Question 1 Consider an economy that has the following production function: Y = zF(K, N) = K1/3N2/3 where Y, z,K and N denote output, total factor productivity, capital stock and labour employment respectively (2 = 1 for simplicity). Assume the depreciation rate d = 0.18, saving rate S = 0.2, and population growth rate 71 = 0.02. a) Write down the production function in per worker terms. (1 mark) h) Calculate capital, income and consumption per capita in the steady state. Use a diagram to illustrate your answer. (2 marks) c) The economy is initially in the steady state that you calculated in part (b). Now suppose that there is a surge in the saving rate such that S = 0.4. i) Calculate capital, income and consumption per capital in the new steady state. (1 mark) ii) Use Excel to determine the path of the change in capital, income and consumption per capita until the new steady state is reached. You will need to attach this Excel sheet with your answers. (1 mark) iii) How long is the transition between the two steady states? (1 mark) iv) Looking at your Excel results, explain how capital per worker reaches the new steady state. Sketch the path of consumption per worker in the transition to the new steady state. Comment on any policy dilemma implied. Use an appropriate set of diagrams to support your answers