Consider the standard equilibrium business-cycle model with labor, rental and asset markets. The economy is populated by many identical households and a representative firm. Denote the real wage rate by w/P and real rental rate by R/P. The firm behaves competitively and produces with a standard Cobb-Douglas function: Y = AKL1, where A, K and L are productivity, capital and labor input, respectively, and > 0. The household's period utility is u(c, l), where c and l are consumption and leisure time, respectively. Households make decisions on consumption c, savings s and leisure time l each period. And they supply the rest of their time to the labor market. Households own the capital stock and the capital utilization rate is exogenous, i.e., = 1. Households live for many periods.

Assume that there is a one-time decrease in the capital stock K, caused by a natural disaster. Before the shock, the economy is in general equilibrium.

1. Analyze in a graph the effect of the natural disaster in capital rental market. Explain carefully. [Hint: You may want to discuss its effects on supply/demand curves and equilibrium.]

2. Analyze in a graph the effect of the natural disaster in labor market. Explain carefully. [Hint: You may want to discuss its effects on supply/demand curves and equilibrium.]

3. How does the price of government bond react to this disaster?

4. How does the nominal rental rate (R) react to this disaster?

5. Further suppose that the utilization rate , can be chosen by households. How does the capital utilization rate react to this disaster? Please show your result carefully and elaborate.