AGGREGATE DEMAND II
IS

LM MODEL
Eva Hrom
á
dkov
á
, 22.3 2010
Macroeconomics ECO 110/1, AAU
Lecture
7
Overview of Lecture
7
IS

LM model of AD curve:
Model for AD curve => analysis of stabilization
policies
IS curve
–
goods market
Fiscal policy
–
expenditures and taxes
LM curve
–
money market
Monetary policy
–
money supply
Equilibrium
–
interest rates
2
IS

LM model
Context
3
We have already introduced the model of aggregate
demand (QTM) and aggregate supply.
Long run
prices
flexible
output determined by
factors of production &
technology
unemployment equals its
natural rate
Short run
prices
fixed
output determined by
aggregate demand
unemployment is
negatively
related to output
IS

LM model
Context II
4
Today we will develop
IS

LM model
, the theory that
explains the aggregate demand curve
First, we focus on the
short run
and assume hat price level
is fixed
Then, we allow price to be
flexible
, and derive AD curve
Finally, we analyze the effect of
fiscal and monetary
policy
on the most important macroeconomic aggregates
–
output and unemployment
IS curve
Keynesian cross
5
A simple closed economy model in which income is
determined by expenditure.
(due to J.M. Keynes)
Notation:
I
= planned investment
E
=
C
+
I
+
G
= planned expenditure
Y
= real GDP = actual expenditure
Difference between actual & planned expenditure:
unplanned inventory investment
IS curve
Elements of the Keynesian cross
6
Consumption function:
C = MPC*(Y

T)
Govt. policy variables:
G, T
Investment:
I = I(r)
Planned expenditure:
E = C(Y

T) + I(r) + G
Equilibrium:
Y = E
IS curve
Graphing planned expenditure
7
income, output,
Y
E
planned
expenditure
E
=
C
+
I
+
G
Slope
is MPC
IS curve
Graphing the equilibrium condition
8
income, output,
Y
E
planned
expenditure
E
=
Y
45
º
IS curve
Equilibrium value of income
9
E>Y: depleting inventories => produce more
E<Y: accumulating inventories=> produce less
income, output,
Y
E
planned
expenditure
E
=
Y
E>Y
E<Y
IS curve
Fiscal policy
10
Fiscal stimulus:
Increase in government expenditures
Cut taxes
Increase transfer payments
Fiscal restraint:
Decrease in government expenditures
Increased taxes
Decreased transfer payments
IS curve
Increase in government purchases
11
Y
E
E
=
C
+
I
+
G
1
E
1
=
Y
1
E
=
C
+
I
+
G
2
E
2
=
Y
2
Y
G
Looks like
Y>
G
IS curve
Why is change in Y > change in G?
12
Def: Government purchases multiplier:
Initially, the increase in
G
causes an equal increase in
Y
:
Y
=
G
.
But
Y
C (Y

T)
further
Y
further
C
further
Y
So the government purchases multiplier will be greater
than one.
IS curve
Change in G

Sum up changes in expenditure
13
IS curve
Increase in taxes
14
Y
E
E
=
C
2
+
I
+
G
E
2
=
Y
2
E
=
C
1
+
I
+
G
E
1
=
Y
1
Y
At
Y
1
, there is now
an unplanned
inventory buildup…
…so firms
reduce output,
and income falls
toward a new
equilibrium
C
=
MPC
T
IS curve
Change in T

Sum up changes in expenditure
15
equilibrium condition
in changes
I
and
G
exogenous
Solving for
Y
:
Final result:
IS curve
Tax multiplier
Question: how is this different from the government spending
multiplier considered previously?
The tax multiplier:
…is
negative:
An increase in taxes reduces consumer spending, which reduces
equilibrium income.
…is
smaller than the
govt
spending multiplier:
(in absolute value) Consumers save the fraction (1

MPC) of a tax
cut, so the initial boost in spending from a tax cut is smaller than
from an equal increase in
G
.
16
IS curve
How to derive the IS curve I
17
def: a graph of all combinations of
r
and
Y
that result in goods
market equilibrium,
i.e.
actual expenditure (output) = planned expenditure
The equation for the
IS
curve is:
Y
= C(
Y

T) + I(
r
) + G
The
IS
curve is
negatively sloped.
Intuition:
A fall in the interest rate motivates firms to increase investment
spending, which drives up total planned spending (
E
).
To restore equilibrium in the goods market, output (a.k.a. actual
expenditure,
Y
) must increase.
Y
2
Y
1
Y
2
Y
1
IS curve
How to derive the IS curve II
r
I
Y
E
r
Y
E
=
C
+
I
(
r
1
)+
G
E
=
C
+
I
(
r
2
)+
G
r
1
r
2
E
=
Y
IS
I
E
Y
Y
2
Y
1
Y
2
Y
1
IS curve
Fiscal policy and IS curve
–
ex. of increase in G
At given value of
r
,
G
E
Y
Y
E
r
Y
E
=
C
+
I
(
r
1
)+
G
1
E
=
C
+
I
(
r
1
)+
G
2
r
1
E
=
Y
IS
1
The horizontal
distance of the
IS shift equals
IS
2
…so the IS curve
shifts
to the right.
Y
LM curve
How to build the LM curve
20
The theory of liquidity preference:
Developed by John Maynard Keynes.
A simple theory in which the interest rate
is determined by money supply and
money demand.
LM curve
Money supply
M/P
real money
balances
r
interest
rate
The supply of real
money balances is
fixed
.
LM curve
Money demand
22
M/P
real money
balances
r
interest
rate
L
(
r,Y
)
The demand for
real money
balances is
negatively
dependent on
interest rate.
LM curve
Equilibrium
23
M/P
real money
balances
r
interest
rate
L
(
r,Y
)
r
1
The interest rate
adjusts
to equate the
supply and
demand for
money
LM curve
Monetary policy
24
LM curve
Monetary policy
–
How can CB affect the interest rate?
25
M/P
real money
balances
r
interest
rate
L
(
r ,Y
)
r
1
r
2
To reduce r, central bank
reduces M.
In reality, this is hardly he
case.
More used technique =
change of
discount rate
.
LM curve
How to derive LM curve?
26
The
LM
curve
is a graph of all combinations of
r
and
Y
that equate the supply and demand for real money
balances.
The equation for the
LM
curve is:
The
LM
curve is
positively sloped
.
Intuition: An increase in income raises money demand.
Since the supply of real balances is fixed, there is now excess
demand in the money market at the initial interest rate. The
interest rate must rise to restore equilibrium in the money market.
LM curve
How to derive LM curve II
M/P
r
L
(
r
,
Y
1
)
r
1
r
2
r
Y
Y
1
r
1
r
2
LM
1
(a)
The market for
real money balances
(b)
The LM curve
LM
2
IS

LM model
Equilibrium
The short

run equilibrium is the
combination of
r
and
Y
that
simultaneously satisfies the
equilibrium conditions in the
goods & money markets:
Y
r
IS
LM
Equilibrium
interest
rate
Equilibrium
level of
income
slide
29
causing output &
income to rise.
IS
1
IS

LM model
Fiscal policy:
An
increase in government purchases
1.
IS
curve shifts right
Y
r
LM
r
1
Y
1
IS
2
Y
2
r
2
1.
2.
This raises money
demand, causing the
interest rate to rise…
2.
3.
…which reduces investment, so the
final increase in
Y
3.
slide
30
IS
1
1.
IS

LM model
Fiscal policy: A tax cut
Y
r
LM
r
1
Y
1
IS
2
Y
2
r
2
Because consumers save
(1
MPC) of the tax cut,
the initial boost in
spending is smaller for
T
than for an equal
G
…
and the
IS
curve
shifts by
1.
2.
2.
…so the effects on
r
and
Y
are smaller for a
T
than
for an equal
G
.
2.
slide
31
2.
…causing the
interest rate to fall
IS
IS

LM model
Monetary
Policy: an increase in
M
1.
M
> 0 shifts
the
LM
curve down
(or to the right)
Y
r
LM
1
r
1
Y
1
Y
2
r
2
LM
2
3.
…which increases
investment, causing
output & income to
rise.
IS

LM model
Shocks I
32
LM
shocks
: exogenous changes in the demand for
money.
Examples:
•
a wave of credit card fraud increases demand for
money
•
more ATMs or the Internet banking reduce money
demand
IS

LM model
Shocks II
33
IS
shocks
: exogenous changes in the demand for goods
& services.
Examples:
•
stock market boom or crash
change in households’ wealth
C
•
change in business or consumer
confidence or expectations
I
and/or
C
Aggregate demand
How to get from IS

LM to AD
34
So far, we’ve been using the
IS

LM
model to
analyze the
short run
, when the price level is
assumed fixed.
However, a change in
P
would shift the
LM
curve and therefore affect
Y
.
The
aggregate demand curve
(
introduced in chap. 9
)
captures this
relationship between
P
and
Y
Y
1
Y
2
Aggregate demand
How to get from IS

LM to AD II
Y
r
Y
P
IS
LM
(
P
1
)
LM
(
P
2
)
AD
P
1
P
2
Y
2
Y
1
r
2
r
1
Intuition for slope
of
AD
curve:
P
(
M
/
P
)
LM
shifts left
r
I
Y
Aggregate demand
Effect of monetary policy
Y
P
IS
LM
(
M
2
/
P
1
)
LM
(
M
1
/
P
1
)
AD
1
P
1
Y
1
Y
1
Y
2
Y
2
r
1
r
2
The Fed can increase
aggregate demand:
M
LM
shifts right
AD
2
Y
r
r
I
Y
at each
value of
P
Y
2
Y
2
r
2
Y
1
Y
1
r
1
Aggregate demand
Effect of fiscal policy
Y
r
Y
P
IS
1
LM
AD
1
P
1
Expansionary fiscal policy
(
G
and/or
T
)
increases agg. demand:
T
C
IS shifts right
Y
at each
value of
P
AD
2
IS
2
slide
38
Aggregate demand
When is fiscal policy more effective?
Fiscal policy is effective
(
Y
will rise much) when:
LM flatter
As the rise in
G
raises Y,
the increase in money demand
does not raise
r
much
:
so investment is not crowded
out as much.
LM’
Y
2
’
2’
Y
2
IS
2
2
LM
Y
1
IS
1
r
1
slide
39
Aggregate demand
When is monetary policy more effective?
Monetary policy is effective
(
Y
will rise much) when:
IS flatter
As a rise in
M
lowers the
interest rate (
r
),
investment rises more
in
response to the fall in
r
,
so output rises more
.
Y
2
LM
2
2
Y
1
LM
1
r
1
Y
2
’
2’
IS
IS’
slide
40
IS

LM and AD

AS model
combination of short & long run
rise
fall
remain constant
In the short

run
equilibrium, if
then over time,
the price level will
IS

LM and AD

AS model
short & long run effect of IS shock I
A negative
IS
shock
shifts
IS
and
AD
left,
causing
Y
to fall.
Y
r
Y
P
LRAS
LRAS
IS
1
SRAS
1
P
1
LM
(
P
1
)
IS
2
AD
2
AD
1
IS

LM and AD

AS model
short & long run effect of IS shock II
Y
r
Y
P
LRAS
LRAS
IS
1
SRAS
1
P
1
LM
(
P
1
)
IS
2
AD
2
AD
1
In the new short

run
equilibrium,
IS

LM and AD

AS model
short & long run effect of IS shock II
Y
r
Y
P
LRAS
LRAS
IS
1
SRAS
1
P
1
LM
(
P
1
)
IS
2
AD
2
AD
1
In the new short

run
equilibrium,
Over time,
P
gradually falls,
which causes
•
SRAS
to move down
•
M
/
P
to increase,
which causes
LM
to move down
AD
2
IS

LM and AD

AS model
short & long run effect of IS shock III
Y
r
Y
P
LRAS
LRAS
IS
1
SRAS
1
P
1
LM
(
P
1
)
IS
2
AD
1
Over time,
P
gradually falls,
which causes
•
SRAS
to move down
•
M
/
P
to increase,
which causes
LM
to move down
SRAS
2
P
2
LM
(
P
2
)
AD
2
SRAS
2
P
2
LM
(
P
2
)
IS

LM and AD

AS model
short & long run effect of IS shock IV
Y
r
Y
P
LRAS
LRAS
IS
1
SRAS
1
P
1
LM
(
P
1
)
IS
2
AD
1
This process continues
until economy reaches
a long

run equilibrium
with
The Great
Depression
CASE STUDY
Unemployment
(right scale)
Real GNP
(left scale)
slide
47
slide
48
The Great Depression
CASE STUDY
Real side of economy
:
Output:
falling
Consumption:
falling
Investment:
falling much
Gov. purchases:
fall (with a delay)
slide
49
slide
50
The Great Depression
CASE STUDY
Nominal side
:
Nominal interest rate:
falling
Money supply (nominal):
falling
Price level:
falling (deflation)
slide
51
The Great Depression
CASE STUDY
The Spending Hypothesis:
Shocks to the IS Curve
asserts
that the Depression was largely due to an
exogenous fall in the demand for goods & services

a leftward shift of the
IS
curve
evidence:
output and interest rates both fell, which is what a
leftward
IS
shift would cause
slide
52
The Spending Hypothesis:
Reasons
for the IS shift
1.
Stock
market crash
exogenous
C
Oct

Dec 1929: S&P 500 fell 17%
Oct 1929

Dec 1933: S&P 500 fell 71%
2.
Drop in investment
“correction” after overbuilding in the 1920s
widespread bank failures made it harder to obtain
financing for investment
3.
Contractionary
fiscal policy
in the face of falling tax revenues and increasing
deficits, politicians raised tax rates and cut spending
slide
53
The Money Hypothesis:
A
Shock to the LM Curve
asserts that the Depression was largely due to
huge fall in the money supply
evidence:
M1 fell 25% during 1929

33.
But, two problems with this hypothesis:
1.
P
fell even more, so
M
/
P
actually rose slightly
during 1929

31.
2.
nominal interest rates fell, which is the opposite
of what would result from a leftward
LM
shift.
slide
54
The Money Hypothesis:
Revision
There was a big deflation:
P
fell 25% 1929

33.
A sudden fall in expected inflation means the ex

ante real
interest rate rises for any given nominal rate (
i
)
ex ante
real interest rate =
i
–
e
This could have discouraged the investment expenditure and
helped cause the depression.
Since the deflation likely was caused by fall in M, monetary
policy may have played a role here.
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