ECON-301: Intermediate Macroeconomics Prof. Boris Gershman Final Exam May 8, 2018 Name: Directions: You have 2 hours and 30 minutes. The use of any class materials, textbooks, or electronic devices including calculators is not allowed. Use the blank space or extra sheets for your answers. Note that often you can answer (fully or partially) one part of the problem without solving the previous parts. The total is 100 points. Good luck! Problem 1. (20 points) Consider two countries, X and Y, that start off in 2010 with the levels of GDP per capita equal to 20 and 10, respectively. 1. (5 points) Both countries are initially growing at the same annual rate of 7% for a period of 10 years. Following this initial period, economic growth stops in country X and its rate remains at zero for 10 years. In contrast, economic growth accelerates in country Y and it catches up with the standard of living in country X in 2025. Find the approximate values of: 1) GDP per capita in 2020 for both countries; 2) the rate of economic growth in country Y after 2020. 2. (5 points) Write down the formulas (with all numbers plugged in) that allow to calculate the exact values of: 1) GDP per capita in country X in 2030; 2) the annual rate of economic growth in country Y between 2020 and 2025. 1 3. (5 points) On the same graph, show the trajectories of GDP per capita in countries X and Y during the period 2010–2030 based on the information provided in part 1. Use the ratio scale of your choice and be careful with slopes. 4. (5 points) What is (approximately) the gap between the living standards in countries Y and X (that is, the ratio of their per capita GDP values) in 2030? Assume that beyond 2030, country Y retains its rate of economic growth achieved during 2020–2030 while country X grows at an annual rate 9%. Calculate the approximate number of years it will take for the gap between the living standards in countries Y and X to double. Problem 2. (20 points) Consider an economy that operates according to the Solow model. In particular, the production function is Yt = A¯K 1/3 t L¯ 2/3, where A¯ is the level of productivity, Kt is the stock of physical capital, and L¯ is the labor force. Each period output is divided between consumption and investment in fixed proportions, that is, It = s¯Yt and Ct = (1− s¯)Yt, where s¯ is the investment rate. Physical capital depreciates at rate d¯. The economy starts off in the steady state in period 0. Note: When answering the questions below, make sure you clearly distinguish between gradual changes and instant jumps (if any). 2 1. (7 points) The government pursues an anti-immigration policy, as a result of which the labor force decreases permanently. Draw a Solow diagram (with investment, output, and depreciation curves) showing the expected impact of this policy in the short run (at the moment of shock) and in the long run (on the new steady state). Show the dynamics of both output and capital over time using arrows. Calculate the percentage change in the steady-state levels of total output and output per capita caused by a 10% reduction in the labor force. 2. (3 points) Draw a diagram showing the dynamics of capital stock over time from period 0 onwards and clearly reflecting the impact of the policy from part 1. 3 3. (7 points) To compensate for the losses in the long-run level of total output caused by the anti-immigration policy, the government encourages savings to boost the in- vestment rate s¯. Assuming the economy starts in the new steady state, draw a Solow diagram (with investment, output, and depreciation curves) showing the impact of this policy in the short run (at the moment of shock) and in the long run (on the new steady state). Show the dynamics of both output and capital over time using arrows. By how much does s¯ have to increase in order to offset the impact of the 10% loss in the labor force on the long-run level of total output. 4. (3 points) Draw a diagram showing the dynamics of total output over time from period 0 onwards and clearly reflecting the impact of policies in parts 1 and 3. 4 Problem 3. (25 points) Use the IS-MP-PC framework to answer the following questions. Assume that the economy starts in period 0 in the no-shock long-run equilibrium, in which a¯ = 0, R = r¯ = 2%, o¯ = 0, Y˜ = 0, and ∆pi = 0, with pi0 = 4%. Assume also that the sensitivity coefficient in the Phillips curve is v¯ = 0.5, and the sensitivity coefficient in the IS curve is b¯ = 2. Be sure to draw the relevant IS-MP-PC diagrams for each of your answers below. 1. (5 points) Suppose that the economy experiences a positive inflation shock o¯ = 2 in period 1 (which goes away in period 2). Use the IS-MP-PC model to illustrate a scenario in which the Fed responds to the shock in order to keep the inflation rate unchanged. Find the values of the real interest rate and short-run output in period 1. 2. (10 points) Now assume that the Fed does not realize that there is an inflation shock in period 1. Instead it believes that there is a positive aggregate demand shock a¯ = 2 in period 1. It responds to this perceived shock in order to not let the inflation rate increase in period 1. Illustrate this situation using the IS-MP-PC diagrams. Be sure to show what actually happens, not what the Fed believes is happening, and mark the location of the economy in period 1 on both of the IS-MP-PC diagrams. 5 Find the values of the real interest rate and the inflation rate in period 1. 3. (10 points) After observing the outcomes of period 1, the Fed realizes its mistake and wants to bring the inflation rate back to its initial level of 4%. In period 2, although the inflation shock goes away, there is a negative aggregate demand shock a¯ = −1 (which is accurately perceived and taken into account by the Fed). Show the events of periods 1 and 2 on the same set of IS-MP-PC diagrams and properly label the locations of all the curves in those two periods. Find the values of the real interest rate and short-run output in period 2. 6 4. (5 points) Now suppose that there is an inflation shock o¯ = 2, as in part 1, but the Fed accurately identifies that shock and responds in order to keep the inflation rate constant. Assume, however, that there is a multiplier effect in the IS curve, such that 1/(1 − x¯) = 4/3. Illustrate this case using the IS-MP-PC diagrams and calculate the values of the real interest rate and short-run output in period 1. Problem 4. (25 points) Use the AS-AD framework to answer the following questions. Assume that the economy starts in period 0 in the no-shock long-run equilibrium, in which a¯ = 0, pi0 = pi−1 = p¯i = 2%, o¯ = 0, Y˜ = 0. Assume also that v¯ = 0.5, b¯ = 2, and m¯ = 1. Be sure to draw the relevant AS-AD diagram for each of your answers below. 1. (10 points) In period 1, the economy is hit by a negative inflation shock o¯ = −4 which lasts for 1 period and goes away in period 2. Examine the consequences of this shock using the AS-AD diagram by showing the locations of AS and AD curves in periods from 0 to 3 and marking the corresponding equilibrium points. Write down the equations for AS and AD curves in period 1 and find pi∗1 and Y˜ ∗ 1 . 7 2. (5 points) Assume that investment demand is less sensitive to the real interest rate, that is, b¯ < 2. Graphically compare this case to the baseline from part 1. Specifically, draw the AS and AD curves in periods 0 and 1 and clearly mark the equilibrium points for both cases on the same AS-AD diagram. 3. (5 points) Consider again the baseline case with b¯ = 2. Assume that, in addition to the inflation shock in period 1 from part 1, in period 2 the economy experiences a positive aggregate demand shock a¯ = 1 which lasts for one period. Illustrate this case using the AS-AD diagram showing the AS and AD curves and marking the equilibrium points in periods 0, 1, 2, and 3. 4. (5 points) Assume that, instead of adaptive expectations, the firms always expect inflation rate to be at the Fed’s target level, so that piet = p¯i. Redo part 3 for this case. 8 Problem 5. (10 points) Consider the government of an economy that exists for two periods. The initial amount of outstanding government debt is B1 = 10. The interest rate on debt is 10% per period. According to the baseline budget proposal, G1 = 4, T1 = 5, and T2 = 15. The government is operating under the assumption that all of the debt has to be repaid before the end of the world, that is, at the end of period 2. 1. (5 points) Calculate the total amount of government debt, with interest, that has to be repayed by the end of period 2 under the baseline budget proposal. Now assume that the government increases its purchases in period 1, G1, by 4. The government expects that these extra purchases will generate economic growth, as a result of which tax revenue in period 2, T2, will go up and fully offset the increased purchases in period 1. However, this does not happen and T2 remains at the baseline level of 15. What will the government have to do with its purchases in period 2 to remain solvent? 2. (5 points) Now consider a scenario in which the expansion of government purchases in period 1 does lead to an increase in T2 due to accelerated economic growth, but only by 2. Furthermore, due to public pressure, the level of government purchases in period 2 must be equal to 4. Given these conditions, how should the government revise T1 in order to satisfy its intertemporal budget constraint? 9 10 11 12
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