DUALITY-THEORY WITH A NONLINEAR CONSTRAINT

A duality theorem between increasing upper semicontinuous utility func tions, upper semicontinuous indirect utility functions and continuous expenditure functions is presented, The constraint is permitted to be non-linear and non-convex, New arguments of proof replace those in the neoclassical theory of the household that rely on the geometry of con vex sets. The duality theorem can be used to prove global and local in tegrability theorems for non-linearly constrained economic behavior.