The number of times by which income increases as a result of increase in investment is called investment multiplier. Investment multiplier shows a relationship between initial increment in investment and the resulting increment in national income.
$\mathrm{K}=\frac{∆\mathrm{Y}}{∆\mathrm{I}}$
where


Relation of multiplier with MPC :
$\mathit{K}=\frac{∆\mathit{Y}}{∆\mathit{I}}$
$\mathit{K}=\frac{∆\mathit{Y}}{∆\mathit{C}}$
(Dividing this equation by $∆\mathrm{Y}$ we get)
$\mathit{K}=\frac{∆\mathit{Y}}{∆\mathit{Y}-∆\mathit{C}}$
$=\frac{\frac{∆\mathit{Y}}{∆\mathit{Y}}}{\frac{∆\mathit{Y}}{∆\mathit{Y}}-\frac{∆\mathit{C}}{∆\mathit{Y}}}=\frac{1}{1-\mathit{M}\mathit{P}\mathit{C}}$
There is a direct relation between $\mathrm{K}$ and MPC. If MPC is high, K will also be high but if MPC is low $\mathrm{K}$ will also be low.