Problem 1 Consider a numerical example using the Solow growth model. Suppose that F( K, N) = 105 /05, with d = 0.1, # = 0.2, a =0.01, and = = 1, and take a period to be a year. (i) Determine capital per worker, income per capita, and consumption per capita in the steady state. (ii) Now, suppose that the coonomy is initially in the steady state that you calculated in part (a). Then, # increases to 0.4. (i) Determine capital per worker, income per capita and consumption per capita in cach of the 10 years following the increase in the savings rate. (ii) Determine capital per worker, income per capita, and consumption per capita in the new steady state. (iii) Discuss your results; in particular comment on the speed of adjustment to new steady state after the change in the savings rate, and the pathe followed by capital per worker, income per worker, and consumption per capita. Problem 2 Consider a numerical example. In the Solow model, assume that n = 0, # = 0.2, d-0.1, F(K, N) = 2103707. Suppose that initially, in period f = 0, that = = 1 and the economy is in a steady state. (i) Determine consumption, investment, savings, and aggregate output in the initial steady state. (ii) Suppose that at t = 1, total factor productivity falls to z = 0.9 and then returns to z = 1 for periods t = 2, 3, 4, . . . Calculate consumption, investment, savings, and aggregate output for each period # = 2,3,4, .. . (iii) Repeat part (ii) for the case where, at { = 1, total factor productivity falls to = = 0.9 and stays there forever. (iv) Comment on what your results in parts (i)-(iii). Problem 3 Consider the following example for the Solow model. Suppose that F(K, N) = =K03 07 The depreciation rated = 0.10, ; The savings rate # = 0.4, ; the population growth rate n = 0.02 ; and the total factor productivity = = 1. The unit period is one year