2.4.4a Multiplier process and marginal propensities
The Multiplier
Definition
Multiplier ratio: the ratio of the final change in national income to the initial change in injections that caused it.
Multiplier process: the sequence of spending rounds by which one person's spending becomes another's income, which is then partly re-spent.
- Because each round of spending becomes new income, the final change in income is larger than the injection that started it.
- Because the multiplier works in both directions, a fall in injections causes a larger eventual fall in income.
Analogy
- An injection is like a stone dropped in a pond, sending out ripples of spending.
- Each ripple is smaller than the last as income leaks into saving, tax and imports.
The Multiplier Process
- An injection first raises income for the group who receive it.
- They spend part of that income, which becomes income for others in the next round.
- Each round is smaller than the last because some income leaks out into saving, tax and imports.
- The rounds continue until the added spending fades away, leaving a total rise larger than the first injection.
Example
- The UK government spends on a new railway, paying construction workers.
- Those workers spend part of their wages in shops, whose staff then earn and spend in turn.
Marginal Propensities
Definition
Marginal propensity to consume (MPC): the fraction of extra income that households spend.
Marginal propensity to save (MPS): the fraction of extra income that is saved.
Marginal propensity to tax (MPT): the fraction of extra income taken in tax.
Marginal propensity to import (MPM): the fraction of extra income spent on imports.
- MPC keeps money flowing round the domestic economy, whereas MPS, MPT and MPM are all withdrawals that leak out of the flow.
- The four propensities sum to 1, so a higher MPC must mean lower total withdrawals and vice versa.
Key Idea
- The multiplier magnifies the effect of any change in injections on real output and employment.
- It works both ways, amplifying booms and deepening downturns.
Size of the Multiplier
- A higher MPC means more of each round is re-spent, giving a larger multiplier.
- MPS, MPT and MPM are withdrawals, so larger propensities to withdraw give a smaller multiplier.
- So the multiplier is larger where households spend a high share of extra income on domestic output.
Example
- In the 2008-09 financial crisis, a sharp fall in investment and confidence was multiplied downwards, deepening the fall in UK national income and employment.
- Because a large share of lost income would otherwise have been re-spent domestically, the initial contraction rippled into further rounds of reduced spending.
Exam technique
- Describe the multiplier as a sequence of spending rounds, not a one-off effect.
- Link a higher MPC or lower withdrawals to a larger multiplier when explaining its size.
Common Mistake
- Do not confuse the multiplier with the accelerator: the accelerator links investment to the rate of change of income, whereas the multiplier links spending rounds to a change in income.
- Do not treat the multiplier's size as fixed, as it depends on the marginal propensities.
Self review
- Define the multiplier ratio.
- Describe how the multiplier process passes spending through the economy.
- Why does the multiplier work in both directions?
- Name the four marginal propensities.
- How does a higher MPC affect the size of the multiplier?
2.4.4b Calculating the multiplier and its significance
The Multiplier Formula
Definition
Multiplier (k): the number by which a change in injections is multiplied to give the final change in national income.
Marginal propensity to withdraw (MPW): the fraction of extra income that leaks out of the flow, made up of saving, tax and imports.
- With no government or trade, the only leakage is saving, so the denominator is 1 − MPC.
- In a full economy, tax and imports are also leakages, so the denominator becomes the MPW.
- The two formulas agree because the fraction of extra income not spent on domestic output, 1 − MPC, is exactly what is withdrawn as MPW.
A Worked Example
Example
- Scenario: households spend 80% of extra income, so MPC = 0.8 and the rest leaks out.
A £10 billion rise in government spending then raises real GDP by £10 billion × 5 = £50 billion.
- Interpretation: each £1 injected ultimately adds £5 to national income, because it is re-spent round after round.
Example
- Scenario: now MPS = 0.1, MPT = 0.15 and MPM = 0.05, so leakages are higher.
A £10 billion injection then raises national income by about £10 billion × 3.33 ≈ £33 billion.
- Interpretation: higher leakages (MPW = 0.3 rather than 0.2) give a smaller multiplier, so the same injection has less effect.
Key Idea
- A larger multiplier means a bigger eventual change in income for a given injection.
- The size of the leakages sets the value of k.
Significance for AD
- A change in an injection shifts AD, and the multiplier scales up the final shift.
- A rise in investment, government spending or exports shifts AD right by the initial amount × the multiplier.
- Because it works both ways, a fall in an injection produces a larger leftward shift in AD.
Example
- If k = 3, a £5 billion rise in investment eventually shifts AD right by about £15 billion.
- The same multiplier means a £5 billion cut in investment shrinks income by about £15 billion.
Policy Implications
- A larger multiplier makes fiscal and other demand-side measures more powerful, while a smaller one weakens them.
- This is why the value of k matters when a government judges how large a stimulus needs to be.
Example
- During the Covid-19 recovery, governments used large infrastructure and support packages, relying on the multiplier to turn each pound of spending into a bigger rise in output.
- The effect was strongest where spare capacity was high and spending stayed in the domestic economy rather than leaking into imports.
How significant is the multiplier for policy?
- It holds because a large multiplier lets a modest injection produce a much bigger rise in output and employment, strengthening fiscal policy.
- But in an open economy with high MPT and MPM the multiplier is small, so the effect on real GDP is more modest than the headline injection suggests.
- On balance, the multiplier's significance depends on the size of the leakages and on spare capacity, since near full capacity extra AD raises prices rather than output.
Exam technique
- Add the propensities to find MPW, then divide 1 by it, or use 1 ÷ (1 − MPC).
- Multiply the initial injection by k to size the final shift in AD and income.
Common Mistake
- Do not divide by the MPC; the denominator is 1 − MPC or the MPW.
- Do not leave out tax or imports, as MPW = MPS + MPT + MPM.
Self review
- State the two formulas for the multiplier.
- What does MPW equal?
- How large is the multiplier if the MPW is 0.3?
- By how much does a £10 billion injection raise income when k is 3.33?
- Why does a larger multiplier matter for a shift in AD?
