## THE PAKISTAN DEVELOPMENT REVIEW

##### Management of Energy Recourses, Marginal Input- Output Coefficients, and Layers of Techniques: A Case Study of US Chemical Industry

The embodied technical change should reduce the cost of production of the commodity. However, price structure, wages and interest rates also will change over time. Thus if a commodity is following a fixed price regime, the adjustment of a historical input-output table to current price wage level will leaves less and less profit per unit of output. The extent of this reduction will indicate the extent of technological change. There are different approaches to the prediction of changes in input-output coefficients. The first approach, attributable to Leontief (1941) and Stone (1962), assumes that input-output matrices change over time in a “biproportional” way. The other approach is to estimate trends in individual coefficients using statistical data. Former approach is used by a number of experts, including Fontela, et al. (1970), Almon, et al. (1974) and Carter (1970). Arrow and Hoffenberg (1959), Henry (1974), Savaldson (1970, 1976), Ozaki (1976), Aujac (1972) and Buzunov (1970). These are examples of the application of the quantitative approach for forecasting input-output coefficients. Still another approach which could not get much attention for forecasting input-output coefficients, is constructing the marginal input-output coefficients [Tilanus (1967); Middelhoek (1970)]. Marginal coefficients for forecasting constructed by Tilanus and Middelhoek are based on average input-output tables, which shows that still new approach (marginal) is based on the old (average) one