The theory of weak revealed preference

We offer a rationalization of the weak axiom of revealed preference (WARP) and of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a "local" utility function. We develop its associated weak revealed-preference theory. We show that preference recoverability and welfare analysis à la Varian (1982) may not be informative enough, when the weak axiom holds, but when consumers are not utility maximizers. We clarify the reasons for this failure and provide new informative bounds for the consumer's true preferences.