Monotone Comparative Statics: Geometric Approach

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.


Published in:
Journal of Optimization Theory and Applications, 137, 3, 641-673
Year:
2008
Publisher:
Springer Verlag
ISSN:
0022-3239
Keywords:
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 Record created 2013-07-15, last modified 2018-09-13

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