Afriat's Theorem for General Budget Sets

Afriat proved the equivalence of a variant of the strong axiom of revealed preference and the existence of a solution to a set of linear inequalities. From this solution he constructed a utility function rationalizing the choices of a competitive consumer. We extend Afriat's theorem to a class of nonlinear, nonconvex budget sets. We thereby obtain testable implications of rational behavior for a wide class of economic environments, and a constructive method to derive individual preferences from observed choices. We also show that by increasing in a regular way the number of observed choices from our class of budget sets one can fully identify the underlying preference relation.

[1]  Johann K. Brunner,et al.  Optimum taxation of life annuities , 2005, Soc. Choice Welf..

[2]  F. Schneider,et al.  Satisfaction with Democracy and the Environment in Western Europe: A Panel Analysis , 2006, SSRN Electronic Journal.

[3]  S. Carson.  African-American and White Living Standards in the 19th Century American South: A Biological Comparison , 2006, SSRN Electronic Journal.

[4]  R. Vohra,et al.  Afrait's Theorem and Negative Cycles , 2003 .

[5]  Una valutazione dele ipotesi di revisione del Metodo Tariffario Normalizzato per il servizio idrico integrato , 2005 .

[6]  H. Raff,et al.  Asset Ownership and Foreign-Market Entry , 2006, SSRN Electronic Journal.

[7]  K. Koch,et al.  Rethinking the Concept of Long-Run Economic Growth , 2006, SSRN Electronic Journal.

[8]  Klaus Wälde,et al.  “Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View , 2006 .

[9]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[10]  Florian Englmaier,et al.  Information, Coordination, and the Industrialization of Countries , 2006, SSRN Electronic Journal.

[11]  Florian Englmaier,et al.  A model of strategic delegation in contests between groups , 2006, SSRN Electronic Journal.

[12]  A. Cigno,et al.  Optimal Policy Towards Families with Different Amounts of Social Capital, in the Presence of Asymmetric Information and Stochastic Fertility , 2006, SSRN Electronic Journal.

[13]  A. Lindbeck,et al.  A Model of Income Insurance and Social Norms , 2006, SSRN Electronic Journal.

[14]  Vincenzo Denicolò,et al.  Nash Bargaining Theory, Nonconvex Problems and Social Welfare Orderings , 2000 .

[15]  Rosa L. Matzkin.  Axioms of Revealed Preference for Nonlinear Choice Sets , 1991 .

[16]  Helge Berger.  Optimal central bank design: Benchmarks for the ECB , 2006, SSRN Electronic Journal.

[17]  P. Samuelson.  A Note on the Pure Theory of Consumer's Behaviour , 1938 .

[18]  Samuel Muehlemann,et al.  Regional Effects on Employer-Provided Training: Evidence from Apprenticeship Training in Switzerland , 2006, SSRN Electronic Journal.

[19]  H. Ursprung,et al.  Evaluation of Researchers: A Life Cycle Analysis of German Academic Economists , 2006, SSRN Electronic Journal.

[20]  P. Dubey,et al.  Price-mediated trade with quantity signals: an axiomatic approach , 2003 .

[21]  H. Varian.  The Nonparametric Approach to Demand Analysis , 1982 .

[22]  Thiess Buettner,et al.  Efficient Revenue Sharing and Upper Level Governments: Theory and Application to Germany , 2006, SSRN Electronic Journal.

[23]  P. Poutvaara,et al.  On human capital formation with exit options: comment and new results , 2006, SSRN Electronic Journal.

[24]  Ondřej Schneider,et al.  What Are Their Words Worth?: The Political Plans and Economic Pains of Fiscal Consolidations in the New EU Member States , 2006 .

[25]  J. Chavas,et al.  On Generalized Revealed Preference Analysis , 1993 .

[26]  H. Gersbach,et al.  Voice and Bargaining Power , 2006 .

[27]  M. J. Todd,et al.  Two new proofs of Afriat’s theorem , 2003 .

[28]  Ludger Woessmann.  Public-Private Partnership and Schooling Outcomes Across Countries , 2006, SSRN Electronic Journal.

[29]  Topi Miettinen,et al.  Political Parties and Network Formation , 2006 .

[30]  Which Plans to Reduce the Digital Divide? Policy Evaluation and Social Interaction , 2005 .

[31]  A dynamic measure of the effective tax rate , 2003 .

[32]  Yoram Barzel,et al.  The Determination of Daily Hours and Wages , 1973 .

[33]  F. van Winden,et al.  Reciprocity and Emotions When Reciprocators Know Each Other , 2006, SSRN Electronic Journal.

[34]  F. van Winden,et al.  Negative Reciprocity and the Interaction of Emotions and Fairness Norms , 2005, SSRN Electronic Journal.

[35]  Moritz Schularick,et al.  Does Financial Integration Spur Economic Growth? New Evidence from the First Era of Financial Globalization , 2006, SSRN Electronic Journal.

[36]  Kurt R. Brekke,et al.  Public Versus Private Health Care in a National Health Service , 2006, Health economics.

[37]  Ron Smith,et al.  Macroeconometric Modelling with a Global Perspective , 2006, SSRN Electronic Journal.

[38]  Yin-Wong Cheung,et al.  An Empirical Model of Daily Highs and Lows , 2006 .

[39]  S. Afriat.  THE CONSTRUCTION OF UTILITY FUNCTIONS FROM EXPENDITURE DATA , 1967 .

[40]  R. Moffitt.  The Estimation of a Joint Wage-Hours Labor Supply Model , 1984, Journal of Labor Economics.

[41]  F. Forges.  The Ex Ante Incentive Compatible Core in Exchange Economies With and Without Indivisibilities , 2006, SSRN Electronic Journal.

[42]  Andreu Mas-Colell,et al.  On Revealed Preference Analysis , 1978 .

[43]  Dirk Schindler,et al.  Company Tax Reform in Europe and its Effect on Collusive Behavior , 2006, SSRN Electronic Journal.

[44]  박상용.  [경제학] 현시선호이론(Revealed Preference Theory) , 1980 .

[45]  Marc-Andreas Muendler,et al.  The Structure of Worker Compensation in Brazil, with a Comparison to France and the United States , 2006, The Review of Economics and Statistics.

[46]  Françoise Forges,et al.  Long Persuasion Games , 2006, J. Econ. Theory.

[47]  K. Angelopoulos,et al.  Rent-Seeking Competition from State Coffers: A Calibrated DSGE Model of the Euro Area , 2006, SSRN Electronic Journal.

[48]  K. Arrow.  Rational Choice Functions and Orderings1 , 1959 .

[49]  H. Verbon,et al.  Cross-Racial Envy and Underinvestment in South Africa , 2006, SSRN Electronic Journal.

[50]  Paolo M. Panteghini,et al.  The capital structure of multinational companies under tax competition , 2006, SSRN Electronic Journal.

[51]  H. Houthakker.  Revealed Preference and the Utility Function , 1950 .

[52]  Steffen R. Henzel,et al.  The New Keynesian Phillips Curve and the Role of Expectations: Evidence from the Ifo World Economic Survey , 2006, SSRN Electronic Journal.

[53]  I. Arnold,et al.  Inflation Expectations and Inflation Uncertainty in the Eurozone: Evidence from Survey Data , 2006, SSRN Electronic Journal.

[54]  Yves Sprumont,et al.  On the Testable Implications of Collective Choice Theories , 2000, J. Econ. Theory.

[55]  L. Goerke.  Bureaucratic corruption and profit tax evasion , 2006, SSRN Electronic Journal.

[56]  M. Funke,et al.  Extracting Leading Indicators of Bank Fragility from Market Prices - Estonia Focus , 2006, SSRN Electronic Journal.

[57]  Andreu Mas-Colell,et al.  The Recoverability of Consumers' Preferences from Market Demand Behavior , 1977 .

[58]  W. Newey,et al.  Nonparametric Estimation With Nonlinear Budget Sets , 1999 .

[59]  Davide Pettenuzzo,et al.  Learning, Structural Instability and Present Value Calculations , 2006, SSRN Electronic Journal.

[60]  B. Heer,et al.  The savings-inflation puzzle , 2006, SSRN Electronic Journal.

[61]  Anders Forslund,et al.  Real and Nominal Wage Adjustment in Open Economies , 2006, SSRN Electronic Journal.

[62]  Something Out of Nothing? Neoclassical Growth and the 'Trivial' Steady State , 2006, SSRN Electronic Journal.

[63]  F. Menoncin.  The role of longevity bonds in optimal portfolios , 2008 .

[64]  B. Heer,et al.  Business Cycle Dynamics of a New Keynesian Overlapping Generations Model with Progressive Income Taxation , 2006, SSRN Electronic Journal.

[65]  Bertrand Crettez,et al.  On the Characterization of Efficient Production Vectors , 2007 .

[66]  F. Menoncin,et al.  Optimal Real Exchange Rate Targeting. A Stochastic Analysis , 2007 .

[67]  Walter Diewert,et al.  Afriat and Revealed Preference Theory , 1973 .

[68]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[69]  L. Shapley,et al.  Trade Using One Commodity as a Means of Payment , 1977, Journal of Political Economy.

[70]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[71]  A. Dreher,et al.  Corruption and the shadow economy: an empirical analysis , 2006, SSRN Electronic Journal.

[72]  Steven A. Y. Lin.  Theory and measurement of economic externalities , 1978 .

[73]  S. Winer,et al.  Political Competition and Convergence to Fundamentals: With Application to the Political Business Cycle and the Size of Government , 2006, SSRN Electronic Journal.

[74]  Apostolos Serletis.  The Nonparametric Approach to Demand Analysis , 2007 .

[75]  E. Minelli,et al.  Credit Market Failures and Policy , 2003 .