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Stability in a non-autonomous iterative system: an application to oligopoly
Institute of Mathematics, National Academy of Sciences, Ukraine.
Umeå University, Faculty of Social Sciences, Centre for Regional Science (CERUM).
2009 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 58, no 10, 2022-2034 p.Article in journal (Refereed) Published
Abstract [en]

This paper reconsiders the relation between oligopoly and perfect competition, more specifically the problem of emergent instability when the number of competitors increases, as pointed out by several authors. A process of mixed short and long run dynamics is set up. In the short run the competitors are subject to capacity limits due to fixed capital stocks, in the long run they may renew these stocks and so in the moments of reinvestment have access to a constant returns technology. The evolution of the system depends on the number of competitors, the interval between their entry on the market, and the durability of capital. The main result is a theorem showing that if capital has a durability of more periods than the spacing of reinvestment times among the firms, multiplied with their total number, then the system always contracts to the Cournot equilibrium state.

Place, publisher, year, edition, pages
Oxford: Pergamon Press, 2009. Vol. 58, no 10, 2022-2034 p.
Keyword [en]
Cournot equilibrium, synchronization, stability, non-autonomous systems, iterative maps
National Category
URN: urn:nbn:se:umu:diva-32448DOI: 10.1016/j.camwa.2009.06.048ISI: 000271794500015OAI: diva2:303257
Available from: 2010-03-11 Created: 2010-03-11 Last updated: 2016-08-30Bibliographically approved

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ReferencesLink to record
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