Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 1976, Volume 44, Issue 5

The Demand Theory of the Weak Axiom of Revealed Preference<971:TDTOTW>2.0.CO;2-I
p. 971-978

Andreu Mas-Colell, Hugo Sonnenschein, Richard Kihlstrom

In this paper we provide a statement of the relationship between the weak axiom of revealed preference (WA) and the negative semidefiniteness of the matrix of substitution terms (NSD). As a corollary we determine the relation between WA and the strong axiom of revealed preference (SA). The latter is equivalent to NSD and the symmetry of the matrix of substitution terms. The former, WA, implies NSD but is not implied by NSD. Also, WA is implied by the condition that the matrix of substitution terms is negative definite (ND), but it does not imply ND. Application of these results yield an infinity of demand functions which satisfy WA but not SA.

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