1) a) Outline the Solow growth model with population growth and technological progress. (15 marks) b) Consider a Cobb-Douglas production function: Y = F(K, EL) = K4/5(EL) 1/5, where K is capital, E is the efficiency of labour, and L is labour. The population is growing at the rate of n = 0.02, the efficiency of labour is growing at the rate g = 0.03, capital depreciates at the rate of o = 0.05, and the saving rate is s = 0.3. i) Show that the production function exhibits positive and diminishing marginal returns, and constant returns to scale. (5 marks) ii) Derive the intensive form of the production function. (3 marks) iii) Solve for the steady-state values of capital, output and consumption per unit of effective labour. (7 marks) iv) Suppose that immigration increases the population growth rate to n' = 0.07. Solve for the new steady-state values of capital, output and consumption per unit of effective labour, and describe the short- and long-run effect on the economy with the help of the appropriate graph. (10 marks) v) If the policy maker could choose the value of the saving rate s, what value would you recommend? Explain your reasoning, and describe the effect of the change in s on the economy using appropriate graphs. (10 marks)