Transformation Problem - Critics of The Theory

Critics of The Theory

Many mathematical economists assert that a set of functions in which Marx's equalities hold does not generally exist at the individual enterprise or aggregate level, so that Chapter 9's transformation problem has no general solution, outside two classes of very special cases. This was first pointed out by, among others, Böhm-Bawerk (1896) and Bortkiewicz (1906). In the second half of the twentieth century, Leontief’s and Sraffa’s work on linear production models provided a framework within which to prove this result in a simple and general way.

Although he never actually mentioned the transformation problem, Sraffa’s (1960) Chapter VI on the "reduction" of prices to "dated" amounts of current and past embodied labour gave implicitly the first general proof, showing that the competitive price of the produced good can be expressed as

,

where is the time lag, is the lagged-labour input coefficient, is the wage and is the "profit" (or net return) rate. Since total embodied labour is defined as

,

it follows from Sraffa’s result that there is generally no function from to, as was made explicit and elaborated upon by later writers, notably Ian Steedman in Marx after Sraffa.

A standard reference – with an extensive survey of the entire literature pre-1971 and a comprehensive bibliography – is Samuelson's (1971) "Understanding the Marxian Notion of Exploitation: A Summary of the So-Called Transformation Problem Between Marxian Values and Competitive Prices" Journal of Economic Literature 9 2 399–431.

Since the 1970s several major schools of Marxian economics have arisen in response to the transformation problem-related challenges of the neoclassical and Sraffian schools. Analytical Marxists held that the transformation problem disproved the Labour Theory of Value and based their Marxian social theory on a combination of the Fundamental Marxian theorem, game theory, and other neoclassical and mathematical tools. Empirical Marxists, including Anwar Shaikh, Moshe Machover, and Paul Cockshott, maintain that since empirical data bears out the correspondence of prices and labour values, the transformation problem is irrelevant. Followers of the Temporal Single System Interpretation and the New Interpretation argue that critics have misunderstood Marx's definition of value and that, correctly defined, there is no difference between value and price.

The lack of any function to transform Marx's "values" to competitive prices has important implications for Marx's theory of labour exploitation and economic dynamics, namely that, some people argue, there is no Tendency of the rate of profit to fall. This means that it is not pre-ordained that capitalists must exploit labour to compensate for a declining rate of profit. This implies that Marx's prophecy that worsening labour exploitation would result in an eventual revolution against the capitalist system and the establishment of communism is logically and mathematically false.

The mathematical proof that Marx's transformation problem has no general solution has been formally questioned by proponents of the Temporal Single System Interpretation, who argue that the determination of prices by simultaneous linear equations (which assumes that prices are the same at the start and end of the production period) is logically inconsistent with the determination of value by labour time. Other Marxian economists accept the proof, but reject its relevance for some key elements of Marxian political economy. Still others reject Marxian economics outright, and emphasise the politics of the assumed relations of production instead. To this extent, the transformation problem—or rather its implications—is still today a controversial question.