1. (16 points) For all of the questions below, draw the relevant curves.

Transcription

1 Intermediate Macroeconomic Theory II, Fall 2006 Solutions to Problem Set 4 (35 points) 1. (16 points) For all of the questions below, draw the relevant curves. (a) (2 points) Suppose that the government wants to raise investment but keep output constant. Using the IS{LM model, what mix of monetary and scal policy would achieve this goal? (b) (2 points) Two classical economies dier only in one respect: in economy A money growth and ination have been low and stable for many years, but in economy B, money growth and ination have uctuated erratically between very low and very high levels. When producers in economy B observe changes in the prices of the goods they produce, from past experience they usually attribute these changes to uctuations in the overall price level, rather than to changes in the relative prices of their goods. Will the slope of the SRAS for economy B be atter or steeper than the slope of the curve for economy A? What about the slope of the Phillips curve? (Hint: draw supply curves and convince yourself that your answer is right.) Use the IS{LM model to determine the short run and long run eects of each of the following on the output (real income), the real interest rate, consumption, investment, the price level, and the real money balances. Draw the relevant diagrams to show how you arrived at your answer. Assume that consumption is not responsive to changes in the real interest rate; and that the economy is initially at the natural level of output. Track the eects for normal cases, i.e., do not bother about vertical/horizontal IS/LM curves. (c) (4 points) The expected rate of ination rises. (d) (4 points) The introduction of automatic teller machines reduces the demand for money. (e) (4 points) An increase in consumer condence, as consumers expect their incomes to be higher in the future. (a) To raise investment, we need to reduce the real interest rate. Thus, we need to adopt a policy that shifts the LM curve to the right, i.e., to pursue an expansionary, loose, monetary policy. For a stable IS curve this will translate into a lower real interest rate, higher investment, and higher output. To maintain output at its previous level, we need to contract spending in the economy and move the IS curve to the left this can be achieved, say, by a decrease in government expenditures. Thus, a loose monetary policy and a tight scal policy would produce the desired outcome. 1

2 (b) The slope of the SRAS curve will be much steeper in the economy B, because producers increase their output only by a small amount in response to an increase in price. The economy A's SRAS curve will be atter, as people are likely to perceive own price changes as changes in the relative prices rather than in the aggregate price level, and thus will respond more strongly to changes in own prices. The short-run Phillips curve will also be steeper in economy B, since unemployment, like output, will not respond much to a change in ination. In economy A, where (un-)employment and output respond more strongly to the price changes, the short-run Phillips curve will be atter. (c) If we consider the IS{LM diagram with the nominal interest rate on the vertical axis (as in your textbook's discussion of the Great Depression), the IS curve will shift up and to the right, leading to an increase in the nominal interest rate and a reduction in the real interest rate. In the short run, this leads to an increase in the real output (income), and therefore an increase in consumption, an increase in investment, no eects on the price level (as the price is stuck in the short run), and no eects on the real money balances (as both the money supply and the level of prices are xed in the short run). Compared to the initial equilibrium, in the SR: Y ", I ", r #, C " (since the real income increases), P, M=P. In the long-run, the price level will increase (and so will ination), LM curve will shift to the left, the nominal interest rate will increase, and the real interest rate will increase, back to its previous level. Investment will fall, output will revert to its previous level, and the real money balance will fall. Compared to the initial equilibrium, in the LR: Y, I (since the real interest rate is at its previous level), r, C (since output is at its previous level, and T is the same), P ", M=P #. Thus, the expectations of rising prices are self-fullling here, i.e., the expected ination leads to actual ination. 2

3 (d) Reduction in the money demand shifts the LM curve to the right for a given output, price and money supply, we will have a lower real interest rate. Since the IS is stable, the real interest rate falls, the investment increases, and the national income increases. Compared to the initial equilibrium, in the SR: Y ", I ", r #, C " (since the real income increases), P, M=P. In the long run, the price level increases in response to an increase in expenditures, M=P falls, and the LM shifts to the left, back to where it was initially. The real interest rate increases to its original level, investment falls and output reverts to its natural level. Compared to the initial equilibrium, in the LR: Y, I, r, C, P ", M=P #. (e) An increase in consumer condence raises planned expenditures and therefore shifts the IS curve to the right, leading to an increase in the real interest rate, and the fall in investment. Compared to the initial equilibrium, in the SR: Y ", I #, r ", C ", P, M=P. In the long run, the price level increases, M=P falls and the LM shifts to the left, increasing the real interest rate and depressing investment even further. Compared to the initial equilibrium, in the LR: Y, I #, r ", C " (since autonomous consumption increases for any level of income), P ", M=P #. 3

4 2. (14 points) Consider the following economy: Planned consumption: C = 1; :5 (Y T ) 200 r. Planned investment: I = r. Real money demand: (M=P ) d = 0:5 Y 200 i. Expected ination: e = 0. (a) (2 points) Suppose T = G = 450 and M = 9; 000. Find an equation for the IS curve. (Hint: Set the national savings to be equal to the national investment, and solve for the relationship between r and Y, given P. Express the IS curve as Y being a function of r.) (b) (2 points) Find an equation for the LM curve. (Hint: Set real money supply and real money demand equal, and solve for the relationship between r and Y, for a given P. Express the LM curve as Y being a function of r.) (c) (2 points) Find an equation for the aggregate demand curve. (Hint: Use the IS and LM equations to nd a relationship between Y and P. Express the AD curve as Y being a function of P.) (d) (2 points) If the full employment output Y = 4; 600, what are the equilibrium values for the level of aggregate prices, output, consumption, investment, and the real interest rate? (e) (2 points) Suppose that the money supply falls to M = 4; 500. What is the equation for the AD now? (Express the AD curve as Y being a function of P.) (f) (2 points) Repeat (2d) given than money supply falls to 4,500. (g) (2 points) Explain what you nd using the IS{LM diagram, and the LRAS curves drawn in the r Y space. Argue whether LM, IS shifted or not and why. (a) r = i e = i. S = Y C G = Y 1; 275 0:5 (Y T )+200 r G = 0:5 Y +200 r 1; 275+0:5 T G. Equating S to I, gives the following equation for the IS curve: 0:5 Y r 1; :5 T G = r, or 0:5 Y = 400 r + 1; 275 0:5 T + G I.e., the IS curve is: Y = 800 r T + 2 G + 4; 350. Plugging G, and T, the IS curve is: Y = 800 r + 4; 800. (b) Equating the demand for real money balances to supply, the LM curve is: 9; 000=P = 0:5 Y 200 i = 0:5 Y 200 r, or Y = 18; 000=P r. (c) From the IS curve, 400 r = 1=2 Y + 2; 400. Plugging 400 r into the LM curve gives the AD: Y = 18; 000=P 1=2 Y + 2; 400, or 18; 000=P + 2; 400 = 3=2 Y, or Y = 12; 000=P + 1; 600. (d) Since our supply curve is Y = 4; 600, equilibrium output is 4,600. Equilibrium level of P is obtained by setting the aggregate quantity of output demanded equal to the quantity supplied: 12; 000=P = 3; 000, and so P = 4. The real interest rate can be obtained from the IS curve: r = 1=4. C = 1; :5 (4; ) 200 (1=4) = 3; 300. I = (1=4) = 850. (e) When the money supply falls to 4,500, the LM curve will be Y = 9; 000=P r, and the new AD curve is: Y = 6; 000=P + 1; 600. (f) Output stays at Y = 4; 600. From the AD curve, P = 6; 000=3; 000 = 2. 4

5 From the IS curve, r = 1=4. C=3,300. I=850. Money is neutral here, i.e. it does not aect the real variables. The fall in the money supply just causes the fall in the aggregate price level. (g) Your IS{LM curve, and the LRAS curve should intersect at the point where r = 1=4, and Y = Y = 4; 600. For a given price level and the real interest rate, there is a shift in the LM curve to the right. But, since the price level drops to P = 2, the real money balances fall to their previous level, and the LM curve shifts back to its original position. Thus, in the end, changes in the money supply lead only to changes in the aggregate price level the monetary neutrality result of classical economics. 3. (5 points) Consider an economy in long-run equilibrium with an ination rate of 12% (=0.12) per year and a natural unemployment rate u n of 6% (=0.06). The Phillips curve is = e 2(u u n ). Assume that Okun's law holds so that a 1% increase in the unemployment rate maintained for one year reduces GDP by 2% of full-employment output. Consider a four-year disination according to the following table: Year e (a) (2 points) What is the cyclical unemployment rate in each of the four years? (b) (2 points) By what percentage does output fall short of full-employment output each year? (c) (1 point) What is the sacrice ratio for this disination? Use equations: u = 0:06 0:5 ( e ). Output shortfall=2.0 (u{0.06). Year e u u u n Output shortfall (a) 7%, 8%, 7%, 6% (see table above). (b) 2%, 4%, 2%, 0% (see table above). (c) Since the overall shortfall in output is 0.08, or 8%, and the disination is (12%{4%)=8%, the sacrice ratio is equal to (0.08/0.08)=1.0. 5