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Harmonic symmetries of imperfect competition on circular city

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Author Info
Hennessy, David A.
Lapan, Harvey E.

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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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Publisher Info
Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 1-2 (January)
Pages: 124-146
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Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:124-146

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Keywords: Cyclic and dihedral symmetries Harmonic analysis Majorization Price and quantity instruments Spatial differentiation;

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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 1133-37, December. [Downloadable!] (restricted)
  2. 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 505-33, May.
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  3. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring. [Downloadable!] (restricted)
  4. Kats, Amoz, 1995. "More on Hotelling's stability in competition," International Journal of Industrial Organization, Elsevier, vol. 13(1), pages 89-93, March. [Downloadable!] (restricted)
  5. 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 107-22, February. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Stephen W. Salant & Greg Shaffer, 1999. "Unequal Treatment of Identical Agents in Cournot Equilibrium," American Economic Review, American Economic Association, vol. 89(3), pages 585-604, June. [Downloadable!] (restricted)
  8. Hennessy, David A. & Lapan, Harvey E., 2004. "Market Cycles for a Non-Storable Product under Adjustment Costs," Staff General Research Papers 12208, Iowa State University, Department of Economics. [Downloadable!]
  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. [Downloadable!] (restricted)
  10. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-19, July. [Downloadable!] (restricted)
  11. Steinmetz, Sebastien, 1998. "Spatial preemption with finitely lived equipments," International Journal of Industrial Organization, Elsevier, vol. 16(2), pages 253-270, March. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
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