The Multiplier Effect
In one line. The multiplier effect is the process by which an initial injection into the economy leads to a larger eventual rise in national income, because the money is re-spent in successive rounds. Its size is given by k = 1 / MPW, where MPW is the marginal propensity to withdraw; the larger the leakages, the smaller the multiplier.
Exam relevance: one of the highest-yield macro ideas, the multiplier appears across fiscal and growth questions almost every year, on ETG analysis. Taught the way an economics tutor who wrote the answer keys teaches it.
01What the multiplier effect is
The multiplier effect is the process by which an initial injection into the economy raises national income by a larger, multiplied amount, because the money is re-spent in successive rounds.
The multiplier effect is the more than proportionate rise in national income that results from an initial injection of expenditure into the circular flow.
An injection is autonomous spending that enters the flow from outside the household to firm circuit: investment, government spending or exports. The multiplier is the reason a dollar of injection raises national income by more than a dollar.
02Why one injection becomes many
The first injection becomes someone's income, and because people re-spend part of what they earn, that spending becomes another round of income, and the process repeats with each round smaller than the last.
Suppose the government spends on building a new MRT line. The construction firms and their workers receive that spending as income. They spend part of it on goods and services, which becomes income for those firms and their workers, who spend again. Each round is smaller than the one before, because some income leaks out as savings, taxes and imports, but the rounds add up to a total rise in national income that is a multiple of the original injection.
03The multiplier formula
The size of the multiplier depends on how much income leaks out at each round, captured in one formula.
k = 1 / MPW, where MPW = MPS + MPT + MPM
The marginal propensity to withdraw (MPW) is the fraction of each extra dollar of income that leaks out, the sum of the marginal propensities to save (MPS), to tax (MPT) and to import (MPM). The larger the leakages, the larger MPW, and the smaller the multiplier. This formula and the marginal propensities are H2 content; H1 students need only the awareness that an injection has a multiplied effect.
04A worked example
- The leakages. If households spend 0.8 of each extra dollar (MPC = 0.8), then 0.2 leaks out, so MPW = 0.2.
- The multiplier. k = 1 / 0.2 = 5.
- The outcome. A 100 million dollar injection raises national income by 5 times 100 million, which is 500 million.
In an open economy do not compute k from MPC alone. In Singapore the leakages include compulsory CPF savings and a high propensity to import, so MPW is larger and k is smaller than a closed economy of the same MPC would suggest.
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05What makes the multiplier large or small
The multiplier is large when leakages are small, and small when leakages are large, which is why the same injection raises national income far more in some economies than in others.
- A large multiplier needs low leakages: low savings, low taxes and low import dependence, so each round keeps most of the spending circulating at home.
- A small multiplier follows from high leakages. Singapore has a small multiplier because compulsory CPF savings and heavy import reliance drain each round.
06Common misconceptions
The multiplier is computed from the marginal propensity to withdraw, not from MPC alone. In an open economy with taxes, k = 1 / (MPS + MPT + MPM). Using 1 / (1 minus MPC) ignores taxes and imports and overstates the multiplier.
A second error is to deploy a mechanical k where the question is really about the relative size of an aggregate demand shift. Not every injection question is a multiplier question, and reading which one is being asked is part of the skill.
07Test yourself
- An economy has MPS = 0.1, MPT = 0.2 and MPM = 0.2. Calculate the multiplier, then the rise in income from a 200 million dollar injection.
- Explain why two economies with the same MPC can have different multipliers.
- Why does a high import dependence reduce the effectiveness of a fiscal injection?
08Questions students ask
It is the way an initial injection into the economy, such as government spending, ends up raising national income by more than the amount first spent. The money is received as income, part of it is re-spent, that becomes someone else's income, and so on through successive rounds, so the total rise is a multiple of the first injection.
The multiplier k = 1 / MPW, where MPW is the marginal propensity to withdraw, the fraction of each extra dollar of income that leaks out as savings, taxes and imports (MPW = MPS + MPT + MPM). If MPW is 0.2, then k = 5, so a 100 million dollar injection raises national income by 500 million. This formula is H2 content.
Because its leakages are large. Compulsory CPF savings raise the marginal propensity to save, and heavy reliance on imports raises the marginal propensity to import, so a large share of each round of spending leaks out of the domestic flow. The smaller multiplier is exactly why a given injection moves Singapore's GDP less than it would a low leakage economy, a point we develop fully in class.