A monopolist faces a market demand function Qd = 1000-4P and has total cost func
ID: 2495522 • Letter: A
Question
A monopolist faces a market demand function Qd = 1000-4P and has total cost function
C(Q) = Q2
a) Write the expressions for:
(i) Average cost
(ii) Marginal cost
(iii) Average revenue
(iv) Marginal revenue
b) Assuming the firm does not price discriminate, find the Profit maximising level of output for the firm and the amount of profit earned.
c) What is the efficient level of output in the market? Calculate the dead-weight loss to society from the monopolist’s operation.
d) If the monopolist can practice first degree price discrimination, find the output level and the amount of profit earned.
*NOTE: it is one question devided into parts.
Explanation / Answer
Q = 1000 - 4P
P = (1000 - Q) / 4 = 250 - 0.25Q
Total revenue, TR = P x Q = 250Q - 0.25Q2
Total cost, C = Q2
(a)
(i) Average cost, AC = C / Q = Q
(ii) Marginal cost, MC = dC / dQ = 2Q
(iii) Average revenue = TR / Q = P = 250 - 0.25Q
(iv) Marginal revenue, MR = dTR / dQ = 250 - 0.5Q
(b) Profit is maximized by equating MR with MC:
250 - 0.5Q = 2Q
2.5Q = 250
Q = 100 (= AC)
P = 250 - 0.25Q = 250 - (0.25 x 100) = 250 - 25 = 225
Profit = Q x (P - AC) = 100 x (225 - 100) = 100 x 125 = 12,500
(c) In efficient production, P = MC
250 - 0.25Q = 2Q
2.25Q = 250
Q = 111 [= AC]
P = MC = 2Q = 222
Deadweight loss = (1/2) x Difference in price x Difference in output
= (1/2) x (225 - 222) x (111 - 100) = (1/2) x 3 x 11 = 16.5
(d) In first degree price discrimination, monopolist charges a Price equal to MC, plus entire consumer surplus.
P = MC = 222 & corresponding Q = 111 (See part (c)).
Profit = Consumer surplus (CS) = Area between demand curve & price
From demand function, when Q = 0, P = 1,000 / 4 = 250 [Reservation price]
CS = (1/2) x (250 - 222) x 111 = (1/2) x 28 x 111 = 1,554