Individual versus Aggregate Income Elasticities for Heterogeneous Populations

This paper deals with different concepts of income elasticities of demand for a heterogenous population and the relationship between individual and aggregate elasticities is analyzed. In general, the aggregate elasticity is  not equal to the mean of individual elasticities. The difference depends on the heterogeneity of the population and is quantified by a covariance term. Sign and  magnitude of this term are determined by an empirical analysis based on the U.K. Family Expenditure Survey. It is shown that the relevant quantities can be identified from cross-section data and, without imposing restrictive structural assumptions, can be estimated by nonparametric techniques. It turns out that the aggregate elasticity significantly overestimates the mean of individual elasticities for many commodity groups.