SFB 303 Discussion Paper No. A - 490

Author: John, Reinhard
Title: A First Order Characterization of Generalized Monotonicity
Abstract: It is shown that a well known necessesary first order condition for pseudomonotone and quasimonotone functions is also sufficient for these properties provided that the functions are regular. This main result extends recent contributions which can be traced back to Kihlstrom, Mas-Colell and Sonnenschein (1976) as well as to Mitjushin and Polterovich (1978) and provides a solution to an open problem posed by Hildenbrand and Jerison (1989). Its application to gradient functions yields immediately a second order characterization of pseudoconcave and quasiconcave functions which generalizes the one by Diewert, Avriel, and Zang (1981). Furthermore, it implies a stability theorem closely related to Hartman and Olech (1962).
Keywords: Weak Axiom of Revealed Preferences, pseudomonotonicity, pseudoconcavity, quasiconcavity
JEL-Classification-Number: C61, C62, D11
Creation-Date: October 1995
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