How the spending multiplier works
Suppose the government pays a contractor to build a bridge. The contractor's crew takes home the money and spends most of it — on groceries, rent, haircuts. The grocer, landlord, and barber now have new income too, and they spend most of theirs. Every round of spending is a fixed fraction of the one before — the marginal propensity to consume, or MPC — so the rounds shrink geometrically but never quite stop. The multiplier is what that infinite series adds up to. The idea was formalized by Richard Kahn in 1931 and put at the center of macroeconomics by Keynes's General Theory (1936); it is still how every intro course explains why a fiscal change moves GDP by more than its own size.
The multiplier formulas
k = 1 ÷ (1 − MPC)
Tax multiplier = −MPC ÷ (1 − MPC)
ΔGDP = k × ΔG
where MPC is the marginal propensity to consume as a decimal and ΔG the initial change in spending. Because MPC + MPS = 1, the spending multiplier can also be written1 ÷ MPS. The two multipliers always sum to exactly 1 — thebalanced-budget multiplier. The series only converges for an MPC below 100%: at 100% every dollar is respent in full forever and the total is unbounded.
Worked example
Take the standard problem: government spending rises by $100B in an economy where households spend 80% of each extra dollar of income (MPC = 0.8). Here is where the total comes from, round by round:
| Step | Amount |
|---|---|
| Round 1 — the government spends ΔGthe injection lands as income for contractors, workers, suppliers | $100B |
| Round 2 — recipients spend 80% of that income80% × $100B, which becomes someone else's income | $80B |
| Rounds 3–5 — respending keeps shrinking by the MPC$64B + $51.20B + $40.96B → $336.16B cumulative after five rounds | $336.16B |
| Multiplier k = 1 ÷ (1 − MPC)1 ÷ (1 − 0.8) = 5 — where the infinite series converges | 5× |
| = Total change in equilibrium GDPk × ΔG = 5 × $100B | $500B |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in your own MPC and fiscal change.
From the classroom model to real fiscal policy
The formula on this page is the closed-economy textbook case, and it is deliberately optimistic. In a real economy each round of respending leaks: part of every new dollar goes to taxes, part is spent on imports, and part is saved — all of which drop out of the domestic respending loop, shrinking the effective MPC and the multiplier with it. Central-bank responses and crowding out of private investment can offset more. That is why empirical estimates of fiscal multipliers are contested and typically come in well below the clean textbook value, and why the same stimulus can pack more punch in a deep recession than near full employment. Use the model for what it teaches best: the respending logic, and why spending and tax changes of equal size do not have equal effects.
Multiplier effects show up in nominal GDP first — use theGDP deflator calculatorto separate real growth from price changes, check what rising prices do to purchasing power with theinflation calculator, or stay on the micro side and measure how buyers respond to prices with theprice elasticity of demand calculator.
Frequently asked questions
What is the spending multiplier?
The spending multiplier is the ratio of the total change in GDP to the initial change in spending that caused it. When the government (or anyone) spends an extra dollar, that dollar becomes someone’s income; they spend part of it, creating income for someone else, and so on. Because each round is a fixed fraction (the MPC) of the last, the rounds form a geometric series that sums to 1 ÷ (1 − MPC). With an MPC of 0.8, the multiplier is 5: a $100B injection ultimately raises equilibrium GDP by $500B in the textbook model.
Why is the tax multiplier smaller — and negative?
A tax change never hits GDP directly; it changes households’ take-home income first, and only the consumed share of that income reaches spending. So the first round of a $100B tax cut is not $100B but MPC × $100B, and every later round shrinks from that smaller start. The result is −MPC ÷ (1 − MPC): one smaller in magnitude than the spending multiplier, and negative because a tax increase pulls spending down while a tax cut pushes it up.
What is the balanced-budget multiplier?
Raise government spending and taxes by the same amount and the two effects do not cancel. The spending side multiplies by 1 ÷ (1 − MPC) while the tax side multiplies by −MPC ÷ (1 − MPC), and their sum is exactly 1 for any MPC. So a $100B spending increase financed dollar-for-dollar by taxes still raises equilibrium GDP by $100B in this model — the government spends the whole first dollar, whereas taxed households would have saved part of it.
What is MPC vs MPS?
The marginal propensity to consume (MPC) is the fraction of each additional dollar of income that households spend; the marginal propensity to save (MPS) is the fraction they save. In the simple model every extra dollar is either spent or saved, so MPC + MPS = 1. The two are mirror images of the same behavior, which is why the multiplier can be written either as 1 ÷ (1 − MPC) or, equivalently, as 1 ÷ MPS: with an MPS of 0.2, the multiplier is 5.
Do real-world multipliers match the textbook number?
No — the formula here is the closed-economy textbook case, and it overstates what economists measure in practice. Real spending leaks out of the respending loop through taxes, imports, and saving at every round, and monetary policy or crowding out can offset part of the stimulus. Empirical estimates are contested and vary with conditions (multipliers tend to be larger in recessions), but most cluster well below the textbook value — often between roughly 0.5 and 2. Treat this calculator as a model for building intuition, not a forecast.
Sources
- OpenStax, Principles of Economics — Appendix D: The Expenditure-Output Model (the multiplier)
- Keynes, The General Theory of Employment, Interest and Money (1936) — Chapter 10, The Marginal Propensity to Consume and the Multiplier
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Disclaimer: This calculator is foreducation and illustration only. It implements the closed-economy textbook multiplier, which ignores taxes, imports, monetary-policy responses, and crowding out — real-world fiscal multipliers are contested and usually smaller. Results are a model calculation, not a forecast, and nothing here is economic, financial, or policy advice.