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. After paying the movie distributors and meeting all other non-interest expenses, the owner expects to net $2.00 per ticket sold. Construction costs are $1,000,000 per screen. (a) Make a table showing the value of the marginal product for each screen from the first through the fifth. What property is illustrated by the behavior of marginal products? # of screens Total # of patrons Additional patrons Value of marginal (marginal product) Product ($1M/screen) 1 40,000 2 75,000 3 105,000 4 130,000 5 150,000 (b) How many screens will be built if the real interest rate is 5.5 percent? (c) If the real interest rate is 7.5 percent? (d) If the real interest rate is 10 percent? (e) If the real interest rate is 5.5 percent, how far would construction costs have to fall before the builder would be willing to build a five-screen complex? 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. After paying the movie distributors and meeting all other non-interest expenses, the owner expects to net $2.00 per ticket sold. Construction costs are $1,000,000 per screen.

Answer 1

Part (a):

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

Solution:

The answer is attached.

Part (b):

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

Answer: 3 screens

Part (c):

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

Answer: 1 screen

Part (d):

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

Answer: 0 screens

Part (e):

If the real interest rate is 5.5 percent, how far would construction costs have to fall before the builder would be willing to build a five-screen complex?

Answer: $727,272.73(approx.)

Step-by-step explanation:

Part (a):

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

Solution:

The solution is attached with working.

Part (b):

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

Solution:

3 screens

The interest cost of each screen = 5.5% x $1,000,000 = $55,000.

There are no other costs mentioned. The value of marginal product exceeds $55,000 for 3 screens.

Therefore, 3 screens should be built.

Part (c):

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

Solution:

1 screen

The value of the marginal product exceeds the interest cost (7.5% of $1,000,000, or $75,000) for only the first screen.

Thus, one screen will be built.

Part (d):

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

Solution:

0 screens

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 screens will be built.

Part (e):

If the real interest rate is 5.5 percent, how far would construction costs have to fall before the builder would be willing to build a five-screen complex?

Solution:

The value of the marginal product of the fifth screen is $40,000. At an interest rate of 5.5%, building five screens is profitable only if 5.5% times the per-screen construction cost is no greater than $40,000.

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

$40, 000 = 5.5% x construction cost per screen Construction cost per screen = $40,000 ÷ 5.5%

= $727,272.73(approx.)