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# Explaining and Calculating the Simple and Extended Multiplier

Level:
AS, A-Level, IB
Board:
AQA, Edexcel, OCR, IB, Eduqas, WJEC

Last updated 13 Dec 2022

Here are two short revision videos explaining the simple and extended multiplier formulae and going through some worked examples.

The multiplier is a number.

It measures the final change in national income that comes from an initial change in one of the components of aggregate demand.

### Multiplier Formula (Simple)

In a closed economy with no government sector, the multiplier shows the impact of a change in investment on national income. There is only one leakage from the circular flow.

Multiplier = 1 / marginal propensity to save

We know that the marginal propensity to consume and to save must equal 1 (unity)

Disposable income can be spent or saved•MPC + MPS = 1

Therefore, the multiplier formula can be written as:

Multiplier = 1 / (1-MPC)

Example:

In a closed economy with no government sector, the marginal propensity to save is 0.2.

What is the value of the multiplier?

The multiplier = 1 / marginal propensity to save (1/MPS)

Multiplier = 1 / 0.2 = 5

### Extended Multiplier

What is the formula for the multiplier in an open economy with a government sector?

Multiplier = 1 / marginal rate of withdrawal

In an open economy with a government sector, there are three withdrawals from the circular flow

• Savings
• Imports
• Taxation

The marginal rate of withdrawal sums together the rate of leakage from savings, imports and taxes

Multiplier = 1 / MPS + MPM + MRT

In an open economy with a government sector, the marginal propensity to import is 0.3, the marginal propensity to tax is 0.3 and the marginal propensity to save is 0.2.

What is the value of the multiplier?
Multiplier = 1 / marginal rate of withdrawal

Multiplier = 1 / sum of (0.3 + 0.3 + 0.2)

Multiplier = 1/ 0.8 = 1.25

### How Big is My Multiplier?

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