Question

1) A monopolist faces two consumer groups: old and young. The inverse demand of old clients for the output of the monopolist is P=180-5Q. The inverse demand of young clients for the output of the monopolist is P=50-5Q. The cost of supplying any type of client is C(Q)=1000. If the monopolist can price discriminate between the two groups (i.e., charge a different uniform price to each group),

a) what price will old clients be charged?

b) what price will young clients be charged?

c) what will be the firm's profit?

Answer 1

C(Q)=1000

Marginal Cost=dC(Q)/dQ=0

a)

In case of old

P=180-5Q

Total Revenue=TRo=P*Q=180Q-5Q^2

Marginal Revenue=MRo=dTRo/dQo=180-10Q

Set MR=MC for profit maximization

180-10Q=0

Q=18

P=180-5Q=180-5*18=90

Old should be charged a price of 90.

b)

In case of young

P=50-5Q

Total Revenue=TRy=P*Q=50Q-5Q^2

Marginal Revenue=MRy=dTRy/dQy=50-10Q

Set MR=MC for profit maximization

50-10Q=0

Q=5

P=50-5Q=50-5*5=25

Young should be charged a price of 25.

c)

Total revenue in case of young=TRy=P*Q=25*5=125

Total revenue in case of old=TRo=P*Q=90*18=1620

Total Revenue=TR=125+1620=1745

C(Q)=TC=1000

Profit=TR-TC=1745-1000=745