Fixed capital

Next Bortkiewicz turned to the case of fixed capital. Ricardo had defined fixed capital in the following way: “According as capital is rapidly perishable, and requires to be fre­quently reproduced, or is of slow consumption, it is classed under the heads of circulat­ing, or of fixed capital” (Ricardo 1951-73, I: 52).

Bortkiewicz (1906-07, pt 2: 27-32) credited Ricardo with having integrated fixed capital in his theory of value and distribution in a satisfactory way. He then formal­ized Ricardo’s approach, which implicitly dealt with the case of constant efficiency of a machine. Assume that a (new) machine can be used for n years and the price of the brand new item is given by p_m0. At the end of the t-th year of its employment its book value is p_{m t}, t = 1, 2,..., n, whereas at the end of its life the price is taken to be nil. (This means implicitly that it has neither a scrap value nor incurs disposal costs.) The differ­ence between the prices of the machine in two consecutive years is equal to the machine’s depreciation. Since the law of one price for the commodity produced holds, this implies that the yearly charge in terms of profits and depreciation - the annuity - must be constant across the entire life of the machine. Let z be the charge, then the following i equations hold true:

The constant annuity represents that component of the price of a commodity that is due to the use of the fixed capital item, as a share of the price of the brand new durable instru­ment of production employed.

Bortkiewicz observed that compared to Ricardo’s treatment of fixed capital, Marx’s was inferior and applied strictly only in the special case of r = 0. In this case the labour theory of value holds as a theory of relative prices and depreciation is linear, that is, it equals period after period the nth fraction of the value of the brand new instrument until it has been entirely written off.