4. Consider a firm that faces the following expected future marginal product of capital: MPK = 1000 - 2K, where MPK is the expected future marginal product of capital and K is the capital stock. The price of capi- tal, 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 capi- tal 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 pur- chased. What is the firm's desired capital stock now? (Hint: An investment tax credit effectively reduces the price of capital to the firm.)