Econometrica: May, 1970, Volume 38, Issue 3
Homothetic Separability and Consumer Budgeting
Charles Blackorby, David Nissen, George Lady, R. Robert Russell
Gorman  has derived necessary and sufficient conditions for the existence of category expenditure functions which yield the optimal allocation of a consumer unit's income to each of a number of groups of commodities as functions of total income and group price indices. These conditions take the form of certain restrictions on the structure of the utility function. Gorman, however, did not address the problem of how these functions are derived. In this paper, we construct an algorithm (a budgeting procedure) for deriving the category expenditure functions and show that the necessary and sufficient condition for this procedure to be consistent is that the utility function be separable into homothetic parts.