Download Chapter 1: Introduction

Chapter 10
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Chapter 10: The IS-LM-AS Framework:
Production, Interest Rates, Unemployment, and
Inflation
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J. Bradford DeLong
http://econ161.berkeley.edu/
[email protected]
9,428 words
Contents
10.1 The LM Curve and the Money Market
10.1.1 Money Market Equilibrium
10.1.2 The LM Curve
10.1.3 The IS-LM Framework
10.1.3.1 IS Shocks
Box 10.1--Example: IS-LM Equilibrium
10.1.3.2 LM Shocks
Box 10.2--Example: An IS Shock
10.1.3.3 Interest Rate Targets
Box 10.3--Example: An LM Shock
10.1.4 Moving Along the LM Curve
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10.2 Fluctuations in Output and Unemployment
10.2.1 Using Okun's Law to Determine the Level of
Unemployment
Box 10.4--Policy: Costs of High Unemployment
10.2.2 Causes of Fluctuations
10.3 IS-LM and the Exchange Rate
10.3.1 Domestic Conditions, the Real Exchange Rate,
and the Balance of Trade
Box 10.5--Example: An LM Shock and Its Effect on the
Balance of Trade
10.3.2 International Shocks and the Domestic
Economy
Box 10.6--Example: A Shock to International Investors'
Expectations
10.4 Inflation and the Price Level
10.4.1 Aggregate Supply and the Phillips Curve
10.4.2 Where Does the Short-Run Aggregate Supply
Relationship Come From?
10.4.3 The Aggregate Demand Relationship
10.5 Chapter Summary
10.5.1 Main Points
10.5.2 Important Concepts
10.5.3 Analytical Exercises
10.5.4 Policy-Relevant Exercises
Questions
What is "money-market equilibrium"?
What is the "LM Curve"?
What determines the equilibrium level of real GDP when the central bank's policy is
to keep the money stock constant?
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What is the IS-LM framework?
What is an IS shock?
What is an LM shock?
Are business cycles in unemployment different from business cycles in output?
What is the relationship between shifts in the equilibrium on the IS-LM diagram and
changes in the real exchange rate and the balance of trade?
What is the aggregate supply curve?
What are the three ways of representing the aggregate supply curve?
What is the aggregate demand curve?
The IS curve built up in chapter 9 is enough to enable one to begin thinking about
business cycles as long as the central bank pegs the real interest rate to some target value.
But the central bank does not always peg interest rates--in fact, there is not always a
central bank to peg interest rates. Alternative monetary arrangements fix not the interest
rate but the quantity of liquid money. And even when central banks do peg interest rates,
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they usually peg not real but nominal interest rates. To understand the determinants of
real interest rates you need to understand the determinants of inflation.
This chapter builds more tools. It builds up an LM curve to serve as a sibling to the IS
curve: the LM curve tells us how interest rates are determined when the stock of liquid
money is fixed. And it begins to build our model of aggregate supply: of what determines
the rate of inflation, and what causes the rate of inflation to change.
10.1 The LM Curve and the Money Market
The IS curve of the previous chapter gave us enough tools to allow us to calculate the
sticky-price equilibrium level of real GDP, as long as the central bank followed a policy
of pegging the real interest rate to a fixed value. But what if the central bank does not
follow a policy of pegging the interest rate at some target value? Or what if there is no
central bank--as was the case in the U.S. back before World War I? Or what if the central
bank wishes to stand back, maintain a constant supply of liquid monetary assets, and have
interest rates determined by market forces?
In that case, the level of interest rates and of real GDP are jointly determined by the
intersection of the IS curve and a "liquidity-money" LM curve that represents equilibrium
in the money market. It must be the case both that real GDP is equal to total income is
equal to aggregate demand--that is what the IS curve represents--and that money supply
be equal to money demand--that is what the LM curve represents.
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10.1.1 Money Market Equilibrium
Recall from chapter seven that the demand for nominal money--the quantity of liquid
readily-spendable assets that people wish to hold--is proportional to total nominal income
P x Y, has a time trend associated with changes in -sector and transactions-processing
technology, and is related inversely related to the nominal interest rate--the sum of the
real interest rate and the current inflation rate. Money balances earn little or no interest.
Over time they lose their power to purchase real, useful goods and services at the rate of
inflation π. If you shifted them into some other part of your portfolio, they would earn the
real interest rate r. Thus the opportunity cost of holding money is the nominal interest rate
I = r + π, the nominal interest rate is the sum of the real interest rate r and the inflation
rate π.
If we ignore for the moment the technologically-driven time trend in velocity, we can
express this in algebra by setting the nominal demand for money to be the function:
M 
d
PY
V (r   )
Real demand for money--demand for real money balances, for the nominal money stock
divided by the price level, for an amount of purchasing power held in readily-spendable
form rather than an amount of pictures of George Washington--is:
M d
Y
  
 P  V(r   )
And our ultimate equations will be simpler if we write this real money demand function
in the form:
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M d
Y
  
 P  V0  Vi  (r  )
The plus sign in front of the Vi parameter makes real money demand a decreasing
function of the nominal interest rate: the higher is r+π, the higher is the velocity of money
and the lower is the demand for real money balances.
For a constant level of real GDP Y, we can plot money demand on a diagram with the
quantity of money demanded on the horizontal axis and the nominal interest rate i=r+π on
the vertical axis.
Figure 10.1: Money Demand and the Nominal Interest Rate
Nominal
Interest
Rate
=r+š
Equilibrium
Nominal
Interest Rate
Y
Money Demand: (V - V i(r+š))
0
Real Quantity of Money
Money
Supply
=Ms
Legend: When the stock of liquid monetary assets is fixed, the equilibrium short-
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term nominal interest rate is that at which households' and businesses' demand for
liquid money is equal to the (fixed) money stock.
Suppose that the current level of the money stock is fixed--by the particular monetary
system adopted, or by the central bank--at a level Ms. Then equilibrium in the money
market means that the nominal interest rate i=r+π has to be at that level where the curves
cross: where the nominal interest rate is such that the quantity of money that households
and businesses wish to hold is just equal to the available money supply.
10.1.2 The LM Curve
Now let's examine how the equilibrium nominal interest rate varies as real GDP and total
income Y vary. The higher is total income, the higher is the demand for money. When
income is high, expenditures are high too: more real money balances are needed to make
sure that the higher volume of expenditures is not interrupted.
For each possible level of total income Y, we can draw a different money demand curve
corresponding to that level of total income. As long as the money supply remains
unchanged, each of the money demand curves will produce a different equilibrium level
of the nominal interest rate.
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Figure 10.2: Money Demand Varies as Total Income Y Varies
Nominal
Interest
Rate
=r+š
Interest rate for
high level of Y
Interest rate for
moderate level
of Y
Money Demand for a high level of Y
Interest rate for
low level of Y
Money Demand for a moderate level of Y
Money Demand for a low level of Y
Real Quantity of Money
Money
Supply
=Ms
Legend: The higher the level of total income, the higher is the quantity of money
demanded for any given interest rate, and (for a fixed money stock) the higher
will
be the equilibrium interest rate.
If we plot on a diagram--with the nominal interest rate i=r+π on the vertical axis and the
level of total income Yon the horizontal axis--the equilibrium level of nominal interest
rates for each potential level of Y, we have plotted the LM curve. The LM curve is drawn
for a given, fixed, particular level of the real money stock Ms/P. And it slopes upwards:
the higher is total income Y, the stronger is demand for money, and the higher is the
equilibrium nominal interest rate i=r+π needed to reduce households' and businesses'
desired money holdings to the level of the money supply.
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Figure 10.3: From Money Demand to the LM Curve
Money Supply and Money Demand
Nominal
Interest
Rate
=r+š
LM Curve
Nominal
Interest
Rate
=r+š
Interest rate for
high level of Y
Interest rate for
moderate level
of Y
Interest rate for
low level of Y
Real Quantity of Money
Total Income Y
Money
Supply
=Ms
Low
Level
of
Y
Moderate
Level
of
Y
High
Level
of
Y
Legend: The LM Curve tells us what the nominal interest rate will be for each
possible value of total income Y.
Simply rewriting the money demand function to get the level of real total income Y on
the left-hand side:
Y  V0  Vi  (r  ) 
M 
 P 
produces a simple algebraic form for the LM curve. Monetary policy changes that
increase the money supply shift the LM curve out to the right. Monetary policy changes
that decrease the money supply shift the LM curve in and to the left. A decline in the
price level will boost the real money supply and shift the LM curve out to the right. A
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rise in the price level will decrease the real money supply and shift the LM curve in to the
left.
10.1.3 The IS-LM Framework
Because the nominal interest rate i is just equal to the real interest rate r + π, as long as
we know the expected inflation rate π we can plot the IS and LM curves on the same set
of axes,
Figure 10.4: The IS-LM Equilibrium
Real
Interest
Rate
r
LM Curve
Equilibrium
Interest
Rate
IS Curve
Real GDP Y
Equilibrium
Real GDP
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Legend: What is the economy's equilibrium? The economy's equilibrium is that
point at which the IS and LM Curves cross. Along the IS Curve, total production
is
equal to aggregate demand. Along the LM Curve, the quantity of money
demanded
by households and businesses is equal to the money stock. Where the curves cross
both the "goods market" and the "money market" are in balance.
Then the equilibrium level of real GDP and of the interest rate is at the point where the IS
curve and the LM curve cross. At that level of real GDP and total income Y, and of the
interest rate r, the economy is in equilibrium in both the goods market and the money
market. Aggregate demand is equal to total production (that's what the IS curve
indicates), and money demand is equal to money supply (that's what the LM curve
indicates).
Box 10.1--Example: IS-LM Equilibrium
Suppose that the economy's marginal propensity to spend [MPS] is 0.5, that the
initial level of baseline autonomous spending A0 is $5000 billion, and that a 1
percentage point increase in the real interest rate reduces the sum of investment
and net exports by $100 billion. Then the economy's initial IS curve is:
Y
A0
I  X  r
$5000 $100
 r
r

 r  $10000  $200  r
1  MPS 1  MPS
1  0.5 1  0.5
If its initial LM curve is represented by the equation:
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Y  $1000  $1000  (r  )
and if the inflation rate π is constant at 3% per year, then the initial equilibrium of
the economy is at the one point which is on both the IS and the LM curves.
Where is that point? Find it by substituting the LM-curve expression for
equilibrium real GDP into the IS curve:
Y  $10000  $200  r  $1000  $1000  (r  3)
$6000  ($200  $1000)  r
r  5%
r equals 5% per year. And if r equals 5% per year, then annual equilibrium real
GDP Y equals $9000 billion.
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Figure: IS-LM Equilibrium Example
Real
Interest
Rate
r
LM Curve: Y=$1000+$1000 x (r+š)
[inflation rate š=3%]
Equilibrium
Interest
Rate:
5%
IS Curve: Y=$10000-$200 x r
Real GDP Y
Equilibrium
Real GDP:
$9000
10.1.3.1 IS Shocks
Any change in economic policy or the economic environment that increases autonomous
spending--like an increase in government purchases, for example--shifts the IS curve out
and to the right. It moves the economy up and to the right along the LM curve. And the
new equilibrium will have both a higher level of real interest rates and a higher
equilibrium level of real GDP.
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Figure 10.5: Effect of a Positive IS Shock
Real
Interest
Rate
r
An increase in autonomous spending
(like an increase in government purchases)
shifts the IS curve to the right...
LM Curve
...It raises the
equilibrium
interest rate...
Old IS Curve
Real GDP Y
...And it raises the
equilibrium level of
real GDP.
Legend: An expansionary shift in the IS curve raises both real GDP Y and the real
interest rate r.
How the consequences of an expansionary shift in the IS curve will be divided between
increases in interest rates and increases in equilibrium real GDP depends on the slope of
the LM curve. If the LM curve is nearly horizontal (or if the central bank is targeting the
money stock--in which case the "LM" curve is horizontal) there will be little or no
increase in interest rates, and the increase in equilibrium real GDP will effectively be the
same as the outward shift in the IS curve. If the LM curve is very steeply sloped--if
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demand for money is extremely interest inelastic, so that it takes a big change in interest
rates to cause a small change in households' and businesses' desired holdings of money-then there will be a big effect on interest rates, and little effect on real GDP.
Any decrease in autonomous spending--a negative IS shock--like a reduction in
government purchases or a sudden shift of beliefs on the part of foreign exchange
speculators in the direction of thinking that the home currency is more valuable will have
opposite effects: shifting the economy down and to the left along the LM curve, resulting
in lower levels of interest rates and a lower level of equilibrium real GDP.
Box 10.2--Example: An IS Shock
Suppose that, as in the previous example, the economy's marginal propensity to
spend [MPS] is 0.5, that the initial level of baseline autonomous spending A0 is
$5000 billion, and that a 1 percentage point increase in the real interest rate
reduces the sum of investment and net exports by $100 billion. Then the
economy's initial IS curve is the same:
Y
A0
I  X  r
$5000 $100
 r
r

 r  $10000  $200  r
1  MPS 1  MPS
1  0.5 1  0.5
And suppose that the economy's initial LM curve is represented by the equation:
Y  $1000  $1000  (r  )
and the inflation rate π is constant at 3% per year. Thus the initial equilibrium of
the economy is--as in the previous example--where equilibrium annual real GDP
is $9000 billion and the real interest rate is 5%.
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Now suppose that there is a positive real shock to the economy: there is no
immediate increase in potential GDP, yet new technological breakthroughs lead
businesses to become more optimistic and generate an increase in baseline
investment I0 (and thus in baseline autonomous spending A0) of $150 billion.
What happens to the economy's equilibrium level of output and interest rates?
The new IS curve is:
Y
A0  I0 I r  X  r
$5000  $150 $100

r 

 r  $10300 $200  r
1  MPS 1  MPS
1  0.5
1 0.5
Thus the IS curve shifts out and to the right by $300 billion--the magnitude of the
shift in baseline autonomous spending divided by one minus the marginal
propensity to spend.
The LM curve remains unchanged at:
Y  $1000  $1000  (r  )
So, with inflation constant at 3% per year, the new equilibrium can be found by
setting the values of Y produced by the IS and LM curve to be equal to each
other:
Y  $10300  $200  r  $1000  $1000  (r  3)
$6300  ($200  $1000)  r
r  5.25%
With the real interest rate r equal to 5.25% per year, annual equilibrium real GDP
Y equals $9250 billion. A $300 billion outward shift in the IS curve has led to an
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0.25% increase in the real interest rate and a $250 billion increase in real GDP.
The higher interest rate has "crowded out" one-sixth of the shift in autonomous
spending.
Figure: IS Curve Expansion Example
Real
Interest
Rate
r
A $150 billion increase in
baseline investment generates,
with an MPS of 0.5, a $300
billion outward shift in the IS curve...
LM Curve: Y=$1000+$1000 x (r+š)
[inflation rate š=3%]
...which raises the
equilibrium real
interest rate by
0.25%...
Old IS Curve: Y=$10000-$200 x r
Real GDP Y
...and raises equilibrium
real GDP by $250.
10.1.3.2 LM Shocks
An increase in the money stock will shift the LM curve out and to the right: the higher
level of the money supply means that a given level of real GDP will be associated with a
lower nominal interest rate when the money market is in equilibrium, for the nominal
interest rate is the "price" of holding money balances in your portfolio, and with a greater
supply of money-like assets in the economy their price will fall.
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Figure 10.6: An Expansionary LM Shock
Real
Interest
Rate
r
An increase in the money stock
shifts the LM curve to the right...
...It lowers the
equilibrium
interest rate...
Old IS Curve
LM Curve
Real GDP Y
...And it raises the
equilibrium level of
real GDP.
Legend: An expansionary shift in the LM curve raises real GDP Y and lowers the
equilibrium interest rate r.
Such an outward LM shift will shift the equilibrium position of the economy down and to
the right along the IS curve. The new equilibrium position will have a higher level of
equilibrium real GDP, and a lower interest rate.
Conversely, a decrease in the money supply or any other contractionary LM shock that
shifts the LM curve in and to the left will shift the economy up and to the left along the IS
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curve, resulting in higher equilibrium interest rates and a lower equilibrium value of real
GDP.
Box 10.3--Example: An LM Shock
Suppose that, as in the previous example, the economy's marginal propensity to
spend [MPS] is 0.5, that the initial level of baseline autonomous spending A0 is
$5000 billion, and that a 1 percentage point increase in the real interest rate
reduces the sum of investment and net exports by $100 billion. Then the
economy's initial IS curve is the same:
Y
A0
I  X  r
$5000 $100
 r
r

 r  $10000  $200  r
1  MPS 1  MPS
1  0.5 1  0.5
And suppose that the economy's initial LM curve is represented by the equation:
Y  $1000  $1000  (r  )
and the inflation rate π is constant at 3% per year. Thus the initial equilibrium of
the economy is--as in the previous example--where equilibrium annual real GDP
is $9000 billion and the real interest rate is 5%.
Now suppose that the central bank conducts expansionary open market
operations: it buys bonds for cash and so increases the supply of money in the
economy to shift the LM curve out to:
Y  $2200  $1000  (r  )
So, with inflation constant at 3% per year, the new equilibrium can be found by
setting the values of Y produced by the IS and LM curve to be equal to each
other:
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Y  $10000  $200  r  $2200  $1000  (r  3)
$4800  ($200  $1000)  r
r  4%
With the real interest rate r equal to 4% per year, annual equilibrium real GDP Y
equals $9200 billion--a $200 billion increase in annual equilibrium real GDP.
Figure: LM Expansion Example:
Real
Interest
Rate
r
Old LM Curve: Y=$1000+$1000 x (r+š)
[inflation rate š=3%]
...which lowers the
equilibrium real
interest rate by
1%...
Expansionary open market
operations shift the LM
curve out by $1200
IS Curve: Y=$10000-$200 x r
Real GDP Y
...and raises equilibrium
real GDP by $200.
10.1.3.3 Interest Rate Targets
The IS-LM diagram thus determines the short-run equilibrium of the economy--real GDP
and interest rates--when the money stock is fixed. It provides a flexible and useful
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framework for analyzing the expenditure-driven determination of output, money market
equilibrium, and interest rates. Even the case in which the central bank is targeting the
interest rate can be viewed in the IS-LM framework: an interest rate target is simply a
flat, horizontal LM curve at the target level of the interest rate.
Figure 10.7: IS-LM Framework with an Interest Rate Target
Real
Interest
Rate
r
Central bank targeting the
interest rate = horizontal LM curve
IS curve
Real GDP Y
Legend: When the central bank targets and fixes the interest rate, we can think of
the
LM curve as being a horizontal line.
10.1.4 Moving Along the LM Curve
The course of the U.S. economy in the early 1980s provides a good example of a
movement along the LM curve in the IS-LM framework. The Federal Reserve sought in
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the early 1980s to keep the rate of growth of the money supply on a stable path in order
to build confidence that inflation was and would remain low.
Figure 10.8: Moving Along the LM Curve
Legend: At the end of the 1970s the Federal Reserve announced that it was
changing its operating procedures to place more emphasis on meeting targets for
the
growth rate of the money stock. This shift in emphasis lasted through the mid-
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1980s. Between the early and the mid-1980s, as the Federal Reserve tried to meet
its
targets for the money stock, the rightward expansionary shift in the IS Curve
driven
by the Reagan budget deficits pushed the U.S. economy up and to the right along
the LM Curve.
Consequently the large outward shift in the IS curve produced by the Reagan
administration fiscal policy expansion of the 1980s moved the economy up and to the
right along the LM curve, raising equilibrium real GDP and also raising real interest
rates.
Thus the IS-LM framework allows us to say even more about the determinants of real
GDP and interest rates when prices are sticky. But it is not enough just to determine what
the current level of real GDP and interest rates are as a function of the economic
environment and of economic policy. The next sections cover natural extensions of the
IS-LM framework--to the determination of unemployment, of the exchange rate and the
balance of trade, and to the rate of inflation.
10.2 Fluctuations in Output and Unemployment
10.2.1 Using Okun's Law to Determine the Level of
Unemployment
Arthur Okun was the first economist to notice exactly how very strong is the relationship
between the unemployment rate and the level of total output. Okun's Law--perhaps the
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strongest empirical real-side regularity in macroeconomics, for the United States at least,
tells us that the unemployment rate U and the level of real GDP Y are related by:
U  U * 0.4 
Y * Y
Y*
where Y* is the level of potential output according to the production function, and U* is
the natural rate of unemployment. Take the relative proportional gap between potential
output and the current level of real GDP: (Y*-Y)/Y*. Multiply it by 0.4. Add it to the
natural rate of unemployment--the rate of unemployment when the economy is at its level
of potential output. The result will be a very good estimate of the current rate of
unemployment.
Whenever actual output grows faster than potential output, unemployment falls.
Whenever actual output grows slower than potential output, unemployment rises. Okun's
law can be written in year-by-year rate-of-change form as:
U  0.4 
Y
 (n  g)
 Y

where U is the year-to-year change in the unemployment rate, Y/Y is the year-to-year
proportional change in real GDP, and n+g is the proportional rate of growth of potential
output from chapter 4.
The strength of Okun's law allows economists to switch back and forth between talking
about business cycles as fluctuations in unemployment relative to the natural rate of
unemployment, and talking about business cycles as fluctuations in total production
relative to potential output. There is no significant distinction between the two: there is
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no point in distinguishing “unemployment business cycles” in any way from “real GDP
business cycles.”
Box 10.4--Policy: Costs of High Unemployment
In a typical post-World War II U.S. recession, unemployment rises by two
percentage points—from around 5 percent to around 7 percent. Okun's law
predicts that, in such a case, total production relative to potential output falls by
about 5%. That's about four years' worth of growth in output per worker. And
recessions are not permanent: they are quickly over, and are followed by periods
of rapid growth that usually serve to return total output to its pre-recession growth
trend.
Even the steepest recession—that of 1982—raised the unemployment rate by only
four percentage points, and lowered output relative to potential by ten percent at
most—about seven years’ worth of economic growth. And within three years of
1982 unemployment had fallen back to what people then considered “normal”
levels.
Yet people fear a typical recession much more than they value an extra four years'
of economic growth. The memory of the 1982 recession has substantially altered
Americans’ perceptions of how the economy works, how much they dare risk in
the search for higher wages, and how confident they can be that their jobs are
secure.
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Why do episodes of high recessionary unemployment have such a psychological
impact? The most likely answer is that recessions are feared because recessions
do not distribute their impact equally. Workers who keep their jobs are only
lightly affected, while those who lose their jobs suffer a near-total loss of income.
People fear a 2% chance of losing half their income much more than they fear a
certain loss of 1%. Thus it is much worse for 2% of the people each to lose half of
their income than for everyone to lose 1%. It is the unequal distribution of the
costs of recessions that makes them so feared—and that makes voters so anxious
to elect economic policymakers who will successfully avoid them.
10.2.2 Causes of Fluctuations
The IS-LM framework allows us to classify many different kinds of changes in the
economic environment and in economic policy into four different groups. It is surprising
howmany different kinds of disturbances to the economy affect the level of aggregate
demand and can be fitted into the IS-LM framework.
Any change in the nominal money stock, in the price level, or in the trend velocity of
money will shift the LM curve's location. Any change in the interest sensitivity of money
demand--in how easy households and businesses find it to economize on their holdings of
real money balances--will change the slope of the LM curve.
Moreover, the fact that the IS-LM diagram is drawn with the real interest rate--the longterm, risky, real interest rate--on the vertical axis has important consequences for how to
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construct the LM curve. The LM relationship is a relationship between the short-run
nominal interest rate and the level of real GDP for a given, fixed level of the real money
supply:
M 
Y  V0  Vi  (i)   
 P 
As long as the spread between the short-term, safe, nominal interest rate i in the LM
equation and the long-term, risky, real interest rate r in the IS equation is constant and
unchanging, there are no complications in drawing the LM curve onto the same diagram
as the IS curve.
But what if the rate of expected inflation π, or the risk premium, or the term premium
between short and long-term interest rates changes? Then the position of the LM shifts
either upward (if expected inflation falls, or if the risk premium rises, or if the term
premium rises) or downward (if expected inflation rises, or if the risk premium falls, or if
the term premium falls).
Thus changes in today’s financial market expectations of future Federal Reserve policy,
of future inflation, or simply changes in the tolerance for risk of bond traders on Wall
Street affect the position of the LM curve. Not only disturbances to the money market,
but broader shifts in financial markets that alter the relationship between the nominal
interest rates on short-term safe bonds and the real interest rate paid by corporations
undertaking long-term risky investments affect the IS-LM equilibrium.
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Figure 10.9: A Rise in Expected Inflation Moves the LM Curve Downward
Real
Interest
Rate
r
A rise in expected inflation means that
the same nominal interest rate is now
associated with a lower real interest rate.
So a fall in expected inflation generates
a downward shift in the LM curve...
...which lowers
the equilibrium
real interest rate...
IS Curve
LM Curve
Real GDP Y
...And raises the
equilibrium level of
real GDP.
Legend: The fact that the interest rate relevant to the IS curve is a real and the
interest rate relevant to the LM curve is a nominal rate is a source of
complications: a
change in expected inflation lowers the real interest rate that corresponds to any
given nominal interest rate, and so shifts the LM curve down on the IS-LM
diagram.
But changes in the IS curve are probably more frequent than changes in the LM curve,
for more types of shifts in the economic environment and economic policy affect planned
expenditure than affect the supply and demand for money. Any change in the effect of a
shift in interest rates on investment spending will change the slope of the IS curve.
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Moreover, so will any change in either the sensitivity of exports to the exchange rate, or
any change in the sensitivity of the level of the exchange rate to the level of domestic
interest rates.
The slope of the IS curve will also be changed by anything that affects the marginal
propensity to spend--the MPS. Moreover, shifts in the MPS will change not just the slope
but also the position of the IS curve, because changes in the MPS change the multiplier
and thus change how much equilibrium real GDP is generated by a given amount of
baseline autonomous spending. Any shift in the marginal propensity to consume Cy will
change the MPS. Thus if households decide that income changes are more likely to be
permanent (raising the marginal propensity to consume) or more likely to be transitory
(lowering the marginal propensity to consume), they will raise or lower the MPS.
Changes in tax rates have a direct effect on the MPS. And so do changes in the propensity
to import. Thus, for example, the imposition or removal of a tariff on imports to
discourage them will affect the marginal propensity to spend, and thus will affect both the
location and the slope of the IS curve.
Last but surely not least, any of a large number of potential changes in the economic
environment and in economic policy can shift the level of autonomous spending, and thus
shift the IS curve in either an expansionary or contractionary direction. Anything that
affects the baseline level of consumption C0 affects autonomous spending--whether it is a
change in demography that changes desired savings behavior, a change in optimism
about future levels of income, or any other cause of a shift in consumer behavior.
Anything that affects the baseline level of investment I0 affects autonomous spending-whether it is a wave of innovation that increases expected future profits and desired
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investment, a wave of irrational overoptimism or overpessimism, a change in tax policy
that affects not the level of revenue collected but the incentives to invest, or any other
cause. Changes in government purchases affect autonomous spending.
In sum, pretty much anything can affect the equilibrium level of aggregate demand. And
pretty much everything does affect it at one time or another. One of the principal merits
of the IS-LM apparatus is that it gives you a framework to use in sorting and classifying
the determinants of the equilibrium level of total output.
Moreover, there is one class of determinants of aggregate demand not mentioned above.
Any of a number of shifts in the determinants of the exchange rate also change the
equilibrium in the IS-LM framework. And it is worth giving this last class a closer look.
10.3 IS-LM and the Exchange Rate
10.3.1 Domestic Conditions, the Real Exchange Rate, and the
Balance of Trade
10.3.1.1 The IS-LM Framework and the Exchange Rate
In our model the real exchange rate  is equal to speculators' opinion of its baseline
fundamental value if there were no gap in interest rates (call it 0), minus a factor r times
the difference between the real interest rate on home currency-denominated assets (r) and
the interest rate on foreign currency-denominated assets (rf):
   0   r r  r f 
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Thus in our model it is easy to read off the effects of changes in domestic conditions on
the value of the real exchange rate. As long as the domestic real interest rate does not
change, domestic conditions have no impact on the exchange rate: if the exchange rate
shifts it is for other, external reasons.
Figure 10.10: IS-LM and the Exchange Rate
Real
Interest
Rate
r
Real
Interest
Rate
r
An outward, expansionary s hift in the LM curve
...which lowers
the equilibrium
real interest rate...
IS Curve
LM Curve
Real Exchange Rate 
Real GDP Y
...will raise the real
exc hange rate...
...and raises the
equilibrium level of
real GDP...
Exports
...and boos t
exports.
Real Exchange Rate 
Legend: Outward shifts in the IS and inward shifts in the LM curve will both
lower
the value of foreign currency and reduce net exports.
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However, changes in the IS curve and the LM curve that do change domestic real interest
rates will also change the real exchange rate by an amount equal to r times the shift in
the domestic interest rate. Outward, expansionary shifts in the IS curve and inward,
contractionary shifts in the LM curve will both lower the value of the exchange rate--the
value of foreign currency. Inward, contractionary shifts in the IS curve and outward,
expansionary shifts in the LM curve will raise the value of the exchange rate--the value
of the foreign currency.
Thus the effects of changes in domestic conditions on the real exchange rate are
straightforward once one has used the IS-LM framework to calculate the effect of the
change in domestic conditions on the real exchange rate. Just one additional step is
needed. In algebra:
  r  r
The change in the exchange rate is proportional to the change in the real interest rate. (If
we had time to go into more detail, we would discuss how the proportionality factor r is
a function of foreign exchange speculators' willingness to bear risk and assessment of
how long interest rate differentials between home and abroad will last; it can and does
change suddenly and rapidly.)
10.3.1.2 The IS-LM Framework and the Balance of Trade
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Unfortunately, the effects of changes in domestic conditions on the balance of net exports
are less straightforward. Changes in the domestic real interest rate affect the exchange
rate, which affects gross exports. Changes in total income Y affect imports.
Figure 10.11: Effect of Change in Domestic Conditions on the Exchange Rate
Change in
Domestic
Conditions
Change in
Exchange Rate
Change in
Equilibrium Values
of Y, r
Change in
Imports
Change in
Gross Exports
Change in
Net Exports
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The effect on net exports is the difference between these two:
NX  GX  IM   r  r IMy  Y
And for this there is no simple two-dimensional graphical and diagrammatic
representation. The ingenuity of economists has been exhausted, and our attempt to have
a diagram for every pair of equations breaks down. You have to calculate it out each
time.
Box 10.5--Example: An LM Shock and Its Effect on the Balance of Trade
Suppose that the economy's marginal propensity to spend [MPS] is 0.5, that the
marginal propensity to import IMy is .15, that the initial level of baseline
autonomous spending A0 is $5000 billion, and that a 1 percentage point increase
in the real interest rate reduces investment spending by $80 billion, and reduces
the value of the exchange rate by 10 percent. Suppose further that each one
percent increase in the exchange rate increases net exports by $2 billion. Then the
economy's initial IS curve is:
Y
A0
I  X  r
$5000 $80 10  $2
 r
r

 r  $10000  $200  r
1  MPS 1  MPS
1  0.5
1  0.5
If the economy's initial LM curve is represented by the equation:
Y  $1000  $1000  (r  )
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and if the inflation rate π is constant at 3% per year, then the initial equilibrium of
the economy is with equilibrium annual real GDP is $9000 billion and the real
interest rate is 5%.
Now suppose the central bank conducts expansionary open market operations to
shift the LM curve out to:
Y  $2200  $1000  (r  )
The new equilibrium can be found by setting the values of Y produced by the IS
and LM curve to be equal to each other:
r  4%
Y  $9200
A $200 billion increase in annual equilibrium real GDP, and a 1 percentage point
decline in the real interest rate.
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Figure: LM Expansion
Real
Interest
Rate
r
Old LM Curve: Y=$1000+$1000 x (r+š)
[inflation rate š=3%]
...which lowers the
equilibrium real
interest rate by
1%...
Expansionary open market
operations shift the LM
curve out by $1200
IS Curve: Y=$10000-$200 x r
Real GDP Y
...and raises equilibrium
real GDP by $200.
The decrease in the real interest rate increases the real exchange rate by:
r  r  10  (1)  10
and the rise in the real exchange rate increases gross exports by:
X    $2 10  $20
The $200 billion increase in real national income increases imports by:
IMy  Y  0.15  $200  $30
Thus the LM shock changes annual net exports by the difference between the two:
NX  GX  Y  $20  $30  $10
It shrinks net exports by $10 billion a year.
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10.3.2 International Shocks and the Domestic Economy
Three different types of internationally-caused shocks affect the IS-LM equilibrium of
the domestic economy. The first are increases or decreases in foreign demand for
domestic exports--the result, usually, of increased or decreased total incomes abroad. The
second are changes in foreign real interest rates, and the third are changes in foreign
exchange speculators' opinions about the fundamental value of the exchange rate.
An increase in foreign demand for home-country exports has effects on the domestic
economy like any other expansionary IS shock: the increase in export demand is an
increase in baseline autonomous spending A0, and shifts the IS curve outward by an
amount A0/(1-MPS). This outward IS shift raises the equilibrium level of real GDP and,
to the extent that the LM curve is upward sloping, raises the real interest rate as well. The
increase in the real interest rate would make exports more expensive to foreigners, and
put some countervailing downward pressure on exports. The increase in the equilibrium
level of real GDP would raise demand for imports.
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Figure 10.12: Effect of an Increase in Foreign Demand for Exports
Real
Interest
Rate
r
An expansion of foreign demand
for exports shifts the IS curve
outward...
LM Curve
...it raises the
equilibrium real
interest rate to
the extent that the
LM curve slopes
upward...
Higher real
interest rates
reduce the
exchange
rate
and put
some downward
countervailing
pressure on
exports
Old IS Curve
Real GDP Y
...and it raises equilibrium
real GDP
which
raises
imports
In the simple case in which the central bank is targeting the real interest rate--if the LM
curve is horizontal--then the change in equilibrium real GDP generated by a rise Yf in
foreign total income is:
Y 
X f  Y f
1  MPS
f

X f  Y


Y 

1 Cy (1 t)  IM y 
And the change in net exports is:
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NX  GX  IM
NX  X f  Y  IMy 
f
X f  Y
f
1  MPS

IMy


NX  X f  Y f  1
 1  Cy (1  t)  IMy 
NX  X f  Y
f

1  Cy (1  t)
 1 C (1 t)  IM
y


y 
An increase in interest rates overseas rf has an immediate impact raising the value of the
exchange rate, and so encouraging exports. The increase in exports shifts the IS curve to
the right, leading to a higher level of equilibrium real GDP and--to the extent that the LM
curve is upward-sloping--to higher real interest rates as well. The consequences of such a
shift are similar to those of an increase in foreign incomes, save for the direction in which
the exchange rate moves. An increase in interest rates overseas raises the value of the
exchange rate. An increase in foreign levels of total income is likely to lower the value of
the exchange rate.
The third type of international shocks that can affect the IS-LM equilibrium is a sudden
change in speculators' expectations 0 of the long-run fundamental exchange rate.
Consider an upward shock to 0. It would have effects identical to an increase in interest
rates overseas: the exchange rate would rise, the IS curve would shift outward,
equilibrium real GDP would increase, and--to the extent that the LM curve is upward
sloping--the domestic real interest rate would increase as well.
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Box 10.6--Example: A Shock to International Investors' Expectations
Suppose that the economy's LM curve is represented by the equation:
Y  $1000  $1000  (r  )
and that the inflation rate π is constant at 3% per year. Suppose further that the
economy's marginal propensity to spend [MPS] is 0.5, that the marginal
propensity to import IMy is .15, that the initial level of baseline autonomous
spending A0 is $5000 billion, that a 1 percentage point increase in the real interest
rate reduces investment spending by $40 billion and reduces the value of the
exchange rate by 10 percent, and that each one percent increase in the exchange
rate increases net exports by $6 billion. Then the economy's initial IS curve is:
Y
A0
I  X  r
$5000 $80 10  $2
 r
r

 r  $10000  $200  r
1  MPS 1  MPS
1  0.5
1  0.5
And the initial equilibrium has annual real GDP of $9000 billion and a real
interest rate of 5%.
Consider a sudden upward shock of ten percent, as foreign exchange speculators'
lose confidence in the value of the domestic currency, to their opinions 0 of the
long-run fundamental value of the real exchange rate. Such a shock shifts the IS
curve to the right--raising the level of real GDP on the IS curve for a given, fixed
level of the real interest rate by an amount:
X   0
1 MPS
The shifted IS curve is then:
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A0  A0 Ir  X  r
A  X    0 Ir  X  r

r  0

r
1 MPS 1 MPS
1  MPS
1  MPS
$5000  $6  10 $80  12  $2
Y

 r  $10120  $200  r
1  0.5
1  0.5
Y
The new equilibrium can be found by setting the values of Y produced by the IS
and LM curve to be equal to each other:
$1000  $1000  (r  )  Y  $10120  $200  r
$6120  $1200  r
r  5.1%
Y  $9100
Equilibrium annual real GDP increases by $100 billion as the raised exchange rate
boosts exports, and the domestic real interest rate rises by 0.1%.
The increase in the domestic real interest rate means that the final change in the
real exchange rate:
    0   r  r
   10  10  0.1  9
is less than the 10 percent magnitude of the initial shock: higher domestic real
interest rates have offset some of the effect of the change in foreign exchange
speculators' opinions. The increase in the domestic real interest rate also means
that some domestic investment has been "crowded out" by the interest rate effects
of the export boom:
I  Ir  r  $40  0.1  $4
The total effect on gross exports from the net change in the exchange rate is:
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GX  X    $6  9  $54
Since the total change in imports is:
IM  IMy  Y  0.15  $100  $15
The total change in net exports from the shift in expectations is +$39 billion.
10.4 Inflation and the Price Level
10.4.1 Aggregate Supply and the Phillips Curve
Inflation is an increase in the general, overall price level. An increase in the price of any
one particular good--even a large increase in the price of any one particular good--is not
inflation. Inflation is an increase in the price of just about everything: the prices of all (or
nearly all) goods (and incomes) have to rise, and they have to rise together by
approximately the same proportional amount for it to be inflation.
Whenever real GDP is greater than potential output, inflation is likely to be higher than
people had previously anticipated. Thus it is likely to speed up. This year's inflation is
likely to be higher than last year's. If total product continues to be higher than potential
output then inflation is likely to continue to accelerate upward. Conversely, whenever the
level of real GDP is below potential output, then inflation is likely to be lower than
people had previously anticipated. The inflation rate is likely to fall toward zero--and
perhaps prices will begin to fall in deflation.
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Economists explain these correlations between real GDP (relative to the level of potential
output) and the rate of inflation (relative to its previously-expected value) by invoking the
idea of a short-run aggregate supply relationship--a relationship between the price level
(or its rate of change) and real GDP that holds in the time span for which the IS-LM
framework is relevant. One algebraic way to write the short-run aggregate supply
function is as the form:
 P  P e 
Y Y*
   
 P e 
Y*
The proportional deviation of real GDP Y from potential output Y* is equal to a
parameter , the slope of the short-run aggregate supply function, times the proportional
deviation of the price level P from its previously-anticipated level Pe.
Since the inflation rate π is simply the proportional rate of change of the price level, we
can replace the price level and the expected price level with the actual inflation rate π and
the previously-expected inflation rate πe to get:
Y Y*
e
      
Y*
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Figure 10.13: Output Relative to Potential and the Inflation Rate
Inflation
Rate
Expected
Inflation
Output Relative to Potential
Potential
Output
Legend: When production is higher than potential output, prices will be higher
than
businesses, consumers, and workers had anticipated--and inflation will be higher
than expected inflation.
And if we invoke Okun's law--that the proportional deviation of real GDP from potential
output is equal to 2.5 times the difference between the natural rate of unemployment and
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the actual unemployment rate--and substitute unemployment for real GDP on the lefthand side, we get:
2.5  (U * U )       e 
which is equivalent to:
      (u  u*)
e
with  = 2.5/. The actual inflation rate is equal to the expected inflation rate, minus the
paramter  times the difference between the actual unemployment rate and the natural
rate of unemployment.
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Figure 10.14: The Phillips Curve
Inflation
Rate
Expected
Inflation
Unemployment Relative to
Its Natural Rate
Natural Rate
Legend: When inflation is higher than expected inflation and production is higher
than potential output, the unemployment rate will be lower than the natural rate of
unemployment. There is thus an inverse relationship in the short run between
inflation and unemployment: the lower unemployment, the higher inflation.
In this form the short-run aggregate supply relationship is called the Phillips curve,
named after the economist A.W. Phillips who first investigated it more than forty years
ago. The Phillips curve turns out to usually be the most convenient of the three forms in
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which to examine aggregate supply. But no matter which of the three forms of the
aggregate supply relationship you look at, the underlying concepts are the same.
Figure 10.15: Three Faces of the Aggregate Supply Relationship
Aggregate Supply--Price Level Form
...subtract off the
price level to
get the....
Price
Level
Aggregate Supply--Inflation Form
Inflation
Rate
Expected
price
level
Expected
inflation
Potential
output
Real GDP Relative
to Potential Output
Potential
output
Real GDP Relative
to Potential Output
...use Okun's law to get the...
Phillips Curve
Inflation
Rate
Expected
inflation
Natural
rate of
unemployment
Unemployment Rate
Legend: We can think of aggregate supply as being a relationship between output
and the price level, between output and the inflation rate, or between the
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unemployment rate and the inflation rate. All three of these are the same
relationship
viewed in different ways. Usually, but not always, the last of the three will be the
most convenient.
If the macroeconomic history of the past forty years has made anything clear, it is that the
short-run aggregate supply curve--the Phillips curve--shifts around a lot from decade to
decade, and sometimes from year to year. The position of the Phillips curve depends on
two concepts--the natural rate of unemployment and the rate of expected inflation--that
are themselves not constants but variables. Increases in the natural rate of unemployment
can--and do--raise the unemployment rate associated with any given value of the inflation
rate. Decreases in expected inflation lower the inflation rate associated with any given
value of the unemployment rate. We will look much more closely at their determinants in
the next chapter.
Figure 10.16: Shifts in the Phillips Curve
Phillips Curve
Inflation
Rate
Phillips Curve
Inflation
Rate
Expected
inflation
Expected
inflation
Unemployment Rate
Natural
rate of
unemployment
Natural
rate of
unemployment
Unemployment Rate
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Legend: When expected inflation changes, the position of the Phillips Curve
changes too.
10.4.2 Where Does the Short-Run Aggregate Supply
Relationship Come From?
There are a large number of reasons why high levels of real GDP (relative to potential
output) and low levels of unemployment (relative to the natural rate) should be associated
with higher inflation and a higher price level (relative to previously expected values).
When demand for products is stronger than anticipated, firms raise prices above what
they had previously planned. When aggregate demand is higher than potential output,
demand is stronger in nearly every single industry. Nearly all firms raise prices and hire
more workers. Employment expands beyond its average proportion of the adult
population and the unemployment rate falls below the "natural" rate of unemployment-the rate at which the rate of inflation is stable. High demand gives workers extra
bargaining power, and they use it to bargain for higher wage levels than they had
previously planned. Unions threaten to strike, knowing that firms will have a hard time
finding replacements. Individuals quit, knowing they can find better jobs elsewhere. Such
a high-pressure economy generates wages that rise faster than previously anticipated, and
they are passed along by firms in higher prices and accelerating inflation. Thus high
aggregate demand generates higher inflation.
When aggregate demand is higher than potential output, individual sectors and industries
in the economy quickly reach the limits of capacity: Bottlenecks emerge. Confronted
with a bottleneck--a vital item, part, or process where production cannot be increased
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quickly--potential purchasers bid up the price of the bottlenecked item: Since a car is
useless without brakes, it is worth it for car manufacturers to pay any price for brake
assemblies if they are in short supply. Such high prices signal to the market that the
bottleneck industry should expand, and triggers investment that in the end boosts
productive capacity. But developing bottlenecks lead to prices that increase faster than
expected--thus to accelerating inflation.
To some degree the puzzle is not why are high levels of real GDP (and low levels of
unemployment) associated with higher prices and inflation, but why is the association as
weak as it is. Back in chapter 7, after all, changes in the total volume of nominal spending
showed up all as changes in prices and none as changes in real GDP. That too is a subject
for the next chapter--on aggregate supply
10.4.3 The Aggregate Demand Relation
One way to integrate the analysis of output and unemployment on the one hand with the
analysis of the price level and the inflation rate on the other is to say that the IS-LM
diagram determines the level of real GDP, and that the aggregate supply relation--in any
or all of its three forms--determines the price level and the inflation rate. On any of the
three sets of axes we have used to plot the aggregate supply relationship, the result of the
IS-LM--call it the aggregate demand relationship--would appear as a vertical line. And
where this aggregate demand relation crosses the aggregate supply curve tells us the
combination of real GDP and the price level, or of unemployment and inflation, for the
economy.
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However, this is not quite right. For the time horizon in which price levels change and
inflation accelerates or decelerates is a time horizon in which the determinants of
aggregate demand, of the IS and LM curves, have time to shift. And usually they shift in
such a way that a higher price level (or inflation rate) generates a lower level of
equilibrium real GDP.
Figure 10.17: Aggregate Supply and Aggregate Demand When Demand Does Not
Depend on Prices
Aggregate Supply--Price Level Form
Aggregate Supply--Inflation Form
Price
Level
Expected
price
level
Expected
inflation
Potential
output
Real GDP Relative
to Potential Output
Phillips Curve
Inflation
Rate
Inflation
Rate
Expected
inflation
Potential
output
Real GDP Relative
to Potential Output
Unemployment Rate
Natural
rate of
unemployment
Aggregate Demand
Legend: When we
Higher prices and inflation generate a lower level of equilibrium real GDP through two
channels, one automatic and the other not so automatic. The automatic channel occurs
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when the central bank, or the monetary system in general, provides the economy with a
fixed value for the nominal money stock. A higher inflation rate then means a higher
price level. A fixed nominal money stock and a higher price level means a lower real
money stock. And a lower real money stock means an LM curve shifted in and to the left-and a lower level of equilibrium real GDP in the IS-LM framework. Thus the higher the
price level (or the inflation rate), the lower is equilibrium real GDP.
The not-so-automatic channel occurs because central banks are as a rule averse to
inflation. A higher level of inflation will induce a central bank to raise real interest rates.
The benchmark rule for setting real interest rates as a function of inflation and
unemployment was set out by Stanford University economist John Taylor, and takes the
form:
r  r *   (  ' )    (u * u)
where r is the real interest rate the central bank chooses, π-π' is the deviation of inflation
from the target level that the central bank has chosen, and u*-u is the difference between
the central bank's estimate of the natural rate of unemployment and the current rate of
unemployment. A central bank following such a rule will set the real interest equal to
some baseline value r*, plus a term that depends on the deviation between actual inflation
and the target inflation level--the higher actual inflation, the higher will the central bank
set real interest rates--and a term that depends on the deviation of unemployment from
the natural rate--the higher actual unemployment, the lower will the central bank set real
interest rates.
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A central bank following a Taylor-like rule or one fixing the nominal money stock will
both tend to behave the same. In both cases, we will find that real GDP as generated by
the IS-LM framework is a decreasing function of the price level or the inflation rate: the
higher are prices, the lower is aggregate demand. In the first case the central bank will
directly respond to higher inflation by raising the real interest rate and reducing aggregate
demand. In the second case the rising price level will lower the real money stock (since
the nominal money stock is fixed), raise interest rates, and reduce aggregate demand.
Figure 10.18: Aggregate Demand and Supply When Demand Depends on the Price
Level
Aggregate Supply--Price Level Form
Aggregate Supply--Inflation Form
Price
Level
Expected
price
level
Expected
inflation
Potential
output
Real GDP Relative
to Potential Output
Phillips Curve
Inflation
Rate
Inflation
Rate
Expected
inflation
Potential
output
Real GDP Relative
to Potential Output
Unemployment Rate
Natural
rate of
unemployment
Aggregate Demand
Like the aggregate supply relationship, the aggregate demand relationship can be drawn
on any of three sets of axes: the information conveyed and the relationship modeled is the
same. For simplicity--and because it is the most useful--in later chapters we drop the
three-fold representation of aggregate demand and supply, and use the Phillips curve
formulation only.
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10.5 Chapter Summary
10.5.1 Main Points
The money market is in equilibrium when the level of total incomes and of the shortterm nominal interest rate is just right to make households and businesses want to
hold all the real money balances that exist in the economy.
When the central bank's policy keeps the money stock fixed--or when there is no
central bank--the LM curve consists of those combinations of interest rates and real
GDP levels at which money demand equals money supply.
When the central bank's policy keeps the money stock fixed--or when there is no
central bank--then the point at which the IS and LM curves cross determines the
equilibrium level of real GDP and the interest rate.
The IS-LM framework consists of two equilibrium conditions: the IS curve shows
those combinations of interest rates and real GDP levels at which aggregate demand
is equal to total production; the LM curve shows those combinations of interest rates
and real GDP levels at which money demand is equal to money supply. Both
equilibrium conditions must be satisfied.
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An IS shock is any shock to the level of aggregate demand: it shifts the IS curve.
An LM shock is a shock to money demand or money supply: it shifts the position of
the LM curve.
Because of Okun's law, there is no point in distinguishing business cycles in
unemployment different from business cycles in output: they are the same thing.
The relationship between shifts in the equilibrium on the IS-LM diagram and changes
in the real exchange rate and the balance of trade is relatively complicated. It is
straightforward to calculate, but has no truly simple representation.
The aggregate supply curve captures the relationship between aggregate demand and
the price level. The higher is real GDP, the higher is the price level likely to be.
The aggregate supply curve can be represented either as a relationship between the
level of output and the level of prices, the level of output and the rate of change of
prices, or the unemployment rate and the rate of change of prices. They all convey the
same information.
The aggregate demand relationship arises because changes in the price level and
inflation rates cause shifts in the determinants of aggregate demand--either directly as
changes in the price level change the money stock, or indirectly as changes in the
inflation rate change the interest rate target of the central bank.
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10.5.2 Important Concepts
Money demand
Real money balances
Money stock
Money supply
Money market equilibrium
LM curve
IS-LM diagram
IS shock
LM shock
Okun's law
Natural rate of unemployment
Expected rate of inflation
Phillips curve
Aggregate supply
International shocks
10.5.3 Analytical Exercises
1. What are the qualitative effects, in the IS-LM model, of…
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…an increase in firms' optimism about future profits?
…a sudden improvement in banking technology that makes checks clear two days
faster?
…a wave of credit card fraud that leads people to use cash for purchsese more
often?
…a banking crisis that diminishes banks' willingness to accept deposits?
…a sudden military spending program?
2. What are the qualitative effects of an increase in real GDP on the rate of inflation?
3. Explain why the LM curve slopes upward. What changes in the economic environment
can you think of that would increase its slope?
4. Suppose that the expected rate of inflation suddenly jumped. What would happen--with
no other changes in the economic environment--to the IS-LM equilibrium? Would
equilibrium real GDP go up or down? Would the equilibrium real interest rate go up or
down?
5. Suppose that the term premium--the gap between short-term and long-term interest
rates--suddenly went up. What would happen--with no other changes in the economic
environment--to the IS-LM equilibrium? Would equilibrium real GDP go up or down?
Would the equilibrium real interest rate in the IS curve go up or down?
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10.5.4 Policy-Relevant Exercises [to be updated every year…]
1. In 1999 the unemployment rate averaged 4.3 percent, and the rate of growth of
potential output was 3.0 percent per year. Assuming that the rate of growth of potential
output remains unchanged and that Okun's law holds, how much higher would you
expect real GDP to be in 2002 than in 1999 if in year 2000 the unemployment rate
averages 6 percent?
2. In 1999 the unemployment rate averaged 4.3 percent. Back in 1995 it averaged 5.6
percent. Real GDP in 1999 stood some 15.8 percent above real GDP in 1995. Assuming
that the natural rate of unemployment remained unchanged between 1995 and 1999,
how much of this growth in real GDP over those four years was due to increases in
potential output? How much was due to "cyclical" factors--fluctuations in
unemployment?
3. Between 1980 and 1986 U.S. net exports shifted from +$10 billion (in 1992 dollars) to
-$164 billion. The unemployment rates in 1980 and 1986 were almost identical. Almost
all observers agreed that this shift in the trade deficit was driven by shifts in U.S.
domestic condition. Do you think that between 1980 and 1986…
…the LM curve shifted right and the IS curve shifted right?
…the LM curve shifted right and the IS curve shifted left?
…the LM curve shifted left and the IS curve shifted right?
…the LM curve shifted left and the IS curve shifted left?
4. Suppose that the Federal Reserve is wondering whether it should follow a policy of
stabilizing the money stock or one of stabilizing the real interest rate. Suppose that all
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shocks to the economy are shocks to autonomous spending: which policy leads to smaller
shifts in real GDP in response to shocks? Suppose that all of the shocks to the economy
are shocks to the parameters of money demand--to the parameters L0 and Li in the money
demand equation:
Y
M 

 P  V0  Vi  (r  )
d
and in the LM equation:
Y  V0  Vi  (r  ) 
M 
 P 
which policy is now best in terms of leading to smaller shifts in real GDP? Suppose that
the only shocks to the economy are changes in assessments of expected inflation π. Now
what is your answer?
5. Suppose that money demand is interest insensitive. That is, suppose that the money
demand function is:
M  Y

 P  V
d
with no dependence on the interest rate at all. What, then, is the LM curve for this
economy? What effect does an increase in government purchases have on the level of real
interest rates and the equilibrium level of annual real GDP?
6. Consider the following data from the 1990s:
Year
1990
Inflation Rate Unemployment Rate Real Interest Rate
4.4%
5.6%
3.1%
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1991
1992
1993
1994
1995
1996
1997
1998
1999
60
3.9%
2.8%
2.6%
2.4%
2.3%
1.9%
1.9%
1.3%
1.8%
6.8%
7.5%
6.9%
6.1%
5.6%
5.4%
4.9%
4.5%
4.3%
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1.5%
0.6%
0.4%
1.9%
3.2%
3.1%
3.2%
3.5%
3.6%
Which particular Taylor rule reaction function for the real interest rate do you think that
the Federal Reserve has been following over the decade of the 1990s? Does it look like
the Federal Reserve has been reacting more to movements in the inflation or movements
in the unemployment rate?