1. The Collegetown movie theater - which is the only theater in the area- serves
ID: 1220147 • Letter: 1
Question
1. The Collegetown movie theater - which is the only theater in the area- serves two kinds of customers: students and professors. There are 900 stu- dents and 100 professors in town. Each students willingness to pay for a movie ticket is $5. Each professors willingness to pay for a movie ticket is $10. Each will buy only one ticket. The movie theaters marginal cost per ticket is constant at $3, and there is no fixed cost. [15 points]
a) Suppose the movie theater cannot price-discriminate and charges both stu- dents and professors the same price per ticket. If the movie theater charges $5, who will buy tickets and what will the movie theaters profit be? How large is consumer surplus?
b) If the movie theater charges $10, who will buy movie tickets and what will the movie theaters profit be? How large is consumer surplus?
c)Now suppose that, if it chooses to, the movie theater can (perfectly) price- discriminate between students and professors by requiring students to show their student ID. If the movie theater charges students $5 and professors $10, how much profit will the movie theater make? How large is consumer surplus?
Explanation / Answer
a. If the movie theater charges $5 per ticket, both students and professors will buy tickets. The movie theater will sell to 1,000 customers (students and professors), at a price of $5 each. Since the movie theater’s cost per ticket is $3, its profit is $2 per ticket for a total profit of 1,000 × $2 = $2,000. Students will experience no consumer surplus, but each of the 100 professors will experience consumer surplus of $10 $5 = $5 for a total consumer surplus of 100 × $5 = $500.
b. If the movie theater charges $10 per ticket, only professors will buy tickets. The movie theater will sell to 100 customers (professors) at a price of $10 each. Since the movie theater’s cost per ticket is $3, its profit is $7 per ticket for a total profit of 100 × $7 = $700. Students experience no consumer surplus since they do not buy any tickets. Each of the 100 professors experiences no consumer surplus since the price is equal to their willingness to pay. So consumer surplus is $0.
c. If the movie theater charges students a price of $5, it sells 900 tickets at a profit of $5 $3 =$2 each for a profit from selling to students of 900 ×$2 =$1,800. Charging professors $10, it sells 100 tickets at a profit of $10 $3 =$7 each for a profit from selling to professors of 100 ×$7 =$700. So the theater’s total profit is $1,800 + $700 =$2,500. Since each customer is charged exactly his or her willingness to pay, there is no consumer surplus.
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