Consider a two period model with investment as we have seen in our lectures. The economy is populated by a representative household, a representative rm, and a govern- ment. The production function of the rm is K = sztht) = szN,l_, for t = U, 1, and K1 = (I. d}K + In, where d = 0.3, or = 0.3, and .30 = :1 = 1. (a) 1What is the optimal value of future capital K1 in terms of r? (b) 1What is the optimal level of investment 10? (c) Disaster! The economy is severely affected by an earthquake. This leads to half the current capital stock to be destroyed. Kn 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. 1What is the main drive for this movement? Illustrate with a graph. (e) IWhat 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 Ga. Would you recommend this? What would be the overall impact on the interest rate. (3;) 1'What if instead, the government decides to lower taxes in the current period {tn goes down). What would be the impact on real variables