The multiplier effect is a fiscal multiplier that measures the increase in overall national income (real GDP) after an initial injection.  It is used to explain and measure why a £10m injection by government into an infrastructure project can cause an increase of £16m to overall real GDP.

So how does this happen?

Consider the following example...

1. The government injects £10m into a local economy to build a new school. 
2. All of the initial costs (materials, labour, energy etc) are now added to real GDP. £10m increase.
3. The construction workers now have money available to spend which came from the initial injection.
4. When the workers go out and purchase goods and services e.g. food from the local cafe, this is also measured as an increase in national income some of the initial injection is spent for a second time.
5. Workers from the cafe will spend some of the initial injection for a third time when they go out and buy their own goods and services.

Measuring the Multiplier Value - A Worked Example

The example in the intro (£10bn up to £16bn) is fictional however the multiplier can be measured.  To do this we need to understand a few new key terms.

Marginal Propensity to Consume - The proportion of a £1 pay rise that would be spent on consumption of goods and services.
Marginal Propensity to Import - The proportion of a £1 pay rise that would be spent on imports.
Marginal Propensity to Tax- The proportion of a £1 pay rise that would be taken by government in tax.
Marginal Propensity to Save- The proportion of a £1 pay rise that would be saved by households.
Marginal Propensity to Withdraw - Imports, taxes and savings are all withdrawals from the circular flow of income and therefore the MPW is MPM + MPT + MPS.

To calculate the multiplier we either need to know the MPC or the MPW. In other words we need to know how much of the initial injection will continue to flow around the UK's circular flow of income and how much will be withdrawn.  ​

The government expect that the MPW is 0.625.  We can then calculate the multiplier in one of two ways outlined below. 

As we know the MPW we can simply do 1/0.625 which gives us a multiplier value of 1.6

we can then take the initial injection (£10m) and use the multiplier value so.....

£10m x 1.6 = £16m total increase in real GDP.

The initial injection for the multiplier to occur can come from the following components of AD,

1. Investment ​
2. Government spending
3. Exports

The diagram below shows how the multiplier can be shown using a macroeconomy diagram.