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Comparative Statics, Stability, and Uniqueness

  • Finn Christensen


    (Department of Economics, Towson University)

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.

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Paper provided by Towson University, Department of Economics in its series Working Papers with number 2014-02.

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Length: 44 pages
Date of creation: Apr 2014
Date of revision: Mar 2015
Handle: RePEc:tow:wpaper:2014-02
Contact details of provider: Postal: Towson, Maryland 21252-0001
Phone: 410-704-2959
Fax: 410-704-3424
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  1. 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.
  2. Plott, Charles R. & Smith, Jared, 1992. "Instability of Equilibria in Experimental Markets: Upward-Sloping Demands, Externalities, and Fad-Like Incentives," Working Papers 816, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Yann Bramoullé & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," Post-Print halshs-00978692, HAL.
  4. Andrew Postlewaite, . ""The Social Basis of Interdependent Preferences''," CARESS Working Papres 97-14, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  5. U. Horst & Jose A. Scheinkman, 2010. "Equilibria in Systems of Social Interactions," Levine's Working Paper Archive 506439000000000119, David K. Levine.
  6. Deb, Rahul, 2009. "A testable model of consumption with externalities," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1804-1816, July.
  7. Finn Christensen & Juergen Jung, 2010. "Global Social Interactions with Sequential Binary Decisions: The Case of Marriage, Divorce, and Stigma," Working Papers 2010-01, Towson University, Department of Economics, revised Jan 2010.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Yann Bramoullé & Rachel Kranton & Martin D'Amours, 2010. "Strategic Interaction and Networks," Cahiers de recherche 1018, CIRPEE.
  13. Guoqiang Tian & Liyan Yang, 2009. "Theory of negative consumption externalities with applications to the economics of happiness," Economic Theory, Springer, vol. 39(3), pages 399-424, June.
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