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The Multiplier Model
Chapter 10
LAUGHER CURVE
“If you put two economists in a room, you get
two opinions, unless one of them is Lord
Keynes, in which case you get three
opinions.”
Winston Churchill
The Multiplier Model


The multiplier model explains how an initial
shift in expenditures changes equilibrium
output when the price level is fixed.
An initial expenditure shift causes additional
induced (multiplier) effects.
The Multiplier Model

The multiplier model quantifies the effect of
changes in aggregate expenditures on
aggregate output.
The AS/AD Model When Prices Are
Fixed
Price
level
Induced shift
(Multiplier effects)
Initial shift
20
P0
Aggregate supply
?
AD
AD
Cumulative shift
Real output
Aggregate Production


Aggregate production –the total amount of
goods and services produced in every
industry in an economy.
Production creates an equal amount of
income.
Aggregate Production

Graphically, aggregate production in the
multiplier model is represented by a 45° line
through the origin
Aggregate Production

Real production (in dollars) is on the vertical
axis, and real income (in dollars) is on the
horizontal axis.

At all points on this curve, income equals
production.
The Aggregate Production Curve
Real
production
B
C
A
$4,000
Potential income
45º
0
Aggregate production
(production = income)
$4,000
Real income
Aggregate Expenditures

Aggregate expenditures – the total amount
of spending on final goods and services in
the economy:
–
–
–
–
Consumption – spending by consumers.
Investment – spending by business.
Spending by government.
Net foreign spending on U.S. goods – the
difference between U.S. exports and imports.
Autonomous and Induced
Expenditures


Autonomous expenditures – expenditures
that do not systematically vary with income.
Induced expenditures – expenditures that
change as income changes.
Autonomous and Induced
Expenditures

Autonomous expenditures is the level of
expenditures at zero income.

They remain constant at all levels of income.
A graph of autonomous expenditures is a
straight, horizontal line.

Autonomous and Induced
Expenditures

Induced expenditures are those that change
as income changes.

When income changes, induced expenditures
change by less than the change in income.
The Marginal Propensity to
Expend



Marginal propensity to expend on
domestically supplied goods (mpe) – the
ratio of the change in aggregate
expenditures to a change in income.
It is composed of the various relationships
between the component of aggregate
expenditures.
Its value is greater than 0 and less than 1.
Components of the Marginal
Propensity to Expend


Marginal propensity to consume (mpc) –
the change in consumption that occurs with a
change in disposable income.
The mpc is less than 1 because individuals
tend to save a portion of an increase in
income.
Components of the Marginal
Propensity to Expend



Income taxes reduce people’s incomes which
lowers their expenditures.
Individuals spend an constant portion of their
incomes on imports.
Marginal propensity to import – the change in
imports that occurs with a change in income.
The Aggregate Expenditures
Function

The relationship between aggregate
expenditures and income can be expressed
mathematically.
AE =
+ mpeY
AE0
autonomous induced
mpe = marginal propensity to expend
Y = income
Expenditures Function

Autonomous expenditures is the sum of the
autonomous components of expenditures:
AE0 = C0 + I0 + G0 + (X0 – M0)

Induced expenditures is the sum of the induced
components of expenditures.
Graphing the Aggregate
Expenditures Function

Situation 1:
–
–
–
–
–
Autonomous consumption = 100
Autonomous investment = 40
Autonomous net exports = 30
Autonomous government spending = 20
The marginal propensity to expend = 0.6
Graphing the Aggregate
Expenditures Function

Situation 2:
–
–
–
–
–
Autonomous consumption = 100
Autonomous investment = 40
Autonomous net exports = 30
Autonomous government spending = 30
The marginal propensity to expend = 0.5
Graphing the Aggregate
Expenditures Function

Situation 3:
–
–
Autonomous expenditures = 140
The marginal propensity to expend = 0.6
Graphing the Expenditures
Function
AE
AE
400
380
310
Slope = 0.6
140
200
(a)
AE
Situation 3
McGraw-Hill/Irwin
200
190
400 600
Real income
200
(b)
Slope = 0.5
Slope = 0.6
400 600
Real income
Situation 1
200
(c)
400 600
Real income
Situation 2
© 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Shifts in the Expenditures
Function

The aggregate expenditure curve shifts in a
parallel fashion when autonomous C, I, G, or
(X – M) change.
Shifts in the Expenditures
Function

Shifts in aggregate expenditures lead to a
change in income from its existing level.

The curve doesn’t determine income
independently of the economy's historical
position.
Determining the Equilibrium Level
of Aggregate Income

In bringing AP and AE together in one
framework, the following is assumed:
–
–
–
The AP curve is a 45º line until the economy
reaches its potential income.
Aggregate expenditures equal aggregate income
at all points on the AP curve.
Planned expenditures on the AE line do not
necessarily equal production or income.
Determining the Equilibrium Level
of Aggregate Income

At equilibrium, planned expenditures must
equal production.

Graphically, it is the income level at which AE
equals AP.
Keynesian Cross (45-deg, AE)
Real expenditures (AE) (in dollars)
Aggregate production
14,000
12,000
Aggregate expenditures
AE = 5,000 + 0.5Y
10,000
Equilibrium
7,000
5,000
AE0 = 5,000
4,000
10,000 14,000
Real income (in dollars)
The Multiplier Equation

The multiplier equation tells us that income
equals the multiplier times autonomous
expenditures.
Change in Y = Multiplier X change in
autonomous expenditures
The Multiplier Equation

Expenditures multiplier – a number that
reveals how much income will change in
response to a change in autonomous
expenditures.
1
Multiplier =
1 - mpe
The Multiplier Equation

As the mpe increases, the multiplier
increases:
mpe
Multiplier =
1/(1-mpe)
mpe
Multiplier =
1/(1-mpe)
0.3
1.4
0.75
4
0.4
1.7
0.8
5
0.5
2.0
0.9
10
The Multiplier Process

When aggregate production do not equal
aggregate expenditures:
–
–
–
–
Businesses change production levels,
Which changes income, which changes
expenditures,
Which changes production, which changes
income,
Which changes . . . etc.
The Multiplier Process

The process ends when aggregate
production equals aggregate expenditures.

Firms are selling all they produce, so they have
no reason to change their production levels.
The Multiplier Process
AP
$7,000
Real expenditures
A1
5,500
4,750
4,000
2,500
2,000
Inventory accumulation
AE
Cut in production
Cut in demand
B
$1,000
B
$4,000
C
$7,000
A
Real income (in dollars)
The Circular Flow Model and the
Multiplier Process


The circular flow model provides the intuition
behind the multiplier process.
The flow of expenditures equals the flow of
income.
The Circular Flow Model and the
Multiplier Process
Aggregate income
Households
Firms
Aggregate expenditures
The Circular Flow Model and the
Multiplier Process

Not all of the flow of income is spent on
domestic goods (the mpe < 1).
–

This represents a leakage from the circular flow.
Autonomous expenditures are injections into the
circular flow.
–
They offset the leakages.
The Circular Flow Model and the
Multiplier Process

The multiplier process is much like a leaking
bathtub.
–
–
The water in the tub represents income in the
economy.
The economy is in equilibrium when water leaking out
equals water flowing in (leakages equal injections).
The Multiplier Model in Action

The multiplier model illustrates how a change
in autonomous expenditures changes the
equilibrium level of income.
The Multiplier Model in Action

Autonomous expenditures are determined
outside the model and are not affected by
changes in income.

When autonomous expenditures shift, the
multiplier process is called into play.
The Steps of the Multiplier
Process


The income adjustment process is directly
related to the multiplier.
Any initial shock (a change in autonomous
AE) is multiplied in the adjustment process.
The Steps of the Multiplier
Process

The multiplier process repeats and repeats
until a new equilibrium level is finally
reached.
Shifts in the Aggregate
Expenditure Curve
C, I
Aggregate production
$4,200
E0
4,160
20
AE0 = 832 + .8Y
AE1 = 812 + .8Y
832
812
0
$20
12.8
20
E1
$100
$4,060
E1
$4,160 Real income
100
D AEA = $20
D AEA = $16
D AEA = $12.8
$16
4,100
4,060
E0
The First Five Steps of Four
Multipliers
mpe = .4
100
mpe = .5
100
50
40
25
16
6.4 2.56
Multiplier = 1/(1-0.4) = 1.7
12.5 6.25
Multiplier = 1/(1-0.5) = 2
The First Five Steps of Four
Multipliers
mpe = .6
100
mpe = .8
100
80
64
60
51.2
40.96
36
21.6
12.9
Multiplier = 1/(1-0.6) = 2.5
Multiplier = 1/(1-0.8) = 5
Examples of the Effect of Shifts in
Aggregate Expenditures

There are many reasons for shifts in
autonomous expenditures:
–
–
–
–
Natural disasters.
Changes in investment causes by technological
developments.
Shifts in government expenditures.
Large changes in the exchange rate.
An Upward Shift of AE
Real
expenditures
$4,210
Aggregate production
AE1
30
AE0
Y =
4,090
1,052.5
= 4 AE0  = 120
30
1,022.5
0
1
AE0 
1 - 0.75
$120
$4,090
$4,210
Real income
An Downward Shift of AE
Real
expenditures
$4,152
Aggregate production
AE0
30 AE1
Y =
4,062
1,412
= 3 AE0  = 90
30
1,382
0
1
AE0 
1 - 0.66
$90
$4,062
$4,152
Real income
The United States at the Turn of
the Millennium

The economy boomed from 1998-2001 and
fell into a recession after September 2001.
–
–
Substantial increases in consumer confidence
increased autonomous consumption through mid2001.
Consumer spending and investment fell after the
terrorist attacks in September 2001.
Japan in the 1990s

Aggregate income and production fell during
the 1990s.
–
–
–
A dramatic rise in the yen cut Japanese exports.
Autonomous consumption decreased as
consumers confidence fell
Suppliers responded by laying off workers and
cutting production.
Fiscal Policy in the Multiplier
Model

Policymakers believe they can use
government policies to shift the AE curve in
an attempt to achieve the desired level of
output.
Fighting Recession: Expansionary
Fiscal Policy


Expansionary fiscal policy is appropriate
when the economy is in a recessionary gap.
The increased spending leads to a multiple
increase in aggregate expenditures, thereby
closing the gap.
Fighting Recession: Expansionary
Fiscal Policy
Aggregate
production
Potential
output
LAS
AE1
AE0
E2
E1
∆G = $60
mpe = 0.67
AE1 = 333 + 0.67Y
Recessionary gap
$1,000 $1,180
McGraw-Hill/Irwin
$60 $120
Initial expenditures
increase
Multiplier effect
Real income
SAS
AD0 AD1
$180
$1,000 $1,180
AD1΄
Real income
© 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Fighting Inflation: Contractionary
Fiscal Policy


Contractionary fiscal policy is appropriate
when the economy is in an inflationary gap.
The decreased spending leads to a multiple
decrease in aggregate expenditures, thereby
closing the gap.
Fighting Inflation: Contractionary
Fiscal Policy
Aggregate
production
Potential
output
AE0
AE1
E1
LAS
P1
B
∆G = $200
$1,000
E2
mpe = 0.8
AE1 = 800 + 0.8Y
Inflationary gap
$4,000 $5,000
McGraw-Hill/Irwin
Real income
P0
A
SAS
AD0
AD1
$4,000 $5,000
Real income
© 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Limitations of the Multiplier Model


On the surface, the multiplier model makes a
lot of intuitive sense.
Surface sense can often be misleading.
The Multiplier Model Is Not a
Complete Model


The multiplier model does not determine
income from scratch.
At best, it can estimate the directions and
rough sizes of autonomous demand or
supply shifts.
Shifts Are Not as Great as Intuition
Suggests

The aggregate expenditure shifts that occur
in response to a shift in autonomous
expenditures may be overemphasized.
The Price Level Will Often Change
in Response to Shifts in Demand


The multiplier model assumes that the price
level is fixed.
The price level can change in response to
changes in aggregate demand.
Forward-Looking Expectations
Complicate the Adjustment


People's forward-looking expectations make
the adjustment process much more
complicated.
Most people, however, act upon their
expectations of the future.
Forward-Looking Expectations
Complicate the Adjustment
Process

Business people may not automatically cut
back production and lay-off workers if they
think a fall in sales is temporary.
Forward-Looking Expectations
Complicate the Adjustment
Process

Rational expectations - all decisions are
based upon the expected equilibrium in the
economy.
Shifts in Expenditures Might
Reflect Desired Shifts in Supply
and Demand


Shifts in demand can occur for many
reasons.
Many shifts can reflect desired shifts in
aggregate production which are
accompanied by shifts in aggregate demand.
Shifts in Expenditures Might
Reflect Desired Shifts in Supply
and Demand

Shifts may be simultaneous shifts in supply
and demand that do not necessarily reflect
suppliers' responding to changes in demand.
Shifts in Expenditures Might
Reflect Desired Shifts in Supply
and Demand

Expansion of this line of thought has led to
the real business cycle theory of the
economy.
Shifts in Expenditures Might
Reflect Desired Shifts in Supply
and Demand

Real business cycle theory of the
economy – fluctuations in the economy
reflect real phenomena such as
simultaneous shifts in supply and demand,
not simply supply responses to demand
shifts.
Expenditures Depend on Much
More Than Current Income


People may base their spending on lifetime
income, not yearly income.
The marginal propensity to consume out of
changes in current income could be very low,
even approaching zero.
Expenditures Depend on Much
More Than Current Income

The expenditures function would essentially
be a flat line.

The multiplier would be one.
There would be no secondary effects of an initial
shift.

Expenditures Depend on Much
More Than Current Income

This set of arguments is called the
permanent income hypothesis.

Permanent income hypothesis -- the
hypothesis that expenditures are determined
by permanent or lifetime income.
The Multiplier Model
End of Chapter 10