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Harmonic symmetries of imperfect competition on circular city

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  • Hennessy, David A.
  • Lapan, Harvey E.

Abstract

Taking location as given, we study imperfect competition on a circular city. In Bertrand oligopoly, we identify price harmonics as a function of firm unit costs and locations. The sum of oligopoly profits is larger when costs and/or locations are more dispersed in the [`]dihedral majorization' sense. This also tends to be the case in which prices are more variable. We study how phase shifts between cost parameters and inter-firm distance parameters change production and oligopoly profits. An exact characterization of production patterns is developed in terms of the eigenvalues for what we call the price harmonics matrix. The same techniques are applied to Cournot oligopoly with spatial externalities on circular city. Solutions are compared with first-best. Production patterns can differ markedly when cost spillovers are negative.

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  • Hennessy, David A. & Lapan, Harvey E., 2009. "Harmonic symmetries of imperfect competition on circular city," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 124-146, January.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:124-146
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    1. d'Aspremont, Claude & Jacquemin, Alexis, 1988. "Cooperative and Noncooperative R&D in Duopoly with Spillovers," American Economic Review, American Economic Association, vol. 78(5), pages 1133-1137, December.
    2. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-1119, July.
    3. Zhao, Jingang, 2001. "A characterization for the negative welfare effects of cost reduction in Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 455-469, March.
    4. Kats, Amoz, 1995. "More on Hotelling's stability in competition," International Journal of Industrial Organization, Elsevier, vol. 13(1), pages 89-93, March.
    5. Fevrier, Philippe & Linnemer, Laurent, 2004. "Idiosyncratic shocks in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 835-848, June.
    6. Russell, Thomas & Farris, Frank, 1993. "The geometric structure of some systems of demand equations," Journal of Mathematical Economics, Elsevier, vol. 22(4), pages 309-325.
    7. Chambers,Robert G. & Quiggin,John, 2000. "Uncertainty, Production, Choice, and Agency," Cambridge Books, Cambridge University Press, number 9780521785235, October.
    8. Barnett, William A. & Choi, Ki-Hong, 2008. "Operational identification of the complete class of superlative index numbers: An application of Galois theory," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 603-612, July.
    9. 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.
    10. Marat Ibragimov & Rustam Ibragimov, 2007. "Market Demand Elasticity and Income Inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 579-587, September.
    11. Long, Ngo Van & Soubeyran, Antoine, 2001. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 505-533, May.
    12. David Hennessy & Harvey Lapan, 2005. "An algebraic theory of multi-product decisions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 819-829, June.
    13. B. Curtis Eaton & Myrna Holtz Wooders, 1985. "Sophisticated Entry in a Model of Spatial Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(2), pages 282-297, Summer.
    14. Yannis Ioannides, 2006. "Topologies of social interactions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 559-584, August.
    15. Hennessy, David A. & Lapan, Harvey E., 2004. "Market Cycles for a Non-Storable Product Under Adjustment Costs," Staff General Research Papers Archive 12208, Iowa State University, Department of Economics.
    16. David A. Hennessy & Harvey E. Lapan, 2003. "An algebraic theory of portfolio allocation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 193-210, August.
    17. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    18. Steinmetz, Sebastien, 1998. "Spatial preemption with finitely lived equipments," International Journal of Industrial Organization, Elsevier, vol. 16(2), pages 253-270, March.
    19. Hennessy, David A. & Lapan, Harvey E., 2003. "Algebraic Theory of Portfolio Allocation, An," Staff General Research Papers Archive 10109, Iowa State University, Department of Economics.
    20. Greg Shaffer & Stephen W. Salant, 1999. "Unequal Treatment of Identical Agents in Cournot Equilibrium," American Economic Review, American Economic Association, vol. 89(3), pages 585-604, June.
    21. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    22. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
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    Cited by:

    1. Qiang Gong & Qihong Liu & Yi Zhang, 2016. "Optimal product differentiation in a circular model," Journal of Economics, Springer, vol. 119(3), pages 219-252, November.

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