Capital
Chapter 17
1.
Suppose a winery is a profit-maximizing firm and is considering when to sell a new wine.
The value of the wine increases as it ages, and the value of the wine in year t is
f(t)=exp(0.18t-0.0025t
2
).
Assume that the real rate of interest is 7 percent. (Hint:
Remember
from calculus that de
x
/dx = e
x
.)
a)
Explain in words and mathematically when the firm will sell the wine.
b)
Explain how an increase in the real interest rate to 10 percent would affect the firm’s
marketing strategy
c)
The owners of the winery decide to store the wine until the value of the wine is
maximized.
How long will they store the wine?
Discuss whether this strategy is in the
owner’s best economic interests.
Answer:
a)
The company will let the wine age until the proportional rate of growth in the value of
the wine equals the interest rate, i.e., r=f’(t)/f(t).
If r=.07 then t=22.
b)
If the interest rate rises, then the firm will sell the wine sooner and invest the money at
the market rate of interest.
They will not accept a proportional rate of growth in the
value of the wine that is less than 0.1, since they can sell the wine and earn a market
rate of return on their profits.
Therefore, the company will sell the wine, when the
wine is appreciating more rapidly than in part a.
If r=.10 then t=16.
d)

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