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Modelling Product Differentiation: An Application of the Theory of Functional Equations

  • Egbert Dierker
  • Konrad Podczeck

Abstract

We consider an oligopolistic market for a differentiated product of which several price setting firms offer one brand each. Firms set prices in order to maximize expected profits. Since the existence of equilibria cannot, in general, be shown without appropriate assumptions on the distribution of consumers’ tastes and since such assumptions cannot be expressed without an algebraic structure, we deal with the conceptual difficulty arising from the fact that there is no natural algebraic structure a priori given on consumers’ tastes. A result on functional equations taken from Eichhorn (1978) is used in order to characterize an algebraic structure lending itself to the formulation of suitable assumptions on the distribution of consumers’ tastes.

Keywords

Functional Equation Algebraic Structure Linear Structure Expected Profit Discrete Choice Model 
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References

  1. ANDERSON, S., de PALMA, A., and THISSE, J.F. (1992): Discrete Choice Theory of Product Differentiation, Cambridge, MIT Press.Google Scholar
  2. CAPLIN, A. and NALEBUFF, B. (1991): “Aggregation and imperfect competition: On the existence of equilibrium”, Econometrica 59, 25–29.CrossRefGoogle Scholar
  3. DIERKER, E. (1991): “Competition for customers”, in: Barnett, W., Cornet, B., d’Aspre¬mont, C., Gabszewicz, J.J., and Mas-Colell, A. (eds.), Equilibrium Theory and Applica¬tions, 383–402, Cambridge, Cambridge University Press.Google Scholar
  4. DIERKER, E. and PODCZECK, K. (1992): “The distribution of consumers’ tastes and the quasiconcavity of the profit function”, preprint, University of Vienna.Google Scholar
  5. EICHHORN, W. (1978): Functional Equations in Economics, London, Addison-Wesley.Google Scholar
  6. MCFADDEN, D. (1986): “The choice theory of market research”, Marketing Science 5, 275–297.CrossRefGoogle Scholar
  7. ROBERTS, J. and SONNENSCHEIN, H. (1977): “On the foundations of the theory of monopolistic competition”, Econometrica 45, 101–113.CrossRefGoogle Scholar
  8. SHAFER, W. and SONNENSCHEIN, H. (1982): “Market demand and excess demand func¬tions”, in: Handbook of Mathematical Economics, vol.11, chapter 14, 671–693, Amsterdam, North-Holland.Google Scholar
  9. VIND, K. with contributions by GRODAL, B. (1990): Additive Utility Functions and Other Special Functions in Economic Theory, University of Copenhagen, preprint.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1993

Authors and Affiliations

  • Egbert Dierker
  • Konrad Podczeck
    • 1
  1. 1.Department of EconomicsUniversity of ViennaViennaAustria

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