The Multiplier Effect

The multiplier is one of the most important and most frequently examined concepts in A-Level economics. It explains why changes in injections (investment, government spending, or exports) lead to a larger change in national income. The concept was originally developed by Richard Kahn (1931) and was then integrated into macroeconomic theory by John Maynard Keynes (1936) in The General Theory of Employment, Interest, and Money.

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The Basic Idea

When an injection of spending enters the circular flow, it does not simply add to national income once. The initial spending generates income for those who receive it. They then spend a proportion of this income (determined by the marginal propensity to consume), which becomes income for others, who also spend a proportion, and so on. Each round of spending is smaller than the last, but the cumulative effect is a change in national income that is larger than the initial injection.

A Numerical Example

Suppose the government increases spending by £100 million, and the MPC is 0.8 (people spend 80% of additional income):

Round	Additional Spending	Cumulative Increase in National Income
1	£100m (initial injection)	£100m
2	£80m (= £100m × 0.8)	£180m
3	£64m (= £80m × 0.8)	£244m
4	£51.2m	£295.2m
5	£40.96m	£336.16m
...	...	...
Total	—	£500m

The initial £100m injection has generated a total increase of £500m in national income — a multiplier of 5.

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The Multiplier Formula

Simple Multiplier (Closed Economy, No Government)

k = 1 / (1 − MPC)

Or equivalently:

k = 1 / MPS

Where:

• k = the multiplier
• MPC = marginal propensity to consume
• MPS = marginal propensity to save (= 1 − MPC)

Examples

MPC	MPS	Multiplier (k)
0.5	0.5	2
0.6	0.4	2.5
0.75	0.25	4
0.8	0.2	5
0.9	0.1	10

The higher the MPC, the larger the multiplier — because more of each round of income is re-spent.

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The Open Economy Multiplier (With Government and Trade)

In an open economy with taxation and imports, the multiplier must account for all withdrawals:

k = 1 / (1 − MPC + MPT + MPM)

Or equivalently:

k = 1 / (MPS + MPT + MPM)

Where:

• MPT = marginal propensity to tax (the fraction of additional income taken in taxation)
• MPM = marginal propensity to import

This is sometimes written as:

k = 1 / MPW

Where MPW = marginal propensity to withdraw = MPS + MPT + MPM

Realistic UK Example

Estimated UK values:

• MPC ≈ 0.35 (marginal propensity to consume domestically from gross income)
• MPS ≈ 0.10
• MPT ≈ 0.30 (including income tax, NI, VAT)
• MPM ≈ 0.25

Note that MPC + MPS + MPT + MPM = 1 (every pound of additional income is either spent domestically, saved, taxed, or spent on imports).

k = 1 / (MPS + MPT + MPM) = 1 / (0.10 + 0.30 + 0.25) = 1 / 0.65 ≈ 1.54

This is much smaller than the simple multiplier would suggest, because taxation and imports are significant withdrawals in the UK economy.

Exam Tip: Always use the open economy multiplier in your analysis — the simple 1/(1−MPC) formula is unrealistic for the UK. Examiners reward candidates who recognise that taxation and imports significantly reduce the multiplier's size. A realistic UK multiplier is approximately 1.3 to 1.6, not the 4 or 5 that the simple formula might suggest.

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Derivation of the Multiplier

For students who want to understand the mathematical derivation:

The total change in national income (ΔY) from an initial injection (ΔJ) is an infinite geometric series:

ΔY = ΔJ + ΔJ(MPC) + ΔJ(MPC)² + ΔJ(MPC)³ + ...

ΔY = ΔJ × [1 + MPC + MPC² + MPC³ + ...]

The sum of this infinite geometric series (where 0 < MPC < 1) is:

ΔY = ΔJ × 1/(1 − MPC)

Therefore the multiplier k = 1/(1 − MPC)

In the open economy version, we replace MPC with MPC net of all withdrawals, giving:

k = 1 / (1 − MPC + MPT + MPM)

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The Multiplier Process: Step by Step

To illustrate the process clearly:

1. Initial injection: Government spends £1 billion on new hospital construction
2. Round 1: Construction workers and suppliers receive £1bn in income
3. Withdrawals: A portion is saved (MPS), taxed (MPT), and spent on imports (MPM)
4. Round 2: The remaining income is spent domestically — creating income for shopkeepers, service providers, etc.
5. Further rounds: Each successive round generates smaller amounts of additional income
6. Final effect: National income rises by £1bn × k

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The Negative Multiplier

The multiplier works in both directions: