Here is the idea in one sentence: the money the government spends does not stop moving when it arrives. It becomes somebody’s income, and they spend part of it, and that becomes somebody else’s income. So a $100 million injection ends up raising national income by much more than $100 million.
📚 What you need to know
The multiplier is the ratio of the change in real income to the injection that caused it.
It works because one person’s spending is another person’s income, round after round.
The size depends entirely on leakages: saving, tax and imports. Bigger leakages, smaller multiplier.
Two formulas: k = 1 ÷ (1 − MPC) or k = 1 ÷ (MPS + MPT + MPM). They give the same answer.
Total change in income = injection × multiplier.
It works in reverse too: a cut in spending shrinks income by a multiple of the cut.
Why the effect is bigger than the injection
Say the government spends $100 million building a bridge. That money goes to a construction firm, which pays wages to workers and buys steel and cement. Those workers now have extra income. They do not save all of it — they spend some in shops and restaurants. That spending becomes income for shopkeepers, who spend some of it too.
Each round is smaller than the last, because some money leaks out at every stage: a bit gets saved, a bit is taken in tax, and a bit is spent on imports, which is income for another country. Eventually the rounds get too small to matter, and the total settles.
Change the leakage and the whole picture changes. If households only spent 50% of extra income, the bars would halve each time and the total would be $200m, not $400m.
The marginal propensities
“Marginal propensity” just means: out of the next dollar you earn, what share goes where? Every extra dollar has to go somewhere, so the four shares add up to 1.
Propensity
What it measures
Injection or leakage?
MPC — to consume
The share of extra income spent on domestic goods and services
Stays in the circular flow
MPS — to save
The share put into savings
Leakage
MPT — to tax
The share taken in tax
Leakage
MPM — to import
The share spent on foreign goods
Leakage
A country with a strong savings habit, high taxes or a heavy reliance on imports will always have a smaller multiplier. That is a ready-made comparison point: the same stimulus package does more in one economy than another.
The two formulas
Using the MPC
k = 1 ÷ (1 − MPC)
Using the leakages
k = 1 ÷ (MPS + MPT + MPM)
Use the first when the question gives you the MPC. Use the second when it gives you the three leakages. They are the same formula, because MPS + MPT + MPM = 1 − MPC.
WORKED EXAMPLE
Find the multiplier and the impact on GDP [4 marks]
An economy has a marginal propensity to save of 0.10, a marginal propensity to tax of 0.25 and a marginal propensity to import of 0.15. The government increases infrastructure spending by $40 million.
(a) Calculate the multiplier. (b) Calculate the total increase in GDP.
Step 1: add up the leakages0.10 + 0.25 + 0.15 = 0.50Step 2: apply the withdrawals formulak = 1 ÷ 0.50 = 2Step 3: multiply the injection by k$40m × 2 = $80mMultiplier = 2, total rise in GDP = $80 millioncheck: MPC must be 1 − 0.5 = 0.5, and 1 ÷ (1 − 0.5) = 2 too
WORKED EXAMPLE
Working backwards from an output gap [3 marks]
An economy faces a recessionary gap of $30 billion. Its MPC is 0.8. Calculate how much extra government spending is needed to close the gap.
Step 1: find the multiplierk = 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5Step 2: the gap is the change in income we want, so divide by k$30bn ÷ 5 = $6bn$6 billion of extra government spendinggoing backwards you DIVIDE by the multiplier — multiplying here is the classic error
Why the multiplier matters
The bigger the MPC, the bigger the multiplier — and the bigger the leakages, the smaller it is.
Anything that changes disposable income changes the multiplier. Higher taxes shrink it. Rising interest rates encourage saving, so they shrink it too. An appreciating currency makes imports cheaper, which also shrinks it. Rising confidence raises consumption, so it grows.
Governments need an estimate of the multiplier before they act, otherwise they cannot judge how large a stimulus to launch.
It runs downwards as well. Cutting spending by $10 million with a multiplier of 3 removes $30 million of income.
On an AD/AS diagram, the initial injection shifts AD right, and the multiplier gives a second, further shift in the same direction.
The evaluation point examiners want. The multiplier takes time — possibly a year and a half for the full effect to work through. During those months confidence can change, and that alone can make the real outcome very different from the calculated one.
💡 Exam tips
Read the data carefully: MPC given, or three leakages? Pick the matching formula.
Never round the multiplier early. A k of 2.5 rounded to 3 changes the final answer badly.
Give the units and the direction: “GDP rises by $80 million”, not just “80”.
To find the spending needed to close a gap, divide the gap by the multiplier.
State the multiplier value in words in an essay even when no calculation is asked for. It upgrades your analysis.
Mention time lags and confidence whenever you are evaluating a multiplier effect.
⚠ Common mix-ups
Using 1 ÷ MPC instead of 1 ÷ (1 − MPC). The denominator is the leakage, not the spending.
Adding MPC to the leakages. MPC is the part that stays in the flow; the other three are what leak out.
Multiplying when you should divide. Injection × k gives the income change; gap ÷ k gives the injection needed.
Forgetting it works in reverse. Austerity has a downward multiplier of exactly the same size.
Thinking the multiplier makes stimulus free. The government still borrowed the original amount.
Assuming it is always large. In an open economy with high taxes and high imports it can be close to 1.
Up next: How Effective Is Fiscal Policy? — automatic stabilisers, crowding out, and the honest limits of using the budget to steer an economy.
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