Monotone Comparative Statics: A Geometric Approach
39 Pages Posted: 15 Oct 2004
Date Written: October 2004
Abstract
We consider comparative statics of solutions to parameterized optimization problems. A geometric method is developed for finding a vector field that, at each point in the parameter space, indicates a direction in which monotone comparative statics obtain. Given such a vector field, we provide sufficient conditions under which the problem can be reparameterized on the parameter space (or a subset thereof) in a way that guarantees monotone comparative statics. A key feature of our method is that it does not require the feasible set to be a lattice and works in the absence of the standard quasi-supermodularity and single-crossing assumptions on the objective function. We illustrate our approach with a variety of applications.
Keywords: Change of Parameters, Parameterized Optimization Problems, Single Crossing, Supermodularity
JEL Classification: C61
Suggested Citation: Suggested Citation