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In 20th century discussions of Karl Marx's economics the transformation problem is the problem of...

In 20th century discussions of Karl Marx's economics the transformation problem is the problem of finding a general rule to transform the "values" of commodities (based on labour according to his labour theory of value) into the "competitive prices" of the marketplace. This problem was first introduced by Marx himself in Chapter 9 of Capital's draft Volume III, where he also tried to solve it. The essential difficulty was this: given that he derived profit ("surplus value") from direct labour inputs and that the amount of direct labour input varied widely between commodities, how could he explain the tendency to an average rate of profit? The production of any commodity generally requires both labour and some produced means of production (or capital goods), like tools and materials. The amount of labour so required is called the direct labour input into the commodity. But also the required capital goods have in their turn been produced (in the past) by labour and other capital goods; and so on for these other capital goods, and so on. The sum of all the amounts of labour, that were direct inputs into this backwards-stretching series of capital goods produced in the past, is called