Professor Oliver Landmann Retake Exam Advanced Macroeconomics I July 2 nd, 2015 ADVANCED MACROECONOMICS I Retake Exam - July 2 nd, 2015 l. Short Questions (1 point each) Mark the following statements as rue () or alse () on the first page of the exam sheets. No explanations required in this part. One point for each correct answer. No points are subtracted for incorrect answers. 1. In the Solow model, an acceleration of technological progress lowers the steadystate level of output per effective labor input. 2. In the Ramsey-Cass-Koopmans model, an acceleration of technological progress increases the steady-state level of output per effective labor input. 3. In the intertemporal theory of consumption choice, the Euler equation is a necessary, but not a sufficient condition for optimal consumption. 4. In the RBC model, more persistent technology shocks cause stronger income and substitution effects. 5. In the Lucas model, a high volatility of aggregate demand weakens the response of aggregate output to an unanticipated aggregate demand shock. 6. In the Lucas model, a high volatility of aggregate demand strengthens the response of individual producers to relative demand shifts. 7. In the menu-cost model of nominal price adjustment, the MC curve measures the menu cost. 8. he Calvo model of the New Keynesian Phillips Curve illustrates the point that real rigidities amplify the consequences of a nominal rigidity. 9. Historically, the stability record of U.S. monetary policy was better when it followed the aylor rule than when it did not. 10. he optimal monetary policy response to an inflationary cost-push shock calls for an increase in the nominal interest rate, but a reduction of the real interest rate. Page 1 of 2
Professor Oliver Landmann Retake Exam Advanced Macroeconomics I July 2 nd, 2015 II. 3 Problems (30 points) Problem 1 (10 points) Consider the Solow model for an economy with production function Y = K ⅓ (AL) ⅔, saving rate s = 32%, population growth n = 1%, labor-augmenting technological progress g = 2%, and depreciation rate δ = 5%. a) Compute steady-state capital k and output y (per effective labor input), respectively. b) Determine the steady-state level of the real wage and its long-term growth rate. c) Now assume that, at some point t, the economy experiences a one-time labor influx from abroad, amounting to 1.5% of the existing labor force. After that, population growth remains unchanged at 1%. i. What is the short-term impact on the real wage? On per-capita income at large? ii. What is the long-term impact on the real wage? On per-capita income at large? Illustrate your reasoning with a suitable diagram. d) If the central bank desires to keep output above potential, then under discretion a suboptimal equilibrium may emerge with no gain in output, but with inflation persistently above target. Explain and discuss each of these propositions within the framework of the New Keynesian theory of optimal monetary policy (a full formal derivation is not required here). Problem 3 (8 points) he diagram below displays the consequences of a fall of the money supply (from M0 to M1) in the world s smallest macroeconomic model (Krugman 2001). Explain the functions displayed and the meaning of points A,B,D,E in the two panels of the diagram. Problem 2 (12 points) Clarida/Galì/Gertler (JEL 1999) present a number of results, among them the following four: a) Cost push inflation confronts the central bank with a trade-off between inflation and output variability. b) Optimal monetary policy incorporates flexible inflation targeting, which calls for aiming at gradual convergence of inflation to its target. c) Optimal monetary policy calls for adjusting the interest rate to perfectly offset demand shocks. Page 2 of 2
Professor Oliver Landmann 1 Retake Exam Advanced Macroeconomics July 2 nd, 2015 ADVANCED MACROECONOMICS Retake Exam, July 2 nd, 2015 l. Short Questions (1 point each) Mark the following statements as rue () or alse (). 1. In the Solow model, an acceleration of technological progress lowers the steady-state level of output per effective labor input. 2. In the Ramsey-Cass-Koopmans model, an acceleration of technological progress increases the steady-state level of output per effective labor input. 3. In the intertemporal theory of consumption choice, the Euler equation is a necessary, but not a sufficient condition for optimal consumption. 4. In the RBC model, more persistent technology shocks cause stronger income and substitution effects. 5. In the Lucas model, a high volatility of aggregate demand weakens the response of aggregate output to an unanticipated aggregate demand shock. 6. In the Lucas model, a high volatility of aggregate demand strengthens the response of individual producers to relative demand shifts. 7. In the menu-cost model of nominal price adjustment, the MC curve measures the menu cost. 8. he Calvo model of the New Keynesian Phillips Curve illustrates the point that real rigidities amplify the consequences of a nominal rigidity. 9. Historically, the stability record of U.S. monetary policy was better when it followed the aylor rule than when it did not. 10. he optimal monetary policy response to an inflationary cost-push shock calls for an increase in the nominal interest rate, but a reduction of the real interest rate.
Professor Oliver Landmann 2 inal Exam Advanced Macroeconomics ebruary 18, 2014 Problem 1 (10 points) a) Y K y = = = k AL AL k = sy ( n + g + δ )k s k = 0 k = n + g + δ 3/ 2 k y 3/ 2. 3/ 2 32 =.01+.02 +.05 = k = 8 = 2 = 4 = 8 Y b) K 2 3 w = = A = 2 1/ 3 2 3 A k = 4 A g w = g L L 3 3 Y 2 3 c) Per-capita income: K Y = A. Real wage: K 2 3 w = = 2 3 A L L L L he production elasticity of labor is 2 /3, which means a 1,5% increase in the labor supply increases output ceteris paribus by 1%. Output per capita thus falls by.5%. So does the marginal productivity of labor (= real wage rate) which is proportional to Y/L. Over time, both variables will gradually recover to their old steady-state growth path where they both grow again at the growth rate of technology (1%). Y ln L -.5% t0 t
Professor Oliver Landmann 3 inal Exam Advanced Macroeconomics ebruary 18, 2014 Problem 2 (10 points) a) In the model of CGG a cost push shock is a shock to the Phillips-curve relation. acing positive cost push inflation, the central bank can use its tool (the short term interest rate) to fight inflation but will thereby create an output gap. Because both inflation and the output gap appear in the loss function, the central bank faces a trade-off. he optimal policy minimizes the total pain inflicted by inflation and output volatility according to the central bank s preferences. b) With a positive weight of the output gap in the loss function (α > 0), the optimal policy of the central bank will let the initial surge of inflation fade out over time according to the autoregressive structure of a cost push shock. In contrast, strict inflation targeting (α = 0) would prevent any departure of inflation form the central bank s target rate, no matter how large the output gap becomes. c) Demand shocks make themselves felt through the IS equation of the model just as the interest-rate policy of the central bank does. herefore, the central bank can always (if it is not in a liquidity trap, that is) adjust the interest rate so as to neutralize any demand shock with regard to output. It is optimal to do so because the stabilization of output in the face of a demand shock also keeps inflation on track. d) If the output gap desired by the central bank is above potential output, the private sector rationally anticipates that the central bank has an incentive to run an interest-rate policy which is more expansionary than would be consistent with target inflation at a zero output gap. As these expectations are built into current pricing decisions, output cannot exceed potential, but the inflation rate exceeds the target rate. Problem 3 (10 points) n Under flexible prices the economy will move from point A to point B according to the displacement d of the notional demand curve C ( ). he flexible response of the price level keeps aggregate demand equal to inelastic supply L so that the economy will stay at full employment. If prices are rigid, the fall in the money supply reduces notional demand to point D. But with the demand constraint now binding, effective demand is now given by M ) so that output falls C d n ( 1 even further to point E. he underlying multiplier process which takes output from A to E is illustrated in the lower panel where effective demand is plotted against output and equilibrium is defined by the condition C = C M ) d. n ( 1