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

The demand curve for the domestic market : y₁=1200-10p₁

The demand curve for the foreign market :  y₂=800-10p₂

C(y)= 50y

Marginal cost = Differentiation of C wrt y= 50

a) Monopolist does not practice price discr,imination means charging uniform price that is:

p = p₁ = p₂

Total demand for the good:

y = y₁ + y₂

y = 1200-10p₁ +800-10p₂

y = 2000-20p Demand function

p= (2000-y)/20 Inverse demand function

pm= Price when y is zero= 100

Total revenue(TR)= y x p= (2000y-y² )/20

Marginal revenue(MR)= Differentiation of TR wrt y= (2000-2y)/20

Profit maximizing condition:

MC= MR

50= (2000-2y)/20

1000 = 2000-2y

2y = 2000-1000

y*= 1000/2= 500 Equilibrium quantity

p*= (2000-500)/20= 1500/20= 75 Equilibrium price

Profit= p* x y* - 50y*= 37500-25000= 12500

b)

Assume that the monopolist practices third-degree price discrimination:

The demand curve for the domestic market : y₁=1200-10p₁

p₁ = (1200-y₁ )/10

pm1= Price in domestic market when y₁ is zero= 120

Total revenue of firm1(TR1)= p₁ x y₁ = (1200y₁ -y₁² )/10

MR1= (1200-2y₁ )/10

MC= 50

Profit maximizing condition(Domestic market):

MC= MR1

50= (1200-2y₁ )/10

500= 1200-2y₁

2y₁ = 700

y₁* = 350 Equilibrium quantity in domestic market

p₁* = (1200-350)/10= 850/10= 85

Profit in domestic market= 350 x 85 - 350 x 50= 12250

The demand curve for the foreign market :  y₂=800-10p₂

p₂ = (800-y₂ )/10

pm2= Price when y₂ is zero= 80

MR2= (800-2y₂ )/10

MC= 50

Profit maximizing condition in foreign market:

MC=MR

50= (800-2y₂ )/10

500= 800-2y₂

2y₂ = 800-500

y₂* = 300/2= 150 Equilibrium quantity in foreign market

p₂*= (800-150)/10= 650/2 = 65 Equilibrium price in foreign market

c.

Consumer surplus before price discrimination= (1/2) (Pm-p*)(y*)= 1/2 (100-75)(500)= 6250

Producer surplus before price discrimination= (1/2) (p*-MC)(y*)= (1/2) (75-50)(500)= 6250

Total surplus before price discrimination= 6250+6250= 12500

Consumer surplus after price discrimination in domestic market= (1/2) (pm1-p₁* )(y₁* )= 1/2 (120-85)(350)= 6125

Producer surplus after price discrimination in domestic market= (1/2) (p₁* - MC)(y₁* )= 1/2 (85-50)(350)= 6125

Total surplus after price discrimination in domestic market= 6125+6125= 12250

Consumer surplus after price discrimination in foreign market= (1/2) (pm2-p₂* )(y₂* )= 1/2 (80-65)(150)= 1125

Producer surplus after price discrimination in foreign market= (1/2) (p₂* - MC)(y₂* )= 1/2 (65-50)(150)= 1125

Total surplus after price discrimination in foreign market= 1125+1125= 2250

Total surplus after price discrimination= 12250+2250= 14500

Change in total surplus= 14500-12500= 2000

The third-degree price discrimination increases welfare by 2000.