AP® Macroeconomics · Unit 3 · Topic 3.2
The Tax Multiplier
The tax multiplier measures how much real GDP changes from a change in taxes, equal to -MPC/(1-MPC). It is smaller in absolute value than the spending multiplier because a tax cut leaks into saving before any of it gets spent.
When the government spends 100 billion directly, every one of those dollars enters the economy as new spending in round one. A tax cut works differently. If households get 100 billion back, they do not spend all of it. Some fraction, the marginal propensity to save, gets saved immediately, and only the MPC share gets spent in that first round. Everything after that first round then multiplies the same way spending does, through the standard 1/(1-MPC) chain. That one missing first round is the whole story of why tax cuts punch below their weight compared to equal-sized spending increases.
This is why the tax multiplier formula is -MPC/(1-MPC) rather than -1/(1-MPC). The negative sign tells you taxes and GDP move in opposite directions: a tax cut raises GDP, a tax hike lowers it. The MPC on top scales down the whole effect, since the first round is diluted by saving. Compare the two formulas side by side and the spending multiplier is always larger in absolute value, for any MPC between 0 and 1.
This matters directly for fiscal policy design. A government trying to close a recessionary gap gets more output per dollar from spending than from tax cuts, so it needs a bigger tax cut to hit the same GDP target. It also explains the balanced budget multiplier: when government raises spending and taxes by the same amount, the spending effect dominates because it enters in full while the tax effect is diluted, so output still rises by exactly the amount of that equal change, a multiplier of 1.
Key terms
- Tax multiplier
- The ratio of change in real GDP to the change in taxes that caused it, equal to -MPC/(1-MPC).
- Marginal propensity to consume (MPC)
- The fraction of each extra dollar of income a household spends rather than saves.
- Spending multiplier
- The ratio of change in real GDP to an initial change in government or autonomous spending, equal to 1/(1-MPC).
- Balanced budget multiplier
- The net effect on GDP of raising government spending and taxes by the same amount, which equals 1.
Watch it explained
- How it worksHow does the first round of a tax cut leak into saving before any spending happens?
- Worked exampleFind the change in GDP produced by a 150 billion tax cut when the MPC is 0.8.
- Common mistakeWhy isn't the tax multiplier simply the negative of the spending multiplier?
- Ties togetherHow does a balanced budget change in spending and taxes still move real output?
Check yourself
End of topic.