From Marx’s fundamental equalities to the solving of the transformation problem - Coherence of the model[Des égalités fondamentales de Marx à la résolution du problème de la transformation - Cohérence du modèle]

Recently, V. Laure van Bambeke used an original approach to solve the famous problem of transformation of values into production prices by considering that capital reallocation to each department (branch) is part of the problem and is required to comply with both Marx's fundamental equalities: between the total sum of values and the total sum of prices, and between the total surplus value and the total profit (in price). Here, we confirm the validity of this consideration in relation with the satisfaction of demand (social need which is able to pay for the given product). However, V. Laure van Bambeke's method of solving an overdetermined system of equations implies that compliance with Marx's fundamental equalities can only be approached, which suggests that Marx's conception would apply approximatively, rather than as a strict law. Here, on the contrary, we show that the transformation problem is solvable from a determined (two-branch models) or an underdetermined system of equations enabling to obtain exact solutions through an algorithm we provide, with no approximation needed. For systems with three branches or more, the solution of the transformation problem belongs to an infinite ensemble and may be determined by an array of factors (e.g., taste of consumers, advertisement, competition between capitalists, politics), accounting for the observed high competition-driven market fluidity. Furthermore, we show that the transformation problem is solvable in the absence of fixed capital, supporting that dealing with the latter is not essential and cannot be seen as a potential flaw of the approach. In these particular cases, the rate of profit can be determined from the eigenvalue of the sociotechnical coefficient matrix, without any information required about the capital allocation to the various branches. Our algorithm enables simulations illustrating how the transient rise in rate of profit predicted by the Okishio theorem is consistent with the tendency of the rate of profit to fall (TRPF) subsequent to capital reallocation, and how the TRPF is governed by the increase of organic composition, in value. We establish that the long-standing transformation problem is not such a problem, since it is easily solved through our algorithm, whatever the number of branches considered. This emphasizes the high coherence of Marx's conception, and its impressive relevance regarding issues such as the TRPF, which have remained intensely debated.