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Bertrand's price competition in markets with fixed costs

We analyze Bertrand's price competition in a homogenous good market with a fixed cost and an increasing marginal cost (i.e., with variable returns to scale). If the fixed cost is avoidable, we show that the non-subadditivity of the cost function at the output corresponding to the oligopoly break-even price, denoted by D(pL(n)), is su±cient to guarantee that the market supports an equilibrium in pure strategies with two or more active 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)). As a by-product, the latter implies that the average cost cannot be decreasing over the range of outputs mentioned before. In addition, we also prove that the existence of a price-taking equilibrium is sufficient, but not necessary, for Bertrand's price competition to possess an equilibrium in pure strategies. This provides a simple existence result for the case where the fixed cost is fully unavoidable.

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_541.pdf
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Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 541.

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Length: 23 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:roc:rocher:541
Contact details of provider: Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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  1. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
  2. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
  3. Grossman, Sanford J, 1981. "Nash Equilibrium and the Industrial Organization of Markets with Large Fixed Costs," Econometrica, Econometric Society, vol. 49(5), pages 1149-72, September.
  4. 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.
  5. 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.
  6. Makoto Yano, 2006. "A price competition game under free entry," Economic Theory, Springer, vol. 29(2), pages 395-414, October.
  7. John Morgan & Michael R. Baye, 2002. "Winner-take-all price competition," Economic Theory, Springer, vol. 19(2), pages 271-282.
  8. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  9. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
  10. Telser, Lester G, 1991. "Industry Total Cost Functions and the Status of the Core," Journal of Industrial Economics, Wiley Blackwell, vol. 39(3), pages 225-40, March.
  11. 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, vol. 2(1), pages 65-71.
  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. 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.
  14. 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 809-22, December.
  15. Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
  16. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
  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. 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. 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.
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