Question: In this problem, we derive an investment function I(r) . Firms choose their level of investment today to maximize future profits AfF(Kf, Nf)-ucfKf-wfNf (4) where

In this problem, we derive an investment functionI(r). Firms choose their level of investment today to maximize future profits

AfF(Kf, Nf)-ucfKf-wfNf(4) whereucf= pK(r+d)is the user cost of capital andKfis desired future capital. For simplicity,

assume thatNfis constant and we can write the production function as

AfF(Kf, Nf) = Af(8890 Kf- 0.5(Kf)2)(5) (a)[3 pts]Write down the maximization problem that firms solve to find the desired future

stock of capital.

(b)[4 pts]Derive the first order condition and solve for investmentIas a function ofpK, r, d,

the current capital stock K andAf.

(c)[3 pts]AssumeAf= 1, pK= 70, d = 0.2, K = 8370. Compute the desired future stock of

capital and corresponding level of investment today as a function ofr.

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