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A multiplier is the ratio of change in income to change in total spending.It explains that a change in total spending induces how much change in the total income, or by what rate a change in total spending induces the income changes.

The formula for the multiplier (k) is as follows:

$k=\frac{â–³Y}{â–³Expenditure}$

Marginal propensity to consume denotes what proportion of total income is consumed by the private individuals.

A larger value of MPC means a smaller value of MPS. As people tend to save less and spend more, the consumption expenditure increases. A greater proportion of income is consumed, and, therefore, the increase in income is greater. This means the value of the multiplier increases.

$k=\frac{1}{1-MPC}$

Therefore, a larger MPC means a larger multiplier.