1} 2} 3} 4} Suppose that a nation's production function can be written as YES-ID iju/m' If the annual rate of growth rate of total factor productivity A 2.0 percent ,capital K growing at 1.5 percent per year and labor N growing at 0.5 percent per year. a) What is the growth fate of output Y'fR points l bl Using the growth rate calculated in part la} if the base year output is $4,000 Billion (assume no inflation )then what would be the value of output in year 20? (2 points ) Consider a constant returns to scale production function given as YGIG'D AAF As usual, Y is total output/income, K is the capital stock and Nis the stock oflabor. The parameter A indicates the level of technology or total factor productivity. a) ShowthatinthecontextoftheSoIowmodelthatthereisaninverserelationshipbetweenthe percentage growthrateofcapitalpercapitaandthelevelofcapitapercapita.Hint recall that the capital stock per capita evolves according to A]; an?!) 3), 5);; En El mtg that there is no growth in TFP. (2 points) bl What does your expression in part (a) say about absolute convergence of living standards between countfies? (2 points) Suppose your economy is at its steady state with a production function is qugm DmAIFfF. The annual growth in output averages 3% percent; the depreciation rate is 4 percent per year; and the capitaloutput ratio is 2.5, meaning, for every unit of output 2.5 units of capital are required. a) What must the saving rate be in the initial steady state? (Hint: Use the steady-state relationship sy 953:9 Tl.\" El d D g'cpointsl b) What is the marginal product of capital in the initial steady state? (2 points) Cl Suppose that a planner has decided to change the savings rate in order to achieve the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product of capital at the Golden rule steady state to the marginal product of capital in the initial steady state. In which direction must the savings rate change? (2 points) Consider population and well -being measured by income per person according to Maithus a} Suppose the mythical ,unpopulated and fertile continent of Atlantis is suddenly discovered .Beginning from the steady state ,show , using the diagrams of Maithus what happens to the worid's income per person and the population growth rate in the short -run and then in the long -run.How does this outcome differ if at all from the neoclassical [Solow model ? (2 points ) bl Suppose instead that millions of benevolent space aliens suddenly appear floating down from the sky in parachutes and take up permanent residence on earth .These aliens have children at the same rate as earthiings and live roughly as long .They have the same nutritional needs and in fact are the same as humans in every way . Use the Maithus diagrams to answer the same question as part (a). (2 points ) Cl Finally , and this is independent of the friendly alien invasion , suppose people begin to have fewet children .Again use the Maithus diagrams to answer the same questions as in part (a). (2 points J