Monotone Comparative Statics: Geometric Approach

Bruno Strulovici and Thomas Weber

Journal of Optimization Theory and Applications, 2008, vol. 137, issue 3, No 11, 673 pages

Abstract: 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.

Keywords: Change of parameters; Parameterized optimization problems; Single-crossing; Supermodularity (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-007-9339-1

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