Simple approach to production functions via factor costs

Abstract

Some common ground between input-output accounting and Cobb-Douglas (C.D.) production functions is explored. The problem of how to express value added as a function of labour, capital stock and time, is re-stated. For a single production process the accountant's model of the growth of value added is examined and the surplus shown to mean a saving of costs. The same growth of value added is now explained by a C.D. production function which includes an exponential time trend for technical progress. Approximate identification o f C.D. parameters with coefficients of the accountant's model is found. Next the form of measurement used for the capital stock is shown to affect the parameters of the C.D. production function - the smaller the apparent volume of capital stock the greater the volume of value added to be explained by technical progress. Fairly obvious conclusions are drawn.