ποΈ Spending Multiplier Calculator
How one dollar of spending ripples through the economy.
Spending multiplier
Estimates for planning only, not financial advice.
When the marginal propensity to consume is 0.8, the spending multiplier is 5: every $1 of new spending eventually lifts GDP by about $5. A $100 billion stimulus package then means roughly $500 billion of total economic activity, as each round of spending becomes someone else's income, which gets partly spent again.
How to Use This Calculator
Enter the marginal propensity to consume, the share of each extra dollar of income that gets spent rather than saved, and the size of the spending change in billions. The calculator returns the multiplier and the total GDP effect, plus the first three rounds of the spending chain so you can see the ripple.
Enter MPC as a decimal between 0 and 1. US estimates usually land between 0.6 and 0.9; 0.8 is a common textbook value.
Enter the spending change in billions. Positive for stimulus, negative to model austerity or spending cuts.
Read the multiplier and GDP effect. Remember this is the simple Keynesian model, a starting point, not a forecast.
The Formula
The logic is a geometric series. The government spends $1. Recipients spend MPC of it, say $0.80. Those recipients' payees spend $0.64, then $0.512, and so on. The infinite sum 1 + MPC + MPC^2 + ... equals 1/(1 - MPC). With MPC of 0.8, that converges to 5. The series converges because each round leaks some money into savings, which is why a higher savings rate means a smaller multiplier.
Worked Example
MPC = 0.8, stimulus = $100 billion. Multiplier: 1 / (1 - 0.8) = 1 / 0.2 = 5. GDP effect: 100 x 5 = $500 billion. The rounds: $100B first, $80B second (100 x 0.8), $64B third (80 x 0.8), $51.2B fourth, shrinking until the total converges on $500B. Flip it: a $100B spending cut with the same MPC shrinks GDP by $500B, which is why austerity during recessions is so contractionary in this model.
What MPC to Use
MPC is not one number. It varies by who gets the money, which is the most useful insight in fiscal policy.
| Recipient | Typical MPC | Implied multiplier |
|---|---|---|
| Low-income households | 0.9 | 10 |
| Middle-income households | 0.7 - 0.8 | 3.3 - 5 |
| High-income households | 0.4 - 0.5 | 1.7 - 2 |
| Corporations (tax cut) | 0.3 - 0.5 | 1.4 - 2 |
This is why stimulus checks to working families score bigger multipliers than corporate tax cuts: the money gets spent, not saved. Empirical estimates of real-world multipliers usually come in lower than the textbook formula, often 1.5 to 2.5 for government spending, because the simple model ignores taxes, imports, and interest-rate responses.
What the Simple Model Leaves Out
Three leakages shrink the real multiplier below 1/(1-MPC). Taxes take a cut of each round. Imports send spending abroad, which is why small open economies have smaller multipliers. And if the economy is near full employment, extra spending mostly bids up prices instead of output, while the central bank may raise rates in response. The textbook multiplier is most accurate in a deep recession with idle workers and low rates, exactly when stimulus is debated. In a booming economy, treat it as an upper bound.
The Tax Multiplier Is Smaller
Cutting taxes by $1 does not have the same punch as spending $1, because households save part of the cut. The tax multiplier is -MPC/(1-MPC): with MPC of 0.8, a $100B tax cut lifts GDP by $400B, versus $500B for $100B of direct spending. Same MPC, smaller effect, because the first round only spends 80 cents of the dollar. Keep this distinction straight when comparing stimulus proposals. For personal tax math rather than macro models, our income tax calculator and tax bracket finder handle the household side.
When the Multiplier Breaks Down
The textbook multiplier of 5 assumes every round of spending stays domestic and gets respent. Reality leaks at every round. Imports are the biggest leak: spending on imported goods sends the next round abroad, which is why small open economies have multipliers near 1 while large relatively closed ones see 1.5 to 2.5 in practice. Savings are the second leak: stimulus paid to high earners or used to pay down debt has a low MPC and fizzles fast, which is why targeted payments to low-income households outperform broad tax cuts per dollar.
Two more caveats. Supply constraints: if the economy is already at capacity, extra spending becomes inflation, not output; multipliers are biggest in recessions with idle workers and factories. And monetary offset: if the central bank raises rates to counter the stimulus, the multiplier shrinks. Empirical estimates cluster around 0.8 to 2 for government spending in normal times, rising toward 2 to 3 in deep recessions at the zero lower bound. Use 5 for the classroom; use 1.5 for the forecast.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is the spending multiplier?
The spending multiplier says how much GDP changes for each $1 change in spending: 1/(1-MPC). With an MPC of 0.8 the multiplier is 5, so $100B of stimulus lifts GDP by about $500B. It works through rounds of respending, where each round's spending becomes someone else's income.
What is marginal propensity to consume (MPC)?
MPC is the share of each additional dollar of income that gets spent rather than saved. An MPC of 0.8 means 80 cents of every extra dollar is spent. It varies by income: low-income households have MPCs near 0.9, high-income households closer to 0.5, since richer households save more of each extra dollar.
How do you calculate the Keynesian multiplier?
Divide 1 by (1 minus MPC). With MPC = 0.75: 1/(1-0.75) = 4. Then multiply the spending change by the multiplier for the GDP effect. The formula is the sum of the infinite geometric series 1 + MPC + MPC^2 + ..., which converges because saving leaks money out each round.
Why is the tax multiplier smaller than the spending multiplier?
A tax cut's first round only spends MPC of each dollar (the rest is saved), so its multiplier is MPC/(1-MPC) instead of 1/(1-MPC). At MPC 0.8, $100B of tax cuts lifts GDP ~$400B versus ~$500B for direct spending. Direct government purchases hit GDP dollar-for-dollar in round one.
What is a realistic value for the multiplier?
Textbook values run 2 to 5, but empirical estimates for US government spending usually land between 1.5 and 2.5. The simple formula overstates because it ignores taxes, imports, and monetary policy responses. Multipliers are biggest in recessions and smallest when the economy runs hot.
Can the multiplier be less than 1?
Yes. If spending mostly leaks into imports or savings, or if it pushes up interest rates that crowd out private investment, each $1 of government spending can produce less than $1 of GDP. This is common for spending in small open economies or when the central bank offsets the stimulus.
Who has the highest MPC?
Low-income households, typically around 0.9, because nearly every extra dollar goes to immediate needs. That is why stimulus targeted at working families generates larger multipliers than tax cuts for high earners or corporations, who save a bigger share of each extra dollar.
Does the multiplier work for spending cuts too?
Yes, symmetrically in the model: cutting $100B of spending with MPC 0.8 shrinks GDP by about $500B. This is the arithmetic behind warnings that austerity during recessions deepens them. In practice the effect depends on what is cut and the state of the economy.
What is the balanced budget multiplier?
If government spending and taxes rise by the same $1, the net effect on GDP is about $1: the spending multiplier 1/(1-MPC) minus the tax multiplier MPC/(1-MPC) equals 1. It is a neat theoretical result showing that even fully tax-financed spending still stimulates, in the simple model.
How does the multiplier relate to inflation?
When the economy has slack (unemployed workers, idle factories), extra spending mostly raises output. Near full employment, it mostly raises prices instead. The textbook multiplier describes real GDP; in a hot economy much of the nominal effect shows up as inflation, which our <a href="/finance/inflation-calculator">inflation calculator</a> can put in perspective.