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Chapter 10
THE
MULTIPLIER
MODEL
McGraw-Hill/Irwin
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-2
Today’s lecture will:
• Explain the difference between
induced and autonomous
expenditures.
• Demonstrate how the level of income
is graphically determined in the
multiplier model.
• Use the multiplier equation to
determine equilibrium income.
McGraw-Hill/Irwin
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-3
Today’s lecture will:
• Explain how the multiplier process
•
•
amplifies shifts in autonomous
expenditures.
Demonstrate how fiscal policy can
eliminate recessionary and inflationary
gaps.
Discuss six reasons why the multiplier
model might be misleading.
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Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-4
The Multiplier Model
• The multiplier model explains how an
•
•
initial change in expenditures changes
equilibrium output when the price level is
fixed.
An initial expenditure causes additional
induced (multiplier) effects.
The multiplier model quantifies the effect
of changes in aggregate expenditures on
aggregate output.
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10-5
The AS/AD Model When
Prices are Fixed
Price
level
Initial shift
Induced shift
(Multiplier effects)
20
P0
?
AD0
AD1
Short-run
aggregate supply
Cumulative shift
Real output
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10-6
Real
production
The Aggregate Production
Curve
•
B
C
A
$4,000
Aggregate production
(production = income)
•
Potential income
45º
0
McGraw-Hill/Irwin
$4,000
Real income
Aggregate
production – the
total amount of
goods and services
produced in an
economy.
Production creates
an equal amount of
income, so the 45°
line represents
production=income.
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-7
Aggregate Expenditures
• Aggregate expenditures – the total
amount of spending on final goods
and services:
 Consumption – spending by consumers
 Investment – spending by businesses
 Government spending
 Net foreign spending – U.S. exports
minus U.S. imports
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10-8
Autonomous and
Induced Expenditures
• Autonomous expenditures –
expenditures that do not systematically
vary with income.
 They remain constant at all levels of
income.
• Induced expenditures – expenditures
that change as income changes.
 When income changes, they change by less
than income.
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10-9
The Marginal Propensity
to Expend
• Marginal propensity to expend (mpe) – the
•
•
ratio of the change in aggregate
expenditures to a change in income.
The mpe is an aggregation of the change
in each of the components of aggregate
expenditures to changes in income.
The mpe, always between 0 and 1, is the
slope of the aggregate expenditures
curve.
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10-10
Real Expenditures
Aggregate Expenditures Curve
Aggregate
Expenditures
$6500
$6000
$5500
Induced
Expenditures
$3000
Autonomous
Expenditures
Real Income
McGraw-Hill/Irwin
$5000 $6000 $7000
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10-11
Components of the MPE
• Marginal propensity to consume (mpc) – the
change in consumption that occurs with a
change in income.
 The mpc is less than one because individuals save
a portion of an increase in income.
• Marginal propensity to import – the change in
•
imports that occurs with a change in income.
Income taxes reduce people’s income which
lowers their expenditures.
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10-12
The Aggregate
Expenditures Function
• The relationship between aggregate
expenditures and income can be
expressed mathematically as:
AE = AE0 +
mpeY
autonomous
induced
AE0 = C0 + I0 + G0 + (X0 – M0)
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10-13
Graphing the Expenditures Function
Autonomous
consumption is 100
AE
310
Slope = 0.6
190
Autonomous
government spending
is 20
Autonomous net
exports is 30
200
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Autonomous
investment is 40
400
600
Real income
Marginal propensity
to expend is 0.6
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10-14
Shifts in the
Expenditures Function
• The aggregate expenditures curve shifts
•
•
when autonomous C, I, G, or (X-M)
change.
The multiplier model is an historical model
most useful for analyzing shifts in
autonomous expenditures.
Shifts in aggregate expenditures lead to a
change in income from its current level.
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10-15
Equilibrium Aggregate Income
AE
Aggregate production
Aggregate
expenditures
14,000
•
12,000
10,000
AE = 5,000 + 0.5Y
Equilibrium
•
7,000
5,000
•
AE0 = 5,000
At equilibrium, AE
($10,000) =
production or Y
($10,000).
At Y = $14,000, AE<Y,
so inventories
increase by $2000.
At Y = $4000, AE>Y,
so inventories fall
below desired levels
by $3000.
4,000
10,000 14,000
Real income (in dollars)
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10-16
The Multiplier Equation
• The multiplier equation can be used to find
•
•
equilibrium income.
The expenditures multiplier reveals how much
income will change in response to a change in
autonomous expenditures.
As the mpe increases, the multiplier increases.
Y = multiplier x autonomous expenditures
1
multiplier 
1- mpe
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10-17
The Multiplier Process
AP
Real expenditures
$7,000
A1
5,500
4,750
4,000
A2
2,500
2,000
•
•
B1
B2
$1,000
$4,000
$7,000
B
C
A
Real income (in dollars)
McGraw-Hill/Irwin
AE
•
At income levels A
and B, the economy
is not in equilibrium.
If the economy is at
A, output > aggregate
expenditures by
$1500.
Businesses decrease
production, which
decreases income
and expenditures
until production and
expenditures are
equal at C.
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-18
The Circular Flow and the
Multiplier Process
•
Aggregate income
•
•
Households
Firms
Aggregate expenditures
McGraw-Hill/Irwin
•
The circular flow model
illustrates the multiplier
process.
The flow of
expenditures equals
the flow of income.
The flow of income
spent on imports is a
leakage from the
circular flow.
Autonomous
expenditures are
injections into the
circular flow.
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-19
The Multiplier Model in Action
• The multiplier model illustrates how a
•
•
change in autonomous expenditures
changes the equilibrium level of
income.
When autonomous expenditures shift,
the multiplier process is called into
play.
Any initial shock (a change in
autonomous AE) is multiplied in the
adjustment process.
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10-20
Shifts in the AE Curve
C, I
E1
500
E1
AE1 = 250 + .5Y
100
A
AE2 = 150 + .5Y
ΔAEA=100
Δ
B
100
300
250
E2
50
100
25
150
0
CCC ΔAEB=50
E2
$200
$300
$500
25
200
Real income
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10-21
The First Steps of Two Multipliers
mpe = .5
100
mpe = .8
100
80
64
51.2
50
40.96
25
12.5 6.25
Multiplier = 1/(1-0.5) = 2
McGraw-Hill/Irwin
Multiplier = 1/(1-0.8) = 5
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-22
Reasons for Shifts in
Aggregate Expenditures
• Natural disasters
• Changes in investment caused by
•
•
•
technological developments
Shifts in government expenditures
Large changes in the exchange rate
Changes in consumer sentiment
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10-23
An Increase in
Autonomous Expenditures
Real
expenditures
Aggregate production
AE1
30
AE0
$4,210
1
AE0
Y 
1- 0.75
4,090
1,052.5
 4AE0   120
30
1,022.5
0
McGraw-Hill/Irwin
$120
$4,090
$4,210
Real income
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-24
Real World Examples of Shifts
in Aggregate Expenditures
• The U.S. economy boomed from 19982001 and fell into a recession after
September, 2001.
 Consumer confidence increased
autonomous consumption through mid2001.
 Consumer spending and investment fell
after the terrorist attacks in September
2001.
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10-25
Real World Examples of Shifts
in Aggregate Expenditures
• Aggregate income and production fell
in Japan during the 1990s.
 A dramatic appreciation of the yen
decreased Japanese exports.
 Autonomous consumption fell as
consumer confidence decreased.
 Suppliers responded by laying off
workers and cutting production.
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10-26
Fiscal Policy and the Multiplier
• Expansionary policy is appropriate
when there is a recessionary gap.
 The increased spending leads to a
multiple increase in AE, thereby closing
the gap.
• Contractionary policy is appropriate
when there is an inflationary gap.
 The decreased spending leads to a
multiple decrease in AE, thereby closing
the gap.
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10-27
Expansionary Fiscal Policy
Aggregate
production
Potential
output
LAS
Initial expenditures
increase
AE1
AE0
E2
$120
∆G = $60
E1
mpe = 0.67
AE1 = 333 + 0.67Y
Recessionary gap
$1,000 $1,180
McGraw-Hill/Irwin
Real income
Multiplier effect
$60
P0
SAS
AD0
AD1΄
$180
AD1
$1,000 $1,180
Real income
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10-28
Contractionary Fiscal Policy
Aggregate
production
Potential
output
AE0
AE1
E1
LAS
P2
B
∆G = $200
$1,000
mpe = 0.8
AE1 = 800 + 0.8Y
E2
Inflationary gap
$4,000 $5,000
McGraw-Hill/Irwin
P1
A
SAS
AD0
AD1
Real income
$4,000 $5,000
Real income
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10-29
Limitations of the
Multiplier Model
• The multiplier model is not a complete
model.
 The multiplier model does not determine
equilibrium income from scratch.
 It can only estimate the direction and rough
sizes of autonomous demand shifts.
• Shifts in aggregate expenditures that
occur in response to autonomous
expenditures may be overstated.
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10-30
Limitations of the
Multiplier Model
• The price level will often change in response to
•
changes in aggregate demand, but the
multiplier model assumes that the price level is
fixed.
Forward-looking expectations complicate the
adjustment process.
 Most people act upon their expectations of the

future.
Rational expectations model – all decisions are
based upon the expected equilibrium in the
economy.
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10-31
Limitations of the
Multiplier Model
• Shifts in expenditures may reflect
desired changes in supply and demand,
rather than simply suppliers responding
to changes in demand.
 Real business cycle theory – fluctuations in
the economy reflect real phenomena such
as simultaneous shifts in supply and
demand, not simply supply responses to
demand shifts.
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10-32
Limitations of the
Multiplier Model
• Expenditures depend on much more
than current income.
 Permanent income hypothesis –
expenditures are determined by
permanent or lifetime income.
 The mpc out of current income could be
zero, which would make the multiplier
equal to one.
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10-33
Summary
• The multiplier model focuses on the induced
•
•
•
effect that a change in production has on
expenditures, which affects production, and so
on.
In equilibrium in the multiplier model, aggregate
production (income) must equal planned
aggregate expenditures (AE).
AE = C + I + G + (X – M)
The mpe tells us the change in expenditures
that occurs with a change in income.
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10-34
Summary
• Equilibrium can be calculated using the
•
•
multiplier equation:
Y = multiplier x autonomous expenditures
The multiplier tells us how much a
change in autonomous expenditures will
change equilibrium income.
The multiplier equals 1(1-mpe).
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10-35
Summary
• Expansionary fiscal policy, increasing
•
government expenditures or decreasing
taxes, is represented as an upward shift
of the AE curve or a rightward shift in the
AD curve.
Contractionary fiscal policy, decreasing
government spending or increasing
taxes, is represented as a downward
shift of the AE curve or a leftward shift of
the AD curve.
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10-36
Summary
• The multiplier model has limitations:
 It is incomplete without information about
where the economy started and what is the
desired level of output.
 It overemphasizes shifts in AE.
 It assumes that the price level is fixed.
 It doesn’t take expectations into account.
 It ignores the possibility that shifts in
expenditures are desired.
 It ignores the possibility that consumption is
based on lifetime income, not current
income.
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10-37
Assume that the mpe is 0.75 and autonomous expenditures are
$1000.
Review Question 10-1 What is the aggregate expenditures function?
AE = 1000 + .75Y
Review Question 10-2 What is equilibrium income?
Y = AE at equilibrium, so:
Y = 1000 + .75Y
.25Y = 1000
Y = $4000
Review Question 10-3 What happens if income is $4800?
AE = 1000 + .75(4800) = $4600
If income is $4800, inventories of $200 accumulate causing
output and income to decrease until output and income equal
aggregate expenditures at $4000.
McGraw-Hill/Irwin
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