Multiplier Calculator
Enter the marginal propensity to consume (or save) and the calculator returns the spending, tax, transfer and balanced-budget multipliers, the change in income from a spending or tax change you choose, and a round-by-round table showing how the effect builds up. A second mode finds the money multiplier from a reserve ratio. Free, no sign-up.
Your numbers
The share of each extra dollar of income that is spent. It must be at least 0 and below 1.
Use any one unit for both — dollars, millions, billions. Enter a tax cut or a spending cut as a negative number. Leave a field at 0 to ignore it.
Results
5
Spending multiplier
-4
Tax multiplier
4
Transfer multiplier
1
Balanced-budget multiplier
500
Change in income from ΔG
0
Change in income from ΔT
500
Total change in income (ΔY)
Working
Spending multiplier = 1 ÷ (1 − MPC) = 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5
Tax multiplier = −MPC ÷ (1 − MPC) = −0.8 ÷ 0.2 = -4
Transfer multiplier = MPC ÷ (1 − MPC) = 0.8 ÷ 0.2 = 4
Balanced budget: 5 + (-4) = 1
ΔY = 5 × 100 + (-4) × 0 = 500
First-round change in spending = ΔG − MPC × ΔT = 100 − 0.8 × 0 = 100
Round by round
Each round, households spend the MPC share of the extra income they just received. After 10 rounds the chain has delivered 89.3% of its final effect.
| Round | New spending | Cumulative change in income | Share of final effect |
|---|---|---|---|
| 1 | 100 | 100 | 20% |
| 2 | 80 | 180 | 36% |
| 3 | 64 | 244 | 48.8% |
| 4 | 51.2 | 295.2 | 59% |
| 5 | 40.96 | 336.16 | 67.2% |
| 6 | 32.77 | 368.93 | 73.8% |
| 7 | 26.21 | 395.14 | 79% |
| 8 | 20.97 | 416.11 | 83.2% |
| 9 | 16.78 | 432.89 | 86.6% |
| 10 | 13.42 | 446.31 | 89.3% |
Show the graph data as a table
| Round of spending | Cumulative change in income | Final change in income (ΔY) |
|---|---|---|
| 1 | 100 | 500 |
| 2 | 180 | 500 |
| 3 | 244 | 500 |
| 4 | 295.2 | 500 |
| 5 | 336.16 | 500 |
| 6 | 368.928 | 500 |
| 7 | 395.1424 | 500 |
| 8 | 416.1139 | 500 |
| 9 | 432.8911 | 500 |
| 10 | 446.3129 | 500 |
Simple-model assumptions: a closed economy (no imports), lump-sum taxes (no income-tax rate), fixed prices, spare capacity, and no crowding out of private spending or investment. Real multipliers are smaller.
How to Use the Multiplier Calculator
- 1. Choose the multiplier. Pick the spending, tax and balanced-budget multipliers for a fiscal-policy question, or the money (deposit) multiplier for a banking question.
- 2. Enter the propensity or the ratios. For fiscal policy, give the MPC or the MPS as a decimal; the other follows because MPC + MPS = 1. For the money multiplier, give the required reserve ratio as a percentage, and add excess reserves or a cash-to-deposit ratio if your course includes them.
- 3. Add the policy change. Enter a change in government spending (ΔG), a change in lump-sum taxes (ΔT), or both. A tax cut is a negative ΔT. For the money multiplier, enter the amount of new reserves.
- 4. Read the working. Each multiplier is written out with your numbers, followed by a round-by-round table and a graph of the cumulative effect.
The Multiplier Formulas
The multiplier exists because one person's spending is another person's income. When the government buys something, the sellers receive income and spend the MPC share of it, which becomes income for someone else, and so on. The rounds form a geometric series whose sum is a simple fraction. OpenStax Principles of Macroeconomics and most other textbooks present this in the Keynesian cross model.
Fiscal multipliers (lump-sum taxes)
Spending multiplier
ΔY ÷ ΔG = 1 ÷ (1 − MPC) = 1 ÷ MPS
Tax multiplier
ΔY ÷ ΔT = −MPC ÷ (1 − MPC)
Transfer multiplier
ΔY ÷ ΔTR = MPC ÷ (1 − MPC)
Balanced budget
1 ÷ (1 − MPC) − MPC ÷ (1 − MPC) = 1
The tax multiplier is smaller in size than the spending multiplier because a tax cut first goes into households' pockets, and they spend only the MPC share of it. That is why raising spending and taxes by the same amount still raises income by exactly that amount: the balanced-budget multiplier is always 1, whatever the MPC.
Worked Example: MPC of 0.8
The calculator opens with an MPC of 0.8 and a $100 increase in government spending. The MPS is 0.2, so each multiplier follows directly.
| Quantity | Calculation | Result |
|---|---|---|
| Spending multiplier | 1 ÷ (1 − 0.8) = 1 ÷ 0.2 | 5 |
| Tax multiplier | −0.8 ÷ 0.2 | −4 |
| Balanced-budget multiplier | 5 + (−4) | 1 |
| Change in income from ΔG = 100 | 5 × 100 | 500 |
| Change in income from a tax cut of 100 (ΔT = −100) | −4 × (−100) | 400 |
In round 1 the extra 100 of spending is income. In round 2 households spend 80 of it, in round 3 they spend 64, and so on; the running total creeps toward 500 and passes 89% of it after ten rounds. The tax cut works the same way but starts one step later, with a first round of 80 (the MPC times the 100 of extra take-home pay).
| MPC | MPS | Spending multiplier | Tax multiplier |
|---|---|---|---|
| 0.50 | 0.50 | 2 | −1 |
| 0.60 | 0.40 | 2.5 | −1.5 |
| 0.75 | 0.25 | 4 | −3 |
| 0.90 | 0.10 | 10 | −9 |
| 0.95 | 0.05 | 20 | −19 |
The Money Multiplier
The same geometric logic describes deposit creation. If banks must hold a fraction rr of deposits as reserves and lend the rest, and every loan is redeposited, then new reserves R can support at most R ÷ rr in deposits. With a 10% reserve ratio the multiplier is 10, so 1,000 of new reserves supports up to 10,000 of deposits and 9,000 of new lending.
Real systems leak. Banks may hold excess reserves (e) and the public may hold some of its money as currency, the cash-to-deposit ratio (c). With those leakages the deposit multiplier becomes 1 ÷ (rr + e + c) and the money multiplier, money supply per unit of monetary base, becomes (1 + c) ÷ (rr + e + c). Leave e and c at zero to get the basic 1 ÷ rr.
What the Simple Model Leaves Out
- Income taxes and imports. A proportional income tax or spending on imports is another leakage, so the true multiplier is smaller than 1 ÷ (1 − MPC). Courses that include them use 1 ÷ (1 − MPC(1 − t) + m).
- Crowding out and prices. If extra government borrowing raises interest rates or the economy is near full employment, some of the effect is offset.
- Timing and expectations. Households may save a temporary tax cut, so the effective MPC out of a one-off change is lower than out of a permanent one.
Frequently Asked Questions
- How do you calculate the spending multiplier?
- Divide 1 by (1 − MPC), which is the same as dividing 1 by the MPS. With an MPC of 0.75 the multiplier is 1 ÷ 0.25 = 4, so a 50 increase in government spending raises equilibrium income by 200 in the simple model.
- Why is the tax multiplier negative?
- A tax increase reduces disposable income, so spending falls and income falls; a tax cut raises both. The sign is negative because taxes and income move in opposite directions. Its size is MPC ÷ (1 − MPC), exactly one less than the spending multiplier.
- Why is the balanced-budget multiplier equal to 1?
- When spending and lump-sum taxes rise by the same amount, the spending multiplier adds 1 ÷ (1 − MPC) times the change and the tax multiplier subtracts MPC ÷ (1 − MPC) times the change. The difference is exactly 1, so income rises by the size of the budget change itself.
- What is the relationship between the MPC and the multiplier?
- The larger the MPC, the larger the multiplier, and the growth is steep near 1. An MPC of 0.5 gives a multiplier of 2, 0.9 gives 10, and 0.99 gives 100. An MPC of exactly 1 has no finite multiplier, which is why the calculator asks for a value below 1.
- What is the money multiplier formula?
- In the basic model it is 1 ÷ rr, where rr is the required reserve ratio as a decimal. With excess reserves e and a cash-to-deposit ratio c, deposits per unit of monetary base are 1 ÷ (rr + e + c), and the M1-style money multiplier is (1 + c) ÷ (rr + e + c).
- Are real-world fiscal multipliers as large as the textbook ones?
- Usually not. Empirical estimates depend on the type of spending, the state of the economy and monetary policy, and are often below 2 and sometimes below 1. The textbook figure is an upper-bound illustration of the mechanism, not a forecast.