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The paper examines under what conditions vertically differentiated duopolists engage in first-degree price discrimination. Each firm decides on a pricing regime at a first stage and sets prices at a second stage. The paper shows that when unit cost is an increasing and convex function of quality, the discriminatory regime is the unique subgame-perfect equilibrium of such two-stage game. In contrast to the case of horizontal differentiation, the discriminatory equilibrium is not necessarily Pareto-dominated by a bilateral commitment to uniform pricing. Also, the quality choices of perfectly discriminating duopolists are welfare maximizing. The paper explains why a threat of entry may elicit price discrimination by an incumbent monopolist. [ABSTRACT FROM AUTHOR]