Chapter 21

The IS Curve

Money and Banking

Deokwoo Nam
Department of Economics and Finance
Hanyang University

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1. INTRODUCTION

1 Introduction

During the Great Depression of the 1930s, aggregate output fell precipitously by 30%.
– To understand why such a contraction in economic activity occur, economists make use of the concept
of aggregate demand, the total amount of output demanded in the economy.
This concept was developed by John Maynard Keynes: he argued that "short-run" changes in
aggregate output, such as the decline during the Great Depression, were determined by changes
in aggregate demand.
The concept of aggregate demand is a central element in the aggregate demand and aggregate
supply (AD-AS) model that is the basic macroeconomic model for explaining "short-run" ‡uctuations
in aggregate output.
In this chapter, we develop the …rst building block to understand aggregate demand, the IS curve, which
describe the relationship between real interest rates and aggregate output when the goods market
(i.e., the market for goods and services) is in equilibrium.
1. We …rst derive the IS curve and then go on to explain what factors cause the IS curve to shift.
2. With our understanding of the IS curve, we will examine why ‡uctuations in economic activity occur and
how the …scal stimulus package of 2009 a¤ected the economy.
Note that in later chapters, we make use of the IS curve to understand the role of monetary policy in economic
‡uctuations.

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2. AGGREGATE DEMAND

2 Aggregate Demand

2.1 Planned Expenditure and Aggregate Demand

We start our analysis by discussing the concept of "planned expenditure."

– Planned expenditure is the total amount of spending on domestically produced goods and services that
households, businesses, the government, and foreigners "want to" make.
In contrast, actual expenditure is the amount that they actually do spend, which equals the total
amount of output produced in the economy.
Note that all the analysis in this chapter is for expenditure in real terms, that is, in terms of actual physical
amounts of goods and services.
The Keynesian view is that aggregate demand, the total amount of output demanded in the economy, is the
same as planned expenditure.
– Thus, planned expenditure— and hence aggregate demand— explains the level of aggregate output when
the goods market is in equilibrium, that is, when aggregate demand for goods and services (i.e., planned
expenditure) is equal to the actual amount of goods and services produced.
The total amount of aggregate demand (planned expenditure) is the sum of four types of spending:
1. Consumption expenditure (C ): the total demand for consumer goods and services (e.g., hamburgers,
visits to the doctor, etc.).
2. Planned investment spending (I ): the total planned spending by business on "new" physical capital
(e.g., machines, factories, etc.) plus planned spending on "new" homes.
3. Government purchases (G): the spending by all levels of government on goods and services (e.g.,
government workers, red tape, etc.), not including transfer payments.
4. Net exports (N X ): the net foreign spending on domestic goods and services, equal to exports minus
imports.

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2. AGGREGATE DEMAND

Therefore, the total aggregate demand Y ad is represented as follows:

Y ad = C + I + G + N X (2.1)

2.2 The Components of Aggregate Demand

2.2.1 Consumption Expenditure

Keynes reasoned that consumption expenditure is related to disposable income, the total income available
for spending that is equal to aggregate output minus taxes:
YD = Y T

Consumption function is expressed as follows:

C = C + mpc YD = C + mpc (Y T) (2.2)

1. C represents autonomous consumption expenditure, the amount of consumption expenditure that is

"exogenous" (independent of variables in the model, such as disposable income).
– Autonomous consumption is related to consumers’optimism about their future income and household
wealth, which induce consumers to increase spending.
2. mpc stands for the marginal propensity to consume and re‡ects the change in consumption expenditure
that results from an additional dollar of disposable income.
– 0 < mpc < 1
– If a $1 increase in YD leads to an increase in C of $0:6, then mpc = 0:6.

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2. AGGREGATE DEMAND

2.2.2 Planned Investment Spending

There are "two" types of investment: …xed and inventory.

1. Fixed investment is planned spending by …rms on equipment (machines) and structures (factories) and
planned spending on new residential housing.
– It is always planned.
2. Inventory investment is spending by …rms on additional holdings of raw materials, parts, and …nished
goods, calculated as the change in holdings of these items in a given time period, say, a year.
– Suppose Ford Motor Company has 100; 000 cars sitting in its factor lots on Dec. 31, 2013, ready to
be shipped to dealers. If each car has a wholesale price of $20; 000, Ford has an inventory worth $2
billion.
If by Dec. 31, 2014, its inventory of cars has risen to 150; 000, with a value of $3 billion, then its
inventory investment in 2014 is $1 billion, the change in the level of its inventory over the course of
the year ($3 billion minus $2 billion).
– An important feature of inventory investment is that some inventory investment can be UN-
PLANNED.
For example, suppose the reason why Ford …nds itself with an additional $1 billion of cars on Dec.
31, 2014 is that $1 billion less of its cars were sold in 2014 than expected— this $1 billion of inventory
investment in 2014 was "unplanned."
In this situation, Ford is producing more cars than it can sell, and it will cut production in order to
keep from accumulating unsold cars.
– Adjusting production to eliminate "unplanned" investment plays a key role in the determination of
aggregate output, as we shall see.
Thus, "planned investment spending" is equal to (planned) …xed investment plus the amount of
inventory investment "planned" by …rms.

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2. AGGREGATE DEMAND

Keynes considered the level of the "real" cost of borrowing rc (e.g., the real interest rate denoted by
r is its main part) to be a key determinant of "planned" investment spending.

– Businesses make investments in physical capital (machines and factories) as long as they expect to earn
more from the physical capital than the real interest cost of a loan to …nance the investment.
For example, when the real interest rate on borrowing is high, say, at 10%, fewer investments in
physical capital will earn more than the 10% cost of borrowed funds, so planned investment spending
will be low.
Keynes also believed that planned investment spending is heavily in‡uenced by business expectations about
the future. Thus, he posited a component of planned investment spending called autonomous investment
I that is completely exogenous (and so is unexplained by variables in the model, such as output or interest
rates).
– Businesses that are optimistic about future pro…t opportunities are willing to spend more.
Note that Keynes believed that changes in "autonomous spending" are dominated by these unstable
exogenous ‡uctuations in planned investment spending, which are in‡uenced by emotional waves of
optimism and pessimism— factors he labeled "animal spirits."
According to the above-mentioned reasonings, investment function is expressed as follows:
I=I d rc (2.3)

1. I represents autonomous investment.

2. d is a parameter re‡ecting how responsive investment is to the real cost of borrowing rc .
3. As we learned in Chapter 9, the real cost of borrowing rc re‡ects not only the real interest rate on
default-free debt instrument r, but also …nancial frictions f , which are additions to the real costs of
borrowing because of asymmetric information problems in …nancial markets:
rc = r + f (2.4)

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2. AGGREGATE DEMAND

Therefore, the investment function above is rewritten as:

I=I d r+f (2.5)

– In words, planned investment spending is positively related to business optimism, as represented

by autonomous investment, and is negatively related to the real interest rate and …nancial
frictions.

2.2.3 Government Purchases and Taxes

The government a¤ects aggregate demand in two ways: through its purchases and taxes.
1. As seen in Equation (2:1), government purchases add directly to aggregate demand.
– We assume that government purchases are exogenous and are set at a …xed amount G:

G=G (2.6)

2. Higher taxes T reduce disposable income for a given level of income (YD = Y T ) and hence cause
consumption expenditure (C ) to fall.
– To make the model simple, we assume that government taxes are exogenous and are set at a …xed
amount T :

T =T (2.7)

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2. AGGREGATE DEMAND

2.2.4 Net Exports

Net exports can be thought of as being made up of two components: the part of net exports that is a¤ected
by changes in the real interest rate and autonomous net exports.
1. The "real" interest rate in‡uences the amount of net exports through the "exchange rate," the
price of one currency (the dollar) in terms of other currencies (the euro).
– When U.S. real interest rates rise, U.S. dollar assets earn higher returns relative to foreign assets. Then,
people want to hold more dollars, thereby increasing the value of dollars relative to other currencies.
That is, a rise in U.S. real interest rates leads to a higher value of the dollar.
– A rise in the value of the dollar makes U.S. goods more expensive in foreign currencies so U.S. exports
will decrease. At the same time, it makes foreign goods less expensive in dollars so that U.S. imports
will increase. As a result, net exports decrease.
– Therefore, a rise in the real interest rate, which leads to an increase in the value of the dollar
(the home currency), in turn leads to a decline in net exports.
2. The amount of exports is a¤ected by the demand by foreigners for domestic goods, while the amount of
imports is a¤ected by the demand by domestic residents for foreign goods.
– For example, if the Chinese have a poor harvest and want to buy more U.S. wheat, U.S. exports will
rise.
– Thus, autonomous net exports N X , which is the level of net exports that is treated as
exogenous also plays a role in determining net exports.
Therefore, the net export function is written as:

NX = NX x r (2.8)

where x is a parameter that indicates how net exports respond to the real interest rate.

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3. GOODS MARKET EQUILIBRIUM AND THE IS CURVE

3 Goods Market Equilibrium and the IS Curve

Keynes believed that equilibrium would occur in the economy when the total quantity of output Y equals the
total amount of aggregate demand Y ad (planned expenditure):
Y = Y ad (3.1)
– In this equilibrium, producers are able to sell all their output and have no reason to change their production
because there is no unplanned inventory investment.
– This analysis explains why aggregate output goes to a certain level by examining the factors that a¤ect
each component of aggregate demand (planned expenditure).
Solving for Goods Market Equilibrium and Deriving the IS Curve
– With our understanding of what drives the components of aggregate demand, we now can see how
aggregate output Y is determined by using the aggregate demand equation (i.e., Equation (2:1)) to
rewrite the equilibrium condition in the goods market (i.e., Equation (3:1)):
Y = C + I + G + NX (3.2)

Substituting all equations for consumption expenditure, planned investment, net exports, government
purchases, and taxes into the above equation gives:

Y = C + mpc Y T
|{z} +I d r + f + |{z}
G +N|X {zx }r
| {z } | {z }

Collecting terms, we rewrite this equation as follows:

Y = C+I df + G + N X mpcT + mpcY (d + x) r

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3. GOODS MARKET EQUILIBRIUM AND THE IS CURVE

Solving for aggregate output yields the following equation explaining how to determine aggregate output
when the goods market is in equilibrium:
1 d+x
Y = C+I df + G + N X mpcT r (3.3)
1 mpc 1 mpc
| {z } | {z }
1 d+x
Since 0 < mpc < 1, 1 mpc
and 1 mpc
are positive.
1 mpc
The term 1 mpc that multiplies G is known as the expenditure multiplier, while the term 1 mpc
that
multiplies T is called the tax multiplier.
Note that the tax multiplier is smaller in absolute value than the expenditure multiplier because
0 < mpc < 1.

– Equation (3:3) is referred to as the IS curve.

It shows the relationship between aggregate output Y and the real interest rate r.
It is made up of two terms:
1. The …rst term tells us that increases in autonomous consumption, investment, government pur-
chases, or net exports, or a decrease in taxes or …nancial frictions leads to an increase in Y at any
given real interest rate. In other words, the …rst term tells us about shifts in the IS curve.
2. The second term tells us that an increase in the real interest rate results in a decline in Y , which
is a movement along the IS curve. That is, it follows from the second term that the IS curve
is downward-sloping.

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4. UNDERSTANDING THE IS CURVE AND FACTORS THAT SHIFTS THE IS CURVE

4 Understanding the IS curve and Factors that Shifts the IS Curve

4.1 The intuition behind the IS curve.

The IS curve traces out the points at which the goods market is in equilibrium.
– More speci…cally, for each given level of the real interest rate, the IS curve tells us what the aggregate
output must be for the goods market to be in equilibrium.
– As the real interest rate rises, planned investment spending and net exports fall, which in turn lowers
aggregate demand, and thus aggregate output must be lower for it to equal aggregate demand and satisfy
goods market equilibrium. Hence, the IS curve is downward-sloping.
For a numerical example, we set the following values for the exogenous variables and for the parameters in
Equation (3:3):
G = $1:4 trillion; I = $1:2 trillion; G = $3:0 trillion;
T = $3:0 trillion; N X = $1:3 trillion;
f = 1; mpc = 0:6; d = 0:3; x = 0:1

Plugging these values in Equation (3:3) yields the IS curve in Figure 1:

4:8 0:4
Y = Y = {z
r)| 12 }r
0:4 0:4
– At the real interest rate r = 3%, equilibrium aggregate output Y = 12 3 = $9 trillion.

This combination of the real interest rate at equilibrium output is plotted as point A in Figure 1.
– When r = 1%, Y = 12 1 = $11 trillion.

This combination is plotted as point B in Figure 1.

– The line connecting these points is the IS curve, and it is downward-sloping.

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4. UNDERSTANDING THE IS CURVE AND FACTORS THAT SHIFTS THE IS CURVE

Why the economy heads toward the equilibrium:

1. When an "excess supply" of goods exists (the economy is located to the right of the IS curve, e.g.,
point G in Figure 1), actual output is above aggregate demand, and thus …rms are saddled with unsold
inventory. To keep from accumulating unsold goods, …rms will continue cutting toward the equilibrium
level (point A).
2. When an "excess demand" for goods exists (the economy is located to the left of the IS curve, e.g.,
point H in Figure 1), actual output is below aggregate demand, and so …rms want to increase production
because inventories are declining more than they desire, thereby making the economy toward the
equilibrium level (point B).

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4. UNDERSTANDING THE IS CURVE AND FACTORS THAT SHIFTS THE IS CURVE

4.2 Factors that Shift the IS Curve

The IS curve describes equilibrium points in the goods market— the combinations of the real interest rate and
equilibrium aggregate output.
– Thus, the IS curve shifts whenever change occurs in "autonomous" factors (factors independent
of aggregate output and the real interest rate).
In Equation (3:3), we identify six candidates as such autonomous factors that can change aggregate demand
and hence a¤ect the level of equilibrium aggregate output:
1 d+x
Y = C+I +G mpcT + N X df r
1 mpc 1 mpc

1. Changes in government purchases G (e.g., G ")

– An increase in government purchases causes aggregate demand to increase at any given real interest
rate.
– Since aggregate output equals aggregate demand when the goods market is in equilibrium, an increase
in government purchases also causes equilibrium aggregate output to rise, thereby shifting the IS curve
to the right.
2. Changes in taxes T (e.g., T ")
– At any given real interest rate, a rise in taxes decreases disposable income and thus causes aggregate
demand and equilibrium aggregate output to fall, there by shifting the IS curve to the left.
3. Changes in autonomous spending (C , I , N X )
– From Equation (3:3), we see that an increase in any of autonomous consumption, planned investment
spending, and net exports (C , I , N X ) has the same impact on the IS curve as an increase in
government purchases. For this reason, we can lump these three variables together as autonomous
spending.

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4. UNDERSTANDING THE IS CURVE AND FACTORS THAT SHIFTS THE IS CURVE

(a) Autonomous consumption (e.g., C ")

– For example, consumers …nd their wealth has increased when the stock market has boomed or
they have become increasingly optimistic about their future income prospects because a positive
productivity shock to the economy has occurred. Both of these events are autonomous (i.e., not
a¤ected by the level of the real interest rate), and increase consumption.
– The resulting rise in autonomous consumption would raise aggregate demand and equilibrium output
at any given real interest rate, shifting the IS curve to the right.
(b) Autonomous investment spending (e.g., I ")
– For example, companies become more con…dent about investment pro…tability after the stock market
rises, and then raise planned investment spending, which is unrelated to the real interest rate.
– The resulting increase in autonomous investment spending increases aggregate demand and equi-
librium output at any given real interest rate, shifting the IS curve to the right.
(c) Autonomous net exports (e.g., N X ")
– For example, foreign countries has a boom and thus buy more U.S. (home) goods, which is unrelated
to the real interest rate. As a result, net exports increases.
– Such an autonomous increase in net exports increases aggregate demand and equilibrium output at
any given real interest rate, shifting the IS curve to the right.
4. Changes in …nancial frictions (e.g., f ")
– An increase in …nancial frictions, as occurred during the …nancial crisis of 2007-2009, raises the real
cost of borrowing to …rms and hence causes investment spending and aggregate demand to fall.
– As a result, an increase in …nancial frictions decreases equilibrium output at any given real interest
rate, shifting the IS curve to the left.

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4. UNDERSTANDING THE IS CURVE AND FACTORS THAT SHIFTS THE IS CURVE

Summary of factors that shift the IS curve:

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5. APPLICATIONS

5 Applications

5.1 The Vietnam War Buildup, 1964–1969

During the Vietnam War period, the increases an overheating of the economy that even-
in U.S. military expenditure raised government tually resulted in high in‡ation, which
purchases. will be discussed in the coming chapters.
– Usually during the period when government
purchases are rising rapidly, central banks raise
real interest rates to keep the economy from
overheating.
– However, the Vietnam War period is unusual
because the Fed decided to keep real interest
rates constant.
– Thus, beginning in 1965, the increases in mil-
itary spending caused the IS curve to shift to
the right from IS1964 to IS1969 .
Because the Fed decided to keep real inter-
est rates constant at 2% this period, equi-
librium output rose from $3 trillion (in 2009
dollars) in 1964 to $3:8 trillion in 1969.
These increases in government purchases
with the real interest rate constant led to

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5. APPLICATIONS

5.2 The Fiscal Stimulus Package of 2009

In the fall of 2008, the U.S. economy was in crisis. However, without the …scal stimulus, the
To stimulate the economy, the Obama administra- IS curve would likely have shifted further
tion proposed a …scal stimulus package that when to the left, resulting in even more unem-
passed by Congress, included (1) $288 billion in tax ployment.
cuts for households and businesses and (2) $499 bil-
lion in increased federal spending, including transfer
payments.
– As our analysis indicates, these tax cuts and
spending increases would increase aggregate
demand, thereby raising the equilibrium level
of aggregate output at any given real interest
rates and so shifting the IS curve to the right.
– Unfortunately, things did not work out quite as
the Obama administration planned.
Most of the government purchases did
not kick in until after 2010, while
the decline in autonomous consumption
and investment were much larger than
anticipated.
The …scal stimulus was much more than o¤-
set by weak consumption and investment,
with the result that the aggregate demand
ended up contracting rather than rising,
and the IS curve shifted to the left rather
than to the right.

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