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The concept of multiplier was originally developed as the employment multiplier by R.F kahn, a Cambridge economist. Keynes used this concept in the General Theory as a powerful tool to analyse the effects of the changes in the planned investment on the level of income and formulated investment multiplier. It shows by how many times the effect of an increment of investment has been multiplied by using repercussions on consumption and thus raising the national income.   
Increase in the planned investment is not always permanent. But, for our analysis, we have assumed that once the investment function bounces up, it stays there period after period. The original equilibrium level of income is replaced by a new higher equilibrium level. A rise in the levels of income and output in response to the increase in the planned investment will be permanent. Nothing in the system pushes them back to their original level.

        To describe the multiplier process whereby the economy moves from one equilibrium level to a new one due to a shift in the planned investment, we consider a simple example.   Suppose, an additional investment (ΔI) of Rs. 100 lakhs is injected   into the economy, which was in the equilibrium. This will generate an income of an equal amount in the first or the immediate round. The recipients of the income (the suppliers of the investment goods or the additional factors employed consequently) will spend the income earned on the consumption goods on the basis of their marginal propensity to consume (MPC). The MPC is assumed to be constant at, say, 0.9. In the second round, the additional income (ΔY) of Rs. 100 lakhs will result in an additional consumption expenditure (ΔC) of Rs.90 lakhs. This is obtained by multiplying the MPC of 0.9 by the initial increase in the investment or the income, i.e., Rs. 100 lakhs. This increase in the consumption expenditure constitutes an increase in the income b Δ I, where ‘b’ is the marginal propensity to consume. This increased income leads to a further increase in the consumption in the third round equal to b.b Δ I or b2 Δ I, which , in turn, generates income of an equal amount. The reason is that an expenditure by one person becomes the income of another person. In the present hypothetical example, the change in the consumption and hence the income in the third round alone amounts to Rs.91 lakhs, obtained by multiplying the MPC of 0.9 by the change in the income, Rs.90 lakhs. This income of Rs.81 lakhs further generates consumption and the process goes on. The amount passed on from one round to the next keeps on diminishing. Ultimately, equilibrium will be reached, when incomes have risen sufficiently to increase the amount that people want to save by an extent equal to the initial rise  in investment. A point will be reached when income rises by an amount equal to the original increase in investment multiplied by the reciprocal of the MPS, as discussed below. The whole process of the multiplier can be summarized in Table 6.1. It is clear from the table that the effect of a permanent increase in the investment expenditure is felt in a number of periods, but its force gets reduced period, after period. if the MPC is less than one.  

Multiplier Process 1

Multiplier Process 3

Multiplier Process 4

Thus, an initial change in the investment of Rs.100 lakhs leads to a total change in the  income of Rs. 1000 lakhs. Equilibrium will be reached when income rises by Rs. 1,000 to induce extra saving of Rs. 100. This happens through a chain of a secondary consumption expenditure by the newly employed or the other income recipients. The multiplier is the ratio of the change in the aggregate income and a change in the investment. In other words, it is number of times a change in the investment is multiplied through the changes in the consumption and finally in the aggregate income.

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