An Interindustry Study of Price Formation

Abstract

M OST interindustry studies have hitherto been made on the assumption of the stability of production coefficients between product and factors. Theoretical justification for these studies may be found in the so-called theorem, which was developed by Professors Arrow [2], Georgescu-Roegen [8], Koopmans [11], and Samuelson [18]. Some empirical economists, however, have doubts about the conclusion that all relative prices as well as production coefficients should be kept constant irrespective of changes in final demand. On the other hand, Professor Klein's substitution theorem [10] claims, on the assumption of the Cobb-Douglas production function and the marginal productivity relationships, that the ratios between the value of output and that of input, or the input coefficients in 'value' terms, should be kept constant while the input coefficients in 'quantity' terms and relative prices are flexible in response to changes in final demands. In this study, I intend to make an empirical analysis of the interdependency of prices and outputs on the basis of the latter theorem. Thus our empirical model is essentially the Walras-Hicks type general equilibrium model in which the production technique of each industry is expressed by a Cobb-Douglas function. In section I general features of this model are explained. Section II gives the estimated results of the model, based on the Japanese economy, which were obtained by using the 1960 input-output table and 19531965 time-series data for Japan. Section III is devoted to a discussion of the implications of the estimates of the excess supply functions. Here I present the estimated effects of a unit change in final demand on price, output, employment, and GNP originating in each industry. In connection with the thoretical problem, it is found that the Jacobian matrix of the estimated excess supply functions approximately realizes the gross substitutability property. Section IV tests our approach. The 1961 values of price, output, employment, and consumption in each industry, which are calculated from our estimated equations based on the 1960 input-output table, are compared with their observed values. The results indicate that our estimated model reproduces, with a tolerable degree of accuracy, the 1960-1961 fluctuation of the whole economy.