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Existence and monotonicity of solutions to moral hazard problems
Affiliation:1. CNRS-University of Cergy-Pontoise (THEMA, UMR 8184), France;2. CNRS-Paris School of Economics (PjSE, UMR 8545), France;1. Department of Quantitative Economics, Maastricht University, Netherlands;2. Economic Research Unit, Indian Statistical Institute, Kolkata, India;1. Department of Economics, College of Business, Florida Atlantic University, Boca Raton, FL 33431, United States;2. Department of Economics, Cornell University, Uris Hall, Ithaca, NY 14850, United States;1. Universidad de Vigo, RGEA-ECOBAS, Spain;2. Universidad de Salamanca, IME, Spain;1. Paris School of Economics, University Paris 1, CES, 106 boulevard de l’Hopital, 75013, Paris, France;2. University of La Rochelle (MIA), Avenue Michel Crepeau, 47042, La Rochelle, France;3. University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Abstract:This paper provides a method to prove existence of solutions to some moral hazard problems with infinite set of outcomes. The argument is based on the concept of nondecreasing rearrangement and on a supermodular version of Hardy–Littlewood’s inequality. The method also provides qualitative properties of solutions. Both the cases of wage contracts and of insurance contracts are studied.
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