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A strong correspondence principle for smooth, monotone environments

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  • Christensen, Finn
  • Cornwell, Christopher R.

Abstract

In discrete time dynamic systems that are locally monotone, we show that comparative statics are well-behaved at a regular equilibrium if and only if equilibrium is exponentially stable. We apply the result to show: (i) if excess demand satisfies the gross substitutes property then the competitive exchange equilibrium is stable iff intuitive comparative statics hold, (ii) the market demand curve for bandwagon (or network) goods slopes upwards only if equilibrium is unstable, and (iii) equilibria of supermodular games are stable iff they exhibit monotone comparative statics. We also provide a non-local version of the result for linear models, and apply the insights to the input–output model and network games with linear best replies and strategic complementarities.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:77:y:2018:i:c:p:15-24
    DOI: 10.1016/j.jmateco.2018.05.005
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    Cited by:

    1. Finn Christensen, 2023. "Comparative Statics for Difference-in-Differences," Working Papers 2023-08, Towson University, Department of Economics, revised Nov 2023.
    2. 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.
    3. 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.
    4. Christensen, Finn, 2022. "Streaming Stimulates the Live Concert Industry: Evidence from YouTube," International Journal of Industrial Organization, Elsevier, vol. 85(C).
    5. 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.
    6. Barthel, Anne-Christine & Hoffmann, Eric, 2022. "On dynamic adjustment and comparative statics via the implicit function theorem," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 52-57.

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    More about this item

    Keywords

    Correspondence principle; Stability; Comparative statics; Best response dynamics; Adaptive dynamics; M−matrix;
    All these keywords.

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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