Question

The builder of a new movie theater is trying to decide how many screens she wants. Below are her estimate of the number of patrons the complex will attract each year depending on the number of screens available. Number of screens: Total number of patrons 1 50,000 2 95,000 3 135,000 4 170,000 5 195,000 The owner expects to net $2 per ticket sold. Construction costs are $1,000,000 per screen. The screen can always be resold for $1,000,000 at the end of the year. However, the builder has to borrow $1,000,000 per screen and pay the lender the prevailing interest rate.

a) What is the marginal product per screen? In other words how much revenue does each screen generate

b) How many screens will be built if the interest rate is 6%

c) How many screens will be built if the interest rate is 8.5%?

d) How many screens will be built if the interest rate is 12%

Answer 1

Part a)

marginal product per screen is the increase in number of patrons for each screen.

marginal revenue of each screen is the marginal product per screen multiplied $2 (price of ticket)

number of screens	total number of patrons	increase in number of patrons for each screen	marginal revenue of each screen
1	50,000	50,000	100,000
2	95,000	45,000	90,000
3	135,000	40,000	80,000
4	170,000	35,000	70,000
5	195,000	25,000	50,000

Part b)

If interest rate is 6%, marginal cost of borrowing is 6% of construction cost per screen ($ 1,000,000) that is equal to $ 60,000.

Assuming firm is maximizing profit, firm invests till the time marginal revenue is greater than or equal to marginal cost. Therefore, builder will build 4 screens

Part c)

If interest rate is 8.5%, marginal cost of borrowing is 8.5% of construction cost per screen ($ 1,000,000) that is equal to $ 85,000.

Assuming firm is maximizing profit, firm invests till the time marginal revenue is greater than or equal to marginal cost. Therefore, builder will build 2 screens

Part d)

If interest rate is 12%, marginal cost of borrowing is 12% of construction cost per screen ($ 1,000,000) that is equal to $ 120,000.

Assuming firm is maximizing profit, firm invests till the time marginal revenue is greater than or equal to marginal cost. Therefore, builder will build 0 screens