Problem Set 3 *Solution* Macroeconomics, ECON 2123 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Part I: True/False/Uncertain Please justify your answer with a short argument for each question and draw a diagram if necessary. 1. Suppose that workers in the Republic of Communia are highly unionized, while workers in the Republic of Individuela are not. In all other respects, the two countries are exactly the same. Then Communia is likely to have a higher natural level of output than Individuela. False. In our model of the labor market, the level of unionization is captured by the Communia is likely to have a higher natural rate of unemployment than Individuela. Hence Communia is likely to have a lower natural level of output than Individuela. 2. Suppose there is a decrease in the price level from P to P’. Given the stock of nominal money, M, this leads to an increase in the real money stock, M/P, which shifts the LM curve down. This implies that the AD curve shifts to the right. 1 Because the AS curve is upward-sloping. not the AS curve. True. Monetary and fiscal policies affect the AD curve. In terms of changing output. if output is below its natural level.3. while fiscal policy is more effective when the AS curve is relatively steep. When output is below the natural level of output. Monetary and fiscal policies 2 . The actual price level equals the expected price level when output is equal to the natural level of output. the actual price level is lower than expected. the actual price level is lower than the expected price level. False. monetary policy is relatively more effective when the AS curve is relatively flat. See diagram: 4. ) the bargaining power of workers is very high relative to firms when the unemployment rate is very low. Keynesia’s economy is described by 3 .are both more effective in changing output when the AS curve is flatter and less effective when the AS curve is steeper. (b) Given your answer to part (a). when the AS curve is vertical. there would be nothing to constrain aggressive wage bargaining. Therefore. so the real wage cannot grow without bound. why is there unemployment in the economy? (What would happen to real wages if the unemployment rate approached zero? Suppose expected price and actual price remain constant. and investment I and output Y fall. (Since a worker could always find a job if the unemployment rate equaled zero. Part III: The IS-LM Model and the AS-AD Model (Chapter 5 and Chapter 7) 1. The existence of unemployment (a) Suppose previously the unemployment rate was relatively high. there is some constraint on workers' bargaining power. As a result. What change happens in terms of the relative bargaining power of workers and firms when the unemployment rate becomes very low? What do your answers imply about what happens to the wage as the unemployment rate gets very low. the real wage would grow without bound as the unemployment rate approached zero since the wage is a decreasing function of unemployment rate. the wage gets very high as the unemployment rate gets very low.) Presumably. consumers wish to purchase fewer goods. But now things change: the unemployment rate becomes very low this year. it is very difficult for firms to find workers to hire and very easy for workers to find jobs. The Republic of Keynesia is a closed economy and obeys our short-run IS-LM model. The AD curve slopes down because an increase in P leads to a fall in M/P. Part II: The Labor Market (Chapter 6) 1. 5. so the nominal interest rate increases. Assume it starts out in equilibrium in both the goods market and the money market. False.) At any positive rate of unemployment. (You can also show this using the wage-setting relation curve in the diagram). neither policy has any effect on output (the only effect of monetary and fiscal policy in this case is a change in the price level). The aggregate demand relation slopes down because at a higher price level. however. given expected price and actual price constant? (When the unemployment rate is very low. In the extreme case. just substitute in for i into the IS equation from the LM equation. and b0 and b1 are positive constants G = G . i is the interest rate. m0 (a positive d constant) represents exogenous changes to M . Derive the expression for aggregate demand using your answer to part (a). where M is nominal money demand. (Hint: To derive the AD curve. where I is investment. P is the price level. and c0 and c1 are positive constants I = b0 – b1 i.m2 i (b) Now suppose 1/[1-c1(1-t)]=λ for simplicity. IS: LM: Ms = Md Ms/P = m0 + m1 Y .the following set of equations: Goods market: C = c0 + c1 (1-t)Y. where C is consumption. You will obtain an equation of Y as a function of P. Y is income. and m1 and m2 are also positive constants Let Ms represent nominal money supply (a) Derive the IS relation and the LM relation equations. where G is a positive constant Money market: d d M = P (m0 + m1Y – m2 i). t represents a proportional tax.) 4 . Suppose the aggregate supply takes the following form: P = Pe + (1/50)( Y − Yn ) and P=1.8 Ms=200 G=100 t=0 Yn=550 Derive the AD equation using these figures.) (d) Use the same condition in part (c).4 m0=400 m1=1 m2=0. Assume we are in the short-run for now.5 b0=300 b1=0. obtain Pe=2.(c) Now let: c0=200 c1=0. Then. you will obtain the equilibrium Y*=500. First. (All figures are in millions of HK dollars. 5 . use the AS equation. Also denote the natural level of output in the diagram. Pe? Draw and label the AS-AD diagram for this case and denote the equilibrium in this economy as point A. use the AD equation from part (c). What is the equilibrium output. substitute P=1. Y*? What is the expected price level. what is the relation between P and Pe? When Y=Yn. and show how the two diagrams are related to each other. P= Pe (f) The Keynesian government is up for reelection soon.(e) If Y happened to be equal to the natural level of output Yn. (We are still in the short run. draw the AS-AD and the IS-LM diagrams. What is the difference between the effects of the two policy options? 6 . For each policy option. and so it wants to achieve the natural level of output.) Propose two different policy options that would do the job. Calculate by how much the government must increase/decrease government spending to achieve the natural level of output. you don’t need to do any calculations. For monetary policy. 7 . ) 8 . What happens as time passes and we get to the “medium run”? (You do not have to do any calculations. The voters apparently think so too. and raises government spending by more than would be required to achieve the natural level of output. and the government gets reelected.(g) The Keynesian government decides not to listen to you. Its argument is that higher output is better. just draw diagrams and give some intuition/explanation. T) + I(Y. (3 marks) (b) Assume that the economy is at a point such that the unemployment rate is equal to the natural rate of unemployment. Describe the channel through which the AS curve slopes up/down. (2 marks) 9 . i) (a) Find the aggregate supply relation. z) Wage Setting Relation: P = (1 + μ) W Goods Market: Y = C(Y.2. i) + G Financial Market: Ms /P = Md (Y. What does this imply about the price level and output? Explain. Closed Economy AS-AD (33 marks) Price Setting Relation: W = Pe F (u. LMMR. ADSR.and medium-run? (2 marks) (e) If the price of oil increases sharply. the short-run equilibrium as point B. (10 points) See in-class notes. where the subscript 0 denotes initial status). and output associated with natural rate of unemployment. what happens in the short-run (SR) and the medium-run (MR)? Start from point A where P = Pe. ASSR. the short-run equilibrium as point B.(c) If the Fed carries out a monetary contraction. where the subscript 0 denotes initial status). the medium-run equilibrium as point C. ADSR. ADMR. what happens in the short-run (SR) and the medium-run (MR)? Start from point A where P = Pe. ASSR. Label the following: all curves including (IS0. Label the following: all curves including (IS0. and output associated with natural rate of unemployment. LMSR. LM0. LM0. (d) What does neutrality of money imply about the effectiveness of contractionary monetary policy in affecting output and interest rate in the short. ISMR. ASMR. LMSR. (10 marks) 10 . the medium-run equilibrium as point C. ADMR. ASMR. LMMR. ISMR. ISSR. ISSR. decrease or remain the same when the price of oil rises sharply.(f) Indicate whether these variables increase.) (6 marks) 11 . (You may use arrows.