The Missing Link Chain-Link Fence Company is
trying to determine how many chain-link fabricating
machines to buy for its factory. If we define
a chain-link fence of some specified length to be
equal to one unit of output, the price of a new fabricating
machine is 60 units of output, and the price
of a one-year-old machine is 51 units of output.
These relative prices are expected to be the same in
the future. The expected future marginal product of
fabricating machines, measured in units of output,
is 165 – 2K, where K is the number of machines in
use. There are no taxes of any sort. The real interest
rate is 10% per year.
a. What is the user cost of capital? Specify the units
in which your answer is measured.
b. Determine the number of machines that will allow
Missing Link to maximize its profit.
c. Suppose that Missing Link must pay a tax equal
to 40% of its gross revenue. What is the optimal
number of machines for the company?
d. Suppose that in addition to the 40% tax on revenue
described in Part (c), the firm can take advantage
of a 20% investment tax credit, which allows it to
reduce its taxes paid by 20% of the cost of any new
machines purchased. What is Missing Link’s desired
capital stock now? (Hint: An investment tax credit
effectively reduces the price of capital to the firm.)
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