Question

Suppose that the BIG CATS  can segment their fans into young fans and senior citizens. Young fans have the demand curve P=120-10G (MR=120-20G). Senior citizens have the demand curve P=60-10G (MR=60-20G). Assume that MC=0.

1. What are the equilibrium price and quantity if the monopoly charges both groups the same price?
2. What are the equilibrium price and quantity for each group if the BIG Cats can segment the market?
3. Calculate producer surplus in each case.

Answer 1

Young fans:

demand curve P=120-10G (MR=120-20G).

Inverse demand curve for Young fans: G= (120-P)/10

Senior citizens: demand curve P=60-10G (MR=60-20G).

Inverse demand curve fro Senior citizens: G = (60-P)/10

Assume that MC=0

a.

If Same price from each segment then:

Total demand in the market:

G' = G+G

G'= (120-P)/10 + (60-P)/10

G'= [120-P+60-P]/10

G'= [180-2P]/10

G'= (90-P)/5 Inverse demand curve for market

5G'= 90-P

P= 90-5G' Demand curve for the market

Total revenue= P x G'= 90G'-5G'²

MR= Differentiation of total revenue wrt G'= 90-10G'

MC=0

Optimal condition:

MR=MC

90-10G'=0

90 = 10G'

G' = 9 Equilibrium Quantity

Use this in demand curve equation:

P= 90-5G' = 90-5(9)= 90-45= 45 Equilibrium price

b)

When there are different prices for the two segments:

For Young fans: Optimal conditon

MR=MC

120-20G=0

20G = 120

G*= 6 Equilibrium quantity for young fans

Use this in demand curve of young fans:

P*=120-10G= 120-60= 60 Equilibrium price for young fans

For senior citizens: Optimal condition

MR=MC

60-20G =0

20G=60

G**= 3 Equilibrium quantity for senior citizens

Use this value in demand curve for senior citizens:

P**= 60-10G= 60-30= 30 Equilibrium quantity for senior citizens

c.

Here as cost is Zero, so

Producer surplus= Profit

When there was a uniform price in the market:

Producer surplus= P x G'= 45 x 9= 405

When price is not uniform:

Producer surplus from young fans segment= P* x G*= 60 x 6= 360

Producer surplus from senior citizen segment= P** x G**= 30 x 3= 90

Total producer surplus= 360+90= 450