Testing Strictly Concave Rationality

We prove that the Strong Axiom of Revealed Preference tests the existence of a strictly quasiconcave (in fact, continuous, generically C(∞), 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 C(∞) way, thus extending a result of Chiappori and Rochet from compact sets to all of R(n).

For finite data sets, one implication of our result is that even some weak types of rational behavior — maximization of pseudotransitive or semtransitive preferences — are observationally equivalent to maximization of continuous, strictly concave, and strictly monotone utility functions.