A Characterization of Rationalizable Consumer Behavior

For an arbitrary finite or infinite dataset D of prices and corresponding chosen bundles, it is shown that the following three conditions are equivalent. (i) D satisfies GARP; (ii) D can be rationalized by a utility function; (iii) D can be rationalized by a strictly increasing, quasiconcave utility function. Examples of infinite datasets satisfying GARP are provided for which every utility rationalization fails to be lower semicontinuous, upper semicontinuous, or concave. Thus condition (iii) cannot be substantively improved upon.