The results of the capital theory controversies and general equilibrium theory

Some reflections on concepts and history

G.C. Harcourt

1.   I was happy to have been asked to write a chapter under the rubric of the results of the capital theory controversies and general equilibrium theory. I once got into hot water with Christopher Bliss when, in a draft of a paper that eventually appeared in two versions (Harcourt 1975, 1976) (one with a title that, in retrospect, I regret having chosen), I tried to reconcile the clash between Christopher Bliss (1970) and Pierangelo Garegnani over Garegnani (1970). Bliss had written a comment on it, in which he expressed surprise at some of Garegnani’s results because, within an Arrow—Debreu framework, the results were not likely to occur. Garegnani’s results 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. (In his Ph.D. dissertation (1959), Garegnani had made much the same point about marginal productivity theory and had used Walras and Wicksell as his guinea pigs.) I suggested that perhaps their difference in opinion might be traced to the fact that Garegnani concentrated (à la Ricardo) on the ultimate long-period outcomes of ‘changes’ in the values of specific variables, whereas Bliss had put more emphasis (à la Malthus) on immediate, short-period results. Bliss interpreted my comments (made in a footnote and subsequently removed) as an assertion that he did not know the difference between the short period and the long period — oh dear me! We eventually sorted out our differences and resumed our restored friendship. With the fullness of time to provide hindsight, I would like now to make a few remarks about the issues involved.¹

Since the 1970s, a number of scholars have looked at the structure and the workings of the Arrow—Debreu intertemporal model and its offshoots. Some have detected, within its own framework, the possibility of perverse results that are akin to those of the capital theory controversies and that are at odds with the fundamental conceptual notion underlying the subjective theory of value that utility is the source of value and that price is an index of scarcity. Furthermore, though not connected directly with these contributions, there are the disquieting results of Hugo Sonnenschein (and others), which, as Abu Rizvi has shown in two fundamental papers (1991, 1994), undermine the mainstream attempt to lay down microeconomic foundations of macroeconomics. Alan Kirman (1989) has also commented on these and other matters and has pointed the way towards the use of social groups rather than isolated individuals as the appropriate starting point for macroeconomic analysis, indeed economic analysis in general. So perhaps a convergent process is starting between poles-apart economists — but I would not bet on it.

As I understand Garegnani’s arguments, he was attempting to show that, in a situation where a tendency to equality of rates of profit in all activities was at work, both the Marshallian and Walrasian frameworks (those that Krishna Bharadwaj called the supply and demand approach) could not guarantee convergence on long-period situations where this was ensured. Or, even if it did occur, the resulting before and after comparisons of the properties of the long-period positions were such as not to be compatible with any observed ‘changes’ in, say, income distribution in actual economies. It was a question concerned, first, with establishing existence (and uniqueness) and, second, with the possibility of the equilibrium, if it existed, exhibiting local and global stability. This last is a much harder task, one that the most thoughtful general equilíbrium theorists seem to have conceded cannot be done unless very special and artificial, arbitrary or, dare I say it, ad hoc, conditions are assumed. Heinz Kurz has written an especially lucid account of the existence and stability arguments in Kurz (1985); there, he set out the ‘critique of economic theory’ implicit in Piero Sraffa’s ‘prelude’ and, more explicitly of course, in the writings of Garegnani and other scholars.

All these expositions are a far cry from the general equilibrium model taught, for example, by Harry Johnson to his graduate students in the 1960s and 1970s and left to us and posterity in his 1970 Yrjó Jahnsson Lectures (Johnson 1971). There, he ensures that capital theoretic puzzles are removed by assumption. The capital good used in the two sectors may be costlessly and timelessly removed and reshaped in response to the pull of changes in relative prices, so that, except for large Giffen good effects (considered to be unlikely), prices in product and factor markets are able to do their thing. Marshall’s dynamical principle of substitution, seen ever at work in both consumption and production, dominates outcomes, which themselves confirm the neoclassical intuition that price is an effective index of scarcity in all markets, product and factor.

Finally, Avi Cohen (1989) had pointed to an incoherence in both approaches to value and distribution once we try to establish the robustness of their insights, intuitions and results outside the confines of one, all-purpose-commodity models. In his 1993 paper, he revives George Stigler’s useful distinction between analytical and empirical propositions, a distinction that dates back at least to Ricardo when Ricardo conceded the effects of the durability of capital goods on the formation of relative values. (His editor, though, would not have accepted such a concession as far as pure, precise theory is concerned.)

In this chapter, I discuss these and other conceptual issues and argue — with hindsight — that they have become obscured at times as the debates have developed over the years. As I wrote in Harcourt (1999), it is far easier to apply an explicit, logical and coherent structure to arguments and events after they have occurred than to be fully, or even dimly, aware of them while they are happening.

2.   I started by reading again Garegnani’s Ph.D. dissertation (1959) (in English; I am ashamcd to say that I have not yet the Italian to read it in its Italian book form. lndeed, when our first grandchild, Caterina, was born, Joan (Harcourt) responded by learning Italian and I, by learning English). There, he makes crystal clear that, in Ricardo, Walras and Wicksell, despite their very different approaches to the theory of value and distribution, there is nevertheless a common source of error associated with the meaning (as Joan Robinson repeatedly stressed) of capital that, in one dimension of the problem, shows itself in its measurement. Garegnani argued — probably he is right — that, in the classical surplus approach, in which the source of value is the difficulty or ease of reproduction (of commodities, by means of commodities), the problem was solvable; but that, in the supply and demand approach of Walras, Wicksell and Marshall and, as Sraffa and Krishna Bharadwaj were to argue, all forms of neoclassical theorising, it was not solvable.

The basic reason is that capital cannot be both an exogenous (determining) variable and an endogenous (determined) variable at one and the same time. Yet, if we are to say that the relative prices of the services of the neoclassical factors of production are ‘low’ or ‘high’ because we have a ‘lot’ or a ‘little’ of their ‘quantities’ (or that more of the services of the relatively cheaper factor will be used if its relative price is low), we must know what we mean by a ‘lot’ or a ‘little’ capital before the analysis starts. That is one reason why the mutual determination nature of general equilibrium theory, and whether Joan Robinson or Sraffa understood the nature of mutual determination (they did), is beside the point. As I said, Johnson was able to dodge this problem (and thus get ‘pleasing’ results) by assuming away virtually all the characteristics of capital goods (and finance capital) as we know them in modern economies.

The ‘lot’ or ‘little’ aspect was seized on by neoclassical economists as a measurement problem and therefore associated with aggregation puzzles. The latter, they argued, were the same (and as easy or as difficult to solve) for labour as for capital goods (or for the collection of heterogeneous goods that make up the national product). In a sense they were right — but about the incoherence in their own approach, not in the alternative approach. For, increasingly, it has been realised that, even in general equilibrium systems, the whole is more than just the sum of the parts, so that starting analysis from isolated individual behaviour virtually ensures that there is a lacuna between individuals’ behaviour, on the one hand, and the collective outcome of all the individuals’ behaviour taken together, on the other.

That I take to be the principal thrust of Kirman’s paper and of his review (1998) of Donald Walker’s fine book (1997) on what Walras really said. Walker argues that Walras always tried to analyse processes, and the formation of prices in particular, as they occurred in real-life markets, even though towards the end of his life he changed his mind on what exactly they were; see also Walker (1987). Kirman argues that, by a process of rational reconstruction, he and other general equilibrium theorists like him imposed an auctioneer on Walras’s analysis as this was the only logical way to make his general equilibrium system coherent and equilibrate (in the sense of proving existence).

This observation also seems to be the crucial thrust of Rizvi’s critique of the mainstream microeconomic foundations of macroeconomics programme stemming from Sonnenschein’s results about the arbitrary nature of the excess demand functions in Arrow—Debreu systems. Jan Kregel (1998) wrote a subtle account of the link between the so-called New Keynesians’ agenda and the fundamental reasons why the markets for labour and investment goods do not ‘clear’ at full employment, even when market structures are competitive. He traces these reasons back to the even more subtle arguments of Keynes about what knowledge (‘information’, as it is fashionable to say today) it is and is not reasonable to assume that people have when making employment and investment decisions, and the implications of making these within an inescapable environment of uncertainty for the (unaided) attainment of full employment. Kregel links these arguments to similar ones to be found in George Richardson’s critique of the coherency of the concept of competition (1959, 1960), to Ronald Coase’s arguments for the existence of firms (1988), and so to the ultimate failure of markets to fulfil the promises its proponents claim they will deliver.

3.   Many of these arguments explicitly point the way to an exciting new theme that Avi Cohen has developed in some of his papers and that will be the subject of his forthcoming book on controversies in capital theory ancient and modern, appropriately subtitled From Böhm-Bawerk to Bliss (the person, not the state). He is convinced that the distinction between history and equilibrium lies at the heart of all the controversies, from those between Böhm-Bawerk and Fisher (and J.B. Clark), through those between Hayek and Knight, up to the modem ones that, started by Joan Robinson in the 1950s, drew fundamentally on the insights of Piero Sraffa. I must, of course, leave Avi to spell out the details of his argument. Suffice it to say here that the equilibrium approach will never be able to capture the essentials of the dynamic problems of accumulation with which the concept of capital is inescapably and crucially associated. (Sraffa shows that there is incoherence even within the confines of an equilibrium system.) All the contestants (in the ancient controversies, anyway) seem to have recognised this, yet vainly sought to find ways around it because they thought that economic theory and equilibrium must always go together.

This conclusion brings to the fore two developments that were occurring simultaneously in the post-war years, in which we know otherwise staunch allies were at loggerheads, for the critique of general equilibrium value and distribution theory by Sraffa and those influenced by him was usually carried out within structures that used the long-period method. One of the by-products of this was to point to the retreat by modern defenders of the subjective theory of value and distribution, a retreat marked by the change in the definition of equilibrium, a move towards temporary equilibrium models and/or the Arrow—Debreu construction; see Garegnani (1990). It would then be argued, incorrectly, that Sraffa’s analysis must be contained within this different but now universal framework, albeit as a (very) special case, as though an overlap of mathematics must automatically imply an overlap of economic conception, intuition and understanding. This movement was not only to be noted in the early Hicks but also in Hayek, who, having recognised the problem in the late 1920s, had hoped to solve it in The pure theory of capital (1941) and so restore coherence to, he hoped, the agreeable results achieved by the traditional method — a task that he admitted he failed to carry out. Yet his intuition (perhaps his fond desire) always told him there must come out of Austrian capital theory a well-behaved, downward-sloping demand curve for the services of capital and that competitive markets, so necessary for his absolute value of freedom in society to be sustained, really did have underlying them stable patterns of relative prices that properly reflected relative scarcities. For him, Dr Pangloss, despite all theoretical and empirical evidence to the contrary, remained alive and well.

Such an act of faith was not, of course, confined to Hayek — it is also reflected in, for example, the opening paragraphs of Ken Arrow’s Nobel Prize Lecture (Arrow 1973) (though not in Hahn’s critique of Kornai’s Anti-equilibrium (Hahn 1973)), nor in the final summing-up in Bliss’s 1975 book). Hayek himself tried to ally this belief with another, that the analysis of dynamic processes was to be the way forward, even though he himself gave up the task and concentrated on the theory of knowledge, the place of law in the good society and the absolute and ultimate value of freedom.

4.   What is the challenge for the heirs of Piero Sraffa, if the general equilibrium approach is not a way forward but a dead end, even a negative achievement in Hahn’s view? One thing that has clearly been exposed as misleading and unacceptable is the use of representative agent models for systemic analysis (not that their use has ceased!). They have served to suppress the attention that Keynes, for example, drew to the dangers of the fallacy of composition when analysing over all behaviour. The general equilibrium theorists thought they could avoid it, but the weight of evidence suggests that they were wrong; too often, as well, post-Keynesians have looked at aggregate relationships and treated them as though they were representative of the behaviour of the firms throwing them up. (An early example of this criticism of post-Keynesian procedures is to be found in Lorie Tarshis’s 1980 American Economic Review paper, where he warns against viewing aggregate flows as an average, when they are often the net outcome of extremely divergent behaviours.) Anyone who has pondered on liquidity preference theory realises that we must have at least two agents, a ‘bull’ and a ‘bear’, whose different desires are reconciled, at least momentarily, in an uneasy truce by the level of the rate of interest. Similarly, anyone who has even the faintest notion of what drives capitalism — the process of accumulation allied with endogenous technical progress — would need to use a model with at least an investment goods sector and a consumption goods sector, with distinct social groups in each. As I have always thought that Piero Sraffa was contributing — deeply, greatly — within a Marxian framework, I would like to think that he would have accepted this too.

Acknowledgements

I thank, but in no way implicate, Stephanie Blankenburg, Peter Kriesler and Ajit Sinha for their comments on a draft of this chapter.

Note

1. I have written the paper in a relatively unscholarly way, i.e. few references and quotes, in order to set out the skeleton of the argument.

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