# Investment Multiplier | Working of Investment Multiplier

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Hi Friends, in today’s article we are going to know about Investment Multiplier (Working of Investment Multiplier). So let’s discuss in details.

## What is investment multiplier?

The concept of investment multiplier is an important contribution of Keynes to the theory of income and employment. It is the co-efficient relating to the ratio of change in investment to change in income.

Investment multiplier express the relationship between an increase in investment and resulting increase in aggregate income. Symbolically,

K = ΔY/ΔI

Where,

K = Multiplier,

ΔY = Change in income,

ΔI = Change in investment.

This is the Formula of investment multiplier or investment multiplier formula.

## Assumption of Investment Multiplier

The multiplier theory is based on the following assumption –

(i) There is change in autonomous investment and that induced investment is absent.

(ii) The MPC is constant.

(iii) Consumption is a function of current income.

(iv) There is no time gap in the multiplier process.

## Working of Investment Multiplier

The multiplier works both forward and backward. In the below paragraph, we explained in details about the working of multiplier.

### Forward working of multiplier

The multiplier explains that a small increment in autonomous investment can lead to a multiple expansion of income. It is term as the forward working of investment multiplier.

The working of multipliers can be explain with the following table –

 Round ΔI ΔY ΔC = MPC ΔS = MPS 1 100 100 50 50 2 – 50 25 25 3 – 25 12.50 12.50 4 – 12.50 6.25 6.25 5 – 6.25 3.125 3.125 – – 3.125 – – Total 100 200 100 100

Suppose there is an initial rise in autonomous investment in a country by Rs.100 crore. In any case some group in the community receives and income of Rs.100 cr.

If every group in the country has MPC = 0.5 or 1/2, the given group will spend Rs.50 crore on consumption and remaining Rs.50 crore will be saved.

Spending Rs.50 crore will be the income of another group. It will spend half of it (Rs.25 cr). Thus this process of income generation from one group to another until aggregate income rises by 200 crore on account of initial increase in investment by Rs.100 crore.

Because K = 2, when the MPC is 1/2 which is shown in the above table.

ΔY = K x ΔI = 2 x 100 = 200 crore

We can explain the working of multiplier with the help of a diagram – In the above figure, income is measured along horizontal scale or axis. Consumption and investment are measured along vertical scale. The 45° line (Y = C) is drawn from origin.

If we add investment to C curve, we get the aggregate demand function C + I, which cuts the 45° line at E1 and the initial equilibrium income is OY1.

If autonomous investment is raised by ΔI, the aggregate demand function shifts to C + I + ΔI, which cuts 45° line at E2 and the equilibrium income is finally OY2.

The vertical distance C + I and C + I + ΔI shows the increased income ( Y1 to Y2) which is due to working of multiplier.

### Backward Working of Multiplier

The backward working of multiplier can be explained by the following example –

Suppose there is a fall in investment by Rs.100 crore and MPC is 0.5 the fall in incomes will be twice the fall in the amount of investment because K = 2 when MPC = 0.5

ΔY = K x ΔI = 2 x (-100) = – 200 crore The backward action of multiplier can be explained by the above mention diagram. If there is a fall in investment by (-ΔI) the C + I curve shifts down to C + I + (-ΔI).

Its intersections with the 45° line determines equilibrium at E2 and final equilibrium income is OY2. The fall in income Y1Y2 is much larger than the fall in investment.

This multiple contraction of income is on account of the reverse operation of investment multiplier.

#### Conclusion

So friends, this was the concept of investment multiplier. Hope you get the full details about it and hope you like this article.

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