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Monotone Comparative Statics: Geometric Approach

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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.

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Authors and Affiliations

  1. Nuffield College, Oxford University, Oxford, UK

    B. H. Strulovici

  2. Department of Management Science and Engineering, 442 Terman Engineering Center, Stanford University, Stanford, CA, 94305-4026, USA

    T. A. Weber

Authors
  1. B. H. Strulovici
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  2. T. A. Weber
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Corresponding author

Correspondence to T. A. Weber.

Additional information

Communicated by D.G. Luenberger.

We are grateful to Kenneth Arrow, Darrell Duffie, David Luenberger, Paul Milgrom, John Quah, and Pete Veinott for helpful comments.

Research in part supported by a David Morgenthaler II Faculty Scholar Award.

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Strulovici, B.H., Weber, T.A. Monotone Comparative Statics: Geometric Approach. J Optim Theory Appl 137, 641–673 (2008). https://doi.org/10.1007/s10957-007-9339-1

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