We study systems of equations, F (x) = 0, given by piecewise differentiable functions F : Rn → Rk, k ≤ n. The focus is on the representability of the solution set locally as an (n − k)-dimensional Lipschitz manifold. For that, nonsmooth versions of inverse function theorems are applied. It...

Many economic models and optimization problems generate (endogenous) shadow prices - alias dual variables or Lagrange multipliers. Frequently the “slopes” of resulting price curves - that is, multiplier derivatives - are of great interest. These objects relate to the Jacobian of the...