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Merger Incentives and Inverse Matrices from Bertrand Competition

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  • Eric Howe
  • Jingang Zhao

Abstract

This paper first inverts a general class of matrices for solving Bertrand equilibria from arbitrary coalition structures in linear Bertand oligopolies. It then studies merger incentives and obtains two main results; 1) for any asymmetric costs, mergers of any size are profitable; 2) a merger will reduce outsiders' profits when there are large cost savings or cost asymmetry. The second result is in sharp constrast to Cournot competition where mergers always increase outsiders' profits. This striking new feature not only supports the belief that Bertrand competition is more general than Cournot competition, but will also open up a new line of arguments in future attempts to block merger proposals

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 586.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:586

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Keywords: Bertrand Equilibrium; Coalition Structure; Inverse Matrix; Merger Incentives;

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References

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  1. Farrell, J. & Shapiro, C., 1988. "Horizontal Mergers: An Equilibrium Analysis," Papers 17, Princeton, Woodrow Wilson School - Discussion Paper.
  2. Shapiro, Carl, 1989. "Theories of oligopoly behavior," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 6, pages 329-414 Elsevier.
  3. 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.
  4. Amir, Rabah & Jin, Jim Y., 2001. "Cournot and Bertrand equilibria compared: substitutability, complementarity and concavity," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 303-317, March.
  5. Jingang Zhao, 1990. "The Hybrid Solutions of an n-Person Game," Cowles Foundation Discussion Papers 956, Cowles Foundation for Research in Economics, Yale University.
  6. Zhao, Jingang, 1991. "The Equilibria of a Multiple Object Game," International Journal of Game Theory, Springer, vol. 20(2), pages 171-82.
  7. Salant, Stephen W & Switzer, Sheldon & Reynolds, Robert J, 1983. "Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 98(2), pages 185-99, May.
  8. Beth Allen, 2000. "The Future of Microeconomic Theory," Journal of Economic Perspectives, American Economic Association, vol. 14(1), pages 143-150, Winter.
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Cited by:
  1. Wang, X. Henry & Zhao, Jingang, 2007. "Welfare reductions from small cost reductions in differentiated oligopoly," International Journal of Industrial Organization, Elsevier, vol. 25(1), pages 173-185, February.

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