Exercise 4 (35 Points) Consider a two period model with investment as we have seen in our lectures. The economy is populated by a representative household, a representative firm, and a govern- ment. The production function of the firm is Yt = =/(Kt, N.) = =KPN!-", for t =0,1, and K1 = (1 - d) Ko + 10; where d = 0.3, a = 0.3, and 20 = 21 = 1. (a) What is the optimal value of future capital Kj in terms of r? (b) What is the optimal level of investment To? (c) Disaster! The economy is severely affected by an earthquake. This leads to half the current capital stock to be destroyed. Ko is cut in half. Holding interest rates constant, what would happen in the labor market? Illustrate with a graph. (d) Holding interest rates constant, what would be the effect on the goods market. What is the main drive for this movement? Illustrate with a graph. (e) What happens to the equilibrium interest rate? What will be the repercussions on the labor market? Illustrate with a graph. (f) Assume that the government decides to intervene, and boosts expenditures Go. Would you recommend this? What would be the overall impact on the interest rate. (g) What if instead, the government decides to lower taxes in the current period (to goes down). What would be the impact on real variables