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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
    DOI: 10.2202/1935-1704.1634
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Renato Soeiro & Alberto A. Pinto, 2023. "Negative network effects and asymmetric pure price equilibria," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 22(1), pages 99-124, January.
    3. 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.
    4. Bos, Iwan & Vermeulen, Dries, 2021. "On pure-strategy Nash equilibria in price–quantity games," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    5. 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.
    6. 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.
    7. Matsumura, Toshihiro, 2012. "Welfare consequence of an asymmetric regulation in a mixed Bertrand duopoly," Economics Letters, Elsevier, vol. 115(1), pages 94-96.
    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. Marie-Laure Cabon-Dhersin & Jonas Didisse, 2017. "Inter-university competition and high tuition fees," Post-Print hal-02356872, HAL.
    10. 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.
    11. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "A general model of price competition with soft capacity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 95-120, July.
    12. 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.
    13. R. R. Routledge & R. A. Edwards, 2020. "Ambiguity and price competition," Theory and Decision, Springer, vol. 88(2), pages 231-256, March.
    14. Robert Routledge, 2010. "On the Bertrand core and equilibrium of a market," Economics Discussion Paper Series 1017, Economics, The University of Manchester.
    15. R. A. Edwards & R. R. Routledge, 2023. "Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 569-586, June.
    16. Dastidar, Krishnendu Ghosh, 2011. "Bertrand equilibrium with subadditive costs," Economics Letters, Elsevier, vol. 112(2), pages 202-204, August.

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