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 government. The production function of the firm is

Yt=zf(Kt, Nt)=zKt^?*Nt^1-? for t=0, 1 and K1=(1-d)K0+I0

where d=0.3, ?=0.3, and z0=z1=1

(a) What is the optimal value of future capital K1 in terms of r?

(b) What is the optimal level of investment I0?

(c) Disaster! The economy is severely affected by an earthquake. This leads to half the current capital stock to be destroyed. K0 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.