Question

Elizabeth Airlines (EA) flies only one route: Chicago–Honolulu. The demand for each flight is Q = 500 - P. EA’s cost of running each flight is \(30,000 plus \)100 per passenger.

1. What is the profit-maximizing price that EA will charge? How many people will be on each flight? What is EA’s profit for each flight?
2. EA learns that the fixed costs per flight are in fact \(41,000 instead of \)30,000. Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that EA faces, EA’s average cost curve when fixed costs are \(30,000, and EA’s average cost curve when fixed costs are \)41,000.
3. Wait! EA finds out that two different types of people fly to Honolulu. Type A consists of business people with a demand of QA = 260 - 0.4P. Type B consists of students whose total demand is QB = 240 - 0.6P. Because the students are easy to spot, EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does it charge other customers? How many of each type are on each flight?
4. What would EA’s profit be for each flight? Would the airline stay in business? Calculate the consumer surplus of each consumer group. What is the total consumer surplus?
5. Before EA started price discriminating, how much consumer surplus was the Type A demand getting from air travel to Honolulu? Type B? Why did total consumer surplus decline with price discrimination, even though total quantity sold remained unchanged?

Short answer

a. EA will charge $300 per ticket.

There will be 200 people per flight.

The profit from each flight will be $10,000.

b. No, EA will not shut down. The below graph shows EA’s average cost curve when fixed costs are $30,000 and EA’s average cost curve when fixed costs are $41,000.

c. Each demand curve and the horizontal sum is shown below:

EA charges the students $250, other customer groups $375. There are 90 students and 110 other customers on each flight.

d. EA’s profit will be $2750 for each flight, and the airline will stay in business. The consumer surplus for the student group will be $6750, and for other customer, groups will be $15,125. The total consumer surplus will be $21,875.

e. Before price discrimination, the consumer surplus for Type A will be $24,500, and for Type B will be $3000. The difference in consumer surplus is that the business consumers have to pay more during the price discrimination, and their demand is inelastic.

Step-by-step solution

Explanation for part (a)

The profit-maximizing price and quantity are calculated below:

$$\begin{gathered} \text{P = 500 - Q} \\ \text{MR = 500 - 2Q} \\ \text{MC = \$ 100} \\ \text{MR = MC} \\ \text{500 - 2Q = 100} \\ \text{2Q = 400} \\ \text{Q = 200} \\ \text{P = 500 - 200} \\ \text{= \$ 300} \end{gathered}$$

The price will be $300 per ticket and 200 people on each flight.

The total profit is calculated below:

$$\begin{gathered} \mathrm{\pi }=\left(300\times 200\right)-30,000-100\left(200\right) \\ =60,000-30,000-20,000 \\ =\$10,000 \end{gathered}$$

The total profit will be $10,000.

Explanation for part (b)

As the fixed cost increases, it will not alter the output level and the price, as the fixed cost does not enter into the marginal cost. With the increase in fixed cost, only the profit reduces. EA cannot shut down immediately as the fixed cost will be more. The shutdown will happen only when the earnings cannot pay the fixed cost.

The graph below shows the change in average cost:

AC₁ represents when the average cost when FC is $30,000, and AC₂ represents when the average cost when FC is $41,000. Here, the average cost is $250 when the FC is $30,000, and the average cost is $305 when the FC is $41,000; $300 represents the price per ticket.

Explanation for part (c)

The price and quantity of Type A customers are calculated below:

$$\begin{gathered} {\text{Q}}_{\text{A}}{\text{= 260 - 0.4P}}_{\text{A}} \\ {\text{P}}_{\text{A}}{\text{= 650 - 2.5Q}}_{\text{A}} \\ {\text{MR}}_{\text{A}}{\text{= 650 - 5Q}}_{\text{A}} \\ \text{MC = 100} \\ {\text{650 - 5Q}}_{\text{A}}\text{= 100} \\ {\text{5Q}}_{\text{A}}\text{= 550} \\ {\text{Q}}_{\text{A}}\text{= 110} \\ {\text{P}}_{\text{A}}\text{= 650 - 2.5}\left(\text{110}\right) \\ \text{= 650 - 275} \\ \text{= \$ 375} \end{gathered}$$

There will be 110 business passengers at a ticket price of $375.

The price and quantity of Type B customers are calculated below:

$$\begin{gathered} {\text{Q}}_{\text{B}}{\text{= 240 - 0.6P}}_{\text{B}} \\ {\text{P}}_{\text{B}}{\text{= 400 - 1.667Q}}_{\text{B}} \\ {\text{MR}}_{\text{B}}{\text{= 400 - 3.33Q}}_{\text{B}} \\ \text{MC = 100} \\ {\text{400 - 3.33Q}}_{\text{B}}\text{= 100} \\ {\text{3.33Q}}_{\text{B}}\text{= 300} \\ {\text{Q}}_{\text{B}}\text{= 90} \\ {\text{P}}_{\text{B}}\text{= 400 - 1.667}\left(\text{90}\right) \\ \text{= 400 - 150} \\ \text{= \$ 250} \end{gathered}$$

There will be 90 student passengers at a ticket price of $250.

The demand curve is shown below:

The price charged to passenger A is higher than that changed for passenger B. Passenger A will have a steep demand curve due to inelastic demand, and passenger B will have a flat demand curve; hence, the demand curve is flat from $400 onwards but steep till $400.

Explanation for part (d)

The profit is calculated below:

$$\begin{gathered} \mathrm{\pi }=\left(250\times 90\right)\left(375\times 110\right)-41,000-100\left(90+110\right) \\ =22,500+41,250-41,000-20,000 \\ =\$2750 \end{gathered}$$

Yes, the airline will stay in business as the profit is positive.

The consumer surplus for both types of the consumer is calculated below:

$$\begin{gathered} C{S}_A=0.5\times 110\times \left(650-375\right) \\ =0.5\times 110\times 275 \\ =\$15,125 \\ C{S}_B=0.5\times 90\times \left(400-250\right) \\ =0.5\times 90\times 150 \\ =\$6,750 \end{gathered}$$

The total consumer surplus will be $21,875 (=15,125 + 6750).

Explanation for part (e)

When the price is $300, then the consumer surplus for Type A customers will be,

$$\begin{gathered} Q_A=260-0.4\left(300\right) \\ =260-120 \\ =140 \\ CS=0.5\times 140\left(650-300\right) \\ =0.5\times 140-350 \\ =\$24,500 \end{gathered}$$

When the price is $300, then the consumer surplus for Type B customers will be,

$$\begin{gathered} Q_B=240-0.6\left(300\right) \\ =240-180 \\ =60 \\ CS=0.5\times 60\left(400-300\right) \\ =0.5\times 60-100 \\ =\$3,000 \end{gathered}$$

The total consumer surplus will be $27500, which is greater than the consumer surplus with the price discrimination. The difference in consumer surplus is that the business consumer has to pay more during the price discrimination, and their demand is inelastic.