IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/17953.html
   My bibliography  Save this paper

A theory of the perturbed consumer with general budgets

Author

Listed:
  • 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
    Note: AG
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w17953.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mogens Fosgerau & Julien Monardo & André de Palma, 2024. "The Inverse Product Differentiation Logit Model," American Economic Journal: Microeconomics, American Economic Association, vol. 16(4), pages 329-370, November.
    2. Mogens Fosgerau & André de Palma, 2016. "Generalized entropy models," Working Papers hal-01291347, 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 & Nikolaj Nielsen & Mads Paulsen & Thomas Kj{ae}r Rasmussen & Rui Yao, 2024. "Substitution in the perturbed utility route choice model," Papers 2409.08347, arXiv.org.
    12. Mogens Fosgerau & Mads Paulsen & Thomas Kj{ae}r Rasmussen, 2021. "A perturbed utility route choice model," Papers 2103.13784, arXiv.org, revised Sep 2021.
    13. 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.
    14. 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.
    15. 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.
    16. 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).
    17. Daniel McFadden, 2017. "Foundations of Welfare Economics and Product Market Applications," NBER Working Papers 23535, National Bureau of Economic Research, Inc.
    18. Allen, Roy & Rehbeck, John, 2024. "Latent utility and permutation invariance: A revealed preference approach," Journal of Econometrics, Elsevier, vol. 244(1).
    19. Daniel L. McFadden, 2013. "The New Science of Pleasure," NBER Working Papers 18687, National Bureau of Economic Research, Inc.
    20. Rehbeck, John, 2024. "A menu dependent Luce model with a numeraire," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    21. Allen, Roy & Rehbeck, John, 2022. "Latent complementarity in bundles models," Journal of Econometrics, Elsevier, vol. 228(2), pages 322-341.
    22. 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.
    23. Mogens Fosgerau & John Rehbeck, 2023. "Nontransitive Preferences and Stochastic Rationalizability: A Behavioral Equivalence," Papers 2304.14631, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Renato Gomes & Jean-Marie Lozachmeur & Alessandro Pavan, 2018. "Differential Taxation and Occupational Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 511-557.
    2. Gan, Li & Ju, Gaosheng & Zhu, Xi, 2015. "Nonparametric estimation of structural labor supply and exact welfare change under nonconvex piecewise-linear budget sets," Journal of Econometrics, Elsevier, vol. 188(2), pages 526-544.
    3. Heim, Bradley T. & Meyer, Bruce D., 2004. "Work costs and nonconvex preferences in the estimation of labor supply models," Journal of Public Economics, Elsevier, vol. 88(11), pages 2323-2338, September.
    4. Gauthier, Stéphane & Laroque, Guy, 2009. "Separability and public finance," Journal of Public Economics, Elsevier, vol. 93(11-12), pages 1168-1174, December.
    5. Koji Miyawaki & Yasuhiro Omori & Akira Hibiki, 2018. "A discrete/continuous choice model on a nonconvex budget set," Econometric Reviews, Taylor & Francis Journals, vol. 37(2), pages 89-113, February.
    6. Wei-Bin Zhang, 2020. "Optimal Taxation in the Solow-Uzawa Growth Model with Public Goods," Journal of Social and Development Sciences, AMH International, vol. 10(3), pages 1-11.
    7. Rainer Niemann & Ulrich Schreiber, 2020. "Herausforderungen und Entwicklungsperspektiven des Steuersystems [Challenges and Development Perspectives of the Tax System]," Schmalenbach Journal of Business Research, Springer, vol. 72(1), pages 1-48, March.
    8. Sanjay K. Chugh & S. Boragan Aruoba, 2009. "Money and Optimal Capital Taxation," 2009 Meeting Papers 69, Society for Economic Dynamics.
    9. Kasy, Maximilian, 2018. "Optimal taxation and insurance using machine learning — Sufficient statistics and beyond," Journal of Public Economics, Elsevier, vol. 167(C), pages 205-219.
    10. Kowalski, Amanda E., 2015. "Estimating the tradeoff between risk protection and moral hazard with a nonlinear budget set model of health insurance," International Journal of Industrial Organization, Elsevier, vol. 43(C), pages 122-135.
    11. Valentini, Edilio, 2015. "Indirect taxation, public pricing and price cap regulation: A synthesis," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 9, pages 1-39.
    12. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    13. Pizer, William A. & Kopp, Raymond, 2005. "Calculating the Costs of Environmental Regulation," Handbook of Environmental Economics, in: K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 3, chapter 25, pages 1307-1351, Elsevier.
    14. Engelson, Leonid & Fosgerau, Mogens, 2016. "The cost of travel time variability: Three measures with properties," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 555-564.
    15. Nelson Lind & Natalia Ramondo, 2023. "Trade with Correlation," American Economic Review, American Economic Association, vol. 113(2), pages 317-353, February.
    16. Ludvig Sinander, 2019. "The converse envelope theorem," Papers 1909.11219, arXiv.org, revised Jun 2022.
    17. Jetlir Duraj & Yi-Hsuan Lin, 2022. "Identification and welfare evaluation in sequential sampling models," Theory and Decision, Springer, vol. 92(2), pages 407-431, March.
    18. John Quah & Hiroki Nishimura & Efe A. Ok, 2013. "A Unified Approach to Revealed Preference Theory: The Case of Rational Choice," Economics Series Working Papers 686, University of Oxford, Department of Economics.
    19. Becko, John Sturm, 2024. "A theory of economic sanctions as terms-of-trade manipulation," Journal of International Economics, Elsevier, vol. 150(C).
    20. Rodrigo Adao & Arnaud Costinot & Dave Donaldson, 2017. "Nonparametric Counterfactual Predictions in Neoclassical Models of International Trade," American Economic Review, American Economic Association, vol. 107(3), pages 633-689, March.

    More about this item

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:17953. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.