The Investment Multiplier

The investment multiplier (k) measures how much TOTAL national income changes for a GIVEN initial change in autonomous investment — capturing the idea that an initial injection of investment spending triggers successive ROUNDS of additional spending throughout the economy (money spent by one person becomes income for another, who in turn spends part of it, and so on), so the ultimate increase in total income is a MULTIPLE of the original investment increase.

The multiplier is derived directly from the MPC (or, equivalently, the MPS):

and the resulting change in income for a given change in investment is:

Why the multiplier depends on MPC. An initial increase in investment spending, $\Delta I$, becomes income for those who receive it (workers, suppliers). They in turn spend a fraction MPC of this new income on further consumption, which becomes income for a further set of people, who again spend MPC of that, and so on — an infinite chain of progressively SMALLER spending rounds. Summing this entire geometric series of successive rounds ($\Delta I+MPC\cdot\Delta I+MPC^{2}\cdot\Delta I+\ldots$) gives exactly $\Delta I \times \dfrac{1}{1-MPC}$, which is precisely the multiplier formula above. …