Economics Chapter 11 Homework Although the textbook does not spend a lot of time on the

255

CHAPTER 11

Aggregate Demand I: Building the

IS–LM Model

Notes to the Instructor

Chapter Summary

Comments

Presentation of IS–LM is greatly facilitated by the fact that students have seen all of the elements

already. This makes it much easier to teach than when it is taught prior to a long–run model. The

amount of time spent on the material in Chapters 11 and 12 is partly a matter of taste. It probably

requires three lectures at a minimum to present basic IS–LM (omitting detailed discussion of the

Great Depression from Chapter 12), although some instructors might 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 with the

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 𝑆𝑌=𝐼(𝑟), where 𝑌 is

exogenous; the IS curve is simply given by S(Y) = I(r), where income is now an endogenous

variable. The Keynesian cross can then be presented as a special case.

Use of the Web Site

The 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–market equilibrium

Use of the Dismal Scientist Web Site

Use the Dismal Scientist Web site to download annual data for the U.S. consumer price index

and the 1–year and 10–year Treasury yields over the last 20 years. Compute the real interest rate

for each of the Treasury yields by subtracting CPI inflation from each yield. Discuss how real

interest rates change with inflation in the short run compared to what you would expect over

longer periods of time.

256 | CHAPTER 11 Aggregate Demand I: Building the IS-LM Model

Chapter Supplements

This chapter includes the following supplements:

11-2 Mr. Keynes and the Classics: The Art of Modeling

11-4 Additional Readings

Lecture Notes | 257

Lecture Notes

Introduction

We now have a basic idea of how the economy functions in the short run. Because in the short

run prices are not completely flexible, changes in aggregate demand affect output, not just

prices. To develop this short–run theory of the economy, we must now consider aggregate

demand and supply in more detail. This chapter and the next present a more detailed analysis of

11–1 The Goods Market and the IS Curve

The building blocks of the IS–LM model are familiar from earlier analysis. The IS side of the

model summarizes equilibrium in the goods market and is based partly on the classical model of

Chapter 3; the LM side of the model summarizes equilibrium in the money market and so is

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 that

C = C(Y – T)

I = I(r)

𝐺=!𝐺

𝑇=!𝑇.

The only difference from our earlier analysis is that we no longer suppose that real GDP is

determined on the supply side, since that is true only in the long run. But this is far from an

innocuous change. Previously, given that Y was fixed at Y, we were able to use this model to

determine the equilibrium interest rate in the economy. Now, there are different combinations of

the interest rate and the level of GDP that are consistent with equilibrium. Writing equilibrium in

terms of the loans market gives

S(Y) = I(r).

Recall from the analysis of the classical model that

So 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 exist in

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 produce

less output. Now recall the circular flow. A decrease in output leads firms to employ fewer

258 | CHAPTER 11 Aggregate Demand I: Building the IS-LM Model

workers and to use their capital less intensively; hence, income goes down. In response to the

decreased income, households consume less. This effect on consumption reinforces the initial

effect, so we get the same conclusion—higher interest rates are associated with lower output,

and vice versa.

The Keynesian Cross

A common means of deriving the IS curve, based on the second explanation above, is known as

the Keynesian cross. The Keynesian cross also gives us insights into how fiscal policy affects

the economy. The key idea of this model is that planned expenditure may differ from actual

expenditure if firms sell less or more than they anticipated and so build up or run down their

inventory. Planned expenditure is simply the amount that households, firms, and the government

intend to spend on goods and services. We write it as

Planned 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 cross

diagram.

The 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 goods to themselves.

Actual expenditure exceeds planned expenditure when firms accumulate inventory. In this

circumstance, firms would cut back on their production, lessening their inventory accumulation

and so decreasing actual expenditure. An analogous situation occurs if planned expenditure

exceeds actual expenditure. In this case, firms are unintentionally getting rid of inventory, giving

them an incentive to increase production. In practice, we think that this adjustment takes place

rapidly, so we focus upon the situation where the economy is in equilibrium.

What happens if planned spending increases? For example, suppose that government

spending increases. That would induce firms to produce more output. Recalling the circular

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

in 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

!Figure 11-3

!Figure 11-4

!Figure 11-5

Lecture Notes | 259

⇒ ∆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

Case Study: Cutting Taxes to Stimulate the Economy:

The Kennedy and Bush Tax Cuts

Cuts 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.

Case Study: Increasing Government Purchases to Stimulate the

Economy: The Obama Stimulus

President Obama’s stimulus plan for the economy was passed by Congress and signed into law

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. Economists debated

the plan, in particular the relatively heavier emphasis on spending as opposed to tax reductions.

In justifying the plan’s larger spending component, Obama administration economists argued

that the multiplier for government purchases was about 50 percent greater than the multiplier for

260 | CHAPTER 11 Aggregate Demand I: Building the IS-LM Model

Case Study: Using Regional Data to Estimate Multipliers

Keynesian theory suggests that changes in taxes and government spending have important

effects on income and output for the economy. But in practice, measuring the effects on the

economy from fiscal policy is difficult because there is no simple way to control for other events

that are also affecting the economy. For example, fiscal stimulus is often adopted in response to

a weak economy, so it is difficult to separate the effects of stimulus from the effects of

prolonged fallout from a recession. Recent studies have attempted to address this problem by

using data from states or provinces within a country. Some regional variation in government

spending is unrelated to other events affecting regional economies, allowing the economic

The Interest Rate, Investment, and the IS Curve

The 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

The 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 Curve

The Theory of Liquidity Preference

To 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).

!Figure 11-7

!Figure 11-8

Lecture Notes | 261

M/P = L(r, Y).

We reintroduce expected inflation in Chapter 11.

Just 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 depends on 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. Note also that changes in the money supply therefore affect the

equilibrium interest rate.

Case Study: Does a Monetary Tightening Raise or Lower

Interest Rates?

In the early 1980s, Paul Volcker, the chairman of the Federal Reserve, slowed the rate of money

growth in a successful attempt to decrease inflation. The Fisher equation teaches us that lower

Income, Money Demand, and the LM Curve

The basic analysis of the LM curve is now straightforward. Higher GDP raises the demand for

money. If the real supply of money is fixed, then interest rates must rise to bring the demand for

money back in line with the supply. So higher GDP is associated with higher interest rates when

the money market is in equilibrium. The LM curve slopes upward.

How Monetary Policy Shifts the LM Curve

The position of the LM curve depends on the real money supply. An increase in the real money

supply for a given level of GDP implies lower interest rates. An increase in the money supply

thus shifts the LM curve downward and conversely.

11–3 Conclusion: The Short–Run Equilibrium

Finally, we can put the IS and LM curves together and find the one {r, Y} combination that is

consistent with equilibrium in both the goods and the money markets. Since points on the IS

!

Figure 11-9

!

Figure 11-10

!

Figure 11-11

!

Figure 11-12

!

Figure 11-13

!Figure 11–14

LECTURE SUPPLEMENT

11–1 The Key Features of the IS–LM Model

The IS–LM analysis is simply a more detailed look at what lies behind aggregate demand. It decomposes

1. The position of the LM curve depends on M/P.

3. Increases in the price level shift the LM curve in.

5. The position of the IS curve depends on G and T.

7. Exogenous spending shocks shift the IS curve.

9. Expansionary fiscal policy works by directly increasing spending but leads to short–run

10. Expansionary monetary policy works by pushing down interest rates and thus encouraging

investment spending.

11. The adjustment of the economy to long–run equilibrium operates through changes in the price

level, leading to changes in M/P, and hence in interest rates and investment. In the IS–LM

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ADDITIONAL CASE STUDY

11–2 Mr. Keynes and the Classics: The Art of Modeling

Keynesian economics was born with the publication of The General Theory of Employment, Interest and

Money, by John Maynard Keynes. In terms of its impact on the discipline, this was surely one of the most

important books in the history of economics. Yet for the modern student of economics, it makes for

difficult reading. Apparently, this was also true for contemporary readers: “It will be admitted by the least

what point the new investment–demand schedule will cut it. If, however, we introduce the state

of liquidity–preference and the quantity of money and these between them tell us that the rate

of interest is r2, then the whole position becomes determinate…. Thus the [investment] curve

and the [saving] curves tell us nothing about the rate of interest. They only tell us what income

will be, if from some other source we can say what the rate of interest is.2

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 Hicks, Critical Essays in Monetary Theory, 135.

264

ADVANCED TOPIC

11–3 The IS–LM Model: A Critical Evaluation

The IS–LM model occupies a curious position in modern macroeconomics. It has been at the heart of much

macroeconomic theory and policy from its invention in 1936 to the present. Professional macroeconomists

in business, government, and academia utilize the model to help them understand the world. Yet, at the

same time, many professional economists— particularly academics—have become increasingly skeptical

of its usefulness. Critics of IS–LM argue that the model is flawed because it is inherently static, lacks

microeconomic underpinnings, and does not provide an adequate treatment of expectations. One such

critic, Robert King, concludes that “the IS–LM model has no greater prospect of being a viable analytical

vehicle for macroeconomics in the 1990s than the Ford Pinto has of being a sporty, reliable car for the

1990s.”1

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 the adjustment 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. Strong demand for

goods and labor would then cause wages and prices to rise. In this setting, the IS–LM model explains

output at a point in time, given the price level, while the specification of price adjustment explains how

prices change, given past values of output. Such an approach will be successful only if we can adequately

capture the complexities of price and wage adjustment by simple, ad hoc price and wage 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 microeconomic

justification for the consumption function, the investment function, and the money demand function that

are used in the IS–LM model. (Much of this work is explained in Part V of the textbook.) More recently,

265

but raising nominal rates. Evidently, the conclusions that we draw are sensitive to our assumptions about

expectations, and the basic IS–LM analysis will be correct only if the expectational effects are small.3

Given this deficiency of the IS–LM model, why do so many still find it a helpful way to think about

the economy? The answer is, perhaps, that it still provides the easiest way to understand the determination

of aggregate demand and the transmission of monetary and fiscal policies in an economy characterized by

significant price stickiness. Unfortunately, macroeconomists have not yet derived simple and tractable

models that both provide a satisfactory treatment of expectations and take into account wage and price

LECTURE SUPPLEMENT

11–4 Additional Readings

John Maynard Keynes’s General Theory is a true classic of economics, although it is a difficult and often

confusing work. Some economists believe that Hicks’s IS–LM model does not really do justice to

Keynes’s ideas, particularly with regard to Keynes’s views on expectations (see Chapter 12 of General

Theory) and wage–price adjustment (see Chapter 19 of General Theory). Readers who wish to make a