The multiplier is defined as the ratio of the change in national income to change in investment.

**Multiplier**

The concept of multiplier was first developed by R.F. Khan in
terms of employment. J.M Keynes redefined it as investment multiplier.

The multiplier is defined as the ratio of the change in national
income to change in investment. If ∆I stands for increase in investment and ∆Y
stands for resultant increase in income, the multiplier K =∆Y/∆I. Since ∆Y
results from ∆I, the multiplier is called investment multiplier.

Keynes’s theory of the multiplier works under certain assumptions
which limit the operation of the multiplier. They are as follows:

1.
There is change in autonomous investment.

2.
There is no induced investment

3.
The marginal propensity to consume is constant.

4.
Consumption is a function of current income.

5.
There are no time lags in the multiplier process.

6.
Consumer goods are available in response to effective demand for
them.

7.
There is a closed economy unaffected by foreign influences.

8.
There are no changes in prices.

9.
There is less than full employment level in the economy.

The propensity to consume refers to the portion of income spent on
consumption. The MPC refers to the relation between change in consumption (C)
and change in income(Y).

Symbolically** MPC = ∆C/∆Y**

The value of multiplier depends on MPC

Multiplier **(K) = 1/1-MPC**

The multiplier is the reciprocal of one minus marginal propensity
to consume. Since marginal propensity to save is 1 - MPC. (MPC+MPS =1).
Multiplier is 1/ MPS. The multiplier is therefore defined as reciprocal of MPS.
Multiplier is inversely related to MPS and directly with MPC.

Numerically if MPC is 0.75, MPS is 0.25 and k is 4.

Using formula k = 1/1- MPC 1/1-0.75 =1/0.25 =4

Table 4.

Taking the following values, we can explain the functioning of
multiplier

C = 100 + 0.8 y; I = 100

I = 10

** Y = C + I **

= 100 + 0.8y + 100

0.2y = 200

Y = 1000

Here, C = 100 + 0.8y = 100 + (1000) = 900;

S = 100 = I

After I is raised by 10, now I = 110,

Y = 100 + 0.8y + 110

0.2y = 210

**Y = 210/0.2 = 1050**

Here C = 100=0.8(1050) = 940; S = 110 = I

**Diagrammatic Explanation.**

At 45° line y = C+ S

It implies the variables in axis and axis are equal.

The MPC is assumed to be at 0.8 (C = 100 + 0.8y)

The aggregate demand (C+I) curve intersects 45° line at point E.

The original national income is 500.

(C = 100 + 0.8y = 100 + 0.8(500) = 500)

When I is 100, y = 1000, C = 900;

S = 100 = I

The new aggregate demand curve is C+I’ = 100 + 0.8y + 100 +10

**Y = 210/0.2 = 1050**

C = 940; S = 110 = I

Suppose the Government undertakes investment expenditure equal to
₹100 crore on some public works, by way of wages, price of materials etc. Thus
income of labourers and suppliers of materials increases by ₹100 crore. Suppose
the MPC is 0.8 that is 80 %. A sum of ₹80 crores is spent on consumption (A sum
of ₹ 20 Crores is saved). As a result, suppliers of goods get an income of ₹80
crores. They inturn spend ₹64 crores (80% of ₹80 cr). In this manner
consumption expenditure and increase in income act in a chain like manner.

The final result is∆Y = 100+100×4/5+100 ×[4/5]2+100×[4/5]3 or,

∆Y = 100 + 100 x 0.8 + 100 x (0.8)2 + 100

x (0.8)3

=100 + 80 + 64 + 51.2...

=500

that is 100×1/1-4/5

100×1/1/5

100×5 = ₹500 crores

For instance if C = 100 + 0.8Y, I = 100, Then Y = 100 + 0.8Y + 100

0.2Y = 200

Y = 200/0.2 = 1000→Point B If I is increased to 110, then

0.2Y =210

Y = 210/0.2 = 1050→Point D

For ₹10 increase in I, Y has increased by ₹50.

This is due to multiplier effect.

At point A, Y = C = 500

C = 100 + 0.8 (500) = 500; S=0

At point B, Y = 1000

C = 100 + 0.8 (1000) = 900; S = 100 = I

At point D, Y = 1050

C = 100 + 0.8 (1050) = 940; S = 110 = I

When I is increased by 10, Y increases by 50.

This is multiplier effect (K = 5)

K = 1/0.2= 5

Static and dynamic multiplier

1. Static and dynamic multiplier

i. **Static multiplier** is otherwise known as
simultaneous multiplier,
timeless multiplier, and logical multiplier.

Under static multiplier the change in investment and the resulting
change in income are simultaneous.There is no time lag. There is also no change
in MPC as the economy moves from one equilibrium position to another.

**ii. Dynamic multiplier **is also known** **as ‘sequence multiplier’.
In real life, income level does not increase instantly with investment. In
fact, there is a time lag between increase in income and consumption
expenditure.

**5. Leakages of multiplier**

The multiplier assumes that those who earn income are likely to
spend a proportion of their additional income on consumption. But in practice,
people tend to spend their additional income on other items. Such expenses are
known as leakages.

If a portion of the additional income is used for repayment of old
loan, the MPC is reduced and as a result the value of multiplier is cut.

If income is used in purchase of existing wealth such as land,
building and shares money is circulated among people and never enters into the
consumption stream. As a result the value of multiplier is affected.

Income spent on imports of goods or services flows out of the
country and has little chance to return to income stream in the country. Thus
imports reduce the value of multiplier.

The multiplier theory assumes instantaneous supply of consumer
goods following demand. But there is often a time lag. During this gap (D>S)
inflation is likely to rise. This reduces the consumption expenditure and
thereby multiplier value.

**Full employment situation**

Under conditions of full employment, resources are almost fully
employed. So, additional investment will lead to inflation only, rather than
generation of additional real income.

1.
Multiplier highlights the importance of investment in income and
employment theory.

2.
The process throws light on the different stages of trade cycle.

3.
It also helps in bringing the equality between **S** and **I**.

4.
It helps in formulating Government policies.

5.
It helps to reduce unemployment and achieve full employment.

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