Fixed Capital, the Cost Criterion, and the Falling Rate of Profit

Abstract

Existing studies that introduce the concept of fixed capital into the Okishio Theorem show that, under an unchanged real wage, cost-reducing technical progress still necessarily raises the equilibrium rate of profit. This paper argues that this conclusion depends on how cost is defined in fixed capital models. In the original model of Okishio (1961), cost corresponds to what is termed operating cost in accounting, which excludes any form of profit; by contrast, the classical fixed capital frameworks adopted by Roemer (1979) and Woods (1985) cannot mathematically separate depreciation from profit, so that cost comparison in fact corresponds to capitalized cost inclusive of profit. This paper employs the annuity method to treat fixed capital, thereby separating depreciation from profit, and grounds the capitalist's technology choice on the basis of operating cost. The results show that two distinct thresholds exist in the fixed capital model: a profit-rate threshold that determines the direction of change in the rate of profit after the diffusion of the new technology, and an operating-cost threshold that determines whether the capitalist will adopt the new technology. When the lifetime of fixed capital exceeds one production period, the two thresholds are strictly separated, giving rise to a nonempty interval. Within this interval, the new technology lowers operating cost and is adopted by capitalists, yet the new equilibrium rate of profit falls below its initial level. The pure circulating capital model corresponds to the special case in which the two thresholds coincide, so that the Okishio Theorem can be regarded as a special case of the results obtained in this paper.