Professor Cassel on the Statistical Determination of Marginal Productivity

In: Canadian journal of economics and political science: the journal of the Canadian Political Science Association = Revue canadienne d'économique et de science politique, Band 4, Heft 1, S. 22-33

Abstract

In recent years, an attempt has been made by the present author to measure the probable slope of the marginal productivity functions of labour and capital in various economies. This has been done by computing indexes of capital (C), labour (L), and product (P) for manufacturing in the United States for the years 1899-1922, Massachusetts 1890-1926, New South Wales 1901-1927, and Victoria 1907-1929. The formula used is that P' (representing an index of computed product) = b LkC(1−k). By making the sum of exponents equal to unity, we assumed for purposes of simplicity that production could be described by a homogeneous function of the first degree and that equal proportionate increases in the quantities of labour and capital would cause the same proportionate increase in product. The exponents of L and C were found by the method of least squares, so that the sum of the squares of the deviation of P′ from P would be reduced to a minimum, and the sum of the arithmetic deviations to zero. The exponents for labour and capital in manufacturing which were found by this method were as follows:It will be noticed that there is a substantial degree of similarity between the exponents found for these economies.A mathematical analysis of the above function discloses: (1) that the share of the net product to be received by a factor should, according to marginal productivity theory, be equal to its exponent; (2) that the elasticity of the marginal productivity curve of, and hence, under competitive conditions, the demand curve for, a factor is the reciprocal of the sum of the exponents of other factors. This would mean a "normal" elasticity of demand for labour of between −2.86 and −4.0, and for capital of between −1.33 and −1.54.