Properties of demand functions for linear consumption aggregates

Abstract

The starting point is the demand functions for homogeneous goods, with properties derived from standard static consumer theory. A linear consumption aggregate of a commodity group is defined as a weighted sum of the physical quantities of the homogeneous goods in the group. By using different types of weights we obtain for the same commodity group, different consumption aggregates with different demand elasticities relevant for different applications. For example, a linear consumption aggregate of alcoholic beverages can be measured in pure alcohol (for health analysis), in litres (for transportation analysis), in alcohol taxes (for fiscal analysis), or in expenditure at (different sets of) constant prices (for macro economic analysis). We derive properties of the demand functions for a general linear consumption aggregate, and relationships between the demand functions for different aggregates of the same commodity groups and across commodity groups. Results are presented in eight theorems, with comments on possible econometric interpretations. A non-Giffen anti law of demand is derived. A possible interpretation in the case of bread consumption implies that the direct Slutsky elasticity for bread measured in weight (kilograms) is positive, and the direct Cournot elasticity even more so, while the demand elasticities for the Hicksian aggregate of bread have normal signs.