E- 1 A country has a production function given by Y = SKIIII , 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 '5 20%, the population growth rate is 596 and depreciation is 10%. 31' h} d} Solve for the steady state capital-labour ratio, output per capita, savings per capita and replacement investment per capita. Illustrate this steady state in {a} on a diagram. Label your diagram completely and carefully including labels for all the ouantih'a calculated in part [a]. . Say the savings rate for this economy increases to 4036. Calculate the value of the total factor productivity parameter that is 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 u nchanged. [5 monks] 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}. Provide an intuitive explanation in words forthe different results in {a} and {c}