KOÇ UNIVERSITY ECON 202 Macroeconomics Fall Problem Set VI C = (Y T) I = 380 G = 400 T = 0.20Y Y = C + I + G.

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1 KOÇ UNIVERSITY ECON 202 Macroeconomics Fall 2007 Problem Set VI 1. Consider the following model of an economy: C = (Y T) I = 380 G = 400 T = 0.20Y Y = C + I + G. (a) What is the value of the MPC in this model? The M P S equals (b) The equation f taxes indicate sthat when Y rises by $100, taxes rise $20. Consequently, when Y rises by $100, disposable income Y T rises by $80 and consumption rises by 0.75(80) = $60. Draw the consumption and planned expenditure curves as a function of Y, and label their slopes and intercepts. Do this yourself. (c) Compute the equilibrium level of income. Y = C + I + G = (Y T) = (Y 0.20Y ) = Y Y = 800/0.4 = (d) At the equilibrium level of income, what is the value of the government budget surplus? T G = 0.20Y G = = 0. (e) Increase G by 10 to 410, calculate the government purchases multiplier, and explain why it is no longer equal to 1/(1 MPC). 1

2 The government purchases multipler is given by whereas Thus, if G = 10, Y = 25. Y G = (1 0.2) = = MPC = 1/0.25 = 4. The reason that the government purchases multiplier is not equal to 1/(1 MPC) is that total taxes now depend on income. Thus, a unit increase in income also increases taxes by 0.2. Thus, the government purchases multiplier is smaller when taxes depend on income. 2. Suppose that the following equations describe an economy: (C, Y, G, T, and Y are measured in billions of dollars, and r is measured as a percent, f example, r = 10 = 10%. C = (Y T) T = 200 I = 100 4r G = 350 (M/P) d = L(r,Y ) = 0.75Y 6r M s /P = M/ P = 735. (a) Derive the equation f the IS curve. (Hint: It is easier to solve f Y here.) The IS curve is given by: Y = C + I + G, Y = (Y 200) r Y = 500 4r Y = r. (b) Derive the equation f the LM curve. (Hint: It is easier to solve f Y.) The LM curve is given by: M s /P = L(r,Y ), M/ P = 0.75Y 6r 735 = 0.75Y 6r Y = r. 2

3 (c) Now express both the IS and LM equations in terms of r. Graph both curves and calculate their slopes. IS : r = Y, and LM : r = 0.125Y (d) Use the equations from Parts (a) and (b) to calculate the equilibrium levels of real output, the interest rate, planned investment, and consumption. Solving f Y yields Y = 0.125Y 122.5, = 0.225Y Y = The equilibrium level of the real interest rate is r = (1100) = = 15. The equilibrium level of consumption is given by C = (Y T) = ( ) = = 710, and the quilibrium level of planned investment is I = 100 4r = 100 4(15) = 40. Notice that at the equilibrium, Y = C + I + G = = (e) At the equilibrium level of real output, calculate the value of the government budget surplus. T G = = Consider the same economy that we analyzed in Question 2 of this problem set. 3

4 (a) Suppose that G increases by 36 to 386. Derive the new IS and LM equations and plot and draw these curves on the graph that you drew f Part (c) in Question 2. The new IS curve is given by: Y = (Y 200) r Y = 536 4r Y = r. The LM curve remains unchanged: LM : Y = r. (b) What is the hizontal shift in the IS curve and/ LM curve in Part (a) (that is, if r remains constant, by how much does Y increases on each curve)? The hizontal shift in the IS curve is given by Y = = 90 = G 1 MPC = (c) Refer to the IS and LM equations you derived in Part (a) With Y on the left-side of the equations, calculate the new equilibrium levels of real output Y, the interest rate r, planned investment I, and consumption C. The new equilibrium real interest rate can be found from r = r, r = The new equilibrium level of output is = 20. Y = r = (20) = Planned consumption at the equilibrium level of output is C = (Y T) = ( ) = = 454, and planned investment is Thus, we again have the identity I = 100 4r = 100 4(20) = 20. Y = C + I + G = =

5 (d) Instead of increasing G, suppose that the Fed sought to achieve the equilibrium level of real output Y in Part (c) through expansionary monetary policy alone. By how much would the Fed have to increase the money supply? (Hint: Start by drawing the appropriate shifts in the IS and/ LM curve in Parts (a) and (d)). Do this yourself. (e) Compare the equilibrium levels of consumption C, government spending G, and planned investment I in Parts (c) and (d) Based on this comparison, why might some economists prefer expansionary fiscal policy while others prefer expansionary monetary policy? Expansionary fiscal policy increases output but it also increases the real interest rate, and crowds out investment. By contrast, expansionary monetary policy increases output but reduces the real interest rate. Thus, investment increases in equilibrium. However, expansionary monetary policy may be inflationary in the long run. 4. Changes in Expected Inflation in the IS LM Model In this exercise, we illustrate how a change in expected inflation will change the IS LM equilibrium. (a) Investment is a function of the real interest rate r, whereas money demand is a function of the nominal interest rate i. Consequently, the IS curve should be drawn as a function of r and the LM curve should be drawn as a function of i. Assume that IS and LM curves are: IS curve : r = Y LM curve : i = Y. Recall that r = i π e. Assume that expected inflation equals zero so that r = i and it does not matter which variable we put on the vertical axis. We ll put the nominal interest rate i on the vertical axis. Draw these two curves, label them IS 1 and LM 1 and label the initial equilibrium point A. Do it yourself. (b) Find the initial equilibrium values of Y and i. Since π e = 0, what is the real interest rate r? Y = Y, which implies Y = 90/0.075 = 1200, 5

6 and i = (1200) = 10. Since π e = 0 r = i = 10. (c) Now suppose that we have deflation and expected inflation falls to π e = 7.5 percent. As a result of this decrease in expected inflation, the real interest rate at the initial value of the nominal interest will rise to r = i π e = 10 ( 7.5) = Consequently, at each level of i, r will now be higher than it was befe the expected deflation. Since the LM curve is a function of the nominal interest rate, it will not shift. The IS curve, on the other hand, is a function of the real interest rate. From the IS equation, it is known that Y = 1,200 when r = 10. When π e = 0, this value of r occurs when i = 10. Now that π e = 7.5 percent, this level of r will occur when i = r + π e = = 2.5 percent. Thus, the same level of investment will occur only if i falls by 7.5 percentage points. Consequently, the IS curve shifts downward by 7.5 percentage points. Draw the new IS curve, label it IS 2, and label the new equilibrium point B. Do this yourself. (d) The equation f the new IS when π e = 7.5 is i = Y. Set this equal to the equation f the LM curve, and compute the new equilibrium values of Y and i. The answer is Y = Y, which implies and Y = 1100 i = (1100) = 5. (e) What is the effect of the decrease in expected inflation on the equilibrium levels of Y, i, and r? The equilibrium levels of Y and i fall, and r = i π e = 5 ( 7.5) = 12.5 increases. 5. In 1993, President Clinton proposed reducing the federal budget deficit by increasing net taxes and reducing government spending. Some economists claimed that this policy would reduce interest rates and increase real GDP as well as cut the deficit. (a) Draw the IS LM graphs to analyze the effects of this mix of fiscal policies on the deficit, interest rates, and real GDP. (Assume that taxes are lump-sum. that is, taxes are an absolute amount that is unrelated to the level of income.) Are these results consistent with the economists predictions? 6

7 An increase in taxes and a reduction in the government spending would certainly reduce interest rates and the budget deficit but this policy would also reduce real output by shifting the IS backwards. (b) Most economists who believe that an increase in taxes and a reduction in government spending would both increase GDP and cut the deficit implicitly assume that the Fed would change its monetary policy if this deficit-reduction plan were enacted. Draw IS LM graphs on a separate sheet of paper to show what kind of monetary policy must accompany this mix of fiscal policy changes in der to decrease the deficit and interest rates, while increasing GDP. The money supply must be increased sufficiently so that the LM curve shifts to intersect the new IS curve at a higher level of income compared to the initial equilibrium. 7