Aggregate Substitutabilities between Factor Demands

Answers to various questions of applied macroeconomics depend on the values given toelasticities of substitution between the demands for factors, these demands being aggregatedacross productive sectors. Such elasticities reflect not only substitutabilities within productiveprocesses, but also substitutabilities in the system of demand functions for goods. The lattersubstitutabilities show how demand for goods react to changes in relative prices of goods,which are themselves induced by changes in factor prices. A fairly general model leads to arelationship directly linking changes in factor prices to changes in the aggregate demands forthese factors. The relation is applied to particular specifications : first, to a simple CESeconomy and, second, to a nested-CES economy with three factors, a case which points todifficulties for the establishment of general transparent properties. A full treatment is,however, provided for the case of two factors only, which may be further specified. Thus, themodel exhibited here lends itself to studies about how, at the aggregate level, factorsubstitutabilities depend not only on the forms of production functions and demand functionsfor goods, but also on heterogeneity across the set of parameters characterizing thesefunctions.