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 ©, 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.)