A corporation produces output with a constant market price of $70 per unit. The marginal product of capital is 1/(2K), where K is units of capital, with each unit assumed to be worth $1. The life span of the capital is 10 years, implying the straight line depreciation rate δ=.10. The financing cost of capital is ρ=.10. Also, assume the discount rate to use in any present value calculations is .10.
a. What is the optimal level of capital for the firm?
b. Suppose the corporate tax rate on accounting profits is 40%. The firm can include depreciation at the rate δ per year in its accounting costs, but not its financing costs. What is the optimal level of capital for the firm?
c. For the scenario in b., what is the effective corporate tax rate?
d. Same assumptions as b. Except, now suppose the government allows the firm to depreciate 25% of its capital costs immediately, while the remainder depreciates at the straight line rate δ, what is the optimal level of capital for the firm?