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ISL244E Macroeconomics Problem Session-6 by Research Assistant Serkan Değirmenci (Ph.D. Candidate) D202/19.03.2012 # Today # • Blanchard (2009), Macroeconomics: #THE SHORT RUN# (CHAPTER 3+4=5) - Chapter 4: Financial Markets: (btw pages: 85-106) Quick Check (page 104-105): 2-3-4 - Chapter 5: Goods and Financial Markets: (btw pages: 107 -131) Quick Check (page 127-128): 2-3-4 Chapter-4-QC-2 (Page: 104) 2. Suppose that a person’s yearly income is $80,000. Also, suppose that this person’s money demand function is given by Md = $Y(0.30 – i) a. b. c. d. e. What is this person’s demand for money when the interest rate is 4%? 8%? Explain how the interest rate affects money demand. Suppose that the interest rate is 4%. In percentage terms, what happens to this person’s demand for money if her yearly income is reduced by 50%? Suppose that the interest rate is 8%. In percentage terms, what happens to this person’s demand for money if her yearly income is reduced by 50%? Summarize the effect of income on money demand. In percentage terms, how does this effect depend on the interest rate? Chapter-4-QC-2 (Page: 104)-answer 2. a. b. i=0.05: Money demand = $80,000(0.30-0.05) = $20,000 i=0.10: Money demand = $80,000(0.30-0.10) = $16,000 Money demand decreases when the interest rate increases because bonds, which pay interest, become more attractive. c. The demand for money falls by 50%. d. The demand for money falls by 50%. e. A 1% increase (decrease) in income leads to a 1% increase (decrease) in money demand. This effect is independent of the interest rate. Chapter-4-QC-3 (Page: 104) 3. Suppose that money demand is given by Md = $Y(0.25 – i) where $Y is $100. Also, suppose that the supply of money is $20. a. What is the equilibrium interest rate? b. If the Federal Reserve Bank wants to increase i by 10 percentage points (e.g., from 2% to 12%), at what level should it set the supply of money? Chapter-4-QC-3 (Page: 104)-answer 3. a. b. MD = MS $20 = MD = $100(0.25-i) i = 5% i = 5% => i* = 15% MD = MS = $100(0.25-0.15) M = $10 Chapter-4-QC-4 (Page: 105) 4. Consider a bond that promises to pay $100 in one year. a. What is the interest rate on the bond if its price today is $75? $85? $95? b. What is the relation between the price of the bond and the interest rate? c. If the interest rate is 8%, what is the price of the bond today? Chapter-4-QC-4 (Page: 105)-answer 4. a. b. c. i = 100/$PB –1 $PB = $75 => i = 33% $PB = $85 => i = 18% $PB = $95 => i = 5% When the bond price rises, the interest rate falls. $PB = 100/(1+i) = 100/(1.08) ≈ $93 Chapter-5-QC-2 (Page: 127-128) 2. Consider first the goods market model with constant investment that we saw in Chapter 3. Consumption is given by C = c0 + c1(Y-T) a. and I, G, and T are given. Solve for equilibrium output. What is the value of the multiplier? Now let investment depend on both sales and the interest rate: b. I = b0 + b1Y – b2i Solve for equilibrium output. At a given interest rate, is the effect of a change in autonomous spending bigger than what it was in part (a)? Why? (Assume c1 + b1 <1.) Next, write the LM relation as M/P = d1Y – d2i c. d. Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM relations.) Derive the multiplier (the effect of a change of one unit in autonomous spending on output). Is the multiplier you obtained in part (c) smaller or larger than the multiplier you derived in part (a)? Explain how your answer depends on the parameters in the behavioral equations for consumption, investment, and money demand. Chapter-5-QC-2 (Page: 127-128)-answer 2. a. Y* = [1/(1-c1)][c0-c1T+I+G] The multiplier is 1/(1-c1). b. Y* = [1/(1-c1-b1)][c0-c1T+b0-b2i+G] The multiplier is 1/(1-c1-b1). Since the multiplier is larger than the multiplier in part (a), the effect of a change in autonomous spending is bigger than in part (a). An increase in autonomous spending now leads to an increase in investment as well as consumption. c. Substituting for the interest rate in the answer to part (b), Y* = [1/(1-c1-b1+b2d1/d2)][c0-c1T+b0+(b2/d2)(M/P)+G]. The multiplier is 1/(1-c1-b1+b2d1/d2). Chapter-5-QC-2 (Page: 127-128)-answer The multiplier is greater (less) than the multiplier in part (a) if (b1-b2d1/d2) is greater (less) than zero. 2. d. The multiplier as measured in part (c) measures the marginal effect of an increase in autonomous spending on equilibrium output. As such, the multiplier is the sum of two effects: a direct effect of output on demand and an indirect effect of output on demand via the interest rate. The direct effect is equivalent to the horizontal shift of the IS curve. The indirect effect depends on the slope of the LM curve (since the equilibrium moves along the LM curve in response to a shift of the IS curve) and the effect of the interest rate on investment demand. The direct effect is captured by the sum c1+b1, which measures the marginal effect of an increase in output on the sum of consumption and investment demand. As this sum increases, the multiplier gets larger. The indirect effect is captured by the expression b2d1/d2 and tends to reduce the size of the multiplier. The ratio d1/d2 is the slope of the LM curve, and the parameter b2 measures the marginal effect of an increase in the interest rate on investment. Note that the slope of the LM curve becomes larger as money demand becomes more sensitive to income (i.e., as d1 increases) and becomes smaller as money demand becomes more sensitive to the interest rate (i.e., as d2 increases). Chapter-5-QC-3 (Page: 128) 3. a. The response of investment to fiscal policy Using the IS-LM diagram, show the effects on output and the interest rate of a decrease in government spending. Can you tell what happens to investment? Why? Now consider the following IS-LM model: C = c0 + c1 (Y-T) I = b0 + b1Y – b2i M/P = d1Y – d2i b. Solve for equilibrium output. Assume c1 + b1 < 1. (Hint: You may want to work through problem 2 if you are having trouble with this step.) c. d. Solve for the equilibrium interest rate. (Hint: Use the LM relation.) Solve for investment. e. Under what conditions on the parameters of the model (i.e., c0, c1, and so on) will investment increase when G decreases? (Hint: If G decreases by one unit, by how much does I increase? Be careful; you want the change in I to be positive when the change in G is negative.) f. Explain the condition you derived in part (e). Chapter-5-QC-3 (Page: 128)-answer 3. a. The IS curve shifts left. Output and the interest rate fall. The effect on investment is ambiguous because the output and interest rate effects work in opposite directions: the fall in output tends to reduce investment, but the fall in the interest rate tends to increase it. b. From the answer to 2(c), Y* = [1/(1-c1-b1+b2d1/d2)][c0-c1T+b0+(b2/d2)(M/P)+G]. c From the LM relation, i = Y(d1/d2)–(M/P)/d2. To obtain the equilibrium interest rate, substitute for equilibrium Y from part (b). i* = Y*(d1/d2)–(M/P)/d2. d. I* = b0+b1Y*-b2i* = b0+(b1-b2d1/d2)Y*+(b2/d2)(M/P) To obtain equilibrium investment, substitute for equilibrium Y from part (b). Chapter-5-QC-3 (Page: 128)-answer 3. e. From part (b), holding M/P constant, equilibrium Y decreases by [1/(1-c1-b1+b2d1/d2)] when G decreases by one unit. From part (d), holding M/P constant, I decreases by (b1- b2d1/d2)/(1-c1-b1+b2d1/d2) when G decreases by one unit. So, if G decreases by one unit, investment will increase when b1<b2d1/d2. f. A fall in G leads to a fall in output (which tends to reduce investment) and to a fall in the interest rate (which tends to increase investment). Therefore, for investment to increase, the output effect (b1) must be smaller than the interest rate effect (b2d1/d2). Note that the interest rate effect is the product of two factors: (i) d1/d2, the slope of the LM curve, which gives the effect of a oneunit change in equilibrium output on the interest rate, and (ii) b2, which gives the effect of a one-unit change in the equilibrium interest rate on investment. Chapter-5-QC-4 (Page: 128) 4. a. b. c. d. e. f. g. Consider the following IS-LM model: C = 400 + 0,25YD I = 300 + 0,25Y – 1500i G = 600 T = 400 (M/P)d = 2Y – 12000i M/P = 3000 Derive the IS relation. (Hint: You want an equation with Y on the left side and everything else on the right.) Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation with i on the left side and everything else on the right.) Solve for equilibrium real output. (Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output.) Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for Y in part (c) into either the IS or LM equations and solve for i. If your algebra is correct, you should get the same answer from both equations.) Solve for the equilibrium values of C and I, and verify the value you obtained for Y by adding C, I, and G. Now suppose that the money supply increases to M/P = 4320. Solve for Y, i, C, and I, and describe in words the effects of an expansionary monetary policy. Set M/P equal to its initial value of 3000. Now suppose that government spending increases to G = 840. Summarize the effects of an expansionary fiscal policy on Y, i, and C. Chapter-5-QC-4 (Page: 128)-answer 4. a. Y=C+I+G=400+.25(Y-400)+300+.25Y-1500i+600 Y=2400-3000i => IS relation b. M/P = 3000 = 2Y-12000i i = Y/6000-1/4 => LM relation c. Substituting from part (b) into part (a) gives Y* = 2100 d. Substituting from part (c) into part (b) gives i* = 10% e. C* = 825; I* = 675; G = 600; C+I+G = 2100 Chapter-5-QC-4 (Page: 128)-answer 4. f. Y* = 2320; i* = 2,67%; C* = 880; I* = 840. A monetary expansion reduces the interest rate and increases output. Consumption increases because output increases. Investment increases because output increases and the interest rate decreases. g. Y* = ?; i* = ? %; C* = ?; I* = ?. (TRY YOURSELF!) A fiscal expansion increases output and the interest rate. Consumption increases because output increases. Investment is affected in two ways: the increase in output tends to increase investment, and the increase in the interest rate tends to reduce investment. In this example, these two effects exactly offset one another, and investment does not change. # Halfway Check List # GNH (2009): Chapters: 1-5-6-11 Blanchard (2009): Chapters: 1-2-3-4-5 Highlights: Measuring National Income and Growth Money, Banking and Financial Markets Goods and Financial Markets: The IS-LM Model to be continued…