TESTING STRICTLY CONCAVE RATIONALITY

We prove that the Strong Axiom of Revealed Preference tests the existence of a strictly quasiconcave (or strictly concave, strictly monotone) utility function generating finitely many demand observations. This sharpens earlier results of Afriat, Diewert, and Varian that tested ("nonparametrically") existence of a piecewise linear utility function. 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. And for infinitely many observations, our result is the basis of several new rationality theorems. © 1991.