91Ó°ÊÓ

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?

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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Demand Curve

In the context of Elizabeth Airlines, a demand curve vividly illustrates consumer interest in flights from Chicago to Honolulu. The demand curve equation is expressed as \(Q=500-P\), where \(Q\) is the quantity demanded and \(P\) represents the price. This linear relationship suggests that when the price is low, more people are willing to fly.

The demand curve is essentially a graph: prices on the vertical axis and quantity on the horizontal axis. As the price decreases, the quantity demanded increase, and vice-versa. This curve is useful for finding an optimal price point where customers are willing to buy without the company missing potential revenue.

For Elizabeth Airlines, understanding the demand curve helps them assess how different pricing might affect the number of passengers. It also helps in analyzing which price points could maximize profits by balancing the potential revenue against customer interest.

Consumer Surplus

Consumer surplus is an economic measure of consumer benefits. It's represented by the area above the price level but below the demand curve. This area reflects how much more consumers would be willing to pay for a service than what they actually do pay.

Before Elizabeth Airlines started engaging in price discrimination, the consumer surplus could be calculated by analyzing the whole group using the original demand equation. Price discrimination occurs when a company charges different prices to different consumer groups for the same service, reducing the consumer surplus because some of it is transferred to the company as additional profit.

For example, business travelers, willing to pay more, might see parts of their surplus captured as additional revenue by the airline charging a higher price. Understanding and calculating consumer surplus is vital since it provides insights into customer's perceived value of the service and monitors how pricing strategies like price discrimination impact consumer well-being.

Profit Maximization

Profit maximization for Elizabeth Airlines involves finding the price and quantity combination that maximizes their revenues while deducting costs. The profit function is determined by the revenue minus costs, expressed as \((500-Q)Q - 30000 - 100Q\). This is derived from the demand curve \(Q=500-P\), where \(P\) is replaced with its equivalent \(500-Q\) based on the relationship between \(P\) and \(Q\).

To determine the optimal quantity and price for maximizing profit, the airline takes a mathematical approach by finding the derivative of the profit function with respect to \(Q\), setting it to zero, and solving for \(Q\). This gives the quantity at which profit is maximized, which in turn helps fix the optimal price by substituting back into the demand curve.

Profit maximization ensures that all factors of cost and revenue are taken into consideration, enabling the airline to make strategic decisions that promote sustainability and long-term success, especially in competitive markets. Understanding the concept of profit maximization helps not only in maintaining viable operations but also in navigating through varying demand conditions effectively.