Spend £200 million on flood defences and national income rises by more than £200 million. That sounds like an accounting trick; it is actually the multiplier, one of the few genuinely surprising results on the A-Level syllabus — and one AQA tests with calculations, not just definitions. Any AQA A-Level economics tutor will tell you the same thing: students lose these marks not on the idea but on the formula they picked. This page fixes both.
1 · The four components of aggregate demand
Aggregate demand is total planned spending on an economy’s output at each price level:
AD = C + I + G + (X − M)
- C — consumption: household spending, comfortably the largest component in the UK.
- I — investment: firms’ spending on capital, the most volatile component.
- G — government spending on goods and services (not transfer payments — pensions and benefits become someone’s C when spent).
- X − M — net exports: overseas spending on our output minus our spending on theirs.
Anything that raises a component shifts AD right. But by how much it shifts national income is the multiplier’s question.
2 · One person’s spending is another’s income
Pay a builder £100 and you have created £100 of income. The builder spends part of it at a café; the café owner spends part of that; and so on. Each round of spending becomes someone else’s income, which funds another, smaller round.
Why smaller? Because at each step some income leaks out of the circular flow through the three withdrawals: saving (S), taxation (T) and imports (M). Only what is spent on domestic output goes round again.
Two fractions run everything. The marginal propensity to consume (MPC) is the share of each extra pound spent on domestic output. The marginal propensity to withdraw (MPW) is the share that leaks: MPW = MPS + MPT + MPM. Since every pound is either respent or withdrawn, MPC + MPW = 1.
3 · The multiplier formula
Add up the shrinking rounds and the total change in national income is a multiple of the first injection:
k = 1 ⁄ (1 − MPC) = 1 ⁄ MPW
Both versions are the same number — use whichever the question’s data makes easy, and state it before you substitute. The bigger the leak, the smaller the multiplier: an open economy with high taxes recycles less of each pound, so its rounds die out faster.
The multiplier also runs in reverse. A £200m cut in spending shrinks income by k × £200m, spread over the same decaying rounds — the downward multiplier that turns local closures into regional slumps.
Worked example — a £200m injection, round by round
The government spends £200m building flood defences. Out of each extra pound of income, people save 20p, pay 10p in tax and spend 10p on imports; the remaining 60p is spent on domestic output. So MPC = 0.6 and MPW = 0.2 + 0.1 + 0.1 = 0.4.
Step 1 — Round one. Contractors and their workers receive the £200m. Income so far: £200m.
Step 2 — Round two. Of that £200m, £40m is saved, £20m taxed, £20m spent on imports — £80m leaks. The other £120m (0.6 × 200) is spent on domestic goods and becomes new income.
Step 3 — Round three. The £120m is respent the same way: 0.6 × 120 = £72m of new income. Each round is 60% of the last: 200, 120, 72, 43.2, 25.9…
Step 4 — Sum the series. The rounds form a geometric series whose total is the injection divided by the leak: 200 ⁄ 0.4 = £500m.
Step 5 — Check with the formula. k = 1 ⁄ (1 − 0.6) = 1 ⁄ 0.4 = 2.5, and 2.5 × £200m = £500m. Both routes agree, as they must.
Step 6 — Watch the convergence. After eight rounds the running total has reached about £491.6m — over 98% of the final effect. The multiplier is front-loaded: the first three rounds alone deliver £392m.
Step 7 — Interpretation. The £500m is the model’s ceiling, not a promise. If the economy is near full capacity, extra rounds bid up prices instead of output; if confidence is low, the MPS rises mid-process and k shrinks. Evaluation marks live exactly there — the multiplier’s size depends on spare capacity and on how stable the withdrawal rates really are.
Sure which multiplier formula the data wants — 1 ⁄ (1 − MPC) or 1 ⁄ MPW? Picking the wrong one is where these gift marks quietly vanish, even when the method is right. Building that choice into a reflex is exactly what a one-on-one A-Level economics tutor drills with you. Book a trial session.
Practice
Q1. In a closed economy with no income tax, MPC = 0.75. Investment rises by £50m. Calculate the multiplier and the total rise in national income.
Q2. An economy has MPS = 0.1, MPT = 0.2 and MPM = 0.2. Government spending rises by £80m. Calculate the multiplier and the total rise in national income.
Q3. MPC = 0.8. The government wants national income to rise by £300m. How large an injection is needed?
Answers. Q1: k = 1 ⁄ (1 − 0.75) = 4, so income rises 4 × 50 = £200m. Q2: MPW = 0.1 + 0.2 + 0.2 = 0.5, so k = 1 ⁄ 0.5 = 2; income rises 2 × 80 = £160m. Q3: k = 1 ⁄ (1 − 0.8) = 5, so the injection must be 300 ⁄ 5 = £60m.
Key takeaways
- AD = C + I + G + (X − M) — know what belongs in each component, and that transfer payments are not G.
- The multiplier exists because spending is income. Each round is MPC of the last; withdrawals make the rounds shrink.
- k = 1 ⁄ (1 − MPC) = 1 ⁄ MPW. Same number, two doors — pick the one the data opens.
- Size depends on leaks and capacity. Big withdrawals or a full-capacity economy mean a small real-output multiplier — that’s your evaluation paragraph.
Why London students choose our A-Level economics tutors
- Calculation drills: AQA sets multiplier arithmetic in Paper 2 data responses, and tutors rehearse the k-formula until choosing between 1 ⁄ (1 − MPC) and 1 ⁄ MPW is automatic.
- One-on-one exam technique: sessions work through your own board’s past papers line by line, showing where a correct idea still drops marks for a missing chain of reasoning.
- PhD-trained tutors: the multiplier connects to everything from fiscal policy to the trade cycle, and tutors who know the subject deeply teach those connections instead of isolated formulas.
FAQ
Q: What is the multiplier effect in simple terms?
A: An initial rise in spending becomes someone’s income, part of which is spent again, creating more income. The total rise in national income ends up larger than the first injection — a multiple of it.
Q: What is the difference between MPC and MPW?
A: The MPC is the fraction of each extra pound spent on domestic output; the MPW is the fraction withdrawn through saving, tax and imports. They always sum to one, which is why 1 ⁄ (1 − MPC) and 1 ⁄ MPW give the same multiplier.
Q: Can the multiplier be negative?
A: The process also works downwards: a fall in injections multiplies into a larger fall in national income through the same rounds. The multiplier itself stays positive — it is the change it multiplies that can be negative.
Q: Why might the real-world multiplier be smaller than the formula says?
A: Near full capacity, extra demand raises prices rather than output; and the withdrawal propensities are not fixed — saving typically rises in uncertain times, cutting the MPC mid-process.
Q: Which formula should I use in the exam?
A: Whichever matches the data given. If the question states an MPC, use 1 ⁄ (1 − MPC); if it gives the three withdrawal propensities, add them and use 1 ⁄ MPW. State the formula before substituting — it usually carries a mark.
Book an AQA A-Level economics tutor in London or online
Multiplier questions are gift marks for students who have drilled the method and a trap for everyone else. One-on-one sessions build the reflexes — components of AD, the right k-formula, the evaluation about capacity and leaks — on real past-paper questions. Tell us your exam board and target grade, and we’ll match you with the right tutor this week, in London or online.
