A Characterization of Rationalizable Consumer Behavior

Econometrica · 2015 · Volume 83 · Issue 1

Abstract

For an arbitrary data setD= {(p,x)} ⊆ (ℝ+m∖ {0}) ×ℝ+m, finite or infinite, it is shown that the following three conditions are equivalent: (a)Dsatisfies GARP; (b)Dcan be rationalized by a utility function; (c)Dcan be rationalized by a utility function that is quasiconcave, nondecreasing, and that strictly increases when all its coordinates strictly increase. Examples of infinite data sets satisfying GARP are provided for which every utility rationalization fails to be lower semicontinuous, upper semicontinuous, or concave. Thus condition (c) cannot be substantively improved upon.

Keywords

Utility representation, integrability, Afriat's theorem

Enable JavaScript for citation tools and additional paper interactions.