Journal of Economics

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

Optimal product differentiation in a circular model

  • Qiang Gong
  • Qihong Liu
  • Yi Zhang


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.


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

JEL Classification

D43 L13 



We would like to thank the Editor Giacomo Corneo and two anonymous referees whose comments allowed us to improve the paper significantly. We would also like to thank Greg Burge, George Deltas, Kostas Serfes, John Turner, Hao Wang, Lixin Ye, Artie Zillante, seminar and conference participants at Southwestern University of Finance and Economics, Shanghai University of Finance and Economics, International Economic Association World Congress (2011), International Industrial Organization Conference (2010), Hong Kong Economic Association Conference (2010) and Five-Star Economics Forum (2010) for helpful comments and suggestions.


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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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