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SOURCE: © Thinkstock Images/Jupiterimages
Picture a crowd watching a football game. Now something ex-
citing happens and the fans rise from their seats. People in the
front rows begin standing first, and those seated behind them are
forced to stand if they want to see the game. Soon everyone in the
stadium is on their feet.
But with everyone standing, no one can see any better than
when everyone was sitting. And the fans are enduring the further
discomfort of being on their feet. (Never mind that stadium seats
are uncomfortable!) Everyone in the stadium would be better off
if everyone sat down, which sometimes happens. But the crowd
rises to its feet again on every exciting play. There is simply no way
to coordinate the individual decisions of tens of thousands of
football fans. The coordination failure idea also helps to explain why it is so
Unemployment poses a similar coordination problem. During a difficult to stop inflation. Virtually everyone prefers stable prices to
deep recession, workers are unemployed and businesses cannot rising prices. But now think of yourself as the seller of a product. If
sell their wares. Figuratively speaking, everyone is “standing” and all other participants in the economy would hold their prices
unhappy about it. If only the firms could agree to hire more work- steady, you would happily hold yours steady, too. But, if you believe
ers, those newly employed people could afford to buy more of the that others will continue to raise their prices at a rate of, say, 5 per-
goods and services the firms want to produce. But, as at the foot- cent per year, you may find it dangerous not to increase your prices
ball stadium, there is no central authority to coordinate these apace. Hence, society may get stuck with 5 percent inflation even
millions of decisions. though everyone agrees that zero inflation is better.




CHANGES ON THE DEMAND SIDE: MULTIPLIER ANALYSIS
We have just learned how demand-side equilibrium depends on the consumption func-
tion and on the amounts spent on investment, government purchases, and net exports.
The multiplier is the ratio
But none of these is a constant of nature; they all change from time to time. How does of the change in equilibrium
equilibrium GDP change when the consumption function shifts or when I, G, or (X 2 IM) GDP (Y) divided by the orig-
changes? As we will see now, the answer is simple: by more! A remarkable result called the inal change in spending that
multiplier says that a change in spending will bring about an even larger change in causes the change in GDP.
equilibrium GDP on the demand side. Let us see why.
TA BL E 3
The Magic of the Multiplier Total Expenditure after a $200 Billion Increase
in Investment Spending
Because it is subject to abrupt swings, investment spend-
(1) (2) (3) (4) (5) (6)
ing often causes business fluctuations in the United
Government Net
States and elsewhere. So let us ask what would happen
Income Consumption Investment Purchases Exports Total
if firms suddenly decided to spend more on investment (X 2 IM) Expenditure
(Y) (C) (I) (G)
goods. As we will see next, such a decision would have
4,800 3,000 1,100 1,300 5,300
2100
a multiplied effect on GDP, that is, each $1 of additional
5,200 3,300 1,100 1,300 5,600
2100
investment spending would add more than $1 to GDP. 5,600 3,600 1,100 1,300 5,900
2100
To see why, refer first to Table 3, which looks very 6,000 3,900 1,100 1,300 6,200
2100
much like Table 1. The only difference is that we now as- 6,400 4,200 1,100 1,300 6,500
2100
6,800 4,500 1,100 1,300 6,800
2100
sume that firms want to invest $200 billion more than
7,200 4,800 1,100 1,300 7,100
2100
previously”for a total of $1,100 billion. As indicated by
the blue numbers, only income level Y 5 $6,800 billion is NOTE: Figures are in billions of dollars per year.




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Part 2
186 The Macroeconomy: Aggregate Supply and Demand



an equilibrium on the demand side of the economy now, because only at this level is total
spending, C 1 I 1 G 1 (X 2 IM), equal to production (Y).
The multiplier principle says that GDP will rise by more than the $200 billion increase in
investment. Specifically, the multiplier is defined as the ratio of the change in equilibrium
GDP (Y) to the original change in spending that caused GDP to change. In shorthand,
when we deal with the multiplier for investment (I), the formula is
Change in Y
Multiplier 5
Change in I
Let us verify that the multiplier is, indeed, greater than 1. Table 3 shows how the new
expenditure schedule is constructed by adding up C, I, G, and (X 2 IM) at each level of Y,
just as we did earlier”only now I is $1,100 billion rather than $900 billion. If you compare
the last columns of Table 1 (page 178) and Table 3 (page 185), you will see that the new
FIGURE 10 expenditure schedule lies uniformly above the old one by $200 billion.
Illustration of the
Figure 10 depicts this change graphically.
Multiplier
The curve marked C 1 I0 1 G 1 (X 2 IM) is
derived from the last column of Table 1,
45°
while the higher curve marked C 1 I1 1 G 1
C + I1 + G + (X “ IM ) (X 2 IM) is derived from the last column of
Table 3. The two expenditure lines are paral-
C + I0 + G + (X “ IM )
E1
lel and $200 billion apart.
So far things look just as you might ex-
Real Expenditure




pect. But one more step will bring the multi-
plier rabbit out of the hat. Let us see what
the upward shift of the expenditure line
does to equilibrium income. In Figure 10,
$200 billion
equilibrium moves outward from point E0
E0
to point E1, or from $6,000 billion to $6,800
billion. The difference is an increase of $800
billion in GDP. All this from a $200 billion
stimulus to investment? That is the magic of
the multiplier.
Because the change in I is $200 billion and
0 6,000 6,800
the change in equilibrium Y is $800 billion,
Real GDP
by applying our definition, the multiplier is
NOTE: Figures are in billions of dollars per year.
Change in Y $800
Multiplier 5 54
5
Change in I $200

This tells us that, in our example, each additional $1 of investment demand will add $4 to
equilibrium GDP!
This result does, indeed, seem mysterious. Can something be created from nothing?
Let™s first check that the graph has not deceived us. The first and last columns of Table 3
show in numbers what Figure 10 shows graphically. Notice that equilibrium now comes
at Y 5 $6,800 billion, because only at that point is total expenditure equal to production
(Y). This equilibrium level of GDP is $800 billion higher than the $6,000 billion level found
when investment was $200 billion lower. Thus, a $200 billion rise in investment does
indeed lead to an $800 billion rise in equilibrium GDP. The multiplier really is 4.


Demystifying the Multiplier: How It Works
The multiplier result seems strange at first, but it loses its mystery once we recall the cir-
cular flow of income and expenditure and the simple fact that one person™s spending is
another person™s income. To illustrate the logic of the multiplier and see why it is exactly
4 in our example, think about what happens when businesses decide to spend $1 million
on investment goods.



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Licensed to:

Chapter 9 187
Demand-Side Equilibrium: Unemployment or Inflation?



Suppose that Microhard”a major corporation in our hypothetical country”decides to
spend $1 million on a new office building. Its $1 million expenditure goes to construction
workers and owners of construction companies as wages and profits. That is, the $1 million
becomes their income.
But the construction firm™s owners and workers will not keep all of their $1 million in
the bank; instead, they will spend most of it. If they are “typical” consumers, their spend-
ing will be $1 million times the marginal propensity to consume (MPC). In our example,
the MPC is 0.75, so assume they spend $750,000 and save the rest. This $750,000 expendi-
ture is a net addition to the nation™s demand for goods and services, just as Microhard™s original
$1 million expenditure was. So, at this stage, the $1 million investment has already pushed
GDP up by some $1.75 million. But the process is by no means over.
Shopkeepers receive the $750,000 spent by construction workers, and TA BL E 4
they in turn also spend 75 percent of their new income. This activity ac- The Multiplier Spending Chain
counts for $562,500 (75 percent of $750,000) in additional consumer
(1) (2) (3)
spending in the “third round.” Next follows a fourth round in which the
Round Spending in Cumulative
recipients of the $562,500 spend 75 percent of this amount, or $421,875,
Number This Round Total
and so on. At each stage in the spending chain, people spend 75 percent
1 $1,000,000 $1,000,000
of the additional income they receive, and the process continues”with
2 750,000 1,750,000
consumption growing in every round.
3 562,500 2,312,500
Where does it all end? Does it all end? The answer is that, yes, it does 4 421,875 2,734,375
eventually end”with GDP a total of $4 million higher than it was before 5 316,406 3,050,781
Microhard built the original $1 million office building. The multiplier is 6 237,305 3,288,086
7 177,979 3,466,065
indeed 4.
8 133,484 3,599,549
Table 4 displays the basis for this conclusion. In the table, “Round 1”
9 100,113 3,699,662
represents Microhard™s initial investment, which creates $1 million in in- 10 75,085 3,774,747
come for construction workers. “Round 2” represents the construction o o o
workers™ spending, which creates $750,000 in income for shopkeepers. The 20 4,228 3,987,317
o o o
rest of the table proceeds accordingly; each entry in column 2 is 75 percent
“Infinity” 0 4,000,000
of the previous entry. Column 3 tabulates the running sum of column 2.
We see that after 10 rounds of spending, the initial $1 million invest-
ment has mushroomed to $3.77 million”and the sum is still growing. After 20 rounds,
the total increase in GDP is over $3.98 million”near its eventual value of $4 million. Al-
though it takes quite a few rounds of spending before the multiplier chain nears 4, we
see from the table that it hits 3 rather quickly. If each income recipient in the chain waits,
say, two months before spending his new income, the multiplier will reach 3 in only FIGURE 11
about ten months.
How the Multiplier
Figure 11 provides a graphical presentation of the Builds
numbers in the last column of Table 4. Notice how the
multiplier builds up rapidly at first and then tapers
off to approach its ultimate value (4 in this example) $4.0
gradually.
And, of course, all this operates exactly the same”
Cumulative Spending Total




but in the opposite direction”when spending falls. 3.0
For example, when the boom in housing in America
ended in 2005 and 2006, spending on new houses be-
gan to decline. As this process progressed, the slow- 2.0
down in housing created a negative multiplier effect
on everything from appliances and furniture to carpet-
ing and insulation. Indeed, the big macroeconomic 1.0
concern in 2007 and 2008 was whether housing would
“pull” the whole economy into a recession.
0 2 4 6 8 10 15 20
Algebraic Statement of the Multiplier Spending Round
Figure 11 and Table 4 probably make a persuasive case
that the multiplier eventually reaches 4. But for the NOTE: Amounts are in millions of dollars.




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Licensed to:
Part 2
188 The Macroeconomy: Aggregate Supply and Demand



remaining skeptics, we offer a simple algebraic proof.5 Most of you learned about some-
thing called an infinite geometric progression in high school. This term refers to an infinite
series of numbers, each one of which is a fixed fraction of the previous one. The fraction is
called the common ratio. A geometric progression beginning with 1 and having a common
ratio of 0.75 looks like this:
1 1 0.75 1 1 0.75 2 2 1 1 0.75 2 3 1 . . .
More generally, a geometric progression beginning with 1 and having a common ratio R
would be
1 1 R 1 R2 1 R3 1 . . .
A simple formula enables us to sum such a progression as long as R is less than 1.6 The
formula is7
1
Sum of infinite geometric progression 5
12R
We now recognize that the multiplier chain in Table 4 is just an infinite geometric pro-
gression with 0.75 as its common ratio. That is, each $1 that Microhard spends leads to a
(0.75) 3 $1 expenditure by construction workers, which in turn leads to a (0.75) 3 (0.75 3
$1) 5 (0.75)2 3 $1 expenditure by the shopkeepers, and so on. Thus, for each initial dollar
of investment spending, the progression is
1 1 0.75 1 1 0.75 2 2 1 1 0.75 2 3 1 1 0.75 2 4 1 . . .
Applying the formula for the sum of such a series, we find that
1 1
Multiplier 5 54
5
1 2 0.75 0.25

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