Cambridge capital controversy

Cambridge capital controversy

The Cambridge capital controversy was a 1960s debate in economics concerning the nature and role of capital goods (or means of production). The name arises because of the location of those most involved in the controversy: the debate was largely between economists such as Joan Robinson and Piero Sraffa at the University of Cambridge in the UK and economists such as Paul Samuelson and Robert Solow at the Massachusetts Institute of Technology, in [ Cambridge] , Massachusetts, USA. The two schools are often labeled "neo-Ricardian" (or "Sraffian") and neoclassical, respectively.

Most of the debate is esoteric and mathematical, but some main elements can be explained in relatively simple terms and as part of the 'aggregation problem' of neoclassical economics. The resolution of the debate, particularly how broad its implications are, is not agreed upon by economists.

Aggregation of "capital"

A core proposition in neoclassical economics, especially textbook neoclassical economics, is that the income earned by each "factor of production" (essentially, labor and "capital") is equal to its marginal product. Thus, the wage is alleged to be equal to the marginal product of labor, and the rate of profit or rate of interest equal to the marginal product of capital. A second core proposition is that a change in the price of a factor of production -- say, a fall in the rate of profit -- will lead to more of that factor being used in production. A fall in this price means that more will be used since the law of diminishing returns implies that greater use of this input will imply a lower marginal product, all else equal.

Piero Sraffa, who originated the Cambridge controversy, pointed out that there was an inherent measurement problem in applying this model of income distribution to capital. Capitalist income is the rate of profit multiplied by the amount of capital, but the measurement of the "amount of capital" involves adding up quite incompatible physical objects -- adding trucks to lasers, for example. That is, just as one cannot add heterogeneous "apples and oranges," we cannot simply add up simple units of "capital" (as a child might add up "pieces of fruit").

Neoclassical economists assumed that there was no real problem here — just add up the money value of all these different capital items to get an aggregate amount of capital. But Sraffa (and Joan Robinson before him) pointed out that this financial measurement of the amount of capital depended in turn on the rate of profit. There was thus a circularity in the argument.

The traditional way to aggregate is to multiply the amount of each type of capital goods by its price and then to add up these multiples. Ideally, this sum would then be corrected for the effects of inflation. A problem with this method arises from variations in the ratio of labor to the value of capital goods used in production across sectors. At different income distributions, prices would have to differ if the competitive market assumption of equal rates of profits in all sectors is to hold. For example, suppose a higher rate of profits and lower wage were to prevail than at the initial situation. The prices of capital goods used in the less capital-intensive sectors would seem to need to rise with respect to the prices of capital goods used in more capital-intensive sectors, thereby ensuring the rate of profits remains identical across sectors. But additional complications arise from the varying capital intensities in the sectors producing capital goods. At any rate, the price of a capital good, or of any arbitrary given set of capital goods, cannot be expected to remain constant across variations in the rate of profits.

In general, this says that physical capital is heterogeneous and cannot be added up the way that financial capital can. For the latter, all units are measured in money terms and can thus be easily summed.

Sraffa suggested a technique (stemming in part from Marxian economics) by which a measure of the amount of capital could be produced: by reducing all machines to "dated labor". A machine produced in the year 2000 can then be treated as the labor and commodity inputs used to produce it in 1999 (multiplied by the rate of profit); and the commodity inputs in 1999 can be further reduced to the labor inputs that made them in 1998 plus the commodity inputs (multiplied by the rate of profit again); and so on until the non-labor component was reduced to a negligible (but non-zero) amount. Then you could add up the dated labor value of a truck to the dated labor value of a laser.

However, Sraffa then pointed out that this accurate measuring technique still involved the rate of profit: the amount of capital depended on the rate of profit. This reversed the direction of causality that neoclassical economics assumed between the rate of profit and the amount of capital. According to neoclassical production theory, an increase in the amount of capital employed should cause a fall in the rate of profit (following diminishing returns). Sraffa instead showed that a change in the rate of profit would change the measured amount of capital, and in highly nonlinear ways: an increase in the rate of profit might initially increase the perceived value of the truck more than the laser, but then reverse the effect at still higher rates of profit. See "Reswitching" below. The analysis further implies that a more intensive use of a factorof production, including other factors than capital, may be associated witha higher, not lower price, of that factor.

According to the Cambridge, England, critics, this analysis is thus a serious challenge, particularly in factor markets, to the neoclassical vision of prices as scarcity indices and the principle of substitution they claim underlies the neoclassical theory of supply and demand.

Aggregate production function

In neoclassical economics, a production function is often assumed, for example,

:: "q" = "A" ƒ("K", "L"),

where "q" is output, "A" is the technology factor, "K" is the sum of the value of capital goods, and "L" is the labor input. The price of the homogeneous output is taken as the numéraire, so that the value of each capital good is taken as homogeneous with output. Different types of labor are assumed reduced to a common unit, usually unskilled labor. Both inputs have a positive impact on output, with diminishing marginal returns. In some more complicated general equilibrium models, labor and capital are assumed to be heterogeneous and measured in physical units. In most versions of neoclassical growth theory (for example, in the Solow growth model), however, the function is assumed to apply to the "entire economy". Then, the neoclassical theory of the distribution of income sketched above is assumed to apply: under perfect competition, the rate of return on capital goods ("r") equals the marginal product of capital goods, while the wage rate ("w") equals the marginal product of labor. The equation of the rate of return on capital goods with the marginal product of capital is true under the simplifying assumption that there exists only one good, other than labor, and that this good can be used both as the consumption and capital good. However, if "K" is understood to be the value of capital goods, whether heterogeneous or homogeneous (but different from the consumption good), a problem arises.

The problem can be understood by thinking about an increase in the "r", the return on capital, (corresponding to a fall in "w", the wage rate, given that initial levels of capital and technology stay constant). This causes a change in the distribution of income, thus a change in the prices of different capital goods, and finally a change in the value of "K" (as discussed above). So the rate of return on "K" (i.e., "r") is not independent of the measure of "K", as assumed in the neoclassical model of growth and distribution. Causation goes both ways, from "K" to "r" and from "r" to "K". This problem is sometimes seen to be analogous to the Sonnenshein-Mantel-Debreu results (e.g., by Mas-Colell 1989) in general equilibrium theory, which show that representative agent models can be theoretically unjustified, except under restrictive conditions (see Kirman, 1992 for an explanation of the Sonnenshein-Mantel-Debreu results as an aggregation problem). Note that this says that it's not simply "K" that is subject to aggregation problems: so is "L".

Some see these technical criticisms of marginal productivity theory as connected to wider arguments with ideological implications. For example, some members of the Marxian school argue that even if the means of production "earned" a return based on their marginal product, that does not imply that their "owners" (i.e., the capitalists) produced the marginal product and should be rewarded. Indeed, the rate of profit is not a price, and it isn't clear that it is determined in a market. In particular, it, at best, only partially reflects the scarcity of the means of production relative to their demand. While the prices of different types of means of production are indeed prices, the rate of profit can be seen as reflecting the social and economic power that owning the means of production gives the capital owners to receive profit. In neoclassical and Austrian economics on the other hand, equilibrium rate of profit is determined by the rate of impatience on part of investors and savers (regardless whether capital is homogeneous or not). These ideological issues seem to have driven much of the rhetoric about this controversy.


Reswitching is a situation in which a technique of production is cost-minimizing at low and high rates of profits, but another technique is cost-minimizing at intermediate rates. Reswitching implies capital reversing, an association between high interest rates (or rates of profit) and more capital-intensive techniques. Thus, reswitching implies the rejection of a simple (monotonic) non-increasing relationship between capital intensity and either the rate of profit or the rate of interest. As rates fall, for example, profit-seeking businesses can switch from using one set of techniques (A) to another (B) and then back to A. This problem arises for either a macroeconomic or a microeconomic production process and so goes beyond the aggregation problems discussed above.

In a 1966 article, the famous neoclassical economist Paul A. Samuelson summarizes the reswitching debate:

: "The phenomenon of switching back at a very low interest rate to a set of techniques that had seemed viable only at a very high interest rate involves more than esoteric difficulties. It shows that the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers — alleging that, as the interest rate falls in consequence of abstention from present consumption in favor of future, technology must become in some sense more 'roundabout,' more 'mechanized' and 'more productive' — cannot be universally valid." ("A Summing Up," "Quarterly Journal of Economics" vol. 80, 1966, p. 568.)

Samuelson gives an example involving both the Sraffian concept of new productsmade with labor using dead or "dated labor" (rather than machines having anindependent role) and the "Austrian" concept of"roundaboutness" — supposedly a physical measure of capital intensity.Instead of simply taking a neoclassical production function for granted,Samuelson follows the Sraffian tradition of constructing a production functionfrom positing alternative methods to produce a product. The posited methodsexhibit different mixes of inputs. Samuelson shows how profit maximizing (costminimizing) indicates the best way of producing the output, given an externallyspecified wage or interest rate. Samuelson's earlier proposition that heterogeneous capital could be treated as a single capital good, homogeneous with the consumption good, through a "surrogate production function" turned out to be mistaken.

In Samuelson's example, there are two techniques, A and B, that use labor at different times ("–1", "–2", and "–3") to produce output of 1 unit at the later time 0.

Then, using this example (and further discussion), Samuelson demonstrates that it is impossible to define the relative "roundaboutness" of the two techniques as in this example, contrary to Austrian assertions. He shows that at an interest rate above 100 percent technique A will be used by a profit-maximizing business; between 50 and 100 percent, technique B will be used; while at an interest rate below 50 percent, technique A will be used again. The interest-rate numbers are extreme, but this phenomenon of reswitching can be shown to occur in other examples using more moderate interest rates.

The second table shows three possible interest rates and the resulting accumulated total labor costs for the two techniques. Since the benefits of each of the two processes is the same, we can simply compare costs. The costs in time 0 are calculated in the standard economic way, assuming that each unit of labor costs $w to hire:

:: cost = (1 + i)w×L–1 + (1 + i)2*w×L–2 + (1 + i)3*w×L–3

where L–n is the amount of labor input in time n previous to time 0.

The results in bold-face indicate which technique is less expensive, showing reswitching. There is no simple (monotonic) relationship between the interest rate and the "capital intensity" or roundaboutness of production, either at the macro- or the microeconomic level of aggregation.

Cambridge Views

Here are some of the Cambridge critics' views:

"Capital reversing renders meaningless the neoclassical concepts of input substitution and capital scarcity or labor scarcity. It puts in jeopardy the neoclassical theory of capital and the notion of input demand curves, both at the economy and industry levels. It also puts in jeopardy the neoclassical theories of output and employment determination, as well as Wicksellian monetary theories, since they are all deprived of stability. The consequences for neoclassical analysis are thus quite devastating. It is usually asserted that only aggregate neoclassical theory of the textbook variety — and hence macroeconomic theory, based on aggregate production functions — is affected by capital reversing. It has been pointed out, however, that when neoclassical general equilibrium models are extended to long-run equilibria, stability proofs require the exclusion of capital reversing (Schefold 1997). In that sense, all neoclassical production models would be affected by capital reversing." (Lavoie 2000)

"These findings destroy, for example, the general validity of Heckscher-Ohlin-Samuelson international trade theory (as authors such as Sergio Parrinello, Stanley Metcalfe, Ian Steedman, and Lynn Mainwaring have demonstrated), of the Hicksian neutrality of technical progress concept (as Steedman has shown), of neoclassical tax incidence theory (as Steedman and Metcalfe have shown), and of the Pigouvian taxation theory applied in environmental economics (as Gehrke and Lager have shown)." (Gehrke and Lager 2000)

Neoclassical views

The neoclassical economist Christopher Bliss comments:

"...what one might call the existential aspect of capital theory has not attracted much interest in the past 25 years. A small bandof ‘true believers’ has kept up the assault on capital theory orthodoxy until today, and from their company comes at least one of my co-editers. 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 from general 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 usually now the model's driver. Finally, the exogenous technical progress of Harrod, and most writers on growth from whatever school in the 1960s and later, has been joined by numerous models which make technical progress endogenous in one of the several possible ways...

...Can the old concerns about capital be taken out, dusted down and addressed to contemporary models? If that could be done, one would hope that its contribution could be more constructive than the mutually assured destruction approach that marred some of the 1960s debates. It is evident that richer models yield richer possibilities. They do not do that in proportion when optimization drives model solutions. However, we know that many-agent models can have multiple equilibria when all agents optimize. There may be fruitful paths forward in that direction.

Old contributions should best be left buried when they involve using capital as a stick to beat 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 the overall solution. It reflects badly on economists and their keenness of intellect that this was not always obvious to everyone." (Bliss 2005)

Part of the problem here is the high level of abstraction and idealization that occurs in the economic model-building on topics such as capital and economic growth. The original neoclassical models of aggregate growth presented by Robert Solow and Trevor Swan were simple mathematical creatures, with simple results and uncomplicated implied predictions about the real, empirical, world. The followers of Robinson and Sraffa then showed that more sophisticated and complicated mathematical models implied that for the Solow-Swan model to say anything about the world, crucial unrealistic assumptions (that Solow and Swan had ignored) must be true.

To choose an example that did not get much attention in the debate (because it was shared by both sides), the Solow-Swan model assumes a continuously-attained equilibrium with 'full employment' of all resources. The fact that the critique was also stated entirely using exactly the same kind of unrealistic assumptions meant that it was very difficult to do anything but 'criticize' Solow and Swan. That is, Sraffian models were explicitly divorced from empirical reality. And, as is very common in serious debates, it was much easier to destroy neoclassical theory than to develop a full-scale alternative that can help us understand the world.

In short, the progress produced by the Cambridge Controversy was from the unrealistic reliance on unstated or unknown assumptions to a clear consciousness about the need to make such assumptions. But this left the Sraffians in a situation where the unreal assumptions prevented most empirical applications, along with further developments of the theory. (Thus, Bliss asks: "what new idea has come out of Anglo-Italian thinking in the past 20 years?")

Most practically-minded neoclassical economists reacted to this problem by simply clinging to the simple model that they had inherited from Solow and Swan. Even though Sraffa, Robinson, and others had undermined its foundations, the Solow-Swan growth model is still a centerpiece of neoclassical macroeconomics and growth theory textbooks, while forming a basis for the so-called "new growth theory." More theoretically-minded neoclassicals such as Bliss (quoted above) have generally accepted the "Anglo-Italian" critique on the mathematical level and have moved on, applying the 'more general' political-economic vision of neoclassical economics to new questions.


Since Samuelson had been one of the main defenders of the idea that heterogeneous capital could be treated as a single capital good, his article conclusively showed that results from simplified models with one capital good do not necessarily hold in more general models. Most experts agree that the one capital good version neoclassical production function is simplistic but, as in all models, the simplistic version is often useful, particularly in empirical work. For this reason, the one capital good model continues to be used by researchers, especially in macroeconomics and growth theory. Samuelson himself has occasionally used multi-sectoral models of the Leontief-Sraffian tradition.

Most mainstream economists continue to use models with aggregateproduction functions, especially in macroeconomics and
growth theory. (See, for example,
new classical economics.) Generally, they justify their use of such simplistic models with an instrumentalist methodology and an appeal about the needs for simplicity in empirical work. But often they just ignore the controversy:

"It is important, for the record, to recognize that keyparticipants in the debate openly admitted their mistakes.Samuelson's seventh edition of "Economics" was purged of errors. Levhari and Samuelson published a paper which began,'We wish to make it clear for the record that thenonreswitching theorem associated with us is definitelyfalse. We are grateful to Dr. Pasinetti...' (Levhari andSamuelson 1966). Leland Yeager and I jointly published anote acknowledging his earlier error and attempting toresolve the conflict between our theoretical perspectives.(Burmeister and Yeager, 1978).

However, the damage had been done, and Cambridge, UK, 'declared victory': Levhari was wrong, Samuelson was wrong, Solow was wrong, MIT was wrong and therefore neoclassical economics was wrong. As a result there are some groups of economists who have abandoned neoclassical economics for their own refinements of classical economics. In the United States, on the other hand, mainstream economics goes on as if the controversy had never occurred. Macroeconomics textbooks discuss 'capital' as if it were a well-defined concept — which it is not, except in a very special one-capital-good world (or under other unrealistically restrictive conditions). The problems of heterogeneous capital goods have also been ignored in the 'rational expectations revolution' and in virtually all econometric work."(Burmeister 2000)

Some theorists, such as Christopher Bliss, Edwin Burmeister, and
Frank Hahn, responded to the controversy by arguing that rigorous neoclassicaltheory is most appropriately set forth in terms of microeconomics andintertemporal general equilibrium models. The critics, such as Pierangelo Garegnani, Fabio Petri, and Bertram Schefold, argue that such models are notempirically applicable and that, in any case, the capital-theoretical problems reappearin such models in a different form. The abstract nature of such models hasmade it more difficult to clearly reveal such problems in as clear a form asthey appear in long-period models.


* Christopher Bliss, "Introduction, The Theory of Capital: A Personal Overview", in C. Bliss, A. Cohen and G.C. Harcourt (eds.) "Capital Theory", (Cheltenham, UK: Edward Elgar, 2005). Vol. I, pp. xxvii–lx.
* Edwin Burmeister, "The Capital Theory Controversy", in "Critical Essays on Piero Sraffa's Legacy in Economics" (edited by Heinz D. Kurz), Cambridge: Cambridge University Press, 2000.
* Avi J. Cohen, G. C. Harcourt, [ "Whatever Happened to the Cambridge Capital Theory Controversies?,"] "Journal of Economic Perspectives", 17(1), Winter 2003, 199–214.
* Christian Gehrke and Christian Lager, "Sraffian Political Economy", "Encyclopedia of Political Economy", Routledge 2000.
* G. C. Harcourt, "Some Cambridge Controversies in the Theory of Capital". Cambridge: Cambridge University Press 1972
* G.C. Harcourt and N.F. Laing, "Capital and Growth", Harmondsworth, UK: Penguin, 1971. (This book includes the Samuelson article cited above and many other relevant articles.)
* John R. Hicks . "Value and Capital", Oxford: Clarendon Press, 1939, 2nd ed. 1946.
* Alan P. Kirman, "Whom or What does the Representative Individual Represent?" "Journal of Economic Perspectives" 6(2), Spring 1992: 117–136.
* Heinz D. Kurz, "capital theory: paradoxes, "The , London and New York: Macmillan and Stockton, 1987, pp. 359–363.
* Marc Lavoie, "Capital Reversing", "Encyclopedia of Political Economy", Routledge, 2000.
* Andreu Mas-Colell, "Capital Theory Paradoxes: Anything Goes", in "Joan Robinson and Modern Economic Theory" (ed. by G. R. Feiwel), New York University Press, 1989
* Luigi L. Pasinetti and Roberto Scazzieri, "capital theory: paradoxes, "The , London and New York: Macmillan and Stockton, 1987, pp. 363–68. .
* Paul A. Samuelson (1987). "Sraffian economics," "The New Palgrave: A Dictionary of Economics", v. 3, pp. 452–60.
* Bertram Schefold, "Normal Prices, Technical Change and Accumulation". London: Macmillan, 1997.
* Joseph E. Stiglitz, [ "The Cambridge-Cambridge Controversy in the Theory of Capital; A View from New Haven: A Review Article,"] "Journal of Political Economy", 82(4), Jul.-Aug. 1974: 893-903.

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