Question

DP Gumby produces sleeveless sweaters. He can separate the demand function into a domestic component:

QD = 32 – 0.4PD and a foreign component QF = 18 – 0.1PF His total cost function is:

C = 50 + 40Q

(f) Imagine his costs are once again C = 50 + 40Q. If Gumby can charge a different price in each market, how many sweaters should he sell domestically? How many sweaters should he sell in the foreign market? What price does he charge in each market?

(g) What is Gumby’s total profit with price discrimination? Is price discrimination profitable for Gumby’s? Comment on your result.

(h) What is the price elasticity of demand in each market? Does these values appear sensible? Explain.

(i) Suppose Gumby can discriminate perfectly among the buyers of sleeveless sweaters. What is his profit maximizing output?

(j) What is the maximum price anyone will pay under perfect price discrimination? What is the minimum price anyone will pay? Explain your choice.

Answer 1

f) domestic demand function of sleeveless sweaters is

QD= 32-0.4PD

or, 0.4PD= 32-QD

or, PD= 80-5/2QD .........(i)

Foreign demand function of sleeveless sweaters is

QF= 18-0.1PF

or, PF= 180-10QF............(ii)

Total cost function is

C= 50+40Q.............(iii)

Total revenue of DP Gumby from domestic market is,

PD.QD= 80QD-5/2QD²

Therefore, marginal revenue of DP gumby from domestic market is

(PD.QD)/QD= 80-5QD ......(iv)

Similarly marginal revenue of DP Gumby from foreign market is

(PF.QF)/QF= 180-20QF .........(v)

and marginal cost is

C/Q= 40 (From eqtn (iii))

Marginal cost is same for both domestic and foreign markets.

Under perfect condition,

marginal revenue = marginal cost

i.e., 80-5QD=40

or, QD= 8 and PD = 80-5/2QD= 80-5/2*8=60

Also, 180-20QF=40

or, QF= 7 and PF= 180-20QF= 180-20*7=40

Therefore, DP Gumby should sell 7 sleeveless sweaters in foreign market. The price of sleeveless sweaters in domestic market is 60 and foreign market 40

g) Q = QD+QF = 8+7= 15

From eqtn(i) total cost (C) = 50+40Q=50+40*15=650

Total revenue of DP Gumby = PD.QD+PF.QF= 8*60+7*40= 480+280= 760

Total profits = Total revenue-total cost = 760-650= 110 which means the price discrimination is profitable for DP Gumby.

h) Price elasticity of demand in domestic market = QD/PD *PD/QD = -0.4*60/8=-3

Price elasticity of demand in foreign market = QF/PF*PF/QF= -0.1*40/7= -0.57

From the results it appear that the price elasticity of demand of domestic market is more elastic than price elasticity of demand of foreign market.

i) From part (f), we get, the profit maximizing output of DP Gumby is

Q= QD+QF= 8+7=15

(j), From part (f), the maximum price of sleeveless sweaters is 60 and minimum price of sleeveless sweater is 40.

DP gumby charges maximum price from domestic customers and minimum price from foreign consumers. As a customer, I shall prefer to purchase sleeveless sweater from foreign market.