Question

# Question 8: Suppose a monopolist faces a market demand of QD=800−PQD=800−P and has a total cost...

Question 8:
Suppose a monopolist faces a market demand of QD=800−PQD=800−P and has a total cost function of TC(Q)=Q2TC(Q)=Q2.
What is the equilibrium price and quantity decided by the monopolist?
What is the average cost at the equilibrium quantity?
How much profit does the monopolist make at the equilibrium price and quantity?

What is the equilibrium price and quantity decided by the monopolist?

The firm produces at MR=MC

converting the demand curve to the inverse demand curve to find MR function

Q=800-P

P=800-Q

MR=800-2Q ........ An MR curve is double sloped than an inverse linear demand curve

MC=change in TC =first differentiation of TC=dTC/dQ=2Q

equating MR=MC

800-2Q=2Q

4Q=800

Q=200

P=800-200=600

the quantity is 200 units and the price is \$600

What is the average cost at the equilibrium quantity?

ATC=TC/Q=Q^2/Q=Q=200

ATC is \$200

How much profit does the monopolist make at the equilibrium price and quantity?

Profit =(P-ATC)*Q

=(600-200)*200

=80000

the profit is \$80000