Spending and tax multipliers, and the GDP change from your tax change, at other values of the MPC with your other settings.
MPC
Spending multiplier
Tax multiplier
Change in GDP
0.50
2.000
−1.000
100.0
0.60
2.500
−1.500
150.0
0.70
3.333
−2.333
233.3
0.75
4.000
−3.000
300.0
◀ yours
0.80
5.000
−4.000
400.0
0.90
10.000
−9.000
900.0
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What it calculates: Tax multiplier, Change in GDP, Spending multiplier, Balanced-budget multiplier.
Updated 22 September 2026 · Transparent assumptions
With an MPC of 0.75 the tax multiplier is −3, so a 100 tax cut raises output by 300
A tax cut raises disposable income by the amount of the cut, and households spend the MPC share of it: 75 of a 100 cut. That 75 becomes someone else’s income, and the usual multiplier rounds follow. The tax multiplier is therefore the spending multiplier applied to the first round’s MPC share: −MPC ÷ (1 − MPC) = −0.75 ÷ 0.25 = −3.
k_T = −MPC ÷ (1 − MPC)
The minus sign means taxes and GDP move in opposite directions: a 100 cut raises GDP by 300; a 100 increase lowers it by 300.
Worked example
MPC = 0.75, ΔT = −100
k_T = −0.75 ÷ 0.25 = −3
ΔY = −3 × (−100)
ΔY = +300
The tax multiplier is always one smaller in size, because the first round is partly saved
A dollar of government purchases is spent in full in the first round; a dollar of tax cut is only spent at the MPC rate, because households save part of it before anything enters the circular flow. With an MPC of 0.75, the spending multiplier is 1 ÷ 0.25 = 4 and the tax multiplier −3: exactly one smaller in size.
|k_T| = k_G − 1
That gap is the arithmetic behind a long-running policy argument: dollar for dollar, purchases move demand more than tax cuts in this model. Real-world comparisons are messier, as the evidence below shows.
Raise spending and taxes by 100 each and GDP still rises by 100
If the government raises purchases by 100 and pays for it with a 100 lump-sum tax, the budget balance is unchanged but GDP is not: spending adds 4 × 100 = 400 and the tax subtracts 3 × 100 = 300, a net rise of 100. The balanced-budget multiplier is 4 + (−3) = 1, a result usually credited to Trygve Haavelmo.
The result holds whatever the MPC in the simple model, because the tax multiplier is always one smaller than the spending multiplier. With income taxes and imports it falls below one; the complex model reports it as (1 − MPC) ÷ the leakage rate.
Balanced budget
ΔG = +100 → +400
ΔT = +100 → −300
ΔY = +100 (multiplier 1)
Add a 20% income tax and a 0.1 import share, and the tax multiplier shrinks from −3 to −1.5
Real economies leak spending through income tax and imports, and some courses also let investment and government spending rise with income. Collecting every share of extra income, the denominator becomes 1 − MPC(1 − t) − i − g + m: re-spending at home subtracts, leaking abroad adds. With MPC 0.75, t = 0.2, m = 0.1 and no induced investment or government spending, that is 1 − 0.6 + 0.1 = 0.5, so the tax multiplier is −0.75 ÷ 0.5 = −1.5 and a 100 cut raises GDP by 150.
k_T = −MPC ÷ (1 − MPC(1 − t) − i − g + m)
Signs matter here. Imports are a leak and enter with a plus; induced investment and government spending are re-spending and enter with a minus. If the re-spent shares outweigh the leaks, the denominator reaches zero and the model has no finite answer — the calculator says so rather than printing a negative multiplier.
Complex model
den = 1 − 0.75 × 0.8 + 0.1 = 0.5
k_T = −0.75 ÷ 0.5 = −1.5
ΔY = −1.5 × (−100) = +150
Romer and Romer estimate that a tax rise of 1% of GDP lowers output by almost 3% over three years
Measuring the real tax multiplier is hard, because governments change taxes in response to the economy. Christina and David Romer read the legislative record to separate tax changes made for reasons unrelated to current conditions, and found those changes strongly contractionary: an exogenous tax increase of 1% of GDP reduced real output by almost 3% within about three years.
That is larger than many estimates for spending multipliers and the reverse of what the simple model predicts, a reminder that the textbook formula captures one channel — spending out of disposable income — and leaves out incentives, expectations and monetary responses.
Transfers carry the tax multiplier with the opposite sign, and a temporary cut is spent less
A transfer payment is a negative tax: it raises disposable income without buying anything, so its multiplier is +MPC ÷ (1 − MPC), the same size as the tax multiplier. Transfers aimed at households with little savings tend to have larger effects, because those households spend more of each dollar.
Timing also matters. A cut people expect to be temporary changes their lifetime income little and is largely saved, lowering the effective MPC and the multiplier; if they expect higher future taxes to repay the borrowing, Ricardian equivalence says they may save all of it.
Frequently Asked Questions
What is the tax multiplier formula?
In the simple model, the tax multiplier is −MPC ÷ (1 − MPC), or −MPC ÷ MPS. With an MPC of 0.8 it is −4.
Why is the tax multiplier negative?
Because higher taxes reduce disposable income and spending, lowering GDP, while tax cuts raise it. The sign records that taxes and output move in opposite directions.
Why is the tax multiplier smaller than the spending multiplier?
Government purchases enter spending in full, but households save part of a tax cut before spending it. In the simple model the tax multiplier is exactly one smaller in size.
What is the complex tax multiplier?
A version with more leakages and induced spending: −MPC ÷ (1 − MPC(1 − t) − i − g + m), where t is the marginal tax rate, m the marginal propensity to import, and i and g induced investment and government spending.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Results are estimates for planning and analysis based on the figures you enter. They are not accounting, tax, or financial advice — verify with your own records and a qualified professional before making decisions.
Spending Multiplier vs Tax Multiplier: Why a Tax Cut Moves GDP Less
Why $100 of government spending raises GDP more than a $100 tax cut in the Keynesian model, the balanced-budget multiplier, and what taxes and imports change.
Published the simple tax multiplier −MPC ÷ MPS and a complex one with income tax and imports, with the GDP change from a tax change and the balanced-budget multiplier.
Added it to an automated formula suite with golden, independent, property, boundary and structural cases.
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