How Does the Keynesian Multiplier Work?
Fiscal policy
What you will learn
- An injection becomes income that is partly spent again.
- Apply the model to an original scenario and justify its limits.
Essential definitions
- Multiplier
- The ratio of the eventual change in national income to the initial autonomous injection.
- Marginal propensity to consume
- The fraction of additional income spent on consumption in the specified model.
- Marginal leakage
- The fraction of additional income withdrawn through saving, taxation or imports.
Follow the spending rounds
An autonomous injection is extra spending not caused by the current income increase. Suppose a firm receives a new 100-unit order and pays the income to workers and suppliers. If recipients spend 80% of extra income, the next round is 80, then 64, then 51.2. Each payment is income for another recipient.
The marginal propensity to consume, MPC, is the share of an additional income unit spent on consumption. With MPC = 0.8, the simple closed-economy multiplier is k = 1 ÷ (1 − MPC) = 5. The multiplier k has no currency unit; it compares the total income change with the initial spending change. This simple version assumes no taxes or imports.
Add the leakages
In an open economy with government, extra income also leaks into saving, taxation and imports. MPS, MPT and MPM are the marginal shares saved, taxed and spent on imports. For this formula, all must refer to the same extra-income base. Do not combine a consumption share of disposable income with tax shares of gross income without adjustment.
The multiplier is k = 1 ÷ (MPS + MPT + MPM). Larger combined leakages leave less for the next round of domestic purchases and reduce k. The income change is ΔY = k × ΔJ, where Δ means change, Y is income and J the autonomous injection. ΔY and ΔJ must use the same currency and period.
Calculate and interpret the result
With marginal leakages 0.20, 0.15 and 0.15, their sum is 0.50 and k = 2. An injection of 12 billion therefore generates a modelled income increase of 24 billion. To close a 30-billion shortfall, reverse the calculation: required injection = 30 ÷ 2 = 15 billion.
The multiplier diagram tracks successive spending or the total output response; it is not a promise of unlimited real growth. Stable propensities, spare capacity and no offsetting changes are essential assumptions. Near capacity, prices may rise instead. A tax cut is not an equal direct-purchase injection because recipients need not spend all of the initial saving.
Hypothetical worked application
- Marginal leakage = 0.20 + 0.15 + 0.15 = 0.50.
- k = 1/0.50 = 2.
- Change in income = 2 × 12 = 24 billion currency units.
A 12-billion autonomous injection produces 24 billion of additional income under the stated assumptions.
Spending rounds and the multiplier
MPS=0.2, MPT=0.15, MPM=0.15. Each round passes on 50% of extra income. k = 1/0.5 = 2; total ΔY = 40 billion from an initial 20 billion. The chart shows only the first nine rounds; the formula sums all rounds.
An autonomous injection becomes someone’s income. The share not saved, taxed or spent on imports becomes further domestic spending. Each round is smaller and the total converges to ΔY = ΔJ/(MPS + MPT + MPM).
How to draw it and model assumptions
- Label spending round horizontally and extra spending vertically.
- Plot the initial injection and each subsequent round.
- Distinguish a single round from the sum of all rounds.
Supplemental visualization: the guide requires multiplier calculation, not this chart. Constant marginal leakages, idle capacity, unchanged prices and no crowding out.
Apply and evaluate
- Stable propensities and spare capacity are essential; inflation and offsetting responses can lower the real-output gain.
Common misconceptions
- The multiplier is the total income change divided by the initial injection, not the injection plus that ratio.
Knowledge check
What happens to k when the marginal propensity to import rises?
Real-world application
Separating the cycle from policy decisions
November 2024: CBO’s report on automatic stabilizers compares US federal budget balances with and without its estimated cyclical effects, alongside actual or projected output gaps.
Model application: a recession can lower tax receipts and increase unemployment-related spending even without a new policy vote. Therefore, a larger observed deficit does not by itself measure a discretionary stimulus. The counterfactual depends on estimates of potential output and is uncertain.
CBO, Effects of automatic stabilizers on the federal budget: 2024 to 2034 ↗Historical evidence checked 9 October 2026. The model interpretation is an original teaching application.
What to remember
An injection becomes income that is partly spent again. Repeated domestic spending makes the total increase larger, while saving, taxes and imports shrink each successive round.
Completion is your own reflection on learning, not a test score. Syllabus references: 3.6.06, 3.6.07.
Sources and applications
Lessons in this section
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