Question 4: Investment (10 points) In this problem, we derive an investment function I(r). Firms choose their level of investment today to maximize future profits AfF(K", N) uc K-WN (4) where udf pk (r+d) is the user cost of capital and Kf is desired future capital. For simplicity, assume that N is constant and we can write the production function as = A F(K', N) = A (8890 K - 0.5(KP)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 investment I as a function of p, r, d, the current capital stock K and Af. (c) [3 pts] Assume Af = 1, pk = 70, d = 0.2, K = 8370. Compute the desired future stock of capital and corresponding level of investment today as a function of r. Question 4: Investment (10 points) In this problem, we derive an investment function I(r). Firms choose their level of investment today to maximize future profits AfF(K", N) uc K-WN (4) where udf pk (r+d) is the user cost of capital and Kf is desired future capital. For simplicity, assume that N is constant and we can write the production function as = A F(K', N) = A (8890 K - 0.5(KP)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 investment I as a function of p, r, d, the current capital stock K and Af. (c) [3 pts] Assume Af = 1, pk = 70, d = 0.2, K = 8370. Compute the desired future stock of capital and corresponding level of investment today as a function of r