Cambridge International AS and A Level Economics: The multiplier and propensities (9708) – Revision Notes

These notes condense outcome 9.1.1 (the multiplier process) of the Cambridge International AS & A Level Economics 9708 syllabus for examination in 2026, 2027 and 2028. Topic 9 is A Level content (topics 7 to 11 are A Level; topics 1 to 6 are AS). Full explanations and longer worked examples are in the study guide. Practise on the practice questions, check your level with the free diagnostics, and tick off topics on the checklist. The Cambridge A Level Economics hub lists every resource. All figures here are invented.

Definitions

• Multiplier: the ratio of the final change in national income to the initial change in injections (or autonomous spending) that caused it.
• Injections: investment, government spending, exports. Withdrawals (leakages): saving, taxation, imports.
• Autonomous spending does not depend on income. Induced spending changes because income changes. The multiplier is applied to autonomous changes.
• Marginal propensity: change in a variable divided by the change in income. Average propensity: the variable divided by income at one level.

Propensities: formulae

Measure	Formula	Note
apc	C / Yd	apc + aps = 1
aps	S / Yd	can be negative at low income
mpc	change in C / change in Yd	mpc + mps = 1
mps	change in S / change in Yd
apm	M / Y
mpm	change in M / change in Y
art	T / Y
mrt	change in T / change in Y	equals art if tax is a flat percentage

Method for any propensity question:

1. Decide average (one row of data) or marginal (the difference between two rows).
2. Put the right total on top and the right income on the bottom (Yd for consumption and saving, Y for imports and tax).
3. Give a decimal or fraction, with no units, since it is a ratio.

Worked reminder. Country E: Y = 800, T = 160, M = 120. Y rises to 900, T = 190, M = 140.

• art at 800 = 160/800 = 0.20; art at 900 = 190/900 = 0.211.
• mrt = (190 - 160)/(900 - 800) = 30/100 = 0.30.
• apm at 800 = 120/800 = 0.15; mpm = 20/100 = 0.20. The art rose because mrt is above art: a progressive tax. The mpm exceeds the apm, so imports are growing faster than income.

Multiplier formulae

Economy	k =
Closed, no government	1/mps or 1/(1 - mpc)
Closed, with government	1/(mps + mrt)
Open, no government	1/(mps + mpm)
Open, with government	1/(mps + mrt + mpm)

• The denominator is the marginal propensity to withdraw, mpw.
• Change in Y = k x change in autonomous spending.
• If mpc is on disposable income and the tax rate is t: k = 1/(1 - mpc(1 - t) + mpm).

Method in steps.

1. Identify which leakages exist (government? foreign trade?).
2. Check the base: are propensities per unit of national income or of disposable income?
3. Add the withdrawals, then take the reciprocal.
4. Multiply the autonomous change by k. Keep the sign.

Worked reminders.

• Country A, closed, no government: mps = 0.2, so k = 1/0.2 = 5.
• Country G, open with government: mps = 0.10, mrt = 0.30, mpm = 0.20. mpw = 0.60, so k = 1/0.60 = 1.667. An investment injection of 90 raises Y by 90 x 1.667 = 150.
• Country H: mpc = 0.9 on disposable income, t = 0.2, mpm = 0.12. k = 1/(1 - 0.9 x 0.8 + 0.12) = 1/0.4 = 2.5. Check: 0.1 x 0.8 + 0.2 + 0.12 = 0.40.

National income determination

Approach	Equilibrium condition
AD (expenditure)	Y = AD = C + I + G + (X - M); AD line cuts the 45-degree line
Income (leakages and injections)	S + T + M = I + G + X

• Working formula: Y = autonomous spending x k, or Y = autonomous spending / (1 - slope of AD line).
• Slope of the AD line = marginal propensity to spend on domestic output = 1 - mpw.
• Above equilibrium: planned AD is less than output, stocks build up, output falls.
• Below equilibrium: planned AD exceeds output, stocks run down, output rises.
• A change in autonomous spending shifts the AD line in parallel. A change in mpc, mrt or mpm changes its slope and so the multiplier.

Worked reminder (Country J). C = 60 + 0.75Yd, I = 90, G = 110, X = 70, T = 0.2Y, M = 0.1Y.

• Autonomous spending = 60 + 90 + 110 + 70 = 330.
• Slope = 0.75 x 0.8 - 0.1 = 0.5, so mpw = 0.5 and k = 2.
• Y = 330 / 0.5 = 660.
• Check: Yd = 528, C = 60 + 396 = 456, S = 528 - 456 = 72, T = 132, M = 66. Withdrawals = 270 = injections (90 + 110 + 70). This is equilibrium.

Effect of a change in AD

• Change in Y = k x change in autonomous spending.
• Required injection for a target rise in Y = target change / k.
• For Country J, G rises by 20: change in Y = 2 x 20 = 40, so new Y = 700. If X falls by 15: change in Y = -30.
• The multiplier works downwards too.

Worked reminder: a change in the tax rate

Back to Country J, but the tax rate rises from 20% to 30% with C = 60 + 0.75Yd and M = 0.1Y unchanged.

• New slope of AD = 0.75 x 0.7 - 0.1 = 0.425, so mpw = 0.575.
• New k = 1/0.575 = 1.739. Autonomous spending is still 330.
• New Y = 330 / 0.575 = 573.9, a fall of 86.1 (13.0%) from 660.
• The fall comes from the lower multiplier, not from a shift in the AD line. Autonomous spending has not changed.

Reading a question

If the question says	Do this
“Calculate the multiplier”	Add the leakages that the economy has, then take the reciprocal
“Final change in national income”	Multiply the autonomous change by k
“Equilibrium national income”	Solve Y = AD, or set withdrawals equal to injections
“Average” and a single row of data	Divide the level by income
“Marginal” and two rows of data	Divide the change by the change in income
“Explain why the effect might be smaller”	Give a link to a leakage, capacity, time or crowding out

Must-know distinctions

• Average versus marginal: the apc can fall while the mpc is constant (when autonomous consumption is positive).
• Movement versus shift: induced spending moves along the AD line. Autonomous spending shifts it.
• Slope change versus shift: a tax-rate rise pivots AD flatter and lowers k. A government spending rise shifts it up.
• Closed versus open: adding imports or taxes adds to the denominator and cuts k.
• Predicted versus actual: the formula gives the full multiplier effect once all rounds are done. Real outcomes depend on spare capacity, time, crowding out and stability of propensities.

Evaluation chains

• High mpw (heavy imports or taxes): smaller k, so fiscal stimulus is less effective, but automatic stabilisers are stronger.
• Near full capacity: the extra AD raises prices, so the real multiplier is smaller than the formula.
• Time lags: the effect builds over many rounds.
• Crowding out: if borrowing raises interest rates, private investment may fall, offsetting some of the effect.

Quick self-test

1. State the multiplier formula for a closed economy with no government, in terms of mps.
2. mps = 0.25 in a closed economy with no government. Find k.
3. Find k for mps = 0.1, mrt = 0.25, mpm = 0.15.
4. An injection of 40 cu with k = 3.5. Find the change in Y.
5. At Yd = 500, C = 450. State the apc and aps.
6. Yd rises from 500 to 600 and C rises to 530. Find the mpc and mps.
7. Y = 1,200 and M = 180. Find the apm.
8. T rises from 300 to 350 as Y rises from 1,500 to 1,700. Find the mrt.
9. AD = 400 + 0.6Y. Find equilibrium Y.
10. Exports fall by 20 and k = 2.5. Find the change in Y.
11. The government wants Y to rise by 150 and k = 3. Find the injection needed.
12. Why does a higher tax rate reduce the multiplier?

Answers

1. k = 1/mps (equivalently 1/(1 - mpc)).
2. k = 1/0.25 = 4.
3. mpw = 0.50, so k = 2.
4. 40 x 3.5 = +140 cu.
5. apc = 450/500 = 0.9; aps = 0.1.
6. Change in C = 80 on a change in Yd of 100: mpc = 0.8, mps = 0.2.
7. 180/1,200 = 0.15.
8. 50/200 = 0.25.
9. Y = 400 + 0.6Y, so 0.4Y = 400 and Y = 1,000.
10. 2.5 x (-20) = -50.
11. 150/3 = 50.
12. A larger share of each extra unit of income is taken in tax, so less is available to spend. Each round of spending is smaller and the total change in income is smaller.

Where marks are usually lost

• Using 1/mpc rather than 1/(1 - mpc).
• Dropping a leakage the question mentions, such as mpm.
• Mixing up average and marginal: dividing the whole of C by the change in Yd.
• Applying k to a total change in AD that includes induced spending.
• Omitting the minus sign on a fall in injections.
• Writing a formula or result with no working, so a slip cannot earn credit.
• Treating the multiplier as certain, with no comment on capacity, time or crowding out.
• Stating that the economy is at full employment because it is in equilibrium.

Official syllabus

Cambridge International AS & A Level Economics 9708 syllabus for examination in 2026, 2027 and 2028, published by Cambridge University Press & Assessment, section 9.1.1.