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Comparative statics and heterogeneity

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  • Finn Christensen

    (Towson University)

Abstract

This paper elucidates the role played by the heterogeneity of interactions between the endogenous variables of a model in determining the model’s behavior. It is known that comparative statics are well-behaved if these interactions are relatively small, but the formal condition imposed on the Jacobian which typically captures this idea–diagonal dominance–ignores the distribution of the interaction terms. I provide a new condition on the Jacobian—mean positive dominance—which better captures a trade-off between the size and heterogeneity of interaction terms. In accord with Samuelson’s (Foundations of economic analysis, Oxford University Press, London, 1947) correspondence principle, I also show that mean positive dominance yields stability and uniqueness results. I apply the results to provide new, or to generalize known, comparative statics results in the following settings: optimization problems, platform monopoly, normality, differentiable games including Cournot oligopoly, and competitive exchange economies.

Suggested Citation

  • Finn Christensen, 2019. "Comparative statics and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 665-702, April.
  • Handle: RePEc:spr:joecth:v:67:y:2019:i:3:d:10.1007_s00199-018-1116-x
    DOI: 10.1007/s00199-018-1116-x
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    Cited by:

    1. Christensen, Finn, 2017. "A necessary and sufficient condition for a unique maximum with an application to potential games," Economics Letters, Elsevier, vol. 161(C), pages 120-123.
    2. Christensen, Finn & Cornwell, Christopher R., 2018. "A strong correspondence principle for smooth, monotone environments," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 15-24.
    3. Luis C. Corchón, 2021. "Aggregative games," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 49-71, March.
    4. Rabah Amir, 2019. "Supermodularity and Complementarity in Economic Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 487-496, April.

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    More about this item

    Keywords

    Comparative statics; Mean positive dominance; B-matrix; Correspondence principle; Cournot oligopoly; Normal goods;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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