## List of issues > Series «Mathematics». 2015. Vol. 13

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The Heterogeneity of Firms Behavior at Oligopolistic Market: Price-makers and Price-takers

The paper considers the model of strategic interaction of firms at the quantity oligopoly market. There are several price-makers maximizing profits using the Cournot strategy, and also several price-takers obtaining outputs from the equivalence of price and marginal costs. The second strategy can be used due to some rational reasons, for example, unavailability of demand function, and competitors’ cost functions essential for reaction curves construction, or due to misunderstanding of its own market power and influence on the equilibrium parameters. Myopic behavior decreases profits comparing to Cournot firms if occurs unilaterally. But the competitors will adapt, and it can unexpectedly make the second strategy effective. The paper analyses the case of linear demand and symmetric firms with quadratic costs. It’s shown that prace-takers’ output is even greater than the output of the Stackelberg leader. The profit can be greater or lower than the original price-makers profits. It depends on the market parameters include the price elasticity of demand and the rate of marginal costs increasing. It’s shown that the probability for price-taker strategy to be efficient is not big, but increases at a large market with inelastic demand and many firms with slowly increasing marginal costs. It’s better for price-taker to be the only one firm with such a strategy.

1. Avdasheva S.B., Rozanova N.M. The Theory of Industrial Organization(in Russian). M., Magistr, 1998.

2. Aizenberg N.I., Kiseleva M.A. Mathematical Models of the Spot Electro-Energy Markets (in Russian). The Proceedings of the Conference «Sustainable Development of the Russian Regions: Innovations, Institutes, and Technological Absorbtion». Ekaterinburg, UrFU, 2010, pp.9-15.

3. Vuros A.D., Rozanova N.M. Industrial Economics (in Russian). M., TEIS, 2000.

4. Aleksandrova I.A., Goncharenko V.M., Denezhkina I.E., Kiselev V.V., Popov V.Yu., Nabatova D.S., Shandra I.G., Shapoval A.B. Methods of optimal decisions in economics and finance. M., Knorus, 2014.

5. Zorkaltsev V.I., Mokryj I.V. Network Model of the Market Coordination (in Russian). The Proceedings of VI Moscow International Conference on Operation Research. M., MAKS Press, 2010, pp. 29-31.

6. Kabral L. Industrial Organization (in Russian). Minsk, Novoe Znanie, 2003.

7. Filatov A.Yu., Aizenberg N.I. Mathematical Models of Imperfect Competition (in Russian). Irkutsk, ISU, 2012.

8. Filatov A.Yu. Heterogeneity and its impact on the Economic Decision Making (in Russian). Irkutsk, ISU, 2013.

9. Yakovlev A., Golikova V., Gonchar K., Kuznetsov B. Russian Industry at the Crossroads: what Prevents our Firms to Become Competitive (in Russian). M., NRU HSE, 2008.

10. Baumol W. On the Theory of Oligopoly. Economica, 1958, no 25, pp. 187-198.

11. Belleflamme P., Peitz M. Industrial Organization. Markets and Strategies Cambridge University Press, 2010.

12. Carlton D., Perloff J. Modern Industrial Organization. Addison-Wesley, 2000.

13. Cournot A. Recherches sur les Principes Mathematiques de la Theorie des Richesses. 1838.

14. Fershtman Ch. Internal Organizations and Managerial Incentives as Strategic Variables in Competitive Environment. International Journal of Industrial Organization, 1985, no 3, pp. 245-253.

15. Fershtman Ch., Judd K. Equilibrium Incentives in Oligopoly. American Economic Review, 1987, no 5(77), pp. 927–940.

16. Filatov A., Makolskaya Ya. Trade-off between competition and increased returns to scale at industrial markets: equilibrium and effective number of firms. Scientific enquiry in the contemporary world: theoretical basics and innovative approach, Titusville, FL, USA: L&L;Publishing, 2012, pp. 51-55.

17. Klemperer P., Meyer M. Supply Function Equilibria in Oligopoly under Uncertainty. Econometrica, 1989, no 6(57), pp. 1243-1277.

18. MasColell A., Whinston M., Green J. Microeconomic Theory. Oxford University Press, 1995.

19. Shy O. Industrial Organization: Theory and Applications. MIT Press, 1995.

20. Tirole J. The Theory of Industrial Organization. MIT Press, 1988.