Prices and profits

Bortkiewicz (1906-07) took Dmitriev’s formalization as the starting point of his own analysis and assumed unidirectional production processes of finite duration, that is, oneway avenues starting from what Ricardo had called “unassisted labour” via a number of intermediate products or capital goods to final outputs.

In such “time-phased” production processes prices of commodities can also be conceived in terms of what Sraffa (1960) called “dated quantities of labour”, with the dated wage bills paid at the consecutive stages of production properly discounted forward at the current rate of profits r. Let l_-1j be the amount of labour expended during the last year before the completion of one unit of commodity j, l_-2j the amount expended two years before, l_-3j three years before, and so on. If the process has been started T years ago, and if wages are paid at the beginning of each year (ante factum), where w is the real wage rate in terms of some commodity, which also serves as standard of value, then we get the following reduction to dated quantities of labour for commodity j:

With a given w and a standard fixed as indicated, there are n equations to determine r and the remaining n - 1 prices. Hence, Ricardo’s determination of the rate of profits was perfectly sound and was not marred by an insufficient number of independent equations to ascertain the unknowns, as critics like William Stanley Jevons and Walras had contended. Bortkiewicz agreed with Knut Wicksell who had defended Ricardo against these accusations.

Bortkiewicz then extended the framework to analyse (1) the problem of a choice of technique, (2) fixed capital and (3) scarce natural resources that are non-exhaustible (land).

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Source: Faccarello G., Kurz H.D.(eds.). Handbook on the History of Economic Analysis, Volume 1: Great Economists Since Petty and Boisguilbert. Cheltenham: Edward Elgar,2016. — 813 p.. 2016

Prices and profits

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