Question

Honolulu Airlines flies only one route: Chicago-Honolulu. The demand for each flight is Q = 500- P. HA’s cost of running each flight is $41,000 plus $100 per passenger.

1. What is the profit maximizing price that HA will charge if the market is a monopoly? How many people will be on each flight? What is HA’s profit for each flight? Will the airline stay in business?

2. HA finds out that two different types of people fly to Honolulu. Type A consists of business people with a demand of Q_{A = 260 - 0.4P.Type B consists of students whose total demand is QB = 240 - 0.6P.} Because the students are easy to spot, HA decides to charge each group different prices. Graph each of these demand curves and their horizontal sum (the market demand curve). What price does HA charge the students? What price does it charge to business customers?

3. What would HA’s profit be for each flight? Would the airline stay in business? Calculate the consumer

surplus of each group. What is the total CS?

4. Before HA started price discrimination, how much CS was the Type A getting? What about Type B? Why did total CS decline with price discrimination? In our price discrimination worksheet, the CS was higher with third degree price discrimination. Explain the discrepancy between the two results.

ANSWER ALL PARTS PLEASE

Answer 1

(1) The profit function of Honululu Airlines is: (500 - Q)Q - 41000 - 100Q

Differentiating the profit function with respect to Q and setting the firdst order codition equal to zero,we get:

500 - 2Q - 100 = 0, or

Q = 200, i.e. 200 passengers will take the flight.

P = 500 - 200 = 300

Total profit = 300*200 - 41000 - 100*200 = -1000

Loss per flight = -1000/200 = -5

(2)The graphs are given below:

The inverse demand function for the two markets is: PA= 650 –2.5QA and PB= 400 –1.667QB.

Marginal revenue curves: MRA= 650 –5QA, and MRB= 400 –3.33QB.

We set marginal revenue equal to marginal cost in each market to find the pprofit maximizing quantities: 650 –5QA= 100, or QA= 110, and

400 –3.33QB= 100, or QB= 90.

Substitute the profit-maximizing quantities into the respective demand curves, we get

PA= 650 –2.5(110) = $375, and

PB= 400 –1.667(90) = $250

(3)Snce profit per flight is positive with price discrimination, HA will stay in business: π = 250(90) + 375(110) –[41,000 + 100(90 + 110)] = $2750.

Consumer surplus for Type A travellers is:CSA= (0.5)(110)(650 –375) = $15,125, and

Type B travellers:CSB= (0.5)(90)(400 –250) = $6750. Total consumer surplus is therefore $21,875.

(4) If HA charges a common price to both the type of customers, the profit function would be:( 260-0.4P)P + (240-0.6P)P - 41000 - 100(500-P)

Differentiating the proft function with resect to P and setting it equal to zero, we get: 600-2P = 0, or P = 300

Hence, QA = 140 and QB = 60

CSA = 0.5(650-300)140 = 24500

CSB = 0.5(400-300)60 = 3000

Total surplus = 27500

Consumer surplus declined because Type A customers had to pay a higher price with price discrimination.