Kindly assist in answering questions 2b, 3 and 4.
'I' 9% nl ,o A. Question Two (20 Marks) a. Suppose that the country of Xanadu saves 30% of its income and has a capitalwutput ratio of 5. i. Using the HarrodDornar model, calculate the rate of growth of total GDP in Xanadu. (5 marks) ii. If population growth were 4% per year and Xanadu wanted to achieve a growth rate of per capita GDP of 5% per year, what would its savings rate have to be to get to this growth rate? (5 marks) b. The production function in an economy is given by Y : K0.35L0.85 where Y is output level, K is capital input, and L is labour input. The saving rate is 28%, the annual population growth rate is 5%, and an nual depreciation rate is 2%. Show that the production function in this economy is neoclassical. (10 marks) Question Three (20 Marks) a. The production function in an economy is given by Y = KD'3L0'7 where Y is output level, K is capital input, and L is labour input. The saving rate is 28%, the annual population growth rate is 5%, and annual depreciation rate is 2%. Determine the steadystate values for per capita capital stock, per capita output level, and per capita consumption level for this economy. (10 marks) b. Consider an economy with labouriaugmenting technological progress. The economy has a CobbDouglas production function in which the share of capital in output is 0.35 while the share of effective labour in output is 0.65. The economy has a saving rate of 30%, the iabour force is growing at 3% per year, the rate of technoiogical progress is 2% per year, and the depreciation rate is 1% per year. What are the steadyistate values of per capita capital stock, per capita output level and per capita consumption? (Assume the initial value of the technological parameter is 1). (10 marks) 3 Question Four (20 Marks) a. Suppose output is growing at 6% per year and capital's and labour's shares of income are 0.3 and 0.7, respectively. If both labour and capital grow at 2% per year, what would the growth rate of total factor productivity have to be? (5 marks) b. Consider an economy with labouraugmenting technological progress. The economy has a CobbDouglas production function in which the share of capital in output is 0.4 while the share of effective labour in output is 0.6. The economy has a saving rate of 30%, the labour force is growing at 4% per year, the rate of technological progress is 3% per year, and the depreciation rate is 1% per year. i. What is the rate of convergence for this economy? (5 marks) ii. Determine the half life of convergence for this economy and interpret it. (5 marks) c. The production function in an economy is given by Y : KDALO'B where Y is output level, K is capital input, and L is labour input. The saving rate is 30%, the annual population growth rate is 3%, and annual depreciation rate is 1%. Determine the golden rule savings rate, SGR, for this economy
