The multiplier

Why an injection raises national income by more than itself, calculating the multiplier from the MPC or MPW and what limits it.

One factory, a whole town.

When a big employer opens or expands, such as a factory, a shipyard or a new hospital, the effect spreads well beyond its gates. Its workers spend wages in local shops, cafés and on trades, those businesses take on staff and those staff spend too. When a big employer closes, the same chain runs in reverse.

How far does a pound of new spending travel, and how much income does it create in the end?

Injections, withdrawals and the multiplier.

Injections add to the circular flow of income: investment, government spending and exports. Withdrawals (leakages) take income out of it: saving, taxes and imports.

The multiplier is the ratio of the final change in national income to the change in injections that caused it.

Out of each extra £1 of income, people spend some on UK goods (the marginal propensity to consume, MPC) and withdraw the rest through saving, tax and imports (the marginal propensity to withdraw, MPW = MPS + MPT + MPM). MPC + MPW = 1.

Multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPW

Think first

The government spends £10bn building new hospitals.

Builders, suppliers and their workers are paid. They spend much of it in shops, cafés and on services.

By how much is national income likely to rise in total?

The £10bn becomes someone’s income, and they spend part of it, which becomes someone else’s income, and so on. Each round is smaller, but the total rise in national income is bigger than the first injection. That is the multiplier.

Step by step

1. The government injects £10bn. The first round alone shifts AD right by the £10bn of spending.

2. With an MPC of 0.75, the builders spend £7.5bn, which becomes others’ income. They spend 0.75 of that, £5.63bn, and so on. Each round is smaller because a quarter leaks out each time.

   Check: MPC is 0.75. The builders receive £10bn. How much do they spend in the second round?

   0.75 × £10bn = £7.5bn spent; £2.5bn is withdrawn in saving, tax and imports.

3. Add up all the rounds: £10bn + £7.5bn + £5.63bn + … = £40bn. The multiplier is 1 ÷ (1 − 0.75) = 4, and 4 × £10bn = £40bn. So AD finally shifts by four times the first shift, to AD2.

4. The bigger the leakages, the smaller the multiplier. The UK is a very open economy, so much extra spending goes on imports, and taxes take a share too: real-world multipliers are much smaller than 4, often estimated at around 1 or below.

   Check: If people save more of each extra pound, the multiplier:

   More leaks out each round (a higher MPW), so the rounds shrink faster.

5. Now run the process the other way.

   Check: A large local employer closes, and its workers lose £100m of wages a year. What happens to total local income?

   The lost wages mean less spending in local shops and firms, which cuts their income too. The rounds shrink, but they add to the first loss, so the total fall is a multiple of £100m.

6. The multiplier works in reverse too. A fall in investment, a fall in exports or a factory closure lowers income by more than the first cut.

A common mistake

The final rise in GDP is the multiplier times the injection: with a multiplier of 4, £40bn. The £10bn is only the first round.

Exam question

Explain how the multiplier process works when the government increases its spending.

Model answer

When the government increases its spending, for example on building hospitals, the money is an injection into the circular flow. It becomes income for construction firms and their workers.

They spend a fraction of this extra income on UK goods and services, the marginal propensity to consume, and withdraw the rest through saving, taxes and spending on imports. The part they spend becomes income for shop owners, suppliers and their staff, who in turn spend a fraction of it. Each round of spending is smaller than the last because some income leaks out each time.

Adding up all the rounds, national income rises by more than the original injection. The final rise equals the injection multiplied by the multiplier, which is 1 ÷ (1 − MPC), or 1 ÷ MPW. For example, with an MPC of 0.75, the multiplier is 4, so £10bn of extra spending raises national income by £40bn. The larger the withdrawals, the smaller the multiplier.

However, the real-world multiplier is uncertain and probably much smaller than 4, because a large share of extra income in the UK goes on imports and tax, and the rounds take time to work through. If the economy is close to full capacity, much of the extra spending raises prices rather than real output.