Comparative Statics, Stability, and Uniqueness
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.
|Date of creation:||Apr 2014|
|Date of revision:||Mar 2015|
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- Micha Gisser & James E. McClure & Giray Ökten & Gary Santoni, 2008.
"Some Anomalies Arising from Bandwagons that Impart Upward-Sloping Segments to Market Demand,"
200804, Ball State University, Department of Economics, revised Dec 2008.
- 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.
- 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.
- U. Horst & Jose A. Scheinkman, 2010.
"Equilibria in Systems of Social Interactions,"
Levine's Working Paper Archive
506439000000000119, David K. Levine.
- Yann Bramoullé & Rachel Kranton & Martin D'Amours, 2010.
"Strategic Interaction and Networks,"
Cahiers de recherche
- Ed Hopkins & Tatiana Kornienko, 2004.
"Running to Keep in the Same Place: Consumer Choice as a Game of Status,"
ESE Discussion Papers
92, Edinburgh School of Economics, University of Edinburgh.
- 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.
- Finn Christensen & Juergen Jung, 2010.
"Global Social Interactions with Sequential Binary Decisions: The Case of Marriage, Divorce, and Stigma,"
2010-01, Towson University, Department of Economics, revised Jan 2010.
- 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.
- 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.
- Deb, Rahul, 2009. "A testable model of consumption with externalities," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1804-1816, July.
- 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.
- 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.
- Charles R. Plott & Jared Smith, 1999.
"Instability of Equilibria in Experimental Markets: Upward-Sloping Demands, Externalities, and Fad-Like Incentives,"
Southern Economic Journal,
Southern Economic Association, vol. 65(3), pages 405-426, January.
- 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.
- 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.
- Karp, Larry & Lee, In Ho & Mason, Robin, 2003. "A global game with strategic substitutes and complements," CUDARE Working Paper Series 940, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
- Karp, Larry & Lee, In Ho & Mason, Robin, 2003. "A global game with strategic substitutes and complements," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt09h2490x, Department of Agricultural & Resource Economics, UC Berkeley.
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