# Solutions to Spring 2015 Week 13 Tutorial Questions (Ch9)

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1 Chapter 9: Q1: Macroeconomics P.324 Review Questions #6 Q2: Macroeconomics P.324 Review Questions #7 Q3: Macroeconomics P.324 Review Questions #8 Q4: Macroeconomics P.325 Numerical Problems #1 Q5: Macroeconomics P.324 Numerical Problems #4 Q1: Define monetary neutrality. Show that after prices adjust completely, money is neutral in the IS-LM model. What are the classical and Keynesian views about whether money is neutral in the short run? In the long run? There is monetary neutrality if a change in the nominal money supply changes the price level but has no effect on real variables. Once prices adjust, money is neutral in the IS-LM model, because a change in the money supply that shifts the LM curve is matched by a proportional change in the price level that returns the real money supply back to its original level and moves the LM curve back to its original location. Classical economists believe that money is neutral in the short run, but Keynesians believe that there may be sluggish adjustment of the price level, so that changes in the money supply affect output and the real interest rate in the short run. Both classicals and Keynesians believe money is neutral in the long run. Q2: What two variables are related by the aggregate demand (AD) curve? Why does the AD curve slope downward? Give two examples of the changes in the economy that shift the AD curve to the right and explain why the shift occurs. The aggregate demand curve relates the price level to the aggregate demand for goods and services. It is downward sloping, because with a fixed nominal money supply, an increase in the price level shifts the LM curve up, so the level of output at the IS-LM intersection is lower. Factors that shift the aggregate demand curve to the right include (1) an increase in expected future output, which reduces desired saving, raises desired consumption, and shifts the IS curve up; (2) an increase in government purchases, which reduces desired saving and shifts the IS curve up; (3) an increase in expected future MPK, which increases desired investment and shifts the IS curve up; (5) an increase in the nominal money supply, which raises the real money supply and shifts the LM curve down; (6) a decrease in the interest rate on money, Which decreases the demand for money and shifts the LM curve down; and (7) an increase in the expected inflation rate, which reduces the demand for money and shifts the LM curve down. Week 13 Page 1

2 Q3: Describe the short run aggregate supply (SRAS) curve and the long run aggregate supply (LRAS) curve. Why is one of these curves horizontal and the other vertical? The short-run aggregate supply curve is horizontal and the long-run aggregate supply curve is vertical. The short-run aggregate supply curve is horizontal because prices remain fixed in the short run. The long-run aggregate supply curve is vertical because the aggregate amount of output supplied is the full-employment level, regardless of the price level. Q4: Desired consumption and investment are C d = r Y; I d = r As usual, Y is output and r is the real interest rate. Government purchases G are 120. a. Find an equation relating desired national saving S d to r and Y. S d = Y C d G= Y ( r+ 0.1 Y) 120 = r+ 0.9Y. b. What value of the real interest rate clears the goods market when Y = 600? Use both forms of the goods market equilibrium condition. What value of the real interest rate clears the goods market when Y = 640? Graph the IS curve. (1) Using the equation that goods supplied equals goods demanded gives Y = C d + I d + G= ( r + 0.1Y) + ( r) + 120= r + 0.1Y. So 0.9Y= r. At full employment, Y = 600. Solving = r, we get r = When Y = 640, we get r = (2)Using the equivalent equation that desired saving equals desired investment gives S d = I d, thus r + 0.9Y= r 0.9Y = r When Y= 600, r = 0.10.So we can use either equation to get the same result. When Y= 640, we get r = Week 13 Page 2

3 r c. Government purchases rise to 132. How does this increase change the equation for national saving in part (a)? What value of the real interest rate clears the goods market when Y = 600? Use both forms of the goods market equilibrium condition. How is the IS curve affected by the increase in G? IS Y When G= 132, desired saving becomes S d = r+ 0.9Y. S d is now 12 less for any given rand Y; this shows up as a shift in the S d line from S 1 to S 2 in the figure below. Setting S d = I d, we get r + 0.9Y= r thus 600r+ 0.9Y= 612.At Y= 600, this is 600r= 612 (0.9 x 600) = 72, so r= The market-clearing real interest rate increases from 0.10 to r S 2 S S d, I d I Week 13 Page 3

4 Q5: The production function in an economy is Y = A(5N N 2 ), where A is productivity. With this production function, the marginal product of labour is MPN = 5A 0.005AN. Suppose that A = 2. The labour supply curve is NS = (1-t)w, where NS is the amount of labour supplied, w is the real wage, and t is the tax rate, which is 0.5. Desired consumption and investment are C d = (Y T) 200r; I d = r. Taxes and government purchases are T = Y; G = 50. Money demand is M d /P = 0.5Y 250(r + π e ). The expected rate of inflation π e is 0.02, and the nominal money supply M is a. What are the general equilibrium levels of the real wage, employment, and output? First, look at labour market equilibrium. Labour supply is NS = (1 t)w NS = w. Labour demand comes from the equation w = MPN = 5A 0.005A ND ND = w. Equating labour supply and labour demand gives N= 100. Using this in either the labour supply or labour demand equation then gives w= 9. Using N in the production function gives Y= 950. b. For any level of output Y, find an equation that gives the real interest rate r that clears the goods market; this equation descries the IS curve. (Hint: write the goods market equilibrium condition and solve for r in terms of Y and other variables.) What are the general equilibrium values of the real interest rate, consumption, and investment? Next, look at goods market equilibrium and the IS curve. S d =Y C d G = Y [ (Y T) 200r] G =Y [300 (0.4Y 16) 200r] G= Y+200r G. Setting S d = I d gives Y + 200r G = r. Solving this for r in terms of Y gives 450r= ( G 0.6 Y. When G= 50, and with full-employment output of 950, using this in the IS curve and solving for r gives r= 0.05.Plugging these results into the consumption and investment equation gives C= 654 and I= 246. c. For any level of output Y, find an equation that gives the real interest rate that clears the asset market; this equation describes the LM curve. (Hint: As in part (b), write the appropriate equilibrium condition and solve for r in terms of Y and other variables.) What is the general equilibrium value of the price level? Next, look at asset market equilibrium and the LM curve. Setting money demand equal to money supply gives 9150/P = 0.5Y 250(r +0.02), which can be solved for r = 0.002Y /P. With Y= 950 and r = Solving for P gives P = 20. Week 13 Page 4

5 d. Suppose that government purchases increase to G = Now what are the general equilibrium values of the real wage, employment, output, the real interest rate, consumption, investment, and the price level? With G= 72.5, the IS curve becomes 450r = Y r = Y. With Y = 950. The IS curve gives r =0.10, the LM curve gives P= 20.56, the consumption equation gives C= 644. And the investment equation gives I= The real wage, employment, and output are unaffected by the change. Week 13 Page 5

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