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A Model of Three Cities

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  • Stefano Colombo

Abstract

We develop a spatial model representing three cities of different size and connected by a road. We study two versions of a two-stage game where firms first decide where to locate and then set quantities or prices. We show that, in the case of quantity competition, maximal dispersion or agglomeration arises. Also, multiple equilibria are possible. In the case of price competition, maximal dispersion or partial dispersion arises. An asymmetric spatial equilibrium is possible even if the model is completely symmetric ex ante. A number of results are also derived when comparing the Cournot and the Bertrand locational equilibria in terms of profits, consumer surplus, and total welfare, and with respect to the welfare-maximizing locations.

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  • Stefano Colombo, 2016. "A Model of Three Cities," International Regional Science Review, , vol. 39(4), pages 386-416, October.
    • Handle: RePEc:sae:inrsre:v:39:y:2016:i:4:p:386-416
    DOI: 10.1177/0160017614543849
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    as
    1. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-640, May.
    2. Ricardo Biscaia & Isabel Mota, 2013. "Models of spatial competition: A critical review," Papers in Regional Science, Wiley Blackwell, vol. 92(4), pages 851-871, November.
    3. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 27-49.
    4. Qihong Liu & Konstantinos Serfes, 2004. "Quality of Information and Oligopolistic Price Discrimination," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 13(4), pages 671-702, December.
    5. Braid, Ralph M., 1989. "Retail competition along intersecting roadways," Regional Science and Urban Economics, Elsevier, vol. 19(1), pages 107-112, February.
    6. Stefano Colombo, 2011. "Taxation and predatory prices in a spatial model," Papers in Regional Science, Wiley Blackwell, vol. 90(3), pages 603-612, August.
    7. Hamilton, Jonathan H. & Thisse, Jacques-Francois & Weskamp, Anita, 1989. "Spatial discrimination : Bertrand vs. Cournot in a model of location choice," Regional Science and Urban Economics, Elsevier, vol. 19(1), pages 87-102, February.
    8. Raphael Thomadsen, 2007. "Product Positioning and Competition: The Role of Location in the Fast Food Industry," Marketing Science, INFORMS, vol. 26(6), pages 792-804, 11-12.
    9. Rath, Kali P. & Zhao, Gongyun, 2001. "Two stage equilibrium and product choice with elastic demand," International Journal of Industrial Organization, Elsevier, vol. 19(9), pages 1441-1455, November.
    10. Matsumura, Toshihiro & Matsushima, Noriaki, 2007. "Congestion-reducing investments and economic welfare in a Hotelling model," Economics Letters, Elsevier, vol. 96(2), pages 161-167, August.
    11. Toshihiro Matsumura & Takao Ohkawa & Daisuke Shimizu, 2005. "Partial Agglomeration or Dispersion in Spatial Cournot Competition," Southern Economic Journal, John Wiley & Sons, vol. 72(1), pages 224-235, July.
    12. Matsumura, Toshihiro & Shimizu, Daisuke, 2005. "Economic welfare in delivered pricing duopoly: Bertrand and Cournot," Economics Letters, Elsevier, vol. 89(1), pages 112-119, October.
    13. Braid, Ralph M., 1988. "Heterogeneous preferences and non-central agglomeration of firms," Regional Science and Urban Economics, Elsevier, vol. 18(1), pages 57-68, February.
    14. Irmen, Andreas & Thisse, Jacques-Francois, 1998. "Competition in Multi-characteristics Spaces: Hotelling Was Almost Right," Journal of Economic Theory, Elsevier, vol. 78(1), pages 76-102, January.
    15. Boyer, Marcel & Laffont, Jean-Jacques & Mahenc, Philippe & Moreaux, Michel, 1994. "Location distortions under incomplete information," Regional Science and Urban Economics, Elsevier, vol. 24(4), pages 409-440, August.
    16. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    17. Toshihiro Matsumura & Noriaki Matsushima, 2012. "Spatial Cournot competition and transportation costs in a circular city," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 48(1), pages 33-44, February.
    18. Thisse, Jacques-Francois & Vives, Xavier, 1988. "On the Strategic Choice of Spatial Price Policy," American Economic Review, American Economic Association, vol. 78(1), pages 122-137, March.
    19. Stefano Colombo, 2014. "Fee versus royalty licensing in spatial Cournot competition," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(3), pages 859-879, May.
    20. Chisholm, Darlene C. & Norman, George, 2004. "Heterogeneous preferences and location choice with multi-product firms," Regional Science and Urban Economics, Elsevier, vol. 34(3), pages 321-339, May.
    21. Toshihiro Matsumura & Daisuke Shimizu, 2008. "A Noncooperative Shipping Cournot Duopoly With Linear‐Quadratic Transport Costs And Circular Space," The Japanese Economic Review, Japanese Economic Association, vol. 59(4), pages 498-518, December.
    22. Kai Andree, 2013. "Collusion in Spatially Separated Markets with Quantity Competition," Journal of Industry, Competition and Trade, Springer, vol. 13(3), pages 309-318, September.
    23. Arnott, Richard & Hochman, Oded & Rausser, Gordon C., 2008. "Pollution and land use: Optimum and decentralization," Journal of Urban Economics, Elsevier, vol. 64(2), pages 390-407, September.
    24. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    25. Chia-Hung Sun & Fu-Chuan Lai, 2014. "Spatial price discrimination in a symmetric barbell model: Bertrand vs. Cournot," Papers in Regional Science, Wiley Blackwell, vol. 93(1), pages 141-158, March.
    26. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 1995. "Asymmetric equilibria in spatial competition," International Journal of Industrial Organization, Elsevier, vol. 13(2), pages 213-227.
    27. Anderson, Simon P. & Goeree, Jacob K. & Ramer, Roald, 1997. "Location, Location, Location," Journal of Economic Theory, Elsevier, vol. 77(1), pages 102-127, November.
    28. Gupta, Barnali & Lai, Fu-Chuan & Pal, Debashis & Sarkar, Jyotirmoy & Yu, Chia-Ming, 2004. "Where to locate in a circular city?," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 759-782, June.
    29. Chen, Chin-Sheng & Lai, Fu-Chuan, 2008. "Location choice and optimal zoning under Cournot competition," Regional Science and Urban Economics, Elsevier, vol. 38(2), pages 119-126, March.
    30. John Gross & William L. Holahan, 2003. "Credible Collusion in Spatially Separated Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 299-312, February.
    31. J. Michael Pogodzinski & Tim R. Sass, 1990. "The Economic Theory of Zoning: A Critical Review," Land Economics, University of Wisconsin Press, vol. 66(3), pages 294-314.
    32. Alessandra Chirco & Marcella Scrimitore & Corrado Benassi, 2007. "Spatial Discrimination with Quantity Competition and High Transportation Costs: a Note," Economics Bulletin, AccessEcon, vol. 12(1), pages 1-7.
    33. Braid, Ralph M., 2003. "A three-input model of the spatial effects of a central-city wage tax," Journal of Urban Economics, Elsevier, vol. 54(1), pages 89-109, July.
    34. Huang, Tao, 2009. "Hotelling competition with demand on parallel line," Economics Letters, Elsevier, vol. 102(3), pages 155-157, March.
    35. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    36. repec:ebl:ecbull:v:12:y:2007:i:1:p:1-7 is not listed on IDEAS
    37. Hong Hwang & Chao‐Cheng Mai & Hiroshi Ohta, 2010. "Who Benefits From Pricing Regulations When Economic Space Matters?," The Japanese Economic Review, Japanese Economic Association, vol. 61(2), pages 218-233, June.
    38. Anderson, Simon P & Neven, Damien J, 1991. "Cournot Competition Yields Spatial Agglomeration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(4), pages 793-808, November.
    39. Matsumura, Toshihiro & Shimizu, Daisuke, 2005. "Spatial Cournot competition and economic welfare: a note," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 658-670, November.
    40. Hwang, Hong & Mai, Chao-cheng, 1990. "Effects of Spatial Price Discrimination on Output, Welfare, and Location," American Economic Review, American Economic Association, vol. 80(3), pages 567-575, June.
    41. José María Chamorro Rivas, 2000. "Spatial dispersion in cournot competition," Spanish Economic Review, Springer;Spanish Economic Association, vol. 2(2), pages 145-152.
    42. Wen-Chung Guo & Fu-Chuan Lai, 2013. "The role of an intermediate market within the barbell model," Letters in Spatial and Resource Sciences, Springer, vol. 6(3), pages 151-161, November.
    43. Stefano Colombo, 2013. "Spatial Cournot competition with non-extreme directional constraints," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 51(3), pages 761-774, December.
    44. Lai, Fu-Chuan & Tsai, Jyh-Fa, 2004. "Duopoly locations and optimal zoning in a small open city," Journal of Urban Economics, Elsevier, vol. 55(3), pages 614-626, May.
    45. Steffen Brenner, 2005. "Hotelling Games with Three, Four, and More Players," Journal of Regional Science, Wiley Blackwell, vol. 45(4), pages 851-864, November.
    46. Harry Garretsen & Ron Martin, 2010. "Rethinking (New) Economic Geography Models: Taking Geography and History More Seriously," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(2), pages 127-160.
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    Cited by:

    1. Stefano Colombo & Zemin Hou, 2021. "Location-Price Equilibria when Traditional Retailers Compete Against an Online Retailer," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 59(3), pages 483-502, November.
    2. Wen-Chung Guo & Fu-Chuan Lai, 2015. "Spatial Cournot competition in a linear–circular market," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(3), pages 819-834, May.

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