Mathematical Modelling in Economics pp 110-120 | Cite as

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

## 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## Preview

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