Question

he inverse demand function faced by a monopoly is given byP=103Q. The monopolyhas a total cost functionTC=Q2+2Q and a marginal cost function MC=2Q+2.

(a) What are the monopolist’s profit maximizing price and quantity? Show these and theassociated deadweight loss on a diagram.

(b) Calculate what price and quantity would prevail if this were a perfectly competitive marketwith the marginal cost curve acting as the supply curve? Show this price on your diagramfor part (a).

(c) If the government imposes a price ceilingPc, which equals to the perfect competitive pricelevel, how much profit (loss) would the monopoly make? Calculate the size of consumersurplus in this case.

(d) Rather than imposing a price ceiling, if the government decides to collect a tax of $1 onevery unit of product sold by the monopoly, what is the monopolist’s new profit-maximizingprice and quantity? What will be the amount of deadweight loss in this case?

Answer 1

A)MR=103-2q

MC=2q+2

103-2q=2q+2

Q=101/4=25.25

P=103-25.25=77.75

B) Perfect competition equilibrium at p= MC

103-Q=2Q+2

Q=101/3=33.67

O=103-33.67=69.33

C) Profit=1/2*33.67*(69.33-2)=0.5*33.67*67.33=1133.5

Consumer surplus=1/2*33.67*(103-69.33)=0.5*33.67*33.67=555.4

D)New MC after tax=2Q+2+1=2Q+3

Profit maximizing quantity;

MR= MC

103-2Q=2Q+3

Q=100/4=25

P=103-25=78

DEADWEIGHT loss=1/2*(33.67-25)*(78-69.33-1)=0.5*8.67*7.67=33.25