Question

3. A market consists of two segments, A and B. An individual in segment A has a demand function of q = 60 − p. An individual in segment B has a demand function of q = 60 − 2p. Suppose that each segment consists of one consumer. There are no costs of production.

a. Suppose that a monopolist must charge the same price to both segments. What is the profit-maximizing price? What are the profits? Briefly explain your approach (maximum 100 words).

[25 marks]

b. Now suppose that the monopolist can observe whether an individual belongs to segment A or B. What price does the monopolist charge to segment A, and what price to segment B? Do profits increase compared to (a)? Which consumers gain by price discrimination? Briefly explain your results (maximum 100 words).

[25 marks]

c. Next, assume that the monopolist cannot observe to which segment an individual belongs. Is price discrimination still possible? If yes, what type of price discrimination can be used. Describe and explain your results (maximum 250 words).

[25 marks]

d. Suppose that the segments A and B become more heterogeneous over time. Demand in segment A is now q = 500−p, whereas demand in segment B remains at q = 60−2p. Should a policy maker ban price discrimination? Justify your answer (maximum 250 words).

[25 marks]

Answer 1

3) a)TR1=60p-p^2

TR2=60p-2p^2

Profit=TR1+TR2{ no Production cost}

Profit=60p-p^2+60p-2p^2

Profit=120p-3p^2

∆profit/∆p=120-6p=0

P=120/6=20

Profit=120*20-3*20*20=2400-1200=1200

B) TRa/ Profit 1=60p-p^2

∆TRa/∆P=60-2p=0

Pa=60/2=30

TRb=60p-2p^2

∆TRb/∆p=60-4p=0

P=60/4=15

Profit=TRa+TRb=60*30-30*30+60*15-2*15*15=1800-900+900-450=1350

Yes Profit Increase.

CONSUMERs type B benefit from price discrimination as they has pay only 15$ per unit compare to before when they pay 20 $ per unit.

C)Yes, The second degree price discrimination or Quantity discrimination is possible.

Seller will add block of Quantity. And set price for each block for Quantity.higher price for low unit of Quantity block and relative low price for high units of Quantity block.

D)If price discrimination would be ban ,then seller won't sell in segment B to maximize Profit because he would earn leaving segment B and selling at higher in segment A.

So from society point of view ,pricr discrimination should not be ban.