Question

Suppose that a monopolist producing bicycles can divide the aggregate demand into two groups: The domestic market and the foreign market. The demand curve for the monopolist’s product in   the   domestic   market is    y₁=1200-10p₁ and the   demand   curve   for   the monopolist’s product in the foreign market is y₂=800-10p₂. The monopolist’s total cost function is given by C(y)= 50y where y=y₁+y₂.

a) Assume that the monopolist does not practice price discrimination. Calculate his/her profit-maximizing price-quantity combination and the maximum profit.

b) Assume that the monopolist practices third-degree price discrimination. Calculate his/her profit-maximizing price-quantity combination and the maximum profit in each market.

c) Check whether the third-degree price discrimination increases or decreases welfare

Answer 1

y₁ = 1200- 10p₁

y₂ = 800 - 10p₂

C(y) = 50y

y = y1 + y2

MC = 50

Monopolist does not practice price discrimination so total market demand would be

y1 + y2 = 1200 - 10p₁ + 800 - 10p₂

y = 2000 - 10p - 10p since p1 = p2 = p

y = 2000 - 20p

20p = 2000 - y

p = 100 - y/20

MR = 100 - 2y/20

MR = 100 - y/10

MR = MC

100 - y/10 = 50

100 - 50 = y/10

50 = y/10

y = 500

p = 100 - y/20

p = 100 - 500/20

p = 100 - 25

p = 75

Profit = py - 50y

= 75×500 - 50×500

= 37500 - 25000

= 12500

b)

Now monopolist practices third degree price discrimination

y₁ = 1200 - 10p₁

p₁ = 120 - y₁/10

MR₁ = 120 - 2y₁/10

y₂ = 800 - 10p₂

_p2 = 80 - y₂/10

_MR2 = 80 - 2y₂/10

MC = 50

MR₁ = MR₂ = MC

MR₁ = MC

120 - 2y₁/10 = 50

120 - 50 = 2y₁/10

70 = y₁/5

y₁ = 350

p₁ =120 - 350/10

= 120 - 35

= 85

MR₂ = MC

80 - 2y₂/10 = 50

80 - 50 = 2y₂/10

30 = y2/5

y2 = 150

p₂ = 80 - 150/10

= 80 - 15

= 65

Profit = p₁y₁ + p₂y₂ - 50y

= 85×350 + 65×150 -50(350 +150)

= 29750 + 9750 - 25000

= 14500

c)

Monopolist's welfare is measured by his/her profit.

Profit of monopolist when he/she practices third degree price discrimination is 14500 and when he/she does not practice third degree price discrimination is 12500. Since profit of monopolist has increased from 12500 to 14500 as he/she practices third degree price discrimination. Therefore welfare of monopolist has gone up or increased after practicing third degree price discrimination.