Theory of Multiplier

The theory of multiplier is a situation where an autonomous increase or decrease in expenditure for output can increase or decrease total expenditure for output by some multiple, by inducing a charge of consumption expenditure in the same direction. 

Multiplier theory is the amount by which a change in net investment is multiplied in terms of income.

It is a measure of change in national income caused by a change in investment. Thus, it explains the relationship between the increase in investment and the resultant increase in income. For example, if an increase in investment of N50,000 causes an increase in national income of N600,000, then the value of the multiplier would be

= \( \frac{600,000}{50,000} \\ = \scriptsize 12 \)

\( \frac{Change \: in \: Income}{Change \: in \: Investment} \\ = \frac{\Delta I}{\Delta Y} \)

Anytime the investment expenditure rises, it will stimulate production and cause income to rise too.

K = \( \frac{1}{\Delta S} \\ \scriptsize or \\ \frac{1}{1 \: – \: \frac{\Delta C}{\Delta Y}} \)

∆C = Change in Consumption

∆S = Change in Savings

∆Y = Change in Income

∆E = Change in expenditure

K = \( \frac{1}{1 \: – \: MPC} \)

or

\( \frac{1}{1 \: – \: b} \)

Where b = Marginal Propensity to consume 

Income multiplier K = \( \frac{1}{1 \: – \: b} \)

While the investment multiplier is given

K = \( \frac{\Delta \: I}{1 \: – \: b} \) where K is the multiplier.

∆I = Change in Income

b = MPC

If the marginal propensity to consume is 50%, what is the multiplier?

If there is 50m rise in investment, what is the change in Income?

K = \( \frac{1}{1 \: – \: b} \\= \frac{1}{1 \: – \: 0.5} \\ = \frac{1}{0.5} \\ = \scriptsize 2 \)

Multiplier = 2

Change in Income ∆Y = \( \frac{\Delta Y}{1 \: – \: b} \\ = \frac{50m}{1 \: – \: 0.5} \\ = \frac{1}{1 \: – \: 0.5} \: \times \: \frac{50m}{1 } \\ = \frac{50m}{0.5} \\= \scriptsize 100m \)

Change in Income ∆Y = 100m