Monotone comparative statics: Geometric approach

B. H. Strulovici, T. A. Weber

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)641-673
Number of pages33
JournalJournal of Optimization Theory and Applications
Volume137
Issue number3
DOIs
StatePublished - Jun 2008

Keywords

  • Change of parameters
  • Parameterized optimization problems
  • Single-crossing
  • Supermodularity

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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