Answer:
Detailed step=wise solution is given below:
Explanation:
a)
P = 120 - Q = 120 - q1 - q2
MC1 = MC2 = 60
For Firm 1, Total revenue (TR1) = P x q1 = 120q1 - q12 - q1q2
Marginal revenue (MR1) = \partial TR1 / \partial q1 = 120 - 2q1 - q2
Equating MR1 and MC1,
120 - 2q1 - q2 = 60
2q1 + q2 = 60 ............(1) (Best response, Firm 1)
For Firm 2, Total revenue (TR2) = P x q2 = 120q2 - q1q2 - q22
Marginal revenue (MR2) = \partial TR2 / \partial Q2 = 120 - q1 - 2q2
Equating MR2 and MC2,
120 - q1 - 2q2 = 60
q1 + 2Q2 = 60 ............(2) (Best response, Firm 2)
Cournot equilibrium is obtained by solving (1) and (2)
2q1 + q2 = 60 ..............(1)
(2) x 2 results in:
2q1 + 4q2 = 120.............(3)
(3) - (1) results in: 3q2 = 60
q2 = 20
q1 = 60 - 2q2 [From (2)] = 60 - (2 x 20) = 60 - 40 = 20
Q = 20 + 20 = 40
P = 120 - 40 = 80
Market share, firm 1 = q1 / Q = 20 / 40 = 0.5 = 50%
Market share, firm 2 = q2 / Q = 20 / 40 = 0.5 = 50%
(b) HHI Index = (50)2 + (50)2 = 2,500 + 2,500 = 5,000
(c) A monopolist maximizes profit by equating MR with MC.
P = 120 - Q
TR = P x Q = 120Q - Q2
MR = dTR / dQ = 120 - 2Q
Equating MR & MC,
120 - 2Q = 60
2Q = 60
Q = 30
P = 120 - 30 = 90
In a monopoly, HHI = 10,000
Change in HHI = 10,000 - 5,000 = 5,000 (Increase)
(d) When MC = 30, equating MR & MC:
120 - 2Q = 30
2Q = 90
Q = 45
P = 120 - 45 = 75
In a monopoly, HHI = 10,000
Change in HHI = 10,000 - 5,000 = 5,000 (Increase)
