The working of multiplier can be explained as follows:
We are given that the value of MPC $=0.8$ and also that initial increase in investment is $\mathit{₹}800$ crore. This implies that with every increase of $\mathit{₹}1$ in the income, people consume 0.8 part of the increased income i.e, ., people consume $\mathit{₹}0.80$and Save ₹ 0.20.
The table shows that initial increase in investment of $\mathit{₹}800$ will lead to a change in income by $\mathit{₹}800$ in the first round. As MPC is 0.8 , so people will consume 0.8 of the increased income (i.e. $\mathit{₹}640$ ), thereby saving $\mathit{₹}160$. This will be termed as leakage (as it is not ploughed back into the economy).
In the next round, due to the increase in the consumption expenditure by $\mathit{₹}640$, there will be an increase in income $\mathit{₹}640$. The people will again spend the increased income i.e. $\mathit{₹}512$ and save the rest part of the income $\mathit{₹}128$.
In the third round, similarly the increased consumption expenditure of $\mathit{₹}512$ will cause a change in the income by $\mathit{₹}512$. They will spend a part of this income on consumption i.e., $\mathit{₹}409.6$ and will save the rest of the increased income $\mathit{₹}102.4$.
This process will continue and the income will go on increasing as a result of increase in consumption. The total change $\left(∆\mathit{Y}\right)=\mathit{₹}4000$ (approx) and the change in the investment $\left(∆\mathrm{I}\right)$ will be 800 .
$\mathit{k}=\frac{1}{1-\mathrm{MPC}}$
$=\frac{∆\mathrm{Y}}{∆\mathrm{I}}$
$\mathit{k}=\frac{1}{1-0.8}$
$=\frac{∆\mathit{Y}}{800}$
or, $\frac{1}{0.2}=\frac{∆\mathit{Y}}{800}$
So, $∆\mathrm{Y}=4,000$
Thus, we can observe that an initial increase in the investment by $\mathit{₹}800$ crore results in increase of income and output by ₹ 4000 crore.