IDEAS home Printed from https://ideas.repec.org/p/roc/rocher/549.html
   My bibliography  Save this paper

Bertrand's price competition in markets with fixed costs

Author

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 supports 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(p(n)).

Suggested Citation

  • Alejandro Saporiti & German Coloma, 2009. "Bertrand's price competition in markets with fixed costs," RCER Working Papers 549, University of Rochester - Center for Economic Research (RCER).
    • Handle: RePEc:roc:rocher:549
    as

    Download full text from publisher

    File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_549.pdf
    File Function: full text
    Download Restriction: None
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. John Morgan & Michael R. Baye, 2002. "Winner-take-all price competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(2), pages 271-282.
    8. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
    9. 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.
    10. 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.
    11. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
    12. 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.
    13. Makoto Yano, 2006. "A price competition game under free entry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 395-414, October.
    14. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
    15. Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
    16. 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.
    17. 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.
    18. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, April.
    19. 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.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sai Bravo & Carole Haritchabalet, 2021. "Certification of low-carbon hydrogen in the transport market," Working Papers hal-03371277, HAL.
    2. Matthew Andrews & Milan Bradonjic & Iraj Saniee, 2017. "Quantifying the Benefits of Infrastructure Sharing," Papers 1706.05735, arXiv.org.
    3. Robert R. Routledge, 2009. "Testable implications of the Bertrand model," Economics Discussion Paper Series 0918, Economics, The University of Manchester.
    4. Sai Bravo & Carole Haritchabalet, 2021. "Certification of low-carbon hydrogen in the transport market," Working papers of Transitions Energétiques et Environnementales (TREE) hal-03371277, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Steffen Hoernig, 2005. "Bertrand equilibria and sharing rules," Nova SBE Working Paper Series wp468, Universidade Nova de Lisboa, Nova School of Business and Economics.
    5. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2021. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Working Papers halshs-03378500, HAL.
    6. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2010. "The end of the Bertrand Paradox?," Post-Print halshs-00542486, HAL.
    7. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2022. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Post-Print halshs-03378500, HAL.
    8. 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.
    9. Roy Chowdhury, Prabal, 2009. "Free Entry Bertrand Competition," MPRA Paper 17837, University Library of Munich, Germany.
    10. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium with a large number of firms," Discussion Papers 04-12, Indian Statistical Institute, Delhi.
    11. Marie‐Laure Cabon‐Dhersin & Nicolas Drouhin, 2023. "Chamberlin without differentiation: Soft capacity constrained price competition with free entry," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(1), pages 118-126, March.
    12. Germán Coloma & Alejandro Saporiti, 2006. "Bertrand equilibria in markets with fixed costs," Economics Discussion Paper Series 0627, Economics, The University of Manchester.
    13. R. R. Routledge & R. A. Edwards, 2020. "Ambiguity and price competition," Theory and Decision, Springer, vol. 88(2), pages 231-256, March.
    14. 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.
    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. repec:ebl:ecbull:v:12:y:2008:i:29:p:1-8 is not listed on IDEAS
    17. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium: Manipulable residual demand," Discussion Papers 04-15, Indian Statistical Institute, Delhi.
    18. Massimo A. De Francesco, 2008. "Existence of pure strategy equilibrium in Bertrand-Edgeworth games with imperfect divisibility of money," Economics Bulletin, AccessEcon, vol. 12(29), pages 1-8.
    19. Matsumura, Toshihiro, 2012. "Welfare consequence of an asymmetric regulation in a mixed Bertrand duopoly," Economics Letters, Elsevier, vol. 115(1), pages 94-96.
    20. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen, 2010. "Robustness to strategic uncertainty in price competition," SSE/EFI Working Paper Series in Economics and Finance 0726, Stockholm School of Economics, revised 08 Apr 2010.
    21. Robert R. Routledge, 2009. "On the existence of Bayesian Bertrand equilibrium," Economics Discussion Paper Series 0917, Economics, The University of Manchester.

    More about this item

    Keywords

    Bertrand competition; cost subadditivity; fixed costs; natural monopoly.;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:roc:rocher:549. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard DiSalvo (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.