Additive Utility Functions with Double-Log Consumer Demand Functions

Frisch (1959) proposed the adoption of direct additive utility functions to facilitate empirical demand analysis. Double-log demand functions resulting therefrom are composed of the real income effect and the relative price effect. I show that the income elasticities and the own-price elasticities of demand are (approximately) constant (an assumption almost invariably made in applications) when the utility function is a generalized CES type. The income elasticity of marginal utility is the overall elasticity of substitution with no cardinal implications that Frisch stressed upon. The paper examines how approximate the constancy assumption is. A comparison is made with the linear expenditure system that is a special case. I suggest that the implied similarity of utility functions among countries provides the missing basis for international comparisons of purchasing power parities.

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