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Chapter 13: Problem 10

The Collegetown movie theater serves 900 students and 100 professors in town. Each student's willingness to pay for a movie ticket is \(\$ 5 .\) Each professor's willingness to pay is \(\$ 10 .\) Each will buy only one ticket. The movie theater's marginal cost per ticket is constant at \(\$ 3,\) 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 \(\$ 5,\) who will buy tickets and what will the movie theater's profit be? How large is consumer surplus? b. If the movie theater charges \(\$ 10,\) 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 \(\$ 5\) and professors \(\$ 10\), how much profit will the movie theater make? How large is consumer surplus?

Short Answer

Expert verified
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

01

a. Movie theater charging \(\$5\) 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 \((900+100)\times\$5=\$5000\). The total cost for supplying these tickets would be \((900+100)\times\$3=\$3000\). Thus, the theater's profit will be \(\$5000 - \$3000 = \$2000\). 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 \(\$5\) and the price charged is \(\$5\). So, the consumer surplus for the students is \(0\). For the professors: The willingness to pay is \(\$10\) and the price charged is \(\$5\). So, the consumer surplus for the professors is \((\$10-\$5)\times100=\$500\).
02

b. Movie theater charging \(\$10\) 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 \(100\times\$10=\$1000\). The total cost for supplying these tickets would be \(100\times\$3=\$300\). Thus, the theater's profit will be \(\$1000 - \$300 = \$700\). 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.
03

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

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

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