Harmonic symmetries of imperfect competition on circular city

David A. Hennessy and Harvey E. Lapan

Staff General Research Papers from Iowa State University, Department of Economics

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 ‘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.

Keywords: cyclic and dihedral symmetries; harmonic analysis; price and quantity instruments; majorization; spatial differentiation (search for similar items in EconPapers)
JEL-codes: C6 E2 M2 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-com, nep-geo and nep-net
Date: Written
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Published in Journal of Mathematical Economics, January 2009, Vol. 45, No. 1-2, pp. 124-146.

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Journal Article: Harmonic symmetries of imperfect competition on circular city (2009)
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Persistent link: http://EconPapers.repec.org/RePEc:isu:genres:12551

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