Modelling Product Differentiation: An Application of the Theory of Functional Equations
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.
KeywordsFunctional Equation Algebraic Structure Linear Structure Expected Profit Discrete Choice Model
Unable to display preview. Download preview PDF.
- ANDERSON, S., de PALMA, A., and THISSE, J.F. (1992): Discrete Choice Theory of Product Differentiation, Cambridge, MIT Press.Google Scholar
- 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
- DIERKER, E. and PODCZECK, K. (1992): “The distribution of consumers’ tastes and the quasiconcavity of the profit function”, preprint, University of Vienna.Google Scholar
- EICHHORN, W. (1978): Functional Equations in Economics, London, Addison-Wesley.Google Scholar
- 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
- VIND, K. with contributions by GRODAL, B. (1990): Additive Utility Functions and Other Special Functions in Economic Theory, University of Copenhagen, preprint.Google Scholar