2.4.4 The Multiplier — Practice Questions

Nine original multiple-choice questions on the multiplier, written to the style and difficulty of Edexcel Paper 2 Section A. Four are calculations.

9 questions Edexcel A-Level Multiple choice Model answers included

Not read the notes yet? Start with the 2.4.4 The Multiplier revision notes.

1. 1. A household receives an extra £100. It spends £55 of it on domestic goods and services, pays £20 in tax and spends £10 on imports. Its marginal propensity to withdraw is

   Calculation

   Select one answer

   A 0.15

   B 0.30

   C 0.45

   D 0.75
   Show model answer

   Answer: C (0.45). Every extra pound is either consumed domestically or withdrawn, so MPW = 1 − MPC.
   MPC here is £55 ÷ £100 = 0.55, so MPW = 1 − 0.55 = 0.45.
   Check it the long way. Of the £100, £45 was not spent on domestic output: £20 in tax, £10 on imports, and the remaining £15 saved. MPW = 0.20 + 0.10 + 0.15 = 0.45. The two routes agree, which is the check worth doing whenever the four propensities appear together.

   Why the other options are wrong

   • A — 0.15 is the marginal propensity to save alone — the £15 left over. Saving is only one of the three leakages.
   • B — 0.30 is the £20 of tax plus the £10 of imports, the two leakages stated explicitly. The £15 saved has been missed.
   • D — 0.75 adds the £55 spent to the £20 of tax. Consumption is not a withdrawal, so it cannot be on that side.

2. 2. Out of every extra £1 of income, households in an economy save 5p, pay 25p in tax and spend 20p on imports. A student uses the saving figure on its own and calculates the multiplier as 20.0. The correct value is

   Calculation

   Select one answer

   A 2.0

   B 4.0

   C 5.0

   D 20.0
   Show model answer

   Answer: A (2.0). The multiplier depends on every leakage, not just saving:
   MPW = 0.05 + 0.25 + 0.20 = 0.50.
   Multiplier = 1 ÷ 0.50 = 2.0.
   The student's answer of 20.0 comes from 1 ÷ 0.05, using saving alone — and it is ten times too large. This is the single most common error on the topic, and it matters: an injection of £1bn would raise national income by £2bn, not £20bn.
   Cross-check with the other formula: MPC = 1 − 0.50 = 0.50, and 1 ÷ (1 − 0.50) = 2.0 as well.

   Why the other options are wrong

   • B — 4.0 is 1 ÷ 0.25, using the tax leakage on its own. The same mistake as the student's, with a different single leakage.
   • C — 5.0 is 1 ÷ 0.20, using the import leakage on its own.
   • D — 20.0 is the student's figure, from 1 ÷ 0.05. The stem gives it precisely because it is the wrong answer.

3. 3. An economy's multiplier is 3. A government wants to raise real GDP by £15 billion. The injection it needs to make is

   Calculation

   Select one answer

   A £5bn

   B £12bn

   C £18bn

   D £45bn
   Show model answer

   Answer: A (£5bn). The multiplier links an injection to the final change in national income:
   final change = injection × multiplier.
   Rearranging, injection = £15bn ÷ 3 = £5bn.
   The check is quick: £5bn × 3 = £15bn. A multiplier greater than 1 always means the injection needed is smaller than the target, which rules out two of the options immediately.

   Why the other options are wrong

   • B — £12bn subtracts the multiplier from the target, £15bn − 3. The multiplier is a ratio, not an amount in pounds.
   • C — £18bn adds it, £15bn + 3, with the same confusion between a ratio and a quantity.
   • D — £45bn multiplies instead of dividing. That is the size of the effect £15bn would produce, not the injection needed.

4. 4. A country's households begin buying a much larger share of their goods from abroad. All other things being equal, the multiplier will

   Applied reasoning

   Select one answer

   A Rise, because imports add to demand.

   B Rise, because the MPW has fallen.

   C Fall, because more income leaks out.

   D Fall, because the MPC has risen.
   Show model answer

   Answer: C (Fall, because more income leaks out.). The marginal propensity to import is one of the three leakages that make up MPW, and the multiplier is 1 ÷ MPW.
   A higher MPM raises MPW, and a larger denominator gives a smaller multiplier. At each round of the process, more of the income being passed on goes abroad rather than to domestic firms, so the rounds shrink faster.
   This is why small open economies typically have smaller multipliers than large, relatively closed ones — the same stimulus leaks away faster.

   Why the other options are wrong

   • A — Imports are spending on output produced elsewhere, so they leave the domestic circular flow rather than adding to demand within it.
   • B — MPW has risen, because MPM is one of its components. A higher MPW gives a smaller multiplier.
   • D — MPC falls when more income goes on imports, since MPC measures spending on domestic goods and services.

5. 5. In an economy the marginal propensity to withdraw is 0.4, so the multiplier calculated as 1 ÷ MPW is 2.5. Calculating it instead as 1 ÷ (1 − MPC) would give

   Applied reasoning

   Select one answer

   A A larger value, because MPC excludes tax.

   B A smaller value, because MPC excludes tax.

   C An undefined value, because MPC is unknown.

   D The same value, because MPC = 1 − MPW.
   Show model answer

   Answer: D (The same value, because MPC = 1 − MPW.). The two formulas are the same equation written differently.
   Since every extra pound is either consumed or withdrawn, MPC + MPW = 1. So MPC = 1 − 0.4 = 0.6, and 1 − MPC = 0.4 — exactly the MPW you started with.
   1 ÷ (1 − 0.6) = 1 ÷ 0.4 = 2.5, the same answer.
   Knowing they agree is genuinely useful: whichever propensities a question happens to give you, you can always reach the multiplier, and working it both ways is a free check on your arithmetic.

   Why the other options are wrong

   • A — MPC does exclude tax, but so does the calculation. Tax is inside MPW, and 1 − MPC recovers MPW in full.
   • B — The same objection. The identity guarantees the two routes give an identical figure, not merely a similar one.
   • C — MPC is not unknown — it is 1 − MPW = 0.6. The identity supplies it whenever MPW is given.

6. 6. Table 1 shows the marginal propensities in an economy.
   Using Table 1, an injection of £3 billion would raise national income by

   Calculation

   Table 1: Marginal propensities in the economy

   Propensity	Value
   Marginal propensity to save	0.05
   Marginal propensity to tax	0.15
   Marginal propensity to import	0.05

   Select one answer

   A £0.75bn

   B £3.0bn

   C £12.0bn

   D £60.0bn
   Show model answer

   Answer: C (£12.0bn). Add the leakages, then invert.
   MPW = 0.05 + 0.15 + 0.05 = 0.25.
   Multiplier = 1 ÷ 0.25 = 4.
   Final change in national income = £3bn × 4 = £12bn.
   The order matters: find MPW first, then the multiplier, then apply it to the injection. Going straight from a single propensity to an answer is where most marks are lost on this topic.

   Why the other options are wrong

   • A — £0.75bn multiplies the injection by MPW instead of by the multiplier. The multiplier is the reciprocal of MPW, not MPW itself.
   • B — £3.0bn is the injection with no multiplier applied at all. The whole point is that the final effect exceeds the initial injection.
   • D — £60.0bn uses saving alone: 1 ÷ 0.05 = 20, times £3bn. Tax and imports are leakages too and must be included in MPW.

7. 7. Households and firms across an economy become markedly more confident about the future. All other things being equal, the size of the multiplier is likely to

   Applied reasoning

   Select one answer

   A Rise, as more of each extra pound is spent.

   B Rise, as the government spends more.

   C Fall, as more income is saved.

   D Fall, as the marginal propensity to withdraw rises.
   Show model answer

   Answer: A (Rise, as more of each extra pound is spent.). Confidence works on the multiplier through the marginal propensity to consume.
   Households who feel secure about their jobs and future income spend a larger share of any extra pound rather than putting it aside. A higher MPC means a lower MPW, and 1 ÷ MPW is therefore larger.
   The practical consequence is that the same fiscal stimulus achieves more when confidence is high — and least when it is low, which is unfortunately when governments most want to use it.

   Why the other options are wrong

   • B — Government spending is an injection. It determines what the multiplier is applied to, not how large the multiplier is.
   • C — Confident households save a smaller share of extra income, not a larger one. Saving rises with caution.
   • D — MPW falls as confidence rises, because more of each pound is spent domestically rather than withdrawn.

8. 8. An economy is operating at full capacity when the government raises its spending. Compared with the same injection made during a deep recession, the effect on real output will be

   Applied reasoning

   Select one answer

   A Larger, because confidence is higher in a boom.

   B Larger, because the multiplier rises with output.

   C Smaller, because extra demand mainly raises prices.

   D The same, because the multiplier is a fixed number.
   Show model answer

   Answer: C (Smaller, because extra demand mainly raises prices.). The multiplier describes what happens to spending. Whether that spending becomes real output depends on whether the economy has the capacity to produce it.
   At full capacity there are no idle workers or machines, so the extra demand meets a vertical or near-vertical supply constraint and pushes the price level up instead of output.
   In a recession the same injection meets plentiful spare capacity, so it is met with real production. This is why the multiplier is usually described as larger in a slump — and why fiscal expansion at the peak of a boom is mostly inflationary.

   Why the other options are wrong

   • A — Confidence may well be higher in a boom, but capacity is the binding constraint. There is nothing spare to produce with.
   • B — The multiplier does not mechanically rise with output. If anything it is larger in a recession, when spare capacity and lower interest rates encourage spending.
   • D — The multiplier is not a fixed number — it depends on the marginal propensities, which change with confidence and conditions.

9. 9. A government cuts its spending by £2 billion in an economy with a multiplier of 3. The most likely effect on national income is

   Applied reasoning

   Select one answer

   A A fall of £2 billion.

   B A fall of £6 billion.

   C A rise of £6 billion.

   D No change, since the multiplier applies only to injections.
   Show model answer

   Answer: B (A fall of £6 billion.). The multiplier works in both directions, and this is the part students most often miss.
   Cutting government spending by £2bn removes £2bn of income from the recipients. They then cut their own spending by a proportion of it, which reduces somebody else's income, and so on down the rounds — the same process as an injection, running in reverse.
   Final change = −£2bn × 3 = a fall of £6bn.
   That asymmetry between the size of the cut and the size of the damage is a central argument against sharp fiscal consolidation in a weak economy.

   Why the other options are wrong

   • A — A fall of £2bn is the initial withdrawal alone, before the knock-on rounds. The multiplier magnifies it.
   • C — The size is right but the direction is wrong. Cutting spending reduces national income; it does not raise it.
   • D — A cut in government spending is a reduction in an injection, and the multiplier applies to it exactly as it would to an increase.