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Recently, V. Laure van Bambeke used an original approach to solve the famousproblem of transformation of values into production prices by considering thatcapital reallocation to each department (branch) was part of the problem. Here,we confirm the validity of this consideration in relation with the satisfactionof demand (social need which is able to pay for the given product). In contrastto V. Laure van Bambeke's method of solving an overdetermined system ofequations (implying that compliance with Marx's fundamental equalities couldonly be approached), we show that the transformation problem is solvable from adetermined (two-branch models) or an underdetermined system of equationsenabling to obtain exact solutions through an algorithm we provide, with noapproximation needed. For systems with three branches or more, the solution ofthe transformation problem belongs to an infinite ensemble, accounting for theobserved high competition-driven market fluidity. Furthermore, we show that thetransformation problem is solvable in the absence of fixed capital, supportingthat dealing with the latter is not essential and cannot be seen as a potentialflaw of the approach. Our algorithm enables simulations illustrating how thetransient rise in the rate of profit predicted by the Okishio theorem isconsistent with the tendency of the rate of profit to fall (TRPF) subsequent tocapital reallocation, and how the TRPF is governed by the increase of organiccomposition, in value. We establish that the long-standing transformationproblem is not such a problem since it is easily solved through our algorithm,whatever the number of branches considered. This emphasizes the high coherenceof Marx's conception, and its impressive relevance regarding issues such as theTRPF, which have remained intensely debated.

From Marx's fundamental equalities to the solving of the transformation problem -- Coherence of the model