Question

The Collegetown movie theater serves 900 students and 100 professors in town. Each student's willingness to pay for a movie ticket is $\mathrm{\$}5.$ Each professor's willingness to pay is $\mathrm{\$}10.$ Each will buy only one ticket. The movie theater's marginal cost per ticket is constant at $\mathrm{\$}3,$ and there is no fixed cost. a. Suppose the movie theater cannot price-discriminate and charges both students and professors the same price per ticket. If the movie theater charges $\mathrm{\$}5,$ who will buy tickets and what will the movie theater's profit be? How large is consumer surplus? b. If the movie theater charges $\mathrm{\$}10,$ who will buy movie tickets and what will the movie theater's profit be? How large is consumer surplus? c. Assume the movie theater can price-discriminate between students and professors by requiring students to show their student ID, charging students $\mathrm{\$}5$ and professors $\mathrm{\$}10$, how much profit will the movie theater make? How large is consumer surplus?

Short answer

Answer: Under the price discrimination scenario, the movie theater's profit is $2500, and the consumer surplus is 0. Comparatively, when charging the same price for both students and professors, the movie theater's profit is lower at $2000 (charging $5 for both) or $700 (charging $10 for both), while the consumer surplus is either $500 (charging $5 for both) or 0 (charging $10 for both).

Step-by-step solution

a. Movie theater charging $\mathrm{\$}5$ for both students and professors tickets#

In this case, all 900 students and 100 professors will buy tickets because the price is within their willingness to pay. The movie theater's revenue would be $(900+100)\times \mathrm{\$}5=\mathrm{\$}5000$. The total cost for supplying these tickets would be $(900+100)\times \mathrm{\$}3=\mathrm{\$}3000$. Thus, the theater's profit will be $\mathrm{\$}5000-\mathrm{\$}3000=\mathrm{\$}2000$. To find consumer surplus, we need to calculate the difference between the willingness to pay and the price charged for each group. For the students: The willingness to pay is $\mathrm{\$}5$ and the price charged is $\mathrm{\$}5$. So, the consumer surplus for the students is $0$. For the professors: The willingness to pay is $\mathrm{\$}10$ and the price charged is $\mathrm{\$}5$. So, the consumer surplus for the professors is $(\mathrm{\$}10-\mathrm{\$}5)\times 100=\mathrm{\$}500$.

b. Movie theater charging $\mathrm{\$}10$ for both students and professors tickets#

In this case, none of the students will buy tickets because the price is higher than their willingness to pay. So, only the 100 professors will buy tickets. Accordingly, the movie theater's revenue would be $100\times \mathrm{\$}10=\mathrm{\$}1000$. The total cost for supplying these tickets would be $100\times \mathrm{\$}3=\mathrm{\$}300$. Thus, the theater's profit will be $\mathrm{\$}1000-\mathrm{\$}300=\mathrm{\$}700$. The consumer surplus would be 0 for both students and professors, as the price is equal to the willingness to pay for professors and higher than the willingness to pay for students.

c. Movie theater price-discriminating between students and professors#

In this case, the movie theater charges students $\mathrm{\$}5$ and professors $\mathrm{\$}10$. All 900 students and 100 professors will buy tickets under this scenario. The movie theater's revenue from students: $900\times \mathrm{\$}5=\mathrm{\$}4500$ The movie theater's revenue from professors: $100\times \mathrm{\$}10=\mathrm{\$}1000$ Total revenue: $\mathrm{\$}4500+\mathrm{\$}1000=\mathrm{\$}5500$ The total cost for supplying these tickets would be $(900+100)\times \mathrm{\$}3=\mathrm{\$}3000$. Thus, the theater's profit will be $\mathrm{\$}5500-\mathrm{\$}3000=\mathrm{\$}2500$. To find consumer surplus, we need to calculate the difference between the willingness to pay and the price charged for each group. For the students: The willingness to pay is $\mathrm{\$}5$ and the price charged is $\mathrm{\$}5$. So, the consumer surplus for the students is $0$. For the professors: The willingness to pay is $\mathrm{\$}10$ and the price charged is $\mathrm{\$}10$. So, the consumer surplus for the professors is $0$. Thus, the total consumer surplus in this case is also $0$.

Key concepts

Consumer Surplus

Consumer surplus is a key economic concept that helps us understand the benefits consumers receive from purchasing a product at a price less than what they're willing to pay. Let's imagine you are at a market, and you're willing to pay $10 for an apple, but you find it for $7. The surplus of $3 represents your consumer surplus. It's a measure of the "bonus" satisfaction you get.

• In our example, when the theater charges $5, professors, who would have paid $10, enjoy a surplus of $5 per ticket.
• Conversely, when tickets are $10, there is no consumer surplus as professors pay just what they are willing to, and students don't buy at all.

This difference in willingness to pay and actual price allows economists to measure how much better off consumers are in monetary terms. It's an essential tool in evaluating the efficiency and equity of market outcomes.

Willingness to Pay

Willingness to pay (WTP) is how much a customer is ready to spend on a product or service. It reflects their maximum budget they're comfortable spending for a particular benefit. Think of it as the threshold of value they assign to the purchase. This concept varies for different groups or individuals, shaped by factors like income, preferences, and the perceived value of the product.

• In our movie theater scenario, students have a WTP of $5, and professors have a higher WTP of $10. It influences their buying decisions directly.
• If the price matches or is below the WTP, they are likely to buy; if higher, they might refrain as seen when students opted out at a $10 ticket price.

Understanding WTP helps sellers in setting prices that maximize revenue and ensure products appeal to different segments of the market.

Marginal Cost

Marginal cost (MC) represents the extra cost incurred by producing one more unit of a good or service. Imagine you’re making cookies and need to calculate the cost of baking an additional batch of cookies. This additional expenditure compared to the cost without that extra batch equals the marginal cost. It's determined by factors like labor, materials, and energy costs.

• In the movie theater example, the MC is constant at $3 per ticket, meaning each ticket sold incurs an additional $3 cost for materials, wages, etc.
• This cost forms a baseline for the minimum price the theater should charge to avoid making a loss on each ticket.

Marginal cost is crucial for businesses to analyze optimal production levels, price-setting, and profitability. If prices don't cover marginal costs, businesses may incur losses or unsustainable profits.