TAILIEUCHUNG - Advances in MATHEMATICAL ECONOMICS - Akira Yamazaki

Managing Editors Akira Yamazaki Meisei University Tokyo, JAPAN Shigeo Kusuoka University of Tokyo Tokyo, JAPAN Editors Robert Anderson University of California, Berkeley Berkeley, . Charles Castaing Universite Montpellier II Montpellier, FRANCE Frank H. Clarke Universite de Lyon I Villeurbanne, FRANCE Egbert Dierker University of Vienna Vienna, AUSTRIA Darrell Duffie Stanford University Stanford, . Lawrence C. Evans University of California, Berkeley Berkeley, . Takao Fujimoto Fukuoka University Fukuoka, JAPAN Jean-Michel Grandmont CREST-CNRS Malakoff, FRANCE Norimichi Hirano Yokohama National University Yokohama, JAPAN Leonid Hurwicz University of Minnesota MinneapoUs, | Advances in MATHEMATICAL ECONOMICS Volume 2 springer Adv. Math. Econ. 7 47-93 2005 Advances in MATHEMATICAL ECONOMICS Springer-V erlag2005 A method in demand analysis connected with the Monge Kantorovich problem Vladimir L. Levin Central Economics and Mathematics Institute of Russian Academy of Sciences 47 Nakhimovskii Prospect 117418 Moscow Russia e-mail vl-levin@ Received February 18 2004 Revised August 6 2004 JEL classification C65 Dll Mathematics Subject Classification 2000 91B42 Abstract. A method in demand analysis based on the Monge-Kantorovich duality is developed. We characterize insatiate demand functions that are rationalized in different meanings by concave utility functions with some additional properties such as upper semi-continuity continuity non-decrease strict concavity positive homogeneity and so on. The characterizations are some kinds of abstract cyclic monotonicity strengthening revealed preference axioms and also they may be considered as an extension of the Afriat-Varian theory to an arbitrary infinite set of observed data . Particular attention is paid to the case of smooth functions. Key words demand function budget set insatiate demand utility function indirect utility function rationalizing strict rationalizing inducing strict inducing Monge-Kantorovich problem MKP with a fixed marginal difference cost function constraint set of a dual MKP concave function strictly concave function positive homogeneous function superdifferential Introduction This article is devoted to concave-utility-rational demand functions. The problem of demand rationalizing is studied in mathematical economics Supported in part by Russian Foundation for Humanitarian Sciences project 03-02-00027 . A part of the material of this paper was presented at the international conference Kantorovich memorial. Mathematics and economics old problems and new approaches January 8-13 2004. 48 . Levin since 1886 Antonelli for history and references see

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