Edexcel A-Level Economics · Revision notes

2.4.4 The multiplier

When an injection into the circular flow changes, national income changes by more than the original amount. The reason is simple: one person's spending is another person's income, and part of that income is spent again. This topic covers the multiplier ratio, the process behind it, the marginal propensities that decide its size, how to calculate it, and why it matters for shifts in aggregate demand (AD).

The multiplier ratio

The multiplier ratio compares the final change in real national income with the initial change in injections that caused it.

multiplier = final change in real national income ÷ initial change in injections

If the government spends an extra £10bn on new railway lines and real national income eventually rises by £25bn, the multiplier is 25 ÷ 10 = 2.5.

The multiplier works in both directions. A fall in an injection, such as a drop in exports, or a rise in a withdrawal, such as households choosing to save more, reduces national income by more than the initial change. This is sometimes called the negative multiplier.

The multiplier process

The process happens in rounds.

Round 1: the injection. The government spends £10bn on new railway lines. That £10bn becomes income for construction firms and their workers.

Round 2: induced spending. The firms and workers do not spend all of their extra income on domestic output. Some is saved, some is taken in tax and some is spent on imports. Suppose 60% is passed on as spending on UK goods and services. That is £6bn of extra spending, which becomes income for shop owners, restaurant staff and their suppliers.

Round 3 and beyond. Those people in turn pass on 60% of their extra income, adding £3.6bn, then £2.16bn, and so on. Each round is smaller than the last, because some income leaks out of the circular flow at every stage.

Adding up every round, 10 + 6 + 3.6 + 2.16 + ... gets closer and closer to £25bn. The initial £10bn injection has raised national income by £25bn, a multiplier of 2.5.

The diagram separates the two parts of the shift in AD. The first shift is the injection itself. The second, larger shift is the induced consumption that follows as the extra income is spent again.

Marginal propensities

A marginal propensity is the proportion of an extra pound of income that is used in a particular way. Marginal means "of the next unit", so these measure what happens to additional income, not to total income.

• Marginal propensity to consume (MPC). The proportion of extra income spent on consumption. If income rises by £100 and spending on domestic output rises by £80, the MPC is 80 ÷ 100 = 0.8, or 80%.
• Marginal propensity to save (MPS). The proportion of extra income saved.
• Marginal propensity to tax (MPT). The proportion of extra income taken in tax, such as income tax, National Insurance and VAT on extra purchases.
• Marginal propensity to import (MPM). The proportion of extra income spent on goods and services produced abroad.

The three withdrawals add up to the marginal propensity to withdraw (MPW):

MPW = MPS + MPT + MPM

Key idea: In the multiplier model, every extra pound is either passed on as spending on domestic output or withdrawn from the circular flow. So MPC + MPW = 1.

If the MPW is 0.4, the MPC is 0.6.

How the propensities affect the multiplier

• A higher MPC means a larger multiplier. More of each round of income is passed on, so the later rounds are bigger.
• A higher MPS, MPT or MPM means a smaller multiplier. More income leaks out at each stage, so the process dies away faster.

Evaluation: This is why the multiplier is smaller in an open economy such as the UK than in simple textbook examples. A large share of extra spending goes on imports, and income tax and National Insurance take a share of every extra pound earned.

Calculating the multiplier

There are two formulae, and they give the same answer.

multiplier = 1 ÷ (1 − MPC)

multiplier = 1 ÷ MPW, where MPW = MPS + MPT + MPM

Worked example 1: using the MPC. The MPC is 0.75. multiplier = 1 ÷ (1 − 0.75) = 1 ÷ 0.25 = 4

Worked example 2: using the MPW. The MPS is 0.1, the MPT is 0.2 and the MPM is 0.2. MPW = 0.1 + 0.2 + 0.2 = 0.5 multiplier = 1 ÷ 0.5 = 2 Check: the MPC is 1 − 0.5 = 0.5, and 1 ÷ (1 − 0.5) = 2.

Worked example 3: using the multiplier. The multiplier is 2 and investment rises by £15bn. Final change in national income = 2 × £15bn = £30bn

Working backwards: if the government wants national income to rise by £40bn and the multiplier is 2.5, the injection needed is £40bn ÷ 2.5 = £16bn.

Effects of the multiplier on the economy

• Policy has a bigger effect. A rise in Government Expenditure raises national income by more than the amount spent, so a smaller injection can be used to reduce a negative output gap.
• Employment rises. As output rises through successive rounds, firms take on more workers, and cyclical unemployment falls.
• Shocks are amplified. A fall in exports during a global downturn, or a collapse in business confidence that cuts investment, reduces national income by more than the initial fall. This helps explain why a recession can deepen.
• Inflation can follow. If the economy is close to full capacity, the multiplied increase in AD mainly pushes up the price level rather than real output.

Why the effect may be smaller or harder to predict

• Time lags. Each round takes time, so the full effect can take months or years to appear.
• Uncertainty about the size. The marginal propensities are not known precisely, and they change. Households worried about losing their jobs may save more of any extra income, which lowers the MPC just when the government wants a large multiplier.
• Leakages in an open economy. Where a high proportion of extra spending goes on imports, much of the multiplier effect benefits other countries.
• Where the extra income goes. Lower-income households tend to spend a higher proportion of extra income than higher-income households, so the size of the multiplier depends on who receives the injection.

The significance of the multiplier for shifts in AD

When an injection changes, AD shifts by more than the initial change:

final shift in AD = multiplier × initial change in injection

What happens to real output then depends on aggregate supply. If there is plenty of spare capacity, most of the shift in AD raises real output and employment. Close to full capacity, more of it raises the price level.

Watch out: When the AS curve slopes upwards, the rise in real output is smaller than the full horizontal shift in AD, because part of the extra demand is absorbed by higher prices.

Key terms

Common mistakes

• Confusing marginal with average. The MPC is the proportion of extra income spent, not the proportion of total income spent.
• Using the wrong formula. If you are given the MPW, use 1 ÷ MPW. If you are given the MPC, use 1 ÷ (1 − MPC). Do not divide 1 by the MPC.
• Leaving out a withdrawal. The MPW includes saving, tax and imports, not saving alone.
• Stopping at the multiplier. If you are asked for the change in national income, multiply the multiplier by the initial injection.
• Assuming the whole shift in AD becomes extra real output. How much becomes real output depends on spare capacity.

How this has been examined

In the Edexcel papers indexed on this site, this topic has appeared in five formats:

• 4-mark calculation — asked twice across 2 series (2022 to 2024)
• 4-mark "Explain" data response — asked twice across 2 series (2020 to 2023)
• 2-mark calculation — asked once (2021)
• 2-mark "Explain" data response — asked once (2017)
• 1-mark multiple choice — asked 3 times across 3 series (2017 to 2020)

Where this goes next

The multiplier builds on 2.4.2 Injections and withdrawals and on the AD/AS analysis in 2.4.3 Equilibrium levels of real national output. The injections that start the process are covered in 2.2.3 Investment (I), 2.2.4 Government expenditure (G) and 2.2.5 Net trade (X-M). The multiplier explains why demand-side policy can close an output gap, covered in 2.5.2 Output gaps and 2.6.2 Demand-side policies.