The authors study a differentiated industry in which two firms compete by offering intervals of qualities to heterogenous consumers. They establish conditions which, for perfect competition and monopoly, imply that different consumers choose different qualities. Under these conditions, they show existence and essential uniqueness of a price equilibrium. At all price equilibria in which both firms make a positive profit, discrimination of consumers is incomplete. The authors also discuss the choice of product lines, and show that the Chamberlinian incentive to differentiate its products from those of its competitor dominates for intermediate qualities.