Objective and subjective product differentiation in a Cournot duopoly

Cournot duopoly is a mathematical model of an imperfectly competitive market, where two profit maximizing firms simultaneously choose the quantities of product to produce, considering each other's behavior. The main objective of this paper is to analytically obtain the equilibrium quantities, prices, and profits of a Cournot duopoly in a market with two objectively differentiated products composed of two properties, and also considering that the consumers subjectively differentiate these properties. We begin by introducing subjective properties differentiation into a Lancaster consumer's choice problem, where the consumer maximizes a symmetrical CES utility function depending on the properties consumed, subject to a budget constraint and to the Lancaster linear transformation of these properties in the final goods. Then we solve this optimization problem through the method of Lagrange multipliers and obtain the final products direct and inverse demand functions, and finally find the equilibrium of the proposed Cournot duopoly. The results show that if the properties are perceived by the consumers as highly differentiated, then a higher subjective properties differentiation implies that the Cournot duopoly has a well-defined equilibrium only for a smaller range of objective product differentiation. Furthermore, an increase in the consumers' subjective differentiation of properties and/or in the objective product differentiation increases the monopoly power of the firms, i.e. with a higher differentiation, the firms produce smaller quantities of products, charge higher prices and earn higher profits. The model proposed here may serve as a basis for the study of imperfectly competitive markets with product differentiation and advertising.