Testing strictly concave rationality
证明强显示偏好公理可以检验有限需求观测是否由严格拟凹（或严格凹、严格单调）效用函数生成，并指出弱理性行为与连续严格凹单调效用最大化在观测上等价。
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.