On Generalising Engel's Law: Commodity Expenditure shares in Hierarchic Demand Systems

Abstract

This paper establishes some simple new properties of hierarchic demand systems as defined in Jackson[l984]. In these systems the number of commodities purchased increases with income. Within hierarchic demand systems with piecewise linear engel curves it is shown that every commodity has the property that the commodity budget share is a decreasing proportion of (i) the expenditure on that commodity and all commodities which enter the budget after that commodity and (ii) total expenditure after the commodity enters the budget. These general propositions give predictions about commodity budget shares in general and as a special case within commodity groups. It is shown that the famous empirical regularity known as Engel's law can be regarded as a special case of these propositions by applying them to the first commodity.