transformation problem

In 20th-century discussions of Karl Marx's economics, the transformation problem is the problem of finding a general rule by which to transform the "values" of commodities (based on their socially necessary labour content, according to his labour theory of value) into the "competitive prices" of the marketplace. This problem was first introduced by marxist economist Conrad Schmidt and later dealt with by Marx in chapter 9 of the draft of volume 3 of Capital. The essential difficulty was this: given that Marx derived profit, in the form of surplus value, from direct labour inputs, and that the ratio of direct labour input to capital input varied widely between commodities, how could he reconcile this with a tendency toward an average rate of profit on all capital invested among industries, if such a tendency (as predicted by Marx and Ricardo) exists? Marx's theory Marx defines value as the number of hours of labor socially necessary to produce a commodity. This includes two elements: First, it includes the hours that a worker of normal skill and dedication would take to produce a commodity under average conditions and with the usual equipment (Marx terms this "living labor"). Second, it includes the labor embodied in raw materials, tools, and machinery used up or worn away during its production (which Marx terms "dead labor"). In capitalism, workers spend a portion of their working day reproducing the value of their means of subsistence, represented as wages (necessary labor), and a portion of their day producing value above and beyond that, referred to as surplus value, which goes to the capitalist (surplus labor). Since, according to Marx, the source of capitalist profit is this surplus labor of the workers, and since in this theory only new, living labor produces value, it would appear logical that enterprises with a low organic composition (a higher proportion of capital spent on living labor) would have a higher rate of profit than would enterprises with a high organic composition (a higher proportion of capital spent on raw materials and means of production). However, in models of classical perfect competition, higher rates of profit are not generally found in enterprises with a low organic composition, and low profit rates are not generally found in enterprises with a high organic composition. Instead, there is a tendency toward equalization of the rate of profit in industries of different organic compositions.