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Preference Scales and Expenditure Systems

S. N. Afriat

Abstract

The classical hypothesis of consumer theory is that expenditures are regulated by a preference order, between all possible compositions of quantities of goods, which selects a best composition on every budget constraint determined by prices and total expenditure. A determination of a composition for every budget constraint defines an expenditure system. The hypothesis applies to any expenditure system, and asserts that it is associated in this way with some preference order. Here there is a statement of definitions and propositions which constitute a structural analysis of expenditure systems, and of the preference systems associated with them by the Samuelson principle of revealed preference. In accordance with the well-known investigation of Houthakker, and the subsequent one by Uzawa, focus is on the admissibility of the preference hypothesis in the usual form, involving a preference scale, for which representation by a numerical function is possible, rather than a general preference order. But there is also a more general analysis involving propositions of a type which appears to be quite new in the subject.