The multiplier: WACE Year 12 Economics Unit 4
“Explain the multiplier process, calculate the multiplier from the marginal propensities, and use it to analyse the effect of a change in injections on the level of economic activity”
The multiplier is the number of times a change in injections is multiplied to give the final change in national income. An initial injection becomes income for someone, who spends part of it, which becomes income for someone else, and so on. The multiplier equals one divided by the marginal propensity to leak, so the more income that leaks out at each round, the smaller the multiplier.
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What this dot point is asking
SCSA wants you to explain the mechanism, calculate the multiplier from the marginal propensities, and apply it to a change in spending. Expect a calculation task and a short response linking the multiplier to the business cycle and to fiscal policy.
The multiplier process
When spending is injected into the economy, it does not stop with the first recipient.
The multiplier is the ratio of the final change in national income to the initial change in injections that caused it. Because each recipient of income spends a portion of it, an injection generates successive rounds of additional spending and income.
The size of each round depends on how much income is passed on as spending and how much leaks out as saving, taxation and imports.
The marginal propensity to consume (MPC) is the fraction of each extra dollar of income that is spent on domestic goods. The marginal propensities to save (MPS), to tax (MPT) and to import (MPM) are the fractions that leak out. They sum with the MPC to one.
Calculating the multiplier
The multiplier depends on the marginal propensity to leak, the combined fraction of extra income withdrawn from the flow at each round.
Multiplier = 1 / MPS + MPT + MPM, that is 1 divided by the marginal propensity to leak. In a simple model with saving as the only leakage, Multiplier = 1 / (1 - MPC).
Suppose for every extra dollar of income, households save 0.10, pay 0.20 in tax and spend 0.15 on imports. The marginal propensity to leak is 0.10 + 0.20 + 0.15 = 0.45. The multiplier is 1 divided by 0.45, which is about 2.22.
Now suppose the government injects 10 billion dollars of infrastructure spending. The final change in national income is 10 billion times 2.22, which is about 22.2 billion dollars. The initial injection has been multiplied because it circulates through successive rounds of spending before it fully leaks away.
Why leakages shrink the multiplier
At each round of spending, the leakages (saving, tax, imports) remove money from the circular flow, so each successive round is smaller than the last. The larger the marginal propensity to leak, the faster the rounds shrink and the smaller the total effect.
Australia is a small open economy with a high marginal propensity to import and a progressive tax system, so a large share of each round of spending leaks out as imports and tax. This makes Australia's expenditure multiplier smaller than in a large, more closed economy, an important point when evaluating how much fiscal stimulus will actually lift domestic activity.
Applying the multiplier
The multiplier works in both directions. A rise in any injection (I, G or X) raises income by the injection times the multiplier; a fall in any injection, or a rise in a leakage, reduces income by the same logic. This is central to:
- Fiscal policy: the impact of government spending depends on the multiplier; a higher multiplier means stronger stimulus per dollar.
- The business cycle: the multiplier amplifies shocks, giving the cycle momentum.
- Confidence shocks: a fall in investment is magnified into a larger fall in income.
Rounds of spending in detail
To see why the multiplier is greater than one, trace the rounds. Suppose the marginal propensity to leak is 0.5 (so half of each extra dollar is spent on domestic goods and half leaks out). An injection of $100 million becomes $100m of income. The recipients spend $50m, which becomes income for others, who spend $25m, then $12.5m, and so on. The series $100 + 50 + 25 + 12.5 + \dots200m, exactly the injection times the multiplier . The geometry shows why a higher leakage rate, which means smaller successive rounds, produces a smaller total.
The multiplier and fiscal policy choices
The size of the multiplier helps explain why governments favour certain stimulus measures over others. Spending that goes to lower-income households or to labour-intensive infrastructure tends to have a higher multiplier, because those recipients have a high MPC and spend most of the money domestically. Tax cuts aimed at higher-income households or measures that leak quickly into imports or saving have a smaller multiplier. During the 2008 to 2009 global financial crisis, the Australian government's cash payments and school-building program were designed to maximise the domestic multiplier and support activity quickly.
A practical limit is that the simple multiplier assumes spare capacity. Near full employment, extra injections push against the economy's productive limits, so the effect shows up more in prices (inflation) than in real output. This is why the multiplier is most powerful during a downturn, when there are idle resources to bring back into use.
Students often calculate the multiplier using saving alone and ignore tax and imports. In a five-sector open economy, the relevant figure is the marginal propensity to leak, which adds the propensities to save, to tax and to import together. Including all three gives a smaller, more realistic multiplier than the saving-only version.
Exam-style questions
Questions in the style of SCSA exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.
WACE 2022-style6 marksAn economy has a marginal propensity to save of 0.15, a marginal propensity to tax of 0.20 and a marginal propensity to import of 0.10. Calculate the simple multiplier and the final change in national income from a $4 billion increase in government investment. Show your working.Show worked answer →
A 6 mark calculation needs the marginal propensity to leak, the multiplier, the final change, and a sentence of interpretation.
Step 1, marginal propensity to leak. .
Step 2, multiplier. .
Step 3, final change in income. billion dollars.
Interpretation. The initial $4 billion injection circulates through successive rounds of spending, raising national income by about $8.9 billion before it fully leaks away.
Markers reward correct identification of all three leakages, the reciprocal formula, accurate arithmetic, and a sentence linking the result back to the multiplier process.
WACE 2023-style8 marksExplain the multiplier process and discuss why the expenditure multiplier tends to be smaller in Australia than in a large, more closed economy.Show worked answer →
An 8 mark response needs the mechanism, the leakage logic, and the open-economy point applied to Australia.
Mechanism. An injection becomes income for its first recipient, who spends a fraction (the MPC) on domestic goods, generating income for the next recipient, and so on. The final change in income is the injection times the multiplier.
Leakage logic. At each round, saving, taxation and imports leak out, so each successive round is smaller. The multiplier equals one divided by the marginal propensity to leak, so larger leakages produce a smaller multiplier.
Australia. As a small open economy with a high marginal propensity to import and a progressive tax system, a large share of each round leaks out as imports and tax. This makes Australia's multiplier modest (often estimated near 1.5 to 2.5), so fiscal stimulus lifts domestic activity by less per dollar than in a large, more closed economy where more spending recirculates at home.
Markers reward a clear round-by-round mechanism, the leakage-multiplier link, and the explicit open-economy comparison applied to Australia.