How the spending multiplier 1 ÷ (1 − MPC) and the resulting change in GDP grow as households spend a larger share of each extra dollar. Your initial change in spending is held fixed across the rows; the row matching your MPC is marked. Figures use the calculator’s own formulas.
MPC
MPS = 1 − MPC
Multiplier
Change in GDP
0.50
0.50
×2.00
$200B
0.60
0.40
×2.50
$250B
0.70
0.30
×3.33
$333B
0.80
0.20
×5.00
$500B
◀ your MPC (×5.00)
0.90
0.10
×10.00
$1,000B
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What it calculates: Spending Multiplier, Change in GDP, Marginal Propensity to Save.
An MPC of 0.8 means each round spends 80% of the last, and the series sums to 5
An injection of 100 becomes income for whoever received it. If they spend 80% of it, 80 becomes someone else’s income, who spends 64, and so on. The sum of that geometric series is 1/(1 − 0.8) = 5, so 100 of spending raises output by 500. The 20% not spent — the marginal propensity to save — is what eventually exhausts the series.
The multiplier is therefore entirely determined by what happens to money at each round. Raise the MPC to 0.9 and the multiplier doubles to 10; lower it to 0.5 and it falls to 2. Because the relationship is 1/(1 − MPC), it is extremely sensitive at the top of the range, which is also where estimating the MPC is hardest.
Tax, imports and saving all remove money from the circuit
The textbook multiplier assumes the only leakage is saving. Real economies leak in three places: income tax takes a share before it can be spent, imports send spending abroad, and saving removes the rest. The fuller expression divides by (1 − MPC(1 − t) + m), and each additional leak shrinks the multiplier substantially.
That is why empirical estimates are so much lower than the textbook figure. Studies of real fiscal stimulus typically find multipliers between 0.5 and 1.5, not 5. A small open economy with high import propensity leaks most of an injection abroad; a large closed economy retains far more. The number this page computes is the upper bound the simplest model allows, not a forecast.
Spare capacity and the interest-rate response decide it
Multipliers are largest when there is slack: unemployed workers and idle capacity mean extra demand raises output rather than prices. At full employment the same injection mostly raises prices, and the real multiplier approaches zero. This is the core reason stimulus timing matters more than stimulus size.
The monetary response matters just as much. If a central bank raises rates in response to fiscal expansion, higher borrowing costs crowd out private investment and offset part of the injection. At the zero lower bound, where rates cannot fall further and are unlikely to rise, estimated multipliers are substantially higher — which is why the same policy can be effective in one environment and ineffective in another.
One closed economy, no time, and a constant propensity to consume
The calculation is static: it gives the eventual total, with no indication of how long the rounds take. Real multiplier effects play out over quarters and years, and a stimulus arriving after a recession has ended does something quite different from one arriving during it.
It also treats the MPC as a single constant. In reality it varies sharply by income — lower-income households spend a much larger share of an extra pound than wealthy ones — which means the same total injection produces very different multipliers depending on who receives it. Targeting is often more consequential than the headline amount.
Frequently Asked Questions
What is the spending multiplier?
It is a number showing how much total GDP changes for each dollar of new spending. Because the recipients of that spending turn around and spend part of it, and their recipients do the same, an initial injection sets off successive rounds that add up to more than the original amount.
How do the MPC and MPS relate?
The marginal propensity to consume is the share of each extra dollar of income that gets spent, and the marginal propensity to save is the share that gets saved. Since a dollar is either spent or saved, MPC and MPS always add up to one, so MPS equals 1 minus MPC.
Why is a higher MPC associated with a larger multiplier?
When people spend a bigger fraction of each dollar they receive, less leaks out into saving at every round, so the money keeps circulating longer. The multiplier, 1 divided by (1 − MPC), grows as MPC approaches one, which is why high-spending economies show stronger multiplier effects.
What is the tax multiplier?
A tax change works through disposable income rather than spending directly, so its multiplier is smaller and has the opposite sign: −MPC/MPS. A tax cut raises income, of which only the MPC fraction is spent, making it less powerful dollar-for-dollar than direct government spending.
What are leakages and why do they matter?
Leakages are the parts of each dollar that do not get re-spent on domestic output: saving, taxes, and spending on imports. The more income that leaks away at each round, the smaller the multiplier, which is why the full-leakage multiplier in practice is well below the simple saving-only version.
Why are real-world multipliers smaller than this model suggests?
The basic formula counts only saving as a leakage and assumes idle resources. In reality taxes and imports drain additional spending each round, and as the economy nears capacity, extra demand pushes up prices rather than output, all of which shrink the realized multiplier below the textbook figure.
What is crowding out?
Crowding out happens when government spending financed by borrowing pushes interest rates up, discouraging private investment and consumption that are sensitive to rates. The private spending lost partly offsets the public spending added, reducing the net effect that the simple multiplier would predict.
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.
Published the calculator with its formula, worked example, assumptions, limitations and a bespoke guide, and added an automated formula test suite covering it.
Verified that the multiplier is the reciprocal of the marginal propensity to save, and that the two propensities always sum to one.
Accepted the MPS as well as the MPC, with the multiplier table built from whichever is known.
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