Investment Multiplier

Investment increases productive capacity, which, in turn, raises the level of output, employment and income. When investment increases by a certain amount, aggregate income increases by a multiple of that investment. This multiple is called the multiplier. Investment multiplier shows a relationship between the initial increment in investment and the resulting increment in national 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 Rs 50 crore causes an increase in national income of Rs 300 crore, the value of multiplier would be 6 (= 300 ÷ 50).

This equals an increase in income divided by an increase in investment. The implication of K = 6 is that for any level of change in investment in the economy income will change 6 times of investment amount. Multiplier (K), thus, is the ratio of increase in national income (ΔY) due to an increase in investment (ΔI). Put in symbols:

Where K = Investment multiplier, ΔY = change in income, ΔI = change in investment.

Investment multiplier indicates the multiplying effect of investment on income. The value of the multiplier determines the rate of growth in the economy. A higher value of the multiplier will attain a higher level of income and growth.

Relationship between Multiplier and MPC:

There exists a direct relationship between MPC and the value of the 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 the case of higher MPC, people will spend a large proportion of their increased income on consumption. In such a case, the value of the multiplier will be more.

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

Mathematical/Algebraic Relationship between Multiplier and MPC

The algebraic relation between Multiplier and MPC can be derived in the following manner:

We know, at equilibrium, income (Y) is the sum total of consumption (C) and investment (I), i.e., Y = C + I.

Similarly, any change in income (ΔY) will also be equal to (ΔC + ΔI).

Dividing both sides by ΔI,

Since c is the marginal propensity to consume, the multiplier K is, by definition, equal to ΔY/ΔI. The multiplier can also be derived from the marginal propensity to save (MPS) and it is the reciprocal of MPS, K = 1/MPS. 

Additional Notes:

MPC + MPS = 1 or c + s=1

MPS = 1 - MPC 

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