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Directional Monotone Comparative Statics

Author

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  • Anne-Christine Barthel

    (Department of Economics, The University of Kansas)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

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. This paper characterizes monotone comparative statics in different directions in finite-dimensional Euclidean space. These new characterizations are ordinal and retain the same flavor as their counterparts in the standard theory, showing new connections to the standard theory. The results are highlighted by several applications in consumer theory, producer theory and game theory. These applications were previously outside the scope of the standard theory of monotone comparative statics.

Suggested Citation

  • Anne-Christine Barthel & Tarun Sabarwal, 2016. "Directional Monotone Comparative Statics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201601, University of Kansas, Department of Economics.
    • Handle: RePEc:kan:wpaper:201601
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    File URL: http://www2.ku.edu/~kuwpaper/2016Papers/201601.pdf
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    Cited by:

    1. Bar Light, 2021. "Stochastic Comparative Statics in Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 797-810, May.
    2. Alexandrov, Alexei & Bedre-Defolie, Özlem, 2017. "LeChatelier–Samuelson principle in games and pass-through of shocks," Journal of Economic Theory, Elsevier, vol. 168(C), pages 44-54.
    3. Rabah Amir & Igor Evstigneev & Adriana Gama, 2021. "Oligopoly with network effects: firm-specific versus single network," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1203-1230, April.
    4. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    5. Rabah Amir, 2018. "Special issue: supermodularity and monotone methods in economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 547-556, October.
    6. 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.
    7. Tarun Sabarwal, 2023. "Universal Theory of Equilibrium in Models with Complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202312, University of Kansas, Department of Economics, revised Nov 2023.
    8. Koch, Caleb M., 2019. "Index-wise comparative statics," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 35-41.
    9. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    monotone comparative statics; directional single-crossing property; directional set order;
    All these keywords.

    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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