Price competition and convex costs
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 622.
Length: 16 pages
Date of creation: 14 Feb 2006
Date of revision: 23 Feb 2006
Contact details of provider:
Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Web page: http://www.hhs.se/
More information through EDIRC
Find related papers by JEL classification:
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-02-19 (All new papers)
- NEP-COM-2006-02-19 (Industrial Competition)
- NEP-IND-2006-02-19 (Industrial Organization)
- NEP-MIC-2006-02-19 (Microeconomics)
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.:
- 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.
- 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.
- Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
- 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.
- Maskin, Eric, 1986. "The Existence of Equilibrium with Price-Setting Firms," American Economic Review, American Economic Association, vol. 76(2), pages 382-86, May.
- Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
- Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
- Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November.
- Noel, Michael, 2004. "Edgeworth Price Cycles: Evidence from the Toronto Retail Gasoline Market," University of California at San Diego, Economics Working Paper Series qt64j579g9, Department of Economics, UC San Diego.
- Andersson, Ola & Argenton, Cédric & Weibull, Jörgen, 2010. "Robustness to strategic uncertainty in price competition," Working Paper Series in Economics and Finance 0726, Stockholm School of Economics, revised 08 Apr 2010.
- Argenton, Cédric & Müller, Wieland, 2012. "Collusion in experimental Bertrand duopolies with convex costs: The role of cost asymmetry," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 508-517.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Helena Lundin).
If references are entirely missing, you can add them using this form.