The multiplier effect is when an initial increase in spending causes a larger increase in national income. Each round of spending becomes income for someone else, who may then spend part of it again.

How do you calculate it?

The multiplier, $k$ , is the total change in national income divided by the initial change in spending:

spendingk=\frac{\text{change in national income}}{\text{initial change in spending}}

In a simple closed economy with no government, you can also calculate it using the marginal propensity to consume, or $M P C$ :

k=11−MPCk=\frac{1}{1-MPC}

The $M P C$ is the proportion of an extra unit of income that households spend. The remainder is saved. For example, if $M P C = 0.8$ , then $k = 1/ (1 - 0.8) = 5$ . An initial increase in investment of $20$ million could therefore increase national income by $100$ million, assuming the full multiplier effect takes place.

What changes the multiplier?

In an open economy, some extra spending goes on imports. Taxation can also take income out of the spending cycle. These are leakages, alongside saving, so they reduce the multiplier. Under a simple model with government and trade:

k=1MPS+MRT+MPMk=\frac{1}{MPS+MRT+MPM}

Here $M P S$ is the marginal propensity to save, $M R T$ is the marginal rate of tax, and $M P M$ is the marginal propensity to import. Each describes what happens to an additional unit of income. Without government, omit $M R T$ ; without trade, omit $M P M$ .

Exam mistake to avoid: do not use the proportion of total income spent or saved. The multiplier calculation uses marginal propensities, based on changes in income. The numerical result is also a modelled effect, not a guarantee: limited spare capacity, for example, may mean more spending raises prices rather than real output.

Specification focus: Cambridge International A Level Economics develops the multiplier calculation in the A Level circular flow of income topic ( $9.1.1$ ). The AS Level introduction to injections and leakages ( $4.2.2$ ) does not require the multiplier.