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Directional monotone comparative statics

Author

Listed:
  • Anne-Christine Barthel

    () (West Texas A & M University)

  • Tarun Sabarwal

    () (University of Kansas)

Abstract

Abstract Many questions of interest in economics can be stated in terms of monotone comparative statics: If a parameter of a constrained optimization problem increases, when does its solution increase as well. We characterize monotone comparative statics in different directions in finite-dimensional Euclidean space by extending the monotonicity theorem of Milgrom and Shannon (Econometrica 62(1):157–180, 1994) to constraint sets ordered in Quah (Econometrica 75(2):401–431, 2007)’s set order. Our characterizations are ordinal and retain the same flavor as their counterparts in the standard theory, showing new connections to the standard theory and presenting new results. The results are highlighted with several applications (in consumer theory, producer theory, and game theory) which were previously outside the scope of the standard theory of monotone comparative statics.

Suggested Citation

  • Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
  • Handle: RePEc:spr:joecth:v:66:y:2018:i:3:d:10.1007_s00199-017-1079-3
    DOI: 10.1007/s00199-017-1079-3
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Alexei Alexandrov & Özlem Bedre-Defolie, 2015. "LeChatelier-Samuelson principle in games and pass-through of shocks," ESMT Research Working Papers ESMT-15-03, ESMT European School of Management and Technology, revised 01 Mar 2016.
    2. repec:spr:joecth:v:66:y:2018:i:3:d:10.1007_s00199-018-1153-5 is not listed on IDEAS
    3. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org.

    More about this item

    Keywords

    Monotone comparative statics; i-Directional single crossing property; i-Directional set order; Quasisupermodular function;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D00 - Microeconomics - - General - - - General

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