Wednesday, October 04, 2006

Interest Rate Unequal To Marginal Product Of Capital (Part 4 Of 4)

4.0 Conclusions
This series of posts has presented a simple explanation of the nonequality of the interest rate and the marginal product of capital, as that equality is understood in macroeconomic models. Thus, neoclassical microeconomics does not imply that equality. Various attempts to defend the macroeconomic models considered here have been examined and have been found wanting. An interesting aspect of this criticism is that it does not seem to be about index number problems. Nor has this argument depended on the phenomena of reswitching at all, and it depended on capital reversing only in criticizing Champernowne's chain index [15]. If the demonstration of the theoretical possibility of these phenomena are taken as central to the Cambridge Capital Controversy, then the implications of that controversy should extend beyond aggregate neoclassical theory [16]. As far as I can see, this argument is fairly well understood on the Cambridge, England side.

It is curious that economists continue to use aggregate production functions despite the clear warnings of this traditional argument. Many of those economists who follow Solow or Lucas do not seem concerned about their inadequate concept of capital. Although these researchers may be interested in technical improvements in their models, capital-theoretic problems do not seem high on their agenda. Furthermore, much of graduate education in economics seems to leave newly emerging economists unaware of capital-theoretic problems with their models. These young economists do not seem to possess the analytical tools that were forged in the CCC, such as the correct analysis of the choice of technique, a correct analysis of the relationship between the theory of rent and income distribution, or even how to analyze depreciation and the economic life of machines in a framework of joint production.

What explains this apparent continuation of the miseducation of economists that Joan Robinson decried over fifty years ago [17]? My hypothesis is partly ideological. Any advanced treatment of capital theory and the appropriate analytical tools [18] would expose the student to the Cambridge Capital Controversy. The student would then learn about some serious questioning of the internal consistency of many claims of neoclassical economists. There are obviously normative overtones to this controversy, for example, over the exploitative nature of profits and the capitalist system as a whole. Neoclassical economics might be claimed to currently fill the social role of "hired prize fighters" for capital, what Marx characterized as "vulgar economics" [19]. This social role is threatened by the CCC.

"The construction of the production function does not even require this refutation via the phenonomenon of returning techniques ('reswitching'), because a production function for which the marginal product equals the factor price already becomes impossible if the wage curves of single techniques are not straight lines (except for a few unimportant cases; see Garegnani, 1970, Hunt and Schwartz, 1972). Contrary to the usual interpretations today, the debate about the possibility of returning techniques is important not only because it proves that the production function with its marginal products is nonsensical, but because, on a more general level, it can be shown that a demand function for capital...cannot be defined." -- Bertram Schefold (1989). Mr. Sraffa on Joint Production and Other Essays, Unwin Hyman: 292.
[O]ne should emphasize the distinction between two types of measurement. First, there was the one in which the statisticians were mainly interested. Second, there was measurement in theory. The statisticians' measures were only approximate and provided a suitable field for work in solving index number problems. The theoretical measures required absolute precision. Any imperfections in these theoretical measures were not merely upsetting, but knocked down the whole theoretical basis. One could measure capital in pounds or dollars and introduce this into a production function. The definition in this case must be absolutely water-tight, for with a given quantity of capital one had a certain rate of interest so that the quantity of capital was an essential part of the mechanism. One therefore had to keep the definition of capital separate from the needs of statistical measurement, which were quite diffent. The work of J. B. Clark, Bohm-Bawerk and others was intended to produce pure definitions of capital, as required by their theories, not as a guide to actual measurement. If we found contradictions, then these pointed to defects in the theory, and an inability to define measures of capital accurately. It was on this - the chief failing of capital theory - that we should concentrate rather than on problems of measurement." -- Piero Sraffa, Interventions in the debate at the Corfu Conference on the "Theory of Capital", 4-11 September 1958.

[17] This miseducation is asserted on slightly different grounds in the following quote:
"Observe that even in neoclassical theory full employment alone is not enough to transform marginal-productivity relationships into a long-run theory of distribution. In long-run neoclassical theory, the capital:labor ratio is endogeneously determined, so that the wage rate cannot be determined solely by marginal productivity of labor at full employment - not even in Chicago. Instead, distribution must reflect household preferences with respect to present and future consumption.

Thus, it is fair to conclude that there are two marginal-productivity theories. The first is a relatively innocuous, general theory that involves nothing more controversial than competitive profit maximization - and provides correspondingly little contribution to the theory of growth and distribution under capitalism. The second is more powerful, and very special, providing by itself a theory of distribution, for the short run at least, whose 'only' defects are (1) that it assumes full employment and (2) that it begs the question of accumulation. The wonder is that it is precisely this theory that so many students come away with from their study of economics. Only slightly more wondrous is that by and large they believe it!" -- Stephen A. Marglin (1984). Growth, Distribution, and Prices, Harvard University Press: 330-331.
Neither version of marginal productivity theory need include the equality of the marginal product of capital and the interest rate in an aggregate production function framework.

[18] Syed Ahmad (1991). Capital in Economic Theory: Neo-classical, Cambridge, and Chaos, Edward-Elgar.

"In summary I believe that Marx's sociology of economic knowledge was quite an impressive achievement, in spite of being flawed by its reliance on functional explanations and the labor theory of value... The recent 'capital controversy' shows that these are not dead issues. Surely some cognitive confusion lay at the origin of the idea that 'capital' can be treated as a homogeneous 'factor of production,' for instance an inference from the fact that capitalists form a fairly homogeneous class. And conceivably the tenacity with which the neoclassical economists stuck to the notion of aggregate capital has something to do with non-cognitive interests. This, admittedly, is sheer speculation, and I may be quite wrong. Vested intellectual interests may suffice to explain the resistance. Be this as it may, the sociology of economic conceptions and economic theory is a field worth cultivating, if proper attention is paid to the many methodological pitfalls in this domain." -- Jon Elster (1985). Making Sense of Marx, Cambridge University Press: 504.

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