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Bertrand's price competition in markets with fixed costs

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)).

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_549.pdf
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Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 549.

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Length: 29 pages
Date of creation: May 2009
Handle: RePEc:roc:rocher:549
Contact details of provider: Postal:
University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

Keywords: Bertrand competition; cost subadditivity; fixed costs; natural monopoly.;

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Find related papers by 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

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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. 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. 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.
  4. 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.
  5. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
  6. Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
  13. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  14. 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.
  15. 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.
  16. 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.
  17. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  18. 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.
  19. 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.
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Cited by:

  1. Robert R. Routledge, 2009. "Testable implications of the Bertrand model," The School of Economics Discussion Paper Series 0918, Economics, The University of Manchester.
  2. Matthew Andrews & Milan Bradonjic & Iraj Saniee, 2017. "Quantifying the Benefits of Infrastructure Sharing," Papers 1706.05735, arXiv.org.

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