A country has a production function given by = 32313 , where Y is total output, K measures total capital in the economy and L is the total amount of labour. Assume that this country's savings rate is 60%, the population growth rate is 2% and depreciation is 1%.

a) Solve for the steady state capital-labour ratio, output per capita, savings per capita and replacement investment per capita. (4 marks)

b) Illustrate this steady state in (a) on a diagram. Label your diagram completely and carefully including labels for all the quantities calculated in part (a). (4 marks)

c) Say the population growth rate for this economy increases to 3%. Calculate the savings rate required to ensure that the economy remains at the initial steady state capital-labour ratio calculated in part (a). Solve for the new steady state output per capita, savings per capita and replacement investment per capita. Assume that everything else remains unchanged. (5 marks)

d) Illustrate the steady state in (c) on a diagram. Label your diagram completely and carefully including labels for all the quantities calculated in part (c). (4 marks)

e) Provide an intuitive explanation in words for the result in (c). (3 marks)