Question

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

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

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., \(π = TR - TC\).

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.

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.

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.

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.

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.

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.

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.

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.

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.

Key concepts

Demand Curve

The demand curve is a visual representation that illustrates how the quantity of a good or service demanded by consumers changes as the price varies. For Elizabeth Airlines (EA), the demand curve for flights between Chicago and Honolulu is given by the equation \(Q = 500 - P\). This linear equation tells us that as the price \(P\) increases, the quantity demanded \(Q\) decreases, and vice versa. It's important to understand that the demand curve slopes downward due to the law of demand: consumers typically buy less of a good as its price increases.

When drawing the demand curve for EA, plot the price \(P\) on the vertical axis and the quantity \(Q\) on the horizontal axis. The interception point on the vertical axis indicates the price at which no consumer would buy the flight tickets, while the axis intercept on the horizontal axis represents the maximum number of tickets the airline could theoretically sell at a price of zero. Understanding the shape and behavior of the demand curve helps EA in setting prices to maximize profits.

Price Discrimination

Price discrimination occurs when a business sells the same product to different consumers at different prices. EA uses this strategy by identifying two distinct groups traveling to Honolulu: business people (Type A) and students (Type B). Each group has its own demand curve: \(Q_A = 260 - 0.4P\) for business travelers and \(Q_B = 240 - 0.6P\) for students.

For EA, practicing price discrimination involves setting different prices for business people and students based on their respective demand curves. Business travelers typically have a lower price sensitivity, allowing EA to charge them a higher price compared to students. To determine the optimal price for each group, EA calculates both curves separately and sets prices that maximize profits while considering the price consumers in each group are willing to pay. By doing this, EA can effectively boost revenue compared to a one-price-fits-all approach.

Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. In the case of EA, consumer surplus represents the area under the demand curve and above the price line for each segment of customers—business travelers and students.

Before EA engaged in price discrimination, each group's consumer surplus was determined by the single price set for all tickets. With price discrimination, the consumer surplus may decrease as EA captures some of this surplus as additional profit by charging higher prices to segments who can afford to pay more. While total quantity sold remains constant, consumer surplus for each group tends to shrink because the price is closer to what each customer is willing to pay, transferring this surplus to EA as increased profits.

Average Cost Curve

The average cost curve displays the cost per unit of output produced, calculated by dividing total costs by the output level. For EA, the average cost consists of fixed costs and variable costs. Initially, fixed costs were \\(30,000 per flight, with a variable cost of \\)100 per passenger. This adds up to an average cost curve, which changes as the number of passengers varies.

EA later finds out the fixed cost per flight increases to \$41,000. This impacts the average cost curve by shifting it upwards, indicating higher average costs at any number of passengers. The average cost curve is crucial for EA's profitability analysis. If the price falls below the average cost, EA will incur a loss. Hence, understanding this curve helps EA determine if it can sustainably cover costs and make a profit, ensuring long-term viability. The position of this curve influences critical pricing and operational decisions by the airline.