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A theory of the perturbed consumer with general budgets

  • Daniel L. McFadden
  • Mogens Fosgerau

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 17953.

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Date of creation: Mar 2012
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Handle: RePEc:nbr:nberwo:17953
Note: AG
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  1. 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 1103-30, December.
  2. Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
  3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  4. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  5. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-86, November.
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