Chapter 3
2. a. The marginal propensity to save, s, equals 1 − c = 1 −. 6 =.4
b. Autonomous planned spending, Ap, equals Ca − cTa + Ip + G + NX = 1,500 − 10r −. 6 (1800) +2400 minus 50r + _2000_− 200 = − 60r. Therefore, at an interest rate equal to 3, autonomous planned spending equals 4620 − 60(3) = 4400.
c. Since the marginal propensity to save equals. _.4________ and the equilibrium level of income equals Ap/s, the equilibrium level of income equals 4400 /. 4 = 11,100 given the interest rate equals 5.
d. Since autonomous consumption changes by four percent of any change in household wealth and the decline in the housing market from 2006–09 and drop in the stock market from 2007-09 reduces household wealth by $3 trillion, the decrease in autonomous consumption that results from the decline in household wealth equals .04(_3T___) = 120 billion.
e. Since the decrease in autonomous consumption that results from the decline in household wealth equals 120 billion, autonomous planned spending decreases by that amount as well. Therefore, the new amount of autonomous planned spending equals 4400− 120 = 4320. Therefore, the new equilibrium level of income equals 4320/. 4 =10,800 , given the interest rate equals 3. f. The multiplier, k, equals ΔY/ΔAp = (10,800 −11,100)/(4,320 −4400) = (−300)/(−120) =2.5. g. Since the multiplier equals 2.5 and income must increase by 300 billion to restore income to its initial equilibrium level of 11,100, fiscal or monetary policymakers must take actions that increase autonomous planned spending by 120 billion in order to restore equilibrium income to 11,100. i. If fiscal policymakers increase government spending, G, and there are no changes in either taxes or the interest rate, then ΔAp = _120 = ΔG. Therefore, fiscal policymakers must increase government spending by 120 billion to restore equilibrium income to 11,100, given no changes in taxes or the interest rate. ii. If fiscal policymakers decrease taxes, Ta, and there are no changes in either government spending or the interest rate, then ΔAp = = −cΔTa = −.6ΔTa. Therefore, /(−.6) = − = ΔTa. Therefore, fiscal policymakers must cut taxes by 200_billion to restore equilibrium income to 11,100, given no changes in government spending or the interest rate. iii. If fiscal policymakers increase government spending and taxes, then given no change in the interest rate, ΔAp = ΔG − .6ΔTa = 120 .Furthermore, since fiscal policymakers at the same time don’t change the government budget balance, then ΔG = ΔTa, so that ΔAp = ΔG− .6ΔG = 120 or .4ΔG = 120 or ΔG = 300 . Therefore, fiscal policymakers increase both government spending and taxes by 300 billion to restore equilibrium income to 11,100, given no changes in the government budget balance or the interest rate. iv. The parameter on the interest rate in the equation for autonomous planned spending indicates that autonomous planned spending increases by 60 billion for every one-percentage point drop in the interest rate. Therefore, since autonomous planned spending must increase by 120 billion to restore equilibrium income to 11,100, monetary policymakers must reduce the interest rate by 2 percentage points to restore equilibrium income to 11,100, given no changes in government spending or taxes.
Chapter 4
1. a. The real demand for money at each combination of the interest rate and income is given in the following table: Income
Interest rate 11,940 12,000 12,060 12,120 12,180
4.4 2,765 2,780 2,795 2,810 2,825
4.7 2,750 2,765 2,780 2,795 2,810
5.0 2,735 2,750 2,765 2,780 2,795
5.3 2,720 2,735 2.750 2,765 2,780
5.6 2,705 2,720 2.735 2,750 2,765
5.9 2,690 2,705 2.720 2,735 2,750
6.2 2,675 2,690 2,705 2,720 2,735 b. The horizontal axis of your graph should be labeled real money balances, and the vertical axis of your graph should be labeled interest rate. The points on demand for money curve when income equals 11,940 are: (2,675, 4.4); (2,750, 4.7); (2,735, 5.0); (2,720, 5.3); (2,705, 5.6); (2,690, 5.9); and (2675, 6.2). The points on demand for money curve when income equals 12,180 are: (2,825, 4.4);
(2,825, 4.4); (2,810, 4.7); (2,795, 5.0); (2,780, 5.3); (2,765, 5.6); (2,750, 5.9); and (2735, 6.2). c. The table in Part a shows that given that the real money supply equals 2,750, the real demand for money and the real supply of money are equal at the following combinations of real income and the interest rate: (11,940, 4.7); (12,000, 5.0); (12,060, 5.3); (12,120, 5.6); and (12,180, 5.9). The horizontal axis of your graph for the LM curve should be labeled real income, and the vertical axis of your graph should be labeled interest rate. The five points on LM0 are listed in the first sentence of this part of the problem. d. The table in Part a shows that given that the real money supply equals 2,780, the real demand for money and the real supply of money are equal at the following combinations of real income and the interest rate: (12,000, 4.4); (12,060, 4.7); (12,120, 5.0); and (12,180_, 5.3). The four points on LM1 are just listed in the previous sentence of this part of the problem. e. The table in Part a shows that given that the real money supply equals 2,720, the real demand for money and the real supply of money are equal at the following combinations of real income and the interest rate: (11,940, 5.3); (12,000, 5.6); (12,060, 5.9); and (12,120, 6.2). The four points on LM2 are just listed in the previous sentence of this part of the problem.