CFA Level I Exam · Fiscal Policy

Fiscal Multiplier and Ricardian Equivalence Explained

Updated 7 October 2026

The fiscal multiplier shows how much GDP changes for each unit of a change in government spending. With a tax rate t and marginal propensity to consume MPC, it equals 1 ÷ [1 − MPC(1 − t)]. Ricardian equivalence argues that deficit-financed tax cuts do not raise demand, because people save to pay future taxes.

Understand Fiscal Multiplier and Ricardian Equivalence

A change in government spending does not stop at the first round. The government buys goods, and that spending becomes income for firms and workers. They spend part of it, which becomes someone else's income. Each round is smaller than the last. The total effect on GDP is larger than the original change. This is the fiscal multiplier.

How big the later rounds are depends on how much of each extra unit of income is spent. The marginal propensity to consume (MPC) is the share of extra disposable income that households spend. The marginal propensity to save (MPS) is 1 − MPC. Taxes reduce the rounds further, because part of each extra unit of income goes to the government before households can spend it.

In the CFA curriculum, income taxes at rate t cut disposable income to (1 − t) of income. So the spending out of each extra unit of income is MPC × (1 − t). A higher tax rate means a smaller multiplier. A higher MPC means a larger one.

A tax cut works through a different route. Households first receive the cut as disposable income, and only part of it (MPC) is spent. So a change in taxes has a smaller effect than the same size change in spending. The spending multiplier is larger than the tax multiplier in absolute size. If the government raises spending and lump-sum taxes by the same amount, GDP still rises. The balanced budget multiplier equals exactly 1 only when taxes are lump-sum. When an income tax rate applies, it is less than 1 but still positive.

Ricardian equivalence is a counter-argument. If the government cuts taxes and funds it by borrowing, taxpayers know the debt must be repaid with higher future taxes. Rational households save the tax cut to pay those future taxes. Private saving rises by the amount of the deficit, so demand does not change. The theory holds only under strict conditions, such as rational forward-looking people and no borrowing constraints. Most economists doubt it fully holds in practice.

Key formulas to remember

Marginal propensity to save: MPS = 1 − MPC; MPC is the share of extra disposable income that is spent.
Spending multiplier (with income tax): Fiscal multiplier = 1 ÷ [1 − MPC(1 − t)]; t is the income tax rate. Set t = 0 to get 1 ÷ (1 − MPC) = 1 ÷ MPS.
Change in GDP from a change in government spending: ΔGDP = ΔG × 1 ÷ [1 − MPC(1 − t)]; Use the same sign as the spending change.
Tax multiplier effect (lump-sum tax change ΔT, in an economy with an income tax rate t): ΔGDP = −ΔT × MPC ÷ [1 − MPC(1 − t)]. When t = 0 (lump-sum taxes only): ΔGDP = −ΔT × MPC ÷ (1 − MPC); ΔT is a lump-sum change in taxes. A tax cut raises GDP. The tax effect is smaller than the spending effect, because only MPC of the change is spent in the first round.
Balanced budget multiplier: ΔG = ΔT (ΔT a lump-sum tax change) gives ΔGDP = ΔG × (1 − MPC) ÷ [1 − MPC(1 − t)]; With t = 0 (lump-sum taxes) this equals 1, so GDP rises by the same amount as the equal spending and tax change. With t > 0 and a lump-sum ΔT, the result is less than 1.
Ricardian equivalence: Deficit-financed tax cut → private saving rises by the cut → no change in aggregate demand; Holds only if households are rational, forward-looking and not borrowing constrained.

How to solve Fiscal Multiplier and Ricardian Equivalence questions

Use this method for any multiplier or Ricardian equivalence question.

1Identify what changes: government spending, taxes, or both.
2Write down MPC. If the question gives MPS, compute MPC = 1 − MPS.
3Check whether an income tax rate t is given. If yes, compute MPC × (1 − t). If no, use t = 0.
4Compute the spending multiplier = 1 ÷ [1 − MPC(1 − t)].
5For a lump-sum tax change, multiply the spending multiplier by MPC and flip the sign (a tax cut raises GDP).
6For equal spending and tax changes, add the spending effect and the tax effect, or use the balanced budget form.
7Multiply the multiplier by the size of the change to get ΔGDP. Check that the sign makes sense.
8If the question asks about Ricardian equivalence, say whether households save the tax cut and whether demand changes.

Quickest way: Three-line multiplier calculation

When to use it: When a question gives MPC or MPS, possibly a tax rate, and asks for the multiplier or the GDP change.

Compute the leakage term: 1 − MPC(1 − t).
Take the reciprocal. On a BA II Plus: enter MPC × (1 − t), press +/−, add 1, then press 1/x. On an HP 12C: compute the same value, then press 1/x.
Multiply by ΔG. For a lump-sum tax change, multiply by MPC as well and flip the sign.
Sanity check: the multiplier is at least 1, and when t > 0 it is smaller than 1 ÷ MPS.

Common mistakes in Fiscal Multiplier and Ricardian Equivalence

Using 1 ÷ MPC instead of 1 ÷ (1 − MPC).
Students mix up the multiplier with the reciprocal of consumption.
Fix: The denominator is the leakage per round. With no tax it is MPS = 1 − MPC.
Ignoring the tax rate or applying it to MPC incorrectly, such as MPC − t.
The formula is memorised without understanding it.
Fix: Taxes reduce income first, then households spend MPC of what is left. So use MPC × (1 − t).
Treating the tax multiplier as equal to the spending multiplier.
Both are called multipliers.
Fix: A tax change starts with MPC of the change, so its effect is the spending multiplier × MPC, with the opposite sign.
Saying the balanced budget multiplier is zero.
The spending and tax changes seem to cancel.
Fix: The spending change has a larger effect than the tax change, so GDP rises. With lump-sum taxes the multiplier is 1.
Claiming that Ricardian equivalence always holds or that it means deficits are harmless.
The argument is remembered as a conclusion, not as a theory with assumptions.
Fix: State the conditions: rational, forward-looking households and no borrowing constraints. Under those, a deficit-financed tax cut leaves demand unchanged.

Worked examples

Example 1

An economy has MPC = 0.80 and an income tax rate of 25%. The government raises spending by $10 billion. What is the change in GDP?

Show the solution

MPC × (1 − t) = 0.80 × 0.75 = 0.60.
Multiplier = 1 ÷ (1 − 0.60) = 1 ÷ 0.40 = 2.5.
ΔGDP = 2.5 × $10 billion = $25 billion.

Answer: GDP rises by $25 billion.

Example 2

An economy has MPC = 0.75 and no income tax. The government cuts lump-sum taxes by $8 billion, financed by government borrowing. What is the change in GDP under the standard multiplier? What is the change in GDP under Ricardian equivalence?

Show the solution

Spending multiplier = 1 ÷ (1 − 0.75) = 4.
Tax multiplier effect = MPC × 4 = 0.75 × 4 = 3.
Standard multiplier: ΔGDP = 3 × $8 billion = $24 billion.
Because the cut is financed by borrowing, Ricardian equivalence can apply. If it holds fully, households expect higher future taxes to repay the debt, save the whole cut, and spend none of it. Demand is unchanged, so ΔGDP = $0.

Answer: Under the standard multiplier, GDP rises by $24 billion. If Ricardian equivalence holds fully, the change in GDP is zero.

Exam tips

Read the question for a tax rate. Many wrong answers come from using 1 ÷ MPS when t is given.
If the question gives MPS, convert to MPC before you apply the tax rate.
For a tax change, always include MPC and the sign. A tax cut raises GDP.
Options are listed smallest to largest. The with-tax multiplier is always smaller than the no-tax multiplier, so you can often remove one option fast.
For Ricardian equivalence, look for the answer that says households save the tax cut because they expect higher future taxes.

Practice questions from Fiscal Policy

Fiscal Multiplier and Ricardian Equivalence: frequently asked questions

What is the fiscal multiplier formula in CFA Level I?

With an income tax rate t, the multiplier is 1 ÷ [1 − MPC(1 − t)]. If there is no income tax, it reduces to 1 ÷ (1 − MPC). Multiply it by the change in government spending to get the change in GDP.

How do you calculate the fiscal multiplier with a tax rate?

First compute MPC × (1 − t). Subtract it from 1 and take the reciprocal. For MPC = 0.8 and t = 0.25, the result is 1 ÷ (1 − 0.6) = 2.5.

What is the balanced budget multiplier?

It is the effect on GDP when government spending and taxes rise by the same amount. Because spending has a bigger effect than the tax change, GDP still rises. With lump-sum taxes the multiplier equals 1.

What does Ricardian equivalence say?

It says a tax cut financed by borrowing does not raise aggregate demand. Households expect future taxes to repay the debt, so they save the cut. It depends on rational, forward-looking households without borrowing constraints.