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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
ANDERSON, S., de PALMA, A., and THISSE, J.F. (1992): Discrete Choice Theory of Product Differentiation, Cambridge, MIT Press.
CAPLIN, A. and NALEBUFF, B. (1991): “Aggregation and imperfect competition: On the existence of equilibrium”, Econometrica 59, 25–29.
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.
DIERKER, E. and PODCZECK, K. (1992): “The distribution of consumers’ tastes and the quasiconcavity of the profit function”, preprint, University of Vienna.
EICHHORN, W. (1978): Functional Equations in Economics, London, Addison-Wesley.
MCFADDEN, D. (1986): “The choice theory of market research”, Marketing Science 5, 275–297.
ROBERTS, J. and SONNENSCHEIN, H. (1977): “On the foundations of the theory of monopolistic competition”, Econometrica 45, 101–113.
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.
VIND, K. with contributions by GRODAL, B. (1990): Additive Utility Functions and Other Special Functions in Economic Theory, University of Copenhagen, preprint.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin · Heidelberg
About this chapter
Cite this chapter
Dierker, E., Podczeck, K. (1993). Modelling Product Differentiation: An Application of the Theory of Functional Equations. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78508-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-78508-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78510-8
Online ISBN: 978-3-642-78508-5
eBook Packages: Springer Book Archive