Question

As the domestic border opens, Qantas Airlines (QA) decides to fly only in one route: Sydney Perth. The demand for each flight on the route is Q=500-P. Qantas’s cost of running each flight is $3000 plus $100 per passenger. a) What is the profit maximizing price that QA will charge? How many people will be on each flight? What is QA’s profit for each flight? b) QA finds out two different types of people fly to Perth. The business people’s demand is Q1=260-0.4P, and the demand for the leisure-travellers (LT) is Q2=240-0.6P. As the LTs are easy to spot from their flexible date of travel QA decides to charge them different prices. What price does QA charge the LTs? What price does QA charge the business people? Will this discrimination reduce the number of passengers? c) Will the new pricing scheme change the profit of QA? d) How much will be the change in total consumer surplus due to this price discrimination? e) Will the deadweight loss be changed due to price discrimination?

Answer 1

Q=500-P

Inverse demand function: P= 500-Q

Cost= 3000+100Q

Where Q is the number of passenger

a)

Firm will set optimal price where:

Marginal revenue(MR)=Marginal cost(MC)

For marginal revenue:

Total revenue(TR)= P x Q= 500Q-Q²

MR= dTR/dQ= 500-2Q

For MC:

Differentiate cost function with respect to Q:

MC= 100

Optimal condition:

MC=MR

100=500-2Q

2Q= 400

Q*= 200 there will be 200 passengers on each flight

Profit maximizng price= P*= 500-Q= 500-200= 300

Profit= P* x Q* - Cost

Profit= 200 x 300 - 3000-100(200)

Profit= 60000-3000-20000= 37000

b)

The business people’s demand is Q1=260-0.4P1

Inverse demand function for business people: P1=650-2.5Q1

MR1= Marginal revenue for business people= 650-5Q1

The demand for the leisure-travellers (LT) is Q2=240-0.6P

Inverse demand function for LT: P2= 400-Q2/0.6

MR2= Marginal revenue for LT= 400-Q2/0.3

MC= 100

Optimal quantity and price for business people:

MC= MR1

100= 650-5Q1

5Q1= 550

Q1*= 110 Optimal quantity of business people

P1*= 650-2.5(110)= 650-275= 375 Price charged from business people

Optimal quantity and price for LT:

MC=MR2

100= 400-Q2/0.3

Q2/0.3= 300

Q2*= 90 Optimal quantity of LT

P2*= 400-90/0.6= 250 Optimal price from LT

Total quantity= Q= Q1*+Q2*= 90+110= 200

No the price discrmination does not cause decrease in number of passengers

c.

Profit after discrimination:

Profit from business people= P1* x Q1* - cost= 110 x 375 - 3000-100(110)= 27250

Profit from LT= P2* x Q2* - Cost= 90 x 250-3000-100(90)= 10500

Total profit= 27250+10500= 37750

Yes the new pricing strategy increases the profit by 750.

d.

Consumer surplus before discrimination:

Q=500-P

Q*=200

P*=300

Pm= Price when Q is 0= 500

Consumer surplus= 1/2 (Pm-P*)Q*= 1/2 (500-300)(200)= 100 x 200= 20000

Consumer surplus after discrimination:

Q1=260-0.4P1

Q1*= 110

P1*= 375

P1m= Price when Q1 is 0= 650

Consumer surplus(of business people)= 1/2 (P1m-P1*)Q1*= 1/2(650-375)(110)=15125

Q2=240-0.6P2

Q2*= 90

P2*= 250

P2m= 400

Consumer surplus(of LT)= 1/2 (P2m-P2*)Q2*= 1/2 (400-250)(90)= 6750

Total consumer surplus after new pricing= 15125+6750= 21875

Due to price discrimination there is an increase in consumer surplus by 1875.