Income and Expenditure chapter: 26 11 ECONOMICS MACROECONOMICS 1. Due to an increase in consumer wealth, there is a $40 billion autonomous increase in consumer spending in the economies of Westlandia and Eastlandia. Assuming that the aggregate price level is constant, the interest rate is fixed in both countries, and there are no taxes and no foreign trade, complete the accompanying tables to show the various rounds of increased spending that will occur in both economies if the marginal propensity to consume is 0.5 in Westlandia and 0.75 in Eastlandia. What do your results indicate about the relationship between the size of the marginal propensity to consume and the multiplier Westlandia Incremental Rounds in GDP in GDP 1 C = $40 billion 2 MPC C = 3 MPC MPC C = 4 MPC MPC MPC C =......... (1/(1 MPC)) C in GDP Eastlandia Incremental Rounds in GDP in GDP 1 C = $40 billion 2 MPC C = 3 MPC MPC C = 4 MPC MPC MPC C =......... in GDP (1/(1 MPC)) C S-147 KrugWellsECPS3e_Macro_CH11.indd S-147
S-148 MACROECONOMICS, CHAPTER 11 ECONOMICS, CHAPTER 26 1. The accompanying tables clearly show that the larger the marginal propensity to consume, the larger the size of the multiplier. In Westlandia, with the marginal propensity to consume of 0.5, the multiplier equals 2. In Eastlandia, with the marginal propensity to consume of 0.75, the multiplier equals 4. Westlandia Incremental Rounds in GDP in GDP 1 C = $40 billion $40 billion 2 MPC C = $20 billion $60 billion 3 MPC MPC C = $10 billion $70 billion 4 MPC MPC MPC C = $5 billion $75 billion......... (1/(1 MPC)) C (1/(1 0.5)) $40 billion $80 billion in GDP Eastlandia Incremental Rounds in GDP in GDP 1 C = $40 billion $40 billion 2 MPC C = $30 billion $70 billion 3 MPC MPC C = $22.5 billion $92.5 billion 4 MPC MPC MPC C = $16.88 billion $109.38 billion......... (1/(1 MPC)) C (1/(1 0.75)) $40 billion $160 billion in GDP 2. Assuming that the aggregate price level is constant, the interest rate is fixed, and there are no taxes and no foreign trade, what will be the in GDP if the following events occur a. There is an autonomous increase in consumer spending of $25 billion; the marginal propensity to consume is 2/3. b. Firms reduce investment spending by $40 billion; the marginal propensity to consume is 0.8. c. The government increases its purchases of military equipment by $60 billion; the marginal propensity to consume is 0.6. 2. a. An autonomous increase in consumer spending of $25 billion, with a marginal propensity to consume of 2/3, will increase GDP by $75 billion: in GDP = (1/(1 MPC)) C in GDP = (1/(1 2/3)) $25 billion in GDP = 3 $25 billion in GDP = $75 billion KrugWellsECPS3e_Macro_CH11.indd S-148
INCOME AND EXPENDITURE S-149 b. If firms reduce investment spending by $40 billion and the marginal propensity to consume is 0.8, GDP will fall by $200 billion: in GDP = (1/(1 MPC)) I in GDP = (1/(1 0.8)) ( $40 billion) in GDP = 5 ( $40 billion) in GDP = $200 billion c. If government purchases of goods and services rise by $60 billion and the marginal propensity to consume is 0.6, GDP will increase by $150 billion: in GDP = (1/(1 MPC)) G in GDP = (1/(1 0.6)) $60 billion in GDP = 2.5 $60 billion in GDP = $150 billion 3. Economists observed the only five residents of a very small economy and estimated each one s consumer spending at various levels of current disposable income. The accompanying table shows each resident s consumer spending at three income levels. Individual consumer spending by Individual current disposable income a. What is each resident s consumption function What is the marginal propensity to consume for each resident b. What is the economy s aggregate consumption function What is the marginal propensity to consume for the economy $0 $20,000 $40,000 Andre 1,000 $15,000 29,000 Barbara 2,500 12,500 22,500 Casey 2,000 20,000 38,000 Declan 5,000 17,000 29,000 Elena 4,000 19,000 34,000 3. a. Each resident s consumption function and marginal propensity to consume are given in the table below. To determine autonomous consumer spending for each resident (the vertical intercept of his or her consumption function), we can look at each one s consumer spending when disposable income is zero. To calculate each resident s marginal propensity to consume (the slope of his or her consumption function), we can calculate the in consumer spending when there is a in disposable income. For example, Andre s marginal propensity to consume is equal to ($29,000 $15,000)/($40,000 $20,000) = 0.70. Autonomous Marginal propensity to Consumption consumption (a) consume (MPC) function (c) Andre $1,000 0.70 $1,000 + 0.70 yd Barbara 2,500 0.50 2,500 + 0.50 yd Casey 2,000 0.90 2,000 + 0.90 yd Declan 5,000 0.60 5,000 + 0.60 yd Elena 4,000 0.75 4,000 + 0.75 yd KrugWellsECPS3e_Macro_CH11.indd S-149
S-150 MACROECONOMICS, CHAPTER 11 ECONOMICS, CHAPTER 26 b. To find the economy s consumption function, we calculate aggregate consumer spending at each level of aggregate disposable income: When each resident earns $0 in disposable income, aggregate consumer spending is $14,500. When each resident earns $20,000 in disposable income, aggregate disposable income is $100,000 and aggregate consumer spending is $83,500. When each resident earns $40,000 in disposable income, aggregate disposable income is $200,000 and aggregate consumer spending is $152,500. Aggregate autonomous consumer spending is $14,500, and the marginal propensity to consume is 0.69 [= ($83,500 $14,500)/($100,000 $0)]. The aggregate consumption function is: C = $14,500 + 0.69 YD 4. From 2003 to 2008, Eastlandia experienced large fluctuations in both aggregate consumer spending and disposable income, but wealth, the interest rate, and expected future disposable income did not. The accompanying table shows the level of aggregate consumer spending and disposable income in millions of dollars for each of these years. Use this information to answer the following questions. Disposable income Consumer spending Year (millions of dollars) (millions of dollars) 2003 $100 $180 2004 350 380 2005 300 340 2006 400 420 2007 375 400 2008 500 500 a. Plot the aggregate consumption function for Eastlandia. b. What is the marginal propensity to consume What is the marginal propensity to save c. What is the aggregate consumption function 4. a. The accompanying diagram shows the aggregate consumption function for Eastlandia. Consumer spending (millions of dollars) $600 500 CF 400 300 200 100 0 $100 200 300 400 500 600 Disposable income (millions of dollars) KrugWellsECPS3e_Macro_CH11.indd S-150
INCOME AND EXPENDITURE S-151 b. The marginal propensity to consume is 0.8, and the marginal propensity to save is 0.2. c. The aggregate consumption function is of the form C = A + MPC YD. We know MPC = 0.8, so we must now solve for A. Rearranging, we have A = C MPC YD. Plugging in the data from the first row of the table, we have A = $180 million 0.8 $100 million = $100 million. Hence, the aggregate consumption function is C = $100 million + 0.8 YD. 5. The Bureau of Economic Analysis reported that, in real terms, overall consumer spending increased by $35.4 billion during October 2010. a. If the marginal propensity to consume is 0.52, by how much will real GDP in response b. If there are no other s to autonomous spending other than the increase in consumer spending in part a, and unplanned inventory investment, I Unplanned, decreased by $50 billion, what is the in real GDP c. GDP at the end of September 2010 was $13,139.5 billion. If GDP were to increase by the amount calculated in part b, what would be the percent increase in GDP 5. a. Real GDP increases as a result of this in consumer spending by (1/(1 MPC)) $35.4 billion = (1/(1 0.52)) $35.4 billion = $73.75 billion. b. If, in addition to the consumer spending in part a, unplanned inventory investment decreases by $50 billion, the resulting in real GDP is $23.75 billion. c. The percent increase in GDP is ($23.75 billion/$13,139.5 billion) 100 = 0.18% approximately the actual percent increase in real GDP over that period. 6. During the early 2000s, the Case Shiller U.S. Home Price Index, a measure of average home prices, rose continuously until it peaked in March 2006. From March 2006 to May 2009, the index lost 32% of its value. Meanwhile, the stock market experienced similar ups and downs. From March 2003 to October 2007, the Standard and Poor s 500 (S&P 500) stock index, a broad measure of stock market prices, almost doubled, from 800.73 to a high of 1,565.15. From that time until March 2009, the index fell by almost 60%, to a low of 676.53. How do you think the movements in home prices both influenced the growth in real GDP during the first half of the decade and added to the concern about maintaining consumer spending after the collapse in the housing market that began in 2006 To what extent did the movements in the stock market hurt or help consumer spending 6. As home prices increased, homeowners experienced a large increase in the value of their wealth held in real estate. At the same time, as the S&P 500 almost doubled from March 2003 to October 2007, stockholders experienced a large increase in the value of their wealth held in stocks. Both of these increased consumer spending in the economy dramatically. However, as home prices plummeted from their peak in early 2006, consumer spending should have fallen, other things equal, as homeowners wealth decreased. And, as the S&P 500 fell almost 60% from its peak in October 2007 to its low in March 2009, there was great concern that the decline in the stock market was exacerbating the decrease in consumers wealth that had occurred because of the collapse in the housing market. 7. How will planned investment spending as the following events occur a. The interest rate falls as a result of Federal Reserve policy. b. The U.S. Environmental Protection Agency decrees that corporations must upgrade or replace their machinery in order to reduce their emissions of sulfur dioxide. c. Baby boomers begin to retire in large numbers and reduce their savings, resulting in higher interest rates. KrugWellsECPS3e_Macro_CH11.indd S-151
S-152 MACROECONOMICS, CHAPTER 11 ECONOMICS, CHAPTER 26 7. a. The lower interest rate will lead to a rise in planned investment spending. b. Firms will need to replace older machinery with newer, less polluting machinery. This will increase planned investment spending. c. As the interest rate rises, planned investment spending will fall. 8. Explain how each of the following actions will affect the level of planned investment spending and unplanned inventory investment. Assume the economy is initially in income expenditure equilibrium. a. The Federal Reserve raises the interest rate. b. There is a rise in the expected growth rate of real GDP. c. A sizable inflow of foreign funds into the country lowers the interest rate. 8. a. A rise in the interest rate will reduce planned investment spending. Planned aggregate spending will now be less than GDP, and inventories will accumulate. So unplanned inventory investment will be positive. b. A rise in the expected growth rate of real GDP will lead firms to increase their planned investment spending. Planned aggregate spending will now exceed GDP. Sales will exceed firms expectations, firms will draw down inventories unexpectedly, and unplanned inventory investment will be negative. c. A fall in the interest rate will lead to an increase in planned investment spending. Planned aggregate spending will now exceed GDP. Sales will exceed firms expectations, firms will draw down inventories unexpectedly, and unplanned inventory investment will be negative. 9. a. The accompanying table shows gross domestic product (GDP), disposable income (YD), consumer spending (C), and planned investment spending (I Planned ) in an economy. Assume there is no government or foreign sector in this economy. Complete the table by calculating planned aggregate spending ( ) and unplanned inventory investment (I Unplanned ). GDP YD C I Planned I Unplanned (billions of dollars) $0 $0 $100 $300 400 400 400 300 800 800 700 300 1,200 1,200 1,000 300 1,600 1,600 1,300 300 2,000 2,000 1,600 300 2,400 2,400 1,900 300 2,800 2,800 2,200 300 3,200 3,200 2,500 300 b. What is the aggregate consumption function c. What is Y*, income expenditure equilibrium GDP d. What is the value of the multiplier e. If planned investment spending falls to $200 billion, what will be the new Y* f. If autonomous consumer spending rises to $200 billion, what will be the new Y* KrugWellsECPS3e_Macro_CH11.indd S-152
INCOME AND EXPENDITURE S-153 9. a. GDP YD C I Planned I Unplanned (billions of dollars) $0 $0 $100 $300 $400 $400 400 400 400 300 700 300 800 800 700 300 1,000 200 1,200 1,200 1,000 300 1,300 100 1,600 1,600 1,300 300 1,600 0 2,000 2,000 1,600 300 1,900 100 2,400 2,400 1,900 300 2,200 200 2,800 2,800 2,200 300 2,500 300 3,200 3,200 2,500 300 2,800 400 b. We can find the aggregate consumption function by calculating aggregate auton omous consumer spending and the marginal propensity to consume. Aggregate autonomous consumer spending equals aggregate consumer spending when disposable income is zero; in this case, aggregate autonomous consumer spending is $100 billion. The marginal propensity to consume is the in aggregate consumer spending divided by the in disposable income; in this case, it is 0.75 [= ($400 $100)/($400 $0)]. The aggregate consumption function is: C = $100 billion + 0.75 YD c. Y* is the level of GDP at which planned aggregate spending equals GDP. From the accompanying table, Y* is $1,600 billion. d. The multiplier equals 1/(1 MPC); the value of the multiplier is 4 = 1/(1 0.75). e. If planned investment spending falls to $200 billion, the new Y* will equal $1,200 billion. If planned investment spending equals $200 billion, it has fallen by $100 billion. Since the multiplier is 4, Y* will by four times the in planned investment spending, or decrease by $400 billion. f. If autonomous consumer spending rises to $200 billion, the new Y* will equal $2,000 billion. If autonomous consumer spending equals $200 billion, it has risen by $100 billion. Since the multiplier is 4, Y* will by four times the in autonomous consumer spending, or increase by $400 billion. 10. In an economy with no government and no foreign sectors, autonomous consumer spending is $250 billion, planned investment spending is $350 billion, and the marginal propensity to consume is 2/3. a. Plot the aggregate consumption function and planned aggregate spending. b. What is unplanned inventory investment when real GDP equals $600 billion c. What is Y*, income expenditure equilibrium GDP d. What is the value of the multiplier e. If planned investment spending rises to $450 billion, what will be the new Y* KrugWellsECPS3e_Macro_CH11.indd S-153
S-154 MACROECONOMICS, CHAPTER 11 ECONOMICS, CHAPTER 26 10. a. If autonomous consumer spending is $250 billion and the marginal propensity to consume is 2 3, the aggregate consumption function is: C = $250 billion + 2 3 YD Planned aggregate spending equals consumer spending plus planned investment spending: = C + I Planned = ($250 billion + 2 3 YD) + $350 billion = $600 billion + 2 3 YD, consumer spending (billions of dollars) $3,000 2,700 2,400 2,100 1,800 45-degree line E CF 1,500 1,200 900 600 300 250 0 $300 600 900 1,200 1,500 1,800 2,100 2,400 2,700 3,000 Real GDP (billions of dollars) b. When real GDP equals $600 billion, planned aggregate spending is $1,000 billion [= $600 billion + 2 3 $600 billion]. Unplanned inventory investment equals real GDP minus planned aggregate spending, or $400 billion. c. Y* occurs where real GDP equals planned aggregate spending. From the accompanying diagram, we can see that this occurs at real GDP equal to $1,800 billion. d. The value of the multiplier is 3 [= 1/(1 2 3)]. e. If planned investment spending rises to $450 billion, that will be an increase of $100 billion in planned investment spending. Given a multiplier of 3, Y* will rise by $300 billion to $2,100 billion. KrugWellsECPS3e_Macro_CH11.indd S-154
INCOME AND EXPENDITURE S-155 11. An economy has a marginal propensity to consume of 0.5, and Y*, income expenditure equilibrium GDP, equals $500 billion. Given an autonomous increase in planned investment of $10 billion, show the rounds of increased spending that take place by completing the accompanying table. The first and second rows are filled in for you. In the first row, the increase of planned investment spending of $10 billion raises real GDP and YD by $10 billion, leading to an increase in consumer spending of $5 billion (MPC in disposable income) in row 2, raising real GDP and YD by a further $5 billion. Rounds a. What is the total in real GDP after the 10 rounds What is the value of the multiplier What would you expect the total in Y* to be based on the multiplier formula How do your answers to the first and third questions compare b. Redo the table starting from round 2, assuming the marginal propensity to consume is 0.75. What is the total in real GDP after 10 rounds What is the value of the multiplier As the marginal propensity to consume increases, what happens to the value of the multiplier Change in I Planned Change in Change in or C real GDP YD (billions of dollars) 1 ΔI Planned = $10.00 $10.00 $10.00 2 ΔC = $ 5.00 $ 5.00 $ 5.00 3 ΔC = 4 ΔC = 5 ΔC = 6 ΔC = 7 ΔC = 8 ΔC = 9 ΔC = 10 ΔC = 11. a. The total in GDP after the 10 rounds is $19.98 billion, obtained by adding up the in GDP for each of the first 10 rounds. The multiplier is 2 [= (1/(1 0.5))]. We would expect the total in Y* to be twice the in planned investment spending. Since the autonomous in planned investment spending was $10 billion, we would expect a in Y* of $20 billion. This is very similar to the in GDP after 10 rounds ($19.98 billion). Change in I Planned or C Change in real GDP Change in YD Rounds (billions of dollars) 1 I Planned = $10.00 $10.00 $10.00 2 C = 5.00 5.00 5.00 3 C = 2.50 2.50 2.50 4 C = 1.25 1.25 1.25 5 C = 0.63 0.63 0.63 6 C = 0.31 0.31 0.31 7 C = 0.16 0.16 0.16 8 C = 0.08 0.08 0.08 9 C = 0.04 0.04 0.04 10 C = 0.02 0.02 0.02 KrugWellsECPS3e_Macro_CH11.indd S-155
S-156 MACROECONOMICS, CHAPTER 11 ECONOMICS, CHAPTER 26 b. The total in GDP after 10 rounds is $37.74 billion, obtained by adding up the in GDP for each of the first 10 rounds. The value of the multiplier is 4. As the marginal propensity to consume increases, so does the value of the multiplier. Change in I Planned or C Change in real GDP Change in YD Rounds (billions of dollars) 1 I Planned = $10.00 $10.00 $10.00 2 C = 7.50 7.50 7.50 3 C = 5.63 5.63 5.63 4 C = 4.22 4.22 4.22 5 C = 3.16 3.16 3.16 6 C = 2.37 2.37 2.37 7 C = 1.78 1.78 1.78 8 C = 1.33 1.33 1.33 9 C = 1.00 1.00 1.00 10 C = 0.75 0.75 0.75 12. Although the United States is one of the richest nations in the world, it is also the world s largest debtor nation. We often hear that the problem is the nation s low savings rate. Suppose policy makers attempt to rectify this by encouraging greater savings in the economy. What effect will their successful attempts have on real GDP 12. If policy makers successfully encouraged greater savings, there would be a decrease in either consumer spending or planned investment spending. A drop in C or in I Planned would decrease the income expenditure equilibrium GDP by several times the in spending. This is the paradox of thrift. If households and producers decrease spending to reduce the nation s debt, these actions will depress the economy, leaving households and producers worse off than they were with the nation s large debt. 13. The U.S. economy slowed significantly in early 2008, and policy makers were extremely concerned about growth. To boost the economy, Congress passed several relief packages (the Economic Stimulus Act of 2008 and the American Recovery and Reinvestment Act of 2009) that combined would deliver about $700 billion in government spending. Assume, for the sake of argument, that this spending was in the form of payments made directly to consumers. The objective was to boost the economy by increasing the disposable income of American consumers. a. Calculate the initial in aggregate consumer spending as a consequence of this policy measure if the marginal propensity to consume (MPC) in the United States is 0.5. Then calculate the resulting in real GDP arising from the $700 billion in payments. b. Illustrate the effect on real GDP with the use of a graph depicting the income expenditure equilibrium. Label the vertical axis Planned aggregate spending, and the horizontal axis Real GDP. Draw two planned aggregate expenditure curves (1 and 2 ) and a 45-degree line to show the effect of the autonomous policy on the equilibrium. KrugWellsECPS3e_Macro_CH11.indd S-156
INCOME AND EXPENDITURE S-157 13. a. Government spending increases the disposable income of American consumers. The MPC can be used to calculate the effect of government spending on consumer spending: ΔC = MPC ΔYD = 0.5 $700 billion = $350 billion. We can then use the in consumer spending along with the multiplier to calculate the resulting in real GDP. ΔY = (1/(1 MPC)) ΔC = (1/(1 0.5)) $350 billion = $700 billion. b. As shown in the accompanying diagram, the payments result in an autonomous increase in planned aggregate spending. This results in an increase in real GDP. Planned aggregate spending, E 1 E 2 2 1 Autonomous Y 1 Y 2 Real GDP KrugWellsECPS3e_Macro_CH11.indd S-157
KrugWellsECPS3e_Macro_CH11.indd S-158
Appendix: Deriving the Multiplier Algebraically 1. In an economy without government purchases, transfers, or taxes, and without imports or exports, aggregate autonomous consumer spending is $500 billion, planned investment spending is $250 billion, and the marginal propensity to consume is 0.5. a. Write the expression for planned aggregate spending as in Equation 26A-1. b. Solve for Y* algebraically. c. What is the value of the multiplier d. How will Y* if autonomous consumer spending falls to $450 billion 1. a. In an economy without government purchases, planned aggregate spending equals the aggregate consumption function plus planned investment spending: = C + I Planned = $500 billion + 0.5 YD + $250 billion b. In an economy without taxes or government transfers, GDP equals disposable income. The economy will be in income expenditure equilibrium when GDP equals planned aggregate spending: Y* = $750 billion + 0.5 Y* 0.5 Y* = $750 billion Y* = $1,500 billion c. The value of the multiplier is 2 [= 1/(1 0.5)]. d. If autonomous consumer spending falls to $450 billion, it will have decreased by $50 billion. Given a multiplier of 2, Y* will fall by $100 billion when autonomous consumer spending falls by $50 billion. The new Y* equals $1,400 billion. 2. Complete the following table by calculating the value of the multiplier and identifying the in Y* due to the in autonomous spending. How does the value of the multiplier with the marginal propensity to consume chapter: 26A 11A ECONOMICS MACROECONOMICS MPC Value of multiplier Change in spending Change in Y* 0.5 0.6 0.75 0.8 0.9 C = + $50 million I = $10 million C = $25 million I = + $20 million C = $2.5 million S-159 KrugWellsECPS3e_Macro_CH11A.indd S-159
S-160 MACROECONOMICS, CHAPTER 11 APPENDIX ECONOMICS, CHAPTER 26 APPENDIX 2. The value of the multiplier increases with an increase in the marginal propensity to consume. MPC Value of multiplier Change in spending Change in Y* 0.5 2 (= 1/(1 0.5)) C = + $50 million 0.6 2.5 (= 1/(1 0.6)) I = $10 million 0.75 4 (= 1/(1 0.75)) C = $25 million 0.8 5 (= 1/(1 0.8)) I = + $20 million 0.9 10 (= 1/(1 0.9)) C = $2.5 million + $100 million $25 million $100 million + $100 million $25 million KrugWellsECPS3e_Macro_CH11A.indd S-160