Capital Theory

8/11/2019 Capital Theory

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Capital Theory

Volume I

Edited by

Christopher BlissNuffield Professor of International Economics

University of Oxford, UK

Avi J. CohenAssociate Professor of Economics

York University, Canada

and

G.C. HarcourtEmeritus Reader in the History of Economic TheoryUniversity of Cambridge, UK

Emeritus Fellow

Jesus College, Cambridge UK

and Professor Emeritus

University of Adelaide, Australia

An Elgar Reference CollectionCheltenham, UK Northampton, MA, USA


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Contents

Acknowledgements ixIntroduction The Theory of Capital: A Personal Overview Christopher Bliss xiIntroduction 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 NewPalgrave: Capital Theory, London: Macmillan Reference Books,10822 3

2. David Ricardo (1951), IV. The Chapter on Value in Edition Iexcerpt from Introduction, excerpt from On Value and OnMachinery, in Piero Sraffa (ed.), The Works and Correspondence ofDavid Ricardo, Volume I, Chapter I, Sections IIIV, Chapter XXXI,Cambridge: Cambridge University Press, xxxxxxvii, 2243, 38697 18

3. Karl Marx ([1891] 1972), Wage Labour and Capital, in Robert C.Tucker (ed.), The MarxEngels Reader, Second Edition, New York:

W.W. Norton and Company, Inc., 16790 604. Luigi L. Pasinetti (1983), The Accumulation of Capital, CambridgeJournal of Economics, 7, 40511 84

PART II FOUNDATIONS OF NEOCLASSICAL CAPITAL THEORY:

IMPATIENCE AND PRODUCTIVITY

5. Nassau William Senior ([1836] 1938), Instruments of Productionand Capital, inAn Outline of the Science of Political Economy,Chapter 3, London: George Allen and Unwin, Ltd, 5760 93

6. Ian Steedman (1972), Jevonss Theory of Capital and Interest,

Manchester School of Economic and Social Studies, XL, 3152 977. Syed Ahmad (1998), Rae, Bhm-Bawerk, and Fisher on the Supplyand 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, 11128, references 119

8. Eugen von Bhm-Bawerk (1959), The Problem of Interest, FinalConclusions and Present and Future in Economic Life, in Capitaland Interest, Translated by George D. Huncke and Hans F. Sennholz,Volume 1, Chapter I, Chapter XV, Volume 2, Chapter I, SouthHolland, IL: Libertarian Press, 17, 34854, 25989, notes 139

9. John B. Clark (1891), Distribution as Determined by a Law of Rent,Quarterly Journal of Economics, 5(3), April, 289318 194


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10. John Bates Clark (1899), Kinds of Capital and of Capital-Goods, inThe Distribution of Wealth: A Theory of Wages, Interest and Profits,Chapter X, New York and London: The Macmillan Company, 14156 224

11. Christopher Bliss (1990), Alfred Marshall and the Theory ofCapital, in John K. Whitaker (ed.), Centenary Essays on AlfredMarshall, Chapter 9, Cambridge: Cambridge University Press,22341 240

12. Knut Wicksell ([1934] 1961), Capitalistic Production, in LionelRobbins (ed.),Lectures on Political Economy, Translated from theSwedish by E. Classen, Volume 1: General Theory, Part II, Chapter2, London: Routledge and Kegan Paul Ltd, 14495 259

13. Knut Wicksell ([1934] 1961), Real Capital and Interest (continued):A Mathematical Analysis of Dr. kermans Problem, in Lionel

Robbins (ed.),Lectures on Political Economy, Translated from theSwedish by E. Classen, Volume 1: General Theory, Appendix 2(b),London: Routledge and Kegan Paul Ltd, 27499 311

14. Paul A. Samuelson (1967), Excerpts from Irving Fisher and theTheory of Capital, in Ten Economic Studies in the Tradition ofIrving Fisher, Chapter 2, New York: John Wiley and Sons, Inc.,1719, 2635 337

15. Joseph A. Schumpeter ([1934] 1983), Interest on Capital, in TheTheory 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, 157211 350

PART III SOME AUSTRIAN AND NEO-AUSTRIAN CONTRIBUTIONS TO

CAPITAL THEORY

16. Carl Menger ([1871] 1976), Excerpt from The Laws Governing theValue of Goods of Higher Order, in Principles of Economics,Translated by James Dingwall and Bert F. Hoselitz, Part III, Chapter3, Sections AD, New York and London: New York UniversityPress, 14965 407

17. Frank A. Fetter (1902), The Roundabout Process in the InterestTheory, Quarterly Journal of Economics, 17(1), November, 16380 424

PART IV EARLY NEOCLASSICAL CAPITAL CONTROVERSIES

18. Thorstein Veblen (1908), Professor Clarks Economics, QuarterlyJournal of Economics, XXII(2), February, 14795 445

19. Avi J. Cohen (1998), Frank Knights Position on Capital andInterest: Foundation of the Knight/Hayek/Kaldor Debate, inMalcolm Rutherford (ed.), The Economic Mind in America: Essaysin the History of American Economics: Perspectives on the History

of Economic Thought, Chapter 10, London and New York:Routledge, 14563 494


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20. Ian Steedman (1994), On The Pure Theory of CapitalbyF.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, 325 51321. Murray Milgate (1979), On the Origin of the Notion ofIntertemporal Equilibrium,Economica, 46(181), New Series,February, 110 536

22. J. Fred Weston (1951), Some Perspectives on Capital Theory,American Economic Review, Papers and Proceedings, 41(2), May,12944 546

Name Index 562

Capital Theory I vii


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Introduction

The Theory of Capital:A Personal OverviewChristopher 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 ofa piece of machinery); it can mean the finance that a particular project requires (as when werefer to the capital market); and it can even mean the risk and entrepreneurship involved inspecific investments (as when we refer to venture capital). The recognition of this basic pointis a great help as one attempts to pick ones way through the diverse and unorganized literaturethat 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 listedabove, sometimes revolve around the distinction between a short-run and a long-run approachto the question of how capital is allocated. A fully successful theory of capital should masterboth cases, because the market system allocates capital in both senses. It determines how andwhere a specific machine tool is used; and it decides how the financial resources directed tocurrent investment will be translated into the purchase of specific machines and structures ofwhat particular designs.

Alfred Marshall, who laid the foundations for an excellent theory of capital, and then failedto deliver,1makes that distinction between specific capital goods and what he called free orfloating 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 sortof rent a Quasi-rent on old investments of capital (Marshall, 1920, p. 412). The distinctionbetween capital in its short-run specific aspect and in its long-run fluid aspect may be calledthefluidity question. It is a troublesome one for economic theory. The second feature especiallyseems to indicate that capital is a natural subject for aggregation. Could it be that in the longrun the detailed micro composition of the capital stock is somewhat irrelevant, and that only abrute total might matter? Only for the case of capital does this question assert itself. If we takelabour, 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 overthe parallel issue with capital, although extreme aggregation of labour has been a commonplace

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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 putup some money to finance a project, an investor might ask: how long before I get my moneyback? Only in the case of particular time structures of the flows of returns from an investmentdoes the answer to that question define the true profitability of an investment. Yet those casesare appealing and intuitive.

In particular, if an investment of $100 generates a flow of $qper 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 theinvestment decision is reduced to an issue of how long the investor has to wait (to get hismoney back). The higher the rate of interest, the shorter is the pay-back period, or the more

impatientis the investor. Or, one might say, the more impatient is the investor, the higher willbe 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 aloneamong revolutionaries in passing themselves off as simple offspring of their predecessors. Theanomalous term neoclassicalillustrates the same point. So John Stuart Mill, the bridge thinkerbetween the classical and the developed neoclassical, presents himself as a mere expositor ofRicardos thought, which he was certainly not. And Alfred Marshall, who could have developeda rich and dynamic capital model consistent with his price theory, trod in Mills footsteps, andsettled 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 theessence of capital, and of capital intensity. Bhm-Bawerk (see his Present and Future inEconomic Life (1959), in Volume I, Chapter 8) shows how there are two sides to the waitingequation. The demand for waiting comes from its productivity: more roundabout methods aremore productive. The supply of waiting is limited by impatience. Is waiting one thing? On thesupply side, that was assumed. On the demand, productivity, side, a positive reply demandedan 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 requireaggregation. Moreover, the concept of waiting would only burden such a model. In one of hismore striking examples, Marshall (1920, p. 351) proposed a beautifully simple model of a manbuilding a house with his own raw labour, where the quality (utility) of the house increasesboth with total effort put into its construction and the time taken to complete the job. He neverworked out this model, though his mathematical technique would have allowed him to do soeasily. 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 topoint out that the idea that the rich are rewarded for postponing their consumption is decidedlynauseating. 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 pricepremium on high-protein wheat is a reward for high protein. And that last example underlines

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the vital consideration that just to state that a premium exists for some feature explains nothinguntil 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 pureimpatience as a fundamental property of human psychology

output for early delivery is more costly to supply than output for later delivery like theirclassical predecessors, neoclassical writers assumed this to be a normal feature oftechnology.

Both branches of the argument are less than completely satisfactory. Assuming a psychologicaltendency appears to be ad hoc. And an innate productivity of waiting sits uncomfortably withthe idea of diminishing returns. Why does capital accumulation not drive the marginalproductivity of waiting down to zero?

The best discussions of these problems both date from about 1930. The first is to be found inIrving Fisher (1930). Fishers book takes the neoclassical arguments about as far as they cango within a static model. He depicts the rate of interest as determined by the joint influences ofproductivity and thrift, with thrift itself powerfully affected by a preference for immediatesatisfaction, which is essentially impatience. In his great paper, Ramsey (1928, Volume II,

Chapter 2), Frank Ramsey showed how the interplay between productivity and impatience isaugmented in a dynamic model. Continuing through von Neumann and Solow, parallel issueswere 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 whythe 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 whatwe would now call factor price determination, they did not have to agonize over the questionof how the determination of the return to capital might, or might not, differ from the determinationof the rent of land. When one factor return is seen as a residual, as Ricardo and Mill, forinstance, modelled the rate of profit, asymmetries between the returns to different factors didnot seem to be anomalous.

That comfortable position was destroyed by the neoclassical revolution. Committed to treatingthe pricing of different factor services symmetrically, these writers had to decide what symmetrywould 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. Thatidentity can only hold in the short run, because capital is accumulated through time via saving

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and investment. The point is easily handled in a dynamic model. The root issue remains whetherit can ever be correct to treat capital as a homogeneous, always-fluid entity. Of course, such anapproach 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 varyfrom 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/rightissue. It was never that. The young, left-leaning Kaldor argued against the conservative FrankKnight in defence of the Austrian period of production aggregation. Later he changed his mindand 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 quotedhere, writes:

the attempts to explain interest, by analogy with wages and rent, as the price of the services of somedefinitely given factor of production has nearly always led to a tendency to regard capital as ahomogeneous substance the quantity of which could be regarded as a datum, and which once it hadbeen properly defined, could be substituted, for the purpose of economic analysis, for the fullerdescription of the concrete elements of which it consisted.

If this quotation has a decidedly Anglo-Italian flavour, that could be misleading. Laterdiscussion makes clear Hayeks view that it is disequilibrium dynamics that require the rejectionof 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, Ihave denied myself one answer to the question: why did a group2 of economists emerge inpostwar Cambridge, England, distinguished, not merely by a general hostility to neoclassicaltheory, but by a particularly focused dislike of capital aggregation and of the concept of themarginal product of capital? While it is true that there were several left-leaning economists inthe 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 itwith his ideas concerning uncertainty, the subjectivity of investment planning, and missingmarkets. While richly suggestive, the theory is incompletely developed. So we end up with theparadoxical conclusion that an indefinite relationship between a single rate of interest andinvestment has a definite negative slope. The indefiniteness comes from the influence of apsychological confidence factor, called animal spirits.

In Chapter 11 of hisGeneral 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 theincrement of value due to the employment of one more value unit of capital. The former involves

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difficulties as to definition of the physical unit of capital, which I believe to be both insoluble andunnecessary.

Keynes could not cite Hayek here; the publication date is later. It is questionable whetherKeynes would have read Wicksell ([1934] 1961, Volume I, Chapter 12), whose more thoroughdiscussion of the marginal product of value capital appeared at this time. He probably did notread 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. Capitalaccumulation is a means to profit maximization, or to optimal inter-temporal consumptionsubstitution. Yet there are many possibilities. Suppose the sudden arrival of a fashion: Beworth a million dollars!, and that many agents then pursue a value target, and the long-runimplications 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 betweenthe rate of interest and the marginal product of capital. Swan (1956) gives us one of the bestdiscussions of the issue.

Whatever influences it may reflect, Keyness throw-away discussion, concerning whetherthe marginal efficiency of capital is an absolute number or a ratio, reflects his real interest lyingelsewhere. This is on the uncertainty of the relationship between immediate returns on aninvestment and the future returns. He writes (1936, p. 145): The schedule of the marginalefficiency 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 thepresent.

In the General Theorypassages, cited above, we find an encapsulated presentation of manyof the ideas that echoed through the classrooms of early 1960s Cambridge; I speak here frompersonal experience as a Cambridge student of that time. I have often wondered whetherKeyness view on the measurement of capital, which does not connect easily with any otherpart of his writings may derive from Piero Sraffa, and the latters participation in the famousGeneral Theoryworkshop. 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 ideasof the General Theoryitself is this: is the Keynesian model just a short-run theory, or arethere 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 theexistence of a long-run under-consumption problem. For certainly, those cathedrals were notrun up in a hurry.

Yet such sections of the General Theoryare informal in the strict sense. Keynes built nomodels of long-run growth, steady or otherwise. Later, when Harrod and Joan Robinsonattempted 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 Italiancritics of neoclassical capital theory is that this theory (often called marginal productivity theory

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in this connection), even if suitable for determining the short-run allocation of specific existingcapital 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 havenot been well exposed by its critics. Probably more problems lie on the side of the supply ofsaving than on the side of market equilibrium with capital, where the emphasis is usuallyplaced. And ultimately, only new theory beats old theory, however bad. In that respect, theanti-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, inparticular, seems to have given up on the job, so that his 1960 book (see the selection inVolume II, Chapter 17), the product of over 30 years work, is subtitled A prelude to a critiqueof economic theory.

To see what has to be done to construct a model, the SolowSwan growth model is a good

starting-point (see Solow (1956), Volume II, Chapter 3). As a beautifully simple aggregatemodel of capital accumulation it clarifies completely how both the short and long run may bedealt with in one model framework. The model treats capital as an aggregate identical withoutput. It is not trivial to dispense with that feature, but it can be done. A deeper and harderproblem 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 fromoptimization, but a constant propensity to save is assumed. It turns out that this last feature isfar more troublesome. We will see, below, how saving can be made endogenous through modelsbased on optimization, due to Ramsey or von Neumann. Meanwhile, consider how the SolowSwan model may be generalized to embrace disaggregated capital.

Let the maximum consumption possible in period tbe:

F(lt;k1,t, k2,t, . . . ,kn,t; k1,t, k2,tt , . . . , kn,t) (1)

where ltis the labour force at time t; k

i,tis the stock of capital of type i(i = 1, . . . ,n) at t; andF(.) is a concave constant-returns function:

ki, t= ki,t+ 1 ki, 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. Thisis similar to the approach used in Dorfman, Samuelson and Solow (1971, Volume II, Chapter4).

Obviously, an infinity of accumulation paths is defined by series of the form:

k1,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 beconsumption feasible, those consumption values should all be non-negative. What features,

aside from consumption feasibility, distinguish those paths which can be market equilibriafrom those which are not?

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Take an arbitrary set of weights at. It can be shown that the market equilibrium solutions are

those which are both consumption feasible and which maximize:

Tt= 1atct (4)

for all T. Note that this is not the same as maximizing equation (4) with T =. The latter wouldrule out steady-state paths with more capital than the golden-rule level, although these aremarket equilibrium solutions.

The above maximizations define a growth path of many capital goods. If F(k1,t, k2,t, . . . , kn, t;k1,t, k2,tt, . . . , kn,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 andconsumption 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 ait should be possible to select from all thevarious growth paths at least one with a constant saving rate. That is correct, although the proofis not trivial and will not be given here. In any case, unlike the simple SolowSwan model,there could be more than one constant saving rate growth path. So aggregation may matterimportantly 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; and2. a capital vector growing at a constant rate equal to the rate of growth of the labour force.

The second condition is:

kt= (1 +g)k

t+ 1 (5)

where gis the growth rate of the labour force. Now we have defined a many-capital-goodsgeneralization of the SolowSwan 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 SolowSwan model and its generalization

SolowSwan Model Many Capital GoodsDynamic Model

Is the equilibrium path from any initialconditions unique? Yes No

Is steady state unique given the saving rate? Yes No

Are model dynamics Markov? Yes Yes

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The meaning of the first two questions in the table will be clear. Allowing capital to bedifferent from other output, particularly consumption, alters conclusions radically. It is notcorrect to say that its rough aggregation of capital is what generates the simple features of the

SolowSwan 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 sameas consumption output. Adding many capital goods is intellectually satisfying but does not adda lot of analytical richness.

What, however, is meant by model dynamics being Markov? In this context, it means thatwhere the system will (or may) move next period is entirely determined by the capital stocknow. 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 uponprices 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 forwardhas to be solved out simultaneously. For this reason, how the system can move forward oneperiod depends upon all the future, and in that feature will be found the clue to multipleequilibrium possibilities. The full set of possibilities for the future, including all sequences ofprices, are limited only by the starting capital stock. For this reason, even the complex dynamicsof 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 questionconcerning the SolowSwan model. This model is highly aggregated and in more than onerespect. At the time there was great concern that capital is treated as a simple aggregate in themodel. Stiglitz addressed the issue that economic agents are treated as if they are one hugerepresentative agent, and he investigated what would happen if agents were to be differentiatedaccording to what shares they enjoy in the ownership of aggregate capital. Assuming thatagents all supply the same quantity of labour, earn the same rate of return on whatever capitalthey 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 willconverge on k*, where k*is the long-run SolowSwan solution for capital per head.

The force driving the Stiglitz result may be explained as follows. For a poor (rich) agentthe share of capital income in total income is low (high). Therefore the rate of growth ofwealth, 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 unevendistribution of wealth is concerned. Such inequalities will disappear with time, although thetime required may be long. In any case, the model behaves in aggregate exactly as if there isno inequality. The conclusion depends upon assumptions which underlie all convergencemodels.

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 historicalgarments, is fundamentally the same. In the same spirit modern -convergence theorists have

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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 benignpolitical 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 theimportance of infrastructure quality, although this may simply be an expression of similiarcauses.

As a matter of fact, neither are saving rates similar for different individuals, nor are theymuch the same for different nations. Edwards (1996) provides a good discussion of why savingrates diverge markedly in the case of Latin America. It seems that to think of the world as amassive SolowSwan model, even with unequal distribution of wealth, is to mis-describe it.Even so, some of the driving force of Stiglitzs theorem may still apply.

The Long-Run Rate of Interest

For all that, it is special: the SolowSwan 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 modeltreats 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 todepend on the growth rate and the aggregate distribution of income. Extensions of the modelmight take some of these influences into account, but only by compromising the elegantsimplicity of the model structure.

We have seen that the many-capital goods, SolowSwan model may have multiple equilibium

steady states. And even for locally stable, isolated steady states, the following conclusions ofthe 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-styledopposition have thrown much light. From the neoclassical side, a SolowSwan constant savingcoefficient 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 aggregatesaving rate. On the anti-neoclassical side, the authors concerned never fully freed themselvesfrom the idea that the rate of interest naturally orders steady states. They just insisted thatcapital intensity does not provide such an order.

Take the popular, double-switching type of example that caused much excitement in the1960s (see Pasinetti (1966), Volume III, Chapter 2). These examples show that the sameproduction equilibrium can be supported by discrete price systems and values of the rate ofinterest. But that is not to say that these two states can be equilibria of the same completeeconomy including a fully specified demand side. If we somehow parameterize steady statessuch 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.

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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 RamseySolowSwan model involves treatingcapital as homogeneous with itself and also with consumption output. A series of papers in the1960s showed that just the separation of consumption from other output leads to richlycomplicated possibilities unknown to the single-sector, neoclassical growth model. Theextract 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 theratio of the value of capital accumulation to the value of gross product), several paradoxes arepossible:

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 SolowSwan model.

Growth Models with Optimal Saving

The Ramsey Model

The SolowSwan production function was the same as that used by Frank Ramsey in hisclassic paper (1928, Volume II, Chapter 2). The critical difference between Ramseys approachand 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 isdetermined by the model itself. The chief purpose of the model is to provide a model of optimalsaving.

The Ramsey model had little impact when it was first published in 1928. It was before itstime, appearing when only a tiny fraction of economists had even a rudimentary mathematicaltraining. 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 planneddevelopment. Recently it has been promoted as a descriptive model, particularly by RobertBarro, 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 SolowSwan model treats thesaving rate as a parameter, it is able, as we have seen, to determine the long-run real rate ofinterest, and to show how it is affected by model parameters. In a simple basic version of theRamsey model, on the other hand, the long-run real rate of interest is in effect a parameter ofthe model. This must be so, because (unless the real interest rate is equal to the rate at whichsavers 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 areboth constant, the real rate of interest is equal to the time discount parameter.

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In such a case, the Ramsey model is not of much use for understanding the determination ofthe long-run real rate of interest. It says that it is determined by how impatient are savers. Andif 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 parametersand the long-run rate of interest is different from that shown by the SolowSwan model (seethe discussion provided by Bliss (1990), Volume I, Chapter 11).

Recall our earlier discussion of Alfred Marshalls (1920) capital theory. There, Marshallwas criticized for an excessive emphasis on impatience without a corresponding emphasis onthe other blade of the demandsupply scissors, namely productivity. Now an examination ofthe Ramsey model tells us that Marshall could have reached the conclusion, as he did withprices, that in the long run only one blade of the scissors cuts. In this case, it would have beenthe impatience blade.

When labour-augmenting technical progress is introduced into the Ramsey model, the optimalsteady 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 SolowSwan 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 toinclude 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(lt;k1t, k2t, . . . ,knt; k1t, k2t, . . . , knt) (6)

Consider the problem of maximizing ct+ 1, subject to ct, k1t, k2t,

. . . , kntand k1,t+ 2, k2, t + 2, . . . ,kn, t+ 2. This problem is well defined, and it establishes a concave functional relationship between

ct+ 1and ct, 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 fallof marginal utility is equal to the rate of return minus the utility discount rate. This result isvalid for the many-capital goods model too. The only difference is that the rate of return is nowa range.

Consider the implications of this last result for the double-switching paradoxes which wereall the rage in the 1960s. Take two stationary states, denoted A and B, which are equilibrium at

rates of interest r1and r3, for A, and r2, for B; with:

r1< r2< r3 (7)

Then by varying the utility discount rates, it will be possible to construct Ramsey-optimalsteady states which use technology A, and where for discount rates in between (where thediscount rate is concerned), there will be a Ramsey-optimal steady state which uses technologyB. 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 anintermediate discount rate, must generate a frontier with an intermediate slope. All this is in the

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spirit of Solow (in Capital Theory and the Rate of Return), and via him Irving Fisher; but it issimpler, because the rate of return is defined as the shortest inter-temporal consumptionsubstitution.

The von Neumann Model

John von Neumanns magisterial paper is of interest for capital theory because it establishedthe first formal model with endogenous growth (see the account provided by Champernowne(19534), Volume II, Chapter 11). The model also provided an early example of many-goodsgeneral equilibrium. Finally, of particular interest is the point that the model, despite its Austriansource, deals a powerful blow to the period-of-production philosophy. For von Neumannsinput and output matrices make all activities last the same single period length. Any economicprocesses 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 Austrianprinciples may not operate behind this structure. A fast but less productive technique and aslower 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.

Diamonds OLG Capital Model

Diamond, whose key paper in this context (see Diamond (1965), Volume II, Chapter 24) marriedSamuelsons pure-consumption loan framework to a neoclassical capital model, with a

production function and investment. Consider a simple version of the model, perfectly adequatefor our purposes, in which the consumer lives for two periods. In the first period of her life, shesupplies 1 unit of labour inelastically and earns the wage rate corresponding to the marginalproduct of the capital that the previous generation saved for its retirement. She may save partof her wage and this becomes the capital which will cooperate with the labour of the nextgeneration. Population grows at rate , so that each generation is (1 +) the size of the previousgeneration. 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, whoplant it in the ground and pay the additional yield of corn resulting next period, when it providesa pension.

Details of how this model works can be found in De La Croix and Michelle (2002). Here aninformal and intuitive discussion serves to show how this approach paints the determination ofthe rate of interest in quite a different hue from that seen in the SolowSwan or Ramsey models.

In the Diamond model the long-run equilibrium rate of interest may not be unique. This is incontrast to the SolowSwan or Ramsey models. Multiple solutions are usually not availablewith the simple functional forms that economic theorists have usually preferred. In particular witha Cobb-Douglas production function, steady-state equilibrium is always unique; De La Croixand Michelle (2002) provide details. Are the more complex cases that can give multiple solutionsimplausible, or are they merely untidy? While we would all like the world to be neat andsimple, 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

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economic analysis, if only because endogenous preference means nothing in a static contextand can only be defined in a dynamic context. And dynamic preferences can easily beinconsistent. 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. Imaginethat saving goes to buy units in a private or public pension fund. The older generation whichco-exists (overlaps) with this young generation will sell all the units which it owns. These willbe sold without dividend i.e. excluding the earnings on the units. In steady state the fund willgrow at rate , issuing new units as required to accommodate population growth. The pensionfund 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 generationworks with less capital than it will save. When they are retired pensioners, these individualswill 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 whichmaps from the Kvalue chosen by one generation into a value of Kchosen by the followinggeneration. The following effects can be demonstrated:

1. the higher are the savings of the previous generation, the higher will be the wage rate of thepresent generation;

2. the higher are the savings of the present generation, the lower will be the gross rate ofreturn which that generation enjoys.

These two effects, together with the assumption of regular preferences, imply the followingresult: assuming future consumption to be a strictly normal good (which rules out the case inwhich 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 ofreturn to saving. But that could only happen if there were more saving. So, there must be moresaving 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, multiplesolution may require variation in the elasticity of inter-temporal substitution , which may notbe readily accepted. In fact the assumption that does not vary, particularly with consumption,is a serious deficiency of much contemporary growth theorizing. If varies with the level ofconsumption the -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 thatthe poor may be reluctant to save. The reason would be that inter-temporal substitution ofconsumption which saving requires may be difficult for the poor particularly not becausethey have a high discount rate, but rather because they have a low value of .

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 chosenthe optimal level of saving, they are by definition indifferent between a slightly smaller and a

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slightly higher level of saving, these two values bridging the precise optimum level. Thefollowing 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 ofreturn on their own savings. In this comparison the divergent interests concern generationsalive (or, at any rate, young) at different times.

In many cases, these apparent externalities do not upset the Pareto optimality of marketequilibrium. In a normal static case when a group of agents form a champagne club, theyimpose positive and negative effects on non-members. The club slightly increases the demandfor champagne, and hence its equilibrium price. That harms all champagne drinkers, but benefitsthe factors used in champagne production. None the less, the standard efficiency result ofgeneral equilibrium (GE) says that banning champagne clubs cannot benefit all, not even ifside payments are made to try to achieve that outcome.

In growth models the GE optimality argument can fail. That happens when the rate of interestris pushed down too low by excess saving. When rfalls below the rate of growth, the effectivelyinfinite number of goods in an infinitely lived economy all count in a value comparison. Suchexcess saving is possible in the Diamond economy. It can also happen in the SolowSwanmodel 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 necessarilyPareto-inefficient by virtue of that fact. This is because one has to find a transition path whichis 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 agoverment 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 mightcall 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 upthe 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. Nosimple name is ideal, but the one I have chosen indicates at least that the influences of PieroSraffa and Joan Robinson, in particular, are of central importance. Even in that case, there is aflavour of necrophilia in the air. If one asks the question: what new idea has come out ofAnglo-Italian thinking in the past 20 years?, one creates an embarrassing social situation. Thisis 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 fromgeneral 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 models driver. Finally, the exogenoustechnical progress of Harrod, and most writers on growth from whatever school in the 1960s

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and later, has been joined by numerous models which make technical progress endogenous inone of the several possible ways.

Endogenous technical progress is not a new concept: the seminal paper is Arrow (1962,

Volume III, Chapter 18). Kaldors idea that a technical progress function should displace theproduction function also makes the rate of technical progress endogenous. The key referenceis Kaldor and Mirrlees (1962). Here endogenous means simply that the rate of technical progressis not a fixed parameter of the model. It is a variable that must be extracted as part of theoverall model solution. These early treatments of variable technical progress are quitemechanical. 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 pharmaceuticaland other research-intensive companies. More work is needed to fully develop this line ofmodelling. Even so, it is striking that old themes emerge in more refined models. Notable is thenon-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 contemporarymodels? If that could be done, one would hope that its contribution could be more constructivethan the mutually assured destruction approach that marred some of the 1960s debates. It isevident that richer models yield richer possibilities. They do not do that in proportion whenoptimization drives model solutions. However, we know that many-agent models can havemultiple equilibria even when all agents optimize. There may be fruitful paths forward in thatdirection.

Old contributions should best be left buried where they involve using capital as a stick tobeat 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 theoverall solution. It reflects badly on economists and their keenness of intellect that this was notalways obvious to everyone.

A Summing Up

The lengthy argument developed above leads to the conclusion that we do not have a goodtheory of the long-run capital equilibrium. That was the view of the Anglo-Italian critics oforthodox 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 savingin the form of capital goods. That is not correct. A far more difficult problem is to build a theoryof 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 importantissues. We can glimpse more convincing models of the supply of capital via saving. They arequite 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 asdisaggregated as realism would dictate. However various influences are weighted, it will bethe case that saving rates, demographics and technical progress will be the grand forces drivingthe 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 getour minds on top of them.

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Notes

1. For a detailed exposition and evaluation of Marshalls 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 (18721944) 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 Americas Saving Rates So Low? An International Comparative

Analysis,Journal of Development Economics, 51, October, 544.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, 17492.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, 16580.Swan, T.W. (1956), Economic Growth and Capital Accumulation,Economic Record, 32(2), 33461.

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Introduction

Capital Theory Controversy:Scarcity, Production,Equilibrium and TimeAvi J. Cohen and G.C Harcourt

When economists reach agreement on the theory of capital they will shortly reach agreement oneverything else. (Bliss, 1975, p. vii)

Capital theory is a subject infamous for the continuous recurrence of controversy. ThisIntroduction1attempts to explain why that is, by linking the controversy to fundamental problemsin capital theory. The singular for controversy is purposeful, as we believe that the same set ofissues fuels most controversies in the history of capital theory, going back to the classicaleconomists and Marx, and continuing through the twentieth century. Major controversy erupted

around the turn of the twentieth century between Eugene von Bhm-Bawerk, J.B. Clark, IrvingFisher and Thorstein Veblen; in the 1930s between Frank Knight, Friedrich von Hayek andNicholas Kaldor; and, most recently, in the Cambridge capital theory controversies.

Capital theory controversy commonalities originate in the dual nature of capital. Economistsconceive of capital both as a heterogeneous collection of specific capital equipment used inproduction, and as a homogeneous fund of financial value that flows among alternative uses toestablish a uniform rate of return. Capital controversy originates in the tension between thesephysical and value conceptions of capital.

In the physical conception of capital, there has been a long-standing neoclassical attempt toground the rate of interest in the technical conditions of diminishing physical returns in

production. This grounding in the objective marginal productivity of capital, coupled withsubjective positive time preference, yields an inverse, monotonic relation between the capitalintensity of production (the quantity of capital) and the rate of interest.2A physical measure ofcapital that is independent of changes in income distribution and prices, akin to measuringlabour in man-hours, would be ideal for this conception. But heterogeneous capital goodscannot be so measured there is no meaningful physical common denominator betweensemiconductors 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, valuingcapital involves the rate of interest to cost the time dimension. The physical conception ofcapital cannot evade a connection to the value conception.

In the financial value conception, capital as investment funds is measured in monetary valueterms, and competition dictates that all investments (adjusted for risk) will expect to receive


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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 thosefunds 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 ofsupply and demand, and with changes in the interest rate which affect the net present value ofthe equipment. The financial value conception of capital cannot evade a connection to theevaluation of physical capital goods.

Economists can usually agree that capital has both physical and value conceptions. Thecontroversies begin when the dual conceptions of capital are integrated into economic models andone 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 twomajor problems: (1) integrating production into the scarcity theory of value, and (2) integratingcapital 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 betweenthe physical and value conceptions of capital, and (4) the role of ideology and vision in fuellingcontroversy, especially when one-commodity results are not robust. This introduction, in fleshingout 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 subjectsuch 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 mechanismallocates scarce resources to their most valuable uses. This vision is intuitively obvious in apure exchange model. But if we allow for capital and production, the intuition becomes lessobvious. 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 aboveterms: vision, value and price. Most economic discussions today begin and end with price, sothe 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 uponanalytic work of any kind we must first single out the set of phenomena we wish to investigate, andacquire intuitively a preliminary notion of how they hang together, or, in other words, of what appearfrom our standpoint to be their fundamental properties. (Schumpeter, 1954, pp. 5612).

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 thePhysiocrats, and with a lineage strongest in Ricardo, Marx, Veblen, Schumpeter, Keynes,

Kalecki, Kaldor, Sraffa and Joan Robinson, envisions the profit-making decisions of capitalistfirms as the driving force of economic activity (see Pasinetti (1983), Volume I, Chapter 4). The

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fundamental economic problem is the allocation of surplus output to ensure reproduction andgrowth. The dependency of individuals on the market makes ones position within the socialdivision 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 rateof profits on capital arises from social relationships in production, and the realization of profitsis brought about by effective demand associated with the different saving and spendingbehaviours of the main classes in the economy and the animal spirits of the capitalists. Therate of profits is the rate of self-expansion of capital, the outcome of the accumulation process.

The more recent neoclassical4vision, originating in Jevons (see Steedman (1972), Volume I,Chapter 6), Walras and Marshall (see Bliss (1990), Volume I, Chapter 11), and integratingcapital in a familiar form in Fisher (see Samuelson (1967), Volume I, Chapter 14), envisionsthe lifetime utility-maximizing consumption decisions of individuals as the driving force of alleconomic 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 ofconsumption (Hirshliefer, 1970, p. 12). (In fact, all capitalist institutions are seen as intermediariesto further the utility-maximizing consumption process.) For capital accumulation, subjectiverates of time preference, marginal productivity and the money rate of interest as the price ofcapital services which clears the market for money loans are fundamental. The rate of interestis the outcome of an inter-temporal optimization process, balancing subjective time preferenceand the objective marginal productivity of capital (more precisely, the technical rates at whichpresent consumption may be transformed into future consumption).

The fundamental properties of each intuitive Vision are embodied in a value theory theanalytical layer between Vision and price theory. Modern economists tend to view value and

price as synonyms e.g. see Debreus (1959) Theory of Value. But the distinction has beenimportant to many capital theorists. What is the difference between price theory and valuetheory? And what is the connection between value theory and vision? We start with the morefamiliar 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 thetechnical conditions of production and the given real wage.5Neoclassical prices depend ongiven 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 simultaneousdetermination 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 ofprice (Lowe, 1981, p. 803). There is a simple, one-direction linkage from underlying cause toeffect on price.7

The two major value theories in the history of economics use either labour or utility as theultimate determinant of price.8For the classical theory of value, the relative price of a commodityreflects 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 quantityof embodied labour.

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For the neoclassical scarcity theory of value, the relative price of a commodity reflects its relativescarcity, 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 valueis 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 theorydid not exist while many of the articles in this collection were written, was not shared by mostof the Cambridge, England, crowd (Sraffas book was both a prelude to a critique of neoclassicaltheory and a revival of classical theory (Meek, 1961)) and because the distinction was madeand 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 allcommodities are gross substitutes, is useful for illustrating the key propositions of the scarcitytheory of value: (1) as a commodity becomes more scarce, its price increases; and (2) if theutility of a commodity increases, its price increases. Price functions as a quantitative index ofresource 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 correspondingpricetheory propositions would be much weaker, stating only that in models with less restrictiveassumptions, prices are determined by preferences and endowments (and technology in modelswith production). Highbrow price theory makes no unequivocal claims about unambiguouslysigned price effects of underlying parameter changes.

In order to focus on the scarcity issue in what follows, utility and demand conditions areassumed not to change. Thus the scarcity theory of value entails, ceteris paribus, a uniqueinverse relationship between a commoditys quantity and its price.

From as far as Bhm-Bawerks (1966 [1898]) controversy with (a posthumous) Marx, allcapital 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 notimmediately obvious, since in what sense are commodities scarce if they can be produced(Bliss, 1975, pp. 34)? But the value theory propositions of price as a scarcity index can besustained if commodities are produced from exogenously given resources under conditions ofconstant returns to scale and diminishing marginal productivity. Capital services are treated asa factor of production the price of which the rate of interest is determined by the relativescarcity of capital. With this extension, the distribution of income to factors of productionbecomes merely a subset of general price determination.10

All of the neoclassical controversies involve models that treat capital as a resource whoseprice 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):

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1. An inverse, monotonic relation between quantity of capital (as well as the capitaloutputratio 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 knowledgeof relative factor scarcities/supplies and of marginal products.

A one-commodity SamuelsonSolowSwan aggregate production function model (VolumeIII, Chapter 1; Volume II, Chapter 3; Swan, 1956) provides the quintessential illustration of theparables:

Q=f (K,L)

where the one produced good (Q) can be consumed directly or stockpiled for use as a capitalgood (K). With the usual well-behaved assumptions, in competitive equilibrium, the price oflabour (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 magnitudesthat are independent of prices. Analogously, the price of capital services (the rate of interest) isdetermined by the relative scarcity and marginal productivity of aggregate capital. The marginalproduct of capital, Q/K, is also a derivative associated with strictly physical quantities.Resources are physical substances measurable independently of distribution that can explaindistribution. Even with production, factor prices (in the form of physical returns to factors ofproduction) reflect relative scarcities.

In these parables, the return on capital stems ultimately from utility and technology. There isone-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 capitalis ideal.

But problems arise for the parables in more general models. Heterogeneous capital goodscannot 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 oras an average of products. In other words, each particular capital-good is measured by a unit extraneousto itself. [This] is a theoretical anomaly which disturbs the correspondence which would otherwiseexist 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 bythe excess or scarcity of similar machines. If capital were to be measured in technical units, the defectwould be remedied and the correspondence would be complete. But, in that case, productive capitalwould have to be distributed into as many categories as there are kinds of tools, machinery, andmaterials, etc., and a unified treatment of the role of capital in production would be impossible. Eventhen we should only know theyield of the various objects at a particular moment, but nothing at allabout the value of the goods themselves, which it is necessary to know in order to calculate the rate ofinterest, which in equilibrium is the same on all capital. (Wicksell [1934] 1961, Volume 1, p. 149;

emphasis in original)

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With heterogeneity of either capital or consumption commodities, price invariance disappears.In aggregate models with heterogeneous commodities, the interest rate is no longer determinedby 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 relativeprices of consumption and capital goods. Once relative prices can vary, the marginal productof capital becomes value output/value capital.11Scarcity, the technical productivity of capitaland prices now help to determine the interest rate. Distribution depends not only on independentphysical magnitudes, but also on prices, which, in turn, depend on distribution. The straightforwardphysical account of the inverse, monotonic relation between capital-intensity and the rate ofinterest 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 parablesof the models. Price Wicksell effects are changes in the value of capital as the wage rate and theinterest 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 theinterest 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 earliercontroversies as well. With capital-reversing, a lower capitallabour ratio is associated with alower interest rate. In comparing two steady-state equilibrium positions, it is as though capitalservices have a lower price in the position where capital is more scarce. Capital-reversingimplies the demand curve for capital is not always downward sloping, and violates parables 1and 2. Reswitching occurs when the same technique (a physical capitallabour ratio) is preferredat 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 associatedwith two different interest rates, violating parables 2 and 3.

In general cases with Wicksell effects, the quantity of capital must be measured in valueterms and the tension between the physical and value conceptions of capital surfaces. Becausethe measure of capital can now change without any change in the physical quantity of capitalgoods, the inverse monotonic relation with the rate of interest need not hold. The rate of interestnow 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 pricetheory 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 unequivocalclaims about unambiguously signed price effects of underlying parameter changes. The onlyclaim is that prices are determined by preferences, endowments and technology, and that ingeneral equilibrium factor returns are equal to or measured by disaggregated marginal products(Blaug, 1975, p. 7; Bliss, 1975, p. 110; Hahn, 1972, pp. 24). No general claims can be madefor the proposition that an increase in the quantity of capital will cause a decrease in the interestrate. In Hahns (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 pointmore forcefully and eloquently:

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Even people who have made no study of economic theory are familiar with the idea that when somethingis more plentiful its price will be lower, and introductory courses on economic theory reinforce thiscommon presumption with various examples. However, there is no support from the theory of generalequilibrium 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 ariseoften turn on a value versus price theory perspective. For example, is it important to be able tomeasure capital in units independent of changes in distribution and prices? Whether or notarguments such as the measurement of the quantity of capital, which is supposed to determinethe rate of interest, itself depends on the rate of interest, are considered, a flawed circularargument or the legitimate mutual interdependence of variables, depends on a value versusprice theory perspective.

Bhm-Bawerk ([1912] 1959a) attacks Fishers (1907) equilibrium model of interest rate

determination (see Volume I, Chapter 8), claiming that simultaneous equations models involvecircular reasoning and thereby fail to provide a causal explanation of interest. Fisher defendshis model as mathematically determinate in terms of numbers of equations and unknowns.Bhm-Bawerk acknowledges Fishers mathematical determination as correct and cogent([1912] 1959a, p. 190). But for Bhm-Bawerk, it is not enough. He says that Fishersdemonstration

would be rather nice if mathematical and causal solutions of problems were the same But to finda certain quantity that matches other given assumptions and to explain this quantity are two entirelydifferent things Certainly a single interest rate corresponds to the state of options that clears themarket; 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 accompanymathematical determination. ([1912] 1959a, pp. 1912; emphasis in original)

Based on this passage, Fisher concluded that Bhm-Bawerks critique was nothing more thanthe misunderstandings of a mathematical innocent. Subsequent commentators agreed. Stigler(1941, p. 181) accuses Bhm-Bawerk of failing to understand some of the most essentialelements 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 equationscontroversy was a fundamental difference between Bhm-Bawerk and Fisher on the need for

value theory, as opposed to price theory, for a complete explanation of economic phenomena.Bhm-Bawerk understood and used extensively simultaneous determination in his ownsubsistence fund model of interest determination.13As an Austrian, Bhm-Bawerk required inaddition to the simultaneous general equilibrium determination, a one-way value theoryexplanation from cause (rooted in subjective preferences and what he considered as the onlyoriginal factors of production labour and land) to effect (Kauder, 1957).

Bhm-Bawerk considers Fishers theory of interest as inadequate, first, because as only apartial 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 labourmarket and production decisions is missing (Bhm-Bawerk, 1891, p. 336).

Second, Fisher focuses on a price theory explanation. Bhm-Bawerk separated the explanationof interest into two questions: the value theory question as to why interest exists, and the price

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theory question of how the rate of interest is determined. Fisher claims that an answer to thesecond question implicitly answers the first question as well. This claim marks the beginningof 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 emergingneoclassical mainstream, he believed that value theory issues were relatively settled.15Bhm-Bawerks Austrian views were not entirely mainstream. For him, there were still importantvalue theory issues to be argued. For those like Fisher, who believed that fundamental valuetheory propositions have been agreed upon, Bhm-Bawerks arguments probably appeared astilting at imaginary windmills.

The value versus price theory perspective also provides insight into the fruitless interchangesduring the Cambridge controversies about simultaneous equations. As early as 1936, Sraffawrote 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 inthe 1950s by Champernowne (19534, Volume II, Chapter 11)16and Joan Robinson (1956),but their full significance was realized only with Sraffas (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 understandthat the equilibrium solution to a set of simultaneous equations does not entail causalrelationships. Von Weizscker (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 ofsimultaneously solvable equations and therefore worries about the derivation of the rate of interestfrom the capital stock, while the definition of the capital stock presumes the knowledge of the interestrate. Where does the puzzle come in all this if one has really understood what a system of interdependentvariable is all about?

While this characterization of simultaneous equations is correct, it ignores the fact that theneoclassical parables were an attempt to go beyond simultaneous interdependence and provideone-directional causal explanations. When that attempt failed conclusively in aggregateproduction function models (outside of the one-commodity model), neoclassicals retreated toa 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 theneoclassicals had sidestepped the point by abandoning the scarcity theory of value. For PieroSraffa, Joan Robinson and others committed to the classical political economy vision, valuetheory issues were still at stake.18But for neoclassicals who presumed value theory questionshad long been settled in their favour, the Cambridge causal critique was misunderstood asmathematically 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 andtime into equilibrium models. Most capital theory controversies of the twentieth century also

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developed into controversies over how, if at all, may the dynamic processes of accumulationand distribution be analysed within an essentially static equilibrium framework? Capital isfundamentally 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) captureswell this particular capital theory controversy commonality in describing the theory of capitalnot as some quite separate section of economic theory, only tenuously related to the rest, butrather as an extension of equilibrium theory and production theory to take into account therole of time. To understand the capitaltimeequilibrium connection, we begin with theconnection 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 inthe representation of capital and time.

Capital and Time

The value of a firms inve

Capital Theory

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