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Monotone Comparative Statics: Geometric Approach

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  • B. H. Strulovici

    (Oxford University)

  • T. A. Weber

    (Stanford University)

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.

Suggested Citation

  • B. H. Strulovici & T. A. Weber, 2008. "Monotone Comparative Statics: Geometric Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 641-673, June.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-007-9339-1
    DOI: 10.1007/s10957-007-9339-1
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    References listed on IDEAS

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    1. Matthews, Steven & Moore, John, 1987. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Econometrica, Econometric Society, vol. 55(2), pages 441-467, March.
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    Cited by:

    1. Weber, Thomas A. & Neuhoff, Karsten, 2010. "Carbon markets and technological innovation," Journal of Environmental Economics and Management, Elsevier, vol. 60(2), pages 115-132, September.
    2. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    3. Thomas Weber, 2010. "Simple methods for evaluating and comparing binary experiments," Theory and Decision, Springer, vol. 69(2), pages 257-288, August.
    4. Bruno Strulovici & Thomas Weber, 2010. "Generalized monotonicity analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 377-406, June.

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