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Do followers really matter in Stackelberg competition?

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  • Ludovic A. Julien
  • Olivier Musy
  • Aurélien W. Saïdi

Abstract

In this note, we consider a generalized T−stage Stackelberg oligopoly. We provide a proof and an interpretation that under the two necessary and sufficient conditions of linear aggregate demand and identical constant marginal costs, followers do not matter for leaders. Leaders act as rational myopic agents, voluntarily ignoring the number of followers and remaining stages, thereby behaving as Cournotian oligopolists. Strategies of incumbent firms are invariant to entry of new cohorts. Their profits can be studied by the way of two discount factors: the first impacting markup and the second impacting output supply. Some implications in terms of welfare and convergence toward competitive equilibrium are derived.

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File URL: http://economix.fr/pdf/dt/2011/WP_EcoX_2011-10.pdf
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Bibliographic Info

Paper provided by University of Paris West - Nanterre la Défense, EconomiX in its series EconomiX Working Papers with number 2011-10.

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Length: 17 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:drm:wpaper:2011-10

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Keywords: Leader’s markup discount factor; linear economy; follower’s output discount factor; myopic behavior;

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  1. John S. Heywood & Matthew McGinty, 2008. "Leading and Merging: Convex Costs, Stackelberg, and the Merger Paradox," Southern Economic Journal, Southern Economic Association, vol. 74(3), pages 879-893, January.
  2. Federico Etro, 2007. "Stackelberg competition with endogenous entry," Working Papers 121, University of Milano-Bicocca, Department of Economics, revised 2007.
  3. Richard Watt, 2002. "A Generalized Oligopoly Model," Metroeconomica, Wiley Blackwell, vol. 53(1), pages 46-55, 02.
  4. Ludovic Julien & Olivier Musy & Aurélien Saïdi, 2012. "On hierarchical competition in oligopoly," Journal of Economics, Springer, vol. 107(3), pages 217-237, November.
  5. Boyer, Marcel & Moreaux, Michel, 1986. "Perfect competition as the limit of a hierarchical market game," Economics Letters, Elsevier, vol. 22(2-3), pages 115-118.
  6. John S. Heywood & Matthew McGinty, 2007. "Mergers among leaders and mergers among followers," Economics Bulletin, AccessEcon, vol. 12(12), pages 1-7.
  7. Ludovic A. Julien & Olivier Musy, 2011. "A Generalized Oligopoly Model With Conjectural Variations," Metroeconomica, Wiley Blackwell, vol. 62(3), pages 411-433, 07.
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