Question

of output respectively, suc. Firm 1 and Firm 2 compete as Cournot duopolists, producing q1 and q units that market output Q = q1 + q2. They face market inverse demand of P-400-20. Firm l's Total cost is given by TG, = 2q3. Finn 2's by TC2-2 . 10, what is Firm l's equilibrium profit maximizing output level, qǐ? 11. What is market output in the Cournot equilibrium for this market (so, what is the value of Q. = qi + qj)? 12. At what price will output be sold in this market in equilibrium?

Answer 1

P = 400 - 2Q = 400 - 2q1 - 2q2

MC1 = dTC1/dq1 = 4q1

MC2 = dTC2/dq2 = 4q2

(10)

For firm 1,

Total revenue (TR1) = P x q1 = 400q1 - 2q1² - 2q1q2

Marginal revenue (MR1) = $\partial$ TR1/$\partial$q1 = 400 - 4q1 - 2q2

Equating MR1 and MC1,

400 - 4q1 - 2q2 = 4q1

8q1 + 2q2 = 400

4q1 + q2 = 200...........(1) [Reaction function, firm 1]

For firm 2,

Total revenue (TR2) = P x q2 = 400q2 - 2q1q2 - 2q2²

Marginal revenue (MR2) = $\partial$ TR2/$\partial$q2 = 400 - 2q1 - 4q2

Equating MR2 and MC2,

400 - 2q1 - 4q2 = 4q2

2q1 + 8q2 = 400

q1 + 4q2 = 200...........(2) [Reaction function, firm 2]

Cournot equilibrium is obtained by solving (1) and (2).

Multiplying (2) by 4,

4q1 + 16q2 = 800.........(3)

4q1 + q2 = 200..........(1)

(3) - (1) yields:

15q2 = 600

q2 = 40

q1 = 200 - 4q2 [From (2)] = 200 - (4 x 40) = 200 - 160 = 40

q1* = 40

(11)

Q = q1 + q2 = 40 + 40 = 80

(12)

P = 400 - (2 x 80) = 400 - 160 = 240