Monotone Comparative Statics: A Geometric Approach

39 Pages Posted: 15 Oct 2004

See all articles by Bruno H. Strulovici

Bruno H. Strulovici

Northwestern University

Thomas A. Weber

Ecole Polytechnique Federale de Lausanne - MTEI

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

Strulovici, Bruno H. and Weber, Thomas A., Monotone Comparative Statics: A Geometric Approach (October 2004). Available at SSRN: https://ssrn.com/abstract=604862 or http://dx.doi.org/10.2139/ssrn.604862

Bruno H. Strulovici (Contact Author)

Northwestern University ( email )

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United States

Thomas A. Weber

Ecole Polytechnique Federale de Lausanne - MTEI ( email )

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Switzerland
+41 (0)21 693 01 41 (Phone)
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