Multiplier

Theory of Multiplier

What Is Multiplier ? Its is an important tool to analyze:

The magnitude (quantum) change in National Income because of change in aggregate demand.

Effects of changes in the Monetary & Budgetary Policy of Government.

Shift in the aggregate demand in a modern economy may be caused by :

Business Investment Government Spending Foreign trade (X+M)

Therefore, multiplier is the tool analyze magnitude of the change because of change in aggregate demand based on above mentioned area.

Business Investment Multiplier

It is the ratio of final change in equilibrium of national income to the initial change in autonomous Investment.

As per Keynes, the increment (decrement) in income would be several times to the initial increment (decrement) in autonomous investment.

m = Y I

If an initial investment of Rs.50/-crores leads to an increase in income by Rs.300/- crores

m= Y/ I = 300/50 m = 6

It suggests that every increment of Rs.1 in investment brings about an increase in income of the order of Rs.6/-

Resultantly, a small increment in investment by the govt. during recession but also provide help for recovery and prosperity of economic system.

Working of Multiplier Process Autonomous Investment Rs.100 Million, b =

80% Rounds of Income

Generation

Consumer Spending

(Rs.Million)

Income Generation

(Rs.Million)

First Round -- 100

Second Round 80 80

Third Round 64 64

Fourth Round 51.20 51.20

Fifth Round 40.96 40.96

Last Round -- 00.00

Total Income 500.00

Graphical Representation Initial equilibrium point is‘E’ where AD intersects ASat Y1 equilibrium level of income.

If autonomous investment takes place pushing up

the AD curve to C+I+ I. Now new equilibrium is At point ‘F’ at Y2 equilibrium level of income.

Y=C+S

C+I+ I

E

F

Y2Y1

C

C+I

R

M

Income

Y- axis Consumption and Investment

AD

As a result of an increase in investment by ‘FM’ the level of income rises by ER.

The increase in Income ‘ER’>‘FM’

It reflects that a given autonomous change in

investment will be associated with a change in

income larger than itself.

Two Limiting Cases of the Value of Multiplier

1. MPC = 1 (Whole income is consumed)

Multiplier will be infinite

2. MPC = 0 (Whole income is saved)

Multiplier = 1

MPC is > 0 but < 1

m is > 1 but < ∞

Assumptions

1. In short run MPC is remain constant.

2. Keynes assumed there is no time-lag between the increase in investment and resultant increment in income. It is known as

instantaneous multiplier.

3. Excess capacity exist in the consumer goods industries. So that increase of demand will not bring inflationary pressure.

Types of Multiplier : Static Multiplier Static Multiplier does not consider the time

path of change in income.

Assumptions: There is no time lag between the receipt of

income and its disposal in the form of consumption.

Investment multiplier varies directly with the ‘MPC’ (Higher the MPC (b) greater will be the magnitude of m and vice-a versa).

Static MultiplierAlgebraic Derivation :

Y = C+I Investment increases by I Consumption increases by C Y = C+ I As change in investment is considered as

independent to income while changes in consumption is function of income. As-

C = b Y

Thus – Y = b Y + I Y – b Y = I Y (1-b) = I

Y = 1 I OR 1-b Y = 1 = m or

I 1-b m = 1_ = 1 = 1 1-b 1-MPC MPS

Example -

I = 200 crore C = 80+0.75Y What will be the equilibrium level of

Income ? What will be the increase in national

income if:

investment increases by Rs. 25 crore

Y = C+I C= 80+0.75Y I = 200 crore

Y= 80+0.75Y+200 Y(1-0.75Y) = 80+200 =280

0.25=280 Y=280 x 100 = 1120

25

m = 1 = __1___

1-b 1-0.75 = 4

I Rs. 25 crore x 4 = 100 crore

Dynamic Multiplier Change in income as a result of change in

investment is not instant.

There is gradual process by which income changes as a result of change in investment.

The gradual process involves the time ‘single period time-lag’ on which consumption is based on.

Consumption in period ‘t’ depends upon the income in ‘t-1’. Investment is assumed to be continuous,

Symbolically-

Yt = Ct+It Ct = a+byt-1 It = It Yt = a+byt-1+It

Example

I = Rs.70 Crore, C = 60+0.80Yd

i) Find the Equilibrium level of Income when

there is a Rs.10 crore increase in auton-omous planned investment increase from Rs. 70 crore to 80 crore.

ii) Establish the multiplier effect of the Rs.10 crore increase in autonomous spending

Solution

i) Y = C+I = 60 + 0.80Y + 70 = 130 +0.80Y

Y -0.80Y = 130 or Y(1-0.80) =130 = 130/0.2 = Rs.650 Crore

ii) Y = C+I = 60 +0.80Y +80 = 140 +0.80Y Y-0.80Y =140 or Y = 140/0.2 = Rs. 700

As a result of 10 crore investment income rises by Rs.50 crore.

Therefore, Multiplier effect – m= 1/1-b = 1/1-0.80 = 1/0.2 = 5

Problem

Assuming the following values of MPC find out the MPS and Multiplier.

MPC = a) 0.20, b)0.50, c)0.90 As - m = 1/MPS As - MPC+MPS =1

Use of Multiplier

Multiplier is important tool to determine investment requirement for a certain planned growth in national income.

Planned Growth ( Y) = Rs. 100billion Multiplier = 5 Invest men Requirement = Y/m = 100/5 = 20 billion

Limitation of Multiplier

This theory does not work practically due to given reasons:

Leakage from the income stream:

Multiplier is based on MPC. Spending takes place as per increased consumption which leads increase in income due to increase in autonomous investment.

In practice this assumption does not hold in reality because people spend their additional income on non-consumption item. Such expenses are known as Leakages because of given reasons:

1. Payment of the Past Debts

2. Purchase of existing wealth

3. Import of Goods and Services

Non Availability of Consumer goods and

Services: There is time-lag between demand and supply. In general supply of goods does not follow instantly the rise in

Demand.

Full Employment Situation: Multiplier does not work in this situation. When resources of the country are fully employed further production will not be possible. Hence additional investment will only lead to INFLATION,

Government Multiplier :

Balanced Budget Multiplier Tax Multiplier

Three Sector Model : Income Determination

Y = C+I+GRedefined C as:

C = a+bYd

Yd = Y-TC= a+b(Y-T)

Equilibrium level of Income:

Y = C+ I +G Y = a +b(Y-T) +I+G

Y=a + b Y – bT + I +G (1-b)Y = a-bT +I+G

Y = 1 ( a –b T + I +G)

1-b

C = 100+ 0.75Yd I = 200 G = T = 100

Y = 1 ( a –b T + I +G)

1-b Y = 1 [100 – (0.75 x100) +200+100] 1-0.75

= 1/0.25 (100-75 +200+100) = 4(325) = 1300

There is no Tax imposition only Gov. expenditure is in economy:

C = 100 +0.75 I = 200 G (Exp.) =100

Y = a + bY+ I + G Y = 100+0.75+200+100

(1– 0.75)Y =100+200+100 Y = 400/0.25

Y =1600

Multiplier –Three Sector Model

Three Sector economy –

Y = C+I+G

This multiplier known as Government expen-diture multiplier. In this case, the equilibrium of national income changes because of change in Government expenditure

Derivation Y = 1 ( a –b T + I +G) (1)

1-b

Gov. Exp. Increases by G Y Y + Y = 1 ( a –bT + I + G + G ) (2)

1-b

Eq.2- 1Eq. Y = 1 /1-b ( G)

Gm = Y/ G = 1 /1-b

Tax Multiplier Equilibrium level of Income:

Y = C+ I +G Y = a +b(Y-T) +I+G

Y=a + bY – bT + I +G (1-b)Y = a-bT +I+G

Y = 1 ( a –b T + I +G)

1-b

Y = 1/1-b [ a –b T + I +G] Eq. (1)

After T Y Y + Y = 1/1-b [ a –b(T+ T)+ I +G] Eq. (2)

= 1/1-b [a- bT- b T + I + G]

Eq. 2 –Eq.1 Y = 1 /1-b (-b T)

Y = (-b T/ 1-b)

Tm = Y/ T = -b /1-b Tax multiplier is always (-) because rise in income tax has negative

impact on national income and vice-a versa.

Example Tax Multiplier Equilibrium with and without Taxes

Assumed - C = 500 + 0.7(Y-T), I=1000, G=500, T=500

Solution Equilibrium when taxes = 0. Y = 1/1-0.7(500+1000+500)

= 3.333 x 2000 = 6667 And since T=500 Y = a +b(Y-T) +I+G

Y = a + bY – bT + I +G C = 500 + 0.7 x Y - 0.7 x 500 = 500 + 0.7 x Y - 350 = 150 + 0.7xY New equilibrium income - Y = 1/1-0.7(150+1000+500)

= 3.333x1650 = 5500 Introduction of a tax of 500 reduced equilibrium income

by 1167.

Tax multiplier = - b/1-b = -0.7/1-0.7 = -0.7/0.3 = 2.333 TM = -2.333

Equilibrium Y = 2.333 x 500 = 1167 Tax multiplier is always (-) because rise in income

tax has negative impact on national income and vice-a versa.

Balanced Budget Multiplier When a Govt. adopts a balanced budget policy, it

spends only as much as it collects through taxation.

It is always equal to unity. It implies that national income increases exactly by the amount of increase in the government expenditure. Because-

Y + Y = 1 + -b = 1

G T 1-b 1-b

Balanced Budget Multiplier : Example

ii) Suppose Govt. finances the entire 10 crore expenditure from lump-sum taxation. What is new equilibrium level of income.

Solution – I = 60 & G = 10 T = Rs.10 crore C = 40+0.80Y(Y-T)

= 40+0.80Y-0.80X10 = 32+0.80Y

= 32+0.80Y+60+10 = 102 +0.80Y

=(1- 0.20)Y =102

Y = 102/0.20 = Rs.510 crore

Four Sector National Income National Income equilibrium in Four sector:

Y = C+I+G+(X-M) Y = a+bYd+I+G+X-(M+mY) (M = M+mY)

= a +b(Y-T)+I+G+X-(M+mY) or

(1-b+m)Y = a +I+G+X-bT-M

Y = 1/1-b+m (a+I+G+X-bT-M)

Example

Suppose Y= C+I+G+(X-M) C = 100+0.75Yd

I = 50, G = 50, X=10, M+m =5+0.1Y, and T = 50

Find Equilibrium level of Income

Solution-

a +b(Y-T)+I+G+X-(M+mY)Y=100+ 0.75 (Y-50) + 50 + 50 +10- (5+0.1Y)

Y = 1/1-b+m (a+I+G+X-bT-M) = (1-0.75+0.1)Y = 100-0.75x50+105 =167.50

167.5/0.35 = 478.57

Y = 478.57

Foreign Trade Multiplier Equilibrium of National Income- Eq.1 Y = 1/1-b+m (a + I + G + X-bT-M )

Suppose level of export rises from X to X then the new level of income equilibrium is –

Y+ Y = 1/1-b+m (a + I+ G + X+ X - bT- M) Eq. 2

Eq. 2 – Eq. 1 = Y/ X = 1/1-b+m

If b = 0.75 What will be multiplier in closed economy-

m = 1/1-b m= 1/1-0.75 = 4

If m = 0.25, what will be the multiplier in open economy-

Fm = 1/1-b+m Fm = 1/1-0.75+0.25 = 2 This is reduced because rising demand is being

challenged off into the purchase of imports.

Example Y= C+I+G+(X-M) C = 100+0.75Yd

I = 50, G = 50, X=10, M+m =5+0.1Y, and T = 50

Solution-Y=100+ 0.75 (Y-50) + 50 + 50 +10 -5-0.1Y

= (1-0.75+0.1)Y = 100-0.75x50+105 =167.50

167.5/0.35 = 478.57 Fm = 1/1-0.75+0.1 = 1/0.35 = 2.86