The multiplier

The multiplier process

Suppose the government spends $10 m on a new hospital. Builders receive $10 m of income. They spend part of it (on food, cars, holidays) and save, pay tax or buy imports with the rest. The spending becomes income for others, who spend part again, and so on. Each round is smaller because of withdrawals. The total rise in national income is a multiple of the original injection.

Change in national income = multiplier x change in injection.

Marginal propensities

• MPC: the fraction of each extra $1 of income that is spent on domestic goods and services (consumed).
• MPS: fraction saved; MPT: fraction taken in tax; MPM: fraction spent on imports.
• MPW (marginal propensity to withdraw) = MPS + MPT + MPM.

In the full model, MPC (on domestic output) + MPW = 1.

Calculating it

Multiplier = 1 / (1 - MPC) = 1 / MPW.

The higher the MPC (the lower the withdrawals), the bigger the multiplier. An open economy with high taxes and lots of imports has a small multiplier.

Note: the multiplier is a number, not a percentage or money value. Pearson mark schemes have deducted a mark for writing a unit after it.

Why it matters

The multiplier means a shift in AD has a larger final effect on output and employment than the initial change in spending. It works in reverse too: a fall in exports or investment causes a bigger fall in national income. Governments need an estimate of the multiplier to judge how big a fiscal stimulus should be; in practice it is hard to measure, takes time to work through, and depends on confidence and spare capacity.

Worked example

MPC = 0.75. Investment rises by $20 bn. Find the multiplier and the final change in national income.

1. Multiplier = 1 / (1 - 0.75) = 1 / 0.25 = 4
2. Change in national income = 4 x 20 = 80

Answer: Multiplier = 4; national income rises by $80 bn

Check yourself

1. The MPC is 0.8. Calculate the multiplier.
   Show answer

   5. 1 / (1 - 0.8) = 1 / 0.2 = 5.

2. MPS = 0.1, MPT = 0.25 and MPM = 0.15. Calculate the multiplier.
   Show answer

   2. MPW = 0.1 + 0.25 + 0.15 = 0.5; multiplier = 1 / 0.5 = 2.

3. MPS = 0.4, MPT = 0.3 and MPM = 0.1. Calculate the multiplier, to 2 decimal places.
   Show answer

   1.25. MPW = 0.8; 1 / 0.8 = 1.25.

4. The multiplier is 2.5 and government spending rises by $8 bn. Find the final change in national income in $ bn.
   Show answer

   $20 bn. 2.5 x 8 = $20 bn.

5. National income needs to rise by $30 bn. The MPW is 0.4. How large an injection is needed, in $ bn?
   Show answer

   $12 bn. Multiplier = 1 / 0.4 = 2.5, so injection = 30 / 2.5 = $12 bn.

6. Exports fall by $6 bn and the MPC is 0.6. Find the change in national income in $ bn (negative for a fall).
   Show answer

   -15 bn. Multiplier = 1 / 0.4 = 2.5; change = 2.5 x -6 = -$15 bn.

7. Which economy is likely to have the smallest multiplier?
   • One with low taxes and few imports
   • One with a high MPC
   • One with high income tax rates and a high share of income spent on imports
   • One with a low MPS and low MPM
   Show answer

   One with high income tax rates and a high share of income spent on imports. High MPT and MPM mean a high MPW, so 1 / MPW is small.

8. A student calculates a multiplier and writes '2.5%'. Why is this marked down?
   • The answer should be in dollars
   • Multipliers are always less than 1
   • It should be written as a fraction
   • The multiplier is a ratio with no unit
   Show answer

   The multiplier is a ratio with no unit. It is a pure number: the ratio of the change in income to the change in injection.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics specification, Issue 2 (June 2018)
• Pearson Edexcel IAL Economics WEC12 Unit 2 mark scheme, January 2025

Last updated 8 November 2026. Spotted a mistake? Tell us.