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

This guide covers outcome 9.1.1 (the multiplier process) in section 9.1, The circular flow of income, of the Cambridge International AS & A Level Economics 9708 syllabus for examination in 2026, 2027 and 2028. Topic 9 is A Level content: the syllabus lists topics 1 to 6 as AS Level and topics 7 to 11 as A Level, and A Level questions on Papers 3 and 4 draw on it. Every country, firm and figure below is invented for illustration and is not real data. Money is in currency units (cu).

Start from the Cambridge A Level Economics hub or the printable checklist. After this guide, use the revision notes and the practice questions. Test yourself with the free diagnostics. Background reading: national income statistics and the circular flow and AD and AS analysis.

What this guide covers

Bullet in 9.1.1	What you must be able to do
Definition	Define the multiplier
Formulae	Calculate the multiplier in a closed and an open economy, with and without a government sector
Propensities	Calculate aps, mps, apc, mpc, apm, mpm, art and mrt
Income determination	Find national income using AD and the income approach, with the multiplier process
Change in AD	Calculate the effect of a change in AD on national income

The components of AD, the accelerator and output gaps are separate outcomes (9.1.2 and 9.1.3) and are not taught here.

The multiplier: definition and process

The multiplier is the ratio of the final change in national income to the initial change in injections (or in autonomous spending) that caused it. An injection is spending that enters the circular flow from outside the domestic household spending loop: investment, government spending and exports.

The reason it exceeds 1 is that one person’s spending is another person’s income. Take a closed economy with no government, where households spend 0.75 of each extra unit of income and save the rest. Firms receive an injection of 100 cu in new investment orders.

Round	New income	Of which spent (75%)	Cumulative income
1	100.00	75.00	100.00
2	75.00	56.25	175.00
3	56.25	42.19	231.25
4	42.19	31.64	273.44

The rounds go on, each smaller than the last, and the total converges on 100 x 1/(1 - 0.75) = 400 cu. The multiplier is 4. The process runs in reverse for a fall in injections, and it takes time: income does not reach the new level at once.

Average and marginal propensities

Average propensities relate a total to income at one level. Marginal propensities relate a change to the change in income that caused it.

Measure	Formula
apc, aps	C / Yd and S / Yd, where Yd is disposable income; apc + aps = 1
mpc, mps	change in C / change in Yd and change in S / change in Yd; mpc + mps = 1
apm, mpm	M / Y and change in M / change in Y
art, mrt	T / Y and change in T / change in Y

Here C is consumption, S is saving, M is imports, T is tax revenue and Y is national income.

Worked example 1. Households in Country A have this data (cu).

Yd	C	S
200	190	10
300	260	40
400	330	70

At Yd = 300: apc = 260/300 = 0.867 and aps = 40/300 = 0.133. From 200 to 300: mpc = (260 - 190)/(300 - 200) = 70/100 = 0.7 and mps = 30/100 = 0.3. The data fit C = 50 + 0.7Yd, with autonomous consumption of 50. Because of that fixed 50, the apc falls as income rises (0.95, 0.867, 0.825) while the mpc stays at 0.7.

Formulae for the multiplier

Every unit of extra income either is spent on domestic output or leaks out. The multiplier is the reciprocal of the share that leaks out:

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

The denominator is the marginal propensity to withdraw (mpw). A larger mpw means a smaller multiplier.

Which base are the propensities measured on? In the table above, mps, mrt and mpm are each a share of an extra unit of national income. Questions sometimes give mpc and mps on disposable income instead. Then convert: each extra unit of income is taxed at rate t, so only (1 - t) becomes disposable income. Saving per unit of national income is mps x (1 - t), and the multiplier is:

k = 1 / (1 - mpc(1 - t) + mpm)  =  1 / (mps(1 - t) + t + mpm)

Worked example 2. Country B has mps = 0.15, mrt = 0.20 and mpm = 0.15, each per unit of national income. mpw = 0.15 + 0.20 + 0.15 = 0.50, so k = 1/0.50 = 2. Government spending rises by 60 cu: change in Y = 2 x 60 = 120 cu.

Worked example 3 (disposable-income form). Country C has mpc = 0.8 on disposable income, a tax rate of 25% and mpm = 0.1. k = 1/(1 - 0.8 x 0.75 + 0.1) = 1/(1 - 0.6 + 0.1) = 1/0.5 = 2. Check through withdrawals: mps(1 - t) + t + mpm = 0.2 x 0.75 + 0.25 + 0.1 = 0.15 + 0.25 + 0.10 = 0.5, so k = 2. Both routes agree.

National income determination

There are two equivalent approaches.

AD approach. Equilibrium national income is where planned aggregate expenditure equals income: Y = AD = C + I + G + (X - M). On a diagram with income on the horizontal axis and planned expenditure on the vertical axis, the equilibrium is where the AD line cuts the 45-degree line. The AD line starts at the autonomous level of spending and slopes upward with a gradient equal to the marginal propensity to spend on domestic output (1 - mpw).

Income approach (injections equal withdrawals). Equilibrium is also where planned injections (I + G + X) equal planned withdrawals (S + T + M). If injections exceed withdrawals, income rises; if withdrawals exceed injections, income falls.

Worked example 4. Country D has these planned behaviours (cu):

C = 100 + 0.8Yd      I = 150      G = 200      X = 120
T = 0.25Y            M = 0.1Y     Yd = Y - T

AD approach:

Y = 100 + 0.8(Y - 0.25Y) + 150 + 200 + 120 - 0.1Y
Y = 570 + 0.6Y - 0.1Y = 570 + 0.5Y
0.5Y = 570, so Y = 1,140

Autonomous spending is 570 and mpw = 0.5, so k = 2 and Y = 2 x 570 = 1,140.

Income approach at Y = 1,140: Yd = 855; S = Yd - C = 855 - (100 + 684) = 71; T = 285; M = 114. Withdrawals = 71 + 285 + 114 = 470. Injections = 150 + 200 + 120 = 470. They match, so Y = 1,140 is equilibrium.

Check why other levels are not equilibrium:

Y	AD = 570 + 0.5Y	AD - Y	Result
900	1,020	+120	Stocks fall, output rises
1,140	1,140	0	Equilibrium
1,400	1,270	-130	Stocks build up, output falls

Equilibrium is not necessarily full employment. The income approach shows only where planned injections and withdrawals balance.

Effect of a change in AD on national income

Change in Y = k x change in autonomous spending. Only autonomous changes shift the AD line; a rise in Y itself moves along it.

Worked example 5 (Country D continued).

• Government spending rises by 40: change in Y = 2 x 40 = +80, so Y = 1,220.
• Exports fall by 30: change in Y = 2 x (-30) = -60, so Y = 1,080.
• Autonomous consumption rises by 25: change in Y = +50, so Y = 1,190.
• To raise income by 90, the required net injection is 90/2 = 45.

A change in a propensity changes the multiplier itself. Suppose the tax rate rises from 25% to 35%, with nothing else altered. k = 1/(1 - 0.8 x 0.65 + 0.1) = 1/0.58 = 1.724. Y = 570 x 1.724 = 982.8, a fall of 157.2 cu (13.8%). The AD line pivots to a flatter slope. Compare this with a change in autonomous spending, which shifts the line in parallel.

Limits of the multiplier. The figure from the formula is a prediction under assumptions. Evaluate it with these points:

• Spare capacity: if the economy is near full capacity, extra spending bids up prices more than output, so the real multiplier is smaller.
• Time lags: each round takes time, so the full effect may be spread over many months, and other changes may occur meanwhile.
• Crowding out: if government borrowing raises interest rates, private investment may fall.
• Stable propensities: the mpc, tax rate and mpm are assumed constant but may change with confidence, expectations or exchange rates.
• High leakages: a country that imports heavily or taxes heavily has a small multiplier, so a given injection achieves less.

Common errors

• Using 1/mpc instead of 1/(1 - mpc) or 1/mps.
• Leaving out a leakage that the question mentions, or adding one the economy lacks.
• Mixing disposable income and national income bases without converting.
• Finding apc from a change in C rather than from the level of C.
• Multiplying by the multiplier a total change in AD that includes induced spending. Apply it to the autonomous change only.
• Giving a change in Y without its sign or units.

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.