Principles of Macroeconomics / Unit 9 MAC 0828 worked example, 60 to 90 seconds
Spending Against an Equal Tax Change
The idea
Compare two policies of the same size in the course's economy, where the multiplier is 2.5 and the propensity to consume is 0.75. Raise government purchases by 100 billion. Alternatively, cut autonomous taxes by 100 billion. Work out what each does to equilibrium output, then put them together.
In practice
Government purchases enter expenditure directly, so the line shifts up by the full 100, and output rises by 2.5 times 100, which is 250. The tax cut reaches households as income, and they spend 0.75 of it, so the line shifts up by 75 and output rises by 2.5 times 75, which is 187.5. The spending increase moves output by more, and the ratio between them is the propensity to consume. Now do both a spending rise and an equal tax rise together: output changes by 250 minus 187.5, which is a rise of 62.5.
Where people slip
In the simplest model, with no income tax and no imports, that last calculation comes out at exactly the change in spending, and the balanced-budget multiplier is said to equal one. With an income tax in the economy it does not, as the 62.5 here shows. The result equals one in a special case, not in general.
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