Equivalence of the weak and strong axioms of revealed preference without demand continuity assumptions: A “regularity condition” approach

The main result of this paper is that, provided the range of the demand function is convex and the whole budget is spent, the strong axiom of revealed preference holds if and only if the weak axiom of revealed preference and a certain “regularity” condition both hold. The regularity condition is a relationship between two definitions of expenditure compensation function that must hold if the strong axiom holds. The paper distinguishes itself from previous work in that no continuity assumptions are made on the demand function. It also discusses the relationship of the regularity condition used in this paper to the one used by Uzawa and van Moeseke.