Transcript
178Miller• Economics Today, Nineteenth Edition
Chapter 12Consumption, Real GDP, and the Multiplier179
Answers to Questions for Critical Analysis
What the Media Actually Report about When Describing Variations in the “Saving Rate” (p. 260)
When the average propensity to save declines as real disposable income increases, what must happen to the average propensity to consume? Explain your reasoning.
When the average propensity to save (APS) declines as real disposable income increases, the average propensity to consume (APC) must rise because APC = 1 ? APS.
Diminished Rightward Shifts in Germany’s Investment Function (p. 264)
In principle, what might be possible causes of the observed diminishment of the rightward shifts of Germany’s investment function over time? (Hint: Recall that changes in productive technology of business taxes affect levels of planned investment spending)
The observed diminishment of the rightward shifts of Germany’s investment function over time might have been the outcome of a decrease in productive technology or an increase in business taxes that would reduce planned investment spending.
Habit Formation in Consumption Spending and the Multiplier Effect (p. 270)
In light of the above discussion, how is a greater degree of habit persistence in consumption likely to affect the marginal propensity to save? Explain your reasoning.
Because the marginal propensity to save is one minus the marginal propensity to consume, a greater degree of habit persistence in consumption that reduces the marginal propensity to consume will result in an increase of the marginal propensity to save.
You Are There
Inferring Low Real GDP Growth from “Restrained” Consumption Spending (p. 273)
1. According to Keynesian theory, what should have determined the actual amount of the response of real consumption expenditures to the small increase in real GDP?
According to Keynesian theory, real consumption expenditures are directly related to real GDP through the marginal propensity to consume.
2. What does the theory of consumption spending predict should have happened to real saving during the particular three-month period that Price was considering? Explain briefly.
According the theory of consumption spending, real consumption and saving decision depends primarily on a household’s current real disposable income. Slow real GDP growth would therefore result in slow growth in real consumption and real saving.
Issues and Applications
An Investment Spending Slowdown Holds Down U.S. Real GDP (pp. 274–275)
1. How could toughened federal regulations of businesses during the current decade have inhibited a rightward shift in the investment function?
Toughened federal regulations of businesses reduce businesses’ profit expectations, thus inhibiting a rightward shift in the investment function.
2. How might recent increases in state and federal tax rates on incomes that businesses derive from capital investment have contributed to the investment function’s failure to rebound?
Recent increases in state and federal tax rates on income that businesses derive from capital investment have induced businesses’ to reduce their planned investment expenditures. As a result, the investment function has failed to shift back to levels prior to the recession.
Research Project
1. To view results from the U.S. Census Bureau’s most recent survey regarding business capital investment, see the Web Links in MyEconLab.
2. For data on the levels of U.S. flows of real investment expenditures, see the Web Links in MyEconLab.
Appendix C—The Keynesian Model and Multiplier
The multiplier effect of can be observed in the Keynesian model as successive rounds of additional spending induced by an autonomous increase in planned expenditures. (See Figure C-1.)
Answers to Problems
12-1. Classify each of the following as either a stock or a flow.
a. Myung Park earns $850 per week.
b. Time Warner purchases $100 million in new telecommunications equipment this month.
c. Sally Schmidt has $1,000 in a savings account at a credit union.
d. XYZ, Inc., produces 200 units of output per week.
e. Giorgio Giannelli owns three private jets.
f. Apple’s production declines by 750 digital devices per month.
g. Russia owes $25 billion to the International Monetary Fund.
a. Flow
b. Flow
c. Stock
d. Flow
e. Stock
f. Flow
g. Stock
12-2. Consider the table below when answering the following questions. For this hypothetical economy, the marginal propensity to save is constant at all levels of real GDP, and investment spending is autonomous. There is no government.
Real GDP Consumption Saving Investment
$ 2,000 $2,200 $______ $400
4,000 4,000 ______ ______
6,000 ______ ______ ______
8,000 ______ ______ ______
10,000 ______ ______ ______
12,000 ______ ______ ______
a. Complete the table. What is the marginal propensity to save? What is the marginal propensity to consume?
b. Draw a graph of the consumption function. Then add the investment function to obtain C + I.
c. Under the graph of C + I, draw another graph showing the saving and investment curves. Note that the C + I curve crosses the 45-degree reference line in the upper graph at the same level of real GDP where the saving and investment curves cross in the lower graph. (If not, redraw your graphs.) What is this level of real GDP?
d. What is the numerical value of the multiplier?
e. What is equilibrium real GDP without investment? What is the multiplier effect from the inclusion of investment?
f. What is the average propensity to consume at equilibrium real GDP?
g. If autonomous investment declines from $400 to $200, what happens to equilibrium
real GDP?
a. The completed table follows (all amounts in dollars):
Real GDP Consumption Saving Investment
2,000 2,200 –200 400
4,000 4,000 0 400
6,000 5,800 200 400
8,000 7,600 400 400
10,000 9,400 600 400
12,000 11,200 800 400
MPS = 200/2,000 = 0.1; MPC = 1,800/2,000 = 0.9.
b. The graph appears below.
c. Yes. The graph appears below. Equilibrium real GDP on both graphs equals $8,000.
d. The multiplier is 1/(1-MPC) = 1/(1 ? 0.9) = 1/0.1 = 10.
e. Without investment, equilibrium real GDP is $4,000. With investment, it is $8,000. The multiplier effect of including the $400 in investment is equal to $400 times 10, or $4,000.
f. At the equilibrium income level of $8,000, the average propensity to consume is $7,600 / $8,000 = 0.95.
g. If autonomous investment declines from $400 to $200, then equilibrium real GDP falls by $200 times 10, or $2,000. The new level of equilibrium real GDP, therefore, is $6,000.
12-3. Consider the table below when answering the following questions. For this economy, the marginal propensity to consume is constant at all levels of real GDP, and investment spending is autonomous. Equilibrium real GDP is equal to $8,000. There is no government.
Real GDP Consumption Saving Investment
$ 2,000 $ 2,000 ______ ______
4,000 3,600 ______ ______
6,000 5,200 ______ ______
8,000 6,800 ______ ______
10,000 8,400 ______ ______
12,000 10,000 ______ ______
a. Complete the table. What is the marginal propensity to consume? What is the marginal propensity to save?
b. Draw a graph of the consumption function. Then add the investment function to
obtain C + I.
c. Under the graph of C + I, draw another graph showing the saving and investment curves. Does the C + I curve cross the 45-degree reference line in the upper graph at the same level of real GDP where the saving and investment curves cross in the lower graph, at the equilibrium real GDP of $8,000? (If not, redraw your graphs.)
d. What is the average propensity to save at equilibrium real GDP?
e. If autonomous consumption were to rise by $100, what would happen to equilibrium
real GDP?
a. The completed table follows (all amounts in dollars):
Real GDP Consumption Saving Investment
2,000 2,000 0 1,200
4,000 3,600 400 1,200
6,000 5,200 800 1,200
8,000 6,800 1,200 1,200
10,000 8,400 1,600 1,200
12,000 10,000 2,000 1,200
Between each row, the change in consumption spending is $1,600 (for instance, between the last two rows, it is $10,000 ?$8,400 = $1,600), and the change in real GDP is $2,000 (for instance, between the last two rows, it is $12,000 ?$10,000 = $2,000), so MPC = 1,600/2000 = 0.8. Between each row, the change in saving is $400 (for instance, between the last two rows, it is $$2,000 ?$1,600 = $400), and the change in income is $2,000, so MPS = 400/2,000 = 0.2.
b. The graph appears below.
c. The graph appears below. Equilibrium real GDP on both graphs equals $8,000.
d. APS = $1,200/$8,000 = 0.15.
e. The multiplier is 1/(1 ? MPC) = 1/(1 ? 0.8) = 1/0.2 = 5. Thus, if autonomous consumption were to rise by $100, then equilibrium real GDP would increase by $100 times 5, or $500.
12-4. Calculate the multiplier for the following cases.
a. MPS = 0.25
b. MPC = 5/6
c. MPS = 0.125
d. MPC= 6/7
a. 1/MPS = 1/0.25 = 1/(1/4) = 4.
b. 1/(1 ? MPC) = 1/(1? 5/6) = 1/(1/6) = 6.
c. 1/MPS = 1/0.125 = 1/(1/8) = 8.
d. 1/(1 ? MPC) = 1/(1? 6/7) = 1/(1/7) = 7.
12-5. Given each of the following values for the multiplier, calculate both the MPC and the MPS.
a. 20
b. 10
c. 8
d. 5
a. The multiplier is 1/MPS = 20, so MPS = 1/20 = 0.05. We know that MPS = 1 ? MPC = 0.05, which implies that MPC = 0.95.
b. The multiplier is 1/MPS = 10, so MPS = 1/10 = 0.10. We know that MPS = 1 ? MPC = 0.10, which implies that MPC = 0.90.
c. The multiplier is 1/MPS = 8, so MPS = 1/8 = 0.125. We know that MPS = 1 ? MPC = 0.125, which implies that MPC = 0.875.
d. The multiplier is 1/MPS = 5, so MPS = 1/5 = 0.20. We know that MPS = 1 ? MPC = 0.20, which implies that MPC = 0.80.
12-6. The marginal propensity to consume is equal to 0.80. An increase in household wealth causes autonomous consumption to rise by $10 billion. By how much will equilibrium real GDP increase at the current price level, other things being equal?
$50 billion
12-7. Assume that the multiplier in a country is equal to 4 and that autonomous real consumption spending is $1 trillion. If current real GDP is $18 trillion, what is the current value of real consumption spending?
The multiplier is 1/(1 ? MPC) = 4, so 1 – MPC = 0.25, which implies that MPC = 0.75. Thus, when real GDP equals $18 trillion, consumption is $1 trillion + (0.75 x $18 trillion) = $1 trillion
+ $13.5 trillion = $14.5 trillion.
12-8. The multiplier in a country is equal to 5, and households pay no taxes. At the current equilibrium real GDP of $14 trillion, total real consumption spending by households is $12 trillion. What is real autonomous consumption in this country?
The multiplier is 1/(1-MPC) = 5, so 1 – MPC = 0.2, which implies that MPC = 0.8. Consumption of $12 trillion is equal to autonomous consumption + (0.8 x $14 trillion), or autonomous consumption plus $11.2 trillion. Thus autonomous consumption is $12 trillion – $11.2 trillion = 0.8 trillion.
12-9. At an initial point on the aggregate demand curve, the price level is 125, and real GDP is
$18 trillion. When the price level falls to a value of 120, total autonomous expenditures increase by $250 billion. The marginal propensity to consume is 0.75. What is the level
of real GDP at the new point on the aggregate demand curve?
The multiplier is 1/(1 ? MPC) = 1/(1 ? 0.75) = 4, so the increase in equilibrium real GDP is $250 billion x 4 = $1 trillion, and the level of real GDP at the new point on the aggregate demand curve is $19 trillion.
12-10. At an initial point on the aggregate demand curve, the price level is 100, and real GDP is $18 trillion. After the price level rises to 110, however, there is an upward movement along the aggregate demand curve, and real GDP declines to $14 trillion. If total planned spending declined by $200 billion in response to the increase in the price level, what is the marginal propensity to consume in this economy?
The multiplier is 1/(1 - MPC) = $1 trillion/$200 billion = 5. Hence, the MPC is equal to 0.80.
12-11. In an economy in which the multiplier has a value of 3, the price level has decreased from 115 to 110. As a consequence, there has been a movement along the aggregate demand curve from $18 trillion in real GDP to $18.9 trillion in real GDP.
a. What is the marginal propensity to save?
b. What was the amount of the change in planned expenditures generated by the decline in the price level?
a. The MPS is equal to 1/3.
b. $0.1 trillion
12-12. Consider the diagram below, which applies to a nation with no government spending, taxes, and net exports. Use the information in the diagram to answer the following questions, and explain your answers.
a. What is the marginal propensity to save?
b. What is the present level of planned investment spending for the present period?
c. What is the equilibrium level of real GDP for the present period?
d. What is the equilibrium level of saving for the present period?
e. If planned investment spending for the present period increases by $25 billion, what will be the resulting change in equilibrium real GDP? What will be the new equilibrium level of real GDP if other things, including the price level, remain unchanged?
a. The MPC is equal to the slope of the consumption function. (See Appendix A for discussion of the slope of a line.) This slope is the “rise,” $3.5 trillion – $0.5 trillion = $3.0 trillion, divided by the corresponding “run,” $4.0 trillion. This is ¾, or 0.75. The MPS equals 1-MPC = 1 – ¾ = ¼, or 0.25.
b. Planned real investment (I) is the difference between total planned real expenditures (C + I) and planned consumption (C) at each level of real GDP per year, or $0.5 trillion.
c. Equilibrium real GDP per year is $4.0 trillion, which is at the point at which the C + I curve crosses the 45-degree reference line.
d. Because there are no taxes, equilibrium real saving equals equilibrium real GDP ($4.0 trillion) minus equilibrium planned consumption spending ($3.5 trillion) or $0.5 trillion. Hence real planned investment equals real saving at the equilibrium level of real GDP.
e. The multiplier equals 1/MPS, or 1/(¼) = 4. Hence, a $25 billion increase in planned investment will generate an increase in equilibrium real GDP of $100 billion, or $0.1 trillion. Equilibrium real GDP will increase from $4.0 trillion to $4.1 trillion.
12-13. Consider movements from points F to K in both panels of Figure 12-1. Use the resulting changes in planned real consumption and saving corresponding to the change in real disposable income to calculate the marginal propensity to consume and to save.
The change in real disposable income between points F and K is $120,000 ?$60,000 = $60,000.
In Figure 12-1, the value of real disposable income at point K is half the distance between $120,000 and $96,000, or $12,000 less than $120,000, which is $108,000. Hence, the change in consumption between point F and point K in the upper diagram is $108,000 ?$60,000 = $48,000, so the marginal propensity to consume is $48,000/$60,000 = 4/5 = 0.8. The change in saving in the lower diagram is $12,000 ?$0 = $12,000, so the marginal propensity to save is $12,000/$60,000
= 1/5 = 0.2.
12-14. Take a look at Figure 12-5. If current real GDP for this nation’s economy is $13 trillion per year, what are the values of planned real investment and actual real investment? What is the amount of the unplanned inventory change, and why does this fact imply that real GDP must change? To what new level will real GDP adjust?
At a real GDP level of $13 trillion, planned investment is $2.8 trillion. Actual investment, however, equals planned and actual saving of $2.4 trillion. Thus, there is an unplanned reduction in business inventories equal to $2.4 trillion ?$2.8 trillion = ?$0.4 trillion. Businesses will respond by increasing production, so real GDP rises to $15 trillion, at which planned investment equals planned saving.
12-15. Consider Table 12-2. What is the average propensity to consume at the equilibrium level of real GDP? What is the average propensity to save?
At the equilibrium real GDP of $18 trillion, real disposable income is $14.8 trillion, and planned real consumption is $12.4 trillion. Thus, APC = planned real consumption/real disposable income = $12.4 trillion/$14.8 trillion = 0.838. The average propensity to save is APS = 1 – APC = 1
– 0.838 = 0.162 or, alternatively, APS = planned real saving/real disposable income = $2.4 trillion/$14.8 trillion = 0.162.
12-16. Take a look at Table 12-2 and consider the changes in planned real consumption and saving associated with an increase in real GDP from $14.0 trillion to $15.0 trillion to calculate the marginal propensity to consume.
A rise in real GDP from $14.0 trillion to $15.0 trillion induces an increase in real disposable income of $10.8 trillion to $11.8 trillion = $1.0 trillion and in planned real consumption of $10.0 trillion ?$9.2 trillion = $0.8 trillion. Hence, the marginal propensity to consume is MPC = change in planned real consumption/change in real disposable income = $0.8 trillion/$1.0 trillion = 0.
12-17. Consider the current equilibrium real GDP level of $18.0 trillion displayed in Table 12-2. Based on your answer to Problem 4, if real government spending were to decrease by $1.0 trillion, what would be the resulting change in real GDP? What would be the new equilibrium level of real GDP? Verify that at the new level of government spending, this new equilibrium real GDP equals C + I + G + X.
The multiplier equals 1 / (1 – MPC) = 1 / (1 – 0.8) = 1/0.2 = 5, so a $1.0 trillion decrease in government spending would cause real GDP to decrease by $5.0 trillion. The new equilibrium
real GDP, therefore, would be $18 trillion ?$5 trillion = $13.0 trillion, at which (given that G is now equal to $2.2 trillion) C + I + G + X = $8.4 trillion + $2.8 trillion + $2.2 trillion ?$0.4 trillion = $13.0 trillion.
12-18. Consider Figure 12-7, which applies to an economy in which the marginal propensity to consume is 0.8. Why does a $0.1 trillion increase in planned real investment spending cause the aggregate demand curve to shift rightward by exactly $0.5 trillion at the initial equilibrium price level of 110?
At the initial equilibrium price level of 110, total planned real spending rises by the $0.1 trillion increase in planned real investment spending times the multiplier, which is equal to 1 / (1 – MPC) = 1 / (1 – 0.8) = 1/0.2 = 5. Hence, the AD curve must shift rightward by the amount of the increase in total planned real spending at this price level, which therefore equals $0.5 trillion.
12-19. Following the rightward shift in the aggregate demand curve generated by the $0.1 trillion rise in real planned investment spending in Problem 12-18, why does the actual equilibrium level of real GDP increase by only $0.3 trillion instead of $0.5 trillion?
The rightward shift in the AD curve generates an upward movement along the SRAS curve. In the short run, the equilibrium price level increases from the initial value of 110 to a higher value of 115. People must expend some of the increase in real disposable income on paying higher prices. Consequently, the real value of goods and services that they actually purchase drops below $18.5 trillion, to $18.3 trillion.
Selected References
Ackley, Gardner, Macroeconomics: Theory and Policy, New York: Macmillan, 1978.
Ando, A. and F. Modigliani, “Velocity and the Investment Multiplier,” American Economic Review,
Vol. LV, No. 4, September 1965, pp. 693–728, 786–790.
Barret, Charles P. and A.A. Walters, “The Stability of Keynesian and Monetary Multipliers in the
United States,” Review of Economics and Statistics, November 1966, pp. 395–405.
Friedman, M. and D. Meiselman, “Reply to Ando and Modigliani and to DePrano and Mayer,”
American Economic Review, Vol. 55, No. 4, September 1965, pp. 753–785.
Gordon, Robert J., Macroeconomics, 4th ed., Boston: Little, Brown, and Company, 1987.
Keynes, John M., The General Theory of Employment, Interest, and Money, New York: Harcourt, 1963.
Klein, Lawrence, The Keynesian Revolution, New York: Macmillan, 1961.
Miller, Roger L. and Robert W. Pulsinelli, Macroeconomics, New York: Harper & Row, 1986.
