A measure theoretical approach of the problem of computing production costs

The problem of determining the costs of generating goods in a production process (productive economy) is approached and it is shown that it can be represented as an equation with additive fuzzy measures as unknowns. These kind of measures are proved to be representable by Lebesgue integrals. This fact is used in order to show that in some 'regularity' conditions concerning the revenue rates of the capital invested in production the problem of determining a 'cost measure' (i.e. a function assigning to each product its producing cost) can be a priori solved and have at least one solution. Moreover, if the speed of variation of the capital's revenue rate with respect to the investments is limited by a sufficiently small upper-bound, then this solution is unique and it can be computed by an algorithmic procedure. Allowing an anticipative evaluation of the production costs, the economic model presented in this work can be of use to study the efficiency of an economy and also to determine prices of produced goods.