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A theory of the perturbed consumer with general budgets

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  • Daniel L. McFadden
  • Mogens Fosgerau

Abstract

We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose subgradients with respect to these perturbations are convex hulls of the utility-maximizing demands. We give necessary as well as sufficient conditions for DGF to be consistent with utility maximization, and establish under quite general conditions that utility-maximizing demands are almost everywhere single-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints.

Suggested Citation

  • Daniel L. McFadden & Mogens Fosgerau, 2012. "A theory of the perturbed consumer with general budgets," NBER Working Papers 17953, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:17953
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    1. John Beshears & James J. Choi & David Laibson & Brigitte C. Madrian, 2010. "The Impact of Employer Matching on Savings Plan Participation under Automatic Enrollment," NBER Chapters, in: Research Findings in the Economics of Aging, pages 311-327, National Bureau of Economic Research, Inc.
    2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    3. Stefan Scholtes & Michael Stöhr, 2001. "How Stringent is the Linear Independence Assumption for Mathematical Programs with Complementarity Constraints?," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 851-863, November.
    4. Diamond, Peter A & Mirrlees, James A, 1971. "Optimal Taxation and Public Production II: Tax Rules," American Economic Review, American Economic Association, vol. 61(3), pages 261-278, June.
    5. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    6. Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
    7. Daniel McFadden, 2010. "Comment on "The Impact of Employer Matching on Savings Plan Participation under Automatic Enrollment"," NBER Chapters, in: Research Findings in the Economics of Aging, pages 327-335, National Bureau of Economic Research, Inc.
    8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    9. A. L. Dontchev, 1998. "A Proof of the Necessity of Linear Independence Condition and Strong Second-Order Sufficient Optimality Condition for Lipschitzian Stability in Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 467-473, August.
    10. Burtless, Gary & Hausman, Jerry A, 1978. "The Effect of Taxation on Labor Supply: Evaluating the Gary Negative Income Tax Experiments," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 1103-1130, December.
    11. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    12. A. B. Levy, 2001. "Lipschitzian Multifunctions and a Lipschitzian Inverse Mapping Theorem," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 105-118, February.
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    Cited by:

    1. Mogens Fosgerau & André de Palma, 2016. "Generalized entropy models," Working Papers hal-01291347, HAL.
    2. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    3. Mattsson, Lars-Göran & Weibull, Jörgen W., 2023. "An analytically solvable principal-agent model," Games and Economic Behavior, Elsevier, vol. 140(C), pages 33-49.
    4. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    5. Mogens Fosgerau & Dennis Kristensen, 2021. "Identification of a class of index models: A topological approach," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 121-133.
    6. Fosgerau, Mogens & de Palma, André, 2015. "Demand systems for market shares," MPRA Paper 62106, University Library of Munich, Germany.
    7. Khai Xiang Chiong & Matthew Shum, 2019. "Random Projection Estimation of Discrete-Choice Models with Large Choice Sets," Management Science, INFORMS, vol. 65(1), pages 256-271, January.
    8. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    9. Roy Allen & John Rehbeck, 2021. "A Generalization of Quantal Response Equilibrium via Perturbed Utility," Games, MDPI, vol. 12(1), pages 1-16, March.
    10. Abi Adams & Richard Blundell & Martin Browning & Ian Crawford, 2015. "Prices versus preferences: taste change and revealed preference," IFS Working Papers W15/11, Institute for Fiscal Studies.
    11. Mogens Fosgerau & Mads Paulsen & Thomas Kj{ae}r Rasmussen, 2021. "A perturbed utility route choice model," Papers 2103.13784, arXiv.org, revised Sep 2021.
    12. Roy Allen & John Rehbeck, 2023. "Revealed stochastic choice with attributes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 91-112, January.
    13. Mogens Fosgerauy & Julien Monardoz & André de Palma, 2023. "The Inverse Product Differentiation LogitModel," THEMA Working Papers 2023-17, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    14. Daniel McFadden, 2014. "The new science of pleasure: consumer choice behavior and the measurement of well-being," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 2, pages 7-48, Edward Elgar Publishing.
    15. Sørensen, Jesper R.-V. & Fosgerau, Mogens, 2022. "How McFadden met Rockafellar and learned to do more with less," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    16. Daniel McFadden, 2017. "Foundations of Welfare Economics and Product Market Applications," NBER Working Papers 23535, National Bureau of Economic Research, Inc.
    17. Daniel L. McFadden, 2013. "The New Science of Pleasure," NBER Working Papers 18687, National Bureau of Economic Research, Inc.
    18. Allen, Roy & Rehbeck, John, 2022. "Latent complementarity in bundles models," Journal of Econometrics, Elsevier, vol. 228(2), pages 322-341.
    19. Roy Allen & John Rehbeck, 2020. "Hicksian complementarity and perturbed utility models," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 245-261, October.
    20. Mogens Fosgerau & John Rehbeck, 2023. "Nontransitive Preferences and Stochastic Rationalizability: A Behavioral Equivalence," Papers 2304.14631, arXiv.org.

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    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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