Chapter # 4 MULTIPLIER and

ACCELERATOR

Chapter`s OutlinesIntroduction and History of MultiplierInvestment Multiplier

Numerical & Graphical Presentation Consumption Multiplier

Numerical & Graphical PresentationGovernment Multiplier

Numerical & Graphical PresentationTax Multiplier

Numerical & Graphical PresentationAccelerator

Numerical Explanation of Acceleration Principle

Introduction of MultiplierThe 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 MultiplierMultiplier 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 consumptionchange in income

For example if the MPC is 0.8 it means 80% of the increase in income is spent.

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 .

For example if mpc is 0.80 then multiplier will be

K= 1 = 1 K = 5

1-mpc

1-0.8

0.2

Size of Multiplier…… cont`d

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 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+I

C+S

0 x

Y

National income

E.

B

2000

C+I+ ΔI

} 100

2500

500

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 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

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 multiplierY=C+I, C= 40 + 0.60Y I0=80

Y=Co+ cY+ I0

Y=40+0.60Y+80Y- 0.60Y=1200.40Y=120dividing both sides by 0.40Y= 300 is initial equilibrium level of income

Numerical example of consumption multiplierNow suppose that autonomous

consumption increases from 40 Afs to 100 Afs

Y=Co+ cY+ IoY=100+0.60Y+80Y-0.6Y=1800.4Y=180, dividing both sides by 0.4Y1=450

so Y1 is the new equilibrium level of income after change in consumption

IS YOUR ANSWER CORRECT..?? VERIFYK = 1 .

1-mpc

K= 1/1-0.60 = 1/0.4 K= 2.5

Now verify your answerY0= 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

C+I

AS=C+SC+ΔCo +I

x

C+IC+S

300 450

E1

E2

ΔCo=60

ΔY=150

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 toAD = 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+sYdGovernment expenditure is autonomous

expenditure i.e. GoTaxes 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+ GoC=Co+ c YC = 40+0.60Y, I0 =80, Go=60Putting the values in income equationY = 40+0.60Y+80+60Y-0.60Y=180Y=450Now 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 multiplierY=C+ I0+ GoC=Co+ c YC = 40+0.60Y, I0=80, Go=100Putting the values in income equationY = 40+0.60Y+80+100Y-0.60Y=220Y1 =220/.40 =550Y1=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= 2.5Now verify your answerY0= 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

AD1=C+I+G1

AD2=C+I+G2AS

Y

AD,AS

E1

E2

450 550

ΔGo=40

Tax multiplierLike 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 MultiplierY=C+ I0+ GoC=Co+ c Yd , Yd =(Y-T)C = 40+0.60Yd, I0=80, Go=60, T= 20Putting the values in income equationY = 40+0.60Yd+80+60Y=40 + 0.60Y - 0.6(20) +80 + 60Y=40 + 0.6Y -12 + 60 + 80 Y-0.60Y=168, => 0.4Y=168 => Y=

420Now 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= 30Putting the values in income equationY = 40+0.60Yd+80+60Y=40 + 0.60Y - 0.6(30) +80 + 60Y=40 + 0.6Y -18 + 60 + 80Y-0.60Y=162 0.4Y=162 Y= 405

Introduction to Acceleration PrincipleCarver 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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