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 ‘dihedralmajorization’ sense. This also tends to be the case in whichprices aremore 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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Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number
12551.
Length: 23 pages Date of creation: 23 Mar 2006 Date of revision: Publication status: Published in Journal of Mathematical Economics, January 2009, Vol. 45, No. 1-2, pp. 124-146. Handle: RePEc:isu:genres:12551
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Find related papers by JEL classification: C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming E2 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment M2 - Business Administration and Business Economics; Marketing; Accounting - - Business Economics
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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.
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