Question

Consiter a firn that wonders how much to invest in future capital, it has current capital stock of K=100, it faces interest rates r=0.05 and capital depreciates with rate d=0.15. The frmm has tha following future marginal product of capital, MP

K
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K
1
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π
1
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(a) Calculate the optimal level of imvosiment, 1= (o) Suppose depreciation rate increases to d=0.17, what happens to optimal imvestment I and why? A. Imvestment goes down because the marginal benefit for investment decreases, and so the optimal K' decreases, which decreases I. 8. Ifwestment goos up since more old capital depreciates, which makes room for new capital which is more productive, which incentives firms to invest more. c. Investment goes up since more current capital stock depreciates, so the firm needs to invest in more future capital to bring them back to same level. D. Invosiment goes down because the marginal cost of investment increases, which decreases optimal K; which decreases I.

Answer 1

The optimal level of investment (I) can be calculated using the formula I = (r + d) * K, where r is the interest rate and d is the depreciation rate. In this case, r = 0.05 and d = 0.15. Substituting these values and the given capital stock (K = 100) into the formula, we get:

I = (0.05 + 0.15) * 100
I = 0.20 * 100
I = 20

Therefore, the optimal level of investment is 20.

If the depreciation rate increases to d = 0.17, the optimal investment level will change. The formula for calculating the optimal investment level remains the same: I = (r + d) * K. Substituting the new depreciation rate into the formula, we get:

I = (0.05 + 0.17) * 100
I = 0.22 * 100
I = 22

So, the optimal investment level increases to 22.

The reason for this change is that with a higher depreciation rate, the firm's capital stock will depreciate at a faster rate. To maintain the same level of capital stock, the firm needs to invest more in future capital. This increased investment is necessary to compensate for the higher rate of depreciation and ensure that the firm's capital stock does not decrease over time.

Therefore, option B is the correct answer: Investment goes up since more old capital depreciates, which makes room for new capital that is more productive, incentivizing firms to invest more.