The Labour Theory of Value and the Problems of Other Theories of Value

This article first shows that one of the main misunderstandings surrounding the labour theory of value arises from the non-distinction between real determination and mathematical determination: although mathematically it is possible to link value prices (values expressed in money) and production prices through a linear transformation that operates in both directions, from the point of view of a realistic economic theory the “real relations of value”, which take place in the real world, are prior to, and determine de facto, univocally, those theoretical-mathematical relationships. Secondly, to study prices appropriately it is necessary to distinguish between actual prices, which are as real as labour-values, and the pair of theoretical-hypothetical prices that would exist if the rate of profit or the rate of surplus value, respectively, were uniform (which they are not in reality). Thirdly, after defining the equations of these prices in the correct way in which they appear in the literature, it is proven that it is possible to read the Marxian Transformation in two steps, showing that the first Marxian definition of both types of prices (defined from actual prices) gives way to a second and definitive definition in which both coincide with the correct definitions. Fourthly, the transformation is framed in a broader framework of various (linear) transformations to show that value prices and production prices are related, also exactly, on the one hand to actual prices and on the other hand to the values and quantities of direct labour represented in the commodities, so that all the vectors involved are calculable simultaneously within a single accounting system. Fifthly, it is explained why a physical theory of value, based on a substance of value alternative to labour, cannot prosper. And finally it is shown that the only productive factor of value is labour, and, although all factors cooperate with labour in the production of wealth (use values), this is an irrelevant question for the determination of prices.