Question

Suppose that the economy wide expected future marginal product of capital is MPKf = 20 - 0.02K, where K is the future capital stock. The depreciation rate of capital, d, is 20% per period. The current capital stock is 900 units of capital. The price of a unit of capital is 1 unit. Firms pay taxes equal to 15%. Suppose that the real interest rate is 10% per period. What are the values of the tax-adjusted user cost of capital, the desired future capital stock, and the desired level of investment?

Answer 1

1.We calculate the marginal product of capital after tax:

adjust for tax rate and depreciation

$\frac{UC}{1-t}=\frac{(r+d)\times Pk}{1-t}$

$UC=\frac{(r+d)\times Pk}{(1-t)}=\frac{(0.1+0.2)\times1}{1-0.15}=0.35$

2.Calculate the future cost of capital:

0.35=20-0.02K

0.2K=20-0.35

Kf=982.5

3.Calculate the desired level of investment:

investments consist of two parts: the desired increase in the stock of capital and the capital needed to recover depreciation (it is disposed of)

$Kf-K=I-(d\times K)$

$982.5-900=I-(0.2\times900)$

I=262.5