Another model of sales. Price discrimination in a differentiated duopoly market

Using a model of horizontal differentiation where a variety dimension is added to Hotelling's (1929) "linear city" duopoly model, I show that even when costs and demand are symmetric, price discrimination may be an equilibrium phenomenon. In the model each customer have a preferred variety and a preferred firm. They have perfect information about all prices and may be induced to switch variety and firm given a sufficient price difference. Price discrimination equilibrium exists when a sufficient fraction of consumers are elastic both with respect to variety and firm.