This paper analyzes a monopolistic market with a continuum of consumers in the linear case. Consumers are vertically differentiated by a one-dimensional preference for quality, and the monopolist is allowed to offer a menu of quality-price pairs. The analysis shows that, in the linear case, the monopolist’s optimal offer endogenously collapses to a single quality-price pair, where the quality equals the highest feasible level. In addition, welfare maximization is achieved if and only if the market is fully served in equilibrium.
Amit Gayer (Mon,) studied this question.