COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 844 "Testing Strictly Concave Rationality" Rosa L. Matzkin and Marcel K. Richter November 1987 We prove that the Strong Axiom of Revealed Preference tests the existence of a strictly quasiconcave (in fact, continuous, generically C(infinity), 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(infinity) 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. JE Classification: 022, 213 Keywords: Nonparametric tests, revealed preference, rational choice, concave utility, strong axiom of revealed preference |
