Question:
1. Two firms produce differentiated products. Firm 1 faces the demand curve Q1=75-P1+0.5P2. Firm 2 faces the 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+0.25P2.
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: P1=P2. Find the firm's equilibrium prices, quantities, and profits.