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(b) under these new circumstances.


| DISCUSSION QUESTIONS |
1. Explain the basic logic behind the multiplier in words. 2. (More difficult) What would happen to the multiplier
Why does it require b, the marginal propensity to con- analysis if b 5 0? If b 5 1?
sume, to be between 0 and 1?



| APPENDIX B | The Multiplier with Variable Imports
In the chapter, we assumed that net exports were a Higher GDP leads to higher incomes, some of which is
fixed number, 2100 in the example. In fact, a nation™s spent on foreign goods. Thus:
imports vary along with its GDP for a simple reason:


Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
Licensed to:

Chapter 9 195
Demand-Side Equilibrium: Unemployment or Inflation?



Our imports rise as our GDP rises and fall as our GDP that once we recognize the dependence of a nation™s
falls. imports on its GDP,
Similarly, our exports are the imports of other countries, International trade lowers the value of the multiplier.
so it is to be expected that our exports depend on their
To see why, we begin with Table 6, which adapts the
GDPs, not on our own. Thus:
example of our hypothetical economy to allow im-
Our exports are relatively insensitive to our own GDP,
ports to depend on GDP. Columns 1 through 4 are the
but are quite sensitive to the GDPs of other countries.
same as in Table 1; they show C, I, and G at alternative
levels of GDP. Columns 5 and 6 record revised as-
This appendix derives the implications of these
sumptions about the behavior of exports and imports.
rather elementary observations. In particular, it shows


TA BL E 6
Equilibrium Income with Variable Imports

(1) (2) (3) (4) (5) (6) (7) (8)
Gross
Domestic Consumer Government Net Total
Product Expenditures Investment Purchases Exports Imports Exports Expenditure
(X 2 IM) (C 1 I 1 G 1 [X 2 IM])
(Y) (C) (I) (G) (X) (IM)
4,800 3,000 900 1,300 650 570 5,280
180
5,200 3,300 900 1,300 650 630 5,520
120
5,600 3,600 900 1,300 650 690 5,760
240
6,000 3,900 900 1,300 650 750 6,000
2100
6,400 4,200 900 1,300 650 810 6,240
2160
6,800 4,500 900 1,300 650 870 6,480
2220
7,200 4,800 900 1,300 650 930 6,720
2280
NOTE: Figures are in billions of dollars per year.




Exports are fixed at $650 billion regard-
FIGURE 13
less of GDP. But imports are assumed to
The Dependence of Net Exports on GDP
rise by $60 billion for every $400 billion
rise in GDP, which is a simple numerical
IM
950 example of the idea that imports depend
Real Exports and Imports




on GDP. Column 7 subtracts imports
850
from exports to get net exports, (X 2 IM),
Negative net
750 and column 8 adds up the four compo-
exports
nents of total expenditure, C 1 I 1 G 1
650 X
Positive net
(X 2 IM). The equilibrium, you can see,
exports
550
occurs at Y 5 $6,000 billion, just as it did
in the chapter.
450
Figures 13 and 14 display the same con-
clusion graphically. The upper panel of
0 4,800 5,200 5,600 6,000 6,400 6,800 7,200
Figure 13 shows that exports are fixed at
Real GDP
$650 billion regardless of GDP, whereas
imports increase as GDP rises, just as in
200 Table 6. The difference between exports
and imports, or net exports, is positive un-
Real Net Exports




100 Positive
Positive net
til GDP approaches $5,300 billion, and
net exports
exports
0
negative once GDP surpasses that amount.
4,800 5,200 6,000 6,400 6,800 7,200
The bottom panel of Figure 13 shows the
“100 Negative net
5,600
exports subtraction explicitly by displaying net ex-
“200
ports. It shows clearly that
“300
Net exports decline as GDP rises.
X “ IM

Real GDP Figure 14 carries this analysis over to
the 45° line diagram. We begin with the
familiar C 1 I 1 G 1 (X 2 IM) line in
NOTE: Figures are in billions of dollars per year.



Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
Licensed to:
Part 2
196 The Macroeconomy: Aggregate Supply and Demand



FIGURE 14 FIGURE 15
Equilibrium GDP with Variable Imports The Multiplier with Variable Imports

45
C + I + G + (X “ IM )
45 C + I + G + (X1 “ IM)
A
(fixed imports)
C + I + G + (X0 “ IM)
C + I + G + (X “ IM )
Rise in
(variable imports)
E




Real Expenditure
Real Expenditure




exports = $160
E




Positive net Rise in GDP = $400
Negative net exports
exports

6,000 6,400
X “ IM
6,000
Real GDP
Real GDP



TA BL E 7
Equilibrium Income after a $160 Billion Increase in Exports

(1) (2) (3) (4) (5) (6) (7) (8)
Gross
Domestic Consumer Government Net Total
Product Expenditures Investment Purchases Exports Imports Exports Expenditure
(X 2 IM) (C 1 I 1 G 1 [X 2 IM])
(Y) (C) (I) (G) (X) (IM)
4,800 3,000 900 1,300 810 570 5,440
1240
5,200 3,300 900 1,300 810 630 5,680
1180
5,600 3,600 900 1,300 810 690 5,920
1120
6,000 3,900 900 1,300 810 750 6,160
160
6,400 4,200 900 1,300 810 810 0 6,400
6,800 4,500 900 1,300 810 870 6,640
260
7,200 4,800 900 1,300 180 930 6,800
2120
NOTE: Figures are in billions of dollars per year.




black. Previously, we simply assumed that net exports This same conclusion is shown graphically in
Figure 15, where the line C 1 I 1 G 1 (X0 2 IM) repre-
were fixed at 2$100 billion regardless of GDP. Now
that we have amended our model to note that net sents the original expenditure schedule and the line
exports decline as GDP rises, the sum C 1 I 1 G 1 C 1 I 1 G 1 (X1 2 IM) represents the expenditure
(X 2 IM) rises more slowly than we previously as- schedule after the $160 billion increase in exports.
Equilibrium shifts from point E to point A, and GDP
sumed. This change is shown by the brick-colored
line. Note that it is less steep than the black line. rises by $400 billion.
Let us now consider what happens if exports rise Notice that the multiplier in this example is 2.5,
by $160 billion while imports remain as in Table 6. whereas in the chapter, with net exports taken to be a
Table 7 shows that equilibrium now occurs at a GDP fixed number, it was 4. This simple example illustrates
of Y 5 $6,400 billion. Naturally, higher exports have a general result: International trade lowers the numerical
value of the multiplier. Why is this so? Because, in an
raised domestic GDP. But consider the magnitude. A
$160 billion increase in exports (from $650 billion to open economy, any autonomous increase in spending
$810 billion) leads to an increase of $400 billion in GDP is partly dissipated in purchases of foreign goods,
which creates additional income for foreigners rather
(from $6,000 billion to $6,400 billion). So the multiplier
is 2.5 (5 $400/$160).9 than for domestic citizens.
Thus, international trade gives us the first of what
will eventually be several reasons why the oversimpli-
Exercise: Construct a version of Table 6 to show what would hap-
9
fied multiplier formula overstates the true value of the
pen if imports rose by $160 billion at every level of GDP while ex-
multiplier.
ports remained at $650 billion. You should be able to show that the
new equilibrium would be Y 5 $5,600.




Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
Licensed to:

Chapter 9 197
Demand-Side Equilibrium: Unemployment or Inflation?



| SUMMARY |
1. Because imports rise as GDP rises, while exports are 2. If imports depend on GDP, international trade reduces
insensitive to (domestic) GDP, net exports decline as the value of the multiplier.
GDP rises.




| TEST YOURSELF |
1. Suppose exports and imports of a country are given by shown in the following table, construct a 45° line dia-
the following: gram and locate the equilibrium level of GDP.

GDP Exports Imports Domestic
GDP Expenditures
$2,500 $400 $250
3,000 400 300 $2,500 $3,100
3,500 400 350 3,000 3,400
4,000 400 400 3,500 3,700

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