Answer:
<u>Part (a):</u>
Make a table showing the value of the marginal product for each screen from the first through the fifth:
<u>Solution: </u>
The answer is attached.
<u>Part (b):</u>
How many screens will be built if the real interest rate is 5.5 percent?
<u>Answer:</u> 3 screens
<u>Part (c): </u>
How many screens will be built if the real interest rate is 7.5 percent?
<u>Answer:</u> 1 screen
<u>Part (d):</u>
How many screens will be built if the real interest rate is 10 percent?
<u>Answer:</u> 0 screens
<u>Part (e): </u>
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?
<u>Answer:</u> $727,272.73(approx.)
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.
<u>Part (b):</u>
<u>How many screens will be built if the real interest rate is 5.5 percent?</u>
<u>Solution:</u>
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.
<u>Part (c): </u>
<u>How many screens will be built if the real interest rate is 7.5 percent?</u>
<u>Solution:</u>
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, <u>one</u> screen will be built.
<u>Part (d):</u>
<u>How many screens will be built if the real interest rate is 10 percent?</u>
<u>Solution:</u>
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.
<u> </u>Thus, no screens will be built.
Part (e):
<u>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?</u>
<u>Solution:</u>
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.
<u>Financial cost per screen = real interest rate x construction cost of per screen </u>
$40, 000 = 5.5% x construction cost per screen Construction cost per screen = $40,000 ÷ 5.5%
= $727,272.73(approx.)
<u></u>
