  We study the budget map and the indirect utility function of a parametric
consumer problem in a Banach space setting by some advanced tools from
set-valued and variational analysis. The Lipschitz-likeness and
differentiability properties of the budget map, as well as formulas for finding
subdifferentials of the infimal nuisance function, which is obtained from the
indirect utility function by changing its sign, are established. Our
investigation is mainly based on the paper by Mordukhovich [J. Global Optim. 28
(2004), 347--362] on coderivative analysis of variational systems and the paper
of Mordukhovich, Nam, and Yen [Math. Program. 116 (2009), 369--396] on
subgradients of marginal functions. Economic meanings of the obtained
subdifferential estimates are explained in details.
