Question

Assume a monopolist faces a market demand curve P = 240 – 1⁄2Q and has the short-run total cost function C = Q2. a. What is the profit-maximizing level of output and price? b. What are profits? c. What would price and output be if the firm priced at the socially efficient (competitive) level? d. What is the magnitude of the deadweight loss caused by monopoly pricing?

Answer 1

a. A monopolist maximizes profits according to the rule that MR = MC.
Total Revenue, TR = P*Q = [240 - (1/2)Q]*Q = 240Q - (1/2)Q²
Marginal Revenue, MR = d(TR)/dQ = 240 - (2/2)Q = 240 - Q

Marginal Cost, MC = dC/dQ = 2Q

Now, MR = MC gives,
240 - Q = 2Q
So, 2Q + Q = 3Q = 240
So, Q = 240/3 = 80

P = 240 – 1⁄2Q = 240 – 1⁄2(80) = 240 - 40 = 200

Thus, P = 200 and Q = 80

b. Profits = TR - C = P*Q - Q² = (200*80) - 80² = 16000 - 6400 = 9600

c. At the socially efficient (competitive) level, P = MC. So, we get,
240 – 1⁄2Q = 2Q
So, 2Q + (1/2)Q = 240
So, (4Q+Q)/2 = 240
So, 5Q = 240*2 = 480
So, Q = 480/5 = 96

P = 240 – 1⁄2Q = 240 – 1⁄2(96) = 240 - 48 = 192

Thus Pc = 192 and Qc = 96

d. MC at Q = 80 is 2(80) = 160
Deadweight loss = area of triangle = (1/2)*(P - MC)*(Qc - Q) = (1/2)*(200-160)*(96-80) = (1/2)*40*16 = 320