multilplier and accelerator
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yMULTIPLIER and
ACCELERATOR
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Introduction of Multiplier
y 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.
y Then J.M. Keynes used it for income analysis.
Keynes believe that an increase in investment
causes a much bigger increase in national income.
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Investment Multiplier
y Multiplier shows that
how an initial change in
investment brings a multiplechange in income.
OR
y Multiplier is the ratio of change in the National
Income to a change investment.
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The Multiplier Process
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Graphical presentation of multiplier
effect
C+I
C+S
0 x
Y
National income
E.
B
2000
C+I+ ¨I
2500
500
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Explanation of Graph
y In this figure the curve C+I intersects the aggregate
production curve line at point E at 2000, the
equilibrium level of the income.
y The new curve showing the additional investmentcurve (C+I+¨I), intersects the total production line
at B. The equilibrium income eventually increases
from 2000 to 2500 in time periods (t).
y Thus the total increase in equilibrium income is
equal to 500
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Algebraic derivation of Multipliery Y=C+I ,In multiplier changes in investment induces
changes in Investment
y Y= C+ I [1]
In the consumption function C=a +b Y Where a is aconstant term, b is MPC which is also assumed tobe constant.
C=b Y, Substituting this in equation 1
Y=b Y, + I or Y -b Y = I
Y(1 ±b)= I ,
Y= I/ 1 ±b or Y = 1 where b =MPC
I 1 ±b
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Size of Investment Multiplier
y The final increase in national income (Y) will be greaterthan the initial injection.
y The investment multiplier is the direct function of
marginal propensity to consume (MPC).y The size of multiplier depends upon how large or small
is the MPC.
y If MPC is high, the value of the multiplier will also be
high.y If MPC is small, the value of the multiplier will also be
small.
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Size of Multiplier
y Marginal Propensity to Consume determine the size of multiplier.Marginal propensity to consume (MPC) is the marginal
increase inC
caused by a marginal increase in disposable income.
y MPC = change in consumption
change in income
y For example if the MPC is 0.8 it means 80% of the increase in incomeis spent.
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Multiplier in a Closed Economyy
Equation
k is equal to the inverse, or, reciprocal, of the marginal
propensity to save or to the reciprocal of 1 minus the marginal
propensity to consume
Reason for income rising more than investment
Investment expenditures rises, producers expand production and
hire more workers and use more capital and other factors of
production. Since the income generated in the process of production
equals the value of the output produced, increasing investment
expenditures also increasing income by the same amount, more
consumption, then further expansion of production and continuing
MPC MPS I
Y k
!!
(
(!
1
11
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Alternate way to find K
y Another way to find out the multiplier is that it is the
reciprocal of MPS,
y For example if MPC is 0.8 then we can easily find MPS ,
as we know that MPS = 1- MPC
y So K= 1/MPS
yK = 1/0.2
yK=5
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ConclusionConclusion
The size of the multiplier depends on marginalpropensity to consume or propensity to save.
The larger the MPC, the larger the multiplier.
The larger the MPS, the smaller the multiplier.
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Assumptions of Multiplier1 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
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Numerical Example for
Multiplier Actiony The investment multiplier tells us that an increase in
investment brings about a multiple increase in aggregate
income.
y
Let us assume that MPC
is 0.8 and an increase in investmentis $100 mn
y The MPC being 0.8 means that the multiplier (K) will be
(1/1-0.8) = 5
y
So the new investment of $100 mn will increase theaggregate income by $ 500 mn.
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Consumption multiplier
y In consumption multiplier we want to show the effect of
consumption on National Income.
y Y=f (c ), that is NI will change many a time more than
the change in consumption.
y Change in consumption will have a multiple effect onincome.
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Consumption Multiplier «.
y How much income change as a result of change in
consumption depends on consumption multiplier (Kc)
y Consumption Multiplier is a ratio of change in NI (Y)
to change in consumption (c)
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Numerical example of consumption
multiplier
y Y=C+I, C= 40 + 0.60Y I0=80
y Y=a+ bY+ I0
y Y=40+0.60Y+80
y Y- 0.60Y=120
y 0.40Y=120
ydividing both sides by 0.40
y Y= 300 is initial equilibrium level of income
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Numerical example of consumption
multiplier
y Now suppose that autonomous consumption increases
from 40 crores to 100 crores
y Y=a+ bY+ Io
y Y=100+0.60Y+80y Y-0.6Y=180
y 0.4Y=180, dividing both sides by 0.4
y
Y1=450soY1 is the new equilibrium level of income after
change in consumption
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Consumption Multiplier Effect (cont«.)
y Graphical presentation of multiplier effect
C+I
AS=C+SC+¨Co +I
x
C+IC+S
300 450
E1
E2
¨Co=60
¨Y=150
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Government Expenditure Multiplier
y Like a change in autonomous investment, change in
gover nment expenditure also has a multiple change in
National Income
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Government expenditure multiplier (cont..)
y How much income changes as a result of change in
Government expenditure is known as Government
Expenditure Multiplier (KG)
OR
y It is the ratio of change in NI (Y) to change in
Government expenditure (G)
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Numerical example of government
expenditure multiplier
y Y=C+ I0+ Go
y C=a+ bY
y C = 40+0.60Y, I0 =80,Go=60
y Putting the values in income equation
y Y = 40+0.60Y+80+60
y Y-0.60Y=180
y Y=450
y Now we assume that government expenditure increases her
expenditure from Rupees 60 crores to rupees 100 crores, theorysuggests that change in government expenditure has multipleeffect on NI, now we will prove it
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Numerical example of government
expenditure multiplier
y Y=C+ I0+ Go
y C=a+ bY
y C = 40+0.60Y, I0=80,Go=100
y
Putting the values in income equationy Y = 40+0.60Y+80+100
y Y-0.60Y=220
y Y1=220/.40 =550
yY1=550, so change inGOVT expenditure is rupees 40 crores,where as change in NI is rupees 100 crores
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Government expenditure multiplier (cont..)
y Graphical presentation of GEM
AD1=C+I+G1
AD2=C+I+G2AS
Y
AD,AS
E1
E2
450 550
¨Go=40
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Tax multiplier
y Like a change in autonomous investment, the change in
autonomous taxes has a multiple effect on level of
national income
y However there is a negative effect on level of national
income. Tax Multiplier is a ratio of change in NI
(Y) to change in Tax (T)
y When tax rate increase, consumption decrease and itleads to decrease in investment and ultimately decreasethe national income.
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Numerical example of Tax
Multiplier««y C = 40+0.60Yd, I0=80,G0=60, T0= 30
y Putting the values in income equation
y Y = 40+0.60Yd+80+60
yY=40 + 0.60Y - 0.6(30) +80 + 60
y Y=40 + 0.6Y -18 + 60 + 80
y Y-0.60Y=162
y 0.4Y=162
y Y= 405
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The Multiplier (cont'd)y Significance of the multiplier
y It is possible that a relatively small change in consumption or
investment can trigger a much larger change in real GDP.
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Introduction to Acceleration Principle
y Carver was the first economist who recognized the
relationship between changes in consumption and net
investment in 1903
y The term ́ acceleration principleµ itself was first
introduced into economics by J.M Clark in 1917.
y It was further developed by Hicks, Samulson and Harrod
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Acceleration
y The principle of acceleration
y The acceleration principle is opposite of multiplier.
y According to this ,when income or consumptionincreases, investment will increase manifold. when
income and therefore consumption of te people
increases, greater amount of commodities will have to be
produced. This will require more capital to producethem .
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Acceleration (cont«)
y 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
y In words of Kurihara ́ acceleration coefficient is the ratio
between induced investment and initial change in
consumption expenditure.
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Acceleration (cont«)
y Symbolically = I/ C
y Where is accelerator coefficient , I is net change in
investment, and C is change in consumptionexpenditure
y If the increase in consumption expenditure of rupees 10
million leads to an increase in investment of rupees 30million then the accelerator coefficient is 3.
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y 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 ininvestment is proportionately more than the rise in
demand for consumption.
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The paradox of thrift
y An attempt by the economy as a whole to increase aggregate savingsnot only will not succeed, but may lower aggregate output, incomeand employment. This is because increased savings at a givenlevel of aggregate income will mean decreased consumption.
Thus a smaller marginal propensity to consume will reducethe simulative effects of investment and other spending.
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