Nonparametric Tests of Maximizing Behavior Subject to Nonlinear Sets

This paper extends the axiomatic theory of revealed preference to choices that are generated by the maximization of a strictly concave and strictly monotone function subject to nonlinear constraint sets. I characterize finite sets of observations on choice behavior that are consistent with the maximization of a strictly concave and strictly monotone objective function. Both nonconvex and convex choice sets are considered. The analysis applies, for example, to consumers who face either regressive or progressive taxes and to households that produce commodities according to either a convex or a concave production function. For choice sets that possess convex and monotone complements, my characterization provides a nonparametric test for the maximization hypothesis. For choice sets that can be supported by unique hyperplanes at the chosen elements, the result provides a nonparametric test for the strict concavity and strict monotonicity of the maximized function.