EQUILIBRIA IN A SPATIAL DUOPOLY: MARKET ASYMMETRY VS. PRODUCT DIFFERENTIATION
Abstract
Introduction. In the theory of industry markets, as a rule, two basic models are used to describe equilibrium states – Cournot and Bertrand. After the famous works of Cournot and Bertrand, economists have been comparing the advantages of quantitative (Cournot) and price (Bertrand) competition for more than a century. In the classical duopoly model, price competition drives prices down to the marginal cost level (Bertrand’s paradox). Consumers will benefit from this, while firms receive minimal profits. Therefore, within the framework of the classical model, firms prefer quantitative competition. It is possible to overcome the Bertrand paradox if other characteristics of real markets are introduced into the model, namely: product differentiation, dynamic interaction of firms, limitation of production capacities, spatial location of firms, etc. The purpose of this paper is to analyze the generalized spatial duopoly model [Liang, W.J., Hwang, H., & Mai, C.C. (2006). Spatial discrimination: Bertrand vs. Cournot with asymmetric demands. Regional Science and Urban Economics, 36, 790–802] under conditions of asymmetric markets and product differentiation. In order to maximize profits, firms first select a location and then the type of competition – Cournot or Bertrand. Results. It is shown that with a sufficiently high level of markets asymmetry, agglomeration in a large market is the only Nash equilibrium in pure strategies, regardless of the type of competition and the nature of product differentiation. It was found that the equilibrium states significantly depend on the relationship between the markets asymmetry, product differentiation and transport tariff. The corresponding dependencies are determined in an analytical form. On the basis of a comparative analysis of equilibria, the optimal strategy of firms for choosing a location and type of competition is substantiated. Conclusions. The analysis carried out in the paper made it possible to formulate the optimal strategy of firms based on the criterion of profit. In the course of a competitive game, firms choose the location and type of competition. Location affects the choice of type of competition, and vice versa. It was found that regardless of the type of competition, it is optimal for firms to be located in a larger market. But the choice of the optimal type of competition depends on product differentiation. With complementarity, the profit of firms will be higher than in price competition. With substitutability, the optimal type of competition will depend on the relationship between market asymmetry, product differentiation and transport tariff.
Downloads
References
2. Zanchettin P. Differentiated duopoly with asymmetric costs. Journal of Economics & Management Strategy. 2006. V. 15. Pp. 999–1015.
3. Anderson S., Neven D. Cournot Competition Yields Spatial Agglomeration. International Economic Review. 1991. V. 32. N 4. Pp. 793–808.
4. Hamilton J., Thisse J.-F., Weskamp A. Spatial discrimination, Bertrand vs. Cournot in a model of location choice. Regional Science and Urban Economics. 1989. N 19. Pp. 87–102.
5. Hamilton J., Klein J., Sheshinski E., Slutsky S. Quantity Competition in a Spatial Model. The Canadian Journal of Economics. 1994. V. 27. N 4. Pp. 903–917.
6. Melnikov S.V. Cournot Competition Yields Spatial Dispersion. Transport Development. 2020. V. 1. N 4. Pp. 57–70.
7. Melnikov S.V. Stackelberg-Nash Equilibrium in the Linear City Model. Automation Remote Control. 2020. N 81. Pp. 358–365.
8. Sun C.-H. Cournot and Bertrand Competition in a Model of Spatial Price Discrimination with Differentiated Products. The B.E. of Theoretical Economics. 2014. N 14. Pp. 251–72.
9. Liang W.J., Hwang H., Mai C.C. Spatial discrimination: Bertrand vs. Cournot with asymmetric demands. Regional Science and Urban Economics. 2006. N 36. Pp. 790–802.
10. Andree K., Calaki J. Product differentiation in a spatial Cournot model with asymmetric demand. Economics Bulletin. 2011. V. 31. N 2. Pp. 1125–1130.
11. Dixit A., Stiglitz J. Monopolistic Competition and Optimum Product Diversity. American Economic Review. 1977. V. 67. N 3. Pp. 297–308.
12. Krugman P.R. Increasing returns, monopolistic competition, and international trade. Journal of International Economics. 1979. V. 9. N 4. Pp. 469–479.
13. Behrens K., Murata Y. General equilibrium models of monopolistic competition: A new approach. Journal of Economic Theory. 2007. V. 136. N 1. Pp. 776–787.
14. Zhelobodko E., Kokovin S., Parenti M., Thisse J-F. Monopolistic Competition in General Equilibrium: Beyond the Constant Elasticity of Substitution. Econometrica. 2012. V. 80. N 6. Pp. 2765–2784.
15. Behrens K. Asymmetric trade and agglomeration. [Research Report] Laboratoire d’analyse et de techniques économiques (LATEC). 2003. 53 p.
16. Sidorov A.V., Zhelobodko E. V. Agglomeration and Spreading in an Asymmetric World. Review of Development Economics. 2013. V. 17. N 2. Pp. 201–219.
