Question

Under patent protection, a firm has a monopoly in its production. Market demand is estimated to be P = 200 – 0.7Q. The firm’s economic costs are given by ATC = MC = $60 per unit.

A. Determine the firm’s optimal output, price and economic profit.  

B. After the firm’s patent expires, predict the new market output and price under perfect competition. Assume that competing suppliers have the same economic costs as the original producer. What is the new market price, quantity, and total industry profit?   

C. Compute the resulting change in consumer surplus.   

Answer 1

a) P = 200 - 0.7Q

ATC = MC = $60

In monopoly, at equilibrium, quantity is determined at MC = MR

R = PQ = (200 - 0.7Q)*Q = 200Q - 0.7Q²

MR = 200 - 1.4Q

Now, at MC = MR

60 = 200 - 1.4Q

So, Q = 100

Hence, optimal output is 100 units

Now, substituting this value in demand function, we have:

P = 200 - 0.7 (100) = $130

Economic profit = Revenue - Cost = 130*100 - 60*100 = $7000

b) Under perfect competition, Demand = MC

Hence, 60 = 200 - 0.7Q

SO, Q = 200 units

Price, P = 200 - 0.7*200 = $60

Industry Payoff = PQ = 60*200 = $12,000

c) Change in Consumer Surplus = 0.5*100*130 - 0.5*200*60 = 500

Hence, consumer surplus decreased by 500.