Theory of Multiplier

The concept of multiplier is one of the important components of Keynesian theory of employment. This theory was propounded by a popular economist F.A. Khan in 1931. Later on J.M Keynes developed and redefined this theory. Hence, where K = multiplier.

= Change in income

= Change in investment

Multiplier is the ratio between change in income with change in investment at particular period of time. In other words, it tells us how many times income increases as a result of increase in investment.

Relationship between multiplier and MPC (Marginal Propensity to Consume)

Let a two sector economy, economy is in equilibrium as follows:                                                                                                               Y = C + I ------------------- (i)

When investment increases them,

Y + = C +   + I +    --------------------- (ii)

Subtract the eqⁿ (i) from (ii)

= + ------------------------ (iii)

Or, =

Or, - =

Or, =

Or,

Substituting the value,

Or, K = ------------------------- (iv)

K =                                                      

This equation shows that the multiplier and marginal propensity to consume have direct relationship. When MPC increases, multiplier also increases and vice versa. This positive relationship can be shown by the help of following table.

MPC	Multiplier K =
0	1
0.25	1.33
0.50	2
0.75	4
-1

Assumption of multiplier effect

1. The original propensity to consume remains constant during the period of multiplier process.
2. There is closed economy.
3. There are no changes in prices.
4. Consumption is function of current income
5. There are no time lags in multiplier process.
6. Consumer goods are available in response to effective demand for them.

Forward working multiplier can be shown with the help of following figure:

Figure:

In the given figure, x-axis represent income and y-axis represent saving / investment. Initial equilibrium is E₁, at point E₁ the equilibrium income is OY. Now there is an increase in the investment () which leads to an increase in the aggregate expenditure. Thus, this cause income to increase ().

Reverse working multiplier

Figure:

In the given figure x-axis and y-axis represents income and saving / investment respectively. Initial equilibrium is E1. At this point income level is OY1. Now there is decrease in investment () which leads to decrease in the aggregate expenditure. Thus, this cause income also decrease by ().

Leakage of multiplier

1. Saving
2. Undistributed profit
3. Taxation
4. Inflation
5. Hoarding of cash balance

1. Saving:

It is the most important cause for the leakage of multiplier process. Since the marginal propensity to consume is less than one, the whole increment in income is not spent on consumption. A part of it is saved which prefer out of the income stream and the increase in income in the next round decline. Thus, the higher the marginal propensity to save, the smaller the size of the income stream and vice versa.

2. Undistributed profit:

If profits acquiring to Joint Stock Company are not distributed to the shareholders in the form of dividend but are kept in the reserve fund, it is a leakage from the income stream. If companies tend to reduce the income and hence, further expenditure on consumption goods thereby weakening the multiplier process.

3. Taxation:

It is also important factor in weakening the multiplier process. Progressive taxes have the effect of lowering the disposable income of tax payers and reducing their consumption expenditure. Thus, increased taxation reduces the income stream and lowers the size of multiplier.

4. Inflation:

When there is a raise in the price of consumption goods, a good part of the increased money expenditure out of the increased income will be dissipated on higher prices instead of promoting consumption, income and employment.

5. Hoarding of cash balance:

This type of leakage will be greater if business prospectuses are bad and smaller. When business prospectus are good. Whenever new created money income is hoarded, it cannot reappear as income in the next round and the multiplier effect will be arrested.