Spending Multiplier Calculator
Turn the marginal propensity to consume into the spending multiplier and the total change in GDP it sets off.
Change in GDP: $500.00 from a $100.00 injection · Tax multiplier: -4 · MPS = 0.2
The spending multiplier is k = 1 ÷ (1 − MPC), where MPC is the marginal propensity to consume. With an MPC of 0.8, the multiplier is 1 ÷ 0.2 = 5, so a $100 injection of new spending ripples through the economy to raise GDP by about $500 as each dollar is re-spent.
What the spending multiplier is
The spending (expenditure) multiplier measures how much total output rises for every dollar of new spending injected into the economy. When the government, a business, or a household spends an extra dollar, the person who receives it spends part of it, the next person spends part of that, and so on. The marginal propensity to consume (MPC) — the fraction of each new dollar that gets spent rather than saved — controls how far that chain reaches. A larger MPC means more of each dollar keeps circulating, so the multiplier is larger.
MPC is the marginal propensity to consume; MPS = 1 − MPC is the marginal propensity to save. Change in GDP = k × initial change in spending.
Worked example
The government spends an extra $100 in an economy where households consume 80% of each new dollar (MPC = 0.8).
- 1 Find the marginal propensity to save. MPS = 1 − MPC = 1 − 0.8 = 0.2 — the fraction of each dollar that is saved.
- 2 Divide 1 by the MPS. k = 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5. This is the spending multiplier.
- 3 Multiply by the initial spending change. ΔGDP = k × $100 = 5 × $100 = $500 — the total rise in output.
- 4 Compare the tax multiplier. Tax multiplier = −MPC ÷ (1 − MPC) = −0.8 ÷ 0.2 = −4, smaller in size and negative.
How the MPC changes the multipliers
As the marginal propensity to consume rises, more of each dollar is re-spent, so both the spending multiplier and the tax multiplier grow in size.
| MPC | MPS (1 − MPC) | Spending multiplier (k) | Tax multiplier |
|---|---|---|---|
| 0.50 | 0.50 | 2 | −1 |
| 0.75 | 0.25 | 4 | −3 |
| 0.80 | 0.20 | 5 | −4 |
| 0.90 | 0.10 | 10 | −9 |
Why spending ripples through the economy
MPC and MPS always add to 1. Every extra dollar of income is either spent or saved, so MPC + MPS = 1. Because the multiplier is 1 ÷ MPS, a smaller propensity to save leaves more money circulating and produces a larger multiplier — that is why the effect balloons as the MPC approaches 1.
The tax multiplier is smaller and negative. A tax change works one step removed: the first dollar of a tax cut is not spending itself — only the MPC share of it gets spent. So the tax multiplier is −MPC ÷ (1 − MPC), always smaller in magnitude than the spending multiplier and opposite in sign, since a tax cut raises spending while a tax rise lowers it.
It assumes a simple closed model. This basic multiplier ignores taxes that rise with income, imports that leak spending abroad, and interest-rate or price responses that can offset the effect. Those leakages shrink the real-world multiplier, so treat these figures as the textbook upper bound rather than a precise forecast.