4 Natural Disaster in the General Equilibrium Model [30 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 price by R/P. The firm behaves competitively and produces with a standard Cobb-Douglas function: Y = AK"LI-a, where A, K and L are productivity, capital and labor input, respectively, and a > 0. The household's period utility is u(c. (), where c and / are consumption and leisure time, respectively. Households make decisions on consumption c, savings s and leisure time / 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.,