On the Dynamics of Capitals in Movement -The Transformation of values into Production Prices

The age-old problem of transforming values into production prices is resolved once it is accepted that solvent social needs are not arbitrarily decreed and that the amounts of capital allocated to the different branches must conform to them. This is why we first demonstrate that a distribution of all capital between branches, consistent with these social needs, follows naturally from Marx's equalities. The solution opens the way to an in-depth understanding of the laws which govern fundamental economic mechanisms. It allows, among other things, to understand how the subjective components intervene in price formation and theoretically clarifies the question of the tendency of the rate of profit to fall by establishing the conditions for its realization. quantity of commodities, but if we assume, even if only as a thought experiment, constant production techniques and more generally all the social-economic conditions, then a fixed monetary quantity must correspond to a quantity of labor 3 and a physical quantity of merchandise. The coherence of Marxist economic theory must, to be established, support this hypothesis without fail. 4. That being said, we do not take into account in this study the role of money, we ignore the effects of credit, financial speculation and fictitious capital, the equivalent of a simple hour of work will be taken implicitly for a monetary unit.V. Laure Van Bambeke [2009, 2013, and 2021] opened the door to a coherent, if not definitive, solution [Harribey, 2022] to the problem of transformation by introducing the need for an adequate distribution of capital that respects solvent social needs. Unfortunately, in wanting to show the possibility of an approximate solution, he rather reinforces the false belief in the non-rigorous nature of Marx's equalities. Of course we understand that reality is actually always "fuzzy" and only allows an approximate verification of the laws, but in its theoretical essence, a law, for example the conservation of energy, cannot be approximate. Furthermore, Marx's equalities must be valid even when the profit rates are not equal, which is not the case in V. Laure Van Bambeke's process. In this paper we present the solution starting from the fundamental model with two branches: raw materials (C) and consumer goods (V), which allows us to highlight, in this specific two-branched model, a fundamental rule of value proportions between branches. From it, we derive an analytical solution for the distribution of capital and the coefficients of transformations of values into prices. With the three-branch model we reveal an infinite number of possible distributions of capital. Then, starting from this three-branch model for a system with, or without, fixed capital, we simulate the transfer of capital towards the most profitable branch and we show that convergence towards a uniform rate of profit leads to the tendency of the rate of profit to fall. These simulations show, through the interconnection of values (objective quantities) and prices (partially subjective quantities) how a "game" with multiple possible scenarios is articulated. Finally, a simple reproduction model with five branches, including a luxury sector, which produces its own fixed capital, allows for generalization to an arbitrary number of branches. In this study, we employ the 3 To simplify, we could consider this quantity of work as a number of hours of work.4 At its core, invoking complex conditions as the TSSI does by rejecting equilibrium, which it considers incompatible with capitalism, serves to obscure the problem of the theory (its own) in dealing with simple situations. This approach contradicts logic. By analogy, the physical law of conservation of energy was first verified in simple cases before being applied, for example, to the complex cases of explosions.'traditional' formalism used by Marx, which does not rely on the physical quantities of commodities nor describe production conditions in detail. The article [Ankri, Marcaggi, 2023] demonstrates how our assumptions can also be applied to a more 'modern' formalism. 2) TWO-BRANCH MODEL:The index "i" is used to designate the branches 5 of the economy reduced to C and V. Capital letters represent extensive quantities that represent monetary values. Lowercase letters represent intensive 6 variables, denoting these same value quantities per unit of capital invested in the branch to which they belong.Ci: The raw materials of branch i or circulating capital.Vi:The means of consumption or variable capital branch i Di: Depreciation of fixed capital of branch i for a production cycle 7 . n: number of periods for complete depreciation of fixed capital Fi: is the fixed capital used for several cycles of branch i.Constant capital: is the sum of