Two firms produce differentiated products. Firm 1 faces the demand curve Q 75-P+5P. (Note that a lower competing price robs the firm of some, but not all, sales. Thus, price competition is not as extreme as in the Bertrand model.) Firm 2 faces the analogous demand curve Q=75-P+5P. For each firm, AC = MC = 30.

a. Confirm that firm 1's optimal price depends on P according to P = 52.5+.25P. Hint Set up the profit expression: (P1-30)Q (P1-30) (75 P+5Pg) and set M = m/ P = 0 to solve for P in terms of P2. Alternatively, set MR, MC and solve for Q and then P in terms of Pg.

b. Explain why a lower price by its competitor should cause the firm to lower its own price.

c. In equilibrium, the firms set identical prices: P Pg. Find the firms' equilibrium prices, quantities, and profits.