Question

A company is a monopolist in the door industry. The total cost is C = 100 - 5Q + Q^2 and the inverse demand is P = 55 - 2Q.

x. Determine the price that the company should set in order to maximize profit. At what output does the firm produce? Determine how much profit and consumer surplus would the company generate.

y. Determine the output if the company was a perfectly competitive firm. What would the profit and consumer surplus be? Explain the difference between part y's (this problem) results and part x's results.

z. Determine the deadweight loss from monopoly power in part x.

Answer 1

MC = dTC/dQ = 2Q - 5

(x)

TR = PQ = 55Q - 2Q²

MR = dTR/dQ = 55 - 4Q

Setting MR = MC,

55 - 4Q = 2Q - 5

6Q = 60

Q = 10

P = 55 - 2 x 10 = 55 - 20 = 35

TR = 35 x 10 = 350

TC = 100 - 5 x 10 + 10 x 10 = 100 - 50 + 100 = 150

Profit = TR - TC = 350 - 150 = 200

When Q = 0, P = 55

CS = (1/2) x (55 - 35) x 10 = 5 x 20 = 100

(y)

In perfect competition, P = MC

55 - 2Q = 2Q - 5

4Q = 60

Q = 15

P = 55 - 2 x 15 = 55 - 30 = 25

TR = 25 x 15 = 375

TC = 100 - 5 x 15 + 15 x 15 = 100 - 75 + 225 = 250

Profit = 375 - 250 = 125

CS = (1/2) x (55 - 25) x 15 = (1/2) x 30 x 15 = 225

There in perfect competition, price is lower, quantity is higher, profit is lower and CS is higher.

(z)

DWL = (1/2) x Change in P x Change in Q = (1/2) x (35 - 25) x (15 - 10) = (1/2) x 10 x 5 = 25