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Bertrand Competition in Markets with Fixed Costs

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  • Saporiti Alejandro

    () (University of Manchester)

  • Coloma Germán

    () (Universidad del CEMA)

Abstract

This paper provides necessary and sufficient conditions for the existence of a pure strategy Bertrand equilibrium in a model of price competition with fixed costs. It unveils an interesting and unexplored relationship between Bertrand competition and natural monopoly. That relationship points out that the non-subadditivity of the cost function at the output level corresponding to the oligopoly break-even price, denoted by D(pL(n)), is sufficient to guarantee that the market sustains a (not necessarily symmetric) Bertrand equilibrium in pure strategies with two or more firms supplying at least D(pL(n)). Conversely, the existence of a pure strategy equilibrium ensures that the cost function is not subadditive at every output greater than or equal to D(pL(n)).

Suggested Citation

  • Saporiti Alejandro & Coloma Germán, 2010. "Bertrand Competition in Markets with Fixed Costs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-30, June.
  • Handle: RePEc:bpj:bejtec:v:10:y:2010:i:1:n:27
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    References listed on IDEAS

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    1. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
    2. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 573-585, June.
    3. Grossman, Sanford J, 1981. "Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs," Econometrica, Econometric Society, vol. 49(5), pages 1149-1172, September.
    4. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
    5. Hoernig, Steffen H., 2002. "Mixed Bertrand equilibria under decreasing returns to scale: an embarrassment of riches," Economics Letters, Elsevier, vol. 74(3), pages 359-362, February.
    6. Novshek, William & Chowdhury, Prabal Roy, 2003. "Bertrand equilibria with entry: limit results," International Journal of Industrial Organization, Elsevier, vol. 21(6), pages 795-808, June.
    7. Panzar, John C., 1989. "Technological determinants of firm and industry structure," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 1, pages 3-59, Elsevier.
    8. Marquez, Robert, 1997. "A note on Bertrand competition with asymmetric fixed costs," Economics Letters, Elsevier, vol. 57(1), pages 87-96, November.
    9. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
    10. Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
    11. Harrington, Joseph Jr., 1989. "A re-evaluation of perfect competition as the solution to the Bertrand price game," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 315-328, June.
    12. Prabal Roy Chowdhury, 2002. "Limit-pricing as Bertrand equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 811-822.
    13. Todd R. Kaplan & David Wettstein, 2000. "The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition," Spanish Economic Review, Springer;Spanish Economic Association, vol. 2(1), pages 65-71.
    14. Telser, Lester G, 1991. "Industry Total Cost Functions and the Status of the Core," Journal of Industrial Economics, Wiley Blackwell, vol. 39(3), pages 225-240, March.
    15. Abbink, Klaus & Brandts, Jordi, 2008. "24. Pricing in Bertrand competition with increasing marginal costs," Games and Economic Behavior, Elsevier, vol. 63(1), pages 1-31, May.
    16. Baumol, William J, 1977. "On the Proper Cost Tests for Natural Monopoly in a Multiproduct Industry," American Economic Review, American Economic Association, vol. 67(5), pages 809-822, December.
    17. 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.
    18. Sharkey, William W. & Sibley, David S., 1993. "A Bertrand model of pricing and entry," Economics Letters, Elsevier, vol. 41(2), pages 199-206.
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    Citations

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    Cited by:

    1. Matsumura, Toshihiro, 2012. "Welfare consequence of an asymmetric regulation in a mixed Bertrand duopoly," Economics Letters, Elsevier, vol. 115(1), pages 94-96.
    2. Cabon-Dhersin Marie-Laure & Drouhin Nicolas, 2017. "A general model of price competition with soft capacity constraints," Working Papers 2017-56, Center for Research in Economics and Statistics.
    3. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2014. "Tacit Collusion in a One-Shot Game of Price Competition with Soft Capacity Constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00974270, HAL.
    4. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2012. "Tacit collusion in a one-shot game of price competition with soft capacity constraints," Working Papers hal-00709093, HAL.
    5. R. R. Routledge, 2017. "Information, ambiguity and price equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 199-214, October.
    6. Robert Routledge, 2010. "On the Bertrand core and equilibrium of a market," The School of Economics Discussion Paper Series 1017, Economics, The University of Manchester.
    7. Cabon-Dhersin Marie-Laure & Drouhin Nicolas, 2017. "A general model of price competition with soft capacity constraints," Working Papers 2017-56, Center for Research in Economics and Statistics.
    8. Delbono, Flavio & Lambertini, Luca, 2016. "Ranking Bertrand, Cournot and supply function equilibria in oligopoly," Energy Economics, Elsevier, vol. 60(C), pages 73-78.
    9. Germán Coloma, 2010. "El número óptimo de empresas bajo competencia de Bertrand," Estudios de Economia, University of Chile, Department of Economics, vol. 37(2 Year 20), pages 189-205, December.
    10. R. R. Routledge, 2013. "On the existence of coalition-proof Bertrand equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 21-31, May.
    11. Marie-Laure Cabon-Dhersin & Jonas Didisse, 2017. "Inter-university competition and high tuition fees," Working Papers halshs-01174291, HAL.
    12. Flavio Delbono & Luca Lambertini, 2016. "Bertrand versus Cournot with convex variable costs," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 73-83, April.
    13. Dastidar, Krishnendu Ghosh, 2011. "Bertrand equilibrium with subadditive costs," Economics Letters, Elsevier, vol. 112(2), pages 202-204, August.
    14. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2014. "Tacit Collusion in a One-Shot Game of Price Competition with Soft Capacity Constraints," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(2), pages 427-442, June.
    15. Makoto Yano & Takashi Komatsubara, 2018. "Price competition or price leadership," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 1023-1057, December.

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