Question

A hotel serves both business and vacation travelers and wishes to price-discriminate. The hotel managers can accurately identify and separate submarkets.

The hotel faces the following cost : MC = AC = 20

Demand by business travelers:          Qb = 400 -5Pb

Demand by vacationer:                          Qv = 400 -10 Pv

3.3. What price should be charged to each type of travelers? Calculate total revenue generated by each submarket.

3.4. Calculate the price elasticity of demand for each submarket based on your answer to 3.3.

3.5. How much profit does the hotel earn?

Answer 1

Pb = (400 - Qb)/5 = 80 - 0.2Qb

Pv = (400 - Qv)/10 = 40 - 0.1Pv

(3.3)

Profit is maximized when MRb = MC and MRv = MC.

(I)

TRb = Pb x Qb = 80Qb - 0.2Qb2

MRb = dTRb/dQb = 80 - 0.4Qb

80 - 0.4Qb = 20

0.4Qb = 60

Qb = 150

Pb = 80 - 0.2 x 150 = 80 - 30 = 50

TRb = 50 x 150 = 7500

(II)

TRv = Pv x Qv = 40Qv - 0.1Qv2

MRv = dTRv/dQv = 40 - 0.2Qv

40 - 0.2Qv = 20

0.2Qv = 20

Qv = 100

Pv = 40 - 0.1 x 100 = 40 - 10 = 30

TRv = 30 x 100 = 3000

(3.4)

Elasticity of demand, Business = (dQb/dPb) x (Pb/Qb) = - 5 x (50/150) = - 1.67

Elasticity of demand, Vacation = (dQv/dPv) x (Pv/Qv) = - 10 x (30/100) = - 3

(3.5)

Total profit = TRb + TRv - MC x (Qb + Qv)

= 7500 + 3000 - 20 x (150 + 100)

= 10500 - 20 x 250

= 10500 - 5000

= 5500