Question

Assume a monopolist who sells a product with a total cost function C=-100Q+1.5Q^2. The market demand is given by the equation P=300-Q. (a) What is the unregulated monopoly quantity and price? (b) Is the monopolist making a profit or loss? How much is the profit or loss? (c) Suppose the monopolist is regulated to charge a rate which covers all unit cost and total cost, what is this rate and how many units will the monopolist produce? (d) If the regulatory agency desires for the monopolist to produce the socially optimal quantity and rate(price), what would they respectively be? (e) Which form of monopoly regulation most commonly used and why?

Answer 1

ANswer a : Unregulated Monopoly quantity and price

P = 300-Q

PQ =300Q- Q²

MR =300-2Q

C = -100Q+1.5Q²

MC =-100+3Q

Unregulated monopoly price

MR =MC (Profit maximisation condition)

300-2Q = -100+3Q

400 =5Q

Q = 400/5

Q = 80 units

P = 300-80 = 220

So at this point quantity they sold is 80 units where as price they charged is $220

Answer b : At this point monopolistic earning a profit because the revenue they generate is more than the cost. They are operating at profit maximisation condition.

Profit = TR-TC

Profit = 300*80-(80)² -(-100(80)+1.5(80)²

Profit = 17600-1600

Profit =$ 16000

At this point monopoly earning a profit of $16000

Answer c : C = -100Q+1.5Q²

ATC =-100+1.5Q

P=300-Q

ATC =P

-100+1.5Q = 300-Q

1.5Q+Q =400

2Q =400

Q =200 units

P = 300-Q

P= 300-200 =100

If monopolist has been regulated than the price charged is $100 where as quantity is 200 units .

ANswer d : Social optiumal price

MC =P

MC =-100+3Q

P =300-Q

-100+3Q =300-Q

4Q =400

Q =100 units

P =300-Q

P =300-100 =$200

Social optiumal price is 200 and output is 100 units

Answer e : A government regulated form of monopoly has been most commonly used because as per this fair price has been charged by the consumer and to cover all fixed as well as variable cost from the price they charged from the producer. Regulated monopoly result in the government make a control and charged a price where ATC=P , the price that has been charged which covered all the cost incurred by them.

Answer b :