MULTIPLIER PART I

The concept of ‘Investment Multiplier’ is an important contribution of Prof. John Maynard Keynes. Keynes believed that an initial increment in investment increases the final income by many times. Multiplier expresses the relationship between an initial increment in investment and the resulting increase in aggregate income.

ALGEBRAIC DERIVATION OF THE MULTIPLIER

When the level of investment increases by some amount, ΔI, the equilibrium level of income will increase by some multiple amount, ΔY. The ratio of change in Y to change in I is called the investment multiplier. It can be derived, as follows, from the equilibrium condition

 Y = C + I .......(i)

 together with the consumption equation 

 C = a + bY

where, a = consumption level when income is zero, i.e., autonomous consumption

            b = marginal propensity to consume(MPC)

 substituting the value of C in equation (i), we get

 Y = a + bY + I

As in the multiplier analysis, we are concerned with changes in income induced by investment. Now, by algebraic manipulation

 ΔY = b ΔY + ΔI 

 ΔY - b ΔY = ΔI 

 (1 - b)ΔY = ΔI

k = ΔY /ΔI = 1 /(1 - b) 

Here,

k = coefficient of multiplier

b = Marginal propensity to consume(MPC)

Suppose an additional investment (∆I) of Rs 4,000 crores in an economy generates an additional income (∆Y) of Rs 16,000 crores. The value of multiplier (k), in this case will be:

k = ΔY /ΔI =16,000/4,000 = 4

It means, income increased 4 times with a single increase in investment.

MULTIPLIER AND MPC

There exists a direct relationship between MPC and the value of multiplier. Higher the MPC, more will be the value of multiplier, arid vice-versa. When investment is increased, it also increases the income of the people. People spend a part of this increased income on consumption. However, the amount of increased income spent on consumption depends on the value of MPC.

1. In case of higher MPC, people will spend a large proportion of their increased income on consumption. In such case, value of multiplier will be more.

2. In case of low MPC, people will spend lesser proportion of their increased income on consumption. In such case, value of multiplier will be comparatively less.

VALUE OF THE MULTIPLIER

The maximum value of multiplier is infinity when the value of MPC is 1. MPC = 1 indicates that the economy decides to consume the whole of its additional income. Here, not even a bit of the additional income is saved. It will lead to a continuous increase in the consumption expenditure and value of multiplier will be infinity.

Proof:

We know: K= 1/(1- MPC)

If MPC = 1,

 then, k = 1/(1 - 1)

k =1/0 

k = ∞ 

Note : Any number, when divided by 0, gives infinity.

The minimum value of multiplier is one when the value of MPC is zero. MPC = 0 indicates that the economy decides to save the whole of its additional income and nothing is spent as consumption expenditure. So, there will be no further increase in income. As a result, the total increase in income (∆Y) will be equal to the increase in investment (∆I), i.e., ∆Y = ∆I Here, the value of multiplier is equal to 1. Proof:

If MPC = 0, then:

k = 1/(1-0)

k = 1/1

k = 1

Therefore, the value of the multiplier lies between one and infinity.

1 < k < ∞

WORKING OF THE MULTIPLIER

The working of multiplier is based on the fact that ‘one person’s expenditure is another person’s income’. When an additional investment is made, then income increases many times more than the increase in investment. Let us understand this with the help of an example.

1. Suppose, an additional investment of Rs 100 crores (∆I) is made to construct a flyover. This extra investment will generate an extra income of Rs 100 crores in the first round. But this is not the end of the story.

2. If MPC is assumed to be 0.90, then recipients of this additional income will spend 90% of Rs 100 crores, i.e. Rs 90 crores as consumption expenditure and the remaining amount will be saved. It will increase the income by Rs 90 crores in the second round.

3. In the next round, 90% of the additional income of Rs 90 crores, i.e. Rs 81 crores will be spent on consumption and the remaining amount will be saved.

4. This multiplier process will go on and the consumption expenditure in every round will be 0.90 times of the additional income received from the previous round.

Thus, an initial investment of Rs 100 crores leads to a total increase of Rs 1,000 crores in the income. As a result, multiplier (k) = ∆Y/∆I= 1,000/100 = 10

DIAGRAMMATIC REPRESENTATION OF THE MULTIPLIER

The multiplier can also be shown graphically using the AD and AS approach. In the figure given below, income is taken on the X-axis and aggregate demand on the Y-axis. Suppose, the initial equilibrium is determined at point E where AD curve intersects the AS curve. The equilibrium level of income is OY. Now, suppose that the investment increases by ∆I, so that the new aggregate demand curve (AD') intersects the aggregate supply curve (AS) at point ‘F’.

Thus, the new equilibrium level of income is OY'. The income rises from OY to OY', in response to an initial increase in investment (∆I ). It is clear from the figure that the increase in income (YY' or ∆Y) is greater than increase in investment (∆I ).