1. Consider the Solow growth model. The dynamic equallon for capital per offoctive unit of labor is given by 1(0 - ,/(14) -(n+g+ 5)ke, where by = " is capital per effective unit of labor, f(la ) is the output per effective unit of labor, s is the constant fraction of output that is waved, 9 - ^ is the growth rare of technology, o is the depre- Ciation rate of capital and my = u is the growth rate of population. Note that in this problems the growth rate of population could vary over time. For simplicity maume that / () = by where a c (0, 1) (a) F'iest assume that n, is constant and equal to a. Draw ake and (n I g to)k, lines on a graph and ahow the steady state level of capital. Denote the steady state capital by &" and comment on the stability of the steady state. [3 marks] (b) Next assume that when & - 0, w - R. When &, e (0, k), where *: > 0, n, doclines at a constant rate, When & 2 5, 74, = 0. This relationship is shown in the figure below. In words, as capital stock increases, the rate of population growth in this economy decreases until it reaches zero when capital stock is equal to f. For capital shocks greater then &, the population is constant. Figure 1: The relationship between wa and k Further assume that a = g +6. Plot (n, -g+ 6)6, curve for this oconomy. Cleary mark A. a marks (c) Continue with the assumptions in part (b) above. Draw ske and (my - g + 8) he lines in a graph and show a steady state such that the steady state capital stock b' > K. [2 marks] (d) Continue with the assumptions in part (b) above. Draw ske and (r I g + dj k, lines in a graph and show a steady-state such that the steady state capital stock kick. 12 marks]