Problem 1 {10 points). Suppose that Buckeyelarld is a closed economy with a labor force that grows by two percent every yearT and that the economy's output in any year t is given as 1'; = IKE-31337, where K; is the capital stock and L; is the size of the labor force in year t. Every year, people in BuokeyeNation save a quarter of their income into investing in new capital, and ve percent of the existing capital stock becomes obsolete. [a] Suppose the capital stock per worker in a given year t is lat = If? \"rhat is the investment per worker from year f? What is the breakeven level of investment per worker from year 1'? Draw a gure representing both of these quantities as a function of k:- TWhat is the change in the capital stock per worker from year t to year t+1? (b) What is the steadystate level of capital per worker? What is the steady-state level of output per worker? [e] Draw a gure representing the output per worker and the breakeven investment as functions of the capital per worker 1What is the Golden Rule level of capital in this economy? 1'ti'li'hat saving rate is required to reach the Golden Rule level