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American Economic Association

IS, LM, and External Equilibrium: A Graphical AnalysisAuthor(s): Dwayne WrightsmanSource: The American Economic Review, Vol. 60, No. 1 (1970), pp. 203-208Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1807870

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COMM UNICATIONS 203

IS, LMA,nd ExternalEquilibrium:A GraphicalAnalysis

By DWAYNE WRIGHTSMAN*The IS-LiMlexposition of general equilib-rium in the domestic money and goods mar-kets excludes the problem of balance of pay-ments equilibrium when the economy en-gages in foreign trade under conditions offixed foreign exchange rates.1 This exposi-

tional shortcoming is easily rectified bysuperimposing an external equilibrium con-dition onto the IS-LM framework. A newexternal equilibrium curve, called the EEcurve, is derived geometrically as shown inthe four-section diagram of Figure 1.In the lower right-hand section of Figure1, net exports of goods and services isshown to vary inversely with the level ofnational income. A change in income isexpected to change demand for imports inthe same direction without having anyappreciable effect on demand for exports. Atlow levels of income, the level of net exportsis positive, meaning that exports exceedimports. But at high income levels, thelevel of net exports is negative indicatingimports in excess of exports.In the upper left-hand section, net foreigninvestment is shown to vary inversely withthe domestic interest rate. A change in theinterest rate is expected to change the do-mestic economy's investment of funds inforeign economies in the opposite direction,and foreign economies' investment of fundsin the domestic economy in the same direc-tion. The net foreign investment sectioil of

the diagram allows for bo h positive andnegative levels of net foreign investment. Atlow interest rates, domestic investors willbe net buyers of foreign securities. But if theinterest rate is high enough, foreigners willbe net buyers of domestic securities, so thatnet foreign investment will be negative.In the lower left-hand section, the 45-degree line represents equality between netexports of goods and services and net foreigninvestment, which, abstracting from prob-lem of unilateral transfers, and net fac-tor income, is the condition for externalequilibrium (meaning no surplus or deficitin the balance of payments). The EE curvein the upper right-hand section of Figure 1is subsequently derived by geometry fromthe two behavioral functions and the equi-librium condition graphed in the other threesections. It contains combinations of theinterest rate level ard the level of incomewhich provide equilibrium in the balance ofpayments.The RE curve has a positive slope as doesthe LM curve. A comparison of the steepnessof the slopes is thus in order. Is EE steeperor less steep than LKv ?And do the twocurves intersect?The absolute slope of the EE curve is theratio between the responsiveness of netexports of goods and services to the level ofincome and the responsiveness of net foreigninvestment to the rate of interest. Theabsolute slope of the LM curve, on the otherhand, is the ratio between the responsivenessof the transactions demand for money to thelevel of income and the responsiveness of theasset demand for mioneyto the rate of inter-est. There is no a priori basis for generalizingthat one of these ratios exceeds the other forall economies at all times. However, a casecan be made for the proposition that theslope of the EE curve is normally steeper

* The author is associate professor of finance at theUniversity of New Hampshire. He is inidebted toWilliam Hosek, James Schulz, Richard Whyte, and themanaging editor for their helpful conmmentsand sug-gestions.1 An IS curve is a curve showing combinations of thelevel of national income and the level of interest rateswhich generate equilibrium in the market for goods andservices. An LM curve does the same for the money

market. For background on the nature of these curves,see John R. Hicks.


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204 THE AMERICAN ECONOMIC REVIEWi (interest rate) i (interest rate)

E

ES curve shows/ I i-Y combinations

- - ~~~~~~~~~~whichigenerateI ,~ _ _ _ _ /7[ ixternalequilibriumNFl= f(i) g

Net Foreign I_ffi

* | a ~~~~~Y ( income)O + Investment 0 - (nm

Net Exports of Net Exports olI Goods & Services Goods & Services |

+ -/- + II 45 et Foreign\

- / Y - Investment Y (income)l - - I

NEGS NFI NEWS= g(Y)(external equilibriumcondition)

FIGURE 1

than the slope of the LM curve and that it(EE) normally intersects LM from below(moving to the right).First, consider an EE-LM intersectionpoint at some positive i and Y. This merelymeans that there is some interest rate abovezero and some level of income above zerocapable of ensuring simultaneous equilib-rium in the domestic money market and thebalance of payments. Surely this is thenormal circumstance. Countries occasion-ally do approach such an equilibrium, andoften those that do not, could, were it notfor pressing internal considerations, for

example, maintenance of high-level employ-ment.Now consider what would happen to aneconomy initially in equilibrium if a generalrecession were to strike (without its beinganticipated by fiscal and monetary au-thorities). Income and the interest ratewould fall. In a financially mobilized countrysuch as the United States, money demanderswould be expected to adjust their cashbalances rapidly so that the lower i-Ycombination would still be on the LM curve,only lower down. Thus the money marketwould soon be back in equilibrium. But


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COMMUNICATIONS 205what would happen to the external equi-librium in the balance of payments? Onewould expect, normally, that a general re-cession would disrupt external equilibriumand create a payments surplus; that is, therecession's income effect of increasing netexports of goods and services would outweighits interest rate effect of inicreasing net for-eign investment. If this is the case, it meansthat the new interest rate is too high and thenew income too low to prevent a paymentssurplus. The EE curve, consequently, liesbelow the LM curve for income values to theleft of the EE-LM intersection. (In the caseof an unanticipated boom accompanied byrapid adjustment in money demand, onewould expect a payments deficit to develop,meaning that EE lies above LM for Yvalues to the right of EE-LA'I equality.)Thus, under these circumstances, which areassumed to be normal, the relation betweenthe EE and LM curves is that they intersectwith the former being steeper than the latter.Unlike the LM and EE curves, the IScurve has a negative slope. However, theIS curve has a steeper negative slope, ceterisparibus,in an open economy than in a closedeconomy. A definition of the IS curve willhelp to explain why this is so. The IS curvedepicts all i-Y combinations which areconsistent with a zero excess demand forgoods and services. For the closed economy,this implies that there is ex ante equality be-tween saving and domestic investment andthat the absolute slope of the IS curve isthe ratio between the responsiveness of sav-ing to the level of income and the respon-siveness of domestic investmient to the rateof interest. For the open econiomy,it impliesthat saving minus net exports of goods andservices equals domestic investment andthat the slope of IS is the ratio between theresponsiveness of saving minus net exportsto the level of income and the responsivenessof domestic investment to the rate of in-terest. Since the response of net exports ofgoods and services to the level of income isnegative, it follows, ceterisparibus, that theabsolute ratio between the responses in theopen economy is greater than that for theclosed economy. However, in both cases theresponses have opposite signs so that IS is

negatively sloped regardless of whether ornot the economy is open or closed.With this as background, it is now ap-propriate to consider the interrelations ofthe IS, LM, and EE curves. Full equilibriumin the money market, the goods market, andthe balance of payments is satisfied only(but not necessarily) when the three curvespass through a common point. If they do not,the resulting disequilibrium is likely to beconcentrated most in that market whichbears the least influence on the rate of in-terest and the level of income. In the UnitedStates the least influential of these threeforces is the balance of payments. Thus, EEis not apt to be as much income and interestrate determining, as are IS and LM. Thepoint toward which i and Y are likely to bemost strongly attracted is the point ofintersection between the IS and LM curves.Passage through a common poirnt is anecessary but not a sufficierit condition forfull equilibrium. If the common point liesbeyond the full-employment income limiton the itncomeaxis, there will be disequilib-rium in the form of inflation because theequilibrium income will be unobtainable;that is, aggregate demand for goods andservices will exceed capacity supply. On theother hand, if the common point lies insidethe full-employment income limit, the in-come disequilibrium problem vanishes butan equally distasteful problem, namely un-employment, emerges.Internal and external problems can beanalyzed separately in the IS, LM, and EEframework, but it is more interesting andinstructive to consider them together. Con-sider, for example, the dual-problem case ofunemployment coupled with a paymentsdeficit. This is the case that gave the UnitedStates much trouble in the late 1950's andearly 1960's and could conceivably re-emerge if and when the Viet Nam conflictends. In Figure 2, IS intersects LM belowand to the right of the EE curve with theresult that joint monetary and product equi-librium produces an income that is too highand an interest rate that is too low to pre-vent a balance of payments deficit. At thesame time, IS intersects LM to the left ofthe F-line (the full-employment income


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206 THE AMERICAN ECONOMIC REVIEWlimit), producing an income which is toolow for full employment.In this case, if the monetary and fiscalauthorities do nothing, the problem of thepayments deficit will solve itself because goldoutflows (in the absence of defensive openmarket operations) will decrease the moneysupply, shifting the LM curve up and to theleft until it intersects the E1 and IS curves.Realistically, the monetary authority is notlikely to let this happen (at least not in theUnited States) because this would make theuinemploy-mentproblem worse. Neverthe-less, monetary contraction is superior tocontractionary fiscal policy for the purposeof restoring external equilibrium. Comparedto contractionary fiscal policy (IS shifteddown and to the left), contractionary mone-tary policy (LM shifted up and to the left)can restore external equilibrium at a smallercost in terms of lost income. In Figure 3,BC is the income lost when contractionarymonetary policy is used to restore externalequilibrium. When contractionary fiscalpolicy is used for this purpose, the incomnelost is AC, or AB plus BC. The net amount ofincome saved by using contractionary mone-tary policy over contractionary fiscal policyis, then, the segment AB.Suppose, however, that full employment,not external equilibrium, is the primary

FI ~~~E

LU E EFIGURE2 UNEM-PLOYMENT-DLFJICITASE

0 YJ ~~A BCFIGURE 3

goal. For this purpose, it turns out thatmonetary policy is not as good a tool asfiscal policy. Expansionary monetary policy(LM shifted down and to the right) restoresfull employment at a greater cost (in termsof a greater payments deficit) than ex-pansionary fiscal policy (IS shifted up andto the right). In Figure 3, QR is the de-ficiency in the interest rate level required forexternal equilibrium when expansionaryfiscal policy is used to restore full emplov-ment. PR, or PQ plus QR, is the interest ratedeficiency when expansionary monetarypolicy is used for this purpose. The netdeficiency in the interest rate required toprovide external equilibrium at full employ-ment avoided by using expansionary fiscalpolicy over expansionary monetary policyis, consequently, the segment PQ.The analysis thus shows that monetarypolicy has a comparative advantage overfiscal policy for the purpose of meeting theexternal equilibrium objective and thatfiscal policy has a comparative advantageover monetary policy for meeting the fullemployment goal. The significance of thecomparative advantage relations betweenmonetary and fiscal policy is that the twoproblems of unemployment and a paymentsdeficit can be simultaneously resolved byapplying a mix of contractionary monetarv


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COMMUNICATIONS 207

S/I~~~~

0 YFIGURE4

policy and expansionary fiscal policy.2 InFigure 4, contractionary monetary policyis applied shifting the LM curve up and tothe left to become L'M'. Expansionary fiscalpolicy is applied at the same time shiftingthe IS curve up and to the right to becomeIl'S'. Where EE, L'M', and I'S' convergeat the F-line the economy is at full employ-ment with external equilibrium. Full emi-ployment income is obtained because asufficient amount of expansionary fiscalpolicy is applied. External equilibrium isachieved because the expansionary fiscalpolicy and the contractionary monetarypolicy raise the interest rate to the necessarylevel. Of course, if an economy is not willingfor various reasons to subject itself tohigher interest rates, the solution just de-scribed is merely academic.8A second interesting, dual-problem case toanalyze is that of inflation coupled with apayments surplus. This case is the converseof the unemployment-deficit case above andsuggests the converse solution of applying

a mix of easy monetary policy and restric-tionist fiscal policy. However, a countryfacing inflation and a surplus may not needto resort to policy measures as it does in theunemployment-deficit case because the twocases are asymmetrical. In the unemploy-ment-deficit case, income is not out ofequilibrium despite the existence of un-employment if there is wage infleyibility inthe labor market. In this situation, govern-ment intervention is used as a substitute fornmarketequilibrating forces to bring theunemployment to an end. In the inflation-surplus case, on the other hand, income isnecessarily out of equilibrium and continuesto be as long as the inflation persists. In thiscase, the rising price level generates equi-librating forces which work to end the pay-ments surplus and the inflation without re-course to monetary and fiscal policy.What is the nature of these equilibratingforces? When a country is confronted withinflation and a balance of payments surplus,its IS, LM, and EE curves are positioned ina way that makes all three curves shift. InFigure 5, IS, LM, and EE are positioned toindicate inflation and a payments surplus.The intersection of IS and LM lies to theleft of the EE curve but to the right of theF-line (the full-employment income limit).The equilibrium level of income correspond-

F

FIGurRE5 TNFLATION-SURPLUS ASE

2 Sucha mix is in accordancewith RobertMundell'sprincipleof matching policy instrumentswith policyobjectives n the basis of comparative dvantage.3 For a discussionof this and relatedproblemsas-sociatedwith the monetaryand fiscalpolicy mix, seeRichard Ablin. Another treatment of a number ofmisgivings about the solution is found in Anne 0.Krueger.


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208 THE AMERICAN ECONOMIC REVIEWing to the IS-LM intersection is, conse-quently, too high to preveint inflation buttoo low to prevent a payments surplus. How-ever, the positioning of the three curves isnot lasting. The LM curve is potentiallyaffected in three ways. First, the paymentssurplus generates an inflow of gold which, inthe absence of defensive open market opera-tions, increases the money supply, shiftingLM to the right. Second, the rising absoluteprice level causes the transactions demandfor nominal cash balances to increase, whichshifts the LM curve to the left. And third,according to Friedman, the rate of inflation,if increasing, reduces the demand for money,shifting LM to the right, and, if decreasing,it increases money demand, shifting LM tothe left. On balance, LM will shift to theright or to the left, depending on the relativestrength of these three effects.Inflation can also cause the IS and EEcurves to shift. First, IS is shifted to the leftif the inflation, working through the realbalance effect, decreases consumption. Thereal balance effect thus serves, in the absenceof elastic price expectations, to make infla-tion self-defeating. Second, EE should shiftto the left because inflation decreases netexports of goods and services for given valuesof real income. A decrease in net exports, inturn, shrinks the payments surplus.The IS curve is further shifted because ofthe now shrinking payments surplus. Withinflation causing net exports of goods andservices to decrease for given values of realincome, IS has to shift to the left to remainconsistent with the zero excess demand con-dition that saving minus net exports equalsdomestic investment. However, if net ex-ports are small relative to total nationalproduct, as they are in the United States,this leftward shift in IS will not be great.The shifts in IS, LM, and EE are gener-ally in the direction of achieving equilibrium.There is, however, a timing consideration inreaching equilibrium. The inflation cannotbe brought to an end before the paymentssurplus is reduced to zero because as long asthere is a surplus there will be an inflow ofgold and an increase in the money supply

(again, assuming no defensive open marketoperations) which will keep the inflationalive. If the inflation is still healthy when thepayments surplus is approaching zero, thesurplus is apt to turn into a deficit. Thecombination of inflation and a deficit willshift the LM curve to the left due to theprice level effect on the demand for moneyand the gold inflow effect on the supply ofmoney. This shift will serve to reduce boththe inflation and the deficit, but it will notreduce the deficit to zero before it eliminatesthe inflation because as long as there is anyinflation, there will be a decrease in net ex-ports of goods and services which will keepthe deficit alive. If the deficit is of any sizewhen the inflation is ended, the money sup-ply will continue to contract (the LM curvewill continue to shift to the left) until exter-nal equilibrium is restored. In the meantime,however, equilibrium income will fall belowthe full-employment income limit producingunemployment. Thus, there is the possibilitythat the inflation-surplus problem can turn,by itself, into the unemployment-deficitproblem discussed earlier. Should this hap-pen, government can intervene to applv theappropriatemix of monetary and fiscalpolicy.

REFERENCESR. Ablin, "Fiscal-Monetary Mix: A Havenfor the Fixed Exchange Rate?" Nat. Bank-ing Rev., Dec. 1966, 4, 199-204.M. Friedman, "The Supply of Money andChanges in Prices and Output," The Re-lationship of Prices to Economic Stabilityand Growth: Compendiumof Papers Sub-mitted by Panelists, Joint Economic Com-

mittee, 85th Cong., 2nd Sess., Washington1958, 241-256.J. R. Hicks, "Mr. Kevnes and the 'Classics':A Suggested Interpretation,"Econometrica,Apr. 1937, 5, 147-159.A. 0. Krueger, "Balance of PaymentsTheory," J. Econ. Lit., Mar. 1969, 7, 1-26.R. A. Mundell, "The Appropriate Use ofMonetary and Fiscal Policy for Internaland External Stability," IntcrnationalMonet. Fund Staf Pap., Mar. 1962, 9, 70-79.

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