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‫الجزء السابع‬
‫أثر المضاعف والسياسة المالية‬
‫‪The multiplier effect and Fiscal Policy‬‬
‫‪1‬‬
The Multiplier effect
Recall: from the Silver Moon economy data we were able to
determine the equilibrium level
For two sectors:
e
Y = 500 m.
When government expenditure were added (100 m)
e
For three sectors with no taxes:
= 700 m.
Y
i.e, an increase in DG = 100
2
e
an increase in D Y= 200
e
Y
Y(AS)
Ye
AE2(C+I+G)
AE1(c+I )
AE
DG =
100
3
500
450
400
350
300
250
200
150
100
50
0
0
100
200
300
400
500
600 700
DY= 200
Y
Note an increase in DY > DG (DI)
or
DY / DG > 1
This is called the multiplier effect
Multiplier effect: Chain reaction of an initial change in income
and spending that leads to a greater change in final income and
spending.
‫ سلسلة من االرتفاع (التغير) في الدخل واإلنفاق الناجمة عن االرتفاع (التغير) في دخل‬:‫مضاعف االتنفاق‬
.‫أو انفاق أولى‬
Change in GDP
The expenditure multiplier =
)‫(مضاعف اإلنفاق‬
initial change in spending (AE)
4
Expenditure Multiplier in a closed economy: (a) with no taxes:
Example 1: For the Silver Moon economy (MPC = 0.5), we
added investment expenditure by $ 100 m. This increased
spending created an equal income in the economy = $100 m.
This income is partly consumed ($ 50 m) and partly saved
($50 m) according to MPC & MPS. The new consumption
expenditure will create a new chain of income in the
economy as follows:
‫( االرتفاع في اإلنفاق‬MPC = 0 .5 ‫في اقتصاد دولة القمر الفضى (حيث‬
. ‫ مليون خلق دخال جديدا في االقتصاد بنفس المقدار‬100 ‫االستثمارى بمقدار‬
.‫ مليون) وادخار النصف اآلخر‬50 ‫هذا الدخل الجديد يتم استهالك نصفه (أي‬
:‫ مليون) سيخلق سلسلة من الدخول كما يلي‬50( ‫اإلنفاق االستهالكى‬
5
Round
1
2
DY
100
50
DC
50
25
DS
50
3
25
12.5
12.5
4
12.5
6.25
6.25
5
6.25
3.125
3.125
200
100
100
25
Note: In this example total income has multiplied by 2.
$ 100 m is a direct increase in AE and the other $100 m is
indirect induced additional spending.
6
Example 2: If for an other economy MPS = 0.25, and the
government increased its spending by DG= $100 m. This initial
increase will DY= $100 m, leading to a chain reaction as follows:
DS
25
Round
1
2
DY
100
75
DC
75
56.25
18.75
3
56.25
42.2
14
400
300
100
Note: In this example total income has multiplied by 4.
$ 100 m is a direct increase in AE and the other $300 m is
indirect induced additional spending.
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Note 1: The multiplier effect increases as MPS decreases
(or as MPC increases ) Why ?
DY
M =
Note 2: See appendix
8
DAE
=
1
MPS
Appendix
Recall, at equilibrium for a simple two sectors economy:
Y
e=
DY
1
DI
DY
DY
DI
M
9
C + I
= DC + DI
DC DI
=
+
DY DY
DC
= 1= 1 - MPC
DY
1
1
=
=
1 - MPC
MPS
1
=
MPS
MPC
Expenditure Multiplier (M)
10
0.9
5
0.8
4
0.75
3
0.67
0. 5
10
2
Examples :
1 – If an increase in autonomous consumption by $50 m
leads to an increase in total income by $250 m. What is the
value of MPC?
DY
1
M =
=
Da
MPS
1
250
=
= 5 =
MPS
50
1
MPS =
5
4
MPC =
5
11
Examples :
2 – If C = 100 + 0.8 Y
I1 = 100
I2 = 200
DY = ?
1
M =
MPS
12
1
0.2
=
DY =
M X
DY =
5 X 100
= 5
DI
= 500
The Tax Multiplier effect
Recall: from the Silver Moon economy data
For three sectors with no taxes:
e
Y
= 700 m.
When government applied a fixed tax of 100 m
e
For three sectors with fixed taxes:
Y = 600 m.
Note the increase in taxes have not reduced DY by a
multiplier = 2
(though MPC = 0.5)
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The Multiplier in a closed economy: (b) with taxes:
MT
D Ye
MPC
=
= DT
MPS
Note 1: MT < MI,G at all values of MPS ( the impact of
DG > DT on equilibrium income) why?
Note 2: See appendix
14
Appendix
1
At T1 : Y1 =
(a - bT1 + I + G)
1- b
1
e
At T2 : Y2 =
(a – bT2 + I + G)
1- b
1
e
DY =
( – bT2 + bT1)
1- b
e
DYe
=
DYe =
DY
=
DT
15
-b
(T2 - T1)
1- b
-b
(DT)
1- b
-b
1- b
MPC
=
MPS
The Expenditure Multiplier in an open economy
Q: for an open economy, imports are considered a leakage from the
economy. Would the effect of the expenditure multiplier in the open
economy be smaller or bigger than
in the case of a closed
economy?
MO
16
D Ye
=
=
D AE
1
MPS + MPM
The GDP gap and Fiscal policy
Recall, the economy maybe below its potential output (GDP)
even at a state of an equilibrium income.
AS (LR)
P
AS(SR)
AD
17
Y
e
Y
f
Q
5
4
f
3
Y
e
2
Y
1
0
0 2 4 6 8 10 12 14 16
First: If
Ye < Yf
there exists a deflationary gap
( ‫)فجوة ركودية‬
This gap may be estimated by two methods:
(1) GDP gap : Yf - Ye
or
(2) Expenditure gap : AE - AS at full employment
Q: What policies a government can apply to reduce this gap?
18
AE
Ye
Y
f
AS
AE
Expenditure
Gap
(deflationary gap)
0
0
GDP Gap
19
Y
There are many policies a government can apply to reduce
the deflationary gap or to generally change the real GDP
and the price level. One of these policies is the Fiscal
Policy.
Fiscal policy: Changes in government spending (on goods
& services and transfer payment) and taxes designed to
influence real GDP and the price level. Government
spending and taxes are tools of the fiscal policy.
‫ التغير في االنفاق الحكومي (على السلع والخدمات و‬:‫السياسة المالية‬
‫المدفوعات التحويلية ) باإلضافة للضرائب بهدف التأثير على الناتج المحلى‬
‫ ان االنفاق الحكومي والضرائب تعتبر أدوات‬.‫الحقيقي و مستوى األسعار‬
.‫السياسة المالية‬
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If an economy is facing a deflationary gap, the
government can increase its spending and/or reduce
taxes : expansionary fiscal policy (‫)سياسة مالية توسعية‬
Note: In this case a budget deficit may occur ( ‫تحقق عجز‬
‫ )في الميزانية‬.
Q: What other policies a government can apply to reduce a
deflationary gap ?
21
Second: If
Ye > Yf
there exists an inflationary gap
( ‫)فجوة تضخمية‬
This gap may be estimated by two methods:
(1) GDP gap : Yf - Ye
or
(2) Expenditure gap : AE - AS at full employment
22
Y
f
AE
Ye
AS
AE
Expenditure
Gap
(inflationary gap)
0
0
GDP Gap
23
Y
If an economy is facing an inflationary gap, the
government can decrease its spending and/or increase
taxes : contractionary fiscal policy (‫)سياسة مالية انكماشية‬
Note: In this case a budget surplus may occur
(‫)تحقق فائض في الميزانية‬
Q1: What other policies a government can apply to reduce
an inflationary gap ?
Q2: Can the government affect the GDP gap with a
balanced budget ?
24
The Balanced Budget Multiplier effect
First: If
Ye < Yf
( deflationary gap)
The government can increase both DG & DT by the same
amount at the same time (DG = DT)
Second: If
Ye > Yf
( inflationary gap)
The government can reduce both DG & DT by the same
amount at the same time (DG = DT)
Q: Recall, that DG & DT have the opposite effect on AD,
would not an equal change in DG & DT leave AD
unaffected?
25
Recall, changing DG & DT will stimulate further changes
in income and spending according to the multipliers MG & MT.
Recall, the impact of MG > MT
M BB = MG
=
+
1
1- b
26
(Why?)
MT
-
b
1- b
=
1 = DY
DG = DT
Note: M BB = DY/ (DG=DT) = 1
always at all values of MPC !
Note: DG = DT (Same direction)
equal change in DY
What are the obstacles facing implementing fiscal
policy?
‫ما هي الصعوبات التي يمكن ان تواجه تطبيق السياسة المالية ؟‬
27
Examples: 1
If MPC = 0.5
Ye = $700m
YF = $1000m
What is the required change in: (1) DG
(2) DT
to eliminate the GDP gap?
Answers
28
MG
= 2
DY
=
DG
DY
300
= M = 2 = 150
MT
= -1
DT
DY
300
= M = -1 = -300
T
YF - Ye
= 300
Examples: 2
If MPS = 0.25
DYe = ?
Answer

29
DG = 200 m
MG
= 4
DYG
= MG
MT
= -3
DYT
= MT X
DY
=
DT = 100
X DG
500
DT
= 4
X 200
= 800
= (-3) X (100) = -300
Examples: 3
If MPC = 0.75
DYe = ?
DG = 50
DT = -50
Answer

30
MG
= 4
MT
= -3
DYG
= 4
DYT
=
(-3) X (-50) = 150
DY
=
350
X 50
= 200
Examples:4
If MPC = 0.8
DY = ?
Answer
MG

Or
31
DG = 200
DT = 200
(a):
MT
= 5
= -4
DY
=
DYG
= 5 X 200 = 1000
DYT = (-4) X 200 = -800
200
(b):
Since DG = DT
 MBB = 1
 DY = DG = DT = 200