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Chapter 11: Problem 6

Elizabeth Airlines (EA) flies only one route: ChicagoHonolulu. The demand for each flight is \(Q=500-P\) EA's cost of running each flight is \(\$ 30,000\) plus \(\$ 100\) per passenger. a. 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? b. 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 \(\mathrm{EA}^{\prime}\) s average cost curve when fixed costs are \(\$ 41,000\) c. Wait! EA finds out that two different types of people fly to Honolulu. Type \(A\) consists of business people with a demand of \(Q_{A}=260-0.4 P\). Type \(B\) consists of students whose total demand is \(Q_{B}=240-0.6 P\) 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? d. 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? e. 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

Expert verified
Profit maximization occurs when marginal cost equals marginal revenue. The change in fixed costs and price discrimination changes the situation in the following ways: the increase in fixed costs may make the business non-profitable, while price discrimination allows the airline to capture more consumer surplus, but does not change the total quantity sold. The total consumer surplus decreases as the producer captures portion of it by charging different prices.

Step by step solution

01

Profit Maximization

The demand curve for EA is \(Q=500-P\). The total cost of each flight is composed of a fixed cost (\$30000) and variable cost per passenger (\$100*Q). Profit is revenue (price*quantity) minus cost. In terms of quantity, this is \((500-Q)*Q - 30000 - 100*Q\). To find the quantity that maximizes profit, take the derivative of the profit function with respect to quantity (Q), set it equal to zero, and solve for Q. This will give the quantity that maximizes profit.
02

Change in Fixed Cost

If the fixed cost increases to \$41000, re-do the calculation in Step 1. If the new quantity that maximizes profit results in a negative profit, EA will not stay in business for long.
03

Price Discrimination

To find the prices EA will charge for both types of customers, find the quantity that maximizes profit for each type, separately (same process as in step 1), using the given demand curves \(Q_{A} = 260 - 0.4P\) and \(Q_{B} = 240 - 0.6P\). The sum of quantities from both types should equal to the capacity of the plane.
04

Calculating Consumer Surplus

Calculate the consumer surplus for each group using the formula \(CS = (1/2)* (Q)*(highest willingness to pay - P)\) where highest willingness to pay is the price at which quantity demanded is 0, obtained from the demand curves in step 3.
05

Price Discrimination and Consumer Surplus

Calculate the consumer surplus before price discrimination using the original demand curve. The decrease in total consumer surplus due to price discrimination occurs because the producer captures some of the surplus by charging different prices.

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