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.
Matzkin, Rosa L. and Richter, Marcel K., "Testing Strictly Concave Rationality" (1987). Cowles Foundation Discussion Papers. 1087.