Multilplier and Accelerator

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yMULTIPLIER and

ACCELERATOR

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.

Investment Multiplier

y Multiplier shows that

how an initial change in

investment brings a multiplechange in income.

y Multiplier is the ratio of change in the National

Income to a change investment.

The Multiplier Process

Graphical presentation of multiplier

effect

National income

C+I+ ¨I

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

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

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.

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.

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

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

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.

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

Numerical Example for

Multiplier Actiony 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 investmentis $100 mn

y 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 theaggregate income by $ 500 mn.

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.

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)

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

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

Y1=450soY1 is the new equilibrium level of income after

change in consumption

Consumption Multiplier Effect (cont«.)

y Graphical presentation of multiplier effect

AS=C+SC+¨Co +I

C+IC+S

300 450

¨Co=60

¨Y=150

Government Expenditure Multiplier

y Like a change in autonomous investment, change in

gover nment expenditure also has a multiple change in

National Income

Government expenditure multiplier (cont..)

y How much income changes as a result of change in

Government expenditure is known as Government

Expenditure Multiplier (KG)

y It is the ratio of change in NI (Y) to change in

Government expenditure (G)

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

Numerical example of government

expenditure multiplier

y Y=C+ I0+ Go

y C=a+ bY

y C = 40+0.60Y, I0=80,Go=100

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

Government expenditure multiplier (cont..)

y Graphical presentation of GEM

AD1=C+I+G1

AD2=C+I+G2AS

450 550

¨Go=40

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.

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

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.

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

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 .

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

y In words of Kurihara ́ acceleration coefficient is the ratio

between induced investment and initial change in

consumption expenditure.

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.

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.

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.

THANK YOU

Multilplier and Accelerator

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