Multidimensional Screening (studies In Economic Theory)

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The book brings into a focus all necessary mathematical knowledge necessary to understand the economics of multidimensional results screening and applies them straightaway to economic models. The first part of this book contains a review of vector calculus, the theory of partial differential equations, and the theory of generalized convexity. These techniques are extensively used in multidimensional screening models. Part II is devoted to the economics of sceening models. It starts with a detailed discussion of economics and mathematics of unidimensional screening problems and three approaches to their solution: direct, dual, and Hamiltonian. It uses the Hamiltonian approach to unify all known results, which were previously obtained using different arguments. Then the major difficulties with direct and dual approach in the multidimensional context are discussed and the Hamiltonian approach is used to provide the most complete characterization of the solution known in the literature.

E-Book Content

Studies in Economic Theory Editors Charalambos D. Aliprantis Purdue University Department of Economics West Lafayette, in 47907-2076 USA Nicholas C. Yannelis University of Illinois Department of Economics Champaign, il 61820 USA Titles in the Series M. A. Khan and N. C. Yannelis (Eds.) Equilibrium Theory in Infinite Dimensional Spaces C. D. Aliprantis, K. C. Border and W. A. J. Luxemburg (Eds.) Positive Operators, Riesz Spaces, and Economics D. G. Saari Geometry of Voting C. D. Aliprantis and K. C. Border Infinite Dimensional Analysis J.-P. Aubin Dynamic Economic Theory M. Kurz (Ed.) Endogenous Economic Fluctuations J.-F. Laslier Tournament Solutions and Majority Voting A. Alkan, C. D. Aliprantis and N. C. Yannelis (Eds.) Theory and Applications J. C. Moore Mathematical Methods for Economic Theory 1 J. C. Moore Mathematical Methods for Economic Theory 2 M. Majumdar, T. Mitra and K. Nishimura Optimization and Chaos K. K. Sieberg Criminal Dilemmas M. Florenzano and C. Le Van Finite Dimensional Convexity and Optimization K. Vind Independence, Additivity, Uncertainty T. Cason and C. Noussair (Eds.) Advances in Experimental Markets F. Aleskerov and B. Monjardet Utility Maximization. Choice and Preference N. Schofield Mathematical Methods in Economics and Social Choice C. D. Aliprantis, K. J. Arrow, P. Hammond, F. Kubler, H.-M. Wu and N. C. Yannelis (Eds.) Assets, Beliefs, and Equilibria in Economic Dynamics D. Glycopantis and N. C. Yannelis (Eds.) Differential Information Economies A. Citanna, J. Donaldson, H. M. Polemarchakis, P. Siconolfi and S. E. Spear (Eds.) Essays in Dynamic General Equilibrium Theory M. Kaneko Game Theory and Mutual Misunderstanding Suren Basov Multidimensional Screening 123 Dr. Suren Basov University of Melbourne Department of Economics Melbourne, Victoria 3010 Australia E-mail: [email protected] Cataloging-in-Publication Data applied for Library of Congress Control Number: 2004115347 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data available in the internet at http://dnb.ddb.de ISBN 3-540-23906-5 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and
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