What is the tax multiplier formula?

The tax multiplier is (-MPC)/(1 - MPC), where MPC is the marginal propensity to consume. With an MPC of 0.8 it equals -0.8/0.2 = -4, so a one-dollar tax cut raises GDP by four dollars.

Why is the tax multiplier negative?

Taxes and GDP move in opposite directions. A tax cut leaves households with more disposable income, so spending and GDP rise; a tax hike does the reverse. The negative sign captures that opposite-direction relationship.

How are the two multipliers related?

In size, the tax multiplier equals the spending multiplier times the MPC. With an MPC of 0.8, the spending multiplier is 5 and the tax multiplier is 5 × 0.8 = 4 (in magnitude). The tax cut simply loses the first full round of spending, so it is smaller by exactly that factor.

What is the balanced-budget multiplier?

If the government raises spending and taxes by the same amount, GDP rises by exactly that amount — the balanced-budget multiplier is 1. The larger spending multiplier and the smaller tax multiplier nearly cancel, leaving a net effect of one.

Does this hold in the real world?

It is a simplified model. Real multipliers are smaller because of leakages (saving, taxes, and imports) and crowding out, where government borrowing nudges up interest rates and dampens private investment. But the ranking usually holds: a dollar of spending moves GDP more than a dollar of tax cuts.

Why is the tax multiplier smaller than the spending multiplier?

Short answer: when the government spends a dollar directly, the whole dollar enters the economy right away. When it cuts taxes by a dollar, households save part of it and spend only a fraction. Less money starts the chain, so the tax multiplier is smaller.

First, the one number that drives everything: the MPC

The marginal propensity to consume (MPC) is the fraction of each extra dollar of income that households spend rather than save. An MPC of 0.8 means people spend 80 cents and save 20 cents of every additional dollar. The MPC sets how much of each new dollar gets passed along to the next person, and that is what powers any multiplier.

The two formulas, side by side

Spending multiplier: $\frac{1}{1 - M P C}$

Tax multiplier: $\frac{- M P C}{1 - M P C}$

The difference is the $M P C$ sitting in the top of the tax formula. A dollar of government spending is a full dollar of new demand on round one. A dollar of tax cut hands households an extra dollar, but they spend only $M P C$ of it and save the rest — so round one is only 80 cents of new demand, not a full dollar. Every later round is scaled down by the same shortfall.

Worked example (MPC = 0.8)

$Spending multiplier = 1/ (1 - 0.8) = 5$

A 100-dollar rise in government spending raises GDP by $5 \times 100 = 500$ dollars.

$Tax multiplier = - 0.8/0.2 = - 4$

A 100-dollar tax cut raises GDP by $4 \times 100 = 400$ dollars.

Same 100 dollars, but direct spending moves GDP by 500 while the tax cut moves it by 400. The missing 100 is the slice of the tax cut that households saved before it ever started circulating.

The clean rule that ties them together

In size, the tax multiplier is just the spending multiplier scaled by the MPC:

∣ Tax multiplier ∣ = Spending multiplier \times M P C = 5 \times 0.8 = 4

Because a tax cut loses exactly the first full round of spending, it always comes out smaller by the factor $M P C$ . That is the whole story in one line.

Common misconception

“A tax cut and an equal spending increase do the same thing to GDP.” They do not. The spending increase enters the economy in full, while the tax-cut dollar is partly saved before it ever circulates. Dollar for dollar, government spending lifts GDP more than a tax cut.

Frequently asked questions

What is the tax multiplier formula?: The tax multiplier is $\frac{- M P C}{1 - M P C}$ , where $M P C$ is the marginal propensity to consume. With an MPC of 0.8 it equals $- 0.8/0.2 = - 4$ , so a one-dollar tax cut raises GDP by four dollars.
Why is the tax multiplier smaller than the spending multiplier?: When the government spends a dollar, the full dollar enters the economy on the first round. When it cuts taxes by a dollar, households save part of it and spend only the MPC fraction, so the chain starts smaller. Less money begins circulating, so the final effect on GDP is smaller.
Why is the tax multiplier negative?: Taxes and GDP move in opposite directions. A tax cut leaves households with more disposable income, so spending and GDP rise; a tax hike does the reverse. The negative sign captures that opposite-direction relationship.
How are the two multipliers related?: In size, the tax multiplier equals the spending multiplier times the MPC. With an MPC of 0.8, the spending multiplier is 5 and the tax multiplier is $5 \times 0.8 = 4$ (in magnitude). The tax cut simply loses the first full round of spending, so it is smaller by exactly that factor.
What is the balanced-budget multiplier?: If the government raises spending and taxes by the same amount, GDP rises by exactly that amount — the balanced-budget multiplier is 1. The larger spending multiplier and the smaller tax multiplier nearly cancel, leaving a net effect of one.
Does this hold in the real world?: It is a simplified model. Real multipliers are smaller because of leakages (saving, taxes, and imports) and crowding out, where government borrowing nudges up interest rates and dampens private investment. But the ranking usually holds: a dollar of spending moves GDP more than a dollar of tax cuts.

Run the numbers yourself

Enter any MPC into Econ Academy's calculator to see the spending, tax, and balanced-budget multipliers and the effect on GDP.

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