A theory of the perturbed consumer with general budgets
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.
Mogens Fosgerau has received support from the Danish Strategic Research Council, and Daniel McFadden has received support from the E. Morris Cox fund at the University of California, Berkeley, the Presidential fund at USC, and National Institute on Aging (NIA) grants No. P01 AG005842 to the NBER and No. RC4 AG039036 to USC The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.