Advanced Search
MyIDEAS: Login

Bertrand's price competition in markets with fixed costs

Contents:

Author Info

Abstract

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.

Download Info

If 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.
File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_541.pdf
File Function: full text
Download Restriction: None

Bibliographic Info

Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 541.

as in new window
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.

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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.:
as in new window
  1. Chaudhuri, Prabal Ray, 1996. "The contestable outcome as a Bertrand equilibrium," Economics Letters, Elsevier, vol. 50(2), pages 237-242, February.
  2. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer, vol. 5(1), pages 19-32, January.
  3. 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.
  4. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
  5. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
  6. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
  7. 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.
  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. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  10. 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.
  11. Makoto Yano, 2006. "A price competition game under free entry," Economic Theory, Springer, vol. 29(2), pages 395-414, October.
  12. 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.
  13. 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.
  14. John Morgan & Michael R. Baye, 2002. "Winner-take-all price competition," Economic Theory, Springer, vol. 19(2), pages 271-282.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
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 in new window

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.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:roc:rocher:541. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Gabriel Mihalache).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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