Two firms produce differentiated products. Firm 1 faces the demand curve Q1 = 75 - P1 + 0.5P2. Firm 2 faces an analogous demand curve Q2 = 75 - P2 + 0.5P1. For each firm, AC=MC=30. a.) Confirm that firm 1's optimal price depends on P2 according to P1=52.5+0.25*P2. b.) describe why a lower price by its competitor should cause the firm to lower its own price. c.) In equilibrium, the firms set identical prices : P1=P2. Find the firms' equilibrium prices, quantities, and profits.