Consistent aggregation of demand functions over restricted income distributions
This paper aims to determine the conditions under which the demands for goods of individual consumers, as functions of prices and individual income, may be summed and aggregatedly represented as a function of prices and community income. With the possible distribution of individual income restricted to be in some set, the economic problem posed reduces to solving Cauchy- and Pexider-type functional equations on restricted domains. The techniques of Zdun, and Daróczy and Losconzi are used to solve the functional equations. The main conclusion is that aggregation of demand is possible if and only if the individual demand functions are essentially linear in income. This rather confining result prompts the formulation of the problem of approximate aggregation of demand functions, the resolution of which would involve determining the stability of functional equations over restricted domains.
scientific article; zbMATH DE number 4008053