IDEAS home Printed from https://ideas.repec.org/p/tow/wpaper/2014-02.html
   My bibliography  Save this paper

Comparative Statics, Stability, and Uniqueness

Author

Listed:
  • Finn Christensen

    (Department of Economics, Towson University)

Abstract

Consider an economic model whose equilibrium can be represented as the fixed point of a system of differentiable equations. Using the theory of B-matrices, I show that comparative statics are well-behaved if the interactions between the equations are not too large, and the negative interactions are not too varied. When there are only positive interactions, for example when strategic complements prevail in a strategic setting, I prove a version of Samuleson's (1947) Correspondence Principle in that equilibrium is nondecreasing for any positive parameter shock if and only if equilibrium is exponentially stable under discrete time best reply dynamics . If there are only negative interactions, like when strategic substitutes prevail in a game theoretic context, I use the theory of inverse M-matrices to significantly relax Dixit's (1986) conditions under which comparative statics are well-behaved. For every comparative statics result I show that if the conditions apply globally then equilibrium is unique. Applications are provided to differentiated products Cournot oligopoly, market demand with interdependent preferences, and games on fixed networks.

Suggested Citation

  • Finn Christensen, 2014. "Comparative Statics, Stability, and Uniqueness," Working Papers 2014-02, Towson University, Department of Economics, revised Mar 2015.
    • Handle: RePEc:tow:wpaper:2014-02
    as

    Download full text from publisher

    File URL: http://webapps.towson.edu/cbe/economics/workingpapers/2014-02.pdf
    File Function: First version, 2014
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
    2. Karp, Larry & Lee, In Ho & Mason, Robin, 2007. "A global game with strategic substitutes and complements," Games and Economic Behavior, Elsevier, vol. 60(1), pages 155-175, July.
    3. Ed Hopkins & Tatiana Kornienko, 2004. "Running to Keep in the Same Place: Consumer Choice as a Game of Status," American Economic Review, American Economic Association, vol. 94(4), pages 1085-1107, September.
    4. Yann Bramoull? & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," American Economic Review, American Economic Association, vol. 104(3), pages 898-930, March.
    5. Deb, Rahul, 2009. "A testable model of consumption with externalities," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1804-1816, July.
    6. Christensen Finn & Jung Juergen, 2010. "Global Social Interactions with Sequential Binary Decisions: The Case of Marriage, Divorce, and Stigma," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-37, October.
    7. Postlewaite, Andrew, 1998. "The social basis of interdependent preferences," European Economic Review, Elsevier, vol. 42(3-5), pages 779-800, May.
    8. Guoqiang Tian & Liyan Yang, 2009. "Theory of negative consumption externalities with applications to the economics of happiness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 399-424, June.
    9. Micha Gisser & James E. McClure & Giray Okten & Gary Santoni, 2009. "Some Anomalies Arising from Bandwagons that Impart Upward Sloping Segments to Market Demand," Econ Journal Watch, Econ Journal Watch, vol. 6(1), pages 21-34, January.
    10. Gary S. Becker & Kevin M. Murphy & Ivan Werning, 2005. "The Equilibrium Distribution of Income and the Market for Status," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 282-310, April.
    11. Jeffrey Rohlfs, 1974. "A Theory of Interdependent Demand for a Communications Service," Bell Journal of Economics, The RAND Corporation, vol. 5(1), pages 16-37, Spring.
    12. Oskar Morgenstern, 1948. "Demand Theory Reconsidered," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 62(2), pages 165-201.
    13. H. Leibenstein, 1950. "Bandwagon, Snob, and Veblen Effects in the Theory of Consumers' Demand," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 64(2), pages 183-207.
    14. Charles R. Plott & Jared Smith, 1999. "Instability of Equilibria in Experimental Markets: Upward-Sloping Demands, Externalities, and Fad-Like Incentives," Southern Economic Journal, John Wiley & Sons, vol. 65(3), pages 405-426, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gamannossi degl’Innocenti, Duccio & Rablen, Matthew D., 2020. "Tax evasion on a social network," Journal of Economic Behavior & Organization, Elsevier, vol. 169(C), pages 79-91.
    2. Ed Hopkins, 2008. "Inequality, happiness and relative concerns: What actually is their relationship?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(4), pages 351-372, December.
    3. König, Tobias & Lausen, Tobias, 2016. "Relative consumption preferences and public provision of private goods," Discussion Papers, Research Unit: Market Behavior SP II 2016-213, WZB Berlin Social Science Center.
    4. Mazali, Rogério & Rodrigues-Neto, José A., 2013. "Dress to impress: Brands as status symbols," Games and Economic Behavior, Elsevier, vol. 82(C), pages 103-131.
    5. Kölln, Volker, 2011. "Produktdiffusion in TIMES-Märkten: Innovation, Kompatibilität und Timing bei Netzeffektgütern," Discussion Papers on Strategy and Innovation 11-01, Philipps-University Marburg, Department of Technology and Innovation Management (TIM).
    6. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115(2), pages 338-363.
    7. Mariano Rojas, 2012. "Do People in Income Poverty Use Their Income Efficiently?: a Subjective Well-Being Approach," WIDER Working Paper Series wp-2012-110, World Institute for Development Economic Research (UNU-WIDER).
    8. Ed Hopkins & Tatiana Kornienko, 2010. "Which Inequality? The Inequality of Endowments versus the Inequality of Rewards," American Economic Journal: Microeconomics, American Economic Association, vol. 2(3), pages 106-137, August.
    9. Bilancini, Ennio & Boncinelli, Leonardo, 2012. "Redistribution and the notion of social status," Journal of Public Economics, Elsevier, vol. 96(9-10), pages 651-657.
    10. Perez Truglia, Ricardo Nicolas, 2007. "Conspicuous consumption in the land of Prince Charming," MPRA Paper 22009, University Library of Munich, Germany, revised 22 Mar 2010.
    11. Chenavaz, Régis Y. & Eynan, Amit, 2021. "Advertising, goodwill, and the Veblen effect," European Journal of Operational Research, Elsevier, vol. 289(2), pages 676-682.
    12. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    13. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2012. "Entanglement between Demand and Supply in Markets with Bandwagon Goods," Papers 1209.1321, arXiv.org, revised Dec 2012.
    14. Ramalingam, Abhijit, 2009. ""Endogenous" Relative Concerns: The Impact of Workers' Characteristics on Status and Pro ts in the Firm," MPRA Paper 18759, University Library of Munich, Germany.
    15. Denis Phan, 2006. "Discrete Choices under Social Influence:Generic Properties," Post-Print halshs-00105857, HAL.
    16. Pradeep Dubey & John Geanakoplos, 2014. "Games with Money and Status: How Best to Incentivize Work," Cowles Foundation Discussion Papers 1954, Cowles Foundation for Research in Economics, Yale University.
    17. Banuri, Sheheryar & Nguyen, Ha, 2023. "Borrowing to keep up (with the Joneses): Inequality, debt, and conspicuous consumption," Journal of Economic Behavior & Organization, Elsevier, vol. 206(C), pages 222-242.
    18. Douch, Mohamed & Bouaddi, Mohammed, 2010. "EQUITY Premium Puzzle in a Data-Rich Environment," MPRA Paper 29440, University Library of Munich, Germany.
    19. Deb, Rahul, 2009. "A testable model of consumption with externalities," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1804-1816, July.
    20. Bilancini, Ennio & Boncinelli, Leonardo, 2014. "Instrumental cardinal concerns for social status in two-sided matching with non-transferable utility," European Economic Review, Elsevier, vol. 67(C), pages 174-189.

    More about this item

    Keywords

    Correspondence principle; interdependent preferences; oligopoly; networks; M-matrices; inverse M-matrices; B-matrices; P-matrices; global univalence.;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tow:wpaper:2014-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Juergen Jung (email available below). General contact details of provider: https://edirc.repec.org/data/detowus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.