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Equilibrium vertical differentiation in a Bertrand model with capacity precommitment


  • BOCCARD, Nicolas
  • WAUTHY, Xavier Y.


Both quality differentiation and capacity commitment have been shown to relax price competition. However, their joint influence on the outcome of price competition has not yet been assessed. In this article, we consider a three-stage game in which firms choose quality, then commit to capacity and, finally, compete in price. When the cost of quality is negligible, we show that firms do not differentiate their products in a subgame perfect equilibrium, in other words, capacity precommitment completely eliminates the incentive to differentiate by quality.
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  • BOCCARD, Nicolas & WAUTHY, Xavier Y., 2010. "Equilibrium vertical differentiation in a Bertrand model with capacity precommitment," CORE Discussion Papers RP 2246, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:2246 Note: In : International Journal of Industrial Organization, 28(3), 288-297, 2010

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    References listed on IDEAS

    1. Lambson Val Eugene, 1994. "Some Results on Optimal Penal Codes in Asymmetric Bertrand Supergames," Journal of Economic Theory, Elsevier, vol. 62(2), pages 444-468, April.
    2. Jean-Pierre Benoit & Vijay Krishna, 1987. "Dynamic Duopoly: Prices and Quantities," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 23-35.
    3. Dastidar, Krishnendu Ghosh, 1997. "Comparing Cournot and Bertrand in a Homogeneous Product Market," Journal of Economic Theory, Elsevier, vol. 75(1), pages 205-212, July.
    4. Davidson, Carl & Deneckere, Raymond J, 1990. "Excess Capacity and Collusion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 521-541, August.
    5. Stefan Lutz, 1997. "Vertical product differentiation and entry deterrence," Journal of Economics, Springer, vol. 65(1), pages 79-102, February.
    6. Motta, Massimo, 1993. "Endogenous Quality Choice: Price vs. Quantity Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 41(2), pages 113-131, June.
    7. Irmen, Andreas & Thisse, Jacques-Francois, 1998. "Competition in Multi-characteristics Spaces: Hotelling Was Almost Right," Journal of Economic Theory, Elsevier, vol. 78(1), pages 76-102, January.
    8. 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.
    9. Avner Shaked & John Sutton, 1982. "Relaxing Price Competition Through Product Differentiation," Review of Economic Studies, Oxford University Press, vol. 49(1), pages 3-13.
    10. Raymond J. Deneckere & Dan Kovenock, 1992. "Price Leadership," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 143-162.
      • Raymond Deneckere & Dan Kovenock, 1988. "Price Leadership," Discussion Papers 773, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    12. de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-781, July.
    13. Economides, Nicholas, 1989. "Quality variations and maximal variety differentiation," Regional Science and Urban Economics, Elsevier, vol. 19(1), pages 21-29, February.
    14. Kuhn, Kai-Uwe, 1994. "Labour Contracts, Product Market Oligopoly, and Involuntary Unemployment," Oxford Economic Papers, Oxford University Press, vol. 46(3), pages 366-384, July.
    15. Dixit, Avinash, 1980. "The Role of Investment in Entry-Deterrence," Economic Journal, Royal Economic Society, vol. 90(357), pages 95-106, March.
    16. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
    17. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    18. William A. Brock & José A. Scheinkman, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 371-382.
    19. Vives, Xavier, 1989. "Cournot and the oligopoly problem," European Economic Review, Elsevier, vol. 33(2-3), pages 503-514, March.
    20. Maggi, Giovanni, 1996. "Strategic Trade Policies with Endogenous Mode of Competition," American Economic Review, American Economic Association, vol. 86(1), pages 237-258, March.
    21. Simon P. Anderson & André De Palma, 1988. "Spatial Price Discrimination with Heterogeneous Products," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 573-592.
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    Cited by:

    1. Makoto Yano & Takashi Komatsubara, 2012. "Price Competition or Tacit Collusion," KIER Working Papers 807, Kyoto University, Institute of Economic Research.
    2. James A. Brander & Barbara J. Spencer, 2015. "Endogenous Horizontal Product Differentiation under Bertrand and Cournot Competition: Revisiting the Bertrand Paradox," NBER Working Papers 20966, National Bureau of Economic Research, Inc.
    3. Xavier Y Wauthy, 2010. "Market coverage and the nature of product differentiation: a note," Economics Bulletin, AccessEcon, vol. 30(2), pages 1129-1136.
    4. Emanuele Bacchiega & Antonio Minniti, 2015. "Training and Product Quality in Unionized Oligopolies," Economica, London School of Economics and Political Science, vol. 82, pages 1261-1301, December.
    5. repec:eee:ecolet:v:156:y:2017:i:c:p:88-91 is not listed on IDEAS
    6. WAUTHY, Xavier Y., 2014. "From Bertrand to Cournot via Kreps and Scheinkman: a hazardous journey," CORE Discussion Papers 2014026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. repec:kap:jincot:v:18:y:2018:i:1:d:10.1007_s10842-017-0253-4 is not listed on IDEAS
    8. Boccard, Nicolas & Wauthy, Xavier, 2003. "Sales Restriction, Quality Selection and the Mode of Competition," Working Papers of the Department of Economics, University of Girona 5, Department of Economics, University of Girona.
    9. Li, Youping, 2014. "Price leadership in a vertically differentiated market," Economic Modelling, Elsevier, vol. 38(C), pages 67-70.
    10. repec:eee:transa:v:100:y:2017:i:c:p:1-15 is not listed on IDEAS
    11. Ibrahima BARRY & Olivier BONROY & Paolo G. GARELLA, 2014. "Labelling by a for-Profit Certifier," Departmental Working Papers 2014-07, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano, revised 27 Feb 2016.
    12. Aigner, Rafael & Weber, Katharina, 2017. "The Fehmarn Belt duopoly – Can the ferry compete with a tunnel?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 100(C), pages 1-15.

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