CHAPTER 10 Aggregate Demand I slide 1
Context
Chapter 9 introduced the model of aggregate
demand 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
CHAPTER 10 Aggregate Demand I slide 2
Context
This chapter develops the IS-LM model,the
theory that yields the aggregate demand curve,
We focus on the short run and assume the
price level is fixed,
CHAPTER 10 Aggregate Demand I slide 3
The Keynesian Cross
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
CHAPTER 10 Aggregate Demand I slide 4
Elements of the Keynesian Cross
()C C Y T
II?
,G G T T
()E C Y T I G
A c t u a l e x p e n d it u r e P la n n e d e x p e n d it u r e
YE
consumption function:
for now,
investment is exogenous:
planned expenditure:
Equilibrium condition:
govt policy variables:
CHAPTER 10 Aggregate Demand I slide 5
Graphing planned expenditure
income,output,Y
E
planned
expenditure
E =C +I +G
MPC
1
CHAPTER 10 Aggregate Demand I slide 6
Graphing the equilibrium condition
income,output,Y
E
planned
expenditure
E =Y
45o
CHAPTER 10 Aggregate Demand I slide 7
The equilibrium value of income
income,output,Y
E
planned
expenditure
E =Y
E =C +I +G
Equilibrium
income
CHAPTER 10 Aggregate Demand I slide 8
An increase in government purchases
Y
E
E =C +I +G1
E1 = Y1
E =C +I +G2
E2 = Y2?Y
At Y1,
there is now an
unplanned drop
in inventory…
…so firms
increase output,
and income
rises toward a
new equilibrium
G
CHAPTER 10 Aggregate Demand I slide 9
Solving for?Y
Y C I G
Y C I G
M P C YG
CG
( 1 M P C ) YG
1
1 M P CYG
equilibrium condition
in changes
because I exogenous
because?C = MPC?Y
Collect terms with?Y
on the left side of the
equals sign:
Finally,solve for?Y,
CHAPTER 10 Aggregate Demand I slide 10
The government purchases multiplier
Example,MPC = 0.8
1
1 M P C
11
5
1 0 8 0 2..
YG
G G G
The increase in G causes income to increase
by 5 times as much!
CHAPTER 10 Aggregate Demand I slide 11
The government purchases multiplier
In the example with MPC = 0.8,
Definition,the increase in income resulting
from a $1 increase in G.
In this model,the G multiplier equals
1
1 M P C
Y
G
1 5
1 0,8
Y
G
CHAPTER 10 Aggregate Demand I slide 12
Why the multiplier is greater than 1
Initially,the increase in G causes an equal
increase in Y,?Y =?G.
But?YC
further?Y
further?C
further?Y
So the final impact on income is much
bigger than the initial?G.
CHAPTER 10 Aggregate Demand I slide 13
An increase in taxes
Y
E
E =C2 +I +G
E2 = Y2
E =C1 +I +G
E1 = Y1?Y
At Y1,there is now
an unplanned
inventory buildup……so firms
reduce output,
and income falls
toward a new
equilibrium
C =?MPC?T
Initially,the tax
increase reduces
consumption,and
therefore E:
CHAPTER 10 Aggregate Demand I slide 14
Solving for?Y
Y C I G
M P C YT
C
( 1 M P C ) M P CYT
eq’m condition in
changes
I and G exogenous
Solving for?Y,
M P C
1 M P CYT
Final result:
CHAPTER 10 Aggregate Demand I slide 15
The Tax Multiplier
def,the change in income resulting from
a $1 increase in T,
M P C
1 M P C
Y
T
0 8 0 8 4
1 0 8 0 2
..
..
Y
T
If MPC = 0.8,then the tax multiplier equals
CHAPTER 10 Aggregate Demand I slide 16
The Tax Multiplier
…is negative:
A tax hike reduces
consumer spending,
which reduces income.
…is greater than one
(in absolute value),
A change in taxes has a
multiplier effect on income,
…is smaller than the govt spending multiplier:
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,
CHAPTER 10 Aggregate Demand I slide 17
The Tax Multiplier
…is negative:
An increase in taxes reduces consumer spending,
which reduces equilibrium income.
…is greater than one (in absolute value),
A change in taxes has a multiplier effect on
income,
…is smaller than the govt spending multiplier:
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,
CHAPTER 10 Aggregate Demand I slide 18
Exercise:
Use a graph of the Keynesian Cross
to show the impact of an increase in
investment on the equilibrium level of
income/output,
CHAPTER 10 Aggregate Demand I slide 19
The IS curve
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
CHAPTER 10 Aggregate Demand I slide 20
Y2Y1
Y2Y1
Deriving the IS curve
rI
Y
E
r
Y
E =C +I(r1 )+G
E =C +I(r2 )+G
r1
r2
E =Y
IS
IE
Y
CHAPTER 10 Aggregate Demand I slide 21
Understanding the IS curve’s slope
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,
CHAPTER 10 Aggregate Demand I slide 22
The IS curve and the Loanable Funds model
S,I
r
I(r )r1
r2
r
YY
1
r1
r2
(a) The L.F,model (b) The IS curve
Y2
S1S2
IS
CHAPTER 10 Aggregate Demand I slide 23
Fiscal Policy and the IS curve
We can use the IS-LM model to see
how fiscal policy (G and T ) can affect
aggregate demand and output,
Let’s start by using the Keynesian Cross
to see how fiscal policy shifts the IS
curve…
CHAPTER 10 Aggregate Demand I slide 24
Y2Y1
Y2Y1
Shifting the IS curve,?G
At any value of r,
GEY
Y
E
r
Y
E =C +I(r1 )+G1
E =C +I(r1 )+G2
r1
E =Y
IS1
The horizontal
distance of the
IS shift equals
IS2
…so the IS curve
shifts to the right.
1
1 M P CYG
Y
CHAPTER 10 Aggregate Demand I slide 25
Exercise,Shifting the IS curve
Use the diagram of the Keynesian Cross
or Loanable Funds model to show how
an increase in taxes shifts the IS curve,
CHAPTER 10 Aggregate Demand I slide 26
The Theory of Liquidity Preference
due to John Maynard Keynes.
A simple theory in which the interest rate
is determined by money supply and
money demand,
CHAPTER 10 Aggregate Demand I slide 27
Money Supply
The supply of
real money
balances
is fixed:
sM P M P?
M/P
real money
balances
r
interest
rate
sMP
MP
CHAPTER 10 Aggregate Demand I slide 28
Money Demand
Demand for
real money
balances:
M/P
real money
balances
r
interest
rate
sMP
MP
()dM P L r?
L(r)
CHAPTER 10 Aggregate Demand I slide 29
Equilibrium
The interest
rate adjusts
to equate the
supply and
demand for
money:
M/P
real money
balances
r
interest
rate
sMP
MP
()M P L r? L(r)
r1
CHAPTER 10 Aggregate Demand I slide 30
How the Fed raises the interest rate
To increase r,
Fed reduces M
M/P
real money
balances
r
interest
rate
1M
P
L(r)
r1
r2
2M
P
CHAPTER 10 Aggregate Demand I slide 31
CASE STUDY
Volcker’s Monetary Tightening
Late 1970s,? > 10%
Oct 1979,Fed Chairman Paul Volcker
announced that monetary policy
would aim to reduce inflation.
Aug 1979-April 1980,
Fed reduces M/P 8.0%
Jan 1983,? = 3.7%
How do you think this policy change
would affect interest rates?
CHAPTER 10 Aggregate Demand I slide 32
Volcker’s Monetary Tightening,cont.
i < 0?i > 0
1/1983,i = 8.2%8/1979,i = 10.4%4/1980,i = 15.8%
flexiblesticky
Quantity Theory,
Fisher Effect
(Classical)
Liquidity Preference
(Keynesian)
prediction
actual
outcome
The effects of a monetary tightening
on nominal interest rates
prices
model
long runshort run
CHAPTER 10 Aggregate Demand I slide 33
The LM curve
Now let’s put Y back into the money demand
function:
(,)M P L r Y?
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:
dM P L r Y? (,)
CHAPTER 10 Aggregate Demand I slide 34
Deriving the LM curve
M/P
r
1M
P
L(r,Y1 )
r1
r2
r
YY
1
r1
L(r,Y2 )
r2
Y2
LM
(a) The market for
real money balances (b) The LM curve
CHAPTER 10 Aggregate Demand I slide 35
Understanding the LM curve’s slope
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.
CHAPTER 10 Aggregate Demand I slide 36
How?M shifts the LM curve
M/P
r
1M
P
L(r,Y1 )r1
r2
r
YY
1
r1
r2
LM1
(a) The market for
real money balances (b) The LM curve
2M
P
LM2
CHAPTER 10 Aggregate Demand I slide 37
Exercise,Shifting the LM curve
Suppose a wave of credit card fraud
causes consumers to use cash more
frequently in transactions,
Use the Liquidity Preference model
to show how these events shift the
LM curve,
CHAPTER 10 Aggregate Demand I slide 38
The short-run equilibrium
The short-run equilibrium is
the combination of r and Y
that simultaneously satisfies
the equilibrium conditions in
the goods & money markets,
( ) ( )Y C Y T I r G
Y
r
(,)M P L r Y?
IS
LM
Equilibrium
interest
rate
Equilibrium
level of
income
CHAPTER 10 Aggregate Demand I slide 39
The Big Picture
Keynesian
Cross
Theory of
Liquidity
Preference
IS
curve
LM
curve
IS-LM
model
Agg,
demand
curve
Agg,
supply
curve
Model of
Agg,
Demand
and Agg,
Supply
Explanation
of short-run
fluctuations
CHAPTER 10 Aggregate Demand I slide 40
Chapter summary
1,Keynesian Cross
basic model of income determination
takes fiscal policy & investment as exogenous
fiscal policy has a multiplied impact on income.
2,IS curve
comes from Keynesian Cross when planned
investment depends negatively on interest rate
shows all combinations of r and Y that
equate planned expenditure with actual
expenditure on goods & services
CHAPTER 10 Aggregate Demand I slide 41
Chapter summary
3,Theory of Liquidity Preference
basic model of interest rate determination
takes money supply & price level as exogenous
an increase in the money supply lowers the
interest rate
4,LM curve
comes from Liquidity Preference Theory when
money demand depends positively on income
shows all combinations of r andY that equate
demand for real money balances with supply
CHAPTER 10 Aggregate Demand I slide 42
Chapter summary
5,IS-LM model
Intersection of IS and LM curves shows the
unique point (Y,r ) that satisfies equilibrium
in both the goods and money markets,
CHAPTER 10 Aggregate Demand I slide 43
Preview of Chapter 11
In Chapter 11,we will
use the IS-LM model to analyze the impact
of policies and shocks
learn how the aggregate demand curve
comes from IS-LM
use the IS-LM and AD-AS models together
to analyze the short-run and long-run
effects of shocks
learn about the Great Depression using our
models
CHAPTER 10 Aggregate Demand I slide 44
Context
Chapter 9 introduced the model of aggregate
demand 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
CHAPTER 10 Aggregate Demand I slide 2
Context
This chapter develops the IS-LM model,the
theory that yields the aggregate demand curve,
We focus on the short run and assume the
price level is fixed,
CHAPTER 10 Aggregate Demand I slide 3
The Keynesian Cross
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
CHAPTER 10 Aggregate Demand I slide 4
Elements of the Keynesian Cross
()C C Y T
II?
,G G T T
()E C Y T I G
A c t u a l e x p e n d it u r e P la n n e d e x p e n d it u r e
YE
consumption function:
for now,
investment is exogenous:
planned expenditure:
Equilibrium condition:
govt policy variables:
CHAPTER 10 Aggregate Demand I slide 5
Graphing planned expenditure
income,output,Y
E
planned
expenditure
E =C +I +G
MPC
1
CHAPTER 10 Aggregate Demand I slide 6
Graphing the equilibrium condition
income,output,Y
E
planned
expenditure
E =Y
45o
CHAPTER 10 Aggregate Demand I slide 7
The equilibrium value of income
income,output,Y
E
planned
expenditure
E =Y
E =C +I +G
Equilibrium
income
CHAPTER 10 Aggregate Demand I slide 8
An increase in government purchases
Y
E
E =C +I +G1
E1 = Y1
E =C +I +G2
E2 = Y2?Y
At Y1,
there is now an
unplanned drop
in inventory…
…so firms
increase output,
and income
rises toward a
new equilibrium
G
CHAPTER 10 Aggregate Demand I slide 9
Solving for?Y
Y C I G
Y C I G
M P C YG
CG
( 1 M P C ) YG
1
1 M P CYG
equilibrium condition
in changes
because I exogenous
because?C = MPC?Y
Collect terms with?Y
on the left side of the
equals sign:
Finally,solve for?Y,
CHAPTER 10 Aggregate Demand I slide 10
The government purchases multiplier
Example,MPC = 0.8
1
1 M P C
11
5
1 0 8 0 2..
YG
G G G
The increase in G causes income to increase
by 5 times as much!
CHAPTER 10 Aggregate Demand I slide 11
The government purchases multiplier
In the example with MPC = 0.8,
Definition,the increase in income resulting
from a $1 increase in G.
In this model,the G multiplier equals
1
1 M P C
Y
G
1 5
1 0,8
Y
G
CHAPTER 10 Aggregate Demand I slide 12
Why the multiplier is greater than 1
Initially,the increase in G causes an equal
increase in Y,?Y =?G.
But?YC
further?Y
further?C
further?Y
So the final impact on income is much
bigger than the initial?G.
CHAPTER 10 Aggregate Demand I slide 13
An increase in taxes
Y
E
E =C2 +I +G
E2 = Y2
E =C1 +I +G
E1 = Y1?Y
At Y1,there is now
an unplanned
inventory buildup……so firms
reduce output,
and income falls
toward a new
equilibrium
C =?MPC?T
Initially,the tax
increase reduces
consumption,and
therefore E:
CHAPTER 10 Aggregate Demand I slide 14
Solving for?Y
Y C I G
M P C YT
C
( 1 M P C ) M P CYT
eq’m condition in
changes
I and G exogenous
Solving for?Y,
M P C
1 M P CYT
Final result:
CHAPTER 10 Aggregate Demand I slide 15
The Tax Multiplier
def,the change in income resulting from
a $1 increase in T,
M P C
1 M P C
Y
T
0 8 0 8 4
1 0 8 0 2
..
..
Y
T
If MPC = 0.8,then the tax multiplier equals
CHAPTER 10 Aggregate Demand I slide 16
The Tax Multiplier
…is negative:
A tax hike reduces
consumer spending,
which reduces income.
…is greater than one
(in absolute value),
A change in taxes has a
multiplier effect on income,
…is smaller than the govt spending multiplier:
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,
CHAPTER 10 Aggregate Demand I slide 17
The Tax Multiplier
…is negative:
An increase in taxes reduces consumer spending,
which reduces equilibrium income.
…is greater than one (in absolute value),
A change in taxes has a multiplier effect on
income,
…is smaller than the govt spending multiplier:
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,
CHAPTER 10 Aggregate Demand I slide 18
Exercise:
Use a graph of the Keynesian Cross
to show the impact of an increase in
investment on the equilibrium level of
income/output,
CHAPTER 10 Aggregate Demand I slide 19
The IS curve
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
CHAPTER 10 Aggregate Demand I slide 20
Y2Y1
Y2Y1
Deriving the IS curve
rI
Y
E
r
Y
E =C +I(r1 )+G
E =C +I(r2 )+G
r1
r2
E =Y
IS
IE
Y
CHAPTER 10 Aggregate Demand I slide 21
Understanding the IS curve’s slope
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,
CHAPTER 10 Aggregate Demand I slide 22
The IS curve and the Loanable Funds model
S,I
r
I(r )r1
r2
r
YY
1
r1
r2
(a) The L.F,model (b) The IS curve
Y2
S1S2
IS
CHAPTER 10 Aggregate Demand I slide 23
Fiscal Policy and the IS curve
We can use the IS-LM model to see
how fiscal policy (G and T ) can affect
aggregate demand and output,
Let’s start by using the Keynesian Cross
to see how fiscal policy shifts the IS
curve…
CHAPTER 10 Aggregate Demand I slide 24
Y2Y1
Y2Y1
Shifting the IS curve,?G
At any value of r,
GEY
Y
E
r
Y
E =C +I(r1 )+G1
E =C +I(r1 )+G2
r1
E =Y
IS1
The horizontal
distance of the
IS shift equals
IS2
…so the IS curve
shifts to the right.
1
1 M P CYG
Y
CHAPTER 10 Aggregate Demand I slide 25
Exercise,Shifting the IS curve
Use the diagram of the Keynesian Cross
or Loanable Funds model to show how
an increase in taxes shifts the IS curve,
CHAPTER 10 Aggregate Demand I slide 26
The Theory of Liquidity Preference
due to John Maynard Keynes.
A simple theory in which the interest rate
is determined by money supply and
money demand,
CHAPTER 10 Aggregate Demand I slide 27
Money Supply
The supply of
real money
balances
is fixed:
sM P M P?
M/P
real money
balances
r
interest
rate
sMP
MP
CHAPTER 10 Aggregate Demand I slide 28
Money Demand
Demand for
real money
balances:
M/P
real money
balances
r
interest
rate
sMP
MP
()dM P L r?
L(r)
CHAPTER 10 Aggregate Demand I slide 29
Equilibrium
The interest
rate adjusts
to equate the
supply and
demand for
money:
M/P
real money
balances
r
interest
rate
sMP
MP
()M P L r? L(r)
r1
CHAPTER 10 Aggregate Demand I slide 30
How the Fed raises the interest rate
To increase r,
Fed reduces M
M/P
real money
balances
r
interest
rate
1M
P
L(r)
r1
r2
2M
P
CHAPTER 10 Aggregate Demand I slide 31
CASE STUDY
Volcker’s Monetary Tightening
Late 1970s,? > 10%
Oct 1979,Fed Chairman Paul Volcker
announced that monetary policy
would aim to reduce inflation.
Aug 1979-April 1980,
Fed reduces M/P 8.0%
Jan 1983,? = 3.7%
How do you think this policy change
would affect interest rates?
CHAPTER 10 Aggregate Demand I slide 32
Volcker’s Monetary Tightening,cont.
i < 0?i > 0
1/1983,i = 8.2%8/1979,i = 10.4%4/1980,i = 15.8%
flexiblesticky
Quantity Theory,
Fisher Effect
(Classical)
Liquidity Preference
(Keynesian)
prediction
actual
outcome
The effects of a monetary tightening
on nominal interest rates
prices
model
long runshort run
CHAPTER 10 Aggregate Demand I slide 33
The LM curve
Now let’s put Y back into the money demand
function:
(,)M P L r Y?
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:
dM P L r Y? (,)
CHAPTER 10 Aggregate Demand I slide 34
Deriving the LM curve
M/P
r
1M
P
L(r,Y1 )
r1
r2
r
YY
1
r1
L(r,Y2 )
r2
Y2
LM
(a) The market for
real money balances (b) The LM curve
CHAPTER 10 Aggregate Demand I slide 35
Understanding the LM curve’s slope
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.
CHAPTER 10 Aggregate Demand I slide 36
How?M shifts the LM curve
M/P
r
1M
P
L(r,Y1 )r1
r2
r
YY
1
r1
r2
LM1
(a) The market for
real money balances (b) The LM curve
2M
P
LM2
CHAPTER 10 Aggregate Demand I slide 37
Exercise,Shifting the LM curve
Suppose a wave of credit card fraud
causes consumers to use cash more
frequently in transactions,
Use the Liquidity Preference model
to show how these events shift the
LM curve,
CHAPTER 10 Aggregate Demand I slide 38
The short-run equilibrium
The short-run equilibrium is
the combination of r and Y
that simultaneously satisfies
the equilibrium conditions in
the goods & money markets,
( ) ( )Y C Y T I r G
Y
r
(,)M P L r Y?
IS
LM
Equilibrium
interest
rate
Equilibrium
level of
income
CHAPTER 10 Aggregate Demand I slide 39
The Big Picture
Keynesian
Cross
Theory of
Liquidity
Preference
IS
curve
LM
curve
IS-LM
model
Agg,
demand
curve
Agg,
supply
curve
Model of
Agg,
Demand
and Agg,
Supply
Explanation
of short-run
fluctuations
CHAPTER 10 Aggregate Demand I slide 40
Chapter summary
1,Keynesian Cross
basic model of income determination
takes fiscal policy & investment as exogenous
fiscal policy has a multiplied impact on income.
2,IS curve
comes from Keynesian Cross when planned
investment depends negatively on interest rate
shows all combinations of r and Y that
equate planned expenditure with actual
expenditure on goods & services
CHAPTER 10 Aggregate Demand I slide 41
Chapter summary
3,Theory of Liquidity Preference
basic model of interest rate determination
takes money supply & price level as exogenous
an increase in the money supply lowers the
interest rate
4,LM curve
comes from Liquidity Preference Theory when
money demand depends positively on income
shows all combinations of r andY that equate
demand for real money balances with supply
CHAPTER 10 Aggregate Demand I slide 42
Chapter summary
5,IS-LM model
Intersection of IS and LM curves shows the
unique point (Y,r ) that satisfies equilibrium
in both the goods and money markets,
CHAPTER 10 Aggregate Demand I slide 43
Preview of Chapter 11
In Chapter 11,we will
use the IS-LM model to analyze the impact
of policies and shocks
learn how the aggregate demand curve
comes from IS-LM
use the IS-LM and AD-AS models together
to analyze the short-run and long-run
effects of shocks
learn about the Great Depression using our
models
CHAPTER 10 Aggregate Demand I slide 44
