Spending Multiplier Calculator
Enter the marginal propensity to consume (MPC) and an initial spending injection to see the spending multiplier, the resulting change in GDP, and the full ripple of spending rounds. Switch to MPS if that is the value you have. You also get the tax multiplier and balanced-budget multiplier alongside a round-by-round breakdown chart, so you can see exactly how each dollar cascades through the economy.
What is the spending multiplier?
The spending multiplier (also called the fiscal multiplier or Keynesian multiplier) measures how much total GDP changes for every one dollar of new spending injected into an economy. It is greater than 1 because each round of spending becomes income for someone else, who then spends a fraction of it again, who passes it on, and so on. The process continues until the sums become negligible, but the total impact is always larger than the original injection. The concept was formalised by John Maynard Keynes and Richard Kahn in the 1930s and remains central to fiscal policy analysis. Governments use it to estimate how a stimulus package will ripple through national income.
How is the spending multiplier calculated?
The formula is Multiplier = 1 / MPS, which is the same as 1 / (1 - MPC). MPC is the marginal propensity to consume: the share of each additional dollar of income that households choose to spend. MPS is the marginal propensity to save: the share they save. Because MPC + MPS = 1, you only need one value. If MPC = 0.8, then MPS = 0.2 and the multiplier is 1 / 0.2 = 5. A $10,000 government injection would therefore be expected to raise GDP by $50,000. The round-by-round chart shows how the initial $10,000 triggers $8,000 of second-round spending, then $6,400, then $5,120, and so on, eventually summing to $50,000.
Tax multiplier and balanced-budget multiplier
A tax change also affects GDP, but less than an equivalent change in spending, because some of the extra after-tax income is saved rather than spent. The tax multiplier is -MPC / MPS. The negative sign reflects that a tax cut raises GDP while a tax increase reduces it. With MPC = 0.8 the tax multiplier is -4, so a $10,000 tax cut raises GDP by $40,000 compared with the $50,000 boost from a $10,000 spending increase. The balanced-budget multiplier is the sum of the spending and tax multipliers: 5 + (-4) = 1. This is the Haavelmo theorem - equal increases in government spending and taxation always raise GDP by exactly the amount of the increase, regardless of the MPC.
Limitations and the open-economy multiplier
The simple Keynesian multiplier assumes a closed economy with no taxes and no imports. In practice, leakages shrink the multiplier significantly. Taxes reduce disposable income (increasing the effective MPS), imports send spending abroad rather than circulating domestically, and rising prices absorb part of any nominal GDP increase. The open-economy multiplier formula is 1 / (MPS + MPM + MPT), where MPM is the marginal propensity to import and MPT is the marginal tax rate. Empirical estimates of government spending multipliers typically range from about 0.6 to 1.5, well below the pure textbook figures for MPC values of 0.8 or higher. The multiplier also varies over the business cycle: it is larger when the economy is operating below capacity and smaller during a boom.
Spending multiplier at common MPC values
| MPC | MPS | Spending Multiplier | Tax Multiplier | Interpretation |
|---|---|---|---|---|
| 0.5 | 0.5 | 2.00 | -1.00 | Moderate - half of each dollar is saved |
| 0.6 | 0.4 | 2.50 | -1.50 | Moderate |
| 0.7 | 0.3 | 3.33 | -2.33 | Strong saving rate is 30% |
| 0.75 | 0.25 | 4.00 | -3.00 | Strong - common textbook value |
| 0.8 | 0.2 | 5.00 | -4.00 | Strong - classic Keynesian example |
| 0.85 | 0.15 | 6.67 | -5.67 | Very strong - low saving rate |
| 0.9 | 0.1 | 10.00 | -9.00 | Very strong - typical of low-income economies |
| 0.95 | 0.05 | 20.00 | -19.00 | Extreme - near-zero saving rate |
The higher the marginal propensity to consume, the larger the spending multiplier and the greater the GDP impact of any injection.
Frequently asked questions
What is the spending multiplier formula?
The spending multiplier equals 1 divided by the marginal propensity to save (MPS), which is the same as 1 divided by (1 minus MPC). If households save 20 cents of every extra dollar (MPS = 0.2, MPC = 0.8), the multiplier is 1 / 0.2 = 5.
What is the difference between MPC and MPS?
MPC (marginal propensity to consume) is the fraction of an additional dollar of income that a household spends on goods and services. MPS (marginal propensity to save) is the fraction that is saved. The two always sum to 1: MPC + MPS = 1. A higher MPC means more spending in each round and therefore a larger multiplier.
Why is the tax multiplier smaller than the spending multiplier?
When the government spends $1 directly, the full dollar enters the economy immediately. When the government cuts taxes by $1, households receive that dollar but save a fraction (MPS) rather than spending all of it. So the first round of the tax cut only injects MPC dollars, making the overall GDP effect smaller by a factor of MPC. The tax multiplier is -MPC / MPS versus 1 / MPS for spending.
What is the balanced-budget multiplier?
If the government simultaneously raises spending and taxes by the same amount, the net effect on GDP equals exactly the size of that increase, no matter what MPC is. This is the Haavelmo theorem. The spending multiplier and the (negative) tax multiplier always cancel out to leave a balanced-budget multiplier of 1.
Why is the real-world multiplier lower than the theoretical one?
The simple formula assumes a closed economy with no taxes and full employment. In practice, part of each spending round leaks out through imports (marginal propensity to import), taxes reduce disposable income, and capacity constraints mean some of the demand boost shows up as higher prices rather than higher output. Empirical estimates for developed economies typically put the government spending multiplier between 0.6 and 1.5, not the 4 or 5 implied by MPC = 0.75 or 0.8.
What MPC is used in AP Macroeconomics?
AP Macroeconomics courses most commonly use an MPC of 0.75 or 0.8 in worked examples, giving multipliers of 4 and 5 respectively. These are convenient round numbers for exam problems. Real-world estimates are lower because open-economy leakages are excluded from the simple formula.