Name Answer all quesions. Each sub-quesion is worh 7 poins (excep 4d). 1. (42 ps) The informaion below describes he curren sae of a growing closed economy. Producion funcion: α 1 Y = K ( Q N ) α Producion per effecive worker Growh rae of echnology g Q Growh rae of workers n Depreciaion rae d Saving rae s α y = k a) Wrie and explain he equaion which deermines he long-run equilibrium value of capial per effecive worker using he noaion and model above. b) Graph he long run equilibrium and label axes, curves, and he value for long-run capial per effecive worker. Assume ha k is less han is long run equilibrium value. Describe how he economy will adjus over ime being explici abou wha happens o savings and invesmen and capial per effecive worker. c) Now assume ha China has he lower value for k on your graph and ha he US has he higher value. Wha is he growh rae of US per capia oupu? Is he growh rae of China s per capia oupu higher or lower? Explain. 1
d) Redraw he Solow diagram for he long-run equilibrium value of capial and label everyhing as before. Now use your graph o analyze he effec of an increase in he savings rae, s, on he long-run value of capial per effecive worker. e) Use he producion funcion and your resuls above o explain how he increase in he savings rae affecs oupu per effecive worker in he long run? Wha is he new value for he longrun rae of growh of per capia oupu? How does i compare o is original value? How does he shor-run value for he growh of per capia oupu compare o he long run value? f) Now, change he model. Se α = QN = 1. Se n = g Q = 0. Redraw he Solow diagram wih he new values, noing especially he new value for α. Label all axes and curves. Pick a value for capial and explain how i changes over ime. Le s increase and illusrae he effec on your graph. Explain how his affecs he rae of growh of capial. 2
2. (14 poins) Use a graph o analyze he effecs of he following shocks on he equilibrium quaniy of savings, invesmen, he ineres rae, and he curren accoun in a small open economy. Assume ha he economy begins wih a balanced curren accoun. Label everyhing in your graphs. Explain why any curve shifs. a) There is an increase in he expeced fuure marginal produciviy of capial. b) A recession oday reduces income oday. Expeced fuure income is unchanged. 3
3. (14 poins) Use wo graphs o analyze he effecs of he following shocks on he equilibrium quaniy of savings, invesmen, he ineres rae, and he curren accoun in a world wih wo large counries. Assume ha boh counries begin wih a balanced curren accoun. Label everyhing in your graphs. Explain why any curve shifs. a) The domesic counry experiences a financial crisis which creaes a large fall in wealh. b) The foreign counry inroduces a policy of axes and subsidies designed o simulae invesmen. 4
4. (30 poins) a) Draw a graph of money marke equilibrium and label all curves, axes, and iniial equilibrium values. Assume ha he price level is fixed. Use your graph o analyze wha he Fed mus do when i wans o reduce he ineres rae. Explain. b) Assume ha he risk premium is zero for all quesions ha follow. For his quesion, assume ha he ineres rae is iniially 4% and is expeced o remain a 4% for he coming wo years. Wha is he price of a discoun bond wih a face value of $10,816? Wha would he ineres rae on a wo-year bond be if each of he wo one-period ineres raes is 4%? Graph he yield curve. c) Now assume ha he Fed insiues a policy which reduces he curren ineres rae o zero. I makes no announcemen abou he fuure rae and people expec i o remain a 4%. Wha is he ineres rae on a wo year bond now? Compare wih your previous resul and graph he new yield curve. 5
d) Wha can he Fed do if i wans o ge he ineres rae on he wo-year bond o fall o zero? e) Wrie an expression for he price of a sock. Assume ha he policy of geing he wo-year bond rae o zero is implemened. Also, assume ha his policy has no effec on expeced fuure dividends. Use your formula o describe wha happens o he price of he sock. 6