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Notice how this result can be generalized. If we did not have a specific number for the
marginal propensity to consume, but simply called it MPC, the geometric progression in
Table 4 would have been
1 1 MPC 1 1 MPC 2 2 1 1 MPC 2 3 1 . . .
This progression uses the MPC as its common ratio. Applying the same formula for sum-
ming a geometric progression to this more general case gives us the following general result:
Oversimplified Multiplier Formula
1
Multiplier 5
1 2 MPC
We call this formula “oversimplified” because it ignores many factors that are impor-
tant in the real world. You can begin to appreciate just how unrealistic the oversimpli-
fied formula is by considering some real numbers for the U.S. economy. The MPC is
over 0.95. From our oversimplified formula, then, it would seem that the multiplier
should be at least
1 1
Multiplier 5 5 20
5
1 2 0.95 0.05
In fact, the actual multiplier for the U.S. economy is less than 2. That is quite a discrepancy!


Students who blanch at the sight of algebra should not be put off. Anyone who can balance a checkbook (even
5

many who cannot!) will be able to follow the argument.
If R exceeds 1, no one can possibly sum it”not even with the aid of a modern computer”because the sum is
6

not a finite number.
The proof of the formula is simple. Let the symbol S stand for the (unknown) sum of the series:
7

S 5 1 1 R 1 R2 1 R3 1 . . .
Then, multiplying by R,
RS 5 R 1 R2 1 R3 1 R4 1 . . .
By subtracting RS from S, we obtain
1
S 2 RS 5 1 or S 5
12R


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Chapter 9 189
Demand-Side Equilibrium: Unemployment or Inflation?



But this discrepancy does not mean that anything we have said about the multiplier so
far is incorrect. Our story is simply incomplete. As we progress through this and subse-
quent chapters, you will learn why the multiplier in the United States is less than 2 even
though the country™s MPC is over 0.95. One such reason relates to international trade”in
particular, the fact that a country™s imports depend on its GDP. We deal with this compli-
cation in Appendix B to this chapter. A second factor is inflation, a complication we will
address in the next chapter. A third factor is income taxation, a point we will elaborate in
Chapter 11. The last important reason arises from the financial system and, after we discuss
money and banking in Chapters 12 and 13, we will explain in Chapter 14 how the finan-
cial system influences the multiplier. As you will see, each of these factors reduces the size
of the multiplier. So:
Although the multiplier is larger than 1 in the real world, it cannot be calculated accu-
rately with the oversimplified multiplier formula. The actual multiplier is much lower
than the formula suggests.




THE MULTIPLIER IS A GENERAL CONCEPT
Although we have used business investment to illustrate the workings of the multiplier, it
should be clear from the logic that any increase in spending can kick off a multiplier chain.
To see how the multiplier works when the process is initiated by an upsurge in consumer
spending, we must distinguish between two types of change in consumer spending.
To do so, look back at Figure 4 on page 181. When C rises because income rises”that
is, when consumers move outward along a fixed consumption function”we call the increase An induced increase
in C an induced increase in consumption. (See the brick-colored arrows in the figure.) in consumption is an
When C rises because the entire consumption function shifts upward (such as from C0 to C2 increase in consumer
in the figure), we call it an autonomous increase in consumption. The name indicates that spending that stems from
consumption changes independently of income. The discussion of the consumption func- an increase in consumer in-
tion in Chapter 8 pointed out that a number of events, such as a change in the value of the comes. It is represented on
a graph as a movement
stock market, can initiate such a shift.
along a fixed consumption
If consumer spending were to rise autonomously by $200 billion, we would revise our function.
table of aggregate demand to look like Table 5. Comparing this new table to Table 3, we
note that each entry in column 2 is $200 billion higher than the corresponding entry in An autonomous increase
Table 3 (because consumption is higher), and each entry in column 3 is $200 billion lower in consumption is an in-
crease in consumer spend-
(because in this case investment is only $900 billion).
ing without any increase in
Column 6, the expenditure schedule, is identical in both tables, so the equilibrium level consumer incomes. It is
of income is clearly Y 5 $6,800 billion once again. The initial rise of $200 billion in con- represented on a graph
sumer spending leads to an eventual rise of $800 billion in GDP, just as it did in the case of as a shift of the entire
higher investment spending. In fact, Figure 10 (page 186) applies directly to this case once consumption function.
we note that the upward shift is now caused by an au-
tonomous change in C rather than in I. The multiplier TA BL E 5
for autonomous changes in consumer spending, then, Total Expenditure after Consumers Decide to Spend
is also 4 (5 $800/$200). $200 Billion More
The reason is straightforward. It does not matter
(1) (2) (3) (4) (5) (6)
who injects an additional dollar of spending into the
Government
economy”business investors or consumers. Whatever
Income Consumption Investment Purchases Net Exports Total
the source of the extra dollar, 75 percent of it will be (X 2 IM) Expenditure
(Y) (C) (I) (G)
respent if the MPC is 0.75, and the recipients of this
4,800 3,200 900 1,300 5,300
2100
second round of spending will, in turn, spend 75 per-
5,200 3,500 900 1,300 5,600
2100
cent of their additional income, and so on. That contin- 5,600 3,800 900 1,300 5,900
2100
ued spending constitutes the multiplier process. Thus 6,000 4,100 900 1,300 6,200
2100
6,400 4,400 900 1,300 6,500
a $200 billion increase in government purchases (G) or 2100
6,800 4,700 900 1,300 6,800
2100
in net exports (X 2 IM) would have the same multi-
7,200 5,000 900 1,300 7,100
2100
plier effect as depicted in Figure 10. The multipliers
are identical because the logic behind them is identical. NOTE: Figures are in billions of dollars per year.




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Part 2
190 The Macroeconomy: Aggregate Supply and Demand



The idea that changes in G have multiplier effects on GDP will play a central role in the
discussion of government stabilization policy that begins in Chapter 11. So it is worth not-
ing here that
Changes in the volume of government purchases of goods and services will change the
equilibrium level of GDP on the demand side in the same direction, but by a multiplied
amount.
To cite a recent example, heavy federal government spending on the war in Iraq since
2003 has boosted the G component of C 1 I 1 G 1 (X 2 IM), which had a multiplier effect
on GDP.
Applying the same multiplier idea to exports and imports teaches us another important
lesson: Booms and recessions tend to be transmitted across national borders. Why is that? Sup-
pose a boom abroad raises GDPs in foreign countries. With rising incomes, foreigners will
buy more American goods”which means that U.S. exports will increase. But an increase
FIGURE 12
in our exports will, via the multiplier, raise GDP in the United States. By this mechanism,
Two View of the
rapid economic growth abroad con-
Multiplier
tributes to rapid economic growth here.
And, of course, the same mechanism
45°
also operates in reverse. Thus:
C + I1 + G + (X “ IM)
The GDPs of the major economies
are linked by trade. A boom in one
C + I0 + G + (X “ IM)
E1
country tends to raise its imports and
hence push up exports and GDP in
Real Expenditure




other countries. Similarly, a recession
in one country tends to pull down
GDP in other countries.
$200 billion

E0
THE MULTIPLIER AND
THE AGGREGATE
DEMAND CURVE
One last mechanical point about the mul-
0 6,000 6,800
tiplier: Recall that income-expenditure
diagrams such as Figure 3 (page 179) can
be drawn only for a given price level.
Different price levels lead to different to-
D0 D1
tal expenditure curves. This means that
our oversimplified multiplier formula in-
dicates the increase in real GDP demanded
that would occur if the price level were fixed.
Graphically, this means that it measures
Price Level




the horizontal shift of the economy™s ag-
gregate demand curve.
E0 E1
Figure 12 illustrates this conclusion
100
by supposing that the price level that
D1 (I = $1,100)
underlies Figure 3 is P 5 100. The top
panel simply repeats Figure 10 (page
D0 (I = $900)
186) and shows how an increase in in-
vestment spending from $900 to $1,100
billion leads to an increase in GDP from
6,000 6,800
$6,000 to $6,800 billion.
The bottom panel shows two
Real GDP
downward-sloping aggregate demand
curves. The first, labeled D0D0, depicts
NOTE: Figures are in billions of dollars per year.




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Licensed to:

Chapter 9 191
Demand-Side Equilibrium: Unemployment or Inflation?



the situation when investment is $900 billion. Point E0 on this curve corresponds exactly
to point E0 in the top panel. It indicates that, at the given price level (P 5 100), the equilib-
rium quantity of GDP demanded is $6,000 billion. The second aggregate demand curve,
D1D1, depicts the situation after investment has risen to $1,100 billion. Point E1 on this
curve indicates that the equilibrium quantity of GDP demanded when P 5 100 has risen
to $6,800 billion, which corresponds exactly to point E1 in the top panel.
As Figure 12 shows, the horizontal distance between the two aggregate demand curves
is exactly equal to the increase in real GDP shown in the income-expenditure diagram”in
this case, $800 billion. Thus:
An autonomous increase in spending leads to a horizontal shift of the aggregate
demand curve by an amount given by the oversimplified multiplier formula.
So everything we have just learned about the multiplier applies to shifts of the economy™s
aggregate demand curve. If businesses decide to increase their investment spending, if the
consumption function shifts upward, or if the government or foreigners decide to buy
more goods, then the aggregate demand curve moves horizontally to the right”as indi-
cated in Figure 12. If any of these variables moves downward instead, the aggregate
demand curve moves horizontally to the left.
Thus, the economy™s aggregate demand curve cannot be expected to stand still for long.
Autonomous changes in one or another of the four components of total spending will
cause it to move around. But to understand the consequences of such shifts of aggregate de-
mand, we must bring the aggregate supply curve back into the picture. That is the task for
the next chapter.



| SUMMARY |
1. The equilibrium level of GDP on the demand side is 7. Equilibrium GDP can be above or below potential GDP,
the level at which total spending just equals production. which is defined as the GDP that would be produced if
Because total spending is the sum of consumption, in- the labor force were fully employed.
vestment, government purchases, and net exports, the 8. If equilibrium GDP exceeds potential GDP, the differ-
condition for equilibrium is Y 5 C 1 I 1 G 1 (X 2 IM). ence is called an inflationary gap. If equilibrium GDP
2. Output levels below equilibrium are bound to rise be- falls short of potential GDP, the resulting difference is
cause when spending exceeds output, firms will see called a recessionary gap.
their inventory stocks being depleted and will react by 9. Such gaps can occur because of the problem of coordi-
stepping up production. nation failure: The saving that consumers want to do at
3. Output levels above equilibrium are bound to fall be- full-employment income levels may differ from the in-
cause when total spending is insufficient to absorb total vesting that investors want to do.
output, inventories will pile up and firms will react by 10. Any autonomous increase in expenditure has a multi-
curtailing production. plier effect on GDP; that is, it increases GDP by more
4. The determination of the equilibrium level of GDP on than the original increase in spending.
the demand side can be portrayed on a convenient 11. The multiplier effect occurs because one person™s addi-
income-expenditure diagram as the point at which the tional expenditure constitutes a new source of income

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