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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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    References listed on IDEAS

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    1. Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    3. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    4. 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.
    5. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
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    Citations

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    Cited by:

    1. Daniel McFadden, 2014. "The new science of pleasure: consumer choice behavior and the measurement of well-being," Chapters,in: Handbook of Choice Modelling, chapter 2, pages 7-48 Edward Elgar Publishing.
    2. Mogens Fosgerau & André De Palma, 2016. "Generalized entropy models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01291347, HAL.
    3. Mogens Fosgerau & Emerson Melo & André De Palma & Matthew Shum, 2017. "Discrete Choice and Rational Inattention: A General Equivalence Result," Working Papers hal-01501313, HAL.
    4. Fosgerau, Mogens & de Palma, André, 2015. "Demand systems for market shares," MPRA Paper 62106, University Library of Munich, Germany.
    5. Daniel McFadden, 2017. "Foundations of Welfare Economics and Product Market Applications," NBER Working Papers 23535, National Bureau of Economic Research, Inc.
    6. Daniel L. McFadden, 2013. "The New Science of Pleasure," NBER Working Papers 18687, National Bureau of Economic Research, Inc.
    7. Mogens Fosgerau & André De Palma, 2016. "Generalized entropy models," Working Papers hal-01291347, HAL.
    8. 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.

    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

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