The Spending & Tax Multipliers

You’ll be able to

Derive the spending multiplier from the marginal propensity to consume
Calculate the total change in GDP from an initial change in spending
Compare the spending multiplier with the smaller tax multiplier

Why spending multiplies

When someone spends a dollar, it becomes income to another person, who spends part of it, which becomes income to a third person, and so on. This chain reaction means an initial injection of spending produces a larger total change in GDP — the multiplier effect. How much each person re-spends depends on the marginal propensity to consume (MPC), the fraction of an extra dollar of income that is spent; the rest, the marginal propensity to save (MPS), leaks out. Since income is either spent or saved, MPC + MPS = 1.

The spending and tax multipliers

The spending multiplier equals 1 / (1 − MPC), or equivalently 1 / MPS. A change in government spending (or investment) is multiplied by this factor to find the total change in GDP. The tax multiplier is smaller in size and works in the opposite direction: a tax cut leaves people with more disposable income, but they save part of it, so only the spent portion enters the multiplier chain. The tax multiplier equals −MPC / (1 − MPC). Because the first round of a tax change is diluted by saving, an equal-sized spending change moves GDP more than a tax change.

The multipliers

Spending multiplier = 1 / (1 − MPC) = 1 / MPS · Tax multiplier = −MPC / (1 − MPC)

MPC + MPS = 1. Total ΔGDP = (multiplier) × (initial change). The tax multiplier is always smaller in absolute value than the spending multiplier.

Worked example

The MPC is 0.8. The government increases spending by $50 billion. Calculate the spending multiplier and the total change in real GDP. Then find the total change if instead the government had cut taxes by $50 billion.

1.Spending multiplier = 1 / (1 − MPC) = 1 / (1 − 0.8) = 1 / 0.2 = 5.
2.ΔGDP from spending = multiplier × ΔG = 5 × $50B = $250B increase.
3.Tax multiplier = −MPC / (1 − MPC) = −0.8 / 0.2 = −4.
4.A $50B tax cut is ΔT = −$50B, so ΔGDP = −4 × (−50) = $200B increase.

Answer: The spending multiplier is 5, so the $50B spending increase raises GDP by $250B. The $50B tax cut raises GDP by only $200B (tax multiplier −4), because households save part of the tax cut before spending begins.

Checkpoint

The marginal propensity to save in an economy is 0.25. If investment spending rises by $40 billion, what is the total change in real GDP?

Watch out

The tax multiplier is always smaller in absolute value than the spending multiplier and carries the opposite sign. A tax cut is a negative ΔT that raises GDP; a tax increase lowers it. Do not apply the spending multiplier to a tax change.

Checkpoint

Why does an equal-dollar increase in government spending raise GDP by more than a tax cut of the same size?

On the exam

Memorize both multiplier formulas and always compute MPS = 1 − MPC first. A frequent free-response task gives you the MPC and asks for the spending needed to close a specific output gap: divide the gap by the spending multiplier.

Answer the 2 checkpoints as you read.