Question

Suppose an airline was able to estimate the demand for passengers traveling for business purposes (B) and for leisure purposes (E) on particular route as follows:

PB = 540 - 0.5 QB

PE = 380 - 0.25 QE

The airline uses a Boeing 747 with a capacity of 400 passengers on the route and which costs $40,000 to operate.

a. How many tickets should the airline sell to each class of customer?

b.   What price should the airline charge for each type of ticket?

c. How much profit would the airline make?

Answer 1

Answer : a) Based on given information, Boeing 747 has the capacity of 400 passengers whose total cost is $40,000. So, per passenger cost or Marginal cost (MC) of airline = 40,000 / 400 = $100.

The demand function for business purposes : P = 540 - 0.5 Q

TR (Total Revenue) = P * Q = (540 - 0.5 Q) * Q

=> TR = 540Q - 0.5Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 540 - Q

At equilibrium condition MR = MC.

=> 540 - Q = 100

=> 540 - 100 = Q

=> Q = 440.

Therefore, the airline should sell 440 tickets for business purposes.

The demand function for leisure purposes : P = 380 - 0.25 Q

TR = P*Q = (380 - 0.25 Q) * Q

=> TR = 380Q - 0.25Q^2

MR = TR / Q

=> MR = 380 - 0.5Q

At equilibrium condition MR = MC.

=> 380 - 0.5Q = 100

=> 380 - 100 = 0.5Q

=> 280 = 0.5Q

=> Q = 280 / 0.5

=> Q = 560

Therefore, the airline should sell 560 tickets for leisure purposes.

b) For business purposes : Q = 440

P = 540 - (0.5 * 440)

=> P = 320

Therefore, the airline should charge $320 per ticket for business purposes.

For leisure purposes : Q = 560

P = 380 - (0.25 * 560)

=> P = 240

Therefore, the airline should charge $240 per ticket for leisure purposes.

c) For business purposes :

TR = P * Q = 320 * 440 = $140,800

Given a Boeing 747 has only 400 passengers capacity whose total cost is $40,000. But as here the airline sells 440 tickets, hence the airline has to use two Boeing 747. So, TC (Total Cost) for airline = 2 * 40,000 = $80,000.

Profit = TR - TC = 140,800 - 80,000

=> Profit = $60,800

For leisure purposes :

TR = P*Q = 240 * 560

=> TR = $134,400

TC = $80,000

Profit = TR - TC = 134,400 - 80,000

=> Profit = $54,400

Therefore, total profit for airline = $60,800 + $54,400 = $115,200.