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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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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