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The Aggregate Expenditures Model
CHAPTER TEN
THE AGGREGATE EXPENDITURES MODEL
CHAPTER OVERVIEW
We have seen in Chapter 9 three basic relationships: how income relates to consumption and saving,
how the interest rate affects investment spending, and how changes in spending work through the system
to create larger changes in output. In this chapter we build the more theoretically rigorous explanation
for these relationships – the Aggregate Expenditures (AE) Model.
The chapter begins with the simple version of the AE model, that of a closed, private economy.
Equilibrium GDP is determined and multiplier effects are briefly reviewed. The simplified “closed”
economy is then “opened” to show how it would be affected by exports and imports. Government
spending and taxes are brought into the model to include the “public” aspects of the system. Finally, the
model is applied to two historical periods in order to consider some of the model’s deficiencies. The
price level is assumed constant in this chapter unless stated otherwise, so the focus is on real GDP.
The Last Word traces briefly the historical development of the AE theory.
WHAT’S NEW
Chapters 10 through 12 are now organized into Part 3, a unit titled “Macroeconomic Models and Fiscal
Policy.” This slight restructuring reflects primarily the changes to Chapters 9 and 10, and otherwise does
not represent a significant change in coverage.
This chapter develops the aggregate expenditures (AE) analysis in its entirety. Instructors that prefer to
bypass the AE model can proceed directly to Chapter 11 (Aggregate Demand / Aggregate Supply)
without students missing the key underlying concepts. In the previous edition the model was covered in
Chapters 9 and 10; now it is in Chapter 10 only.
Discussion of the balanced budget multiplier has been replaced with a brief discussion of the “differential
impacts” of government purchases (G) and taxes (T).
New applications of recessionary gaps (recession of 2001) and inflationary gaps (late 1980s) have
replaced previous edition references to the Great Depression, Vietnam War inflation, and Japan’s 1990s
recession.
The closing section, “Limitations of the Model,” now includes “It does not allow for ‘self-correction’.”
The “Last Word” on “Say’s Law, the Great Depression, and Keynes” replaces the multiplier piece that
appeared in the previous edition and now appears in Chapter 9.
End-of-chapter and web-based questions have been revised and edited.
There is no “Consider This” box in this chapter, but there are two potentially useful “Concept
Illustrations” that appear in the COMMENTS AND TEACHING SUGGESTIONS.
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INSTRUCTIONAL OBJECTIVES
After completing this chapter, students should be able to
1. Identify the simplifying assumptions of the Aggregate Expenditures (AE) model.
2. Explain the relationship between the investment demand curve and the investment schedule.
3. Use the consumption and investment schedules to determine the equilibrium level of GDP.
4. Explain verbally and graphically the equilibrium level of GDP.
5. Explain why above-equilibrium or below-equilibrium GDP levels will not persist.
6. Explain the basics of the classical view that the economy would generally provide full employment
levels of output.
7. Trace the changes in GDP that will occur when there is a discrepancy between saving and planned
investment.
8. Use the multiplier to find changes in GDP resulting from changes in spending.
9. Define the net export schedule.
10. Explain the impact of positive (or negative) net exports on aggregate expenditures and the
equilibrium level of real GDP.
11. Explain the effect of increases (or decreases) in exports on real GDP.
12. Explain the effect of increases (or decreases) in imports on real GDP.
13. Describe how government purchases affect equilibrium GDP.
14. Describe how personal taxes affect equilibrium GDP.
15. Explain why an equal amount of government purchases and taxes will have a differential impact
on GDP.
16. Identify a recessionary gap and explain how it relates to the U.S. recession of 2001.
17. Identify an inflationary gap and explain how it relates to the inflationary experience of the late
1980s.
18. List five limitations of the aggregate expenditures model.
19. Explain how the aggregate expenditures model emerged as a critique of Classical economics and
in response to the Great Depression.
20. Define and identify terms and concepts listed at the end of the chapter.
COMMENTS AND TEACHING SUGGESTIONS
1. As stated earlier, some instructors may choose to skip this chapter. However, students could still
benefit from the Last Word for Chapter 10.
2. Note that net exports are kept as independent of the level of GDP to keep the analysis simple. You
may want to note in passing that, in fact, there tends to be a direct relationship between import
spending and the level of GDP.
3. The Last Word for this chapter provides a historical backdrop for Keynesian theory. Impress upon
students that Keynes developed the theory that emphasizes the importance of aggregate demand
for economic performance. You may want to point out that his theory changed the way
economists viewed the modern capitalist system and that he has been credited with the
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development of macroeconomics as a separate field. Stress that debate still lingers over whether
the system is self-correcting during periods of unemployment or inflation.
4. Data to update Figure 9-1 may be found in the most recent issue of Survey of Current Business or
Economic Indicators. Web-based questions at the end of the chapter also point to sources.
5. The following “Concept Illustration” may be useful in conveying the leakages-injections approach
to equilibrium GDP.
Concept Illustration … Leakages and Injections
A bathtub analogy is useful in illustrating the injections-leakages approach to equilibrium real
domestic output and income (real GDP) in the private, closed economy. A tub’s faucet enables an
inflow of water and the tub’s drain allows an outflow of water. The level of water in the tub
remains constant when the inflow from the faucet equals the outflow from the drain. If the inflow
exceeds the outflow, the level of water rises. If the inflow is less than the outflow, the level of
water level recedes.
The inflow, outflow, and level of water in the tub are analogous to investment (Ig), saving (S), and
real GDP, respectively, in a private, closed economy. Equilibrium real GDP occurs where the
investment injection (inflow) just equals the saving leakage (drain). If the investment injection
exceeds the saving leakage, real GDP expands until saving increases sufficiently to equal the level
of investment. If the investment injection is less than the saving leakage, real GDP declines until
saving falls sufficiently to equal investment. In both cases equilibrium is achieved where
investment equals saving.
In the economy represented in Table 9-4, equilibrium real GDP is $470 billion. In view of the
bathtub analogy, it is not surprising to discover that investment and saving flows are each $20
billion.
6. After learning the AE model, students may reach the conclusion that increasing saving is bad
because of the contractionary impact it has on consumption and, by extension, aggregate spending.
This is, of course, the famous “paradox of thrift,” and if you choose to include such a discussion in
your course, you may find the following “Concept Illustration” useful.
Concept Illustration … The Paradox of Thrift
In Chapter 2 we said that a higher rate of saving is good for society because it frees resources from
consumption uses and directs them toward investment goods. More machinery and equipment
means a greater capacity for the economy to produce goods and services.
But implicit within this “saving is good” proposition is the assumption that increased saving will
be borrowed and spent for investment goods. If investment does not increase along with saving, a
curious irony called the paradox of thrift may arise. The attempt to save more may simply reduce
GDP and leave actual saving unchanged.
Our analysis of the multiplier process helps explain this possibility. Suppose an economy that has
a MPC of .75, a MPS of .25, and a multiplier of 4, decides to save an additional $200 billion.
From the social viewpoint, a penny saved that is not invested is a penny not spent and therefore a
decline in someone’s income. Through the multiplier process, the $200 billion of reduced
consumption spending lowers real GDP by $800 billion (4 x $200 billion).
The $800 billion decline of real GDP, in turn, reduces saving by $200 billion (= MPS of .25 x
$800 billion), which completely cancels the initial $200 billion increase of saving. Here, the
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attempt to increase saving is bad for the economy: it creates a recession and leaves saving
unchanged.
For increased saving to be good for an economy, greater investment must accompany greater
saving. If investment replaces consumption dollar-for-dollar, aggregate expenditures stay constant
and the higher level of investment raises the economy’s future growth rate.
STUDENT STUMBLING BLOCKS
1. When introducing the investment, net export, and government purchases schedules, be sure to
emphasize that the graphs are horizontal because of the exogenous nature of the variables, not
because the values are unchanging.
2. When the model is complete (GDP = C + Ig + Xn + G), students may confuse the equilibrium
equation with the accounting identity presented in Chapter 7. You may need to visually separate
planned and unplanned investment in the equation to help them see the difference between the two
equations.
3. Some students will need to be reminded that in the AE model, unplanned inventory build-ups or
depletions are corrected by adjusting production, not by altering prices.
LECTURE NOTES
I.
Introduction—What Determines GDP?
A. This chapter focuses on the aggregate expenditures model. We use the definitions and facts
from previous chapters to shift our study to the analysis of economic performance. The
aggregate expenditures model is one tool in this analysis. Recall that “aggregate” means
total.
B. As explained in this chapter’s Last Word, the model originated with John Maynard Keynes
(pronounced “Canes”).
C. The focus is on the relationship between income and consumption and savings.
D. Investment spending, net exports, and government purchases, important parts of aggregate
expenditures, are also examined.
E. Finally, these spending categories are combined to explain the equilibrium levels output and
employment in at first a private (no government), domestic (no foreign sector) economy.
Therefore, GDP = NI = PI = DI in this very simple model.
F. The revised model adds realism by including the foreign sector and government in the
aggregate expenditures model.
G. Applications of the new model include two U.S. historical periods (the 2001 recession and
the late 1980s inflation).
II.
Simplifying Assumptions for the Private Closed-Economy model
A. We first assume a “closed economy” with no international trade.
B. Government is ignored.
C. Although both households and businesses save, we assume here that all saving is personal.
D. Depreciation and net foreign income are assumed to be zero for simplicity.
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E. There are two reminders concerning these assumptions.
1. They leave out two key components of aggregate demand (government spending and
foreign trade), because they are largely affected by influences outside the domestic
market system.
2. With no government or foreign trade, GDP, national income (NI), personal income (PI),
and disposable income (DI) are all the same.
III.
Tools of Aggregate Expenditures Theory: Consumption and Investment Schedules
A. The theory assumes that the level of output and employment depend directly on the level of
aggregate expenditures. Changes in output reflect changes in aggregate spending.
B. In a closed private economy the two components of aggregate expenditures are consumption
and gross investment.
C. The consumption schedule was developed in Chapter 9 (see Figure 9-2a).
D. In addition to the investment demand schedule, economists also define an investment
schedule that shows the amounts business firms collectively intend to invest at each possible
level of GDP or DI.
1. In developing the investment schedule, it is assumed that investment is independent of
the current income. The line Ig (gross investment) in Figure 10-1b shows this to be
graphically related to the level determined by Figure 10-1a.
2. The assumption that investment is independent of income is a simplification, but it will
be used here.
3. Figure 10-1a shows the investment schedule from GDP levels given in Table 9-1.
IV.
Equilibrium GDP: Expenditures-Output Approach
A. Look at Table 10-2, which combines data of Tables 9-1 and 10-1.
B. Real domestic output in column 2 shows ten possible levels that producers are willing to
offer, assuming their sales would meet the output planned. In other words, they will produce
$370 billion of output if they expect to receive $370 billion in revenue.
C. Ten levels of aggregate expenditures are shown in column 6. The column shows the amount
of consumption and planned gross investment spending (C + Ig) forthcoming at each output
level.
1. Recall that consumption level is directly related to the level of income and that here
income is equal to output level.
2. Investment is independent of income here and is planned or intended regardless of the
current income situation.
D. Equilibrium GDP is the level of output whose production will create total spending just
sufficient to purchase that output. Otherwise there will be a disequilibrium situation.
1. In Table 10-2, this occurs only at $470 billion.
2. At $410 billion GDP level, total expenditures (C + Ig) would be $425 = $405(C) + $20
(Ig) and businesses will adjust to this excess demand (revealed by the declining
inventories) by stepping up production. They will expand production at any level of
GDP less than the $470 billion equilibrium.
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3. At levels of GDP above $470 billion, such as $510 billion, aggregate expenditures will
be less than GDP. At $510 billion level, C + Ig = $500 billion. Businesses will have
unsold, unplanned inventory investment and will cut back on the rate of production. As
GDP declines, the number of jobs and total income will also decline, but eventually the
GDP and aggregate spending will be in equilibrium at $470 billion.
E. Graphical analysis is shown in Figure 10-2 (Key Graph). At $470 billion it shows the C + Ig
schedule intersecting the 45-degree line which is where output = aggregate expenditures, or
the equilibrium position.
1. Observe that the aggregate expenditures line rises with output and income, but not as
much as income, due to the marginal propensity to consume (the slope) being less than 1.
2. A part of every increase in disposable income will not be spent but will be saved.
3. Test yourself with Quick Quiz 10-2.
V.
Two Other Features of Equilibrium GDP
A. Savings and planned investment are equal.
1. It is important to note that in our analysis above we spoke of “planned” investment. At
GDP = $470 billion in Table 10-2, both saving and planned investment are $20 billion.
2. Saving represents a “leakage” from spending stream and causes C to be less than GDP.
3. Some of output is planned for business investment and not consumption, so this
investment spending can replace the leakage due to saving.
a. If aggregate spending is less than equilibrium GDP as it is in Table 10-2, line 8,
when GDP is $510 billion, then businesses will find themselves with unplanned
inventory investment on top of what was already planned. This unplanned portion is
reflected as a business expenditure, even though the business may not have desired
it, because the total output has a value that belongs to someone—either as a planned
purchase or as an unplanned inventory.
b. If aggregate expenditures exceed GDP, then there will be less inventory investment
than businesses planned as businesses sell more than they expected. This is reflected
as a negative amount of unplanned investment in inventory. For example, at $450
billion GDP, there will be $435 billion of consumer spending, $20 billion of planned
investment, so businesses must have experienced a $5 billion unplanned decline in
inventory because sales exceed that expected.
B. In equilibrium there are no unplanned changes in inventory.
1. Consider row 7 of Table 10-2 where GDP is $490 billion; here C + Ig is only $485
billion and will be less than output by $5 billion. Firms retain the extra $5 billion as
unplanned inventory investment. Actual investment is $25 billion, or $5 billion more
than the $20 billion planned. So $490 billion is an above-equilibrium output level.
2. Consider row 5, Table 10-2. Here $450 billion is a below-equilibrium output level
because actual investment will be $5 billion less than planned. Inventories decline below
what was planned. GDP will rise to $470 billion.
C.
Quick Review:
output.
1.
Equilibrium GDP is where aggregate expenditures equal real domestic
C + planned Ig = GDP
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2. A difference between saving and planned investment causes a difference between the
production and spending plans of the economy as a whole.
3. This difference between production and spending plans leads to unintended inventory
investment or unintended decline in inventories.
4. As long as unplanned changes in inventories occur, businesses will revise their
production plans upward or downward until the investment in inventory is equal to what
they planned. This will occur at the point that household saving is equal to planned
investment.
5. Only where planned investment and saving are equal will there be no unintended
investment or disinvestment in inventories to drive the GDP down or up.
VI.
Changes in Equilibrium GDP and the Multiplier
A. As developed in Chapter 9, an initial change in spending will be acted on by the multiplier to
produce larger changes in output.
1. The “initial change” represented in the text and Figure 10-3 is in planned investment
spending. It could also result from a nonincome-induced change in consumption.
2. The multiplier in Figure 10-3 is 4 (=1/MPS)
B. Figure 10-3 shows the impact of changes in investment. Suppose investment spending rises
(due to a rise in profit expectations or to a decline in interest rates).
1. Figure 10-3 shows the increase in aggregate expenditures from (C + Ig)0 to (C + Ig)1. In
this case, the $5 billion increase in investment leads to a $20 billion increase in
equilibrium GDP.
2. Conversely, a decline in investment spending of $5 billion is shown to create a decrease
in equilibrium GDP of $20 billion to $450 billion.
VII.
International Trade and Equilibrium Output
A. Net exports (exports minus imports) affect aggregate expenditures in an open economy.
Exports expand and imports contract aggregate spending on domestic output.
1. Exports (X) create domestic production, income, and employment due to foreign
spending on U.S. produced goods and services.
2. Imports (M) reduce the sum of consumption and investment expenditures by the amount
expended on imported goods, so this figure must be subtracted so as not to overstate
aggregate expenditures on U.S. produced goods and services.
B. The net export schedule (Table 10-3):
1. Shows hypothetical amount of net exports (X - M) that will occur at each level of GDP
given in Table 10-2.
2. Assumes that net exports are autonomous or independent of the current GDP level.
3. Figure 10-4b shows Table 10-3 graphically.
a. Xn1 shows a positive $5 billion in net exports.
b. Xn2 shows a negative $5 billion in net exports.
C. The impact of net exports on equilibrium GDP is illustrated in Figure 10-4a.
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1. Positive net exports increase aggregate expenditures beyond what they would be in a
closed economy and thus have an expansionary effect. The multiplier effect also is at
work. In Figure 10-4a we see that positive net exports of $5 billion lead to a positive
change in equilibrium GDP of $20 billion (to $490 from $470 billion). This comes from
Table 10-2 and Figure 10-3.
2. Negative net exports decrease aggregate expenditures beyond what they would be in a
closed economy and thus have a contractionary effect. The multiplier effect also is at
work here. In Figure 10-4a we see that negative net exports of $5 billion lead to a
negative change in equilibrium GDP of $20 billion (to $450 from $470 billion).
D. Global Perspective 10-1 shows 2001 net exports for various nations.
E. International economic linkages:
1. Prosperity abroad generally raises our exports and transfers some of their prosperity to
us. (Conversely, recession abroad has the reverse effect.)
2. Tariffs on U.S. products may reduce our exports and depress our economy, causing us to
retaliate and worsen the situation. Trade barriers in the 1930s contributed to the Great
Depression.
3. Depreciation of the dollar (Chapter 6) lowers the cost of American goods to foreigners
and encourages exports from the U.S. while discouraging the purchase of imports in the
U.S. This could lead to higher real GDP or to inflation, depending on the domestic
employment situation. Appreciation of the dollar could have the opposite impact.
VIII.
Adding the Public Sector
A. Simplifying assumptions are helpful for clarity when we include the government sector in
our analysis. (Many of these simplifications are dropped in Chapter 12, where there is
further analysis on the government sector.)
1. Simplified investment and net export schedules are used.
independent of the level of current GDP.
We assume they are
2. We assume government purchases do not impact private spending schedules.
3. We assume that net tax revenues are derived entirely from personal taxes so that GDP,
NI, and PI remain equal. DI is PI minus net personal taxes.
4. We assume that tax collections are independent of GDP level (a lump-sum tax)
5. The price level is assumed to be constant unless otherwise indicated.
B. Table 10-4 gives a tabular example of including $20 billion in government spending and
Figure 10-5 gives the graphical illustration. Note that the previous section’s net export
information has also been included.
1. Increases in government spending boost aggregate expenditures.
2. Government spending is subject to the multiplier.
C. Table 10-5 and Figure 10-6 show the impact of a tax increase. (Key Question 12)
1. Taxes reduce DI and, therefore, consumption and saving at each level of GDP.
2. An increase in taxes will lower the aggregate expenditures schedule relative to the 45degree line and reduce the equilibrium GDP.
3. Table 10-5 confirms that, at equilibrium GDP, the sum of leakages equals the sum of
injections. Saving + Imports + Taxes = Investment + Exports + Government Purchases.
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D. Government purchases and taxes have different impacts.
1. In our example, equal additions in government spending and taxation increase the
equilibrium GDP.
a. If G and T are each increased by a particular amount, the equilibrium level of real
output will rise by that same amount.
b. In the text’s example, an increase of $20 billion in G and an offsetting increase of
$20 billion in T will increase equilibrium GDP by $20 billion (from $470 billion to
$490 billion).
2. The example reveals the rationale.
a. An increase in G is direct and adds $20 billion to aggregate expenditures.
b. An increase in T has an indirect effect on aggregate expenditures because T reduces
disposable incomes first, and then C falls by the amount of the tax times MPC.
c. The overall result is a rise in initial spending of $20 billion minus a fall in initial
spending of $15 billion (.75 x $20 billion), which is a net upward shift in aggregate
expenditures of $5 billion. When this is subject to the multiplier effect, which is 4 in
this example, the increase in GDP will be equal to $4 x $5 billion or $20 billion,
which is the size of the change in G.
IX.
Injections, Leakages, and Unplanned Changes in Inventories – Equilibrium revisited
A. As demonstrated earlier, in a closed private economy equilibrium occurs when saving (a
leakage) equals planned investment (an injection).
B. With the introduction of a foreign sector (net exports) and a public sector (government), new
leakages and injections are introduced.
1. Imports and taxes are added leakages.
2. Exports and government purchases are added injections.
C. Equilibrium is found when the leakages equal the injections.
1. When leakages equal injections, there are no unplanned changes in inventories.
2. Symbolically, equilibrium occurs when Sa + M + T = Ig + X + G, where Sa is after-tax
saving, M is imports, T is taxes, Ig is (gross) planned investment, X is exports, and G is
government purchases.
X.
Equilibrium vs. Full-Employment GDP
A. A recessionary gap exists when equilibrium GDP is below full-employment GDP. (See
Figure 10-7a)
1. A recessionary gap of $5 billion is the amount by which aggregate expenditures fall short
of those required to achieve the full-employment level of GDP.
2. In Table 10-5, assuming the full-employment GDP is $510 billion, the corresponding
level of total expenditures there is only $505 billion. The gap would be $5 billion, the
amount by which the schedule would have to shift upward to realize the full-employment
GDP.
3. Graphically, the recessionary gap is the vertical distance by which the aggregate
expenditures schedule (Ca + Ig + Xn + G)1 lies below the full-employment point on the
45-degree line.
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4. Because the multiplier is 4, we observe a $20-billion differential (the recessionary gap of
$5 billion times the multiplier of 4) between the equilibrium GDP and the fullemployment GDP. This is the $20 billion GDP gap we encountered in Chapter 8’s
Figure 8-3.
B. An inflationary gap exists when aggregate expenditures exceed full-employment GDP.
1. Figure 10-7b shows that a demand-pull inflationary gap of $5 billion exists when
aggregate spending exceeds what is necessary to achieve full employment.
2. The inflationary gap is the amount by which the aggregate expenditures schedule must
shift downward to realize the full-employment noninflationary GDP.
3. The effect of the inflationary gap is to pull up the prices of the economy’s output.
4. In this model, if output can’t expand, pure demand-pull inflation will occur (Key
Question 10).
XI.
Historical Applications
A. The U.S. recession of 2001 provides a good illustration of a recessionary gap.
1. U.S. overcapacity and business insolvency resulted from excessive expansion by
businesses in the 1990s, a period of prosperity.
2. Internet-related companies proliferated during the 1990s, despite their lack of
profitability, but fueled by speculative interest in the stocks of these start-up firms.
3. Consumer debt grew as people borrowed against their expectations of rising wealth in
financial markets.
4. Fraud by executives and accountants led to speculative excesses and set up firms to fail.
5. Beginning in 2000, a dramatic drop in stock market values occurred, causing pessimism
and highly unfavorable conditions for acquiring additional investment funds.
6. In March 2001 aggregate expenditures declined and the economy fell into its 9 th
recession since 1950.
7. The terrorist attacks on September 11, 2001, further undermined consumer confidence
and contributed to the downturn.
8. Unemployment has remained high (by the standards of the last decade), at or above 6%,
despite other signs pointing toward recovery. As of summer 2003, the upturn was still
being referred to as a “jobless recovery,” where output rises, but labor market conditions
remain weak.
B. U.S. Inflation in the late 1980s provides an example of an inflationary gap period.
1. Strong economic growth in the late 1980s gave way to increasing rates of inflation.
2. Inflation rose from 1.9% in 1986 and to 3.6, 4.1, and 4.8% in the years that followed.
3. Inflationary pressure subsided with the 1990-91 recession and the recessionary gap that
emerged.
XII.
Limitations of the Model
A. The aggregate expenditures model has five limitations.
1. The model can account for demand-pull inflation, but it does not indicate the extent of
inflation when there is an inflationary gap. It doesn’t measure inflation.
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2. It doesn’t explain how inflation can occur before the economy reaches full employment
(premature demand-pull inflation).
3. It doesn’t indicate how the economy could produce beyond full-employment output for a
time.
4. The model does not address the possibility of cost-push type of inflation.
5. It doesn’t allow for “self-correction,” built-in features of the economy that tend to
ameliorate recessionary and inflationary gaps.
B. In Chapter 11, these deficiencies are remedied with a related aggregate demand-aggregate
supply model.
XIII. Last Word: Say’s Law, The Great Depression, and Keynes
A. Until the Great Depression of the 1930, most economists going back to Adam Smith had
believed that a market system would ensure full employment of the economy’s resources
except for temporary, short-term upheavals.
B. If there were deviations, they would be self-correcting. A slump in output and employment
would reduce prices, which would increase consumer spending; would lower wages, which
would increase employment again; and would lower interest rates, which would expand
investment spending.
C. Say’s law, attributed to the French economist J. B. Say in the early 1800s, summarized the
view in a few words: “Supply creates its own demand.”
D. Say’s law is easiest to understand in terms of barter. The woodworker produces furniture in
order to trade for other needed products and services. All the products would be traded for
something, or else there would be no need to make them. Thus, supply creates its own
demand.
E. Reformulated versions of these classical views are still prevalent among some modern
economists today.
F. The Great Depression of the 1930s was worldwide. GDP fell by 40 percent in U.S. and the
unemployment rate rose to nearly 25 percent (when most families had only one
breadwinner). The Depression seemed to refute the classical idea that markets were selfcorrecting and would provide full employment.
G. John Maynard Keynes in 1936 in his General Theory of Employment, Interest, and Money,
provided an alternative to classical theory, which helped explain periods of recession.
1. Not all income is always spent, contrary to Say’s law.
2. Producers may respond to unsold inventories by reducing output rather than cutting
prices.
3. A recession or depression could follow this decline in employment and incomes.
H. The modern aggregate expenditures model is based on Keynesian economics or the ideas that
have arisen from Keynes and his followers since. It is based on the idea that saving and
investment decisions may not be coordinated, and prices and wages are not very flexible
downward. Internal market forces can therefore cause depressions and government should
play an active role in stabilizing the economy.
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ANSWERS TO END-OF-CHAPTER QUESTIONS
10-1
What is an investment schedule and how does it differ from an investment demand curve?
An investment schedule shows the level of investment spending for a given level of GDP.
An investment demand curve shows how expected rates of profit and real interest rates
determine the level of investment spending. In the simple AE model, investment spending is
assumed to be independent of the level of real GDP.
10-2
(Key Question) Assuming the level of investment is $16 billion and independent of the level of
total output, complete the following table and determine the equilibrium levels of output and
employment in this private closed economy. What are the sizes of the MPC and MPS?
Possible levels
of employment
(millions)
Real domestic
output (GDP = DI)
(billions)
Consumption
(billions)
Saving
(billions)
40
45
50
55
60
65
70
75
80
$240
260
280
300
320
340
360
380
400
$244
260
276
292
308
324
340
356
372
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
Saving data for completing the table (top to bottom): $-4; $0; $4; $8; $12; $16; $20; $24; $28.
Equilibrium GDP = $340 billion, determined where (1) aggregate expenditures equal GDP (C of
$324 billion + I of $16 billion = GDP of $340 billion); or (2) where planned I = S (I of $16
billion = S of $16 billion). Equilibrium level of employment = 65 million; MPC = .8; MPS = .2.
10-3
Using the consumption and saving data in question 2 and assuming investment is $16 billion,
what are saving and planned investment at the $380 billion level of domestic output? What are
saving and actual investment at that level? What are saving and planned investment at the $300
billion level of domestic output? What are the levels of saving and actual investment? Use the
concept of unplanned investment to explain adjustments toward equilibrium from both the $380
and $300 billion levels of domestic output.
At the $380 billion level of GDP, saving = $24 billion; planned investment = $16 billion (from
the question). This deficiency of $8 billion of planned investment causes an unplanned $8
billion increase in inventories. Actual investment is $24 billion (= $16 billion of planned
investment plus $8 billion of unplanned inventory investment), matching the $24 billion of actual
saving.
At the $300 billion level of GDP, saving = $8 billion; planned investment = $16 billion (from the
question). This excess of $8 billion of planned investment causes an unplanned $8 billion
decline in inventories. Actual investment is $8 billion (= $16 billion of planned investment
minus $8 billion of unplanned inventory disinvestment) matching the actual of $8 billion.
When unplanned investments in inventories occur, as at the $380 billion level of GDP,
businesses revise their production plans downward and GDP falls. When unplanned
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The Aggregate Expenditures Model
disinvestments in inventories occur, as at the $300 billion level of GDP; businesses revise their
production plans upward and GDP rises. Equilibrium GDP—in this case, $340 billion—occurs
where planned investment equals saving.
10-4
Why is saving called a leakage? Why is planned investment called an injection? Why must
saving equal planned investment at equilibrium GDP in the private closed economy? Are
unplanned changes in inventories rising, falling, or constant at equilibrium GDP? Explain.
Saving is like a leakage from the flow of aggregate consumption expenditures because saving
represents income not spent. Planned investment is an injection because it is spending on capital
goods that businesses plan to make regardless of their current level of income. If the two are
unequal, there will be a discrepancy between spending and production that will result in
unplanned inventory changes. Firms, not wanting inventory levels to change, will change
production, implying that equilibrium can only occur when the saving leakage equals the
injection of investment spending in a private closed economy.
At equilibrium GDP there will be no changes in unplanned inventories because expenditures will
exactly equal planned output levels which include consumer goods and services and planned
investment. Thus there is no unplanned investment including no unplanned inventory changes.
10-5
What effect will each of the changes designated in question 3 at the end of Chapter 9 have on the
equilibrium level of GDP? Explain your answers.
a. A large increase in the value of real estate, including private houses.
b. A decline in the real interest rate.
c. A sharp, sustained decline in stock prices.
d. An increase in the rate of population growth.
e. The development of a cheaper method of manufacturing computer chips.
f.
A sizable increase in the retirement age for collecting Social Security benefits.
g. The expectation that mild inflation will persist in the next decade.
h. An increase in the Federal personal income tax.
(a) If this means that people have become wealthier, then their consumption schedule will shift
up and GDP will rise by a multiple of the increase in consumption.
(b) This will increase interest-sensitive consumer purchases and investment, causing GDP to
increase.
(c) By reducing consumption (because households will feel—or be—less wealthy, or because
they fear a recession) and by decreasing investment, the AE schedule will shift downward,
causing the GDP to decline.
(d) This will increase AE, causing GDP to increase.
(e) Investment will increase both because of increased profitability and because of increased
innovations, causing GDP to increase.
(f) The announcement will lead to an upward shift of the current saving schedule (downward
shift of the consumption schedule), causing GDP to decline.
(g) An increase in the personal income tax will decrease the level of disposable income, and
decrease consumer spending, which could mean a decline in aggregate expenditures. But if
the government increases its purchases to the extent of the tax increase, then aggregate
161
The Aggregate Expenditures Model
expenditures will actually increase, since consumer expenditures fall only by a fraction of the
decline in income and government spending is more than offsetting this decline. If this
happens, the equilibrium level of GDP should rise. On the other hand, if government
spending does not rise, then the equilibrium level of GDP may fall as private spending falls.
10-6
By how much will GDP change if firms increase their investment by $8 billion and the
MPC is .80? If the MPC is .67?
GDP will increase $40 billion if the MPC is .80. An MPC of .80 will produce a multiplier of 5.
The multiplier times the $8 billion change in spending will change GDP by $40 billion.
Change in GDP = Change in Investment x (1/(1 - MPC))
$40 billion = $8 billion x (1/(1 - .8))
GDP will increase by approximately $24 billion when the MPC is .67
$24 billion = $8 billion x (1/(1 - .67)) Note: The multiplier for an MPC of .67 is actually 3.03.
10-7
Depict graphically the aggregate expenditures model for a private closed economy. Now show a
decrease in the aggregate expenditures schedule and explain why the decrease in real GDP in
your diagram is greater than the initial decline in aggregate expenditures. What would be the
ratio of a decline in real GDP to the initial drop in aggregate expenditures if the slope of your
aggregate expenditures schedule were .75?
If the slope of the aggregate expenditures schedule were .8, then the MPC = .8 and the MPS = .2.
Therefore, the multiplier would be 1/(.2) = 5. The ratio of decline in real GDP to the initial drop
of expenditures would be a ratio of 5:1. That is, if expenditures declined by $4 billion, GDP
should decline by $20 billion. On the graph it can be seen that a one-unit decline in (C + I) leads
to a five-unit decline in real GDP.
10-8
Suppose that a certain country has an MPC of .9 and real GDP of $400 billion. If its investment
spending decreases by $4 billion, what will be its new level of real GDP?
The multiplier is 10 or 1/(1-.9) so 10 x -$4 billion = -$40 billion. The new GDP is $400 billion $40 billion = $360 billion.
10-9
(Key Question) The data in columns 1 and 2 of the table below are for a private closed economy.
162
The Aggregate Expenditures Model
(1)
Real
domestic
output
(GDP = DI)
billions
(2)
Aggregate
expenditures
private closed
economy,
billions
$200
$250
$300
$350
$400
$450
$500
$550
$240
$280
$320
$360
$400
$440
$480
$520
(3)
(4)
(5)
(6)
Exports,
billions
Imports,
billions
Net
exports,
private
economy
Aggregate
expenditures,
open,
billions
$20
$20
$20
$20
$20
$20
$20
$20
$30
$30
$30
$30
$30
$30
$30
$30
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
a. Use columns 1 and 2 to determine the equilibrium GDP for this hypothetical economy.
b. Now open up this economy to international trade by including the export and import figures
of columns 3 and 4. Fill in columns 5 and 6 to determine the equilibrium GDP for the open
economy. Explain why this equilibrium GDP differs from that of the closed economy.
c. Given the original $20 billion level of exports, what would be the equilibrium GDP if
imports were $10 billion greater at each level of GDP?
d. What is the multiplier in this example?
(a) Equilibrium GDP for closed economy = $400 billion.
(b) Net export data for column 5 (top to bottom); $-10 billion in each space. Aggregate
expenditure data for column 6 (top to bottom): $230; $270; $310; $350; $390; $430; $470;
$510. Equilibrium GDP for the open economy is $350 billion, $50 billion below the $400
billion equilibrium GDP for the closed economy. The $-10 billion of net exports is a leakage
that reduces equilibrium GDP by $50 billion.
(c) Imports = $40 billion: Aggregate expenditures in the private open economy would fall by
$10 billion at each GDP level and the new equilibrium GDP would be $300 billion.
(d) Since every rise of $50 billion in GDP increases aggregate expenditures by $40 billion, the
MPC is .8 and so the multiplier is 5.
10-10 Assume that, without taxes, the consumption schedule of an economy is as shown below:
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The Aggregate Expenditures Model
GDP,
billions
Consumption,
Billions
$100
200
300
400
500
600
700
$120
200
280
360
440
520
600
a. Graph this consumption schedule and determine the MPC.
b. Assume now that a lump-sum tax system is imposed such that the government collects $10
billion in taxes at all levels of GDP. Graph the resulting consumption schedule, and compare
the MPC and the multiplier with that of the pretax consumption schedule.
Refer to Figures 9-2 and 9-4 for the graphs for (a) and (b), respectively.
(a) The size of the MPC is 80/100 or .8 because consumption changes by 80 when GDP changes
by 100.
(b) The resulting consumption schedule will be exactly $8 billion below the original at all levels
of GDP (or income). After-tax income will fall by $10 billion. Given the MPC of .8,
consumption therefore will fall by $8 billion at each level of GDP. The multiplier is 5
because the MPS is .2. The MPC and multiplier don’t change from of a lump-sum tax.
10-11 Explain graphically the determination of equilibrium GDP for a private economy through the
aggregate expenditures model. Now add government spending (any amount that you choose) to
your graph, showing its impact on equilibrium GDP. Finally, add taxation (any amount of lumpsum tax that you choose) to your graph and show its effect on equilibrium GDP. Looking at your
graph, determine whether equilibrium GDP has increased, decreased, or stayed the same in view
of the sizes of the government spending and taxes that you selected.
Figures 10-5 and 10-6 show how to do this. Graphs and answers will differ depending on
magnitude of changes.
10-12 (Key Question) Refer to columns 1 and 6 of the tabular data for question 9. Incorporate
government into the table by assuming that it plans to tax and spend $20 billion at each possible
level of GDP. Also assume that all taxes are personal taxes and that government spending does
not induce a shift in the private aggregate expenditures schedule. Compute and explain the
changes in equilibrium GDP caused by the addition of government.
Before G is added, open private sector equilibrium will be at $350. The addition of government
expenditures of G to our analysis raises the aggregate expenditures (C + Ig +Xn + G) schedule
and increases the equilibrium level of GDP as would an increase in C, Ig, or Xn. Note that
changes in government spending are subject to the multiplier effect. Government spending
supplements private investment and export spending (Ig + X + G), increasing the equilibrium
GDP to $450.
The addition of $20 billion of government expenditures and $20 billion of personal taxes
increases equilibrium GDP from $350 to $370 billion. The $20 billion increase in G raises
equilibrium GDP by $100 billion (= $20 billion x the multiplier of 5); the $20 billion increase in
T reduces consumption by $16 billion at every level. (= $20 billion x the MPC of .8). This $16
billion decline in turn reduces equilibrium GDP by $80 billion ($16 billion x multiplier of 5).
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The Aggregate Expenditures Model
The net change from including balanced government spending and taxes is $20 billion (= $100
billion - $80 billion).
10-13 (Key Question) Refer to the table below in answering the questions that follow:
(1)
Possible levels
of employment,
millions
(2)
Real domestic
output,
billions
(3)
Aggregate
Expenditures
(Ca+Ig+Xn+G),
billions
90
100
110
120
130
$500
550
600
650
700
$520
560
600
640
680
a. If full employment in this economy is 130 million, will there be an inflationary gap or a
recessionary gap? What will be the consequence of this gap? By how much would
aggregate expenditures in column 3 have to change at each level of GDP to eliminate the
inflationary or recessionary gap? Explain. What is the multiplier in this example?
b. Will there be an inflationary or recessionary gap if the full-employment level of output is
$500 billion? Explain the consequences. By how much would aggregate expenditures in
column 3 have to change at each level of GDP to eliminate the gap? Explain. What is the
multiplier in this example?
c. Assuming that investment, net exports, and government expenditures do not change with
changes in real GDP, what are the sizes of the MPC, the MPS, and the multiplier?
(a) A recessionary gap. Equilibrium GDP is $600 billion, while full employment GDP is $700
billion. Employment will be 20 million less than at full employment. Aggregate
expenditures would have to increase by $20 billion (= $700 billion -$680 billion) at each
level of GDP to eliminate the recessionary gap. The MPC is .8, so the multiplier is 5.
(b) An inflationary gap. Aggregate expenditures will be excessive, causing demand-pull
inflation. Aggregate expenditures would have to fall by $20 billion (= $520 billion -$500
billion) at each level of GDP to eliminate the inflationary gap. The multiplier is still 5 – the
level of full employment GDP does not affect the multiplier.
(c) MPC = .8 (= $40 billion/$50 billion); MPS = .2 (= 1 -.8); multiplier = 5 (= 1/.2).
10-14 (Advanced analysis) Assume the consumption schedule for a private open economy is such that
C = 50 + 0.8Y. Assume further that planned investment and net exports are independent of the
level of income and constant at Ig = 30 and Xn = 10. Recall also that, in equilibrium, the real
output produced (Y) is equal to the aggregate expenditures: Y = C + Ig + Xn.
a
Calculate the equilibrium level of income or real GDP for this economy.
b
What happens to equilibrium Y if Ig changes to 10? What does this tell you about the size of
the multiplier?
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The Aggregate Expenditures Model
(a) Y  C  I g  X n  $50  0.8Y  $30  $10  0.8Y  $90
Therefore Y  0.8Y  $90, and 0.2Y  $90, so Y  $450 at equilibriu m.
Real domestic
output
(GDP = YI)
$ 0
50
100
150
200
250
300
350
400
450
500
C
Ig
Xn
Aggregate
expenditures,
open economy
$ 50
90
130
170
210
250
290
330
370
410
450
$30
30
30
30
30
30
30
30
30
30
30
$10
10
10
10
10
10
10
10
10
10
10
$90
130
170
210
250
290
330
370
410
450
490
(b) If Ig decreases from $30 to $10, the new equilibrium GDP will be at GDP of $350, for with
Ig now $10 this is where AE also equals $350. This indicates that the multiplier equals 5, for
a decline in AE of $20 has led to a decline in equilibrium GDP of $100. The size of the
multiplier could also have been calculated directly from the MPC of 0.8.
10-15 Answer the following questions, which relate to the aggregate expenditures model.
a. If Ca is $100, Ig is $50, Xn is -$10, and G is $30, what is the economy’s equilibrium GDP?
b. If real GDP in an economy is currently $200, Ca is $100, Ig is $50, Xn is -$10, and G is $30,
will the economy’s real GDP rise, fall, or stay the same?
c. Suppose that full-employment (and full-capacity) output in an economy is $200. If Ca is
$150, Ig is $50, Xn is -$10, and G is $30, what will be the macroeconomic result?
(a) Assuming that there is no unplanned inventory investment at these expenditure levels,
equilibrium GDP is $170. (= Ca+Ig+Xn+G)
(b) If real GDP is $200, aggregate expenditures of $170 will result in positive unplanned
inventory investment. GDP will fall as firms respond to the inventory build-up by reducing
output.
(c) Assuming that the economy is in equilibrium at these expenditure levels, real GDP is $170,
below the full employment level of output. There is a recessionary gap, and employment
levels are lower than they would be at full employment.
10-16 (Last Word) What is Say’s law? How does it relate to the view held by classical economists that
the economy generally will operate at a position on its production possibilities curve (Chapter 2).
Use production possibilities to demonstrate Keynes’s view on this matter.
Say’s law states “supply creates its own demand.” People work in order to earn income and
plan to spend the income on output – why else would they work? Basically, the classical
economists would say that the economy will operate at full employment or on the production
possibilities curve because income earned will be recycled or spent on output. Thus the spending
166
The Aggregate Expenditures Model
flow is continuously recycled in production and earning income. If consumers don’t spend all
their income, it would be redirected via saving to investment spending on capital goods.
The Keynesian perspective, on the other hand, suggests that society’s savings will not necessarily
all be channeled into investment spending. If this occurs, we have a situation in which aggregate
demand is less than potential production. Because producers cannot sell all of the output
produced at a full employment level, they will reduce output and employment to meet the
aggregate demand (consumption plus investment) and the equilibrium output will be at a point
inside the production possibilities curve at less than full employment.
167