The Multiplier Process (Cambridge International A-Level Economics)

Bridge from AS Level

• At AS Level, you established that an economy reaches equilibrium in the circular flow when injections = leakages (I + G + X = S + T + M)

• You also knew that any rise in injections would raise national income, but you were not required to calculate how much

• At A Level, you now quantify that change

  • A $1bn rise in investment does not raise national income by $1bn - it raises it by some multiple of $1bn, because the initial spending becomes someone else's income and is re-spent in successive rounds
  • The multiplier measures the size of that total change

What is the multiplier?

• The multiplier (k) is the ratio of the change in equilibrium national income to the initial change in autonomous expenditure that caused it

$k=\frac{\Delta Y}{\Delta J}$

• Where ΔY is the change in national income and ΔJ is the initial change in an injection (investment, government spending or exports)

  • A multiplier of 3 means that a $100m rise in government spending ultimately raises national income by $300m
  • The multiplier operates in both directions - a fall in injections causes a larger fall in national income (the reverse multiplier)
  • The multiplier is always greater than 1 in a functioning economy, because part of each round of income is re-spent

The intuition: rounds of spending

• Assume an economy where households spend 80% of any extra income (MPC = 0.8) and save the other 20% (MPS = 0.2). The government injects $100m of new spending

• Each round is smaller than the last because some income leaks out as savings
• The rounds continue until cumulative leakages equal the original injection ($100m)
• Final rise in national income = $500m, giving a multiplier of 5

The four pairs of propensities

• A propensity measures the proportion of income allocated to a particular use

  • An average propensity measures the proportion of total income allocated to a given use
  • A marginal propensity measures the proportion of any additional income allocated to that use

• You are required to calculate both the average and the marginal value for consumption, saving, imports and taxation:

  • Consumption (APC, MPC) - the proportion of income spent on goods and services
  • Saving (APS, MPS) - the proportion of income not spent, i.e. added to savings
  • Imports (APM, MPM) - the proportion of income spent on goods and services produced abroad
  • Taxation (ART, MRT) - the proportion of income paid to the government in tax

Key points about these propensities

• In any economy, all additional income is accounted for by one of these four uses, so the sum of the four marginal propensities always equals 1: MPC + MPS + MPM + MRT = 1

• Average and marginal values are not the same

  • APC tends to fall as income rises (richer households save a larger proportion), while MPC is the rate at which the next unit of income is spent

Worked Example

calculating the propensities

A household's income rises from $40,000 to $50,000. Its consumption rises from $32,000 to $38,000, savings rise from $4,000 to $6,000, imports rise from $3,000 to $4,000, and tax paid rises from $1,000 to $2,000.

Calculation	Working	Value
MPC	$\mathrm{MPC}=\frac{\Delta C}{\Delta Y}=\frac{6000}{10000}$	0.6
MPS	$\mathrm{MPS}=\frac{\Delta S}{\Delta Y}=\frac{2000}{10000}$	0.2
MPM	$\mathrm{MPM}=\frac{\Delta M}{\Delta Y}=\frac{1000}{10000}$	0.1
MRT	$MRT=\frac{\Delta T}{\Delta Y}=\frac{1000}{10000}$	0.1
APC (at new income)	$\mathrm{APC}=\frac{C}{Y}=\frac{38000}{50000}$	0.76
APS (at new income)	$\mathrm{APS}=\frac{S}{Y}=\frac{6000}{50000}$	0.12

Note that the marginal propensities sum to 1 (0.6 + 0.2 + 0.1 + 0.1 = 1), confirming all additional income has been accounted for

Formulae for the multiplier

• The multiplier takes a different form depending on how many sectors the economy contains. In every case, the formula is:

$\mathrm{k} = \frac{1}{The \text{marginal} \text{propensities} \text{to} withdraw}

\mathrm{k} = \frac{1}{( \text{MPS} + \text{MRT} + \text{MPM} )}$

• A withdrawal (leakage) is any income not passed on as consumption of domestic output - saving, tax and imports

• The more leakages present, the smaller the multiplier

  • Adding sectors always reduces k because each new leakage represents income lost from the domestic spending chain

Worked Example

multiplier in different economies

Given MPS = 0.2, MRT = 0.15, MPM = 0.15:

Economy	Calculation	Multiplier
Closed, no government	$k=\frac{1}{\mathrm{MPS}}=\frac{1}{0.2}$	5.00
Closed, with government	$\mathrm{k} = \frac{1}{( \text{MPS} + \text{MRT} )} \\ k = \frac{1}{( 0.2 + 0.15 )}$	2.86
Open, no government	$\mathrm{k} = \frac{1}{( \text{MPS} + \text{MRT} )} \\ k = \frac{1}{( 0.2 + 0.15 )}$	2.86
Open, with government	$\mathrm{k} = \frac{1}{( \text{MPS} + \text{MRT} + \text{MPM} )} \\ \mathrm{k} = \frac{1}{( 0.2 + 0.15 = 0.15 )}$	2.00

The open economy with government has the smallest multiplier because 50 cents of every additional dollar of income leaks out of the domestic circular flow

Factors that determine the size of the multiplier

Exam Hint The single most common error is confusing MPC with the multiplier itself. MPC is a propensity (a number between 0 and 1); the multiplier is 1 divided by the sum of withdrawal propensities. Always write out the formula in full before calculating.

For essay questions asking how a change in injections affects national income, the strongest answers explicitly name the multiplier process, state the relevant formula, and link the size of the multiplier to the economy's openness and tax regime. Writing "the multiplier effect will amplify the increase" without quantifying or qualifying will score for analysis but not for evaluation.

For evaluation, the two highest-value points are:

• the multiplier only raises real output if spare capacity exists - at full employment it raises prices instead, and
• small open economies have low multipliers because of high import leakage.

Supporting these with country-specific examples lifts answers into the top band