Introduction to Keynesian Dynamics 9780231884648

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INTRODUCTION

TO

KEYNESIAN DYNAMICS

by Kenneth Κ.

Kurìhara

Monetary Theory and Public Policy Post-Keynesian Economics (Editor)

INTRODUCTION TO KEYNESIAN DYNAMICS

Kenneth K.

Kurihara

Rutgers University

NEW COLUMBIA

YORK UNIVERSITY

FIRST PUBLISHED IN

1956

All rights reserved

Printed

in

Great

Britain

PREFACE T H I S book is concerned with that part of economic theory which deals with the functioning of the economy as a dynamic whole, and in particular the temporal behaviour of national income, employment, and general prices. It is in the main a formal analysis of dynamic systems involving discrete and continuous changes, the sequence of cause-and-effect events, and the time paths of macro-variables and aggregative relationships in given socio-historical contexts. The macro-dynamic models of the 'building-block' type constructed for such an analysis are important, not so much for precise forecasting, but for the light they throw upon what is and what is not relevant for understanding economic change. They are also helpful in the selection of those strategic variables which are operationally most significant for the kind of society in which we actually live. Moreover, these dynamic models give us a deeper insight into the intricate equilibrium mechanism of an actual economy than do the macro-static models to which we have all grown accustomed. The aim of this volume is to provide a coherent and compact study of macro-dynamic analysis in general and particularly the two outstanding 'post-Keynesian' developments 1 in the field—(i) dynamic theories of cyclical fluctuations and (2) secular growth analysis. With this aim in mind, I have endeavoured to lay greater stress on the laws of motion than on manipulative technique. Bibliographical footnotes have been included for further inquiries, appropriate diagrams designed for expository purposes, and institutional materials and policy statements inserted where they seemed essential to the clarity of perception. Part I of this book provides a general base of reference for substantive analysis. Comparative-statics here is an indispens1 In this regard the reader may wish to see Post-Ktynesian Economics (a symposium by an international group of able economists), New Brunswick: Rutgers University Press, and London: George Allen and Unwin Ltd., 1954.

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able preliminary to the macro-dynamics discussed elsewhere in the volume. Care was taken to bring out in full relief the technical details of basic functional relationships and their economic significance. Part II contains fairly definitive materials, dealing as it does with the modus operandi of cyclical fluctuations, the dynamics of inflation and deflation, the stability conditions of equilibrium, a non-linear model of dynamic switches, the interaction of endogenous and exogenous variables, and international oscillatory processes. Part I I I explores the technical possibility and difficulty of securing maximum economic growth with minimum instability—in the perspective of history and in the light of modern analysis. T h e concluding chapter critically examines the twin problems of steady growth for advanced economies and rapid development for underdeveloped economies in a w a y that would suggest a common solution. In closing these prefatory remarks I wish to express my appreciation to President Howard Bowen of Grinnell College, Professor Broadus Mitchell of Rutgers University, M r . R o y Harrod of Oxford University, Professor Austin Robinson of Cambridge University, Professor J . R . Hicks of Oxford University, and Professor Shinichi Ichimura of Osaka University—for their stimulation, encouragement, and counsel in the formative stages of this writing. I am especially indebted to Professor William Vickery of Columbia University whose rigorous criticisms and constructive suggestions did so much to help improve the contents of this book. However, the thoughts contemplated here do not necessarily reflect their imprimatur. KENNETH K. KURIHARA

Rutgers University

CONTENTS page

PREFACE I.

MACRO-ECONOMIC

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METHODOLOGY—

INTRODUCTION

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Micro-Economic Method Development of Aggregative Thinking Macro-Dynamic Method P A R T ONE: B A S I C F U N C T I O N A L R E L A T I O N S H I P S 2.

THE

CONSUMPTION

FUNCTION

2g

Income and Consumption Objective Determinants of the C Function Subjective Determinants of the C Function 3.

THE

4.

THE

5.

THE

INVESTMENT

FUNCTION

LIQUIDITY

FUNCTION

Motives for Liquidity Equilibrium Market Rate of Interest Significance of the Monetary Theory of Interest SAVINGS-INVESTMENT

Income, Savings, and Investment Under-, Full-, and Over-Employment Equilibria Concepts of the Multiplier and the Accelerator THE

MULTIPLIER

AND

63

ADJUSTING

FUNCTION

6.

44

Autonomous and Induced Investment Marginal Efficiency of Capital Theory Interest Elasticity and Shift Factors of Investment

INCOME

76

93

FLUCTUATIONS

Investment Multiplier Action Accelerator-Multiplier Combined Action 7.

THE

DYNAMIC

STABILITY

OF

EQUILIBRIUM

AC/ΔΓ and Stability Conditions Δ / / A T and Stability Conditions Non-Linear Investment Function and Dynamic Switches 7

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KEYNESIAN

8.

THE

9.

INCOME, EMPLOYMENT, AND NATIONAL EQUILIBRIUM

DYNAMICS

INFLATION

Inflationary Gap in terms of S and I Price Multiplier in a Full-Employment Economy Hyperinflation and Forced Saving INTER-

Domestic Employment and Foreign Trade Multiplier in an Open Economy Induced Imports, Investment, and International Equilibrium IO.

PRICE FLEXIBILITY FULL EMPLOYMENT

AND

I2g

144

AUTOMATIC I59

Wages and Employment 'Pigou Effect' and Employment

PART THREE: SECULAR ECONOMIC DYNAMICS 11.

12.

SECULAR

MACRO-ECONOMIC

THEOREMS

Long-Run Multiplier Theorems Long-Run Acceleration Theorems CAPITAL ACCUMULATION EQUILIBRIUM

AND

Paradox of Investment Interest Rate and Long-Run Equilibrium Capital Widening and Deepening

13.

DOMESTIC G R O W T H AND INTERNATIONAL DEVELOPMENT

Growth Mechanism Stability Conditions of Dynamic Equilibrium International Implications

INDEX

173

185

I98

219

Chapter ι

MACRO-ECONOMIC METHODOLOGYINTRODUCTION economic theory integrates, in varying proportions, an analysis of the behaviour of the economy as a whole and an analysis of the behaviour of the individual firm.1 The former analysis has been termed 'macro-economics' and the latter 'micro-economics'. Though economists have always been concerned with the phenomena affecting both the whole economic system and the individual firm, the recent shift of emphasis from traditional concern with the individual firm to concern with the whole economic system is considered a 'Keynesian phenomenon'. For, as K. Boulding has observed, 'the modern developments in macro-economics . . . are most closely associated with the work of Mr. J. M. Keynes'.8 This chapter compares the development, nature and usefulness of the macro-economic method with those of the micro-economic method. MODERN

THE

MICRO-ECONOMIC

METHOD

The analytical significance and practical importance of the micro-economic method can best be seen in the light of the nature and development of micro-economics. It seems useful, therefore, to review briefly the traditional technique of economic thinking. 1 Cf., e.g., L. Tarshis, The Elements of Economics, Houghton Mifflin, Boston, 1947; P. Samuelson, Foundations of Economic Analysis, Harvard University Press, Cambridge, 1948, and also Economics, McGraw-Hill, N.Y., 1948; K . Boulding, Economic Analysis, Harpers, N.Y., 1948, and also A Reconstruction of Economics, John Wiley, N.Y., 1950; J. F. Due, Intermediate Economic Analysis, Irwin, Chicago, 1950. * For controversial methodological discussions, see A . F. Burns, Economic Research and the Keynesian Thinking of our Times, National Bureau of Economic Research, N.Y., 1946; A . H. Hansen, 'Dr. Burns on Keynesian Economics', Review of Economic Statistics, November 1947; J. Tinbergen, 'The Significance of Keynes's Theories from the Econometric Point of View', in The New Economics (S. E. Harris, ed.), Knopf, N.Y., 1948; W. Leontief, 'Econometrics', in A Survey of Contemporary Economics (H. S. Ellis, ed.), Blakiston, Philadelphia, 1948.

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Individual Prices and Quantities Micro-economics owes its systematic origin to A d a m Smith, and it culminated with Alfred Marshall. 1 The method of analysis associated with economists from Smith down to Marshall consists in explaining and describing the way in which self-interest determines what particular goods are produced, how various inputs of factors will be combined to produce them, and how the value of the final product will be distributed between those factors—on the fundamental assumption of a given total output. Thus if the volume of total output is taken as given or, what is the same, if the economy's entire resources are supposed to be fully employed, there remains as only relevant the question of how best those employed resources can be allocated between different lines of production. It was supposed that self-interest, working through the pricing mechanism, would automatically lead to an optimum allocation of resources. Tacit Assumptions It is interesting to observe that Keynes considered the above type of analysis logically unobjectionable; what he found objectionable were the tacit assumptions that a full-employment volume of total output is maintained by some inexplicable forces2 and that self-interest always operates in the public interest. 3 These assumptions Keynes considered as being 'seldom or never satisfied' and as rendering economics incapable of solving 'the economic problems of the actual world'. 4 It was only on those assumptions that economists could justify their preoccupation with an explanation of how individual prices and quantities came into existence. For if self-interest does not automatically bring about full employment or if it does not always operate in the public interest, 'a study of the forces which 1 Cf. Smith's An Inquiry into the Nature and Cotises of the Wealth of Nations, published in 1776 and available in the Modern Library series; Marshall's Principles of Economics, Macmillan, London, 1890. For a good summary of post-Marshallian developments in micro-economics, see B. F. Haley, 'Value and Distribution', in A Survey of Contemporary Economics. 1 See J. M . Keynes, Essays in Persuasion, Harcourt Brace, N.Y., 1932, p. 312. ' J . M. Keynes, The General Theory of Employment, Interest and Money, Harcourt Brace, N.Y., 1936, pp. 378-9. 1 Keynes, General Theory, p. 378.

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II

determine changes in the scale of output and employment as a whole' becomes necessary. Ironically, therefore, the microeconomic approach based on the above assumptions appears to be really more applicable to a completely regulated economy than to an unregulated economy, since in the former type of economy, with its inevitable full employment, it is the allocation of resources, not the total employment of those resources, that is significant. Accordingly Keynes envisaged a full-employment economy as providing a point of departure from which onward 'the classical theory comes into its own again'. 1 A Self-Adjusting Economy It may be asked why economists traditionally took aggregate output as given or assumed full employment. T o answer this question it is necessary to digress a little and look at history. T h e view that the 'invisible hand' automatically and necessarily brings about full employment was originally based on a crude analogy between the order of nature and a self-adjusting economic system. Economists entrusted the 'invisible hand' with the task of running the whole economic system as smoothly as the order of nature. Specifically the law of supply and demand, like the law of natural order, was supposed to govern the behaviour of the economy as a whole in such a way that there was nothing for economists to do but concentrate on the atomistic elements of the economy. Early capitalism did appear to be a perfect 'natural' order—so much so that what few frictions and disturbances there were could easily be explained away merely as exceptions to the rule. T h e entrepreneur could always be relied upon, so it seemed, for co-ordinating the producers' market and the consumers' market, to avoid a periodic glut of unsold good and services. It was but natural that J . B. Say, the French expositor of A d a m Smith's political economy, should have expounded his famous 'Law of Markets' to deny the possibility of general overproduction. 2 Nor did it surprise any one that David Ricardo should have won his personal debate with T . R. Malthus (compare 'Robert Malthus : T h e First of the Ibid. * Cf. his Traité d'economie politique, 1803. According to Say's L a w , economic man's self-interest and market forces are such that the whole of the costs of production must inevitably be spent on buying the product, thus rendering general overproduction logically inadmissible. 1

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Cambridge Economists', in J . M. Keynes, Essays in Biography, Horizon Press, N.Y., 1951) over the theoretical possibility of general overproduction, with the former taking the negative position and the latter the affirmative position. It is not hard to see, either, why Sismondi and Marx vainly attacked Say's Law. Thus a self-adjusting economy, whether by hypothesis or in fact, is conducive to the tacit assumption of full employment. Individualistic Milieu A. H. Hansen attributes 'the atomistic individualism of the mid-nineteenth century' to 'the old individualistic pattern of work and living'.1 To appreciate this statement, it is only necessary to recall how favourable the loosely-knit colonial economy, with its independent, self-sufficient households and handicrafts and extensive barter, must have been to individualistic thinking in early America. One might wonder why economists persisted in their individualistic approach even after the disappearance of the individualistic modes of work and living. Intellectual inertia is one answer, but a more serious answer seems to be that, despite technological and institutional developments making for aggregative thinking, the economic system remained relatively free from such profound disturbances as mass unemployment and world-wide depression or hyperinflation. So long as the economic system was functioning progressively and smoothly, economists naturally took the economy as a whole for granted, thus tending to study the determination of individual prices and quantities rather than that of general prices, output and employment. Mrs. Ursula K . Hicks, of Oxford University, has declared it to be 'no accident that the marginal analysis, with its primary interest in the individual, was developed in a period (1870-90), when the business cycle, in England at least, was showing less than its usual activity'.2 This may be taken as a good illustration of a high correlation between micro-economic developments and a current milieu devoid of uprooting economic fluctuations. Mrs. Hicks considers it inevitable that aggregative thinking in economics up to the thirties should have been narrowly confined to the field of 1 See his Economic Policy and Full Employment, Whittlesey, N.Y., 1947, pp. 14-5. * In correspondence with the author.

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METHODOLOGY—INTRODUCTION

I3

money and general prices, owing to (i) 'the small size of public sectors', (2) 'the inevitably limited effect of fiscal policy', and (3) 'the unfeasibility of using direct controls'. 1 T h e Great Depression and the Second World War changed these conditions almost as a matter of course. Limited, Applicability While the micro-economic method, with its analysis of the behaviour of the individual market, firm or industry, is a necessary 'part of one's apparatus of thought', even as Keynes recognized, 2 its applicability in the real world will remain limited to the extent that a full-employment economy actually prevails. 'It may well be,' says Keynes, 'that the classical theory represents the way in which we should like our Economy to behave.' 3 'But', he says further, 'to assume that it actually does so is to assume our difficulties away.' Meanwhile he urges economists to endeavour to rid economics of unrealistic assumptions regarding self-interest, aggregate output, full employment, 'errors of compositions', and the danger of getting lost in the hopeless confusion of 'micro-statics'. 4

DEVELOPMENT

OF

AGGREGATIVE

THINKING

Aggregative thinking in economic matters, like its individualistic counterpart, has closely followed changing milieu, as indicated in what follows. Pre-Classical Contribution Even before A d a m Smith, a group of economic thinkers known as 'Mercantilists' had been largely concerned with the functioning of the whole economic system. One might find, as Keynes did, in mercantilism, 'a contribution to statecraft, which is concerned with the economic system as a whole and securing 1 Ibid. * General Theory, p. 340. 3 Ibid., p. 34. 4 ' Micro-statics ' refers to that method of analysis which treats the relation between individual phenomena (e.g., particular prices, outputs, inputs, demands, supplies and other statistical micro-units) as if they were a series of 'still' pictures. This is the method associated with partial equilibrium analysis. A study of disequilibria at instants of time would be called 'micro-dynamics'.

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INTRODUCTION

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DYNAMICS

the optimum employment of the system's entire resources'.1 Mercantilists perceived the cause-and-effect relation between a favourable balance of trade and national prosperity, between gold-inflow and the domestic rate of interest, between the rate of interest and the volume of investment, and between the volume of investment and the level of employment, according to Keynes. 2 They therefore were interested in practical policies aimed at promoting domestic prosperity and progress. In deciphering the unsuspected wisdom of Mercantilists, Keynes has indicated the possibility of profiting by their technique of thinking without accepting their nationalistic and monolithic doctrines. Classical Developments T . R . Malthus, better known for his Essays on Population (i 798) than for his Principles of Political Economy (1820), might be regarded as an important forerunner of macro-economics. 3 He ventured the view that aggregate demand could be insufficient, contrary to the then prevailing notion of an automatic selfadjusting economy. He challenged Say's Law on the reasoning that the parsimony which Adam Smith and others had sanctioned would, if pushed to excess, 'destroy the motive to production' and lead to the 'stagnation of capital, and subsequent stagnation in the demand for labour'. Malthus was thus among the first to cast a serious doubt on the reliability of the economic 'invisible hand', thereby presaging the emergence of the modern theory of the behaviour of the economy as a whole. K . Marx is perhaps the most conspicuous exception to the classical tradition (roughly from Adam Smith to John Stuart Mill) in more ways than one. According to K . Boulding, the Marx of Capital made 'the first attempt to deal with the problems of the whole economic system', to build 'a picture of economic life and relationships as a whole'—'a task of synthesis which previous economists had neglected'. 4 Also, Marx may have anticipated modern growth analysis, for 'the idea that a General Theory, p. 340. * For an extended discussion, see ibid., C h . 23. ' Malthus's basic macro-notions will be found in his letters to Ricardo and in the Preface of his Principles of Political Economy; also see J. M . Keynes, Essays in Biography, Macmillan, London, 1933, pp. '39-47· * Cf. The Economics of Peace, Prentice-Hail, N.Y., 1946, p, 223. 1

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METHODOLOGY—INTRODUCTION

I5

capitalist economy needs growth goes back, in one form or another, at least to M a r x ' , to quote E. D . Domar. 1 This is plausible, since Marx's aggregative analysis is considered predominantly 'organistic' in the sense that it is concerned with the organism of capitalism as a developing whole. By contrast, it is to be noticed, Keynes's analysis ran largely in terms of 'mechanistic' equilibrium analysis, since his method consisted in investigating the quilibrium mechanism of capitalism in a historically given situation. This, then, is the fundamental difference in methodology between M a r x and Keynes, apart from the fact that 'Keynes wanted to apologize and preserve, while M a r x wanted to criticize and destroy', as L . R . Klein alludes to their diametrically opposed ideological bearings. 8 Modem Developments O n e might mention many other writers before and along with Keynes who contributed to macro-economic developments, such, for example, as L . Walras, K . Wicksell and I. Fisher. But if the modern developments in macro-economics are 'most closely' associated with the works of Keynes, a brief survey of conditions leading up to the appearance of his General Theory may be considered appropriate. W h a t once appeared to be a perfect 'natural' order did not prove so perfect after all, for the economic system periodically failed to function smoothly, thus calling forth a series of inquiries into the behaviour of the economy as a whole. T h e classical debate between Ricardo, Say, and Mill (J. S.) on the one side and Malthus, Sismondi, and M a r x on the other side is not hard to see in the above light. As Hansen observed, 'industrialization and urbanization' surely, though slowly no doubt, made for aggregative thinking, with the result that economists were made to feel rather uneasy about living, however consistently, in a Ricardian transcendental world of 1 See his 'Expansion and Employment', American Economic Review, March 1947. • S e e Klein, The Keynesian Revolution, Macmillan, N.Y., 1947, p. 131. J. A . Schumpeter informs us that, while 'quite different', the 'breakdown theories' of Marx and Keynes had at least this in common, that general instability is 'motivated by causes inherent to the working of the economic engine, not by the action of factors external to it'. (See his 'John Maynard Keynes, 1883-1946', American Economic Review, September 1946.) Schumpeter's own theory of economic development was doubtless influenced by Marx's 'organistic' approach as well as by L. Walras's 'mechanistic' equilibrium analysis.

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certainty and stability. If mass production and other technological developments rendered 'atomistic individualism' untenable, at least in economic analysis, periodic 'commercial crises', 'technological unemployment' and other accompaniments of industrialization called for a critical examination of the forces that governed the behaviour of the economy as a whole. Thus economists were impelled to develop a theory of money and general prices and finally a general theory of output and employment as a whole. The theory of money and general prices was spurred by the widespread inflationary conditions after World War I, and was developed by such economists as G. Cassel, A. Marshall, A. C. Pigou, D. H. Robertson, R. G. Hawtrey, I. Fisher and F. Hayek—beyond but along the lines of the original quantity theory expounded by J . Locke, author of On Money (1752). Keynes also made a contribution to this development in his A Treatise on Money (Macmillan, London, 1930). Those economists, including Keynes, were then concerned with the stabilization of general prices and therefore with the stable value of money. Apart from any particular monetary doctrines, they pushed forward the frontiers of macro-economics along with those of micro-economics. Coming as it did against the background of that devastating depression of the thirties, Keynes's General Theory, with its overall diagnosis and its heavy emphasis on the fiscal cure, caught the imagination of the depression-weary generation, and also had a dramatic impact on aggregative thinking in economic matters. Thus the Great Depression furnished a convincing background for the new theory of the behaviour of the economy as a whole and a convenient testing ground for its validity and fruitfulness. World War II, with its total mobilization of manpower and materials, and the postwar transition, with its inflation, reconstruction, balance of payments difficulties, development of underdeveloped economies, and other global problems, required a general frame of reference for bold fiscal experiments, direct controls, international economic plans, and other measures of public policy. Summary of Objective Factors The economic developments underlying the evolution of

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aggregative thinking, which culminated in the appearance of Keynes's General Theory, may be summarized thus: (i) industrialization and urbanization in general and mass production in particular; (2) the increasing public sectors of the economy and the welling importance of the role of government finance for stability and welfare; (3) the growing complexity and multiplicity of the phenomena affecting modern economic life, requiring more and more over-all information and broader policies ; and (4) the Great Depression of the thirties, calling for an over-all stocktaking of the existing economic system, 1 with its characteristic business cycles and great disparities of income and wealth. All these factors, except perhaps the Great Depression which may be replaced by the spectre of 'secular inflation', are likely to persist into the future. Anticipation of this likelihood is reflected in 'post-Keynesian' thinking along the lines of macro-dynamic and secular analyses. It might be added, in this connexion, that disaggregative econometric models based on cross-section and other micro-data are the direct outcome of attempts to test Keynes's aggregative hypotheses.*

THE

MACRO-DYNAMIC

METHOD

Apart from the social milieu favouring the growth of aggregative thinking in economics, it seems fruitful to inquire into the 'general' and presumably 'dynamic' nature of Keynes's General Theory. General and Special Cases What has passed for 'general' economics before Keynes was in fact largely an explanation of why and how the individual firm behaved the way it did, while, on the other hand, what was in fact an explanation of general prices was regarded as a 'special' case of that 'general' economics. Thus the theory of 1 It is an interesting commentary on 'the Keynesian thinking of our times' as well as on the ideological issue of the postwar period that the American Economic Association in 1949 defined the central theme of its Annual Meeting as Ά Stocktaking of American Capitalism'. * See, e.g., T . Haavelmo, 'Family Expenditures and the Marginal Propensity to Consume', Econometrica, 15 (1947); also L. R. Klein, A Textbook of Econometria, Row Peterson, Evanston, Illinois, 1953, esp. Ch. V.

Β

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money and general prices, which is concerned with the money economy as a whole, was treated like a stepchild. Instead of showing the full blood relationship between individual and general prices, economists had explained the former in familiar terms of supply and demand and the latter in vague and strange terms of 'the quantity of money', 'the velocity of money', &c. Accordingly economists found themselves 'sometimes on the one side of the moon and sometimes on the other, without knowing what route or journey connects them', according to Keynes. 1 His General Theory was, in a way, an attempt to show the 'route' connecting individual and general prices. As a consequence one can see the relation between particular and general prices in proper perspective, since the micro-economics of individual prices has turned out to be really a special case of the macro-economic theory of output and employment as a whole. Both the behaviour of particular prices and that of general prices can now be seen as being broadly governed by the same forces of supply and demand. The apparatus of Keynes's General Theory is capable of explaining alternatively what happens to general prices when the supply of everything becomes completely inelastic relatively to elastic demand and what happens to output and employment when effective demand changes relatively to elastic supply. However, the doctrine of the General Theory, as distinguished from its analytic apparatus, is one-sidedly concerned with the determination of output up to full employment at the expense of the determination of general prices beyond full employment. T o this extent Keynes's General Theory lacks generality. Yet Keynes's book may properly be viewed as containing a general theory in the sense that it is concerned with the determination of the equilibrium level of total national income through the interaction of some opposite forces with some strategic force. Thus the desire to save and the desire to invest are shown to be such opposite forces which nevertheless depend on income so crucially that their mutual relation changes with income 1 General Theory, pp. 292-3. Also see J. Robinson's prophetic article, ' T h e Theory of Money and the Analysis of the Output', Review of Economic Studies, October 1933. T h e Keynes of 'Treatise' (1930) was still writing his 'Fundamental Equation' (Ρ = E/O + /' — SjR) on the assumption that the rate of factor earnings is constant, as when full-employment output is taken as given.

MACRO-ECONOMIC

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ig

change until their conflict is resolved by a unique level of income. This, in a nutshell, is Keynes's 'building-block' type of a general theory centred around the strategic income variable. O n yet a higher level of abstraction, P. A . Samuelson considers the simple model as outlined by Keynes's General Theory as a 'special case' of a still 'more general dynamic system' involving time-lags, rates of change, explicit stability conditions, &c. x This will become clear in due course. It is interesting, in retrospect, that E. G . Nourse, ex-president of the American Economic Association and then chairman of the President's Council of Economic Advisers, publicly called on economists to develop 'a technique for continuous examination of the entire economy as a functioning and dynamic whole'. 2 It is equally interesting that Samuelson, this time in his elementary analysis (Economics, p. 394), made this significant statement: O f course, as economists and citizens, we are primarily interested in the fluctuations in total jobs, total production, and total (real) national income.' O n e may doubt if either of these statements could have been made prior to the appearance of Keynes's General Theory, with a definite accent on 'General'. Aggregative Models T h e macro-economic approach is directly concerned with the relations among large statistical aggregates, such as national income, general prices, total consumption, total savings, and total investment. T o understand such relations is in effect to understand the behaviour of the economy as a whole. Economists m a y build aggregative models (schemata) on the basis of a priori assumptions or empirical data or both, e.g., a general picture of how the community's saving may be expected to behave on the basis of hypotheses or data concerning the behaviour of individual savers or of groups of individual savers. 3 Keynes selected the above aggregates not only became they, on some assumptions, influence the behaviour of general economic activity most significantly but because they 'can be Foundations of Economic Analysis, p. 278. • 'Economics in the Public Service', American Economic Review, M a y 1947. s Cf. L . R . Klein, 'Macroeconomics and the Theory of Rational Behaviour', Econometrica, April 1946; also K . M a y , 'Technological Change and Aggregation', ibid., January 1947. 1

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deliberately controlled or managed' in the public interest.1 T h e pedagogic advantage of thinking in rather simple macroeconomic terms is, as Tinbergen has observed, that it provides 'a way of making the elimination process understandable and transparent'.* For example, though one may disagree on the exact and adequate definition of any particular variable involved in the truistic exchange equation (P = MV¡Τ or some variant of it) or on the best method of weighting different prices as in computing an average index number, one may still find the notion of the general price level helpful in explaining the behaviour of the economy as a whole. Similarly one may disagree on particular assumptions, institutional or psychological, regarding the saving patterns of individuals or groups of individuals, and yet may find the concept of aggregate savings useful in describing the actual or probable behaviour of national income. T h e necessary reservation to bear in mind in all these cases of simple macro-relations is that many statistical and conceptual difficulties are involved. None the less, macro-model building is the necessary technique for predicting and controlling the behaviour of the economy as a whole. Macro-Dynamics and Macro-Statics The traditional theory, when it deals with the economy as a whole, is interested in explaining certain aggregative relations which obtain in the stationary position without any attempt to show how the economy got there temporally or spatially. This type of method is called 'macro-statics'. In comparison with this traditional theory of stationary equilibrium, Keynes considered his own 'dynamic', thus christening it 'the theory of shifting equilibrium'. 3 This latter theory is considered dynamic in the sense that it explains 'a system in which changing views about the future are capable of influencing the present situation'. 4 His emphasis on the role of 'expectations' lends some plausibility to his claim. Perhaps a more cogent interpretation of the 'dynamic' nature of Keynes's theory of shifting equilibrium is that he is thinking dynamically, since there can be no General Theory, p. 247. * See his ' T h e Significance of Keynes's Theories from the Econometric Point of V i e w ' , op. cit. * General Theory, p. 293. * Ibid. 1

MACRO-ECONOMIC

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21

shift from one position of equilibrium to another without prior movements of variables through time. Keynes made no formal attempt to show the process of transition from one position of equilibrium to another, however. His method of comparing different equilibrium levels of income corresponding to changes in the consumption and investment variables, that is, changes in the values of macro-variables, has been termed 'comparative statics'. O n the other hand, 'macro-dynamics' treats discrete movements or rates of change of macro-variables. 1 This method separates the process of trial and error into a series of continuously changing reactions and indicates, step by step, what is cause and what is effect. It describes the changing universe as it is related to previous or subsequent adjustments ; it analyses the discrete or continuous changes of aggregates, the sequence of cause-and-effect events arising from some initial disturbance, and the time paths of macro-variables and aggregative relationships. Thus the macro-dynamic method enables one to see a 'motion-picture' of the functioning of the economy as a progressive whole. This technique has been developed by such economists as D . H. Robertson, R . Frisch, M . Kalecki, J . Tinbergen, P. A . Samuelson, R . F. Harrod and J . R . Hicks. I f Keynes's 'comparative statics' is concerned with the level of employment 'at any time', the macro-dynamics of those other economists may be said to focus attention on the fluctuations of employment 'at instants of time'. If the former is interested in the precise effects of a change in some aggregate upon the stationary or equilibrium position of the economy as a whole, the latter may be said to describe the temporal processes of deviations or disequilibria.

1 Cf. P. A. Samuelson, Foundations of Economic Analysis, C h . 11, and his 'Dynamic Process Analysis', in A Survey of Contemporary Economics, J. Tinbergen, The Dynamics of Business Cycles, University of Chicago Press, 1950,pp. 102-8; R. Frisch,'On the Notion of Equilibrium and Disequilibrium', Review of Economic Studies, III (193536), and his 'Propagation Problems and Impulse Problems in Dynamics', in Economic Essays in Honour of Gustav Cassel, Allen and Unwin, London, 1933 ; M . Kalecki, Ά Macrodynamic Theory of Business Cycles', Econometrica, July 1935, and his Theory of Economic Dynamits, Rinehart, N.Y., 1954; R. F. Harrod, Towards a Dynamic Economics, Macmillan, London, 1948, Lec. 1 ; J. R. Hicks, A Contribution to the Theory of the Trade Cycle, Oxford, 1950, C h . 1; G . F. Stigler, The Theory of Price, Macmillan, Ν . Y . , 1950, pp. 24-31.

22

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

I t seems convenient to categorize the above-mentioned methods as follows. Macro-Statics If the object is to show a 'still-picture' of the economy as a whole, the macro-static method is the appropriate technique. For this technique is one of investigating the relations between macro-variables in the final position of equilibrium without reference to the process of adjustment implicit in that final position. Such a final position of equilibrium may be reflected by the familiar equation

r = c +1,

where î"is total income, C total consumption expenditure, and I total investment. There is no indication of any adjusting mechanism; all that we can see is that total income is identically equal to total consumption plus total investment. Considered as the condition of equilibrium to be satisfied, however, this timeless identity equation implies that total income will increase or decrease unless an amount equal to it is spent on consumergoods and capital-goods. From the fact that total income is neither rising nor falling, it may be inferred that consumers and businessmen as a whole desire to spend no more or less than what they are earning in the current period. But one needs much more information to know how total income has gotten into that position of equilibrium which is assumed to be established without regard to the time involved. Something of this 'know-how' can be seen in the following discussion of the comparative macro-static method. Comparative Macro-Statics If the object is to show different 'still-pictures' of the economy as a whole, the comparative-static method is what is needed. For this technique is one of investigating various equilibrium values of an economic quantity corresponding to various values of the variables taken as independent data. For instance, the simple identity equation Τ = C + I must now be transformed into a behaviour equation of the form Τ = C(T) + / on the assumptions that consumption depends in a specified way on the level of income

MACRO-ECONOMIC

METHODOLOGY—INTRODUCTION

23

a n d that i n v e s t m e n t is a fixed a m o u n t at a n y one time. 1 T h i s is essentially K e y n e s ' s t e c h n i q u e o f 'shifting e q u i l i b r i u m ' analysis. O n these assumptions r e g a r d i n g c o n s u m p t i o n a n d investment, different e q u i l i b r i u m v a l u e s o f total i n c o m e c a n be seen as resulting f r o m c h a n g e s in total investment a n d c o n s u m p t i o n t h r o u g h s o m e a d j u s t m e n t m e c h a n i s m , as in the f o l l o w i n g system o f e q u a t i o n s AT = AC + AI

(1)

AC = a AT

(2)

B y substitution w e get the instantaneous a d j u s t m e n t m e c h a n i s m AT = — - — A I ι — a

(3)

Here Δ Τ is a n i n c r e m e n t o f i n c o m e , AC a n i n c r e m e n t o f c o n s u m p t i o n , AI an i n c r e m e n t o f investment, a a fixed ratio o f changes o f c o n s u m p t i o n to changes o f i n c o m e . I n this system, a n y new level (higher or lower) of i n c o m e c a n be seen as c o m i n g into existence instantaneously because the original level o f income c h a n g e s b y Δ Τ w h i c h e q u a l s the reciprocal o f some definite f r a c t i o n o f i n c o m e not spent o n c o n s u m p t i o n , 1/(1 — a), times a n i n c r e m e n t of investment i n d e p e n d e n t o f the level o f income, AI. T h i s 'instantaneous multiplier' t h e o r y i n v o l v e d i n K e y n e s ' s c o m p a r a t i v e statics will b e a n a l y s e d m o r e c a r e f u l l y later, a l b e i t in contrast w i t h the d y n a m i c multiplier principle. T o see the transition f r o m o n e position o f e q u i l i b r i u m to a n o t h e r through time orj the process of disequilibrium, it is necessary to adopt t h e f o l l o w i n g t e c h n i q u e . Macro-Dynamics M a c r o - d y n a m i c s is a m e t h o d o f s t u d y i n g the process of temporal equilibrium adjustment or the relations between variables which are functions of time and the values of which are therefore lagged in an economically significant way, s u c h as s h o w n in t h e d y n a m i c system

r, = ct+ Λ a(Tt^ -T0)

Ct =

(O +C0

(2)

B y substitution w e h a v e the d y n a m i c a d j u s t m e n t m e c h a n i s m

rt = a{Tt_, - T0) +C0+It

(3)

1 For a helpful exposition of this aspect see P. A . Samuelson, ' T h e Simple Mathematics of Income Determination', in Income, Employment and Public Policy (Essays in Honor of A l v i n H. Hansen), Norton, N . Y . , 1948.

24

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

Here Yt is income at time /, T0 initial or base period income, a a fixed rate of change of consumption, T t _ 1 — T0 the amount by which the income of the preceding period exceeds the base period income, C0 initial or base period consumption, and I t investment at time t. In the above system, income, consumption and investment are all functions of time ; consumption depends on the income of the preceding period, (t — ι ) ; investment is also dependent on time, /(*), but is held constant, / ; income in any period can be seen as the resultant of the interaction of 'lagged' consumption and investment; the process of income expansion (or contraction) may converge to or diverge from equilibrium, depending on the value of α (or a combination of α and some other coefficient, as when 'induced' investment is involved). All this requires detailed explanations, as will be attempted in later chapters. Here the intention is merely to indicate what the macro-dynamic method purports to show, namely, the behaviour of aggregate income, employment, output or prices through discrete stages in time, if not in space as well. Fluctuations of these aggregates may be adequately explained by the macro-dynamic method to the extent that the underlying assumptions regarding the behaviour of individual units of the economy are realistic in the historical, institutional and psychological senses. Diagrammatic Representations The above systems of equations could be represented diagrammatically, as is attempted below in order to give a bird'seye view of the static, comparative-static, and dynamic models. c c+ I

Y o Y FIG. I . Macro-Static Model

MACRO-ECONOMIC

METHODOLOGY—INTRODUCTION

25

Here the economy may be said to be in the final position of equilibrium represented by the point E or, alternatively, by the equilibrium level of income Τ somehow predetermined by the interaction of total expenditure, C +1, and total income represented by the 45 0 line. The detailed explanations of this model and the following two models will be found in subsequent chapters.

In Fig. 2, the economy can be seen as having shifted from the original position of equilibrium E1 to the new higher position Et as a result of the reactions of AI on C and I. Here the point of view taken is that there is no need to specify time lags (which may or may not be involved in practice) so as to focus attention on the final outcome, Tt, vis-à-ms the initial position, Tlt corresponding to changes in C and I.

FIG. 3. Dynamic Model

26

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

In Fig. 3, the economy is seen as moving from E to En or from Γ0 to T„ through the time paths represented by the dotted vertical and horizontal lines between the C + Δ/ and C schedules or through the transition income levels of Y¡ in period ι and Y t in period 2. It will be found that the difference between the income of period o and that of period 1 or, for that matter, any two successive periods, equals the difference between investment and 'lagged' savings. Practical Importance J. Tinbergen, in his appraisal of Keynes's theories, says that 'working with macro-economic concepts is a bare necessity for the modern theorist who wishes to contribute to the solutions of the great problems of our times'.1 He further states that the great economic problems of our times are 'those of explaining the course of total national employment and production, of explaining why they could shrink as they have sometimes, and of indicating possibilities of influencing them'. 2 There is much practical advantage in seeing through all the complex interrelationships of the economy as a whole and so in concentrating on those large statistical aggregates which strategically affect the behaviour of the whole economy. Otherwise there is danger that one will get lost in the turbulent details of economic behaviour and so lose sight of perspective altogether. Moreover, those aggregates lend themselves to measurement, thus facilitating over-all purposes of control and prediction. Else, the Council of Economic Advisers, for instance, would have nothing to say about 'foreseeable trends'. Macro-dynamics not only enriches our understanding of the functioning of the economy as a dynamic whole but also throws useful light on the practica! problem of economic stabilization both in the short run and long run.

1 Cf. 'The Significance of Keynes's Theories from the Econometric Point of View', op. cit. » Ibid.

Parti

BASIC FUNCTIONAL

RELATIONSHIPS

Chapter 2 THE

CONSUMPTION

FUNCTION

THIS chapter deals with the relation between consumption and income or the consumption function, its technical characteristics and its objective and subjective determinants. The savings function will be analysed simply as the complement of the consumption function. The consumption function or the propensity to consume is, on any definition, considered as one of the strategic relationships affecting the behaviour of the economy as a whole. 1 As such, it is a basic macro-relationship which deserves a separate careful analysis. This relationship will be analysed in such a way as to facilitate the later discussions of dynamic systems. INCOME

AND

CONSUMPTION

Income is generally considered to be the greatest single influence on consumption expenditures, individual and aggregate. Abstracting from other influences, it is possible to construct an aggregate schedule showing the various possible amounts of consumption oudays to be expected out of various levels of income. Consumption and Income Concepts Consumption may be regarded as a function of real income if 'money illusion' is supposed to exert no significant influence on 1 For refinements and reappraisals see W. S. Vickrey, 'Resource Distribution and the Classification of Families', Studies in Income and Wealth, National Bureau of Economic Research, 1947; M. Bronfenbrenner, 'The Consumption Function Controversy', Southern Economic Journal, January 1948; F. Modigliani, 'Fluctuations in the Savings-Income Ratio', Studies in Income and Wealth, 1949; J. S. Duesenberry, Income, Saving, and Theory of Consumer Behaviour, Harvard University Press, 1950; J. Tobin, 'Relative Income, Absolute Income, and Saving', Money, Trade, and Economic Growth (In Honor of J. H. Williams), Macmillan, N.Y., 1951 ; H. G. Johnson, Ά Note on the Effect of Income Redistribution on Aggregative Consumption with Interdependent Consumer Preferences', Economica, August 1951 ; L. R . Klein, 'Estimating Patterns of Savings Behaviour from Sample Survey Data', Econometrica, October 1951 ; S. F. James and W. Beckerman, 'Interdependence of Consumer Preferences in the Theory of Income Redistribution', Economic Journal, March 1953.

29

30

INTRODUCTION

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KEYNESIAN

DYNAMICS

consumer decisions. 1 T h e complication of treating prices as a separate variable can then be avoided. This presumes that consuming units would not alter their real consumption if money incomes and prices were to change by the same proportion (e.g., a doubling of both). Consumption may be considered a function of gross national product if disposable income is itself a function of gross national product for widely separated periods. 2 It is more usual to make consumption depend on net national income largely in order to stress the psychological importance of allowing for depreciation before deciding how much is to be spent on consumption (i.e., how much of total income to be set aside for replacement before distributing it as wages, dividends, & c . ) . Consumption is sometimes related to disposable income on the ground that income after personal taxes is a more reliable independent variable for purposes of prediction. These and other hypotheses regarding the consumption-income relation are matters for empirical testing. For purposes of simple theoretical analysis, however, consumption may be thought of in terms of total income, though total income should be defined for the particular purpose at hand. I n T a b l e ι the first column records various possible levels of real income, or Tm[P, where Tm is money income and Ρ the general price index. If, for example, money income is $300 billion and the price index 150 in a given period (as compared 1 Keynes makes his consumption function depend uniquely on real income by defining it in terms of wage-units, C „ = x(Tv), where the subscript K denotes the variables measured in wage-units. (See General Theory, pp. 90-1.) In the above equation, income in terms of wage-units (T"w) represents real income, since

where Τ is money income, Ρ the price index, W the money wage-rate, YjP real income, and WjP real wages. T h e equation implies that a change in the money wage-rate, which changes the level of money incomes and prices, would have no influence on the real demand for consumer-goods and hence on output and employment. If 'money illusion' does not affect consumption decisions, money-wage changes relative to prices, which are relevant to the classical employment function, become irrelevant to employment determination. Thus Keynes seems to have defined consumption in terms of wage-units partly to eliminate wage-flexibility as an explanatory variable of aggregate employment. (For further discussion on this Last point, see C h . 10 of this book.) * Cf. Ta-Chung Liu and Ching-Gwan Chang, 'Consumption and Investment Propensities', American Economic Review, September 1950; comments thereon by F. M . Bator, T . Mayer, and G . C . Means, ibid., March 1953.

THE

CONSUMPTION TABLE

FUNCTION

31

I

Consumption Schedule (In constant billion dolían) r = r j p

I

0 50 100 '5° 200 250 300

C =

C(T)

f 20 60 100 140 180 220 260

with the base period selected), real income in the period is $200 billion (300/1 -5). Each level of income, which is assumed to change by $50 billion, might be considered a change in income compared with previous periods. T h e second column refers to various amounts of real consumption expenditure out of current real income. The whole schedule relating various amounts of consumption and various levels of income is what Keynes calls 'the propensity to consume' or simply the consumption function. Table 1 shows that consumption is an increasing function of income (dC/dT > o), since the Τ and C variables move in the same direction. It should be noticed that consumption is assumed to change by $40 billion for each $50-billion change in income. W e may explain the above schedule further in terms of Fig. 4.

Figure 4 is a diagrammatic representation of the consumption schedule of Table 1. Consumption and its inverse, savings, are

32

I N T R O D U C T I O N TO K E Y N E S I A N

DYNAMICS

measured vertically and income is measured horizontally. The 45° line is the indicator of zero savings, since the consumers as a whole spend on consumption all of their income by moving along that line. The C curve is a linear function on our simplifying assumption that consumption changes by the same amount, or $40 billion. This explains the constant slope of the C curve. Consistent with the data of Table 1, the C curve does not start from the origin because consumption is not zero when income is zero, that is, C = $20 billion when Τ = o. The C curve slopes upward to the right, indicating that consumption expenditure increases as income increases. This accounts for the shape of the C curve, that is, consumption as an increasing function of income. The point of intersection Β is the break-even point, where C = Τ and where the division is drawn between positive and negative savings. In terms of Table 1 the break-even point is reached when both income and consumption are S100 billion. Going beyond the break-even point is to have positive savings, as indicated by the widening gap between the 45 0 line and tthe C curve. Conversely going below the break-even point is to have negative savings or 'dissavings'. Since a 45 e line is nothing but income itself plotted against income, a savings curve may be drawn against the income axis. Thus the S curve is seen as cutting the î^axis from below through point B' corresponding; to the break-even point B. The vertical distance between thœ S curve and the Τ axis at any level of income is exacdy the same as that between the 45 0 line and the C curve. In terms of Tablie 1 the community dissaves at all levels of income below S1100 billion and saves at all higher levels of income than $100 billiion. Thus the S curve, which measures various amounts of savimgs corresponding to various levels of income, is simply the complement of the C curve inasmuch as a propensity to consume alwiays implies a propensity not to save. Technical Attributes of the C Function Let us turn to the important matter of the technical attribuâtes of the consumption function in order to see their econoimic significance. The first attribute of the C function is 'the averrage propensity to consume', which may be defined as the ratiio of consumption expenditure to any particular level of income, or C¡Yr. If C = $100 billion when Τ = $ιοο billion, as in Table; 1,

THE

CONSUMPTION

FUNCTION

33

C Υ = ι, or unity. I f C = $180 billion when Y - $200 billion, C Y = o-g, or 90%. I f C = S220 billion when Y = $250 billion, C Y = 0-88, or 88%. It follows that the average propensity to save is respectively ο, ο·ι, and 0-12, since the average propensity to save, SIY, is the inverse of C, Y, that is, S¡ Υ = ι — (C, Y). Thus the proportion of income spent on consumption decreases as income increases and the proportion of income saved increases as income increases. If C/Y and S/Y do not actually behave in this way, it means that some other influences are permitted to enter into the consumption and savings functions. As for the economic significance of the concept of the average propensity to consume, it tells us what proportion of the total cost of a given output from planned employment may be expected to be recovered in the sales of consumer-goods alone. It tells us what proportion of the total amount of goods and services demanded by the community depends on the demand for consumer-goods as a source. The average propensity to save, on the other hand, tells us what percentage of the total cost of a given output will have to be made good by the sale of capitalgoods. The relative development of consumer-goods and capital goods industries in an economy depends on C¡ Y and SI Y, other things being equal. This suggests that in highly industrialized economies the average propensity to consume is persistently low and the average propensity to save persistently high. The average propensity to consume or to save will be found particularly important in the long-run analysis. The other attribute of the C function is 'the marginal propensity to consume', which measures the rate of change of total consumption expenditure, or the derivative of the total consumption function C = C(Y). Symbolically it may be expressed as dCjdY if the changes in C and Y are infinitesimally divisible or as ACι AY if the changes are discrete. Suppose, for example, that C increases by $40 billion (from 100 to 140) as Y increases by S50 billion (from 100 to 150). Then we have ACjAY = 40/50, or 0-8. A linear consumption function, as in Fig. 4, presupposes, among others, a constant marginal propensity to consume at any level of income. O n some other assumption regarding consumer behaviour we should expect a non-linear consumption function, as will be indicated later. The marginal propensity to c

34

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

seme, is 0-2 in the above example, since AS ¡AT = ι — (AC¡AT) znd(AC¡AT) + (AS¡AT) = ι , or unity. T h e economic significance of the marginal propensity to consume lies in that it throws light on the possible division of any extra income between consumption a n d investment, thus facilitating the planning of investment to maintain the desired level of income. Suppose AC = $18 billion w h e n AT = $30 billion, so that AC/AT — ο·6. T h e producers as a whole would lose $12 billion (30-18) by expanding output at an extra cost of $30 billion, since the consumers as a whole, b y hypothesis, spend only 60 per cent, of an increment of income, that is, $18 billion out of a n extra income of S30 billion (as a first approximation, total cost = total income = total profits + wages, where total profits include interest, rents and other property incomes). This example illustrates, though crudely, the analytical usefulness of the concept of the marginal propensity to consume, since there can be no increase in output and employment without an amount of investment equal to that part of an additional income which is not spent on consumption. T h e full significance of this concept will become clear in connexion w i t h the multiplier theory. Diagrammatic Representations T h e technical properties of the C and S functions can be described in terms of Fig. 5. (A)

to the left of the intersection point, short demand, D < to the right of it, a n d effective demand, D = Z> only where the C + / schedule intersects the 45 o line. Let us see how variations in effective d e m a n d may, cet. par., make producers content with more or less than fullemployment output. I n Fig. 13 the consumption function is not shown b u t implicit in the aggregate demand schedules C + / , C + / ' , and C + /". T h e constant level of autonomous investment, 7, is also implicit in each aggregate demand schedule, since it can be represented by a straight line superimposed on a consumption function. T h e aggregate d e m a n d schedules intersect the 45 o line at various points to generate uwfer-employment equilibrium income Tu,

86

INTRODUCTION

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KEYNESIAN

DYNAMICS

^ / / - e m p l o y m e n t equilibrium income Y¡, and oiw-employment equilibrium income Ym. W e m a y interpret these different equilibria corresponding to the C + I, C + /' and C + I" positions of aggregate d e m a n d as o w i n g to deficient, adequate and excessive 'effective d e m a n d ' . So interpreted, the alternatives o f an under-employment equilibrium and an over-employment equilibrium can be avoided only by maintaining the C + Γ

level of aggregate demand so that this demand is effective at Τ = Yf. I f the consumption function is given, as it is in Fig. 13, an increase or a decrease in 'effective d e m a n d ' compatible w i t h full employment must be due to similar changes in expected proceeds from the sale of capital goods alone. In other words, desired capital outlays or investment must be supposed to exceed desired savings to generate over-employment income Ym or fall short of desired savings to yield under-employment income Yu. T h u s it is possible to analyse economic fluctuations in terms of v a r y i n g 'effective d e m a n d ' as well as in terms of saving and investment.

THE

CONCEPTS

OF

THE

MULTIPLIER

AND

THE

ACCELERATOR

T o facilitate the next analysis of the temporal process of equilibrium adjustment, it seems useful to get acquainted with

THE

SAVINGS-INVESTMENT

ADJUSTING

FUNCTION

87

the concepts of the 'multiplier' and the 'accelerator'—incomemagnifying coefficients that are derived from the consumption (or savings) and investment functions. The

Multiplier

The 'investment multiplier' is the term Keynes gives to the coefficient by which a given change in investment is multiplied to show the final change in income. The simplifying assumptions underlying Keynes's 'logical theory of the multiplier' are ( ι ) that a change in investment is autonomously given, (2) that consumption is a function of current income, and (3) that the marginal propensity to consume is a constant. Then the value of the multiplier is given by the reciprocal of the marginal propensity to save, since the extent to which an increase in investment will expand income is structurally limited by the magnitude of a 'leakage' that AS¡AT is. We may express the idea of the multiplier by writing k

ι

=

AC AT

ι

leverage

AS ΔΤ

leakage

The magnifying coefficient k is what Keynes calls the 'investment multiplier', 1 which is based on a combination of AC

=

a AT,

AT=AC

(1) +

AI,

(2)

where AC is an increment of consumption, a the marginal propensity to consume, AT an increment of income, and AI an increment of investment. By substitution, we have the multiplier form A T = - - L _ A I , ι —a =

(3)

kAI.

By transposition, we get A

Ir

k

r

/

\

(3Λ) A/" Thus the multiplier, k, can be seen as the coefficient measuring a change in income, AT, relative to a change in investment, 1

=

For Iiis dynamic qualifications, see Central Theory, pp. 122-5.

88

INTRODUCTION

TO

REYNESIAN

DYNAMICS

Al. Now to give a numerical example, if a = 0-8, k = 5, and Δ/ = $10 billion, then AT = $50 billion, according to AT = kAI. Given AY = $50 billion as a desideratum and a = 0-8 as a structural parameter, the required amount of AI = $10 billion, according to AI = AT/k. Lastly, given AT = $50 billion and AI = $10 billion, the required value of k and inferentially that of a will be 5 and 0-8 respectively, according to k = AT/AI and a = AC/AT = 1 — i/k. The policy implications of all this manipulation are by no means without interest. More important for our purpose, it is possible to dynamize the above static multiplier, as we shall attempt to do shortly. The

Accelerator

The acceleration coefficient was formerly confined to the ratio between induced investment and an initial change in consumption expenditure, but it has come to be more broadly interpreted as the ratio of induced investment to a prior change in income or output on the ground that the demand for capitalgoods can be 'derived' not only from consumer demand but from any 'direct' demand. It is a good first approximation to think of this coefficient in terms of the marginal propensity to invest, since a change in the level of income reflecting the profit outlook is likely to induce a change in investment. Leaving the necessary qualifications to later discussions, we may write down our notion of the 'accelerator' as AI

=

(4)

bAT, AI

b =

Δ ί

.

(4.i)

where b is the marginal propensity to invest or the acceleration coefficient in the above short-run sense (the long-run accelerator will be discussed in Part III). By combining equations (1) and (4), we have the 'supermultiplier' form 1 ι

— a — b

s — b '

(5)

1 For variants see R . F. Harrod, The Trade Cycle, Oxford, 1936; J . R . Hicks, Trade Cycle·, P. A . Samuelson, 'Interaction between the Multiplier Analysis and the Principle of Acceleration', Review of Economic Statistics, M a y 1939.

THE

SAVINGS-INVESTMENT

ADJUSTING

FUNCTION

89

where k' is the 'super-multiplier' and s the marginal propensity to save. T h e term (i — a — b) refers to the net leakage in the sense that what consumers permit to be leaked into savings is pardy made good by what entrepreneurs pour into the income stream. For example, if a = 0-6 and b = 0 2, the net leakage equals 1 — ο·6 — ο·2, and the 'super-multiplier' equals 1/(1 — 0-6 — 0-2) or 5. Compounding the multiplier and the 'accelerator' in the present sense, we have the general 'super-multiplier' form ΔΓ =

1 ,AI, ι —a —b '

(61 K

= k'M. It will be found that the combined action of the accelerator and the multiplier is capable of rendering the system highly unstable, as demonstrated in Part II.

Part II

DYNAMIC INCOME BEHAVIOUR

Chapter 6 THE

MULTIPLIER AND FLUCTUATIONS

INCOME

THE theory of the multiplier establishes a precise relationship between aggregate income and the rate of investment, given the marginal propensity to consume. T h e 'investment multiplier' is the term Keynes gives to that endogenous force inherent in the economic mechanism which absorbs, assimilates, and propagates an exogenous 'shock'. As such, it is an indicator of what employment fluctuation is to be expected from a given fluctuation in investment. This chapter is devoted to analysis of the multiplying mechanism of income behaviour not only in terms of multiplier action but also in terms of acceleration-multiplier combined action.

INVESTMENT

MULTIPLIER

ACTION

A Static Model T o appreciate the dynamic multiplier, it seems useful to build a static model first. For this latter purpose let us assume (i) that no time lags are involved, (2) that induced investment is absent, (3) that there is a chance change in autonomous investment, and (4) that the marginal propensity to consume remains constant. Specifically let AI = $10 billion and AC/AT = ο·6 and therefore k — 2-5. O u r expectation is then that income will expand by an amount equal to k times $10 billion, or $25 billion. Figure 14 depicts the static or instantaneous result of investment multiplier action. In Fig. 14(A) consumption and investment are measured vertically and income is measured horizontally. These magnitudes are all in real terms. T h e consumption function C has a constant slope of ο·6, thus yielding a multiplier of 2-5. T h e original level of income is Tit that is, before a chance increase in autonomous investment. Now suppose that investment is increased by an amount equal to AÌ and held constant at that 93

94

INTRODUCTION

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KEYNESIAN

DYNAMICS

level. T h e economy can be seen as directly and instantaneously settled down to a new higher level of income, Yt· What is important to notice here is that the horizontal distance between Υ ι and Yt, or Δ Y exactly equals an amount 2 5 times Δ/, that is, the vertical distance between the C + I and C + I + Δ/ schedules. Since the value of Δ / i s assumed to be S10 billion, the value of Δ Γ must be S25 billion, according to AY = kAI. (A)

ι»'

C

C FIG. 14. Static Multiplier Action

The same result is shown in Fig. 14(B) in terms of savings and investment. In both cases the multiplier action, starting where S = I, increases income to augment savings enough to offset the increment of investment, with the result that the economy settles down to a new stationary level of income. As long as the investment continues at the same rate of Δ/, the new equilibrium level of income can be maintained indefinitely. However, we are left in the dark as to what happens between the Y x level of income before the investment change and the Y2 level after that change. This is where we leave Keynes's 'logical theory of the multiplier' and begin with the dynamic theory of the multiplier'. 1 The Dynamic Multiplier Form

If there is an economically significant time lag between an 1 Cf. J . R . Hicks, Trade Cycle, pp. 1 1 - 3 6 ; P. A. Samuelson, 'Dynamic Process Analysis', op. cit.; R . M. Goodwin, 'Secular and Cylical Aspects of the Multiplier and the Accelerator', in Income, Employment and Public Policy.

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initial investment outlay and its reappearance as income, difference equations expressing lagged consumption and investment must replace static equations in order that the discrete steps involved in the multiplier process may be traced. We may build a simple dynamic system involving a consumption lag but no investment lag, such as ct = a(Tt_, - r 0 ) + C«

(0 (2)

rt=ct+ it) (3) = air,., - r0) +C0+I, (4) where Ct is consumption at time t, a the marginal propensity to consume, Tt_l previous income, Y0 initial income, C0 initial consumption, /, investment at time t, and I constant autonomous investment. The essential point to notice about the general multiplier equation (4) is that consumption is lagged, that is, dependent on the income of the preceding period over and above some arbitrary initial income. To see the propagation mechanism clearly, it is convenient to contemplate a constant rate of autonomous investment, say, to the tune of $10 billion per unit of time beginning with period 1. If α = 0 5 and therefore k = 2, $10 billion of new investment will expand income in a manner indicated below. Since it is assumed that the increment of consumption occurs one period later, extra consumption after the investment change must be zero in period 1, and the amount of investment, $10 billion, is the amount by which the income of period 1 increases over period o. In period 2, income again increases but, this time, by the amount of consumption which is half of the previous increment of income, or by $5 billion, and so on. This continues into the future indefinitely until the constant autonomous investment plus all the subsequent fractional increments of consumption expenditure add up to exactly S20 billion. Thus the income propagation initiated by the $io-billion investment takes the form of a dwindling series of increases in the rate of consumption, which eventually gives rise to a final increment of income equal to k times S10 billion. Such an expansion of income at a decreasing rate of change is due to our assumption of a < 1, and will be illustrated by a more detailed numerical example presently.

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The Geometric Progression Form In the above example the final increment of income is the sum of $10 billion in period 1, $5 billion in period 2, $2-5 billion in period 3, and so forth, or a total of $20 billion. Puttingy(t) as the increase of income (jt — J 0 ) o v e r the initial income j „ , the geometric progression can be shown as A°)

= (T, - J o ) = o,

Αι) = Δ/, J(2) = Δ / + ¿ Δ / = ( I + A3) •

A«)

=[!+* '}

+

= [ ! + * +

(*)']*/, (i)2 + · · · + (i)"]*/.

I f η becomes infinite, the last equation comes to ΑΓ = kid, as in the static theory. T h e important difference, however, is that the above sequence involved in the difference equations is what the static equation fails to show. T h e successive periods ι, 2, 3, . . . involved refer to 'rounds' of consumption expenditure subsequent to the initial injection of $10 billion. T h e actual length of the interval between one 'round* and another depends on the complex nature of the 'lag structure' in a particular economy. 1 I f each 'round' is only one month, the initial investment will reach its limit rather quickly. 2 This suggests that in an advanced economy, where all sorts of uncertainties and rigidities exist, consumption expenditure may lag considerably behind the receipt of income, production behind sales, and dividend payments behind corporate profits—all tending to lengthen each 'round' and so to slow up the speed of income propagation. The Dynamic Process of Income Propagation Let us now analyse carefully the dynamic process of successive income changes in terms of Fig. 15. For this purpose we shall make consumption depend on the income of the preceding 1 Cf. L. Metzler, 'Three Lags in the Circular Flow of Income', in Income, Employmint and Public Polity. * J. R. Hicks has observed that if the lag between wage payments and their expenditure were the only lag to be considered (which is nearly zero), 'we could then treat the system as having an instantaneous adjustment in the Keynesian manner'. (See his Tradt ÇycU, p. a I.)

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period, C = C, = aTt_l (where a stands for the marginal propensity to consume), and also assume investment to be a function of time and an autonomous constant, / = /, = /. (.a = 0 5; k = 2)

In Fig. 12 consumption, investment, and savings are measured along the vertical axis and income is measured along the horizontal axis—all magnitudes being in real terms. The C curve relates consumption to the income of the preceding period and it has a constant slope of 0-5. The original investment schedule is the vertical distance between the C curve and the C + I curve, while the new investment schedule is that between the C curve and the C + / + Δ/curve, which gives a constant level of investment equal to Δ/. Savings out of previous income are measured by the vertical distance between the 45o line and the C curve. T h e system may be seen as initially settled at equilibrium point Eq, where savings and investment are equal {Eff ! — E f J . This is our starting-point. In period o, before the change, consumption is c ^ and income OT0 or Eoro, thus leaving E0c1 both as savings and investment. Now investment increases by Δ/ from period o to period ι and stays at this level. What happens? Consumption remains the same, since consumers have not yet had a chance to adjust themselves to the change. Similarly intended savings remain unchanged. This means that investment exceeds intended G

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savings by an amount equal to the increment of investment, or by j>iE 0 . This excess of investment over intended savings for period ι (equal to actual savings for period o) accounts for the unexpected increment of income from period o to period ι . In period ι there is an equal horizontal change, = r . r O , for the vertical change o f j j i v In other words, income increases over OT0 by the amount of excess investment in period ι after the injection of Δ/. The total income received in period ι is therefore 0 1 r i ( = 0 T e + J ^ i ) · What of the savings-investment relation in this period ? Investment is again / + Δ/, or y ¡¡¿a and savings corresponding to previous income O r 0 is /jCa, thus making intended savings fall short of investment by = y ¿ 2 ~ h c i ) · This excess investment is what causes income to increase from period ι to the next, that is, by ( =J>i*l)· Although consumption increases from c1T0 to ctT1 corresponding to the increased total income of 0 T t , this extra consumption amounts to half of extra income J^î^. Likewise savings increase by half of extra income T0T1. This is the reason why intended savings in period ι fall short of investment. Accordingly income expands by an amount equal to the above excess of investment over intended savings, or by y^t^ which amount is equal to the horizontal change oiy2t2. It is thus that period 2 is ushered in and total income received is 0 Y 2 . But investment in this period still exceeds savings by jy3t2( =y3c3 — t¡c3), since intended savings corresponding to previous income OTl amount to t2c3, which amount isj 3 < 2 short of a total investment ofy¿c 3 (constant I + Δ/). This excess of investment over intended savings in period 2 is instrumental in increasing income from period 2 to period 3. And so on. It is to be noticed that the gap between intended savings and intended investment (the vertical distance between the C + / + Δ/ curve and the 4 5 0 line) becomes smaller and smaller, and the increment of income which it produces, until the gap is completely wiped out. The constant stream of new investment has developed its full effect, and aggregate income has reached the stationary higher level of Tn in the nth period. T h e system has at last found peace and quiet, as it were, at the new and higher equilibrium point En. Income has reached there via E0,yu t¡,y2, t2,y3, . . ., E„. The multiplier has done its job,

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for it has caused income to expand to cause intended savings to expand up to the new level of investment, that is, where Sn = /„. Thus in the nth period the savings gap (the vertical distance between the 4 5 0 line and the C curve at Y„) exactly equals the sum of old investment plus new investment (the vertical distance between the C + I + Δ / curve and the C curve at T„). This is merely another way of saying that the multiplier action stops when it has been exhausted by the very expansion of income and therefore savings which it calls forth. A Numerical Example of Dynamic Multiplier Action In interpreting the numerical sequence of Table 7 the following points are to be stressed by way of precaution at the outset : Total savings (S) or the increment of savings (AS) represent the amount that the consumers planned to save on the basis of the preceding period's income, not what they find themselves to have actually saved at the end of the period ; planned investment (I) may fail, contrary to the assumptions of Table 7, to be carried out because of entrepreneurial reactions to unexpected changes in unintended inventories, that is, stocks of goods which businessmen are forced to hold because the market will not absorb them; if inventories accumulate as a result of an unexpected decline in market demand, production is cut down and demand is met 'out of stock', with the result that planned investment which includes outlays on inventories decreases relatively to planned savings. Conversely if inventories are being depleted as a result of an unanticipated rise in demand, production is increased and with it planned investment relatively to planned savings. It follows that savings and investment are equal when the rate of change of unintended inventories is zero, that is, when stocks of goods are neither accumulating nor decumulating. These remarks apply to similar models elsewhere. In T a b l e 7 the economy is shown as starting out from a low position of equilibrium, where income in period 0 equals consumption conditioned by previous income plus current investment, or 100 = 80 + 20, and where S = I. As a result of a sudden increment of investment, 10, income increases by 10 to increase total income to 110. But consumption does not immediately react to the increment of income and remains at

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80. Investment has gone up to 30, and yet intended savings remain at 20. Thus the difference between investment and intended savings equals unexpected extra income, or AC + Al = A T (o + 10 = 10). So ends period 1 and period 2 begins. In period 2 consumption increases by 5, which is half of previous extra income 10. Intended savings likewise increase by 5. Income increases by the increment of consumption or, what is the same, by the difference between investment and savings. Total income earned or produced in period 2 equals 115, which TABLE 7

Dynamic Multiplier and S - 1 Equilibrium Process (In billion constant dollars) Period

! Λ/

AC Ar

o

$

0

0

C

I

s

r

Position

$

s

80

20

20

100

20

IIO

>

25

"5

Transition

_

30

120

New Higher Equilibrium

%

0 IO

0

80

30

10

5

5

5

85

30

0

0

90

30

(/ = /,=/;£ =

< >

0

$

10

• 00 i IO il 0o k = 2.)

$

AS

¿ • ( r . , ) ; Ar

= r - r0; AC = C-

s

j

Initial Equilibrium

C 0 ; Δ 5 = S - Sa; a = ο · 5 ;

is 5 over the preceding period. Since the unchanged investment still exceeds intended savings by 5 in period 2, this is the amount by which income in the next period will expand. And so on. In period n, extra investment of 10 reaches its limit, for it is no longer capable of generating additional consumption and savings on a 50 per cent, basis. Total savings have increased enough to cancel out the extra investment plus the original investment, or 30 = 30. The multiplier has caused total income to reach the asymptote, and consumption and savings with it. Notice that total income at the final stationary level is exactly 20 more than at the initial level, according to AT = kAI. Yet it has taken time for extra investment of 1 o to lift total income by an amount equal to k times AI. Thus, by showing income be-

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haviour through discrete stages the dynamic multiplier analysis based on difference equations makes an important contribution to the theory of economic fluctuations. Let us, however, observe some qualifications. Qualifications

ι. The assumption of a given increment of investment in the multiplier analysis is useful but may have to be dropped, in some contexts, in order to allow for the possibility that the multiplied income may in turn induce fluctuations in investment. If so, the total effect on income would be greater than if the multiplier effect on consumption alone was considered. We shall consider this problem in the subsequent analysis of the acceleration process. 2. Allowance must be made for the possibility that the marginal propensity to consume may not remain constant as income increases through the multiplier action. The value of k in any multiplier period would be smaller if the consumers chose to save a larger proportion of extra income or if corporations decided to withhold a larger proportion of extra profitincome from dividend payments. The magnifying effect of an increment of investment on income will decrease to the extent that income recipients allow all sorts of 'leakages' to take place for whatever reasons. 3. Output and employment will stop growing, however high the marginal propensity to consume may be, once full employment has been reached. Only up to this point will increasing employment be associated with a multiplier expansion of income. Beyond that point a further increment of investment would merely increase general prices instead of output and employment, as will be shown later. For the supply of labour curve will probably have zero elasticity and there simply may not be any more labour available to increase output, in the short run at least. 4. Allowance must also be made for the possibility that a part of the magnified income may leak out to the benefit of employment elsewhere, as far as an open system with foreign-trade relations is concerned. Keynes adds the cheerful thought that the 'leakage' might be partly recovered through foreign balances accompanying the magnified incomes in other

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countries. 1 This is to presuppose a world economy in which all trading nations simultaneously pursue expansionary employment and trade policies to mutual advantage. We shall explore this possibility later.

ACCELERATOR-MULTIPLIER

COMBINED

ACTION

Thus far we have taken investment as autonomously given, but we may now modify this assumption in order to consider the effect of a given fluctuation in income on a fluctuation in investment. The question now is: How does income behave when an autonomous change in investment calls forth not only induced consumption but also induced investment ? The answer to this question requires an analysis of the action of the 'supermultiplier' mentioned earlier. A Dynamic Accelerator-Multiplier System T h e endogenous instability of an income system is greatly exaggerated by the combined action of the accelerator and the multiplier. If we think of induced investment in terms of the marginal propensity to invest, we can represent a 'supermultiplier' system by r

t

= c

t

+ i

(O

t

C, = a{rt_,

-

T0) + C0,

(2)

Λ = b{Yt_,

-

r 0 ) + /„.

(3)

By combining (2) and (3), we have the fundamental accelerator-multiplier form rt = (a + 6 ) ( r , _ 1 -

r 0 ) +c0

+/.,

(4)

where T t is current income, C, current consumption, /, current investment, a the marginal propensity to consume, b the marginal propensity to invest, T t _ t previous income, T0 initial income, C0 initial consumption, and I 0 initial investment. The last equation (4) tells us that total income in the current period equals initial income (C0 + /0 = T0) plus subsequent induced consumption and investment. This will be further clarified by a numerical example, but for the moment the following geometric progression form may help reveal the way in which 1 General Theory, pp. 121-2.

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income p r o p a g a t i o n leads an accelerator-multiplier system to a final position of equilibrium for certain values of a, b, a n d Al. J>(o)

=

o,

j(I) = M, J(2) = ι + ( i

+έ)Δ/=(ι

v(3) = ( ! + * +

+ J +έ)Δ7,

έ 2 )Δ/,

A " ) = [ι + ( i + Ì) + ( i + i ) ' + · · · + (* + i)"J Δ7. In the a b o v e system w e assume a marginal propensity to consume o f 0-5 and a m a r g i n a l propensity to invest o f 0-25. I f Si of a u t o n o m o u s investment is injected once and for all, income will e x p a n d a c c o r d i n g to S i + So*75 + §0-5625 + . . . until it adds u p to S4. T h i s is w h a t must be expected to h a p p e n , since the 'super-multiplier' k' = 1/(1 — 0 5 — 0-25), or 4. It w o u l d b e fruitful to analyse the d y n a m i c interaction o f the accelerator and the multiplier in terms of the savings a n d investment schedules, since s u c h an a p p r o a c h at once reveals the equilibrium mechanism o f a d y n a m i c income system as the analogue of the familiar m a r k e t price mechanism. L e t us turn to this analysis. Autonomous Investment and the

'Super-Multiplier'

For purposes of d i a g r a m m a t i c analysis, assume (1) a constant level of autonomous investment d u e to innovation or public policy, (2) a marginal propensity to consume of 0-6 and therefore a m a r g i n a l propensity to save o f 0-4, and (3) a m a r g i n a l propensity to invest o f 0-2. F i g u r e 16 lays a basis for explaining a d y n a m i c equilibrium solution for this system. (A)

(B)

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In Fig. ι6(A) the / and S schedules represent induced investment and savings, as indicated by equation (3) and implied by equation (2) of the 'super-multiplier' system. They have the slopes of b = ο·2 and 1 — a — 0-4 respectively. These schedules intersect to generate initial equilibrium income T0. Now a constant rate of autonomous investment, Δ/, puts in its appearance, thus giving rise to the / + Δ7 curve. Consequently total investment becomes larger than intended savings by an amount equal to Δ/. This excess of investment over savings is the amount by which income increases from period o to period 1, for T1 exceeds T0 by an amount equal to the difference between current investment and current savings which depend on the preceding period's income, or Tt — Yt-1 = It — S(Yt-j). To get an equal horizontal increase of income from each vertical excess of investment over intended savings, draw a 45 0 line from the S curve at Y0 to let it intersect a horizontal drawn from a point on the / + Δ7 curve corresponding to T0. Then draw a vertical through the intersection point obtained in the above manner, to find the exact increment of income horizontally as well as the induced savings and investment vertically. These steps can be repeated to get all the other equal horizontal increments of income for all the vertical excesses of investment over savings. Thus the increased income of period ι, Y0Y1, equals the vertical distance between the I + AI and 5 curves corresponding to the Y0 level of income. The same is true of the subsequent income increases, TlT2, Y2Y3, . . . When the income expansion terminates in period n, the total increment of income, Y0Y„, will be found equal to k' = 1/(1 — 0-6 — 0-2). It can be seen that in period η total investment (autonomous plus induced plus original) equals total savings, as these quantities may be read off the I + Δ7 and S curves at the Yn level of income. This equilibrium solution of the dynamic 'super-multiplier' system is due to our assumption of (1 — a) > b. A Dynamical Equilibrium Solution Turning now to Fig. I 6 ( B ) , we can see a dynamical equilibrium solution from the time-shape of income behaviour, in comparison with a comparative-statical equilibrium. Income is measured vertically and time measured horizontally. The Y{t)

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curve represents the temporal behaviour of income due to the accelerator-multiplier interaction. This curve starts from baseperiod constant income T, rising with time and finally flattening out, and so indicates that income increases at a decreasing rate. When the T(t) curve has a zero rate of increase, the system may be said to have grown into a new higher income plateau. The Τ + A g l i n e paralleling the t axis represents such a plateau from the standpoint of comparative-statics, i.e., if we are to ignore any prior movements of variables. This is Keynes's procedure, as he would compare ΐ with f + AT without reference to T(t). In dynamics, on the other hand, all three, f , T{t), and f + ΔΥ, must be duly considered. This part of the analysis may be clinched by the numerical model of Table 8. TABLE 8

Accelerator-Multiplier

Interaction

(In billion constant dollars)

( o) as well as a decreasing function of capital (81/δΚ < o). Now the investment function is believed to deviate from linearity in a S-shaped fashion, for these reasons: At extremely low levels of activity there is so much idle capacity (surplus inventories and unutilized plant and equipment) as to yield small dl/dT; at extremely high levels of activity, on the other hand, it is a combination of rising factor costs, increasing resource immobility, and pressing material-labour shortages that tends to make for small dl/dY·, at intermediate levels the using-up of idle capacity in the upswing or the piling-up of idle capacity in the contraction phase gives rise to large dl/dT. Let us see in light of Fig. 21 how a nonlinear investment and a linear savings function of the above sort can, between them, generate a purely endogenous cycle with the customary phases of recovery, boom, recession, and slump.

Upper turningpoint

I.S

O

Y.

S

γ.

Y,

Y

FIG. 21. Non-Linear Investment Function and Cyclical Turning-Points

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The Switch from Upswing to Downswing Suppose that the system is initially in equilibrium at point E, with Y — Y0 and S = I. Equilibrium income Y0 is given by the intersection of the S and I curves. For reasons yet to be explained, the I curve in time shifts from the position of / to that of /', to touch the S curve at point B. This latter point is a critical or 'branch' point at which the position of the system becomes unstable in an upward direction, since investment exceeds savings in its neighbourhood. How quickly the system can move from E to B, that is, from the state of slump to the critical phase of the upswing depends on the rapidity with which the whole investment curve shifts upward. The rapidity of the shift of the investment curve in turn depends on a number of initiating conditions, such as specified later. Given the 5-shaped investment curve, the behaviour of investment after the critical point looks as though the system would 'explode' since the marginal propensity to invest far exceeds the marginal propensity to save in the middle range. Soon, however, nonlinearity asserts itself to lead the system to a stable equilibrium, as may be seen from the flattening out of the / ' curve. The / ' and S curves intersect at E' to generate equilibrium income Yn, which may fall short of assumed full-employment equilibrium income Yf. If the marginal propensity to invest were larger at extremely high levels of activity than assumed here, the / ' curve would be steeper so as to intersect the S curve possibly at some point corresponding to full-employment income Yf. The reason why the Γ curve is so flat toward E' is that we consider it more likely for an actual peacetime economy to experience all sorts of 'botdenecks' (factor immobility, special shortages, rising factor prices, and the like) even before it reaches a position of full-employment boom—in addition to the narrowing range of profitable investment opportunities due to the possible overexpansion of plant and equipment during the later stage of the upswing. What is more, the system cannot remain indefinitely even at that less-than-full employment equilibrium point, E'. Let us see why it cannot do so. To be sure, high equilibrium point E' represents a stable equilibrium position since savings exceed investment above it and investment exceeds savings below it. But this position in

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I25

time becomes unmaintainable, as the rate of capital accumulation to sustain the high Tn level of activity gives rise to the diminishing effects of capital on investment and to the gradual shift of the / ' curve in a downward direction. As a result of this downward shift, the system moves from E ' to new 'branch' point B', where the position becomes unstable downwards since it is flanked by the excess of savings over investment on both sides. Point E ' can therefore be considered 'the upper turningpoint' where the fluctuation of income takes a downturn, where the boom switches to a downswing, and where the expansionary forces propelled by I > S are substituted by the contractionary forces impelled by S > I. This upper turning-point might also be ascribed to what Hicks characterizes as 'a collapse in the accelerator' due to 'real limitation of resources' 1 near or at full employment or to what Keynes calls 'the collapse of the marginal efficiency of capital' [schedule] due to the disillusioning impact of 'their [capital-goods] growing abundance and their rising costs of production'. 2 These two explanations are integrated in our investment function, since investment is made to vary directly with income and inversely with capital. If the switch to a downswing is explained solely in terms of the weakening of the accelerator or the marginal ratio of investment to output, the criticism becomes unavoidable that the 'capacity-creating' aspect of investment due to the accumulation of capital stock is unrealistically ignored. If, on the other hand, the switch to a downswing is explained exclusively in terms of the falling level of investment due to the depressing effect of capital accumulation, the criticism becomes inevitable that the 'income-generating' aspect of investment via the acceleration principle is unrealistically overlooked. These remarks apply to the switch to an upswing as well. Let us now turn to this other switch of behaviour. The Switch from Downswing to Upswing If the system is initially in equilibrium at E ' with Y = T n and S = /, it in time switches to a downswing for the above reasons. The I curve below B' is seen sloping downward as steeply as if 1 2

Trade Cycle, 125-7. General Theory, pp. 315-16.

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the system were bound for an explosive deflation of income and employment. In the words of Keynes, 'when disillusion falls upon an over-optimistic and over-bought market, it [the marginal efficiency of capital schedule] should fall with sudden and even catastrophic force'. 1 Yet the downward fluctuation of income is terminated by the I curve flattening out to intersect the S curve at E to generate equilibrium income T0 above zero income. In other words, the marginal propensity to invest becomes smaller relatively to the marginal propensity to save as the system approaches lower equilibrium point E, owing to the fact that there is always some constant long-run investment of an autonomous nature such as represented by the virtually horizontal straight part of the / curve around E. Otherwise the / curve might be so steep as to cause the system to find a 'zero employment' solution or, at worst, no stable solution at all. Though gross investment is positive at Ta, it is so much below replacement that there is negative net investment. If activity continues at this low level, capital will be decumulated to the point where the marginal efficiency of capital once again rises high enough to bring forth positive net investment. Moreover, the reduced pressure on resources decreases the marginal cost of producing capital-goods, the decreased demand for transaction money relieves pressure on speculative money to lower interest rates, the replacement demand increases as a result of unpostponable depreciation and obsolescence—all tending to restore business confidence in the profitability of new investment. Thus the / curve gradually shifts upward to the position o f / ' , to start the cycle all over again. Point E can therefore be considered 'the lowering turning-point' where the depression switches to an upswing and where there occurs a revival in induced investment. A more complete explanation of turning-points, however, would have to take into account not only the role of a nonlinear savings function 2 but also the roles of such exogenous forces as innovations. 3 Nevertheless the above provides a simple General Theory, p. 316. S e e K a l d o r , op. cit. 3 S e e , e.g., J . A . S c h u m p e t e r , ' T h e D e c a d e of the T w e n t i e s ' , American Economic Review, M a y 1946. 1

2

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127

yet plausible explanation for the existence of an endogenous cycle. The Time-Shape of a Real Cycle Although no two historical cycles are completely alike, they may nevertheless share in common the recurrent phases of (1) upswing, (2) boom, (3) downswing, and (4) slump. The foregoing analysis suggests that a boom is likely to be limited by a full-employment ceiling and that a slump is likewise limited by a zero-saving floor. Figure 22 illustrates the temporal fluctuation of real income within these theoretical limits. γ Full-Employment Ceiling / / / V ü

\ Boorn^N.

/ (1) Upswing

\ V \

y

(3) D o w n s w i n g V .

(4) Slump

.

Zero-Saving Hoor 1

FIG. 22. Ceiling and Floor of a Fluctuation In Fig. 22 real income is measured vertically and time measured horizontally. The Y = Yf line is a full-employment ceiling or an upper limit which is drawn horizontal by abstracting from secular growth, while the Y = C line is a zero-saving floor or a lower limit which is also drawn by abstracting from secular growth. Starting from where Y = C and S = 0, the solid curve can be seen moving up slowly during the early period of the upswing, goes into high gear during the latter part of this phase, and slows down to the peak or boom. If, on the other hand, the boom were stronger, it would hit the fullemployment ceiling, as indicated by the broken curve. For the reasons already mentioned, the boom takes a downturn and the downswing follows the gradually steepening curve and

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then slowly tapers off into a slump or depression. I f the slump were more severe, it would break through the zero-saving floor, as indicated by the broken curve below the Τ = C line. Although this latter possibility is borne out by experience, it is likely to be a rather short-lived phenomenon since an actual economy cannot long endure 'capital consumption'. T h e 1932-34 personal dissaving of the United States is a case in point. Even if real income stays on the zero-saving line, the level of employment associated with that low level of income may be 'so low that it would provoke revolutionary action if long maintained', as Dillard has suggested. 1 T h e time-shape of income fluctuation in Fig. 22 is consistent with the non-linear behaviour of the investment function previously discussed. It is to be noticed, too, that the fluctuation of income tends to return to the Y = C level in due course, owing to the tendency of that fluctuation to reverse itself. T h e arguments involved in Fig. 21 and Fig. 22 seem to provide a plausible explanation for the observable fact that a modern industrial economy, while subject to significant fluctuations, is not generally so 'violently unstable', thanks to the stabilizing influence of a marginal propensity to consume of less than unity or to the damping transformation of a marginal propensity to invest into dl/dT < dS[d¥ both at extremely high and low levels of activity. Y e t when price is introduced as a separate and independent variable, the behaviour of income, that is, of money national income may well be so asymmetrical as to pierce through the fullemployment ceiling, while there may not be a corresponding tendency to go below the zero-saving floor. W e shall now turn to this subject of inflation dynamics.

1

See D. Dillard, op. cit., p. 39.

Chapter 8 THE

DYNAMICS

OF

INFLATION

far we have analysed income behaviour on the assumption that changes in money income were also changes in real income, that is, on the assumption of constant prices. We must now drop this assumption in order to see what happens to money national income when effective demand increases beyond the full-employment level. This chapter is concerned with the dynamic behaviour of general prices, the stability conditions of over-employment equilibrium, and the multiplier in a full-employment economy. The basic equation of an income system involved in this chapter is Τ = Tm = P(t) Tf, where Τ is national income, Tm money national income, P(t) the price level at time t, and Y constant full-employment real national income. THUS

THE

INFLATIONARY

GAP

IN

TERMS

OF

S

AND

/

Our first lesson in the economics of full employment is the 'gap analysis' associated with the name of Keynes. 1 This refers to a technique whereby the gap between expected total expenditure and the money value of available output at base prices is measured with a view to estimating the implied magnitude of price increases. Through this technique the level of money national income can be determined in familiar savingsand-investment terms. For simplicity we may initially assume investment to be entirely autonomous and lagless and savings to be dependent on current income alone. O n these assumptions an inflationary gap will be found identical with a disequilibrium state of desired full-employment investment exceeding desired full-employment savings. An increase in income resulting from such an excess of investment over savings reflects higher general prices rather than greater output and employment. Let us analyse gap potentials in terms of Fig. 23. 1

I

See his How to Pay for the War, Harcourt Brace, N.Y., 1940. 199

I30

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

In Fig. 23 investment and savings are measured along the vertical axis and income is measured along the horizontal axis. W e may suppose that the savings and investment schedules are such as to intersect to generate constant full-employment equilibrium real income Tf. In conditions of full employment total output is no longer expansible, and yet there is no such limit to total demand. If businessmen are willing to increase their expenditure on new capital goods at all levels of income, the investment schedule may shift upward to the position o f / ' , as in Fig. 23(A). If the propensity to consume remains the same,

(A)

(B)

the propensity to save will be unchanged, as represented by the S curve of Fig. 23(A). Because total demand has increased to the extent that desired investment has increased, while total supply remains inelastic, an inflationary gap must develop inevitably. Such a gap is shown to be the vertical excess of investment over savings at the full-employment level of income. The money value of full-employment output is the sum total of the value of consumer and capital goods at existing prices, while desired total expenditure consists of what the consumers and the businessmen are disposed to spend at all levels of income. It follows that if desired total expenditure corresponding to the full-employment level of income exceeds the money value of full-employment output, general prices will tend to rise, as measured by the horizontal distance between Yf and Tm. The T m level of money income is given by the intersection of the

THE

DYNAMICS

OF

INFLATION

131

S and / ' curves. At this level of income, money savings and money investment are equal. If we express constant full-employment real investment by If and desired savings out of constant full-employment real income by S(l~f), an inflationary gap takes the form

if - s(rf) > o.

Unless the above gap is wiped out, it will inevitably lead to general price increases according to Ym = P(t) Yf.\i Y = Yf is desired, then the condition of equilibrium I¡ = S(Yj) will have to be satisfied. If, on the other hand, some price increases are to be allowed so that Y = Ym, the expansion of money national income will come to rest when Im = Sm, where Im is realized money investment and Sm realized money savings. Figure 23(B) shows that an inflationary gap develops as a result of a decreased propensity to save or, what is the same, as a result of an increased propensity to consume, given constant full-employment investment. Thus the savings schedule can be seen shifting to the position of 5", thereby creating a gap between investment and savings corresponding to the Yf level of income. As in Fig. 2 3 ( A ) , the intersection of the savings and investment schedules beyond the full-employment level generates equilibrium money income Ym. Implicit here is the assumption that consumer habits in conditions of full employment have changed so that the consuming public is disposed to spend more or save less at all levels of income. Figure 23 suggests that there are an infinite number of solutions to the savings-investment equation in order to maintain the constant level of full-employment real income without price inflation. The theoretical requirement to satisfy is that the savings and investment schedules should intersect at Y = Yy, that is, if over-employment equilibrium income Ym is to be avoided. This can be done by making the investment schedule shift downward to intersect the savings schedule at Y = YfOT, alternatively, by making the savings schedule shift upward to intersect the investment schedule at Y = Y¡. It is a matter of policy which of these alternatives is translated into action.1 1 Cf. S. E. Harris, The Economics of Mobilization and Inflation, Norton, N.Y., 1951 ; also K . K . Kurihara, Monetary Theory and Public Policy.

132 THE

INTRODUCTION

PRICE

TO

MULTIPLIER

KEYNESIAN

IN

A

DYNAMICS

FULL-EMPLOYMENT

ECONOMY

T h e above gap analysis is a necessary explanation of general price increases in a full-employment economy, but it is not a sufficient explanation of the behaviour of general prices. 1 T o ward such a sufficient explanation the following multiplier analysis may be one step farther. A Dynamic Money Income System A full-employment money income system may be generally represented by rm(t) = cm(t) +im(t), where Tm(t) is money national income at time t, Cm(t) money consumption (i.e., consumption in money terms) at time t, and Im(t) money investment at time t. As mentioned before, Tm(t) = P(t)Yj, where P(t) is the average price at time t and Y j constant full-employment real income.

Cm(t) =a'[rm(t - I) - Tf] +C,

(2)

where a' is the marginal propensity to consume in money terms, or a' = ACm/AYm - ACm/(AP)Yf (where ΔC m is an increment of money consumption and A P an increment of average price), Ym(t — ι) — Tf previous money income over the initial fullemployment level, and C¡ constant full-employment real consumption. This implies that the marginal propensity to save out of inflated money income, ASm¡AYm = ASm/(AP) Yf) could be different from the marginal propensity to save out of real income alone, that is, at constant prices. Thus, for example, we should expect the marginal propensity to save out of money income to rise if a rise in general prices leads to a significant redistribution of real income in favour of profit-takers whose marginal propensity to save out of real income is generally 1 For various models based on special assumptions see R . M . Goodwin, ' T h e Multiplier', in The New Economics·, A . Smithies, ' T h e Behavior of Money National Income under Inflationary Conditions', Quarterly Journal of Economics, November ig42; R . Turvey, 'Period Analysis and Inflation', Economica, August 1949; D. Holzman, 'Income Determination in Open Inflation', Review of Economics and Statistics, M a y 1950; T . Koopmans, ' T h e Dynamics of Inflation', Review of Economic Statistics, M a y 1942.

(i)

THE

DYNAMICS

OF

INFLATION

!33

higher than that of wage-earners. W e shall return to this point later.

/m(0 = nrm(t -1) - rf] + if,

where b' is the marginal propensity to invest in money terms, or b' — AIn/ATm = AIm/(AP)Yf (where AIm is an increment of money investment), and 1¡ constant full-employment real investment. T h e marginal propensity to invest out of inflated money income could also differ from the marginal propensity to invest out of real income alone, that is, if entrepreneurial reactions to price changes are explicitly taken into account, as will be shown in the course of the present analysis. By combining (2) and (3), we get the price super-multiplier form rm(t)

= («' + b')[Tm(t

-

I) -

Tf] +C,+

lf.

(4)

Designating the price multiplier by kp, we may write down ι =

ΔC m

ι _ Mm

(ΔΡ)2)

=

ι

a'

b'

β)

(AP) Τ,

W h a t will happen to this system when an inflationary shock is introduced by a constant stream of autonomous real investment (fixed amount regardless of price increases, such as associated with war expenditure, deficit spending, and a net foreign balance) ? Such a shock will determine the level of money national income, given the propensities to consume and to invest, but convergence and divergence will depend on the values of a' and b', not on the size of that shock. Let us first analyse the dynamic determination of money income and general prices in terms of Fig. 24. Dynamic Price-Multiplier Action For the purpose of the following diagrammatic analysis let us assume that the supply of money is perfectly elastic, that the full-employment inelasticity of output is already reached, that the marginal propensities to consume (or to save) and to invest in money terms are constant, and that excess demand or a shock is introduced autonomously and kept constant. In Fig. 24, investment and savings are measured vertically and income is measured horizontally. U p to Yf all magnitudes

(3)

134

INTRODUCTION

TO K E Y N E S I A N

DYNAMICS

.+ ΔΙ

FIG. 24. Money Income Determination and the Price

Multiplier

are in real terms, but beyond it they are in money terms. Initially full-employment real income Yj is given by the intersection of the broken real savings and investment curves, Sr and Ir. At this level total output ceases to be expansible, by hypothesis. This implies that any attempt to increase real investment will necessarily increase general prices, given the propensity to save. Let such an attempt be represented by a constant stream of autonomous real investment equal to Δ/Γ. We may suppose that this inflationary pressure or shock is associated with war expenditure, deficit spending, a net foreign balance, or any other excess demand. If the autonomous investment, as such, is kept constant with rising prices, that is, a fixed proportion of fullemployment real income regardless of inflated prices, or pxYf\OY¡, the proportion of money national income invested will remain unaffected by the progress of inflation. Thus we follow along a straight line from the origin through plt to get a total money investment, induced and autonomous, schedule, I m -+• A/m. The average (and marginal) propensity to invest out of inflated money income is the same as that of constant fullemployment real income. As for the ES'm line, it is the money savings schedule whose slope is larger than that of the real savings schedule, Sm = 7m, on the assumption that higher prices beyond Yf have the effect of redistributing real income in favour of profit-takers who generally have a high marginal propensity to save. This deviation from the Sm — Im may be represented by an aggregate marginal propensity to save out of money income, or s' = 1 —

THE

DYNAMICS

OF

INFLATION

135

a' = Δ5,ηι/(Δ/>) Yj. Such a marginal propensity to save is implicit in the price super-multiplier equation (4) and explicit in the larger slope of the money savings schedule S'm. I f the desire to save depended on real income alone, that is, if it were unaffected by redistribution effects of higher money income and prices on, e.g., profit-takers and wage-earners with different marginal propensities to save, the slope of the S'm curve would be the same as that of the Sm = Im line which in turn equals that of the O E line. T h e marginal propensity to invest (before the autonomous investment) at Y}, or the slope of OE, is the same as that at any level of Ym, or the slope of the Sm = Im, that is, when the desire to invest depends on real income alone. If prices are permitted to exercise their redistribution influence on the propensity to invest, the result will be quite different, as shown later. T h e main point to be stressed is that the money savings schedule intersects the induced plus autonomous money investment schedule at E ' to generate equilibrium money income Ym. T h e cumulative upward movement of money income and prices follows along the dotted 45 o and vertical lines between the Im + AIm and S'm curves, since the vertical excess of investment over intended savings for each period causes the income of the next period to increase proportionately. T h e cumulative movement, however, is terminated at E ' corresponding to Ym, where the money value of savings equals the money value of investment. N e w equilibrium money income Ym may be thought of as the resultant of 1 + (a' + b') + (a' + δ') 2 + ...+(

THE

DYNAMICS

OF

INFLATION

137

As to the interpretation of Table 9. The model is initially in a full-employment equilibrium. At time o, since P(t) = 100 (base period index), full-employment real consumption, investment, savings, and income have the same magnitudes as money consumption, etc. The initial equilibrium position is characterized by the condition 7m = Sm, or 20 = 20. After the appearance of a constant real investment of 10, the model is disturbed into disequilibrium, since investment thereby exceeds intended savings. At time 1, after the investment change, there are no reactions on consumption and investment as there was no prior increment of income to induce consumption and investment. Accordingly the money income of time 1 is increased by an amount equal to the constant investment, or by 10. The money value of total investment at time 1 is therefore increased to 30, while that of total savings remains 20. As explained before, the total money income of time 1 exceeds that of the base period by an amount exactly equal to the excess of money investment over money savings. The final result is a proportional increase in the average price, that is, proportional to the above increment of money income. Thus P{t) at time 1 reads 110. At time 2, money consumption is increased by 5, since the marginal propensity to consume is 0-5; money savings increased by 5, since the marginal propensity to save is also 0-5; induced money investment is increased by 4, since the marginal propensity to invest is 0 4; hence money income is increased by 9 (see definition below Table 9). Consequently total consumption is increased to 85, total savings to 25, total investment to 44, and total income to 129. It is to be noticed again that this increment of total money income at time 2 equals the excess of investment over savings from time 1 to time 2. The relevant result is the increase of the average price to 1-19. Money income and general prices will keep on rising as long as savings fall short of investment in each discrete period. At time n, however, the limit of expansion is reached, since enough money savings have been generated to offset money investment. The total money income of this finite period equals all prior increments of income plus the initial equilibrium income, which is exactly equal to the price-multiplier [kp = 1/(1 — 0-5 — 0-4) = 10] times the constant investment plus

138

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

the initial constant income, or 200 = 10 χ 10 + 100. Since the total increment of money i n c o m e is 100 (10 χ i o ) and since a = 0-5, the total consumption of this period equals the summation of all prior increments o f consumption plus the initial consumption, or 130 = 50 + 80. It follows that the total savings of the period is 70. Since the marginal propensity to invest is 0 4 and since all the increments of investment amount to 40(100 χ 0 4), the total investment of the nth period equals constant autonomous investment of 10 plus initial investment of 20 plus the increments of investment of 40, or 70. T h e net result of all this is that the average price has doubled from 1 ·οο to 2ΌΟ. Nevertheless, it should be noticed that the average price has been increasing at a declining rate of ο · ι ο , 0-09, 0 08, 0-07, . . ., o-oo. F r o m the above analysis it can be laid d o w n that the stability condition of equilibrium in a full-employment economy is

1

_

ACM

AIM

(δρ) rf > (AP)

rf

o r

ASM (AP) rf >

A/M (AP) rf '

In other words, unless the marginal propensity to save out of money income exceeds the marginal propensity to invest out of money income, there will be no stable determination of m o n e y income and general prices in a full-employment economy. T h a t the marginal propensity to save far exceeds the marginal propensity to invest in Fig. 24 presupposes Keynes's normal law of consumption asserting itself eventually, no matter h o w m u c h the marginal propensity to consume m a y deviate f r o m the normal level from one multiplier period to another. T h i s m a y mean, as a first approximation, that rising prices redistribute real income against wage-earners w h o do most of the total consuming in favour of profit-takers w h o do most of the total saving. T h e usual inference that therefore money wages should be stabilized while allowing prices to increase abstracts f r o m the possible reactions of a redistribution of real income in favour of profit-takers on the marginal propensity to invest. W h e n such reactions are taken into account, the d y n a m i c behaviour of money income and prices will be very different from that w h i c h is shown in Fig. 24, as will be discussed in the subsequent limiting case of 'out-and-out inflation'.

THE

DYNAMICS

HYPERINFLATION

OF

AND

INFLATION

FORCED

I39

SAVING

T o complete our story of inflation, let us consider (1) the limiting case of hyperinflation and (2) forced saving. The first of these is due to the abnormal behaviour of the marginal propensity to consume or to invest, while the second is a ramification of credit inflation in conditions of full employment. Hyperinflation That 'range of instability' which Keynes hinted as the limiting case may prove wide and long enough to warrant a serious consideration, especially as most economies today are likely to maintain full employment by design or by accident and as some of them are disposed to operate on the principle that 'all is for the best in the best of all possible worlds provided we will let well enough alone'. Indeed postwar experience is replete with examples of 'out-and-out inflation'. If the reasonable stability of the value of money, which is a prerequisite of the smooth functioning of a money economy, is to be maintained, contemplations of explosive inflation would serve to emphasize anti-inflation 'operationalism' along the lines suggested by Keynes's How to Pay for the War. Policy considerations aside, let us look into the theoretical possibility of hyperinflation. We may distinguish between hyperinflation due to a marginal propensity to consume of unity or greater than unity and that due to a marginal propensity to invest exceeding a marginal propensity to save. As for the first case, various explanations may be offered to account for the abnormal behaviour of consumers, such as income redistribution in favour of wageearners, progressive tax rates, aggressive trade-union action, the 'money illusion' produced by large paper gains, and liberal dividend payments. As for the second case, income redistribution in favour of profit-takers, errors of entrepreneurial optimism concerning the marginal efficiency of capital, the 'money illusion' generated by rising money profits, regressive tax rates, and the expectation of continued inflationary pressures may account for an exceptionally high marginal propensity to invest out of inflated money income, at least for a while until disillusionment with the over-accumulated inventories or

I4O

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

o v e r - e x p a n d e d p l a n t a n d e q u i p m e n t sets in. F i g u r e 25 illustrates the l i m i t i n g case. I n F i g . 25(A), c o n s u m p t i o n a n d i n v e s t m e n t are m e a s u r e d vertically a n d i n c o m e is m e a s u r e d horizontally. Fulle m p l o y m e n t e q u i l i b r i u m real i n c o m e Yf is g i v e n b y the intersection o f the real c o n s u m p t i o n plus i n v e s t m e n t c u r v e , Cr + Δ/ Γ , w i t h the 45 o line. N o w suppose t h a t the m a r g i n a l propensity to c o n s u m e o u t o f m o n e y i n c o m e b e c o m e s g r e a t e r t h a n u n i t y for s u c h reasons as m e n t i o n e d a b o v e . S u c h c o n s u m e r beh a v i o u r is represented b y the m o n e y c o n s u m p t i o n schedule Cm

(A)

(SI

w h i c h cuts the 45 o line f r o m b e l o w . T h i s is t h e schedule on w h i c h a constant s t r e a m o f a u t o n o m o u s real i n v e s t m e n t , Alr, m u s t be superimposed, thus g i v i n g rise to the m o n e y c o n s u m p tion plus m o n e y i n v e s t m e n t schedule, Cm f AIm. W i t h the a p p e a r a n c e o f a u t o n o m o u s investment I r , the system is t h r o w n into disequilibrium. A s a c o n s e q u e n c e m o n e y i n c o m e e x p a n d s indefinitely, a n d general prices w i t h it. N o t i c e that there is a h o r i z o n t a l i n c r e m e n t of m o n e y i n c o m e b y an a m o u n t e q u a l to a vertical i n c r e m e n t o f c o n s u m p t i o n , as e x p l a i n e d earlier. Since the investment multiplier is n e g a t i v e in this case, there can be n o stable m o n e y i n c o m e d e t e r m i n a t i o n for this system. E c o n o m i c m a n is b o u n d to e x p e r i e n c e a n 'explosive' or 'sky's-thel i m i t ' i n f l a t i o n — u n l e s s some artificial brake is a p p l i e d from

THE

DYNAMICS

OF

INFLATION

I4I

without (e.g., the inelasticity of money supply). Thus Fig. 25(A) shows the possibility that even if induced investment is completely absent, a marginal propensity to consume of greater than unity will produce hyperinflation, given an initiating inflationary shock. If an actual economy is spared this kind of hyperinflation, it means, among other things, that consumer behaviour obeys the normal law of consumption, ο < a < i. Figure 25(B) is the same as Fig. 24 except that the marginal propensity to invest out of inflated money income exceeds that out of constant full-employment real income for abovementioned reasons, while the marginal propensity to save out of both money and real income remains identical. Thus the money investment schedule, after the inflationary shock, is shifted to the position of I' m . Accordingly the induced plus autonomous money investment schedule now is / ' „ + AImy not I m + ΔI m (the distance between the /' m + ΔI m and I m + Alm lines must be equal to that between the I'm and Sm = Im lines at all levels of Ym). It is evident from Fig. 25(B) that the expansion of money income and prices has no upper limit for the simple reason that there is no 'leakage' in this system. For a marginal propensity to invest exceeding a marginal propensity to save signifies that businessmen pour back into the income stream more than what consumers let leak into savings. If entrepreneurial behaviour is of this sort in an actual economy, money profits may have to be stabilized to discourage an excessive desire to invest, along with money wages to keep the propensity to consume under control. Forced Saving In a full-employment economy the quantity theory of money comes of age, even as Keynes remarked that 'when there is full employment, prices will change in the same proportion as the quantity of money'. 1 This is because an increase in the quantity of money, insofar as it increases effective demand, fully spends itself on a proportionate increase in prices when output is no longer expansible. It is in this connexion that 'forced saving' may be fruitfully discussed. T h e following analysis will show some peculiar modern 'twists' to the neoclassical notion of 'forced saving'. 1

General Theory, p. 296.

I42

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

The sequence involved in forced saving is this: The fullemployment inelasticity of output is our starting-point. Let there be bank credit expansion for whatever purpose (e.g., to finance investment or consumption). Excess demand so financed relatively to the fixed amount of goods and services inevitably bids up general prices. Now a rise in general prices leads to a fall in the real income of fixed-income groups and hence to a decline in their real consumption. Total savings will increase if the credit-stimulated rise of prices significantly shifts real income against fixed-income groups (esp. rentiers) in favour of flexible-income groups (esp. equity holders), and if the latter have a higher propensity to save than the former. For in these circumstances fixed-income groups are likely to constrain their demand for consumer-goods, that is, to increase 'forced saving', even though they will themselves experience a reduction in their own real savings. In this way additional resources can be made available to the capital-goods industries, though there are many alternative ways to accomplish the same aim (e.g., capital formation financed by taxation or by undistributed business profits, compulsory pay-roll savings, and priority resource allocations). Such is the traditional explanation of the way inflation makes more 'capitalistic' (roundabout) production possible, quite apart from voluntary saving associated with the increase of income. There are some interesting implications of forced saving that may be pointed out below. First, in the postwar condition of general capital scarcities (i.e., in the war-devastated countries) the expansion of bank credit at full employment actually had the effect of 'reconstructing' the capital-goods industries at the expense of the consumergoods industries via forced saving. Japan was a typical case in point. 1 T o the extent, however, that fixed-income groups succeed in improving their real income position, they will be less constrained to save. In this case voluntary saving will have to be relied upon for shifting employed resources from the consumer-goods industries to the capital-goods industries. In some less developed economies 'development through inflation' has found popular expression on the theory that 'inflationary development financing' (via government deficits) 1 See, e.g., S. Tsuru, ' T h e Examination of the Gross National Product: Estimates of Postwar Japan', Hitolsubashi University Economic Review, October 1951.

THE

DYNAMICS

OF

INFLATION

I43

would not only squeeze 'forced saving' out of those economies but also provide the 'money illusion' necessary to stimulate investment activity. 1 Apart from the difficulties that such a method of 'development' may generate in a less developed economy's balance of payments position (i.e., inflated export prices as well as a diversion of resources from the export industry), there seems to be little doubt that, at least in the short run, 'forced saving' via inflationary credit expansion does have a favourable effect on industrialization and capital development in less developed economies. Lastly, the marginal propensity to invest may rise to an unusual height, not only because resources are made available to the capital-goods industries at the expense of the consumergoods industries, but because the very inflationary method of effecting 'forced saving' at full employment keeps money profits rising with prices. If this happens, the stabilizing influence of forced saving on the community's propensity to consume may be considerably offset by the destabilizing effect of the accompanying 'money illusion' on the inducement to invest. Thus the argument that rising profits increase the marginal propensity to save so as eventually to set an upper limit to inflation must abstract from, among others, the above destabilizing influence of increasing money profits on the marginal propensity to invest.

1 Cf. H. C . Wallich, 'Underdeveloped Countries and the International Monetary Mechanism', in Money, Trade, and Economic Growth ; Ε. M . Bernstein and I. G . Patel 'Inflation in Relation to Economic Development', International Monetary Fund Staff Papers, November 1952.

Chapter 9 INCOME, EMPLOYMENT AND INTERNATIONAL EQUILIBRIUM chapter is primarily concerned with the behaviour of national income in an open system with less than full employment, and secondarily with the repercussions of national income fluctuations upon international equilibrium. T h e modern income approach is an indispensable supplement to the familiar classical price approach to international trade, for the former explains international equilibrium adjustments in terms of relative income movements on the assumption of variable employment and the latter in terms of relative price-cost movements on the assumption of full employment. Much, however, remains yet to be refined and developed in this field,1 if we are, in the words of Keynes, 'to use what we have learnt from modern experience and modern analysis, not to defeat, but to implement, the wisdom of A d a m Smith'. 2 THIS

DOMESTIC

EMPLOYMENT

AND

FOREIGN

TRADE

Ά willing and unimpeded exchange of goods and services in conditions to mutual advantage' will become possible only when international trade ceases to be 'a desperate expedient to maintain employment at home by forcing sales on foreign markets and restricting purchases'. 3 In these words Keynes strikes home to us a fundamental conflict between domestic 1 O n Keynes's influence on modern international trade theory see S. E. Harris, 'International Economics: Introduction' and R . Nurkse, 'Domestic and International Equilibrium', in The New Economics; L. A . Metzler, 'The Theory of International Trade', in A Survey of Contemporary Economics; also Κ . K . Kurihara, Monetary Theory and Public Policy, Part 3. For early applications of the income approach see J. Robinson, Essays in the Theory of Employment, Macmillan, London, 1937; R . F. Harrod, International Economics, London 1939; F. Machlup, International Trade and National Income Multiplier, Blakiston, Philadelphia, 1943. The most epitomic of all in recent years is the United Nations' National and International Measures for Full Employment. * Keynes's speech before the House of Lords, 18 December 1945. 3 Keynes, General Theory, pp. 382-3.

144

INCOME, EMPLOYMENT, INTERNATIONAL EQUILIBRIUM

I45

employment and foreign trade. An understanding of this conflict is essential to the present analysis. In a classical world of full employment there is perfect harmony between domestic employment and foreign trade for the simple reason that foreign trade in that world is only a medium through which the optimum allocation of the product of fullyemployed world resources is effected. In such a world price adjustments (money wages, export-import prices, interest rates, and exchange rates) are what brings about equilibrium in international balances of payments without affecting income and employment which are taken as given. This does not of course mean that income and employment do not change as a result of price adjustments; rather that on the classical assumption of full employment it is unnecessary to take into account the consequences of fluctuations in income and employment. On this assumption the only thing that matters is the most efficient allocation of the product resulting from the employment of a given quantity of world resources. And the pricing mechanism is what does the allocating in the international field as it is in the domestic field with full employment. Thus it is logically consistent to insist that the main business of the economist in the international field is to demonstrate how 'the wealth of nations' can be enhanced through the international division of labour based on comparative advantage. With each and every nation enjoying full employment, it is obvious that the world would be materially benefited by letting each produce and trade with others those goods and services which each could manufacture to better advantage. This of course is the celebrated doctrine of comparative advantage, which R. F. Harrod rightly reminds us as being 'never out of date and never to be despised'.1 It is to be feared, however, that in the context of an under-employment world or of an underdeveloped economy the principle of comparative advantage cannot and will not be embraced as so dear an 'old friend' as some would like to see. Apropos, the authors of the United Nations' National and International Measures for Full Employment 'knew that the theory of comparative costs did not apply in a country where there was a hypothetical reserve of unemployed 1

Κ

Sec his Dynamit Economici, p. 109.

I46

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

labour capable of undertaking any competitive production'. 1 If an 'open economy' (i.e., an economy in the analysis of which exports, imports, and other foreign-trade quantities are introduced as explicit variables) is confronted with domestic unemployment, it is but natural that it should try to export unemployment by producing anything, regardless of comparative costs, just to provide more jobs and by 'forcing sales on foreign markets', if possible. Similarly, if an underdeveloped economy is bent on industrialization, it is not unnatural that it should try to 'protect' indigenous capital-goods industries, however inefficient, by means of tariff and exchange-rate manipulations (e.g., multiple exchange rates). These remarks are not of course a justification of international attempts at discriminatory trade practices and beggar-myneighbour policies, rather a painful recognition of the fundamental conflict between domestic full employment and international 'free trade'. Keynes was among the first to recognize this stark contradiction, for he rebelled against the international gold standard on the ground that it involved the whole world in 'a competitive campaign of deflation, each of us trying to get our prices down faster than the others, a campaign which had intensified unemployment and business losses to an unendurable pitch'. 2 It is not necessary here to explain the well-known 'specie-flow-price mechanism' in order to show how inadequate it is in a world of mass unemployment and depression. Suffice it to observe that for the first time in the history of international economic thinking the classical theory of free trade based on international specialization was challenged as untenable in an under-employment world and its equilibrating mechanism in the form of an international gold standard as utterly inappropriate to a generally contracting world economy. In this challenge Keynes was supported by the course of events that followed the World War I. For nations plagued with domestic unemployment were all disposed to disregard comparative advantage by producing anything and everything within national borders if for no other reason than to increase domestic employment. 1 Cf. United Nations' Economic and Social Council, Official Records (358th Meeting, 21 February 1950), p. ιοο. * Persuasion, p. 293.

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This bit of historical digression serves to emphasize the fact that the goal of free trade, while it is, in the words of Keynes, 'the only policy which is technically sound and intellectually right... in the long run and in general', 1 is difficult of realization so long as the majority of trading nations have unemployment. Keynes sounded the keynote of a future compatibility of domestic full employment with international equilibrium when he advocated 'the simultaneous pursuit' of measures to maintain domestic full employment and expanding world trade 'by all countries together' so that 'economic health and strength, whether we measure it by the level of domestic employment or by the volume of international trade', might be restored.* With the above as the background, we shall be in a better position to understand the economic significance of the foreigntrade multiplier which follows. 3

THE

MULTIPLIER

IN

AN

OPEN

ECONOMY

The foreign-trade multiplier analysis is designed to show the probable effects on national income and employment of changes in an open economy's foreign trade position during a period of less than full employment. T o isolate such effects, it is customary to assume all prices (commodity prices, wages, interest rates, exchange rates, &c.) to be given, as implied in the above qualifying phrase 'less than full employment'. We shall compare the static and dynamic foreign-trade multipliers as well as the ordinary and 'super' multipliers in due course. Let us begin with a preliminary survey of the relevant factors affecting the Op. cit., p. 326. • General Theory, p. 349. Coincidentally we find the following significant statements by the United Nations' experts: " . . . failure to maintain economic prosperity in one part of the world makes it more difficult to pursue policies aimed at economic expansion in other parts; and may, in addition, force other countries to adopt restrictionist measures in international trade, which react unfavourably on the prosperity of the countries whose exports are thereby reduced. The pursuit of policies aiming at economic prosperity and stability is consistent with a relatively free system of international trade only if, in pursuing full-employment policies, all countries keep in step, so that the efforts of some are not frustrated by the failure of others.' (See National and International Measures for Full Employment, p. 29.) ' Cf. Machlup, op. cit. ; D. H. Robertson, 'Mr. Clark and the Foreign Trade Multiplier', Economic Journal, June 1939; J. £. Meade, 'National Income, National Expenditure and the Balance of Payments', Economic Journal, December 1948. 1

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foreign-trade multiplier process, namely, (1) autonomous exports, AE, (2) a marginal propensity to import, AM/AT, and (3) a marginal propensity to save, AS/AT. The Export Multiplier As for the first of these factors, AE, it is an exogenously given parameter whose value is subject to change pari passu with alterations in foreign countries' tastes, needs, abilities and policies. Concretely, AE refers to any autonomous increase in exports in terms of money, that is, sale-proceeds from exports of merchandise and services on current account. As such, AE is in the nature of an 'injection' into the domestic income stream, otherwise known as a 'multiplicand'. Formally AE has the same stimulating or magnifying effect on an open economy's domestic income as extra domestic investment, AI, has on that of a closed economy (opposite of an open economy explained earlier, where the income system is considered 'closed' by abstracting from foreign-trade influences on its behaviour, as might be justified in the case of a highly self-sufficient economy). The second factor, AM ¡AT, is in the nature of a 'leakage', since it means that there is always a certain fraction of extra domestic income going to purchases of imports and therefore out of the domestic income stream. Accordingly a marginal propensity to import is in the same category as a marginal propensity to save. The marginal propensity to import of any particular economy is larger or smaller, 1 depending on its tariff structure, its degree of self-sufficiency, relative prices of domestic vis-à-vis foreign goods, import control, tastes, and perhaps other influences. Whatever the actual value of AM J AT may be, the extent of domestic income expansion due to new exports will be limited in part by this coefficient being positive. The last factor, AS/AT, is an old timer, but it must be reinterpreted in the present connexion. To be sure, AS/AT is an additional 'leakage' or a damping-down factor in the foreigntrade multiplier process, but it is not the inverse of the marginal propensity to consume in the usual sense of this latter term. For 1 For rough estimates see T . C. Chang, 'International Comparison of the Demand for Imports', Review of Economic Studies, 1945-46, and Ά Statistical Note on World Demand for Exports', Review of Economics and Statistics, M a y 1948. H b figure for America's AAf/AT"is 0-07, which is far smaller than the figures for other countries.

INCOME, E M P L O Y M E N T ,

INTERNATIONAL

EQUILIBRIUM

149

the marginal propensity to consume, AC/AT, in the present context refers to consumption of domestically produced goods or, for brevity, domestic goods. Hence its inverse (i — AC/AT) equals the marginal propensity to save plus the marginal propensity to import (AS/AT + AM/AT). This is on the assumption that any extra domestic income is spent partly on domestic goods and partly on imports and then saved. In other words, a marginal propensity to import plus a marginal propensity to save plus a marginal propensity to consume domestic goods equals unity. By denoting AM ¡AT and AS/AT respectively by m and s, we can derive a foreign-trade or export multiplier coefficient from AT AÉ

=

kf =

ι i_ ι - a = m +s '

where kf stands for the foreign-trade or export multiplier and a for the marginal propensity to consume domestic goods. We are tacitly assuming that all imports are consumer-goods and that exports include such invisible incomes as net interest and dividends from abroad, so that the income governing AC, and AM, as in Τ = (C 4 M) 4-/ + (/?— M) may approximate the income governing the employment of an open system, as in Τ = C + / + E. Ignoring lags for the moment, we have a final increment of income due to an increment of exports in a given period, or AT = — L m+ j = kfAE

=

Î χ $i = $2.50, 0 - 1 + 0-3

=2-5 χ $1

= $2.50,

for m • 0 1 , s — 0-3, and AE = $1. Thus for every $1 of new exports there will be $2.50 of additional domestic income, given the multiplier of 2 5. The smaller the combined 'leakage' is, the larger will be the foreigntrade multiplier and the larger also will be the increment of domestic national income relatively to a given increase in exports. This implies that an open system whose marginal propensity to import is high should not, cet. par., expect a greatly magnified income as a result of an increase in its exports. Let us now dynamize our foreign-trade multiplier analysis.

I50

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

Dynamic Foreign-Trade Multiplier For purposes of dynamic analysis we shall regard consumption, savings and imports as depending on previous income, investment and exports as constant functions of time, and the marginal propensities to consume and to import as constants. Specifically we may define r,=ct+it+Et,

(0

where Tt is domestic national income at time t, Ct consumption of domestic goods at time t, / , domestic investment at time t, and Ε, exports at time t. Imports and savings are implicit in thi» equation since Yt—Ct=It+Et = St + Mt, where St is domestic savings at time t and Mt imports at time t. In other words, domestic investment plus exports must in equilibrium equal domestic savings plus imports. ct = a{Yt_1 - r0) + C0,

(2)

where a is the marginal propensity to consume domestic goods, T,_1 previous income, T0 initial income, C0 initial consumption of domestic goods, and Ti_l — Y„ previous income in excess of the initial income. By substitution, we have the dynamic foreign-trade multiplier form r, = « ( * · , _ , -

r 0 ) + c 0 + / , + Et.

(3)

For certain arbitrary values of a, s, and AE, and designating the discrete increment of income, Τ — T0, as y{x) and the autonomous increase of exports, AE, as AE, the geometric progression over time is A o) = MO = ΔΕ, jr(9) = ΔΕ + JAË = = (. + *)ΔΕ A3) - [" + i + (έ) ι ]ΔΕ

[' + i + (i)' + · · • + (Ι)"]ΔΕ

$ι + $0.50 = = (i + J) X $I = $1.50, (ι + ο·5 + 0-25) χ $ι = $1.75, (ι + 0-5 + 0-35 + . . .) X $1 I I - 05 X $1 = $2.00

Thus we can see that $ 1 of new exports leads to an eventual increase of national income 2 times as much as that initial $1, or $2, given the marginal propensity to consume of 0-5, the

INCOME,

EMPLOYMENT,

INTERNATIONAL

EQUILIBRIUM

I5I

marginal propensity to import of ο· ι, and the marginal propensity to save of 0-4. If the latter two coefficients were smaller than assumed here, the combined 'leakage' would be correspondingly smaller, to yield a larger multiplier and so to generate a larger increment of domestic national income. With the above definitions and assumptions in mind, let us analyse the dynamic behaviour of domestic national income in terms of the specific model of Fig. 26. (a = 0-5, m = ο·ι, s = 0 4, kf = 2) C,I,E

In Fig. 26 the vertical axis measures consumption, investment, and exports in real terms, while the horizontal axis measures income also in real terms. T h e C curve represents the consumption function of an open economy and has a constant slope of 0 5 according to a = 0 5. The vertical distance between the C curve and the 45 o line (indicated by shading) therefore measures savings plus import leakage. We are assuming a marginal propensity to consume of 0-5, a marginal propensity to import of o-i, and a marginal propensity to save of 0-4 for this system. The C + I + E curve represents a consumption plus autonomous investment plus exports schedule, and its intersection with the 45 o line at point E determines the initial value of equilibrium income T0. With the appearance of a constant stream of autonomous exports (possibly as a result of changes in other countries' import policies) equal to ΔΕ, the

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INTRODUCTION

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KEYNESIAN

DYNAMICS

open system is disturbed into disequilibrium. T h e constant amount of exports is superimposed on the old C + / + E curve so that the total 'demand' schedule of the economy now is shifted to the position of C + 1 + E + AE. Let us trace the discrete change of income after the disturbance. In period o, before the export change, the system was in equilibrium, since total savings plus imports were equal to total investment plus exports, as can be seen from the equality of the distance between the C + / + E curve and the C curve measuring investment plus exports and the distance between the 45 0 line and the C curve measuring savings plus imports—corresponding to equilibrium income Y0. After the export change, however, the system can no longer remain in equilibrium, since investment plus exports now exceeds intended savings plus imports by an amount equal to Ais. If AE = $1, the income of period ι is increased by $1. Thereafter income is increased by $0-50, $0 25, and so on in a dwindling series. At each round $ of the extra income earned leaks into savings and out as imports, since s = 0 4 and m = ο·ι. Income keeps on expanding as long as there is a vertical gap between the C + / + E +AE curve and the 45 0 line to be wiped out. Thus we can see that there is an equal horizontal increment of income (e.g.,^/,) for each vertical excess of investment plus exports over intended savings plus imports (e.g., yxE). From this analysis follows the theorem that the income of each discrete multiplier period in an open system is increased by an amount exactly equal to the excess of investment plus exports over intended savings plus imports out ofprevious income. The cumulative expansion of income comes to a halt when sufficient savings and imports have been generated to oflset investment plus exports. The intersection of the C + / + E + AE curve with the 45 0 line at point E' determines new equilibrium income T n . At this new level of income total intended investment plus exports equals total intended savings plus imports (the vertical distance between the 45 o line and the C curve measuring savings plus imports exactly equals that between the C + / + E + AE curve and the C curve measuring investment plus exports). This outcome conforms to equation (1), or r , = Ct + It + Et and hence Yt - Ct = It + Et = St + Mt, which will be remembered as the approximate dynamization of static equation Τ = (C + M) + / + ( £ — M)

INCOME, EMPLOYMENT, INTERNATIONAL EQUILIBRIUM

153

on the specified assumptions. Notice that the horizontal distance between Tt and Tu is twice as great as the vertical length since the multiplier involved is 1/(1 — 0-5), or 2. T h e total income of the nth period, OT n , equals initial constant income OT0 plus the sum total of all the succeeding increments of income. Another point to be noticed is that the system, once disturbed into disequilibrium, converges to a new equilibrium, owing to our assumption of o < a < 1. Were it not for this assumption, there will be divergence from equilibrium. 1 INDUCED

IMPORTS,

INTERNATIONAL

INVESTMENT,

AND

EQUILIBRIUM

Thus far we have only considered the effects of foreign trade on domestic income and employment, but we must now shift our attention to the possible repercussions of domestic income change on international equilibrium. First, we shall consider the relation of induced imports to international equilibrium on the assumption that induced investment at home is zero. Second, we shall introduce induced investment to see what difference it makes to international equilibrium. Induced Imports and International Equilibrium By 'induced imports' we may understand an increment of imports corresponding to a given marginal propensity to import out of an export-generated increment of domestic income. Let AM - increment of imports, AT = increment of income, and AE = increment of exports. Further, let a = ο·6, m = 0 1 , and s = 0-3. Then we can write for AT and AM respectively, when AE = $1 AT --

1 AE = — 1 χ Si = $2.50, ι —α ι — 0-6 ι Δ Μ = mAT = m AE = 0 1 χ 2-5 χ $ι = $0 25, ι —a

=

m ο· ι AE = — χ $1 = $0.25. ι —a 0-4

1 Such a case of unstable equilibrium is conceived i n j . E. Meade, op. cit. For the general problem of stability conditions in an open economy at less than full employment see L. A . Meteler, 'Underemployment Equilibrium in International Trade', Econometrica, April 1942.

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DYNAMICS

This means that Si of new exports has increased domestic income by $2.50, that $2.50 of increased domestic income has in turn induced $0.25 of imports, and that $0.25 of imports has compensated for $1 of initial exports. Thus only J of our original $ ι-exports is recouped by other countries through our induced imports. To put it differently, we compensate for other countries' loss of $1 to us by letting them gain $0-25 through subsequent exports to us. From our standpoint this is a satisfactory state of affairs, since we have ended up with a positive balance of $0.75. But from the standpoint of international equilibrium it is rather regrettable, since the rest of the world has ended up with a negative balance of $0.75. Equilibrium in the international balance of payments will not be attained unless we increase autonomous imports (in contradistinction to induced imports) by reducing our tariffs, by shifting our demand from domestic to foreign goods, &c., irrespective of domestic income change or unless the rest of the world decreases its current imports from us through import quotas, increased tariffs, exchange control, &c. The result is a worldwide shrinkage of trade. Worse yet, a negative balance will give rise to the reverse operation of the foreign-trade multiplier in the rest of the world, only to intensify its desperate attempt to 'export' unemployment to us. Now the pertinent question to ask is why our induced imports amount to only J of one unit of our exports to the rest of the world, to begin with. Why is not an increment of imports, ΔΜ, as large as or greater than an increment of exports, AE, so that the international accounts may be balanced or temporarily overbalanced? The answer is that when and where the marginal propensity to save is positive, an open economy's induced imports are always smaller than the initial exports. This theorem is based on the assumption that induced investment is zero. On this assumption there is no escape from the conclusion that we cannot count upon induced imports for fully compensating for our exports. Thus it is believed by some writers that the importance of income effects in achieving equilibrium in the international balance of payments has been overstressed. Before turning to a criticism of the above assumption, let us test the logical validity of the theorem. Let a + m + s = ι, so that 1 — a = m + s. We shall take

INCOME, EMPLOYMENT, INTERNATIONAL EQUILIBRIUM

155

up three cases where s > o, s = o and s < o. Only for the first case of s > o does it follow that AM < AE. For we have AM = hence where s > o, '

m m AE = —,—AE, ι —a m + s — — < ι. m + s

and

AM < AE.

If we assume, for example, that a = ο·6, m = ο·ι, s ~ 0-3, and AE = i, we have AM =

ο·ι ο·ι τ. — - 0-25. ι — ο·6 ο·ι + ο·3

Thus the conclusion is inevitable that where the marginal propensity to save is positive, s > o, the increment of imports, AM, is necessarily smaller than the increment of exports, AE. Since the marginal propensity to save is certainly positive in most modern communities, the presumption is against AM = 1, when AE — 1. The point is that if and when an open system possesses a positive marginal propensity to save so as to permit some fraction of an increment of domestic income to leak into domestic savings, $1 of exports cannot, cet. par., magnify domestic income (via the foreign-trade multiplier) sufficiently to induce $1 of further imports—to contribute toward smooth adjustments in the international balance of payments. For the second case, where s = o, AM =

m m AE = —--AE ι —a m + s

m _ = -AE = AE. m

If we take for illustration a = 0-9, m = ο·ι, AE = ι , 1—0-9

s = o, and

o-i + o

Thus if all trading countries had a marginal propensity to save of zero and if induced investment were completely absent, an export-generated income would induce imports exactly proportional to the initial value of exports, thereby balancing the international payments all around. The fact that some countries experience a persistent disequilibrium in their balances of

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INTRODUCTION

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KEYNESIAN

DYNAMICS

payments is indicative of some other countries having marginal propensity to save which is positive, s > o. Lastly, let us take up the case of s < 0 . Again we have AM =

m ι — a

AE =

a

m ——AE. m + s

But now where s < o, m + s > ι, and AM > AE. If we assume that a --- 0-9, m = ο·2, and s = —ο·ι, so that 0-9 + ο·2 — ο·ι = ι and 1 — 0-9 = ο·2 — ο·ι, then when A E = ι the induced imports are AM =

0-2 0-2 — = — > 0*2 — o-i O-I

ι.

Thus when the marginal propensity to save is negative, induced imports will exceed the initial increment of exports. This is obviously a case of'overcompensation'. If the United States could be supposed to have a negative marginal propensity to save, other things equal, the third case would signify a chronic dollar excess in the rest of the world. Conversely, if the rest of the world had a negative marginal propensity to save, the third case would, cet. par., mean a chronic 'dollar shortage' in the rest of the world and a chronic surplus in the American balance of payments. Actually the problem of 'dollar shortage' is not of course as simple as our theorem would indicate, since the marginal propensity to save does not remain constantly negative, if at all, and since other things do not remain equal. 1 Let us therefore turn to a case where AM > AE can occur even though the marginal propensity to save is positive. Induced Investment and International Equilibrium Domestic investment may be 'induced' by a favourable change in domestic income resulting from an increment of exports. Some writers seem to dismiss the possibility of such induced investment on the grounds that there may be unused capacity in the export industry and that a secular tendency to underinvest may exist.1 Unused capacity, however, is known to disappear in the later stage of the upswing. Moreover, 1 Cf. T . Balogh, The Dollar Cruis, Oxford, 1949; C . P. Kindleberger, The Dollar Shortage, John Wiley, N.Y., «950. * E.g., Kindleberger, op. cit., p. 99.

INCOME, EMPLOYMENT, INTERNATIONAL EQUILIBRIUM

I57

expectations and other variables will have to be taken into consideration before making a conclusive argument about the absence of induced investment. Induced investment, I(Y), must be taken into account (a) when entrepreneurs make investment decisions according to current and projected national income trends, (A) when aggregate demand is expected to continue increasing 'permanently', and (c) when the economy is underequipped for one reason or another relatively to current and expected aggregate demand. Under these circumstances the marginal propensity to invest is likely to be positive, dljdT > o. Induced investment may make a significant difference not only to the foreign-trade multiplier but also to international equilibrium. Denoting dI[dT as b and assuming ι — a = m + s, we may express a sort of 'super-multiplier' as

\r __

ι

ι

AE ~ m + s — b

~ m + s —b

If m = 0-3, s = o-i, b = 0-3, and AE = $i, an autonomous rise in exports will increase domestic national income by τ 03 + 01 - 03

χ $i = $10.

Now we know that induced imports are given by AM = m\T=—rm ,AE, m + s —b 03 χ $1 = $3. 0-3 + 0 1 - 0 3 Hence AM > AE. Thus if the marginal propensity to invest is larger than the marginal propensity to save, i.e., if b > s, the induced imports will be larger than the original increment of exports. In other words, if and when induced investment reinforces induced consumption of domestic goods (via the 'super-multiplier'), domestic national income can increase sufficiently to induce additional imports in excess of original exports—even though a fraction of any extra domestic national income always leaks into savings. Theoretically, therefore, a positive marginal propensity to save cannot be said never to induce imports larger than

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DYNAMICS

initial exports without reference to induced investment. Moreover, if our analysis is correct, the practical significance of the above demonstration is not at all hard to see: that a positive marginal propensity to save is capable of balancing or overbalancing equilibrium in the international balance of payments as well as of leading the foreign-trade multiplier expansion of domestic national income to a stable equilibrium. Even if the open system had b > (m + s) so that its income determination was unstable, there still would remain the above beneficial effect on international equilibrium.

Chapter io PRICE

FLEXIBILITY AND A U T O M A T I C FULL EMPLOYMENT

chaptcr is a digression on the controversial question of whether the pricing mechanism is theoretically capable of generating an automatic full-employment equilibrium. 1 This question is a matter of great theoretical significance and practical importance, quite apart from one's predisposition toward any particular school of thought. It is of theoretical significance because the controversy involved reveals the fundamental dichotomy between the static and dynamic schemes of economic thinking. It is of practical importance because fullemployment policy recommendations are often based on conflicting theoretical considerations. For expository convenience, we shall divide this chapter into two sections, namely, (i) wages and employment and (2) the 'Pigou effect' (otherwise known as the wealth effect) and employment.

THIS

WAGES

AND

EMPLOYMENT

Let us first consider wage flexibility as the mechanism for equilibrating the demand for and supply of labour to generate a full-employment equilibrium. 1 1 Cf. W . Leontiff, 'Postulates: Keynes's General Theory and the Classicists', in The New Economics·, J . Tobin, 'Money Wage Rates and Employment', ibid.; Keynes, General Theory, C h . 19 (including 'Appendix on Prof. Pigou's Theory of Employment') ; A . C . Pigou, Employment and Equilibrium, Macmillan, London 1941, and also 'Economic Progress in a Stable Environment', Economica, 14, 1947; D. Patinkin, 'Price Flexibility and Full Employment', American Economic Review, September 1948; O . Lange, Price Flexibility and Employment, Bloomington, Indiana, 1945; N . Kaldor, 'Prof. Pigou on Money Wages in Relation to Unemployment', Economic Journal, 47, 1937; L . R . Klein, The Keynestan Revolution, C h . 4; J. M . Clark, 'Separate Concurring Statement', in National and International Measures for Full Employment (United Nations, New York, 1949).

* Compare: 'When . . . money wages are reduced, this entails, in general, a fall in money wages relatively to prices, i.e. of real wage-rates, which makes it profitable to employers to engage more men.' (Pigou, Employment and Equilibrium, p. 81.) 'There is, therefore, no ground for the belief that a flexible wage policy is capable of maintaining a state of continuous full employment. . . . T h e economic system cannot be made self-adjusting along these lines.' (Keynes, General Theory, p. 267.)

«59

ΐ6θ

INTRODUCTION

TO

KEYNESIAN

DYNAMICS

Short-Run Classical Employment Model T h e simplest classical short-run employment model involves the following relations and assumptions: (i) the supply of labour is an increasing function of real wage-rates; (2) the demand for labour is a decreasing function of real wage-rates ; (3) there are no institutional rigidities in the labour market; (4) no changes are anticipated; (5) aggregate demand (for goods and services) remains constant; and (6) population, technology, and tastes are given. O n these definitions and assumptions, the theorem is advanced that unemployment is incompatible with equilibrium. Let us analyse this theorem in terms of the model of Fig. 27.

In Fig. 27 the vertical axis measures real wage-rates, that is, the average money wage deflated by the price level, or W/P, while the horizontal axis measures various amounts of employment, or N. The demand for labour is represented by the D curve, the shape of which indicates that more labour will be hired for lower real wage-rates, according to the law of diminishing marginal productivity. The supply of labour is represented by the S curve, the shape of which tells us that more labour will be offered for higher real wage-rates on the general principle of increasing marginal disutility (of employment), that is, by abstracting from 'income effects' (which yield a backward sloping supply curve for labour over the range of high real wagerates).

PRICE

FLEXIBILITY

AND

FULL

EMPLOYMENT

l6l

Suppose that the entire labour market is in disequilibrium at the real wage-rate of (WjP)^, so that there is unemployment equal to the horizontal distance between d and s. But then the ds amount of unemployment makes workmen bid down money wages relatively to prices to the level of ( W¡P)„, thus wiping out the excess of labour supplied over labour demanded. It can be seen that the D and S curves intersect at point E to determine full employment N 0 and that at the equilibrium or ruling real wage-rate of (JV¡P)0 the amount of labour demanded and the amount supplied are equal. N0 is full employment, since money wages are, by hypothesis, allowed to be cut relatively to prices until all those who are willing to work at the ruling real wagerate are employed. Anybody unwilling to work at that wagerate is therefore considered 'voluntarily unemployed' like members of 'the leisure class', to borrow Veblen's phrase. In brief, the demand for and supply of labour are related to real wages such that any discrepancy between the amount demanded and the amount supplied in relation to real wages tends to cause real wages to change until full employment is reached. In equilibrium, therefore, we have D{W¡P) — S(W¡P) - o and Ν = If unemployment exists, the system must be in disequilibrium, as at ( W¡P)i. Hence unemployment is considered incompatible with equilibrium. Such is a self-adjusting classical system which engenders an automatic full-employment equilibrium. If, however, an actual economy is found not so self-adjusting, it must be explained in terms of different models based on different assumptions concerning economic activities, decisions, and expectations. It is interesting to observe, in this connexion, that Keynes, while trying to rebut the classical theory of an automatic fullemployment equilibrium, finds himself involved in a rigid wage policy to prove his case of 'involuntary unemployment'. For this is what is implied in his perfectly elastic supply of labour curve at the going rate of money wages.1 His dynamic suggestions are considered a more successful answer to the classical argument, however. Many economists have come to consider it utterly illicit to assume that aggregate demand remains unaffected by money-wage reductions, especially of a general 1 General Theory, pp. 10-8. pp. 80-7.

L

See also L. R . Klein, The Keynesùm Revolution,

IÖ2

INTRODUCTION

TO K E Y N E S I A N

DYNAMICS

nature, regardless of the wage elasticity of demand for labour. This leads lis to a consideration of the possible repercussions of wage reductions on the components of aggregate demand. Repercussions of Overall Wage Reductions Keynes, while granting that money-wage reductions unaccompanied by reductions in aggregate demand will lead to an increase in total employment, nevertheless argues: 'The precise question at issue is whether the reduction in moneywages will or will not be accompanied by the same aggregate effective demand as before.' 1 Specifically, he raises the question : 'Does a reduction in money-wages have a direct tendency, cet. par., to increase employment, "cet. par." being taken to mean that the propensity to consume, the schedule of the marginal efficiency of capital and the rate of interest are the same as before?' 2 He suggests that all these other things are not likely to remain unchanged when money-wages are reduced and that aggregate demand is most likely to fall to a level short of full employment. We may outline the possible repercussions of money-wage reductions on aggregate demand, as follows. ι. A general cut in money wages will lead to some price decreases, though probably not proportionately. Consequently there will be some redistribution of real income from wageearners to non-wage-earners. Since the wage groups generally have a higher marginal propensity to consume than the nonwage groups, such a redistribution of real income will probably decrease total consumption. If a general cut in money wages is expected to be repeated over and over again, there is likely to be the anticipatory withholding of consumer demand as a matter of precaution. In other words, the savings function is 1 General 'Theory, p. 260. See also R . C . O . Matthews, ' T h e Effect of Wage-Cuts on Employment', Economic Journal, September 1951. * General Theory, p. 260. Mrs. J. Robinson offers this interpretation of the implied answer: 'It is true for any one employer, or for any one industry . . . that a cut in wages, by lowering the price of the commodity produced, will increase its sales, and so lead to an increase of employment in making it. But if all wages are cut, all prices fall, all money incomes fall, and demand is reduced as much as costs. N o one employer then has any motive to take on more men." (See her Collected Economic Papers, Augustus M . Kelley, N . Y . , 1951, p. 135·) She is well aware of course that such a simple reference to the fallacy of composition would have to be reinforced by a disaggregative analysis of the specific effects of anticipatory wage-price falls on wage-earners vis-à-vis profit-takers, rentiers vis-à-vis entrepreneurs, debtors vis-à-vis creditors, & c .

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FLEXIBILITY

AND

FULL

EMPLOYMENT

163

most likely to shift upward relatively to the investment function as real income is redistributed in favour of high savers against high consumers, to cause income and employment to decline. 2. I f money-wage reductions are expected to continue, people's liquidity-preference will probably increase, especially to satisfy the speculative motive, that is, to hold money as a 'store of wealth' against the increasing uncertainty that the deflation of wages generates. As a consequence two things may happen. First, the demand for consumer-goods is cut down in favour of the demand for money as a 'store of wealth', i.e., to save and hold a larger portion of consumer income in the form of liquid assets. In the next place, the liquidity function may become so elastic with respect to interest that the monetary authority will be unable to decrease the interest rate by varying the quantity of money, as mentioned earlier. T h e first of these possible results obviously affects the consumption function, while the second will affect the investment function to the extent that investment decisions require a favourable 'monetary atmosphere'. 3. A general wage-cut, both when repeated and unrepeated, is bound to influence the behaviour of the investment function. I f the marginal propensity to consume is normally less than unity, producers, acting on the expectation that since their own costs have been reduced by a money-wage reduction, they will be able to sell more at a larger profit, may well meet a bitter disappointment. For the sale-proceeds from the increased output and employment will be found short of the total cost of production, given a marginal propensity to consume of less than unity—unless investment can be supposed to increase by an amount equal to the absolute gap between income and consumption. Moreover, the expectation of further wage-cuts is likely to induce producers to postpone investment decisions. T h e postponement of investment in new capital-goods so caused will in turn lead to a further decrease in consumption, which will in turn aggravate deficient investment, and so on. T h e effects of all this may well be 'those of the economics of hyperdeflation and social revolution', to borrow L . R . Klein's warning phrase. 1 Such dynamic considerations as outlined above would probably make one hesitate to regard wage 1

Klein, op. cit., p.^89.

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flexibility as a deus ex machina for bringing about a state of continuous full employment. These dynamic qualifications need to be explained further in connexion with the so-called 'Pigou effect' which is discussed subsequently. Finally when the actual imperfections of the labour market due to institutional rigidities are taken into account, there may not be much left of an automatic full-employment equilibrium via wage flexibility.

THE

'PIGOU

EFFECT'

AND

EMPLOYMENT

There is yet another w a y in which price-flexibility may affect the volume of employment, namely, via a combination of flexible wages, prices, and interest rates or, in the narrower technical language of pure theorists, via the 'Pigou effect' associated with the name of A . C . Pigou. For clarity of perspective it seems fruitful to begin this part of discussion with an analysis of the classical theory of savings and investment. Interest as the Equilibrating Mechanism T h e pre-Keynesian theory of savings and investment runs roughly as follows. If the desire to save out of full-employment income exceeds the desire to invest at full employment, the rate of interest will tend to fall to diminish savings and at the same time to increase investment, with the ultimate result that full-employment savings and investment are brought into equality to make full employment self-maintaining. Conversely, if the desire to invest exceeds the desire to save, the rate of interest will tend to rise to decrease investment and to increase savings, so that income may not expand beyond the fullemployment level to entail inflation. T h e relationships and assumptions involved in this theory are (a) non-interference with the money market, (b) rigid money wages as an institutionally given constant, (c) savings as a function of both interest and income, ( o. Since the capital-goods industries produce less capital-goods than the 'required' saving ratio would make resources available in terms of real savings, ST — fT < o, the resulting shortage of capital-goods has the effect of increasing the marginal efficiency of capital in general and hence of widening scope for profitable new investment. The rising investment opportunities so effected tend to keep the propensity to invest persistently above the propensity to save in conditions of full employment. Consequently general prices will rise in accordance with the same money-income adjustment

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mechanism mentioned above. This is the other possible case of an inflationary divergence due to 'undercapacity'. But, again, the paradoxical thing is that the economy, while it may be thought following the lower line of steady growth in real output due to hjb < f/b or π < β, nevertheless is more likely to be found moving in an upward direction, that is, along a higher divergent path of chronic inflation for the reasons stated. Deflationary Divergences W e now turn to a consideration of opposite possible cases of 'real' deflation due to 'oversaving' and 'overcapacity'. As a frame of reference we may put down general propositions as follows : I I I . If the 'potential' saving ratio is more than the 'required' saving ratio, forces are released to make for a possible case of chronic deflation due to 'oversaving or 'underconsumption'. I V . If the feasible' investment ratio is more than the 'required' saving ratio, forces are engendered to make for a case of chronic deflation due to 'overcapacity. T o begin with a possible case of deflation due to 'oversaving', we m a y let the initiating shock of the form sp > f do the displacing (from equilibrium) while keeping the 'feasible' investment ratio adjusted to the 'required' saving ratio so that / = δ. T h e excess of the 'potential' saving ratio over the 'required' saving ratio, sp > sr, means that there exists 'oversaving' due to spY — fY > o or, what amounts to the same, 'underconsumption' demand due to (i — sp)Y — ( i — f ) Y < 0. Consumer-goods industries, whose stock of equipment is adjusted to the consumption demand, (i — sr)Y, that had prevailed before the savings change, now find themselves with excess capacity relative to the new demand, (i — sp)Y, and so cut down orders for capital-goods. This drop in the 'derived' demand for capital-goods creates excess capacity in capital-goods industries, thus tending to lower the marginal efficiency of capital and so to depress new investment opportunities. This leads to a chronic state of affairs in which the propensity to invest at full employment is persistently less than the propensity to save out of full-employment real income. Thus the economy, once displaced out of progressive equilibrium by

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sp > j', will be driven into a 'real' deflation of output and employment; it is very likely to be found on a divergent path along which real income will decrease in accordance with dYjdt = f(S — /), where T, S, and I are all in real terms. Once again the asymmetry to be noticed is that the economy, while it may be thought advancing at a higher rate of growth in money income due to splb > sr¡b or μ > β, nevertheless will be found diverging downward owing to 'oversaving' or 'underconsumption'. The higher rate of growth, if it represented the actual line of advance, would be associated with the rising value of output inasmuch as physical output could not increase faster than is allowed by the population growth and technological progress associated with the 'required' rate of growth. This point will be made clearer later by means of diagrammatic analysis. As for the other possible case of deflation due to 'overcapacity', we may suppose the initiating shock to take the form δ > s* and the 'required' and 'potential' saving ratios to be in equality, s* = sp. The excess of the 'feasible' investment ratio over the 'required' saving ratio means that there exists the 'overcapacity' output of capital-goods due to S Y — f Y > o or, conversely, the 'undercapacity' output of consumer-goods due to (ι — δ)Y — (ι — f)Y< o. Now the 'overcapacity' production of capital-goods leads to excess capacity relative to demand in capital-goods industries, thus tending to depress the marginal efficiency of capital and so to narrow scope for profitable new investment. In consequence the propensity to invest at full employment tends to be persistently smaller than the propensity to save at full employment. Output and employment must therefore fall in accordance with the same income-adjustment mechanism mentioned in the previous case. For these reasons the economy is likely to diverge downward from the path of dynamic equilibrium with full employment, though it might otherwise be thought following a higher line of steady growth in money income due to δ/Α > f/b or π > β. This latter line of advance might be followed if it were not for the fact that the same phenomenon of 'overcapacity' has contradictory effects on the economy's income-level adjustment mechanism and on its growth mechanism, as in all the previous paradoxes mentioned.

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Diagrammatical Supplements The foregoing analysis may be made more vivid by diagrammatical illustrations, as in Fig. 33. There the vertical axis measures output on a semi-logarithmic scale and the horizontal axis measures time. The expression 2"(o) = Tf at the origin indicates that the percentage growth of output is associated with full employment when t = o. The T{t) curve represents the percentage growth of real output from full employment and, as such, also represents the path of dynamic equilibrium with a positive constant rate of change.1 Its slope is given by β = f¡b. The rest can be described in connexion with (A) and (B) respectively. (A) log Y

Y W = Y.

(U log Y

Y W = Y. FIG. 33. Divergences from Dynamic Equilibrium

Figure 33(A) depicts a situation where the appearance of 'undersaving' or 'undercapacity' at some point of time gives rise to an upward deviation in money terms and, on the other side, to a downward trend of growth in real output. There the economy can be thought of as diverging away from dynamic equilibrium with full employment and as following along the path of chronic inflation represented by the upward rising broken curve above the T{t) curve, while it might be supposed to be following along the lower line of steady advance represented 1 The percentage rate of increase of output over time is given by β = {dT¡T)¡dt, and its dynamic equilibrasi solution by Υ — î"(o)(i+/?) , where β = s'¡b.

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by the solid Y' (/) curve below the Y{t) curve. A s stated already, the economy would be on the lower line o f steady advance were it not for the buoyant effect of 'undersaving' or 'undercapacity' on its income-expenditure behaviour (savingsinvestment relation) in conditions of full employment. Here is the paradox o f actual price inflation in the midst of potential output deflation mentioned a little earlier. As for Fig. 33(B), it illustrates the opposite situation where 'oversaving' or 'overcapacity' leads to a downward deviation in real terms and, on the other side, to an upward trend of growth in money income. T h e Y'{t) curve above the Y(t) curve represents the hypothetical growth of money income which is greater than that which population growth and technological advance allow, and which would obtain were it not for the depressing impact of 'oversaving' or 'overcapacity' on the economy's income-expenditure behaviour. In other words, the Y'(t) curve here is associated with steadily rising prices, not with increasing physical output, since that curve lies above the Y(t) curve representing the m a x i m u m possible rate o f growth of output from full employment allowed by a growing population with an increasing productivity of labour. Here again the basic paradox involved is that an economy attempting to grow faster than w h a t population growth and technological progress allow is likely to find itself actually on a divergent path of chronic deflation in real terms. Stability Conditions and Qualifications ι . T h e foregoing analysis leads to the following conditions necessary for the stability of dynamic equilibrium with full employment : sp

= f = δ or μ = β = TT so that sfiY = fi"

= BY =

b{dY¡dt).

For that analysis has shown : I f j*

< β > ^j

inflationary divergences occur.

I sp > sr < S ) If I > β < J t h e n deflationary divergences occur. 2. It m a y be presumed that if 'undersaving' or 'oversaving' has the effect o f disturbing dynamic equilibrium in an in-

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flationary or a deflationary way, the institutional-psychological complex of society will be adjusted in the long run to make sp = sr or μ = β. If so, the propensity to save at full employment presumably remains in harmony with the propensity to invest at full employment, or spT = s'T = b[dTjdt). So it is usually argued that when the 'required' rate of growth exceeds the 'potential' rate of growth, β > μ, more saving or thrift is a force making for progressive equilibrium without inflation. Conversely, it is usually argued that when the 'required' rate of growth is less than the 'potential' rate of growth, β < μ, less saving is a force making for the stability of a growing economy without deflation. But these Keynesian arguments1 are based on the classical simplifying assumptions regarding the composition of output and the structure of industry, that is, validated by abstracting from the problems of specificity. 3. Since the composition of output is not actually so homogeneous and the structure of industry not so frictionless as are commonly supposed, the stability of dynamic equilibrium with full employment but without inflationary or deflationary tendencies would require the additional stability condition that the 'feasible' investment ratio be in equality with the 'required' saving ratio, or 8 = i r so that the propensity to invest at full employment may be kept in equality with the propensity to save at full employment, or b(dT¡dt) = 8T = s'T. Thus viewed, both the classical formula for 'progress through thrift' as a corrective to sp < f and Keynes's proposal for 'prosperity through spending' as a remedy for sp > sr can be seen as special cases of a more general case where the community's thriftiness is not perfectly identifiable with the economy's capacity to produce capital-goods. For we have seen that the growing economy could still be left vulnerable to chronic instability due to δ ^ sr even if the 'potential' saving ratio were adjusted to the 'required' saving ratio, sp = sr. 4. It is theoretically possible to keep the economy on an even keel with full employment by controlling the 'autonomous' component of total investment, that is, if the condition of progressive equilibrium to be satisfied always takes the form 1 Compare Harrod, Dynamic Economics, pp. 87-8. Kaldor and Fellner have modified these usual Keynesian arguments somewhat by calling attention to the specific structural difficulties involved, as mentioned earlier.

o

2IO

INTRODUCTION

TO KEYNESIAN

DYNAMICS

b(dY¡df) = (f — X)Y, where λ stands for public investment in the Keynesian sense of 'a balancing factor' considered as a fraction of full-employment real income. T h u s if 'undersaving' threatens chronic inflation, the excess of the propensity to invest at full employment over the propensity to save at full employment, b(dTldt) — (f — X)T > o, could be corrected by reducing Λ so as to make b(dYldt) = (f — λ ) T . Conversely if 'oversaving' makes for chronic deflation, the deficient propensity to invest, b(dTldt) — (s* — X)T < o, could be rectified by increasing λ so as to make b(dYldt) = (j* — λ)Υ. Such operations are of great practical significance if and when public investment makes up a quantitatively significant proportion of aggregate investment. T h e same principle would hold if chronic inflation or deflation were to arise from 'undercapacity' or 'overcapacity'. 5. There are a number of powerful reasons w h y chronic inflation should be considered preferable to chronic deflation if the choice had to be made between the former associated with 'undersaving' and the latter associated with 'oversaving'. First, 'undersaving' will not necessarily impair the required growth of output if the 'feasible' investment ratio is kept above the 'potential' saving ratio and equal to the 'required' saving ratio, sp < δ = f . For the economy could then expand output at a rate consistent with full employment while general prices tended to rise from time to time under the inflationary pressure of 'undersaving' or 'overconsumption' demand, sp < f , accompanied by excess investment-demand. Second, there is no conflict between a 'high-consumption, low-saving' state of affairs catering to consumer-preferences and a maximum of productive efforts riding on inflationary waves. For that 'highconsumption' state of affairs implicit in sp < f helps rather than hinders the private inducement to invest via the acceleration form /, = F{dC,dt). A n y contrary view must assume, and unrealistically, that the 'undersaving' characterized by s" < sr would necessarily break down the propensity to invest for sheer lack of the resources saved in terms of real income without taking into account the possibility of a capacity to produce capital-goods in excess of saving, or S > sp. 6. Moreover, it is plausibly arguable that the privateenterprise economy needs the general environment of rising

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prices for net capital formation. If so, instead of looking upon 'money illusion' as 'irrational', as classical economists were in the habit of doing, it may be looked upon as a perfectly rational modus operandi of private investment in a money economy. This argument is reinforced by the Keynesian argument that the distributive inequity (in favour of flexible-income groups against fixed-income groups) involved in price inflation is a lesser evil than the business losses and economic wastes involved in the deflation of output and employment. This Keynesian reasoning is further strengthened by the experience that it is easier to control inflation through practicable fiscal-monetary policies than to stimulate recovery through the same policies, albeit in a reverse direction. 1 INTERNATIONAL

IMPLICATIONS

T o sharpen the contrast, it seems best to discuss international implications mainly from the standpoint of underdeveloped economies. 2 T h e major problem facing all underdeveloped economies alike seems to be that of increasing capital accumulation for the purpose of developing their available and hidden resources, with an ultimate view to raising their per capita standard of living. If the maintenance of steady growth is the chief concern of advanced economies, the attainment of greater growth can be said to constitute the principal interest of underdeveloped economies. But the formidable difficulty with underdeveloped economies lies in the fact that they are in the nature of the case 'capital-poor' or short of capital in relation to that 1 J. R . Hicks, by way of conclusion, significantly recommends 'monetary reform to re-establish monetary security, combined with a moderate use of public investment and fiscal controls, designed to quieten, but hardly to eliminate, the real cycle'. (See his Trade Cycle, p. 168.) 2 For various insights see Harrod, Dynamic Economics (especially Lec. 4) ; J. Robinson, 'Mr Harrod's Dynamics', op. cit.; C. Clark, Conditions of Economic Progress (2nd ed.), Macmillan, London, 1951, and also his 'The World Will Save Money in the 1950's', Fortune, July 1950; R. Nurkse, Problems of Capital Formation in Underdeveloped Countries, Oxford University Press, N.Y., 1953; T. Haavelmo, A Study in the Theory of Economic Evolution, op. cit.; J. Viner, International Trade and Economic Development, Free Press, Glencoe, 111., 1952; United Nations, Measures for the Economic Development of Underdeveloped Countries; K . K . Kurihara, 'Growth Analysis and the Problem of Capital Accumulation in Underdeveloped Countries', op. cit., and also his 'The United Nations and Economic Development', Indian Economic Journal, April 1954.

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which is required for greater growth. We may begin by illustrating the order of magnitude of capital required for a given rate of growth. Required Capital Accumulation As before, we shall assume that the capital-output ratio is technologically given. From β = f¡b, we have s* = bß, f being the unknown this time. The required saving ratio as a measure of capital accumulation can then be illustrated as follows : If β — o-oi, b = 4, then ? — 0-04. If β = 0 02, b = 4, then f = 0 08. If β = 0-03, b = 4, then f = 0-12. Given the constant capital-output ratio of 4, the economy must accumulate capital at the rate of 0-04 in order to grow at the rate of ο·οι, to cite the first example. The higher the given growth rate of output, the higher will have to be the rate of capital accumulation, if the capital-output ratio remains unaltered. Now suppose that the needs of a growing population are such as to require a 3 per cent, rate of output growth, while the state of technology is such as to give a constant capitaloutput ratio of 4 and the institutional-psychological complex is such as to provide a constant saving ratio of 6 per cent. Then clearly the economy would have to increase capital accumulation at a faster rate of 12 per cent, by its own efforts or else import the difference—unless the needs of a growing population could be supposed to decline somehow. Thus the economy possessing a 'potential' saving ratio less than the 'required' saving ratio could get into trouble in the absence of access to external capital. The trouble might be settled to the mutual advantage of the 'capital-poor' economy and some 'capitalrich' economy, as we shall see presently. The Need for External Capital: Case I Abstracting from the problems of specificity mentioned earlier, we may first take up the possible case of an underdeveloped economy needing external capital, owing to the discrepancy between the 'required' and 'potential' saving ratios. We saw above that one possible remedy for this shortage

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2I3

of capital consists in the borrowing of 'surplus savings' from industrially advanced economies, 'surplus savings' which may arise from the excess of the 'potential' saving ratio over the 'required' saving ratio in the latter economies. Leaving out the necessary qualifications for later discussion, we may set out the above possibility as follows : If s* > sp, (s* — sp)Y: short capital must be imported. If s* < sp, (sp — s*) Y: excess capital must be exported. T h e first of these representations illustrates the need of a 'capital-poor' economy for external capital for the purpose of economic development. In the present context the term 'capital' refers to a money claim to the supply of real capital made available by saving in terms of real income. Thus an underdeveloped economy short of capital in this sense is passing through the 'borrowing stage' of its development. If the 'required' saving ratio exceeds the 'potential' saving ratio, as in the first representation, then the underdeveloped economy must import capital equal to the difference between the 'required' and 'potential' savings, or (¿r — sp) Y. Failure to import that much external capital would, cet. par., make it impossible for the underdeveloped economy to grow at the required rate of 3 per cent., in our example. T h e implications of such a failure for the employment of a growing labour force and for the standard of living are not at all hard to surmise. In the second representation we see that the 'required' saving ratio is smaller than the 'potential' saving ratio. This we might suppose to be the case of an advanced economy, which has such a slow rate of population growth as to require a much lower rate of capital accumulation than its potential saving allows. Since this latter saving is associated with full-employment real income, it is not difficult to see why the advanced economy in question might be well-disposed to export the resulting 'surplus savings', or (sf — s*) Y. For the failure to export that much excess savings might entail a tendency to chronic deflation, as we have already discussed. Thus it would appear to the advantage of a 'capital-rich' economy to export part or all of its excess savings, on at least formal grounds. But even if the underdeveloped economy is in a position to secure the necessary capital for its required development, it

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will still have to overcome the problems of specificity. This is where we turn to Case II. The Need for External Capital: Case II Suppose that the underdeveloped economy's composition of output and structure of industry are such that it can produce capital-goods at the 'feasible' rate of δ. Now suppose that this 'feasible' investment ratio is less than the 'required' saving ratio, owing to a variety of technical bottlenecks associated with the heterogeneous composition of output and the maladjusted structure of industry. It is this excess of the 'required' saving ratio over the 'feasible' investment ratio which occasions the need for external capital in the specific form of capital-£oo¿r. We may compare this with the opposite situation where the need is exports of capital-goods, as follows : If f > δ, (f — δ) Y: short capital-goods must be imported. If i ' < δ, (δ — s') Y: excess capital-goods must be exported. In the first representation the economy must import the necessary capital-goods by paying as much for such imports as it can afford by its potential saving or in exchange for its excess consumer-goods, (ι — — (i — s')Y > o. Here the underdeveloped economy must import capital-goods, not because it cannot save in terms of domestic real income, but because it cannot produce the amount of capital-goods necessary for the required growth. By contrast, the second representation characterizes an advanced economy which must export capital-goods because it can produce more capital-goods than the community's thrift allows in conditions of full employment. Since this 'overcapacity' output of capital-goods implies the 'undercapacity' output of consumer-goods, (ι — B)Y — (i — sT)Y < o, it stands to reason that the advanced economy should desire to export its excess capital-goods in exchange for consumer-goods from elsewhere. Moreover, the failure to export excess capital-goods on the part of the advanced economy might result in the kind of chronic deflation that is associated with 'overcapacity', as was described earlier. Summary

If there exists sT = δ $ sp, there will take place international lending and borrowing for developmental purposes, not exports

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and imports of capital-goods. In the absence of international capital movements the institutional-psychological complex presumably changes in the long run so as to make sp = f . If there exists f — sp $ δ, there will take place exports and imports of capital-goods, not international lending and borrowing. In the absence of trade presumably structural readjustments will occur in the long run so as to make δ = f . If there exists δ $ f $ sp, there will be exports and imports of both capital and capital-goods. Failure or inability to carry out such exports and imports would presumably result in longrun readjustments in both the institutional complex of society and the structure of industry so as to make δ = f = sp. In the past these exports and imports of capital and capitalgoods were left to the vagaries of international finance and commerce, but in the future they are likely to be increasingly guided by the proposition that the economic development of the world should be viewed essentially as a technical problem of making the saving propensities of its capital-rich members compatible with the development needs of its capital-poor members in a mutually advantageous manner. Qualifications

ι. To the extent that superfluous labour, such as is applied to inefficient agricultural production, can be utilized in capitalgoods industries proper, the underdeveloped economy will to that extent be able to increase the supply of real capital without reducing real consumption significantly. If domestic capital can be increased in this way, the usual dependence on external capital for developmental purposes will be somewhat reduced. This qualification is particularly applicable to those underdeveloped economies which have rapid population growth coupled with preponderant agriculture.1 2. Even if the necessary amount of capital were imported to supplement deficient domestic capital so that the underdeveloped economy had (j™ + sp)T = fY, where s" is imported savings considered as a fraction of domestic income, there would still be a practical problem of equating the demand for capital-goods with the supply of real capital, that is, the 1 C f . Ε. M. Bernstein and I. G. Patel, 'Inflation in Relation to Economic Development', International Monetary Fund Staff Papers, November 1952.

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left-hand side of the equation of the form b(dTjdt) = (J™ + s')Y. Here Keynes's theory of the marginal efficiency of capital a n d Schumpeter's theory of innovation (a member of the famous trio of innovation, enterprise, and credit) will be found helpful for those underdeveloped economies mainly operating along private-enterprise lines. For their theories throw much light on the private motives behind the inducement to invest—in short, on the behaviour structure of a developing economy. 1 T h e fact that, in some underdeveloped economies, the general atmosphere of inflationary buoyancy is considered necessary to stimulate private capital formation is indicative of the existence of demand problems along with supply problems.* 3. T h e need for external capital will be considerably reduced if an underdeveloped economy happens to be developing mostly along the lines of light manufacturing industries, instead of along those of heavy industry. For the former type of development is likely to require less capital per unit of output than the latter type, with the possible result that a reasonably high rate of growth is feasible with a relatively small saving ratio. If so, the capital-output ratio need not be so formidable an obstacle to economic development as is usually supposed. Here disaggregative studies of various capital-output ratios in various lines of industrial production would greatly help determine the realistic magnitude of the capital-output ratio for the economy as a whole and therefore that of required savings to be provided by domestic efforts or supplemented by external capital, It is conceivable that the capital-requirement coefficient, b, may be lowered in underdeveloped areas of the world in the future as a consequence of peaceful application of atomic energy. 4. T h e underdeveloped economy can have a higher per capita standard of living either by increasing the rate of output growth with the same rate of population growth or by reducing the rate of population growth with the unchanged rate of output growth. Accordingly there still is some scope for the Malthusian medicine in the case of especially 'overpopulated' 1 Mrs. J. Robinson stresses this point with respect to advanced economics operating mainly in conditions of laissez-faire. See her ' M r . Harrod's Dynamics', op. cit. * H . C . Wallich makes allusion to this, in his 'Underdeveloped Countries and the International Monetary Mechanism,' Money, Trade, and Economic Growth (In Honor of J. H. Williams).

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underdeveloped economies. If the rate of population growth is deliberately controlled, the required rate of output growth will be correspondingly lower. If the required rate of growth is so reduced, the amount of external capital needed to supplement domestic capital for the required growth will be correspondingly smaller, given the capital-output ratio. It may be presumed, however, that the process of industrialization carries with it the long-run implication that the rate of population growth in industrializing economies will gradually slow down. But in the meantime a high rate of population growth remains a strong presumption against a self-sufficiency of domestic capital in many actual underdeveloped economies, thus necessitating some external capital for the required growth. So it may be the part of wisdom to operate with the growth rate of output, β, via the control of the rate of population growth, AP/P.

5. A possible alternative to exports of capital open to an advanced economy is one of gradually readjusting the industrial structure to what Hansen calls a 'high-consumption, lowsaving' state of affairs. 1 In the colourful language of D. H. Robertson we must 'make up our minds that too much progress is a bad thing, adjust the distribution of our national income accordingly, and train a larger proportion of our population to make cakes and ale.' 8 For this alternative is a basic way to minimize the marked instability arising from the preponderance of capital-goods industries or to reduce 'the price of progress', to borrow Robertson's phrase. However, this alternative may prove neither necessary nor desirable. It may prove unnecessary if, as in our previous analysis, it is feasible to counterbalance the destabilizing impact of 'oversaving' or 'underconsumption' by making an upward adjustment in the policy parameter λ, that is, to let public investment absorb the part of full-employment savings not absorbed by induced private investment alone. It may prove undesirable if, as in the foregoing analysis, it is to the mutual advantage of 'capitalrich' and 'capital-poor' economies to export and import excess savings. The above alternative might be considered both Sec his Economic Policy and Full Employment, p. 48. See his 'The Trade Cycle—An Academic View', Lloyds Bank Review, September '937· 1 1

ai8

INTRODUCTION

TO KEYNESIAN

DYNAMICS

necessary and desirable if public investment and developmental foreign investment were deemed impracticable. Thus we are led to the conclusion that it is economically sound and perhaps politically sensible to narrow the existing gap between the underdeveloped and developed areas of the world by making the saving propensities of its 'capital-rich' members compatible with the development needs of its 'capitalpoor' members. It seems fitting to end our discussion by reference to Keynes's prescience: 'It is likely, in my judgement, that the field of reconstruction from the consequences of war will mainly occupy the proposed Bank [International Bank for Reconstruction and Development! in its early days. But as soon as possible, and with increasing emphasis as time goes on, there is a second primary duty laid upon it, namely, to develop the resources and productive capacity of the world, with special attention to the less developed countries, to raising the standard of life and the conditions of labour everywhere, to make the resources of the world more fully available to all mankind, and so to order its operations as to promote and maintain equilibrium in the international balances of payments of all member countries.' (Opening Remarks at the First Meeting of the Second Commission on the World Bank, 3 July, 1944.)

INDEX Accelerator, 88-9, 103-6, 117-22, 123-8, 133-8, 179-84 Accounting equality, of saving and investment, 76-7 Alexander, S. S., 107 Andrews, P. W. S., 166 Autonomous investment. See Investment Average propensity to consume, defined 32 Average propensity to invest, defined, 47 Average propensity to save, defined, 32 Balogh, T., 156 Bator, F. M., 30 Baumol, W. J . , 63, 73 Beckerman, W., 29 Bennion, E. G., 37 Bernstein, E. M., 143, 215 Beveridge, Lord, 42 Bishop, R. L., 38 Boulding, K . E., 9, 14 Bowen, H. R., vi 'Branch' point. See Trade cycle Bronfenbrenner, M., 29, 198 Building-block models, v, 19-20 Bums, A. F., 9, 107 Business cycle. See Trade cycle Capital accumulation. See Investment Capital deepening, 194-7 Capital imports, 2 1 1 - 8 Capital-output ratio, 180, 200 Capital widening, 194-7 Capitalized value. See Discounting process Chang, T. C., 148 Ching-Gwan, C., 30 Clark, J . M., 159 Clark, Colin, 196, 2 1 1 Comparative statics, defined, s 1-2 'Conspicuous consumption', 42 Consumption Function: attributes of, 32-6 ; and corporate financial policies, 39-9; and income concepts, 29-30; 2

and income distribution, 37-8; and liquid assets, 39-40; postwar controversy over, 37; refinements of, 29; subjective motives of, 42 fr. Also see Saving function Corporate saving, 39, 43 Deflationary divergence, 113-6, 1 1 9 22, 124-5, 205^6- Also see Unstable equilibrium Dillard, D., 48, 128 Discounting process, 51-2, 58 Dollar shortage, 156 Domar, E. D., 15, 185, 198 Due, J . F., 9 Duesenberry, J . S., 29, 36, 42 Dynamic accelerator, 102-8, 133-8 Dynamic consumption function, 23, 95-101, 132 Dynamic equilibrium, stability conditions of, 179-81, 202-11 Dynamic foreign-trade multiplier, 1503 Dynamic general price behaviour, 132-9 Dynamic income adjustment function, 73, 80-1,84-5 Dynamic interest adjustment function, 73 Dynamic investment function, 48, 1026, 122-8, 133-8 Dynamic multiplier, 94-102, 132-3, >73-9 Dynamic saving function, 36, 187. Also see Dynamic consumption function Dynamic switches, 122-8. Also see Trade cycle Dynamics, defined, 21, 23 Ebersole, J . R., 166 Effective demand, defined, 84, 85 Ellis, H. S., 9, 69 Endogenous variables, 60-2 Employment model: Keynesian, 81-6; η eo-Classical, 160-2, 164-70 Exchange equation, 20

220

INDEX

Exogenous variables, 60-2 Expectations, dynamic role of, 49, 60-2 Export multiplier. See Foreign-trade multiplier Feasible growth rate, 201-a Fellner, W., 198, 202, 209 Fisher, I., 15, 16 Forced saving, 141-3 Foreign-trade multiplier, 147-53, 1769. Alio see Multiplier Frisch, R., 21 Functional equality, of saving and investment, 77-80 Goodwin, R . M . , 94, 107, 122, 132, 185, 198 Growth equations, 179-80, 199-201 Haavelmo, T . , 17, 198, 211 Haberler, G., 40, 169 Haley, B. F., 10 Hansen, A. H., 9, 12, 15, 23, 39, 40, 42, 185, 194, 196, 198, 217 Hak ism, G., 196 Harris, S. E., 9, 131, 144 Harrod, R . F., vi, 21, 44, 72, 88, 109, 122, 144, 145, 179, 180, 185, 193, 198, 199, 200, 209, 211 Hawtrey, R . G., 16 Hayek, F., 16 Hicks, J. R., vi, 21, 36, 72, 88, 94, 96, 107, 108, 109, 115, 122, 125, 198, 211 Hicks, Ursula K . , 12-3 Higgins, B., 179 Hoarding, defined, 74 Holzman, D., 132 Hyperinflation, dynamic model of, •39-4' Ichimura, S., vi, 122 Induced imports, 153-6 Inflationary divergence, 139-41, 203-5 Inflationary gap, 129-3: 'Instantaneous' multiplier. See Static multiplier Interest: equilibrium rate of, 67-70; as equilibrium mechanism, 73-4; flexibility, 71, 164-7; irreducible minimum rate of, 192-3; and marginal productivity of capital, 74; 'natural' rate of, 193; and profit rate, 74, 191-3; and wage rate, 71, 167-79

International Bank for Reconstruction and Development, 218 Inventory valuation, 49 Investment function: attributes of, 44-8; autonomous, 44-6; dynamic, 48, 102-6, 122-8, 133-8; induced, 46-8, 156-8; intercst-elasticity of, 57-60, 166-7; paradoxical nature of, 185-7; shift parameters of, 61-2, 194-6; unstable nature of, 60—2, 119-28, 194-7 James, S. F., 29 Johnson, H. G., 29, 42 Kaldor, N., 107, 122, 126, 159, 198, 200, 202, 209 Kalecki, M . , 21, 122, 185, 190, 198 Katona, G., 37, 40 Keynes, J . M . : and 'breakdown' theory, 15; on classical theory, 10—1, 13; on consumption in terms of real wages, 30; on consumption motives, 42-3; on corporate saving, 39 ; on dynamics of fixed capital, 49; on 'dynamic' nature of General Theory, 17-9; econometric significance of, 26; on economic development, 218; on effective demand, 84; on elastic liquidity function, 70-1 ; as founder of modern macroeconomics, 9; on free trade, 146-7; and 'fundamental equation', 18; and 'general' nature oí Generai Theory, 17-9; on inflationary gap, 129-31; on interest inelasticity of investment, 166-7; a n d 'investment multiplier', 87; on marginal efficiency of capital, secular decline of, 55, 187, 196-7; marginal propensity to consume, estimate for U . K . and U.S., 36; and Marx, 15; on mercantilism, 13-4; and secular multiplier behavior, 173-9; o n 'shifting equilibrium', 82; on stability conditions of equilibrium, 109; on wage-employment relation, 159, 1624. 170 'Keynesian Day of Judgment', 190 'Keynesian phenomenon', 9 'Keynesian' savings-investment schedules, 76 Kindleberger. C. P., 156

INDEX Klein, L. R . , 15, 17, 19, 29, 37, 159, 1 6 1 , 163, 169 Knox, A. D., 107 Koopmans, T., 13a Kurihara, K . K . , vi, 4 1 , 1 3 1 , 144, 173, 198, 199, 2 1 1 Kuznets, S., 176 Labour-output ratio, 199 Lange, O., 159 Lansing, J . B., 40 Leontief, W., 9, 159 Lerner, A. P., 72, 77 Likert, R., 37, 40 Liquidity function: and income variable, 64-5, 67, 69-70; interest elasticity of, 70-1 ; and money market, 67-70, 72; motives of, 63-6 Locke, J . , 16 Lorenz-curve distribution, distinguished from functional distribution,

37-8

Machlup, F., 144, 147 Macrodynamics, defined, 21, 23 Macrostatics, defined, 20, 22 Malthus, T., i l , 14, 1 5 Malthusian medicine, 2 1 6 Marginal efficiency of capital, defined, 51 Marginal efficiency of capital equation, 56 Marginal propensity to consume, defined, 33 Marginal propensity to import, 'leakage' nature of, 148 Marginal propensity to invest, defined, 47 Marginal propensity to save, defined, 33-4. 35 Marshall, Α., io, 16 Marshallian partial equilibrium, 76 Marx, K . , 12, 14, 15, 55, 185 Matthews, R . C. O., 162 May, K . , 19 Mayer, T., 30 Maynes, E. S., 40 Meade, J . E., 109, 147, 153, 166 Means, G. C., 30 Mercantilists, 1 3 - 4 Metzler, L . Α., 96, 144, 153 Microdynamics, defined, 13 Microstatics, defined, 13

221

Midas, fate of, 190 Mill, J . S., 14, 15 Mitchell, B., vi Modigliani, F., 29, 63, 71, 169 Monetary theory, development of, 16, 18 Money: dynamic role of, 7 2 - 3 ; as medium of exchange, 63, 67; as store of value, 72-3. See also Quantity theory; Liquidity function Multiplier: dynamic, 23, 94-101 ; foreign-trade, 147-58, 176-8; overemployment price, 1 3 2 - 8 ; static, 23, 87-8. 93-4! 'super', 88-9, 102-8, '33-8 Musgrave, R . Α., 40, 63 National income, basic determination of, 76-86 Natural growth rate, 199 Nonlinear model, 122-8. See alio Trade cycle Nourse, E. G., 19 Nurkse, R . , 144, 21 : Over-employment equilibrium, defined, 81 Over-production, general, 12 Partial equilibrium, 76 Patel, I. G., 143, 2 1 5 Patinkin, D., 40, 159, 169, 170 Perloff, H. S., 42 Pigou, A. C., 16, 40, 159, 164, 167, 190, ' 9 · . >94-5. '96 'Pigou effect', 40, 167-70, 197 Population problem, 183, 194, 196-7, 199-200, 2 1 2 - 8 'Post-Keynesian' thinking, v, 17 Potential growth rate, 200-1 Precautionary motive, 64-5 Price super-multiplier, 133-8 Profit rate. See Marginal efficiency of capital Progressive equilibrium. See Dynamic equilibrium Propensity to consume. See Consumption function Propensity to hoard. See Liquidity function Propensity to invest. See Investment function Propensity to save. See Saving function

222

INDEX

Quantity theory, ι6, 18, 141 Ricardo, D . , 11, 14, 15, 55, 185, 193 Robertson, D . H . , i6, a i , 72, 147, 217 Robinson, E . A . G . , vi Robinson, Joan, 18, 37, 38, 63, 72, 144, 162, 185, 198, 211, 216 Rosa, R . V . , 69 'Roundabout' production, 49 Ruggles, R . , 76 Samuelson, P. Α . , g, 19, 21, 23, 88, 94, 109, 122, 170, 180 Saving function: attributes of, 35-6; nonlinear, 126; long-run, 34-6, 187; short-run, 34-6. See alio Consumption function Say, J . B., i t , 15 Say's L a w , stated, 11 Schumpeter, J . Α . , 15, i22, 126, 194, 216 Secular inflation, 203-5, 207-11 Secular stagnation, 186-97, 205-11 Security motive, of saving, 42 Shifting equilibrium, 20-1, 23, 82-4 Shift parameters, defined, 60 Sismondi, J . C . L . S. de, 12, 15 Smith, A d a m , 10, 11, 13, 14 Smithies, Α . , 132 Speculative motive, 65-6, 72-3 Sproul, Α., 6g Stable equilibrium, 109-13, 117—9, 138, 202-8 Static multiplier, 23, 87-8, 93-4. Also see Multiplier Stern, E. H., 185 Stigler, G . F., 21 Stock market, destabilizing influence of, 72 Super-multiplier, 88-9, ion-8, 133-8. Also see Multiplier T a - C h u n g , L . , 30 Tarshis, L., 9

Technological parameters, 180, 183, 199-200, 216. See also Capital-output ratio; Labour-output ratio Technological unemployment, 16 T h o r p , W . L., 196 Tinbergen, J . , 9 , 2 0 , 2 1 , 2 6 , 4 6 , 1 0 7 , 108 Tobin, J., 29, 159 Transaction motive, 63-4 Trade cycle: 'branch' points of, 124; endogenous mechanism of, 109-22; exogenous factors of, 122; lower turning-point of, 125-6; nonlinear model of, 122-7; phases of, 123; regularity of, 109, 122; time-shape of, 127-8; upper turning-point of, >84-5 Tsuru, S., 142 Turvey, R . , 132 Underdeveloped economies, 2 1 1 - 8 Underemployment equilibrium, 81-3, 179-84, 187-90, 199-203, 205-6 United Nations, 144, 145, 146, 147, 196, 211 Unstable equilibrium, 113-6, 119-22, ' 5 3 . 203-8 Veblen, T . , 42, 161 Vickrey, W., vi, 29 Viner, J., 211 Voluntary unemployment, 161 Wages: dynamic effects of general re» duction, 162-4; and employment, 30, 159-64; and inflation, 132, 135, 138; reduction as substitute for interest policy, 71 Warranted growth rate, 200 Walras, L., 15 Wallich, H . C . , 143, 216 Wealth effect. See Pigou effect Wicksell, K . , 15, 185, 193 Williams, J . H., 29, 198, 216 Wilson, T . W . , 166 World Bank. See International Bank Wright, D. M . , 198