ECON 141: Macroeconomics
Expenditure Multiplier
Fixed Prices and Expenditure Plans
• From the AD-AS chapter, we studied that:
• In the long run, LAS is vertical and price
level and prices of factors of production are
all variables. The RGDP is constant at the
potential GDP.
• Hence,
H
AD d
determines
t
i
only
l th
the price
i in
i the
th
LR.
Chapter 7
Expenditure Multiplier
Dr. Mohammed Alwosabi
1
• In the short run, price level varies along SAS
but every thing else remain constant.
• So AD determines both P and the amount of
RGDP.
• Firms increase prices if their sales increase
more than they planned and reduce prices if
the quantity sold is less than the planned
sales
3
2
• However, firms' prices are fixed in the very
short run.
• It is costly to change prices every hour or
every day (menu cost plus other costs).
• Supply curve in the very SR is horizontal at
fixed price
• So
S the
th quantities
titi that
th t firms
fi
sell
ll depend
d
d on
demand not supply (the shifts of AD).
4
• Thus, in the Keynesian model of aggregate
expenditure, real GDP is determined by the
level of aggregate demand because this
model assumes that individual prices and
the price level are fixed in the very short
run.
• Because in the very short run prices are
fixed, it is easy for people to plan their
expenditure.
P
LAS
SAS
P
Dr. Mohammed Alwosabi
VSAS
RGDP
Y
5
6
1
ECON 141: Macroeconomics
Expenditure Multiplier
• Aggregate planned expenditure (AE) is the
sum of the planned amounts of
consumption expenditure (C), investment (I),
government purchase (G), net exports (NX)
• So, Planned aggregate expenditure equal
AE = C + I + G + (X – M)
7
• Since RGDP influence C and M, and since C
and M are components of AE, an increase in
RGDP leads to an increase in AE, and an
increase in AE leads to an increase in
RGDP. Hence, there is a two-way link
between AE and RGDP.
• Before discussing the equilibrium
expenditure (or equilibrium RGDP) and
before studying the multiplier let us have a
look at each component of the planned
aggregate expenditures (AE).
9
• Disposable income (Yd) equals to income (Y)
minus tax plus transfer payments.
• If we define net tax (T) as tax minus transfer
payments then,
Yd = Y – T.
Yd = Y when T = 0
• Disposable income (Yd) is divided into
consumption (C) and saving (S).
Yd = C + S
11
Dr. Mohammed Alwosabi
• In the very SR, AE can be divided into two
main components
1. Autonomous expenditures: They are fixed.
They do not vary with RGDP. They exist
even if RGDP = 0. They include I, G, and X.
2. Induced expenditures: They are not fixed.
They depend on RGDP.
RGDP They include C and
M. But C and M have their autonomous parts
as we will discuss later.
8
Disposable Income, Consumption Function,
and Saving Function
• Consumption and saving are influenced by:
(1) Disposable income,
(2) The real interest rate,
(3) Wealth,
(4) Expected future income.
10
• Consumption function shows the positive
relationship between consumption
expenditure (C) and disposable income (Yd),
other things remaining the same.
• It shows how much all households plan to
consume at each level of real disposable
income.
• Consumption function: C = a + bYd
• Movements along C is a result of changes in
Yd
• Consumption function is divided into two
parts:
12
2
ECON 141: Macroeconomics
Expenditure Multiplier
1. Autonomous consumption is consumption
expenditure that does not depend on the
level of GDP or disposable income.
• It is the amount of consumption
expenditure that would occur in the SR
even if Yd = 0. a > 0.
• It is the vertical axis intercept (a)
2. Induced consumption, which is bYd, is
equal to consumption caused by an
increase in disposable income.
• b is the slope of the consumption function.
b = ∆C/∆Yd , 0 ≤ b ≤ 1
Dr. Mohammed Alwosabi
• Saving function shows the negative
relationship between S and Yd.
• Saving (S) is not part of AE but can be
derived from the consumption function.
• S = Yd – C = Yd – a - bYd = - a + (1 - b)Yd,
where (- a) is the intercept and (1-b) is the
slope that is equal to 1-b
1 b = ∆S/∆Yd
• Example
If C = 35 + 0.8Yd
S = - 35 + (1-0.8)Yd
13
14
• The following table and diagram shows the
relationship among Yd, C and S
Yd
C
S
A
0
1.5
-1.5
B
2
3.0
-1.0
C
4
4.5
-0.5
D
6
6.0
0
E
8
7.5
+0.5
F
10
9.0
+1.0
C
450
saving
C
6
dissaving
1.5
0
Yd
6
S
S
0
15
• where the vertical and horizontal axes are
scaled the same, the 45° line is the line that
extends out from the origin and has a slope
of one.
• Any point on the 45° line represents an
equilibrium between the disposable income
to the consumption function (Yd = C).
• The slope of the consumption function is
less than the slope of the 45-degree line but
not equal to zero
• The vertical distance between the 45-degree
line and the consumption line represents
17
saving or dissaving.
-1.5
6
Yd
16
1. If C is above the 45° line ⇒ C > Yd ⇒
Dissaving (negative saving) (dissaving: the
use of past saving)
2. If C is on the 45° line ⇒ C = Yd ⇒ zero
saving
3. If C is below the 45° line ⇒ C < Yd ⇒
positive saving
• A change in Yd leads to changes in C and
S, and brings movement along the
consumption function and saving function;
all other influences on C and S are fixed.
18
3
ECON 141: Macroeconomics
Expenditure Multiplier
Marginal Propensities to Consume and Save:
• The extent to which C changes when Yd
changes depends on the marginal
propensity to consume.
• The marginal propensity to consume (MPC)
is the fraction of a change in Yd that is
consumed.
consumed
• It represents how much of the increase in
income will be spent on goods and services,
as opposed to saving it.
MPC = ∆C/∆Yd = b = the slope of the
consumption function, 0 ≤ MPC ≤1
19
• The marginal propensity to save (MPS) is
the fraction of a change in Yd that is saved
• MPS = ∆S/∆Yd = (1 – b) = the slope of the
saving function, 0 ≤ MPS ≤1
• Since C + S = Yd, any increase in Yd is either
consumed or saved
∆C + ∆S = ∆Yd
• Divide both sides by ∆Yd
∆C/∆Yd + ∆S/∆Yd = 1
MPC + MPS = 1
• Thus, MPS = 1 – MPC, and MPC = 1- MPS
21
• Exercise:
Suppose Yd increased by $100 and as a
result C increased by $ 60 what is the MPS?
MPC = 60/100 = 0.60
Since MPS = 1 – MPC ⇒ MPS = 1- 0.60 = 0.40
23
Dr. Mohammed Alwosabi
• For linear consumption function, MPC is
constant at every level of Yd.
• But it is not necessarily to be this way.
• In general, the lower is the Yd the higher the
MPC and the higher the income the lower
the MPC.
• The
Th MPC is
i affected
ff t d by
b the
th consumers’’
confidence and the interest rates.
• Mostly, C would increase by less amount
than the increase in Yd
20
• Example:
If the increase of Yd from $4 billions to $6
billions lead to an increase in C from $2
billion to $3.6 billion,
MPC = ∆C/∆Yd = (3.6-2)/(6-4) = = 0.80
⇒ 80 % of the increase in Yd will go to
consumption
ti
off goods
d and
d services.
i
• Since b = MPC = 0.80 then
MPS = 1- MPC = 1- b = 1- 0.80 = 0.20
22
Other influences on C and S (Shifts of the
Curves)
• Some other factors that influence C and S
includes
1. Real interest rate (r)
2. Wealth
3. Expected future income
24
4
ECON 141: Macroeconomics
Expenditure Multiplier
• While the change in disposable income
results in a movement along the
consumption function, a change in any of
these other influences leads to a change in
autonomous consumption and results in a
parallel shifts of the consumption function
and the saving
g function.
• Slope does not change because it depends
on the Yd which is assumed fixed.
25
• Consumption function could rotate if the
autonomous part does not change but there
is a change in the slope and the induced
component as a result of change in Yd.
• Consumption function could shift and rotate
if changes in autonomous and induced
components occur simultaneously. That is if
Yd and the one of the other influences
change at the same time.
27
• The marginal propensity to import (MPI) is
the fraction of an increase in RGDP that is
devoted to imports.
• MPI is the change in imports divided by the
change in disposable income.
• MPI = ∆M/∆RGDP = ∆M/∆Y = ∆NX/∆Y,
0 ≤ MPI ≤1
• (Since we assumed X is fixed in the very SR,
the change in NX is a result of change in M)
29
Dr. Mohammed Alwosabi
• When r↓, or when wealth or expected
income↑, C↑ and shifts consumption
function upward, and S↓ and shifts saving
function downward. These usually occur
during the expansion phase of business
cycle.
• When r↑ or when wealth or expected
income↓, C↓ and shifts consumption
function downward, and S↑ and shifts
saving function upward. Such shifts often
occur when a recession begins.
26
Import Function
• Like consumption, import is also influenced
by RGDP. The import function is M = a + mY.
If assumed a = 0 then, M = mY.
• M depends on income (RGDP). Other things
remaining the same, the greater the RGDP
the larger is the quantity of imports.
imports
• The relationship between M and RGDP is
determined by the marginal propensity to
import (MPI)
28
• With MPI = 0.05. If income (Y) rises by $100,
imports will rise by $5.
• MPI = 0 if we assume the country has no
economic relations with the rest of the world
(closed economy)
30
5
ECON 141: Macroeconomics
Expenditure Multiplier
Autonomous Expenditures
• As mentioned earlier, planned I, G, and X are
autonomous (independent of RGDP) in the
very SR.
• Their effect will be an upward or downward
shift of AE
• The
Th slope
l
off the
th aggregate
t expenditure
dit
curve = b = ∆AE/∆RGDP, 0 ≤ b ≤1
• Aggregate expenditure curve slopes upward
because, in part, consumption expenditure
increases when real GDP increases.
450
AE
C+I+G+X
C+I+G+X‐M
C+I+G
C+I
C
0
31
Dr. Mohammed Alwosabi
RGDP
32
Determination of Equilibrium Expenditures
• Aggregate expenditure function explains the
relationship between aggregate planned
expenditure and real GDP
• Actual aggregate expenditure is always
equal to RGDP.
• But
B t planned
l
d aggregate
t expenditure
dit
(AE) is
i
not necessarily equal to actual aggregate
expenditure and therefore is not equal to
RGDP.
• Actual expenditure and planned expenditure
differ from each other because of
"unintended inventory accumulation". 33
• Firms might end up with inventories that are
greater or smaller than planned.
• Planned investment does not include
"unintended inventory accumulation".
• Therefore, actual expenditure might differ
from planned expenditure because actual
investment differs from planned investment
investment.
• For example, if a company produces 100
cars, expecting to sell all of them this year
but only sells 70 cars this year, then the
remaining 30 are counted in GDP as
unplanned inventory investment.
Equilibrium expenditure
• Equilibrium expenditure is the level of
aggregate expenditure that occurs when
planned aggregate expenditures equal the
actual aggregate expenditure (i.e., equal to
RGDP) (and planned investment equals
actual investment)
RGDP = AE = C + I + G + NX
• When the price level is fixed, equilibrium
expenditure determines RGDP. When
planned aggregate expenditure and actual
aggregate expenditure (RGDP) are unequal,
a process of convergence toward
equilibrium expenditure (equilibrium RGDP)
occurs.
• At the equilibrium expenditure consumers
are willing to buy exactly the amount of
output that is produced and unplanned
changes in inventory must be zero.
35
34
36
6
ECON 141: Macroeconomics
Expenditure Multiplier
• Example:
AE
450
Actual AE Planned Change in Unplanned RGDP &
(RGDP) AE
Inventory (Y – AE) Employment
0
200
400
600
800
1000
Dr. Mohammed Alwosabi
200
300
400
500
600
700
-200
-100
0
100
200
300
unplanned increase
AE
in inventories
Increasingg
Increasing
Constant
Decreasing
Decreasing
Decreasing
400
200
unplanned reduction
in inventories
RGDP
400
37
• In this example, equilibrium expenditure is
at $400 million where AE = RGDP at which
45° line intersects AE line. (At equilibrium,
what is the autonomous expenditure? What
is the induced expenditure?)
• How the economy achieves equilibrium
RGDP?
• When RGDP, for example, is at $200 million
actual expenditure is also 200 million but AE
is 300 million, so AE is greater than Y.
39
• Therefore, firms' inventories fall by $100
million. Because the change in inventory is
part of the investment, actual investment is
now $100 million less than planned
investment. To restore inventories to their
target level, firms hire additional labor and
increase p
production. So RGDP increases.
This process ends when RGDP equals AE
and unplanned inventory change is zero.
• Thus, wherever RGDP (or Y) is less than AE,
unplanned decrease in inventories and
investment decreases which leads RGDP
(and employment) to increase.
41
38
• When people plan to spend $300 million and
firms produce goods and services worth
only $200 million, firms will try to meet the
planned spending by taking from
inventories what is worth to $100, which is
the difference between planned spending
and actual production.
p
40
• If RGDP is above the equilibrium
expenditure which means firms are
producing more than they can sell, firms'
would experience unplanned increase in
inventories and in response firms decrease
production and RGDP (and employment)
decreases until it reaches equilibrium.
q
At
equilibrium, where RGDP = AE, firms do not
change their production.
42
7
ECON 141: Macroeconomics
Expenditure Multiplier
Changes in the Equilibrium RGDP
• When autonomous expenditure increases,
AE increases and AE curve shifts up, and as
a result the equilibrium RGDP (Y) increases.
But we can observe that the increase in the
equilibrium RGDP is larger than the increase
in the autonomous expenditure.
• Example:
Suppose AE increases by $100 million
because of an increase in investment (I) by
$100 million.
43
450
AE1
AE0
400
200
400
600
Original New
AE
AE
200
300
200 300
400
400 400
500
600 500
600
800 600
700
1000 700
800
0
44
• As a result of an increase in investment by
100 million AE increases by a 100 million
and AE curve shifts up by a 100 million from
AE0 to AE1, at each level of RGDP.
• This upward shift in the AE resulted in a
new equilibrium expenditure point where AE
= RGDP = $600 million.
• Thus, an increase in investment by $100
million resulted in an increase in the
equilibrium RGDP by $200 million.
AE
600
Y
Dr. Mohammed Alwosabi
RGDP
45
• The increase in equilibrium expenditure by
more than the increase in the autonomous
expenditure is due to the multiplier effect.
• The concept of the multiplier process
became important in the 1930s when
Keynes suggested it as a means to
achieving full employment. This approach
meant to help overcome a shortage of
business capital investment.
47
46
The Multiplier and Equilibrium RGDP
• In the above example, when planned
investment (I) increased by $100 millions,
AE increases and RGDP (Y) increases.
• When Y increases Yd increases and as a
result C increases. The increase in C will
lead to an increase in AE which in turn
cause Y to increase and these multiples will
continue.
• Consumption expenditure of one person
would be the income of another person who
would spend some of this income on
48
consumption.
8
ECON 141: Macroeconomics
Expenditure Multiplier
• The chain of spending continues until
there's nothing left to spend.
• Thus, the initial increase in investment (I)
brings a bigger increase in AE since I does
not increases only by itself but it induces an
increase in C.
• Therefore,
Therefore the equilibrium expenditure
increases by the sum of the initial increase
in the autonomous expenditure and the
increase in the induced expenditure as well.
• The same analysis applies to a decrease in
autonomous expenditure.
49
Dr. Mohammed Alwosabi
• The multiplier indicates how many times (or
multiples) the equilibrium RGDP would
increase when an initial increase in
autonomous expenditure occurs.
• When autonomous expenditure increases,
equilibrium aggregate expenditure
increases by a greater amount due to the
multiplier.
• The multiplier effect magnifies small
changes in spending into larger changes in
output and income.
50
• Since the equilibrium RGDP increases by
more than the increase in autonomous
expenditure, this means the multiplier,
which is the change in the equilibrium
expenditure divided by the change in the
autonomous expenditure, is greater than
one.
• Multiplier = m = ∆Y/∆I , m > 1
• Example:
Find the multiplier if I increased by a $100
million and as a result Y increased by $200
millions.
51
m = ∆Y/∆I = 200/100 = 2
• Example:
Suppose I increased by $100 million and the
multiplier was found to be equal to 2, what
is the increase in the RGDP?
∆Y = (m)(∆I) = (2)(100) = 200
• Example:
Suppose the country's equilibrium RGDP
$1000 million and the multiplier = 2.5. Now,
if the country wants to increase its RGDP by
$200 million how much should the country
spend in investment?
∆I = ∆Y/m = 200/2.5 = 80
Marginal Propensities and the Multiplier
• The marginal propensity to consume (MPC)
determines the magnitude of the multiplier.
• The larger is the MPC the larger is the
multiplier.
• Assuming, the change in Y results from
change
h
in
i I plus
l change
h
in
i C,
C everything
thi
else remaining the same,
∆Y = ∆C + ∆I
Since MPC = ∆C/ ∆Y,
∆C = MPC * ∆Y
Thus, ∆Y = (MPC)(∆Y) + ∆I
By rearrangement, (1-MPC) ∆Y = ∆I
∆Y = ∆I / (1-MPC)
(
)
Divide both sides by ∆I results in the
multiplier
m = ∆Y/∆I = 1 / (1-MPC)
Since MPS = 1- MPC, m = 1/MPS
• The higher the MPC (the lower the MPS), the
54
greater is the multiplier effect.
53
52
9
ECON 141: Macroeconomics
Expenditure Multiplier
• Example:
If MPC is 0.80 and the autonomous
investment increases by $200, what is the
amount of the increase in RGDP?
The output multiplier is m = 1/(1-0.8) = 5
So the $200 initial increase in investment
ultimately
lti t l increases
i
RGDP by
b 5 x $200 =
$1,000.
• In general, the steeper the aggregate
expenditure curve the larger the multiplier;
and the flatter the aggregate expenditure
curve the smaller the multiplier.
55
• Imports make the multiplier smaller than it
otherwise would be because spending on
imports does not increase real GDP
domestically. RGDP increases only by
goods and services produced inside the
country. Hence, the larger is the MPI, the
smaller is the changes
g in the country's
y
RGDP.
• The multiplier increases if MPC increases,
MPS decreases or MPI decreases
57
• Example:
Find equilibrium RGDP given the following
consumption and investment functions.
Assume that government spending, taxes,
and net exports are all zero:
C = 100 + 0.9Y, I = 100
St (1)
Step
(1): multiplier
lti li = 1/(1-MPC)
1/(1 MPC) = 1/(1-0.9)
1/(1 0 9)
= 1/0.1 = 10
Step (2): total autonomous spending
= a + I + G + NX
= 100 + 100 + 0 + 0 = 200
59
Step (3): Y = 10 * 200 = 2000
Dr. Mohammed Alwosabi
The Output Multiplier with Imports
• When domestic income rises, consumers
wish to purchase more goods and services.
Some of the things they wish to consume
are imports. Thus, demand for foreign
goods and services also rises.
• Using the same method as before we can
add MPI and obtain the multiplier as
m = ∆Y/∆I = 1/(1-MPC+MPI) = 1/(MPS+MPI)
56
• From the multiplier equation we conclude
∆Y =1/(1-MPC+MPI) ∆I = 1/(MPS+MPI) ∆I
∆I = (1-MPC+MPI) ∆Y = (MPS+MPI) ∆Y
• Example:
Suppose the MPC = 0.8 and MPI = 0.05. The
value of the output multiplier is
m = 1/(1-0.8+0.05) = 1/(0.25) = 4
• The MPI tends to lower the multiplier effect
because demand for domestically produced
final goods and services falls.
58
The Multiplier and the Price Level
• To study the simultaneous determination of
RGDP and the price level we use AS-AD
model and the equilibrium RGDP
(equilibrium expenditure) model. The
difference between AD and AE, everything
else remaining the same
60
10
ECON 141: Macroeconomics
Expenditure Multiplier
AD curve
• AD curve is the negative relationship
between the quantity of RGDP demanded
and the price level.
• Price level is variable along AD curve.
• A change in price level brings a movement
along
l
AD curve
AE curve
• AE curve is the positive relationship
between AE and RGDP.
• Price level is fixed along AE curve.
• A change in price level shifts the AE curve
61
• It is important to note that along an AE
curve price level is fixed. But when P rises,
each of wealth effect and substitution effect
reduces AE at each level of RGDP and shifts
AE curve downward. When P falls, the AE
curve shifts upward.
Dr. Mohammed Alwosabi
AE and the Price Level:
• Because the short-run aggregate
expenditure model assumes that the price
level is fixed, its predicted effect of changes
in autonomous expenditure on equilibrium
output is greater than the prediction of the
AD/AS model.
• When price level changes, AE changes and
the quantity of RGDP demanded changes.
62
AE
450
C
600
200
AE0 (P=110)
A
400
AE2 (P=100)
AE1 (P=120)
B
400
200
RGDP
600
P
120
B
A
110
C
100
63
• Along AEo curve, price level is fixed at Po =
110 and equilibrium expenditure is 400
million at point A.
• When P increases to 120, AE decreases at
each level of RGDP. So AE curve shifts
downward to AE1 curve and the equilibrium
expenditure is 200 million at point B.
• When P decreases to 100, AE shifts upward
to AE2 and the equilibrium expenditure is
600 million at point C.
• Points A, B, and C on the AD curve
correspond to the equilibrium expenditure
65
points A, B and C in the AE curves.
AD
200
400
600
RGDP
64
• When autonomous expenditure changes,
the horizontal distance by which the
aggregate demand curve shifts depends on
the size of the multiplier.
66
11
ECON 141: Macroeconomics
Expenditure Multiplier
Shifts in AE and AD
• Now suppose investment (I) increased by
100 million at P = 110, AE curve shifts
upward to AE1 and the equilibrium
expenditure is 600 at point B. This
equilibrium expenditure of 600 million is the
new RGDP demanded at P = 110 and AD
curve shifts to AD1.
• A decrease in autonomous expenditure
shifts the AE curve downward and shifts AD
curve leftward
67
AE
450
AE1 (P=110)
AE0 (P=110)
B
600
400
A
200
200
RGDP
600
400
P
110
A
Dr. Mohammed Alwosabi
• How much AD curve shifts depends on the
multiplier. The larger is the multiplier, the
larger is the shift in the AD curve that
results from a given change in autonomous
expenditure.
68
The conclusion
• A change in P shifts AE curve and brings a
movement along the AD curve.
• A change in any other influence on AE shifts
both AE curve and AD curve. For example,
an increase in I or X increases both AE and
AD and shifts AE curve upward and AD
curve rightward.
B
AD1
AD0
400
RGDP
600
69
Exercise:
• Refer to the following table for a country
with no tax. The data includes RGDP and
planned aggregate expenditures. (All
numbers are in millions of dollars)
Y
50
100
150
200
250
C
40
75
110
145
180
I
15
15
15
15
15
G
30
30
30
30
30
NX
5
0
-5
-10
-15
71
70
a. What would be the MPC?
b. What would be the country’s autonomous
consumption?
c. What would be the slope of the AE?
d. What would be the country’s MPI?
e. What is the multiplier?
f. What is the country’s
y equilibrium
q
RGDP?
g. If the country wants to increase equilibrium
RGDP by 30, how much investment must be
changed?
h. If investment were to increase by 10, what would
be the change in equilibrium expenditures
i. What is the unplanned inventory change when
72
GDP = 50?
12
ECON 141: Macroeconomics
Expenditure Multiplier
Dr. Mohammed Alwosabi
• Exercise:
Suppose C = 40 + 0.8Y, MPI = 0.30, I = 100,
and RGDP = 500. Now suppose P decreases
from 110 to 100 and as a result consumption
function becomes C = 60 + 0.8Y and I
becomes 120
a
a.
How much is the change in the
autonomous expenditures?
b. What would be the country’s new
equilibrium RGDP?
73
74
13