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CHAPTER
25
AGGREGATE DEMAND AND
OUTPUT IN THE SHORT RUN
■
hen one of the authors of this book was a small boy, he used to
spend some time every summer with his grandparents, who lived a
few hours from his home. A favorite activity of his during these visits was to spend a summer evening on the front porch with his grandmother,
listening to her stories. For some reason Grandma’s recounting of her own life
was particularly fascinating to her grandson.
Grandma had spent the early years of her marriage in New England during the worst part of the Great Depression. In one of her reminiscences she
remarked that at that time, in the mid-1930s, it had been a satisfaction to her
to be able to buy her children a new pair of shoes every year. In the small
town where she and her family lived, many children had to wear their shoes
until they fell apart, and a few unlucky boys and girls went to school barefoot. Her grandson thought this was scandalous: “Why didn’t their parents
just buy them new shoes?” he demanded.
“They couldn’t,” said Grandma. “They didn’t have the money. Most of
the fathers had lost their jobs because of the Depression.”
“What kind of jobs did they have?”
“They worked in the shoe factories, which had to close down.”
“Why did the factories close down?”
“Because,” Grandma explained, “nobody had any money to buy shoes.”
The grandson was only 6 or 7 years old at the time, but even he could
see that there was something badly wrong with Grandma’s logic. On the one
side were boarded-up shoe factories and shoe workers with no jobs; on the
other, children without shoes. Why couldn’t the shoe factories just open and
W
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CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
produce the shoes the children so badly needed? He made his point quite firmly,
but Grandma just shrugged and said it didn’t work that way.
The story of the closed-down shoe factories illustrates in a microcosm the
cost to society of an output gap. In an economy with a recessionary gap, available resources that could in principle be used to produce valuable goods and services are instead allowed to lie fallow. This waste of resources lowers the economy’s output and economic welfare, compared to its potential.
Grandma’s account also suggests how such an unfortunate situation might
come about. Suppose factory owners and other producers, being reluctant to
accumulate unsold goods on their shelves, produce just enough output to satisfy
the demand for their products. And suppose that for some reason the public’s
willingness or ability to spend declines. If spending declines, factories will respond
by cutting their production (because they don’t want to produce goods they can’t
sell) and by laying off workers who are no longer needed. And because the workers who are laid off will lose most of their income—a particularly serious loss in
the 1930s, in the days before government-sponsored unemployment insurance—
they must reduce their own spending. As their spending declines, factories will
reduce their production again, laying off more workers, who in turn reduce their
spending, and so on, in a vicious circle. In this scenario, the problem is not a
lack of productive capacity—the factories have not lost their ability to produce—
but rather insufficient spending to support the normal level of production.
The idea that a decline in aggregate spending may cause output to fall below
potential output was one of the key insights of John Maynard Keynes, a highly
influential British economist of the first half of the twentieth century. Box 25.1
gives a brief account of Keynes’s life and ideas. The goal of this chapter is to
BOX 25.1: JOHN MAYNARD KEYNES AND THE KEYNESIAN
REVOLUTION
John Maynard Keynes (1883–1946), perhaps the most influential economist of the twentieth century, was a remarkable individual who combined a brilliant career as an economic theorist with an active life in
diplomacy, finance, journalism, and the arts. Keynes (pronounced
“canes”) first came to prominence at the end of World War I when he
attended the Versailles peace conference as a representative of the British
Treasury. He was appalled by the shortsightedness of the diplomats at
the conference, particularly their insistence that the defeated Germans
make huge compensatory payments (called reparations) to the victorious
nations. In his widely read book The Economic Consequences of the
Peace (1919), Keynes argued that the reparations imposed on Germany
were impossibly large and that attempts to extract the payments would
prevent Germany’s economic recovery and perhaps lead to another war.
Unfortunately for the world, he turned out to be right.
In the period between the two world wars, Keynes held a professorship
at Cambridge, where his father had taught economics. Keynes’s early writings had been on mathematics and logic, but after his experience in Versailles he began to work primarily on economics, producing several wellregarded books. He developed an imposing intellectual reputation, editing
Great Britain’s leading scholarly journal in economics, writing articles for
newspapers and magazines, advising the government, and playing a major
role in the political and economic debates of the day. On the side, Keynes
made fortunes both for himself and for King’s College (a part of Cambridge
University) by speculating in international currencies and commodities. He
was also an active member of the Bloomsbury Group, a circle of leading
artists, performers, and writers that included E. M. Forster and Virginia
JOHN MAYNARD KEYNES AND THE KEYNESIAN REVOLUTION
657
Woolf. In 1925 Keynes married the glamorous Russian ballerina Lydia
Lopokova. Theirs was by all accounts a very successful marriage, and
Keynes devoted significant energies to managing his wife’s career and promoting the arts in Britain.
Like other economists of the time, Keynes struggled to understand the Great
Depression that gripped the world in the 1930s. His work on the problem led
to the publication in 1936 of The General Theory of Employment, Interest,
and Money. In The General Theory, Keynes tried to explain how economies
can remain at low levels of output and employment for protracted periods.
He stressed a number of factors, most notably that aggregate spending may
be too low to permit full employment during such periods. Keynes recommended increases in government spending as the most effective way to increase
aggregate spending and restore full employment.
The General Theory is a difficult book, reflecting Keynes’s own struggle to
understand the complex causes of the Depression. In retrospect, some of The
General Theory’s arguments seem unclear or even inconsistent. Yet the book
is full of fertile ideas, many of which had a worldwide impact and eventually
led to what has been called the Keynesian revolution. Over the years many
economists have added to or modified Keynes’s conception, to the point that
Keynes himself, were he alive today, probably would not recognize much of
what is now called Keynesian economics. But the ideas that insufficient aggregate spending can lead to recession and that government policies can help to
restore full employment are still critical to Keynesian theory.
In 1937 a heart attack curtailed Keynes’s activities, but he remained an
important figure on the world scene. In 1944 he led the British delegation
to the international conference in Bretton Woods, New Hampshire, which
established the key elements of the postwar international monetary and
financial system, including the International Monetary Fund and the World
Bank. Keynes died in 1946.
© Bettman/Corbis
develop a model of how recessions and expansions may arise from fluctuations
in aggregate spending, along the lines first suggested by Keynes. This model,
which we call the basic Keynesian model, is also known as the Keynesian cross,
after the diagram that is used to illustrate the theory. In the body of the chapter
we will emphasize a numerical and graphical approach to the basic Keynesian
model. The appendix to this chapter provides a more general algebraic analysis.
We will begin with a brief discussion of the key assumptions of the basic
Keynesian model. We will then turn to the important concept of aggregate demand,
or total planned spending in the economy. We will show how, in the short run,
aggregate demand helps to determine the level of output, which can be greater than
or less than potential output. In other words, depending on the level of spending,
the economy may develop an output gap. “Too little” spending leads to a recessionary output gap, while “too much” creates an expansionary output gap.
An implication of the basic Keynesian model is that government policies that
affect the level of spending can be used to reduce or eliminate output gaps. Policies used in this way are called stabilization policies. Keynes himself argued for the
active use of fiscal policy—policy relating to government spending and taxes—to
eliminate output gaps and stabilize the economy. In the latter part of this chapter
we will show why Keynes thought fiscal policy could help to stabilize the economy, and we will discuss the usefulness of fiscal policy as a stabilization tool.
As we foreshadowed in Chapter 24, the basic Keynesian model is not a complete or entirely realistic model of the economy, since it applies only to the short
period during which firms do not adjust their prices but instead meet the demand
forthcoming at preset prices. Furthermore, by treating prices as fixed, the basic
Keynesian model presented in this chapter does not address the determination of
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CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
inflation. Nevertheless, this model is a key building block of current theories of
short-run economic fluctuations and stabilization policies. In subsequent chapters
we will extend the basic Keynesian model to incorporate inflation and other
important features of the economy.
THE BASIC KEYNESIAN MODEL
The basic Keynesian model, on which we will focus in this chapter, is built on
two key assumptions, given below. Of these two assumptions, the second—
that, in the short run, firms meet the demand for their products at preset
prices—is the crucial one. As we will see in this chapter, if firms respond to
changes in demand primarily by changing their production levels instead of
their prices, then changes in aggregate spending will have a powerful effect on
aggregate output.
KEY ASSUMPTIONS OF THE BASIC KEYNESIAN MODEL
1. Aggregate demand fluctuates. Total planned spending in an economy, called
aggregate demand, depends on the prevailing level of real GDP as well as
other factors. Changes in either real GDP or in other factors that affect total
spending will cause aggregate demand to fluctuate.
2. In the short run, firms meet the demand for their products at preset prices.
Firms do not respond to every change in the demand for their products by
changing their prices. Instead, they typically set a price for some period, then
meet the demand at that price. By “meeting the demand,” we mean that firms
produce just enough to satisfy their customers.
menu costs the costs of
changing prices
The assumption that over short periods of time firms will meet the demand
for their products at preset prices is generally realistic. Think of the stores where
you shop: The price of a pair of jeans does not fluctuate with the number of customers who enter the store or the latest news about the price of denim. Instead,
the store posts a price and sells jeans to any customer who wants to buy at that
price, at least until the store runs out of stock. Similarly, the corner pizza restaurant may leave the price of its large pie unchanged for months or longer, allowing its pizza production to be determined by the number of customers who want
to buy at the preset price.
Firms do not change their prices frequently because doing so would be costly.
Economists refer to the costs of changing prices as menu costs. In the case of the
pizza restaurant, the menu cost is literally just that—the cost of printing up a
new menu when prices change. Similarly, the clothing store faces the cost of remarking all its merchandise if the manager changes prices. But menu costs may
also include other kinds of costs, including, for example, the cost of doing a market survey to determine what price to charge and the cost of informing customers
about price changes.
Menu costs will not prevent firms from changing their prices indefinitely. As
we saw in Chapter 24 for the case of Al’s ice cream store, too great an imbalance between demand and supply, as reflected by a difference between sales and
potential output, will eventually lead to a change in price. If no one is buying
jeans, for example, at some point the clothing store will mark down their jeans
prices. Or if the pizza restaurant becomes the local hot spot, with a line of customers stretching out the door, eventually the manager will raise the price of a
large pie. Like other economic decisions, the decision to change prices reflects a
cost-benefit comparison: Prices should be changed if the benefit of doing so—
the fact that sales will be brought more nearly in line with the firm’s normal
production capacity—outweighs the menu costs associated with making the
change. As we have stressed, the basic Keynesian model developed in this chapter
AGGREGATE DEMAND
ignores the fact that prices will eventually adjust, and should therefore be interpreted as applying to the short run.
AGGREGATE DEMAND
In the Keynesian theory discussed in this chapter, output at each point in time is
determined by the amount that people want to spend—what economists call
aggregate demand. Specifically, aggregate demand (AD) is total planned spending
on final goods and services.
The four components of total, or aggregate, spending on final goods and services were introduced in Chapter 18:
1. Consumer expenditure, or simply consumption (C), is spending by households on final goods and services. Examples of consumer expenditure are
spending on food, clothes, and entertainment, and on consumer durable
goods like automobiles and furniture.
2. Investment (I) is spending by firms on new capital goods, such as office buildings, factories, and equipment. Spending on new houses and apartment buildings (residential investment) and increases in inventories (inventory investment) are also included in investment.
3. Government purchases (G) is spending by governments (federal, state, and
local) on goods and services. Examples of government purchases include new
schools and hospitals, military hardware, equipment for the space program,
and the services of government employees, such as soldiers, police, and government office workers. Recall from Chapter 18 that transfer payments, such
as Social Security benefits and unemployment insurance, and interest on the
government debt are not included in government purchases.
4. Net exports (NX) equals exports minus imports. Exports are sales of domestically produced goods and services to foreigners; imports are purchases by
domestic residents of goods and services produced abroad. Net exports represents the net demand for domestic goods by foreigners.
Together these four types of spending—by households, firms, the government,
and the rest of the world—sum to total, or aggregate, spending.
PLANNED SPENDING VERSUS ACTUAL SPENDING
Aggregate demand, we have just noted, equals total planned spending. Could
planned spending ever differ from actual spending? The answer is yes. The most
important case is that of a firm that sells either less or more of its product than
expected. As was noted in Chapter 18, additions to the stocks of goods sitting
in a firm’s warehouse are treated in official government statistics as inventory
investment by the firm. In effect, government statisticians assume that the firm
buys its unsold output from itself; they then count those purchases as part of the
firm’s investment spending.1
Suppose, then, that a firm’s actual sales are less than expected so that part of
what it had planned to sell remains in the warehouse. In this case, the firm’s actual
investment, including the unexpected increases in its inventory, is greater than its
planned investment, which did not include added inventory. Suppose we agree to
let I p equal the firm’s planned investment, including planned inventory investment.
A firm that sells less of its output than planned, and therefore adds more to its
inventory than planned, will find that its actual investment (including unplanned
inventory investment) exceeds its planned investment so that I I p.
1
For the purposes of measuring GDP, treating unsold output as being purchased by its producer has
the virtue of ensuring that actual production and actual expenditure are equal.
aggregate demand (AD) total
planned spending on final goods
and services
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CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
What about a firm that sells more of its output than expected? In that case,
the firm will add less to its inventory than it planned, so actual investment will
be less than planned investment, or I I p. Example 25.1 gives a numerical illustration.
EXAMPLE 25.1
Actual and planned investment
The Fly-by-Night Kite Company produces $5,000,000 worth of kites during the
year. It expects sales of $4,800,000 for the year, leaving $200,000 worth of kites
to be stored in the warehouse for future sale. During the year, Fly-by-Night adds
$1,000,000 in new production equipment as part of an expansion plan. Find Flyby-Night’s actual investment I and its planned investment I p if actual kite sales
turn out to be $4,600,000. What if sales are $4,800,000? What if they are
$5,000,000?
Fly-by-Night’s planned investment I p equals its purchases of new production
equipment ($1,000,000) plus its planned additions to inventory ($200,000), for
a total of $1,200,000 in planned investment. The company’s planned investment
does not depend on how much it actually sells.
If Fly-by-Night sells only $4,600,000 worth of kites, it will add $400,000 in
kites to its inventory instead of the $200,000 worth originally planned. In this case,
actual investment equals the $1,000,000 in new equipment plus the $400,000 in
inventory investment, so I $1,400,000. We see that when the firm sells less output than planned, actual investment exceeds planned investment (I I p).
If Fly-by-Night has $4,800,000 in sales, then it will add $200,000 in kites to
inventory, just as planned. In this case, actual and planned investment are the
same: I I p $1,200,000.
Finally, if Fly-by-Night sells $5,000,000 worth of kites, it will have no output to add to inventory. Its inventory investment will be zero, and its total actual
investment (including the new equipment) will equal $1,000,000, which is less
than its planned investment of $1,200,000 ( I I p).
Because firms that are meeting the demand for their product or service at preset prices cannot control how much they sell, their actual investment (including
inventory investment) may well differ from their planned investment. However,
for households, the government, and foreign purchasers, we may reasonably
assume that actual spending and planned spending are the same. Thus, from now
on we will assume that for consumption, government purchases, and net exports,
actual spending equals planned spending.
With these assumptions, we can define aggregate demand by the equation
AD C I p G NX.
Definition of aggregate demand
(25.1)
Equation 25.1 says that aggregate demand equals the economy’s total planned
spending, which in turn is the sum of planned spending by households, firms,
governments, and foreigners. We use a superscript p to distinguish planned investment spending by firms I p from actual investment spending I. However, because
planned spending equals actual spending for households, the government, and
foreigners, we do not need to use superscripts for consumption, government purchases, or net exports.
DETERMINING AGGREGATE DEMAND: THE
CONSUMPTION FUNCTION
When we study the demand for a particular good or service, say Danish pastries,
our first task is to specify the factors that determine how much people want to
spend on it—factors such as the price of pastries, the incomes of pastry-loving
consumers, the prices of competing items like cinnamon buns, the health effects
AGGREGATE DEMAND
661
of carbohydrate consumption, and so on. In the same way, to study aggregate
demand we need to specify the factors that determine how much households plan
to consume, how much firms plan to invest, and so on.
The largest component of aggregate demand—nearly two-thirds of total
spending—is consumption spending, or C. What determines how much people
plan to spend on consumer goods and services in a given period? While many
factors may be relevant, a particularly important determinant of the amount people plan to consume is their after-tax, or disposable, income. All else being equal,
households and individuals with higher disposable incomes will consume more
than those with lower disposable incomes. Keynes himself stressed the importance
of disposable income in determining household consumption decisions, claiming
a “psychological law” that people would tie their spending closely to their
incomes.
Recall from Chapter 22 that the disposable income of the private sector is
the total production of the economy, Y, less net taxes (taxes minus transfers), or
T. So we can assume that consumption spending (C) increases as disposable
income (Y T) increases. As already mentioned, other factors may also affect
consumption, such as the real interest rate, also discussed in Chapter 22. For now
we will ignore those other factors, returning to some of them later.
An equation that captures the link between consumption and the private sector’s disposable income is
_
C C c(Y T).
(25.2)
This equation, which we will dissect in a moment, is known as the consumption
function. The consumption function relates consumption spending to its determinants, such as disposable (after-tax) income.
Let’s look at the consumption function, Equation
25.2, more carefully. The
_
_
right side of the equation contains two terms, C and c(Y T). The first term, C,
is a constant term in the equation that is intended to capture factors other than
disposable income that affect consumption. For example, suppose consumers
were to become more optimistic about the future so that they desire to consume more and save less at any given level of their current disposable incomes.
An increase in desired consumption at any given level of disposable income
would be represented
_ in the consumption function, Equation 25.2, as an
increase in the term C.
The second term on the right side of Equation 25.2, c(Y T), reflects the
effect of disposable income Y T on consumption. The parameter c, a fixed
number, is called the marginal propensity to consume. The marginal propensity
to consume, or MPC, is the amount by which consumption rises when current
disposable income rises by $1. Presumably, if people receive an extra dollar of
income, they will consume part of the dollar and save the rest. In other words,
their consumption will increase but by less than the full dollar of extra income.
Thus we assume that the marginal propensity to consume is greater than 0 (an
increase in income leads to an increase in consumption), but less than 1 (the
increase in consumption will be less than the full increase in income). These
assumptions can be written symbolically as 0 c 1.
Figure 25.1 shows a hypothetical consumption function, with consumption
spending (C) on the vertical axis and disposable income (Y T) on the horizontal axis. The intercept
of the consumption function on the vertical axis equals
_
the constant term C, and the slope of the consumption function equals the marginal propensity to consume c.
To see how this consumption function fits reality, compare Figure 25.1 to
Figure 25.2, which shows the relationship between aggregate real consumption
expenditures and real disposable income in the United States for the period 1960
through 1999. Figure 25.2, a scatter plot, shows aggregate real consumption on
the vertical axis and aggregate real disposable income on the horizontal axis. Each
consumption function the
relationship between
consumption spending and its
determinants, such as disposable
(after-tax) income
marginal propensity to
consume (MPC) the amount by
which consumption rises when
disposable income rises by $1;
we assume that 0 MPC 1
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
Consumption spending C
FIGURE 25.1
A Consumption
Function.
The consumption function
relates households’
consumption spending C to
disposable income Y T.
The vertical intercept of _this
consumption function is C,
and the slope of the line
equals the marginal
propensity to consume c.
Consumption
function
C
Slope c
Disposable income YT
FIGURE 25.2
The U.S. Consumption
–1999.
Function, 1960–
Each point on this figure
represents a combination of
aggregate real consumption
and aggregate real disposable
income for a specific year
between 1960 and 1999.
Note the strong positive
relationship between
consumption and disposable
income.
Consumption (1996 dollars, billions)
662
7,000.0
6,000.0
1995
5,000.0
1985
4,000.0
1990
1980
1975
1970
1965
3,000.0
2,000.0
1,000.0
0.0
0
1,000
2,000
3,000
4,000
5,000
6,000
Disposable income (1996 dollars, billions)
7,000
point on the graph corresponds to a year between 1960 and 1999 (selected
years are indicated in the figure). The position of each point is determined by
the combination of consumption and disposable income associated with that
year. As you can see, there is indeed a close relationship between aggregate
consumption and disposable income: Higher disposable income implies higher
consumption.
AGGREGATE DEMAND AND OUTPUT
Thinking back to Grandma’s reminiscences, recall that an important element of
her story involved the links among production, income, and spending. As the
shoe factories in Grandma’s town reduced production, the incomes of both factory workers and factory owners fell. Workers’ incomes fell as the number of
hours of work per week were reduced (a common practice during the Depression), as some workers were laid off, or as wages were cut. Factory owners’
AGGREGATE DEMAND
663
income fell as profits declined. Reduced incomes, in turn, forced both workers
and factory owners to curtail their spending, which led to still lower production
and further reductions in income.
To capture these links in our model, we need to show how aggregate demand
AD is affected by changes in aggregate income Y—which is the same, you may
recall, as aggregate output, or GDP. The consumption function, which relates desired
consumption to disposable income, helps to establish this relationship. Because consumption spending C is a large part of aggregate demand and because consumption depends on output Y, aggregate demand as a whole depends on output.
To express the connection between aggregate demand and output in an equation, we start with the definition of aggregate demand, Equation 25.1:
AD C I p G NX.
If we substitute the consumption function, Equation 25.2, for consumption C in
the definition of aggregate demand just given, the result is
_
AD [C c (Y T)] I p G NX.
Although we have discussed the determinants of consumption, we have not yet
said anything about the other three components of spending. For now, we will
simply assume that planned investment, government purchases, and net exports
are given, fixed quantities that are determined outside our model of the economy.
Using an overbar to denote a fixed value, we can write this assumption as
_
I p I,
_
G G,
__
NX NX.
We will also assume for now that net taxes T are fixed by the government.
Because
_ the amount of net taxes collected is assumed to be fixed, we can write
T T.
Substituting the fixed values for investment, government purchases, net
exports, and taxes into the equation defining aggregate demand, we get
_
_
_ _
__
AD [C c(Y T)] I G NX.
Finally, let’s rearrange this equation to group together those terms that depend
on output Y and those that do not. This rearrangement yields
_
_
_ _
__
AD (C cT I G NX) cY.
(25.3)
Equation 25.3 shows that if real output Y increases by one unit, then aggregate
demand AD increases by c units, where c, the marginal propensity to consume,
is between 0 and 1. Thus Equation 25.3 captures the key idea that as real output (Y) changes, aggregate demand (AD) changes with it, in the same direction.
Equation 25.3 also shows that aggregate demand can be divided into two
parts, a part that is determined outside the model and a part that is determined
within the model. The portion of aggregate demand that is determined outside
the model is called autonomous aggregate demand. In this example, autonomous
aggregate
_
_ demand
_
_ is given
__ by the first term on the right side of Equation 25.3,
(C cT I G NX). The portion of aggregate demand that is determined
within the model is called induced aggregate demand. Algebraically, induced
aggregate demand is given by cY, the second term on the right side of Equation
autonomous aggregate
demand the portion of
aggregate demand that is
determined outside the model
induced aggregate demand
the portion of aggregate demand
that is determined within the
model (because it depends on
output Y)
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CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
25.3. This portion of aggregate demand is determined within the model because
it changes as income Y changes. Autonomous aggregate demand and induced
aggregate demand together equal total aggregate demand. Example 25.2 illustrates these ideas numerically.
EXAMPLE 25.2
Linking aggregate demand to output
In a particular economy, the following parameter values hold:
_
_
_
__
_
C 620, c 0.8, I 220, G 300, NX 20, T 250.
a. Write an equation linking aggregate demand to output.
b. Find autonomous aggregate demand and induced aggregate demand.
Substituting the consumption function for consumption C, and treating the
other components of aggregate demand as fixed numbers, the algebraic expression for aggregate demand can be written as (see Equation 25.3)
_
_
_ _
__
AD [C cT I G NX] cY.
Plugging in the numbers in Example 25.2, we have
AD [620 0.8(250) 220 300 20] 0.8Y 960 0.8Y.
This equation links aggregate demand AD to output Y. As Y increases, aggregate
demand increases as well.
Autonomous aggregate demand is the part of aggregate demand that is determined outside the model and hence does not depend on output Y. Induced aggregate demand is the part of aggregate demand that does depend on output. In this
example, AD 960 0.8Y, so autonomous aggregate demand is 960 and
induced aggregate demand is 0.8Y. Notice that the numerical value of induced
aggregate demand depends on the value taken by output.
RECAP
AGGREGATE DEMAND
Aggregate demand (AD) is total planned spending on final goods and services. The four components of aggregate demand are consumer expenditure
(C), planned investment (I p), government purchases (G), and net exports
(NX). Planned investment differs from actual investment when firms’ sales
are different from what they expected so that additions to inventory (a component of investment) are different from what firms anticipated.
The largest component of aggregate demand is consumer expenditure, or
simply consumption. Consumption depends on disposable, or after-tax,
income, according to a relationship known as the consumption function.
The slope of the consumption function equals the marginal propensity to
consume c. The marginal propensity to consume, a number between 0 and
1, is the amount by which consumption rises when disposable income rises
by $1.
Increases in output, which imply increases in income, cause consumption
to rise. As consumption is part of aggregate demand, aggregate demand
depends on output as well. The portion of aggregate demand that depends
on output, and hence is determined within the model, is called induced
aggregate demand. The portion of aggregate demand determined outside the
model is autonomous aggregate demand.
AGGREGATE DEMAND
665
SHORT-RUN EQUILIBRIUM OUTPUT
Now that we have defined aggregate demand and seen how it is related to output, the next task is to determine what output will be. Recall the assumption of
the basic Keynesian model: that in the short run, producers leave prices at preset levels and simply meet the demand at those prices. In other words, during the
short-run period in which prices are preset, firms produce an amount that is equal
to aggregate demand. Accordingly, we define short-run equilibrium output as the
level of output at which output Y equals aggregate demand AD:
Y AD.
Definition of short-run equilibrium output
(25.4)
Short-run equilibrium output is the level of output that prevails during the period
in which prices are predetermined.
We can find the short-run equilibrium output for the economy described
in Example 25.2 using Table 25.1. Column 1 in the table gives some possible
values for short-run equilibrium output. To find the correct one, we must comTABLE 25.1
Numerical Determination of Short-Run Equilibrium Output
(1)
(3)
(4)
Output Y
(2)
Aggregate demand
AD 960 0.8Y
Y AD
Y AD?
4,000
4,160
160
No
4,200
4,320
120
No
4,400
4,480
80
No
4,600
4,640
40
No
4,800
4,800
0
Yes
5,000
4,960
40
No
5,200
5,120
80
No
pare each to the value of aggregate demand at that output level. Column 2
shows the value of aggregate demand corresponding to the values of output
in column 1. Recall that in this example, aggregate demand is determined by
the equation
AD 960 0.8Y
(see Example 25.2). Because consumption rises with output, aggregate demand
(which includes consumption) rises also. But if you compare columns 1 and 2,
you will see that when output rises by 200, aggregate demand rises by only 160.
That is because the marginal propensity to consume in this economy is 0.8, so
each dollar in added income raises consumption and aggregate demand by 80
cents.
Again, short-run equilibrium output is the level of output at which Y AD,
or equivalently, Y AD 0. Looking at Table 25.1, we can see there is only
one level of output that satisfies that condition, Y 4,800. At that level, output
and aggregate demand are precisely equal, so the producers are just meeting the
demand.
In this economy, what would happen if output happened to differ from its
equilibrium value of 4,800? Suppose, for example, that output were 4,000. Looking at column 2 of Table 25.1, we can see that when output is 4,000, aggregate
demand equals 960 0.8(4,000), or 4,160. Thus if output is 4.000, firms are
short-run equilibrium output
the level of output at which
output Y equals aggregate
demand AD; the level of output
that prevails during the period in
which prices are predetermined
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CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
not producing enough to meet the demand. They will find that as sales exceed
the amounts they are producing, their inventories of finished goods are being
depleted by 160 per year, and that actual investment is less than planned investment. Under the assumption that firms are committed to meeting their customers’
demand, firms will respond by expanding their production.
Would expanding production to 4,160, the level of aggregate demand firms
faced when output was 4,000, be enough? The answer is no, because of induced
aggregate demand. That is, as firms expand their output, aggregate income (wages
and profits) rises with it, which in turn leads to higher levels of consumption.
Indeed, if output expands to 4,160, aggregate demand will increase as well, to
960 0.8(4,160), or 4,288. So an output level of 4,160 will still be insufficient
to meet demand. As Table 25.1 shows, output will not be sufficient to meet aggregate demand until it expands to its short-run equilibrium value of 4,800.
What if output were initially greater than its equilibrium value—say, 5,000?
From Table 25.1 we can see that when output equals 5,000, aggregate demand
equals only 4,960— less than what firms are producing. So at an output level of
5,000, firms will not sell all they produce and will find that their merchandise is
piling up on store shelves and in warehouses (actual investment is greater than
planned investment). In response, firms will cut their production runs. As Table
25.1 shows, they will have to reduce production to its equilibrium value of 4,800
before output just matches aggregate demand.
EXERCISE 25.1
Construct a table like Table 25.1 for an economy like the one we have
been working with. Use the following values for the parameters:
_
_
_
__
_
C 820, c 0.7, I 600, G 600, NX 200, T 600.
What is short-run equilibrium output in this economy? (Hint: Try using
values for output above 5,000.)
Table 25.1 is useful for understanding why short-run equilibrium output
equals 4,800 in the economy described in Example 25.2, but it is a laborious way
to find the equilibrium value of output. Example 25.3 illustrates the more direct
approach to solving for short-run equilibrium output numerically.
EXAMPLE 25.3
Finding short-run equilibrium output (numerical approach)
Solve numerically for short-run equilibrium output for the economy described in
Example 25.2.
We can solve numerically for short-run equilibrium output in two steps.
First, we know that in this example aggregate demand is related to output by
the equation
AD 960 0.8Y.
Recall that we found this equation by substituting the values given in the problem for each of the four components of aggregate demand into the definition of
aggregate demand, Equation 25.1.
Second, we know that short-run equilibrium output must satisfy the equation Y AD. Using the equation AD 960 0.8Y to substitute for AD in the
definition of short-run equilibrium output, we get
Y 960 0.8Y.
AGGREGATE DEMAND
The solution to this equation gives us short-run equilibrium output, the level of
output at which production equals aggregate demand. Solving for Y we get
Y 4,800,
which is the same value obtained from Table 25.1. Box 25.2 summarizes the
process of solving the basic Keynesian model numerically.
BOX 25.2: SOLVING THE BASIC KEYNESIAN MODEL
NUMERICALLY
Step 1. Find the relationship between aggregate demand AD and output Y.
■
Write the definition of aggregate demand, Equation 25.1:
AD C I p G NX.
■
Substitute for each of the four components of aggregate demand, and simplify. For example, Example 25.2 assumes
C 620 0.8(Y T),
_
I p I 220,
_
G G 300,
___
NX NX 20,
_
T T 250.
Substituting for the components of aggregate demand in Equation 25.1 gives
AD [620 0.8(Y 250)] 220 300 20.
Simplifying this equation yields the relationship of AD to Y:
AD 960 0.8Y.
Step 2. Use the definition of short-run equilibrium output, Y AD, to solve
for Y.
■
Write the definition of short-run equilibrium output, Equation 25.4:
Y AD.
■
Replace AD with the expression found in step 1:
Y 960 0.8Y.
■
Solve the resulting equation for short-run equilibrium output Y:
Y(1 0.8) 960,
0.2Y 960,
667
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
Y 960/0.2,
Y 4,800.
This answer is the same as the one shown in Table 25.1.
Short-run equilibrium output can also be determined graphically, as Example
25.4 shows.
EXAMPLE 25.4
Finding short-run equilibrium output (graphical approach)
Using a graphical approach, find short-run equilibrium output for the economy
described in Example 25.2.
Figure 25.3 shows the graphical determination of short-run equilibrium output for the economy described in Example 25.2. Output Y is plotted on the horizontal axis and aggregate demand AD on the vertical axis. The figure contains
two lines, one of which is a 45° line extending from the origin. In general, a 45°
line from the origin includes the points at which the variable on the vertical axis
equals the variable on the horizontal axis. In this case, the 45° line represents the
equation Y AD. Recall that short-run equilibrium output must satisfy the condition Y AD. So we know that the value of short-run equilibrium output
demand must lie somewhere on the Y AD line.
The second line in Figure 25.3, less steep than the 45° line, shows the relationship between aggregate demand AD and output Y. Because it summarizes how
FIGURE 25.3
Determination of ShortRun Equilibrium Output
(Keynesian Cross).
The 45° line represents the
short-run equilibrium
condition Y AD. The line
AD 960 0.8Y, referred
to as the expenditure line,
shows the relationship of
aggregate demand to output.
Short-run equilibrium output
(4,800) is determined at the
intersection of the two lines,
point E. This type of diagram
is known as a Keynesian
cross.
Y AD
Aggregate demand AD
668
Expenditure line
AD 960 0.8Y
Slope 0.8
E
960
45°
4,800
Output Y
total expenditure depends on output, we will call this line the expenditure line.
In this example, we know that the relationship between aggregate demand and
output (the equation for the expenditure line) is
AD 960 0.8Y.
According to this equation, when Y 0, the value of AD is 960. Thus 960 is
the intercept of the expenditure line, as shown in Figure 25.3. The slope of the
line relating aggregate demand to output is 0.8, the value of the coefficient of
output in the equation AD 960 0.8Y. Where does the number 0.8 come
from? (Hint: What determines by how much aggregate demand increases when
output rises by a dollar?)
AGGREGATE DEMAND
Only one point in Figure 25.3 is consistent with both the definition of shortrun equilibrium output Y AD and the given relationship between aggregate
demand and output, AD 960 0.8Y. That point is the intersection of the
two lines, point E. At point E, short-run equilibrium output equals 4,800, which
is the same value that we obtained using Table 25.2 and by a direct numerical
solution. Notice that at points to the right of E, output exceeds aggregate
demand. Hence, to the right of point E, firms will be producing more than they
can sell and will tend to reduce their production. Similarly, to the left of point
E, aggregate demand exceeds output. In that region, firms will not be producing enough to meet demand and will tend to increase their production. Only at
point E, where output equals 4,800, will firms be producing enough to just satisfy aggregate demand.
The diagram in Figure 25.3 is often called the Keynesian cross, after its characteristic shape. The Keynesian cross shows graphically how short-run equilibrium output is determined in a world in which producers meet demand at predetermined prices.
EXERCISE 25.2
Find short-run equilibrium output for the economy described in Exercise
25.1 using a Keynesian cross diagram. What are the intercept and the
slope of the expenditure line?
AGGREGATE DEMAND AND THE OUTPUT GAP
We are now ready to use the basic Keynesian model to show how insufficient aggregate demand can lead to a recession. To illustrate this idea, we will continue to
work with the economy introduced in Example 25.2. We have shown that in this
economy, short-run equilibrium output equals 4,800. Let’s now make the additional
assumption that potential output in this economy also equals 4,800, or Y* 4,800.
In other words, we will assume that at first, actual output equals potential output
so that there is no output gap. Starting from this position of full employment, Example 25.5 shows how a fall in aggregate demand can lead to a recession.
A fall in spending leads to a recession
For the economy introduced in Example 25.2, we have found that short-run equilibrium output Y equals 4,800. Assume also that potential output Y* 4,800 so
that the output gap Y* Y equals zero.
Suppose, though, that consumers become more pessimistic about the future,
so they begin to spend less at every level
_ of current disposable income. We can
capture this change by assuming that C, the vertical intercept of the consumption function, falls from its initial value of 620 to 610. What is the effect of this
reduction in aggregate
demand on the economy?
_
The fall in C implies a reduction in autonomous aggregate demand, which
will affect short-run equilibrium output. To find out precisely what this
_ effect is,
let’s solve for short-run equilibrium output under the assumption that C has fallen
from 620 to 610. Once more we can use the steps outlined in Box 25.2. The first
step is to find the
_ relationship between aggregate demand AD and output Y after
the decline in C.
Recall the definition of aggregate demand, Equation 25.1:
AD C I p G NX.
To find the relationship of aggregate demand to output, we can substitute for the
four components of spending. Planned investment, government purchases,
net
_
exports, and net tax collections take the same fixed values as before: I 220,
EXAMPLE 25.5
669
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
_
__
_
_
G 300, NX 20, T 250. However, because of the assumed decline in C
from 620 to 610, consumption is now given by
_
C C c(Y T ) 610 0.8(Y 250).
If we substitute these values for the four components of spending in the definition of aggregate demand, we get
AD [610 0.8(Y 250)] 220 300 20.
Simplifying, we find that the relationship of aggregate demand to output is
AD 950 0.8Y.
Comparing_ this equation to the result in Example 25.2, we see that the 10-unit
decline in C has caused autonomous aggregate demand to fall by 10 units, from
960 to 950.
Following the method of Box 25.2, the second step is to solve for short-run
equilibrium output Y. We use the relationship AD 950 0.8Y to substitute for
AD in the definition of short-run equilibrium output Y AD, which gives us
Y 950 0.8Y.
Solving this equation for Y, we get
Y 4,750.
Thus the decline in consumers’ willingness to spend has caused short-run equilibrium output to fall from 4,800 to 4,750. The output gap, which was zero, now
equals Y* Y 4,800 4,750 50. We conclude that the fall in consumer
spending has led to a recession. From Okun’s law, we know that this fall in output also implies an increase in cyclical unemployment.
The same result can be obtained graphically. Figure 25.4 shows the original
short-run equilibrium point of the model (E), at the intersection of the Y AD
line and the original expenditure line, representing the equation AD 960 0.8Y. As before, the initial value of short-run equilibrium output_ is 4,800, which
corresponds to potential output Y*. But what happens when C declines by 10
from 620 to 610? We have just found that the equation for the expenditure line
FIGURE 25.4
A Decline in Spending
Leads to a Recession.
A decline in consumers’
willingness to spend at any
current level of disposable
income reduces autonomous
aggregate demand and shifts
the expenditure line down.
The short-run equilibrium
point drops from E to F,
reducing output and opening
up a recessionary gap.
Y AD
Aggregate demand AD
670
Expenditure line
AD 960 0.8Y
Expenditure line
AD 950 0.8Y
E
A decline in autonomous
aggregate demand shifts
the expenditure line down
F
960
950
Recessionary gap
45°
4,750 4,800
Y*
Output Y
AGGREGATE DEMAND
after the drop in consumer spending is AD 950 0.8Y. Since the intercept of
the expenditure line has decreased, from 960 to 950, but its slope has not
changed, the effect of the decline in consumer spending will be to shift the expenditure line down in parallel fashion by 10 units. The blue line in Figure 25.4 indicates this downward shift. The new short-run equilibrium point is F.
As Figure 25.4 shows, the downward shift in aggregate demand reduces shortrun equilibrium output from 4,800 to 4,750, opening up a recessionary gap of 50.
EXERCISE 25.3
In Example 25.5, we found a recessionary gap of 50, relative to potential
output of 4,800. Suppose that in this economy the natural rate of unemployment u* is 5 percent. What will the actual unemployment rate be
after the recessionary gap appears?
EXERCISE 25.4
© The New Yorker Collection 1990 Robert Weber from cartoonbank.com.
All Rights Reserved.
For the economy described in Exercise 25.1, suppose planned investment
I p rises from 600 to 630.Assuming the economy had no output gap before
the increase in planned investment, show numerically that the change in
investment leads to an expansionary output gap.
“These are hard times for retailers, so we should show them
our support in every way we can.”
–1991 recession?
What caused the 1990–
As we saw in Chapter 24, the 1990–1991 recession came at the wrong time for President Bush.What caused the output of the U.S. economy to fall below its potential during that period?
Two factors have received a substantial part of the blame for the 1990–1991
recession, one being a decline in consumer confidence. Organizations such as the Conference Board and the Survey Research Center of the University of Michigan perform regular consumer surveys, in which people are asked their views about the
future of the economy in general, and their own fortunes in particular. Consumer
responses are then summarized in measures of “consumer confidence.” A high level
of confidence implies that people are optimistic about both their own economic futures
and the future of the economy in general. Economists have found that when consumers
25.1
671
672
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
are optimistic, they are more likely to spend, particularly on “big-ticket” items such as
cars and furniture. Hence, when consumer confidence took its sharpest-ever plunge following Iraq’s invasion of Kuwait and the associated spike in oil prices in August 1990,
economists and policymakers winced. As Americans became increasingly concerned both
about U.S. energy security and the possibility of a ground war in the Middle East, aggregate demand and hence output fell, as suggested by Example 25.5.
The second factor, a credit crunch, arose from problems in the U.S. banking system.
During the 1980s, many U.S. banks had made large real estate loans, taking undeveloped
land or commercial real estate as collateral. When land and other real estate prices fell
sharply in the late 1980s, banks suffered serious losses. Some regions of the country, such
as New England, were hit especially hard. Many financially distressed banks either had no
new funds to lend or were not permitted to lend by government regulators.This decline
in the supply of credit from banks made credit costlier and more difficult to obtain for
many borrowers, especially small- and medium-sized firms.Without access to credit, these
firms could not make capital investments, further reducing aggregate demand and output.
In terms of the model presented in this chapter, a decline in planned
_ investment spending
brought
about
by
a
credit
crunch
can
be
thought
of
as
a
fall
in
I.
Like the decline in
_
_
C illustrated in Example 25.5, a fall in I reduces short-run equilibrium output (see Problem 5 at the end of the chapter).
Why was the deep Japanese recession of the 1990s bad news for the rest of
East Asia?
25.2
Economic Naturalist 24.1 discussed the severe economic slump in Japan during the 1990s.
Japan’s economic problems were a major concern not only of the Japanese but of policymakers in other East Asian countries, such as Thailand and Singapore. Why did East Asian
policymakers worry about the effects of the Japanese slump on their own economies?
Although the economies of Japan and its East Asian neighbors are intertwined in
many ways, one of the most important links is through trade. Much of the economic
success of East Asia has been based on the development of export industries, and over
the years Japan has been the most important customer for East Asian goods.When the
economy slumped in the 1990s, Japanese households and firms reduced their purchases
of imported goods sharply. This fall in demand dealt a major blow to the export industries of other East Asian countries. Not just the owners and workers of export industries were affected, though. The decline in exports to Japan reduced net exports, and
thus autonomous aggregate demand, in East Asian countries. Falling aggregate demand
in turn reduced their short-run equilibrium GDP and contributed to recessionary output gaps. Graphically, the effects were similar to those shown in Figure 25.4.
Japan is not the only country whose economic ups and downs have had a major
impact on its trading partners. Because the United States is the most important trading partner of both Canada and Mexico, a recession in the United States would be
likely to reduce Canadian and Mexican GDPs as well by reducing U.S. demand for the
exports of its neighbors.
THE MULTIPLIER
Note that in Example 25.5,
although the initial decline in consumer spending (as
_
measured by the fall in C) was only 10 units, short-run equilibrium output fell by
50 units. The reason the impact on output and aggregate demand was greater than
the initial change in spending is the “vicious circle” effect suggested by Grandma’s
reminiscences about the Great Depression. Specifically, a fall in consumer spending
not only decreases aggregate demand, it also reduces the incomes of workers and
owners in the industries that produce consumer goods. As their incomes fall, these
workers and capital owners reduce their spending, which reduces the output and
incomes of other producers in the economy. And these reductions in income lead
to still further cuts in spending. Ultimately, these successive rounds of declines in
AGGREGATE DEMAND
spending and income may lead to a decrease in aggregate demand that is significantly greater than the change in spending that started the process.
The idea that a change in spending may lead to a much larger change in
short-run equilibrium output is an important feature of the basic Keynesian
model. In Example 25.5 we considered the effects of a decrease in spending, but
an increase in spending produces the same effect in reverse. For example, if
desired consumption had increased rather than decreased by 10, it would have
set off successive rounds of increases in income and spending, culminating in a
final increase of 50 in short-run equilibrium output. The same type of effect also
applies to changes in other components of autonomous aggregate demand. For
example, in
desired investment
_ this hypothetical economy,_ an increase of 10 in__
spending I, in government purchases G, or in net exports NX would increase
short-run equilibrium output by 50.
The effect on short-run equilibrium output of a one-unit increase in
autonomous aggregate demand is called the income-expenditure multiplier, or the
multiplier for short. In the economy of Example 25.5 the multiplier is 5. That is,
each $1 increase in autonomous aggregate demand leads to a $5 increase in shortrun equilibrium output, and each $1 decrease in autonomous aggregate demand
implies a $5 decrease in short-run equilibrium output. Box 25.3 provides more
information about the economics of the multiplier and shows how to calculate
its numerical value in specific examples.
We stress that, because the basic Keynesian model omits some important features of the real economy, it tends to yield unrealistically high values of the multiplier. Indeed, virtually no one believes that the multiplier in the U.S. economy is
as high as 5. Later we will discuss why the basic Keynesian model tends to overstate the value of the multiplier. Nevertheless, the idea that changes in aggregate
demand can have important effects on short-run equilibrium output remains a central tenet of Keynesian economics and a major factor in modern policymaking.
BOX 25.3: THE MULTIPLIER IN THE BASIC KEYNESIAN MODEL
In Example 25.5, a drop in autonomous aggregate demand of 10 units caused
a decline in short-run equilibrium output five times as great—an illustration
of the income-expenditure multiplier in action. To see more precisely why this
multiplier effect occurs, note that the initial decrease of 10 in consumer spending in Example 25.5 has two effects. First, because consumption spending is
part of aggregate demand, the fall in consumer spending directly reduces
aggregate demand by 10. Second, the fall in spending also reduces by 10 the
incomes of producers (workers and firm owners) of consumer goods. Under
our assumption that the marginal propensity to consume is 0.8, the producers of consumer goods will therefore reduce their consumption spending by
8, or 0.8 times their income loss of 10. This reduction in spending cuts the
income of other producers by 8, leading them to reduce their spending by 6.4,
or 0.8 times their income loss of 8. These income reductions of 6.4 lead still
other producers to cut their spending by 5.12, or 0.8 times 6.4, and so on.
In principle this process continues indefinitely, although after many rounds of
spending and income reductions the effects become quite small.
Adding up all these “rounds” of income and spending reductions, the
total effect on aggregate demand of the initial reduction of 10 in consumer
spending is
10 8 6.4 5.12 ... .
The three dots indicate that the series of reductions continues indefinitely. The
total effect of the initial decrease in consumption can also be written as
673
income-expenditure multiplier
the effect of a one-unit increase
in autonomous aggregate
demand on short-run
equilibrium output
674
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
10[1 0.8 (0.8)2 (0.8)3 ...].
This expression highlights the fact that the spending that takes place in each
round is 0.8 times the spending in the previous round—0.8, because that
is the marginal propensity to consume out of the income generated by the
previous round of spending.
A useful algebraic relationship, which applies to any number x greater
than 0 but less than 1, is
1
1 x x2 x3 ... ____.
1x
If we set x 0.8, this formula implies that the total effect of the decline in
consumption spending on aggregate demand and output is
1
1
10 ________ 10 ____ 10 5 50.
1 0.8
0.2
(
)
( )
This answer is consistent with our earlier calculation, which showed that
short-run equilibrium output fell by 50 units, from 4,800 to 4,750.
By a similar analysis we can also find a general algebraic expression for
the multiplier in the basic Keynesian model. Recalling that c is the marginal
propensity to consume out of disposable income, we know that a one-unit
increase in autonomous aggregate demand raises spending and income by
one unit in the first round, by c 1 c units in the second round, by
c c c2 units in the second round, by c c2 c3 units in the third
round, and so on. Thus the total effect on short-run equilibrium output of
a one-unit increase in autonomous aggregate demand is given by
1 c c2 c3 ... .
Applying the algebraic formula given above, and recalling that 0 c 1,
we can rewrite this expression as 1/(1 c). Thus, in a basic Keynesian
model with a marginal propensity to consume of c, the multiplier equals
1/(1 c). To check this result, we can substitute our assumed numerical
value of 0.8 for c and calculate the multiplier in our example as 1/(1 0.8)
1/0.2 5, which is the same value we obtained earlier.
RECAP
SHORT-RUN EQUILIBRIUM OUTPUT
Short-run equilibrium output is the level of output at which output equals
aggregate demand; or in symbols, Y AD. For a specific example economy, short-run equilibrium output can be solved for numerically (see Box
25.2) or graphically. The graphical solution is based on a diagram called
the Keynesian cross. The Keynesian cross diagram includes two lines: a 45°
line that captures the condition Y AD and the expenditure line, which
shows the relationship of aggregate demand to output. Short-run equilibrium output is determined at the intersection of the two lines. If short-run
equilibrium output differs from potential output, an output gap exists.
Increases in autonomous aggregate demand shift the expenditure line
upward, increasing short-run equilibrium output, and decreases in
autonomous aggregate demand induce declines in short-run equilibrium output. Decreases in autonomous aggregate demand that drive actual output
below potential output are a possible source of recessions. Generally, a one-
STABILIZING AGGREGATE DEMAND: THE ROLE OF FISCAL POLICY
675
unit increase in autonomous aggregate demand leads to a larger increase in
short-run equilibrium output, a result of the income-expenditure multiplier.
The multiplier arises because a given initial increase in spending raises the
incomes of producers, which leads them to spend more, raising the incomes
and spending of other producers, and so on.
STABILIZING AGGREGATE DEMAND: THE ROLE
OF FISCAL POLICY
According to the basic Keynesian model, inadequate spending is an important cause
of recessions. To fight recessions—at least, those caused by insufficient demand
rather than slow growth of potential output—policymakers must find ways to
increase aggregate demand. Policies that are used to affect aggregate demand, with
the objective of eliminating output gaps, are called stabilization policies.
The two major types of stabilization policy, monetary policy and fiscal policy,
were introduced in Chapter 17. Recall that monetary policy refers to decisions
about the size of the money supply, while fiscal policy refers to decisions about the
government’s budget—how much the government spends and how much tax revenue it collects. In the remainder of this chapter we will focus on fiscal policy (monetary policy will be discussed in Chapters 26 and 27). Specifically, we will consider
how fiscal policy works in the basic Keynesian model, looking first at the effects
of changes in government purchases of goods and services and then at changes in
tax collections. We will conclude the chapter with a discussion of some practical
issues that arise in the application of fiscal policy.
stabilization policies
government policies that are
used to affect aggregate demand,
with the objective of eliminating
output gaps
GOVERNMENT PURCHASES AND AGGREGATE DEMAND
Decisions about government spending represent one of the two main components
of fiscal policy, the other being decisions about the level and type of taxes. As was
mentioned earlier (see Box 25.1), Keynes himself felt that changes in government
spending were probably the most effective tool for reducing or eliminating output
gaps. His basic argument was straightforward: Government purchases of goods and
services are a component of aggregate demand, so aggregate demand is directly
affected by changes in government purchases. If output gaps are caused by too much
or too little aggregate demand, then the government can help to guide the economy
toward full employment by changing its own level of spending. Keynes’s views
seemed to be vindicated by the events of the 1930s, notably the fact that the Depression did not finally end until governments greatly increased their military spending
in the latter part of the decade. Ironically, Adolf Hitler may have been the most
successful of all the era’s leaders at applying Keynes’s prescription (although no evidence suggests that the Nazi dictator was familiar with Keynes’s writings). Economic
historians credit Hitler’s massive rearmament and road-building programs with
greatly reducing unemployment in Germany in the 1930s.
Example 25.6 shows how increased government purchases of goods and services can help to eliminate a recessionary gap. (The effects of government spending on transfer programs, such as unemployment benefits, are a bit different. We
will return to that case shortly.)
An increase in the government’s purchases eliminates a recessionary gap
In Example 25.5, we found that a drop of 10 units in consumer spending creates a recessionary gap of 50. _Show that in _that economy, a 10-unit increase in
government purchases, from G 300 to G 310, will eliminate the output
gap and restore full employment.
EXAMPLE 25.6
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
Intuitively, the 10-unit increase in government purchases should be just
enough to offset the 10-unit decline in autonomous consumption expenditures
and restore actual output to the full-employment level of 4,800. Let’s confirm this
result by solving for the value of short-run equilibrium output after the increase
in government purchases.
As before, the first step is to write the relationship between aggregate demand
AD and output Y. To do so, we write the definition of aggregate demand, AD C I p G NX, and substitute for each of the four components. The first
component, consumption spending, is given by
C 610 0.8(Y 250),
_
_
where C 610 and taxes T T 250 (see Example 25.5). As before, planned
investment I p equals 220, and net exports NX equals 20. However, government
purchases of goods and services, G, has increased from 300 to 310.
Substituting for these four components of aggregate demand yields
AD [610 0.8(Y 250)] 220 310 20.
Simplifying, we get the relationship between aggregate demand and output:
AD 960 0.8Y,
which is the same relationship we found for this economy in Examples 25.3 and 25.4.
The second step is to substitute the expression for aggregate demand into the
definition of short-run equilibrium output, Y AD. Doing so, we get
Y 960 0.8Y.
Finally, solving this equation for the value of short-run equilibrium output, we get
Y 4,800, which is the same value assumed for potential output Y*. Thus in this
example the increase in government purchases eliminates the recessionary output gap.
The effect of the increase in government purchases is shown graphically _
in
Figure 25.5. After the 10-unit decline in autonomous consumption spending C,
FIGURE 25.5
An Increase in
Government Purchases
Eliminates a Recessionary
Gap.
After a 10-unit decline in
autonomous
_ consumer
spending C, the economy is at
point F, with a recessionary
gap of 50 (see Figure 25.4).A
10-unit increase in
government purchases raises
autonomous aggregate
demand by 10 units, shifting
the expenditure line back to
its original position and raising
the equilibrium point from F
to E. At point E, where output
equals potential output
(Y Y* 4,800), the output
gap has been eliminated.
Y AD
Aggregate demand AD
676
Expenditure line
AD 960 0.8Y
Expenditure line
AD 950 0.8Y
E
An increase in G
shifts the expenditure
line upward
F
960
950
Recessionary gap
45°
4,750 4,800
Y*
Output Y
STABILIZING AGGREGATE DEMAND: THE ROLE OF FISCAL POLICY
the economy is at point F, with a 50-unit recessionary gap. The 10-unit increase
in government purchases raises the intercept of the expenditure line 10 units, causing the expenditure line to shift upward in parallel fashion. The economy returns
to point E, where short-run equilibrium output equals potential output (Y Y*
4,800), and the output gap has been eliminated.
EXERCISE 25.5
In Exercise 25.4, you found that for the economy described in Exercise 25.1,
an increase in planned investment from 600 to 630 leads to an expansionary output gap. Show how a change in government purchases could be used
to eliminate this output gap. Confirm your answer numerically.
To this point we have been considering the effect of fiscal policy on a hypothetical economy. Economic Naturalists 25.3 and 25.4 illustrate the application
of fiscal policy in real economies.
Why is Japan building roads nobody wants to use?
Japanese officials recently decided to build a toll road on the northern island of
Hokkaido. About 32 miles of the planned 160-mile highway has been completed, at a
cost of $1.9 billion, or $60 million per mile. Very few drivers use the road, largely
because an existing highway that runs parallel to the new toll road is free. Officials
tried to attract drivers by offering prizes and running promotional contests.Though the
campaign succeeded in increasing the average number of cars on the road to 862 per
day, the route is still the least used highway in Japan (The New York Times, Nov. 25, 1999,
p. A1). Why is Japan building roads nobody wants to use?
Japan spent most of the 1990s in a deep recession (see Economic Naturalist
24.1), and the government has periodically initiated large spending programs to try
to stimulate the economy. Indeed, during the 1990s the Japanese government spent
more than $1 trillion on public works projects. More than $10 billion was spent
on the Tokyo subway system, an amount so far over budget that subway tokens
will have to cost an estimated $9.50 each if the investment is ever to be recouped.
(Even more frustrating is that the subway does not run in a complete circle, requiring passengers to make inconvenient transfers to traverse the city.) Other examples of government spending programs include the construction of multimillion-dollar concert halls in small towns, elaborate tunnels where simple roads would have
been adequate, and the digging up and relaying of cobblestone sidewalks. Despite
all this spending, the Japanese recession has dragged on.
The basic Keynesian model implies that increases in government spending such
as those undertaken in Japan should help to increase output and employment.
Japanese public works projects do appear to have stimulated the economy, though
not enough to pull Japan out of the recession. Why has Japan’s fiscal policy proved
inadequate to the task? Some critics have argued that the Japanese government was
unconscionably slow in initiating the fiscal expansion, and that when spending was
finally increased, it was simply not enough, relative to the size of the Japanese economy and the depth of the recession. Another possibility, which lies outside the basic
Keynesian model, is that the wasteful nature of much of the government spending
demoralized Japanese consumers, who realized that as taxpayers they would at
some point be responsible for the costs incurred in building roads nobody wants
to use. Reduced consumer confidence implies reduced consumption spending, which
may to some extent have offset the stimulus from government spending. Very possibly, more productive investments of Japanese public funds would have had a
greater impact on aggregate demand (by avoiding the fall in consumer confidence);
certainly, they would have had a greater long-term benefit in terms of increasing
the potential output of the economy.
25.3
677
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
Does military spending stimulate aggregate demand?
40
World War II
35
Defense spending/GDP
30
25
20
Korean War
Peak of Vietnam War
15
Reagan military
buildup
10
1996
1992
1988
1984
1980
1976
1972
1968
1964
1960
1956
1952
0
1948
5
1944
FIGURE 25.6
U.S. Military
Expenditures as a Share
–1999.
of GDP, 1940–
Military expenditures as a
share of GDP rose during
World War II, the Korean
War, the Vietnam War, and
the Reagan military buildup
of the early 1980s. Increased
military spending is generally
associated with an expanding
economy and declining
unemployment.The blue
areas indicate periods of
recession.
1940
25.4
An antiwar poster from the 1960s bore the message “War is good business. Invest your
son.” War itself poses too many economic and human costs to be good for business,
but military spending could be a different matter. According to the basic Keynesian
model, increases in aggregate demand created by increased government spending may
help bring an economy out of a recession or depression. Does military spending stimulate aggregate demand?
Figure 25.6 shows U.S. military spending as a share of GDP from 1940 to 1999.
The blue areas in the figure correspond to periods of recession as shown in Table 24.1.
Note the spike that occurred during World War II (1941–1945), when military spending reached nearly 38 percent of U.S. GDP, as well as the surge during the Korean War
(1950–1953). Smaller increases in military spending relative to GDP occurred at the
peak of the Vietnam War in 1967–1969 and during the Reagan military buildup of the
1980s.
Share of GDP (%)
678
Year
Figure 25.6 provides some support for the idea that expanded military spending tends to promote growth in aggregate demand. The clearest case is the World
War II era, during which massive military spending helped the U.S. economy to
recover from the Great Depression. The U.S. unemployment rate fell from 17.2 percent of the workforce in 1939 (when defense spending was less than 2 percent of
GDP) to 1.2 percent in 1944 (when defense spending was greater than 37 percent
of GDP). Two brief recessions, in 1945 and 1948–1949, followed the end of the
war and the sharp decline in military spending. At the time, though, many people
feared that the war’s end would bring a resumption of the Depression, so the relative mildness of the two postwar recessions was something of a relief.
Increases in defense spending during the post-World War II period were also
associated with economic expansions. The Korean War of 1950–1953 occurred
simultaneously with a strong expansion, during which the unemployment rate
dropped from 5.9 percent in 1949 to 2.9 percent in 1953. A recession began the
year the war ended, 1954, though military spending had not yet declined much.
Finally, economic expansions also occurred during the Vietnam-era military buildup
in the 1960s and the Reagan buildup of the 1980s. These episodes support the idea
that increases in government spending—in this case, for weapons and military supplies—can help to stimulate the economy.
© The New Yorker Collection 1992 Dana Fradon from cartoonbank.com.
All Rights Reserved.
STABILIZING AGGREGATE DEMAND: THE ROLE OF FISCAL POLICY
“Your majesty, my voyage will not only forge a new route to the spices of the
East but also create over three thousand new jobs.”
TAXES, TRANSFERS, AND AGGREGATE DEMAND
Besides making decisions about government purchases of goods and services, fiscal policymakers also determine the level of tax collections (payments from the
private sector to the government) and transfer payments (payments from the government to the private sector, such as welfare payments and Social Security). The
basic Keynesian model implies that like changes in government purchases, changes
in the level of taxes or transfers can be used to affect aggregate demand and thus
to eliminate output gaps.
Unlike changes in government purchases, however, changes in taxes or transfers do not affect aggregate demand directly. Instead they work indirectly by
changing disposable income in the private sector. Specifically, either a tax cut or
an increase in government transfer payments increases disposable income in the
private sector, which according to the consumption function should encourage
households to spend more on consumer goods and services. In short, changes in
taxes and transfers affect aggregate demand only to the extent that they change
the level of spending in the private sector. Example 25.7 shows the effect of a
tax cut (or an equal-size increase in transfers) on aggregate demand and shortrun equilibrium output.
Using a tax cut to close a recessionary gap
In Example 25.5, we found that in our hypothetical economy, an initial drop in
consumer spending of 10 units creates a recessionary gap of 50. Example 25.6
showed that this recessionary gap could be eliminated by a 10-unit increase in government purchases. Suppose that, instead of increasing government purchases, fiscal policymakers decided to stabilize aggregate demand by changing the level of tax
collections. By how much should they change taxes to eliminate the output gap?
A common first guess at the answer to this problem is that policymakers
should cut taxes by 10, but that guess is not correct. Let’s see why.
The source of the recessionary gap in Example 25.5 is the assumption that
households have reduced their consumption spending by 10 units at each level of
output Y. To eliminate this recessionary gap, the change in taxes must induce
households to increase their consumption spending by 10 units at each output
level. However, if taxes T are cut by 10 units, raising disposable income Y T
by 10 units, consumption at each level of output Y will increase by only 8 units.
The reason is that the marginal propensity to consume out of disposable income
is 0.8, so consumption spending increases by only 0.8 times the amount of the
tax cut. (The rest of the tax cut is saved.)
EXAMPLE 25.7
679
680
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
To raise consumption
spending_by 10 units, fiscal policymakers must cut taxes
_
by 12.5 units, from T 250 to T 237.5. Because 0.8(12.5) 10, a tax cut
of 12.5 will spur households to increase their consumption by 10 units at each
level of output.
_ That increase will just offset the 10-unit decrease in autonomous
consumption C, restoring the economy_to full employment.
We can check to see that setting
_ T 237.5 will eliminate the recessionary
_
gap. Under the assumptions that C takes its lower value of 610 and T 237.5,
the consumption function is
C 610 0.8(Y 237.5).
Using the values for planned investment, government purchases, and net exports
given in Example 25.2, we can write aggregate demand as
AD [610 0.8(Y 237.5)] 220 300 20.
Simplifying in the usual way, we get
AD 960 0.8Y,
which is the same expression we found in Example 25.2. Using this equation to substitute for AD in the definition of short-run equilibrium output Y AD, we obtain
Y 960 0.8Y.
Solving for Y, we find Y 4,800, which is also the value of potential output.
We conclude that a tax cut of 12.5 will eliminate the recessionary gap and restore
full employment in this economy.
Note that since T refers to net taxes, or taxes less transfers, the same result
could be obtained by increasing transfer payments by 12.5 units. Because households spend 0.8 times any increase in transfer payments they receive, this policy
would also raise consumption spending by 10 units at any level of output.
Graphically, the effect of the tax cut is identical to the effect of the increase
in government purchases, shown in Figure 25.5. Because it leads to a 10-unit
increase in consumption at any level of output, the tax cut shifts the expenditure
line up by 10 units. Equilibrium is attained at point E in Figure 25.5, where output again equals potential output.
EXERCISE 25.6
In Exercise 25.5, you eliminated an expansionary output gap from the
economy described in Exercise 25.1 by changing government purchases.
How could the same effect be achieved by changing tax collections?
RECAP
FISCAL POLICY AND AGGREGATE DEMAND
Stabilization policies are policies used to affect aggregate demand with the
objective of eliminating output gaps. Fiscal policy includes two methods for
affecting aggregate demand: changes in government purchases and changes
in taxes or transfer payments. An increase in government purchases
increases autonomous aggregate demand by an equal amount. A reduction
in taxes or an increase in transfer payments increases autonomous aggregate demand by an amount equal to the marginal propensity to consume
times the reduction in taxes or increase in transfers. The ultimate effect of
FISCAL POLICY AS A STABILIZATION TOOL: TWO QUALIFICATIONS
a fiscal policy change on short-run equilibrium output equals the change in
autonomous aggregate demand times the multiplier.
Accordingly, if the economy is in recession, an increase in government
purchases, a cut in taxes, or an increase in transfers can be used to stimulate spending and eliminate the recessionary gap.
FISCAL POLICY AS A STABILIZATION TOOL:
TWO QUALIFICATIONS
The basic Keynesian model might lead you to think that fiscal policy can be used
quite precisely to eliminate output gaps. But as is often the case, the real world
is more complicated than economic models. We close the chapter with two qualifications about the use of fiscal policy as a stabilization tool.
First, fiscal policy may affect potential output as well as aggregate demand.
In the examples in this chapter we assumed that changes in government purchases, taxes, and transfer payments change aggregate demand without affecting
the supply side of the economy, as represented by potential output. But as we
saw in Chapter 20, this assumption often is not correct. On the spending side,
for example, investments in public capital, such as roads, airports, and schools,
can play a major role in the growth of potential output. On the other side of the
ledger, tax and transfer programs may well affect the incentives, and thus the economic behavior, of households and firms. For example, a high tax rate on interest income reduces the after-tax return on saving, which may cause people to save
less, while a tax break on new investment may encourage firms to increase their
rate of capital formation. Such changes in saving or investment will in turn affect
potential output. Many other examples could be given of how taxes and transfers affect economic behavior and thus potential output.
Some critics of the Keynesian theory have gone so far as to argue that the
only effects of fiscal policy that matter are its effects on potential output. This
was essentially the view of the so-called supply-siders, a group of economists and
journalists whose influence reached a high point during the first Reagan administration (1981–1985). Through their arguments that lower taxes would substantially increase potential output, with no significant effect on aggregate
demand, the supply-siders provided crucial support for the large tax cuts that
took place under the Reagan administration.
A more balanced view is that fiscal policy affects both aggregate demand and
potential output. Thus, government policymakers should take into account not
only the need to stabilize aggregate demand but also the potential effects of government spending, taxes, and transfers on the economy’s productive capacity.
The second qualification about the use of fiscal policy is that fiscal policy is
not always flexible enough to be useful for stabilization. Our examples have
implicitly assumed that the government can change spending or taxes relatively
quickly in order to eliminate output gaps. In reality, changes in government spending or taxes must usually go through a lengthy legislative process, which reduces
the ability of fiscal policy to respond in a timely way to economic conditions.
Budget and tax changes proposed by the President must be submitted to Congress 18 months or more before they actually go into effect. Another factor that
limits the flexibility of fiscal policy is that fiscal policymakers have many other
objectives besides stabilizing aggregate demand, from assuring an adequate
national defense to providing income support to the poor. What happens if, say,
the need to strengthen the national defense requires an increase in government
spending but the need to stabilize aggregate demand requires a decrease in spending? Such conflicts can be difficult to resolve through the political process.
681
682
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
automatic stabilizers
provisions in the law that imply
automatic increases in
government spending or
decreases in taxes when real
output declines
This lack of flexibility means that fiscal policy is less useful for stabilizing
aggregate demand than the basic Keynesian model suggests. Nevertheless, most
economists view fiscal policy as an important stabilizing force for two reasons.
The first is the presence of automatic stabilizers, provisions in the law that imply
automatic increases in government spending or decreases in taxes when real output declines. For example, some government spending is earmarked as “recession
aid”; it flows to communities automatically when the unemployment rate reaches
a certain level. Taxes and transfer payments also respond automatically to output gaps: When GDP declines, income tax collections fall (because households’
taxable incomes fall), while unemployment insurance payments and welfare benefits rise—all without any explicit action by Congress. These automatic changes
in government spending and tax collections help to increase aggregate demand
during recessions and reduce it during expansions, without the delays inherent in
the legislative process.
The second reason that fiscal policy is an important stabilizing force is that
while fiscal policy may be difficult to change quickly, it may still be useful for
dealing with prolonged episodes of recession. The Great Depression of the 1930s
and the Japanese slump of the 1990s are two cases in point. However, because
of the relative lack of flexibility of fiscal policy, in modern economies aggregate
demand is more usually stabilized through monetary policy. The role of monetary policy in stabilizing aggregate demand is the subject of the next chapter.
■
SUMMARY
• The basic Keynesian model shows how fluctuations in
aggregate spending, or aggregate demand, can cause actual
output to differ from potential output. Too little spending
leads to a recessionary output gap, while too much spending creates an expansionary output gap. This model relies
on two basic assumptions: that aggregate demand fluctuates, and that in the short run, firms will meet the demand
for their products at preset prices.
• Aggregate demand is total planned spending on final goods
and services. The four components of total spending are consumption, investment, government purchases, and net
exports. Planned and actual consumption, government purchases, and net exports are assumed to be the same. Actual
investment may differ from planned investment, because
firms may sell a greater or lesser amount of their production
than they expected. If firms sell less than they expected, for
example, they are forced to add more goods to inventory than
anticipated. And because additions to inventory are counted
as part of investment, in this case actual investment (including inventory investment) is greater than planned investment.
■
aggregate demand is the portion of aggregate demand that
is determined outside the model; induced aggregate demand
is the portion that is determined within the model. In the
model presented in this chapter, induced aggregate demand
is the part of aggregate demand that depends on current
output.
• At predetermined prices, short-run equilibrium output is
the level of output that equals aggregate demand. Short-run
equilibrium can be determined graphically in a Keynesian
cross diagram, drawn with aggregate demand on the vertical axis and output on the horizontal axis. The Keynesian
cross contains two lines: an expenditure line, which relates
aggregate demand to output, and a 45° line, which represents the condition that short-run equilibrium output
equals aggregate demand. Short-run equilibrium output is
determined at the point at which these two lines intersect.
Algebraically, short-run equilibrium output can be found by
setting output equal to aggregate demand and solving for
the value of output (see Box 25.2).
• Changes in autonomous aggregate demand will lead to
• Consumption is related to disposable, or after-tax, income
by a relationship called the consumption function. The
amount by which desired consumption rises when disposable income rises by $1 is called the marginal propensity to
consume (MPC). The marginal propensity to consume is
always greater than 0 but less than 1.
• An increase in real output raises aggregate demand, since
higher output (and equivalently, higher income) encourages
households to consume more. Aggregate demand can be
broken down into two components, autonomous aggregate
demand and induced aggregate demand. Autonomous
changes in short-run equilibrium output. In particular, if the
economy is initially at full employment, a fall in autonomous aggregate demand will create a recessionary gap and
a rise in autonomous aggregate demand will create an
expansionary gap. The effect of a one-unit increase in
autonomous aggregate demand on short-run equilibrium
output is called the multiplier. An increase in autonomous
aggregate demand not only raises spending directly, it also
raises the incomes of producers, who in turn increase their
spending, and so on. Hence the multiplier is greater than 1;
that is, a $1 increase in autonomous aggregate demand
raises short-run equilibrium output by more than $1.
PROBLEMS
683
• To eliminate output gaps and restore full employment, the
• Two qualifications must be made to the use of fiscal policy
government employs stabilization policies. The two major
types of stabilization policy are monetary policy and fiscal
policy. Stabilization policies work by changing aggregate
demand, and hence short-run equilibrium output. For
example, an increase in government purchases raises aggregate demand, so it can be used to reduce or eliminate a
recessionary gap. Similarly, a cut in taxes or an increase in
transfer payments increases the public’s disposable income,
raising consumption and aggregate demand. Higher aggregate demand, in turn, raises short-run equilibrium output.
as a stabilization tool. First, fiscal policy may affect potential output as well as aggregate demand. And second,
because changes in fiscal policy must go through a lengthy
legislative process, fiscal policy is not always flexible
enough to be useful for short-run stabilization. However,
automatic stabilizers—provisions in the law that imply
automatic increases in government spending or reductions
in taxes when output declines—can overcome the problem
of legislative delays to some extent and contribute to economic stability.
■
KEY TERMS
■
menu costs (658)
short-run equilibrium output (665)
stabilization policies (675)
income-expenditure multiplier (673)
induced aggregate demand (663)
marginal propensity to consume
(MPC) (661)
aggregate demand (AD) (659)
automatic stabilizers (682)
autonomous aggregate demand (663)
consumption function (661)
■
REVIEW QUESTIONS
1. What are the two key assumptions of the basic Keynesian
model? Explain why each of the two assumptions is necessary if one is to accept the view that aggregate spending
is a driving force behind short-term economic fluctuations.
2. Give an example of a good or service whose price
changes very frequently and one whose price changes relatively infrequently. What accounts for the difference?
3. Define aggregate demand and list its components. Why
does aggregate demand change when output changes?
4. Explain how planned spending and actual spending can
differ. Illustrate with an example.
5. Sketch a graph of the consumption function, labeling the
axes of the graph. Discuss the economic meaning of (a) a
movement from left to right along the graph of the consumption function and of (b) a parallel upward shift of
the consumption function.
■
■
6. Sketch the Keynesian cross diagram. Explain in words
the economic significance of the two lines graphed in the
diagram. Given only this diagram, how could you determine autonomous aggregate demand, induced aggregate
demand, the marginal propensity to consume, and shortrun equilibrium output?
7. Using the Keynesian cross diagram, illustrate the two
causes of the 1990–1991 recession discussed in Economic Naturalist 25.1.
8. Define the multiplier. In economic terms, why is the multiplier greater than 1?
9. The government is considering two alternative policies,
one involving increased government purchases of 50, the
other involving a tax cut of 50. Which policy will stimulate aggregate demand by more? Why?
PROBLEMS
■
1. Acme Manufacturing is producing $4,000,000 worth of goods this year and is expecting to sell its entire production. It is also planning to purchase $1,500,000 in new
equipment during the year. At the beginning of the year the company has $500,000
in inventory in its warehouse. Find actual investment and planned investment if:
a. Acme actually sells $3,850,000 worth of goods.
b. Acme actually sells $4,000,000 worth of goods.
c. Acme actually sells $4,200,000 worth of goods.
Assuming that Acme’s situation is similar to that of other firms, in which of these
three cases is output equal to short-run equilibrium output?
2. Data on before-tax income, taxes paid, and consumption spending for the Simpson
family in various years are given below.
684
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
Before-tax income ($)
Taxes paid ($)
Consumption spending ($)
25,000
3,000
20,000
27,000
3,500
21,350
28,000
3,700
22,070
30,000
4,000
23,600
a. Graph the Simpsons’ consumption function, and find their household’s marginal
propensity to consume.
b. How much would you expect the Simpsons to consume if their income was
$32,000 and they paid taxes of $5,000?
c. Homer Simpson wins a lottery prize. As a result, the Simpson family increases its
consumption by $1,000 at each level of after-tax income. (“Income” does not
include the prize money.) How does this change affect the graph of their consumption function? How does it affect their marginal propensity to consume?
3. An economy is described by the following equations:
C 1,800 0.6(Y T),
_
I p I 900,
_
G G 1,500,
___
NX NX 100,
_
T T 1,500,
Y* 9,000.
a. Find an equation linking aggregate demand to output.
b. Find autonomous aggregate demand and induced aggregate demand.
4. For the economy described in Problem 3:
a. Construct a table like Table 25.1 to find short-run equilibrium output. Consider
possible values for short-run equilibrium output ranging from 8,200 to 9,000.
b. Solve numerically for short-run equilibrium output.
c. Show the determination of short-run equilibrium output for this economy using
the Keynesian cross diagram.
d. What is the output gap for this economy? If the natural rate of unemployment is
4 percent, what is the actual unemployment rate for this economy (use Okun’s
law)?
5. For the economy described in Problem 3, find the effect on short-run equilibrium output of each of the following changes, taken one at a time:
a. An increase in government purchases from 1,500 to 1,600
b. A decrease in tax collections from 1,500 to 1,400
c. A decrease in planned investment spending from 900 to 800
What is the value of the multiplier for this economy?
6. For the following economy, find autonomous aggregate demand, the multiplier, shortrun equilibrium output, and the output gap. By how much would autonomous aggregate demand have to change to eliminate the output gap?
C 3,000 0.5(Y T),
_
I p I 1,500,
_
G G 2,500,
PROBLEMS
___
NX NX 200,
_
T T 2,000,
Y* 12,000.
__
7. An economy has zero net exports (NX 0). Otherwise, it is identical to the economy described in Problem 6.
a. Find short-run equilibrium output.
b. Economic
__ recovery abroad increases the demand for the country’s exports; as a
result, NX rises to 100. What happens to short-run equilibrium output?
c. Repeat part b, but this time assume that foreign
__economies are slowing, reducing
the demand for the country’s exports so that NX 100. (A negative value of
net exports means that exports are less than imports.)
d. How do your results help to explain the tendency of recessions and expansions to
spread across countries?
8. In a particular economy, planned investment spending is given by the equation
I p 300 0.1Y.
This equation captures the idea that when real GDP rises, firms find it more profitable to make capital investments. Specifically, in this economy, when real GDP rises
by a dollar, planned investment spending rises by 10 cents. All the other equations
describing this economy are the same as in Problem 6. Find autonomous aggregate
demand, the multiplier, short-run equilibrium output, and the output gap. (Be careful:
The multiplier is no longer given by the formula 1/(1c). You will need to calculate
directly the effect of a change in autonomous aggregate demand on short-run equilibrium output.) By how much would autonomous aggregate demand have to change to
eliminate any output gap?
9. An economy is described by the following equations:
C 40 0.8(Y T),
_
I p I 70,
_
G G 120,
__
NX NX 10,
_
T T 150.
a. Potential output Y* equals 580. By how much would government purchases have
to change to eliminate any output gap? By how much would taxes have to change?
Show the effects of these fiscal policy changes in a Keynesian cross diagram.
b. Repeat part a assuming that Y* 630.
10. (More difficult) This problem illustrates the workings of automatic stabilizers. Suppose that
an economy take their usual forms:
_ demand in __
_ aggregate
_ the components of
C C c(Y T), I p I, G G, and NX NX. However, suppose that, realistically, taxes are not fixed but depend on income. Specifically, we assume
T tY,
where t (a number between 0 and 1) is the fraction of income paid in taxes (the tax
rate). As we will see in this problem, a tax system of this sort serves as an automatic
stabilizer, because taxes collected automatically fall when incomes fall.
a. Find an algebraic expression for short-run equilibrium output in this economy.
685
686
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
b. Find an algebraic expression for the multiplier, that is, the amount that output
changes when autonomous aggregate demand changes by one unit. Compare the
expression you found to the formula for the multiplier when taxes are fixed. Show
that making taxes proportional to income reduces the multiplier.
c. Explain how reducing the size of the multiplier helps to stabilize the economy,
holding constant
fluctuations
in_the components
_
_
__ of autonomous aggregate demand.
d. Suppose C 500, I 1,500, G 2,000, NX 0, c 0.8, and t 0.25. Calculate numerical values for short-run equilibrium output and the multiplier.
■
ANSWERS TO IN-CHAPTER EXERCISES
■
25.1 First we need to find an equation that relates aggregate demand to output. We start
with the definition of aggregate demand and substitute the numerical values given
in the problem:
AD C I p G NX,
_
_ _
___
[ C c (Y T)] I G NX,
[820 0.7(Y 600)] 600 600 200,
1,800 0.7Y.
Using this relationship we construct a table analogous to Table 25.1. Some trial and
error is necessary to find an appropriate range of guesses for output (column 1).
Determination of Short-Run Equilibrium Output
(1)
(3)
(4)
Output Y
(2)
Aggregate demand
AD 1,800 0.7Y
Y AD
Y AD?
5,000
5,300
300
No
5,200
5,440
240
No
5,400
5,580
180
No
5,600
5,720
120
No
5,800
5,860
60
No
6,000
6,000
0
Yes
6,200
6,140
60
No
6,400
6,280
120
No
6,600
6,420
180
No
Short-run equilibrium output equals 6,000, as that is the only level of output that
satisfies the condition Y AD.
25.2 The graph shows the determination of short-run equilibrium output, Y 6,000.
The intercept of the expenditure line is 1,800, and its slope is 0.7. Notice that the
intercept equals autonomous aggregate demand and the slope equals the marginal
propensity to consume.
ANSWERS TO IN-CHAPTER EXERCISES
Aggregate demand AD
Y AD
Expenditure line
AD 1,800 0.7Y
Slope 0.7
1,800
45°
6,000
Output Y
25.3 This problem is an application of Okun’s law, introduced in Chapter 24. The recessionary gap in this example is 50/4,800, or about 1.04 percent, of potential output.
By Okun’s law, cyclical unemployment is one-half the percentage size of the output
gap, or 0.52 percent. As the natural rate of unemployment is 5 percent, total unemployment rate after the recessionary gap appears will be approximately 5.52 percent.
25.4 To find short-run equilibrium output after the increase in planned investment spending, we first find the relationship between aggregate demand
_ and output. The steps
are the same as in Exercise 25.1 except now we assume I 630.
AD C I p G NX
_
_ _
___
[ C c(Y T)] I G NX
[820 0.7(Y 600)] 630 600 200
1,830 0.7Y.
Comparing with Exercise 25.1, we see that the increase of 30 in planned investment
spending raises the intercept of the expenditure line by 30.
To solve for short-run equilibrium output, set Y AD, use the expression above
to substitute for AD, and solve for Y:
Y AD
1,830 0.7Y
6,100.
Hence the increase in planned investment causes output to increase from 6,000 (see
Exercise 25.1) to 6,100. If the economy had no output gap before the increase in
planned investment, the increase leads to an expansionary output gap of 6,100 6,000 100.
25.5 The increase in planned investment raised autonomous aggregate demand by 30. A
reduction of 30 in government purchases will restore autonomous aggregate demand
to its original level
_ It is straightforward to show
_ and thus eliminate the output gap.
directly that if I 630 and government purchases G are lowered from 600 to 570,
then
687
688
CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN
AD 1,800 0.7Y.
Setting Y AD and solving for Y, we find that short-run equilibrium output is
6,000, its original value.
25.6 An increase of 30 in planned investment created the output gap, so to eliminate the
output gap autonomous aggregate demand must be reduced by 30. The marginal
propensity to consume is 0.7 in this economy, so an increase in taxes of 30/0.7 42.9 will achieve a reduction of 30 (or 0.7 42.9)
in autonomous
consumption
_
_
spending. To confirm the answer, show that if I 630 and T 600 42.9 557.1 then short-run equilibrium output equals 6,000, its original value.
APPENDIX
AN ALGEBRAIC
SOLUTION OF THE BASIC
KEYNESIAN MODEL
■
his chapter showed how to solve the basic Keynesian model in two
steps, given specific numerical values for the parameters. In this
appendix we will show that the same steps can be used to find a
more general algebraic solution for short-run equilibrium output in the basic
Keynesian model. This solution has the advantage of showing clearly the links
between short-run equilibrium output, the multiplier, and autonomous aggregate demand. The general method can also be applied when we make changes
to the basic Keynesian model, as we will see in subsequent chapters.
The model we will work with is the same one presented earlier. It is based
on the consumption function, Equation 25.2, and the assumption that the
other three components of aggregate demand are fixed. We assume also that
tax collections are fixed. These assumptions may be summarized as follows:
T
_
C C c(Y T),
_
I p I,
_
G G,
__
NX NX,
690
CHAPTER 25 APPENDIX AN ALGEBRAIC SOLUTION OF THE BASIC KEYNESIAN MODEL
_
T T.
The first step in solving the model is to relate aggregate demand to output.
The definition of aggregate demand, Equation 25.1, is
AD C I p G NX.
As before, we substitute for the components of aggregate demand to get
_ _
_
_
__
AD [C c(Y T)] I G NX.
Rearranging this equation to separate the terms that do and do not depend
on output Y, we obtain
_ _
_
_
__
AD (C cT I G NX) cY.
This is Equation 25.3. The term in parentheses on the right side of the equation
represents autonomous aggregate demand, and the term cY represents induced
aggregate demand.
The second step in solving for short-run equilibrium output begins with its
definition, Y AD. Using the equation just above to substitute for AD, we have
_ _
_
__
Y (C cT I G NX) cY.
To solve this equation for Y, it is convenient to group all terms involving Y on
the left side of the equation:
_ _
_
_
__
Y cY (C cT I G NX),
or
_ _
_
_
__
Y(1 c) (C cT I G NX).
Dividing both sides of the equation by (1 c) gives the answer:
_ _
_
_
__
1
Y _____
(C cT I G NX).
1 c
(
)
(A.1)
Equation A.1 gives
output for our model economy in terms
_ _ __ equilibrium
_ short-run
_
of the values of C, I, G, NX, and T and the marginal propensity to consume c.
We can use this formula to solve for short-run equilibrium output in specific
numerical examples. For example,
suppose
we_ plug in the
_
_
__ numerical
_ values
assumed in Example 25.2: C 620, I 220, G 300, NX 20, T 250,
and c 0.8. We get
(
)
1
Y _______
[620 0.8(250) 220 300 20]
1 0.8
1 (960) 5 960 4,800,
___
0.2
which is the same answer found earlier.
Equation A.1 shows clearly the relationship between autonomous aggregate
demand and short-run equilibrium output. Autonomous _aggregate
the
_ _ is__
_ demand
second term on the right side of Equation A.1, equal to C cT I G NX.
The equation shows that a one-unit increase in autonomous aggregate demand
increases short-run equilibrium output by 1/(1 c) units. In other words, we can
see from Equation A.1 that the multiplier for this model equals 1/(1 c), a result
that we found more indirectly in Box 25.3.