AGGREGATE DEMAND AND OUTPUT IN THE SHORT · PDF fileafter the diagram that is used to...

C H A P T E R

25A G G R E G A T E D E M A N D A N D

O U T P U T I N T H E S H O R T R U N■

hen one of the authors of this book was a small boy, he used tospend some time every summer with his grandparents, who lived afew hours from his home. A favorite activity of his during these vis-

its 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 lifewas particularly fascinating to her grandson.

Grandma had spent the early years of her marriage in New England dur-ing the worst part of the Great Depression. In one of her reminiscences sheremarked that at that time, in the mid-1930s, it had been a satisfaction to herto be able to buy her children a new pair of shoes every year. In the smalltown where she and her family lived, many children had to wear their shoesuntil they fell apart, and a few unlucky boys and girls went to school bare-foot. Her grandson thought this was scandalous: “Why didn’t their parentsjust buy them new shoes?” he demanded.

“They couldn’t,” said Grandma. “They didn’t have the money. Most ofthe 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 oneside were boarded-up shoe factories and shoe workers with no jobs; on theother, children without shoes. Why couldn’t the shoe factories just open and

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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 thecost to society of an output gap. In an economy with a recessionary gap, avail-able resources that could in principle be used to produce valuable goods and ser-vices are instead allowed to lie fallow. This waste of resources lowers the econ-omy’s output and economic welfare, compared to its potential.

Grandma’s account also suggests how such an unfortunate situation mightcome about. Suppose factory owners and other producers, being reluctant toaccumulate unsold goods on their shelves, produce just enough output to satisfythe demand for their products. And suppose that for some reason the public’swillingness or ability to spend declines. If spending declines, factories will respondby cutting their production (because they don’t want to produce goods they can’tsell) and by laying off workers who are no longer needed. And because the work-ers who are laid off will lose most of their income—a particularly serious loss inthe 1930s, in the days before government-sponsored unemployment insurance—

they must reduce their own spending. As their spending declines, factories willreduce their production again, laying off more workers, who in turn reduce theirspending, and so on, in a vicious circle. In this scenario, the problem is not alack 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 highlyinfluential British economist of the first half of the twentieth century. Box 25.1gives a brief account of Keynes’s life and ideas. The goal of this chapter is to

656 CHAPTER 25 AGGREGATE DEMAND AND OUTPUT IN THE SHORT RUN

BOX 25.1: JOHN MAYNARD KEYNES AND THE KEYNESIANREVOLUTION

John Maynard Keynes (1883–1946), perhaps the most influential econ-omist of the twentieth century, was a remarkable individual who com-bined a brilliant career as an economic theorist with an active life indiplomacy, finance, journalism, and the arts. Keynes (pronounced“canes”) first came to prominence at the end of World War I when heattended the Versailles peace conference as a representative of the BritishTreasury. He was appalled by the shortsightedness of the diplomats atthe conference, particularly their insistence that the defeated Germansmake huge compensatory payments (called reparations) to the victoriousnations. In his widely read book The Economic Consequences of thePeace (1919), Keynes argued that the reparations imposed on Germanywere impossibly large and that attempts to extract the payments wouldprevent 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 professorshipat Cambridge, where his father had taught economics. Keynes’s early writ-ings had been on mathematics and logic, but after his experience in Ver-sailles he began to work primarily on economics, producing several well-regarded books. He developed an imposing intellectual reputation, editingGreat Britain’s leading scholarly journal in economics, writing articles fornewspapers and magazines, advising the government, and playing a majorrole in the political and economic debates of the day. On the side, Keynesmade fortunes both for himself and for King’s College (a part of CambridgeUniversity) by speculating in international currencies and commodities. Hewas also an active member of the Bloomsbury Group, a circle of leadingartists, performers, and writers that included E. M. Forster and Virginia

develop a model of how recessions and expansions may arise from fluctuationsin 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 chapterwe will emphasize a numerical and graphical approach to the basic Keynesianmodel. The appendix to this chapter provides a more general algebraic analysis.

We will begin with a brief discussion of the key assumptions of the basicKeynesian 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 thanor 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 reces-sionary output gap, while “too much” creates an expansionary output gap.

An implication of the basic Keynesian model is that government policies thataffect the level of spending can be used to reduce or eliminate output gaps. Poli-cies used in this way are called stabilization policies. Keynes himself argued for theactive use of fiscal policy—policy relating to government spending and taxes—toeliminate output gaps and stabilize the economy. In the latter part of this chapterwe will show why Keynes thought fiscal policy could help to stabilize the econ-omy, 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 com-plete or entirely realistic model of the economy, since it applies only to the shortperiod during which firms do not adjust their prices but instead meet the demandforthcoming at preset prices. Furthermore, by treating prices as fixed, the basicKeynesian model presented in this chapter does not address the determination of

JOHN MAYNARD KEYNES AND THE KEYNESIAN REVOLUTION 657

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Woolf. In 1925 Keynes married the glamorous Russian ballerina LydiaLopokova. Theirs was by all accounts a very successful marriage, andKeynes devoted significant energies to managing his wife’s career and pro-moting the arts in Britain.

Like other economists of the time, Keynes struggled to understand the GreatDepression that gripped the world in the 1930s. His work on the problem ledto the publication in 1936 of The General Theory of Employment, Interest,and Money. In The General Theory, Keynes tried to explain how economiescan remain at low levels of output and employment for protracted periods.He stressed a number of factors, most notably that aggregate spending maybe too low to permit full employment during such periods. Keynes recom-mended increases in government spending as the most effective way to increaseaggregate spending and restore full employment.

The General Theory is a difficult book, reflecting Keynes’s own struggle tounderstand the complex causes of the Depression. In retrospect, some of TheGeneral Theory’s arguments seem unclear or even inconsistent. Yet the bookis full of fertile ideas, many of which had a worldwide impact and eventuallyled to what has been called the Keynesian revolution. Over the years manyeconomists have added to or modified Keynes’s conception, to the point thatKeynes himself, were he alive today, probably would not recognize much ofwhat is now called Keynesian economics. But the ideas that insufficient aggre-gate spending can lead to recession and that government policies can help torestore full employment are still critical to Keynesian theory.

In 1937 a heart attack curtailed Keynes’s activities, but he remained animportant figure on the world scene. In 1944 he led the British delegationto the international conference in Bretton Woods, New Hampshire, whichestablished the key elements of the postwar international monetary andfinancial system, including the International Monetary Fund and the WorldBank. Keynes died in 1946.

inflation. Nevertheless, this model is a key building block of current theories ofshort-run economic fluctuations and stabilization policies. In subsequent chapterswe will extend the basic Keynesian model to incorporate inflation and otherimportant features of the economy.

THE BASIC KEYNESIAN MODELThe basic Keynesian model, on which we will focus in this chapter, is built ontwo key assumptions, given below. Of these two assumptions, the second—

that, in the short run, firms meet the demand for their products at presetprices—is the crucial one. As we will see in this chapter, if firms respond tochanges in demand primarily by changing their production levels instead oftheir prices, then changes in aggregate spending will have a powerful effect onaggregate output.

KEY ASSUMPTIONS OF THE BASIC KEYNESIAN MODEL

1. Aggregate demand fluctuates. Total planned spending in an economy, calledaggregate demand, depends on the prevailing level of real GDP as well asother factors. Changes in either real GDP or in other factors that affect totalspending 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 bychanging their prices. Instead, they typically set a price for some period, thenmeet the demand at that price. By “meeting the demand,” we mean that firmsproduce just enough to satisfy their customers.

The assumption that over short periods of time firms will meet the demandfor their products at preset prices is generally realistic. Think of the stores whereyou shop: The price of a pair of jeans does not fluctuate with the number of cus-tomers 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 thatprice, at least until the store runs out of stock. Similarly, the corner pizza restau-rant may leave the price of its large pie unchanged for months or longer, allow-ing its pizza production to be determined by the number of customers who wantto 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 thepizza restaurant, the menu cost is literally just that—the cost of printing up anew menu when prices change. Similarly, the clothing store faces the cost of re-marking all its merchandise if the manager changes prices. But menu costs mayalso include other kinds of costs, including, for example, the cost of doing a mar-ket survey to determine what price to charge and the cost of informing customersabout price changes.

Menu costs will not prevent firms from changing their prices indefinitely. Aswe saw in Chapter 24 for the case of Al’s ice cream store, too great an imbal-ance between demand and supply, as reflected by a difference between sales andpotential output, will eventually lead to a change in price. If no one is buyingjeans, for example, at some point the clothing store will mark down their jeansprices. Or if the pizza restaurant becomes the local hot spot, with a line of cus-tomers stretching out the door, eventually the manager will raise the price of alarge pie. Like other economic decisions, the decision to change prices reflects acost-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 normalproduction capacity—outweighs the menu costs associated with making thechange. As we have stressed, the basic Keynesian model developed in this chapter


menu costs the costs of changing prices

ignores the fact that prices will eventually adjust, and should therefore be inter-preted as applying to the short run.

AGGREGATE DEMANDIn the Keynesian theory discussed in this chapter, output at each point in time isdetermined by the amount that people want to spend—what economists callaggregate demand. Specifically, aggregate demand (AD) is total planned spendingon final goods and services.

The four components of total, or aggregate, spending on final goods and ser-vices were introduced in Chapter 18:

1. Consumer expenditure, or simply consumption (C), is spending by house-holds on final goods and services. Examples of consumer expenditure arespending on food, clothes, and entertainment, and on consumer durablegoods like automobiles and furniture.

2. Investment (I) is spending by firms on new capital goods, such as office build-ings, factories, and equipment. Spending on new houses and apartment build-ings (residential investment) and increases in inventories (inventory invest-ment) are also included in investment.

3. Government purchases (G) is spending by governments (federal, state, andlocal) on goods and services. Examples of government purchases include newschools and hospitals, military hardware, equipment for the space program,and the services of government employees, such as soldiers, police, and gov-ernment office workers. Recall from Chapter 18 that transfer payments, suchas Social Security benefits and unemployment insurance, and interest on thegovernment debt are not included in government purchases.

4. Net exports (NX) equals exports minus imports. Exports are sales of domes-tically produced goods and services to foreigners; imports are purchases bydomestic residents of goods and services produced abroad. Net exports rep-resents 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. Couldplanned spending ever differ from actual spending? The answer is yes. The mostimportant case is that of a firm that sells either less or more of its product thanexpected. As was noted in Chapter 18, additions to the stocks of goods sittingin a firm’s warehouse are treated in official government statistics as inventoryinvestment by the firm. In effect, government statisticians assume that the firmbuys its unsold output from itself; they then count those purchases as part of thefirm’s investment spending.1

Suppose, then, that a firm’s actual sales are less than expected so that part ofwhat it had planned to sell remains in the warehouse. In this case, the firm’s actualinvestment, including the unexpected increases in its inventory, is greater than itsplanned investment, which did not include added inventory. Suppose we agree tolet 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 itsinventory than planned, will find that its actual investment (including unplannedinventory investment) exceeds its planned investment so that I � I p.

AGGREGATE DEMAND 659

aggregate demand (AD) totalplanned spending on final goodsand services

1For the purposes of measuring GDP, treating unsold output as being purchased by its producer hasthe virtue of ensuring that actual production and actual expenditure are equal.

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 willbe less than planned investment, or I � I p. Example 25.1 gives a numerical illus-tration.

Actual and planned investment

The Fly-by-Night Kite Company produces $5,000,000 worth of kites during theyear. It expects sales of $4,800,000 for the year, leaving $200,000 worth of kitesto 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 Fly-by-Night’s actual investment I and its planned investment I p if actual kite salesturn 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 productionequipment ($1,000,000) plus its planned additions to inventory ($200,000), fora total of $1,200,000 in planned investment. The company’s planned investmentdoes 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 inkites 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 ininventory investment, so I � $1,400,000. We see that when the firm sells less out-put 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 toinventory, just as planned. In this case, actual and planned investment are thesame: I � I p � $1,200,000.

Finally, if Fly-by-Night sells $5,000,000 worth of kites, it will have no out-put to add to inventory. Its inventory investment will be zero, and its total actualinvestment (including the new equipment) will equal $1,000,000, which is lessthan its planned investment of $1,200,000 ( I � I p).

Because firms that are meeting the demand for their product or service at pre-set prices cannot control how much they sell, their actual investment (includinginventory investment) may well differ from their planned investment. However,for households, the government, and foreign purchasers, we may reasonablyassume that actual spending and planned spending are the same. Thus, from nowon 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 plannedspending, which in turn is the sum of planned spending by households, firms,governments, and foreigners. We use a superscript p to distinguish planned invest-ment spending by firms I p from actual investment spending I. However, becauseplanned spending equals actual spending for households, the government, andforeigners, we do not need to use superscripts for consumption, government pur-chases, or net exports.

DETERMINING AGGREGATE DEMAND: THECONSUMPTION 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 tospend on it—factors such as the price of pastries, the incomes of pastry-lovingconsumers, the prices of competing items like cinnamon buns, the health effects


EXAMPLE 25.1

of carbohydrate consumption, and so on. In the same way, to study aggregatedemand we need to specify the factors that determine how much households planto consume, how much firms plan to invest, and so on.

The largest component of aggregate demand—nearly two-thirds of totalspending—is consumption spending, or C. What determines how much peopleplan to spend on consumer goods and services in a given period? While manyfactors may be relevant, a particularly important determinant of the amount peo-ple plan to consume is their after-tax, or disposable, income. All else being equal,households and individuals with higher disposable incomes will consume morethan those with lower disposable incomes. Keynes himself stressed the importanceof disposable income in determining household consumption decisions, claiminga “psychological law” that people would tie their spending closely to theirincomes.

Recall from Chapter 22 that the disposable income of the private sector isthe total production of the economy, Y, less net taxes (taxes minus transfers), orT. So we can assume that consumption spending (C) increases as disposableincome (Y � T) increases. As already mentioned, other factors may also affectconsumption, such as the real interest rate, also discussed in Chapter 22. For nowwe will ignore those other factors, returning to some of them later.

An equation that captures the link between consumption and the private sec-tor’s disposable income is

C �_C � c(Y � T). (25.2)

This equation, which we will dissect in a moment, is known as the consumptionfunction. The consumption function relates consumption spending to its deter-minants, such as disposable (after-tax) income.

Let’s look at the consumption function, Equation 25.2, more carefully. Theright 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 thandisposable income that affect consumption. For example, suppose consumerswere to become more optimistic about the future so that they desire to con-sume more and save less at any given level of their current disposable incomes.An increase in desired consumption at any given level of disposable incomewould be represented in the consumption function, Equation 25.2, as anincrease in the term

_C.

The second term on the right side of Equation 25.2, c(Y � T), reflects theeffect of disposable income Y � T on consumption. The parameter c, a fixednumber, is called the marginal propensity to consume. The marginal propensityto consume, or MPC, is the amount by which consumption rises when currentdisposable income rises by $1. Presumably, if people receive an extra dollar ofincome, 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 (anincrease in income leads to an increase in consumption), but less than 1 (theincrease in consumption will be less than the full increase in income). Theseassumptions can be written symbolically as 0 � c � 1.

Figure 25.1 shows a hypothetical consumption function, with consumptionspending (C) on the vertical axis and disposable income (Y � T) on the hori-zontal axis. The intercept of the consumption function on the vertical axis equalsthe constant term

_C, and the slope of the consumption function equals the mar-

ginal 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 consumptionexpenditures and real disposable income in the United States for the period 1960through 1999. Figure 25.2, a scatter plot, shows aggregate real consumption onthe vertical axis and aggregate real disposable income on the horizontal axis. Each


consumption function the relationship between consumption spending and itsdeterminants, such as disposable(after-tax) income

marginal propensity toconsume (MPC) the amount bywhich consumption rises whendisposable income rises by $1;we assume that 0 � MPC � 1

point on the graph corresponds to a year between 1960 and 1999 (selectedyears are indicated in the figure). The position of each point is determined bythe combination of consumption and disposable income associated with thatyear. As you can see, there is indeed a close relationship between aggregateconsumption and disposable income: Higher disposable income implies higherconsumption.

AGGREGATE DEMAND AND OUTPUT

Thinking back to Grandma’s reminiscences, recall that an important element ofher story involved the links among production, income, and spending. As theshoe factories in Grandma’s town reduced production, the incomes of both fac-tory workers and factory owners fell. Workers’ incomes fell as the number ofhours of work per week were reduced (a common practice during the Depres-sion), as some workers were laid off, or as wages were cut. Factory owners’


FIGURE 25.1A ConsumptionFunction.The consumption functionrelates households’ consumption spending C todisposable income Y � T.The vertical intercept of thisconsumption function is

_C,

and the slope of the lineequals the marginal propensity to consume c.

Slope � c

Disposable income Y�T

Consumptionfunction

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FIGURE 25.2The U.S. ConsumptionFunction, 1960––1999.Each point on this figure represents a combination ofaggregate real consumptionand aggregate real disposableincome for a specific yearbetween 1960 and 1999.Note the strong positiverelationship between consumption and disposableincome.

0.0

7,000.0

6,000.0

5,000.0

4,000.0

3,000.0

2,000.0

1,000.0

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1995

199019851980

1975

19651970

Disposable income (1996 dollars, billions)1,000 2,000 3,000 4,000 5,000 6,000 7,0000

income fell as profits declined. Reduced incomes, in turn, forced both workersand factory owners to curtail their spending, which led to still lower productionand further reductions in income.

To capture these links in our model, we need to show how aggregate demandAD is affected by changes in aggregate income Y—which is the same, you mayrecall, as aggregate output, or GDP. The consumption function, which relates desiredconsumption to disposable income, helps to establish this relationship. Because con-sumption spending C is a large part of aggregate demand and because consump-tion depends on output Y, aggregate demand as a whole depends on output.

To express the connection between aggregate demand and output in an equa-tion, 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 inthe 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 yetsaid anything about the other three components of spending. For now, we willsimply assume that planned investment, government purchases, and net exportsare 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 writeT �

_T.

Substituting the fixed values for investment, government purchases, netexports, 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 dependon output Y and those that do not. This rearrangement yields

AD � (_C � c

_T �

_I �

_G �

__NX) � cY. (25.3)

Equation 25.3 shows that if real output Y increases by one unit, then aggregatedemand 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 out-put (Y) changes, aggregate demand (AD) changes with it, in the same direction.

Equation 25.3 also shows that aggregate demand can be divided into twoparts, a part that is determined outside the model and a part that is determinedwithin the model. The portion of aggregate demand that is determined outsidethe model is called autonomous aggregate demand. In this example, autonomousaggregate demand is given by the first term on the right side of Equation 25.3,(_C � c

_T �

_I �

_G �

__NX). The portion of aggregate demand that is determined

within the model is called induced aggregate demand. Algebraically, inducedaggregate demand is given by cY, the second term on the right side of Equation


autonomous aggregatedemand the portion of aggregate demand that is determined outside the model

induced aggregate demandthe portion of aggregate demandthat is determined within themodel (because it depends onoutput Y)

25.3. This portion of aggregate demand is determined within the model becauseit changes as income Y changes. Autonomous aggregate demand and inducedaggregate demand together equal total aggregate demand. Example 25.2 illus-trates these ideas numerically.

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 theother components of aggregate demand as fixed numbers, the algebraic expres-sion for aggregate demand can be written as (see Equation 25.3)

AD � [_C � c

_T �

_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, aggregatedemand increases as well.

Autonomous aggregate demand is the part of aggregate demand that is deter-mined outside the model and hence does not depend on output Y. Induced aggre-gate demand is the part of aggregate demand that does depend on output. In thisexample, AD � 960 � 0.8Y, so autonomous aggregate demand is 960 andinduced aggregate demand is 0.8Y. Notice that the numerical value of inducedaggregate demand depends on the value taken by output.


EXAMPLE 25.2

AGGREGATE DEMAND

Aggregate demand (AD) is total planned spending on final goods and ser-vices. 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’ salesare different from what they expected so that additions to inventory (a com-ponent of investment) are different from what firms anticipated.

The largest component of aggregate demand is consumer expenditure, orsimply 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 toconsume c. The marginal propensity to consume, a number between 0 and1, is the amount by which consumption rises when disposable income risesby $1.

Increases in output, which imply increases in income, cause consumptionto rise. As consumption is part of aggregate demand, aggregate demanddepends on output as well. The portion of aggregate demand that dependson output, and hence is determined within the model, is called inducedaggregate demand. The portion of aggregate demand determined outside themodel is autonomous aggregate demand.

RECAP

SHORT-RUN EQUILIBRIUM OUTPUT

Now that we have defined aggregate demand and seen how it is related to out-put, the next task is to determine what output will be. Recall the assumption ofthe basic Keynesian model: that in the short run, producers leave prices at pre-set levels and simply meet the demand at those prices. In other words, during theshort-run period in which prices are preset, firms produce an amount that is equalto aggregate demand. Accordingly, we define short-run equilibrium output as thelevel 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 periodin which prices are predetermined.

We can find the short-run equilibrium output for the economy describedin Example 25.2 using Table 25.1. Column 1 in the table gives some possiblevalues for short-run equilibrium output. To find the correct one, we must com-


short-run equilibrium outputthe level of output at which output Y equals aggregatedemand AD; the level of outputthat prevails during the period inwhich prices are predetermined

TABLE 25.1Numerical Determination of Short-Run Equilibrium Output

(1) (2) (3) (4)Aggregate demand

Output Y 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 2shows the value of aggregate demand corresponding to the values of outputin column 1. Recall that in this example, aggregate demand is determined bythe 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, soeach dollar in added income raises consumption and aggregate demand by 80cents.

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 onlyone level of output that satisfies that condition, Y � 4,800. At that level, outputand aggregate demand are precisely equal, so the producers are just meeting thedemand.

In this economy, what would happen if output happened to differ from itsequilibrium value of 4,800? Suppose, for example, that output were 4,000. Look-ing at column 2 of Table 25.1, we can see that when output is 4,000, aggregatedemand equals 960 � 0.8(4,000), or 4,160. Thus if output is 4.000, firms are

not producing enough to meet the demand. They will find that as sales exceedthe amounts they are producing, their inventories of finished goods are beingdepleted by 160 per year, and that actual investment is less than planned invest-ment. 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 firmsfaced when output was 4,000, be enough? The answer is no, because of inducedaggregate demand. That is, as firms expand their output, aggregate income (wagesand 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, to960 � 0.8(4,160), or 4,288. So an output level of 4,160 will still be insufficientto meet demand. As Table 25.1 shows, output will not be sufficient to meet aggre-gate 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 demandequals only 4,960— less than what firms are producing. So at an output level of5,000, firms will not sell all they produce and will find that their merchandise ispiling up on store shelves and in warehouses (actual investment is greater thanplanned investment). In response, firms will cut their production runs. As Table25.1 shows, they will have to reduce production to its equilibrium value of 4,800before output just matches aggregate demand.

EXERCISE 25.1

Construct a table like Table 25.1 for an economy like the one we havebeen 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 usingvalues for output above 5,000.)

Table 25.1 is useful for understanding why short-run equilibrium outputequals 4,800 in the economy described in Example 25.2, but it is a laborious wayto find the equilibrium value of output. Example 25.3 illustrates the more directapproach to solving for short-run equilibrium output numerically.

Finding short-run equilibrium output (numerical approach)

Solve numerically for short-run equilibrium output for the economy described inExample 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 bythe equation

AD � 960 � 0.8Y.

Recall that we found this equation by substituting the values given in the prob-lem for each of the four components of aggregate demand into the definition ofaggregate demand, Equation 25.1.

Second, we know that short-run equilibrium output must satisfy the equa-tion Y � AD. Using the equation AD � 960 � 0.8Y to substitute for AD in thedefinition of short-run equilibrium output, we get

Y � 960 � 0.8Y.


EXAMPLE 25.3

The solution to this equation gives us short-run equilibrium output, the level ofoutput 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 theprocess of solving the basic Keynesian model numerically.


BOX 25.2: SOLVING THE BASIC KEYNESIAN MODELNUMERICALLY

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 sim-plify. 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 solvefor 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,

Short-run equilibrium output can also be determined graphically, as Example25.4 shows.

Finding short-run equilibrium output (graphical approach)

Using a graphical approach, find short-run equilibrium output for the economydescribed in Example 25.2.

Figure 25.3 shows the graphical determination of short-run equilibrium out-put for the economy described in Example 25.2. Output Y is plotted on the hor-izontal axis and aggregate demand AD on the vertical axis. The figure containstwo 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 axisequals the variable on the horizontal axis. In this case, the 45° line represents theequation Y � AD. Recall that short-run equilibrium output must satisfy the con-dition Y � AD. So we know that the value of short-run equilibrium outputdemand must lie somewhere on the Y � AD line.

The second line in Figure 25.3, less steep than the 45° line, shows the rela-tionship between aggregate demand AD and output Y. Because it summarizes how


Y � 960/0.2,

Y � 4,800.

This answer is the same as the one shown in Table 25.1.

EXAMPLE 25.4

FIGURE 25.3Determination of Short-Run Equilibrium Output(Keynesian Cross).The 45° line represents theshort-run equilibrium condition Y � AD. The lineAD � 960 � 0.8Y, referredto as the expenditure line,shows the relationship ofaggregate demand to output.Short-run equilibrium output(4,800) is determined at theintersection of the two lines,point E. This type of diagramis known as a Keynesiancross.

45°

Slope � 0.8

Output Y4,800

E

Y � AD

Expenditure lineAD � 960 � 0.8Y

Agg

rega

te d

eman

d A

D

960

total expenditure depends on output, we will call this line the expenditure line.In this example, we know that the relationship between aggregate demand andoutput (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 isthe intercept of the expenditure line, as shown in Figure 25.3. The slope of theline relating aggregate demand to output is 0.8, the value of the coefficient ofoutput in the equation AD � 960 � 0.8Y. Where does the number 0.8 comefrom? (Hint: What determines by how much aggregate demand increases whenoutput rises by a dollar?)

Only one point in Figure 25.3 is consistent with both the definition of short-run equilibrium output Y � AD and the given relationship between aggregatedemand and output, AD � 960 � 0.8Y. That point is the intersection of thetwo lines, point E. At point E, short-run equilibrium output equals 4,800, whichis the same value that we obtained using Table 25.2 and by a direct numericalsolution. Notice that at points to the right of E, output exceeds aggregatedemand. Hence, to the right of point E, firms will be producing more than theycan sell and will tend to reduce their production. Similarly, to the left of pointE, aggregate demand exceeds output. In that region, firms will not be produc-ing enough to meet demand and will tend to increase their production. Only atpoint E, where output equals 4,800, will firms be producing enough to just sat-isfy aggregate demand.

The diagram in Figure 25.3 is often called the Keynesian cross, after its char-acteristic shape. The Keynesian cross shows graphically how short-run equilib-rium output is determined in a world in which producers meet demand at pre-determined prices.

EXERCISE 25.2

Find short-run equilibrium output for the economy described in Exercise25.1 using a Keynesian cross diagram. What are the intercept and theslope of the expenditure line?

AGGREGATE DEMAND AND THE OUTPUT GAP

We are now ready to use the basic Keynesian model to show how insufficient aggre-gate demand can lead to a recession. To illustrate this idea, we will continue towork with the economy introduced in Example 25.2. We have shown that in thiseconomy, short-run equilibrium output equals 4,800. Let’s now make the additionalassumption 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 outputso that there is no output gap. Starting from this position of full employment, Exam-ple 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 equi-librium output Y equals 4,800. Assume also that potential output Y* � 4,800 sothat 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 cancapture this change by assuming that

_C, the vertical intercept of the consump-

tion function, falls from its initial value of 620 to 610. What is the effect of thisreduction 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 firststep is to find the relationship between aggregate demand AD and output Y afterthe 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 thefour components of spending. Planned investment, government purchases, netexports, and net tax collections take the same fixed values as before:

_I � 220,


EXAMPLE 25.5

_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 def-inition 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-unitdecline 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 forAD 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 equi-librium output to fall from 4,800 to 4,750. The output gap, which was zero, nowequals Y* � Y � 4,800 � 4,750 � 50. We conclude that the fall in consumerspending has led to a recession. From Okun’s law, we know that this fall in out-put also implies an increase in cyclical unemployment.

The same result can be obtained graphically. Figure 25.4 shows the originalshort-run equilibrium point of the model (E), at the intersection of the Y � ADline 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, whichcorresponds 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 25.4A Decline in SpendingLeads to a Recession.A decline in consumers’ willingness to spend at anycurrent level of disposableincome reduces autonomousaggregate demand and shiftsthe expenditure line down.The short-run equilibriumpoint drops from E to F,reducing output and openingup a recessionary gap.

45°Recessionary gap

Output Y4,750 4,800

E

F

Y � AD

Expenditure lineAD � 960 � 0.8YExpenditure lineAD � 950 � 0.8Y

Y *

Agg

rega

te d

eman

d A

D

950960

A decline in autonomousaggregate demand shiftsthe expenditure line down

25.1

after the drop in consumer spending is AD � 950 � 0.8Y. Since the intercept ofthe expenditure line has decreased, from 960 to 950, but its slope has notchanged, the effect of the decline in consumer spending will be to shift the expen-diture line down in parallel fashion by 10 units. The blue line in Figure 25.4 indi-cates this downward shift. The new short-run equilibrium point is F.

As Figure 25.4 shows, the downward shift in aggregate demand reduces short-run 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 potentialoutput of 4,800. Suppose that in this economy the natural rate of unem-ployment u* is 5 percent. What will the actual unemployment rate beafter the recessionary gap appears?

EXERCISE 25.4

For the economy described in Exercise 25.1, suppose planned investmentI p rises from 600 to 630.Assuming the economy had no output gap beforethe increase in planned investment, show numerically that the change ininvestment leads to an expansionary output gap.


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What caused the 1990––1991 recession?

As we saw in Chapter 24, the 1990–1991 recession came at the wrong time for Pres-ident Bush.What caused the output of the U.S. economy to fall below its potential dur-ing that period?

Two factors have received a substantial part of the blame for the 1990–1991recession, one being a decline in consumer confidence. Organizations such as the Con-ference Board and the Survey Research Center of the University of Michigan per-form regular consumer surveys, in which people are asked their views about thefuture of the economy in general, and their own fortunes in particular. Consumerresponses are then summarized in measures of “consumer confidence.” A high levelof confidence implies that people are optimistic about both their own economic futuresand the future of the economy in general. Economists have found that when consumers

“These are hard times for retailers, so we should show themour support in every way we can.”

25.2

are optimistic, they are more likely to spend, particularly on “big-ticket” items such ascars and furniture. Hence, when consumer confidence took its sharpest-ever plunge fol-lowing Iraq’s invasion of Kuwait and the associated spike in oil prices in August 1990,economists and policymakers winced.As Americans became increasingly concerned bothabout U.S. energy security and the possibility of a ground war in the Middle East, aggre-gate 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 undevelopedland or commercial real estate as collateral. When land and other real estate prices fellsharply in the late 1980s, banks suffered serious losses. Some regions of the country, suchas New England, were hit especially hard. Many financially distressed banks either had nonew funds to lend or were not permitted to lend by government regulators.This declinein the supply of credit from banks made credit costlier and more difficult to obtain formany borrowers, especially small- and medium-sized firms.Without access to credit, thesefirms 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 spend-ing 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 Prob-

lem 5 at the end of the chapter).

Why was the deep Japanese recession of the 1990s bad news for the rest ofEast Asia?

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 policy-makers in other East Asian countries, such as Thailand and Singapore.Why did East Asianpolicymakers worry about the effects of the Japanese slump on their own economies?

Although the economies of Japan and its East Asian neighbors are intertwined inmany ways, one of the most important links is through trade. Much of the economicsuccess of East Asia has been based on the development of export industries, and overthe years Japan has been the most important customer for East Asian goods.When theeconomy slumped in the 1990s, Japanese households and firms reduced their purchasesof imported goods sharply.This fall in demand dealt a major blow to the export indus-tries of other East Asian countries. Not just the owners and workers of export indus-tries were affected, though. The decline in exports to Japan reduced net exports, andthus autonomous aggregate demand, in East Asian countries. Falling aggregate demandin turn reduced their short-run equilibrium GDP and contributed to recessionary out-put 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 majorimpact on its trading partners. Because the United States is the most important trad-ing partner of both Canada and Mexico, a recession in the United States would belikely to reduce Canadian and Mexican GDPs as well by reducing U.S. demand for theexports of its neighbors.

THE MULTIPLIER

Note that in Example 25.5, although the initial decline in consumer spending (asmeasured 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 thanthe initial change in spending is the “vicious circle” effect suggested by Grandma’sreminiscences about the Great Depression. Specifically, a fall in consumer spendingnot only decreases aggregate demand, it also reduces the incomes of workers andowners in the industries that produce consumer goods. As their incomes fall, theseworkers and capital owners reduce their spending, which reduces the output andincomes of other producers in the economy. And these reductions in income leadto still further cuts in spending. Ultimately, these successive rounds of declines in


spending and income may lead to a decrease in aggregate demand that is signifi-cantly greater than the change in spending that started the process.

The idea that a change in spending may lead to a much larger change inshort-run equilibrium output is an important feature of the basic Keynesianmodel. In Example 25.5 we considered the effects of a decrease in spending, butan increase in spending produces the same effect in reverse. For example, ifdesired consumption had increased rather than decreased by 10, it would haveset off successive rounds of increases in income and spending, culminating in afinal increase of 50 in short-run equilibrium output. The same type of effect alsoapplies to changes in other components of autonomous aggregate demand. Forexample, in this hypothetical economy, an increase of 10 in desired investmentspending

_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 themultiplier 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 short-run equilibrium output, and each $1 decrease in autonomous aggregate demandimplies a $5 decrease in short-run equilibrium output. Box 25.3 provides moreinformation about the economics of the multiplier and shows how to calculateits numerical value in specific examples.

We stress that, because the basic Keynesian model omits some important fea-tures of the real economy, it tends to yield unrealistically high values of the mul-tiplier. Indeed, virtually no one believes that the multiplier in the U.S. economy isas high as 5. Later we will discuss why the basic Keynesian model tends to over-state the value of the multiplier. Nevertheless, the idea that changes in aggregatedemand can have important effects on short-run equilibrium output remains a cen-tral tenet of Keynesian economics and a major factor in modern policymaking.


income-expenditure multiplierthe effect of a one-unit increasein autonomous aggregatedemand on short-runequilibrium output

BOX 25.3: THE MULTIPLIER IN THE BASIC KEYNESIAN MODEL

In Example 25.5, a drop in autonomous aggregate demand of 10 units causeda decline in short-run equilibrium output five times as great—an illustrationof the income-expenditure multiplier in action. To see more precisely why thismultiplier effect occurs, note that the initial decrease of 10 in consumer spend-ing in Example 25.5 has two effects. First, because consumption spending ispart of aggregate demand, the fall in consumer spending directly reducesaggregate demand by 10. Second, the fall in spending also reduces by 10 theincomes of producers (workers and firm owners) of consumer goods. Underour assumption that the marginal propensity to consume is 0.8, the produc-ers of consumer goods will therefore reduce their consumption spending by8, or 0.8 times their income loss of 10. This reduction in spending cuts theincome 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 stillother 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 ofspending and income reductions the effects become quite small.

Adding up all these “rounds” of income and spending reductions, thetotal effect on aggregate demand of the initial reduction of 10 in consumerspending is

10 � 8 � 6.4 � 5.12 � ... .

The three dots indicate that the series of reductions continues indefinitely. Thetotal effect of the initial decrease in consumption can also be written as


10[1 � 0.8 � (0.8)2 � (0.8)3 � ...].

This expression highlights the fact that the spending that takes place in eachround is 0.8 times the spending in the previous round—0.8, because thatis the marginal propensity to consume out of the income generated by theprevious round of spending.

A useful algebraic relationship, which applies to any number x greaterthan 0 but less than 1, is

11 � x � x2 � x3 � ... � ____.

1�x

If we set x � 0.8, this formula implies that the total effect of the decline inconsumption spending on aggregate demand and output is

1 110(________) � 10(____) � 10 � 5 � 50.

1 � 0.8 0.2

This answer is consistent with our earlier calculation, which showed thatshort-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 forthe multiplier in the basic Keynesian model. Recalling that c is the marginalpropensity to consume out of disposable income, we know that a one-unitincrease in autonomous aggregate demand raises spending and income byone unit in the first round, by c � 1 � c units in the second round, byc � c � c2 units in the second round, by c � c2 � c3 units in the thirdround, and so on. Thus the total effect on short-run equilibrium output ofa 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 Keynesianmodel with a marginal propensity to consume of c, the multiplier equals1/(1 � c). To check this result, we can substitute our assumed numericalvalue 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.

SHORT-RUN EQUILIBRIUM OUTPUT

Short-run equilibrium output is the level of output at which output equalsaggregate demand; or in symbols, Y � AD. For a specific example econ-omy, short-run equilibrium output can be solved for numerically (see Box25.2) or graphically. The graphical solution is based on a diagram calledthe Keynesian cross. The Keynesian cross diagram includes two lines: a 45°line that captures the condition Y � AD and the expenditure line, whichshows the relationship of aggregate demand to output. Short-run equilib-rium output is determined at the intersection of the two lines. If short-runequilibrium output differs from potential output, an output gap exists.

Increases in autonomous aggregate demand shift the expenditure lineupward, increasing short-run equilibrium output, and decreases inautonomous aggregate demand induce declines in short-run equilibrium out-put. Decreases in autonomous aggregate demand that drive actual outputbelow potential output are a possible source of recessions. Generally, a one-

RECAP

STABILIZING AGGREGATE DEMAND: THE ROLEOF FISCAL POLICYAccording to the basic Keynesian model, inadequate spending is an important causeof recessions. To fight recessions—at least, those caused by insufficient demandrather than slow growth of potential output—policymakers must find ways toincrease aggregate demand. Policies that are used to affect aggregate demand, withthe 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 decisionsabout the size of the money supply, while fiscal policy refers to decisions about thegovernment’s budget—how much the government spends and how much tax rev-enue it collects. In the remainder of this chapter we will focus on fiscal policy (mon-etary policy will be discussed in Chapters 26 and 27). Specifically, we will considerhow fiscal policy works in the basic Keynesian model, looking first at the effectsof changes in government purchases of goods and services and then at changes intax collections. We will conclude the chapter with a discussion of some practicalissues that arise in the application of fiscal policy.

GOVERNMENT PURCHASES AND AGGREGATE DEMAND

Decisions about government spending represent one of the two main componentsof fiscal policy, the other being decisions about the level and type of taxes. As wasmentioned earlier (see Box 25.1), Keynes himself felt that changes in governmentspending were probably the most effective tool for reducing or eliminating outputgaps. His basic argument was straightforward: Government purchases of goods andservices are a component of aggregate demand, so aggregate demand is directlyaffected by changes in government purchases. If output gaps are caused by too muchor too little aggregate demand, then the government can help to guide the economytoward full employment by changing its own level of spending. Keynes’s viewsseemed to be vindicated by the events of the 1930s, notably the fact that the Depres-sion did not finally end until governments greatly increased their military spendingin the latter part of the decade. Ironically, Adolf Hitler may have been the mostsuccessful of all the era’s leaders at applying Keynes’s prescription (although no evi-dence suggests that the Nazi dictator was familiar with Keynes’s writings). Economichistorians credit Hitler’s massive rearmament and road-building programs withgreatly reducing unemployment in Germany in the 1930s.

Example 25.6 shows how increased government purchases of goods and ser-vices can help to eliminate a recessionary gap. (The effects of government spend-ing on transfer programs, such as unemployment benefits, are a bit different. Wewill 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 cre-ates a recessionary gap of 50. Show that in that economy, a 10-unit increase ingovernment purchases, from

_G � 300 to

_G � 310, will eliminate the output

gap and restore full employment.

STABILIZING AGGREGATE DEMAND: THE ROLE OF FISCAL POLICY 675

stabilization policiesgovernment policies that areused to affect aggregate demand,with the objective of eliminating output gaps

unit increase in autonomous aggregate demand leads to a larger increase inshort-run equilibrium output, a result of the income-expenditure multiplier.The multiplier arises because a given initial increase in spending raises theincomes of producers, which leads them to spend more, raising the incomesand spending of other producers, and so on.

EXAMPLE 25.6

Intuitively, the 10-unit increase in government purchases should be justenough to offset the 10-unit decline in autonomous consumption expendituresand restore actual output to the full-employment level of 4,800. Let’s confirm thisresult by solving for the value of short-run equilibrium output after the increasein government purchases.

As before, the first step is to write the relationship between aggregate demandAD 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 firstcomponent, 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, governmentpurchases 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 getY � 4,800, which is the same value assumed for potential output Y*. Thus in thisexample the increase in government purchases eliminates the recessionary output gap.

The effect of the increase in government purchases is shown graphically inFigure 25.5. After the 10-unit decline in autonomous consumption spending

_C,


FIGURE 25.5An Increase inGovernment PurchasesEliminates a RecessionaryGap.After a 10-unit decline inautonomous consumerspending

_C, the economy is at

point F, with a recessionarygap of 50 (see Figure 25.4).A10-unit increase in government purchases raisesautonomous aggregatedemand by 10 units, shiftingthe expenditure line back toits original position and raisingthe equilibrium point from Fto E. At point E, where outputequals potential output (Y � Y* � 4,800), the outputgap has been eliminated.

45°Recessionary gap

Output Y4,750 4,800

E

F

Y � AD



Y *

Agg

rega

te d

eman

d A

D

950

960

An increase in Gshifts the expenditureline upward

25.3

the economy is at point F, with a 50-unit recessionary gap. The 10-unit increasein government purchases raises the intercept of the expenditure line 10 units, caus-ing the expenditure line to shift upward in parallel fashion. The economy returnsto 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 expansion-ary output gap. Show how a change in government purchases could be usedto eliminate this output gap. Confirm your answer numerically.

To this point we have been considering the effect of fiscal policy on a hypo-thetical economy. Economic Naturalists 25.3 and 25.4 illustrate the applicationof 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 ofHokkaido. About 32 miles of the planned 160-mile highway has been completed, at acost of $1.9 billion, or $60 million per mile. Very few drivers use the road, largelybecause an existing highway that runs parallel to the new toll road is free. Officialstried to attract drivers by offering prizes and running promotional contests.Though thecampaign succeeded in increasing the average number of cars on the road to 862 perday, 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 Naturalist24.1), and the government has periodically initiated large spending programs to tryto stimulate the economy. Indeed, during the 1990s the Japanese government spentmore than $1 trillion on public works projects. More than $10 billion was spenton the Tokyo subway system, an amount so far over budget that subway tokenswill 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, requir-ing passengers to make inconvenient transfers to traverse the city.) Other exam-ples of government spending programs include the construction of multimillion-dol-lar concert halls in small towns, elaborate tunnels where simple roads would havebeen adequate, and the digging up and relaying of cobblestone sidewalks. Despiteall this spending, the Japanese recession has dragged on.

The basic Keynesian model implies that increases in government spending suchas those undertaken in Japan should help to increase output and employment.Japanese public works projects do appear to have stimulated the economy, thoughnot enough to pull Japan out of the recession. Why has Japan’s fiscal policy provedinadequate to the task? Some critics have argued that the Japanese government wasunconscionably slow in initiating the fiscal expansion, and that when spending wasfinally increased, it was simply not enough, relative to the size of the Japanese econ-omy and the depth of the recession. Another possibility, which lies outside the basicKeynesian model, is that the wasteful nature of much of the government spendingdemoralized Japanese consumers, who realized that as taxpayers they would atsome point be responsible for the costs incurred in building roads nobody wantsto use. Reduced consumer confidence implies reduced consumption spending, whichmay to some extent have offset the stimulus from government spending. Very pos-sibly, more productive investments of Japanese public funds would have had agreater impact on aggregate demand (by avoiding the fall in consumer confidence);certainly, they would have had a greater long-term benefit in terms of increasingthe potential output of the economy.


25.4

Does military spending stimulate aggregate demand?

An antiwar poster from the 1960s bore the message “War is good business. Invest yourson.” 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 Keynesianmodel, increases in aggregate demand created by increased government spending mayhelp bring an economy out of a recession or depression. Does military spending stim-ulate 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 spend-ing 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 thepeak of the Vietnam War in 1967–1969 and during the Reagan military buildup of the1980s.


FIGURE 25.6U.S. MilitaryExpenditures as a Shareof GDP, 1940––1999.Military expenditures as ashare of GDP rose duringWorld War II, the KoreanWar, the Vietnam War, andthe Reagan military buildupof the early 1980s. Increasedmilitary spending is generallyassociated with an expandingeconomy and decliningunemployment.The blueareas indicate periods ofrecession.

Year

0

40

35

30

25

20

15

10

5

1940

1944

1948

1952

1956

1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

Sha

re o

f GD

P (

%)

Defense spending/GDP

World War II

Korean War Peak of Vietnam War

Reagan militarybuildup

Figure 25.6 provides some support for the idea that expanded military spend-ing tends to promote growth in aggregate demand. The clearest case is the WorldWar II era, during which massive military spending helped the U.S. economy torecover from the Great Depression.The U.S. unemployment rate fell from 17.2 per-cent of the workforce in 1939 (when defense spending was less than 2 percent ofGDP) to 1.2 percent in 1944 (when defense spending was greater than 37 percentof GDP). Two brief recessions, in 1945 and 1948–1949, followed the end of thewar and the sharp decline in military spending. At the time, though, many peoplefeared that the war’s end would bring a resumption of the Depression, so the rel-ative mildness of the two postwar recessions was something of a relief.

Increases in defense spending during the post-World War II period were alsoassociated with economic expansions. The Korean War of 1950–1953 occurredsimultaneously with a strong expansion, during which the unemployment ratedropped from 5.9 percent in 1949 to 2.9 percent in 1953. A recession began theyear the war ended, 1954, though military spending had not yet declined much.Finally, economic expansions also occurred during the Vietnam-era military buildupin the 1960s and the Reagan buildup of the 1980s.These episodes support the ideathat increases in government spending—in this case, for weapons and military sup-plies—can help to stimulate the economy.

TAXES, TRANSFERS, AND AGGREGATE DEMAND

Besides making decisions about government purchases of goods and services, fis-cal policymakers also determine the level of tax collections (payments from theprivate sector to the government) and transfer payments (payments from the gov-ernment to the private sector, such as welfare payments and Social Security). Thebasic Keynesian model implies that like changes in government purchases, changesin the level of taxes or transfers can be used to affect aggregate demand and thusto eliminate output gaps.

Unlike changes in government purchases, however, changes in taxes or trans-fers do not affect aggregate demand directly. Instead they work indirectly bychanging disposable income in the private sector. Specifically, either a tax cut oran increase in government transfer payments increases disposable income in theprivate sector, which according to the consumption function should encouragehouseholds to spend more on consumer goods and services. In short, changes intaxes and transfers affect aggregate demand only to the extent that they changethe level of spending in the private sector. Example 25.7 shows the effect of atax cut (or an equal-size increase in transfers) on aggregate demand and short-run 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 inconsumer spending of 10 units creates a recessionary gap of 50. Example 25.6showed that this recessionary gap could be eliminated by a 10-unit increase in gov-ernment purchases. Suppose that, instead of increasing government purchases, fis-cal policymakers decided to stabilize aggregate demand by changing the level of taxcollections. By how much should they change taxes to eliminate the output gap?

A common first guess at the answer to this problem is that policymakersshould 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 thathouseholds have reduced their consumption spending by 10 units at each level ofoutput Y. To eliminate this recessionary gap, the change in taxes must inducehouseholds to increase their consumption spending by 10 units at each outputlevel. However, if taxes T are cut by 10 units, raising disposable income Y � Tby 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 incomeis 0.8, so consumption spending increases by only 0.8 times the amount of thetax cut. (The rest of the tax cut is saved.)


“Your majesty, my voyage will not only forge a new route to the spices of theEast but also create over three thousand new jobs.”

EXAMPLE 25.7

© T

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ew Y

orke

rC

olle

ctio

n 19

92 D

ana

Frad

on fr

om c

arto

onba

nk.c

om.

All

Rig

hts

Res

erve

d.

To raise consumption spending by 10 units, fiscal policymakers must cut taxesby 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 eachlevel of output. That increase will just offset the 10-unit decrease in autonomousconsumption

_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 exportsgiven 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 sub-stitute 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 restorefull employment in this economy.

Note that since T refers to net taxes, or taxes less transfers, the same resultcould be obtained by increasing transfer payments by 12.5 units. Because house-holds spend 0.8 times any increase in transfer payments they receive, this policywould 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 increasein government purchases, shown in Figure 25.5. Because it leads to a 10-unitincrease in consumption at any level of output, the tax cut shifts the expenditureline up by 10 units. Equilibrium is attained at point E in Figure 25.5, where out-put again equals potential output.

EXERCISE 25.6

In Exercise 25.5, you eliminated an expansionary output gap from theeconomy described in Exercise 25.1 by changing government purchases.How could the same effect be achieved by changing tax collections?


FISCAL POLICY AND AGGREGATE DEMAND

Stabilization policies are policies used to affect aggregate demand with theobjective of eliminating output gaps. Fiscal policy includes two methods foraffecting aggregate demand: changes in government purchases and changesin taxes or transfer payments. An increase in government purchasesincreases autonomous aggregate demand by an equal amount. A reductionin taxes or an increase in transfer payments increases autonomous aggre-gate demand by an amount equal to the marginal propensity to consumetimes the reduction in taxes or increase in transfers. The ultimate effect of

RECAP

FISCAL POLICY AS A STABILIZATION TOOL:TWO QUALIFICATIONSThe basic Keynesian model might lead you to think that fiscal policy can be usedquite precisely to eliminate output gaps. But as is often the case, the real worldis more complicated than economic models. We close the chapter with two qual-ifications 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 pur-chases, taxes, and transfer payments change aggregate demand without affectingthe supply side of the economy, as represented by potential output. But as wesaw 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 theledger, tax and transfer programs may well affect the incentives, and thus the eco-nomic behavior, of households and firms. For example, a high tax rate on inter-est income reduces the after-tax return on saving, which may cause people to saveless, while a tax break on new investment may encourage firms to increase theirrate of capital formation. Such changes in saving or investment will in turn affectpotential output. Many other examples could be given of how taxes and trans-fers affect economic behavior and thus potential output.

Some critics of the Keynesian theory have gone so far as to argue that theonly effects of fiscal policy that matter are its effects on potential output. Thiswas essentially the view of the so-called supply-siders, a group of economists andjournalists whose influence reached a high point during the first Reagan admin-istration (1981–1985). Through their arguments that lower taxes would sub-stantially increase potential output, with no significant effect on aggregatedemand, the supply-siders provided crucial support for the large tax cuts thattook place under the Reagan administration.

A more balanced view is that fiscal policy affects both aggregate demand andpotential output. Thus, government policymakers should take into account notonly the need to stabilize aggregate demand but also the potential effects of gov-ernment spending, taxes, and transfers on the economy’s productive capacity.

The second qualification about the use of fiscal policy is that fiscal policy isnot always flexible enough to be useful for stabilization. Our examples haveimplicitly assumed that the government can change spending or taxes relativelyquickly in order to eliminate output gaps. In reality, changes in government spend-ing or taxes must usually go through a lengthy legislative process, which reducesthe 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 Con-gress 18 months or more before they actually go into effect. Another factor thatlimits the flexibility of fiscal policy is that fiscal policymakers have many otherobjectives besides stabilizing aggregate demand, from assuring an adequatenational defense to providing income support to the poor. What happens if, say,the need to strengthen the national defense requires an increase in governmentspending but the need to stabilize aggregate demand requires a decrease in spend-ing? Such conflicts can be difficult to resolve through the political process.

FISCAL POLICY AS A STABILIZATION TOOL: TWO QUALIFICATIONS 681

a fiscal policy change on short-run equilibrium output equals the change inautonomous aggregate demand times the multiplier.

Accordingly, if the economy is in recession, an increase in governmentpurchases, a cut in taxes, or an increase in transfers can be used to stimu-late spending and eliminate the recessionary gap.

This lack of flexibility means that fiscal policy is less useful for stabilizingaggregate demand than the basic Keynesian model suggests. Nevertheless, mosteconomists view fiscal policy as an important stabilizing force for two reasons.The first is the presence of automatic stabilizers, provisions in the law that implyautomatic increases in government spending or decreases in taxes when real out-put declines. For example, some government spending is earmarked as “recessionaid”; it flows to communities automatically when the unemployment rate reachesa certain level. Taxes and transfer payments also respond automatically to out-put gaps: When GDP declines, income tax collections fall (because households’taxable incomes fall), while unemployment insurance payments and welfare ben-efits rise—all without any explicit action by Congress. These automatic changesin government spending and tax collections help to increase aggregate demandduring recessions and reduce it during expansions, without the delays inherent inthe legislative process.

The second reason that fiscal policy is an important stabilizing force is thatwhile fiscal policy may be difficult to change quickly, it may still be useful fordealing with prolonged episodes of recession. The Great Depression of the 1930sand the Japanese slump of the 1990s are two cases in point. However, becauseof the relative lack of flexibility of fiscal policy, in modern economies aggregatedemand is more usually stabilized through monetary policy. The role of mone-tary policy in stabilizing aggregate demand is the subject of the next chapter.


• The basic Keynesian model shows how fluctuations inaggregate spending, or aggregate demand, can cause actualoutput to differ from potential output. Too little spendingleads to a recessionary output gap, while too much spend-ing creates an expansionary output gap. This model relieson two basic assumptions: that aggregate demand fluctu-ates, and that in the short run, firms will meet the demandfor their products at preset prices.

• Aggregate demand is total planned spending on final goodsand services. The four components of total spending are con-sumption, investment, government purchases, and netexports. Planned and actual consumption, government pur-chases, and net exports are assumed to be the same. Actualinvestment may differ from planned investment, becausefirms may sell a greater or lesser amount of their productionthan they expected. If firms sell less than they expected, forexample, they are forced to add more goods to inventory thananticipated. And because additions to inventory are countedas part of investment, in this case actual investment (includ-ing inventory investment) is greater than planned investment.

• Consumption is related to disposable, or after-tax, incomeby a relationship called the consumption function. Theamount by which desired consumption rises when dispos-able income rises by $1 is called the marginal propensity toconsume (MPC). The marginal propensity to consume isalways greater than 0 but less than 1.

• An increase in real output raises aggregate demand, sincehigher output (and equivalently, higher income) encourageshouseholds to consume more. Aggregate demand can bebroken down into two components, autonomous aggregatedemand and induced aggregate demand. Autonomous

aggregate demand is the portion of aggregate demand thatis determined outside the model; induced aggregate demandis the portion that is determined within the model. In themodel presented in this chapter, induced aggregate demandis the part of aggregate demand that depends on currentoutput.

• At predetermined prices, short-run equilibrium output isthe level of output that equals aggregate demand. Short-runequilibrium can be determined graphically in a Keynesiancross diagram, drawn with aggregate demand on the verti-cal axis and output on the horizontal axis. The Keynesiancross contains two lines: an expenditure line, which relatesaggregate demand to output, and a 45° line, which repre-sents the condition that short-run equilibrium outputequals aggregate demand. Short-run equilibrium output isdetermined at the point at which these two lines intersect.Algebraically, short-run equilibrium output can be found bysetting output equal to aggregate demand and solving forthe value of output (see Box 25.2).

• Changes in autonomous aggregate demand will lead tochanges in short-run equilibrium output. In particular, if theeconomy is initially at full employment, a fall in autono-mous aggregate demand will create a recessionary gap anda rise in autonomous aggregate demand will create anexpansionary gap. The effect of a one-unit increase inautonomous aggregate demand on short-run equilibriumoutput is called the multiplier. An increase in autonomousaggregate demand not only raises spending directly, it alsoraises the incomes of producers, who in turn increase theirspending, and so on. Hence the multiplier is greater than 1;that is, a $1 increase in autonomous aggregate demandraises short-run equilibrium output by more than $1.

automatic stabilizersprovisions in the law that implyautomatic increases in government spending ordecreases in taxes when realoutput declines

■ S U M M A R Y ■

• To eliminate output gaps and restore full employment, thegovernment employs stabilization policies. The two majortypes of stabilization policy are monetary policy and fiscalpolicy. Stabilization policies work by changing aggregatedemand, and hence short-run equilibrium output. Forexample, an increase in government purchases raises aggre-gate demand, so it can be used to reduce or eliminate arecessionary gap. Similarly, a cut in taxes or an increase intransfer payments increases the public’s disposable income,raising consumption and aggregate demand. Higher aggre-gate demand, in turn, raises short-run equilibrium output.

• Two qualifications must be made to the use of fiscal policyas a stabilization tool. First, fiscal policy may affect poten-tial output as well as aggregate demand. And second,because changes in fiscal policy must go through a lengthylegislative process, fiscal policy is not always flexibleenough to be useful for short-run stabilization. However,automatic stabilizers—provisions in the law that implyautomatic increases in government spending or reductionsin taxes when output declines—can overcome the problemof legislative delays to some extent and contribute to eco-nomic stability.

PROBLEMS 683

■ K E Y T E R M S ■

aggregate demand (AD) (659)automatic stabilizers (682)autonomous aggregate demand (663)consumption function (661)

income-expenditure multiplier (673)induced aggregate demand (663)marginal propensity to consume

(MPC) (661)

menu costs (658)short-run equilibrium output (665)stabilization policies (675)

■ R E V I E W Q U E S T I O N S ■

1. What are the two key assumptions of the basic Keynesianmodel? Explain why each of the two assumptions is nec-essary if one is to accept the view that aggregate spendingis a driving force behind short-term economic fluctua-tions.

2. Give an example of a good or service whose pricechanges very frequently and one whose price changes rel-atively infrequently. What accounts for the difference?

3. Define aggregate demand and list its components. Whydoes aggregate demand change when output changes?

4. Explain how planned spending and actual spending candiffer. Illustrate with an example.

5. Sketch a graph of the consumption function, labeling theaxes of the graph. Discuss the economic meaning of (a) amovement from left to right along the graph of the con-sumption function and of (b) a parallel upward shift ofthe consumption function.

6. Sketch the Keynesian cross diagram. Explain in wordsthe economic significance of the two lines graphed in thediagram. Given only this diagram, how could you deter-mine autonomous aggregate demand, induced aggregatedemand, the marginal propensity to consume, and short-run equilibrium output?

7. Using the Keynesian cross diagram, illustrate the twocauses of the 1990–1991 recession discussed in Eco-nomic Naturalist 25.1.

8. Define the multiplier. In economic terms, why is the mul-tiplier greater than 1?

9. The government is considering two alternative policies,one involving increased government purchases of 50, theother involving a tax cut of 50. Which policy will stimu-late aggregate demand by more? Why?

■ P R O B L E M S ■

1. Acme Manufacturing is producing $4,000,000 worth of goods this year and is expect-ing to sell its entire production. It is also planning to purchase $1,500,000 in newequipment during the year. At the beginning of the year the company has $500,000in 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 thesethree cases is output equal to short-run equilibrium output?

2. Data on before-tax income, taxes paid, and consumption spending for the Simpsonfamily in various years are given below.


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 marginalpropensity 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 itsconsumption by $1,000 at each level of after-tax income. (“Income” does notinclude the prize money.) How does this change affect the graph of their con-sumption 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’slaw)?

5. For the economy described in Problem 3, find the effect on short-run equilibrium out-put of each of the following changes, taken one at a time:a. An increase in government purchases from 1,500 to 1,600b. A decrease in tax collections from 1,500 to 1,400 c. A decrease in planned investment spending from 900 to 800What is the value of the multiplier for this economy?

6. For the following economy, find autonomous aggregate demand, the multiplier, short-run equilibrium output, and the output gap. By how much would autonomous aggre-gate 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 685

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 econ-

omy 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, reducingthe 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 prof-itable to make capital investments. Specifically, in this economy, when real GDP risesby a dollar, planned investment spending rises by 10 cents. All the other equationsdescribing this economy are the same as in Problem 6. Find autonomous aggregatedemand, the multiplier, short-run equilibrium output, and the output gap. (Be careful:The multiplier is no longer given by the formula 1/(1�c). You will need to calculatedirectly the effect of a change in autonomous aggregate demand on short-run equilib-rium output.) By how much would autonomous aggregate demand have to change toeliminate 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 haveto 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. Sup-pose that the components of aggregate demand in an economy take their usual forms:C �

_C � c(Y � T), I p �

_I, G �

_G, and NX �

__NX. However, suppose that, realis-

tically, 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 taxrate). As we will see in this problem, a tax system of this sort serves as an automaticstabilizer, because taxes collected automatically fall when incomes fall.a. Find an algebraic expression for short-run equilibrium output in this economy.


(1) (2) (3) (4)Aggregate demand

Output Y 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

b. Find an algebraic expression for the multiplier, that is, the amount that outputchanges when autonomous aggregate demand changes by one unit. Compare theexpression you found to the formula for the multiplier when taxes are fixed. Showthat 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. Cal-

culate numerical values for short-run equilibrium output and the multiplier.

■ A N S W E R S T O I N - C H A P T E R E X E R C I S E S ■

25.1 First we need to find an equation that relates aggregate demand to output. We startwith the definition of aggregate demand and substitute the numerical values givenin 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 anderror is necessary to find an appropriate range of guesses for output (column 1).

Determination of Short-Run Equilibrium Output

Short-run equilibrium output equals 6,000, as that is the only level of output thatsatisfies 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 theintercept equals autonomous aggregate demand and the slope equals the marginalpropensity to consume.

25.3 This problem is an application of Okun’s law, introduced in Chapter 24. The reces-sionary 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 outputgap, or 0.52 percent. As the natural rate of unemployment is 5 percent, total unem-ployment 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 spend-ing, we first find the relationship between aggregate demand and output. The stepsare 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 investmentspending raises the intercept of the expenditure line by 30.

To solve for short-run equilibrium output, set Y � AD, use the expression aboveto 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 (seeExercise 25.1) to 6,100. If the economy had no output gap before the increase inplanned 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. Areduction of 30 in government purchases will restore autonomous aggregate demandto its original level and thus eliminate the output gap. It is straightforward to showdirectly that if

_I � 630 and government purchases

_G are lowered from 600 to 570,

then

ANSWERS TO IN-CHAPTER EXERCISES 687

45°

Output Y6,000

Y � AD

Expenditure lineAD � 1,800 � 0.7Y

Agg

rega

te d

eman

d A

D

1,800

Slope � 0.7


AD � 1,800 � 0.7Y.

Setting Y � AD and solving for Y, we find that short-run equilibrium output is6,000, its original value.

25.6 An increase of 30 in planned investment created the output gap, so to eliminate theoutput gap autonomous aggregate demand must be reduced by 30. The marginalpropensity 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 consumptionspending. 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.

A P P E N D I X

A N A L G E B R A I CS O L U T I O N O F T H E B A S I C

K E Y N E S I A N M O D E L■

his chapter showed how to solve the basic Keynesian model in twosteps, given specific numerical values for the parameters. In thisappendix we will show that the same steps can be used to find a

more general algebraic solution for short-run equilibrium output in the basicKeynesian model. This solution has the advantage of showing clearly the linksbetween short-run equilibrium output, the multiplier, and autonomous aggre-gate demand. The general method can also be applied when we make changesto 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 basedon the consumption function, Equation 25.2, and the assumption that theother three components of aggregate demand are fixed. We assume also thattax collections are fixed. These assumptions may be summarized as follows:

C �_C � c(Y � T),

I p �_I,

G �_G,

NX �__NX,

T

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 dependon output Y, we obtain

AD � (_C � c

_T �

_I �

_G �

__NX) � cY.

This is Equation 25.3. The term in parentheses on the right side of the equationrepresents autonomous aggregate demand, and the term cY represents inducedaggregate demand.

The second step in solving for short-run equilibrium output begins with itsdefinition, Y � AD. Using the equation just above to substitute for AD, we have

Y � (C � c_T �

_I �

_G �

__NX) � cY.

To solve this equation for Y, it is convenient to group all terms involving Y onthe left side of the equation:

Y � cY � (_C � c

_T �

_I �

_G �

__NX),

or

Y(1 � c) � (_C � c

_T �

_I �

_G �

__NX).

Dividing both sides of the equation by (1 � c) gives the answer:

1Y � (_____) (_C � c

_T �

_I �

_G �

__NX). (A.1)

1 �c

Equation A.1 gives short-run equilibrium output for our model economy in termsof 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 specificnumerical examples. For example, suppose we plug in the numerical valuesassumed in Example 25.2:

_C � 620,

_I � 220,

_G � 300,

__NX � 20,

_T � 250,

and c � 0.8. We get

1Y � (_______)[620 � 0.8(250) � 220 � 300 � 20]1 � 0.81

� ___(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 demand is thesecond term on the right side of Equation A.1, equal to

_C � c

_T �

_I �

_G �

__NX.

The equation shows that a one-unit increase in autonomous aggregate demandincreases short-run equilibrium output by 1/(1 � c) units. In other words, we cansee from Equation A.1 that the multiplier for this model equals 1/(1 � c), a resultthat we found more indirectly in Box 25.3.

690 CHAPTER 25 APPENDIX AN ALGEBRAIC SOLUTION OF THE BASIC KEYNESIAN MODEL

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