Monopoly and Endogenous Single Highest Quality

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.