Consider a firm that faces the following expected future marginal product of capital:
MPKf = 1000 - 2K,
where MPKf is the expected future marginal product of capital and K is the capital stock. The price of capital, pK, is 1000, the real interest rate, r, is 10%, and the depreciation rate, d, is 15%.
a. What is the user cost of capital?
b. What is the value of the firm's desired capital stock?
c. Now suppose that the firm must pay a 50% tax on its revenue. What is the value of the desired capital stock?
d. Now suppose that in addition to the 50% tax rate on revenue, the firm can take advantage of a 20% investment tax credit, which allows it to reduce its taxes paid by 20% of the value of new capital purchased. What is the firm's desired capital stock now? (Hint: An investment tax credit effectively reduces the price of capital to the firm.)