Question I -~ Solow Model without Population or Technology Growth Consider the Solow growth model with no population growth and no technology growth, e, n = x = 0. Output is created by a Cobb-Douglas production [unetion combining Labor, Ly, and capital, K, such that ouiput ; is given Ly Yy = A KL . liecall that, without population growth, L; = Lg and assume that Ly = 1. Forthermore, recall that, without technology growth, Ay = Ap and assume that Ag = 1. The law of motion for capital is given by Kigr = (1 8) Ky + sAKELT (1) Assume that the savings rate is 5 = 1.2, the depreciation rate is & = (1.1, and that the capital share is o = (1.3, L. Use equation (1) to solve for the steady siate level of capital, K., and show that 1 ':] T o What is the steady state level of capital? (Replace the numbers in the expression) . Suppose that Ky = 1. Does capital grow or [all over time? What is the maximum level of capital this economy will ever have? Suppose that Ky = 5. Does capital grow or fall over time? What is the maximum level of capital this economy will ever have? . Suppose that this economy was at its steady staie level ol capital K, when it is hit by a natural disasier that destroys 10 percent of the capital stock. This catastrophe means that the economy musi start anew with Ky =09 = K. Useequation (1) to compute K, for the next 10 years. How long does it take to recover at least, half of the lost capital stock, Le., in which year is K; = 0.95 x K. . Suppose thai the government conducis a program of incentivizing invesiment and is able to take s = 0.21, i.e., the government increases the savings rate by | percentage point. Use the same Ky as in question 4, and compute the new path Ky for the next 10 yvears. Now, how long does it take to recover at least hall of the lost capital stock, i.e., in which year is Ky > 095 x K. ls convergence faster or slower with this new savings rate? Explain why