Question

1. A monopolist sells in two states and practices price discrimination by charging different prices in each state. The monopolist produces at constant marginal cost MC = 10, Demand in market 1 is Q₁ = 50-P₁. Market 2 demand is Q₂ = 90-5P₂.
   1. What price will be charge in each market?
   2. Find elasticities of demand for each market.
   3. Suppose a third party enters the market, no as a producer but as a reseller, capable of reselling by transporting the goods from market to market at a cost of $4/unit. How does this affect the monopolist?

Answer 1

a)

Market 1

Q1=50-P1

or P1=50-Q1

Total Revenue in Market 1=TR1=P1*Q1=50Q1-Q1²

Marginal Revenue in Market 1=MR1=dTR1/dQ1=50-2Q1

Set MR1=MC for profit maximization

50-2Q1=10

2Q1=40

Q1*=20 -------Profit maximizing output in market 1

P1*=50-Q1=50-20=$30 --------Profit maximizing price in market 1

Market 2

Q2=90-5P2

or 5P2=90-Q2

P2=18-0.2Q2

Total Revenue in Market 2=TR2=P2*Q2=18Q2-0.2Q2²

Marginal Revenue in Market 2=MR2=dTR2/dQ2=18-0.4Q2

Set MR2=MC for profit maximization

18-0.4Q2=10

0.4Q2=8

Q2*=20 -------Profit maximizing output in market 2

P2*=18-0.2*Q2=18-0.2*20=$14 --------Profit maximizing price in market 2

b)

Market 1

Q1=50-P1

dQ1/dP1=-1

Price elasticity of demand at optimal level for market 1=(dQ1/dP1)*(P/Q)=-1*(30/20)=-1.50

Market 2

Q2=90-5P2

dQ2/dP2=-5

Price elasticity of demand at optimal level for market 2=(dQ2/dP2)*(P/Q)=-5*(14/20)=-3.50

c)

Suppose a third party enters from market 2 to market 1,

Cost of third party=14+4=18

Third party can start selling at a price above $18 i.e. $19.Monopolist will have to reduce the price to 19

This will increase the quantity demanded but profit will be reduced.