ANALYTICAL UTILITY FUNCTIONS UNDERLYING FRACTIONAL EXPENDITURE ALLOCATION MODELS

Abstract

This paper •shows conditions and procedures for deriving direct utility functions (D.U.F.) from indirect utility functions (I.U.F.) - provided that the latter can be written explicitly. For the fractional expenditure allocation model (F.E.A.M.) the I.U.F. appears to become a fairly simple integral. Derivation of D.U.F. from the I.U.F., however, appears to impose rather severe restrictions on parameters of the F.E.A.M., if not the number of commodities distinguished. For the power version of the F.E.A.M., this implies either constraints on the number and different values of the power parameters or the requirement that one of them become 1; mutatis mutandis the same applies to the generalized version of that model, viz. cross-bred with the linear expenditure system. In other cases approximate but still acceptable analytical D.U.F. might be derived provided that this would require but minor adjustments in one or more parameter estimates.