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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 EA'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 \(Q_{\lambda}=260-0.4 P\). Type \(B\) consists of students whose total demand is \(Q_{\mathrm{B}}=240-0.6 P\) 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
This is a comprehensive exercise detailing how businesses price their products or services in response to several scenarios, such as varying costs and customer segmentation. The solution involves calculating the profit maximizing price, determining business viability based on costs, calculating profit and consumer surplus, and understanding the impact of price discrimination on consumer surplus.

Step by step solution

01

Understanding Part a

To understand the problem, we need to use the cost and demand equations which are \(Q=500-P\) and the total cost is \(\$ 30000 +\$100*Q\). Profit \(π\) is calculated by the difference between Total Revenue (TR) and Total Cost (TC), i.e., \(π = TR - TC\).
02

Calculating Profit Maximizing Price: Part a

Start solving by substituting Q in the profit equation. So \(TR = P*Q\) becomes \(TR = P*(500-P)\). The cost equation \(TC = \$30000 +\$ 100*Q\) becomes \(TC =\$30000 + \$100*(500-P)\). Hence the profit equation becomes \(π = P*(500-P) - (\$30000 + \$100*(500-P))\). Derive the first order condition by differentiating profit with respect to price P, equate it to zero, solve for P which is the profit maximizing price and hence demand Q.
03

Understanding Part b

Accounting for the change in costs \$41000, we need to plug it into our profit equation and find the prices that allows EA to at least break even.
04

Predicting EA's Business Sustainability: Part b

Draw the new TC curve and find the lowest point of average cost curve, equate it with price and then calculate.\nNow, determine if EA can still make a profit at the profit optimizing price P and demand Q, to decide if it will stay in business.
05

Understanding Part c

Given the demand functions for two types of customers, we need to consider the pricing strategy for each segment separately and aggregate them together.
06

Calculating pricing for different customers: Part c

We need to maximize the profit functions for both the groups separately and add them in order to get the combined profit. Hence, the profit function becomes a weighted sum of both the profits; differentiate and solve for price P for both the demand functions.
07

Understanding Part d

Calculate the profit based on the new pricing strategy and evaluate if EA will stay in business. Consumer surplus is the area between the price line and the demand curve and hence, can also be determined.
08

Calculating profit and consumer surplus: Part d

By substituting the prices for two types of customers in profit function and calculating, we will get the profit for EA. If it's still making profit, EA will remain in business. Consumer surplus is the area between the price line and the demand curve and hence, can also be determined.
09

Understanding Part e

Price discrimination can shift consumer surplus to producer surplus. So, it's necessary to figure out the previous situation before discrimination to see the changes.
10

Evaluating effects of price discrimination: Part e

Calculate the consumer surplus before discrimination by determining the areas under the demand curves but above the price line for both Type A and B customers. Then compare the results with the situation after price discrimination. This will help us understand the impact of price discrimination on consumer surplus.

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Most popular questions from this chapter

A monopolist is deciding how to allocate output between two geographically separated markets (East Coast and Midwest), Demand and marginal revenue for the two markets are $$\begin{array}{ll}P_{1}=15-Q_{1} & \mathrm{MR}_{1}=15-2 Q_{1} \\ P_{2}=25-2 Q_{2} & \mathrm{MR}_{2}=25-4 Q_{2}\end{array}$$ The monopolist's total cost is \(C=5+3\left(Q_{1}+Q_{2}\right)\) What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions?

Many retail video stores offer two alternative plans for renting films: A two-part tariff: Pay an annual membership fee (e.g., \(\$ 40\) ) and then pay a small fee for the daily rental of each film (e.g., \(\$ 2\) per film per day). A straight rental fee: Pay no membership fee, but pay a higher daily rental fee (e.g., \$4 per film per day). What is the logic behind the two-part tariff in this case? Why offer the customer a choice of two plans rather than simply a two-part tariff?

You are an executive for Super Computer, Inc. (SC), which rents out super computers. SC receives a fixed rental payment per time period in exchange for the right to unlimited computing at a rate of \(P\) cents per second. SC has two types of potential customers of equal number-10 businesses and 10 academic institutions. Each business customer has the demand function \(Q=10-P,\) where \(Q\) is in millions of seconds per month; each academic institution has the demand \(Q=8-P\). The marginal cost to \(\mathrm{SC}\) of additional computing is 2 cents per second, regardless of volume. a. Suppose that you could separate business and academic customers. What rental fee and usage fee would you charge each group? What would be your profits? b. Suppose you were unable to keep the two types of customers separate and charged a zero rental fee. What usage fee would maximize your profits? What would be your profits? c. Suppose you set up one two-part tariff-that is, you set one rental and one usage fee that both business and academic customers pay. What usage and rental fees would you set? What would be your profits? Explain why price would not be equal to marginal cost.

If the demand for drive-in movies is more elastic for couples than for single individuals, it will be optimal for theaters to charge one admission fee for the driver of the car and an extra fee for passengers. True or false? Explain.

As the owner of the only tennis club in an isolated wealthy community, you must decide on membership dues and fees for court time, There are two types of tennis players. "Serious" players have demand $$Q_{1}=10-P$$ where \(Q_{1}\) is court hours per week and \(P\) is the fee per hour for each individual player. There are also "occasional" players with demand $$Q_{2}=4-0.25 P$$ Assume that there are 1000 players of each type. Because you have plenty of courts, the marginal cost of court time is zero. You have fixed costs of \(\$ 10,000\) per week. Serious and occasional players look alike, so you must charge them the same prices. a. Suppose that to maintain a "professional" atmosphere, you want to limit membership to serious players. How should you set the anmul membership dues and court fees (assume 52 weeks per year) to maximize profits, keeping in mind the constraint that only serious players choose to join? What would profits be (per week)? b. A friend tells you that you could make greater profits by encouraging both types of players to join. Is your friend right? What annual dues and court fees would maximize weekly profits? What would these profits be? c. Suppose that over the years, young, upwardly mobile professionals move to your community, all of whom are serious players. You believe there are now 3000 serious players and 1000 occasional players. Would it still be profitable to cater to the occasional player? What would be the profitmaximizing annual dues and court fees? What would profits be per week?
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