Question 24 (30 marks) Suppose that the production function for output in an economy is given by =1/2..The number of workers, N, is constant. The saving rate is s, and the depreciation rate of physical capital is .

a) Write down the equation showing the evolution of the physical capital stock over time. Explain in words. (4 marks)

b) Derive the steady state levels of capital per worker and output per worker in terms of the saving rate (s) and the depreciation rate ( ). (6 marks)

c) Show these steady state values in a well-labelled diagram of the Solow-Swan growth model. (5 marks)

d) Suppose that = 10% (=0.10). Calculate the steady-state level of consumption per worker (C/N) as a function of the saving rate.Show this relationship between C/N and s in a diagram. (5 marks)

e) At what value of s would C/N be maximized? (2 marks)

f) If s = 0.4 compute the steady state level of Y/N, K/N and C/N. (4 marks)

g) If the government wants to increase the economic growth rate, should it be aiming to increase or decrease the saving rate? (2 mark)

h) If the government cares about the standard of living, should it be aiming to increase, decrease or leave unchanged the saving rate? (2 mark)