Capital Theory

Capital TheoryVolume I Edited by Christopher Bliss Nuffield Professor of International Economics University of Oxford, UK Avi J. Cohen Associate Professor of Economics York University, Canada and G.C. Harcourt Emeritus Reader in the History of Economic Theory University of Cambridge, UK Emeritus Fellow Jesus College, Cambridge UK and Professor Emeritus University of Adelaide, Australia An Elgar Reference Collection Cheltenham, UK • Northampton, MA, USA © Christopher Bliss, Avi J. Cohen and G.C. Harcourt 2005. For copyright of individual articles, please refer to the Acknowledgements. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of the publisher. Published by Edward Elgar Publishing Limited Glensanda House Montpellier Parade Cheltenham Glos GL50 1UA UK Edward Elgar Publishing, Inc. 136 West Street Suite 202 Northampton Massachusetts 01060 USA A catalogue record for this book is available from the British Library ISBN 1 84064 481 8 (3 volume set) Printed and bound in Great Britain by MPG Books Ltd, Bodmin, Cornwall. Contents Acknowledgements ix Introduction The Theory of Capital: A Personal Overview Christopher Bliss xi Introduction Capital Theory Controversy: Scarcity, Production, Equilibrium and Time Avi J. Cohen and G.C. Harcourt xxvii PART I CLASSICAL AND MARXIAN CONCEPTIONS OF CAPITAL 1. K.H. Hennings ([1987] 1990), ‘Capital as a Factor of Production’, in John Eatwell, Murray Milgate and Peter Newman (eds), The New Palgrave: Capital Theory, London: Macmillan Reference Books, 108–22 3 2. David Ricardo (1951), ‘IV. The Chapter on Value in Edition I’ excerpt from ‘Introduction’, excerpt from ‘On Value’ and ‘On Machinery’, in Piero Sraffa (ed.), The Works and Correspondence of David Ricardo, Volume I, Chapter I, Sections III–V, Chapter XXXI, Cambridge: Cambridge University Press, xxx–xxxvii, 22–43, 386–97 18 3. Karl Marx ([1891] 1972), ‘Wage Labour and Capital’, in Robert C. Tucker (ed.), The Marx–Engels Reader, Second Edition, New York: W.W. Norton and Company, Inc., 167–90 60 4. Luigi L. Pasinetti (1983), ‘The Accumulation of Capital’, Cambridge Journal of Economics, 7, 405–11 84 PART II FOUNDATIONS OF NEOCLASSICAL CAPITAL THEORY: IMPATIENCE AND PRODUCTIVITY 5. Nassau William Senior ([1836] 1938), ‘Instruments of Production’ and ‘Capital’, in An Outline of the Science of Political Economy, Chapter 3, London: George Allen and Unwin, Ltd, 57–60 93 6. Ian Steedman (1972), ‘Jevons’s Theory of Capital and Interest’, Manchester School of Economic and Social Studies, XL, 31–52 97 7. Syed Ahmad (1998), ‘Rae, Böhm-Bawerk, and Fisher on the Supply and Demand of Capital’, in O.F. Hamouda, C. Lee and D. Mair (eds), The Economics of John Rae, Chapter 6, London and New York: Routledge, 111–28, references 119 8. Eugen von Böhm-Bawerk (1959), ‘The Problem of Interest’, ‘Final Conclusions’ and ‘Present and Future in Economic Life’, in Capital and Interest, Translated by George D. Huncke and Hans F. Sennholz, Volume 1, Chapter I, Chapter XV, Volume 2, Chapter I, South Holland, IL: Libertarian Press, 1–7, 348–54, 259–89, notes 139 9. John B. Clark (1891), ‘Distribution as Determined by a Law of Rent’, Quarterly Journal of Economics, 5 (3), April, 289–318 194 vi Capital Theory I 10. John Bates Clark (1899), ‘Kinds of Capital and of Capital-Goods’, in The Distribution of Wealth: A Theory of Wages, Interest and Profits, Chapter X, New York and London: The Macmillan Company, 141–56 224 11. Christopher Bliss (1990), ‘Alfred Marshall and the Theory of Capital’, in John K. Whitaker (ed.), Centenary Essays on Alfred Marshall, Chapter 9, Cambridge: Cambridge University Press, 223–41 240 12. Knut Wicksell ([1934] 1961), ‘Capitalistic Production’, in Lionel Robbins (ed.), Lectures on Political Economy, Translated from the Swedish by E. Classen, Volume 1: General Theory, Part II, Chapter 2, London: Routledge and Kegan Paul Ltd, 144–95 259 13. Knut Wicksell ([1934] 1961), ‘Real Capital and Interest (continued): A Mathematical Analysis of Dr. Åkerman’s Problem’, in Lionel Robbins (ed.), Lectures on Political Economy, Translated from the Swedish by E. Classen, Volume 1: General Theory, Appendix 2(b), London: Routledge and Kegan Paul Ltd, 274–99 311 14. Paul A. Samuelson (1967), Excerpts from ‘Irving Fisher and the Theory of Capital’, in Ten Economic Studies in the Tradition of Irving Fisher, Chapter 2, New York: John Wiley and Sons, Inc., 17–19, 26–35 337 15. Joseph A. Schumpeter ([1934] 1983), ‘Interest on Capital’, in The Theory of Economic Development: An Inquiry into Profits, Capital, Credit, Interest, and the Business Cycle, Translated from the German by Redvers Opie, Chapter V, New Brunswick and London: Transaction Books, 157–211 350 PART III SOME AUSTRIAN AND NEO-AUSTRIAN CONTRIBUTIONS TO CAPITAL THEORY 16. Carl Menger ([1871] 1976), Excerpt from ‘The Laws Governing the Value of Goods of Higher Order’, in Principles of Economics, Translated by James Dingwall and Bert F. Hoselitz, Part III, Chapter 3, Sections A–D, New York and London: New York University Press, 149–65 407 17. Frank A. Fetter (1902), ‘The “Roundabout Process” in the Interest Theory’, Quarterly Journal of Economics, 17 (1), November, 163–80 424 PART IV EARLY NEOCLASSICAL CAPITAL CONTROVERSIES 18. Thorstein Veblen (1908), ‘Professor Clark’s Economics’, Quarterly Journal of Economics, XXII (2), February, 147–95 445 19. Avi J. Cohen (1998), ‘Frank Knight’s Position on Capital and Interest: Foundation of the Knight/Hayek/Kaldor Debate’, in Malcolm Rutherford (ed.), The Economic Mind in America: Essays in the History of American Economics: Perspectives on the History of Economic Thought, Chapter 10, London and New York: Routledge, 145–63 494 20. Ian Steedman (1994), ‘On The Pure Theory of Capital by F.A. Hayek’, in M. Colonna, H. Hagemann and O.F. Hamouda (eds), The Economics of F.A. Hayek, Volume II: Capitalism, Socialism and Knowledge, Chapter 1, Aldershot: Edward Elgar, 3–25 513 21. Murray Milgate (1979), ‘On the Origin of the Notion of “Intertemporal Equilibrium”’, Economica, 46 (181), New Series, February, 1–10 536 22. J. Fred Weston (1951), ‘Some Perspectives on Capital Theory’, American Economic Review, Papers and Proceedings, 41 (2), May, 129–44 546 Name Index 562 Capital Theory I vii Introduction The Theory of Capital: A Personal Overview Christopher Bliss What Is Capital Theory About? It is a fallacy to suppose that if we have a name for something there must be something, particularly a single something, which that name defines. So it is with the ‘theory of capital’, and even with the term ‘capital’ itself. Capital can mean specific capital goods (as in the case of a piece of machinery); it can mean the finance that a particular project requires (as when we refer to the capital market); and it can even mean the risk and entrepreneurship involved in specific investments (as when we refer to venture capital). The recognition of this basic point is a great help as one attempts to pick one’s way through the diverse and unorganized literature that has been thrown up by 200 years, at least, of thinking about capital. Different ways of viewing capital, which is what is involved in the various terms listed above, sometimes revolve around the distinction between a short-run and a long-run approach to the question of how capital is allocated. A fully successful theory of capital should master both cases, because the market system allocates capital in both senses. It determines how and where a specific machine tool is used; and it decides how the financial resources directed to current investment will be translated into the purchase of specific machines and structures of what particular designs. Alfred Marshall, who laid the foundations for an excellent theory of capital, and then failed to deliver, 1 makes that distinction between specific capital goods and what he called ‘free’ or ‘floating’ capital most clearly when he writes: ‘That which is rightly regarded as interest on “free” or “floating” capital, or on new investments of capital, is most properly treated as a sort of rent – a Quasi-rent – on old investments of capital’ (Marshall, 1920, p. 412). The distinction between capital in its short-run specific aspect and in its long-run fluid aspect may be called the fluidity question. It is a troublesome one for economic theory. The second feature especially seems to indicate that capital is a natural subject for aggregation. Could it be that in the long run the detailed micro composition of the capital stock is somewhat irrelevant, and that only a brute total might matter? Only for the case of capital does this question assert itself. If we take labour, by way of contrast, there is no presumption that there might be a natural aggregation. Strangely, this has caused much less blood to be spilt over the aggregation of labour than over the parallel issue with capital, although extreme aggregation of labour has been a commonplace practice among economic theorists. Capital Theory I From Mill to Irving Fisher: Impatience and Productivity The classical economists, which would include here Smith, Ricardo and Torrens (but not John Rae) viewed investment, and hence capital, from a somewhat limited perspective. Asked to put up some money to finance a project, an investor might ask: how long before I get my money back? Only in the case of particular time structures of the flows of returns from an investment does the answer to that question define the true profitability of an investment. Yet those cases are appealing and intuitive. In particular, if an investment of $100 generates a flow of $q per period for ever, the pay- back period is 100/q. If the rate of interest is r, the project will show a net profit if q ≥ 100r. This is the same as requiring that the pay-back period should be no greater than 1/r, and the investment decision is reduced to an issue of how long the investor has to wait (to get his money back). The higher the rate of interest, the shorter is the pay-back period, or the more impatient is the investor. Or, one might say, the more impatient is the investor, the higher will be the rate of interest. This fatally attractive equation of the supply constraint on capital and waiting dogged capital theory for more than 100 years. It did not help that the neoclassical economists were not alone among revolutionaries in passing themselves off as simple offspring of their predecessors. The anomalous term neoclassical illustrates the same point. So John Stuart Mill, the bridge thinker between the classical and the developed neoclassical, presents himself as a mere expositor of Ricardo’s thought, which he was certainly not. And Alfred Marshall, who could have developed a rich and dynamic capital model consistent with his price theory, trod in Mill’s footsteps, and settled for waiting as a component of long-run cost, with all the lack of clarity and problems which that view entails. What Ricardo had started the Austrians took to its logical conclusion. They made time the essence of capital, and of capital intensity. Böhm-Bawerk (see his ‘Present and Future in Economic Life’ (1959), in Volume I, Chapter 8) shows how there are two sides to the waiting equation. The demand for waiting comes from its productivity: more roundabout methods are more productive. The supply of waiting is limited by impatience. Is waiting one thing? On the supply side, that was assumed. On the demand, productivity, side, a positive reply demanded an aggregate, an average period of production. This is the concept which Frank Knight attacked, and which the young Nicholas Kaldor defended (see the account provided by Weston (1951), Volume I, Chapter 22). Really these are side issues. A general equilibrium model of capital does not require aggregation. Moreover, the concept of waiting would only burden such a model. In one of his more striking examples, Marshall (1920, p. 351) proposed a beautifully simple model of a man building a house with his own raw labour, where the quality (utility) of the house increases both with total effort put into its construction and the time taken to complete the job. He never worked out this model, though his mathematical technique would have allowed him to do so easily. That simple model shows that capital has two components: intensity and waiting. The most popular case against the idea that the rate of interest is a reward for waiting is to point out that the idea that the rich are rewarded for postponing their consumption is decidedly nauseating. Yet the term ‘reward’, as used, for example, by Marshall, has an analytical content which identifies the rate of interest as the reward for waiting in exactly the sense that a price premium on high-protein wheat is a reward for high protein. And that last example underlines xii Capital Theory I the vital consideration that just to state that a premium exists for some feature explains nothing until it has been shown why: • the feature is demanded – high protein wheat makes better bread; • the feature is costly to supply – high protein wheats have lower yields. Exactly by analogy to the wheat case, a theory of capital built on waiting needs to detail why: • early consumption is preferred to later – neoclassical writers usually assumed pure impatience as a fundamental property of human psychology • output for early delivery is more costly to supply than output for later delivery – like their classical predecessors, neoclassical writers assumed this to be a normal feature of technology. Both branches of the argument are less than completely satisfactory. Assuming a psychological tendency appears to be ad hoc. And an innate productivity of waiting sits uncomfortably with the idea of diminishing returns. Why does capital accumulation not drive the marginal productivity of waiting down to zero? The best discussions of these problems both date from about 1930. The first is to be found in Irving Fisher (1930). Fisher’s book takes the neoclassical arguments about as far as they can go within a static model. He depicts the rate of interest as determined by the joint influences of productivity and thrift, with thrift itself powerfully affected by a preference for immediate satisfaction, which is essentially impatience. In his great paper, Ramsey (1928, Volume II, Chapter 2), Frank Ramsey showed how the interplay between productivity and impatience is augmented in a dynamic model. Continuing through von Neumann and Solow, parallel issues were treated in terms of a model of economic growth. The Aggregation of Capital Once the fluidity issue has been given the prominence that it deserves, it is not hard to see why the question of whether and how capital can be aggregated regularly comes into consideration. The classical economists tended to consider capital as fluid, uncommitted financial resources. As such, one might say that it is naturally aggregated. Adopting a piecemeal approach to what we would now call factor price determination, they did not have to agonize over the question of how the determination of the return to capital might, or might not, differ from the determination of the rent of land. When one factor return is seen as a residual, as Ricardo and Mill, for instance, modelled the rate of profit, asymmetries between the returns to different factors did not seem to be anomalous. That comfortable position was destroyed by the neoclassical revolution. Committed to treating the pricing of different factor services symmetrically, these writers had to decide what symmetry would mean in the case particularly of capital, on the one hand, and land, on the other hand. And the answer to that question is by no means trivial. The easiest manner of dealing with the issue (actually ducking it) is to assume that capital to be exactly like homogeneous land. That identity can only hold in the short run, because capital is accumulated through time via saving xiii Capital Theory I and investment. The point is easily handled in a dynamic model. The root issue remains whether it can ever be correct to treat capital as a homogeneous, always-fluid entity. Of course, such an approach cannot be right. Nothing in economic theory is exactly right. The crucial issue, which can and has divided reasonable opinion, is how seriously it matters. The answer might vary from one application to another. The late Joan Robinson did the debate no favour by politicizing the question; presenting it as a struggle between ‘neoclassicals’, wearing black hats, and their white-hat opponents (Robinson, 1958). Most misleading is the script that writes the division of opinion concerned as a left/right issue. It was never that. The young, left-leaning Kaldor argued against the conservative Frank Knight in defence of the Austrian period of production aggregation. Later he changed his mind and defected to the anti-aggregation camp, while his politics remained much the same. The conservative Hayek (1941, ch. 1, p. 5), in the part of a single elaborate sentence quoted here, writes: the attempts to explain interest, by analogy with wages and rent, as the price of the services of some definitely given ‘factor’ of production has nearly always led to a tendency to regard capital as a homogeneous substance the ‘quantity’ of which could be regarded as a ‘datum’, and which once it had been properly defined, could be substituted, for the purpose of economic analysis, for the fuller description of the concrete elements of which it consisted. If this quotation has a decidedly ‘Anglo-Italian’ flavour, that could be misleading. Later discussion makes clear Hayek’s view that it is disequilibrium dynamics that require the rejection of aggregate capital, an angle which is at best subsidiary to the Anglo-Italian case. Keynes and the Cambridge School By emphasizing that scepticism concerning capital aggregation never divided left from right, I have denied myself one answer to the question: why did a group 2 of economists emerge in postwar Cambridge, England, distinguished, not merely by a general hostility to neoclassical theory, but by a particularly focused dislike of capital aggregation and of the concept of the marginal product of capital? While it is true that there were several left-leaning economists in the Cambridge of that time who held such views, the key influence here is not left-wing politics. Rather it is the influence of Keynes. The idea that the quantity of capital, and with it its marginal product, cannot be measured, leads back in this case directly to Keynes. In his General Theory, Keynes (1936) merged it with his ideas concerning uncertainty, the subjectivity of investment planning, and missing markets. While richly suggestive, the theory is incompletely developed. So we end up with the paradoxical conclusion that an indefinite relationship between a single rate of interest and investment has a definite negative slope. The indefiniteness comes from the influence of a psychological confidence factor, called ‘animal spirits’. In Chapter 11 of his General Theory (1936, p. 138), Keynes writes: There is, to begin with, the ambiguity whether we are concerned with the increment of physical product per unit of time due to the employment of one more physical unit of capital, or with the increment of value due to the employment of one more value unit of capital. The former involves xiv Capital Theory I difficulties as to definition of the physical unit of capital, which I believe to be both insoluble and unnecessary. Keynes could not cite Hayek here; the publication date is later. It is questionable whether Keynes would have read Wicksell ([1934] 1961, Volume I, Chapter 12), whose more thorough discussion of the marginal product of value capital appeared at this time. He probably did not read Wicksell with any care ever. Wicksell intertwined the notion of capital as monetary finance (value capital) with long-run equilibrium conditions. This is a legitimate, if strange, exercise. Usually those who accumulate capital do not pursue any specific quantitative target. Capital accumulation is a means to profit maximization, or to optimal inter-temporal consumption substitution. Yet there are many possibilities. Suppose the sudden arrival of a fashion: ‘Be worth a million dollars!’, and that many agents then pursue a value target, and the long-run implications are as analysed by Wicksell. The problem with the Wicksell argument is the supposition that this comparative static exercise has anything to do with the relation between the rate of interest and the marginal product of capital. Swan (1956) gives us one of the best discussions of the issue. Whatever influences it may reflect, Keynes’s throw-away discussion, concerning whether the marginal efficiency of capital is an absolute number or a ratio, reflects his real interest lying elsewhere. This is on the uncertainty of the relationship between immediate returns on an investment and the future returns. He writes (1936, p. 145): ‘The schedule of the marginal efficiency of capital is of fundamental importance because it is mainly through this factor (much more than through the rate of interest) that the expectation of the future influences the present.’ In the General Theory passages, cited above, we find an encapsulated presentation of many of the ideas that echoed through the classrooms of early 1960s Cambridge; I speak here from personal experience as a Cambridge student of that time. I have often wondered whether Keynes’s view on the measurement of capital, which does not connect easily with any other part of his writings may derive from Piero Sraffa, and the latter’s participation in the famous General Theory workshop. If that connection exists, I have not been able to document it. A critical question for a Keynes-influenced approach to capital – and indeed for the ideas of the General Theory itself – is this: is the Keynesian model just a short-run theory, or are there long-run ‘Keynes problems’? If one selects the right passages from the General Theory, the answer seems to be an unambiguous yes. If Keynes was wholly serious in proposing that the construction of mediaeval cathedrals was good for effective demand, then he believed in the existence of a long-run ‘under-consumption’ problem. For certainly, those cathedrals were not run up in a hurry. Yet such sections of the General Theory are informal in the strict sense. Keynes built no models of long-run growth, steady or otherwise. Later, when Harrod and Joan Robinson attempted to fill the gap, their models leave a Heath-Robinson (no relation to Joan) 3 impression. Long-Run Equilibrium with Capital To summarize brutally, a leading line of argument employed by the Cambridge and Italian critics of neoclassical capital theory is that this theory (often called marginal productivity theory xv Capital Theory I in this connection), even if suitable for determining the short-run allocation of specific existing capital goods, cannot provide a theory of long-run equilibrium. This view is hard to understand. Yes, there are problems around the definition of a long-run equilibrium, and an examination of the issues involved can be enlightening. The critical weaknesses in orthodox theory have not been well exposed by its critics. Probably more problems lie on the side of the supply of saving than on the side of market equilibrium with capital, where the emphasis is usually placed. And ultimately, only new theory beats old theory, however bad. In that respect, the anti-neoclassicals have been notably unsuccessful. There really is not a well-worked-out, alternative long-run capital theory to set against the various orthodox models. Piero Sraffa, in particular, seems to have given up on the job, so that his 1960 book (see the selection in Volume II, Chapter 17), the product of over 30 years’ work, is subtitled ‘A prelude to a critique of economic theory’. To see what has to be done to construct a model, the Solow–Swan growth model is a good starting-point (see Solow (1956), Volume II, Chapter 3). As a beautifully simple aggregate model of capital accumulation it clarifies completely how both the short and long run may be dealt with in one model framework. The model treats capital as an aggregate identical with output. It is not trivial to dispense with that feature, but it can be done. A deeper and harder problem is that both Solow and Swan, following Harrod, treat saving in a non-neoclassical – one might almost say, in a Keynesian – manner. Saving decisions are not derived from optimization, but a constant propensity to save is assumed. It turns out that this last feature is far more troublesome. We will see, below, how saving can be made endogenous through models based on optimization, due to Ramsey or von Neumann. Meanwhile, consider how the Solow– Swan model may be generalized to embrace disaggregated capital. Let the maximum consumption possible in period t be: F(l t ; k 1, t , k 2, t , . . . , k n, t ; ∆k 1, t , ∆k 2, tt , . . . , ∆k n, t ) (1) where l t is the labour force at time t; k i, t is the stock of capital of type i (i = 1, . . . , n) at t; and F(.) is a concave constant-returns function: ∆k i, t = k i, t + 1 – k i, t (2) Notice how the consumption possibility function makes consumption depend upon the capital stock at t, and also upon the additions for next period of each item in that stock. This is similar to the approach used in Dorfman, Samuelson and Solow (1971, Volume II, Chapter 4). Obviously, an infinity of accumulation paths is defined by series of the form: k → 1 , k → 2 , . . . , k → t , . . . (3) where the superscript → indicates that these are vectors of capital stocks at the various times. Given equation (3), a sequence of consumptions are defined via equation (1). For a path to be consumption feasible, those consumption values should all be non-negative. What features, aside from consumption feasibility, distinguish those paths which can be market equilibria from those which are not? xvi Capital Theory I Take an arbitrary set of weights a t . It can be shown that the market equilibrium solutions are those which are both consumption feasible and which maximize: ∑ T t = 1 a t ⋅c t (4) for all T. Note that this is not the same as maximizing equation (4) with T = ∞. The latter would rule out steady-state paths with more capital than the golden-rule level, although these are market equilibrium solutions. The above maximizations define a growth path of many capital goods. If F(k 1, t , k 2, t , . . . , k n, t ; ∆k 1, t , ∆k 2, tt , . . . , ∆k n, t ) is differentiable in its various arguments (the smooth, neoclassical case), we obtain unique time-varying capital goods prices and consumption interest rates. In the non- differentiable case favoured by the critics of neoclassical theory, we still obtain prices and consumption interest rates; but now these values need not be unique. From the prices in either case come saving rates as shares of current value devoted to investment. Intuition will suggest that adjusting the weights a it should be possible to select from all the various growth paths at least one with a constant saving rate. That is correct, although the proof is not trivial and will not be given here. In any case, unlike the simple Solow–Swan model, there could be more than one constant saving rate growth path. So aggregation may matter importantly for dynamics, just as Hayek believed. Now it is easy to define a steady state solution. A steady state solution consists of: 1. a constant saving rate market equilibrium as defined above; and 2. a capital vector growing at a constant rate equal to the rate of growth of the labour force. The second condition is: k → t = (1 + g) k → t + 1 (5) where g is the growth rate of the labour force. Now we have defined a many-capital-goods generalization of the Solow–Swan model in both its dynamic and its steady-state realizations. The important differences are shown in Table 1 and clarified below. Table 1. A comparison of the Solow–Swan model and its generalization Solow–Swan Model Many Capital Goods Dynamic Model Is the equilibrium path from any initial conditions unique? Yes No Is steady state unique given the saving rate? Yes No Are model dynamics Markov? Yes Yes xvii Capital Theory I The meaning of the first two questions in the table will be clear. Allowing capital to be different from other output, particularly consumption, alters conclusions radically. It is not correct to say that its rough aggregation of capital is what generates the simple features of the Solow–Swan model. The differences advertised in the table already arise with the neoclassical, two-sector models (see below), in which capital is completely aggregated, but is not the same as consumption output. Adding many capital goods is intellectually satisfying but does not add a lot of analytical richness. What, however, is meant by model dynamics being Markov? In this context, it means that where the system will (or may) move next period is entirely determined by the capital stock now. In no other respect does history have an influence. Plainly, as the model has been specified, this property must hold on the technological side. How about the saving rate? Beyond the one-good model, the saving rate depends upon prices – that is, the relative values of various capital goods and the consumption good. And since all saving rates into the future depend upon all future prices, everything looking forward has to be solved out simultaneously. For this reason, how the system can move forward one period depends upon all the future, and in that feature will be found the clue to multiple equilibrium possibilities. The full set of possibilities for the future, including all sequences of prices, are limited only by the starting capital stock. For this reason, even the complex dynamics of the many-capital goods model are Markov. Income Inequality and Convergence In a superb paper, Stiglitz (1969, Volume II, Chapter 25) asked and answered a pointed question concerning the Solow–Swan model. This model is highly aggregated and in more than one respect. At the time there was great concern that capital is treated as a simple aggregate in the model. Stiglitz addressed the issue that economic agents are treated as if they are one huge representative agent, and he investigated what would happen if agents were to be differentiated according to what shares they enjoy in the ownership of aggregate capital. Assuming that agents all supply the same quantity of labour, earn the same rate of return on whatever capital they own, and all save the same share of total income, Stiglitz establishes the following result. Regardless of the initial distribution of wealth, the per capita wealth holdings of all agents will converge on k * , where k * is the long-run Solow–Swan solution for capital per head. The force driving the Stiglitz result may be explained as follows. For a poor (rich) agent the share of capital income in total income is low (high). Therefore the rate of growth of wealth, which is proportional to income given a constant saving rate, is high (low) for poor (rich) agents. The Stiglitz result tells us not to worry about aggregation, at least not where the uneven distribution of wealth is concerned. Such inequalities will disappear with time, although the time required may be long. In any case, the model behaves in aggregate exactly as if there is no inequality. The conclusion depends upon assumptions which underlie all convergence models. David Hume, and following him Adam Smith, in tune with the tenor of enlightenment thinking, took it for granted that all humanity, divested of its contingent cultural and historical garments, is fundamentally the same. In the same spirit modern β-convergence theorists have xviii Capital Theory I arrived at the concept of so-called ‘conditional’ convergence (see Barro and Sala-i-Martin (1992), Volume III, Chapter 22). This means that such influences as an economically benign political system, or a good standard of education, need to be right before a nation can participate in the process of globalized converging economic growth. Others have emphasized the importance of infrastructure quality, although this may simply be an expression of similiar causes. As a matter of fact, neither are saving rates similar for different individuals, nor are they much the same for different nations. Edwards (1996) provides a good discussion of why saving rates diverge markedly in the case of Latin America. It seems that to think of the world as a massive Solow–Swan model, even with unequal distribution of wealth, is to mis-describe it. Even so, some of the driving force of Stiglitz’s theorem may still apply. The Long-Run Rate of Interest For all that, it is special: the Solow–Swan model (in the steady state which we have generalized) is useful for depicting the operation of the grand influences on the rate of interest. The model treats the growth of the working population, and similarly, technical change of the labour- augmenting variety, as exogenous. The saving rate is also taken as given. In fact it is likely to depend on the growth rate and the aggregate distribution of income. Extensions of the model might take some of these influences into account, but only by compromising the elegant simplicity of the model structure. We have seen that the many-capital goods, Solow–Swan model may have multiple equilibium steady states. And even for locally stable, isolated steady states, the following conclusions of the one good model will not necessarily be robust: • A rise in the saving rate lowers the long-run rate of interest. • A rise in either the rate of population growth or the rate of technical progress raises the long-run rate of interest. This is a field on which neither the orthodox neoclassical approach nor its self-styled opposition have thrown much light. From the neoclassical side, a Solow–Swan constant saving coefficient becomes a can of worms in a many-capital goods model with variable prices. There is every possibility of model discontinuites when solutions are parameterized by the aggregate saving rate. On the anti-neoclassical side, the authors concerned never fully freed themselves from the idea that the rate of interest naturally orders steady states. They just insisted that capital intensity does not provide such an order. Take the popular, double-switching type of example that caused much excitement in the 1960s (see Pasinetti (1966), Volume III, Chapter 2). These examples show that the same production equilibrium can be supported by discrete price systems and values of the rate of interest. But that is not to say that these two states can be equilibria of the same complete economy – including a fully specified demand side. If we somehow parameterize steady states such that we move from one to the other in the direction of ‘more capital’ in a chain index sense, it is inconceivable that the rate of interest will move monotonically (or even continuously), or that we will visit the same state twice. xix Capital Theory I The Two-Sector Models It is a fallacy to suppose that economic models behave sweetly so long as capital is a single aggregate. The extreme aggregation of the Ramsey–Solow–Swan model involves treating capital as homogeneous with itself and also with consumption output. A series of papers in the 1960s showed that just the separation of consumption from other output leads to richly complicated possibilities unknown to the single-sector, neoclassical growth model. The extract here from Hahn and Matthews (1964, Volume II, Chapter 7) gives a good overview. Even with a fixed constant saving coefficient (which, in this context, has of necessity to be the ratio of the value of capital accumulation to the value of gross product), several ‘paradoxes’ are possible: 1. Short-run equilibrium may not be unique. 2. Even if unique, short-run equilibrium may not be stable. 3. Long-run, steady-state equilibrium may not be unique. The last possibility reiterates what has been written above concerning a generalized Solow– Swan model. Growth Models with Optimal Saving The Ramsey Model The Solow–Swan production function was the same as that used by Frank Ramsey in his classic paper (1928, Volume II, Chapter 2). The critical difference between Ramsey’s approach and that adopted by Solow and Swan is that, while in the latter the saving rate is a parameter, determined by forces not explicitly examined within the model, in the Ramsey model saving is determined by the model itself. The chief purpose of the model is to provide a model of optimal saving. The Ramsey model had little impact when it was first published in 1928. It was before its time, appearing when only a tiny fraction of economists had even a rudimentary mathematical training. When it attracted great interest in the 1960s, as part of a huge flowering of mathematical economics at that time, it was seen almost exclusively as a model of optimal planned development. Recently it has been promoted as a descriptive model, particularly by Robert Barro, who has made it the linchpin of his theory of economic convergence. Barro (1997) provides an up-to-date survey. The merits of two models are not all on one side. While the Solow–Swan model treats the saving rate as a parameter, it is able, as we have seen, to determine the long-run real rate of interest, and to show how it is affected by model parameters. In a simple basic version of the Ramsey model, on the other hand, the long-run real rate of interest is in effect a parameter of the model. This must be so, because (unless the real interest rate is equal to the rate at which savers discount utility) it is always optimal to accumulate more capital, or to decumulate capital. Therefore in a steady state, in which capital per head and consumption per head are both constant, the real rate of interest is equal to the time discount parameter. xx Capital Theory I In such a case, the Ramsey model is not of much use for understanding the determination of the long-run real rate of interest. It says that it is determined by how impatient are savers. And if there are changes in the long-run real rate, these must be explained by alterations in the impatience of savers. And what would explain such alterations? Ignoring these root questions, it is interesting to note that in the Ramsey model the relationship between model parameters and the long-run rate of interest is different from that shown by the Solow–Swan model (see the discussion provided by Bliss (1990), Volume I, Chapter 11). Recall our earlier discussion of Alfred Marshall’s (1920) capital theory. There, Marshall was criticized for an excessive emphasis on impatience without a corresponding emphasis on the other blade of the demand–supply scissors, namely productivity. Now an examination of the Ramsey model tells us that Marshall could have reached the conclusion, as he did with prices, that in the long run only one blade of the scissors cuts. In this case, it would have been the impatience blade. When labour-augmenting technical progress is introduced into the Ramsey model, the optimal steady state has growing consumption per head. To have an optimal stationary state in that case, the utility function of individuals has to take a particular constant-elasticity form. In this case, as with the Solow–Swan model, more rapid technical progress raises the long-run rate of interest. The Ramsey model throws great light on capital theory issues when it is generalized to include many capital goods, as in the model in the long-run equilibrium with capital section, above. Maximum consumption in period t, c t , is given by: F(l t ; k 1t , k 2t , . . . , k nt ; ∆k 1t , ∆k 2t , . . . , ∆k nt ) (6) Consider the problem of maximizing c t + 1 , subject to c t , k 1t , k 2t , . . . , k nt and k 1, t + 2 , k 2, t + 2 , . . . , k n, t + 2 . This problem is well defined, and it establishes a concave functional relationship between c t + 1 and c t , which being concave is weakly differentiable in the sense that it has well-defined left- and right-hand derivatives everywhere. These derivatives measure everywhere not- necessarily-unique consumption rates of return. In the simple Ramsey solution, the rate of fall of marginal utility is equal to the rate of return minus the utility discount rate. This result is valid for the many-capital goods model too. The only difference is that the rate of return is now a range. Consider the implications of this last result for the double-switching paradoxes which were all the rage in the 1960s. Take two stationary states, denoted A and B, which are equilibrium at rates of interest r 1 and r 3 , for A, and r 2 , for B; with: r 1 < r 2 < r 3 (7) Then by varying the utility discount rates, it will be possible to construct Ramsey-optimal steady states which use technology A, and where for discount rates in between (where the discount rate is concerned), there will be a Ramsey-optimal steady state which uses technology B. What can we infer from this? First, because the consumption rate of return frontier is uniquely defined by the technology (A in this case), that frontier must have a corner which enables the Ramsey equilibrium condition to be satisfied with two distinct discount rates. The technology B, which is supported by an intermediate discount rate, must generate a frontier with an intermediate slope. All this is in the xxi Capital Theory I spirit of Solow (in Capital Theory and the Rate of Return), and via him Irving Fisher; but it is simpler, because the rate of return is defined as the shortest inter-temporal consumption substitution. The von Neumann Model John von Neumann’s magisterial paper is of interest for capital theory because it established the first formal model with endogenous growth (see the account provided by Champernowne (1953–4), Volume II, Chapter 11). The model also provided an early example of many-goods general equilibrium. Finally, of particular interest is the point that the model, despite its Austrian source, deals a powerful blow to the period-of-production philosophy. For von Neumann’s input and output matrices make all activities last the same single period length. Any economic processes that last a long time are broken down into a sequence of one-period activities, which produce intermediate goods including part-finished work. This is not to say that Austrian principles may not operate behind this structure. A fast but less productive technique and a slower but more productive technique may both be represented within the von Neumann set- up. And the model solution will decide which technique best serves rapid growth. Diamond’s OLG Capital Model Diamond, whose key paper in this context (see Diamond (1965), Volume II, Chapter 24) married Samuelson’s pure-consumption loan framework to a neoclassical capital model, with a production function and investment. Consider a simple version of the model, perfectly adequate for our purposes, in which the consumer lives for two periods. In the first period of her life, she supplies 1 unit of labour inelastically and earns the wage rate corresponding to the marginal product of the capital that the previous generation saved for its retirement. She may save part of her wage and this becomes the capital which will cooperate with the labour of the next generation. Population grows at rate α, so that each generation is (1 + α) the size of the previous generation. Let the production function give gross output as a function of gross capital. It is, then, as if capital is corn, and young workers lend part of their corn wages to farmers, who plant it in the ground and pay the additional yield of corn resulting next period, when it provides a pension. Details of how this model works can be found in De La Croix and Michelle (2002). Here an informal and intuitive discussion serves to show how this approach paints the determination of the rate of interest in quite a different hue from that seen in the Solow–Swan or Ramsey models. In the Diamond model the long-run equilibrium rate of interest may not be unique. This is in contrast to the Solow–Swan or Ramsey models. Multiple solutions are usually not available with the simple functional forms that economic theorists have usually preferred. In particular with a Cobb-Douglas production function, steady-state equilibrium is always unique; De La Croix and Michelle (2002) provide details. Are the more complex cases that can give multiple solutions implausible, or are they merely untidy? While we would all like the world to be neat and simple, it may not oblige us. In fact deeper issues can also be involved. For example, a ready route to multiple solutions is to make the elasticity of intertemporal substitution endogenous, depending upon the level of prosperity. However, endogenous preferences hugely complicate xxii Capital Theory I economic analysis, if only because endogenous preference means nothing in a static context and can only be defined in a dynamic context. And dynamic preferences can easily be inconsistent. This was shown long ago by Strotz (1956) for time discounting, and the point is far more general. In any case, whether or not it is unique, an equilibrium solution may not be optimal. Imagine that saving goes to buy units in a private or public pension fund. The older generation which co-exists (overlaps) with this young generation will sell all the units which it owns. These will be sold without dividend – i.e. excluding the earnings on the units. In steady state the fund will grow at rate α, issuing new units as required to accommodate population growth. The pension fund lends its capital to firms. These can be represented by a single competitive profit- maximizing firm with one production function. With population growth, the young generation works with less capital than it will save. When they are retired pensioners, these individuals will consume the with-dividend value of their units. The gross rate of return to saving is treated as a constant by workers who decide how much to save, although collectively they influence it. One can usefully view the optimizing decision of a single generation as a mechanism which maps from the K value chosen by one generation into a value of K chosen by the following generation. The following effects can be demonstrated: 1. the higher are the savings of the previous generation, the higher will be the wage rate of the present generation; 2. the higher are the savings of the present generation, the lower will be the gross rate of return which that generation enjoys. These two effects, together with the assumption of regular preferences, imply the following result: assuming future consumption to be a strictly normal good (which rules out the case in which the consumer has a fixed target for the pension) if the previous generation saves more, then so will the present generation. That result is true because a higher wage implies a higher demand for future consumption (regular income effect). Therefore that higher demand must manifest itself in higher saving, unless a price effect resists that movement. That price effect would be a fall in the gross rate of return to saving. But that could only happen if there were more saving. So, there must be more saving in any case. While the slope of the relationship between past and current saving must be positive, it may be greater or less than 1, and this permits multiple steady states. As has been remarked, multiple solution may require variation in the elasticity of inter-temporal substitution σ, which may not be readily accepted. In fact the assumption that σ does not vary, particularly with consumption, is a serious deficiency of much contemporary growth theorizing. If σ varies with the level of consumption the β-convergence of Barro and Sala-i-Martin (1992, Volume III, Chapter 22) can be undermined. This is no mere curiosum point. It is in fact quite plausible to suppose that the poor may be reluctant to save. The reason would be that inter-temporal substitution of consumption which saving requires may be difficult for the poor particularly – not because they have a high discount rate, but rather because they have a low value of σ. Consider a substantial (in this context, substantial means ‘non-atomistic’, so it can be quite small) group of identical young individuals deciding how much to save. When they have chosen the optimal level of saving, they are by definition indifferent between a slightly smaller and a xxiii Capital Theory I slightly higher level of saving, these two values bridging the precise optimum level. The following generation would strictly prefer the higher of the savings levels. The higher the rate, the better the wage rate that they will enjoy. The existing generation, regarded as a collective, would prefer a lower rate of saving from this group, because that would raise the gross rate of return on their own savings. In this comparison the divergent interests concern generations alive (or, at any rate, young) at different times. In many cases, these apparent externalities do not upset the Pareto optimality of market equilibrium. In a normal static case when a group of agents form a champagne club, they impose positive and negative effects on non-members. The club slightly increases the demand for champagne, and hence its equilibrium price. That harms all champagne drinkers, but benefits the factors used in champagne production. None the less, the standard efficiency result of general equilibrium (GE) says that banning champagne clubs cannot benefit all, not even if side payments are made to try to achieve that outcome. In growth models the GE optimality argument can fail. That happens when the rate of interest r is pushed down too low by excess saving. When r falls below the rate of growth, the effectively infinite number of goods in an infinitely lived economy all count in a value comparison. Such excess saving is possible in the Diamond economy. It can also happen in the Solow–Swan model if the saving coefficient is large. It can never happen in a Ramsey-style optimal economy, as inefficiency is plainly non-optimal. A parallel problem can arise in this last case, however, as no optimum need exists where discounting turns out to be too weak. Notice that a steady state which can be dominated by another steady state is not necessarily Pareto-inefficient by virtue of that fact. This is because one has to find a transition path which is Pareto-superior. Even so, for the Diamond model, if a given steady state is dominated by one with a lower saving rate, it is trivial to find such a transition path. Unfortunately, while a goverment can readily enforce a higher rate of saving, it cannot easily enforce a lower rate. Bringing the Arguments Forward Some of the papers assembled in this volume are old, reflecting the fact that what one might call the existential aspect of capital theory has not attracted much interest in the past 25 years. That description applies to the profession at large. A small band of ‘true believers’ has kept up the assault on capital theory orthodoxy until today, and from their company comes at least one of my co-editors; I shall call that loosely connected school the Anglo-Italian theorists. No simple name is ideal, but the one I have chosen indicates at least that the influences of Piero Sraffa and Joan Robinson, in particular, are of central importance. Even in that case, there is a flavour of necrophilia in the air. If one asks the question: what new idea has come out of Anglo-Italian thinking in the past 20 years?, one creates an embarrassing social situation. This is because it is not clear that anything new has come out of the old, bitter debates. Meanwhile mainstream theorizing has taken different directions. Interest has shifted from general equilibrium style (high-dimension) models to simple, mainly one-good models. Ramsey- style dynamic-optimization models have largely displaced the fixed-saving coefficient approach. The many consumers that Stiglitz implanted into neoclassical growth modelling did not flourish there. Instead the representative agent is now usually the model’s driver. Finally, the exogenous technical progress of Harrod, and most writers on growth from whatever school in the 1960s xxiv Capital Theory I and later, has been joined by numerous models which make technical progress endogenous in one of the several possible ways. Endogenous technical progress is not a new concept: the seminal paper is Arrow (1962, Volume III, Chapter 18). Kaldor’s idea that a technical progress function should displace the production function also makes the rate of technical progress endogenous. The key reference is Kaldor and Mirrlees (1962). Here endogenous means simply that the rate of technical progress is not a fixed parameter of the model. It is a variable that must be extracted as part of the overall model solution. These early treatments of variable technical progress are quite mechanical. More recent work has represented technical progress as the output of a profit- driven sector. This view fits better with the fact of huge R&D departments in pharmaceutical and other research-intensive companies. More work is needed to fully develop this line of modelling. Even so, it is striking that old themes emerge in more refined models. Notable is the non-optimality of decentralized market solutions in the presence of endogenous technical change. Arrow had already noted this point. Can the old concerns about capital be taken out, dusted down and addressed to contemporary models? If that could be done, one would hope that its contribution could be more constructive than the mutually assured destruction approach that marred some of the 1960s debates. It is evident that richer models yield richer possibilities. They do not do that in proportion when optimization drives model solutions. However, we know that many-agent models can have multiple equilibria even when all agents optimize. There may be fruitful paths forward in that direction. Old contributions should best be left buried where they involve using capital as a stick to beat marginal theory. All optima imply marginal conditions in some form. These conditions are part of an overall solution. Neither they nor the quantities involved in them are prior to the overall solution. It reflects badly on economists and their keenness of intellect that this was not always obvious to everyone. A Summing Up The lengthy argument developed above leads to the conclusion that we do not have a good theory of the long-run capital equilibrium. That was the view of the Anglo-Italian critics of orthodox capital theory in the 1960s and 1970s. They located the problems of building a long- run theory of the rate of interest in the market equilibrium conditions for the demand for saving in the form of capital goods. That is not correct. A far more difficult problem is to build a theory of the long-run supply of savings. For that problem the Anglo-Italians had nothing to offer. Simple models seem to be inadequate, although they may throw light on some important issues. We can glimpse more convincing models of the supply of capital via saving. They are quite complicated, and have sometimes not been developed explicitly. To be really insightful, it is imperative that a model should be disaggregated, although no usable model can be as disaggregated as realism would dictate. However various influences are weighted, it will be the case that saving rates, demographics and technical progress will be the grand forces driving the long-run interest rate. There is no reason to suppose that the same would not be true for better and more complicated models, if these could be further developed, and if we could get our minds on top of them. xxv Capital Theory I Notes 1. For a detailed exposition and evaluation of Marshall’s capital theory see Bliss (1990). 2. I have deliberately avoided the use of the term ‘school’, as these individuals were far too disunited to merit that description. 3. William Heath Robinson (1872–1944) made his fame by drawing bizarre and absurdly constructed machines. References Barro, Robert J. (1997) Determinants of Economic Growth. Cambridge, MA: MIT Press. Bliss, Christopher (1990), ‘Marshall and the Theory of Capital’, in John K. Whitaker (ed.), Centenary Essays on Alfred Marshall. Cambridge: Cambridge University Press. De La Croix, David and Michel, Phillippe (2002), A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations. Cambridge: Cambridge University Press. Edwards, Sebastian (1996), ‘Why are Latin America’s Saving Rates So Low? An International Comparative Analysis’, Journal of Development Economics, 51, October, 5–44. Fisher, Irving (1930), The Theory of Interest. New York: Macmillan. Hayek, Friedrich A. (1941), The Pure Theory of Capital. London: Routledge & Kegan Paul. Kaldor, N. and Mirrlees, J. (1962), ‘A New Model of Economic Growth’, Review of Economic Studies, 29, 174–92. Keynes, John Maynard (1936), The General Theory of Employment, Interest, and Money. London: Macmillan. Marshall, Alfred (1920), Principles of Economics (8th edn). London: Macmillan. Robinson, Joan (1958), The Accumulation of Capital. London: Macmillan. Sraffa, Piero (1960), The Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press. Strotz, R.H. (1956), ‘Myopia and Inconsistency in Dynamic Utility Maximization’, Review of Economic Studies, 3, 165–80. Swan, T.W. (1956), ‘Economic Growth and Capital Accumulation’, Economic Record, 32 (2), 334–61. xxvi Introduction Capital Theory Controversy: Scarcity, Production, Equilibrium and Time Avi J. Cohen and G.C Harcourt When economists reach agreement on the theory of capital they will shortly reach agreement on everything else. (Bliss, 1975, p. vii) Capital theory is a subject infamous for the continuous recurrence of controversy. This Introduction 1 attempts to explain why that is, by linking the controversy to fundamental problems in capital theory. The singular for controversy is purposeful, as we believe that the same set of issues fuels most controversies in the history of capital theory, going back to the classical economists and Marx, and continuing through the twentieth century. Major controversy erupted around the turn of the twentieth century between Eugene von Böhm-Bawerk, J.B. Clark, Irving Fisher and Thorstein Veblen; in the 1930s between Frank Knight, Friedrich von Hayek and Nicholas Kaldor; and, most recently, in the Cambridge capital theory controversies. Capital theory controversy commonalities originate in the dual nature of capital. Economists conceive of capital both as a heterogeneous collection of specific capital equipment used in production, and as a homogeneous fund of financial value that flows among alternative uses to establish a uniform rate of return. Capital controversy originates in the tension between these physical and value conceptions of capital. In the physical conception of capital, there has been a long-standing neoclassical attempt to ground the rate of interest in the technical conditions of diminishing physical returns in production. This grounding in the objective marginal productivity of capital, coupled with subjective positive time preference, yields an inverse, monotonic relation between the capital intensity of production (the quantity of capital) and the rate of interest. 2 A physical measure of capital that is independent of changes in income distribution and prices, akin to measuring labour in man-hours, would be ideal for this conception. But heterogeneous capital goods cannot be so measured – there is no meaningful physical common denominator between semiconductors and shovels. So capital equipment must be measured in monetary value terms. Because capital equipment takes time to build and yields productive output over time, valuing capital involves the rate of interest to cost the time dimension. The physical conception of capital cannot evade a connection to the value conception. In the financial value conception, capital as investment funds is measured in monetary value terms, and competition dictates that all investments (adjusted for risk) will expect to receive Capital Theory I equal rates of return. Otherwise, investors shift funds from low-return to high-return sectors, until expected returns are equalized. But what about the capital equipment in which those funds are invested? Existing capital equipment might be shifted between sectors, but more often, the physical equipment stays put while its value changes with changing conditions of supply and demand, and with changes in the interest rate which affect the net present value of the equipment. The financial value conception of capital cannot evade a connection to the evaluation of physical capital goods. Economists can usually agree that ‘capital’ has both physical and value conceptions. The controversies begin when the dual conceptions of capital are integrated into economic models and one conception is emphasized to the relative neglect of the other (see Hennings ([1987] 1990), in Volume I, Chapter 1). Most capital controversies of the last 100 years revolve around two major problems: (1) integrating production into the scarcity theory of value, and (2) integrating capital and time into equilibrium models. Two further commonalities exist in attempts to deal with these problems: (3) the panacea of one-commodity models in eliminating the tension between the physical and value conceptions of capital, and (4) the role of ideology and vision in fuelling controversy, especially when one-commodity results are not robust. This introduction, in fleshing out these four common themes, will provide a context for situating the articles that follow. Vision, Value and Price Contemporary first-year economics students are presented with an initial vision of the subject such as this: economics is about scarcity, and scarcity necessitates choices. Resources are finite, wants are infinite and goods have value because they are scarce. The price mechanism allocates scarce resources to their most valuable uses. This vision is intuitively obvious in a pure exchange model. But if we allow for capital and production, the intuition becomes less obvious. In what sense are goods scarce if they can be produced without limit (see Ricardo, 1951, ch. 1, Volume I, Chapter 2)? Before answering that question, we must examine much more carefully three of the above terms: vision, value and price. Most economic discussions today begin and end with price, so the discussions of vision and value may be unfamiliar and, for many economists, unwelcome. But these terms are essential for understanding capital theory controversies. Schumpeter (1954, p. 41) defines Vision as ‘a preanalytic cognitive act that supplies the raw material for the analytic effort’. He later elaborates: 3 In every scientific venture, the thing that comes first is Vision. That is to say, before embarking upon analytic work of any kind we must first single out the set of phenomena we wish to investigate, and acquire ‘intuitively’ a preliminary notion of how they hang together, or, in other words, of what appear from our standpoint to be their fundamental properties. (Schumpeter, 1954, pp. 561–2). Economists’ attempts to understand the complex interdependence of production, consumption, distribution and exchange in capitalist economies can be divided into two major visions (Hennings, 1985). The earlier vision of classical political economy, originating with the Physiocrats, and with a lineage strongest in Ricardo, Marx, Veblen, Schumpeter, Keynes, Kalecki, Kaldor, Sraffa and Joan Robinson, envisions the profit-making decisions of capitalist firms as the driving force of economic activity (see Pasinetti (1983), Volume I, Chapter 4). The xxviii Capital Theory I fundamental economic problem is the allocation of surplus output to ensure reproduction and growth. The dependency of individuals on the market makes one’s position within the social division of labour (social class) the fundamental unit of analysis. Consumption is conceived of as an indirect form of exchange for the purpose of satisfying the goal of production. The rate of profits on capital arises from social relationships in production, and the realization of profits is brought about by effective demand associated with the different saving and spending behaviours of the main classes in the economy and the ‘animal spirits’ of the capitalists. The rate of profits is the rate of self-expansion of capital, the outcome of the accumulation process. The more recent neoclassical 4 vision, originating in Jevons (see Steedman (1972), Volume I, Chapter 6), Walras and Marshall (see Bliss (1990), Volume I, Chapter 11), and integrating capital in a familiar form in Fisher (see Samuelson (1967), Volume I, Chapter 14), envisions the lifetime utility-maximizing consumption decisions of individuals as the driving force of all economic activity, with the allocation of given, scarce resources as the fundamental economic problem. Production is an indirect form of exchange for the purpose of satisfying the goal of consumption (Hirshliefer, 1970, p. 12). (In fact, all capitalist institutions are seen as intermediaries to further the utility-maximizing consumption process.) For capital accumulation, subjective rates of time preference, marginal productivity and the money rate of interest as the price of capital services which clears the market for money loans are fundamental. The rate of interest is the outcome of an inter-temporal optimization process, balancing subjective time preference and the objective marginal productivity of capital (more precisely, the technical rates at which present consumption may be transformed into future consumption). The fundamental properties of each intuitive Vision are embodied in a value theory – the analytical layer between Vision and price theory. Modern economists tend to view value and price as synonyms – e.g. see Debreu’s (1959) Theory of Value. But the distinction has been important to many capital theorists. What is the difference between price theory and value theory? And what is the connection between value theory and vision? We start with the more familiar price theory and work backwards. Corresponding to the two visions are two major price theories in the history of economics (Walsh and Gram, 1980; Pasinetti, 1986). In the earlier classical cost of production theory, natural prices or ‘prices of production’ in Marx and Sraffa depend for a given output, on the technical conditions of production and the given real wage. 5 Neoclassical prices depend on given preferences, endowments and the technology. Using a set of simultaneous equations, price theory captures how the interdependence of production, consumption, distribution and exchange determines relative prices. The focus is on interdependence and simultaneous determination within a general equilibrium framework. Value theory, while recognizing the simultaneous determination of price, goes beyond interdependence to provide an ‘underlying’ or ‘ultimate’ explanation of why goods have value (Pasinetti, 1974, 1986). 6 It identifies a price-independent parameter which is the source of price (Lowe, 1981, p. 803). There is a simple, one-direction linkage from underlying cause to effect on price. 7 The two major value theories in the history of economics use either labour or utility as the ultimate determinant of price. 8 For the classical theory of value, the relative price of a commodity reflects its difficulty of production, which is determined by its price-independent quantity of embodied labour. Increases in relative price are ultimately caused by increases in the quantity of embodied labour. xxix Capital Theory I For the neoclassical scarcity theory of value, the relative price of a commodity reflects its relative scarcity, which is determined by its utility and its quantity, both of which are price independent. Increases in relative price are ultimately caused by increases in utility or scarcity. Although the neoclassical value theory is usually called the utility theory, the term ‘scarcity theory of value’ is equally appropriate, and provides a sharper focus for understanding issues in capital theory. To a modern economist, the value/price distinction sounds decidedly antiquarian – the overwhelming consensus about the validity of neoclassical value theory makes it a non-issue. But the value/price distinction is essential here because the modern consensus on value theory did not exist while many of the articles in this collection were written, was not shared by most of the Cambridge, England, crowd (Sraffa’s book was both a ‘prelude to a critique’ of neoclassical theory and a revival of classical theory (Meek, 1961)) and because the distinction was made and used by most of the capital theorists themselves. Integrating Production into the Scarcity Theory of Value The scarcity theory of value is associated with the task of optimally allocating scarce resources. A pure exchange model (Malinvaud, 1985, ch. 5), with the strong assumption that all commodities are gross substitutes, is useful for illustrating the key propositions of the scarcity theory of value: (1) as a commodity becomes more scarce, its price increases; and (2) if the utility of a commodity increases, its price increases. Price functions as a quantitative index of resource scarcity relative to consumption demand. These two propositions are value theory propositions, in that changes in price are explained causally by changes in underlying, price-independent determinants. 9 The corresponding price theory propositions would be much weaker, stating only that in models with less restrictive assumptions, prices are determined by preferences and endowments (and technology in models with production). Highbrow price theory makes no unequivocal claims about unambiguously signed price effects of underlying parameter changes. In order to focus on the scarcity issue in what follows, utility and demand conditions are assumed not to change. Thus the scarcity theory of value entails, ceteris paribus, a unique inverse relationship between a commodity’s quantity and its price. From as far as Böhm-Bawerk’s (1966 [1898]) controversy with (a posthumous) Marx, all capital theory controversies involve attempts to extend proposition (1) of the scarcity theory of value to models including capital and production. The legitimacy of this extension is not immediately obvious, since in what sense are commodities scarce if they can be produced (Bliss, 1975, pp. 3–4)? But the value theory propositions of price as a scarcity index can be sustained if commodities are produced from exogenously given resources under conditions of constant returns to scale and diminishing marginal productivity. Capital services are treated as a factor of production the price of which – the rate of interest – is determined by the relative scarcity of capital. With this extension, the distribution of income to factors of production becomes merely a subset of general price determination. 10 All of the neoclassical controversies involve models that treat capital as a resource whose price is determined by its relative scarcity. While the models differ in details depending on the author, all share three key ‘parables’. Harcourt (1972, p. 122) took the term from Samuelson (1962, see Volume III, Chapter 1): xxx Capital Theory I 1. An inverse, monotonic relation between quantity of capital (as well as the capital–output ratio and sustainable levels of consumption per head) and rate of interest; 2. Grounding the return on capital (rate of interest) in the natural or technical properties of the diminishing marginal productivity of capital or roundabout production; 3. Explaining the distribution of income between capitalists and labourers from a knowledge of relative factor scarcities/supplies and of marginal products. A one-commodity Samuelson–Solow–Swan aggregate production function model (Volume III, Chapter 1; Volume II, Chapter 3; Swan, 1956) provides the quintessential illustration of the parables: Q = f (K, L) where the one produced good (Q) can be consumed directly or stockpiled for use as a capital good (K). With the usual well-behaved assumptions, in competitive equilibrium, the price of labour (the wage rate) is determined by the relative scarcity and marginal productivity of labour (L). The marginal product of labour, ∂Q/∂L, is a derivative associated with physical magnitudes that are independent of prices. Analogously, the price of capital services (the rate of interest) is determined by the relative scarcity and marginal productivity of aggregate capital. The marginal product of capital, ∂Q/∂K, is also a derivative associated with strictly physical quantities. Resources are physical substances measurable independently of distribution that can explain distribution. Even with production, factor prices (in the form of physical returns to factors of production) reflect relative scarcities. In these parables, the return on capital stems ultimately from utility and technology. There is one-directional causation – from factor scarcities and technology to relative factor prices. Changes in factor quantities cause inverse changes in factor prices, allowing powerful, unambiguous predictions. For these value theory explanations, a physical conception of capital is ideal. But problems arise for the parables in more general models. Heterogeneous capital goods cannot be measured and aggregated in physical units; capital valuation must be used instead, as Wicksell ([1934] 1961, Volume I, Chapter 12) stated so clearly: Whereas labour and land are measured each in terms of its own technical unit (e.g. working days or months, acre per annum) capital … is reckoned … as a sum of exchange value – whether in money or as an average of products. In other words, each particular capital-good is measured by a unit extraneous to itself. [This] is a theoretical anomaly which disturbs the correspondence which would otherwise exist between all the factors of production. The productive contribution of a piece of technical capital, such as a steam engine, is determined not by its cost but by the horse-power which it develops, and by the excess or scarcity of similar machines. If capital were to be measured in technical units, the defect would be remedied and the correspondence would be complete. But, in that case, productive capital would have to be distributed into as many categories as there are kinds of tools, machinery, and materials, etc., and a unified treatment of the role of capital in production would be impossible. Even then we should only know the yield of the various objects at a particular moment, but nothing at all about the value of the goods themselves, which it is necessary to know in order to calculate the rate of interest, which in equilibrium is the same on all capital. (Wicksell [1934] 1961, Volume 1, p. 149; emphasis in original) xxxi Capital Theory I With heterogeneity of either capital or consumption commodities, price invariance disappears. In aggregate models with heterogeneous commodities, the interest rate is no longer determined by a purely physically defined marginal product of capital. Changes in the relative scarcity of a capital good no longer affect just the technical productivity of capital, but also the relative prices of consumption and capital goods. Once relative prices can vary, the marginal product of capital becomes ∂ value output/∂ value capital. 11 Scarcity, the technical productivity of capital and prices now help to determine the interest rate. Distribution depends not only on independent physical magnitudes, but also on prices, which, in turn, depend on distribution. The straightforward physical account of the inverse, monotonic relation between capital-intensity and the rate of interest now becomes a partially circular account with the addition of price changes. The complication of price changes, or Wicksell effects, causes problems for the three parables of the models. Price Wicksell effects are changes in the value of capital as the wage rate and the interest rate take on different values but techniques do not change. Real Wicksell effects are changes in the value of capital associated with changes in techniques as the wage rate and the interest rate take on different values. In the Cambridge controversies, the problems created for the neoclassical parables by Wicksell effects were termed capital-reversing and reswitching. These problems arose in the earlier controversies as well. With capital-reversing, a lower capital–labour ratio is associated with a lower interest rate. In comparing two steady-state equilibrium positions, it is as though capital services have a lower price in the position where capital is ‘more scarce’. Capital-reversing implies the demand curve for capital is not always downward sloping, and violates parables 1 and 2. Reswitching occurs when the same technique (a physical capital–labour ratio) is preferred at two or more rates of interest, while other techniques are preferred at intermediate rates. As the interest rate falls, the cost-minimizing technique switches from a to b and then (reswitches) back to a. Thus the same physical technique (and marginal product of capital) is associated with two different interest rates, violating parables 2 and 3. In general cases with Wicksell effects, the quantity of capital must be measured in value terms and the tension between the physical and value conceptions of capital surfaces. Because the measure of capital can now change without any change in the physical quantity of capital goods, the inverse monotonic relation with the rate of interest need not hold. The rate of interest now depends not only on exogenous technical properties of capital like marginal productivity, but also on endogenously determined prices. This endogeneity of prices complicates the one- way value theory explanation of income distribution based on factor scarcities and technology. Changes in underlying determinants no longer yield unambiguously signed price effects. These problems arise for the underlying value theory explanations. The corresponding price theory explanations are less affected, because they are much weaker to start with. Price theory, with its focus on simultaneous equations and mutual determination, makes no unequivocal claims about unambiguously signed price effects of underlying parameter changes. The only claim is that prices are determined by preferences, endowments and technology, and that in general equilibrium factor returns are equal to or measured by disaggregated marginal products (Blaug, 1975, p. 7; Bliss, 1975, p. 110; Hahn, 1972, pp. 2–4). No general claims can be made for the proposition that an increase in the quantity of capital will cause a decrease in the interest rate. In Hahn’s (1981, p. 128) words, neoclassical price theory ‘is not committed to a relative scarcity theory of distribution’. Bliss (1975, p. 85; see Volume II, Chapter 21) makes the point more forcefully and eloquently: xxxii Capital Theory I Even people who have made no study of economic theory are familiar with the idea that when something is more plentiful its price will be lower, and introductory courses on economic theory reinforce this common presumption with various examples. However, there is no support from the theory of general equilibrium for the proposition that an input to production will be cheaper in an economy where more of it is available. When production is integrated into the scarcity theory of value, the controversies that arise often turn on a value versus price theory perspective. For example, is it important to be able to measure capital in units independent of changes in distribution and prices? Whether or not arguments such as the measurement of the quantity of capital, which is supposed to determine the rate of interest, itself depends on the rate of interest, are considered, a flawed circular argument or the legitimate mutual interdependence of variables, depends on a value versus price theory perspective. Böhm-Bawerk ([1912] 1959a) attacks Fisher’s (1907) equilibrium model of interest rate determination (see Volume I, Chapter 8), claiming that simultaneous equations models involve circular reasoning and thereby fail to provide a ‘causal’ explanation of interest. Fisher defends his model as mathematically determinate in terms of numbers of equations and unknowns. Böhm-Bawerk acknowledges Fisher’s mathematical determination as ‘correct’ and ‘cogent’ ([1912] 1959a, p. 190). But for Böhm-Bawerk, it is not enough. He says that Fisher’s demonstration would be rather nice if mathematical and causal ‘solutions’ of problems were the same … But to find a certain quantity that matches other given assumptions and to explain this quantity are two entirely different things … Certainly a single interest rate corresponds to the state of options that ‘clears’ the market; the problem is solved mathematically. But this mathematical determination fails to inform us on the sequence of causality between the facts. Therefore causal interpretation must accompany mathematical determination. ([1912] 1959a, pp. 191–2; emphasis in original) Based on this passage, Fisher concluded that Böhm-Bawerk’s critique was nothing more than the misunderstandings of a mathematical innocent. Subsequent commentators agreed. Stigler (1941, p. 181) accuses Böhm-Bawerk of ‘failing to understand some of the most essential elements of modern economic theory, the concepts of mutual determination and equilibrium (developed by the use of the theory of simultaneous equations)’. 12 But Stigler is the one who fails to understand that the real source of the simultaneous equations controversy was a fundamental difference between Böhm-Bawerk and Fisher on the need for value theory, as opposed to price theory, for a complete explanation of economic phenomena. Böhm-Bawerk understood and used extensively simultaneous determination in his own subsistence fund model of interest determination. 13 As an Austrian, Böhm-Bawerk required in addition to the simultaneous general equilibrium determination, a one-way value theory explanation from cause (rooted in subjective preferences and what he considered as the only original factors of production – labour and land) to effect (Kauder, 1957). Böhm-Bawerk considers Fisher’s theory of interest as inadequate, first, because as only a partial equilibrium theory, not only are prices given, there is no analysis of factor markets, factor substitution or production. The underlying analysis tracing interest back to the labour market and production decisions is missing (Böhm-Bawerk, 1891, p. 336). Second, Fisher focuses on a price theory explanation. Böhm-Bawerk separated the explanation of interest into two questions: the value theory question as to why interest exists, and the price xxxiii Capital Theory I theory question of how the rate of interest is determined. Fisher claims that an answer to the second question implicitly answers the first question as well. This claim marks the beginning of the modern subsuming of value theory explanations under price theory explanations of the rate of interest. 14 Fisher was willing to bypass value theory concerns because, as part of the emerging neoclassical mainstream, he believed that value theory issues were relatively settled. 15 Böhm- Bawerk’s Austrian views were not entirely mainstream. For him, there were still important value theory issues to be argued. For those like Fisher, who believed that fundamental value theory propositions have been agreed upon, Böhm-Bawerk’s arguments probably appeared as tilting at imaginary windmills. The value versus price theory perspective also provides insight into the fruitless interchanges during the Cambridge controversies about simultaneous equations. As early as 1936, Sraffa wrote Joan Robinson a letter explaining the essence of this measurement problem for neoclassical theory of capital (see Volume II, Chapter 16). Capital-reversing and reswitching were noted in the 1950s by Champernowne (1953–4, Volume II, Chapter 11) 16 and Joan Robinson (1956), but their full significance was realized only with Sraffa’s (1960, Volume II, Chapter 17) book. Sraffa (1962, p. 479) posed the key question regarding the meaning and measurement of capital: ‘What is the good of a quantity of capital … which, since it depends on the rate of interest, cannot be used for its traditional purpose … to determine the rate of interest [?]’ Neoclassicals often complained that Cambridge, England, economists did not understand that the equilibrium solution to a set of simultaneous equations does not entail causal relationships. Von Weizsäcker (quoted in Harcourt, 1982, p. 249) provides a typical example: 17 I really fear that Joan Robinson … has not really understood the basic principle of a system of simultaneously solvable equations and therefore worries about the derivation of the rate of interest from the capital stock, while the definition of the capital stock presumes the knowledge of the interest rate. Where does the puzzle come in all this if one has really understood what a system of interdependent variable is all about? While this characterization of simultaneous equations is correct, it ignores the fact that the neoclassical parables were an attempt to go beyond simultaneous interdependence and provide one-directional causal explanations. When that attempt failed conclusively in aggregate production function models (outside of the one-commodity model), neoclassicals retreated to a defence of simultaneous equations and general equilibrium. The Cambridge, England, critics continued to press the causal point that had been at issue in the neoclassical parables, but the neoclassicals had sidestepped the point by abandoning the scarcity theory of value. For Piero Sraffa, Joan Robinson and others committed to the classical political economy vision, value theory issues were still at stake. 18 But for neoclassicals who presumed value theory questions had long been settled in their favour, the Cambridge causal critique was misunderstood as mathematically ignorant carping (see also Harcourt ([1969] 1986, Volume III, Chapter 9). Integrating Capital and Time into Equilibrium Models These differences in perspective also enter into controversies about integrating capital and time into equilibrium models. Most capital theory controversies of the twentieth century also xxxiv Capital Theory I developed into controversies over how, if at all, may the dynamic processes of accumulation and distribution be analysed within an essentially static equilibrium framework? Capital is fundamentally intertwined with issues of time, and a state of equilibrium, as Hicks (1976, p. 140) notes, ‘is a signal that time … has been put to one side’. Bliss (1975, p. 346) captures well this particular capital theory controversy commonality in describing the theory of capital ‘not as some quite separate section of economic theory, only tenuously related to the rest, but rather as an extension of equilibrium theory and production theory to take into account the role of time’. To understand the capital–time–equilibrium connection, we begin with the connection between capital and time before looking at its integration into equilibrium models. The distinction between the physical and value conceptions of capital also comes into play in the representation of capital and time. Capital and Time The value of a firm’s investment in capital goods can be calculated in terms of cost-of-production or net present value. Both calculations use the interest rate either to cost the time money is tied up in construction or to discount the stream of expected future returns. While time is obviously involved in valuing capital goods, many capital theorists have gone much further, identifying capital as time. Starting with Böhm-Bawerk, capital theorists have claimed that ‘time is productive’ or that the productivity of capital is the productivity of time itself. Examples include Wicksell’s ([1934] 1961) and subsequently Samuelson’s (1966a, Volume III, Chapter 4) wine maturing in casks, J.B. Clark’s forests producing firewood, Fisher’s orchards and Knight’s Crusonia plant (1944, Volume III, Chapter 17), all of which grow at a constant rate, increasing in value over time without human aid. One of Böhm-Bawerk’s (1959, Volume I, Chapter 8) many contributions was to transform this natural productivity of time into a social conception of the productivity of roundabout methods of production. His classic example was catching fish. Human labour alone, unaided by capital, could catch fish (albeit poorly). But if instead of catching fish directly, the fisherman were to spend some time first making a net, that more ‘roundabout’ method of production would increase the productivity of fishing. And further extensions of roundaboutness (building a boat, better nets, etc.) by the fisherman or by capital goods firms, would further increase productivity, but at a diminishing rate. Böhm-Bawerk’s period of production attempted to measure both roundaboutness and the capital intensity of production. With these measures in place, the interest rate was determined by the marginal productivity of additional roundaboutness = capital = time. While the mathematical formalizations of these propositions has grown exponentially since Böhm-Bawerk’s contributions, what has remained constant is the essential idea of the (diminishing marginal) productivity of more capital-intensive/roundabout production processes as a determinant of the interest rate. Capital, Time and Equilibrium To see why capital theory controversies become equilibrium controversies consider what happens when we integrate the time-dependent measures of capital into a simple, two-factor isoquant model of production, à la Joan Robinson (1953–4, Volume II, Chapter 10). xxxv Capital Theory I Capital Theory – Fig unnumbered Labour Capital 0 A 1 2 B xxxvi The quantity of labour input (in hours) is measured on the vertical axis. The quantity of capital input is measured on the horizontal axis. Capital must be measured in value units because of the heterogeneity of capital goods. The isoquant represents all of the technical factor substitution possibilities between labour and capital for producing a given output. The convex shape of the isoquant reflects the diminishing (but positive) returns to increasing the factor intensity of production in either direction. For a given set of factor prices (wage rate and interest rate) represented by the slope of the isocost line, the tangency point with the isoquant represents the lowest-cost method of producing that quantity of output. For that method of production, marginal factor products are equal to factor returns. If the economy is in long-period equilibrium at the prices represented by isocost line A, then today’s prices have remained constant over a long past and are expected to remain constant over a long future. A firm considering investing its financial capital into a new factory will choose the method of production represented by point 1. At that point, the quantity of capital, whether measured as a dollar amount of investment, the cost of production or the expected net present value of the factory, is the same. Similarly, if the economy is in long-period equilibrium at the prices represented by the isocost line B, then a firm investing in a new factory will choose the method of production represented by point 2, and all three measures of capital will be equivalent at that point. But what if, under the initial long-period conditions, the firm builds the factory of point 1. Then factor prices change (unexpectedly) to those of isocost line B where the interest rate is lower relative to the wage rate. This is where all of the problems begin: ‘When an unexpected event occurs, the three ways of evaluating the stock of goods part company and no amount of juggling with units will bring them together again’ (J. Robinson, 1953–54, p. 84, Volume II, Chapter 10). With different values of the interest rate, the net present value will no longer be equal to the initial investment or the cost of production. A measure of the firm’s capital can have three different quantitative values. Nor is it clear how the isoquant could be made coherent because each point on it is associated with a different price system and so an attempt to ‘move’ from one point to another will ‘change’ their positions. The time-related questions this raises about the transition from technique 1 to technique 2 are therefore even more problematic and important. Economists traditionally use comparative statics to tell the transition story. When factor prices Capital Theory I change, profit-maximizing (or cost-minimizing) firms change production techniques, substituting away from the relatively more expensive factor and making more use of the relatively cheaper factor. With a relative fall in the interest rate, this implies that the firm operating at point 1 will move to the more capital-intensive production process at point 2. But in comparing points 1 and 2, is the increase in the quantity of capital simply an increase in the net present value of the existing capital goods (due to the lower interest rate), or is it an increase in physical capital goods? 19 Furthermore, will the firm actually move to technique 2? After all, technique 2 represents the factory the firm would have built ab ovo, if factor prices always had been and were expected to be those of isocost curve B. Will a firm with installed equipment of technique 1 necessarily move to the same technique? Does the existence of specific physical capital goods create any path dependence that affects the firm’s decisions? And what about the stability of the existing or new equilibrium positions? Once the firm is out of equilibrium, to what point does it return, and what are the disequilibrium dynamics? All of these questions, pertaining to the comparison of equilibrium positions in a simple static equilibrium model, persist and are only multiplied in comparing different equilibrium stationary states or steady-state equilibrium growth paths or inter-temporal general equilibrium models of economies along different semi-stationary growth paths. Can differences in equilibrium positions be used to accurately represent or explain changes taking place over time? The term ‘comparative statics’ (and the analogous ‘comparative dynamics’) is descriptive of the comparison of different static (or stationary or steady-state) equilibrium states (or growth paths). But do those comparisons represent the outcome of the actual process set in motion by a change in prices or in some other parameter of the model? These questions troubled most capital theorists and generated much controversy. Böhm- Bawerk, Veblen (1908, Volume I, Chapter 18), Knight (1944, Volume III, Chapter 17), Kaldor, Hayek, Hicks and Joan Robinson (1975, Volume III, Chapter 13) all had serious concerns about using differences in equilibrium positions to explain changes over time. Joan Robinson’s answers to the questions in the preceding paragraph are most famous. Throughout the Cambridge capital theory controversies, she ‘frequently had occasion to complain of the inability of neoclassical writers to distinguish between a difference in the parameters of an equilibrium model and the effects of a change taking place at a moment of time’ (1980b, p. vii; emphasis in original). One of her clearest, and typically confrontational, statements is: It is an absurd, though unfortunately common, error to suppose that substitution between labour and capital is exhibited by a movement from one point to another along a pseudo-production function. Each point represents a situation in which prices and wages have been expected, over a long past, to be what they are today, so that all investments have been made in the form that promises to yield the maximum net return to the investor. The effect of a change in factor prices cannot be discussed in these terms. Time, so to say, runs at right angles to the page at each point on the curve. To move from one point to another we would have either to rewrite past history or embark upon a long future. (1971, pp. 103–4) Whether or not the concerns Joan Robinson and the others voiced about comparative statics are justified depends on the stability underpinnings of equilibrium models. And even if the comparative static results are theoretically justified, the question of their empirical significance remains to be assessed. xxxvii Capital Theory I Equilibrium, Path Dependence and Stability Economics’ claim as a discipline to scientific status is rooted in the use of equilibrium concepts and the empirical testing of equilibrium models to explain the complexities of economic life. To be able to go beyond descriptive statements like ‘everything depends on everything else’, economists construct simplified models that attempt to capture the most important forces operating in complex, interdependent economies that are changing over time. Simultaneous equation models attempt to capture the essential interdependencies. But with simultaneous determination, there is no sequence of events over time, and hence no causation. As equilibrium models, however, simultaneous equations also attempt to capture the outcomes of the key forces of self-interest and competition that move the economy over time to predictable, objective outcomes. These forces are seen as operating like natural laws. Self-interest, in the form of utility maximization, is presented as a characteristic of human nature, independent of social organization. When the assumption of nonsatiation is coupled with finite resources and diminishing returns, scarcity becomes an unavoidable natural condition. Combining self-interest with competition provides causal explanatory stories that are a core strength of economics – the inevitable exploitation of all unexploited opportunities for gain, and the competitive enforcement of objective outcomes. The equilibrium outcomes of these models represent a balance of the forces of self-interest and competition, where no agent can do any better and resources are allocated efficiently. To use equilibrium models to explain a process in time, we make the further assumption that the equilibrium is a useful reference point of the actual expected outcome of the economy, a stable outcome of a disequilibrium process. In our simple isoquant model, given the factor prices of isocost line A, if the firm does not choose technique 1, it will not be minimizing its costs and will ultimately be competed out of business. A similar stability story applies to comparative statics. If the relative price of capital services falls (the isocost line shifts from A to B), firms who shift to the more capital-intensive technique 2 will minimize their costs and gain a competitive edge. The equilibrium ‘is said to be like the vertical position of a pendulum’ (Joan Robinson, 1962, p. 22). Any perturbation away from equilibrium will be self-correcting, just like the pendulum returning to the vertical position. The stability stories of price adjustment to a single equilibrium position or of comparative statics adjustments to a change in parameters do ‘run at right angles to the page at each point on the curve’. The stability stories describe a putative sequence of out-of-equilibrium positions that is not represented explicitly in the simultaneous equations of the equilibrium model, but rather in the stability literature which we will examine momentarily. Among capital theorists, Joan Robinson’s questions about whether equilibrium is the end of an actual economic process are the most extreme (and often characterized as theoretically nihilistic – see Cohen (1993)). But to focus on her shared concerns with others about the limitations of equilibrium, 20 Bliss’s (1975, p. 27) distinction between two conceptions of equilibrium is instructive. One conception is of equilibrium as an actual outcome ‘which would be expected to be realized, because the dynamic forces which operate … bring the economy to an equilibrium’. The other is of equilibrium as ‘no more than an analytical stepping stone, as a necessary simplification to render possible some progress in an otherwise hopelessly difficult analytical endeavour’. All capital theorists, including Joan Robinson, accept the second conception. 21 Controversy centres on the first conception. xxxviii Capital Theory I When economists build equilibrium models and then subject them to empirical test, there is an implicit if not explicit belief that the outcomes of the model will be detected in the data. There is a belief that the equilibrium outcome captures the effect of the most important forces actually operating in the economy. This entails the stronger conception of equilibrium as an actual outcome of dynamic forces, which concerned so many capital theorists. This belief presupposes the stability of equilibrium outcomes, and the general equilibrium stability literature has validated the concerns of Robinson and others. The stability literature is one of the major theoretical concerns of the Arrow–Debreu general equilibrium project: demonstrations of existence, uniqueness and stability of an equilibrium price vector. 22 Stability implies that when a model is not in equilibrium, prices will increase with excess demand and decrease with excess supply. Scarf (1960) was the first to show that perfectly well-behaved general equilibrium models, each with a unique equilibrium, will none the less be characterized by the global instability of competitive equilibrium. His counter- example ended the hope that tâtonnement models would be generally stable under ordinary microeconomic assumptions. Subsequently, the Sonnenschein–Mantel–Debreu (SMD) results on the lack of restrictions on aggregate excess demand functions have made it easier to produce examples of Walrasian economies that lack stability. Stability holds in only a few, quite restrictive, special cases. 23 Based on these results, Hahn (1984, p. 53) admits that ‘the Arrow– Debreu construction … must relinquish the claim of providing necessary descriptions of terminal states of economic processes’ (see also Hahn, 1966, Volume II, Chapter 20). The concern with dynamic stability was also tied to determinate comparative statics results through Samuelson’s (1941, 1942, 1947) ‘Correspondence Principle’. Samuelson hoped to demonstrate a one-to-one correspondence between the stability of the price adjustment mechanism and the signs of the comparative statics expressions associated with changes in system parameters. During the 1960s and 1970s, attempts were made to apply the correspondence principle to the Walrasian general equilibrium model. But the sign of the effect on prices of a given change in the parameters of a general equilibrium model turns out to be, with few exceptions, indeterminate. 24 Arrow and Hahn (1971, p. 245), after investigating ‘the power of general equilibrium models in giving unambiguous predictions of how the equilibrium of an economy will be affected by a given parameter change’, find that even with the strong assumptions necessary to guarantee the uniqueness of an equilibrium, ‘the kind of parameter changes for which predictions become possible is pretty limited’. They conclude that ‘the correspondence principle isn’t’ (1971, p. 321). The lack of adequate stability results calls into question the conception of equilibrium as the end of an economic process, the adequacy of comparative statics as reliable explanations of the process of change following a parameter shift, 25 and the basic neoclassical vision of the utility- maximizing consumption decisions of individuals driving an optimal allocation of resources through the mechanism of prices as scarcity indexes: 26 If one thinks of a competitive economy as a dynamic system driven by the self-seeking actions of individual agents, does that system have competitive equilibria as stable rest points? If so, are such equilibria attained so quickly that the system can be studied without attention to its disequilibrium behaviour? The answers to these crucial questions remain unclear … we have no rigorous basis for believing that equilibria can be achieved or maintained if disturbed. (F. Fisher, 1989, pp. 36, 37) xxxix Capital Theory I Given these results, believers in Bliss’s conception of equilibrium as the actual outcome of an economic process (and this would be the vast majority of economists) must resort either to ‘faith’ that the disequilibrium dynamic results will someday arrive, or to an ‘as if’ methodological justification. Bliss (1975, p. 28) nicely characterizes the resort of ‘faith’: In the face of all the [disequilibrium dynamics] problems it may seem more sensible to simply assume that equilibrium will prevail … [W]e could attempt to justify this procedure as a useful starting point to what one might eventually hope to see realized in a complete account of the behaviour of the economy, including a full specification of its disequilibrium dynamics. This approach … may seem to be more attractive, if only because more tractable, than the Herculean programme of constructing a complete theory of the behaviour of the economy out of equilibrium. Bliss’s suggestion amounts to sidestepping the stability problems by declaring faith in their eventual solution through future research. The ‘as if’ methodological justification – associated most closely with Friedman (1953) – makes no claims that the outcomes of an equilibrium model actually occur. The model simply predicts empirical outcomes that are the same ‘as if’ they were the result of an equilibrating process. Whether or not the model’s equilibrium outcomes are the end of an actual economic process is irrelevant. All that matters is the predictive accuracy of the model. Equilibrium modelling continues to dominate the economics profession, regardless of the paucity of stability results. All economists use equilibrium as an ‘analytical stepping stone’, and the dual defences of ‘faith’ and the ‘as if’ methodological justification clearly suffice for most economists to view an equilibrium as an actual outcome. To even raise questions about the limitations of comparative statics explanations is to be identified as an outsider to the profession. But over the past century, these questions about the limitations of equilibrium models were an acceptable and constant theme in controversies over integrating capital and time into equilibrium models. Capital theory controversies often developed into controversies over the limitations of equilibrium for dealing with time, through the dual nature of capital as both financial value and physical equipment. A comparison of equilibrium points on an isoquant diagram (like points 1 and 2) makes perfect sense for financial capital which is perfectly mobile. But if physical capital is installed at point 1 and prices change, issues of path dependence arise. Many controversies occurred over whether the equilibrium models capture what happens in actual time, and an author’s position on equilibrium is often correlated with the author’s emphasis on either the financial aspect of capital (equilibrium models are fine) or on the physical aspect (equilibrium models are inadequate). Böhm-Bawerk, in arguing against J.B. Clark’s concepts of ‘pure’ financial capital and static equilibrium states, claimed that out of equilibrium, ‘in a dynamic economy … where concrete capital goods are … changing’ (1895, p. 127), then ‘the whole subject of the transfer of capital must be studied with reference to capital-goods’ (1906, p. 18). Veblen’s interest in the physical and institutional aspects of capital coupled with an evolutionary methodology of cumulative causal sequences led him to criticize equilibrium as an inadequate concept for analysing these issues. 27 Irving Fisher’s emphasis on financial aspects of capital left him a defender of equilibrium modelling against Böhm-Bawerk’s criticisms of the need for a one-directional ‘causal’ explanation. 28 Knight conflates the physical and financial aspects of capital in his famous Crusonia plant, and believes that that ‘normal-equilibrium price analysis has no application to xl Capital Theory I a situation of … the capital market’ (1936: p. 614). 29 Kaldor (1938, p. 164), like Knight, melds the physical and financial aspects of capital, and attacks Hayek’s theory as not a ‘tenable explanation of the nature of capital’ for a society in a ‘process of change’. Kaldor also believes that ‘the method of comparative statics (which treats change as a result, and not as a process) is applicable to problems of capital accumulation’ only for short-period analysis. 30 Hayek’s interest in the role of specific physical capital goods in causing business cycles led him to de- emphasize the concept of equilibrium 31 in favour of what he called dynamics: When it is used in contrast to equilibrium analysis in general, it refers to an explanation of the economic process as it proceeds in time, an explanation in terms of causation which must necessarily be treated as a chain of historical sequences. What we find here is not mutual interdependence between all phenomena but a unilateral dependence of the succeeding event on the preceding one. This kind of causal explanation of the process in time is of course the ultimate goal of all economic analysis, and equilibrium analysis is significant only in so far as it is preparatory to this main task. (1941, p. 17) All of the authors above get into controversies about equilibrium as a result of the problems of integrating the physical and financial aspects of capital into equilibrium models. The Panacea of One-Commodity Models The essential tension between the physical and financial conceptions of capital is at the root of most capital theory controversies per se, as well as contributing to controversies over the adequacy of equilibrium models for dealing with time. That tension, however, can be dissolved instantly and completely with a single assumption – by limiting the model to one commodity. There are two other modelling assumptions that can yield the same results as one-commodity models. One is the assumption of ‘putty’ capital, which can instantaneously and costlessly change physical form. The other is the assumption of equal factor proportions in all industries. These assumptions eliminate the two major classes of problems underlying all capital theory controversies: (1) problems integrating production into the scarcity theory of value, and (2) problems integrating capital and time into equilibrium models. The power of the one-commodity, putty capital and equal factor proportions assumptions lies in merging the physical and financial aspects of capital, thereby eliminating the effects of interdependence and time. With the assumptions of one-commodity/putty capital/equal factor proportions, the three neoclassical parables are preserved: (1) an inverse, monotonic relation between the quantity of capital (as well as the capital–output ratio and sustainable levels of consumption per head) and rate of interest; (2) grounding the return on capital (rate of interest) in the natural or technical properties of the diminishing marginal productivity of capital or roundabout production; and (3) explaining the distribution of income between capitalists and labourers from a knowledge of relative factor scarcities/supplies and of marginal products. One-Commodity Models Samuelson’s (1962, Volume III, Chapter 1) prototypical one-commodity model (see, above, p. xxxi) has all of these characteristics. 32 With only one commodity, there is no interdependence xli Capital Theory I between sectors since there are no relative prices of commodities that can vary. A change in distribution between wages and profits has no impact on relative prices. This eliminates the complication of price changes resulting from the differing factor proportions underlying the production of heterogeneous commodities. With price invariance, all resources, including capital, can be defined in exogenously given physical quantities. There are no aggregation problems since there is only one (capital) good. The rate of interest is determined by the physical marginal product of capital, depending solely on the technology and the scarcity of capital relative to consumption demand. There can be no Wicksell effects. All prices, including the price of capital services, reflect the relative scarcity of the exogenously given resources. The one-direction causation of value theory explanations remains intact in a model with capital and production, that determines relative prices (at least the prices of labour and capital services) according to the scarcity (and utility) of commodities. The one-commodity model not only sustains the scarcity theory of value, it also eliminates problems arising from integrating capital and time in equilibrium models. To start, a change in the interest/profit rate has no impact on the measurement of capital in a one-commodity model. As a result, an equilibrium position with more capital is unambiguously a position with more physical capital. Problems comparing equilibrium positions also disappear in a one-commodity model. Substitution between capital and labour as factor prices change is straightforward. With a single homogeneous (capital) good, as the interest rate falls, a firm with an existing technique can increase its capital intensity simply by adding more capital. There are no problems of heterogeneous capital goods with specific uses becoming inappropriate as factor prices change. This eliminates any path dependence, allowing all existing techniques to be costlessly and timelessly transformed into new techniques with different factor proportions. Physical capital goods take on the same properties as financial capital, flowing costlessly between investment opportunities. Without path dependence or the interdependence of prices across sectors, any deviation from equilibrium will be costlessly corrected. The stability and disequilibrium dynamics problems from general equilibrium models do not arise. This is not surprising, since in simple general equilibrium models where all goods are gross substitutes, such problems are also absent and the scarcity theory of value propositions hold. The logical limit of a model where all goods are gross substitutes is a one-commodity model. One-commodity models sustain the strong conception of equilibrium as an actual outcome of dynamic disequilibrium forces. Comparative statics provide a full explanation of the process of change resulting from a change in underlying parameters, and the Correspondence Principle holds. Putty Capital Even if capital is a separate good from the consumption good, the assumption of putty capital also preserves the results of the one-commodity neoclassical model and avoids problems of integrating both production and capital into the scarcity theory of value, and capital and time into equilibrium models. By assuming capital goods to be perfectly malleable and composed of a homogeneous ‘putty’, physical specific capital goods acquire the same quality as financial capital – the ability to flow costlessly between investment opportunities. In the capital theory controversies surveyed here, Böhm-Bawerk was the first to note this equivalence in Clark’s concept of true capital: ‘Clark thinks of capital as a quantum of value xlii Capital Theory I “imputed” in material goods. He strips off everything which may suggest material existence, and retains only a value jelly, existing eternally, never destroyed’ (Böhm-Bawerk, 1907, p. 280; emphasis added).This ‘value jelly’ flows costlessly (is ‘never destroyed’) between investment opportunities. 33 Swan (1956) introduced putty capital in the Cambridge capital controversies through the analogy of meccano sets, the pieces of which can be timelessly and costlessly transformed into appropriate quantities of ‘capital’ in response to the pull of relative factor prices. Separate putty capital goods function almost identically as one-commodity capital. Putty capital can be aggregated without problem, is not revalued through Wicksell effects and still has a determinate physical marginal product (∂Y /∂K). While this marginal product is not a pure number as in the one-commodity model, it is still a derivative associated with two physical magnitudes that do not change with changes in distribution or in prices. In comparing equilibrium positions, the assumption of putty capital avoids any path dependence. The existing capital stock can be costlessly and timelessly remoulded to the form most appropriate for the new equilibrium conditions. As time progresses and conditions change, making the initial stock of capital goods non-optimal, putty capital restores optimality, so that there is no need to resort to a historical, out-of-equilibrium dynamics story. 34 Salter (1965, p. 268; and Salter 1966, Volume II, Chapter 6) provides one of the best descriptions of the consequence of putty capital assumptions: one consequence of the assumptions of fluid capital and instantaneous adjustment is that they prevent analysis of the actual time path of an economy … the assumption of fluid capital effectively cuts off an economy from its own past history. At each point of time, the economy is assumed to start off, as it were, with a clean slate independent of its past history and techniques. Equal Factor Proportions The parable results of the neoclassical model can also be preserved by the assumption of equal factor proportions in all consumption commodity and capital good industries. Equal factor proportions ensures price invariance, so that the relative prices of consumption and capital commodities do not change with changes in the distribution of income between wages and profits. This is the assumption Samuelson (1962, Volume III, Chapter 1) made in an attempt to introduce what looked like heterogeneous capital goods into his initial one-commodity model. But this assumption effectively collapses the model into a one-commodity model, as Samuelson (1966a, Volume III, Chapter 4) and others (Garegnani, 1970, Volume III, Chapter 3; Ferguson and Hooks, 1971; Pasinetti, 1969 (Volume III, Chapter 5); Spaventa, 1970; Harcourt, 1969 (Volume III, Chapter 9), 1972, ch. 4) subsequently recognized. Too Much of a Panacea? Because of the power of the assumptions of one-commodity (or equivalently, putty capital or equal factor proportions), most participants in capital theory controversies used the assumptions in their models. But the use of one-commodity models is a double-edged sword. By simplifying so extensively, one-commodity models allow many competing theories to demonstrate their results. As distinct subsets within the basic neoclassical approach of extending the scarcity theory of value to equilibrium models with production and time, Böhm-Bawerk, Hayek and Kaldor get Austrian capital theory results from their one-commodity models; Solow, Swan and xliii Capital Theory I Samuelson get the standard neoclassical parable results; and Knight’s Crusonia plant model justifies his unique perspective. But one-commodity models can also be used to validate the other dominant value theory in the history of economics – the classical theory of value which conceives of price as an index of the difficulty of production. Sraffa’s reconstruction of Ricardo’s corn model in the Essay on Profits is the classical (in all senses of the word!) one-commodity model. Labour and seed corn produce more corn. With less fertile soil, the technical difficulty of producing corn increases as does the labour requirement. Because the real wage is defined in corn, the technical and distributional determinants of the ‘implicit corn price’ collapse into a unidimensional quantity of corn inputs that increases monotonically with the difficulty of production. 35 Ricardo’s explicit illustration of the labour theory of value comes in the equal factor proportions model of Chapter 1 of the Principles (1951, Volume I, Chapter 2). By assuming equal factor proportions (and capitals of equal durability), prices are independent of distribution and are proportional to the exogenously given quantity of (direct and indirect) labour embodied in each commodity. Marx’s equal factor proportions model (equal organic composition of capital) in Volume I of Capital goes beyond Ricardo’s proportionality of prices to embodied labour. Marx’s ‘prices of production’ are equal to embodied labour values, and profit is attributable to surplus value exploited from labour. 36 What is the source of the power of one-commodity models to validate so many, and such differing, visions of economic activity (Cohen, 1989, Volume III, Chapter 16)? Why can the neoclassical scarcity theory of value (in many variations) and the radically different classical theory of value both be substantiated in one-commodity models? The key is the price invariance that suppresses mutual interdependence. A change in any of the interdependent elements of production, consumption, distribution and exchange normally causes a change in prices. The price invariance of the one-commodity model neutralizes that interdependence, allowing a theory to focus attention on some elements while downplaying others. The relative neoclassical focus is on consumption and exchange, the relative classical focus is on production and distribution. Both neoclassical and classical theories of value are sustained when prices are invariant to changes in distribution. This condition holds in a one-commodity model, and in putty capital and equal factor proportions models that are effectively equivalent to a one-commodity model. In more general heterogeneous commodity models of each theory, prices vary with changes in distribution. This causes critical exogenous conditions of each one-commodity model to become endogenous. Instead of being determined by exogenously given physical magnitudes, the rate of interest in neoclassical theory depends on prices, which, in turn, depend on the rate of interest. The internalization of the measure of capital is the source of the possibilities of capital reversal and reswitching. As a result, the rate of interest (or, more generally, the cost of capital services) will not necessarily reflect the relative scarcity of capital, and the inverse monotonic relation between the quantity of capital and the rate of interest need not obtain. Once prices vary with changes in distribution, the strong classical conception of price as an index of the exogenous difficulty of production is immediately violated. The rate of profits, which previously depended only on exogenously given physical magnitudes of outputs and inputs, comes to depend on the prices of outputs and inputs, which, in turn, depend on the rate of profits. The internalization of the measure of inputs to production eliminates the necessity of an inverse relation between the real wage and the rate of profits. xliv Capital Theory I Thus the price invariance of one-commodity models allow the key parameters of value theory explanations to remain exogenous, preserving unambiguous, one-directional cause-and- effect explanations. By eliminating the effects of interdependence, price invariance also eliminates the source of the stability and disequilibrium dynamics in general equilibrium models. Once prices vary with changes in the mutually interdependent realms of production, consumption, distribution and exchange, the simultaneous determination of price theory takes over. And in the realm of price theory, the simple, parable-like explanations like ‘an increase in capital causes a decrease in the price of capital services’ cannot be supported. In a famous passage about one-commodity models in ‘Parable and Realism in Capital Theory: The Surrogate Production Function’, Samuelson (1962, p. 193; Volume III, Chapter 1) is too correct by half when he notes that: ‘Such simple models or parables do, I think, have considerable heuristic value in giving insights into the fundamentals of interest theory in all its complexities.’ While heuristically valuable, the insights one-commodity models provide do not allow us to distinguish between competing theories that view interest or profits as payment for the marginal productivity of capital, or as exploitation of workers. This leads us to one of the key questions for the final section of this Introduction. What happens when the robust results of one-commodity models do not generalize to heterogeneous commodity models where prices can vary? Ideology and Vision Capital controversies often centre on abstract technical questions like the importance of Wicksell effects and the measurement of the period of production or of the capital stock generally. But, as Bliss (1975, p. 346) notes, ‘a consideration of technical questions alone will never reveal why the theory of capital is such hotly contested territory. Everyone understands that there is a strongly ideological element to the debates, but the element is an elusive one.’ While the role of ideology is elusive, it is simultaneously pervasive as a ‘sub-text’ to controversies over seemingly dry technical questions. Ideology has two important entry points into the past century of capital controversies. First, ideology is involved in the ethical justification of profit and interest. Second, ideology plays a role in sustaining the ‘faith’ that disputants maintain in their fundamental theories when their one-commodity results do not generalize, and in motivating the faith (articulated previously by Bliss) that equilibrium outcomes are the result of processes of adjustment, despite the lack of stability results for disequilibrium dynamics. Ideology is deeply embedded in capital theory controversy at the level of Schumpeter’s (1954, p. 42) ‘Vision’: Analytical work begins with material provided by our vision of things, and this vision is ideological almost by definition. It embodies the picture of things as we see them, and wherever there is any possible motive for wishing to see them in a given rather than another light, the way in which we see things can hardly be distinguished from the way in which we wish to see them. To understand the complex interdependencies in the economy, theorists must make choices about which factors to focus on as essential for understanding, and which to relegate to secondary importance. While ideology does not affect the logic of a proof or the derivation of a theorem, ideology is embedded in our choices of models, of assumptions, of topics deemed worthy of xlv Capital Theory I our investigative efforts. These choices at the level of vision cannot be evaluated as true or false by checking facts, and so there is room for ideology to enter. 37 The Ethical Justification of Profit and Interest In the neoclassical vision, the distribution of income to factors of production is a subset of general price determination. Scarcity determines the margin, and marginal productivity determines factor returns. Capital services are treated as a factor of production the price of which – the rate of interest – is determined by the relative scarcity of capital. The return on capital is grounded in natural or technical conditions that are exogenous to society – utility and technology. Interest is a payment for a service, the productivity of capital, on a par with wages as payment for the productivity of labour. The neoclassical vision contrasts sharply with other vision prominent at the time when neoclassical capital theory controversies began – Marx’s vision of profit as exploitation and the associated labour theory of value (see Marx ([1891] 1972), Volume I, Chapter 3). Profit for Marx (the classical term for the return to capital) is the appropriation by the capitalist of surplus value actually produced by the labourer, made possible by the dominant power position of capitalists in bargaining relationships. Marx defines capital as ‘a social power’. Without direct access to finance and the means of production and unable to subsist independently, labourers (as a class) must enter into a bargain with capitalists (as a class) on unequal terms. The labour theory of value ‘enables’ the analysis to penetrate below the sphere of exchange and prices (where there is an ‘illusion’ of voluntary exchange and mutual benefit) to illuminate the sphere of production where there is an underlying exploitative relation between capitalists and labourers, even under normal competitive conditions. Most disputants in the late-nineteenth- and early-twentieth-century capital theory controversies (Böhm-Bawerk, Clark, Irving Fisher) were consciously engaged in countering Marx by constructing an alternative theory of profit/interest (Tobin, 1990, p. 166). J.M Clark (1931, p. 170), looking back on that era of his father, notes that: The marginal theories of distribution were developed after Marx; their bearing on the doctrines of Marxian socialism is so striking as to suggest that the challenge of Marxism acted as a stimulus to the search for more satisfactory explanations. They undermine the basis of Marxian surplus value doctrine by basing value on utility instead of on labour cost and furnish a substitute for all forms of exploitation doctrine, Marxian or other, in the theory that all factors of production are not only productive but receive rewards based on their assignable contributions to the joint product. Böhm-Bawerk certainly fits this description. His 1884 history of capital and interest theories criticized Marx’s theories of value and surplus value from Volume I of Capital, and noted Marx’s promise in a future work to explain the discrepancies between labour values and prices of production. Two years after the third volume of Marx’s Capital was published posthumously, Böhm-Bawerk published a book-length review of 115 pages entitled Zum Abschluss des Marxschen Systems (1896). This was translated in English as Karl Marx and the Close of His System ([1898], 1966). The English title calls attention to Marx’s attempt to keep his promise to complete his system of analysis by linking values to prices. Böhm-Bawerk, writing from the perspective of subjective value theory, condemns Marx’s system as built on ‘a house of cards’ ([1898] 1966, p. 118). 38 xlvi Capital Theory I J.B Clark, in the Distribution of Wealth (1899, Volume I, Chapter 10), introduces his work as an explicit counter-argument to Marx’s ideas. Clark is worth quoting at length, as evidence of the explicit ideological motivation behind his marginal productivity theory: The welfare of the laboring classes depends on whether they get much or little; but their attitude toward other classes – and, therefore, the stability of the social state – depends chiefly on the question, whether the amount that they get, be it large or small, is what they produce. If they create a small amount of wealth and get the whole of it, they may not seek to revolutionize society; but if it were to appear that they produce an ample amount and get only a part of it, many of them would become revolutionists, and all would have the right to do so. The indictment that hangs over society is that of ‘exploiting labor’. ‘Workmen’ it is said, ‘are regularly robbed of what they produce. This is done within the forms of law, and by the natural working of competition.’ If this charge were proved, every right-minded man should become a socialist; and his zeal in transforming the industrial system would then measure and express his sense of justice. If we are to test the charge, however, we must enter the realm of production. We must resolve the product of social industry into its component elements, in order to see whether the natural effect of competition is or is not to give to each producer the amount of wealth that he specifically brings into existence. (1899, p. 4) Clark’s answer to Marx’s charge of exploitation forms the thesis of his book and is best expressed in Clark’s famous claim that ‘what a social class gets is, under natural law, what it contributes to the general output of industry’ (1891, p. 312) (see Volume I, Chapter 9). More than 30 years after Clark’s statements, Irving Fisher (1930b, p. 1) acknowledges the continuing ideological controversy surrounding the theory of interest: The controversy over the moral and economic problems of interest has endured for centuries and is still raging … While it is now agreed almost unanimously [except for ‘Marxian socialists’ and ‘communists’] that interest-taking is morally just and economically sound, there still remains much confusion and wide differences of opinion regarding the economic explanation of the causes which create interest and make it necessary. The last disputant in the early set of controversies, Thorstein Veblen, was also influenced by Marx, but in a positive way. Veblen developed Marx’s position on the origin of profits, which he used in attacking ‘Professor Clark’s Economics’ (1908, Volume I, Chapter 18). Veblen took issue with Clark’s attempt to ground the justification of profits in natural laws of physical matter which make capital productive. Instead, Veblen argued that profit was grounded in the social power of the capitalists which enabled them to appropriate the technological achievements of the society as a whole. For Veblen (1908, pp. 166–7), ‘industrial capital – capital considered as a productive agent – is substantially a capitalisation of technological expedients’. Veblen claims it is extremely difficult to determine what share of the value of the joint product of capital and labor should, under a rule of ‘natural’ equity, go to the capitalist as an equitable return for his monopolisation of a given portion of the intangible assets of the community at large. The returns accruing to him under competitive conditions would be a measure of the differential advantage held by him by virtue of his having become legally seized of the material contrivances by which the technological achievements of the community are put into effect. While Marx’s vision has not occupied centre stage in the controversies since the 1930s (exceptions are Bhaduri (1969), Volume III, Chapter 11; Harcourt (1972, 1976), Volume III, xlvii Capital Theory I Chapter 14), his influence remains in the legacy of how the early debates helped shape later debates. The intensity and passion surrounding later capital theory debates, and ‘the strongly ideological overtones which attach to seemingly technical debates … must be unintelligible’ (Bliss 1975, p. 347) without understanding the impetus (both con and pro) provided by the original Marxian vision. In recent debates, Joan Robinson was one of the few to explicitly raise the role of ideology. And she referred not to Marx, but to Veblen: ‘I only recently discovered that Thorstein Veblen had made my point, much better than I did, in 1908’ (1980b, p. 116). She goes on to quote from Veblen’s article ‘Professor Clark’s Economics’: The continuum in which the ‘abiding entity’ of capital resides is a continuity of ownership, not a physical fact. The continuity, in fact, is of an immaterial nature, a matter of legal rights, of contract, of purchase and sale. Just why this patent state of the case is overlooked, as it somewhat elaborately is, is not easily seen. Robinson interpreted the significance of capital to lie in the property owned by the capitalist class, ownership of which confers on capitalists the legal right and economic authority to take a share of the surplus created by the production process (Harcourt and Laing, 1971, p. 10). Faith The second entry point for ideology is the faith professed by many capital controversy combatants that disequilibrium dynamics will converge to equilibrium outcomes, or their faith in underlying visions when one-commodity results are not robust. Because this entry point is more controversial, the historical evidence from the numerous debates will be important, we suspect, in convincing most readers of the role of ideology. J.B. Clark (1891, Volume I, Chapter 9) uses comparative statics to get his inverse relation between the quantity of capital and the rate of interest, and uses a putty capital model to claim his results will be sustained in the face of disequilibrium dynamics. 39 He recognizes that his comparative static thought experiments, where the quantity of labour also can vary, violate his static state assumptions and ‘makes the study for the moment dynamic, since, in addition to the change in the number of the workers, it involves changes in the forms that the fixed fund of capital assumes’. Clark asserts, without further justification, that ‘Such a dynamic study is, however, admissible as an introduction to a study of a static condition’ (1891, p. 305). With the exception of a sketchy foray into economic dynamics in Essentials of Economic Theory (1907), Clark’s analysis was confined to the explication of static laws. But Clark none the less has faith in the dominance of the static forces over the complications introduced by dynamic forces. The last sentence of his 1899 opus reads ‘Yet, whatever movements the dynamic division of economic science may discover and explain, static laws will never cease to be dominant. All real knowledge of the laws of movement depends upon an adequate knowledge of the laws of rest’ (1899, p. 442). Böhm-Bawerk uses a number of one-commodity models to illustrate his claims that increases in roundaboutness will increase productivity, but at a decreasing rate. As part of those illustrations, he also assumes (incorrectly) that interest accrues on a simple rather than compound basis. xlviii Capital Theory I In debates with Irving Fisher and Fetter, Böhm-Bawerk claims that ignoring compound interest was a mere expository simplification: ‘I have not been guilty of any error in principle. Ignoring compound interest merely changes the figures which are in any event only chosen at random and for illustrative purposes’ (1959c, Vol. II, p. 457n; emphasis in original). Fisher and Fetter challenge Böhm-Bawerk results because compound interest makes the measure of capital depend on the rate of interest, with the consequence that in general cases, outside of Böhm-Bawerk’s one-commodity examples, Böhm-Bawerk’s claims need not hold true. But Böhm-Bawerk ([1912] 1959a, p. 68) refuses to back down, although he offers little in the way of rebuttal other than polemics, accusing Fetter and Fisher of using a ‘deceitful dialectic’. Böhm-Bawerk retains his faith in the one-commodity result of an inverse monotonic relation between the interest rate and the capital intensity, roundaboutness and productivity. Irving Fisher (1907) constructs partial equilibrium examples with a single output, heterogeneous capital goods and fixed prices that do not depend on the rate of interest. These numerical examples for investors choosing between different income streams illustrate diminishing returns to increased capital intensity – the inverse monotonic relation. With his sophisticated mathematical knowledge, Fisher realizes that a complete analysis must allow for general equilibrium interactions between the rate of interest, prices and the values of income- streams. 40 He relaxes the assumption of fixed prices and constructs new numerical examples that preserve both the inverse monotonic relationship between the rate of interest and the value of the capital/investment opportunity, and the movement to more roundabout production processes as the interest rate falls. Fisher seems to realize that his results are arbitrary in saying that ‘It is true in this case that the change in the [income-stream values] does not affect the final result’ (1907, p. 173; emphasis added). None the less, Fisher, like Böhm-Bawerk (1959a, Vol. II, p. 457n), claims that these feedback effects will not make any difference: ‘But, whatever the final outcome of all the readjustments, it is evident that the introduction of the influence of the rate of interest on the [values of the income stream] does not in any material way affect the reasoning already given in regard to the determination of interest’ (1907, p. 174; emphasis added). Fisher acknowledges the limitation of his partial equilibrium theory of interest, but goes on to make a claim on faith that many others have made but have been unable to prove: ‘Afterwards it will be easy to dovetail together this interest theory, which assumes prices predetermined, with price theory which assumes interest predetermined, thus reaching a synthesis in which the previously assumed constants become variables. But all the principles remain valid’ (1930a, p. 131n). But Fisher never explicitly addresses the implications of variable prices for his rate of return calculations or his rankings of the capital intensity of production processes. Hayek continues to insist on an inverse relation between capital and interest (and roundaboutness) despite complications of measuring capital in heterogeneous goods models. Outside of a model with a single, homogeneous input and one-commodity output, Hayek freely acknowledges that: ‘All attempts to reduce the complex structure of waiting periods … are bound to fail, because the different waiting periods cannot be reduced to a common denominator in purely technical terms’ (1941, pp. 141–2). But Hayek steadfastly maintains that decreases in the interest rate will prompt more roundabout, capital-intensive production, even though he cannot prove this result in heterogeneous goods models. In debating Kaldor’s simple one-commodity models, both Kaldor and Knight agree on the quantification of capital and the calculation of an index of capital intensity, given the simplifying xlix Capital Theory I assumptions. They also agree that the results of the simple models – the inverse, monotonic relation between capital intensity and the interest rate – are not sustained in heterogeneous commodity models. The basic disagreement between Kaldor and Knight is whether the simple models provide useful and true insights about the world. Kaldor and Knight debate this problem by the not very fruitful tack of challenging the realism of each other’s assumptions. Despite being unable to sustain the results of his simple models under less restrictive assumptions, Kaldor (at this time) continues to believe in the conception of capital as a factor of production whose return, like the returns of all factors, is a function of its scarcity and marginal productivity. Knight’s one-commodity Crusonia-plant results also cannot be generalized, leaving him open to the same claims of ‘unrealism’ and the challenge to abandon the simple model and search for a better explanation in a different direction. Knight sticks to his fundamental theoretical conception of capital (just as Kaldor stuck to his) as a permanent, timeless homogeneous fund of value which is embodied in all ‘so-called factors of production’. Knight and Kaldor both have faith in their respective underlying theoretical visions of capital, and will not discard what each believes are the useful, heuristic insights of their simple models. And since they both acknowledge the problems in more ‘realistic’ and general models, any empirical testing of those models would not sway their beliefs. What is the point of testing a generalized model that you acknowledge does not have clear theoretical results on an issue like an inverse relation between capital intensity and the interest rate? The role of empirical testing in settling divergences between one-commodity model results and results in more general heterogeneous commodity models comes to the fore again in the Cambridge capital theory controversies. Ferguson’s (1969) book moved faith over to the realm of empirical testing. Ferguson (1969, pp. xvii–xviii) says this about the Cambridge criticism of neoclassical theory: Its validity is unquestionable, but its importance is an empirical or an econometric matter that depends upon the amount of substitutability there is in the system. Until the econometricians have the answer for us, placing reliance upon neoclassical economic theory is a matter of faith. I personally have the faith; but at present the best I can do to convince others is to invoke the weight of Samuelson’s authority as represented, for example, by the flyleaf quotation. Ferguson’s argument was that the empirical likelihood of re-switching and capital reversing depended on the substitution possibilities between factors of production, and this was an empirical question. The Samuelson quotation to which he refers (1966b, pp. 444–5) is also an important example of faith in the results of one-commodity models: Until the laws of thermodynamics are repealed, I shall continue to relate outputs to inputs – i.e. to believe in production functions. Until factors cease to have their rewards determined by bidding in quasi- competitive markets, I shall adhere to (generalized) neoclassical approximations in which relative factor supplies are important in explaining their market remunerations … a many-sectored neoclassical model with heterogeneous capital goods and somewhat limited factor substitutions can fail to have some of the simple properties of the idealized J.B. Clark neoclassical model. Recognizing these complications does not justify nihilism or refuge in theories that neglect short-term microeconomic pricing. Continuing in a footnote, Samuelson adds, ‘In my model … I do confine myself to well-behaved properties in which … the relative share of factors does depend on relative factor supplies’. l Capital Theory I These professions of faith, especially Ferguson’s, were often ridiculed as antithetical to scientific standards of inquiry. But Blaug (1975, pp. 42–3) did not hesitate to defend Ferguson on methodological grounds: ‘The history of both the physical and social sciences is replete with such examples of “faith”, that is, a determination to ignore logical anomalies in a theory until they are shown to be empirically important, rather than to leave whole areas of intellectual endeavour devoid of any theoretical framework.’ After listing examples, Blaug concludes that ‘there is nothing irrational about the tendency of scientists to hang on to a theory despite anomalies if no better rival theory is available’. Blaug (1975, Volume III, Chapter 10) is correct that there is nothing irrational about this kind of faith. It is a corollary to the Duhem–Quine thesis – why would not a researcher, in the face of disconfirming evidence, first question the least important links in the chain of reasoning that must be tested jointly. Suspicion first focuses on empirical data, testing techniques and other secondary hypotheses before a researcher contemplates jettisoning a primary theory or underlying vision. But since this is faith without strong evidence, there is plenty of room for ideology to play a role in the decision to hang on to a theory or vision. That decision is not irrational, but it is certainly not a purely positive rational decision either. Ideology plays a role. Thus, when proof is lacking that disequilibrium dynamics will converge to equilibrium outcomes, or when one-commodity results are not robust, capital theorists keep the faith in the results of their one-commodity models and their underlying visions. And ideology enters in the choice of an (unproven) vision and in the faith that it eventually will be proven. Conclusion We hope that the major themes of this Introduction will make more intelligible the articles that follow, whether they are part of the literatures of previous capital controversies, or positive contributions to the development of differing capital theories. Keep in mind that ‘capital’ has both physical and value conceptions. Most controversies begin when the dual conceptions of capital are integrated into economic models and one conception is emphasized to the relative neglect of the other. Neoclassical models treat capital as a resource (sometimes physical, sometimes value) whose price is determined by its relative scarcity. While the models differ in details depending on the author, all share three key ‘parables’: 1. An inverse, monotonic relation between quantity of capital (as well as the capital–output ratio and sustainable levels of consumption per head) and rate of interest; 2. Grounding the return on capital (rate of interest) in the natural or technical properties of the diminishing marginal productivity of capital or roundabout production; 3. Explaining the distribution of income between capitalists and labourers from a knowledge of relative factor scarcities/supplies and of marginal products. Most capital controversies of the past 100 years revolve around two major problems: (1) integrating production into the scarcity theory of value, and (2) integrating capital and time into equilibrium models. Two further commonalities exist in attempts to deal with these li Capital Theory I problems: (3) the panacea of one-commodity models in eliminating the tension between the physical and value conceptions of capital, and (4) the role of ideology and vision in fuelling controversy, especially when one-commodity results are not robust. All three editors had wished to include the articles below in the Table of Contents but were unable to secure permission to reprint. Volume I, Part II Foundations of Neoclassical Capital Theory: Impatience and Productivity Irving Fisher (1930), Excerpts from ‘Time Preference (Human Impatience)’ and ‘The Investment Opportunity Principles’, in The Theory of Interest: As Determined by Impatience to Spend Income and Opportunity to Invest It, Chapter 4, Sections 1–8, Chapter 7, Sections 1–5, New York: The Macmillan Company, 61–80, 150–61 Volume I, Part III Some Austrian and Neo-Austrian Contributions to Capital Theory J.R. Hicks ([1939] 1946), ‘Interest’ and ‘The Planning of Production’, in Value and Capital, Second Edition, Chapters XI and XV, Oxford University Press, 141–52, 191–201 John Hicks (1973), ‘The Standard Case and the Simple Profile’ and ‘The Measurement of Capital – Value and Volume’, in Capital and Time: A Neo-Austrian Theory, Chapters VII and XIII, Oxford: Clarendon Press, 81–8 and 151–66 John Hicks (1983), ‘The Austrian Theory of Capital and its Re-birth in the Modern Economics’, in Collected Essays on Economic Theory, Volume 3: Classics and Moderns, Cambridge, MA: Harvard University Press, 96–112 Volume II, Part I Capital in One-Commodity Neoclassical Growth Models T.W. Swan (1956), ‘Economic Growth and Capital Accumulation’, Economic Record, 32, 343– 61 Volume II, Part IV Keynes and the Cambridge School John Maynard Keynes (1936), ‘The Marginal Efficiency of Capital’, in The General Theory of Employment Interest and Money, Chapter 11, London: Macmillan and Co., 135–46 lii Capital Theory I Notes 1. This introduction was developed jointly from Chapter 2 in a book (long) in progress by Cohen titled ‘A Century of Capital Controversy from Böhm-Bawerk to Bliss: Scarcity, Production, Equilibrium and Time’. We thank but in no way implicate Mark Blaug, Christopher Bliss, Ian Steedman and an anonymous referee for their comments on a previous draft. 2. In the classical, Marxian and Keynesian approach, the rate of profits (r) is distinguished completely from the rate of interest. Profit is the return, expected and actual, on investment in capital goods. Interest is the hire price of finance (and, as Joan Robinson (Robinson, 1971, p. 28) reminds us), the yields of placements are the rates of return rentiers receive on the capital values of their assets. In the neoclassical approach, these amounts are regarded as indissoluble in size, as rates and also conceptually. 3. See also Dobb (1973, ch. 1). 4. Neoclassical is here used as the equivalent to Krishna Bharadwaj’s (1978) ‘supply and demand theories’. 5. Piero Sraffa and his closest colleagues and/or followers – especially Krishna Bharadwaj, Pierangelo Garegnani, Luigi Pasinetti and, of the younger generation, Alessandro Roncaglia, Bertram Schefold and Ian Steedman – concentrated on the organizing concept of classical political economy, the surplus. Sraffa himself was mainly concerned with the distribution, taking as read the classical- Marxian story of its creation, production and subsequent use. Following the classics, Sraffa (and Garegnani) do not do as the neoclassicals do, that is to say, determine prices, quantities and distribution simultaneously. Rather they argue for a different level of abstraction for the determination of wages (w) or r and levels of output and employment than for the determination of relative prices and either w or r, taking the methods of production and the levels of output and employment as givens for this purpose. 6. ‘One of the tasks of the economic theorist [is] to specify which variables are sufficiently interdependent to be best represented by simultaneous relations, and which variable exhibit such an overwhelming dependence in one direction (and such a small dependence in the opposite direction) as to be best represented by one-way-direction relations’ (Pasinetti, 1974, p. 44). 7. Schumpeter (1954, p. 590) describes value theory as ‘the factors that account for a thing’s having exchange value’, and as ‘views on the problem of causal explanation of the phenomenon of value’ (p. 309). According to Meek (1977, p. 151), value theory involves ‘the postulation of some kind of (relatively) independent “determining constant” from which one proceeds to the final conclusion by means of a simple one-directional catena of causes’. See also Dobb (1940, p. 12). 8. Ian Steedman reminds us that there is also a tradition of physical quantities in an explanation associated with the Physiocrats, Torrens, Ramsey (see Steedman (1994), Volume I, Chapter 20) and Sraffa, which is distinct from both. 9. These value theory propositions are a modern restatement of Walras’s (1954, p. 148) claims about his pure exchange model: ‘Given two commodities in a market in a state of equilibrium, if all other things being equal, the utility of one of these two commodities increases or decreases for one or more parties, the value of this commodity in relation to the value of the other commodity, i.e. its price, will increase or decrease. If, all other things being equal, the quantity of one of the two commodities in the hands of one or more holders increases or decreases, the price of this commodity will decrease or increase.’ 10. Böhm-Bawerk (1959b, Vol. II, p. 347) makes the earliest explicit statement of this principle: ‘The exchange … which constitutes the source of the phenomenon of interest, is merely one special case under the rubric of the exchange of goods in general … determination of price in this field cannot proceed under any laws other than those which govern determination of price in all economic exchange.’ And the general laws which determine price or exchange value stem from the fact that goods ‘are useful and … they are scarce’ (Böhm-Bawerk 1959b, Vol I, p. 91; emphasis added). Regarding the 1930s controversy, Kaldor (1937, p. 230) states that ‘“real productivity”, and thus the real rate of return, on any resource will depend upon the relative scarcity of the services of that resource’. Solow (1963, p. 14; see Volume II, Chapter 5) notes ‘the theory of capital is after all just liii Capital Theory I a part of the fundamentally microeconomic theory of the allocation of resources, necessary to allow for the fact that commodities can be transformed into other commodities over time’. 11. Ian Steedman points out that Edwin Burmeister (see Burmeister (1976), Volume III, Chapter 8) and others have insisted that the focus should be on p∂q/p∂k, not ∂(pq)/∂(pk). Call us old-fashioned, but how can we have p∂k if we cannot measure k? 12. Kuenne (1971, p. 35) claims that Böhm-Bawerk did not ‘understand the idea of simultaneity of variation’ and that this was the ‘most punishing deficiency of his analytical vision’. 13. But even Kuenne (1971, p. 35) acknowledges that Böhm-Bawerk’s own model involved the interdependence of general equilibrium, and gives Böhm-Bawerk ‘credit for an analytical sally of the most impressive ambition, namely an attempt to formulate a general equilibrium model inclusive of the economy’s capital and interest variation’. 14. ‘It is, therefore, not necessary in beginning our study of interest to distinguish, as many writers do, between the principles which lead to the existence of interest and those which regulate the rate of interest. By the existence of interest these writers mean that the rate is greater than zero. It seems preferable to reverse the order of the two problems and seek first to find the principles which fix the terms on which present and future goods exchange, without restricting ourselves in advance to the thesis that, always and necessarily, present goods command a premium over future goods … [68] After these general principles have been established a special study will then be in order to discover why the rate of interest is, in actual experience, almost never zero or negative’ (Fisher, 1930a, pp. 67–8; emphasis in original). 15. According to Dorfman (1959, Vol. 5, p. 464), by Fisher’s time ‘the dominant neoclassicists … felt that value theory was largely a settled issue’. 16. David Champernowne’s chain index method of measuring capital (1953–54) seemed to restore the parables of the ‘good old theory’ under carefully specified conditions which ruled out capital reversing and re-switching by assumption. But his measure was not independent of distribution and prices and his marginal products, while related in simple ways to r and w, were subtly different concepts to those of traditional neoclassical theory (Bliss, 1975, ch. 8; Harcourt, 1972, p. 45, and 1995, p. 42). 17. See also Bliss (1975, ch. 5), Hahn (1975, p. 362) and Stiglitz (1974, p. 894). 18. Sraffa’s classic 1960 book was concerned to show why a unit which was independent of distribution and prices in which to measure capital, so vital for neoclassical theory, could not be found. In the sections of the book on reduction to dated quantities of labour, fixed capital and the choice of technique, Sraffa comments on the changes in relative prices of commodities as different values of the rate of profits (r) were considered: ‘The reversals in the direction of the movement of relative prices, in the face of unchanged methods of production, cannot be reconciled with any notion of capital as a measurable quantity independent of distribution and prices’ (Sraffa, 1960, p. 38; emphasis in original). In the sections on fixed capital, Sraffa discusses the value of capital within the context of a balanced stock of machines. He shows that its value rises as the value of r rises, for Sraffa ‘a remarkable effect’ (p. 70) because it implies that it is impossible to have a measure of capital which is invariant to changes in distribution. Finally, and for Sraffa and his followers, the real knock- down blow, he shows in the section on the choice of technique, that the phenomena of capital- reversing and reswitching contradict the agreeable neoclassical parable of a downward-sloping demand curve for capital. Garegnani (1970, Volume III, Chapter 3) and Pasinetti (1969, Volume III, Chapter 5), in particular, were to pick up this ball from here and run. Duncan Foley (2001, Volume II, Chapter 18) surveys admirably Garegnani’s achievements and the limitations of his agenda. By being so single-minded in pursuing the critique of the neoclassical project, Garegnani and his followers have not developed sufficiently a persuasive alternative approach to the grand classical problems of value, growth and distribution. 19. Frank Fetter (1902, Volume I, Chapter 17) made this point 50 years before Joan Robinson: ‘With a value concept the “amount of capital” … varies with the rate of discount in capitalization’ (1902, p. 177). Therefore, the measurement of ‘a greater capital’ can mean either ‘more physical instruments’ or it can mean the same physical ‘instruments of greater value’ (1902, p. 183). 20. Her shared concerns do not extend to Sraffa’s followers. Garegnani, for example, is a staunch defender of the long-period method in high theory – the view that rigorous results may only be liv Capital Theory I established within a framework which captures the effects of sustained and persistent forces which create the characteristics of the long-period positions – e.g. the natural prices of the Classical Political Economists, the prices of production of Marx and the long-period normal equilibrium prices of Marshall, all of which are the economist’s counterpart of the natural sciences’ traditional centres of gravitation. Garegnani’s (1970, Volume III, Chapter 3) results, for example, related to comparisons of values of relative factor prices and shares following a ‘change’ in accumulation which he thought were unable to be reconciled with any real-world observations. Insistence on the use of this method is why Joan Robinson directly and Kaldor indirectly fell out with the Sraffians (or so-called neo- Ricardians), of whom Garegnani is the outstanding example on method, but see also Kurz and Salvadori (1995), Schefold (1997) and Cozzi and Marchionatti (2001). 21. Later in her life, Joan Robinson accepted equilibrium as a concept only in the context of doctrinal debates. 22. The stability discussion draws heavily on Hands and Mirowski (1998). 23. The pioneering papers include Sonnenschein (1972, 1973), Mantel (1974), Debreu (1974) and McFadden et al. (1974). See also the literature survey in Shafer and Sonnenschein (1982), and summaries in Mas-Colell (1985) and Rizvi (1994). 24. The most important exceptions take the form of gross substitute systems, which include the case of ‘binary changes’ that affect only two goods. Such a restricted change can be used to show that if there is an exogenous increase in the amount of a factor (‘capital’) available, ‘the equilibrium with more capital, other things constant, must also have a lower rental of capital’ (Arrow and Hahn 1971, 247). This result, however, will not generalize for non-binary changes. 25. Even if we move past tâtonnement processes to trading processes for analysing reactions to a parameter shift, problems remain: ‘If stability requires trading (or production and consumption) to take place before equilibrium is reached, then the adjustment process itself changes the givens of the equilibrium problem (the endowments of agents, for example). This makes the set of equilibria also change in the course of adjustment, so that the equilibrium finally reached (assuming stability) differs from that computed by algorithms taking the initial situation as fixed. Moreover, comparative static analysis, that major tool of theory, will miscompute the effects of a displacement of equilibrium, for the equilibrium reached will depend on the adjustment process and not merely on the displacement itself. While such effects may be small, they are certainly not known to be small. The argument that they are likely to be negligible because prices adjust much faster than quantities is unconvincing. The limiting case of such relative speeds of adjustment is tâtonnement and is known to lack general convergence properties’ (F. Fisher, 1989, p. 38). 26. In a comprehensive survey of the significance of poor stability results for the general equilibrium research programme, Ingrao and Israel (1985, pp. 101–2, and 1990) draw the following conclusions: ‘the analysis of the global stability of a perfectly competitive market does not produce satisfactory results, and the general … tendency has been to play down the importance of these negative results … [But] if we accept that one essential aspect of the notion of general equilibrium is the idea that “a social system moved by independent actions in pursuit of different values is consistent with a final coherent state of balance” (Arrow and Hahn, 1971, p. 1), it would be very odd indeed to accept the validity of any model which, while demonstrating the existences of a “final coherent state of balance”, did not admit the system’s capacity to place itself in that state by a price adjustment process. It would be a model in which the market forces are unable to lead the market to equilibrium, or in which Adam Smith’s “invisible hand” is waving, Sisyphus-like around the equilibrium without managing to “push” the system into it.’ (See also Harcourt (2001).) 27. ‘The word [statics] is borrowed from the jargon of physics, where it is used to designate the theory of bodies at rest or of forces in equilibrium. But there is much in the received economic theories to which the analogy of bodies at rest or of forces in equilibrium will not apply’ (Veblen, 1899, p. 122). 28. Fisher (1930a, 484, fn. 39) writes that ‘The advance of all science has required the abandonment of such simplified conceptions of causal relationship for the more realistic conception of equilibrium … The mathematical solution of the problem of interest by means of simultaneous equations recognizes the mutual interdependence of all the factors in the interest problem and, at the same time, yields a determinate solution for the problem.’ lv Capital Theory I 29. Because the stock of capital can grow or fall ‘without a definite prospect of coming to a stationary level’ (1936, p. 616), Knight argues that equilibrium price theory is inapplicable. What is needed instead is ‘a special methodology’ (1936, p. 617): ‘long-run historical changes must be faced as problems of historical causality and treated in terms of concepts very different from those of given supply and demand functions and a tendency toward equilibrium under given conditions’ (Knight, 1931, p. 210). 30. A concern with process – ‘the problem of how prices come into being rather than what system of prices will secure equilibrium’ (Kaldor, 1934, p. 128) – stayed with Kaldor throughout his career, and came to fruition explicitly in ‘The Irrelevance of Equilibrium Economics’ (Kaldor, 1972) and Economics without Equilibrium (Kaldor, 1985). See also Kaldor’s 1984 Mattioli lectures (only published in 1996) in Causes of Growth and Stagnation in the World Economy. 31. ‘[T]he fundamental problem of all economic theory … is … the question of the significance of the concept of equilibrium and its relevance to the explanation of a process which takes place in time … some of the formulations of the theory of equilibrium prove to be of little use and … not only their particular content but also the idea of equilibrium as such which they use will require a certain amount of revision’ (Hayek [1933] 1939, p. 138). 32. Pasinetti (1969, p. 519, see Volume III, Chapter 5) states that in a one-commodity (corn) model the ‘inverse monotonic relationship between physical rate of profit and existing stock of corn would permit an extension to the rate of profit[s] of the marginal theory of prices (which, as is well known, interprets prices as indexes of scarcity). The smaller – i.e. the scarcer – the existing quantity of corn, the higher the physical rate of return (and of profit[s])’. Harry Johnson’s (1971) two-sector general equilibrium model of the 1970s also exhibits these characteristics. 33. Here is Clark’s (1888, pp. 9–10; emphasis in original) description of true capital flowing among specific physical capital goods: ‘Ask a manufacturer, “What is your capital?” and he will probably express his answer in dollars. Ask him, “In what is your capital invested?” and he will specify the buildings, machines, land, materials, etc., in which his productive fund now chances to be embodied. These concrete things will figure in his thoughts as the containers of his capital; while the content itself will appear to him to be a value, an abstract quantum of wealth. He will think of it as a fund that is permanently his, though it may not retain for a single day its exact present form of embodiment … Capital is, in this view, an abstract fund, the destiny of which is to migrate thru an endless series of outward forms.’ 34. In his controversy with Knight, Hayek (1934, pp. 228–9; emphasis in original) clearly describes and then rejects the putty capital assumption because it eliminates the historical process of investment in specific capital goods: ‘The notion that capital … is completely mobile and can at will and without any loss of value be transformed in any concrete form … would be true only if the concrete capital goods were just so many units of homogeneous “energy” which could be put to any use, i.e. if they were completely non-specific. But this … corresponds even less to reality than the assumption of complete specificity … all the capital goods existing at any one moment are at least partly the result of an historical process which again and again has put existing capital goods to other uses than those for which they were originally intended, and that in consequence the actual form that capital takes will be very different from what it would be if the structure could be built up ab ovo with the help of an equivalent fund of free capital.’ 35. See Cohen (1989, pp. 237–44; Volume III, Chapter 16) for the detailed argument. 36. Harcourt (1972, pp. 133–4) and Dobb (1973, p. 256) both pointed out the irony that Samuelson’s assumption of equal factor proportions in the Surrogate Production Function would also justify Marx’s labour theory of value. Indeed, the supreme irony is that the assumption which Böhm- Bawerk argued (wrongly, as it happened) supported Marx’s entire system is rather the assumption which is essential for the alternative neoclassical theory to ‘go through’. 37. Ian Steedman queries whether economists have to have one vision only. Could not issues be looked at from alternative points of view and perhaps their implications could be combined? 38. 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Wicksell, K. ([1934] 1961), Lectures on Political Economy, Vol. 1. London: George Routledge. lx Capital Theory Volume II Edited by Christopher Bliss Nuffield Professor of International Economics University of Oxford, UK Avi J. Cohen Associate Professor of Economics York University, Canada and G.C. Harcourt Emeritus Reader in the History of Economic Theory University of Cambridge, UK Emeritus Fellow Jesus College, Cambridge UK and Professor Emeritus University of Adelaide, Australia An Elgar Reference Collection Cheltenham, UK • Northampton, MA, USA © Christopher Bliss, Avi J. Cohen and G.C. Harcourt 2005. For copyright of individual articles, please refer to the Acknowledgements. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of the publisher. Published by Edward Elgar Publishing Limited Glensanda House Montpellier Parade Cheltenham Glos GL50 1UA UK Edward Elgar Publishing, Inc. 136 West Street Suite 202 Northampton Massachusetts 01060 USA A catalogue record for this book is available from the British Library ISBN 1 84064 481 8 (3 volume set) Printed and bound in Great Britain by MPG Books Ltd, Bodmin, Cornwall. Contents Acknowledgements ix Introductions by the editors to all three volumes appear in Volume I PART I CAPITAL IN ONE-COMMODITY NEOCLASSICAL GROWTH MODELS 1. D.G. Champernowne (1945–1946), ‘A Note on J. v. Neumann’s Article on “A Model of Economic Equilibrium”’, Review of Economic Studies, 13 (1), 10–18 3 2. F.P. Ramsey (1928), ‘A Mathematical Theory of Saving’, Economic Journal, XXXVIII (152), December, 543–59 12 3. Robert M. Solow (1956), ‘A Contribution to the Theory of Economic Growth’, Quarterly Journal of Economics, 70 (1), February, 65–94 29 PART II VARIATIONS ON SIMPLE NEOCLASSICAL GROWTH MODELS: HETEROGENEOUS CAPITAL GOODS, TWO-SECTOR MODELS AND MORE 4. R. Dorfman, P.A. Samuelson and R.M. Solow (1971), ‘Efficient Programmes of Capital Accumulation’, in G.C. Harcourt and N.F. Laing (eds), Capital and Growth, Chapter 18, Harmondsworth: Penguin Education, 348–68 61 5. Robert M. Solow (1963), ‘The Rate of Return on Investment’, in Capital Theory and the Rate of Return, Excerpt from Chapter 1, Amsterdam: North-Holland Publishing Company, 16–28 82 6. W.E.G. Salter (1966), ‘A Model of the Delay in the Utilisation of New Techniques of Production’, in Productivity and Technical Change, Second Edition, Chapter IV, Cambridge: Cambridge University Press, 48–65 95 7. F.H. Hahn and R.C.O. Matthews (1964), ‘Two-sector Models’, excerpt from ‘The Theory of Economic Growth: A Survey’, Economic Journal, 74 (296) December, 812–21, references 113 8. Milton Friedman (1976), ‘The Theory of Capital and the Rate of Interest’, in Price Theory, Chapter 17, New York: Aldine de Gruyter, 283–322 124 PART III PRODUCTION FUNCTIONS AND AGGREGATE CAPITAL 9. Charles W. Cobb and Paul H. Douglas (1928), ‘A Theory of Production’, American Economic Review, Papers and Proceedings, 18 (1), Supplement, March, 139–65 167 vi Capital Theory II 10. Joan Robinson (1953–1954), ‘The Production Function and the Theory of Capital’, Review of Economic Studies, 21 (2), 81–106 194 11. D.G. Champernowne (1953–1954), ‘The Production Function and the Theory of Capital: A Comment’, Review of Economic Studies, 21 (2), 112–35 220 12. Robert M. Solow (1955–56), ‘The Production Function and the Theory of Capital’, Review of Economic Studies, 23 (2), 101–8 244 13. Franklin M. Fisher (1971), ‘Aggregate Production Functions and the Explanation of Wages: A Simulation Experiment’, Review of Economics and Statistics, LIII (4), November, 305–25 252 PART IV KEYNES AND THE CAMBRIDGE SCHOOL 14. R.F. Kahn (1959), ‘Exercises in the Analysis of Growth’, Oxford Economic Papers, 11 (2), June, 143–56 275 15. Colin Rogers (1989), excerpts from ‘Wicksellian Monetary Theory’ in Money, Interest and Capital, Chapter 2, Cambridge: Cambridge University Press, 21–35, 39–43, references 289 PART V SRAFFA AND SRAFFIANS 16. Piero Sraffa (1936), Letter to Joan Robinson, 27 October, Archives, King’s College, Cambridge 313 17. Piero Sraffa (1960), ‘Reduction to Dated Quantities of Labour’ and ‘Fixed Capital’, in Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory, Chapters VI and X, Cambridge: Cambridge University Press, 34–40, 63–73 316 18. Duncan K. Foley (2001), ‘Value, Distribution and Capital: A Review Essay’, Review of Political Economy, 13 (3), 365–81 334 PART VI DISAGGREGATED CAPITAL, ACCUMULATION AND GENERAL EQUILIBRIUM 19. Edmond Malinvaud (1953), ‘Capital Accumulation and Efficient Allocation of Resources’, Econometrica, 21 (2), April, 233–68 353 20. F.H. Hahn (1966), ‘Equilibrium Dynamics with Heterogeneous Capital Goods’, Quarterly Journal of Economics, 80 (4), November, 633–46 389 21. C.J. Bliss (1975), ‘The Orthodox Vision’, in Capital Theory and the Distribution of Income, Chapter 12, Amsterdam and Oxford: North Holland Publishing Company, 279–97, references 403 22. Avinash Dixit (1977), ‘The Accumulation of Capital Theory’, Oxford Economic Papers, 29 (1), March, 1–29 423 PART VII CAPITAL AND OVERLAPPING GENERATIONS 23. Paul A. Samuelson (1958), ‘An Exact Consumption-Loan Model of Interest With or Without the Social Contrivance of Money’, Journal of Political Economy, LXVI (6), December, 467–82 455 24. Peter A. Diamond (1965), ‘National Debt in a Neoclassical Growth Model’, American Economic Review, 55 (5), December, 1126–50 471 25. J.E. Stiglitz (1969), ‘Distribution of Income and Wealth Among Individuals’, Econometrica, 37 (3), July, 382–97 496 Name Index 513 Capital Theory II vii Capital Theory Volume III Edited by Christopher Bliss Nuffield Professor of International Economics University of Oxford, UK Avi J. Cohen Associate Professor of Economics York University, Canada and G.C. Harcourt Emeritus Reader in the History of Economic Theory University of Cambridge, UK Emeritus Fellow Jesus College, Cambridge UK and Professor Emeritus University of Adelaide, Australia An Elgar Reference Collection Cheltenham, UK • Northampton, MA, USA © Christopher Bliss, Avi J. Cohen and G.C. Harcourt 2005. For copyright of individual articles, please refer to the Acknowledgements. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of the publisher. Published by Edward Elgar Publishing Limited Glensanda House Montpellier Parade Cheltenham Glos GL50 1UA UK Edward Elgar Publishing, Inc. 136 West Street Suite 202 Northampton Massachusetts 01060 USA A catalogue record for this book is available from the British Library ISBN 1 84064 481 8 (3 volume set) Printed and bound in Great Britain by MPG Books Ltd, Bodmin, Cornwall. Contents Acknowledgements vii Introductions by the editors to all three volumes appear in Volume I PART I RESWITCHING AND CAPITAL REVERSING 1. Paul A. Samuelson (1962), ‘Parable and Realism in Capital Theory: The Surrogate Production Function’, Review of Economic Studies, XXIX (3), June, 193–206 3 2. Luigi L. Pasinetti (1966), ‘Changes in the Rate of Profit and Switches of Techniques’, Quarterly Journal of Economics, LXXX (4), November, 503–17 17 3. P. Garegnani (1970), ‘Heterogeneous Capital, the Production Function and the Theory of Distribution’, Review of Economic Studies, 37 (3), July, 407–36 32 4. Paul A. Samuelson (1966), ‘A Summing Up’, Quarterly Journal of Economics, 80 (4), November, 568–83 62 5. Luigi L. Pasinetti (1969), ‘Switches of Technique and the “Rate of Return” in Capital Theory’, Economic Journal, LXXIX (315), September, 508–31 78 6. Robert M. Solow (1970), ‘On the Rate of Return: Reply to Pasinetti’, Economic Journal, LXXX (318), June, 423–8 102 7. Luigi L. Pasinetti (1970), ‘Again on Capital Theory and Solow’s “Rate of Return”’, Economic Journal, LXXX (318), June, 428–31 108 8. Edwin Burmeister (1976), ‘Real Wicksell Effects and Regular Economies’, in Murray Brown, Kazuo Sato and Paul Zarembka (eds), Essays in Modern Capital Theory, Amsterdam, New York and Oxford: North-Holland Publishing Company, 145–64 112 PART II ASSESSMENTS OF THE CAMBRIDGE CAPITAL THEORY CONTROVERSIES 9. G.C. Harcourt ([1969] 1986), ‘Some Cambridge Controversies in the Theory of Capital’, in O.F. Hamouda (ed.), Controversies in Political Economy: Selected Essays of G.C. Harcourt, Chapter 7, Brighton: Wheatsheaf Books Ltd, 145–206 135 10. Mark Blaug (1975), ‘A Final Judgement’, in The Cambridge Revolution: Success or Failure? A Critical Analysis of Cambridge Theories of Value and Distribution, Revised Edition, Chapter VIII, London: The Institute of Economic Affairs, 79–86, references 197 vi Capital Theory III 11. Amit Bhaduri (1969), ‘On the Significance of Recent Controversies on Capital Theory: A Marxian View’, Economic Journal, LXXIX (315), September, 532–9 206 12. Joan Robinson ([1974] 1979), ‘History versus Equilibrium’, in Collected Economic Papers, Volume 5, Chapter 4, Oxford: Basil Blackwell, 48–58 214 13. Joan Robinson (1975), ‘The Unimportance of Reswitching’, Quarterly Journal of Economics, 89 (1), February, 32–9 225 14. G.C. Harcourt (1976), ‘The Cambridge Controversies: Old Ways and New Horizons – Or Dead End?’, Oxford Economic Papers, 28 (1), March, 25–65 233 15. Frank Hahn (1982), ‘The Neo-Ricardians’, Cambridge Journal of Economics, 6 (4), December, 353–74 274 16. Avi J. Cohen (1989), ‘Prices, Capital, and the One-commodity Model in Neoclassical and Classical Theories’, History of Political Economy, 21 (2), Summer, 231–51 296 PART III CAPITAL, INCREASING RETURNS AND ENDOGENOUS GROWTH 17. Frank H. Knight (1944), ‘Diminishing Returns from Investment’, Journal of Political Economy, 52 (1), March, 26–47 319 18. Kenneth J. Arrow (1962), ‘The Economic Implications of Learning by Doing’, Review of Economic Studies, XXIX (3), 155–73 341 19. Paul M. Romer (1986), ‘Increasing Returns and Long-Run Growth’, Journal of Political Economy, 94 (5), October, 1002–37 360 20. Paul M. Romer (1990), ‘Endogenous Technological Change’, Journal of Political Economy, 98 (5, Part 2), October, S71–S102 396 21. Kevin M. Murphy, Andrei Shleifer and Robert W. Vishny (1989), ‘Industrialization and the Big Push’, Journal of Political Economy, 97 (5), October, 1003–26 428 22. Robert J. Barro and Xavier Sala-i-Martin (1992), ‘Convergence’, Journal of Political Economy, 100 (2), April, 223–51 452 23. Philippe Aghion and Peter Howitt (1998), ‘Market Structure’, in Endogenous Growth Theory, Chapter 7, Cambridge, MA and London: MIT Press, 205–32, references 481 24. Robert M. Solow (2000), ‘Lessons and Suggestions for Aggregative Growth Theory’, in Growth Theory: An Exposition, Second Edition, Chapter 12, New York and Oxford: Oxford University Press, 180–86, references 510 Name Index 519