Capital controversy

From Academic Kids

The capital controversy refers to a debate in economics concerning the nature and role of capital goods (or means of production) that occurred during the 1960s, largely between economists such as Joan Robinson and Piero Sraffa at the University of Cambridge in England and economists such as Paul Samuelson and Robert Solow at the Massachusetts Institute of Technology, in Cambridge, MA. It is thus sometimes called the Cambridge capital controversy.

Most of the debate is esoteric and mathematical, but there are some main elements that can be explained in relatively simple terms.

Contents

Aggregation of "capital"

A core proposition in neoclassical economics, especially textbook neoclassical economics, is that the income earned by each of "factors 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 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.

Pierro 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 an 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.

This aggregation problem was thus a serious challenge to the neoclassical theories of income distribution and of production, which is why the debate was so important.

Aggregate production function

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

q = f(K, L),

where q is the sum of all output, K is the sum of all capital goods, and L is the sum of all labor input. Both of the inputs have a positive impact on output, with diminishing marginal returns.

In neoclassical growth theory (for example, in the Solow growth model), this 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 problem here can be understood by thinking about an increase in the r (corresponding to a fall in w). 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 is a problem that is also indicated by general equilibrium theory as with the Sonnenshein-Mantel-Debreu theorem, which rejects all representative agent models and other inappropriate aggregations, except under very restrictive conditions (see Kirman, 1992). Note that this says that it's not simply K that is subject to aggregation problems: so is L.

There are other criticisms of the marginal productivity theory of distribution that are not part of the Cambridge Critique. For example, the Marxian school argues that even if the means of production "earned" a return based on their marginal product, that does not mean that their owners (i.e., the capitalists) produced the marginal product and should be rewarded. Indeed, the rate of profit is not a price, since it isn't determined in markets and only partially reflects the scarcity of (and demand for) means of production. While the prices of different types of means of production are indeed prices, the rate of profit reflects the social and economic power that owning the means of production gives this minority that allows them to exploit the majority of workers and to receive profit.

Reswitching

Reswitching refers to 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 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 interest 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 that involves both the Sraffian concept that new products are made by labor using dead or dated labor (rather than machines having an independent role) and the "Austrian" concept of "roundaboutness" -- a measure of capital intensity. Instead of simply taking a neoclassical production function for granted, Samuelson follows the Sraffian tradition of positing that more than one way to produce a product exists (with different mixes of inputs) and then shows how profit maximizing (cost minimizing) indicates the best way of producing, given economic variables.

First, 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.

Two Production Techniques
time periodinput or outputtechnique Atechnique B
–3labor input02
–270
–106
0output11

Then, using this example (and further discussion), Samuelson demonstrates that it is impossible to define the relative "roundaboutness" of the two techniques in this example, contrary to Austrian assertions (and that it is possible for techniques to differ in this way). More importantly, 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.

Reswitching
interest ratetechnique Atechnique B
150%$43.75$46.25
75%$21.44$21.22
0%$7.00$8.00

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.

Conclusion

Since Samuelson had been one of the main defenders of the neoclassical canon against the critics from Cambridge, England, his article represents a major admission of defeat. Most experts would thus agree that the neoclassical production function is excessively simplistic (internally inconsistent). Samuelson himself now uses multi-sectoral models of the Leontief-Sraffian tradition. However, that model continues to be used by neoclassicals, especially in macroeconomics and growth theory. (See, for example, new classical economics.) Many or most microeconomists have moved to using general equilibrium theory instead of aggregate production functions. But these economists ignore the fact that reswitching can apply at the microeconomic level. The vast majority of neoclassicals, however, seem to never have heard of the controversy.

Sources

  • 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.)
  • Alan P. Kirman, "Whom or What does the Representative Individual Represent?" Journal of Economic Perspectives 6(2), Spring 1992: 117-136.
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