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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.
References
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
