Cambridge capital controversy

This vision produces a core proposition in textbook [[neoclassical economics]], i.e., that the income earned by each "[[factor of production]]" (essentially, labor and "capital") is equal to its marginal product. Thus, with perfect product and input markets, the wage (divided by the price of the product) is alleged to equal the [[marginal product|marginal physical product]] of labor. More importantly for the discussion here, the [[rate of profit]] (sometimes confused with the [[rate of interest]], i.e., the cost of borrowing funds) is supposed to equal the marginal physical product of capital. (For simplicity, abbreviate "capital goods" as "capital.") A second core proposition is that a change in the price of a factor of production will lead to a change in the use of that factor – an increase in the [[rate of profit]] (associated with falling wages) will lead to more of that factor being used in production. The [[Diminishing returns|law of diminishing marginal returns]] implies that greater use of this input will imply a lower marginal product, [[ceteris paribus|all else equal]]: since a firm is getting less from adding a unit of capital goods than is received from the previous one, the rate of profit must increase to encourage the employment of that extra unit, assuming [[profit maximization]].

This vision produces a core proposition in textbook [[neoclassical economics]], i.e., that the income earned by each "[[factor of production]]" (essentially, labor and "capital") is equal to its marginal product. Thus, with perfect product and input markets, the wage (divided by the price of the product) is alleged to equal the [[marginal product|marginal physical product]] of labor. More importantly for the discussion here, the [[rate of profit]] (sometimes confused with the [[rate of interest]], i.e., the cost of borrowing funds) is supposed to equal the marginal physical product of capital. (For simplicity, abbreviate "capital goods" as "capital.") A second core proposition is that a change in the price of a factor of production will lead to a change in the use of that factor – an increase in the [[rate of profit]] (associated with falling wages) will lead to more of that factor being used in production. The [[Diminishing returns|law of diminishing marginal returns]] implies that greater use of this input will imply a lower marginal product, [[ceteris paribus|all else equal]]: since a firm is getting less from adding a unit of capital goods than is received from the previous one, the rate of profit must increase to encourage the employment of that extra unit, assuming [[profit maximization]].

[[Piero Sraffa]] and [[Joan Robinson]], whose work set off the Cambridge controversy, pointed out that there was an inherent measurement problem in applying this model of [[income distribution]] to capital. Capitalist income (total profit or property income) is defined as the rate of profit multiplied by the amount of capital, but the measurement of the "amount of capital" involves adding up quite incomparable physical objects – adding the number of trucks to the number of lasers, for example. That is, just as one cannot add heterogeneous "apples and oranges," we cannot simply add up simple units of "capital." As Robinson argued, there is no such thing as "leets," an inherent element of each capital good that can be added up independent of the prices of those goods.

[[Piero Sraffa]] and [[Joan Robinson]], whose work set off the Cambridge controversy, pointed out that there was an inherent measurement problem in applying this model of [[income distribution]] to capital. Robinson developed her contribution to this critique in her 1953 paper “The Production Function and the Theory of Capital,” where she addressed the question of what units of capital could be measured in. She argued that valuing a stock of capital goods cannot be done without first knowing the rate of profit, since capital goods are valued by the income they are expected to generate. However, the production function is supposed to determine the rate of profit. As she put it, a student of economics is taught to write output as a function of labor and capital but is then “hurried on to the next question, in the hope that he will forget to ask in what units C is measured.” Robinson identified that this was a methodological error, since valuing capital requires the rate of interest to be taken as given, rather than determined by the theory itself. She insisted that this problem could not be resolved by only adding up monetary values of capital goods, since those values shift as the rate of profit changes. She concluded that this rendered “the major part of neo-classical doctrine spurious.”{{Cite journal |last=Robinson |first=Joan |date=1953 |title=The Production Function and the Theory of Capital |journal=Review of Economic Studies |volume=21 |issue=2 |pages=81-106}}

Capitalist income (total profit or property income) is defined as the rate of profit multiplied by the amount of capital, but the measurement of the "amount of capital" involves adding up quite incomparable physical objects – adding the number of trucks to the number of lasers, for example. That is, just as one cannot add heterogeneous "apples and oranges," we cannot simply add up simple units of "capital." As Robinson argued, there is no such thing as "leets," an inherent element of each capital good that can be added up independent of the prices of those goods.

===Sraffian presentation===

===Sraffian presentation===