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Page 1: Shapiro Chapter 12

This chapter combine~ the theory of income andoutput and the theory of money and interest in atwo-market equilibrium model that shows how thegoods and money markets interact to determinethe level of output and the rate of interest. Theprice level is not a variable in this model becausethe model retains the assumptions of Part 2: Theaggregate supply curve is perfectly elastic up tothe full employment level of output and does notshift; and the economy's level of output variesalong the range belOw the full employment level.Therefore, changes in aggregate spending canaffeCt only the output level; the price level is fixed.

The first part of the chapter explains the deri-vation of the IS and LM functions on which themodel is built. At the particular combination ofincome level and interest rate at which IS equalsLId. there is eqUilibrium in both the goods and themoney markets. The IS and LM functions havelong been the most basic tools of macroecon-omics. The balance of the chapter uses them toexamine questions that could not be handledadequately with the tools at hand in earlier chap-ters. Following the derivation of the IS and LMfunctions is the derivation of the aggregatedemand function or curve. This is found from theintersection formed by the IS and LM functions.To simplify in this chapter, the assumptions aresuch as to produce a perfectly inelastic aggregatedemand curve.

234------~----...::...-----------

OVERVIEW _

ThehteModel: Fi ePrice Lev

The next part of the chapter analyzes the sep-arate and combined effects of increases in invest-ment and the money supply on the income leveland the interest rate. The conclusions reachedthrough the use of the I5-LM tool differ fromthose reached when the goods and monetaryaspects of the analysis were considered sepa-rately. For example, the simple Keynesian multi-pliers developed for the two-sector economy InChapter 5 are now seen to apply only whenevents in the monetary sector are such that theinterest rate remains constant as aggregatespending for goods and services changes.

The same sort of general analysis is carriedout in the next part of the chapter for changes ingovernment spending and taxation. Here againthe simple government spending and tax multi-pliers presented in Chapter 6 are found to applyonly when the monetary authority acts to maintaina constant interest rate.

Page 2: Shapiro Chapter 12

The last part of the chapter turns to the ques-tic1nof the elasticities of the IS and LM functions,and to the closely related Question of the effec-tiveness of monetary and fiscal policies. The elas-ticities of the two functions are analyzed to clarifythe difference between the extreme version of theclassical theory-which argues that only mone-tary policy can be effective in raising the incomelevel-and the extreme version of the Keynesian

theory-which argues that only fiscal policy canbe effective. On the basis of this analysis, the LMfunction, if it is assumed to vary from perfect ine-lasticity at one extreme to perfect elasticity at theother, can be divided into a segment consistentwith classical theory, a segment consistent withKeynesian theory, and an intermediate segmentlying between the extreme versions of the two the-ories.

Inprevious chapters, we developed sepa-rately the theories of income determinationand money and interest. Although this pro-

cedure provided an orderly introduction to therelevant theory, it must now be recognized ashighly simplistic. The two parts are actually sorelated that what happens in one depends onwhat happens ioJhe other. In developing the sim-ple Keynesian theory of income determination inChapters 4-7, we found that a rise in investmentspending would raise the equilibrium level ofincome by an q.mount equal to the multipliertimes the rise in investment spending. However,we implicitly assumed that the interest rate wasgiven. If we now admit the interest rate as a var-iable in the system, the rise in investment spend-ing will, by raising the level of income, also forceup the interest rate. This in turn will discourageinvestment, and the actual rise in the equilibriumlevel of income will be less than it would other-wise be. Similarly, in developing the theory ofmoney and interest in Chapter 11, we saw thatan increase in the money supply would reducethe interest rate, as shown by the movementdown the given demand curve for money. How-ever, this curve assumed a given level of income.If we nQw admit the income level as a variable inthe system, the increase in the money supply will,by lowering the interest rate, stimulate investmentspending and raise the level of income. This will~ncrease the transactions demand for money,and the actual fall in the interest rate will be lessthan it would otherwise be. Therefore, it appears

that the interest rate and the level at Income arelinked in a complicated manner. In this and thefollowing two chapters, we will construct andemploy an extended model that can accommo-date this and other complications.1

The Goods Marketand theMoney Market _

Our model consists of two parts: The first drawstogether the determinants of equilibrium in themarket for goods, and the second draws togetherthe determinants of equilibrium-in the market formoney. For a two-sector economy, we found inChapter 4 that goods market equilibrium is foundat that level of Y at which the sum of C + I is justequal to that level of Y.Goods market equilibriumis also defined by an equality between saving

'The construction here will be almost entirely graphic.For an algebraic formulation of the same elementarymodel covered in this chapter, see the Appendix to Chap-ter 12 of E Shapiro, Macroeconomic Analysis-A StudentWorkbook, 5th ed.. Harcourt Brace Jovanovich, 1982. Aconcise algebraic treatment of a less elementary IS-LMmodel is provided in WL. Smith and R.L. Teigen,Readingsin Money, National Income, and Stabilization Policy,4th ed., Irwin, 1978, pp 1-22 The model, Including a var-iable price level, is developed in R.S.Holbrook, "The Inter-est Rate, Price Level, and Aggregate Output," in the same.volume, pp. 38-54.

Page 3: Shapiro Chapter 12

236

and investment. At the level of Y at which S = I,the leakage from the income stream into S isexactly offset by I. Money market equilibrium isdefined by an equality between the supply of andthe demand for money-m s = md-the conditionthat gave us the equilibrium interest rate. In otherwords, at the interest rate at which ms = md• thereis money market equilibrium.2

The particular level of income at which thereis goods market equilibrium depends in part onconditions in the money market. The particularinterest rate at which there is money market equi-librium depends in part on conditions in thegoods market. For a preliminary look at what isinvolved, let us briefly review the simplest pos-sible Keynesian model as shown in Figure 12-1 .Given the C + I, curve in Part A and the SandI, curves in Part B, the equilibrium level of Y is Y,.If investment depends at all on the interest rate,the C + I, curve in Part A and the I, curve inPart B must have been drawn on the assumptionof some particular interest rate. Other thingsbeing equal, a lower interest rate would indicatea different position for the C + I curve-say C~+ 12instead of C + I,-and a different positionfor the I curve-say /2 instead of I,. This, in turn,would indicate a different equilibrium incomelevel, Y2 instead of Y,. Figure 12-1, however, doesnot reveal what the interest rate may be-itassumes some rate and proceeds from there.

2A more complete general equilibrium model will alsoinclude the market for factors of production. which,because of the short-run assumption 01 a fixed capitalstock, becomes the marKet lor labor. Equilibrium in thismarket requires equality between the supply of and thedemand for labor. From a Keynesian viewpoint. disequi-librium in this market in the form of an excess supply oflabor-that is. unemployment-can be corrected by pol-icies designed to raise the level of output-that is, to shiftthe equilibrium In the goods market to a higher level ofgoods output whose production in turn calls for employ-ment of more labor. From a classical viewpoint. the samedisequilibrium would be removed automatically by fallingwages and prices in a system characterized by such flex-ibility. Following the development '')1 the basic model,which is limited to the goods and mo,1eymarkets, attentionwill be given to these other questions in Chapter 13.

FIGURE 1~·1Equilibrium Levels of Income

Figure 12-2 shows the determination of theequilibrium interest rate. Given the ms and md\

curves, the equilibrium rate is (" at which thedemand for and the supply of money are equal,or mIl + msp, = md, = ms' However, the demandfor money is composed in part of the transactionsdemand which depends on the level of income.Therefore, the md1 curve must have been drawnon the basis of some assumed income level thatdefined mil' Other things being equal. a higherincome level would indicate a different position

Page 4: Shapiro Chapter 12

mlZ

rzr----Ir, '-"---

m'l

FIGURE 1.1·~Equilibriwn Levels of the

Interest Rate

for the curve-say md2 instead of md . This wouldindicate a different equilibrium rate ~f interest r., 2'

at which mt2 + m~ = md2 = m2. Figure 12-2,however, does not reveal what the level of incomemay be-it assumes some income level and pro-ce~ds from there:'

It appears that we cannot determine the equi-librium income level without first knowing theinterest rate and that we cannot determine theequilibrium interest rate without first knowing theincome level. Somehow Y and r must be deter-mined simUltaneously. Although this cannot bedone through Figures 12-1 and 12-2, there arenonetheless a particular income level and inter-E'st rate that simultaneously provide equilibriumin the goods market behind Figure 12-1 and inlhe money market behind Figure 12-2. The modelto be developed in this chapter provides thissimultaneous solution of the two equilibriumvalues and clarifies some other important prob-I~s and policy questions. 3

,

.J .

3This model was originally developed by J.R. Hicks inhiI article MMr. Keynes and the 'Classics': A ~gest~Interpretation,· in Econometrica. April 1937, pp. 147-59.reprinted in W. Fellner and B,F. Haley, eds., Readings'iJJ \the Theory of Income Distribution, Irwin, 1946.pp:- 461-76.

EquDibriumin the GoodsMarketBecause equilibrium in the goods market requiresthat Y = C + I and S = I, all the factors thatcause the consumption function and thereforethe saving function to shift and all the factors thatcause the investment function to shift influencethe determination of this equilibrium. Althoughother factors may be introduced once the basicmodel is developed, we assume here that invest-

Tn ment is a function of the interest rate alone andthat consumption and therefore saving is a func-tion of income alone. From the C + 1 approach,we then have, in general terms, the followingthree equations to cover the g00ds market:

Consumptfon function: C = C(Y)Investment function: 1 = I(r)

Equilibrium condition: Y = C(Y) + I(r)

From the S, 1 approach, we have, in generalterms, the following three equations to cover thegoods market:

Saving function: S = S(Y)Investment function: I = I(r)

Equilibrium condition: S(Y) = I(r)

One may develop the diagrammatic an~lysis thatfollows on the basis of either or both of theapproaches. tlut attention here will be limited tothat based on the S, I approach.

The set of equations for that approach maybe shown graphically as in Figure 12-3. Part Agives the investment spending schedule. show-ing that investment spending varies inversely withthe interest rate. The straight line in Part B isdrawn at a 45° angle from the origin. Whateverthe amount of planned investment measured

See also F. Modigliani, "Liquidity Preference and the The-ory of Interest and Morley," in FA. Lutz and L.w. Mints,,005 .• Reaoings in Monetary Theory, Irwin, 1951, partlcu-lcirlypp. 190-206.

Page 5: Shapiro Chapter 12

____ 1_

o 40

I

'l

C Saving FunctionS = S(Y)

IIII

IS IIII IE---------- -1--------I----------:r-

F I II II II II II II II I! ,I !

40 80 120 160 200 Y

D Goods Market EquilibriumS(Y) = I(r)

SI

100 -

B Saving Inv8strnenl Equality5 c- I

-- 1 1 __

o 20 40 60

A Investment FunctionI = I(r)

FIGURE 12·~Goods Market ~quilibrium

5, ~

Page 6: Shapiro Chapter 12

along the horizontal axis of Part B. equilibriumrequires that planned saving measured along thevertical axis of Part B be the same. Therefore. allpoints along the 45° line in Part B indicate equal-ity of saving and investment. Part C brings in thesaving function. showing that saving varies directlywith income.

The 15 curve in Part 0 is derived from theother parts of the figure. For example, assumean interest rate of 6 percent in Part A, indicatingthat investment is $20 per time periOd:4 In Part Bto satisfy the equality between 5 and I, savingmust also be $20, as shown on the vertical axis.In Part C. saving will be $20 only at an incomelevel of $120.5 Finally. bringing together Yof $120from Part C and r of 6 percent from Part A yieldsone combination of Y and r at which 5 = I (andY = C + I). If we assume the lower interest rateof 5 percent, Part A indicates that investment willbe $30, which yields an income level of $140 inPart C. Therefore. Y of $140 and r of 5 percent isanother combinatidn of Y and r at which 5 = f.Other combinations could be found in the sameway. Connecting th~se combinations gives us the15 ctJrve in Part 0.6'

There is no longer a single level of income atwhich 5 = t, but a different level for each differentinterest rate. The higher the interest rate, thelower will be the level of income at which 5 = I.Viewed in one way. this follows from the fact thata high r means a low f. A low I, through the mul-tiplier.means a low Y. Viewed in another way, itfollows from the fact that a low Y means a low 5.Because equilibrium requires that 5 = f, a low 5

4AII dollar amounts are in billions.sThe saving function S = Sa + sY is here S = -$40

+ 'I2Y.6A!ternatively, the combinations of Y and , at which S

= 1could just as well be determined graphically by start-ing with assumed levels of Y.Assuming Y of $120, Part Cshows ~hat S will be $20. Moving from Part·C throughP".,I B to,Part A. 1of $20 is consistent with" pf 6 Pf;rcent.Therefore, in-Part D. Yof $120 and, of 6 percent identifyone combination at which S = ,.

means a low I. A low t is the resuJt of a high r.Although the 15 function indicates that equilib-rium in the goods market will be found 'at a lowerlevel of income for a higher interest rate, it alonedoes not reveal what particular combination of Yand r will be found in any specific time period. Allcombinations on the 15 function are equally pos-sible equilibrium combinations of Y and r in thegoods market.

Identifying all equilibrium combinations doesnot. however, mean that the actual combinationin each time period will be one of them. Theremay be disequilibrium in the goods market. Sup-pose that tile actual combination is the disequi-librium combination of Y = $140 and r =6 percent indicated as point E in Part 0 of Figure12-3. At the income level of $140. 5 will equal Ionly if the interest rate is 5 percent. Therefore,given this $140 income level and an interest rateof 6 percent. 5 must exceed t because I will besmaller at a rate higher than 5 per£ent, but 5 willbe unchanged. 5 depends only on the level ofincome, which is here unchanged at $140. Thecombination of Y = $140 and r = 6 percent isalso a disequilibrium from a second point of view.At the interest rate of 6 percent, 5 will equalf onlyif the income level is $120. Therefore. given thecombimition of this 6 percent interest rate and anincome level of $140 as at point~, 5 must exceedI because 5 will be larger at an income levelabove $120. but iwill be unchanged. t dependsonly on the interes~ rate, which is here unchangedat 6 percen.t. It follows that for any combinationof Y and r located anywhere in the space to theright of the 15 curve. the same conclusion maybe drawn that was drawn for point E: There is adisequilibrium in which 5 exceeds I and Yexceeds (C + I).

By the same line of reasoning, the combina-tion of Y = $120 and r = 5 percent indicated aspoint F is a disequilibrium of the opposite kind:Here f must exceed 5. Generalizing as before,f~r, any combination of Y and r anywhere in thespace to the left of the f5 curve, there is a dise-qui!ibrium in which I exceeds 5 and (C + I)

Page 7: Shapiro Chapter 12

240----------------------rC~H~APTED:mR;-:lWE~iVCLVE

exceeds Y. In other words. the aggregate spend-ing on goods exceeds the aggregate output ofgoods.

Equilibriumin the MoneyMarketEquilibrium in the money market requires anequa1ity between the supply of and the demandfor money. The Keynesian theory of the demandfor money makes the transactions demand (herecombined with the precautionary demand) adirect function of the income level alone. orm,= k(Y) . .It makes the speculative demand aninverse function of the interest rate alone. or msp

= h(r). Total demand for money is md = mr +ms = k(Y) + h(r). The supply of money ms isdetermined outside the model--it is exogenous.This may be written ms = mar in which m8 is sim-ply the am0unt of money that exists, an amountdetermined by the monetary authorities. (Themonetary authorities determine only the nominalstock of money, Ms. but with P assumed to bestable. determination of Ms also determines ms')

This .gives us three equations to cover the moneymarket:

Demand for money: md = k(Y) + h(r)Supply of money: ms = mil

Equilibrium condition: md = ms

This set of equations is shown graphically inFigure 12-4. Part A shows the speculative demandfor money as a function of r. Part B is drawn toshow a total money supply of $100. all of whichmust be held in either transactions or speculativebalances. The points along the line indicate allthe possible ways in which the given money sup-ply may be divided between m, and map' Part Cshows the amount of money required for trans-actions purposes at each level of income on theassumption that k = 1/2. The LM curve of Part 0is derived from the other parts as follows, .

Assume in Part A an interest rate of 6 percent,at which the public will want to hold $40 in spec-ulative balances. In Part B, subtracting the $40of speculative balances from a total money sup-ply of $100 leaves $60 of transactions balances,an amount consistent with an income level of$120 as shown in Part C. Finally, in Part D, bring-ing together y of $120 from Part C and r of6 percent from Part A yields one combination ofYand r at which md = ms or at which there isequilibrium in the money market. If we assumethe lower interest rate of 5 percent, Part A indi-cates that speculative balances will be $50,Part B indicates that transactions balances willbe $50. and Part C indicates the income level of$100 as that consistent with transactions bal-ances of $50. This yields another combination ofY and r~100 and 5 percent-at which md =ms' Other such combinations can be determi~edin the same way. In Part D, th~ function labeledLM results when these combinations are con-nected.7

Although particular characteristics of the LMfunction will call for attention later, in general thefunction slopes upward to the right. With a givenstock of money. money market equilibrium isfound at combinations of high interest rates andhigh income levels or low interest rates and lowincome levels. Viewed in one way, this followsfrom the fact that a high level of income calls forrelatively large transactions balances, which,with a given money supply, can be drawn out ofspeculative balances only by pushing up theinterest rate. Viewed in another way, it followsfrom the fact that at a high interest rate specu-lative balances will be low; this releases more of

7 As with the IS curve. the combinations of Y and r atwhich md = m. could just as well be determined graphi-cally by starting with assumed levels of Y. Therefore,assuming Yof $120, Part C ShONSthat m, will be $60.Subtracting S60 from the total money supply of $100leaves $40. As Part A shoNs. this is an amount the publicwill be willing to hold in speculative balances, msp. at r of6 percent. In Part D. Yof $120 and r of 6 percent thereforeidentify one combination of Yand r at which md = m.,

Page 8: Shapiro Chapter 12

m,I

100 I1

!III

_j J..80

C Transactions Demandmt = k(Y)

;10 ~-

!IIIIIII

Fi6 ---------t-

I I-1-----------I EI II II II II II II

o Money Market Equilibriumm, == k(Y) -;- h(r)

60 ------i ms = $100

---------1-III!IIII

8 Supply of Moneym. = mr + msp

A Speculative Demandm.p = h(r)

FIGURE 1;1..4Money Market EquWbrium

Page 9: Shapiro Chapter 12

the money supply for transactions balances. Thismoney wil! be held in such balances only at acorrespondingly high level of income. Althoughthe LM function indicates why equilibrium inthe money market wil! occur at a higher interestrate for a higher level of income, it alone cannotreveal what particular combination of Y and (-"will be f0und in any given time period. All combi-nations on the LM function are equally possibleequilibrium combinations in the money market.

As with the IS curve. identifying all combi-nations at which md = ms does not mean that theactual combination in each time period will beone of them. The actual combination may involvea disequilibrium in the money market. For exam-ple. consider the disequilibrium combinationindicated by poin,t E in Part D of Fig!Jre 12-4. Atthe income level of $120, md will equal ms only if( is 6 percent. Therefore. if we combine this $120income level with an interest rate of 5 percent.md must exceed ms because md will be larger at( = 5 percent. The quantity of money demandedfor speculative purposes rises with a lower inter-est rate. but the total supply of money is fixed.Alternatively. if we start with the interes1 rate of5 percent, md will equal ms only -if the incomelevel is $100. Therefore. if we combine this5 percent interest rate with an income level of$120 shown as point E, md must exceed ms

because md WIll. be larger at an income level'&i>ove$100 than it will be at $100. The quantityof money demanded for transactions rises witha higher income. but the total money suppiy is.as before. fixed. What has been concluded forthe combination indicated by point E holds truefor any combination located in the space to theright of the LM curve; any combination of Y and( in this space is necessarily a disequilibriumcombi[1ation in which md exceeds ms'

By the same reasoning. the combination ofY = $100 and r = 6 percent indicated as pointF is a disequilibrium of the opposite kind: ms musthere exceed md. Generalizing as before. there isa disequilibrium in which ms exceeds mCI for anycombination of Y and ( located in the space totr-18 ieTt of the L:'v1 curve.

Two ..MarketEquilibriUni-The Goods and MoneyMarketsEquilibrium between Hie supply of and demandfor goods is possible at all combinations of Yandr iridicated by the IS curve; similarly, equilibrium .between the supply of and demand for money ispossible at ail combinations of Y and r indicatedby the LM curve. However, there is only one com-bination of Y and ( at which the supply of goodsequals the demand for goods and the supply.ofmoney equals the demand for money This com-bination is defined by the intersection of the ISand LM curves derived in Figures 12-3 and 12-4and brought together in Figure 12-5. in this dlus-tration, equilibrium in both markets occurs withY = $120 and ( =-= 6 percent.

I

"I ~10 r

i "-81- "-I IV

Iq-----------I

/IIII

) I- :I :1 1. .1 , _-L- , __I vo 1 4L: 80 1~c: 1CJ 200 ;l4q 1

__ I ._. . _FIG1JP..J: 1295

Equilibrium in 'the Goods andMoney Markets

Page 10: Shapiro Chapter 12

From Disequilibrium toEquilibriumEvery possible combination of Y and r in Figure12-5 other than that given by the intersection ofthe IS and LM curves is one at which there isdisequilibrium in the goods market, the moneymarket, or both. All those combinations that donot lie on either the IS or the LM curve fall intothis last category. Because all such combinationsdo not lie on a line, they necessarily jie in one ofthe four areas identified by the Roman numeralsI through IV As we saw earlier, any combinationof Y andr that lies anywhere to the right of the IScurve is a combination at which S > I and Y >(C + I). The opposite is true for any combinationof Y and r anywhere to the left of the IS curve.Similarly, any combination of Y and r anywhereto the right of the LM curve is a combination atwhich md > ms' The opposite is true for any com-bination to the left of the LM curve. Accordingly,each of the four spa~s may be distinguishedfrom the other three in terms of the relationshipsbetween the supply of and demand for goodsand between·the supply of and demand formoney for any-'combination of Y and r that fallswithin that space:

In Space I:In Space II:In Space III:In Space IV:

Goods Marketf < S, (C + I) < Y1< S, (C + I) < YI> S, (C + I) > YI> S, (C + I) > Y

MoneyMarket

md < ms

md> ms

md> ms

md < ms

From the analysis of the goods market con-sidered in isolation, we know that a situation inwhich' I > S or (C + I) :> Y will lead to a rise inincome and vice versa. From the analysis of themoney market considered in isolation, we knowthat a situation in which md >ms will lead to a risein the interest rate and vice versa. What we nowhave in the four spaces laid out in Figure 12-5are various combinations of IS and LM disequi-.Iibrium situations. Because we know the directionin which the income .level tends to move in

. response to an excess supply or excess demand

for goods and the direction in which the interestrate tends to move in response to an excess sup-ply or excess demand for money, we can traceout in a nonrigorous fashion a possible path thatthe income level and the interest rate may followin response to any given disequilibrium situation.

if) Figure 12-6 we assume the economy islocated at the disequilibrium combination of Yand r indicated by A, which is in Space IiI. Herethere is an excess demand for goods and anexcess demand for money. The excess demandfor goods tends to raise the income level. asindicated by the horizontal arrow originating at A.The excess demand for money tends to push upthe interest rate, as indicated by the verticalarrow originating at A. With these forces at work,it is not unreasonable to expect the economy tomove along the path designated by the arrowfrom A~to B. Next, with the economy at B, thesupply of and demand for goods are equal,

FIGURE 12-6Possible Paths of Movement toEquilibrium in the Goods an4

Money Markets

Page 11: Shapiro Chapter 12

because we are on the IS curve. But we are stillat a point to the right of the LM curve, so thedemand for money exceeds the supply of money.Therefore, a force is at work to push up the inter-est rate and the next movement may be alongthe arrowfrom B to C. At C there is still an excessdemand for money, which again tends to pushup the inlerest rate as indicated by the verticalarrow originating at C. However, at C there is anexcess supply of goods, "thich tends to reduc€the income level as shown by the horizontal arroworiginating at C. These forces may on balancecause the economy to move along the pathdescribed by the arrow running from C to D. At0, the forces are the same as at C; the result isa movelTocnt of the same kind. The combinationof income level and interest rate may change inthis way over time until finally the system reachesthat one combination of Y and r at which bothmarkets clear. Although the several discretesteps traced out here help reveal the-underlyingprocess at work, the actual process would be acontinuous one in which Y and r might movealong a path like that indicated by the dashed..line running from A to 0 and then to the intersec-tion of the two curves.

Instead of starting at A, we could start at anyother disequilibrium point in Figure 12-6 andtrace the movement of Y and r toward the singlepair of equilibrium values in the same way. Nomatter what disequilibrium point one starts with,all one need do is (1) identify whether I > S, 1<S, or I = S, or in terms of aggregate spendingwhether (C + !) > Y, (C + I) < Y, or (C + I) =Y, which te!ls whether Y will tend to rise, fall, orremain unchanged; (2) identify whether md >ms'

md < ms' or md = ms' which tells whether r willtend to rise, tall, or remain unchanged; and (3)establish the direction of movement at the Y, rcombination indicated by the forces found to beat work in (1) and (2). For example, starting withany point in Space I such as E, forces tend toreduce both the income level and the interestrate. The reader may trace the discr€te stepsfrom E thrOi !gh H, which are different In directionbut exactly symmetrical with those from A through

D. As was shown for themovement-from-A.t6 theintersection, the continuous;pa.th-th_at;t~~ ~omy might follow fro~ E to H and then to theintersection is indicated by a dashed line. Onceat the intersection. the combination of Y and ,provides equilibrium in both markets; the incomelevel and the interest rate will remain unchangeduntil the existing equilibrium is upset by a shift inthe IS or LM curve. or in both.8

E5-LM Equilibrium and theAggregate Demand CurveIn th~simple classical theory of Chapter 9, theaggregate demand curve was derived from thequantity of money and appeared graphically asa downward sloping curve (rectangular hyper-bola). Given the classical theory's conclusionthat the aggregate supply curve is a perfectlyinelastic line situated at the full employment levelof output, the intersection of the AD curve withthe AS curve did no more than determine theprice level of the full employment output.

The model being constructed in this chapterincludes the opposite extreme for the AS curve-that is. one that is perfectly elastic up to the fullemployment level of output but perfectly inelasticat that level. This kind of AS curve is shown inPart B of Figure 12-7. The present model alsoassumes that the economy operates below thefull employment level of output-that is, along theperfectly elastic portion of the AS curve. Some

8Although it is quite illuminating to trace the path fol-lowed by Yand' as we have done here. the IS-LM model

, now before us does not in itself reveal that Y and , willfollow the path here described or any other particular pathfrom an initial disequilibrium position like A or E. As brieflyexplained in Chapter 3. to trace the process of change inthe values of a model's variables from one period toanother can be done only with a dynamic model. TheIS-LM model isnot dynamic, but completely static. It iden-tifies the values the variables must exhibit in order thatthere be equilibrium. but it does not show the sequence

- of changes by which these values will be reached if westart off with any values eltler than Ihese equilibriumvalues.

Page 12: Shapiro Chapter 12

i12 r-

4,

2 ,-IS

'- - ... -' .0 40 80 160 200 240 Y

A

P

AD AS43

2"'~ 1

i. ......... -0 40 80 120 160 200 240 Y

~

FIGURE12·7The IS-LM Curves and theAggregate Demand Curve

:other assumptions finally yield the conclusionthat the level of output is determined entirely-p¥'aggregate-demand. In this case, aggregate'sup-

1,~lyonly determines the' price level at which that'output will sell.

.:. ,:.J,n this model, the derivation of the AD curveis more complicated than in the simple classicalmodel in which it only depends on the supply ofmoney Here it depends on all the factors thatdetermine the positions of the IS and LM curves.The supply of money is only one of these factors.At any time, these factors will determine partic~

ular IS and LM curves, and it is from the inter-section of this pair of curves that the AD curve isderived in the present model. To derive the ADcurve, we make one final assumption-that nei-ther the IS nor the LM curve shifts with changesin the price level. This assumption enables us topostpone dealing with some major complicationsuntil Chapter 13.

With this 3ssumption, whatever the price levelmight be-1, 2, 3, 4, or any other level in Part Bof Figure 12-7-the IS and LM curves remain inthe position shown in Part A. Therefore, corre-sponding to each possible price level on the ver-tical axis of Part B, we have the same pair of ISand LM curves and the same equilibrium figureof 120 for the output level found in Part A. TheAD curve shows the toial amount of goodsdemanded at various price levels, but on thepresent assumption that amount is a constant120. Therefore, the aggregate AD c.urve is per-fectly inelastic at the output level of 120, asshown in Part B. Throughout the balance of thischapter we will assume that the IS andLM curvesdo not shift with the price level; therefore all ofthe AD curves will be perfectly inelastic. How-ever, these AD curves can shift :to the right or theleft, and we next look at some of the factors· thatwill produce such shifts.

q,.;mges in AggregateDemand_· _' _

,...--- .,-//

The eqUilibrium combination of Yand r identifiedby the intersection of the IS and LMfunct~ons will,of course, change in response to any.$hift inthose functions, and the AD curve will s~ift to thelevel of Y identified by the new infers~ctiof) ...Shifts

.in the IS function are caused by shifts· in theinvestment or the saving function (parts A"and ..cof Figure 12-3); ,shifts in the LM, -function ar~caused by shifts in the, money supply, transac-·tions demand, or speculative demand functions(Parts B, C, and A, respectively, of Figure 12-4).Finally, a shift in any of the functions on which the

Page 13: Shapiro Chapter 12

Is and LM curves are based may result from achange in the factors that determine the positionsof the-se functions. This givBs us a method of ana-lyzing the effects of a change in any of theseunderlying factors. We can trace a change in anyfactor through the system to its final effect on theincome level and interest rate-assuming, ofcourse, that all other factors remain unchanged.Given the assumed shape of the aggregate sup-ply curve, none of these changes will affect theprice .Ievel.

A Change in InvestmentAmong the various possibilities, a shift in theinvestment curve is one of the most important.Suppose a change in an underlying factor-for-example, an improvement in business expecta-tions-causes this'curve to shift $20 to the rightat each rate~of interest. In Part A of Figure 12-8,the original curve is labeled I, and the new one12, In Figure 12-3, an IS curve was derived graph-ically from the investment and saving curvesgiven there. Similarly, in Figure 12-8, a separateIS curve may be derived from each of the invest-ment curves in combination with the given savingcurve. In Part D, the IS, and IS2 curves are basedon the I, and 12 curves, respectively. At eachinterest rate, IS2 lies $40 to the right of IS,. Inother words, at each interest rate the level ofincome at which S = I is now $40 greater thanit was before the shift in the investment schedule.This follows from the fact that, with an increaseof $20 in investment, income must rise by $40 toinduce an increase of $20 in saving, given thatthe MPS is 1/2. This is nothing more than thesimple multiplier in action, ~ Y(1 /MPS~/, whichgives us $40 = 2'· $20.

, The original equilibrium was earlier -found atY pf $120 and r of 6 percent. Here it is showna@ainby the intersection of IS, and L,M in Part Dof Fig'Jre 12-8. As before, this gives us the AD,curve positioned at Y of $120 in Part E. The LMcurve here is the sa\Tle as the one derived in Fig-ure 12-4. The new equilibrium that results fromthe shift in the investment curve is at Y of $140and r of 7 percent (an 'increase of one percent-

age point) as shown by the intersection of IS2 andLM in Part D. As the increase in investment

, .spending starts an upward movement in income,the rising income level increases the money bal-ances needed for transactions purposes. Thisleads to a rising interest rate, which in turn feedsback to make the increase in investment spend-ing less than the $20 and the increase in incomeless than the $40 they would have been with norise in the interest rate. In the present illustration,with the LM curve as given, the shift in the IScurve caused by a rightward shift of $20 in theinvestment curve raises Y by $20 and r by onepercentage point. The $20 rise in Y means anincrease of $10 in required transactions bal-ances, given k = 0.5. The rise in r of one pe~-centage point is just sufficient to reduce th~amount of money the public wishes to hold inspeculative balances by $10, thereby supplyingthe additional $10 needed for transactions bakances. Therefore, with ~ Y = $20 and ~r of onepercentage point, the supply of and demand formoney will again be in balance.

The same one percentage point rise in r willdecrease investment from $20 to $10. As may be -seen in Part A of Figure 12-8, investment-whichwould have risen from its original $20 at r -of6 percent (point E) to $40 with no change in r(Point F)-only rises from $20 to $30 (point G)because one half of what would have been thelarger increase is choked off by the rise in r from6 to 7 percent. The final increase in investmentof $10 turns out to be the same amount as theincrease in saving that occurs with a rise inincome of $20. From ~S = s(~Y), we here have$1g- = 0.5($20). With ~ Y = $20 and ~r of onepercentage point, S will again equal I and Y willagain equal C + '- No other combination ofchanges in Y and r will be consistent with equi-librium in both the goods and money rn'arkets,assuming the indicated rightward shift in theinvestment schedule with all else as given.

For a leftward shift in the investment sched-ule, the results will be the opposite. If the invest-

- ment schedule of Part A were to shift to the leftby $20 or from " to '3' the new equilibrium inPart D wQuld show Yof $100 and r of 5 percent.

Page 14: Shapiro Chapter 12

S!

100 l-

I80 I

::~

I20 r-

l~_l.-__1,---------- --

..J _l. ----I I

--1..--_1 _...L__ ..l...--. _

120 160 200 Y

C

_ ..

I I - .l- ....1.- __ ..... _

160 200 Y

sS- 100 ~

80 \-

I

6d-II

40 t·!

.....L..-..__...L__..._L.. __

60 80 100

B

2 ~.

I[ ~ ~ G..__ •• .....L..-. •• _ .••L_ .._.L_ ..._L .__L.-..._. ...__.

o 20 40 60 80 100 I

FIGURE12·8A Change in Investment and the Change in Aggregate Demapd

'(

Page 15: Shapiro Chapter 12

Relative to the original equilibrium, t'1is would bea decrease in Yof $20 and in r of one percentagepoint.9 No other combination of changes in Yorr would be consistent with equilibrium in both thegoods and money markets, assuming the indi-cated shift in the investment schedule with allelse as given.

Just as the intersection of IS1 and LM inPart D established the AD1 curve in Part E, theintersections of the IS2 and LM curves and of theIS3 and LM curves establish the AD2 and AD3

curves, respectively, in Part E. Given the LMcurve in Part D, the shifts in the I curve of. Part Awhich cause the indicated sh:fts in the IS curvein Part D also produce the shifts here noted inthe AD curve in Part E.

A Changein th'e Money SupplyAs a second illustration of a shift in the AD curve,assume a $20 increase in the money supply. Thisshifts the ms curve in Part B of Figure 12-9 fromits original position of mS1 to the new positionms2. With no change in the speculative demandfunction or the transactions demand function, the$20 increase in ms shifts the LM function right-ward by $40 at each rate of interest, or from LM 1

to LM2. What lies behind this may be seen asfollows. Equilibrium between md and ms requiresa rise in Y sufficient to absorb the ms increase of$20 in transactions balances, ml, if the interestrate is assumed to be given. Because mt = k(Y),we ' .J.veY = m,lk and ~ Y = tun,lk. Accordingly,with k given as 0.5, aY must be $40 to producea new equilibrium between md and ms at eachjntere~t rate.

9For simplicity, here we. assume that the LM curve islinear over the range of interest rates (5 to 7 percent) rel-evant to our illustrations. (This requires that we alsoassume that the underlying speculative demand curve islinear over this same range.) Specifically, the slope of LMis taken to be 0.05 (r changes by 0.05 percentage pointfor each $1 billion change in Yor by 1.00 percp-ntage pointfor a $20 billion change in V). Any dE:;J~lrture from linearitywould give actual numerical resultsdifferent from the sym-metrical ones found in the illustrations.

The original eqUilibrium at Y of $120 and r of6 percent is shown here again by the intersectionof IS and LM1 in Part 0 of Figure 12-9. The IScurve here is the same as ·the one originallyderived in Figure 12-3. The new equilibrium thatresults from the increase in the money supply is ..at Y of $140 and r of 5 percent. Although the $20increase in ms will shift the LM curve $40 to theright at each interest rate. it will not raise theequilibrium level of Y by $40, because, with-no·shift in the IS curve, a rise in the equilibrium levelof income cannot occur unless r falls. However,a fall in r will increase the amount of money peo-ple choose to hold in speculative balances. Inthe present illustration, $10 of the $20 increasein M will be absorbed in speculative balances asr falls from 6 to 5 percent (as may be seen fromPart A of Figure 12-9). This same fall in r is alsojust sufficient to raise f by $10 (as may be seenfrom Part A of Figure 12-8) and, through the mul-tiplier, raise Y by $20. A rise in Yof $20 increase~required transactions balances by $10, whichaccounts for the balance of the $20 increase inms' Nu other possible combination of changes inYand r but this $20 increase and one percentagepoint decrease will be consistent with equilib-rium, assuming the indicated increase in themoney supply with all else as given.

If the change were in the opposite direction-a $20 decrease in the money supply that shiftsthe curve from ms to ms -the new equilibrium

1 3combination of Y and r would be at $100 and7 percent, or a decrease in )l of $20 and a risein r of one percentage point. By the reasoning ofthe preceding paragraph, no other combinationof changes in Y and r will provide a new equilib-rium within the assumptions of the present illus-tration.

Because the LM 1 and IS curves in Figure12-9 are identical with the LM and IS1 curves inFigure 12-8, they intersect at Y = $120 and r =6 percent. With the eqUilibrium interest rate setat 6 percent, S = I and Y = C + I at Yof $120.As in Figure 12-8, this establishes the AD; curvein Part E at Y = $120. An increase from m.

lto

ms shifts the LM curve from LM1 to LM21 lowers2 •

the equilibrium interest rate, and makes S = J

Page 16: Shapiro Chapter 12

249

.....J _

I-1- -+ - - - - - - - - - - -

I II II II II II I

I I I__ -L __L.L__L_--.L ..L.._ ...__. _

40 80 120 160 200 Y

10I8~

6~

I.~ I

II

2 II

, I( I~ l----l- L. __ l L ......L. . _

o 40 80 120 160 200 Y

"-';

.'_.,

I I I I

,I40 t-,

,

2 ~i -L .l-..., .L L

o 20 40 60

_ ... .c. . L. L.80 100 120 msp

" FIGURE 12-9AG •• p :Inthe Money Supply and the Change in Aggregate Demand

Page 17: Shapiro Chapter 12

and Y = C + I at Y of $140. This establishes theAD2 curve at Y of $140 in Part E. In the same way,the LM3 curve based on mS3 yields the AD3 curveat Y of $100 in Part E.

Although the present illustration involv~snothing more than a purely monetary change,one result is still a change in the level of .realincome. In short, given the IS and LM curves asin Figure 12-9, monetary policy can influence theeconomy's level of output. As will be explainedlater, the effect on the income level of an increasein the mqney supply depends on (1) how greatthe fall in the interest rate is, which in turndepends on the elasticity of the speculativedemand function, and (2) how much investmentspending rises as a result of any given drop inthe interest rate, which in turn depends on theinterest elasticity of the investment function. If theinterest rate falls with a rise in the money supplyand if investment 'spending rises with a fall in theinterest rate, the income level will rise.

A Simultaneous Increasein Investment andthe Money Supply A

Now suppose that the two increases we have dis-cussed separately occur simultaneously. The risein the investment function moves the IS curvefrom IS, to IS2, and the rise in the money supplymoves the LM curve from LM, to LM2, as shownin Part A of Figure 12-10. The result is a shift inthe equilibrium position from Y of $120 and r of6 percent to Yof $160 and r of 6 percent. The ADcurve of Part B correspondingly shifts from itsposition at Y of $120 to a position at Y of $160. Arise in investment spending, with no change inthe money supply, produces a rise in income thatis dampened by a rise in the interest rate result-ing from it. If the money supply increases by justthe amount necessary to prevent this rise in theinterest rate, the full i'ncome-expansionary effectof the rise in investmeAt will be realized. Theincrease in Yfrom $120 to $160, with an increasein investment of $20 and an MPC of 1/2, is justthe result we found in the simple Keynesian

III

rI

2 I: I IS,

I ,I'- __----.--L-_-----l-..._-L --.L ----.--L-o. 40 80 120 160 200

I

240 Y

AAD, AD2 AS

FIGURE 12-10Effect on Aggregate Demand of a

Simultaneous Increase inInvestment and the Money

Supply

model in Chapter 5. Now we see that this resultwill be realized only if an appropriately expan-sionary monetary policy-here an increase in msof $20-is pursued to prevent what otherwisewould be a rise in the interest rate and conse-quently a smaller rise in the income level.

The effects of shifts in other functions may betraced in the same way. For example, an increasein "thrift," which appears as an upward shift in the

Page 18: Shapiro Chapter 12

saving function (Part C of Figure 12-3), will shift· the IS curv,eto the left and lower rand Y. An· increase in the demand for money to be held inidle balances, which appears as a shift to theright in the speculative demand function (Part A

\ of,Figure 12-4), will shift the LM curve to the left,. ,,\raiser, and lower Y.A change in payments prac-·)ices that makes it possible for each dollar ofmoney to handle a larger volume of transaCtionsper time period reduces k,and appears as a lesssteeply inclined, transactions demand function(Part C of Figure 12-4), This will shift'the LM curveto the right. lower r, and raise Y.

, Government Spending,Taxation, and AggregateDemand, _Once government spending and taxation havebeen added to the model, the equilibrium con-dition S = I in the goods market foi' a two-sectoreconomy becomes S + T = I + G for a three-sector economy. This simply means that theaggregate spending for goods and aggregateoutput of goods will be equal when the sum ofthe diversions, S + T, from the real incomestream is just matched by the sum of compen-sating injections, I + G, into the real..'income·stream. Alternatively, the equilibrium condition inthe goods market may be expressed as Y =C + I + G. The equilibrium condition in themoney'market is md = ms' as before.

As in the first fiscal model of Chapter 6. bothgovernment purchases of goods and servicesand net tax receipts'are assumed to be indepen-dent of the level of income. Part A of Figure 12-11shows $20 9f :government purchases added.to the investment .schedule- of Figure 12-3.

'Bec.~use these Pwchases are also regardedas independent of the interest rate, the I + Gcurve lies $20 to the right of the I curve at allinterest rates. Whatever the interest rate, the sumof I -+- G will be $20 greater than I alone. In terms-of its'effecton Y,a dollar of G is no different from

, a dollar of I. Adding $20 of G therefore shifts the

IS curve $40 to the right. from IS1 to IS2, for the,same reason that the increase in investment of$20 shifted the IS curve to the right by $40 inFigure 12_8.10 Part 0 of Figure 12-11 includes thesame LM function derived in Figure 12-4.

Other things being eElual, the introduction ofdeficit-financed government purchases of $20moves the Y, r equilibrium in' Part 0 from $120and 6 percent to $140 and 7 percent and shiftsthe AD curve in Part E from AD1 to AD2• Again

.the result shown is the same _as that in Figure12-8 for a $20 shift in the investment demandschedule. What otherwise would be an expan-sion in Yof $40, as indicat.ed by the simple mul-tiplier of 2, becomes the lesser expansion of $20due to the effect of the rise in r that accompaniesthe rise in Y. However, there is a difference: G of$20 is unaffected by the rise in r it causes, butthe rise in r reduces I by $10, which makes thenet change in I + G only $10 and the rise inincome~:only $20. The full income-expansionaryeffect of G,is not realized, because tfie resultingrise in r crowds out $10 of private investmentspending. Therefore, a fiscal policy designed toraise the income level through a deficit-'financedexpansion of government spending may not pro-duce the maximum possible rise of income unlessit is accompanied by an appropriately expansion-ary monetary policy. 1.1

Let us now suppo~e that there is abalancedbudget and that the government collects taxesof $20 to match its spending of $20,thefeby

1°lt would be more correct to designate the curve asIG-ST instead of IS, but the simpler notation will beretained. Note. however. that in Parts A-C the axes pre-viou_slylabeled I are now I + G. and the axes previouslylabeled S are now S + T.

11 Because government spending in this example isentirely deficit financed, we are concerned with themethod of deficit financing employed, If entirely financed-by thesale oLgovernment securities to the public. therewill be no increase in the money supply; the results are asdescribed above. If financed by the appropriate "mix" ofsales to the public and the banking system, there will be~n incr¢ase in the money :;upply that permits the full $40 ;potentiat expansion in Y. .

Page 19: Shapiro Chapter 12

,I

60 ~

!40 r

I20 r-

I1.__ .__ ..1...- .

o 40

_1. _I

I I I______.Ll_L__~____----.L.. _

00 lW 100 200 Y

rI

10 \--!

- '" :\

120 f ~ 160130 140

S+T100 L

I!

:: f401-··-----

~---- Ir---I I

20!-- -- I! I I I II I I, 45° I I I, .__'-_....L1_L ' __ ..l- ._----L __.. _

G 20 40 60 80 100 I + G

6,i

4 ~-

i,I

2 r-I I+~IL .....L.__ i_. ..l- ..l_. .1.__... _

o 20 40 60 80 100

fiGURE 12-·1iEffect on Aggregate D'emand of Changes in Government Spending

and Taxation

Page 20: Shapiro Chapter 12

avoiding deficit spending,. In the present model,. taxes of $20 reduce disposable income by $20.With,the" MPS of 1/2, the reduction in saving isone-~alf of this amount. Consequently, at each.'- (

level of Y, T of $20 reduces 5 by $10 and C by$10, which appears in Part C of Figure 12-11 asa downward shift of $10 from 51 to 52 in the savingfunction. To the leakage from income made upof saving must now be added the leakage of $20for taxes. This gives us the curve 52 + T, the sumof saving and taxes, or that portion of the incomeflow that does not appear as consumptionspending at each level of income.12

I of Part A and 51 of Part C gave us 151 ofPart 0; I + G of Part A with T of zero gave us 152

of Part 0; finally, I + G of Part A with 52 + T ofPart C gives us 153 of Part D. The new equilibriumposition indicated by the intersection of 153 andLM in Part 0 is found at Y of $130 and r of 6.5percent. Corresponding to this is AD3 positionedat Y of $130 in Part E. In our illustration, addingG of $20 and an equal amount of T raises theequilibrium level of Y by one-half the increase inthe size of the b'udget.13

With G and T both independent of the levelof Y,we have a model similar to the one that gaveus the unit multiplier in Chapter 6. In that model,the rise in Y was equal to the increase in the sizeof the budget. However, because the interest rateis now part of the model, we' firiOtha:t the adualmultiplier is less than the balanced-budget mul-tiplier of 1 that appears in the simpler model. Anexpansion in the size of the budget, with thebudget'balanced, will raise the income level, butthe rise in income-which would otherwise be

12Forexample, with Y of $140 and T of zero, Yd' or Y- T, would be $140; C would be $110, or $40 + 1/2($140- 0); and $ would be $30, or - $40 + %($140 - 0), thelast figure as shown on the $, curve of Part C of Figure 12-11 at.y of.$140. The imposition of T of $20 reduces Yd to$120 when Y is $140. This reduces C to $100, or $4.0 +%($140 - $20), and $ to $20; or -$40 + %($140.-$20), the latter figure as shown on the $2 curve at Y of$140. Finally, adding T of $20 makes total diversions fromincome $40 at Y'of $140, as shown on the $2 + T curve,

13Theoriginal budget was one in which both G and Twere zero.

equal to the expansion in the size of the budget-will be dampened by the tendency for the interestrate to rise with the rise in income. In other words,a fiscal policy designed to produce a rise inincome while maintaining a balanced bUdget willprodu~e the maximum possible income increaseonly if it is accompanied by an expansionarymonetary policy that prevents what otherwis~might be a rise in the interest rate and a conse-quent reduction in private investment spending.

We have seen that a rise in the income levelm'ay be expected from an expansion in G with nochange in T and even from an expansion in Gthat is matched by T. The third possibility, ofcourse, is a reduction in Twith no reduction in G,a commonly cited example of which was the taxcut of 1964. This major reduction cut federal taxreceipts about 10 percent below what they other~wise would have been; in contrast. the morerecent anti-reCE:fssionary Tax Reduction Act' of1975 reduced receipts about 5 percent belowwhat they otherwise would have been. Figure12-11 may bE?used to illustrate an aspect of the1964 tax cut much discussed at the Jime.-SUp-pose the original equilibrium is definedf/by)theintersection of 153 and LM at Y otl$)3(j,~'nd r of6.5' percent; this is the equilibriurl consistent with1 + G of Part A and 52 + T ~f ParVJ. of Figure12-11. With no change in G ~ ~Jax cut of $20,the I + G curve remains ~ 1's.' ~crthe 52 + Tcurve shifts downward to.8,. 't'fis'in turn causesthe 15 curve to shift from 153 'to 152, But the fullexpansionary effect of the tax cut-a rise in Yfrom $130 to $150-is not realized because theinterest rate rises. Therefore, in judging the pro-spective effectiveness of the 1964 tax cut, oneconsideration was whether or not the expected'increase in aggregate spending would be smallerthan otherwise obtainable due to adverse mon-etary effects, In President Johnson's words, ,''Itwould be self-defeating to cancel the,stimulus,oftax reduction by tightening money. Monetary anddebt policy should be directed toward maintain-jng interest rates and credit conditions thatencourage private investment.,,14 The model In

Page 21: Shapiro Chapter 12

254Figure 12-11 is far tOb simple.to come to gripswith the questions' involved, but it suggests. invery general terms, that what is called-for is anincre~~e in the money supply. This' Jncrease.should be"sufficient to shift the LM cu~e to theright 'by the amount necessary to s.ecure thegreater rise in income-from $130 to $"1~~thatwill follow f(om the increase in aggregate spend-ing to be exp~cted at ,a stable interest rate.

~Itpough we will not go beyond the simplemodel in which both G and T are assumed to beindependent of Y, the- IS-LM analysis of Figure12-11 may be elaborated by introducing morerealistic fiscal assumptions. In Part C, for exam-ple. T may be treated as a function of Y, and theeffects of this more realistic fiscal assumption onthe..Y, r equilibrium combination may readily betr~ced. This ..model will show how the potentialincome-expansionary effect of, say, a rise ininvestment. spending may be restrainec.by botha rise in the interest rate and a rise in tax receiptsas income expands. Although it adds somethingto the simpler model of this section, like any othermodel of this kind it will again bring out our prin-cipal conclusion: An increase in aggregatespending-whether it is the result of a shift in theinvestment function. consumption function, or achange in government spending or taxation-willnot produce the effect on income ~uggested bythe crude multipliers in earlier ch~ers. When,we recognize the r<>leplayed by money and inter-est, we see how an otherwise greater expansionof income suggested by crude multipliers maybe prevented by the rise in the interest rate thatmay accompany a rise in income.

The :IS and LMElasticitiesand MOftetaryiFiscaJ.Policies ' ,

81) far, we have intentionally avoided specific ref-erence to the elasticities of the IS and LM tunc:'tions so that we might concentrate on the general

characteristics at th~' present stab!e-ptice modeland the general conclusions it suggests. As weallow for the elasticities of these functions. we willfind that some ofthese conclusions must be qual-ified and that some must even be abandoneq inthe extreme cases' of perfectly elastic or inelasticfunctions. For example, an expansionary fiscal.policy may rais,e only the interest rate and leavethe income level unchanged; conversely, it mayraise only the income level and leave the interestrate unchanged. An expansionary monetary pol-icy may lower only the interest rate and leave theincome level unchanged; or it may change nei-ther the interest rate nor the level of income. Thereverse is possible for contractionary policies.

Elasticity of the IS and LMFunctionsWith a fixed money supply, the LM function asderived in Figure 12-4 slopes upward to the right.However, at one extreme the function may becomeperfectly elastic, and at the other extreme it maybecome perfectly inelastic, with a range of vary-ing elasticities in between. In general, the higherthe interest rate, the less elastic the correspond-ing point on the L~ function will be. These threeranges are delineated in Part A of Figure 12-12,in which the perfectly elastic section is the"Keynesian range," the perfectly inelastic sectionis the "classical range," and the section betweenis the "intermediate range."

Why this particular shape with perfect elas-ticity at one extreme and perfect inelasticity atthe other? Remember that at sonie very low inter-est rate th~ speculative demand for money maybecome perfectly elastic due to a consensus bywealth-holders that the interest rate will fall nolower and that security prices will rise no higherWealth-holders accordingly stand ready toexchange seGurities for cash at existing securityprices. which produces the liquidity trap on thespeculative demand function. Here,' on the LM" ,function: it produces what is known as the Keynes-ian range. At the other extreme, at some veryhigh int~rest rate, the speculative demand for

-~~-.---

Page 22: Shapiro Chapter 12

! 'I I 1L. t.L_L _

FIGtJRE 1:1·12Effects of Shifts m the is andLM FWtctions with Various

Elasticities of the LM FwtCtiOfi

money may become zero and perfectly inelasticat interest rates above this if wealth-holdersbelieve the interest rate will rise no higher andthat security prices will fall no lower. At this or anyhigher rate, wealth-holders accordingly prefer tohold only securities and no idle cash. This per-fectly inelastic section of the speculative demandfunction is known as the classical range on theLM function.

Why are the three sections into which the LMfunction has be-en diVIded labeled in this fash-

ion? In our simplified version of the classical the-ory, money is demanded only for transactionspurposes. Therefore, in Figure 12-4, classicaltheory assumes that the speculative demand formoney is zero at each inter~st rate. In effect.Part A of that figure vanishes. If the total moneysupply given in Part B is $100. that $100 will beheld in transactions balances or msp = 0 and ms=: tnr With k of 1/2 in Part C. the LM curve ofPart 0 becomes a perfectly vertical line at theincome level of $200. if the public holds, moneyonly for transactions purposes and if it holdsmoney balances equal to one-half of a period'sincome, money market equiiibrium is found at an

. income level of $200 at all interest rates. 15

With the exception of the perfectly. inelasticsection-the so-called classical range-it wouldnot be altogether incorrect to include the remain-der of the LM function in the Keynesian range.However, because of Keynes' emphasis on theineffectiveness of monetary policy, the Iiquidity-trap section alone has been identified. as theKeynesian range. Within this range, monetarypolicy is completely ineffective; therefore .. thisrange most closely fits Keynes' emphasis.

The IS function as derived in Figure 12-3slopes downward to the right. Its elasticitydepends on the responsiver:'ess of investment ./spending to changes in the interest rate and onthe magnitude.of the mUltiplier. If the investmentspending schedule is perfectly inelastic (indi-pating that investment sRending is completelytnsensitive to the interest rate). the IS curvederived in Part 0 will' be perfectly inelastic.regardless of the magnitude of the multiplier. If,on the other hand, the investment demandschedule shows some elasticity, as se~ms to bethe case, the IS curvewili be- more ela,stic, thelower the MPS. The lower the MPS, the higher willbe the mutliplier and the greater will be _thechange in income for any increase in investmentresulting from a fall in the interest rate. Part A of .Figure 12-13 shows three pairs of IS curves, each

''''The graphic derivation of a perlect!V inelastic LMcurve is shoM1 in Chsptei 13 on p. 268.

Page 23: Shapiro Chapter 12

·. .._,..... '-0 Y4 y

A

PAD3 ADs

,AD, AD2 AD4 AS

IPI

FIGURE 12·13Effects of Elastic and Inelastic ISFunctions in Different Ranges of

the LM Function

~ made up of one highly inelastic and one elasticIS curve.

Parts B of both Figures 12-12 and 12-13show AD curves corresponding to the variouslevels of Y set off on the Y axis in Part A of eachof those figures. As in previous figures of thischapter, the AS curve is assumed to be perfectlyelastic up to the full employment level of output.Also as before, the full employment leve! isassumed to be greater than the highest leve! of

output attained, Ys in Part A. Consequently, all ofthe changes in AD shown in each figure from Y1

to Ys are accompanied by proportional changesin y"6

Monetary and Fiscal PolicyMonetary policy is the exercise of the centralbank's control over the money supply as aninstrument for achieving the objectives of generaleconomic policy. Fiscal policy is the exercise ofthe government's control over public spendingand tax collections for the same purpose. We willconfine ourselves here to the single policy objec-tive of raising the level of real income. The IS-LMframework then provides a basis for comparing'the effect of the two types of policy on the incomelevel and the interest rate and for comparing con-ditions under which each type of policy will oeeffective or ineffective in prodt.i'ciftg the; desiredchange in income. For this purpose, tHe discus-sion is conveniently divided into three parts, eachcorresponding to a range of the LM function inPart A of Figure 12-12.

....The Keynesian Range Consider first· the Yl'r, equilibrium in the Keynesian range. An increasein the money supply shifts the LM curve to theright, from LM1 to LM2. This means that for eachpossible level of income md = ms only at a lowerinterest rate; the rate must fall by the amount nec-essary to make the public willing to hold largeridle cash balances. But this is not true in the

16Although the present model contains a classical ele-ment in the form of the perfectly inelastic range of the LMcurve, the model is essentially Keynesian because itshows that the equilibrium level of output may be belowit-Ie level consistent with full employment. Remember fromChapter 9 that the simple classical model with its assump-tion of perfect wage and price flexibility yields a perfectlyinelastic AS curve, which is located at the full employmentievel of output. This makes the full employment level ofoutput the only equilibrium level, a result altogether dif-ferent from that found in Figures 12-12 and 12-13. Further

". comparisons between the classical and Keynesian modelsin terms of the IS-U.If framework will be presented in thefollowing chapter.

Page 24: Shapiro Chapter 12

"liquidity trap." Here the interest rate is alreadyat an irreducible minimum for the time.being. Asthe monetary authority purchases securities,security-holders are willing to exchange them forcash at the existing prices. Therefore, expansion?f the money supply cannot cause the interestrate to fall below the rate given by the trap. Allthat happens is that the public holds more inspeculative balances and less in securities. Fur-ther increases in the money supply would shiftthe LM curve still farther to the right, but the lowerend of the curve would remain anchored in thesame liquidity trap. If the economy is already inthe trap, monetary policy is powerless to raisethe income level. It cannot reduce the interestrate any further to produce a movement down theIS1 curve to a higher equilibrium income level.The belief that the economy was in the trap dur-ing the early thirties led Keynes to his then unor-thodox fiscal policy' prescriptions. Because gov-ernment cannot raise the income level throughmonetary policy, it can only try to do so throughfiscal policy. If a rise in income cannot beacnieved by producing a movement down the IS 1

curve through monetary expansion, it can beachieved by producing a shift in the IS curve. 1Itself, say from IS1 to IS'l' Fiscal measures suchas increased government spending or reducedtaxes .that could shift the IS curve become theorder of the day.. :0 t~~ extent that monetary policy operates byraising Investment spending through a reductionin t.he cost of money, the impasse of monetarypolicy for an economy caught in the trap meansthat the elasticity or inelasticity of the IS functionis no longer relevant. In Part A of Figure 12-13, forexample, it does not matter Wh~eh r the IS func-tion is th~ el.a~ticIS1 or the inelasti IS"1.17

The liqUidity trap is an extre e case thatcould occur only during a dee depression, ifeven then. A prosperous economy and a liquiditytrap do not go hand in hand. Because the pure

17As we will see, the elasticity of the IS function does::>ecomerelevaAt elsewhere, but not in the Keynesian·ange.

Keynesian range is the range of the liquidity trap,one can",now appreciate what Professor Hicksmeant by his observation, made shortly after theappearance of Keynes' book, that "the GeneralTheory of Employment is the Economics ofDepression.,,18

"The Classical 'Range Next let us examine theY4' r4 equilibrium defined by the intersection ofIS3 and LM 1 in Part A of Figure 12-12. Someincrease in the money supply will shift the LM_ 1

curVe to LM2. In contrast to the result in theKeynesian range, the result is now an increasein the inc.ome level from Y4 to Y5 and a fall in theinterest rate from r4 to r3' In the classical range I

the i~terest rate is so high that speculative bal-ances are zero; money is held for transactionspurposes only. Under these circumstances, if themonetary authority enters the market to purchasesecurities, security-holders can be induced toexchange securitjes for cash only at higherprices. As security prices are bid up and theinterest rate is pushed down, investment is stim-ulated (and, in classical theory, saving is dis-couraged). Because nobody chooses to holdidle cash, expansion of the mo"ney supply willproduce a new equilibrium only by reducing theinterest rate by whatever amount is necessary toincrease the income level sufficiently to absorbthe full increase in the money supply in transac-tions balances. If in the present case we assumethat ilms = $20 and k = 1/2, equilibrium will berestored only when Y has risen by $40, or, in gen-eral, when ilY = ilmjk. In the classical range,the result follows the simple classical quantitytheory of money as a theory of aggregatedemand. Y rises proportionally with the increasein ms' If V = 2 or k = 1/2, the rise in Y must betwice the rise in ms in order to satisfy the equilib-rium condition: msV = Y and ms = k(Y).

18J.R. Hicks, "Mr. Keynes and the 'Classics': A Sug,gested Interpretation," reprinted in W. Fellner and B.F.Haley,eds., Readings in the Theory of Income DistributionIrwin, 1946, p. 472. . '

Page 25: Shapiro Chapter 12

In contrast to the Keynesian range, in whichmonetary policy is completely ineffective, in theclassical range it appears to be completely effec·tive. No part of any increase in the money supplydisappears into idle cash balances. The increasein the money supply leads to increased spendingthat raises the income !evel to the point at whichthe total increase in the money supply is absorbedinto transactions balances. Because all incomechanges are real changes in the present model,the increase in the money supply that i>hifts LM 1

to LM2 causes an increase horn Y4 to Y5 in outputas well as in income.

Again in contrast to the Keynesian range, inwhich fiscal policy alone can be effective, fiscalpolicy it') the classical range is completely inef-fective. IAn upward shift in the IS function from IS3to is' 3 in P?rt A of Figure 12-12 can raise only theinterest rate, from r4 to r5; the incdrne level staysunchanged at Y4• Given the increase in spendingthat lies behind the upward shift in the IS function,the interest rate will rise sufficiently to crowd outenough spending to leave aggregate spendingunchanged. Therefore, if the 'rise in spendingresulted from increased government spending,the r.ise in the interest rate would crowd out an-.amount of private spending equal to the rise ingovernment spending. The level of income is ashigh as the given money supply can support. Inthe classical range, an increase in income istherefore impossible without an increase in themoney supply, and monetary policy becomes anall-powerful method of controlling the income'8"'e~

How does the elasticity of the IS functron affectthe equilibrium positions in the classical range?Let us compare the elastic IS3 function and theInelastic IS" 3 function shown in Part A of Figure12-13. Given the IS" 3 function, no increase in themoney supply and no reduction in the interestrate is capable of raising the income level fromy 4 to Y 5' Monetary policy will raise Y, but not bythe multiple of ms given by 11k. Although thisseems to upset the result suggested by classicaltheory, classical theorists woutd deny that the IScurve could be so inelastic. Remember that in

both classical and Keynesian theory investmenti.sa function of the interest rate, but that in clas-sical theory saving also is a function of the inter-

. est rate. Consequently, only if both saving andinvestment are quite irisensitive to the interestrate could there be an inelastic curve of the sortdescribed by /S" 3 in Part A of Figure 12-13.19 As

..long as one or the other is elastic, the reSUltingIS function will also be elastic; with an elastic ISfunction, the result of a change in the money sup- .ply in the present model is d Y = dmslk.

The Intennediate Range Finally, let us exam-ine the equilibrium of Y2, r2, as defined by !.heintersection of /S2 and LM1 in Part A of Figu~e12-12. Here again we see that some increase in themoney supply will shift the LM1 function to LM

2.

In the Keynesian range, this increase in themoney supply left both Y and r unchangedbecause that total increase was absorbed inspeculative balances at the existing interest rate. -.In the classical range, this increase in the money ,supply raised Y by the amount necessarY toabsorb the full increase in transactions balances.This worked itself out through the interest ratereduction that raised spending by the amountneeded to produce the required rise in income.In the intermediate range, however, the increasein the money supply is partially absorbed in bothspeculative and transactions balances. The levelof income rises, but by an amount less than thatwhich would require the full increase in themoney supply for transactions purposes.

For example, suppose that the increase in themoney suppiy is $20 and k is 1/2. Although theresultant shift in the LM function is $40, here therise in income (Y3 - Y2) is only ha~fthat amount.

191nterms of Part C of Figure 12-3, we may show savingas a function of both Y and r by drawing in a similar fashionsuccessively higher saving functions to correspond witl1successively higher interest rates. An inelastic investmentfunction in Part A combined with this income-elastic andint8rest-elastic saving function in Part C will still producean elastic IS function in Part D.

Page 26: Shapiro Chapter 12

In reducing the interest rate by the amount thatproduce"s the increase in spending needed toraise the income level by $20, $10 (one-half ofthe increase in the money supply) is absorbed ins"peGulative balances. The remaining· $10 isexactly the additional amount of money neededfor transactions purposes with the income levelup by $20.

In ~he intermediate range, monetary policyhas sume degree of effectiveness but not thecomplete effectiveness it has in the classicnlrange. In general, the closer the equilibrium inter-section is to the classical range, the more effec-tive monetary policy becomes; the closer theintersection is to the Keynesian range, the lesseffective it becomes.

Within this range, fiscal policy is also effectiveto some extent. Fiscal measures that shift the ISfunction from IS2 to IS' 2' for example, will raisethe level of income and the interest rate to thenew equilibrium defined by the intersection ofIS'2 and LM1• If the shift in the IS function stemsfrom a deficH-financed increase in governmentspending, the interest fate must rise. We areassuming a fixed money supply described byLM1, so the increased government spending isbeing financed by borrowing from the public. Thp.sale of additional securities by the governmentdepresses security prices, raises the interestrate, and chokes off some amount of privatespending. The rise in the interest rate followingany given increase in government spending will

be greater or smaller depending on how high inthe intermediate range the equilibrium happensto be Although fiscal policy is somewhat effec-tive anywhere in the intermediat~ range, in gen-eral it will be more effective the closer equilibriumis to the Keynesian range and less effective thecloser equilibrium is to the classical range.

Although both monetary and fiscal policieshave. varying degrees of effectiveness in theintermediate range, the relative effectiveness ofeach depends in large part on the elasticity ofthe IS function. If the IS function is the inelasticIS"2 in Part A of Figure 12-13, monetary poli~ycan do very littie to raise the level of income, evenin the intermediate range; fiscal policy alone is

.effective in such a situation. Furth~rrTlore, anexpansionary fiscal policy need not be con-cerned with adverse monetary effects in thiscase. A shift in an inelastic IS function will raisethe interest rate, but this higher rate will have littlefeedback on spending. Keynes maintained thatthe investDlent schedule (as well as the savingschedule) was interest inelastic. If this is thecase, the IS schedule must also be inelastic, andfiscal policy, which is completely effective in theKeynesian range, must be almost as effective inthe intermediate range. If the IS sch~dule isindeed interest inelastic, tl1en the Keynesianrange becomes, in effect, the complete LMcurve, more applicable at the lower end than atthe upper end, but with some applicabilitythroughout.


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