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This article summarizes a longer study reflecting on the main academic theories dealing with the transformation of value into production cost, all based on homogenous systems of equations. A departure from this theoretical corpus is needed, and should be built around a number of principles: First, the value of the production of a given period is the sum of values transferred from the previous periods and the added value created in the current period. Meanwhile, fixed capital (machinery) transmits its value in constant fractions over its useful life without redefining its value. Second, systems consisting of linear equations are preferred to the usual homogenous systems. Competition leads to capital transfers between branches, satisfying in the process the social need. The total engaged capital is not modified by variations in the price structure, and the equilibrium is restored by a change in the distribution of social work. Based on these hypotheses, it is possible to change the value of goods to production price, with the option of an algebraic or an arithmetic route.