CFDP 844

Testing Strictly Concave Rationality


Publication Date: July 1987

Pages: 20


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.


Nonparametric tests, Revealed preference, Rational choice, Concave utility, Strong axiom of revealed preference

JEL Classification Codes: 022, 213

See CFP: 782