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. Economics (from the Greek οίκος [oikos], house, and νομος [nomos], rule, hence household management) is a social science that studies the production, distribution, trade and consumption of goods and services. ... In politics, a capital (also called capital city or political capital — although the latter phrase has an alternative meaning based on an alternative meaning of capital) is the principal city or town associated with its government. ... The means of production are physical, non-human, inputs used in production. ... Joan Violet Robinson (1903 in Surrey - 1983) was a Keynesian economist who was well known for her knowledge of monetary economics and wide-ranging contributions to economic theory. ... Piero Sraffa (1898-1983) was an influential economist. ... The University of Cambridge is the second-oldest university in the English-speaking world, with one of the most selective sets of entry requirements in the United Kingdom. ... Paul A. Samuelson (born May 15, 1915) is an American economist known for his work in many fields of economics. ... Robert Merton Solow (born August 23, 1924) is an American economist particularly known for his work on the theory of economic growth. ... The Massachusetts Institute of Technology, or MIT, is a university located in the city of Cambridge, Massachusetts, USA. MIT is one of the worlds leading research institutions in science and technology, as well as in numerous other fields, including management, economics, linguistics, political science, and philosophy. ...

Most of the debate is esoteric and mathematical, but there are some main elements that can be explained in relatively simple terms. The resolution of the debate, particularly how broad its implications are, is not agreed upon by economists. Here are some of the Cambridge critics' views:

Capital reversing renders meaningless the neoclassical concepts of input substitution and capital 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 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)

Aggregation of "capital"

A core proposition in neoclassical economics, especially textbook neoclassical economics, is that the income earned by each "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. Neoclassical economics refers to a general approach (a metatheory) to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. ... Factors of production are resources used in the production of goods and services in economics. ... In economics, the marginal product or marginal physical product of an input to production during a specific time period is as follows, assuming that no other inputs to production change: marginal product of X used in producing Y = ΔY/ΔX = (the change of Y)/(the change of X). ... In economics, the profit rate refers to the relative profitability of an investment project or of an capitalist enterprise or for the capitalist economy as a whole. ... In economics, the profit rate refers to the relative profitability of an investment project or of an capitalist enterprise or for the capitalist economy as a whole. ... In economics, diminishing returns is the short form of diminishing marginal returns. ... Ceteris paribus is a Latin phrase, literally translated as with other things [being] the same, and usually rendered in English as all other things being 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. Financial capital, or economic capital, is any liquid medium or mechanism that represents wealth, or other styles of capital. ... An example of Money. ...

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. Marxian economics refers to a body of economic thought stemming from the work of Karl Marx. ...

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 factor of production, including other factors than capital, may be associated with a 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, Neoclassical economics refers to a general approach (a metatheory) to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. ... In microeconomics, a production function expresses the relationship between an organizations inputs and its outputs. ...

q = f(K, L),

where q is output, K is the sum of the value of capital goods, and L is the labor input. Output is taken as the numeraire, so that the value of each capital good is taken as homogenerous 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 economics, diminishing returns is the short form of diminishing marginal returns. ... General Equilbrium (linear) supply and demand curves. ...

In most versions of neoclassical growth theory (for example, in the Solow growth model), 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. Neo-classical growth model is a term used to sum up the contributions by various authors in the framework of neoclassical economics. ... Robert Merton Solow (born August 23, 1924) is an American economist particularly known for his work on the theory of economic growth. ... In economics, the marginal product or marginal physical product of an input to production during a specific time period is as follows, assuming that no other inputs to production change: marginal product of X used in producing Y = ΔY/ΔX = (the change of Y)/(the change of X). ...

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 (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 problem is sometimes seen to be analogous to the Sonnenshein-Mantel-Debreu results in general equilibrium theory, which show all representative agent models and other inappropriate aggregations are theoretically unjustified, 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. Gerard Debreu was a naturalized US citizen from France Gerard Debreu (July 4, 1921 – December 31, 2004) was a French-born American economist who won the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel. ... General Equilbrium (linear) supply and demand curves. ... // History The notion of a representative agent is a hypothetical construct in economics. ...

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 this minority to exploit the majority of workers and to receive profit. These ideological issues seems to have driven much of the rhetoric about this controversy. In economics, the marginal product or marginal physical product of an input to production during a specific time period is as follows, assuming that no other inputs to production change: marginal product of X used in producing Y = ΔY/ΔX = (the change of Y)/(the change of X). ... Marxian economics refers to a body of economic thought stemming from the work of Karl Marx. ... In economics, a capitalist is someone who owns capital, presumably within the economic system of capitalism. ... In economics, the profit rate refers to the relative profitability of an investment project or of an capitalist enterprise or for the capitalist economy as a whole. ... A social class is, at its most basic, a group of people that have similar status. ... There is no agreed-upon definition of power in economics. ... The term exploitation may carry two distinct meanings: The act of utilizing something for any purpose. ... Profit is a positive return made on an investment by an individual or by business operations. ...

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. Capital intensity is the term in economics for the amount of fixed or real capital present in relation to other factors of production, especially labor. ... In economics, the profit rate refers to the relative profitability of an investment project or of an capitalist enterprise or for the capitalist economy as a whole. ... An interest rate is the price a borrower pays for the use of money he does not own, and the return a lender receives for deferring his consumption, by lending to the borrower. ...

In a 1966 article, the famous neoclassical economist Paul A. Samuelson summarizes the reswitching debate: Neoclassical economics refers to a general approach (a metatheory) to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. ... Paul Samuelson (born May 15, 1915) is an American economist known for his work in many fields of economics. ...

"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 products made with labor using dead or "dated labor" (rather than machines having an independent 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 function from positing alternative methods to produce a product. The posited methods exhibit different mixes of inputs. Samuelson shows how profit maximizing (cost minimizing) indicates the best way of producing the output, given an externally specified wage or interest rate. Samuelson's earlier proposition that heterogenous capital could be treated as a single capital good, homogeneous with the consumption good, through a "surrogate production function" turned out to be mistaken. William Stanley Jevons (September 1, 1835 - August 13, 1882), English economist and logician, was born in Liverpool. ... Eugen von Böhm-Bawerk Eugen von Böhm-Bawerk (February 12, 1851 - August 27, 1914) made important contributions to the development of Austrian economics. ... Johan Gustaf Knut Wicksell, (December 20, 1851-May 3, 1926), Swedish economist. ... Roundaboutness, or roundabout methods of production is the term used to describe the process whereby capital goods are produced first and then, with the help of the capital goods, the desired consumer goods are produced. ... Capital intensity is the term in economics for the amount of fixed or real capital present in relation to other factors of production, especially labor. ...

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.

Conclusion

Since Samuelson had been one of the main defenders of the idea that heterogenous 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. Wassily Leontief (August 5, 1906 – February 5, 1999), born at St. ...

Most mainstream economists continue to use models with aggregate production 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: Macroeconomics is the economics sub-field of study that considers aggregate behavior, i. ... Neo-classical growth model is a term used to sum up the contributions by various authors in the framework of neoclassical economics. ... New Classical Economics emerged as a school in Macroeconomics during the 1970s. ...

It is important, for the record, to recognize that key participants 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 the nonreswitching theorem associated with us is definitely false. We are grateful to Dr. Pasinetti...' (Levhari and Samuelson 1966). Leland Yeager and I jointly published a note acknowledging his earlier error and attempting to resolve 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 neoclassical theory is most appropriately set forth in terms of microeconomics and intertemporal general equilibrium models. The critics, such as Pierangelo Garegnani, Fabio Petri, and Bertram Schefold, argue that such models are not empirically applicable and that, in any case, the capital-theoretical problems reappear in such models in a different form. The abstract nature of such models has made it more difficult to clearly reveal such problems in as clear a form as they appear in long-period models. This article does not cite its references or sources. ... General Equilbrium (linear) supply and demand curves. ...

Sources

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.

• Christian Gehrke and Christian Lager, "Sraffian Political Economy", Encyclopedia of Political Economy, Routledge 2000.

• 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.

• Marc Lavoie, "Capital Reversing", Encyclopedia of Political Economy, Routledge, 2000.

• Bertram Schefold, Normal Prices, Technical Change and Accumulation. London: Macmillan, 1997.