2. The Multiplier
The number of times a rise in GDP exceeds the rise in injections that caused it.
Eg. if £10M increase in net injections results in £10.4 increase in GDP then the multiplier is 1.4

4. Injections of new demand for goods and services into the circular flow of income stimulate further rounds of spending – “one person’s spending is another’s income”.
This leads to a bigger eventual effect on output and employment as the money is circulated around the economy.

5. The larger the multiplier, the larger the final effect on the economy of an initial injection.
Formula based on how much of £1 extra will be re-spent in the economy – any money not re-spent is ‘leaked’ and so doesn’t go round the circle again.
The % re-spent is the ‘Marginal Propensity to Consume.’ Eg. If we tend to re-spend 70% of what we earn, MPC is 0.7.

6. Reminder: What do we mean by ‘injection’?
What do we mean by ‘change in national income’

7. The Multiplier Example:
If MPC = 0.6, then out of each injected £1, £0.60 will be re-spent, and so on
So, total GDP will rise by: £1 + £ £ £ £ £ £0.05 …

8. The Multiplier
Consider a £300 million increase in capital investment – eg. an overseas company decides to build a new production plant in the UK.
This sets off a chain reaction of increases in expenditures. Firms who produce the capital goods and construction businesses who win contracts to build the new factory will see an increase in their incomes and profits.
If they and their employees in turn, collectively spend about 3/5 of that additional income, then £180m will be added to the incomes of others.
At this point, total income has grown by £300m + (0.6 x £300m).
The sum will continue to increase as the producers of the additional goods and services realize an increase in their incomes, of which they in turn spend 60% on even more goods and services.
The increase in total income will then be £300m + (0.6 x £300m) + (0.6 x £180m).
Each time, the extra spending and income is a fraction of the previous addition to the circular flow.

9. How to Calculate The Multiplier
How much is leaked or ‘withdrawn’ from the economy determines the size of the multiplier.
MPS = Marginal propensity to save (MPS)
MPT = Marginal propensity to tax
MPM = Marginal propensity to import
The total proportion of an increase in income that is withdrawn: MPW = MPS + MPT + MPM

10. How to Calculate The Multiplier
The larger the multiplier, the larger the final effect on the economy of an initial injection.
The multiplier = 1/MPW
So, if: MPS is 0.1 (10%) MPT is 0.2 (20%) MPM is 0.2 (20%) Then MPW is 0.5 (50%)
So, the multiplier = 1/0.5 = 2
If AD is increased by an initial injection of £100m, the final increase in AD will be £200m

11. How to Calculate The Multiplier
The multiplier = 1/MPW
MPW = 1 – MPC (marginal propensity to consume)
So, the multiplier is also 1 / 1-MPC
If MPC = 70% or 0.7
Multiplier = 1 / = 1 / 0.3 = 3.33
If AD is increased by an initial injection of £100m, the final increase in AD will be £333m

12. The multiplier on an AD/AS diagram
Price
Level
The initial increase in aggregate demand from building the hospital is £500m and is represented by a shift from AD1 to AD2
The multiplier effect is shown by the further increase in AD from AD2 to AD3 and then to AD4
Notice that successive shifts are smaller and smaller as money is leaked out with every trip round the circular flow
SRAS P4 P3 P2 P1
AD4
AD3
AD2
AD1 Y1 Y2 Y3 Y3
Real Output

13. Examples
Calculate the value of the multiplier and the change in income if:
Animal spirits rise leading to an increase in investment of £2 billion. MPW is 0.3
Chinese economy collapses, so exports fall by £1.5 billion. MPS is 0.1, MPT 0.1 and MPM is 0.2
The government wants to reduce the deficit, so cuts government spending by £1 billion. Savings rate is 10%, MPT is 25% and MPM is 25%
What happens to the multiplier if:
MPW was 0.6, but new pension rules means the savings rate increases from 5% to 15%
Government reduces taxes so MPT falls from 0.25 to 0.2. Old MPW was 0.6

14. More sample questions:
Which of the following would cause the value of the multiplier to fall: ↓MPM, ↓MPT, ↓MPC, ↓MPS
A final increase in national income of £6bn, following an increase in state spending of £4bn, means that the value of the multiplier is: 0.66, -1.5, 1.5
The value of the multiplier is 1.2 and there is an estimated negative output gap of £450m. What extra injection of government spending will close this gap?
If MPC is 0.75 and investment increased by £30bn, by how much would national income increase?
If worries about the EU referendum decreased investment by firms by £50bn and the MPC is 0.6, what change would we expect to see on national income?
MPC
1.5
3.75
120
-125

16. Evaluation: Time lags and the multiplier effect
It is important to remember that the multiplier effect will take time to come into full effect
A good example is the fiscal stimulus introduced into the US economy by the Obama government. They have set aside many billions of dollars of extra spending on infrastructure spending but these capital projects can take years to be completed. Delays in sourcing raw materials, components and finding sufficient skilled labour can limit the initial impact of the spending projects.