A Characterization of Rationalizable Consumer Behavior - Reny, Philip J. (Econometrica, 2015)
For an arbitrary data set D = {(p, x)} ⊆ (ℝ+m∖ {0}) × ℝ+m, finite or infinite, it is shown that the following three conditions are equivalent: (a) D satisfies GARP; (b) D can be rationalized by a utility function; (c) D can be rationalized by a utility function that is quasiconcave, nondecreasing, and that strictly increases when all its coordinates strictly increase. Examples of infinite data sets satisfying GARP are provided for which every utility rationalization fails to be lower semicontinuous, upper semicontinuous, or concave. Thus condition (c) cannot be substantively improved upon.