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A Note on Separability in Demand Analysis

S. M. Goldman
H. Uzawa

Abstract

Three separability concepts in demand analysis have been introduced by Sono [9], Leontief [5, 6], Strotz [10, 11], Gorman [3], Frisch [2], Houthakker [4], and Pearce [7]. These concepts have been used effectively to analyze the structure of consumers' preference fields, and their implications have been shown to be of primary importance to empirical study in demand analysis. In this note, we are interested in clarifying the basic structure of the three separability concepts. Necessary and sufficient conditions for a grouping of commodities to be separable in the three criteria are first stated in terms of utility functions, and then they are characterized by the Slutsky terms of the corresponding demand functions.^2