Testing Strictly Concave Rationality

Abstract

We prove that the Strong Axiom of Revealed Preference tests the existence of a strictly quasiconcave (in fact, continuous, generically Coo, strictly concave, and strictly monotone) utility function generating finitely many demand observations. This sharpens earlier results of Afriat, Diewert, and Varian that tested ("nonparametrically") the existence of a piecewise linear utility function that could only weakly generate those demand observations. When observed demand is also invertible, we show that the rationalizing can be done in a Coo way, thus extending a result of Chiappori and Rochet from compact sets to all of Rn. For finite data sets, one implication of our result is that even some weak types of rational behavior - maximization of pseudotransitive or semitransitive preferences -- are observationally equivalent to maximization of continuous, strictly concave, and strictly monotone utility functions.