The Big Picture
Keynesian
Cross
IS
curve
Theory of
Liquidity
Preference
LM
curve
Planned Expenditure


IS-LM
model
Agg.
demand
curve
Agg.
supply
curve
Determinants of planned expenditure (PE)
Explanation
of short-run
fluctuations



C = C(Y − T) = a + b(Y − T)
II
G  G and T  T
PE  C  I  G
 a  b(Y  T )  I  G
 (a  I  G  bT )  bY
Model of
Agg.
Demand
and Agg.
Supply
autonomous
expenditure
1
Planned Expenditure
induced
expenditure
2
Goods Market Equilibrium

PE
planned
expenditure
PE =C +I +G
The goods market is in equilibrium when actual
expenditure equals planned expenditure.
the equilibrium condition: Y = PE

1
b=MPC
Reason: Y = PE implies



a  I  G  bT

actual investment equals planned investment
unplanned changes in inventories equal zero
total sales (demand) equals total production (supply)
equilibrium in the goods market
income, output, Y
3
4
Graphing the Equilibrium Condition
The Keynesian Cross
PE
planned
expenditure
PE
planned
expenditure
PE =Y
(the equilibrium cond.)
PE =Y (“supply curve”)
PE =C +I +G
(“demand curve”)
45º
income, output, Y
income, output, Y
Equilibrium
income
5
Goods Market Equilibrium

Government-Purchases Multiplier
How does the economy get to the equilibrium?
PE
At Y1,
there is now an
unplanned drop
in inventory…
PE
planned
expenditure
PE =Y (“supply curve”)
Unplanned
increase in
inventories
Unplanned
decrease in
inventories
Y
PE =C +I +G2
PE =C +I +G1
G > 0
PE =C +I +G
(“demand curve”)
Y*
6
7
…so firms
increase output,
and income rises
toward a new
equilibrium.
Y
PE1 = Y1
Y > 0
PE2 = Y2
8
Government-Purchases Multiplier

According to the Keynesian Cross





G↑
Y↑
∆Y > ∆G


Government-Purchases Multiplier

The ratio ∆Y/∆G is called the government-purchases multiplier,
which tells you how much income rises in responses to a $1
increase in government purchases.
∆Y/∆G > 1.
Q1: Why does a $1 increase in G result in a more
than $1 increase in Y (the multiplier effect)?
Q2: How big is the government purchases multiplier
effect?
Q1: Why does a $1 increase in G result in a more than $1
increase in Y (the multiplier effect)?
A1: Initially, the increase in G causes an equal increase in
Y: Y = G = 1. But
Y
 C (by b)
 further Y (by b)
 further C (by b2)
 further Y (by b2)
 further C (by b3)
 further Y (by b3)
…
9
Government-Purchases Multiplier


Government-Purchases Multiplier
Q2: How big is the government-purchase multiplier
effect?
1
1
Y


A2:
G 1  b 1  MPC

10
Y  C  I  G
equilibrium condition
Y  C  I  G
in changes

C
 G
 MPC  Y  G
Example: If MPC = 0.75, then
1
1
Y


4
G 1  MPC 1  0.75
Collect terms with Y on
the left side of the equals
sign:
An increase in G causes income to increase 4 times as
much.
(1  MPC)  Y  G
11
because I exogenous
because C = MPC Y
Solve for Y :


1
Y  
  G
1

MPC


12
Tax Multiplier
Tax Multiplier
PE

Initially, the tax
increase reduces
consumption, and
therefore PE:
PE =C1 +I +G

PE =C2 +I +G

At Y1, there is now an
unplanned
inventory buildup…

Y
PE2 = Y2
Y
PE1 = Y1


The ratio ∆Y/∆T is called the tax multiplier, which tells you
how much income decreases in responses to a $1 increase in
taxes.
Q1: Why does a $1 increase in T result in a more
than $1 decrease in Y (the multiplier effect)?
Q2: How big is the tax multiplier effect?
13
14
Tax Multiplier

T↑
Y↓
|∆Y| > |∆T|

C = MPC T
…so firms reduce
output, and
income falls
toward a new
equilibrium
According to the Keynesian Cross
Tax Multiplier
Q1: Why does a $1 increase in T result in a more than $1
decrease in Y (the multiplier effect)?
A1: The increase in T causes a decrease in C and thus Y:
T (by 1)
 ↓ C (by b)
 ↓ Y (by b)
 further ↓C (by b2)
 further ↓ Y (by b2)
 further ↓ C (by b3)
 further ↓ Y (by b3)
…

Q2: How big is the tax multiplier effect?

A2:

Y  b
 MPC


T 1  b 1  MPC
Example: If MPC = 0.75, then
Y  b
 MPC
 0.75



 3
T 1  b 1  MPC 1  0.75
An increase in T causes income to decrease 3 times as
much.
15
16
Tax Multiplier
Tax Multiplier
eq’m condition in
changes
Y  C  I  G
 C
I and G exogenous
 MPC   Y  T
Solving for Y :
Final result:
…is negative:
A tax increase reduces C,
which reduces income.
…is greater than one
(in absolute value):
A change in taxes has a
multiplier effect on income.

(1  MPC)  Y   MPC  T
…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.
  MPC 
Y  
  T
 1  MPC 
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18
Government-Purchases Multiplier
G (by 1)  Y (by 1)
 C (by b)
 further Y (by b)
 further C (by b2)
 further Y (by b2)
 further C (by b3)
 further Y (by b3)
…
The IS Curve
T (by 1)  ↓ C (by b)
 ↓ Y (by b)
 further ↓C (by b2)
 further ↓ Y (by b2)
 further ↓ C (by b3)
 further ↓ Y (by b3)
…
19


Definition: A curve that shows the combinations
of the interest rate (r) and the level of income (Y)
that are consistent with equilibrium in the market
of goods and services.
Need to modify the Keynesian Cross so that a
relationship between r and Y can be shown.
20
The IS Curve


The IS Curve
Determinants of planned expenditure

C = C(Y − T) = a + b(Y − T)

I  I (r )

G  G and T  T
PE
planned
expenditure
PE =C +I +G
PE  C  I  G
1
 a  b(Y  T )  I (r )  G
 [a  I (r )  G  bT ]  bY
autonomous
expenditure
a  I (r )  G  bT
income, output, Y
induced
expenditure
21
22
The IS Curve
The IS Curve
PE =Y
PE
r
 I
 PE
b=MPC
PE =C +I (r2 )+G

PE =C +I (r1 )+G
I
 Y
r
Y1
Y
Y2
r1
Why is the IS curve downward sloping?
 A fall in the interest rate motivates firms to
increase investment spending, which drives up
total planned expenditure (PE).
 To restore equilibrium in the goods market,
output must increase.
r2
IS
Y1
Y2
Y
23
24
Fiscal Policy and The IS Curve


Shifting the IS Curve: ↑G
At any value of r, G
We can use the IS-LM model to see how fiscal
policy (G and T ) affects aggregate demand and
output.
Let’s start by using the Keynesian cross
to see how fiscal policy shifts the IS curve…
 PE  Y
PE =C +I (r1 )+G1
…so the IS curve
shifts to the right.
The horizontal
distance of the
IS shift equals
Y 
r

Y
Y2
1
G
1MPC
Y
Y1
IS1
Y2
IS2
Y
26
The Big Picture
Fiscal Policy and The IS Curve

Y1
r1
25

PE =Y PE =C +I (r )+G
1
2
PE
The IS curve is constructed holding G and T
fixed. That is, the IS curve is drawn for a given
fiscal policy.
An expansionary fiscal policy (G or T) shifts
the IS curve to the right.
A contractionary fiscal policy (G or T) shifts
the IS curve to the left.
Keynesian
Cross
IS
curve
Theory of
Liquidity
Preference
LM
curve
IS-LM
model
Agg.
demand
curve
27
Agg.
supply
curve
Explanation
of short-run
fluctuations
Model of
Agg.
Demand
and Agg.
Supply
28
Theory of Liquidity Preference

Theory of Liquidity Preference
A simple theory in which the interest rate is
determined by money supply and money demand.

The supply of real money balances is fixed.


Nominal money supply is a exogenous variable chosen by
the Fed.
The average price level is fixed in the short run.
r
The supply of
real money
balances
is fixed:
M
interest
rate
M
P
s
P M P
s
M P
M/P
real money
balances
29
Theory of Liquidity Preference

Theory of Liquidity Preference
A simple theory in which the interest rate is
determined by money supply and money demand.

The demand for real money balances: (M/P )d = L(i,
Y) = L(r + Eπ, Y) = L(r, Y).

30
r
Demand for
real money
balances:
interest
rate
M
P
s
(M/P )d = L(r, Y)
Eπ is fixed in the short run.
L (r, Y )
M P
31
M/P
real money
balances
32
Theory of Liquidity Preference
r
M P 
interest
rate
The interest rate adjusts
to equate the supply and
demand for money:
(M/P)s = (M/P)d.
The LM Curve

s
Definition: A curve that shows the combinations
of the interest rate (r) and the level of income (Y)
that are consistent with equilibrium in the money
market.

r1
LM curve represents
L (r, Y )
M/P
M P
real money
balances
34
The LM Curve
(a)
The LM Curve
The market for
real money balances
(b) The LM curve
r

r
LM
r2
r2
L (r , Y2 )
r1
r1
L (r , Y1 )
M1
P
M/P
Y1
Y2
Why is the LM curve upward sloping?
 An increase in income raises money demand.
 Since the supply of real money 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.
Y
35
36
Monetary Policy and The LM Curve
(a)
r
The market for
real money balances
r
Monetary Policy and The LM Curve
(b) The LM curve

LM2
LM1

r2
r2
r1
L (r , Y1 )
M2
P
M1
P

r1
M/P
Y
Y1
37
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:
r
Y  C (Y  T )  I (r )  G
LM
IS
M P  L (r ,Y )
Equilibrium
interest
rate
The LM curve is constructed holding M fixed.
That is, the LM curve is drawn for a given
monetary policy.
Expansionary monetary policy shifts the LM
curve to the right.
Contractionary monetary policy shifts the LM
curve to the left.
Y
Equilibrium
level of
income
39
38