Abstract
We consider utility functions defined on P̄, the closure of the positive orthant of R l , that satisfy the differentiable monotonicity and differentiable convexity conditions. We show that the demand function derived from such a utility function is piecewise smooth in a strong sense. We use this result to show that the Pareto optimal subset of a pure exchange economy derived from the kind of utility functions we consider is generically the union of a finite number of compact manifolds-with-corners.
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