Consider a numerical example. In the Solow model, assume that n = 0, s = 0.2, d=0.1, F(K, N) = zK0.3NO.7. Suppose that initially, in period t = 0, that z = 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 t = 2, 3, 4, ... (iii) Repeat part (b) for the case where, at t = 1, total factor productivity falls to z = 0.9 and stays there forever. (iv) Comment on what your results in parts (a)-(c). Problem 2: Problem 10 from Chapter 10 in the textbook Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience, and that there is a labour-augmenting technological progress, with a production function Y = F(K, bN), (1) where b denotes the number of units of "human capital" per worker, and bN is "efficiency units" of labour. Letting b' denote future human capital per worker, assume that b' = (1 + f)b, where f is the growth rate of human capital. (i) Show that the long run equilibrium has the property that ** = py is a constant. At what rate does aggregate output, aggregate consumption, aggregate investment, and per capita income grow in this steady state? Explain. (ii) What is the effect of an increase in f on the growth of the per capita income? Discuss how