2 Natural Disaster in the General Equilibrium Model (25 Points] 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-a, where A, K and L are productivity, capital and labor input, respectively, and a> 0. The household's period utility is u(cl), where c and I 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., k = 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 k, can be chosen by households. How does the capital utilization rate react to this disaster? Please show your result carefully and elaborate. 2 Natural Disaster in the General Equilibrium Model (25 Points] 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-a, where A, K and L are productivity, capital and labor input, respectively, and a> 0. The household's period utility is u(cl), where c and I 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., k = 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 k, can be chosen by households. How does the capital utilization rate react to this disaster? Please show your result carefully and elaborate