Answer:
Consider the following calculations
Explanation:
a. π1 = P Q1 − C1 = (300 − Q1 − Q2 )Q1 − 60Q1 = 300Q1 − Q1^2 − Q1 Q2 − 60Q1
π2 = P Q2 − C2 = (300 − Q1 − Q2 )Q2 − 60Q2 = 300Q2 − Q1 Q2 − Q2^2-60Q2
Take the FOCs:
∂π/(∂Q1)= 300 − 2Q1 − Q2 = 0 ⇒ Q1 = 120 − 0.5Q2
∂π/(∂Q2)= 300 − Q1 − 2Q2 = 0 ⇒ Q2 = 120 − 0.5Q1
Q1 = 120 − 0.5[120 − 0.5Q1 ] = 60 − 0.25Q1 ⇒ Q1 = 80
Similarly find Q2 = 80 such that π1 = π2 = 6, 400.
b. The two firms act as a monopolist, where each firm produces an equal share of total output. Demand is given by P = 300 − Q, M R = 300 − 2Q, and M C = 60. Set M C = M R tofind that Q = 120 and Q1 = Q2 = 60, respectively. Therefore:
π1 = π2 = 180 × 60 − 60 × 60 = 7, 200.
c. It would be higher because they could make more money.
d. Firm 2 knows that Q1 = 60 and given the reaction function derived in part (a) firm 2 sets Q2 = 120 − 0.5 × 60 = 90. Overall, QT = 150 and P = 300 − 150 = 150. Hence:
π1 = 150 × 60 − 60 × 60 = 5, 400
π2 = 150 × 90 − 60 × 90 = 8, 100.
