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Quantitative Comparative Statics for a Multimarket Paradox

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  • Tobias Harks
  • Philipp von Falkenhausen
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    Abstract

    Comparative statics is a well established research field where one analyzes how marginal changes in parameters of a strategic game affect the resulting equilibria. While classic comparative statics is mainly concerned with qualitative approaches (e.g., deciding whether a parameter change improves or hurts equilibrium profits or welfare), we provide a framework to expose the extend (not monotonicity) of a discrete (not marginal) parameter change, with the additional benefit that our results can even be used when there is uncertainty about the exact model instance. We apply our quantitative approach to the multimarket oligopoly model introduced by Bulow, Geanakoplos and Klemperer (1985). They describe the counterintuitive example of a positive price shock in the firm's monopoly market resulting in a reduction of the firm's equilibrium profit. We quantify for the first time the worst case profit reduction for multimarket oligopolies with an arbitrary number of markets exhibiting arbitrary positive price shocks. For markets with affine price functions and firms with convex cost technologies, we show that the relative loss of any firm is at most 25% no matter how many firms compete in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on consumer surplus. We find tight bounds also for these measures showing that total profit and consumer surplus decreases by at most 25% and 16.6%, respectively.

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    File URL: http://arxiv.org/pdf/1307.5617
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1307.5617.

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    Date of creation: Jul 2013
    Date of revision: Dec 2013
    Handle: RePEc:arx:papers:1307.5617

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    1. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
    2. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    3. Jonathan Eaton & Gene M. Grossman, 1983. "Optimal Trade and Industrial Policy Under Oligopoly," NBER Working Papers 1236, National Bureau of Economic Research, Inc.
    4. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    5. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    6. Brander, James A. & Spencer, Barbara J., 1985. "Export subsidies and international market share rivalry," Journal of International Economics, Elsevier, vol. 18(1-2), pages 83-100, February.
    7. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-22, February.
    8. Gaudet, Gerard & Salant, Stephen W, 1991. "Increasing the Profits of a Subset of Firms in Oligopoly Models with Strategic Substitutes," American Economic Review, American Economic Association, vol. 81(3), pages 658-65, June.
    9. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    10. Fevrier, Philippe & Linnemer, Laurent, 2004. "Idiosyncratic shocks in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 835-848, June.
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