A monopolist sells travel services to two groups of people with the following de

Question

A monopolist sells travel services to two groups of people with the following demand curves Q1 = 100 – 2P1 (and MR1 = 50 – Q1) and Q2 = 60 – P2 (and MR2 = 60 – 2Q2) . The marginal cost of providing one unit of travel service to either of the groups is the same for the monopolist, i.e., MC = $10 per unit.

(a) Identify whether group 1 or group 2 has more elastic demand. (b) If the monopolist can price discriminate, then what prices would the monopolist charge the two groups for travel services? What quantities will the monopolist sell to each group?

(c) Suppose the monopolist is forced to charge a single price to all consumers regardless of which group they belong to. What is the profit maximizing price and quantity? Who benefits from this policy? Who loses?

(d) What would be equilibrium price and quantity if the market was competitive?

Explanation / Answer

a)

For group 1, For Profit maximization

MR=MC

50-Q1=10

Q1=40

P1=(100-Q1)/2=(100-40)/2=30

Elasticity=dQ1/dP1*(P1/Q1)

Q1 = 100 – 2P1

dQ1/dP1=-2

Elasticity=(-2)*(30/40)= -1.5

For group 2, For Profit maximization

MR=MC

60-2Q2=10

Q2=25

P2=60-Q2=(60-25)=35

Elasticity=dQ2/dP2*(P2/Q2)

Q2 = 60-P2

dQ2/dP2=-1

Elasticity=(-1)*(35/25)= -1.4

Thus Group 1(-1.5) has more elasticity than group 2(-1.4)

b)

For group 1, For Profit maximization

MR=MC

50-Q1=10

Q1=40

P1=(100-Q1)/2=(100-40)/2=30

For group 2, For Profit maximization

MR=MC

60-2Q2=10

Q2=25

P2=60-Q2=(60-25)=35

Thus group1 should charge $30 and sell 40 unit and group 2 should charge $25 and sell 25 unit

c)

Let both are charging the same price=P

Net Quantity=Q1+Q2=100-2P+60-P=160-3P

Total quantiy=35+40=75(as calculated above)

Thus 160-3P=75

3P=85

P=$28.3

Thus both should charge $28.3

Thus group 1 will lose as it was charging $30 and now have to charge $28.3 and group 2 will benefit as it will be charging $28.3 from $25

d)

For perfect Competition

P=MC=MR=$10

Thus Quantity supplied by group A =100-2P1=100-2*10=80 unit

Quantity supplied by group B=60-P2=60-10=50 unit

Thus equilibrium price=$10

Equilibrium quantity=80+50=130 unit

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.