3 The Collegetown movie theater serves two kinds of customer

3. The Collegetown movie theater serves two kinds of customers: students and professors. There are 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 for a movie ticket is $10. Each will buy only one ticket. The movie theater\'s marginal cost er ticket is constant at $3, and there is no fixed cost. 3a. Suppose the movie theater can not price-discriminate and charges both students and professors the same price per ticket. If the movie theater charges $5, determine number of tickets bought and calculate the movie theater\'s profit. 3b. If the movie theater charges $10, determine number of tickets bought and calculate the movie theater\'s profit. 3c. Now suppose that, if it chooses to, the movie theater can price-discriminate between students and professors by requiring students to show their student ID. If the movie theater charges students $5 and professors $10, calculate the profit the movie theater wil make.

Solution

Question 3

(a)

If movie theater charges $5, both students and professors will buy the ticket as price is equal to or lower than the maximum willingness to pay of both.

So, a total of 1,000 tickets would be bought.

Calculate profit -

Profit = Total Revenue - Total Cost

Profit = (P * Q) - (MC * Q)

Profit = ($5 * 1,000) - ($3 * 1,000) = $5,000 - $3,000 = $2,000

So,

The number of tickets bought would be 1,000 tickets.

The movie theater\'s profit is $2,000.

(b)

If movie theater charges $10 then only professors would purchase the tickets as price is equal to maximum willingness to pay of professors.

Students will not purchase the ticket as price is greater than their maximum willingness to pay.

There are 100 professors in the town.

So,

The number of tickets bought would be 100.

Calculate profit -

Profit = TR - TC

Profit = (P*Q) - (MC*Q)

Profit = ($10 * 100) - ($3 * 100) = $1,000 - $300 = $700

The movie theater\'s profit is $700.

(c)

The movie theater price discriminates and charges $5 from students and $10 from professors.

Calculate the profit -

Profit = TR - TC

Profit = ($10 * 100) + ($5 * 900) - ($3 * 1,000) = $1,000 + $4,500 - $3,000 = $2,500

The movie theater will make a profit of $2,500.