255CHAPTER 11Aggregate Demand I: Building the IS–LM ModelNotes to the InstructorChapter SummaryChapter 11 introduces students to the IS –LM model. The chapter is taken up principally withthe derivation of the IS and LM curves, prior to the use of the model in Chapter 12.CommentsPresentation of IS –LM is greatly facilitated by the fact that students have seen all of theelements already. This makes it much easier to teach than when it is taught prior to a long-runmodel. The amount of time spent on the material in Chapters 11 and 12 is partly a matter oftaste. It probably requires three lectures at a minimum to present basic IS –LM (omittingdetailed discussion of the Great Depression from Chapter 12), although some instructorsmight prefer to spend up to six lectures on this material.When teaching the IS curve, some instructors may find that it is preferable to start withthe loanable-funds derivation of the IS curve. The advantage of this approach is that it builds on the Chapter 3 model: equilibrium in Chapter 3 is summarized by ()()S Y I r =, where Y is exogenous; the IS curve is simply given by S (Y ) = I (r ), where income is now anendogenous variable. The Keynesian cross can then be presented as a special case. Use of the WebsiteThe model exercises for Chapter 3 can be used as an alternative way to derive the IS curve.Students can calculate and graph all of the {r , Y } pairs consistent with goods-marketequilibrium and also see how changes in exogenous variables shift this curve.Although the textbook does not spend a lot of time on the monetary/fiscal policy debate,the website material can be used to go through the standard exercises on the relative efficacyof monetary and fiscal policy under different assumptions on the parameters.Use of the WebsiteUse the website to download annual data for the U.S. consumer price indexand the 1-year and 10-year Treasury yields over the past 20 years. Compute the real interestrate for each of the Treasury yields by subtracting CPI inflation from each yield. Discuss howreal interest rates change with inflation in the short run compared to what you would expectover longer periods of time.258 | CHAPTER 11Aggregate Demand I: Building the IS–LM ModelChapter SupplementsThis chapter includes the following supplements:11-1The Key Features of the IS–LM Model11-2Mr. Keynes and the Classics: The Art of Modeling11-3The IS–LM Model: A Critical Evaluation11-4Additional ReadingsLecture Notes | 257 Lecture NotesIntroduction➢Figure 11-1We now have a basic idea of how the economy functions in the short run. Because in the shortrun prices are not completely flexible, changes in aggregate demand affect output, not justprices. To develop this short-run theory of the economy, we must now consider aggregatedemand and supply in more detail. This chapter and the next present a more detailed analysisof aggregate demand based on the IS–LM model. This model was developed by John Hicksin the 1930s as an interpretation of John Maynard Keynes’s seminal work, The GeneralTheory of Employment, Interest and Money, and is based on an analysis of equilibrium in thegoods and money markets, supposing that the price level is fixed. We can interpret the IS–LMmodel in two distinct ways: first, as a theory of GDP determination, supposing that the pricelevel is fixed; second, as a theory of aggregate demand and so as part of an aggregate demand–aggregate supply model.11-1 The Goods Market and the IS CurveThe building blocks of the IS–LM model are familiar from earlier analysis. The IS side of themodel summarizes equilibrium in the goods market and is based partly on the classical modelof Chapter 3; the LM side of the model summarizes equilibrium in the money market and sois related to the analysis of money in Chapter 5.The basic equation summarizing equilibrium in the goods market, for a closed economy, is familiar:Y = C + I + G.As before, we suppose thatC = C(Y – T)I = I(r)G=GT=T.The only difference from our earlier analysis is that we no longer suppose that real GDP isdetermined on the supply side, since that is true only in the long run. But this is far from aninnocuous change. Previously, given that Y was fixed at Y, we were able to use this model todetermine the equilibrium interest rate in the economy. Now, there are different combinationsof the interest rate and the level of GDP that are consistent with equilibrium. Writingequilibrium in terms of the loans market givesS(Y) = I(r).Recall from the analysis of the classical model thatS p = Y – T – CS g = T – G⇒ S = Y – C(Y – T) – G.Now, consider how changes in GDP change saving. An increase in GDP (∆Y), from thisequation, raises saving directly by ∆Y and lowers it by an amount equal to MPC × ∆Y. Thus,the total change in saving is∆S = (1 – MPC)∆Y > 0.258 | CHAPTER 11Aggregate Demand I: Building the IS–LM ModelSo an increase in income increases total saving, other things being equal. We know, therefore,that it decreases the interest rate. Thus, we draw the conclusion that, for equilibrium to existin the goods market, higher levels of GDP must be associated with lower interest rates.We can tell the same story another way. Suppose that interest rates increase. This decreases the level of investment. In response to this fall in investment demand, firms produceless output. Now recall the circular flow. A decrease in output leads firms to employ fewerworkers and to use their capital less intensively; hence, income goes down. In response to thedecreased income, households consume less. This effect on consumption reinforces the initialeffect, so we get the same conclusion—higher interest rates are associated with lower outputand vice versa.We summarize this reasoning in terms of the IS curve. This is defined as {r, Y} combinations such that the goods market (equivalently, the loanable-funds market) is inequilibrium. The previous reasoning tells us that it slopes downward.The Keynesian CrossA common means of deriving the IS curve, based on the second explanation above, is knownas the Keynesian cross. The Keynesian cross also gives us insights into how fiscal policyaffects the economy. The key idea of this model is that planned expenditure may differ fromactual expenditure if firms sell less or more than they anticipated and so build up or run downtheir inventory. Planned expenditure is simply the amount that households, firms, and thegovernment intend to spend on goods and services. We write it asPE = C + I + G.Suppose, for the moment, that the interest rate is fixed at r so that the level of plannedinvestment is exogenous [I(r)]. Then, we can write planned expenditure as()+I r()+G.PE=C Y-T➢Figure 11-2Planned expenditure is thus an increasing function of income.In equilibrium, planned expenditure equals actual expenditure, which, of course, equals GDP:PE = Y.We can graph both planned and actual expenditure against income to get the Keynesian crossdiagram.➢Figure 11-3The adjustment to equilibrium takes the form of changes in inventory. If actual expenditure exceeds planned expenditure, this means that firms produced too much.Remember that inventory investment is counted as expenditure; it is as if firms sell the goodsto themselves. Actual expenditure exceeds planned expenditure when firms accumulateinventory. In this circumstance, firms would cut back on their production, lessening theirinventory accumulation and so decreasing actual expenditure. An analogous situation occursif planned expenditure exceeds actual expenditure. In this case, firms are unintentionallygetting rid of inventory, giving them an incentive to increase production. In practice, we thinkthat this adjustment takes place rapidly, so we focus upon the situation where the economy isin equilibrium.➢Figure 11-4What happens if planned spending increases? For example, suppose that government spending increases. That would induce firms to produce more output. Recalling the circularLecture Notes | 257 flow, this implies that workers and owners of firms obtain more income and so increase their consumption. Planned spending and, ultimately, output go up by more than the original increase➢Figure 11-5in government spending. To put it another way, government spending has a multiplier effect on output through the government-purchases multiplier.What is the economics behind this process? The answer can be found in the circular flow of income. An increase in government purchases (say, ∆G = $1 billion) directly increases GDP by the same amount. Firms hire workers to produce this extra output, so wages and profits, hence income, rise by an equal amount. This induces extra consumption equal to MPC × ∆G (for example, if MPC = 0.75, then consumption increases by $750 million). Thus, expenditures, which originally rose by ∆G, now rise by (1 + MPC)∆G = $1.75 billion.The story does not stop here. Since this additional consumption again increases income, consumption rises even further, by an amount equal to MPC × (MPC × ∆G). In this example, consumption increases by an additional $563 million. And the process continues. The ultimate increase in GDP is given by∆Y = (1 + MPC + MPC2 + MPC3 + . . .)∆G= [1/(1 – MPC)]∆G⇒ ∆Y/∆G = 1/(1 – MPC).The multiplier has a couple of interpretations—one benign, the other less so. From one perspective, we can think about the multiplier as telling us that we have the power to use fiscal policy to affect the economy dramatically in the short run. This suggests that fiscal policy might be a potent tool for stimulating the economy in a recession, for example. But another implication is that fluctuations in spending have magnified effects on GDP. The reasoning that we have just considered would apply equally well if the initial change were an exogenous shock to planned investment or consumption. Keynes suggested that fluctuations in GDP might be caused by initial fluctuations in investment due to the capricious behavior of investors (which he called their animal spirits).➢Figure 11-6Just as increases in spending increase GDP, so do cuts in taxes. The mechanism is similar: tax cuts increase disposable income and hence stimulate consumption. The only difference comes from the fact that a tax cut of ∆T increases consumption initially by MPC × ∆T. Thus, the tax multiplier equals the government-purchases multiplier multiplied by –MPC:∆Y/∆T = – MPC/(1 – MPC).Case Study: Cutting Taxes to Stimulate the Economy:The Kennedy and Bush Tax CutsCuts in personal and corporate income taxes were used by President Kennedy to stimulate the economy in 1964, on the advice of his Council of Economic Advisers. The economy grew rapidly in the wake of these cuts. Keynesian economists think that this experience supports the idea, embodied in the Keynesian cross model, that tax cuts stimulate aggregate demand and boost the economy. Tax cuts may also increase people’s incentive to supply labor, thus increasing the aggregate supply of goods and services.When George W. Bush proposed tax cuts during his campaign in 2000, the economy was near full employment, and some economists were concerned that a tax cut might raise aggregate demand and spur inflation. But candidate Bush’s advisers argued that reductions in marginal tax rates would increase labor supply and thus increase aggregate supply. After the election, as the economy began to weaken, President Bush’s advisers began touting the tax-cut proposal as a way to stimulate spending and thus increase aggregate demand. The tax cut258 | CHAPTER 11Aggregate Demand I: Building the IS–LM Modelthat finally passed in May 2001 included a “rebate” mailed to taxpayers that was intended tospeed up the stimulus to the economy. A subsequent tax cut in 2003 further stimulated theeconomy, turning a relatively weak recovery into a more robust one.Case Study:Increasing Government Purchases to Stimulate the Economy:The Obama StimulusPresident Obama’s stimulus plan for the economy was passed by Congress and signed intolaw in February 2009. The plan, which totaled nearly $800 billion in spending and tax cuts,represented a classic Keynesian-style response to the worsening recession. Economistsdebated the plan, in particular the relatively heavier emphasis on spending as opposed to taxreductions. In justifying the plan’s larger spending component, Obama administrationeconomists argued that the multiplier for government purchases was about 50 percent greaterthan the multiplier for tax cuts. Some economists criticized the plan as being too small, giventhe magnitude of the recession. They argued that the stimulus spending needed to be muchlarger if it were to offset the recession. Other economists, however, doubted whether moneyallocated for spending on infrastructure would have immediate effects on the economy. Theywere concerned that much of the spending would not occur in the first year and that therecession could well be over by then. These economists generally favored greater emphasison tax cuts that might have more immediate effects on households’ income and thus spending.The economy finally did recover from the recession, but much more slowly than the Obamaadministration had forecast. Whether this represented a failure of the stimulus policy orsimply a recession more severe than economists initially believed remains a question ofdebate.Case Study: Using Regional Data to Estimate MultipliersKeynesian theory suggests that changes in taxes and government spending have importanteffects on income and output for the economy. But in practice, measuring the effects on theeconomy from fiscal policy is difficult because there is no simple way to control for otherevents that are also affecting the economy. For example, fiscal stimulus is often adopted inresponse to a weak economy, so it is difficult to separate the effects of stimulus from theeffects of prolonged fallout from a recession. Recent studies have attempted to address thisproblem by using data from states or provinces within a country. Some regional variation ingovernment spending is unrelated to other events affecting regional economies, allowing theeconomic impact of government spending to be more precisely measured.One study considers variation in U.S. federal defense spending at the state level and computes its impact on state GDP. Another study considers variation in public investmentspending in Italian provinces as a result of crackdowns on organized crime (investment fallstemporarily following crackdowns) and assesses the effect on province-level GDP. Bothstudies find government spending multipliers of about 1.5.These estimates may overstate the true size of national government spending multipliers because this spending is financed with taxes at the national, not regional, level, and such taxeswould dampen the stimulus effects. Also, the national multiplier may be smaller becausecentral banks respond to national rather than regional conditions and may offset some of thestimulus from government spending by raising interest rates. One feature, however, thatwould imply a larger national multiplier is leakage of spending into imports of goods andservices. For a state or region, imports from other states and regions are a much higherpercentage of GDP than are imports from abroad for a nation as a whole. Leakage into importsreduces the marginal propensity to spend on regionally produced goods and services andthereby reduces the size of the multiplier.Lecture Notes | 257The Interest Rate, Investment, and the IS Curve➢Figure 11-7The transition from the Keynesian cross model to the IS curve is achieved by noting that planned investment changes if the real interest rate changes. The Keynesian cross analysis tells us that changes in planned investment change GDP. For example, if interest rates increase, planned investment falls, and so does output. Thus, higher levels of the interest rate are associated with lower levels of output.How Fiscal Policy Shifts the IS Curve➢Figure 11-8The position of the IS curve depends on fiscal-policy variables. Increases in government spending or decreases in taxes increase the equilibrium level of output at any given interest rate. Thus they are associated with outward shifts in the IS curve.11-2 The Money Market and the LM CurveThe Theory of Liquidity PreferenceTo understand the determination of interest rates, we turn to the money market. Again, our building blocks are familiar from the classical model. Our starting point is the condition for equilibrium in the money market:M/P = L(i, Y).According to this equation, the demand for real balances equals the real supply of money M/P. The demand for real balances, as explained in Chapter 4, depends on the level of GDP and the nominal interest rate; this is known as the theory of liquidity preference. The real supply of money depends on the nominal money supply, which is an exogenous policy variable, and the price level, which is also taken to be exogenous in the IS–LM model.Recall from the Fisher equation that the nominal interest rate equals the real interest rate plus the expected inflation rate. If expected inflation is zero, i = r. For simplicity, we suppose for the moment that this is the case, so we can writeM/P = L(r, Y).We reintroduce expected inflation in Chapter 12.➢Figure 11-9Just as the IS curve gives us {r, Y} combinations consistent with equilibrium in the goods market, the LM curve gives us {r, Y} combinations consistent with equilibrium in the money market. To see how this works, consider a diagram of the market for money. Notice that the demand for money is a function of r and Y. Increases in r decrease the demand for money; increases in Y increase the demand for money. The supply of and demand for money determine the equilibrium interest rate. Changes in the money supply therefore affect the equilibrium interest rate.Case Study: Does a Monetary Tightening Raise or Lower Interest Rates?➢Figure 11-10In the early 1980s, Paul V olcker, the chair of the Federal Reserve, slowed the rate of money growth in a successful attempt to decrease inflation. The Fisher equation teaches us that lower258 | CHAPTER 11Aggregate Demand I: Building the IS–LM Modelinflation tends to reduce nominal interest rates in the long run. Our analysis of the moneymarket reveals that when prices are sticky, anti-inflationary monetary policy reduces realmoney balances and increases interest rates in the short run. Both effects are visible in the1980s data.Income, Money Demand, and the LM Curve➢Figure 11-11The basic analysis of the LM curve is now straightforward. Higher GDP raises the demandfor money. If the real supply of money is fixed, then interest rates must rise to bring thedemand for money back in line with the supply. So higher GDP is associated with higherinterest rates when the money market is in equilibrium. The LM curve slopes upward.How Monetary Policy Shifts the LM Curve➢Figure 11-12The position of the LM curve depends on the real money supply. An increase in the real moneysupply for a given level of GDP implies lower interest rates. An increase in the money supplythus shifts the LM curve downward and conversely.11-3 Conclusion: The Short-Run Equilibrium➢Figure 11-13➢Figure 11-14➢Supplement 11-1, “The Key Features of the IS–LM Model”➢Supplement 11-2, “Mr. Keynes and the Classics: The Art of Modeling”➢Supplement 11-3, “The IS–LM Model: A Critical Evaluation”Finally, we can put together the IS and LM curves and find the one {r, Y} combination that isconsistent with equilibrium in both the goods and the money markets. Since points on the IScurve are consistent with equilibrium in the goods market and points on the LM curve areconsistent with equilibrium in the money market, the point where the two curves intersectgives the one combination of the real interest rate and GDP for which both markets are inequilibrium.If used carefully, IS–LM is a simple but powerful model for understanding the short-run behavior of the economy; it is a model that helps many economists answer macroeconomicquestions. We make much use of it from here on.LECTURE SUPPLEMENT11-1 The Key Features of the IS–LM ModelThe IS–LM analysis is simply a more detailed look at what lies behind aggregate demand. It decomposes aggregate demand into its two constituent markets: money and goods. The money market is summarized in the LM curve, the goods market in the IS curve. The advantages of the analysis are that it allows us to look at the two markets separately, to examine the determination of interest rates, and to distinguish clearly between fiscal and monetary policy. It is a very useful tool for short-run analysis of the economy.The key things to understand about the IS–LM analysis are as follows:1.The position of the LM curve depends on M/P.2.Expansionary monetary policy shifts the LM curve out.3.Increases in the price level shift the LM curve in.4.Exogenous shocks to money demand shift the LM curve.5.The position of the IS curve depends on G and T.6.Expansionary fiscal policy shifts the IS curve out.7.Exogenous spending shocks shift the IS curve.8.The slopes of the IS and LM curves depend on various parameters that indicate the sensitivityof money demand, investment demand, and consumption demand to income and interestrates.9.Expansionary fiscal policy works by directly increasing spending but leads to short-runcrowding out because increased money demand pushes up interest rates and discouragesinvestment.10.Expansionary monetary policy works by pushing down interest rates and thus encouraginginvestment spending.11.The adjustment of the economy to long-run equilibrium operates through changes in theprice level, leading to changes in M/P, and hence in interest rates and investment. In the IS–LM diagram, long-run adjustment entails shifts in the LM curve.267ADDITIONAL CASE STUDY11-2 Mr. Keynes and the Classics: The Art of Modeling Keynesian economics was born with the publication of The General Theory of Employment, Interestand Money, by John Maynard Keynes. In terms of its impact on the discipline, this was surely one ofthe most important books in the history of economics. Yet for the modern student of economics, itmakes for difficult reading. Apparently, this was also true for contemporary readers: “It will be admittedby the least charitable reader that the entertainment value of Mr. Keynes’s General Theory ofEmployment is considerably enhanced by it satiric aspect. But it is also clear that many readers havebeen left very bewildered by this Dunciad.”1One reason why Keynes’s work had such impact was that the Nobel prize–winning economist John Hicks found a way to translate Keynes’s ideas into a simple and easily understood diagram: the IS–LMmodel. If Keynes’s book was one of the most influential in the history of economics, then Hicks musttake much of the credit. Compare, for example, the following:Now if the investment-demand schedule shifts,…income will, in general, shift also. But theabove [saving/investment] diagram does not contain enough data to tell us what its newvalue will be; and, therefore, not knowing which is the appropriate [saving] curve, we donot know at what point the new investment-demand schedule will cut it. If, however, weintroduce the state of liquidity-preference and the quantity of money and these betweenthem tell us that the rate of interest is r2, then the whole position becomesdeterminate….Thus the [investment] curve and the [saving] curves tell us nothing about therate of interest. They only tell us what income will be, if from some other source we can saywhat the rate of interest is.2The curve IS can therefore be drawn showing the relation between income and interestwhich must be maintained in order to make saving equal to investment.3It is a tribute to Hicks’s modeling skills that IS–LM analysis survives to this day in textbooks and in journal articles. It has become such a standard tool that writers usually do not even bother to citeHicks when using it. And whereas some criticize the model and others claim that it misrepresentsKeynes’s work, it seems likely to endure as a useful tool for short-run macroeconomic analysis. Hickscannot have suspected his understatement when he wrote that “in order to elucidate the relation betweenMr. Keynes and the ‘Classics,’ we have invented a little apparatus. It does not appear that we haveexhausted the uses of that apparatus.”41 J.R. Hicks, “Mr. Keynes and the Classics,” Econometrica 5, no.2 (April 1937), reprinted in J. Hicks, Critical Essays in Monetary Theory (Oxford: Oxford University Press, 1967), 126–42.2 J.M. Keynes, The General Theory of Employment, Interest and Money (London: Macmillan, 1936), 181.3 Hicks, Critical Essays in Monetary Theory, 135.4 Ibid., 135.264ADVANCED TOPIC11-3 The IS–LM Model: A Critical EvaluationThe IS–LM model occupies a curious position in modern macroeconomics. It has been at the heart ofmuch macroeconomic theory and policy from its invention in 1936 to the present. Professionalmacroeconomists in business, government, and academia utilize the model to help them understand theworld. Yet, at the same time, many professional economists— particularly academics—have becomeincreasingly skeptical of its usefulness. Critics of IS–LM argue that the model is flawed because it isinherently static, lacks microeconomic underpinnings, and does not provide an adequate treatment ofexpectations. One such critic, Robert King, concludes that “the IS–LM model has no greater prospectof being a viable analytical vehicle for macroeconomics in the 1990s than the Ford Pinto has of beinga sporty, reliable car for the 1990s.”1The IS–LM model is static because it makes no attempt to explain the behavior of the economy over time. Rather, the model yields values of certain endogenous variables at a point in time, given thevalues of other exogenously specified variables. In the simple IS–LM model, there is no attempt toanalyze how the endogenous variables evolve over time, despite that many of the underlyingrelationships in the model are meant to capture decisions with an explicit time dimension. For example,the consumption function is meant to reflect the consumption–saving choices of households, and theinvestment function is based on firms’ decisions to undertake current expenditures in the anticipationof future benefits.One way to introduce dynamics into an IS–LM model is to make price adjustment endogenous.Much Keynesian modeling in the 1960s and 1970s took this approach. The idea was to explain theadjustment of wages and prices over time based on supply and demand in the labor and goods markets.For example, if output is above its natural rate, then unemployment will be below its natural rate. Strongdemand for goods and labor would then cause wages and prices to rise. In this setting, the IS–LM modelexplains output at a point in time, given the price level, while the specification of price adjustmentexplains how prices change, given past values of output. Such an approach will be successful only ifwe can adequately capture the complexities of price and wage adjustment by simple, ad hoc price andwage equations. And that, in turn, brings us back to the question of microeconomic underpinnings.The search for solid microeconomic foundations for the IS–LM model has been going on since the early days of Keynesian economics. Researchers in the 1950s and 1960s provided microeconomicjustification for the consumption function, the investment function, and the money demand functionthat are used in the IS–LM model. (Much of this work is explained in Part V of the textbook.) Morerecently, researchers have analyzed how firms set prices and wages and have thus developed muchbetter microfoundations for wage and price stickiness (see Chapter 14 of the textbook). As this workprogressed, however, it became evident that expectations have a critical influence on the economy: anindividual’s decision on how much to consume and how much to save depends on what he expects hisfuture income to be; a firm’s investment decisions depend on expectations of future sales. Likewise,the price- and wage-setting decisions of firms and workers depend on expectations of future inflationand other variables.Because the IS–LM model is static, anticipations of future events cannot be handled endogenously.Rather, the IS–LM model treats shifts in expectations as exogenous. If firms anticipate strong demandand so increase investment, or if rising consumer confidence leads to increased consumption, thisshows up in the IS–LM model as an exogenous outward shift of the IS curve. If expected inflationincreases, the nominal interest rate will be higher for any given value of the real rate and money demandwill fall. This shows up in the IS–LM model as an exogenous outward shift of the LM curve.2 The problem is that expectations might themselves be affected by changes in other exogenous variables. Suppose that the money supply is increased. The basic IS–LM model predicts that the LMcurve will shift out, leading to higher output and lower interest rates. But firms and consumers mighttake the change in the money supply as a signal that the Fed has adopted a more expansionary monetarypolicy. Anticipations of higher demand and higher income might then increase investment andconsumption, shifting the IS curve out and conceivably causing real interest rates to rise. Anticipations1 R. King, “Will the New Keynesian Macroeconomists Resurrect the IS–LM Model?” Journal of Economic Perspectives 7 (Winter 1993): 67–82.2 This assumes that the IS–LM diagram is drawn with the real interest rate on the axis; otherwise, it is the IS curve that shifts.267。
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