A Note on Bertrand Competition under Quadratic Cost Functions
The authors focus on a model of competition known in economics as Bertrand competition. They investigate how the outcome of Bertrand competition changes when linear cost functions are replaced by quadratic functions in the model. Named after French mathematician Joseph Louis Francois Bertrand (1822-1900), Bertrand competition describes interactions among firms and a market situation in which firms make their output and pricing decisions based on the assumption that their competitors will not change their own prices. Prokop, Ramsza and Wiśnicki show that the introduction of quadratic cost functions in the model leads to a qualitative change in competition between firms. In this case, the standard assumption that a firm with a lower price is interested in taking over the entire market is not only unrealistic (even in the absence of capacity constraints), but also irrational from the profit-maximization viewpoint, the authors say. Therefore the results of previous studies are misleading, according to Prokop, Ramsza and Wiśnicki. They argue that the so-called Bertrand duopoly model should be adjusted to better capture the behavior of firms under quadratic cost functions. The authors relax the assumption that the output of firms is determined by existing demand. They offer a modified Bertrand duopoly model in which firms competing in prices are free to choose their level of production depending on the market demand for their products at specific prices. “Under the modified assumptions, the static price competition game of identical duopolists has no symmetric equilibrium in pure stra- tegies,” the authors conclude. Their research shows that, under quadratic cost functions, it is possible to expect price fluctuations on oligopolistic markets rather than a stable equilibrium situation described by the standard model of price competition.
Volume (Year): (2015)
Issue (Month): 2 ()
|Contact details of provider:|| Postal: Al. Niepodleglosci 162, 02-554 Warszawa|
Phone: + (48)(22) 49 12 51
Fax: + (48)(22) 49 53 12
Web page: http://gospodarkanarodowa.sgh.waw.pl/
More information through EDIRC
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.:
- Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, July.
- Atsuhiro Satoh & Yasuhito Tanaka, 2013.
"Relative profit maximization and Bertrand equilibrium with quadratic cost functions,"
Economics and Business Letters,
Oviedo University Press, vol. 2(3), pages 134-139.
- Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and Bertrand equilibrium with quadratic cost functions," MPRA Paper 55893, University Library of Munich, Germany.
When requesting a correction, please mention this item's handle: RePEc:sgh:gosnar:y:2015:i:2:p:5-14. 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: (Dariusz Nojszewski)
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.