We consider the 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 obtains. 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.
- Change of parameters
- Parameterized optimization problems
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics