Consider a version of the Solow model where the population, Lt, grows at rate n, and labour efficiency grows at rate g. A fraction s = 1/5 of income is invested in capital, Kt, every period and capital depreciates at rate 8. The production technology is Cobb-Douglas and given by: Yt = K/³ (Lt Et) 2/3 a. Derive an expression for the accumulation of capital per efficiency unit of labour in this economy, i.e. Akt+1, where kt Kt/Lt Et. (5 points) b. What is the steady state condition in this economy? Illustrate the equilibrium in a diagram. (4 points) c. Suppose that n = 1/10, 8 = 1/20 and g = 1/20. Compute the steady-state level of capital per efficiency unit of labour, i.e. k*. (4 points) d. Suppose that the economy starts out with a capital stock that is greater than k*. Explain how the economy reaches the steady state, i.e. describe the mechanism. (4 points)