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A Characterization of Rationalizable Consumer Behavior
Author(s) -
Reny Philip J.
Publication year - 2015
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta12345
Subject(s) - characterization (materials science) , mathematical economics , mathematics , economics , econometrics , microeconomics , computer science , mathematical optimization , physics , optics
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.