# SFB 303 Discussion Paper No. A - 163

**Author**: Hildenbrand, Werner, and Michael Jerison

**Title**: The Demand Theory of the Weak Axioms of Revealed Preference

**Abstract**: If in individual demand function f satisfies the Weak Axiom of Revealed Preference then the Slutsky
substitution matrix of f is negative semidefinite. This is well-known since Samuelson formulated the Weak
Axiom of Revealed Preference in 1938. The converse implication is not true. However, a slightly weaker axiom,
referred to here as the Weak Axiom (first formulated by Hicks, 1956, p. 110), is in fact equivalent to the negative
semidefiniteness of the Slutsky substitution matrix. This was shown by Kihlstrom, Mas-Colell and Sonnenschein
(1976).Since characterizations of these revealed preference axioms are fundamental for demand theory, it is of
interest of have available complete statements and simple proofs. These will be given in the paper.

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**Creation-Date**: March 1988

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