Journal of Economics

, Volume 119, Issue 3, pp 219–252 | Cite as

Optimal product differentiation in a circular model

Article
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Abstract

Since circular model was introduced in Salop (Bell J Econ 10:141–156, 1979), it has been the workhorse for analyzing spatial competition among differentiated firms. A common assumption in this literature is that firms are evenly spaced on the circle, even when entry is allowed. We characterize conditions for even spacing to be an equilibrium, using a two-stage (location-then-price) circular model with general transport cost function. Under duopoly competition, we characterize a mild sufficient condition—the first derivative of transport cost is concave (together with an assumption governing the transport cost difference to the two firms). If one only considers pure strategy equilibrium in prices, this sufficient condition is weakened to the first derivative of transport cost being \(-\)1-concave. These conditions ensure that firms’ profits are concave in their prices when firms are evenly spaced and that even spacing maximizes profits. Under oligopoly competition (\(N\ge 2\) firms), we characterize a necessary condition for even spacing to be an equilibrium. This necessary condition requires a firm’s profit to be concave in location at the symmetric location. It involves the third derivative of transport cost function, so having convex transport cost in general is neither necessary nor sufficient to determine equilibrium location choice. Our results have implications for studies employing circular models, especially in terms of welfare analysis which depends on firms’ location choices.

Keywords

Product differentiation Circular model Location choice \(\rho \)-Concavity 

JEL Classification

D43 L13 

References

  1. Aghion P, Schankerman M (2004) On the welfare effects and political economy of competition-enhancing policies. Econ J 114(498):800–824CrossRefGoogle Scholar
  2. Anderson S (1986) Equilibrium existence in the circle model of product differentiation. Lond Papers Reg Sci Ser 16:19–29Google Scholar
  3. Anderson S, Goeree J, Ramer R (1997) Location, location, location. J Econ Theory 77(1):102–127CrossRefGoogle Scholar
  4. Bae S, Choi J (2007) The optimal number of firms with an application to professional sports leagues. J Sports Econ 8(1):99–108CrossRefGoogle Scholar
  5. Bhaskar V, To T (2004) Is perfect price discrimination really efficient? An analysis of free entry. Rand J Econ 35(4):762–776CrossRefGoogle Scholar
  6. Brekke K, Siciliani L, Straume O (2008) Competition and waiting times in hospital markets. J Public Econ 92(7):1607–1628CrossRefGoogle Scholar
  7. Caplin A, Nalebuff B (1991) Aggregation and imperfect competition: on the existence of equilibrium. Econometrica 59:25–59CrossRefGoogle Scholar
  8. Coibion O, Einav L, Hallak J (2007) Equilibrium demand elasticities across quality segments. Int J Ind Org 25(1):13–30CrossRefGoogle Scholar
  9. D’Aspremont C, Gabszewicz J, Thisse J (1979) Hotellings stability in competition. Econometrica 47(5):1145–1150CrossRefGoogle Scholar
  10. de Frutos MA, Hamoudi H, Jarquec X (1999) Equilibrium existence in the circle model with linear quadratic transport cost. Reg Sci Urban Econ 29(5):605–615CrossRefGoogle Scholar
  11. de Frutos MA, Hamoudi H, Jarquec X (2002) Spatial competition with concave transport costs. Reg Sci Urban Econ 32(4):531–540CrossRefGoogle Scholar
  12. Economides N (1986) Minimal and maximal product differentiation in Hotelling duopoly. Econ Lett 21(1):67–71CrossRefGoogle Scholar
  13. Economides N (1989) Symmetric equilibrium existence and optimality in differentiated product markets. J Econ Theory 47(1):178–194CrossRefGoogle Scholar
  14. Gong Q, Zhang Y (2011) The optimal product position choice. China Econ Q 10(2):619–634Google Scholar
  15. Gopinath G, Gourinchas P, Hsieh C, Li N (2011) International prices, costs, and markup differences. Am Econ Rev 101(6):2450–2486CrossRefGoogle Scholar
  16. Grossman G, Shapiro C (1984) Informative advertising with differentiated products. Rev Econ Stud 51(1):63–81CrossRefGoogle Scholar
  17. Gupta B, Lai F, Pal D, Sarkar J, Yu C (2004) Where to locate in a circular city? Int J Ind Org 22(6):759–782CrossRefGoogle Scholar
  18. Hennessy D, Lapan H (2009) Harmonic symmetries of imperfect competition on circular city. J Math Econ 45:124–146CrossRefGoogle Scholar
  19. Hotelling H (1929) Stability in competition. Econ J 39:41–57CrossRefGoogle Scholar
  20. Kats A (1995) More on Hotelling stability in competition. Int J Ind Org 13(1):89–93CrossRefGoogle Scholar
  21. Kim J (2009) Competition intensity and strategies in a market with differentiated products. IUPUI (in press)Google Scholar
  22. Liu Q, Serfes K (2005) Imperfect price discrimination, market structure, and efficiency. Can J Econ 38(4):1191–1203CrossRefGoogle Scholar
  23. Loertscher S, Muehlheusser G (2011) Sequential location games. Rand J Econ 42(4):639–663CrossRefGoogle Scholar
  24. Matsumura T, Okamura M (2006) A note on the excess entry theorem in spatial markets. Int J Ind Org 24(5):1071–1076CrossRefGoogle Scholar
  25. Osborne M, Pitchik C (1987) Equilibrium in Hotellings model of spatial competition. Econometrica 55(4):911–922CrossRefGoogle Scholar
  26. Picard P, Tabuchi T (2010) Self-organized agglomerations and transport costs. Econ Theory 42:565–589CrossRefGoogle Scholar
  27. Salop S (1979) Monopolistic competition with outside goods. Bell J Econ 10:141–156CrossRefGoogle Scholar
  28. Selten R, Apesteguia J (2005) Experimentally observed imitation and cooperation in price competition on the circle. Games Econ Behav 51(1):171–192CrossRefGoogle Scholar
  29. Shapiro D, Shi X (2008) Market segmentation: the role of opaque travel agencies. J Econ Manag Strategy 17(4):803–837CrossRefGoogle Scholar
  30. Vogel J (2008) Spatial competition with heterogeneous firms. J Polit Econ 116(3):423–466CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Wenlan School of BusinessZhongnan University of Economics and LawWuhanChina
  2. 2.Department of EconomicsUniversity of OklahomaNormanUSA
  3. 3.Department of EconomicsUniversity of Wisconsin-MadisonMadisonUSA

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