The Multiplier Process (Cambridge (CIE) A Level Economics): Revision Note

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

$\mathrm{k}=\frac{∆\mathrm{Y}}{∆\mathrm{J}}$

• 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

Formulae for the multiplier

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

$$\begin{gathered} \mathrm{k}=\frac{1}{\mathrm{The}\mathrm{marginal}\mathrm{propensities}\mathrm{to}\mathrm{withdraw}} \\ \mathrm{k}=\frac{1}{\left(\mathrm{MPS}+\mathrm{MRT}+\mathrm{MPM}\right)} \end{gathered}$$

• 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

Factors that determine the size of the multiplier