keynesian income determination

W,WffiffiWfi rc$l{inth

Robert J.rris Professor in the Social SciencesStanley G. Ha

Northwestern University

Ssston Sa,n Frnneisco New York

London Toronto $ydney Tokyo Singapore Madrid

Mexico City Munirh Paris C*pe Town llong Kong Montreal

CHAPTER

Endogenous variables arethose explained by an eco-nomic theory.

Exogenous variables arethose that are relevant butwhose behavior the theorydoes not attempt toexplain; their values aretaken as given.

The Simple Keynesian Theoryof Income Determination

Att ltoncsf ttntt is orta utlttt kliozrrs tlnf lu ctttt't cottsrnttc ntorL'tlnrt ltt'ltns Ttrt;tlttct'tl.

-Avn Rar-rc1, 1c)66

This chapter begins a two-part unit, spanning Chapters 3-8, that develops a the-ory of business cycles and the potential role of monetary and fiscal policy indampening the amplitude of cycles. Our first interest is in fluctuations in realGDP and interest rates; subsequently we link these fluctuations to the govern-ment budget, foreign trade, price movements, and inflation.

3-l Business Cycles, Unemployment, and lncomeDetermination

In section 2-70 you learned that fluctuations in unemployment are the mirrorimage of fluctuations in output or, more precisely, in the difference (gup)between actual and natural real CDP. When that gap rises into positive territoryas the economy expands, the unemployment rate falls; when that gap becomesnegative as the economy slides into a recession, the unemployment rate rises.Thus thekey to tmderstnnding the causes of fluctttations in unemployment is to deuelop

a theory of fluctuntions in resl CDP.

What We Explain and What We Take as Given

Any theoretical model in economics sets limits on what it tries to explain. Thelimited number of variables to be explained are called endogenous variables.The large number of variables that are taken as given and are not explained are

called exogenous variables.In macroeconomic theory we begin with a short list of endogenous vari-

ables and treat most as exogenous. Gradually, we move some from the exoge-nous list to the endogenous list as our theory becomes more realistic. Table 3-1

shows the major variables that we analyze and their status as endogenous orexogenous.

This list excludes some variables that are treated as exogenous throughout,especially the money supply, the level of government spending, and tax rates.Although not included in the list, other exogenous elements, sometimes called

61

(i2 THI.l SIIlf)l.E IiEYNF,SI'\N 'f Hli()li\- oI I\('()Iill I)i)f iiRllI\A'l'i()-\i

3-1 Endogenous and Exogenous Variables in the Theoryof Business Cvclesr-' -- -t

I

-i

Chapter 3

Chapte'r 4

l, nclogcrt orrs

Real outputConsumptionPrice le,u'el

Real outpr,rtConsumptionInvestmentLrterest rate

Real outputConsr-rmptionInvestmentInterest ratePrice level

F)rog'rn itrr s

InvestmentInterest rate

Price level

Chapter 7

tJt'nuutd shocks, are some of the basic causes of business cycles; they include theeffects of wars and other political crises, and unpredictable changes in spendingon consumption, investment spending, ancl net exports. Finally, other exoge-nous variables, supply shocks, include major changes in the price of oil or otherraw nraterials.

Lc'ar,,ing aside these excluded exogenous varial'rles, we see from Table 3-1that our theory develops one element at a time, successively movir'rg variablesfrorn the exogenous to the endogenous category. We begin in the next sectionwith a simple theory that explains consumption and real output, treating invest-ment, the interest rate, and the price level as exogenous.

3-2 PlannedExpenditure

Our study of national income accounting in Chapter 2 identified four types ofexpenditure on CDP. By definition, total expencliture orl GDP (E ) is equal to thesum of these four components: consumption (C), investment (I), governmentspending on goods and services (C), arrd net exports (NX).

E:C+IIC+NX (3.i)

The Consumption Function

At the beginning, we treat only consLlmption spending (O as endogenous, orexplained by the theory, and treat the other three types of plannecl spending as

exogenous. An obvious way to explairr consumption is that people spend morewhen their incomes go up and vice versa. The income that matters for con-sumption decisions is income after taxes, or disposable personal income. Thiscan be written as total real incom e (Y) minus personal taxes paicl (T), or Y - T.r

1'Ihe rrotatjon T in this ch.lpter continues, ;rs in Chapter 2, to mean "total taxes mintrs transferpayments."

t],)

An autonomous magni-tude is independent of thelevel of income.

The marginal propensityto consume is the dollarchange in consumptionexpenditures per dollarchange in disposableincome.

Induced consumption isthe portion of consump-tion spending thatresponds to changes inincome.

How do households divide their disposable income between consumptionand saving? Households consume a fixed amount that does not depend on theirdisposable income, plus a fraction of each dollar of disposable income:

(,r'nr'r',il I int'.rr iorn

C: Co + ,U -;; (3.2)

The fixed amount is called autonomous consumption, abbreviated (Cr), andthis is completely independent of disposable income. The amount by whichconsumption expenditures increase for each extra dollar of disposable incomeis a fraction called the marginal propensity to consume, abbreviated (c). Thisequation (3.2) says in words that consumption spending (C) equals autonomousconsumption (C) plus the marginal propensity to consume times disposableincome lc(Y - T)]. Another name for this last term is induced consumption.

The consumptionfunction is any relationship that describes the determinantsof consumption spending. This function can be written as a general expression,as in equation (3.2), or as a numerical example. For instance, if we choose $500billion to be the value of autonomous consumption and 0.75 to be the value ofthe marginal propensity to consume, the consumption function can be written

\ttrtrt't'ic,ti I r.trrr;,lt'

C:500+0.75(Y-T)

Either way of writing the consumption function, either in the general version ofequation (3.2) or in the specific numerical example, states that total consump-tion is the sum of autonomous consumption and induced consumption.

The consumption function can also be shown graphically, as in Figure3-1. The thick red line shows on the vertical axis the amount of consumption foralternative values of disposable income (measured along the horizontal axis).When disposable income is zero, total consumption consists just of theautonomous component ($5OO billion). For each extra $1,000 billion of dispos-able income, as we move to the right on the graph, the red consumption func-tion line rises by $750 billion, since its slope (the marginal propensity toconsume) is 0.75. For instance, at point D disposable income is $8,000 billion andtotal consumption is $6,500 billion (consisting of $6,000 billion of induced con-sumption and $500 billion of autonomous consumption).

L. If a person's disposable income is zero, what is that person's level of con-sumption spending in the general linear form of equation (3.2)? In thenumerical example?

2. How can that person consume a positive amount with a zero disposableincome? Think of yourself-what options are open to you to buy some-thing even if you had no income?

Induced Saving and the Marginal Propensity to Save

The simplest way to show the amount of saving is to use a graph like Figure 3-1.The thick black line shows the amount of disposable income in both a horizon-tal and a vertical direction; this line is often called the "45-degree" line. Since thethick red line shows the consumption function, the distance between the twolines indicates the total amount of saving.

64 (.}]APTF]R :J . TFIE SI\IPL}.] KIIYNESIAN THEORY OF'INI]f)T{!] DETERNIINATIC)N

FIGURI' 3.1A Simple Hypothesis RegardingConsumption BehaviorThe red line passing through F and Dillustrates the consumption function. It showsthat consumption is 75 percent of disposableincome pltrs an autonomous conlponent of$500 billion that is spent regardless of thelerrel of disposable income. The red sl-radedarea shows tire amount of positive saving thatoccurs when income exceeds consumption;the grav area shows the arnount of negativesaving (dissaving) that occurs whenconsumption exceeds income.

HOW DISPOSABLE INCOME IS DIVIDED BETWEEN CONSUMPTIONAND SAVING

10,00t)

8,000

6,5006,000

4,000

2,000 4,000 6,000 8,000 I0,000

Real disposable income (Y-f)

Uq)

=.=7,co_X

Co.Fo_EfCo

GCJu

I---l rotal

l----l total s.rving negative Disposable income

To the right of point F, total saving is positive because disposable incomeexceeds consumprtion; this is indicated by the red shading. To the left of point F,total saving is negative because consumption exceeds disposable income; this isindicated by the gray shading. How can sarring be negative? Individuals canconsume more tl-ran they earn, at least for a while, by withdrawing funds fron-ra savings account, by selling stocks and bonds, or by borrowing. Negative sav-ing is quite typical for many students who borrow to finance tl-reir education.

Figure 3-2 illustrates the relationship between induced saving, autono-mous consumption, and total saving. The top frame duplicates Figure 3-1 buthighlights the division of disposable income between induced consumption[0.75(Y - T)] and induced saving [0.25U - T)]. The bottom frame subtractsinduced consumption from the top frame and isolates the relationship betweenautonomolrs consumption and induced saving.

The shaded rrertical distance between the black and red lines represents sav-ing (S), that is, the difference between disposable income and consumption:

Ct,rrcr.rl Linear Frttrm

S: Y-T-C: Y-T-Cn-c(Y-T) 5

: -Cu + 0. - c)(Y -T) (3.3)

This sazring fiutction starts with the definition of saving as personal disposableincome minus consulnption; then it substitutes the consumptior-r function fromequatiorl (3.2). The last line simplifies the saving fur-rction, which now states that

N r,r nrt'ric.r I Era ur ple

- Y-T-C: Y-T-500 -0.75U-T): -500 + 0.25(y -T)

PLANN]jD iiX PIN t)t'l't. titi 6ir

FIGURE 3.2The Relation Between InducedConsumption, Induced Saving, andthe Consumption FunctionThe upper frame duplicates Figure 3-1. Thethin black line shows the dividing linebetween induced saving and inducedconsumption. Starting at zero disposableincome, each dollar of disposabie income isdivided between 75 cents of inducedconsumption and 25 cents of inducedsaving. The lower frame subtracts inducedconsumption from the upper frame. Itshows the relation between induced savingand autonomous consumption. Totalsaving in both parts of the diagram isshown by the red and gray shading andequals induced saving minus autonomousconsumption.

ANY CHANGE IN DISPOSABLE INCOME IS DIVIDED BETWEENINDUCED CONSUMPTION AND INDUCED SAVING

lnducedsavi ng

= 0.25 (Y-T)

lnducedconsumption= 0.75 (Y_T)

2,000 4,000 6,000 8,000 10,000


2,000 4,000 5,000 8,000 10,000


Inducedsaving

= 0.25 (Y-T)

Marginal propensity tosave is the change inpersonal saving inducedby a $1 change in personaldisposable income.

personal saving equals minus the amount of autonomous consumption (-C,r)plus the marginal propensity to save (7 - c) times disposable income U - T).

Notice the three points in both frames of Figure 3-2 marked with letters cor-responding to different levels of disposable income. At H, disposable income iszero, so consumption is C,,, or 500, and saving from equation (3.3) is -Cn, or-500. AtF, disposable income and consumption are equal, so saving is zero. AtD, consumption of 6,500 is less than disposable income of 8,000, so saving is apositive 1,500.

ffiN$ 1,.

2.

Can you derive a general expression showing how the level of consump-tion and disposable income at point F depend on autonomous consump-tion (Co) and the marginal propensity to consume (c)?

If disposable income is 5,000 rather than 8,000, the economy in Figure3-2 will be at a point between points F and D. Calculate the values of con-sumption (C) and saving (5) when disposable income is 5,000.

(i6

Wuv Drn U"S. Savmc Alnnosr VaNrsH rN 2001?

Figure 3-3 is arranged exactly like Figure 3-1 and shows the actual values of dis-posable income and consumption spending in the United States during theyears 7929-2001. As in Figure 3-1, the amount of personal saving' is shown bythe light red shaded area between the black and red lines.

Four major conclusions can be drawn from the evidence. First, consumptionincreased as disposable income grew during the years since World War II.Second, in the worst years of the Great Depression, in 7932 and 1933, house-holds consumed more than their entire disposable incomes, so the fractionsaved was negative (-0.9 percent in7932 and -1.5 percent in 1933). Third, theseusual peacetime relationships were interrupted during World War II (794215),when consumer goods were unavailable or rationed. In that period, households

F-[(;URII 3-:iConsumption, Saving,and DisposableIncome, 1929-2001In 2001 saving was bareiypositive and amounted toa mere 1.6 percent ofdisposable income. Savingwas unusualiy high cluringWorld War II becauseconsumer goods wererationed. During the fourdecades before 2001,personal saving as a

percentage of disposableincome ranged from 5.3 to9.7 percent.

HOW ACTUAL U.S. DISPOSABLE INCOME HAS BEEN SPLIT

BETWEEN CONSUMPTION AND SAVING

8,000

=--oO)O)

oC

::o

.Fo-E

C

?M.

7,OOO

6,000

5,000

4,0O0

3,000

2,O00

'1,000

0

[_-] Area inclicates disposableincome minus consumption,or personal s.rving

t19291 933

1,000 2,000 3,000 4,000 5,000 6,000 7 ,oo0 8,000

Real disposable income (billions of 1996 clollars)

World War llsaving bulge

'Be careful to distinguish between "savings" (with a terminal "s"), which is the stock of assets thathouseholds have in savings accounts or under the mattress, from "savrng" (rvithout a terminal "s"),which is thefTozr per unit of time that leaks out of disposable income and is unavailable for pur-clrases of consumption goods. It is the flow of sauittg that is designatecl by the symbol S.

THE ECONON'IY IN AND OI,IT (X' EOIIII-IBRII]II 67

were forced to consume much less and save much more than is normal in peace-time, fully 26 percent of disposable income tn7944. After the war, consumersrushed out to spend their accumulated savings, helping to maintain prosperity.

The fourth conclusion is quite surprising. In the late 1980s and throughoutthe 1990s, real personal saving decreased, from about 9447 billion in79}4,to$272billion in7996, to a mere $121 billion in 2001. The gradual shrinking of saving inthe 1990s was generally attributed to the long stock market boom following 1982,during which the average value of stock prices increased tenfold. Consumerswere able to raise their consumption relative to their disposable income by sell-ing some of their stocks that had enjoyed large capital gains. Also, consumerswere able to boost their consumption by taking advantage of lower interest ratesand refinancing their home mortgages. In Chapters 4 and 15 we return to theinfluence of interest rates and stock prices on consumption behavior.

3-4 The Economy In and Out of Equilibrium

Until now we have seen that the level of consumption spending depends ondisposable income. But so far we have no idea what the level of income willactually be. $5,000 billion? $10,000 billion? We need an extra element, besidesthe consumption function, to construct our theory of income determination.

This extra element is that expenditure is not always what is desired orplanned, and if some expenditure is unplanned, business firms will adjust pro-duction until the unplanned component of expenditure is eliminated. The totalamount of spending that people want to do includes only the planned compo-nent, called planned expenditure (Ep). The rest of expenditwe (E - Er,) isunplanned and undesired. To simplify, we assume that investment (I) is the bnlycomponent of total expenditure that can contain an unplanned component,whereas consumption (C), government spending (G), and net exports (I,JX) areakuays equal to the planned ctmount.

Er:C+Ip+G+l/XThe four components of expenditure are exactly the same as in equation (3.1),except that we use a subscript "p" for investment, since only for that componentof expenditure do we need to distinguish between the planned amount (lr,) andthe unplanned amount (1,,).

The next step is to combine the consumption function from equation (3.2)with the definition of planned expenditure from equation (3.a):

Er,: Cn + c(Y - T) + It) + G + ^/x

(3.4)

(3.s)

A parameter is a valuetaken as given or knownr.t'ithin a particularanalvsis.

In words, this states that planned expenditure equals autonomous consump-tion, plus the part of consumption that depends on disposable income (inducedconsumption), plus the fixed values of planned investment, government spend-ing, and net exports.

The word parameter means something that is taken as given, including notonly exogenous variables but also fixed elements of a function. In the case of theconsumption function, there are two such fixed elements (Co and c), andwe willtake both as given. In addition, the three components of planned expenditureother than consumption (1r,, G, and NX) can be considered as both exogenousvariables and parameters.

tis

ffi

Autonomous Planned Spending

It helps to simplify the subsequent anaiysis if we take all the elements of equa-tion (3.5) that do not depend on total income (Y) and call them sutonontousplnnned spending ( A,,, ):

( ,t'nt'r'al I inr'.l l ()l nt

Ap: E, - cY : Cn - cTn + Ip + G + l/XIn words, this states that autonomous planned spending consists of all the com-ponents of planned spending that do not depend on income, that is, excludingonly induced consumption (cY).3 To summarize, the five components ofautonomous planned spending are autonomous consumption (C,r), the effect ofautonomous taxes in reducing consumption (-cTn), planned investment 0,,),government spending (C), and net exports (l/X).

As our numerical example, we will continue to assume that autonomousconsumPtton(C) equals 500 and the marginal propensity to consume (c) equals0.75, and add assumed values of 7,200 for planned investment (Ir) and -200 fornet exports (NX). Government spending and autonomous taxed are set to zero.These imply that autonomous planned spending is equal to a total of 1,500:

\rrrrr,'r'i,,rl i .,,rirr1'1,.

At, : 500 - 0.75 (0) + 7,200 + 0 - 200 : 1,500

Overall, we have learned that totai planned expenditure (Er,) has two parts,autonomous planned spending (Ar) and induced consumption (cy).

( ,r'nr't',t I I-irrt'.t r l:orrlr

Er: A, + cY

\ ttittclir.rl i r,tntl-rli'

E,,: 7,500 + 0.75Y

(3 6)

(3.7)

Equilibrium is a state inwhich there exists nopressure for change.

When Is the Hconomy in Bquilibrium?A basic lesson of Chapte r 2 w as that actual expendi ture (E ) and total income (y )are always equal by definition. But there is no reason for income (Y)always toequal plnnned expenditure (Er). Only when the economy is in equilibrium isincome equal to planned expenditure. Only then do households, business firms,the government, and the foreign sector want to spend exactly the amount ofincome that is being generated by the current level of production.

Equilibrium is a situation in uthich there is no pressure for change. When theeconomy is out of equilibrium, production and income are out of line withplanned expenditure, and business firms will be forced to raise or lower pro-duction. When the economy is in equilibrium, production and income are equalto planned expenditure, and on the average, business firms are happy to con-tinue the current level of production.

This idea is illustrated in Figure 3-4. The thick black line in the top frame, asin Figure 3-3, has a slope of 45 degrees; everywhere along it the level of incomeplotted on the horizontal axis is equal to the level of expenditure plotted on thevertical axis. Hence the black line is labeled E : Y. The red line is the totai levelof planned expenditures (E,,) given by equation (3.7), namely, 1,500 plus 0.25

rWe exclude only cY rather than c(Y - l") because we assume that all tax revenues are autonomous(now designated Ir) and do not depend on income.

THE EOONONTY IN AND OUT OF EQUILIBRIT-INI 69

FIGURE 3.4How Equilibrium IncomeIs DeterminedThe ecottcrmv is in equilibrium in tl'retop frame at point B, where the redplanned expenditure (E,,) line crosses

the,lS-c-legrce income line. At any otherlevel of income, the economy is out ofequilibrium, causing pressure on

L-rusiness firms to increase ol reduceproduction ancl income. ln the lowerframe, equilibrium occurs art point B,

rvhere inducecl saving (sY) equalsautonomous plernned spencling (4,,).

THE ECONOMY IS IN EQUILIBRIUM ONLYWHERETHE RED

AND BLACK LINES CROSS

10,000

8,0007,500

6,000

'+,00t)

2,000

2,00t) 4,000 (),(X)0

Real inconre

tA = 1.500 {r'

Io

0,

=.=-oCc)o_X.J

-(,OCcc-

CJ

l-=-oCa)c_Xa,

-a

cc

*cf,>

c-tr=

<':

8,000 -l0,000 12,000

4,Ot)O (r,000 8,000 10,000 12,00(l

Real incomc (Y)

lnducecl saving,

times income (Y). Only where the black and red lines cross at point B is incomeequal to planned expenditure, with no pressure for change. Householcls andbusiness firms \ /ant to spend $6,000 billion when income is $6,000 billion. Andthis amount of income is created by the $6,000 billion of production of the goodsand services that householcls and business finns wallt to buy.*

What Happens Out of Equilibrium?

The economy is out of equilibrium at all points other than B along the 45-clegree

line. For instance, at point /, income is $8,000 billion. How much do households

4Note that the horizontal axis in Figure 3-4 is income (Y) rather than clisposable income (Y - T) as irr

Figr-rres 3-1 atrd 3-2. This reflects our assumption that taxes are arttot-totttous .lt-Id are iuclttdec-l in 4,,on thc' r,erticirl axis.

70 (IHAPTER ll . 'fIIE SIN'IPL11 KEYNFISIAN THllOIi\'f)F IN('OIIE IlliTFlt'illtN.\l'l()\

and business firms want to spend when incotne is $8,000? The two componentsof planned expenditure are:

autonomous planned spending (A,,) : 1,500

induced consLunption (0.75Y ) : 6,000

Unintended inventoryinvestment is the amountbtisiness firms are forcedto accun'rttlate whenplanned expenditr,rre isless than income.

planned expenditure (Er) -- 7,500

Thtrs at an income level of $8,000 billion, planned expendit:u.re (Et) is only $2500billion (point H on the E,, line), leaving business firms with $500 billion of mer-

chandise that nobody wAnts to purchase.The $500 billion of unsold production is counted as inventory investment in

the official national income accoullts. But businesses do not desire this inr,'en-

tory buildup (if they did, they would have included it in their planned invest-

ment,1,,). To bring inventories back to the original desired level, businesses react

to the dituation at I by cutting production and income, which moves the econ-

omy left toward point B. In the diagram, the distance between points I and H,

amounting to $500 billion, is labeled 1,,, which stands for unintended inventoryinvestment.

The distance /H measures the excess of income over planned expenditure-that is, the positive'n,alue of /,,. Production and income will be cut until this dis-

crepancy disappears and the unwanted inventory buildup ceases (1,,: 0). This

occurs only when the economy arrives at B. Only at B are businesses producingexactly the amount that is demanded.

1. What happens in the top frame of Figure 3-4 when income is only $4,000

billion?2. Describe the forces that move the economy back to equilibrium at B.

At point /, as in every situation, income and actual expenditttre are equal by

definition:

income (Y) = expenditure (E)

: planned expenditure (Er,) +

unintended inrrentory investment (1,, )

By contrast, the economy is in equilibrium only when unintended inventoryacctrmulation or decumulation is equal to zero (1,,-- 0). When we substitute(1,, -- 0) into the equation (3.8), we obtain the economy's equilibrium situation:

(3 B)

(3.e)Y:l-t,

Table 3-2 summarizes the differences between what is always true and what is

true only in equilibrium.

Autonomous Planned Spending Equals Induced Saving

The lower frarne of Figure 3-4 illustrates the determination of equilibriumincome in an equivalent way. It subtracts induced consttmption from both

income and plannecl expenditure. The red horizontal line is total autonomous

planned spending (A,,) of $1,500 billion.

t^IIg!s

Comparison of the Economy's 'Always True" and Equilibrium Situations

A;it ri., s ll ur, ii..' illii;tiliritl

Actual expenditure includingunintended inventory accumulation

Can be any amount, positiveor negative

(3.8) Y:E:Eu*1,,

Any point on 45-degree incomeline (example: point / )

At point /,Y(8,000) : E(8,000)

: Er,(7,500) + Ir,(5oo)

i't'i r, , ,ii ii r

2.

J.

What concept of expenditureis equal to income?

Amount of unintendedinventory investment (I,, )

Which equation is valid,(3.8) or (3.9)?

Where does the economy operatein the top frame of Figure 3-4?

Numerical example in Figure3-4 of nonequilibrium andeqtrilibrium situa tions.

Planned expenditure

Must be zero

(3.9) Y : E,,

Only at point B where E,, linecrosses 45-degree income line

At point B,

Y(6,000) : Er, (6,000)

Take the definition of equilibrium in equation (3.9) and subtract inducedconsumption (cY) from both sides of that equation:

Y-cY--Et)-cY

We can replace Ep - cY on the right-hand side by its equivalent, autonomousplanned spending, Ar, (Why? See equation 3-7):

(7-c)Y:At,

Because the marginal propensity to save equals 1.0 minus the marginal propen-sity to consume (s : 1 - c), we can rewrite (3.10) as

(3.10)

(3.11)

(3.12)

sY:4,

Thus equilibrium can occur only if induced saving (sY) equals autonomousplanned spending (Au ). The black sloped induced saving line in the lower frameof Figure 3-4 rises by $0.25 per $1.00 of income and crosses the red A,, line atpoint B, which is at an income level of $6,000 billion and lies directly beneath thetop frame's point B. The economy is in equilibrium at B in the top frame becauseproduction (Y) equals planned spending (Ep). When this occurs, point B in thelower frame shows that the induced leakage into saving (sY) just balancesautonomous planned spending (A, ).

The equilibrium level of income is always equal to autonomous plannedspending (Ar,) divided by the marginal propensity to save (s), as we can see

when both sides of (3.11) are divided by s:

(,('rt{'1,,1 I ril,.',ri I l|.itl

t1.,,\/_ rI-

s

In the numerical example, $6,000 billion of income is required to generate the$1,500 billion of induced saving needed to balance $1,500 billion of autonomousplanned spending.

'..::1,, l j.. .l l ..,ri,l;, .

0.25Y : 1,500

lnduced saving is theportion of saving thatresponds to changes inincome.

":';:rT:6,ooo

72 C]HAP'fER I] . THE SI\,{PLE K!]YNESIAN THEORY OF INCO\IE DETERX'iINATION

3-5 The Multiplier EffectOur conclusion thus far that equilibrium income equals $6,000 billion is

absolutely dependent on our assumption that autonomous planned spending(Ar,) equals $1,500 billion. Any change in autonomous planned spending willcairse a change in equilibrium income. To illustrate the consequences of a change

in A., we shall assume that business firms become more optimistic, raising theirg.t"dr as to the likely profitability of new investment projects. They increase theirinvestment spending by $500 billion, boosting Ao from $1,500 billion to $2,000

billion. In each situation where a change is described, a numbered subscript isused to distinguish the original from the new situation. Thus 4o6 denotes the orig-inal level of A, ($1,500 billion), and A4 denotes the new level ($2,000 billion).

Calculating the MultiplierWe can use (3.12) to calculate the equilibrium level of income in the new and old

situations. Note that only A,, changes; there is no change in the marginal Propen-sity to save (s).

(,1'tl('l'.11 I itlt',ll Iittl'tll N r-r nrclic.r I F ra rtrp it'

2,000Y,:; ^- : 8,000- u./-31,500

Y' : iru : 6'ooo

Take new situation Y1 --

Subtract old situation Y,, :

A

^p7s

4qs

The multiplier is the ratioof the change in output tothe change in autonomousplanned spending thatcauses it. It is also 1.0

divided by the marginalpropensity to save.

(,t'rlet.ai I-tttc.lt' lrot rtt

AY 1multiplier (k) : :

LAt, s

Equais change in income

multiplier (k)

AY:#:2,ooo (3.13)AA,,AY: -r

s

The top line of the table calculates the new level of income when A7,1rs at

the new value of 2,000. The second line calculates the original level of incomewhen,4,,,, is at the old value of 1,500. The change in income, abbreviated AY, is

simply the first line minus the second. The multiplier (k) is defined as the ratio

of the change in income (LY) to the change in planned autonomous spending(LA) that causes it:

\ Lr nit't'ica I l:x.t rrr ;r ie

Ar: 1 :4.0LAr, 0.25

In Figure 3-5 we can see why the multiplier (k) is 7f s, or 4.0. Figure 3-5

reproduces from Figure 3-4 the original situation, with A, at its original value of

$1,500 billion.The 9500 billion increase in A,causes the A,, line to shift upward by $500 bil-

lion and to intersect the fixed induced saving line at point /. Because only 25 per-

cent of extra income is saved, income must rise by $2,000 billion to generate the

required $500 billion increase in induced saving. In terms of the line segments:

R/ 1.. RB,

RB: s(slnces: Rl)

Example of the Multiplier Effect in Action

How does the magic of the multiplier work? One answer is given by Figure

3-5, which is based on the idea that the economy can be in equilibrium only

(3.14)

THE NILILTIPLIETi Ii F'F'F,(I'I'rJ t)t,)

FIGURE 3-5The Change in EquilibriumIncome Caused by a $SOO BillionIncrease in Autonomous PlannedSpendingIncreasing autonomous planned spending(At) by $500 billion raises the horizontalred Ar line by $500 billion, moving theequilibrium position from B to /. Thus a

change in A, has a multiplier effect,raising income by $2,000 billion.

HOW HIGHE,R AUTONOMOUS PLANNED SPENDINGRAISES INCOME

,,,,,,,, f1,s00

l-1,O00,

.gco_

cc

_Cf>-(!

v d)c-YJ

{-1 t l r r t

5,000 6,000 7,OOO il.()0o

Real income (Y)

9,000

Induced saving

= 0.25Y

when induced saving (sY) is equal to autonomous planned spending (A).If At:,

rises, sY must rise by exactly the same amount, and this can happen'only ifincome (Y) rises by 7 / s times the increase in A,,.

A real-life example provides another answer. An example of an increasein planned investment is the decision by Southwest Airlines in 2000 to pur-chase $4 billion of Boeing 737 airuaft. Initially the $4 billion of new investmentspending would raise income by the $4 billion earned by Boeing workers inSeattle, where the aircraft plant is located. But, using our example of a marginalpropensity to consume (c) of 0.75, the Boeing workers would soon spend 0.75of the $4 billion, or $3 billion, on goods and services at Seattle stores. The storeswould have to reorder $3 billion of additional goods, causing production andincome to rise at plants all over the country that supply the goods to the storesin Seattle. Workers at these supplying plants also have a marginal propensityto consume of 0.75, adding another $2.25 billion of spending and income. Sofar, in the first three rounds of spending, income has gone up by $4.0 plus $3.0plus $2.25 billion, or $9.25 billion. But the process continues, as induced con-sumption is increased in each successive round of spending. Eventually, thetotal increase in income will be four times the initial increase in plannedinvestment, or $16 billion (: $4 billion times 7/.25),just as in Figure 3-5.)

'It is possible to use an algebraic trick to prove that the sum of A1,, plus the inclr.rcecl consumptionat each round of spending is exactly equal to the multiplier pi times AA,,. The first rouncl of con-

sumption is cAA,,. The second is c times the first, c(cLAr), or c2A,,. Thus the total AY is the series ofall the infinite number of rounds of spending:

L,Y : L,A,, + cLA,, + c2L,A,,+ .. . + c-AA,,

Factor out the common element AA,,on the right-hand side of equation (a):

AY : AA,,(1.0 + c + c2 +"' + c-)

Multiply both sides of equation (b) by ci

- cAY: AA,,(- c - cl -... c-)

The difference between lines (b) and (c) is

(1 - c) AY : AA,,

We can neglect the c- term, since any fraction raised to the infinity power is zerosides of equation (d) by (7 - c), we obtain the familiar:

AA,,AY: '1-c

(a)

(b)

(c)

(d)

Dividing both

;i

3-G Fiscal Policv

Is a multiplier J*Ounrtnn or contraction of output following a change inautonomous planned spending desirable or not?

Assume that the desired level of real CDP is $8,000 billion. In Figure 3-5, a

level of autonomous planned spending (Ar,) of $2,000 billion would be perfect,for it would bring about an equilibrium level of actual real GDP of $8,000 billionat point /, the desired level. On the other hand, a decline in A, by $500 billionwould cut equilibrium income to $6,000 billion at B and would open up a gapof $2,000 billion between sctunl and the desired level of real CDP.

What might calrse actual real CDP to decline below the desired level? Adrop in planned investment, a major component of Ar,, car. be and has been amajor cause of actual real-world recessions and depressions. In the CreatDepression, for instance, fixed inrzestment dropped by 81 percent, and this con-tributed to the 27 percent decline in actual real GDP between 7929 and7933.

Government Spending and Taxation

The government can adjust its expenditures on goods and services as well as itstax revenues in an attempt to offset fluctuations in real GDP caused by move-ments in autonomous consumption, in planned investment, and in net exports.Our definition of autonomous planned spending (Ar,) rn equation (3.6) alreadyincludes government sprending (G) and the effect of autonomous taxes (T,r) onconsumption. For convenience we repeat equation (3.6):

( 't'ttt'r'.tl I irtr'.tt' l ot'tt'i

Ar,: cn- cTu+ lr,+ G + l'Ix (3.6)

1". Why is 1, written with a p subscript, but the other components of autono-mous planned spending (Co, - cT* C, and NX) are not?

2. Why does the (cf) term appear with a minus sign but all the other sumsappear with a plus sign?

Equation (3.6) states that autonomous planned spending equals the sum of fivecomponents. It also implies that the chnnge in autonomous planned spendingequals the sum of the clnnge in each of the same five components. We can statethis idea as an equation if we insert the "change in" symbol, A, in front of eachelement in equation (3.6). The only remaining element without a A symbol is themarginal propensity to consume (c), which we are assuming to be fixedthrougirout this discussion:

LA, -- ACn - cAf + A1,, + AC + Al/X

ln sum, the five causes of changes in A,, are:

1. A $1 change in autonomous consumption (Cn) changes A,,by $1 in the samedirection

2. A $1 change in autonomolrs tax revenue (7,,,) changes Arby c (the marginalpropensity to consume) tirnes $1 in the opposite direction.

(3.15)

F'ISCAL POLICY 7 l-t

3. A$1 change inplanned investment(Ir,) changes A,by $1 in the same direction.

4. A $1 change in government spending (G) changes A, by $1 in the same

net exports (l/X) changes Auby $1 in the same direction.

Once the change in Arhas been calculated from this list, our basic multiplierexpression from equation (3.13) determines the resulting change in equilibriumincome:

direction.

5. A $1 change in

LA,.AY: t's

(3.13)

1. Notice that there is no A in front of the c in equation (3.15). Why?2. Notice that there is no A in front of the s in equation (3.13). Why?3. How is s defined in terms of c?

Fiscal Expansion

To provide an example of a situation in which higher government spending canexpand real income, let us assume that initially the level of autonomousplanned spending (A,,) is 1,500. This means that the level of real income will be6,000, as shown at point B in Figure 3-5. This is unsatisfactory, because thedesired level of real CDP is at the higher level of $8,000 billion. Thus point Brepresents a situation in which actual real GDP and real income are $2,000 bil-lion lower than desired. How can government fiscal policy correct this situationthrough its control over the level of government expenditure?

It is clear from our basic income-determination formula (3.13) that therequired $2,000 billion increase in real income and real GDP can be achieved byany action that raises autonomous planned spendrng (Ar) by $500 billion. TWopossibilities are (1) a $500 billion increase in G (government spending on goodsand services) and (2) a $667 billion reduction in autonomous tax revenue.o

The $500 billion change in government spending (AC : 500) in Figure 3-5has exactly the same effect on income as any other $500 billion increase in A,,.The economy reaches a new equilibrium at point /. The multiplier (k) for AG isalso the same, already given by equation (3.14) in the preceding section.

The Government Budget Deficit and Its Financing

Any change in government expenditure or tax revenue has consequences for thegovernment's budget. The government budget surplus has already been

nwhy $667 billion? Because according to equation (3.15), a reduction in taxes raises A,,by c times

the reduction. If c : 0.75, as in our numerical example, then

LAt,- c AT: -0.75(-667) : 500

Recall that transfer payments (welfare, Social Security, and unemployment benefits) are equivalentto negative taxes, so that a $667 billion reductiort in taxes has the same impact on A,, as a $667 bil-lion increase in transfer pavments.

76 CHAPTER i] . THE SIMPLE KEYNESIAN THEORY OF INCOI\'IE DETERNIINATION

defined in Section 2-4 as tax revenue minus government expenditure (T - G),which in turn equals investment plus net exports minus private saving.'

T-C=1+l/X-S

Similarly, the change in the left side of the equation must balance the change inthe right side:

AT-AC-A/-Al/X-AS (3.16)

When the government boosts its spending by 500, the movement in Figure3-5 from point B to point / assumes that autonomoLrs consumption, investment,and net exports are fixed (ACu : A1 : Al/X : 0) and that tax revenue remainsat zero (AT : 0). Thus the only elements of (3.16) that are changing are AS andAC. The value of AG is the fiscal stimulus of 500. But what is the value of AS?Recall from the saving function shown in equation (3.3) that saving changes bythe marginal propensity to save times the change in disposable income,AS : r^(AY - AT). Using this expression for saving, we can substitute the num-bers for this example into equation (3.16) and obtain:

AT - AC : AI + Al/X - s(AY - LT)

0-AC:0+0-s(AY-0)0 - 500 : 0 + 0 - 0.25(2,000) : -500

The $2,000 billion increase in output induces $500 billion of extra saving. Eachextra dollar of saving is available for households to purchase the $500 billion ofgovernment bonds that the government must sell to finance its $500 billion gov-ernment budget deficit. The payoff of this government deficit is the $2,000 boostin income needed to raise income to its desired amount.

The Tax MultiplierAs an alternative to stimulating the economy by raising government spendir-rgby $500 billion, it could choose to reduce autonomous taxes by $667 billion. Aswe have seen, these two actions have exactly the same effect, which is to boostautonomous planned spending by $500 billion and to raise income through themultiplier effect by $2,000 billion.

How is the multiplier for a change in autonomous taxes stated? As before,the change in income (AY) is equal to the change in autonomous planned spend-ing (LA,,) divided by the marginal propensity to save (s):

C,t'ncr.r I L.it'tt'ir r Fonrr

A\,, - LA,

- -cLTn_\r : ' :5S

NLrnrt'ricaI []r.trlplc

Ay : - (q4I 667) : :19 : 2,ooo (2.17)0.25 0.25

Here we replace (LAr) by the effect of autonomous taxes on autonomousplanned spending (-cLT).

TSee equation (2.5) on p. 36.

The multiplier for an increase in taxes is(3.17) divided by ATn.

Clcncrr-rl l.i rrt:a r []orrn

FISCAL POI,ICY 77

the income change in equation

NunrcricaI l:xitnrPlc

-g : 4!: -'L:, _ -c ^l : -gf!: _3.0 (3.18)A4 sAL sAl] s 4L 0.25 J'v

Financing a Tax Cut

When the government decides to stimulate the economy with a tax cut, as didthe Bush administration in 2001, then the reduction in tax revenues raises thegovernment budget deficit. In fact, to achieve the same degree of stimulus,enough to raise income by $2,000 billion, the government must cut taxes by $667billion and run that amount of extra deficit, more than is needed when the econ-omy is stimulated by the alternative method of boosting government spendingby $500 billion.

To see how this larger government budget deficit is financed, we use thesame equation (3.16) as before and substitute the example of a$667 billion tax cut:

AT - AG : AI + Al{X - s(AY - AT)

-667- 0 : 0 + 0 - 0.25[2,000 - (-667)l

-667 : -0.25(2,667) : -667The $2,000 billion increase in output plus the fi667 billion tax cut boosts dispos-able income by $2,667 billion, thus inducing 0.25 times 2,667 or $667 billion inextra saving. Each extra dollar of saving is available for households to purchasethe $667 billion of government bonds that the government must sell to financeits $667 billion government br"rdget deficit.

1. If govemment spending is reduced by $500 billion and the rest of theexample in the text is retained, how much does saving change?

2. What is the government doing when it runs a surplus, and how do privatesavers react?

3. If taxes are raised by $667 billion and the rest of the example in the text isretained, how much does saving change? How do private households payfor the higher taxes?

The Balanced Budget MultiplierIn the previous example, the government could boost income by $2,000 billioneither by raising government spending by $500 billion or by cutting taxes by$667 billion. Yet either method would create a large increase in the governmentdeficit, which may be undesirable. Yet, surprisingly, the government can stimu-late the economy even if it needs to maintain a balanced budget. To see this, wesimply add the multipliers for government spending (k : 1/s) and that for achange in taxes (tnx change multiplier : -c/s):

-c \ - c: :1.0ss

1I

I

I

sBalanced budget multiplier (3.1e)

78 T]IIAT'TUR I] . THE SIXIPI,E KEYNESIAN TH!]ORY OF IN['[)NIE DETER\'TINA'IION

II'{TERI{ATIOI\AL

PERSPECTIVE

\.-/ne method to stabilize the economy by reducingthe arnpiitude of business cycles is to ttse "counter-

cyclical" fiscal policy. Such a poiicy operates "counter"or "against" the bttsiness cycle by using fiscal stimulus(higher spending or lower taxes) when the economy is

weak and using the reverse when the economy is

strong. Hor.t,ever, fiscal policy in practice rtlns upagainst major problerns. If government spending isused, then government spending on what? If the gov-ernment takes a long time to develop plans for projectslike highways, hospitals, or schools, the economy'scondition in the meantime may have changed from tooweak to too strong. If tax cuts are used, they may be

delayed by political debates, and households mav

decide to save the tax cut money rather than spending it.Cor-rntercyclical fiscal policy in the United States has

primarily used tax changes, and spending changes

have rarely been used since the New Deal era of the1930s. Tax reductions were used to stimulate the econ-

orny in 1,964_-65, for restraint in 7968, and again forstimulus in 7975 and 1981-83. However the tax cuts ofthe early 1980s left the government budget mired inpersistent cleficits until the late 1990s, and this experi-

I ence gave fiscal policy a bad name.

I ttris changed in 2001 when Congress ratified the] p,'.h .,-lminicfrqfinn'c nrnr-rnqnl fnt cionificenf nrfq ofBush ;rdministration's proposal for significant cuts of

How the United States and Japan UseFiscal Policy

income tax rates to be spread over the next half-decade,starting with checks of $300 (for single filers) or $600(for joint returns) sent in the mail to American taxpay-ers in the sumrner of 2001. Skepticism seemed to be

warranted when the personal saving rate jumpecl, indi-cating that a substantial fraction of the payments hadbeen saved rather than spent. A more novel use of fis-cal policy n'as to help U.S. airlines with $5 billion inemergency aid after the September 11, 2001, attacksand to offer airlines up to an additional $10 billion inloans, contingent on a complex set of criteria. Furtherfiscal stimulus became caught in a political stalemate,as Republicans and Democrats disagreed on the formthat the stimulus should take.

Since the early I990s, the Japanese econorny has

been depressed, aud numerous fortns of fiscal stimu-lus have been employed as the Japanese governmentstruggles to find a route back to prosperity. In contrastto the United States, the Japanese place much moreernphasis on public works projects. To avoid time lagsin starting new projects, the Japanese have a set ofplans ready and vary fiscal expenditures to speed upor slow down completion of particular projects. Forinstance, the 115-mile Tokyo Coastal Bay Expresswaywas under construction for two decades. Manyobservers are skeptical of the usefulness of many ofLll__

This states that the multiplier for a balanced-budget fiscal expansion is always1.0, no matter what the value of c! Why? The positive multiplier occurs because

one dollar of government spending raises autonomous planned expenditure byexactly one dollar, whereas the extra dollar of taxes only reduces autonomous

planned expenditure by c times one dollar, and c (the marginal propensity to con-

sume) is normally substantially less than unity. Thus, the government can achieve

any desired increase in income and real GDP by a sufficiently large increase ingovernlnent spending accompanied by exactly the same increase in tax rates.b

Conclusion

This completes our analysis of the simple Keynesian model of income determi-nation. As explained at the beginning of the chapter, we have maintained twocrucial assumptions-that both the interest rate and the price level are fixed. We

now turn in Chapter 4 to a more realistic model that builds on what you have

learned but allows the interest rate to vary and to influence the level ofautonomous planned spending. We retain the assumption of a fixed price levelthroughout Chapters 4 and 5 before allowing the price level to be flexible, start-ing in Chapters 6 and7.

8The app-,endix to this chapter shorvs that this simple expression for the balanced budget multiplierdoes not apply to a more realistic world in which tax revenues and imports deper-rd on income.

these public works projects, pointing to roads thatlead nowhere and a report that 60 percent of theJapanese coastline is encased in concrete. However;the Chapter 3 multiplier for government spendingdoes not require that the spending must be useful tostimulate spending, and recent evidence has sup-ported that textbook view.

Although tax cuts have also been introduced injapan, these have been ineffective, as they have been

announced as temporary and have soon been followe-dby even larger tax increases. For instance, a reduction inthe income tax in 7994 was followed by an increase inthe value-added tax in 1996 that was three times aslarge. Overall, Japanese policymakers continue tostruggle to extricate their economy from its decade-longslump. We return in Chapter 5 to a deeper look at the

Japanese policy dilemma, al-rd at sonle of the mistakes l

and misconceptions that htrve plagued 1-rolicymakers.

1. This chapter presents a simple theory for determiningreal income. Important simplifying assumptionsinclude the constancy of tl're interest rate and the. pricelevel.

2. Disposable income is divided between consumptionand saving. Throughout the chapter consumption isassumed to be a fixed autonomolls amount, $500 bil-lion in the numerical example, plus 0.75 of disposableincome. Saving is the remaining 0.25 of disposableincome minus the $500 billion of autonomous con-sumption.

3. During the twentieth century, U.S.consumption was aroughly constant fraction of disposable income.Exceptions were during World War II, when rationingprevented households from obtairring the goods theydesired and forced them to sar.e an abnormal fractionof their income, and in the late 1990s when savingalmost r,'anishecl.

4. Output and income (Y) are equal by definition to totalexperrditures (E), which in turn can be di','ided upbetween planned expenditure (E,,) and urintendedinventory accumulation (1,,). We convert this defini-tion into a theory by assuming that business firmsadjust production whenever /,, is not zero. The econ-omy is in equilibrium, with no pressllre for produc-tion to change, only when there is no unintendedinventory accumtrlation or decumulation (1,, : 0/.

5. Autonomous plannecl spendirrg (At,) equals totalplanned expenditurc minus induced consumption.The five compollents of autonomous planned expen-diture are autonomous consumption (C,,), planneclinvestmen t (It,), government spending (G), nef exports(NX), and the effect ol1 consumption of autonornoustax revenue (-cT.).

6. Any change in autonomous planned spending (LAt,)lras a rnultiplier effect: An incretrse raises income and

EO

induced consumption over and above the initial boost

in A-. Income must increase until enough extra saving

has been induced (sAY) to balance the iniection of

extra autonomous planned spending (LAr)'For this

reason, the multipliea the ratio of the change in

income to the change in autonomous planned spend-

ing (LY / LAr), is the inverse of the marginal Propen-sity to save (1/s).

7. The same multiplier is valid for a change in any com-

ponent in A,,.Thus, if private spending components of

A, are weak, the government can raise its spending(G) or cut taxes Q) to maintain stability in Arand thus

in real output,8. The multiplier for government spending changes is

(I/s). The multiplier for autonomous tax changes is

(-c/s).The multiplier for a balanced budget expansion

is 1.0, but this conclusion is not valid if taxes and/orimports depend on income, as shown in the Appendix

to Chapter 3.

Note:Asterisks designate Concepts, Questions, and Problems that require the Appendix to Chapter 3'

endogenous variablesexogenous variablesautonomous magnitudemarginal propensitY to consumeinduced consumptionmarginal propensitY to save

parameter

equilibriumunintended inventorY investmentinduced savingmultiplier*marginal leakage rate*automatic stabilization

QUESTIONS

1. Explain the distinction between exogenous variabies

and endogenous variables. Explain the distinction, ifany, between a parameter and an exogenous variable'For the most complete model used in this chapter,

which of the following variables are endogenous?

Which are exogenous?(a) autonomous taxes(b) consumption(c) margirral propensity to consume(d) exports(e) net exports(f) GDP(g) Price level(h) interest rate(i) investment(i) tax revenue(k) disposable income(l) saving(m)foreign trade surplus (deficit)(n) government budget surplus (deficit)

2. Why do we distinguish between autonomous con-

sumption and induced consumPtion?

-* 3. Using the consumption ftmction, describe what hap-

pened to U.S. consumption and saving starting in the

iate 1990s. How did these trends affect Ar,, Er, and

equilibrium income?4. D-oes the existence of positive inventory change

imply that the economy is out of equilibrium? Why or

why not?-' 5. What moves the economy toward equilibrium when

unintended inventory investment is either positirre or

negative rather than zero?

6. Assume that there is an increase in atttonomous

investment of $100 billion. Under which circumstance

will the ultimate impact on the level of equilibriumGDP be greater: (a) with a relatively high marginal

propensity to consume, or (b) with a relatively lor'r'

marginal propensity to consume? Explain'7. Is it more desirable for an economy to have a large

multiplier or a small multiPlier?8. Explain why government action that increases the

deficit is expansionary fiscal policy. what about action

that decreases the surPlus?9. Why are imports considered to be a leakage in the

economy? How are imports included in the model

presented in this chaPter?

The following four questions assume knowledge ofthe appendix.

*10. Civen a consumption function of the formC: Cu + c(Y - T) and T : To * fl write the formulafor the expanded consumption function. Write theformula for the expanded saving function that isimplied by the stated consumption function.

*11. How would your answer in question 6 change if thealternatives read: (a) with a relatively high marginalleakage rate, or (b) with a relatively low marginalleakage rate? Explain.

*12. What is the effect on the multiplier of includinginduced taxes in the model of income determinationpresented in this chapter?

*13. When all taxes and net exports are autonomous, thebalanced budget multiplier is one. Find the balancedbudget multiplier when all taxes are autonomous,but net exports have an autonomous and inducedcomponent. Is this new balanced budget multiplierless than, greater than, or equal to one?

PROBLEMS" 1. Consider an economy in which all taxes are autonomous

and the following values of autonomous consumption,planned investment, government expenditure, taxes,and the marginal propensity to consume are given:

C,r:1,200 1,,:700 C:400 T:500 c:0.6

(a) What is the level of consumption when the level ofincome (Y) equals $3,800?

(b) What is the level of saving when the level ofincome (Y) equals $3,800?

(c) What is the level of planned investment when thelevel of income (Y) equals $3,800? What is the levelof actual investment? What is the level of unin-tended inventory inr.estment?

(d) Show that injections equal leakages when income(Y) equals $3,800.

(e) Is the economy in equilibrium when income(YS : $3,800? If not, what is the equilibrium level ofincome for the economy described in this question?

*Z.C:Cn*c(y_T)

where:C,, : 300 Ir,: 400 T -

NX:400 c:0.5 C-(a) Determine the equilibrium

sumption, saving, and taxes.(b) What is the value of the

200

500

levels of CDP, con-

marginal propensityto save?

(c) Is there a surplus or deficit in the government bud-get? How much?

(d) Show that leakages equal injections.(e) What is the new equilibrium level of GDP if gor,-

ernment spending increases by $30 billion?

QTIESTTONS AND PROBT.TIXIS Bl

*3. Assume that the marginal propensity to consumeequals 0.6 for every consumer in the economy. Youhave just been paid $20,000 to produce a researchreport for the Commerce Department. How will thisaction by the government affect your spending plans?What would be the total effect on the economy of thisaction? (Assume that f : 0 and rrx : 0.)

*4. Given a consumption function in the formC : Co + c(Y - T) and T : T + tY, ancl given thefollowing values,

Cn : 300 c : 0.8 T: 100 t :0.25

(a) What is the level of tax revenue when y : $5,000billion?

(b) What is tl-re level of disposable income (Y - T)when Y: $5,000billion?

(c) What is the level of consumption when Y : $5,000billion?

(cl) Assuming that saving and taxes are the only leak-ages in this economy, what is the value of the mar-ginal leakage rate?

(e) Assuming that the only other source of spendingin the economy is government spending, whatmust the value of G be in order to generate anequilibrium value of Y : $5,000?

(0 What is the value of the. govenlment budget sur-plus or deficit in this example?

*5. Assume an economy in which the marginal propen-sity to collsume, c, is 0.8, the income tax rate, t, is 0.2,and the share of imports in CDP, nx, is 0.04.Autonomous consumption, a, is 660; autonomoustaxes, T, are 200; autonomous net exports, NX,,, are300; planned investment, 1,,, is 500; and governmentspending, C, is 500.(a) What is the value of autonomous planned spend-

ing (A,,)?

(b) What is the value of the multiplier?(c) What is the equilibrium value of income (Y)?(d) What is the value of consumption in equilibrium?(e) Show that leakages equal injections.(0 Suppose government expenditures decline by 150.

Describe the economic process by which the newequilibrium value of Y is attained.

(g) What is the new equilibrium value of Y?

What would be the total effect on the economy of theaction described in problem 3 if t :0.2 and n"r : 0.08?

Assume an economy in which c is0.75, t is0.25, and rrris 0.0625. Autonomous planned spending, A, is 500.(a) What is the equilibrium value of income (Y)?

(b) Suppose C increases by 50 and the governmentadjusts autonomous taxes to keep the budget bal-anced. What is the value of the balanced buclgetmultiplier and the new equilibrium value of Y?

(c) In part (b), by how much cloes f rise to keep thebudget balanced?

'o.

*7.

1r.63 0) C = Cn in the general linear form, C = 500 in thenumerical example. (2) Your options are to borrow,reduce your savings account, and to sell stocks, bonds,or any other assets yoLr may o\vn.

p.65 At point F consumption and disposable income areeqtral. Thus consumption, C,, + c(Y - T), equals dis-posable irrcome, or Y - T. Setting these two equal, rvecan subtra ct c(Y - T) from Y - T to obtain C, : (7 - c)(Y - T). Dividing by 7 - c, we obtain the answer thatdisposable income (Y - T) is equal to Cn/ 0 - c) and sois consumption. Thus at point F consumption equals500 /0.25, or 2,000, while saving equals zero. (2) Whendisposable income is 5,000, consumption C = 500 +

0.75(5,000) : 4,250. Saving - Y - T - C : 5,000 - 4,250 =750.

7t. 70 (1) When incorne is only 4,000, planned expenditureis equal to autonomous spending (1,200 + 500 - 200)

plus induced consumption (0.75 times 4,000 : 3,000), fora total of 4,500. Thus planned expenditure exceedsincome, forcing firms to reduce their inventoriesin order to meet demand. (2) Unintended inventoryirrvcstnrent is -500, and fimrs raise productionin order to provicle goods to meet planned expenditures;this increase ir-r production moves the economy towardthe equilibrium income level of 6,000.

p. 7a Q) We write planned investment as l) with a p sub-script, to reflect our assumption that consrttttcrs, tJtc

goaernnrcttt, nnd exportars nntl importcrs nre ahonrls nble

to realize their plnns, so that there is no such thingas autonomous unplanned consumption, autonomousunplanned tax revenues, unfilamed govemment spend-ing, or unplanned net exports. Only busine.ss firms areforced to make unplanned expenditures, as occurs lt heninvestrnent (1) is not equal to what they plan (1,, ), but alsoincludes unplanned inventory (1,,). (2) cT,, appears with aminus sign because an increase in taxes will reduce,rather than increase, autonornous planned spending bythe amotmt of the tax times the fraction of the tax thatwoulcl have been consumed rather than saved.

p.75 (7) We are assuming that the marginal propensity toconsllme does not change. (2) When we assume themarginal propensity to consume does not change, themarginal propensity to save will not change either.u (3)

s:1-c.p. 77 (1) Income will decline by 2,000 and saving will

decline by one quarter of 2,000, the exact amount of thedecline in government expenditures. (2) Tax revenuesexceed government spending. Private savers no longerpurchase go\/enlment boncls. Sa'"'ing will equal theamount that total investment exceeds the surplus. (3) Iftaxes are raised by $667 billion, saving declines byexactly $667 billion. Private households pay for thehigher taxes by reducing their level of savirrg.

"Using thc calculus formula for the change in a ratirr, thechange in income whcn both ,4,, and -s are ;rllor,r'ed to changc is:

1Y : JA, /: .4,,Is/..:

Equation (3.13) in the te'xt simply sets Is equal to zero in this expression.

AI)PIINDIX T(] CHAPTER IJ E:]

Nlowing for Income Taxes and Income-Dependent Net Exports

EFFECT OF II{COME TAXESWhen the government raises some of its tax re\/enue (T) 1'111l an income tax in additionto the autonomous tax (7,), its total tax revenue is:

T:7,, ltY

The first component is the autonomous tax, for which we continue to use the symbol(7,,).The second component is income tax rer.enue, the tax rate (f) times income (Y).Disposable income (Y - T) is total income minus tax re.v'enue:

Yo: Y - T - "

- r,,- tY :(1 - f)Y - Tn

Leakages from the Spending StreamFollowing any change in total income (Y), disprosable income changes by only a fraction(1 - f) as much. For iustance, if the tax rate ( t) is 0.2, then disposable incorne changes by80 percent of the change irr total income. Any change in tcltal income (AY) is now dividedinto induced consttmption, incluced saving, and induced income tax revenue. The frac-tion of AY going into consumption is the marginal propensity to consume disposableincotne (c) times the fraction of income going into clispctsable income (1 - 1). Thus thechange in total income is divided up as shown in the following table.

(1)

(2)

l"r'ltt'1 iotl goi tl!r tr):

1. Induced consumption2. Induced savirrg3. Induced tax revenue

Total

(]enerai Liuear F'ourr

c(1 -f)s(1 - r)t

+s)(1-t)+t7-t+f:1.0

Numt'rical Exanrple

0.75(1 - 0.2): 0.60.25(1 0.21 - g.'0.2

1.0

income equals

(3)

IAs in equation (3.9) on p.70,the economy is in equilibrir"rm rvhen

planrred expenditures :

Y:E,,

As before, we can subtract induced consumption from both sides of the equilibrium coll-dition. According to the preceding table, income (Y) minus induced consumption is thetotal of induced saving plus induced tax revenlte. Plernned expenditure (E,,,) minusinduced consumption is autonomous planned spencling(Ap). Thus the equilibrium con-dition is

induced saving * inducecl tax revenue : autonomous planned spending (,4,,) (4)

From the table just given, equation (4) can be written in symbols as:

[s(1 - t) + tlY : A,, (5)

The term in brackets on the left-hand side is the fraction of a change in income thatdoes ruof go into induced consttmption-that is, the sum of the fraction going to inducedsaving s(1 - f ) and the fraction going to the go\/ernment as income tax revenr.re (f). The

84 (IHAPTFiR ll . 'fFIE SIIIPLE KEYNIISIANI THEORY OI" lN(lONIf DETIItriNI[N'\TION

The marginal leakage rateis the fraction of incomethat is taxed or savedrather than being spent onconsumption.

Automatic stabilization isthe effect of income taxesin lowering the multipliereffect of changes inautonomous plannedspending.

sum of these two fractions within the bracketsequilibrium value for Y can be calculated whenthe term in brackets:

is called the marginal leakage rate. Thewe divide both sides of equation (5) by

\ rr rlcric.r I lrr.t Ittfrltr

2,000 2,000 - 5,000 (6)0.25(0.8) r 0.2 0.4

Cle Ircr.rl l,irrcirr [rortrr

4,,V_ r' Y:t- s(1-t)+t

The numerical example shows that if autonomous planned spending (At,) is $2,000 bil-lion, income will be only $5,000 billion, rather than $8,000 billion as in the example

used previously in Chapter 3. Why? A greater fraction of each dollar of income nowleaks out of the spending stream-0.4 in this numerical example-than occurred due

to the savinp; rate of 0.25 by itself. This allows the injection of autonomous plannedspending (Ar, 2,000) to be balancecl by leakages out of the spending stream at a lowerlevel of income.

INCOME TAXES AND THE MULTIPLIERThe change in income (AY) is simply the change in autonomous planned spending(LA,,)divided by the marginal leakage rate:

AY: ^ol.- (7)s(1-t)+t

The multiplier (AYl AA,,) is simply 1.0 divided by the marginal leakage rate. The multi-plier was 1/s when there was no income tax. Now, with an income tax:

11mtrltiplier marginal t"nt og*rate:s(1 -f) f f

(8)

In Chapter 3, where the income tax rate is assumed to be zero, the numerical exam-

ple of the multiplier was 4. This was a special case of equation (8), valid when f : 0, so

that the marginal leakage rate equals simply s, or 0.25.

Now that we have introduced an income tax rate of 0.2, the marginal leakage rate

is 0.4 [see equation (6)] and the multiplier is I /0.4 or 2.5. Thus raising the income taxrate reduces the multiplier and vice versa. This gives the government a new tool forstabilizing income. When the government wants to stimulate the economy and raise

income, it can raise income in equation (6) and the mr-rltiplier in equation (8)by cuttingincome tax rates. This occurred most recently in 2001. And, when the governmentIt'ants to restrain the economy, it can raise income tax rates, as occurred most recentlyin 7993.

THE GOVERNMENT BUDGETThe government budget surplus is defined as before; it equals tax revenue minus gov-

ernment spending;, T - G. Substituting the definition in equation (1), which expresses tax

revenue (T) as the sum of autonomous and induced tax revenue, we can write the gov-

ernment surplus as:

governmentbudgetsurplus -T - G:Tn+ tY - G (9)

Thus the government budget surplus automatically rises when the level of income

expands. This consequence of the income tax is sometimes called automatic stabiliza-tion. This name reflects the automatic rise and fall of income tax rer.,enues as income rises

and falls. When income rises, income tax revenues rise and siphon off some of the incomebefore households have a chance to spend it. Similarly, when incorne falls, income taxrevenues fall arrd help minimize the drop in disposable income. This is why the presenceof an income tax makes the multiplier smaller.

AUTONOMOUS AND TNDUCED NET EXPORTSIhe theory of income determination in equation (6) states that equilibrium income equalsautonomous planned spending (A,,) divided by the marginal leakage rate. When theUnited States trades with nations abroad, U.S. producers sell part of domestic output asexports. Householcls and business firms purchase imports from abroad, so part of U.S.expenditure does not generate U.S. production.

How do exports and inlports affect the determination of income? We learned inChapter 2 that the difference between exports and imports is called net exports ancl is partof GDP. When exports increase, net exports increase. When imports increase, net exportsdecrease. Designating net exports by NX, we can write the relationship between netexports ancl income (Y) as:

ly'X : NX. - nxY (10)

Net exports contains an autonomous component (NX,?), reflecting the factthat tire level of exports depends mainly on income in foreign countries (which is exoge-nous, not explained by our theory) rather than on domestic income (Y). Net exports alsocontains an induced component (-nxY), reflecting the fact that imports rise if domesticincome (Y) rises, thus reducing net exports. The meaning of "nx" can be stated as "theshare of imports in GDP."

Because we now have a new component of autonomous expenditure, theautonomous component of net exports (NXr), we can rewrite our definition of A,, as thefollowing in place of equation:

Ap: Cn- cTn+ Ip+ G + NX,, (1i)

Because imports depend on income (Y), tlne induced component of net exports (-nxY)has exactly the same effect on equilibrium income and the multiplier as does the incometax. Imports represent a leakage from the spending stream, a portion of a change inincome that is not part of the disposable income of U.S. citizens and thus not availablefor consumption. The fraction of a change in income that is spent on net exports (nx) ispart of the economy's marginal leakage rate.

T.vpes of'leakage's

Saving onlySaving and income taxSaving, income tax, and imports

N'larginal lealiirgc' r'irtc

s

s(1-t)+ts(1 -t)*t-trtx

FULL EQUATIONS FOR EQUILIBRIUM INCOMEAND THE MULTIPI",IER,When we combine equation (6), equation (11), and the table, equilibrium incorne becomes:

- cr, +Ji qjly4s(1-t)+t +ny

Ld

marginal leakage rate(r2)

8ri {'if-\t'T'l.lli

F$i

It

bst

F

The change in income then becomes

AY : ,.*gn*l*;s" r^t"'

where LAt,: AC,, - cATn + AIt, + AG + ANX,' and the marginal leakage rate is the sameas the denominator of equation (12).

THE BALANCED BUDGET MULTIPLIERThe balanced budget multiplier may be generalized from equation (3.19) in Chapter 3 byreplacing s in the denominator by the marginal leakage rate:

I-cbalanced budget niultil'rlier : -...:, _ -1 , _,' margrnal leaKage rate

CFIAPTER

The IS-LM Model

It itttttl ltt'lnitl dtttt,tt tts tt ttttttittt, tlnf ,r.,lr(rt'r,(r t trt'nt dt'nl cntt L,t' ntntlt'i,y tltc rr.sr'o/tltonL'U,0 lrt'rtt lcnl i'ill .()ntnt()itlU bt uit,ut.fttr tltc ttsc o.f it.

;\clant Srrritlr. i 77(.

4-l Introduction

The basic theme of the last chapter was that income and real CDP change by amultiple of any change in autonomous planned spending. But changes inautonomous planned spending (LAr,) were assumed to be already known; thatis, they were exogenous and were not explained. In this chapter we accept every-thing in Chapter 3 as valid. But we go further and relate the level of autonomousplanned spending to the level of the interest rate.

If autonomous planned spending depends partly on the interest rate, whatdetermines the interest rate? First we will explore the connection between theinterest rate and the supply of money. Then we will see how the governmentuses its control over the money supply to influence the interest rate, and thusthe equilibrium level of income. We will learn that both the level of income andthe level of the interest rate can be affected by monetary and fiscal policy, work-ing separately or in combination.

This chapter adds to our understanding of the process of income determi-nation, and begins our investigation of the key questions at the heart of recenteconomic debates:

1. How does monetary policy work? By what mechanism did the U.S. FederalReserve hope to stimulate the economy by reducing interest rates 11 separatetimes during the year 2007?

2. What difference did it make that the federal government ran persistent bud-get deficits from 1980 to 7997, followed by budget surpluses during 7998-2007and then a return to deficits in 2002 and perhaps beyond? Why did this shiftfrom deficit to surplus back to deficit occur?

3. Does the multiplier effect of fiscal policy, previously examined in Chapter 3,

depend on the conduct of monetary policy? Does the multiplier effect of monetarypolicy depend on the conduct of fiscal policy?

4. If real GDP is higher or lower than desired, so that a policy action restrain-ing or stimulating the economy is needed, should that policy action be carriedout in the form of monetary or fiscal policy, or by a combination of the two?

87

,.1,8

In this chapteq, as in Chapter 3, we will assume that the price level is fixed. Allchanges in real income and real GDP are accompanied by the same change in nom-inal income and nominal GDP. A11 effects of spending on inflation and of inflationon the interest rate are postponed for treatment later in ChaptersT,B, and 9.

4-Z Interest Rates and Rates of Return

The central focus of this chapter is on the interest rate. While in the real worldthere are many different interest rates, here we simplify by assuming that thereis only a single interest rate. Savers receive this rate as a return on their savingsaccounts and holdings of bonds. And both business firms and consumers paythis interest rate when they borrow from financial institutions.

Functions of Interest Rates

Interest rates help the econolny allocate saving among alternative uses. Forsavers, the interest rate is a reward for abstaining from consumption and wait-ing to consume at some future time. The higher the interest rate, the greater theincentive to save. For borrowers, the interest rate is the cost of borrowing fundsto invest or buy consumption goods. At a higher interest rate, people will bor-row fewer funds and purchase fewer goods. Thus if the desire to borrowexceeds the willingness to save sufficient funds, the interest rate tends to rise.

Interest rates are central to the role of monetary policy. Since the govern-ment, through the Federal Reserve Board (the Fed), can influence the interestrate, it can affect the cost of borrowed funds to private borrowers.

Types of Interest Rates

Banks offer a variety of interest rates on checking and savings accounts. Sometypes of accounts allow customers to earn interest instantly; others requirecustomers to leave funds on deposit for a year or more. The phrase "short-term interest rate" refers to interest that is paid on funds deposited for threemonths or less; "long-term interest rate" refers to interest on funds depositedfor a year or more.

In addition to short-term interest rates on bank deposits, there are short-term interest rates that apply to funds borrowed by the government (theTreasury bill rate), by businesses (the commercial paper rate), and by banks (thefederal funds rate). Similarly, in addition to long-term rates on bank deposits,there are long-term interest rates that apply to funds borrowed by the govern-ment (the Treasury bond rate), by businesses (the corporate bond rate), and byhouseholds (the mortgage rate). The business sections of most local newspa-pers and The Wnll Street lournal publish the daily values of these rates.

The hallmark of a good theory is its ability to spotlight important relation-ships and to ignore unnecessary details. For most purposes, the differencesbetween alternative interest rates fall into that category of detail, in contrast tothe important overall rl)urge level of interest rates. Thus "the" interest rate dis-cussed in this chapter can be regarded as an average of all the different interestrates listed in the previous paragraph.

The rate of return on aninvestment project is itsannual earnings dividedbv its total cost.

,ITlii RI|LATION OF'ALIT()NOtrTOLIS PLANI'IED SPEI{DING TO THF] INl'I'ItI'S'I'ITA'IIJ E9

4-3 The Relation of Autonomous PlannedSpending to the Interest Rate

We begin by asking why planned investment (a component of autonomousplanned spending) depends on the interest rate. Business firms attempt to profitby borrowing funds to buy investment goods-office buildings, shopping cen-ters, factories, machine tools, computers, airplanes. Obviously, firms can stay inbusiness only if the earnings of investment goods are at least enough to pay theinterest on the borrowed funds (or to attract enough investors to warrant a newissue of stock).

Bxample of an Airline's Investment Decision

American Airlines calculates that it can earn $10 million per year from one addi-tional Boeing 757 jet airliner after paying all expenses for employee salaries, fuel,food, and airplane maintenance-that is, all expenses besides interest paymentson the borrowed funds. If the 757 costs $50 million, that level of earnings repre-sents a 20 percent rate of return ($10,000,000/$50,000,000), defined as annualearnings divided by the cost of the airplane. If American must pay 10 percentinterest to obtain the funds for the airplane, the 20 percent rate of return is morethan sufficient to pay the interest expense.

In the top frame of Figurc 4-7, point A shows that the 20 percent rate ofreturn on the ftrst 757 exceeds the 10 percent interest rate on borrowed funds.The steplike red line in the top frame of Figure 4-1 shows the rate of return onthe first through fifth planes. The gray area between point A and the 10 percentinterest rate represents the annual profit rate made on the first plane. Point B forthe second plane also indicates a profit. Point C shows that purchase of a thirdextra 757 earns only a 10 percent rate of return, or $5 million (10 percent of $50million) in extra earnings after payment of all noninterest expenses.

Why do the second and third planes earn less than the first? The first planeis operated on the most profitable routes; the second and third must fly onroutes that are less likely to yield full passenger loads. A fourth plane (at pointD) would have an even lower rate of return, insufficient to pay the interest costof borrowed funds. How many planes will be purchased? The third can pay itsinterest expense and will be purchased, but the fourth will not. If the interestcost of borrowed funds were to rise above 10 percent but remain below 15 per-cent, American would purchase two planes instead of three. If the interest ratewere to fall to 5 percent or below, then American would purchase four planes.

The Interest Rate and the Rate-of-Return Line

The interest rate not only influences the level of business investment but alsoaffects the level of household consumption. For instance, households decidingwhether to purchase a dishwasher or a second automobile will consider the sizeof the monthly payment, which depends on the interest rate. In the bottomframe of Figure 4-\, the rate-of-return line shows that the return on plannedinvestment and autonomous consumption spending (lr, + Co) declines as thelevel of spending increases. As for American Airlines, each successive invest-ment good purchased by business firms is less profitable than the last. Similarly,each successive consumption good purchasedby households provides fewer

1)i) ('l l \l ''l'1._li I ' 'fI IE /.s L 11 ]l( )l)Ei.

!'IGURI,i 4-lThe Pavoff to Investment for an Airlineand the Economy

The red steplike line in the top frame showsthe rate of return to American Airlines forpurchases of additionalTSTs.If the interestrate is 10 percent, a profit is made bypurchasing the first two pianes, and thecompany breaks even by buying the thirdplane. Purchase of a fourth or fifth planewould be a mistake, because the pianes wouldnot generate enough additional profit to payfor the cost of borrowing the money to buythem. The bottom frame shows the samephenomenon for the economy as a whole.

AN ]NCREASE IN PLANNED PRIVATE SPENDING REDUCES THE RATE

OF RETURN

12345Numlter of erlra 757s

ttttl50 1 00 1 50 200 250 300

Cost ($ millions)

500 1,000 1,500 2,000 2,500 3,000

Real private autonomous planned spending (f * C,l

15

10

C

o--c=

Otr

cZ .=

20

15

10

c

o_-c'.=

q)tr

cZ .=

Profit on firstand second planesr'--t&*r

Loss made on fourthand fifth planes

Interest rate

----Loss area

services than the last (for instance, a family's second car is less important anduseful than its first car).

Determination of the level of It) + Cors a two-step process. First we plot therate-of-return line representing firms' and consumers' expectations of the bene-fit of additional purchases. Second, we find the level of In + Co at the pointwhere the rate-of-return line crosses the interest rate level.

When the interest rate is 10 percent, as in Figure 4-1, autonomous plannedspending (1, + Cr) will be $1,500 billion at point C, as long as the level of busi-ness and consumer optimism remains constant. A decrease in the interest ratewill increase purchases (10 + Co);for instance, a decrease from 10 percent to 5

percent moves autonomous planned spending from $1,500 billion at C to $2,000billion at D.

Business and Consumer Optimism

Can purchases ever change when the interest rate is held constant at 10 percent?Certainly-an increase in business and consumer optimism about the expectedpayoff of additional purchases can shift the entire rate-of-return line to the right,

TI{E RELATION OF' r\LI'fON0\lOLfS PL;\N}iFlD SI)l.lNDlN(; TO l'lIE IN'l'|,tilt>'t li,\'l'11 91

FIGURE 4.2Effect on Autonomous PlannedSpending of an Increase in Businessand Consumer ConfidenceThe dashed red "original rate-of-return line"is an exact copy of the solid red "rate-of-return line" in Figure 4-1.If the level ofbusiness and consumer confidence were toincrease, the spending schedule would shiftrightward to the solid red "ne\ / rate-of-return line." If the interest rate were to stayconstant at 10 percent, then autonomousplanned spending (Ao)would increase from$1,500 billion at point C to $2,000 billion atpoint F.

HIGHER BUSINESS AND CONSUMER CONFIDENCE RAISES

AUTONOMOUS SPENDING

Pc\J

b 15o_

-cL tl)Y.

v :w

o3 5

u. .*

500 -|,000 1,500 I (XX) 2,500 3,000

Real private autonomous planned spending (t, + C,,)

F Interest rate

as indicated by the red "ne\M rate-of-return line" in Figure 4-2. This shifts to theright (to point F ) the intersection of the rate-of-return line with the fixed hori-zontal interest rate line.

The events of September \7,2007, caused a sharp decline in business andconsumer confidence, shifting the rate of return line to the left. Among the ini-tial effects were massive cancellations by airlines of their previous orders fornew aircraft.

Summarizing, we can show the amount of lt, + Cn spending that wouldoccur at different interest rates and different levels of confidence.

Demand for Io * Co

Interest rate

15

It)5

Original ritte-of'-return line(pessinristic

c'xpcctations )

1,000 (at B)

1,5(X) (,rt C )

2,000 (at D)

Neu' higherr rltte-oI-rctunr lirrc'(optirnistic

t'x1)t'r'tlrtirrti> i

1,500

2,(XX) (at / )

2,500

The left-hand column (pessimistic expectations) is plotted as the "originalrate-of-return line" (red dashes) in Figure 4-2.The right-hand column (optimisticexpectations) is plotted as the solid red "new rate-of-return line."

The Demand for Autonomous Planned Spending

You learned earlier that there are five components of autonomous plannedspending (Ar): planned investment, autonomous consumption, governmentspending, the effect of autonomous taxes on consumption, and net exports. Wehave already seen that planned investment and autonomous consumption bothdepend on the interest rate; both types of spending are stimulated by a lowerinterest rate.

92 CilAPTFtR 4 .

FIGURE 4.3Relation of the VariousComponents of AutonomousPlanned Spending to theInterest RateThe rrertical black line shows that threecomponents of autonornous plannedspending do not clepend on the interestrate. These are governmcnt sperrding(C), the effect of autonomclus taxes(-cT), and net exports (NX). The slopredline shor,r,s that autonomous consumption(C,,) and planne.d investment (1,,,) depcndinversely on thc interest rate. Hence, thetotal dernand fclr arutonomous planneclspending, as showrr by the "A' clemandschedlrle," also clepends inversely onthe interest rate.

BOTH CONSUMPTION AND INVESTMENT BY BUSINESS F'IRMS

RESPOND TO THE.INTEREST RATE,

Autonomous p lanrrecl sperrcli rrg (A,,)

c)

AJ

C

\1,' r

,-\ clt'nr.rncl

sc ht'rlLrlt'

In Figure 4-3 we plot the relationship of the compollents of autonomousplanned spending on the horizontal axis to the interest rate on the vertical axis,

The negative relationship between the interest rate and both planned invest-rnerrt and autonomolls consumption (/,, + C{,) is copied from Figure 4-2. Theother three components of atrtonomous spending do not depend on the interestrate.l Accordingly, the total amount of government spending, the effect ofautonomous taxes on consumption, ancl net exports G - cTo + NX) are plottedas a black vertical line in Figure 4-3.

Total autonomous planned spending also consists of autonornous con-sumption (C,,) ancl planned investment (1,,), both of which depend negatively on

the interest rate, so thc sl1lout1t of tlrcse trtto s1111rroneris ttdcled to tlrc first flrccdeptctuls on tlrc intcrest rntc.The lower the interest rate, the larger C,, and the larger1,,. The total of all five components is shown by the line on the right labeled "4,,

demand schedule." This schedule shows that the total of all autonomousplanned spending depends orr the interest rate.

Shifts in the Ao Demand Schedule

As before, government spencling, taxes, and net exports are given exogenorlsamounts. A chernge in any of these will shift the A,, demand schedule. As youpreviously leamed, a shift of business expectations toward optimism and confi-dence i,t,ill boost planned investment at any given interest rate, so such attitudeswill also shift the A,, demand schedule. Finally, an improvement in consumerconfidence will raise autonomous consumer spending and shift the schedule in

the sarne wav.

lChapter 6 identifics an indirect iink between the interest rate arnr-l net cxports, workirrg throtrgh the

foreign exchange rate. Tlris link is ignorecl lrere.

THE RELATION OF AUTONON,IOUS PI,ANNED SPENDING TO TI{E INTEREST RATE 93

J,Vlonetary poiicy is carried out by the FederalReserve System (or the "Fed" for short). Roughlyevery five weeks, an important meeting is held by theFederal Open Market Committee (FOMC), which con-sists of the seven governors of the Fed plus the presi-dents of the twelve regional Fed banks (e.9., theFederal Reserve Banks of New York, Chicago, andAtlanta). At precisely 2:75 P.M. Eastern time, anannouncement is issued as to whether the FOMC hasdecided to raise, reduce, or leave unchanged the fed-eral funds rate, an interest rate that banks charge eachother for lending or borrowing bank reserves (see

Chapter 13). In 2001 and early 2002, the FOMCresponded to perceived weakness in the economywith unprecedented speed, cutting the federal fundsrate at eleven straight meetings from 6.5 percent at theend of 2000 to 1.75 percent in January 2002.In otherperiods in the past, the Fed perceived that the econ-omy was too strong and raised interest rates, mostrecently Ln7994 and again in7999-2000.

How do these changes in the federal funds rateinfluence spending? In the text, the effect of lowerinterest rates is depicted in Figures 4-1 and 4-2 as stim-ulating an increase in planned investment andautonomous consumption. Indeed, in 2001-02, thre

rapid decreases in interest rates achieved by the FOMCstimulated consumer spending, especially on autosand houses. Because of low interest rates, auto compa-nies could afford to charge very low interest rates totheir customers, even zero interest rates in the fall of2001. Auto purchasers who might have waited formonths or years raced to showrooms and bought carsat a record pace. Similarly, low interest rates allowedmore home buyers to qualify for mortgages, or allowedthem to buy bigger houses. In addition, many otherhomeowners were able to refinance their mortgages,lowering their monthly payments (leaving moremoney for other purchases) and/or raising the amountof the mortgage in order to obtain extra cash withoutan increase in the monthly payment.

The effect of lower interest rates on consumptionexpenditures is one of four "channels" by which theFed influences total spending. And the potent impactof lower interest rates on consumption spending in

2001-02 suggests that this first channel was operatingwith great efficacy. However, there are three otherchannels of monetary influence, and none of these wasoperating normally.

The second channel is the influence of lower inter-est rates on planned investment. The 2001 recessionhad been caused primarily by a collapse in high-techinrrestment, particularly investment in computers,software, and telecommunications equipment. Lowerinterest rates did not stimulate spending on thoseproducts because the economy was awash in excesshigh-tech equipment; if a firm owns 100 computersand is only using 50 of them, lower interest rates willnot induce the firm to buy more computers.

The third channel of monetary influence worksthrough the stock market. Normally lower interestrates boost stock prices, thus stimulating both con-sumption and investment spending. But stock pricesfell in both 2000 and 2001 and by May 2A02were 30 per-cent below their values of two years earlier.

The fourth and final channel works through theexchange rate. As we will learn in Chapter 6, lowerinterest rates cause the exchange rate of the dollar todepreciate, making U. S. exports cheaper for foreignersto buy, thus boosting net exports (a component ofCDP). However, instead of depreciating, the dollarappreciated (became more expensive) throughout 2001.

The first channel of monetary influence, the effect oflower interest rates in stimulating consumption, wasclearly a very important reason why the recession of2001 was so mild. But, nevertheless, the economyremained weak and unemployment rose despite therapid action of the FOMC. Some commentators havedescribed the Fecl in 2001 as "a four-cylinder enginerunning on only one cylinder."

9+ ('ll,\l)'l'flli ,1 . l'Hli IS-l.ll IlOt)El-

ffiNi' Explain how the A, demand schedule will shift to the left, right, or not at allin response to the following events:

1. A reduction in auto imports from |apan as the quality of American-builtcars improves.

2. The stimulus to housing given by lower mortgage interest rates.3. Higher taxes levied by the government in an attempt to reduce the budget

deficit.4. Higher government spending on security at airports.5. A reduction in consumer confidence after the September 11 attacks.

The 15 curve is theschedule that identifies thecombinations of incomeand the interest rate atwhich the commoditymarket is in equilibrium;everywhere along the 15

curve the demand forcommodities equals thesupply.

4-4 The /S Curve

You have now learned that total autonomous planned spendrng (Ar) dependson the interest rate. And in Chapter 3 you learned that the total level bf real GDPand real income depends on the total level of autonomous planned spending.Now, if we put these two relationships together, we conclude that total real GDPand real income must depend on the interest rate. In this section we derive a

graphical schedule that shows the different possible combinations of the interestrate and real income that are compatible with equilibrium, given the state of busi-ness and consumer confidence, the marginal propensity to save, and the level ofgovernment spending, taxes, and net exports. This schedule is the fS curve.

How to Derive the /S Curve

The lower left-hand corner of Figure 4-4 shows the first ingredient in the deriva-tion of the 15 curve. The " Au demand schedule" shows the demand forautonomous planned spending at different levels of the interest rate and is

copied from the "original rate-of-return line" in Figure 4-2. Notice that at a 10

percent interest rate (point C), At)will be $1,500 billion, just the same as (at pointC) in Figure 4-2.To simplify the discussion, initially we assume that there are nogovernment spending, tax revenue, or net exports, so total autonomous spend-ing consists simply of the two components, 11., + Cn, both of which depend neg-atively on the interest rate.'

\Mhat will be the equilibrium level of real income if A,, equals $1,500 billion? We

answer this question, just as in Chapter 3,by plotting the level of A, in the upperright-hand corner of Figure 4-4 as the horizontal red line (with a height of $1,500 bil-lion). Wrere the An: 1,500line crosses the upward-sloping induced saving line at

point C, equilibrium real income is $6,000 billion. In the lower right-hand side of

Figure 4-4ts plotted the equilibrium level of real income of $6,000 billion against the

assumed 10 percent level of the interest rate.The figure also shows other possibilities; for instance, at point B in the lower

right-hand frame the assumed 15 percent interest rate is plotted against the

$4,000 billion level of real income that is compatible with it. Point B in the otherframes shows the determination of autonomous spending and induced saving.

'The equation of the A,, demand schedule in the lower left quadrant of Figure 4-4 is:

2,500 - 100r

Thus, when the interest rate is at 10 percent, the level of autonomous planned spending along the

,4,, demand schedule is 2,500 - (100 x 10) : 1,539.

WHY EQUILIBRIUM REAL INCOME DEPENDS ON THE INTEREST RATE

4,000 4,000c;co_

zcc(g

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c;,

<.=

nc)cc

efo

u.=--i*

2,000

1,000

0

/t | |

ali,soo '

1,000 2,000 4,000

Autonomousplanned

spendi ng

2,O00

1,500

1,000

0

20

c

O-

o 10P

;c

c

o_qJ l(J

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In this area, real

income is too high

In this area, real

income is too low

1,000 2,000 4,000 0

Autonomous plannedspending (Au)

FIGURE 4-4 Relation of the IS Curve to the Demand for Autonomous Spendingand the Amount of Induced SavingIn the lower left frame, the "A, demand schedule" is copied from the dashed red line inFigure 4-2.\t shows that the demand for autonomous planned spending depends onthe interest rate. For instance, at a 10 percent interest rate the level of A, is $1,500 billionat point C. Following the thin dashed black line up from point C and over to the upperright frame, we see that the economy is in equilibrium at point C, where both A, andinduced savings are equal. This equilibrium level of income is $6,000 billion and isplotted directly below in the lower right-hand frame at point C, opposite the 10 percentinterest rate that we assumed at the beginning.

1. What interest rate is compatible with an $8,000 billion level of equilibriumreal income?At what point does this equilibrium occur inof Figure 4-4?At what point does this equilibrium occur inof Figure 4-4?

the lower right-hand frame

the upper right-hand frame

!)ir

Induced saving

10,000 12,ooo

Real income (Y)

/S curve

10,000 12,000

Real income (Y)

9(i ('H,\Pl'llR -1 . 'IIJE IS LXI XIODEL

,^{D r.,." the /S curve is so important and useful, wepause here to study it more closely. (A full algebraictreatment of the IS-LM model is given in the appendixto Chapter 5.)

increase in transfers). Opposite changes will shiftthe IS curve to the left.

Figure 4-5 illustrates the effect of a rightward shift inthe Ao demand schedule. The result is a rightwardshift in the 15 curve by an amount equal to the A,shift times the multiplier.

The multiplier (k) transforms the A,, demand scheduleinto the 15 curve. An increase in the multiplier (due,for instance, to a smailer marginal propensity tosave) rotates or twists the 15 curve outward aroundits intercept on the vertical interest rate axis. Thusthe higher the multiplier, the flatter the IS curve.

Anything that makes investment or consumptiondemand less sensitive to the interest rate (forinstance, a tendency for firms to pay for investmentgoods with internal funds rather than borrowedfunds) rotates or twists the IS curve upward aroundits intercept on the horizontal income axis. Thus theless sensitive the response of autonomous spendingto the interest rate, the steeper the 1S curve.

Diagram Ingredients andReasons for SlopeThe vertical axis is the interest rate and the horizontal

axis is the level of income.The 15 curve takes information from two other graphs,

the A, demand schedule and the equilibriumbetwei:n induced saving and autonomous plannedspending. Because A, depends on the interest rate,and because equilibrium income is a multiple k) ofA' equilibrium income becomes a negative func-tion of the interest rate.

The horizontal position (equilibrium income) along theIS curve is equal to the horizontal position along theA,, demand schedule times the multiplier k.

The 15 curve slopes down because income is a multipieof A, and A, depends negatively on the interestrate. The IS curve becomes flatter, the more respon-sive is A,to the interest rate, and the larger the mul-tiplier. The 1S curve becomes steeper, the less

responsive is A, to the interest rate, and the smallerthe multiplier.

What Shifts and Rotates the /SCurve?The IS curve is equal to the interest-dependent level of

A,, times the multiplier (k). Anything that shifts theA,, demand schedule will shift the IS curve in thesd*e direction. The factors that shift the IS curve tothe right include an increase in business or con-sumer confidence, an increase in governmentspending or net exports, and a decrease in taxes (or

What Is True of Points That Are offthe /S Curve?The entire area to the left of each IS curve is character-

izedby too low a level of production and income forthe economy to be in equilibrium. There is unde-sired inventory decumulation (negative unplannedinvestment, lr,).

The entire area to the right of each IS curve is charac-terized by too high a level of production and incomefor the economy to be in equilibrium. There is unde-sired inventory accumulation (positive unplannedinvestment, Ir,).

At any point off the /S curve there is pressure for busi-ness firms to adjust production until the economyreturns to the 15 curve.

Because A, depends on the interest rate, equilibrium income does also. The15 ctrrve in Figure 4-4plots the values of equilibrium real income when the mar-ginal propensity to save is 0.25 and the multiplier is 4.0, as in the preceding chap-ter. Notice that points B, C, and D along the 15 curve are all plotted at a horizontaldistance exactly 4.0 times the value of the A, line in the lower left-hand frame.

What the /S Curve Shows

The 15 curve shows all the different combinations of the interest rate (r) andincome (Y ) atwhich the economy's market for commodities (goods and services)

cl7

is in equilibrium, which occurs only when income equals planned expenditures.At any point off the 15 curve the economy is out of equilibrium.

It will be convenient to have a label for the horizontal position of the A,,line,since this in turn will affect the horizontal position of the 1S curve.'' Let us deJine

A',, as the unlue of autonomous plnnned spendiug thnt would take plnce at 0n interestrnte of zero.In Figure 4-4 the A, line intersects the horizontal axis at $2,500 bil-iion, so our label for this A,, line will be A'rn : 2,500. The IS curve always lies ata horizontal distance 4.0'times the A,, line, because the multiplier (k) rs 4.0.

Notice in Figure 4-4that the 15 curve intersects the horizontal axis at $10,000 bil-lion, exactly 4.0 times the level of A'po: 2,500.

What Shifts the IS Curve?

Figure 4-4 demonstrates that the horizontal intercept of the 15 curve is alwaysequal to the multiplier (k) times A',,0, tL.e amount of autonomous plannedspending that would occur at a zero interest rate. Anything that changes Ai,n toanother value like Ai,r will shift the 1S curve. Anything that changes the multi-plier (k) will rotate the 15 clrrve.

Both the A, demand schedule and the 15 curve will shift to the right if busi-nesses and consumers become more optimistic and desire to spend more at anygiven interest rate.

In Figure 4-5, the ieft-hand frame shows two A,lines. Along the left-hand"old An demand schedule" confidence is relatively low, but the "new A,deman& schedule" reflects a higher level of confidence and lies everywherbexactly $500 billion farther to the right. Since the mtrltiplier is 4.0, the "new 15

curve" lies $2,000 billion to the right, so that at an interest rate of 10 percent,equilibrium real income is $8,000 billion at point F.

Once again, it is convenient to label each IS curve by the amount ofautonomous planned spending that would occur at an interest rate of zero-that is, A'p, : 2,500 along the "old ,,4.,, demand schedule" and A'u, : 3,000 alongthe "new A,, demand schedule."

The Missing Relation

The 15 curve is like a menu, providing us with innumerable combinations ofinterest rates and income that are consistent with equilibrium in the commoditymarket. But which item on the menu should we choose? There is not enoughinformation here to make a choice. We need to find another relationship to linkincome and the interest rate in order to tie down the economy's position alongthe 15 curve. In the familiar langr-rage of elementary algebra, we have twounknowns but only one equation. In the next sections, we supply the missingequation and arrive at a complete theory of how income and the interest rate are

determined."

3We call the IS schedule a " cLrrve," even though we have drawn it as a straight line-, becanse in thereal world the relationship might be a cun'e. Also the' term "IS cttrve" h.ls t'reen iamiliair to genera-tions of economists since its invention by the late Sir John Hicks iu a classic article, "Mr. Keynes andthe Classics: A Suggested Interpretation," Ecortornctricn, r.ol. 5 (April 7937), pp. 747 -159 .

aDespite its nerme, the 15 cllrve has no unique connection with investment (1) clr saving /S). It shiftswhenever there is a shift in the A,, demand schedule, which can tre causecl by a change in govern-ment spending, in taxes or transfdrs, or in net exports, as well as by changes in business and con-sumer confidence.

98 CHAPTI]R ,1 . 'l'l{E IS-L,l,I \lOD]ll,

HOW INCREASED CONFIDENCE SHIF'TS THE /S CURVE

2020

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c

_+

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t\t\l'I

I

I

1 ( )lri /.S,,

1\ .-

\lIt\

0 2,000 4,000 0

Autonomous plannedspending (Ar)

FIGURE 4-5 Effect on the .[S Curve of a Rightward Shift in theDemand for Autonomous Planned SpendingThe "old" A,, demand schedule and IS curve are copied from Figure 4-4. Now weassume that an increase in the level of business and consumer confidence shifts the Ai,line $500 billion to the right, just as occurred in Figure 4-2. The 15 curve shifts to tl'reright by four times as much. Notice that the horizontal intercept of the new IS curve at12,000 is four times the horizontal intercept of the A',,line-that is, A'yt : 3,000.

4-5 Why People Use Money

The second relationship between real income and the interest rate (in additionto the IS curve) occLrrs in the "money market," a general expression for thefinancial sector of the economy. In reality, the financial sector consists of manyassets in addition to money, including short-term debt of corporations and thegovernment, as well as bonds, stocks, and mutual funds of various types. In thischapter we n'ill limit our attention to the segment of the financial sector gener-ally referred to as "money."

The money supply (M') consists of two parts: currency and checkingaccounts at banks and thrift institutions. At this stage in the book, the moneysupply may be considered to be a policy instrument that the Federal ReserveBoard (the Fed) can set exactly at any desired value, just as we have been assum-ing that the government can precisely set the level of its fiscal policy instru-ments-that is, its purchases of goods and services and tax revenues. Later, inChapter 13, we will learn how the Fed achieves its control over the money sLrp-

ply in actual practice.The theory developed in this chapter establishes a link between the rnoney

supply, income, and interest rates. In order to understand the hypothesis

6,000 8,000 10,000 12,000

Real income (Y)

The money supplyconsists of currency andtransactions accounts,including checkingaccounts at banks andthrift institutions.

[u'gf*',+; +rftr rS]

a - l curve to the right

c)cl

A medium of exchange isusecl for br-rying and seli-ing goods and services andis a universal alternative tothe barter system.

A store of value is amethod of storing pur-chasing power whenreceipts and expendituresare not perfectlv synchro-rrized.

A unit of account is a

way of recording receipts,expenditures, assets, andliabilities.

underlying the demand for money, we begin by examining the three traditionalfunctions of money-its roles as a medium of exchange, a store of value, and a

unit of account.

A Medium of Exchange

The most important function that differentiates money from other assets is itsrole as a medium of exchange. Money is one of the most important inventionsin human history because it has allowed society to rise above the cumbersomemethod of exchange known as the barter system. With barter, one good or ser-vice is exchanged directly for another.If , as a professor, I want a leaky faucetfixed, I must find a plumber who wants to learn about economics. It might takeweeks or months to find such a plumber, since the matching of services requiresa "double coincidence of wants."

A barter society remains primitive because people have to spend so muchtime arranging exchanges that they have little time remaining to produce effi-cientiy. As a result, to avoid arranging exchanges they mustbecome self-strfficient(I would have to fix my own leaking faucet), thus failing to take advantage of theessential role of specialization in the development of an advanced economic sys-tem. Money eliminates the need for barter and the double coincidence of wants.

Which types of assets serve as a medium of exchange? Thirty years agoalmost all exchanges in the United States involved coins, currency, or checkingaccounts that paid no interest. Cradually other methods of exchange havedeveloped, including interest-bearing checking accounts, savings accounts, andmoney market mutual funds against which checks can be written. The recluire-ments for an asset to qualify as a medium of exchange include ready accept-ability, protection from counterfeiting, and divisibility (ability to use for smalltransactions).

A Store of Value

People do not always spend the entirety of their income the instant they receiveit. Some receipts may be spent a day or two iater, but others may be saved for a

substantial period of time. People need some way of storing the purchasingpower of their receipts until a later time. Any asset that performs this functionis called a store of value. There are many financial instruments that serve as astore of value but not as a medium of exchange, including passbook savingsaccounts that do not provide check-writing services, as well as bonds andstocks. Money can be used both as a medium of exchange and as a store of value.

A Unit cf Account

Money is also used for accounting purposes. How much your employer will payyou in wages, how much you owe the bank, how much a firm has earned, andhow much a bond is worth are all recorded in some unit of account. This unit iscalled dollars in the United States, pounds sterling in the United Kingdom, yen inJapan, and so on. The dollars entered on accounting records do not physicallyexist, in the sense that no coin or piece of currency corresponding to each oneexists in a particular location. Some dollars that serve as bookkeeping entries canalso serve as a medium of exchange without any piece of paper actually changinghands, as in wire transfers between bank accounts.

I0()

Real money balanceseqr-ral the total moneysupply divided by theprice level.

4-G Income, the Interest Rate, andthe Demand for Money

The hypothesis that links the money supply, income, and the interest rate statesthat tlrc anrourtt of ntoney tlnt peopla tlemnntl in renl terms tleytends botlr on ilrconrcand on the interest rate. Why do households give up interest earnings to holdmoney balances that pay no interest? The main reason is that at least sottc hold-ing of money is necessary to facilitate transactions, due to the role of money as

a medium of exchange.

Income and the Demand for Money

Funds held in the form of stocks or bonds pay interest but cannot be used fortransactions. People have to carry currency in their pockets or have money intheir bank accounts to back up a check bdfore they can buy anything. (Even iithey use credit cards, they need money in their bank accounts to keep up withtheir credit card bills.) Because rich people make more purchases, they generallyneed a larger arnount of currency and larger bank deposits. Thus the demandfor real money balances increases when everyone becomes richer-that is,when the total of real income. increases.

Changes in real income alter the demand for money in real terms-that is,adjusted for changes in the price level. Let us assume that the demand for realmoney balances M/P) equals half of real income (Y ):

0.5v

The superscript d means "the demand for."If real income (Y) is $8,000 billion, the demand for real money balances

(M/P)'t wiil be $4,000 billion, as shown in Figure a-6 by the vertical line (L')drawn at $4,000 billion. The line is vertical because we are assuming initially thatthe demand for real balan ces (M/P)'1 does not depend on the interest rate (r).

The Interest Rate and the Demand for Money

The L' line is unreaiistic, however, because individuals will not hold as muchmoney at a 10 percent interest rate as at a zero interest rate. Why? Because theinterest rate plotted on the vertical axis is paid on asscfs otlrcr thnn ntoney, such as

bonds and savings certificates. The higher the reward (r) for holding interest-earning financial assets (that are not money), the less money will be held.

If the interest rate (r) paid on nonmoney assets were less than the interestpaid on money, there would be no point in holding them. Individuals wotrldhold all of their financial assets in the form of money to take advantage of itsconvenience. But if the interest rate on them were higher than the interest paidon money, individuals would cut down on their averafle money holding irr

order to earn the higher interest availabie on aiternative assets. They would con-sider these higher interest earnings sufficient compensation for the nuisance ofperiodically converting these assets into money.

In Figure 4-5 the downward slope of the Lo line through points F and D indi-cates that when real income is $8,000 billion and the interest rate is zero, the

(ryr\' _tl\P/

THE I;iI CURVE 101

F'I(;URI'.1.6The Demand for Money, the Interest Rate,and Real IncomeThe vertical line L'is drawn on the unrealisticassumption that the demand for real balances is equal tcr

half of real income ($8,000 billion in this case), but doesnot depend on the interest rate. The L,, curve maintainsincome at $8,000, but it allows the demand for realbalances to decrease by $1,000 billion for each 5 percentincrease in the interest rate. The gray area shor,t,s theamount shifted into other assets, an amount that growsas the interest rate rises, leaving a smaller and smalleramount to be held as money.

HOW INCOME AND THE INTEREST RATE DETERMINETHE DEMAND FOR RE,AL BALANCES

4,000

Real nroney b;rlances WIP)

20

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p

c)

c)

C

6,000

Amount shifted inton0nmtlney assets

1,, {Y - 8,000)

demand for real balances is $4,000 billion. But when the interest rate rises fromzero to 5 percent, people suffer inconvenience to cut down their money holdingsfrom $4,000 billion to $3,000 billion (point D). When tl-re interest rate is 10 per-cent, only $2,000 billion of money is demanded (point F ). The new !o line canbe summarized as showing that the real demand for money (M/P)" is half ofincome minus S200 billion times the interest rate:

0.5Y - 200r

A change in the interest rate moves the economy up and down its realmoney demand schedule, whereas a change in real output (Y) shifts that sched-ule to the left or right, as shown in Figure 4-7.

(MYtt:\P /

L.

2.

J.

ffi What are the two determinants of the real demand for money?What is the effect of each determinant on the real demand for money?Does a change in either determinant shift the /S curve?

4-7 The LM Curve

Thus far we have learned that the supply of money (M') is controlled by the Fed,and that the real quantity of money demanded by households (M/P)'/ dependson both income and the interest rate. Now we can tie these two relationshipstogether by assuming that the money market is always in e quilibriunt (a situation

102 ('il,\Pt'F)i I .

F'IGURE 4.7Effect on the Money Demand Schedule of aDecline in Real Income from $8,000 to$6,000 BillionThe L,, line is copiecl from Figure 4-6 and shor,r,s thedemand for real balances at different rates of interest,assuming that real income is $8,000 billion. A $2,000billion drop in the level of incorne to $6,000 billiorrcalrses the dernancl for real bzrlances to drop by half as

much, or $1,000 billion, at each interest rate level. Forinsttrnce, at an interest rarte of 10 percent the dem;tnd forreal balances falls from $2,000 billion at point F to $1,000billion at point C.

A DROP IN THE LEVEL OF'INCOME SHIF-ISTHE MONEY DEMAND SCHEDULE TO THE LEFI

| .-)

1,000 2,000 4,000

Real money balances (MlP)

20

E(/!,a)go 1O.3

CJ

C

6,000

(Y = tl.O00)

where there is no pressure for change), with the real supply of money equal to

the real demand for money. This equilibriurn condition for the money rnarketallows us to derive a relationship called the LM umte, just as we prer.iouslyderived an equilibrium condition for the commodity market called the 15 currtc,

To achieve equilibrium in the rnoney market,,the real supply of money (Mt/P)

must equal the demarrd for real money (M/P)":

0.5Y - 200rM' IM\N

-tt-P -\p/ - (4 1)

If the amount of money supplied by the government is $2,000 billion and the

price index (P) is set at a constant value of 1.0, then M' /P equals $2,000 billion.To simplify the analysis, we assume that the supply of money does not clependon the interest rate, so Mt / P is drawn in the left frame of Figure 4- B as a verti-cal line at a level of $2,000 billior-r for every interest rate. The two money demandschedules, L,, and L1, ate- copied from Figure 4-7.

How to Derive the LM Curve

The sloped money clemand line Ls, drawncrosses the Mt/P line at point F, whereThe demand for money at F is $2,000 billion,$2,000 biilion. Because the two are equal, the

for an income of $8,000 billion,the interest rate is 10 percent.and the supply of money is also

money market is in equilibrium

10ll

A FIXED MONEY SUPPLY IS CONSISTENT WITH MANY DIFFERENT LEVELS OF'INCOME

0 2,000 4,000

Real money balances (MlP)

F'IGURE 4-8 Derivation of t}ne LM CurveIn the left frame the Ln and L., schedules are copied from the previous figure. Thevertical M' / P line shows the available supply of money provided by the government.The money market is in equilibrium where the supply line (M'/P) ..om"s the demandline (Lo or L1). When income is $8,000 billion, equilibrium occurs at point l, plotted

:.'iJl'#;:[:11TeH$,'ff :r,"Jt-if :fl ll*?i!:'iH:ffJil:'.il]"n"shows all combinations of Y and r consistent with equilibrium in the money market.

20

C

I ls_o_

P

3 ioc

0 2,000 4,000 6,000 8,000 .l 0,000 12,000

Real income (Y)

I (V-Ll \ ' -

6,000)

when Y : 8,000 (assumed in drawing the Lo line) and r : 10 percent. Thisequilibrium combination of values is plotted at point F in the right frame ofFigure 4-8.'

If income is $6,000 billion instead of $8,000 billion, the demand for money isshown by schedule L, passing through points C and G in the left frame of Figure4-8. Now the demand for real money balances can be equal to thefixed real supply of money only at point G, where the interest rate is 5 percent.Thus Y : 6,000 and r : 5 is another combination consistent with equilibriu.t-t ilthe money market, and this is plotted at point G in the right frame of Figure 4-B.n

sThrs, in equation (4.1)

6Thus, in equation (4.1)

2,000 - 0.5(8,000) 200(10)

- 4,000 2,000

- 2,000

2,000 : 0.5(6,000) - 200(5): 3,000 - 1,000: 2,000

104 CI{APTEIT 4 . THII IS-LA,I N,l0DEL

rrrI he LM curve is as important and useful as the IS

cLlrve. This box explains the slope of the curve andwhat makes it shift and rotate its position.

Diagram Ingredients andReasons for SlopeThe verticai axis is the interest rate and the horizontal

axis is the level of income (same as the 15 curve).The LM curve shows the different combinations of the

interest rate and income consistent with setting thedemand for money equal to afixed supply of money.Since the demand for money is fixed everywherealong the LM curve, but income increases as wemove to the right, "something" must happen to off-set the higher demand for money that results fromhigher income. That "something" is the higherinterest rate, which induces people to shift someassets into nonmonetary assets, freeing up more ofthe fixed available money to be used for the higherlevel of transactions.

Along any given LM curve, the level of real money bal-ances (Mt/P) is fixecl, but real income (Y) varies. Theratio of real income to real balances is called theaelocity of money (7);

velocity (Iz) = #": #The right-hand expression states that velocity is also

equal to nominal income QY) divrded by the nomi-nal money supply (Mt).Tlne higher the interest rate,the higher is velocity. Why? If r increases, peoplewish to hold less money. But the money supply isfixed. To maintain equilibrium in the money market,there must be an increase in income to induce house-hoids to hold the fixed existing quantity of money.Anything that can cause the economy to move up

and down along a fixed LM curve achieves a changeof velocity by altering Y while M' / P is fixed.

What Shifts and Rotates theLM Curve?The LM curve is drawn for a fixed real supply of money

i

(M'/P). Ahigher nominal supply of money (M') will i

shift the LM curve to the right, as in Figure 4-9, and i

a lower nominal supply of money will shift the LM i

curve to the left. An increase in the price level (P) :

will shift the LM curve to the left, and vice versa i

Anything that makes the demand for money less sen- l

sitive to the interest rate makes both the money ,

demand schedule, L(Y), and the LM curve steeper "

(rotating it upward around its horizontal intercept). ',

Anything that makes the demand for money less i

responsive to changes in income will make the LM i

curve flatter and also shift it outward. .

What Is True of Points That Are offthe LM Curve?The entire area to the left of the LM curve has an excess

supply of money because income is lower than thatneeded to create a sufficient demand for money tomatch the supply.

The entire area to the right of the LM curve has anexcess demand for money because income is higherthan required to match the demand for money tothe fixed supply.

At any point off the LM curve there is pressure forinterest rates to change. For instance, when there isan excess demand for money, people try to obtainmoney by selling bonds and other financial assets,and this pushes up the interest rates on bonds andother financial assets.

The LM curve is theschedule that identifies thecombinations of incomeand the interest rate atwhich the money marketis in equilibrium; on theLM curve the demand formoney equals the supplyof monev.

What the LM Curve Shows

The line connecting points G and F in the right-hand frame of Figure 4-B is calledthe LM curye. The LM curve represents all combinations of income (Y) andinterest rate (r) where the money market is in eguilibrium-that is, where thereal supply of money equals the real demand for money.

At any point off the LM curve, say point D, the money market is not inequilibrium. The problem at D and all other points in the red shaded area isthat the demand for real money exceeds the available supply.At point C and all

TTIE I,T4 CLTRVE 105

other points in the white area there is an excess supply of money that exceedsthe demand.

How does the economy adjust to guarantee that the given supply of moneycreated by the government is exactly equal to the demand when the money mar-ket is out of equilibrium, as at point D? One possible adjustment, a reduction inthe price level, will be considered later. In this chapter we continue to assumethat the price index (P) is fixed at 1.0. Without changing prices, the economymight achieve money market equilibrium from point Dby increasing the inter-est rate from 5 to 10 percent. This would move it to point l, cutting the demandfor money. Or,instead, income might fall from $8,000 billion to $6,000 billionwhile the interest rate remains fixed. This would cause a movement to point Gand would also cut the demand for money. Or some other combination mightoccllL with a partial drop in income and a partial increase in the interest rate.

1. By how much does the demand for money change when the economymoves from point D to point F in Figure 4-B?

2. From point D to point C?3. From point C to point F?

4. From point C to point C?

What Makes the LM Curve Shift?

The position of the LM curve is determined by the size of the money supply, andany change in the money supply will cause the LM curve to shift its position.What happens when the Fed decides to alter Ms, the nominal money supply? Ifthe price level (P) is fixed, this will alter the real money supply (Ms/P).In Figure4-9, for instance, a $1,000 billion increase in the money supply from 92,000 to$3,000 billion shifts the LM curve from the left-hand dashed line (LMi to theright-hand solid hne (LM). Since each dollar of extra available money makes pos-sible 2.0 extra dollars of income , the LM curve shifts horizontallv bv $2,000 billion.

Another way to interpret the effect of a higher money supply is also shownin Figure 4-9. How does the economy adjust if real income remains fixed atY : 8,000? In the left frame of Figure 4-9, the demand-for-money line, labeledLr(y : 8,000), shows the amount by which the demand for money increases asthe interest rate declines, holding the level of income fixed at Y : 8,000. If themoney supply is at its original value of 2,000, the money market is in equilibriumat point I, with an interest rate of 10 percent. When the money supply increasesfrom 2,000 to 3,000, the left frame shows that the interest rate must decline from10 percent at point F to 5 percent at point D in order to maintain equilibrium inthe money marketbyboosting the demand for moneyby the same amount as themoney supply has risen-that is, from 2,000 to 3,000.

In the right frame of Figure 4-9, points F and D are plotted at the samehorizontal position, since the level of income is assumed to be 8,000. Whenthe money supply is at the original level of 2,000, the economy operates alongthe original LMo curve at point F. When the money supply increases to the newvalue of 3,000, the LM curve shifts rightward to its new position LM, at point D.

Which outcome will occur following an increase in the money supply? Willincome increase while the interest rate remains constant? Or will the interestrate decline (as from point F to point D) while income remains constant? Onceagain, we cnnnot determine the unlue of two tmknowns with only one relntion-thnt is,

-

106 ('l[APTI']R -l ' TIIFI IS'L]'I N'I()DEI.

HOW A HIGHER REAL MONEY SUPPLY CAN REDUCE THE INTEREST RATE

Higher moneysupply shiftsLM curve to right

0 2,000 4,000

Real money balances WIP)

FIGURE 4-g The Effect on the LM Curve of an Increase in the Real Money Supplyfrom $2,000 Billion to $3,000 BillionThe dashe d LM'line in the figure is identical to LM in Figure 4-8. When the money

supply is increaied, the money available to support output increases and the LM curve

rnifir .ightwa.d by 2.0 dollars per dollar of extra money to the new LM, line.

20

c

9 1s0.)1

;O IU

C

0 2,000 4,000 6,000 8,000 10,000 12,000

Real income (Y)

New lM, curve

(+ = 3,ooo)

1,, (Y= 8,000)

the LM curae. We must use both relations, the 1S curve and the LM curve, to

cletermine the two unknown variables-income and the interest rate' The next

section joins together the 15 and LM curves to determine the level of both

unknown variables.

4-8 The /S Curve Meets the LM Curve

Now we are ready to examine the economy's "general equilibrium," which

takes account of behavior in both the commodity and money markets. We do

this by bringing together the ISo curve from Figure 4-5 with the LMo curve from

Figure 4-9.Equilibrium in the commodity market occurs only at points on the 1S curve'

Figure 4-10 copies the 1S,, schedule from Figure 4-5 drawn for a value of

Aiur: 2,500. Ai any point off tne ISo curve-, for instance G and l, the commod-

ity market is out of equilibrium. C, D, and E,, all represent different combina-

tions of income and the interest rate that are compatible with

commodity-market equilibrium. At which equilibrium point will the economv

come to rest? The single ISo schedule does not provide enough information to

cjetermin e both income and the interest rate. Truo schedules are needed to pin

down the equilibrium values of two unknown variables.

NI0NETA1TY I)OI,I('\' IN A(]'I-i0\ 107

FIGURE 4.10The /S and, LM Schedules Crossat LastThe 156 schedule is copied from Figure 4-5; theLMo schedule is copied from Figure 4-9. Onlyat the red point, E0, is the economy in "gen-eral" equilibrium, with the conditions for equi-librium attained in both the commodity market(along 15) and the money market (along LM).At points U, V, G, and E, the commodity mar-ket is out of equilibrium. At points U, V, C, andD, the money market is out of equilibrium.

THE ECONOMY'S "CENERAL" EQUTLTBRTUM

20

15

Pc

o_

.g 10

a)

c

4,000 6,000 - , ( )( !0 8,000 1 0,000

Real income (Y)

2,55A, ft = 4,0)

General equilibrium is asituation of simultaneouseouilibrium in all themirkets of the economy.

The LM curve provides the necessary additional information, showingall combinations of income and the interest rate at which the money market isin equilibrium for a given real money supply-in this case, $2,000 billion. Figure4-10 copies the LMo schedule from Figure 4-9 drawn for a value of Ms/P : 2,000.At any point off the LMo curve, for instance points C and D, the money marketis out of equilibrium. At D income is too high and the real demand for moneyexceeds the real supply. At C income is too low and the real demand for moneyis below the real supply. Equilibrium in the money market occurs only at pointssuch as G, F, and Es, each representing combinations of income and the interestrate at which the real demand for money is equal to a real money supply of$2,000 billion.

How does the economy arrive at its general equilibrium at point E. if itstarts out at the wrong place, such as at points U or V ? If the commodity mar-ket is out of equilibrium and involuntary inventory decumulation or accumula-tion occurs, firms will step up or cut production, pushing the economy in thedirection needed to reach E0. If the money market is out of equilibrium, therewill be pressure to adjust interest rates, since people will have to sell stocks andbonds if they cannot otherwise satisfy their demand for money. Either way theeconomy arrives at En.

4-g Monetary Policy in Action

The IS-LM model uses two relations (or schedules) to determine the twoendogenous variables, real income and the interest rate. The exogenous vari-ables, which the model does not explain, are the level of business and consumer

108 CHAPTER 4 . THE ls-tfll NIODEL

An expansionarymonetary policy is onethat has the effect oflowering interest rates andraising GDP.

A contractionarymonetary policy is onethat has the effect oflowering CDP and raisinginterest rates.

optimism, the single instrument of monetary policy (the money supply), thetwo instruments of fiscal policy (government sper-rding and tax revenues), andnet exports. Whenever there is a change in one of the exogenous variables, theresult will be a change in either or both of the two endogenous variables, realincome and the interest rate. In this section we will see that a decision by the Fedto change the money supply will normally lead to a change in both real incomeand the interest rate.

What level of real GDP does the Fed desire? We shall assume that thedesired level of income, "natural real GDP," is $8,000 billion. In Figure 4-10 theequilibrium level of real income (GDP) at point En is only $7,000 billion. Thusthere is a $1,000 billion "gup" between actual and natural real GDP that needsto be filled. What should the Fed do?

To raise CDP by the required $1,000 billion, the Fed must increase the moneysupply. This action is called an expansionary monetary policy. Conversely, ifnatural real GDP is lower than actual real CDP, the Fed can decrease the moneysupply. This is an example of a contractionary monetary policy.

Normal Effects of an Increase in the Money Supply

Wili an increase in the money supply increase real income, reduce the interestrate, or both? If the 1S and LM curves have the "normal" shapes displayed inFigure 4-70, the answer is "both." As we shall see in the next chapter, there are

extreme cases in which the 15 and / or the LM cur\res are vertical or horizontal,and the entire impact of a change in the money supply may fall just on real

income or just on the interest rate. But here, where the 15 curve has its normalnegative slope and the LM curve has its normal positive slope, monetary policvchanges both real income and the interest rate.

Figure 4-11 repeats the LMo curve of Figure 4-70, drawn on the assumptionthat the real money supply is $2,000 billion. Also repeated is the lSo curve of

Figure 4-10, which assumes that A'po:2,500 and k: 4.0. The economy's gen-

eral equilibrium, the point where both the money and commodity markets are

in equilibrium, occurs at point E,,.

Assume that the Fed now raises the nominal money supply from $2,000 bil-lion to $3,000 billion. As long as the price level stays fixed at 1.0, the real moneysupply increases by the same amount. The LM curve shifts to the right by $2,000billion. Now, at the new higher real money supply of $3,000 billion, there is an

"excess supply of money" of $1,000 billion. How can the economy generate the

$1,000 billion increase in the real demand for money needed to balance the neu'

higher supply?Finding themselves with more money than they need, individuals transfer

some money into savings accounts and use some to buy stocks, bonds, and com-

modities. This raises the prices of bonds and stocks and reduces the interest rate.

The lower interest rate raises the desired level of autonomous consumption and

investment spending, requiring an increase in production. Only at point E,,

with an income level of $8,000 billion and interest rate of 5 percent, are both the

money and commodity markets in equilibrium. Compared to the starting pointEn, the increase in the real money supply has caused both an increase in real

income and a reduction in the interest rate.Monetary policy works exactly the same in reverse. If the desired ler.,el oi

real income was not $8,000 billion but rather $7,000 billion, the Fed could

move the economy leftward from point E, in Figure 4-11 to point E6, simplv

HO\V F'ISI]AL EXPANSION CAN "CROWD OUT'' I}.iVEST1\I}'NT 109

FIGURE 4.11The Effect of a $1,000 Billionin the Money Supply with aNormal LM Curve

fncrease 2o

We repeat the $1,000 billion increase in themoney supply that was shown in Figure 4-9.In order to maintain equilibrium in both thecomrnodity and money markets here, twoeffects occLrr: equilibrium income rises and theinterest rate declines, as indicated by themovement from Eo to Er.

A HIGHER MONEY SUPPLY BOOSTS INCOME AND CUTS THE INTEREST RATE

c

o 10

oCJ

c

2,OOO 4,000 6,000 7,000 ii,(xx) 10,000 12,000

Real income (Y)

Old lM,,curve /(ry = 2.ooo) |\ P '/

New lM, curve

(+:3,ooo)

Equilibriunrmoves to nere

by reducing the real money supply from $3,000 billionresult, the LM, curve would shift leftwards to LMo, andfrom $8.000 billion to $7,000 billion.

to $2,000 billion. As a

income would decline

4-10 How Fiscal Expansion Can "Crowd Out"Investment

In the last section we exarnined the effects on real income and the interest rateof changes in monetary policy by shifting the LM curve along a fixed 15 curve.Now we shall do the reverse and shift the 15 curve along a fixed LM cun,e. Theoriginal 15 curve is copied from Figure 4-10 and is labeled in Figure 4-12 (onpage 772) as the "old lSo curve " ; it is drawn on the assumption that the amountof autonomous planned spending that would occur at a zero interest rate (Ai,o)

is equal to $2,500 billion.

Expansionary Fiscal Policy Shifts the /S Curve

An expansionary fiscal policy taking the form of a $500 billion increase in gov-ernment purchases shifts the 1S curve to the right. Note that the horizontal dis-tance between the old and new 15 curves is not $500 billion but $2,000 billion,since the horizontal shift of 15 is $500 billion times the multiplier, still assumedto be 4.0.

Figure 4-72 demonstrates that the effect of an expansionary fiscal policy onreal income is not indicated by our original Chapter 3 multiplier (k : 4.0) once

110

II{TERNATIONAL i The Wbrldwide Effects on ConsumerPERSPECTIVE i Confidence of the September 11 Attacks

la\

I

rnI he September 77, 2007, attacks were felt most

directly in downtown Manhattan and at the Pentagon.But the first significant foreign attack on the Americanhomeland, lr,,hich had been immune in previous wars,dealt a blou, to the American psyche. Trips were can-celled and vacation plans postponed, and the airlineand hotel industries went into a tailspin. Sales of lux-ury goods suffered, as wealthy individuals felt Llrlcorn-fortable inclulging themseives while others weresuffering.

The arnalysis in Chapter 4 singles out consumer andbusiness confidence as factors that can shift autonomousplanned spe.nding and the 1S curve. The September 11

attacks stand out as a clarssic case of an adverse "shock"to consumer ancl business confidence. In terms of ourmacroeconomic model, the attacks caused the 1S

curve to shift to the left, thus reducing the level ofplanned expenditures at any given interest rate.Monthlv surveys measure the state of consumer con-fidence in the United States; the figure displays theIrrdex of Consumer Confidence for 7988-2002 as com-piled by the Conference Board.

Clearly, there was a sharp drop in consumer confi-dence in October and November 2001 as a result of theattacks. Hor,r,ever, several remarkable facts stand outfrom the graph. First, the e.ffect of September 11 wasshort-lived, since confiderrce snapped back over thenext few, months. Second, the post-;'rttack drop in con-sumer confidence was much smaller than the sharn

decline in confidence that began in mid-2000, which inturn represented a reaction to the beginning of a

decline in the stock market and a turnaround in the jobmarket from rapid job growth to layoffs and vanishingjobs. The post-attack drop in consumer confidence wasalso much smaller than that which occurred after theAugust 1990 invasion of Kuwait by Iraq or in severalother episodes in the early 1990s. Overall, while thepost-attack period provides an example of a drop inconsumer confidence that shifts the IS curve to the left,it was relatively minor and short-lived compared toother episodes.

The effects of the September 11 attacks were notlirnited to the United States. Many other nations lostcitizens who had been working in the World TradeCenter that morning-hundreds in the case of theUnited Kingdom and Japan. Yet the impact of theattacks on consumer confidence in other countrieswas even smalier than in the United States, perhapsbecause these citizens were farther away from thc.

World Tiade Center and were concerned with differ-ent issues.

For instance, Japan had been mired in a decade-longslump (we will learn more about this in Chapter 5).Consumer and business confidence had been decliningfor a long time, and the attacks barely registered a rip-ple on a sea of pessimism caused by a persistentdecline of industrial production, a continuing loss ofjobs, and the seeming inability of policymakers to take

i

the money market is taken into consideration. The full fiscal multiplier of k : 4.0

would move the economy horizontally from the initial equilibrium position at

En to point E2, where income is $2,000 billion higher. At E2, however, the moneymarket is not in equilibrium, because E, is off the LMo curve. Income is higherthan at Es, raising the dernand for money, but the real supply of money remainsunchanged at the original assumed value Mt/P :2,000. There is an excess

demand for money.To cut the demand for money back to the level of the fixed supply, the inter-

est rate must rise. But an increase in the interest rate makes point E, untenableby reducingplanned consumption and investment expenditlrres. Only nt poinf E.

are both the commodity and money markets in equilibrium. Real income does

not increase by the full $2,000 billion, but only by half as much, $1,000 billion.The higher interest rate accounts for the fact that the fiscai policy multiplier

is 2.0, rather than 4.0, r,t'hen the requirement for money market equilibrium is

FIO\V I'I S(]AL EXPANSION (]AN *CRO\\'D (]T]T" I N V I,] S1' N I E NT 111

the strong actions that many observers agreed wereneeded. At the other extreme was France, where con-sumer confidence hit all-time highs in late 2001 andearly 2002. The French economy was expected to con-tinue growing at the most rapid rate of all the largeEuropean countries, and French consumers reported a

record-high readiness to purchase cars and houses, as

well as optimism about the outlook for their ownhousehold finances.

The ripple effects of the September 11 attacksimpacted the U.S. economy, and this amplified a sharpdecline in U.S. imports that was already underway andthat reduced net exports in many economies, particu-larly in Asia. But, aside from the effect on foreign trade,the attacks had virtually no separate impact on con-sumer confidence in other countries, while even withinthe United States, the slide in consumer confidencewas surprisingly small and short-lived.

.,1'

oL1 9BB 1 989 1 990 1991 1992 1993 1994 1 995 1996 1997 ',r 998 1999 2000 2001 2002 2003

Source: The Conference Board

taken into account. The increase in the interest rate from 7.5 to 10 percent cutsprivate autonomous planned consumption and investment spending by $250billion, fully half of the $500 billion increase in government spending. Thus fullyhalf of the original multiplier of 4.0 is "crowded out."

Comparison of Equilibrium Positions Eo and Eg

120

110

100

il90

x ---oc

70

Initial8,,

Interest rate (r) 7.5

Private autonomous spending Qp + C,,: 2,500 - 100r) 7,750Government spending (C) 0

Total autonomous spending (A, : I, I C,? + C) 1,750Income (Y : 4.04t)) 7,000

Ncu, E,

10.0

1,500

5002,0008,000

E

II2 tlltAPTb'It .1 . THI| I,S-LXI IIODiil,

THE CROWDING OUT EFFECT CUTS THE, FISCAL MTJLTIPLIER

tur(# = 2,ooo)

0 2,000 4,000 6,000 7,000 8,000 (),i)00 10,000 12,000

Real income (Y)

FIG{JRE 4-12 The Effect on Real Income and the Interest Rate of a $500 Billionlncrease in Government SpendingAlong the original 1S., curve, the autonomous spending desired at a zero interest rate(A1,,) is 2,500 ancl the economy's equilibrium occurs at point Eo.A $500 billion increase

in governrnent spending boosts spending from A'ro : 2,500 to A'4 : 3,000, ancl shifts

l;ilr#ffi j;#ll#;;:Irfi*iHLfrii#*r"ilsf:;ilt:ffi-is partial, not complete.

15

a.)

gd,

(-)

0)CJ

I

I

-t

l

I\i

i

I

Crowdingout effect

The crowding out effectdescribes the effect of anincrease in governmentspending or a reduction oftax rates in reducing tlreamount of one or moreother components ofprivate expenditures.

The Crowding Out Effect

Some economists and journalists use the phrase crowding out effect to comparepoints such as E, and E, in Figure 4-I2. The $1,000 billion difference in real

income between points Erand E, results from the investment and consumptionspending crowded out by the higher interest rate. Point Er, used in calculatingthe size of the crowding out effect, is a purely hypothetical position that the

economy cannot and does not reach. Actually, far from being crowded out, total

private spending is higher in the new eqlrilibrium situation at E. than at the

original situation at Eo-real income has increased by $1,000 billion, of which

only $500 billion represents higher government purchases, leaving the remain-

ing $500 billion for extra private expenditures. The composition of private

spending changes, however, as a result of the higher interest rate. Induced con-

sumption spending increases, but autonomous private spending decreases,

Expenditlrres are divided up as follows in the two situations:

SL]NIIIARY

At O.,

5001,500

6,000

8,000

113

Covernment purchasesAutonomous private spending (lp + Ca)

lndtrced consumptionTotal real expenditures

At E0

0

7,7505 ?50

z;,ntoo

Can Crowding Out Be Avoided?

The fundamental cause of crowding out is an increase in the interest rate that isrequired whenever income rises and the supply of money is fixed while thedemand for money responds positively to an increase in income. To offset theincrease in the demand for money caused by higher income, it is necessary forthe interest rate to rise by enough to offset the effects of higher income on thedemand for money.

The simplest way to avoid crowding out would be for the Fed to increase themoney supply, thus allowing the LM curve to shift rightward by the sameamount as the /S curve. Another possible exception to crowding out would be ifthe demand for money did not depend on income. Other hypothetical situationsin which crowding out would be avoided are when the 15 curve is vertical (thatis, the interest responsiveness of spending is zero) or when the LM curve is hor-izontal (that is, the interest responsiveness of the demand for money is infinite).

In the next chapter we will begin by examining some of these situations inwhich monetary policy and fiscal policy are unusually strong or weak, then studyinteractions among monetary and fiscal policy, and finally learn about effects ofthe government budget surplus or deficit on trade, investment, and growth.

1. Interest rates allocate the supply of funds availablefrom savers to alternative borrowers. Not only do pri-vate households and firms borrow in order to buyconsumption and investment goods, but the govern-ment also borrows to finance its budget deficit.

2. Private autonomous plannecl spending W) dependspartly on the interest rate. The higher the interest rate,the lower is A,,.

3. Private autoiomous planned spending (Ar) alsodepends on the optimism or pessimism of investorsand consumers about the future. An increase in optr-mism tends to raise A, for any given level of the inter-est rate.

4. The 1S curve indicates all the combinations of theinterest rate and real income at which the economy'scommodity market is in equilibrium. At any pointoff the IS curve, the commoditv market is out ofequilibrium.

5. The main functions of money are its use as a mediumof exchange, a store of value, and a trnit of account.

6. The real quantity of money that people demanddepends both on real income and on the interest rate.Equilibrium in the money market requires that the realsupply of money equal the demand for real moneybalances.

7. The LM curve represents all the combinations of realincome and of the interest rate where the money mar-ket is in equilibrium.

8. An increase in the money supply raises real incomeand reduces the interest rate when the 15 curve has itsnormal negative slope and the LM curve has its nor-mal positive slope.

9. A fiscal expansion raises reai income and the interestrate, causing crowding out if the money supply is heldconstant and both the 15 and LM curves have theirnormai slopes.

i1+

Note: Asterisks designate Concepts, Questions, and Problems that require the Appendix to Chapter 3.

rate of return15 curvemonev supplymedium of exchangestore oi valueunit of account

real money balancesLM curvegeneral equilibriumexpansionary monetary policycontractionary monetary policycrowding out effect

,i:r r

QUITSTTONS1. Which among the exogenous variables listed in ques-

tion 1 at the end of Chapter 3 have become endoge-nous in the cornplete IS-LM model of this chapter? Isthis true as well for autonomous consumption expen-cliture? Velocity? Have any othe.r endogenous vari-atrles been introducecl in this chapter? Exogenousvariables?

2. Suppose that in early 2001 many econornic forecasterspreclict that a rnajor recession will occur in late 2001 orearly 2002. How might these forecasts affect the actualperformance of the economy in 2001 and2002?

3. Describe the automatic adjustment that will take placein the economy when the current position of the econ-orny is off the 15 curve.

4. Describe the automatic adjustment that will take placein the economv when the current position of the econ-omy is off the LM curvc.

5. Why is the distinction between autonomous expendi-ture and induced expenditure crucial to an under-st;rnding of the crort'ding out effect?

6. Under r,r,hat circumstances could government spend-ing (federal, state, and local) be crowded out? Do youthink this is likely to be the case?

7. Whart happens to the velocity of rnoney (defined in thebox on p.10a) when the economy mo\res along a givenLM cr,rrve? Why does velocity behave this way?

8. Describe the situation in the commodity market anclthe money rnarket at point V in Figure 4-10. What willhappen to the econolny if the current position is atpoint 7?

9. During the 1980s the size of the federal governmentdebt became so large that servicing the interest pay-ments became a significant portion of total federalexpenditure. In response, many representatives andsenators felt that the federal deficit needed to bereduced. If government spending (G) became nega-tively sensitive to changes in the interest rate, whateffect would this have on the slope of the 15 curve? Ifatttonornous taxes (tr) become positively sensitive tochanges in the interest rate, what effect would thishave on the slope of the IS curve?

10. A change in which of the follor,r'ing would cause the IS

curve to shift? To rotate? To both shift and rotate?Which do not affect the position or slope of the 15

curve?(a) autonomous planned expenditure at zero interest

(A")@) mdrginal tax rate (t)(c) rnarginal propensity to 531rs (s)

(d) share of imports in GDP (irr)(e) interest rate (r)(f) multiplier (k)

(g) interest sensitivity of the An demand schedule(h) business and consumer confidence

11. A change in which of the following would cause theLM curve to shift? To rotate? To both shift and rotate?Which do not affect the position or slope of the LMcurve?(a) nominal rnoney supply (M')(b) responsiveness of the demand for money to the

interest rate

\tz.

(c) responsiveness of the demand for money toincome

(d) business and consumer confidence(e) interest rate (r)(0 price level (P)

Suppose Congress raises autonomous taxes. How willthis tax hike affect real income? The interest rate?Consumption? Planned investment?

13. If the A,, demand schedule shifts to the right, r.l'hathappens to the real interest rate? Does the chan5;e inreal interest rate amplify or dampen the swings inincome that result from changes in,4,,?

14. You learned in Chapter 1 that infltrtion speeds upwhen actual real GDP exceeds natural real GDP. If pol-icymakers believe that actual real CDP is too high andfear that inflation r.t,ill rise, how could they use lnone-tary and fiscal policies to reduce actual real GDP?Describe how each policy woulcl work ancl its effectson the economy.

15. Evaluate the follou,ing argument trsing the 1S-LMmodel: When consumer and business confidellce are

high and the economy is booming, the interest rate ishigh. Therefore, cluring a recession the Fed could pro-mote tr higher ler.el of income if it trsed monetary pol-icv to raise the interest rate.

PR(}I]LEMS*1. Let the structure of the commodity rnarket be repre-

sented by the following equations: C : Cu +0.75(Y T), C,, : 200 70r, T : 200 + 0.2Y,

1,. : 300 - 3]r,ernd C : 400.

thl Wnat is the value of the multiplier (k)7

(b) What is the equation of the autonomous plannedexpenditure iurrctir-rn? (Hirtt: Just substitute theerluations given above for C,,, T, and 1,, .rnd thevalue given above for G into the geueral formttlafor A,,: A,,: C,, - cTn + It, + G + NX,/. In this prob-lem NX,, : 0.)

(Jlrt]sTloi{s r\NI) f,R( )BLF}tS I 1 ir

and parameters /r and/in the LM curve: Mt /P = 300,h:0.1, and/:50.(a) What is the horizontal intercept of the LM curve?(b) What is the slope (Lr / LY ) of the LM curve?(c) What is the equtrtion of tlre LM cun,e?(d) If the Fed increased the money supply by 100, at

r.vhart value on the horizontal axis r.r,ould the LMcurve intersect it? What happens to the slope ofthe LM curve?

*3. Using the inforrntrtion contained in problems 1 and 2,

what is equilibrium real income (Y) and the interestrate (r)(a) in the inititil situation (i.e., G : 400, M' / P - 300)?(b) if C increases to 450? What is the amount of

autonomous spending that is crolt'ded out irr thissitu.-rtion? What happens to velocitv?

(c) if M'/P increases to -100?

(d) if both C antl M'/P increase (i.e., C : 450 ancl

M' /P - 4oo)?*4. Assume that the economv is initially in equilibriunr at

a ler..el of real output (Y) oi $5,000 ancl an interest rate(r) ctf 5 perccnt. If as a result of an incrcase in govern-ment spending of $500, the economy rrloves to a neweqr-rilibritrm at Y : $5,750 trncl r : 6.5 percent (.rud

given that k : 3), how much Y woulcl be crowded otttdue to the increasc in the interest rate? How muchautonor-rrous spencling r,t,oulc1 be cror,r,ded out? Whatis the value of the cocfficient for intercst-rate r€'spon-

\o siveness of the 15 curve? Of the A,, dernand schcdule?*5. Assume that the following ecl,rations summarize. the

structnre of an ecolromy.C: C,, + 0.8(Y - T);C,,: 700 - 15r;T :200 + 0.2Y;(M/P|l : 0.7Y - 70r; M'/P: -1.10;

/,, : 500 25r;i - 1,100;

NX: 100 - 0.04Y.

Answer the follovviug questions:(a) What is the ecluation of the 15 cun,e?(b) Whtrt is the eclttation of the LM cun,e?(c) What is the equilibritrm retrl output?(d) What is the erprilibrium interest rate?(e) What is the level of saving at equilibrium?(f) What is the level of planned investment at eqr.ri-

libriurn?(g) Determine r.t,hether leakages equ;rl injectiorrs at

equilibrium.(h) Assr.rme that r : 4 arrcl Y : 5,t100. Is there an

excess denrtrnd for money or cxcess suprply ofmoney in this situatictrr? Hort, mttch? Is thereunplanned inventory change? If so, what is thevahre of the urrplannerl irrventory change?

What is the equation of the IS curr.e? (Hirrf: Thegeneral equation for tht. 15 curve is Y : kA,,.)

Wlrat is the slope of the /S curve (\r / LY )?If government spencling increased by 50, zrt whatvalue on the horizontal axis would the new 1S

cllrve intersect it? What would happen to theslope of the 15 cun'e?

*2. The equation of the LM ctrrve is given by the follow-ing formula: Y : l(M'/P) + frl/lt, where M'/P is thereal money sr-rpply, /r is the response of moneyderr-rand to a $1 change in income at a fixecl interestrate, and/ is the response of money demand to a onepercentage point change in the interest rate. Assumethe folkrvving values for the exogenous yariable M'/P

(c)

/.-t \\Ll/

(e)

1 16 CHAI'}I'ER .1 . l'HIi IS-LM IIOllitL

p. 94 (1) A reduction of imports raises net exports andshifts the A,, demand schedule to the right. (2) A changein interest rates moves the economy nktug the schedulebut does not shift it. (3) Higher taxes reduce consunp-tion and thus shift the A.. demand schedule to the left.(4) Higher go\.cmment spendirrg shifts the A,, demandschedule to the right. (5) A recluction in consumer con-fidence shifts the 4.. demand schedule to the left.

p.95 (l)An irrterest rhte of 5 percent is compatible with a

$4,000 billion level of equilibrium retrl income. (2) Thisoccurs at point D on the 15 curve in the lower right-handframe oi Figure 1-4. (3) This eqr-rilibrir-rm occrlrs at pointD in the upper right-hancl frame of Figure 4-4.

p.101 (1) The levels of it'rcome (Y) and the interest rate onassets other than money (r) are the tn o determinants ofthe real demernd for money, (M/P)'t. (2) An increase in Y

raises the real demand for money, and an increase in theinterest rate reduces the real demand for money.(3) Ne.ither determinant shifts the 15 cLrrve, because theaxes of the /S crlr\/e diagrarn are these very determi-nants, Y and r.

p.105 (1) ln going from D to E, the irrterest rate rises from5 to 10 percent, ancl the demand for money decreases bvthe interest responsiveness (200) times the change in theinterest rate (S)-that is, by 1000. (2) In going frorn D toG, the level of real income falls from 8,000 to 6,000. Thedemand for money decreases by the income respon-siverress (0.5) times the change in real incorne (2,000)-that is, by 1000. (3) This is the reverse of Part (2); thedemand for money increases by 1000. (-1) This is thereverse of Part (1). The dernand for money increases by1000.

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keynesian income determination

Economy & Finance