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A Comment on: “Monotone Comparative Statics”

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  • Rabah Amir
  • David Rietzke

Abstract

Milgrom and Shannon (1994) provide necessary and sufficient conditions on parameterized optimization problems for their solution sets to be globally monotone in the parameter. We establish that their conditions may be significantly relaxed when focusing on discrete, binary comparisons between solution sets. Such binary comparisons are ubiquitous in economics and may involve comparing the same decision maker across two distinct regimes or two distinct decision makers with related objectives (e.g., a monopolist firm versus a social planner). While the single‐crossing property remains prominent in the theory, quasisupermodularity of the objective functions of interest is not needed. Our approach relies upon a novel method of embedding a new optimization problem with a quasisupermodular objective function “between” the two original problems of interest. In smooth problems, sufficient conditions for our new assumptions may be verified by elementary differential comparisons, making them well suited for applied work. We illustrate the relevance of this novel approach with several economic applications.

Suggested Citation

  • Rabah Amir & David Rietzke, 2025. "A Comment on: “Monotone Comparative Statics”," Econometrica, Econometric Society, vol. 93(4), pages 1481-1490, July.
    • Handle: RePEc:wly:emetrp:v:93:y:2025:i:4:p:1481-1490
    DOI: 10.3982/ECTA23292
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    References listed on IDEAS

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    1. Amir, R., 1996. "Cournot oligopoly and theory of supermodular games," LIDAM Reprints CORE 1228, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    3. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    4. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    5. Fischer, Carolyn & Newell, Richard G., 2008. "Environmental and technology policies for climate mitigation," Journal of Environmental Economics and Management, Elsevier, vol. 55(2), pages 142-162, March.
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    Cited by:

    1. Wei He & Yeneng Sun & Hanping Xu, 2025. "Monotone Perfection," Papers 2509.01358, arXiv.org, revised Oct 2025.

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