchase of capital goods is an income for the capital goods-producing firms). This same logic applies for the capital goods sector. Those firms need to borrow credit to cover expenses related to production and the purchase of capital goods too. The point of departure of the theory of the monetary circuit is therefore debt and the creation of incomes. The emphasis on the nature of money as debt – as opposed to its roles and functions – suggests that money creation implies an eventual destruction of money. Debt incurred during production must be reimbursed; otherwise the debtor is incurring unnecessary interest costs. Firms generate the necessary revenues by capturing a portion of household incomes by selling their goods. Hence, what is initially injected into the system is eventually returned to firms, from which they can reimburse their initial debt towards the bank. Money flows through the system, changes hands, but ultimately returns to its point of departure.7 The emphasis on debt is a strong one. One can see right away that if firms need to reimburse their initial loans, they cannot use the proceeds from sales to expand the cycle. The logic of the reflux mechanism is such that it cannot be denied – and it is this same reflux mechanism, as we will see in the next section – that is at the heart of my approach to the multiplier process. In a recent article, however, Pressman (2000) objects strongly to the reflux mechanism. As he claims, ‘The most disturbing aspect of the circuit mechanism is the process by which money finds its way back to banks’ (p. 971). Pressman’s argument rests on the notion that bank credit need not be reimbursed ‘immediately’; rather firms can simply roll over their debt. In this respect, there is a ‘time lag that allows for the possibility of a greater multiplier’. Pressman’s argument is an important one. Indeed, if firms were not obligated to reimburse banks their initial loans, then they could use the proceeds from the initial injection of money, such as from fiscal policy, to continue the production cycle and hence generate additional income in the process. Therefore, an initial

174  Rochon injection of money can be used over and over again and generate a large multiplier effect. But such an approach, I believe, is flawed as it fails to recognize the role of banks in refinancing continuing production cycles. It is unrealistic to argue that banks supply an initial loan and then turn their backs on their customers by allowing them to take their time in reimbursing the loan. Moreover, even this arrangement would require the tacit approval of the banks. In other words, even the act of rolling over an existing debt requires the consent of the bank. Hence, banks are active agents who have an important role in determining the extent of the multiplier effect.

The role of banks and Keynesian multiplier analysis Post-Keynesians accord banks a pivotal role in the endogenous creation of money. By placing the emphasis on the loans–deposit–reserves process, post-Keynesians recognize that banks are a component of production. Strangely enough, once money is created, once a credit has been extended, once the production process has been engaged, banks seem to disappear from the analysis. This section tries to integrate banks into Keynesian multiplier analysis and attempts to show how the existence of the multiplier depends on the ‘co-operation of the banking system’, as Kahn puts it. Since banks are active agents in the credit and money-creation process, their actions will influence the value of the multiplier through the cycle of production. It is the actions of banks that give meaning to the multiplier. To do so, we need a theory of the supply of credit. The crucial question is, what affects this supply of credit, and how is this linked to the theory of the multiplier? Let us begin with a rather banal statement: banks are firms whose liabilities are accepted as money. This gives them a very special role to play in the economy and, as we will see, in the multiplier analysis. As we saw earlier, and as postKeynesians argue, production cannot take place before credit is secured. If the multiplier is tied to the production and consumption of goods, then it must also be tied to credit. Yet, in the standard multiplier analysis, once the output and incomes are created, the consumption of goods given the marginal propensity to consume creates more output and income. While banks intervene at the beginning of the initial process, and are instrumental in the financing of production and the creation of incomes, they disappear completely in subsequent rounds of output and income creation. In other words, we now have output creating output! Yet, this is at odds with post-Keynesian and circuit theories: only bank credit can create incomes. Including banks in this analysis, however, must be done while taking into account the banks’ management of the supply of funds (see Wolfson, 1996; and Rochon, 2006). Indeed, banks are active players in the credit-supply process and do not lend indiscriminately. They lend only to creditworthy borrowers. Horizontalists have always emphasized this point: while the supply of loans is demand determined, only creditworthy demand will be met. In this sense, horizontalism is

The Keynesian multiplier  175 fully consistent with Keynes’s ‘fringe of unsatisfied customers’. While the money supply is credit-led and demand-determined, it is also supply-constrained by the willingness of banks to lend. Banks, just as firms and households, operate in a state of pure uncertainty regarding the future. They are concerned primarily with the ability of firms to reimburse their debt in the future: in this sense, creditworthiness is synonymous with the bank’s trust in their customers’ ability to honour their contractual obligations. Lavoie (1996, p.  284) writes, ‘Because of uncertainty and the complexities of decision making, bank lending depends on whether or not the potential borrower fulfils various norms and customs.’ Of course, this can be found in Keynes of the Treatise on Money (1971b, p. 212), in a now famous passage: There is apt to be an unsatisfied fringe of borrowers, the size of which can be expanded or contracted, so that banks can influence the volume of investment by expanding or contracting the volume of their loans, without there being necessarily any change in the level of the bank-rate, in the demand-schedule of borrowers, or in the volume of lending otherwise than through the banks. This phenomenon is capable, when it exists, of having great practical importance. But how does uncertainty affect the supply of bank credit and, more specifically, how does this affect the multiplier process? In making their lending decisions, banks will typically face two different sources of uncertainty, which can be labelled microuncertainty and macrouncertainty (see Rochon, 2006). Microuncertainty is defined as arising from the ‘probability’ (perhaps a poor choice of words) that a particular bank borrower will default due to insufficient sales from which to reimburse his debt to the bank. The important point is that this inability exists irrespective of the business cycle. Microuncertainty is present regardless of the level of effective demand and hence of where we are on the business cycle. For instance, even if effective demand is strong and the economy is growing, inevitably some firms may still be unable to meet their contractual agreements with banks and will default, resulting from mismanagement or poor sales. This may be called a bad loan. In this sense, responsibility must be shared with the bank for failure to properly evaluate borrowers due to asymmetric information, which may arise for a number of reasons. Banks may not have all the relevant information about a firm, the competence of its managerial team or other pertinent issues. Whether this information is asymmetric or simply unknown to both parties is not the issue. From the bank’s point of view, it may not be able to properly assess the potential of a firm to generate profits in the future. Ex post, of course, it is always easy to identity the bad loans; ex ante, the bank must place a ‘bet’ – to borrow Parguez’s expression – despite its best efforts to evaluate the borrower. Macrouncertainty, on the other hand, is defined as the possibility that a firm may not reimburse its existing debt with the bank because of the consequences of

176  Rochon the business cycle. A general fall in effective demand (from a recession or from a central bank decision to raise interest rates) will have an impact on all the firms’ ability to meet their contractual obligations to the banks. Macrouncertainty will affect all firms equally. A general downturn in the cycle will pose a risk to all firms. This is the concept of uncertainty post-Keynesians often discuss: we ‘simply do not know’ the future course of the cycle and how it will affect firms. While post-Keynesians have emphasized uncertainty and incorporated it within their theories of investment and consumption, little has been done to incorporate it within a theory of banking (see Wolfson, 1996). Banks, just like firms and households, are unaware of the future and how it will subsequently impact on firms overall. Lending is in fact a ‘bet’ on the future of the business cycle and on the future of interest rates. For instance, an increase in the rate of interest may have microuncertainty effects. A rise in the rate may translate into higher costs of servicing loans, and hence affect the borrower’s cash flow. Weak firms may not be able to survive this increase in the rate of interest. In Minskian terminology, borrowers may go first from hedge, to speculative, and finally to Ponzi situations. I believe that the New Keynesian ‘financial accelerator’ principle or the balance sheet channel is indicative of the ‘microuncertain’ environment of firms. As rates rise, some firms may face cash flow problems. As a result of the presence of two uncertainties, banks place two bets. In the first instance they place a bet on the borrower they then place a bet on their expectations of the business cycle. Both bets are related in a sense. If the economy slows down, revenues and profits fall, and firms may default. However, firms may default irrespective of the health of the economy. Lavoie (1992, p. 106) emphasizes these two sources of uncertainty facing banks, and writes that ‘the uncertainty about the future, as well as the lack of relevant knowledge about the competence of the managerial team and about the profitability of the project, forces bankers to rely on the performance record of the past, that is the profits generated in the past by the firm.’ Hence, when faced with uncertainty, banks will either make it more difficult to borrow money or simply refuse to roll over existing debt. Hence, pessimism about the future level of aggregate demand, and therefore the ability of firms to pay back their debt, will lead banks to reduce the supply of credit. Banks will typically raise their minimum creditworthiness criteria (lending standards), eliminating a number of potential borrowers in the process and thereby leading to credit constraints: to ensure that their new credit demand is honoured (or existing credit rolled over), borrowers must ensure that they meet the new, stricter guidelines. Through the cycle, then, creditworthiness criteria will vary because banks will be subject to ‘sudden bursts of optimism and pessimism’. For instance, at the beginning of a cycle when animal spirits are high, creditworthiness criteria will be lower and banks will seek out potential borrowers. Banks generally relax their lending practices. As the economy grows, banks may fear an eventual downturn, become more pessimistic about the future and raise the minimum required criteria. They may also fear that as the economy heats up, the central bank will raise

The Keynesian multiplier  177 the rate of interest to discourage economic expansion. We would therefore expect banks to tighten credit conditions at the height of the business cycle, and to relax them at its trough. The above analysis is instrumental in understanding the multiplier process. If only finance can finance production, then each round of new output must be financed by credit. This implies that as firms reimburse their loans, they must secure new credit. Assume therefore an initial spending financed by bank credit. Consistent with the theory of the monetary circuit, the debt incurred during the production process must be reimbursed. For that increase in income to create additional income, new credit must be secured, and this depends on the banking system. The ‘co-operation of the banking system’ is therefore required. If banks decide not to renew credit, spending cannot continue. This suggests not only that the multiplier depends on the banking system, but that it will vary through the cycle. In periods of optimism, when banks are more ‘co-operative’, that is when credit is easier to obtain, there will be a greater multiplier. However, in economic downturns, when banks are more guarded and credit is therefore more difficult to obtain, the multiplier will be smaller. This analysis makes fiscal policy even more relevant. Without fiscal stimulus, it is difficult for banks to get out of the pessimism trap. In this sense, the role of fiscal policy is to ensure that banks are sufficiently optimistic to keep the credit tap open and running. By stimulating aggregate demand, fiscal policy will ensure that firms are always considered creditworthy.

Conclusion The theory of the monetary circuit relies on the role of banks in the production process. In this sense, it is faithful to Keynes’s argument that banks ‘hold the key’ to increases in output. This point, however, holds in the static short-run period, as it does over the longer run of succeeding periods of production. The analysis presented above is not necessarily a refutation of post-Keynesian analysis, but rather seeks to integrate the two by claiming that the multiplier is not an automatic phenomenon. It can hold, provided initial injections into the circuit lead to increased private revenues sufficient to guarantee the renewal debt commitment and the extension of bank credit to renew production. The analysis developed here also contains important policy implications. Fiscal policy plays an important role in the multiplier analysis. Fiscal expenditures become revenues for various firms in the economy and income for workers who then purchase consumption goods. These revenues play an integral role in maintaining and enhancing the creditworthiness of firms. This role is all the more important during periods of bleak economic outlook. Moreover, monetary policies favouring low interest rates are always preferable for their positive income distributional effects and their positive effects on firms’ balance sheets and cash flow situations. In both situations, the bottom line must always be the effects of fiscal and monetary policies on the creditworthiness of firms. In this sense, the Keynesian multiplier, if it exists, arises over several periods

178  Rochon of production. In this sense, it is no surprise that Pressman (1995) found evidence of a large multiplier. This is not denied. What is denied is that government expenditures necessarily, or automatically, lead to a multiplier process. This reasoning is misleading. What is needed is the added argument that banks must be willing and ready to lend, provided their expectations of the future are good. Similarly, the analysis contained herein can help explain why the value of the multiplier can change through the business cycle. Indeed, when banks become pessimistic they curtail their lending, thus denying some firms the ability to renew their production plans. Hence, the effect of fiscal policy may be ambiguous. This is certainly consistent with post-Keynesian theory: in periods of depressed output, fiscal policy should be expansive, while during periods of robust growth, fiscal policy should be curtailed. Of course, more discussion is needed of the appropriate mix of fiscal and monetary policy. But the analysis here should lead to one important conclusion: if banks indeed ‘hold the key’ to stronger growth, as Keynes makes clear in his articles on the finance motive, then it is necessary to create the appropriate macroenvironment and take steps to reduce foremost macrouncertainty. In this sense, fiscal policy can be seen as a supplement to firms’ income by allowing them to inflate their revenues and compensate for household hoards. Thus, fiscal policy is primarily used to help firms reimburse their initial debt.

Notes 1 This criticism has been answered – at least tentatively – by Amadeo (1987), who proposes a shifting equilibrium or a long-period equilibrium. As expectations change and affect levels of investment, ‘to different states of long-period expectations there corresponds different levels of investment and, therefore, different levels of longperiod levels of employment.’ So Amadeo is arguing that, despite a non-ergodic environment, a long-period (normal) position of equilibrium exists for every level of investment or expectations. 2 In Rochon (1999), it is argued that even if central banks are non-accommodating, the supply of credit money is still seen as horizontal. The lack of reserves pushes the curve upward to a new, higher rate of interest. See Lavoie (1992) for details. 3 The analysis does not exclude governments and deficits. 4 Keynes argues that the ‘finance required during the interregnum between the intentions to invest and its achievement is mainly supplied by specialists, in particular by the banks’ (1973b, p. 219). In the following paragraph, Keynes claims that the finance is ‘wholly supplied . . . by the banks’. Keynes also writes: ‘It is the rôle of the credit system to provide the liquid funds which are required first of all by entrepreneurs during the period before his actual expenditure, and then by the recipients of this expenditure during the period before they have decided to employ it’ (1973b, p. 285). 5 We should be clear that banks do not meet all the forthcoming demand for credit. Banks have strict guidelines by which they judge the creditworthiness of potential borrowers. There may well be a ‘fringe of unsatisfied borrowers’ (Keynes, 1971a, p. 327). The demand for credit that banks meet is the creditworthy demand for credit (see Rochon, 1999; Lavoie, 1996). 6 One may argue, of course, that uncertainty affects the private agents’ demand for bank credit or the banks’ decision to expand credit. 7 Of course, in addition to what households spend on consumption goods, firms also

The Keynesian multiplier  179 succeed in capturing back what households spend on financial markets (see Graziani, 1990). However, firms cannot capture households’ hoarded savings. Simply put, firms do not reimburse the totality of their initial loans because households hoard a portion of their income.

Acknowledgement The author would like to thank Claude Gnos for his very insightful arguments. The usual caveats apply.

References Amadeo, E. (1987) ‘Multiplier Analysis,’ in J. Eatwell, M. Milgate and P. Newman (eds), The New Palgrave: A Dictionary of Economics, London: Macmillan. Cottrell, A. (1994) ‘Endogenous Money and the Multiplier,’ Journal of Post Keynesian Economics, 17 (10), Fall, 111–20. Davidson, P. (1990) Money and Employment: The Collected Writings of Paul Davidson 1, London: Macmillan. Davidson, P. (1994) Post Keynesian Macroeconomic Theory: A Foundation for Successful Economic Policies in the Twenty-First Century, Aldershot: Edward Elgar. Deleplace, G. and Nell, E. (eds) (1996), Money in Motion, London: Macmillan. Godley, W. and Cripps, F. (1983), Macroeconomics, London: Fontana. Graziani, A. (1990), ‘The Theory of the Monetary Circuit’, Économies et Sociétés. Monnaie et Production, July, 24 (7), 7–36. Kahn, R. (1931) ‘The Relation of Home Investment to Unemployment’, Economic Journal, June, 173–98. Keynes, J. M. (1971a) The Collected Writings of John Maynard Keynes. Vol. 2: The Economic Consequences of the Peace, D. Moggridge (ed.), London: Macmillan and Cambridge University Press. Keynes, J. M. (1971b) The Collected Writings of John Maynard Keynes. Vol. 5: A Treatise on Money. The Pure Theory of Money, D. Moggridge (ed.), London: Macmillan and Cambridge University Press. Keynes, J. M. (1973a) The Collected Writings of John Maynard Keynes. Vol. 7: The General Theory of Employment, Money and Interest, D. Moggridge (ed.), London: Macmillan and St Martin’s Press. Keynes, J. M. (1973b) The Collected Writings of John Maynard Keynes. Volume 14: The General Theory and After – Defence and Development, D. Moggridge (ed.), London: Macmillan and Cambridge University Press. Lavoie, M. (1987) ‘Monnaie et production: une synthèse de la théorie du circuit’, Économies et Sociétés, 9 (September), 65–101. Lavoie, M. (1992) Foundations of Post-Keynesian Economic Analysis, Aldershot: Edward Elgar. Lavoie, M. (1996) ‘The Endogenous Supply of Credit–Money, Liquidity Preference and the Principle of Increasing Risk: Horizontalism versus the Loanable Funds Approach’, Scottish Journal of Political Economy, 43 (3), 275–300. Moore, Basil (1988) Horizontalists and Verticalists: The Macroeconomics of Credit Money, Cambridge: Cambridge University Press. Moore, B. (1994) ‘The Demise of the Keynesian Multiplier: A Reply to Cottrell,’ Journal of Post Keynesian Economics, 17 (10), 121–34.

180  Rochon Parguez, A. (1975) Monnaie et macroéconomie, Paris: Économica. Pressman, S. (1995) ‘Deficits, Full Employment and the Use of Fiscal Policy’, Review of Political Economy, (7), 2, 212–26. Pressman, S. (2000) ‘A Note of Money and the Circuit Approach,’ Journal of Economic Issues, 34 (4), December, 969–73. Rochon, L.-P. (1999) Credit, Money and Production: An Alternative Post-Keynesian Approach, Cheltenham: Edward Elgar. Rochon, L.-P. (2006) ‘Endogenous Money, Central Banks and the Banking System: Basil Moore and the Supply of Money’. In M. Setterfiled (ed.), Complexity, Endogenous Money and Macroeconomic Theory: Essays in Honour of Basil J. Moore, Cheltenham: Edward Elgar Publishing, pp. 220–43. Rochon, L.-P. and Rossi, S. (2003), Studies in Modern Theories of Money, Cheltenham: Edward Elgar. Trevithick, J. (1994) ‘The Monetary Prerequisites for the Multiplier: An Adumbration of the Crowding-Out Hypothesis’, Cambridge Journal of Economics, February, 18 (1), 77–90. Wolfson, M. H. (1996) ‘A Post Keynesian Theory of Credit Rationing’, Journal of Post Keynesian Economics, 18 (3), 443–70.

10 The multiplier, the principle of effective demand and the finance motive A single coherent framework Claude Gnos

Introduction In his celebrated 1988 book Horizontalists and Verticalists, as well as in his subsequent work (for example, Moore, 1994), Basil Moore severely criticized the Keynesian multiplier theory. According to him, the identity of saving and investment, which is tied in with the endogeneity of money, refutes ‘the Keynesian notion that the level of income adjusts to bring planned saving and planned investment . . . into equality by a “multiplier” process’ (Moore, 1988, p. 309). This chapter examines this argument. It will conclude that Moore’s criticism of the multiplier is well grounded, although it is not the end of the multiplier story. It is instead, I shall claim, a half-way point toward a better understanding of the originality of Keynes’s analysis, as opposed to its standard interpretation. To begin with, the next section presents Moore’s argument in some detail and then examines it with reference to the famous distinction between actual and planned saving and investment. According to Cottrell (1994), Moore namely underestimates the implications of this distinction for the multiplier theory. The third section shows, however, that Moore, just as Schmitt (1960, 1972) previously, accurately questions the standard interpretation of the Keynesian multiplier: the I–S identity is undoubtedly at variance with the standard multiplier expansion path. The next section shows that Keynes would not have disputed the arguments against the multiplier. But how could he state the identity and simultaneously adopt the multiplier? To answer this crucial question, the following section seriously assesses the static or logical dimension of the multiplier depicted by Keynes. In the sixth section, we are in a position to confirm that Keynes’s conception of the multiplier cannot be reduced to the standard version of it and so deserves a full reappraisal within the framework of his actual theory of employment as characterized by the principle of effective demand and the finance motive. The seventh section concludes.

Is the multiplier theory rebutted by I–S identity? Moore’s criticism is closely related to the analysis of bank money and the endogeneity thesis he advocates in his book. Bank money, Moore points out, is created

182  Gnos in response to borrowers’ demand for credit, in the form of bank deposits. Thus, present-day money is ‘the liability of the issuing financial institution and, behind the institution, the institution’s borrower’ (Moore, 1988, p. 14). By reference to double-entry bookkeeping, which stipulates the equality of sources and applications of funds, he insists that deposits imply lending: they are a source of financing for banks matching the credit that banks grant to borrowers. The double-entry principle precludes banks from granting credit to borrowers without the banks themselves being granted equivalent credit by depositors.1 Depositors are therefore creditors of banks and ‘ultimately the creditors of bank borrowers’ (ibid., p. 20). Moore terms deposits ‘convenience lending’ since the public hold them for convenience before spending them on goods or non-monetary financial assets. He then insists that this convenience lending is voluntary; banks are quantity-takers: no money could be created unless sellers of goods and services (workers who hire out their services in the case of the multiplier process) were to accept it as a means of payment and so demand it in exchange for goods and services (ibid., p. 314). As he puts it, ‘The quantity of money is always demand-determined, and the supply of money is always credit-driven’ (ibid., p. 313). The multiplier process is concerned with these features of bank money in so far as the increment in investment that initiates it has to be financed. According to Moore, that is what is fundamentally flawed in the standard Keynesian analysis: it ‘never addresses the issue of how planned spending in excess of current income is financed’ (ibid., p. 312). As soon as this issue is accounted for, the author argues, it clearly appears that planned investment and planned saving are necessarily equal. Then, no room is left for any process by which income would adjust to bring them into equality: Income does not adjust to equate planned investment with planned saving. What then is left of Keynes’s income–expenditure multiplier analysis of the equilibrium level of income? The answer must be – nothing. (Moore, 1988, p. 314) To make his point, Moore first assumes that the velocity of money is stable. In this case, the increment in I, defined as an ‘autonomous’ expenditure – that is, an expenditure not made out of a pre-existent income – implies that firms deficitspend and so have recourse to banks, which purposefully create money. According to Moore, ‘So long as velocity is stable, such net deficit spending must be financed by an increase in net bank credit and new money creation’ (ibid., p. 313). Hence, since bank money is necessarily deposited with banks, money creation means new lending. Banks grant credit to the firms that perform the increment in investment (∆I) and thus become indebted to the factors the services of which firms pay. This means that there is a strictly equivalent increase in planned saving, that is, in the bank deposits that the factors have voluntarily accepted as a means of payment, and in investment (∆I) that has been planned by firms. Therefore, there is no scope for an adjustment process matching this planned ∆S to the initial increment in investment, ∆I, decided upon by firms.

The multiplier, the principle of effective demand and the finance motive  183 Moore also assumes, as a second step, that the velocity of money is likely to increase. In this case, there is no need for banks to create a supplementary quantity of money: pre-existent deposits are used for financing new payments by firms. This means that firms borrow cash from depositors, the latter buying assets from the former. According to Moore (ibid., p. 312), ‘When borrowing is from a non-bank unit, it is financed out of increased volitional lending, that is, the conscious decision by economic units to accumulate income-yielding nonmonetary financial assets out of current income.’ Firms then transfer the cash to the factors they employ. Irrespective of whether firms’ outlays are financed by banks or non-banks, the result is the same: the creation of income deposits by the factors of production, which, as stated above, amounts to convenience lending for the benefit of firms through the intermediation of banks. What is crucial here is that this convenience lending is additional to the volitional lending granted by those economic units who changed their cash into non-monetary financial assets, and forms the counterpart to the new investment. So Moore’s conclusion remains unchanged: All increases in investment spending, whether financed internally or externally, from non-banks or banks, are thus accompanied by equal increases in saving in the same period . . . The Keynesian multiplier analysis is thus flawed. (ibid., p. 312) What are we to make of Moore’s argument? Despite the author’s insistence on the fact that bank deposits would not exist if the general public were not to accept holding them, we may surmise that his conception of ‘convenience saving’ does not precisely correspond to the conception of ‘planned saving’ that the proponents of the multiplier theory are usually referring to. This is a point that Cottrell (1994) raises in defence of the multiplier theory: according to him, Moore fails to distinguish between ‘actual’ investment and saving that ‘are indeed identically equal’, and ‘planned’ or ‘intended’ investment and saving that ‘are not identical, and must be brought into equality by means of some mechanism or other’ (p. 114). According to the standard approach to the Keynesian multiplier, Cottrell emphasizes, an increase in investment generates an increase in income which is then (at least partially, depending on income-holders’ marginal propensity to consume) spent on inventories of consumption goods. The consequent fall in inventories induces entrepreneurs to employ more workers and produce more: The actual mechanism whereby Y changes in response to I is typically explicated in terms of inventory accumulation or decumulation. So long as planned investment exceeds planned saving, sales will exceed production and producers experience an unplanned fall in inventory levels. They react by employing more workers and producing more. (ibid., p. 111)

184  Gnos In Cottrell’s words, this adjustment process, which is defined primarily in real terms, entails a monetary counterpart (cf. ibid., pp. 118–19). For one thing, producers meeting the supplementary demand out of inventory do not immediately step up their production as their takings increase. For another, newly employed workers do not spend their incomes at once. Thus, producers and workers temporarily hold money balances that they will soon spend ‘all round, just as in Keynes’ (ibid., p. 119). Cottrell then argues that Moore’s ‘convenience saving’ corresponds to these temporary holdings. Indeed, there is not doubt that the increase in investment is accompanied by an equal increase in saving. But, defined in this way, ∆I and ∆S are actual magnitudes that may be not in accordance with investment and saving as planned by economic agents, that is, with long-run values of investment and saving (ibid., p. 114). What then is left of Moore’s criticism?

I–S identity at variance with the supposed multiplier expansion path In his reply to Cottrell, Moore acknowledges the relevance of the distinction between actual and planned or intended saving and investment. He even concedes (Moore, 1994, p.  126) that his conceptions of ‘convenience lending’ and ‘convenience saving’ have much to do with the transitional ‘monetary counterpart’ Cottrell assigns to the adjustment process inherent in the Keynesian multiplier. In doing so, is he not undermining his initial argument for good? In fact, what he claims is that he has ‘no quarrel with this interpretation of course, other than it presumes the existence of the multiplier result’ (ibid., p. 127). Let us examine this latter point. Indeed, Moore (1994) comes up here with further arguments. On the one hand, he criticizes the very reference to any long-term position of equilibrium. With reference to Davidson’s non-ergodicity axiom (cf. Davidson, 1972, 2002), he is namely in a position to claim the following: Our expectations of the unknown future change continuously. As a result, in a non-ergodic world it is impossible even to conceive of any stable macroeconomic equilibrium configuration towards which the system is tending. Ergo, there can be no Keynesian income multiplier. (Moore, 1994, p. 127) On the other hand, he goes deeper into his initial argument by which: The fatal flaw in the textbook treatment of the multiplier is that it never addresses how an autonomous increase in investment spending is financed. (ibid.; emphasis in original) He then concludes: ‘As a result, real-world economies can never move along their multiplier expansion path’ (ibid., p. 131). The determination of current output (Y1) is simply subject to the principle of effective demand, just as the deter-

The multiplier, the principle of effective demand and the finance motive  185 mination of the output of the year before (Y0) was: ‘The situation at Y1 is, from the viewpoint of the expected future change in income, no different from that at Y0’ (ibid.). Without underestimating the consequences of the non-ergodicity axiom, we may have a closer look at Moore’s initial argument relating to the financing of investment spending and the I–S identity. The latter proves, in the final analysis, to be relevant in refuting the existence of the expansion path inherent in the multiplier theory, irrespective of any consideration of the plans of economic agents. This is so because the identity denotes that, in a world of endogenous money, when firms invest money in production they do not spend any pre-existent savings but on the contrary generate a new amount of savings: ‘an increase in investment expenditures always creates the increase in nominal saving required to finance it. In short, investment determines saving, and not the other way round’ (Moore, 1988, p.  315). This means that no income is ever induced from pre-existent income. Any supposed chain of events by which the spending of income feeds income is a figment of the imagination. The multiplier expansion path depicted by standard analysis is actually denied by the I–S identity. In support of Moore’s argument, it is worth observing that this very same point was made earlier by Schmitt (1960, 1972), a leader of the Franco-Italian circuit school. Examining the monetary conditions for the economic circuit, that is, for the successive outlays and receipts of firms, which have to pay for factor costs and then to recoup the money they spent, Schmitt came to the conclusion that ‘the hypothesis of the dynamic sequence of incomes is entirely destroyed’ (Schmitt, 1972, p. 138). As confirmed above, the payment of factor costs generates incomes that are not taken out of pre-existent incomes. From this, Schmitt concludes that expenditures on goods do not generate incomes but on the contrary annihilate them: ‘If incomes take shape “initially” through an expenditure which is not an income expenditure, it follows that incomes are spent and not reproduced by purchases; they leak out’ (ibid., p. 137). Schmitt finds confirmation of this statement in the nature of bank money. Being dematerialized, bank money is paper or book money with no intrinsic value or purchasing power. Its purchasing power is derived from the goods that are being produced when firms pay for factor costs, and this purchasing power is destroyed when factors pay for the goods they purchase from firms. In the time interval, the purchasing power of money is saved: investment in new production generates an equivalent saving by income-holders. This is why the use of pre-existent deposits in the payment of factor costs does not exhaust any pre-existent saved income but simply transforms it into illiquid saving. This pre-existent saving continues to exist so long as it is not spent on goods. Then, just as would happen with the use of newly created deposits, the use of pre-existent deposits in the payment of factor costs forms a new saving (income deposits) corresponding to the newly produced goods. By the same token, the identity of I and S also means, in macroeconomic terms, that no income formed in the sector producing capital goods can be spent on consumption goods. In other words, when workers producing the supplementary capital goods spend their wages on consumption goods, holders of incomes

186  Gnos formed in the production of consumption goods necessarily spend them on capital goods or save them. Moreover, if they spend it on stocked goods, the conclusion is unchanged; this amounts to saying that the workers who produced the latter goods keep saving the incomes they earned in that production. Schmitt concludes that the multiplier is necessarily equal to one: the autonomous investment generates a strictly equivalent income which is tied up in financing this same investment (cf. Schmitt, pp. 125–38). There is no extra income available that could be spent on consumption goods out of inventories and so generate new incomes until such time as – as the standard theory of the multiplier argues – planned saving is equated to the initial increase in investment.

Keynes’s own statement of the I–S identity We may surmise that Keynes would not have disputed the arguments against the multiplier examined in the previous sections. He states the identity of I and S in a way that clearly anticipates the analysis put forward by Moore and Schmitt. This is specifically the case in the General Theory when he writes that: The prevalence of the idea that saving and investment . . .  can differ from one another, is to be explained, I think, by an optical illusion due to regarding an individual depositor’s relation to his bank as being a one-sided transaction, instead of seeing it as the two-sided transaction which it actually is . . . It is impossible that the intention of the entrepreneur who has borrowed in order to increase investment can become effective . . . at a faster rate than the public decide to increase their savings. (1936, pp. 81–3) We are thus confronted with a puzzling situation: how could Keynes acknowledge the identity of saving and investment and simultaneously adopt the multiplier? Before looking for an answer to this question in the two last sections, we may examine Keynes’s statement of the I–S identity in some detail. Let us consider the initial increase in investment involved in the standard multiplier process. This increment in I pertains to the payment of an increased quantity of employment in the production of investment goods. In Keynes’s own words, ‘The fluctuations in real income under consideration in this book are those which result from applying different quantities of employment (i.e. of labour units) to a given capital equipment, so that real income increases and decreases with the number of labour-units employed’ (ibid., p. 114). The term ‘investment’ is usually used to designate spending for the accumulation of capital, especially in the form of capital equipment. Such spending exhausts incomes that were saved by their holders. Here (with regard to the multiplier process), ∆I is not meant to pay for goods, but to pay for the labour units necessary for a new production of capital goods. Expenditures met in this way do not exhaust existing saving, but instead form new incomes and so new saving. Keynes did not expand much on this in the General Theory but he did so in his famous 1937 articles on the theory of the rate of interest (Keynes, 1937a,b). As he then explained, firms have to

The multiplier, the principle of effective demand and the finance motive  187 secure finance, that is, an ‘advance provision of cash’ (Keynes, 1937a, p. 208), when they decide to start production. Such finance may be provided by banks or by the market, if not by firms from their own cash balances. Whichever way it is provided, this cash, when spent in the payment of wages, does not exhaust any pre-existent saving. On the contrary, it generates new net saving attached to the new net investment (ibid., p. 209). This analysis clearly ties in with the nature of bank money (see also Keynes, 1936, pp. 79–85) discussed above with reference to Moore and Schmitt. Being mere paper or book money (these types are not mutually exclusive since paper money is recorded in the books of the central bank) with no intrinsic purchasing power, bank money has to be interpreted with reference to the economic operations in which it is involved. When spent in paying workers’ wages, money represents new incomes that allow their recipients to buy goods currently produced. So long as recipients do not buy goods, goods remain in the hands of firms, whether they are still in the making or stocked in stores. Thus, the payment of factor costs finally resolves itself both in saving, in the form of deposits held by income recipients, and in investment, that is, the capitalization of goods; in the final analysis, the term ‘investment’ is not misused here. Keynes emphasizes that while borrowing cash for paying wages, firms successively benefit from two kinds of credit, credit in the sense of ‘finance’ (which allows them ‘to go ahead with assurance’) and credit in the sense of ‘saving’ (so long as the goods produced are not sold, after wages have been paid, firms are in the debt of banks and, through them, of depositors who save their income in the form of bank deposits). As Keynes (1937a, p. 209) puts it, Credit, in the sense of ‘finance’, looks after a flow of investment. It is a revolving fund which can be used over and over again. It does not absorb or exhaust any resources. The same ‘finance’ can tackle one investment after another. But credit, in Professor Ohlin’s sense of ‘saving’, relates to a stock. Each new net investment has new net saving attached to it. The saving can be used once only. It relates to the net addition to the stock of actual assets. The unity of the views of Keynes and his two modern followers quoted above is beyond dispute. How then are we to explain Keynes’s stance in favour of the multiplier? To answer this question, let us consider in the next section Keynes’s ‘logical theory of the multiplier’, as he termed it.

Keynes’s ‘logical theory of the multiplier’ and its critique Let us return to the General Theory. Keynes bases the multiplier on the marginal propensity to consume that ‘tells us how the next increment of output will have to be divided between consumption and investment.’ Hence he writes: For ∆Yw = ∆Cw + ∆Iw, where ∆Cw and ∆Iw are the increments of consumption and investment; so that we can write ∆Yw = k∆Iw, where 1 – 1/k is equal to the marginal propensity to consume. Let us call k the investment multiplier. It

188  Gnos tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment (1936, p. 115). In Keynes’s words, this presentation corresponds to the ‘logical theory of the multiplier, which holds good continuously, without time-lag, at all moments of time’ (ibid., p. 122). In general, however, he suggests that we consider ‘the consequences of an expansion in the capital goods industries which take gradual effect, subject to time-lag and only after an interval’ (ibid., pp.  122–3). I believe this distinction is crucial, but has been misinterpreted by Keynes’s followers. Typically, Hansen, who made a major contribution to the development of the standard Keynesian analysis, considered that Keynes had analysed the process of expansion inherent in the multiplier theory all too briefly ‘to ensure understanding by the reader’ (1953, p. 108). He deplored Keynes’s focus on the logical theory of the multiplier, which Hansen thought depicted a ‘mere arithmetic multiplier’, which was ‘tautological’, and also on what may be called ‘the comparative-statics multiplier’, ‘which is “timeless” in the sense that it leaps over the time interval between two successive static equilibrium positions’ (ibid., p. 108). To make good this failing, Hansen promoted a ‘true behaviour multiplier’ designed to provide ‘a true analysis of causal factors’ based on behaviour patterns. This is the point of entry of the distinction between actual and planned (or desired) saving and investment, and also of the expansion path based on the successive increases in expenditures and incomes referred to in the third section above. Thereafter, as we know, it became commonplace to claim that: Keynes’s treatment of the multiplier is thus incomplete. It is always necessary to keep in mind that the passage of time is not dealt with in comparative static analysis, and this time element must be introduced in any application of the analysis that is concerned with the effects of changes. Keynes’s language in referring to the multiplier sometimes gives the impression that he is dealing with changes, but his treatment of it is confined to comparative statics (Asimakopulos, 1991, p. 68). We shall not re-examine the conception of the multiplier promoted by Keynes’s followers, but challenge the suggestion that Keynes is dealing with changes within an inappropriate framework. Keynes’s distinction between the logical multiplier and the general case in which capital goods industries gradually expand is grounded on the state of forecasts: The discussion has been carried on, so far, on the basis of a change in aggregate investment which has been foreseen sufficiently in advance for the consumption industries to advance pari passu with the capital-goods industries . . . In general, however, we have to take account of the case where the

The multiplier, the principle of effective demand and the finance motive  189 initiative comes from an increase in the output of the capital-goods industries which was not fully foreseen. (1936, p. 122) It is true that Keynes is not very explicit, then, as regards the way imperfect forecasts induce the multiplier process. He simply emphasizes that ‘an expansion in the capital goods industries causes a series of increments in aggregate investment occurring in successive periods over an interval of time’ (ibid., p.  123). It was legitimate for Hansen to consider that a missing piece had to be replaced. However, an alternative suggestion might be made: the multiplier effect may hinge on a mechanism that Keynes had already explored in full, namely the principle of effective demand. Here is my point.

The coherence of Keynes’s theory of employment The principle of effective demand brings entrepreneurs’ forecasts to centre stage. Entrepreneurs determine the employment they offer on the basis of the proceeds of sales they are expecting, which are dependent on the volume of employment they pay for. They require that these proceeds reimburse their factor costs and, in addition, earn them a (maximum) profit (Keynes 1936, pp. 23–6). On this view, what will be the consequences of an increase in investment, which amounts to the payment of increased wages in the capital goods industries? This question does not actually require a more detailed answer. Entrepreneurs will anticipate an increase in demand for consumption goods, which, proportionally to the marginal propensity to consume, is dependent on the extra wages paid in the production of capital goods and on the wages paid in the production of an increased quantity of consumption goods. Without reference to any further mechanism, we thus reach a conclusion which draws specifically on the theory of the investment multiplier. The increase in Y is k∆Iw, where k is the logical multiplier as previously defined. Of course, entrepreneurs are not likely to be able to foresee in full what the increased demand for consumption goods will be. Accordingly, just as Keynes puts it, we may expect that they will gradually adapt their supply to demand in connection with their actual proceeds in the market. However, The fact that an unforeseen change only exercises its full effect on employment over a period of time . . . does not in any way affect the significance of the theory of the multiplier as set forth in this chapter. (ibid., p. 124) In other words, Keynes’s focus on the logical multiplier is not a flaw in his analysis, as the standard Keynesian literature claims. He did not fail to shift from a static analysis to a dynamic one, that is, on the standard view, to explain how purchases of consumption goods could increase incomes and so feed new purchases along a

190  Gnos given multiplier path. In reality, by Keynes’s analysis, any change in employment, and so in income, is determined in accordance with the principle of effective demand, which applies whether changes in demand are accurately foreseen or not. This means that the multiplier path, as posited in standard Keynesian literature, does not exist. The determination of aggregate income, just as Schmitt argues, ‘is static in that each period requires its own analysis’ (Schmitt, 1972, p. 113; see also Moore, 1988, p. 131 quoted above, for whom ‘the situation at Y1 is . . . no different from that at Y0′). To depict the adjustment process he refers to, Keynes takes the extreme case where the increase in I was not foreseen. In this event the efforts of those employed in the capital-goods industries to consume a proportion of their increased incomes will raise the prices of consumption-goods until a temporary equilibrium between demand and supply has been brought about partly by a redistribution of income in favour of the saving classes as an effect of the increased profits resulting from the higher prices, and partly by the higher prices causing a depletion of stocks. So far as the balance is restored by a postponement of consumption there is a temporary reduction of the marginal propensity to consume, i.e. of the multiplier itself, and in so far as there is a depletion of stocks, aggregate investment increases for the time being by less than the increment of investment in the capital-goods industries. As time goes on, however, the consumption-goods industries adjust themselves to the new demand, so that when the deferred consumption is enjoyed, the marginal propensity to consume rises temporarily above its normal level, to compensate for the extent to which it previously fell below it, and eventually returns to its normal level; whilst the restoration of stocks to their previous figure causes the increment of aggregate investment to be temporarily greater than the increment of investment in the capital-goods industries. (1936, pp. 123–4) This passage is very instructive. We have confirmation that the multiplier does not represent a process defining an expansion path that would come to an end when planned saving and investment have been equated. As noted above, for Keynes, the significance of the multiplier is in no way affected by the fact that entrepreneurs gradually adapt their supply to demand. The multiplier, which is thus definitively logical or static, applies strictly at every moment of time; it shows how entrepreneurs’ expectations and hence employment are affected by a supplementary investment. At the very most, forecasts concerning demand being imperfect, the quantities of capital and consumption goods may be produced in such a proportion that the current value of the propensity to consume (‘i.e. of the multiplier itself’) may differ from its ‘normal level’, which will prevail later on (probably after a brief interval, according to Keynes, 1936, pp. 124–5). Here, Keynes might well have used the distinction between planned and actual saving and investment magnitudes. Moreover, he certainly would have agreed with Hansen, who consid-

The multiplier, the principle of effective demand and the finance motive  191 ered that behaviour patterns should be taken into account to describe the dynamics of the expansion of an economy. The originality of Keynes’s analysis would have remained intact, however, in that, in his view, which is supported by the finance motive and the principle of effective demand, there is no dynamic chain of events by which the spending of incomes would generate incomes. Interestingly enough, Hansen observes in a footnote (1953, p. 113) that the critical literature on Keynes has generally missed the point that Keynes, in his chapter on the multiplier, did not actually adopt the comparative-statics framework but, somehow, the concept of ‘a moving equilibrium’. This insight is judicious in that Keynes’s concept of the multiplier is static but may be combined with the analysis of the dynamics of the economy; what is actually hard for us to understand is why Hansen was dissatisfied with this view and why he did graft a dynamic multiplier onto Keynes’s analysis.

Conclusion As Cottrell emphasizes, the debate about the multiplier is part of a more general discussion about the extent to which ‘the arguments of Keynes’ General Theory have to be revised in the light of endogenous money’ (1994, p. 111). It is a fruitful discussion indeed, particularly with regard to our understanding of the originality of Keynes’s theory. This is at least one conclusion we can draw from our examination of the debate about the multiplier. It namely turns out that endogenous money does not run counter to Keynes’s actual conception of the multiplier but counter to the standard interpretation of it. According to the standard interpretation of the Keynesian multiplier, an autonomous investment, that is, an investment which is not financed out of current income, induces purchases of consumption goods that generate a succession of supplementary incomes and purchases until planned saving is equated to the initial increment in investment. This multiplier expansion path is undoubtedly at variance with the features of bank money, which cannot finance (on demand) any investment by firms without simultaneously generating an equivalent saving by income recipients. Whatever the distinction between planned and actual magnitudes, then, every investment ties up the corresponding saving, which cannot therefore be spent on consumption goods and generate new incomes. The very idea that the spending of incomes on purchases could feed new incomes is refuted at once, because, just as Keynes put it when he explained the ‘finance motive’ in his 1937 articles, the financing of the factor costs of any production does not rely on pre-existent resources. On the contrary, Keynes’s own conception of the multiplier is not challenged by endogenous money. This is so because Keynes did not conceive of the multiplier as a dynamic process in itself. The multiplier is, in fact, static or logical. It can, however, be combined with the dynamics of the economy resulting from behaviour patterns, through the principle of effective demand by which entrepreneurs decide on the scale of their production with regard to their expected proceeds from sales, which of course may be influenced by an increase in investment.

192  Gnos

Notes 1 This is an inference Keynes already made in the General Theory.

References Asimakopulos, A. (1991), Keynes’s General Theory and Accumulation, Cambridge: Cambridge University Press. Cottrell, A. (1994), ‘Endogenous Money and the Multiplier’, Journal of Post Keynesian Economics, Fall, Vol. 17, 1, pp. 111–20. Davidson, P. (1972), Money and the Real World, New York: John Wiley and Sons. Davidson, P. (2002), Financial Markets, Money and the Real World, Cheltenham: Edward Elgar. Hansen, A. H. (1953), A Guide to Keynes, London: McGraw-Hill. Keynes, J. M. (1936) The General Theory of Employment, Interest and Money, London: Macmillan. Keynes, J. M. (1937a) ‘Ex post and ex ante’, in (1973) The Collected Writings of John Maynard Keynes, Vol. 14, London, Macmillan. Keynes, J.M. (1937b) ‘The ‘ex ante’ theory of the rate of interest’, in (1973) The Collected Writings of John Maynard Keynes, Vol. 14, London: Macmillan. Moore, B. (1988), Horizontalists and Verticalists: The Macroeconomics of Credit Money, New York: Cambridge University Press. Moore, B. (1994), ‘The Demise of the Keynesian Multiplier: A Reply to Cottrell’, Journal of Post Keynesian Economics, Fall, Vol. 17, 1, pp. 121–33. Schmitt, B. (1960), La formation du pouvoir d’achat, Paris: Sirey. Schmitt, B. (1972), Macroeconomic Theory. A fundamental revision, Albeuve, Switzerland: Castella.

Index

about this book: multiplier process, criticism of 1–3; structure 3–5 ‘accelerator principle’ 33, 54, 55, 79, 176 Aftalion, Albert 33, 64 aggregate demand (AD) 1, 17, 28n15, 29n26, 35, 68, 91, 124, 137, 171, 176–7; aggregate supply (AS) and 120–3 aggregate investment 13, 24, 62, 73, 89, 91, 102n9, 134, 137, 138, 144, 188–9, 190 aggregate supply (AS) 16, 68, 120–3 Amadeo, Edward 170, 178n1 American Economic Review 34, 39, 47 Angell, J. W. 37, 43–4n13, 52 Arestis, P., Dunn, S. P. and Sawyer, M. 15 Arestis, Philip 64, 82 Asimakopulos, Athanasios 2, 27–8n14, 140, 167n5, 188 assets 115, 116, 183; acquisition of 102n10; banks’ liabilities and 110, 111, 162; investment reserves and 162; liquid assets 92; non-monetary financial assets 182, 183; profits, assets and liabilities 112, 113; stock of 111, 187; value of, security of 111 Asso, Pier Francesco 43n1, 46 autonomous expenditures 58, 62, 63, 71–2, 77–8, 92, 100, 102n14, 153, 160, 182 autonomous variables 61, 69, 74, 75, 77–8 Bagehot, Walter 56 Bailly, Jean-Luc 4 banks: bank credit in business cycles 153–4; bank loans for consumption 114; bank money and Keynesian multiplier 4, 109, 113, 173, 181–2, 185, 187, 191; liabilities of 110, 111, 113

Barrière, A. 142 Becher’s principle 95 behaviour, coordination of 75–6 Bhaduri, A. 18, 19, 23, 28n19, 29n25, 29n27 Bickerdicke, Charles 33 Böhm-Bawerk, Eugen von 48 Bortis, Heinrich 4, 58, 59, 61, 63, 64, 66, 73–5, 76, 79, 82 Bradley, Xavier 4, 147 Brookings Institution 57 budget deficits 154, 159, 160, 163 business cycles 24, 54, 59, 61, 175; bank credit in 153–4; behaviour, coordination by system and 75–6; investment, economic activity and 154; investment and stimulation of 162, 163; macrouncertainty and 75–6; mediumterm multiplier and 67; in monetary production economy 75–7; multiplier, change through 178; multiplier and, Clark’s perspective 35–6, 37–8; profits and investment in generation of 156–7; trend and cycle, relationship between 72–3; Wicksell’s analysis of 64 business expansion 38, 40, 44n17, 162 Business Organization and the Myth of the Market Economy (Lazonick, W.) 82 capacity utilisation 66, 72, 173 capital: capitalist consumption, lagged profits and 158; liquid capital 90, 92, 93–4, 102n9, 111, 113, 114, 115, 117, 119n7; value, variable capital and 19–24 Carver, Thomas Nixon 33 Casarosa, C. 27–8n14 cash balances, ratio to business volume 38

194  Index causal relations of equilibrium 140 Chick, Victoria 15, 18, 27n12, 91, 102n8, 102n14, 119n1, 134 circuit theories, post-Keynesians and 106–9, 110–11, 116–17, 172–4, 177–8 circuit velocity of money, concept of 37–8, 39–40, 421 circulation: circular process of production 58, 64; circulating media and production volume, ratio between 37; of consumer spending 95; demand for money in 161, 162; income propagation period and velocity of 37; of incomes 95; period of 43n12; production and, processes of 59; of stamp money 50; time deposits and circulating money 43–4n13; velocity of circulation of money 33, 34, 36, 38, 39, 40, 41, 125 Clark, John Bates 32, 56 Clark, John Maurice 4, 32–44; ‘accelerator principle,’ father of 33; ambivalent nature of thought 32–3; business cycles, multiplier and 35–6; cash balances, ratio to business volume 38; circuit velocity of money, concept of 37–8, 39–40, 42; Hegeland’s view on multiplier analysis of 40–1; income propagation period, concept of 37–8, 40; ‘institutionalized’ attitude of 33, 43; inventory accumulation, deaccumulation 38; Johannsen’s work, denial of influence of 34; ‘leakages,’ income velocity and 36, 39; letter from Alvin H. Hansen (1934) 50–2; letter from Paul A. Samuelson (1953) 53–4; letter to G. S. Hauge (1937) 52–3; letter to Joseph Dorfman (1956) 55–7; letter to Maurice Roche-Agussol (1918) 46–50; letter to Paul A. Samuelson (1953) 54–5; multiplier, role in development 33–5, 39; multiplier analysis, awareness of intrinsic limitations of 41–2; multiplier analysis, individuation of approaches to 36–7; multiplier as ‘rough approximation’ 42–3; public expenditures in multiplier analysis 36–7 Cobb, Charley 55 Collected Writings (Keynes, J. M.) 14 Colm, Gerhard 39 Columbia Commission 50 comparative-static analysis 13–14, 91 comparative-static equilibrium 123

constant propensity, idea of 40, 42 consumer spending 95, 132 consumption: consumption function 27n3, 65, 155; consumption goods, production of investment goods and 133–8, 138–47; investment and 127–48; postponement of, marginal propensity to consume and 62 Cooley, Charles H. 56 The Costs of the World War to the American Public (Clark, J. M.) 34, 35, 56 Cottrell, Allin 3, 29n24, 104n30, 143, 148n5, 168, 171, 181, 183–4, 191 credit: ‘credit inflation’ 161–2; creditworthiness 175, 178n5; ‘finance’ and investment 187 crowding out argument 165–6 Crystal, Bernard 46 customers, fringe of unsatisfied 175, 178n5 D-curve 17, 19, 28n15, 28n16, 29n26; see also aggregate demand (AD) Dalziel, P. 29n24, 104n30, 140 Davenport, Herbert J. 48, 56 Davidson, P. 16, 27n13, 171, 184 Davis, Ronnie 33 deferred consumption: hypothesis of 143–7; and marginal propensity to consume 62, 143–5, 190 Deficit Spending and the National Income (Villard, H. H.) 40 Deleplace, G. and Nell, E. 172 demand for money 119n2, 161, 162 Dimand, Robert W. 33–4, 43n7, 101–2n7 direct employment 11, 14, 101n3 The Distribution of Wealth (Clark, J. B.) 32, 52 Domar, Evsey 61, 69–72 Dorfman, Joseph 32, 33, 34, 35, 43n4, 43n5, 43n10, 44n18, 44n19, 46, 55–7 double-entry bookkeeping 182 Douglas, Paul 34 dynamic theory of multiplier 94–5, 95–9, 102n14, 102n15, 127, 128–33, 132–3; dynamic period analysis, abandonment of 13–14; logical form of multiplier and 13–14, 26–7, 62–3, 128–33; and marginal propensity to consume 95, 133 ‘dynamiting’ effect of marginal propensity to consume 138–9

Index  195 Eastern Economic Association 3 economic activity and investment, Kalecki’s analytical modes on 154 Economic Journal 64, 65 The Economic Mind in American Civilization (Dorfman, J.) 33 economic reality and Keynesian multiplier 14–15 Economics of Planning Public Works (Clark, J. M.) 34, 36, 39, 40 effective demand: autonomous and derived 58; capacity output and 76; components of 73–4; decline in 69; inherent instability of 69–71; and Keynesian multiplier 9, 15–16, 17–18, 26, 59, 168; long-period demand 75; principle of 15–18, 26–7, 60–1, 66, 82, 91–2; problem in money terms 59; sources of 80; unifying agenda for postKeynesians 15–18 Ely, Richard 56 employment: direct and indirect, distinction between 87–8; direct employment 11, 14, 101n3; indirect employment 11, 87, 88 101n3; primary employment 14, 65, 88, 101n3, 142; secondary employment 65, 89, 101n3; volume and direction of 102–3n16 employment multiplier 68, 89, 90, 132 employment theory, coherence of 189–91 endogenous money 3–4, 29n24, 116–17, 168–9, 185, 191 Essays in Business Cycle Theory (Kalecki, M.) 155, 167n2 Euler’s theorem 55 expenditure, primary and secondary 11 export surpluses 154, 159, 160, 165 ‘external markets’ 159–60 Fetter, Frank A. 48 finance motive: Keynes’ writings on 119n6, 161; and Keynesian multiplier 1, 5, 41, 119n6, 134, 161, 178, 181, 191 financial machine 28n21 financing 2, 38, 104n29, 138; of additional investment 154; bank deposits and 182, 183; deficit financing 41; of factor costs 191; funding and 160–3, 165; of investment spending 185–6; long- and short-term financing 2; refinancing of production cycles 174; state financing 116; storage financing 96 finite value of multiplier, search for 87–90

Fiorito, Luca 4, 39 Fisher, Irving 50, 64 Fitzgibbons, A. 61 Flux, A. W. 55 Fontana, G. 24, 27n10 forecasts, state of 188–9 foreign trade multiplier 79–81 free profits 111–12, 113, 114, 115, 117 Freund, Ernst 56 fundamental psychological law 9, 12, 13, 19, 20, 21, 23, 25, 27n5, 89, 92, 135 Garegnani, P. 60, 73 General Theory (Keynes, J. M.) 33, 41, 42, 69, 87, 97, 99, 134, 141, 153; basic tenet of 80; causal relations of equilibrium 140; central focus of post-Kenesian macroeconomics 1; dynamic period analysis, abandonment of 13–14; effective demand and the multiplier 9, 15–16, 17–18, 26, 59, 168; endogenous money and 191; explicit reference to two different types of multiplier 90; focus on multiplication of incomes 89; income disposal by workers and entrepreneurs 20; indirect and primary employment in 88; interest rate, monetary phenomenon 169; investment and saving, difference as optical illusion 186–7; investment and saving, justification for necessary equality between 90–1; investment and structural multipliers in 26; investment multiplier in 63–4, 89; logical multiplier, dynamic multiplier and 13–14, 26–7, 62–3, 128–33; middle way perspective of 61; money, fundamental future uncertainty on 119n5; multiplier as dynamic process 12, 128–33; multiplier as logical relation between investment and income 12–13, 26–7, 29n28, 58–82, 91–4, 102n13, 128–33; multiplier in terms of ex ante expectation 25; reimbursement constraint 109; saving and household behaviour 171; shortperiod employment multiplier in 68; time dimension and 2; see also marginal propensity to consume Gilbert, J. C. 13–14, 43 Gilbert–Humphrey attitude 43 Gnos, C. and Rasera, J.-B. 103n22 Gnos, Claude 3, 4–5, 82, 169, 171, 179

196  Index Godley, W. and Cripps, F. 173 Graziani, Augusto 43n1, 134, 148n1, 178–9n7 Haberler, G. 104n25, 104n31 Hagemann, H. and Rühl, C. 43n6 Hamilton, Walton H. 32, 46, 47, 48 Hansen, Alvin 36–7, 43n9, 43n10, 43n13, 50–2, 144, 188, 190–1 Harcourt, Geoffrey 60, 82 Harrod, Roy F. 61, 69–72, 75; Harrod Paradox 70 Harrod–Domar growth model 69–72 Hartwig, Jochen 3, 27n1 Hauge, G. S. 43n2, 52–3 Hawtrey, Ralph George 2, 33, 139 Hegeland, Hugo 40–1, 43n8 Hicks, J. R. 24, 27n10, 29n27, 60, 72 hoarding: of money, impossibility of 111; propensity towards 93, 108, 109 Hobsbawm, Eric 78 Hobson, John A. 49 Hofmann, Werner 14–15 horizontalist re-interpretation of Keynesian multiplier 168–79 Horizontalists and Verticalists (Moore, B. J.) 126n2, 168, 181 income: circulation of 95; consumptiongoods and investment-goods 25–6; earners’ net indebtedness, retained profits and 112, 114–16; holders and marginal propensity to consume 143, 183; income disposal by workers and entrepreneurs 20; investment, ‘prime mover’ in income generation 10; multiplication, Keynes’ focus on 89; ordered by spending, hypothesis of 139–41; output value and 19; propagation period, Clarke’s concept of 37–8, 40; velocity of circulation of 37–8, 43n12, 44n14 Income Stabilization for Developing Democracy (Millikan, M. F., Ed.) 53 indirect employment 11, 87, 88 101n3 industrial system, inflexibility of 58 inherent instability, multiplier and 69–72 institutions and system in monetary production economy 72–5 interest rates 11, 60, 93, 111, 164, 165–6, 172, 176, 177; Keynes’ rejection of natural rate of 1–2; rate as monetary phenomenon 169; rates and spending, short-period influence 20–1

‘internal’ multiplier 79 intertemporal transmission of money: in endogenous monetary economy 106–18; process of 107, 109, 112, 114, 115, 116, 117, 118 inventories 20, 28n17; accumulation and deaccumulation of 38 investment: accounting equality between saving and 2–3; aggregate investment 102n9; convergence of investment, savings and marginal propensity to consume 171; credit, ‘finance’ and 187; decision-making on 153, 155–6, 157–8; economic activity and business cycles 154; economic activity and investment, Kalecki’s analytical modes 154; finance motive and saving 1; goods, consumption goods and production 133–8, 138–47; investment–savings (I–S) identity, Keynes’ statement on 12, 186–7; investment spending, Keynes’ ‘animal spirits’ and 120; Keynes’ definition of 148n4; long- and shortterm financing of 2; national income and investment demand 10–11; ‘prime mover’ in income generation 10; and profits, relationships between 159, 165; profits and investment in generation of business cycles 156–7; public investment 10, 11; purchasing power and 154, 162; saving and 102n11, 102n12; saving and, difference as optical illusion 186–7; saving and, justification for necessary equality between 90–1; savings, role in 11–12; and stimulation of business cycles 162, 163; structural multipliers 26 investment multiplier: Clark’s role in development 33–5, 39; consumption, investment and 127–48; deferred consumption, hypothesis of 143–7; determined by marginal propensity to consume 136–7; as dynamic process 12, 128–33; dynamic view of 12, 13, 14, 18, 26–7, 94–5, 99, 100, 102n15; finite value of multiplier, search for 87–90; illumination on logical and applied theories 81–2; incomes ordered by spending them, hypothesis of 139–41; in Keynes’ General Theory 63–4, 89; logical form of multiplier 130–2; as logical relation between investment and income 12–13, 26–7, 29n28, 58–82, 91–4, 102n13, 128–33;

Index  197 logical theory of 12–13, 25, 26–7, 29n28, 58–82, 91–4, 102n13, 128–33; logical v. dynamic multiplier 127–33; moving equilibrium and the 190–1; multiplication process, engagement of 141–3; multiplication process, investment–savings relationship 95–101; multiplier conceived as process 132–3; multiplier relation in monetary production economy 58–82; multiplier tradition, post-Keynesian defence of 1, 3, 81–2, 106–7, 109, 168–9; production of investment goods, producers of consumption goods’ anticipation of 133–8, 147–8; production of investment goods, producers of consumption goods failure in anticipation of 138–47, 147–8; proportionality, factor of 133–5, 135–8; as ‘rough approximation’ 42–3; savings, exchanges of 101; savings from income and 87–101; stocks, funding and investment-savings relationship 90–5; in terms of ex ante expectation 25; as transactions velocity of money concept 50–1; wage unit multiplication 135–8; see also Keynesian multiplier investment reserves 161, 162 involuntary unemployment, equilibrium in 58–9 James, William 56 Johannsen, Nicholas 34, 43n6, 56, 64, 66 Journal of Political Economy 47, 53 Junankar, P. N. 33 Kahn, Richard F. 1, 4, 33, 34, 36, 39, 55, 57, 64, 65, 88–9, 96, 101–2n7, 101n1, 101n3, 126n1, 132, 169, 174 Kahn–Keynes approach 33, 34, 36, 38, 39, 42 Kahn–Keynes multiplier 98, 101 Kahn–Meade relation 41 Kaldor, Nicolas 35, 41, 57, 61, 76, 79–80, 81; multipliers, long-period and shortperiod 66–9 Kalecki, Michal 4, 68, 72–3, 76, 119n8, 153–67, 169; on bank credit and business cycle 153–4; budget deficits 154, 159, 160, 163; capitalist consumption, lagged profits and 158; ‘credit inflation’ 161–2; crowding out argument 165–6; economic activity and

investment, analytical modes on 154; export surpluses 154, 159, 160, 165; ‘external markets’ 159–60; financing and funding 160–3; investment and profits, relationships between 159, 165; on investment decision-making 153, 155–6, 157–8; investment reserves 162; Keynesian multiplier, perspective on 153–66; marginal propensity to consume, view on 155; money, creation through loans 163–4; money, production levels and circulation of 161–2; output and ‘natural state of unemployment’ 166; purchasing power and investment 154, 162; saving, forcing of 156–7, 164; savings and investment, causal links 156–7, 163–5, 166; short-term equilibrium 157; simple multipliers in analysis of 155–9; trade cycle analysis 164–5; ‘unattached’ deposits 162 Kent, R. 5n1 Keynes, J. M. and Henderson, H. 11, 22 Keynes, John Maynard: aggregate demand (AD) 1, 17, 28n15, 29n26, 35, 68, 91, 124, 137, 171, 176–7; aggregate demand (AD), aggregate supply (AS) and 120–3; aggregate supply (AS) 16, 68, 120–3; autonomous expenditures 78; capacity utilisation 66, 72, 173; coherence of employment theory 189–91; comparative-static equilibrium, implication of 123; consumption goods, production of investment goods and 133–8, 138–47; credit, ‘finance’ and investment 187; creditworthiness 175, 178n5; customers, fringe of unsatisfied 175, 178n5; employment, direct and indirect, distinction between 87–8; employment, volume and direction of 102–3n16; employment theory, coherence of 189–91; finance motive, writings on 119n6, 161; financial machine 28n21; focus on multiplication of incomes 89; forecasts, state of 188–9; fundamental psychological law of 9, 12, 13, 19, 20, 21, 23, 25, 27n5, 89, 92, 135; income, consumption-goods and investmentgoods 25–6; income and output value 19; income multiplication, focus on 89; industrial system, inflexibility of 58; interest, rejection of natural rate of 1–2; interest rates and spending, short-

198  Index period influence 20–1; investment, definition of 148n4; investment, finance motive and saving 1; investment goods, consumption goods and production of 133–8, 138–47; investment spending, ‘animal spirits’ and 120; liquidity, credit system and 172, 178n4; monetary critique 60; monetary macro-analysis, need for 102–3n16; multiplier, dynamic theory of 94–5, 95–9, 102n14, 102n15, 128–33; multiplier, dynamic view of 12, 13, 14, 18, 26–7, 94–5, 99, 100, 102n15; multiplier, illumination on logical and applied theories 81–2; multiplier, logical theory of 12–13, 25, 26–7, 29n28, 58–82, 91–4, 102n13, 128–33; multiplier, moving equilibrium and the 190–1; multiplier as transactions velocity of money concept 50–1; multiplier concepts, meaning of both 62–3; multiplier process, description of 11; prices and quantities, equilibrating role 15; production period 16; profit maximisation 17; proportionality 133–5; pyramid building 66; saving, behavioural phenomenon 171; saving, finance motive and investment 1; shifting equilibrium, theory of 24; ‘third view’ of multiplier 24–6; see also marginal propensity to consume Keynes–Henderson assertion 65 Keynesian multiplier: bank money and 4, 109, 113, 173, 181–2, 185, 187, 191; birth of 65–6; business cycles and, Clark’s perspective 35–6, 37–8; change through business cycles 178; comparative-static analysis 13–14, 91; contradictory nature of concept 13–14; dynamic theory of 94–5, 95–9, 102n14, 102n15, 128–33; economic reality and 14–15; effective demand, principle of 15–18, 26–7; endogenous money and 3–4, 29n24, 116–17, 168–9, 185, 191; finance motive and 1, 5, 41, 119n6, 134, 161, 178, 181, 191; horizontalist re-interpretation 168–79; investment– savings (I–S) identity, Keynes’ statement on 12, 186–7; Kalecki’s perspective 153–66; Keynes and ‘third view’ of 24–6; Keynes’ employment theory, coherence of 189–91; logical theory, description and critique of 187–9; marginal propensity to consume

in traditional interpretation of 10, 11, 12, 13, 26, 120–1, 127, 174–5, 189, 190; medium-term multiplier and business cycles 67; Moore’s criticism of 3, 181–4, 184–6; Moore’s rejection of, defence of 120–6; multiplier process 10, 11; policy prescriptions and multiplier process 11; price adjustment 23, 25, 29n27; problems with traditional interpretation 13–15; reproduction schemes and 18–24; structural change, business cycle and 24; surplus value and 19–24; traditional interpretation of 9–13; unrealistic assumptions of traditional views 26–7; value, variable capital and 19–24; see also investment multiplier Kinley, David 55 Knopf, Alfred A. 57 Koenig, G. 27–8n14 Kregel, J. 21–2, 24, 148n6, 167n5 Landry, Adolphe 49 Lautenbach, Wilhelm 39 Lavoie, Marc 64, 82, 169, 172, 175, 176, 178n2, 178n5 Lazonick, William 61, 82 ‘leakages,’ income velocity and 36, 39 Lee, Frederic S. 64, 82 Leijonhufvud, A. 15, 27n7 letters: Alvin H. Hansen (1934) to Clark, John Maurice 50–2; Clark, John Maurice (1937) to G. S. Hauge 52–3; Clark, John Maurice (1956) to Joseph Dorfman 55–7; Clark, John Maurice (1918) to Maurice Roche-Agussol 46–50; Clark, John Maurice (1953) to Paul A. Samuelson 54–5; Paul A. Samuelson (1953) to Clark, John Maurice 53–4 Lindahl, E. 27n10 liquidity: credit system and 172, 178n4; liquidity preference 93, 109, 113, 114, 119n5, 142, 148n6; ultimate destruction of money and liquidity preference 111 logical form of multiplier 127–8, 130–2; dynamic multiplier and 13–14, 26–7, 62–3, 128–33 logical theory of multiplier: description and critique of 187–9; and marginal propensity to consume 26, 29n28, 91, 127, 132, 187–8; in monetary production economy 62–3, 81–2 long-term cycles in monetary production economy 72, 77–8

Index  199 losses, emergence of 104n29 Lutz, F. 90 Machlup, F. 43n11, 103n18, 103n19, 103n20, 103n23, 104n26 macrouncertainty 175–6, 178 Mäki, U. 14, 27n2 Malthus, Robert 64 marginal propensity to consume 19, 27n3, 28n16, 29n23, 89, 122, 129; aggregate increase in production and 140; assumption of differences in 20; constant propensity, idea of 40, 42; consumption postponement and 62; convergence of investment and savings and 171; deferred consumption and 62, 143–5, 190; dynamic theory of multiplier and 95, 133; ‘dynamiting’ effect of 138–9; income holders and 143, 183; Kalecki’s perspective 155; logical theory of multiplier and 26, 29n28, 91, 127, 132, 187–8; multiplier determined by 136–7; ‘positive and less than unity’ 9; productive resources and 24; proportionality and 134; structural function within logical theory 127; in traditional interpretation of multiplier 10, 11, 12, 13, 26, 120–1, 127, 174–5, 189, 190; variable ‘psychological’ magnitude 25; for workers as well as entrepreneurs 21 Marschak, Jacob 39 Marshall, Alfred 4, 48, 59, 62, 82; Marshallian provenance 20 Marx, Karl 43, 64; Marx-Keynes reproduction scheme 19; production and circulation, scheme of 59; reproduction schemes 18–19 Meade, James 10, 11–12, 14, 23, 26, 101–2n7 ‘The Means to Prosperity’ (Keynes, J. M.) 11, 34 Medio, A. 35 medium-term cycles in monetary production economy 77–8 middle way perspective of General Theory 61 Milgate, M. 27n8 Mill, John Stuart 47–8, 49 Milliken, M. F. 53 Mini, P. 61 Minskian terminology 176 Mitchell, Wesley C. 47, 54, 56 monetary circuit, multiplier and 106–9, 110–11

monetary critique by Keynes 60 monetary macro-analysis, need for 102–3n16 monetary production economy: autonomous and derived effective demand 58; autonomous variable, role of 77–8; behaviour, coordination of 75–6; business cycle 75–6; capacity output and effective demand 76; components of effective demand 73–4; coordination of behaviour 75–6; decline in effective demand 69; foreign trade multiplier 79–81; historical perspective 63–6; inherent instability, multiplier and 69–72; inherent instability of effective demand 69–71; institutions and system 72–5; ‘internal’ multiplier 79; involuntary unemployment, equilibrium in 58–9; Kaldor’s multipliers 66–9; logical theory of the multiplier 62–3, 81–2; long-period effective demand 75; long-term cycles 72, 77–8; mediumterm cycles 77–8; money, neoclassical exchange model 59–60; multiple coefficient 58; multiplier relation in 58–82; price rigidity, inherent in 59; principle of effective demand 60–1, 66, 82, 91–2; principles as fundamental elements 63; problem in money terms of effective demand 59; sources of effective demand 80; supermultiplier relation 78–9; supermultiplier trend 72–5 money: bank loans for consumption 114; bank money and Keynesian multiplier 4, 109, 113, 173, 181–2, 185, 187, 191; banks’ liabilities 110, 111, 113; circuit velocity of money, concept of 37–8, 39–40, 421; circulation of stamp money 50; creation through loans 163–4; demand for 119n2; demand for money in circulation 161, 162; effective demand, problem in money terms 59; endogenous money and Keynesian multiplier 3–4, 29n24, 116–17, 168–9, 185, 191; free profits in, firms and 111–12; fundamental future, uncertainty on 119n5; hoarding of, impossibility of 111; incomeearners’ net indebtedness and retained profits 112, 114–16; intertemporal transmission in endogenous monetary economy 106–18; intertemporal transmission process 107, 109, 112,

200  Index 114, 115, 116, 117, 118; liquidity preference and ultimate destruction of 111; monetary circuit, multiplier and 106–9, 110–11; neoclassical exchange model 59–60; production levels and circulation of 161–2; quantity theory of money 125; reimbursement constraint, multiplier and 109–10; retained profits, conditions for existence of 116–17; retained profits, economic policy and 112, 113–14, 114–16, 116–17; stamp money 50; state deficit and retained profits 112, 113–14; time deposits and circulating money 43–4n13; ultimate destruction of money and liquidity preference 111; velocity of circulation of 33, 34, 36, 38, 39, 40, 41, 125 Moore, Basil J. 2, 4, 29n24, 103n17, 104n24, 121, 126n2, 140, 168, 169–70, 171, 187, 190, 234; criticism of Keynesian multiplier 3, 181–4, 184–6; rejection of Keynesian multiplier, defence of 120–6 Morgan, M. and Rutherford, M. 43n3 Moulton, H. G. 46 multiple coefficient 58 multiplication process: engagement of 141–3; and investment–savings relationship 95–101 multiplier analysis: banks’ role, postKeynesians and 174–7, 178; Clark’s awareness of intrinsic limitations of 41–2; individuation of approaches to 36–7; post-Keynesian criticism of 169–72 multiplier process 10, 11; description of 11; post-Keynesian perspective 108, 177–8 national income and investment demand 10–11 Neisser, H. 39 Nell, Edward J. 23–4 Nelson, C. R. and Plosser, C. I. 125 The New Economics and the Old Economists (Davis, R.) 33 The New Palgrave: A Dictionary of Economics 35 New York Times 53 O’Donnell, R. M. 61 Ohlin, Bertil 187 Oncken, A. 63

Parguez, A. and Seccareccia, M. 119n3 Parguez, Alain 4, 110, 168, 175 Parinello, S. 17 Parker, Carleton H. 47, 56 Pasinetti, L. L. 63, 73 Patinkin, D. 26, 29n29, 101n1, 101n6 Patten, Simon N. 56 The Philosophy of Wealth (Clark, J. B.) 32, 46, 48, 49, 53 Pigou, A. C. 2, 49, 52, 56 Poincaré, Henri 54 policy prescriptions and multiplier process 11 Ponzi situations 176 post-Keynesians 63, 64, 79; and circuit theories 106–9, 110–11, 116–17, 172–4, 177–8; effective demand, unifying agenda for 15–18; free profits in, firms and 111–12; hoarding of money, impossibility of 111; income-earners’ net indebtedness and retained profits 112, 114–16; liquidity preference and ultimate destruction of money 111; marginal propensity to consume, assumption of differences in 20; Moore’s rejection of multiplier, objections of 3; multiplier analysis, banks’ role and 174–7, 178; multiplier analysis, criticism of 169–72; multiplier processes 108, 177–8; multiplier tradition, defence of 1, 3, 81–2, 106–7, 109, 168–9; profit rates and growth rates for 76; reimbursement constraint, multiplier and 109–10; retained profits, economic policy and 112, 113–14, 114–16, 116–17; state deficit and retained profits 112, 113–14 Pound, Roscoe 56 Pressman, S. 173–4, 178 price adjustment 23, 25, 29n27 price and quantity, equilibrating role 15 price rigidity, inherent in monetary production economy 59 primary employment 14, 65, 88, 101n3, 142 Principles of Economics (Marshall, A.) 62 production: aggregate increase in production and marginal propensity to consume 140; circular process of production 58, 64; circulating media and production volume, ratio between 37; circulation and, processes of 59; of investment goods, producers of consumption goods’ anticipation of

Index  201 133–8, 147–8; of investment goods, producers of consumption goods failure in anticipation of 138–47, 147–8; Keynes’ production period 15, 16, 17, 18, 19, 20, 22, 23, 24, 27n10, 28n17, 29n27; money, production levels and circulation of 161–2; productive resources and marginal propensity to consume 24 Production of Commodities by Means of Commodities (Sraffa, P.) 64 profits: free profits 111–12, 113, 114, 115, 117; and investment in generation of business cycles 156–7; profit maximisation 16, 17; rates of, and growth rates for post-Keynesians 76 proportionality 133–5, 135–8; marginal propensity to consume and 134 psychological law 9, 12, 13, 19, 20, 21, 23, 25, 27n5, 89, 92, 135 public expenditures in multiplier analysis 36–7 public investment 10, 11 purchasing power and investment 154, 162 pyramid building 66 quantity theory of money 125 Quarterly Journal of Economics 39 Quesnay, François 63–4, 66 Ramson, Baldwin 32 reimbursement constraint 109–10 reproduction: ‘completely successful’ 9, 19, 20, 21–2, 23, 28n21; schemes for, Keynesian multiplier and 18–24 retained profits: conditions for existence of 116–17; economic policy and 112, 113–14, 114–16, 116–17 Ricardo, David 43; Ricardianism 44n18 Robertson, D. H. 2, 104n25, 131 Robinson, Joan 27n6, 76, 132, 155, 163 Roche-Agussoll, Maurice 32, 43n4, 46–50 Rochon, L.-P. and Rossi, S. 172 Rochon, Louis-Philippe 1, 4, 28n21, 82, 109, 124, 172, 174, 175, 178n2, 178n5 Rossi, Sergio 82 Samuels, Warren J. 43n1 Samuelson, Paul A. 32, 39–40, 53–4, 54–5 saving: accounting equality between investment and 2–3; behavioural phenomenon 171; convergence of investment, savings and marginal propensity to consume 171; exchanges

of 101; finance motive, investment and 1; forcing of 156–7, 164; household behaviour and 171; from income, investment multiplier and 87–101; investment and 102n11, 102n12; investment and, causal links 156–7, 163–5, 166; investment and, difference as optical illusion 186–7; investment and, justification for necessary equality between 90–1; investment–savings (I–S) identity, Keynes’ statement on 12, 186–7; liquid savings 93, 94, 96, 97, 99, 113; multiplication process and investment–savings relationship 95–101; role of 11–12; stocks, funding and investment–savings relationship 90–5; of workers 28n21 Sawyer, Malcolm 4, 169 Say’s law 1, 15, 16 Schmitt, B. 96, 97, 104n27, 129, 130–1, 142, 146, 181, 185–6, 187, 190 Schneider, E. 64, 65, 66 Schumpeter, J. A. 103n21 Screpanti, Ernesto 43n1 secondary employment 65, 89, 101n3 Setterfield, M. 27n6 Shackle, G. L. S. 33 Shaking the Invisible Hand (Moore, B.) 3 shifting equilibrium, theory of 24 short-period employment multiplier 68 short-term equilibrium 157 Shute, Laurence 33 Sidgwick, Henry 48, 49 Skidelsky, R. 58, 64, 65 Slichter, Sumner H. 39 Smith, Adam 47 Social Economics , Preface to (Clark, J. M.) 34 Spiegel, Henry William 54 Sraffa, Piero 60, 64 Sraffa–Leontief–Pasinetti production coefficients 58 stamp money 50 state deficit, retained profits and 112, 113–14 state investment 104n33 Die Steuer der Zukunft (Johannsen, N.) 64 stocks, funding and investment-savings relationship 90–5 Strategic Factors in Business Cycles (Clark, J. M.) 33 structural change, business cycle and 24 structural function within logical theory 127

202  Index structural multiplier 26 supermultiplier relation 78–9 supermultiplier trend 72–5 surplus value and Keynesian multiplier 19–24 Targetti, F. 69 Theory of Economic Dynamics (Kalecki, M.) 158 time deposits and circulating money 43–4n13 time dimension and General Theory 2 trade cycle analysis 164–5 Treatise on Money (Keynes, J. M.) 13, 61, 68, 69, 89, 99, 175 trend and cycle, relationship between 72–3 Trevithick, J. 169 ‘unattached’ deposits 162 unemployment 1, 3, 33, 64, 91; frictional unemployment 60; ‘global’ perspective for 92; involuntary unemployment 4, 58, 59, 61, 62, 63, 69, 80, 81, 82, 100; long-period unemployment 73; output

and ‘natural state of unemployment’ 166; persistent unemployment 81; systemic unemployment 63 value, variable capital and 19–24 variable ‘psychological’ magnitude 25 Veblen, Thorstein B. 49, 56 velocity of circulation of money 33, 34, 36, 38, 39, 40, 41, 125 Vickers, D. 16, 27n9, 27n13 Villard, Henry H. 40, 42 wage unit multiplication 135–8 Warming, Jens 65, 89, 101–2n7 Wells, P. 27–8n14 Wicksell, Knut 64 Wicksteed, Philip H. 55 Wiles, R. C. 44n16 Wolfson, M. H. 174, 176 Wray, L. R. 28n18, 145 Z-curve 17, 19, 27n13, 28n15, 28n16; see also aggregate supply (AS)