The Production Function and the Theory of Capital

The dominance in neo-classical economic teaching of the concept of a production function, in which the relative prices of the factors of production are exhibited as a function of the ratio in which they are employed in a given state of technical knowledge, has had an enervating effect upon the development of the subject, for by concentrating upon the question of the proportions of factors it has distracted attention from the more difficult but more rewarding questions of the influences governing the supplies of the factors and of the causes and consequences of changes in technical knowledge. Moreover, the production function has been a powerful instrument of miseducation. The student of economic theory is taught to write 0 f f (L, C) where L is a quantity of labour, C a quantity of capital and 0 a rate of output of commodities.' He is instructed to assume all workers alike, and to measure L in man-hours of labour; he is told something about the index-number problem involved in choosing a unit of output ; and then he is hurried on to the next question, in the hope that he will forget to ask in what units C is measured. Before ever he does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next. The question is certainly not an easy one to answer. The capital in existence at any moment may be treated simply as " part of the environment in which labour works."2 We then have a production function in terms of labour alone. This is the right procedure for the short period within which the supply of concrete capital goods does not alter, but outside the short period it is a very weak line to take, for it means that we cannot distinguish a change in the stock of capital (which can be made over the long run by accumulation) from a change in the weather (an act of God). We may look upon a stock of capital as the specific list of all the goods in existence at any moment (including work-in-progress in the pipe lines of production). But this again is of no use outside the strict bounds of the short period, for any change in the ratio of capital to labour involves a re-organisation of methods of production and requires a change in the shapes, sizes and specifications of many or all the goods appearing in the original list. 3 As soon as we leave the short period, however, a host of difficulties appear. Should capital be valued according to its future earning power or its past costs ? When we know the future expected rate of output associated with a certain capital good, and expected future prices and costs, then, if we are given a rate of interest, we can value the capital good as a discounted stream of future profit which it will earn. But to do so, we have to begin by taking the rate of interest as given, whereas the main purpose of the production function is to show how wages and the rate of interest (regarded as the wages of capital) are determined by technical conditions and the factor ratio.