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Price competition and convex costs

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Author Info
Weibull, Jörgen () (Dept. of Economics, Stockholm School of Economics)

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Abstract

In the original model of pure price competition, due to Joseph Bertrand (1883), firms have linear cost functions. For any number of identical such price-setting firms, this results in the perfectly competitive outcome; the equilibrium price equal the firms’ (constant) marginal cost. This paper provides a generalization of Bertrand’s model from linear to convex cost functions. I analyze pure price competition both in a static setting - where the firms interact once and for all - and in dynamic setting - where they interact repeatedly over an indefinite future. Sufficient conditions are given for the existence of Nash equilibrium in the static setting and for subgame perfect equilibrium in the dynamic setting. These equilibrium sets are characterized, and it is shown that there typically exists a whole interval of Nash equilibrium prices in the static setting and subgame perfect equilibria in the dynamic setting. It is shown that firms may earn sizable profits and that their equilibrium profits may increase if their production costs go up.

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Publisher Info
Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 622.

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Length: 16 pages
Date of creation: 14 Feb 2006
Date of revision: 23 Feb 2006
Handle: RePEc:hhs:hastef:0622

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Related research
Keywords: Bertrand competition;

Find related papers by JEL classification:
D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  2. 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. [Downloadable!] (restricted)
  3. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
  4. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-99, May. [Downloadable!] (restricted)
  5. Allen, Beth & Hellwig, Martin, 1986. "Price-Setting Firms and the Oligopolistic Foundations of Perfect Competition," American Economic Review, American Economic Association, vol. 76(2), pages 387-92, May. [Downloadable!] (restricted)
  6. Michael Noel, 2004. "Edgeworth Price Cycles: Evidence from the Toronto Retail Gasoline Market," University of California at San Diego, Economics Working Paper Series 2004-03, Department of Economics, UC San Diego. [Downloadable!]
  7. Maskin, Eric, 1986. "The Existence of Equilibrium with Price-Setting Firms," American Economic Review, American Economic Association, vol. 76(2), pages 382-86, May. [Downloadable!] (restricted)
  8. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November. [Downloadable!] (restricted)
  9. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October. [Downloadable!] (restricted)
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