Chapter 11
The IS Curve
11.1 Introduction
In this chapter, we learn
• the foundation of the short-run model: the IS curve
• Depicts the inverse relationship between the real
interest rate and short-run output
• how shocks to consumption, investment,
government purchases, or net exports—“aggregate
demand shocks”—can shift the IS curve.
• the life-cycle/permanent-income hypothesis, which
describes consumption behavior.
• that investment is the key channel through which
changes in real interest rates affect GDP in the short
run.
Introduction
The Federal Reserve influences the level of economic
activity in the short run.
• The Fed targets the federal funds rate.
• The Fed is highly correlated with the short-term
nominal interest rate at which people borrow and lend
in financial markets.
The basic story is as follows:
The IS curve
• Illustrates the negative relationship between interest
rates and short-run output
Introducing the IS Curve
11.2 Setting Up the Economy
The national income accounting identity
• Implies that the total resources available to the
economy equal total uses
• One equation and six unknown variables
• where
Setting Up the Economy
Five additional equations to solve the model:
Ac is determined and is
A fixed share of potential output
Same for all the others.
where a bar denotes an exogenous variable
“Ai” exogenous investment
expenditure , fixed
proportional of potential
output b(Rt – r) , r = “mpk” ,
determined in the long run
model therefore given as
seen with the bar. Rt = real
interest rate. If short run
output is 0 the eco is at its
long run potential, then Rt =
r.
Potential Output
Recall:
The definition of potential output
That potential output is smoother than actual GDP
• A shock to actual GDP will leave potential output
unchanged.
That the equation depends on potential output
• Shocks to income are “smoothed” to keep consumption
steady.
• If income is reduced people will try remain consuming
how they previously have consumed, people
consumption is based on their constant income.
The Model—1
Assume 𝐶𝑡, 𝐺𝑡, 𝐼𝑀𝑡, and 𝐸𝑋𝑡 are given exogenously.
Example: 𝐶𝑡 is a constant fraction of potential output given
by
• is empirically estimated to be approximately 2/3
Consumption
• About two out of every three dollars of GDP is attributed
to consumption.
The Model—2
Now we use our national income accounting identity:
and substitute in the four equations that contain only
parameters:
such that
The Investment Equation

Investment is given by:
Marginal Product of Capital (MPK)—1
Amount of additional output the firm can produce by
investing in one more unit of capital
In the long run, MPK = 𝑟, and 𝑟 is
• Exogenous
• Time invariant
Recall the equation for investment:
Multiply each side by
parentheses:
the
through the
Marginal Product of Capital (MPK)—2
Now, we can use the following equation for investment
to understand how the gap between MPK and the real
interest rate helps determine investment:
In the short run, MPK and can be different .
If MPK
• Firms should save and not invest in capital.
• Investment will decline.
If MPK
• Firms should borrow and invest in capital.
• Investment will increase.
The Setup of the Economy for the IS Curve
11.3 Deriving the IS Curve
Begin with the national income accounting identity:
Divide both sides by potential output:
Substitute the five remaining equations into the equation above:
Simplifying yields:
Deriving the IS Curve—1
Recall the definition of short-run output:
Subtract 1 from both sides of the equation:
Deriving the IS Curve—2
After simplifying:
• The gap between the real interest rate and the MPK
is what determines output fluctuations.
• The parameter 𝑎 is called the aggregate demand
shock.
• Note: When
then
and
Case Study: Why Is It Called the "IS Curve"?
Introduced by John R. Hicks
"IS" stands for "investment equals savings."
𝑌 = 𝐶 + 𝐼 + 𝐺 + 𝐸𝑋 − 𝐼𝑀
𝑌 − 𝐶 − 𝐺 + 𝐼𝑀 − 𝐸𝑋 = 𝐼
11.4 Using the IS Curve
A Change in the Interest Rate—1
A change in the real interest rate moves the economy
along the IS curve.
An Increase in the Real Interest Rate to R′
Ricardian equivalence – We maximize
utility and try max for whole life-time ,
with a consistent consumption , people.
Tax now or later doesn’t matter but wont
effect people as they will always try to
consume the same amount regardless of
the tax / rate of inflation.
A Change in the Interest Rate—2
If the sensitivity to the interest rate (𝑏) were higher:
• The IS curve would be flatter.
• A change in the interest rate would be associated
with larger changes in output.
A Change in the Interest Rate—3
Rearranging the IS equation
and solving for 𝑅𝑡:
•
•
•
The slope of the IS curve is negative.
As increases, the slope decreases, and the IS curve
becomes flatter.
An Aggregate Demand Shock—1
Suppose that information technology improvements
create an investment boom.
An Aggregate Demand Shock—2
Real interest rate, R
A
r
B
IS
IS
0
a
~
Output, Y
Case Study: Move Along or Shift?
• A change in R shows up as a movement along the IS
curve.
• The curve tells you the level of short-run output
that corresponds to any interest rate.
• Any other change in the parameters of the short-run
model causes the IS curve to shift.
A Shock to Potential Output
Suppose there is a discovery of a new technology:
↑ Potential output
↑ Actual output
Short-run output unchanged
Recall the definition of short-run output:
If 𝑌𝑡 and increase by the same amount, the ratio
equal to 1 and
.
will be
11.5 Microfoundations of the IS Curve
Microfoundations:
• Explain the microeconomic behavior that establishes
the demands for 𝐶, 𝐼, 𝐺, EX, and 𝐼𝑀
Theories of consumption behavior:
• Individuals prefer to smooth their consumption
spending over time.
• The permanent-income hypothesis: People will base
their consumption on an average of their income over
time rather than on their current income.
• The life-cycle model of consumption suggests that
consumption is based on average lifetime income
rather than on income at any given age.
Consumption
Consider an example: You are given the choice between
Option A and Option B:
Option A:
• Consumption: one piece of cake ($3) every day Monday
through Friday
• Income: $15 on Friday, but you may borrow $3 a day (at
no interest) to consume during the week.
Option B:
• Consumption: five pieces of cake ($15) on Friday
• Income: $15 on Friday
The permanent income hypothesis predicts that people will
choose Option A.
The Life-Cycle Model of Consumption
Empirical Evidence—1
Case study
• Alaska – How do consumers respond to two
different types of income shocks?
• Annual payment from the State of Alaska’s
Permanent Fund (from oil revenues)
• Federal tax refunds
Empirical Evidence—2
The LC/PI hypothesis predicts that consumption
should not change when the Permanent Fund check is
received.
• Hsieh finds that this is the case for the Permanent
Fund.
• But the same is not true in response to a tax refund.
• For every $1 of a tax refund, consumers spend 0.30
cents.
Hsieh concludes that the LC/PI hypothesis applies to
large and anticipated changes.
Multiplier Effects—1
Suppose we conclude that consumption also depends
on temporary changes in income.
• This yields a multiplier effect.
Consumption equals
where is a parameter that determines how much
consumption rises when the economy expands.
We assume is between 0 and 1.
Multiplier Effects—2
Solving for the IS curve, assuming that consumption
also depends on temporary changes in income:
• We begin with the national income accounting
identity and divide both sides by potential GDP.
• Substituting the new consumption equation yields:
Multiplier Effects—3
After simplifying:
Subtract 1 from both sides of the equation:
𝑌𝑡
− 1 = 𝒙𝒀𝒕 + 𝑎𝑖 − 𝑏𝑅𝑡 + 𝑏𝑟 + 𝑎𝑐 + 𝑎𝑔 + 𝑎𝑒𝑥 − 𝑎𝑖𝑚 − 1
𝑌𝑡
Simplifying further:
𝟏
𝑌𝑡 =
𝑎 − 𝑏(𝑅𝑡 − 𝑟)
𝟏−𝒙
Multiplier Effects—4
The new IS curve:
Multiplier Effects—5
Positive
AD
shock
↑ 𝐶𝑡
↑𝑎
↑ 𝑌𝑡
Note: In this case,
short-run output .
, and consumption is affected by changes in
Investment—1
Recall the equation for investment:
There are two main determinants of investment at the
firm level:
• The gap between the real interest rate and the MPK
• Cash flow
Investment—2
How do we calculate the return to capital?
• In a simple model, the return on capital = MPK –
depreciation.
• A richer framework includes:
• Corporate income taxes
• Investment tax credits
• Depreciation allowances
Agency Problems
Investment spending can be financed through:
• Cash flow
• Borrowing (which tends to be more costly)
Borrowing introduces agency problems.
• Asymmetric information between individuals
involved in a transaction
• Two main types of agency problems:
• Adverse selection
• Moral hazard
Government Purchases—1
Government purchases of goods and services are an
important source of demand.
• In recent years, government purchases are about
20% of GDP.
Government purchases can be
• a source of short-run fluctuations.
• an instrument to reduce fluctuations.
Government Purchases—2
Discretionary fiscal policy
• Purchases of new goods or services
• American Recovery and Reinvestment Act of 2009
• Tax rate changes
• Investment tax credit of 1961
• Economic Growth and Tax Relief Reconciliation
Act of 2001
Fiscal Policy
Automatic stabilizers
• Transfer spending programs (e.g., unemployment
insurance, Medicare)
The impact of fiscal policy depends on
• timing.
• the “no free lunch” principle.
Ricardian Equivalence
Analogous to the permanent-income hypothesis
According to Ricardian equivalence:
• The timing of tax changes does not matter for
consumer behavior.
• The present value of government tax collection
determines behavior.
Consider an example:
• Suppose Congress decides to hire more teachers,
increasing government purchases by $500 million.
OR
Case Study: The Macroeconomic Effects of the American Recovery and
Reinvestment Act (ARRA) of 2009
Net Exports—1
Trade balance = Net exports
• = 𝐸𝑋 − 𝐼𝑀
•=
•=
If 𝐸𝑋 > 𝐼𝑀
• 𝑁𝑋 > 0
• Trade surplus
If 𝐸𝑋 < 𝐼𝑀
• 𝑁𝑋 < 0
• Trade deficit
Net Exports—2
Suppose there is
• an increase in demand for U.S. goods from the rest
of the world (↑ ) → IS shifts right → ↑ short-run
output.
• an increase in demand for imports from the rest of
the world (↑ ) → IS shifts left→ ↓ short-run
output.
11.6 Conclusion
The foundation of the short-run model (IS curve)
• describes the relationship between the real interest rate
(𝑹𝒕) and economic activity.
• There is an inverse relationship between 𝑅𝑡.
• The mechanism operates through investment
.
Clicker Question 1
If the marginal product of capital decreases, what
happens to the IS curve?
a. It shifts outward.
b. It shifts inward.
c. There is movement along the curve.
d. It remains the same.
Clicker Question 1 – Answer
If the marginal product of capital decreases, what
happens to the IS curve?
a. It shifts outward.
b. It shifts inward.
c. There is movement along the curve.
d. It remains the same.
Clicker Question 2
Which of the following explains why an increase in the
interest rate reduces short-run output?
a. The cost of borrowing increases for firms.
b. The cost of borrowing increases for households.
c. Firms reduce business investment.
d. All of these choices are correct.
Clicker Question 2 – Answer
Which of the following explains why an increase in the
interest rate reduces short-run output?
a. The cost of borrowing increases for firms.
b. The cost of borrowing increases for households.
c. Firms reduce business investment.
d. All of these choices are correct.
Clicker Question 3
In our model, a hurricane that damages some physical
capital in an economy will typically
a. increase short-run output and potential output.
b. decrease short-run output and potential output.
c. decrease short-run output and increase potential
output.
d. increase short-run output and decrease potential
output.
Clicker Question 3 – Answer
In our model, a hurricane that damages some physical
capital in an economy will typically
a. increase short-run output and potential output.
b. decrease short-run output and potential output.
c. decrease short-run output and increase potential
output.
d. increase short-run output and decrease
potential output.
Clicker Question 4
The LC/PI hypothesis implies that an individual will
make consumption decisions based on
a. current income.
b. average income.
c. short-run output.
d. actual output.
Clicker Question 4 – Answer
The LC/PI hypothesis implies that an individual will
make consumption decisions based on
a. current income.
b. average income.
c. short-run output.
d. actual output.
Clicker Question 5
Which of the following is not an example of an
automatic stabilizer?
a. Medicaid
b. unemployment insurance
c. discretionary spending on highways
d. welfare transfer payments
Clicker Question 5 – Answer
Which of the following is not an example of an
automatic stabilizer?
a. Medicaid
b. unemployment insurance
c. discretionary spending on highways
d. welfare transfer payments
Clicker Question 6
According to the LC/PI hypothesis, a college student
should
a. consume more than she has in income.
b. consume less than she has in income.
c. consume exactly her income.
d. not consume.
Clicker Question 6 – Answer
According to the LC/PI hypothesis, a college student
should
a. consume more than she has in income.
b. consume less than she has in income.
c. consume exactly her income.
d. not consume.
Clicker Question 7
Suppose the United States is currently at its trend level
of potential output. All economies are open. Europe
enters into a recession. Short-run output in the United
States will be
a. negative.
b. positive.
c. unchanged because European fluctuations do not
impact the United States.
d. uncertain.
Clicker Question 7 – Answer
Suppose the United States is currently at its trend level
of potential output. All economies are open. Europe
enters into a recession. Short-run output in the United
States will be
a. negative.
b. positive.
c. unchanged because European fluctuations do not
impact the United States.
d. uncertain.
Clicker Question 8
The marginal product of capital can differ from the real
interest rate because
a. the MPK is exogenous while the real interest rate is
endogenous.
b. installing new capital takes time to equalize the
MPK and the real interest rate.
c. the MPK depends on how sensitive firms are to
changes in the economy.
d. the MPK and the real interest rate are always equal
to each other.
Clicker Question 8 – Answer
The marginal product of capital can differ from the real
interest rate because
a. the MPK is exogenous while the real interest rate is
endogenous.
b. installing new capital takes time to equalize the
MPK and the real interest rate.
c. the MPK depends on how sensitive firms are to
changes in the economy.
d. the MPK and the real interest rate are always equal
to each other.
Clicker Question 9
a. true
b. false
Clicker Question 9 – Answer
a. true
b. false
Clicker Question 10
If an economy has actual output equal to potential
output, then the aggregate demand shock equals 0.
a. true
b. false
Clicker Question 10 – Answer
If an economy has actual output equal to potential
output, then the aggregate demand shock equals 0.
a. true
b. false
Clicker Question 11
A person who speeds faster on the highway because he
or she is wearing a seatbelt is an example of moral
hazard.
a. true
b. false
Clicker Question 11 – Answer
A person who speeds faster on the highway because he
or she is wearing a seatbelt is an example of moral
hazard.
a. true
b. false
Clicker Question 12
An increase in the aggregate demand parameter for
imports will shift the IS curve in the same direction as
an increase in the aggregate demand parameter for
consumption.
a. true
b. false
Clicker Question 12 – Answer
An increase in the aggregate demand parameter for
imports will shift the IS curve in the same direction as
an increase in the aggregate demand parameter for
consumption.
a. true
b. false
Clicker Question 13
If aggregate consumption responds to changes in
temporary income, fluctuations in short-run output
will be larger than if consumption is unresponsive to a
temporary change in income.
a. true
b. false
Clicker Question 13 – Answer
If aggregate consumption responds to changes in
temporary income, fluctuations in short-run output
will be larger than if consumption is unresponsive to a
temporary change in income.
a. true
b. false
Clicker Question 14
Suppose the government increases discretionary
spending. Ricardian equivalence implies that
consumption will be higher today if the government
announces that taxes will be increased next year as
opposed to if it announces taxes will be increased in
two years.
a. true
b. false
Clicker Question 14 – Answer
Suppose the government increases discretionary
spending. Ricardian equivalence implies that
consumption will be higher today if the government
announces that taxes will be increased next year as
opposed to if it announces taxes will be increased in
two years.
a. true
b. false
Clicker Question 15
Foreign savings is equal to exports minus imports.
a. true
b. false
Clicker Question 15 – Answer
Foreign savings is equal to exports minus imports.
a. true
b. false
Clicker Question 16
a. a decrease in the marginal product of capital.
b. a decrease in the real interest rate.
c. firms being optimistic about the future and
willing to invest more at any level of the interest
rate.
d. firms being pessimistic about the future and
willing to invest less at any level of the interest
rate.
Clicker Question 16 – Answer
a. a decrease in the marginal product of capital.
b. a decrease in the real interest rate.
c. firms being optimistic about the future and
willing to invest more at any level of the interest
rate.
d. firms being pessimistic about the future and
willing to invest less at any level of the interest
rate.
Clicker Question 17
In the LC/PI model, do individuals prefer a smooth
consumption path (corresponding to their permanent
income) to a fluctuating consumption path (corresponding
to their actual income)?
a. No, they are indifferent because the utility of every
additional unit of consumption does not change.
b. No, they don’t, because the utility of every additional
unit of consumption is smaller.
c. No, they don’t, because the utility of every additional
unit of consumption is larger.
d. Yes, they do, because the utility of every additional
unit of consumption is smaller.
e. Yes, they do, because the utility of every additional
unit of consumption is larger.
Clicker Question 17 – Answer
In the LC/PI model, do individuals prefer a smooth
consumption path (corresponding to their permanent
income) to a fluctuating consumption path (corresponding
to their actual income)?
a. No, they are indifferent because the utility of every
additional unit of consumption does not change.
b. No, they don’t, because the utility of every additional
unit of consumption is smaller.
c. No, they don’t, because the utility of every additional
unit of consumption is larger.
d. Yes, they do, because the utility of every
additional unit of consumption is smaller.
e. Yes, they do, because the utility of every additional
unit of consumption is larger.
Clicker Question 18
Suppose a negative aggregate demand shock causes shortrun output to drop to -1 percent. To stimulate investment
and bring the economy back to potential output, the
interest rate decreases by 1 percentage point. However, as a
result, investment increases more than expected and shortrun output reaches 1 percent. This result could be caused
by
a. an increase in the consumption share of potential
output.
b. an increase in the government purchases share of
potential output.
c. a decrease in the import share of potential output.
d. the presence of a consumption multiplier.
e. All of these are correct.
Clicker Question 18 – Answer
Suppose a negative aggregate demand shock causes shortrun output to drop to -1 percent. To stimulate investment
and bring the economy back to potential output, the
interest rate decreases by 1 percentage point. However, as a
result, investment increases more than expected and shortrun output reaches 1 percent. This result could be caused
by
a. an increase in the consumption share of potential
output.
b. an increase in the government purchases share of
potential output.
c. a decrease in the import share of potential output.
d. the presence of a consumption multiplier.
e. All of these are correct.
Clicker Question 19
According to the life-cycle model, ___________ is much
smoother than __________ over one's lifetime.
a. income, consumption
b. borrowing, dissaving
c. consumption, income
d. none of the above
Clicker Question 19 – Answer
According to the life-cycle model, ___________ is much
smoother than __________ over one's lifetime.
a. income, consumption
b. borrowing, dissaving
c. consumption, income
d. none of the above
Clicker Question 20
Assume that Country A has a larger IS multiplier than
Country B. Further, assume that both countries receive an
aggregate demand shock of 3 percent. Given this
information, what do we expect to be the difference in
short-run output between the two countries, ceteris
paribus?
a. Country A and Country B will have no change in shortrun output.
b. Country A will have a larger change in short-run output
than Country B.
c. Country A will have a smaller change in short-run
output than Country B.
d. The change in short-run output will be the same for
Countries A and B.
Clicker Question 20 – Answer
Assume that Country A has a larger IS multiplier than
Country B. Further, assume that both countries receive an
aggregate demand shock of 3 percent. Given this
information, what do we expect to be the difference in
short-run output between the two countries, ceteris
paribus?
a. Country A and Country B will have no change in shortrun output.
b. Country A will have a larger change in short-run
output than Country B.
c. Country A will have a smaller change in short-run
output than Country B.
d. The change in short-run output will be the same for
Countries A and B.
Credits
This concludes the Lecture PowerPoint presentation for Chapter 11, The IS Curve, of Macroeconomics, 5e by Charles I. Jones
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