Question

The builder of a new movie theater complex is trying to decide how many screens she wants. Below are her estimates 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	40,000
2	75,000
3	105,000
4	130,000
5	150,000

After paying the movie distributors and meeting all other noninterest expenses, the owner expects to net $2.5 per ticket sold. Construction costs are $1,000,000 per screen.

Instructions: Enter your responses as whole numbers.

a. Make a table showing the value of marginal product for each screen from the first through the fifth.

Number of screens	Value of marginal product
1	$
2	$
3	$
4	$
5	$

What property is illustrated by the behavior of marginal products?

• Diminishing returns to capital

• Increasing returns to capital

• Negative returns to capital

b. How many screens will be built if the real interest rate is 5.5 percent?

screen(s)


c. How many screens will be built if the real interest rate is 7.5 percent?

screen(s)


d. How many screens will be built if the real interest rate is 10 percent?

screen(s)

e. If the real interest rate is 5.5 percent, what is the highest construction cost per screen that would make a five-screen complex profitable?

Answer 1

a) calculation of screens :-

Value of marginal product = additional patrons * price

b) The interest cost of each screen is (5.5%) * ($1,000,000) = $55,000 ​​​​​​. There are no other costs mentioned. The value of marginal product exceeds $55,000 for 4 screens.

Thus, four screens should be built .

c) The value of marginal product exceeds the internet rate (7.5% of $1,000,000 or $75,000) for 2 screens.

Thus, two screens should be built.

d) At 10% interest the interest cost of a screen is $100,000 more than the value of the marginal product of even the first screen.

Thus, no screen should be built.

e) The value of the marginal product of the fifth screen is $50,000. At an interest rate of 5.5%, building five screens is profitable only if 5.5% times the per screen constitution cost is no greater than $50,000.

Financial cost per screen = real interest rate * construction cost of per screen

$50,000 = 5.5% * constitution cost per screen

Construction cost per screen = $50,000 / 5.5%

= $909,090.91

That is, the constitution cost would have to fall to $909,090.91 per screen to make the five screen complex profitable.

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