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ECON 202 CHAPTER 4 SOLUTIONS Question 9 (a) Shift (for a given Y, (Ms/P) (M/P)d at a lower r. (b) Rotate (the horizontal intercept is unchanged). (c) Shift and rotate (both horizontal intercept and slope change). (d) No effect on position or slope of LM curve. (e) Causes movement along LM curve, but does not affect its position or slope. (f) Shift (for a given Ms, changes the real money supply). Question 10 If government spending becomes negatively sensitive to changes in the interest rate, then autonomous spending declines by a larger amount for any given change in the interest rate. Therefore the IS curve becomes flatter and, other things being equal, any given fiscal expansion results in smaller increases in output and the interest rate. However, because the fiscal expansion causes a smaller increase the interest rate, it also means that less autonomous consumption and planned investment is crowded out by the fiscal expansion. Likewise, if autonomous taxes become positively sensitive to changes in the interest rate, then disposable income declines when the interest rate rises. That means that autonomous spending becomes more sensitive to the interest rate. Therefore the IS curve becomes flatter and, other things being equal, any given fiscal expansion results in smaller increases in output and the interest rate. However, because the fiscal expansion causes a smaller increase the interest rate, it also means that less autonomous consumption and planned investment is crowded out by the fiscal expansion. Question 11 If private sector spending is highly sensitive to a change in the interest rate, then the IS curve is relatively flat. The main effect of a fiscal expansion will be a higher interest rate that reduces private sector spending almost as much as the fiscal expansion increases autonomous spending. As a result, the fiscal expansion causes very little increase in output. In the case of a fiscal contraction, the effect of the lower interest rate on private sector spending almost offsets the effect of the fiscal contraction. As a result, fiscal policy is unable to have much of an impact on output. On the other hand, monetary policy is quite capable of changing output if private sector spending is highly sensitive to a change in the interest rate. A policy of tight money will result in a sharp contraction of private sector spending as the interest rate rises. Easy money will provide a large stimulus to private sector spending as the interest rate falls. 1 Question 13 An increase in autonomous taxes shifts the IS curve to the left. To maintain equilibrium in the commodity and money markets both equilibrium income and the interest rate fall. Consumption falls as a decline in induced consumption dominates any boost the lower interest rate gives autonomous consumption. Planned investment rises because of the lower interest rate. Problem 1 (a) To compute the equilibrium interest rate, set the equation for the IS curve equal to the equation for the LM curve to get 11,000 – 250r 8,000 250r. Adding 250r to and subtracting 8,000 from both sides yields 500r 3,000. Dividing both sides by 500 yields the equilibrium interest rate r 6. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 11,000 – 250(6) 8,000 250(6) 9,500. (b) To compute the new equilibrium interest rate, set the equation for the new IS curve equal to the equation for the LM curve to get 10,000 – 250r 8,000 250r. Adding 250r to and subtracting 8,000 from both sides yields 500r 2,000. Dividing both sides by 500 yields the equilibrium interest rate r 4. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 10,000 – 250(4) 8,000 250(4) 9,000. (c) To compute the new equilibrium interest rate, set the equation for the IS curve equal to the new equation for the LM curve to get 11,000 – 250r 7,000 250r. Adding 250r to and subtracting 7,000 from both sides yields 500r 4,000. Dividing both sides by 500 yields the equilibrium interest rate r 8. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 11,000 – 250(8) 7,000 250(8) 9,000. Problem 2 The slope of the LM curve is r/Y. The equation for the LM curve in problem 1 tells us that Y/r 250. Therefore in problem 1, the slope of the LM curve, r/Y, equals 1/250 0.004. The equation for the LM curve in this problem states that Y/r 150. Therefore in this problem, the slope of the LM curve, r/Y, equals 1/150 0.0067. The slope of the LM is larger in this problem than in problem 1, indicating that the LM curve is steeper in this problem. Since the LM curve is steeper in this problem than in problem 1, it takes a larger increase in the interest rate to restore equilibrium in the money market, given the increase in the demand for money due to a rise in income. That means that the demand for money is less sensitive to a change in the interest rate for this problem’s LM curve when compared to that of problem 1. 36 Gordon • Macroeconomics, Tenth Edition To verify that the equilibrium interest rate (r) and the equilibrium level of income are the same as in part (a) of problem 1, set the equation for the IS curve equal to the new equation for the LM curve to get 11,000 – 250r 8,600 150r. Adding 250r to and subtracting 8,600 from both sides yields 400r 2,400. Dividing both sides by 400 yields the equilibrium interest rate r 6. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 11,000 – 250(6) 8,600 150(6) 9,500. (b) To compute the new equilibrium interest rate, set the equation for the new IS curve equal to the 2 equation for the LM curve to get 10,000 – 250r 8,600 150r. Adding 250r to and subtracting 8,600 from both sides yields 400r 1,400. Dividing both sides by 400 yields the equilibrium interest rate r 3.5. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 10,000 – 250(3.5) 8,600 150(3.5) 9,125. (c) To compute the new equilibrium interest rate, set the equation for the IS curve equal to the new equation for the LM curve to get 11,000 – 250r 7,600 150r. Adding 250r to and subtracting 7,600 from both sides yields 400r 3,400. Dividing both sides by 400 yields the equilibrium interest rate r 8.5. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 11,000 – 250(8.5) 7,600 150(8.5) 8,875. (d) When compared to part (b) of problem 1, part b of this problem illustrates that the effect of fiscal policy on output weakens at the demand for money becomes less sensitive to a change in the interest rate. Part (c) of this problem, when compared to part (c) of problem 1, shows that the effect of monetary policy on output strengthens as the demand for money becomes less sensitive to a change in the interest rate. These results are exactly the text states in terms of the effectiveness of monetary and fiscal policies as the demand for money becomes less sensitive to a change in the interest rate. Problem 3 (a) The slope of the IS curve is r/Y. The equation for the IS curve in problem 1 tells us that Y/r –250. Therefore in problem 1, the slope of the IS curve, r/Y, equals –1/250 –0.004. The equation for the IS curve in this problem states that Y/r –150. Therefore in this problem, the slope of the IS curve, r/Y, equals –1/150 –0.0067. The absolute value of slope of the IS is larger in this problem than in problem 1, indicating that the IS curve is steeper in this problem. Since the IS curve is steeper in this problem than in problem 1, a decrease in the interest rate results in a smaller increase in income in the commodity market, indicating that autonomous planned spending is more responsive to a change in the interest rate in problem 1. To verify that the equilibrium interest rate (r) and the equilibrium level of income are the same as in part a of problem 1, set the equation for the new IS curve equal to the equation for the LM curve to get 10,400 – 150r 8,000 250r. Adding 150r to and subtracting 8,000 from both sides yields 400r 2,400. Dividing both sides by 400 yields the equilibrium interest rate r 6. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 10,400 – 150(6) 8,000 250(6) 9,500. (b) To compute the new equilibrium interest rate, set the equation for the new IS curve equal to the equation for the LM curve to get 9,400 – 150r 8,000 250r. Adding 150r to and subtracting 8,000 from both sides yields 400r 1,400. Dividing both sides by 400 yields the equilibrium interest rate r 3.5. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 9,400 – 150(3.5) 8,000 250(3.5) 8,875. Chapter 4 Monetary and Fiscal Policy in the IS-LM Model 37 (c) To compute the new equilibrium interest rate, set the equation for the IS curve equal to the new equation for the LM curve to get 10,400 – 150r 7,000 250r. Adding 150r to and subtracting 3 7,000 from both sides yields 400r 3,400. Dividing both sides by 400 yields the equilibrium interest rate r 8.5. To compute equilibrium real output, substitute the equilibrium interest rate into the equations for the IS and LM curves to get Y 10,000 – 150(8.5) 7,000 250(8.5) 9,125. (d) When compared to part b of problem 1, part (b) of this problem illustrates that the effect of fiscal policy on output strengthens as autonomous planned spending becomes less responsive to a change in the interest rate. Part (c) of this problem, when compared to part (c) of problem 1, shows that the effect of monetary policy on output weakens as autonomous planned spending becomes less responsive to a change in the interest rate. These results are exactly the text states in terms of the effectiveness of monetary and fiscal policies as autonomous planned spending becomes less responsive to a change in the interest rate. 4

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posted: | 9/29/2011 |

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