5. Actual Labor Values in a General Model of Production

In contrast to counterfactual linear programming definitions of labor values this chapter introduces an at least equivalent definition of such values for the general case of joint production which is exclusively based on actual data. This task is accomplished by extending Marx’s concept of “individual values” from multiple activities to joint production by means of certain price ratios at those points where production data are insufficient to ensure the positiveness of “embodied labor time”. Our approach generalizes the simple formula that relates labor values to monetary input–output tables, and it reformulates the labor theory of value in such a way that the “theoretical priority” of the case of a uniform composition of capital is reaffirmed. In the concluding pages of his book, Marx’s Economics, it is suggested by Morishima that Marxian economists “ought radically to change their attitude towards the labor theory of value” since in general the value system of the methods of production actually adopted in a capitalistic economy “may be determined to be negative, indefinite or even contradictory to the postulate of the uniform rate of exploitation” (Morishima 1973, p. 193). He then continues by proposing that “optimal labor values”, the shadow prices of certain linear programming problems which minimize the amount of labor needed to produce given bundles of net output, should take the place of “actual labor values” when production models of a more general kind than the simple Leontief model are to be considered, an interpretation of labor values which has been worked out in detail in Morishima (1974) and has become a widely accepted approach to labor values and the labor theory of value for all types of multiple production systems.