(20pts) 5. Xanadu is a closed economy where the population grows at the rate of n, where the saving rate is $1, and where capital depreciates at the rate of 8 where 0 < <1. (12pts) (a) (5pts) (i) What is the fundamental equation of the Solow growth model that describes the growth of the capital stock per worker? (4pts) (ii) Suppose that the production function is given by F (K, L) = K1/2 11/2. The initial capital stock per worker is ko 2, the saving rate s = = 0.4,8 = 0.1 and the population growth rate is n = 0.02. Calculate the steady-state capital stock per worker ki. (Recall that k = K/L). (3pts) (iii) Draw a graph to illustrate the steady state of the economy. Be sure to label the axes, the curves and the steady-state capital stock per worker ki. (8pts) (b) A few years ago, the government of Xanadu decided to reduce the GST from 5.75% to 4.25% to stimulate consumption. The impact of this policy action was to reduce the saving rate from s = 0.4 to $2 =0.3. What will happen to the steady-state capital stock per worker as a result of this reduction in the saving rate? (i) Explain graphically and in words. In your explanation, refer to the fundamental equation of the Solow model. Draw a graph to illustrate the initial and the new steady-state of the economy. Be sure to label the axes, the curves, the initial steady-state capital stock and the new steady-state capital stock. (ii)Calculate the new steady-state capital stock k2 using the value of $2 = 0.3 together with the other values given in part (a)(iii) above.