Chapter # 4
MULTIPLIER and
ACCELERATOR
Chapter`s Outlines
 Introduction and History of Multiplier
 Investment Multiplier
 Numerical & Graphical Presentation
 Consumption Multiplier
 Numerical & Graphical Presentation
 Government Multiplier
 Numerical & Graphical Presentation
 Tax Multiplier
 Numerical & Graphical Presentation
 Accelerator
 Numerical Explanation of Acceleration Principle
Introduction of Multiplier
 The concept of Multiplier was first developed by R.F.
Kahn in early 1930`s. He traced the effect of an increase
in investment on employment.
 Then J.M. Keynes used it for income analysis.
Keynes believe that an increase in investment causes a
much bigger increase in national income.
Introduction of Multiplier
 When we change investment, it will bring a
multiple change in national income, but the
question arise to what extent NI changes as a
result of change in investment.
Definition of Multiplier
 An initial change in aggregate demand will lead to
greater increase in the final level of equilibrium National
Income.
Investment Multiplier
 Multiplier shows that
how an initial change in
investment brings a multiple
change in income.
OR
 Multiplier is the ratio of change in the National
Income to a change investment.
Example:
 The government decides to build new roads across the
Afghanistan. They pay a contractor $300m to do this.
 This creates a $300 million increase in spending in
the Afghan economy.
 This will create a chain reaction of increases in expenditures.
 The firm who gets the contract to build the roads will spend
this $300m on materials, equipment, wages & profits. This
will create additional incomes for other firms and
households
 If they spend approx 60% of that additional income, then
$180m will be added to the incomes of others.
 At this point, total income has grown by ($300m + (0.6 x
$300m).
 The sum will continue to increase as the producers of the
additional goods and services gain an increase in their
incomes, of which they in turn spend 60% on even more
goods and services.
 The increase in total income will then be ($300m + (0.6 x
$300m) + (0.6 x $180m).
 The process can continue indefinitely. But each time, the
additional rise in spending and income is a fraction of the
previous addition to the circular flow.
Size of Investment Multiplier...??
 The final increase in national income (Y) will be
greater than the initial injection.
 The size of the multiplier depends on how much
of an increase in income is spent in Afghanistan
economy.
Size of Multiplier…… cont`d
 Marginal Propensity to Consume determine the size of
multiplier.
 MPC = change in consumption
change in income
 For example if the MPC is 0.8 it means 80% of the increase
in income is spent.
Size of Multiplier…… cont`d
 The investment multiplier is the direct function of marginal
propensity to consume (MPC). The size of multiplier
depends upon how large or small is the MPC.
 If MPC is high, the value of the multiplier will also be high.
 If MPC is small, the value of the multiplier will also be small.
Size of Multiplier…… cont`d
 The value of Multiplier can be obtained by following formula
K= 1 .
1-mpc
For example if mpc is 0.80 then multiplier will be
K= 1 = 1 K = 5
0.2
1-0.8
Alternate way to find K…???
 Another way to find out the multiplier is that it is the
reciprocal of MPS,
 For example if MPC is 0.8 then we can easily find MPS ,
as we know that MPS = 1- MPC
 So K = 1/MPS
 K = 1/0.2
 K=5
Conclusion

The size of the multiplier depends on marginal
propensity to consume or propensity to save.

The larger the MPC, the larger the multiplier.

The larger the MPS, the smaller the multiplier.
Numerical Example for
Multiplier Action
 The investment multiplier tells us that an increase in
investment brings about a multiple increase in aggregate
income.
 Let us assume that MPC is 0.8 and an increase in investment
is $100 mn
 The MPC being 0.8 means that the multiplier (K) will be
(1/1-0.8) = 5
 So the new investment of $100 mn will increase the
aggregate income by $ 500 mn.
Graphical presentation of multiplier
effect
C+S
Y
B
C+I+ ΔI
C+I
.
E
500
0
2000
2500
National income
x
Explanation of Graph
 In this figure the curve C+I intersects the aggregate
production curve line at point E at 2000, the
equilibrium level of the income.
 The new curve showing the additional investment
curve (C+I+∆I), intersects the total production line
at B. The equilibrium income eventually increases
from 2000 to 2500 in time periods (t).
 Thus the total increase in equilibrium income is
equal to 500
Assumptions of Multiplier
1
MPC is constant.
2
There is no changes in prices of commodities.
3
There is closed economy unaffected by foreign influence.
4
There is no change in autonomous investment
Consumption multiplier
 In consumption multiplier we want to show the effect of
consumption on National Income.
 Y=f (c ), that is NI will change many a time more than
the change in consumption.
 Change in consumption will have a multiple effect on
income.
Consumption Multiplier ….
 How much income change as a result of change in
consumption depends on consumption multiplier (Kc)
 Consumption Multiplier is a ratio of change in NI (ΔY)
to change in consumption (Δc)
Numerical example of consumption
multiplier
 Y=C+I,
C= 40 + 0.60Y
I0=80
 Y=Co+ cY+ I0
 Y=40+0.60Y+80
 Y- 0.60Y=120
 0.40Y=120
 dividing both sides by 0.40
 Y= 300 is initial equilibrium level of income
Numerical example of consumption
multiplier
 Now suppose that autonomous consumption increases
from 40 Afs to 100 Afs
 Y=Co+ cY+ Io
 Y=100+0.60Y+80
 Y-0.6Y=180
 0.4Y=180, dividing both sides by 0.4
 Y1=450
so Y1 is the new equilibrium level of income after
change in consumption
IS YOUR ANSWER CORRECT..?? VERIFY
 K=
1 .
1-mpc
K= 1/1-0.60
= 1/0.4
K= 2.5
Now verify your answer
Y0= 300 & Y1 = 450 ∆Y = 450-300= 150
C= 40, C1 = 100, ∆C =100-40= 60
K = ∆Y/ ∆C
K= 150/60 = 2.5
Consumption Multiplier Effect (cont….)
 Graphical presentation of multiplier effect
AS=C+S
C+ΔCo +I
C+I
C+S
E2
ΔCo=60
C+I
E1
ΔY=150
300
450
x
Government Expenditure Multiplier
 Like a change in autonomous investment, change in
government expenditure also has a multiple change in
National Income
 Now our NI, Y will be equivalent to
 AD = C+I+G , AS=C+I+S
 Where C= Co+cYd ,where Yd is personal disposable
income which is equal to Y-T
Government Expenditure Multiplier…..
 Investment is equal to autonomous
investment i.e. Io
 The saving equation is S=-So+sYd
 Government expenditure is autonomous
expenditure i.e. Go
 Taxes are also autonomous i.e. To
Government expenditure multiplier (cont..)
 How much income changes as a result of change in
Government expenditure is known as Government
Expenditure Multiplier (KG)
OR
 It is the ratio of change in NI (ΔY) to change in
Government expenditure (ΔG)
Numerical example of government
expenditure multiplier
 Y=C+ I0+ Go
 C=Co+ c Y
 C = 40+0.60Y, I0 =80, Go=60
 Putting the values in income equation
 Y = 40+0.60Y+80+60
 Y-0.60Y=180
 Y=450
 Now we assume that government expenditure increases her
expenditure from 60 Afs to 100 Afs, theory suggests that change in
government expenditure has multiple effect on NI, now we will
prove it
Numerical example of government
expenditure multiplier
 Y=C+ I0+ Go
 C=Co+ c Y
 C = 40+0.60Y, I0=80, Go=100
 Putting the values in income equation
 Y = 40+0.60Y+80+100
 Y-0.60Y=220
 Y1 =220/.40 =550
 Y1=550, so change in GOVT expenditure is 40 Afs ,where as
change in NI is 100 Afs
VERIFY YOUR ANSWER..??
 As we know that
K= 1 .
1-mpc
K= 1/1-0.60
= 1/0.4
K= 2.5
Now verify your answer
Y0= 450 & Y1 = 550 ∆Y = 550-450= 100
G= 60, G1 = 100, ∆G =100-60= 40
K = ∆Y/ ∆G
K= 100/40 = 2.5
Government expenditure multiplier (cont..)
 Graphical presentation of GEM
AS
AD2=C+I+G2
E2
AD,AS
AD1=C+I+G1
ΔGo=40 E1
450
550
Y
Tax multiplier
 Like a change in autonomous investment, the change in
autonomous taxes has a multiple effect on level of
national income
 However there is a negative effect on level of national
income
 When tax rate increase, consumption decrease and it
leads to decrease in investment and ultimately decrease
the national income.
Tax multiplier (cont…)
 As a result, NI decrease many a time
depending upon the value of Kt
 Through KT we find How much income
change as a result of change in Tax (Kt)
 Tax Multiplier is a ratio of change in NI
(ΔY) to change in Tax (ΔT)
Numerical example of Tax Multiplier
 Y=C+ I0+ Go
 C=Co+ c Yd ,Yd =(Y-T)
 C = 40+0.60Yd, I0=80, Go=60, T= 20
 Putting the values in income equation
 Y = 40+0.60Yd+80+60
 Y=40 + 0.60Y - 0.6(20) +80 + 60
 Y=40 + 0.6Y -12 + 60 + 80
 Y-0.60Y=168, => 0.4Y=168 =>
Y= 420
 Now we assume that government increases Tax from 20
Afs to 30 Afs
Numerical example of Tax
Multiplier……
 C = 40+0.60Yd, I0=80, G0=60, T0= 30
 Putting the values in income equation
 Y = 40+0.60Yd+80+60
 Y=40 + 0.60Y - 0.6(30) +80 + 60
 Y=40 + 0.6Y -18 + 60 + 80
 Y-0.60Y=162
 0.4Y=162
 Y= 405
Introduction to Acceleration Principle
 Carver was the first economist who recognized the
relationship between changes in consumption and net
investment in 1903
 The term “acceleration principle” itself was first
introduced into economics by J.M Clark in 1917.
 It was further developed by Hicks, Samulson and Harrod
Acceleration
 The principle of acceleration
The principle of acceleration is based on the fact
that demand for capital goods is derived from the
demand for Consumer goods, it means that if there is
demand of consumer goods in market, investment will
take place and demand for capital goods will increase.
Acceleration (cont…)
 Acceleration principle explains the process by which an
increase or (decrease) in demand for consumption goods
leads to an increase or decrease in investment or capital
goods
 In words of Kurihara “ acceleration coefficient is the ratio
between induced investment and initial change in
consumption expenditure.
Acceleration (cont…)
 Symbolically
β = ΔI/ ΔC
 Where β is accelerator coefficient , ΔI is net change in
investment, and ΔC is change in consumption
expenditure
 If the increase in consumption expenditure of 10 million
Afs leads to an increase in investment of 30 million Afs
the accelerator coefficient is 3.
 This means that when the income of a community rises
the purchasing power of the people increases. They begin
to buy more commodities. The higher the demand for
consumer goods leads to greater investment. The rise in
investment is proportionately more than the rise in
demand for consumption.
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