How this instrument works
The Keynesian spending multiplier answers a narrow question: if MPC — the share of an extra dollar of income a household spends rather than saves — holds steady at some level, how many total dollars of activity does one new dollar of spending eventually generate as it changes hands? The idea traces to Richard Kahn's 1931 'employment multiplier' and was folded into John Maynard Keynes's 1936 General Theory as the mechanism behind fiscal stimulus arguments. This instrument treats MPC as a given assumption you supply — a figure pulled from a textbook problem, a published estimate, or a policy debate — rather than something it measures from a spending and income change itself.
The formula's shape comes from summing an infinite geometric series. The first dollar spent becomes someone else's income; that person spends MPC of it, the next recipient spends MPC of that smaller amount, and so on. Add the whole chain and the total collapses to 1 ⁄ (1 − MPC) — a clean result because a geometric series with ratio MPC sums exactly that way once MPC sits strictly between 0 and 1. Near MPC = 0, almost nothing gets re-spent and the result sits close to 1; push MPC toward 100% and the denominator shrinks toward zero, so the output climbs without any upper bound.
That climb is a mathematical property of the model, not evidence that a high MPC guarantees a large real economic payoff. This version of the formula assumes a closed system with no taxes, no imports, and no leakage besides the saved share of each round — assumptions that published estimates of actual fiscal multipliers, which typically land well below this simple output even for MPCs near 80% or 90%, are built to relax. A policy analyst comparing a textbook figure against a modeled stimulus number, an instructor illustrating why the simple chain overstates real spillovers, and a forecaster stress-testing how sensitive a projection is near the 100% edge case all reach for this ratio directly, distinct from someone still trying to measure MPC itself from raw spending and income data.
- Enter the assumed share of each extra dollar spent into "Marginal propensity to consume, %" — for example, 80 for an MPC of 80%.
- Read "Spending (Keynesian) multiplier" — the total dollars of activity that figure implies for every $1 of new spending.
- Raise the percentage toward 100 to watch the reading climb sharply, since the formula's denominator is shrinking toward zero.
- Lower the percentage to watch the reading fall toward 1, the floor reached only as the input approaches 0.
- Compare the output against a published fiscal-multiplier estimate for the same scenario to see how far the leakages this formula excludes pull the real figure down.
Worked example — an MPC of 80%
Set "Marginal propensity to consume, %" to 80, describing a population that spends 80 cents of every additional dollar of income. The formula returns multiplier = 1 ⁄ (1 − 0.8) = 5.0 exactly — the case this page is built to reproduce. Trace the chain by hand: a $1 injection becomes $0.80 of new spending in the first round, $0.64 in the second, $0.512 in the third, and so on; sum the whole infinite chain and it totals $5.00, matching the formula's output to the cent.
Nudge the input and the sensitivity near the top of the range shows up fast: an MPC of 90% pushes the reading to 10.0, and 95% pushes it to 20.0, even though the underlying spending habit barely changed. That steepness is exactly why economists publishing real fiscal-multiplier estimates for stimulus packages rarely quote a number built from MPC alone — a modeled figure that also accounts for tax withholding, imported goods, and interest-rate responses typically comes in well under 2, regardless of how high the underlying MPC assumption runs.
Questions
Why does the multiplier grow so fast as MPC nears 100%?
Because the formula divides by (1 − MPC), and that denominator is shrinking toward zero. At MPC = 90% the result is 10; at 99% it is 100. The growth is a property of dividing by a number approaching zero, not a sign the underlying economy is becoming ten or a hundred times more responsive — small changes in an already-high MPC swing the ratio disproportionately.
Does this match the multiplier economists cite for a stimulus package?
Rarely, and usually not closely. This formula assumes a closed system where the only leakage is the saved share of each round; real fiscal-multiplier estimates also subtract taxes withheld, spending that goes toward imports, and any offsetting rise in interest rates, so published estimates for government spending commonly sit between roughly 0.5 and 2 even when the underlying MPC assumption is 80% or higher.
Where does the 1 ⁄ (1 − MPC) formula come from?
It sums an infinite geometric series. Each dollar spent becomes someone else's income, that person spends MPC of it, the next recipient spends MPC of that amount, and the pattern repeats; the sum of that shrinking sequence reduces algebraically to 1 divided by (1 − MPC). Richard Kahn described the mechanism in 1931 and Keynes built it into the General Theory in 1936.
What MPC figure should I actually enter?
This instrument does not estimate MPC for you — enter whatever figure the scenario calls for: a textbook assumption, a published research estimate for a specific income group, or a value you are stress-testing. A companion tool that derives MPC from an observed change in spending and income is the right instrument if you need to measure the figure first rather than assume it.
Why won't the calculator accept an MPC of 100 or more?
At MPC = 100% the denominator (1 − MPC) hits zero and the ratio is mathematically undefined — an infinite chain that never shrinks. The instrument requires a value below 100% so the geometric series actually converges to a finite sum; economically, an MPC of 100% would mean a household saves nothing at all from any extra dollar, an edge case models avoid for exactly this reason.
Can a small MPC change meaningfully shift the multiplier?
Yes, especially at high MPC levels. Moving MPC from 80% to 90% lifts the reading from 5.0 to 10.0 — a ten-percentage-point shift in the input doubles the output. The same ten-point move near the bottom of the range, say from 20% to 30%, only lifts the reading from 1.25 to about 1.43. The formula's sensitivity is concentrated entirely near its upper edge.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.