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A multiplier gives the proportion of change in real GDP due to a unit change in spending.A change in spending induces a change in real GDP. The following formula gives the multiplier effect:

$â–³\mathrm{Y}=\mathrm{k}â–³\mathrm{I}$, where k is the multiplier.

The above formula shows that the change in real GDP is positively related to the change in spending. For example, if the change in investment is $2000 and MPC is 0.1, then the change in income will be $200 (2000×0.1).

Since the multiplier is the effect of change in total spending, a larger MPC means greater income generation through private consumption. Therefore, the multiplier has a positive relation with MPC.

Therefore, for the large size of the multiplier, the MPC should be large.

$$\begin{gathered} k=\frac{â–³Y}{â–³Spending} \\ k=\frac{â–³Y}{\left(1-MPC\right)â–³Y} \\ k=\frac{1}{1-MPC} \end{gathered}$$

Thus, the multiplier is directly related to MPC.

The multiplier effect measures the result of changes in expenditure components on the income. A smaller MPS means larger spending through private consumption and a higher increase in the real GDP. Therefore, the multiplier is inversely related to MPS.

$$\begin{gathered} k=\frac{â–³Y}{â–³I} \\ k=\frac{â–³Y}{MPS\left(â–³Y\right)} \\ k=\frac{1}{MPS} \end{gathered}$$

MPC measures the propensity to consume out of a unit increase in income. The greater the value of MPC, the greater proportion of the income will be consumed. Greater consumption expenditure will result in greater demand for goods and services and will encourage firms to increase production and investment. An investment increase will further encourage the demand by distributing higher income in society.

Thus, the increase in GDP is higher than before (when the MPC was smaller). The multiplier effect is greater due to the higher MPC value.