Reduction to dated quantities of labour

Dmitriev investigated first how the total amount of labour expended in the production of a commodity can be ascertained. He considered a single product system that can be represented, in matrix notation, as:

where A is the n?n matrix of commodity inputs, l is the n-vector of direct labour inputs, and r is the n-vector of direct and indirect labour inputs.

or

where l_t = A^tl. Dmitriev set out the simultaneous equation system (1) and concluded that since there are as many equations as unknowns r is determined, given A and l. He thus disposed of the common misconception that a “historical digression” would be needed in order to ascertain the total labour contents of commodities:

[W]e can always find the total sum of the labour directly and indirectly expended on the produc­tion of any product under present-day production conditions.... the fact that all capital under present-day conditions is itself produced with the assistance of other capital in no way hinders a precise solution of the problem. (Dmitriev 1974: 44)

However, in the following, Dmitriev then assumed that the series of dated quantities of labour in (2) is finite, and thus implicitly adopted an “Austrian” perspective: Dmitriev’s representation of production processes in terms of a finite series of dated quantities of labour corresponds to Austrian processes of the “flow input-point output” type, and presupposes the non-existence of basic commodities (Kurz and Salvadori 1995: 176-8). Within this framework, Dmitriev then confirmed the proposition, originally proposed by Smith and adopted by Ricardo, that the price of every commodity can be entirely resolved into wages and profits. Following the classical authors, wages are supposed to be paid ante factum and prices are explained in terms of a reduction to a finite stream of dated quantities of labour, that is:

or