# Cambridge Capital Controversy

# Cambridge Capital Controversy

The Cambridge capital controversy refers to a debate that started in the 1950s and continued through the 1970s. The core of the debate concerns the measurement of capital goods in a way that is consistent with the requirements of neoclassical economic theory. The debate involved economists such as Piero Sraffa, Joan Robinson, Piero Garegnani, and Luigi Pasinetti at the University of Cambridge in England and Paul Samuelson and Robert Solow at the Massachusetts Institute of Technology in Cambridge, Massachusetts. In a now-famous *Quarterly Journal of Economics* publication from 1966, Samuelson admitted the logical validity of the British critique of the neoclassical theory of capital (Samuelson 1966). Yet, Solow (1963) claimed the debate was largely a sideshow to the core of neoclassical analysis.

The essence of the debate revolved around the fundamental premises of the theories of value, distribution, and growth, each of which depends upon an aggregate production function where the inputs or factors of production for capital and labor are aggregated in some fashion prior to the determination of the rate of profit (interest) and the wage rate. According to neoclassical theory, the price of each factor of production is determined by its marginal contribution to production; furthermore, there exists substitutability between factors of production that gives rise to diminishing returns. As a consequence, the rate of profit (or interest) is the price of capital and as such reflects capital’s relative scarcity; more specifically, a relative abundance of capital, in combination with the law of diminishing returns of a factor of production (whereby the greater use of an input will imply a lower marginal product, other things being equal) will give rise to a low rate of profit (interest). The opposite would be true in the case of a relative scarcity of capital. Capital income would amount to the product of the rate of profit times the amount of capital employed.

Piero Sraffa pointed out that there was an inherent measurement problem in applying the neoclassical model of value and income distribution, because the estimation of the rate of profit requires the prior measurement of capital. The problem is that capital—unlike labor or land, which can be reduced to homogenous units stated in their own terms (for example, hours of the same skill and intensity or land of the same fertility)—is an ensemble of heterogeneously produced goods, which must be added in such a way as to enable a cost-minimizing choice of techniques. From the various alternatives, neoclassical theory chooses to measure capital goods in value terms; that is, the product of physical units (buildings, machines, etc.) times their respective (equilibrium) prices. Joan Robinson (1953), inspired by Sraffa’s teaching and early writings, and later Sraffa himself (1960), argued that the value measurement of capital requires the prior knowledge of equilibrium prices, which in turn requires an equilibrium rate of profit that cannot be obtained unless we have estimated the value of capital.

Clearly, there is a problem of circularity here that the Cambridge, Massachusetts, economists sought to resolve. Paul Samuelson, in particular, presented a model based on the heroic assumption that capital-intensity is uniform across sectors, which is equivalent to saying that there is a one-commodity world. In such an economy, as income distribution varies, the subsequent revaluation of capital gives rise to results that are absolutely consistent with the requirements of neoclassical theory. In fact, Samuelson derived a straight-line wage–profit rate frontier (the mirror image of the usual convex isoquant curves), each one representing a cost-minimizing technique, and this gave rise to a well-behaved demand-for-capital schedule. Parenthetically, Samuelson attacked Marxian value theory for its alleged inability to explain relative prices. However, if one applies Samuelson’s heroic assumption of an equal capital intensity across all industries to Marx’s labor theory of value, then all of Samuelson’s criticisms of Marx become irrelevant. This irony was not unnoticed by the British participants in the capital debates.

Samuelson’s assumption was attacked for lack of realism by Garegnani, Pasinetti, and Amartya Sen, among others, who showed that once we hypothesize different capital intensities across industries, the neoclassical results do not necessarily hold. The idea is that as relative prices change the revaluation of capital can go either way, and it is possible for an industry that is capital-intensive in one income distribution to become labor-intensive in another. As a consequence, we no longer derive Samuelson’s straight-line wage–profit rate frontiers, which are consistent with the cost-minimizing choice of technique and give rise to well-behaved demand-for-capital schedules. In the presence of many capital goods and various capital intensities across industries it follows that the wage–profit rate frontiers are nonlinear and may cross over each other more than once, which means that for a low rate of profit one may choose a capital-intensive technique. As the rate of profit increases, the technique with a lower capital intensity may be chosen, and for a higher rate of profit the original technique of higher capital intensity is chosen again. We observe that a capital-intensive technique may be chosen for both low and high rates of profit, a result that runs contrary to the neoclassical theory of value and income distribution. Under these circumstances we cannot determine a well-behaved demand for capital schedule and so the whole neoclassical construction is under question.

It is important to point out that the capital theory critique does not affect the classical theory of value and income distribution, because the classical theory does not claim that relative prices of factors of production reflect relative scarcities; additionally this theory assumes one of the distributive variables, usually the real wage, as a datum that in combination with the given technology and output level determines the relative equilibrium prices together with the equilibrium rate of profit. Furthermore, the evaluation of heterogeneous capital goods can be achieved in terms of labor values; hence there might be a problem of consistency because variables estimated in terms of labor values will differ from those estimated in terms of equilibrium prices. This, however, is mainly an empirical question and the empirical research has shown that the two types of prices are close to each other, and variables estimated in labor values or equilibrium prices are approximately equal to each other (Shaikh and Tonak 1994, p. 143).

The capital controversy had an initial effect on neoclassical economics, but soon it was forgotten to the point that the new generation of neoclassical economists either dismisses it or simply does not know it. As a result, both theoretical and empirical neoclassical research makes use of aggregate production functions, where capital is still used along with labor in the determination of output and the marginal products of these inputs are estimated on the assumption of substitutability between factors of production, as if the capital controversy never happened. At the close of the twentieth century, there were new efforts by the so-called modern classical economists to revive the classical approach, and once again the capital theory began to surface in mainstream journals, which may revive theoretical questions that puzzled the best Cambridge economists in England and the United States.

The Cambridge capital controversy revived interest in Marxian economics, contributed to the founding of neo-Ricardian or Sraffian economics, and inspired the development of post-Keynesian economics. Indeed, it was Sraffa’s 1920s critique of the neoclassical theory of the firm and Sraffa’s proto-critique of neoclassical value theory that greatly influenced Keynes’s *General Theory of Employment, Interest, and Money* (1936). British interpretation of Keynes’s influential publication assumed a classical theory of value and distribution, while the U.S. interpretation sought to integrate Keynes into the neoclassical theory of value and distribution. This difference in understanding Keynes led Joan Robinson to refer to her American counterparts as “bastard Keynesians” (Harcourt 1982, p. 347). Finally, in another famous barb, Robinson once said that because she never learned math she was always forced to think. Robinson’s mathematics never went beyond basic algebra and very elementary geometry—the kind of math mastered by many American students in the first two years of high school. On the other hand, Samuelson’s economic analysis has led the way in the use of calculus, linear algebra, differential equations, real analysis, and mathematical programming. Robinson’s biting comment is a warning to economists to not allow mathematical technique to triumph over substantive understanding of how real-world economies operate.

**SEE ALSO** *Capital; Pasinetti, Luigi; Robinson, Joan; Samuelson, Paul A.; Sen, Amartya Kumar; Solow, Robert M.; Sraffa, Piero; Substitutability*

## BIBLIOGRAPHY

Cohen, Avi J., and G. C. Harcourt. 2003. Whatever Happened to the Cambridge Capital Theory Controversies? *Journal of Economic Perspectives* 17 (1): 199–214.

Harcourt, Geoffrey. 1982. *The Social Science Imperialists*. London: Routledge & Kegan Paul.

Keynes, John Maynard. 1936. *General Theory of Employment, Interest, and Money*. New York: Harcourt, Brace and World.

Robinson, Joan. 1953. The Production Function and the Theory of Capital. *Review of Economic Studies* 21 (2): 81–106.

Samuelson, Paul A. 1966. A Summing Up. *Quarterly Journal of Economics* 80 (4): 568–583.

Shaikh, Anwar, and Tonak Ahmet. 1994. *Measuring the Wealth of Nations*. Cambridge, U.K.: Cambridge University Press.

Solow, Robert. 1963. *Capital Theory and the Rate of Return*. Amsterdam: North-Holland.

Sraffa, Piero. 1960. *Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory*. Cambridge, U.K.: Cambridge University Press.

*Lefteris Tsoulfidis*

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