Abstract

In this paper we show first of all how to calculate the magnitude of the vector of labour values without having recourse previously to the vector of direct (abstract or concrete) labour that is usually considered as a necessary condition for it. We show that, apart from its total volume, which is supposed here to be equal to the total volume of concrete labour, the magnitude of direct abstract labour per unit of commodity is not needed for the calculation of values, either as one of the ingredients of value (to be added to a second ingredient: the amount of indirect abstract labour embodied in the means of production) or as a “coefficient of labour” that becomes value once vertically integrated. We will show then, beginning from unit values, how to compute the vector of abstract labour, both per unit of output and as a fraction of total labour, and their respective “coefficients of reduction” by means of which they can be considered a multiple of the quantities of concrete labour. Both things are discussed at the theoretical level and also by means of a numerical example that helps to understand the implications of the new definitions. The main implication is that, though “physical” data suffice to determine the vector of “relative” values (or any of their infinite multiples), labour is not redundant for a theory of value because the latter requires the determination of “absolute” values as a unique vector, for which the magnitude of total labour expended is needed.

As a second aim of the paper, we intend to show that Rubin’s ideas on both the
qualitative and quantitative determination of abstract labour and the role of exchange, demand, and social need in the quantitative definition of values—ideas that have often been misunderstood—are a necessary presupposition of the modern, correct quantification of abstract labour and value.

1) The definition of values and abstract labour, p. 1; 2) Absolute values and abstract labour, p. 4; 3) A numerical example, p. 8; 4) Production, exchange and abstract labour, p. 10; 5) Rubin and abstract labour, p. 14; 6) Rubin on demand and social need, p. 18; 7) A graphical representation of abstract labour, p. 21; Bibliography, p. 24.

The quantitative determination of abstract labour and values