Spending Multiplier Calculator

What Is the Spending Multiplier?

The spending multiplier is the number of units by which total output (GDP) changes when spending changes by one unit. It is also called the expenditure multiplier or the Keynesian multiplier. A multiplier of 5 means that 1 of new spending ends up adding 5 to total output.

The effect is larger than the first spending because one person's spending is another person's income. The people who receive the money spend part of it, the people they pay spend part of that, and so on. The new spending can come from the government, from firms investing, from households or from export sales. The simple formula treats them all the same way.

Spending Multiplier Formula

• MPC: the marginal propensity to consume, the fraction of extra income that is spent.
• MPS: the marginal propensity to save, equal to 1 − MPC.
• ΔSpending: the first change in spending, also called the injection.
• ΔY: the total change in output once every round of re-spending is counted.

The MPC must be at least 0 and less than 1. At an MPC of 1 the formula divides by 0, because every round would be as large as the one before and the total would never settle.

How to Calculate the Spending Multiplier

Households spend 0.8 of each extra unit of income, and the government raises its spending by 500:

1. Subtract the MPC from 1. 1 − 0.8 = 0.2. This is the MPS.
2. Divide 1 by the answer. 1 ÷ 0.2 = 5. This is the spending multiplier.
3. Multiply by the change in spending. 5 × 500 = 2,500.

Output rises by 2,500 in total. The first 500 is the government's own spending, and the other 2,000 is induced spending by households as the money is passed along.

The Multiplier Round by Round

The formula is a shortcut for adding up a long chain of spending. In round 1 the government spends 500. The people paid that 500 spend 0.8 of it, which is 400. The people paid that 400 spend 320, and so on:

The rounds form a geometric series, and its sum is the multiplier formula:

Most of the effect arrives early. After 10 rounds the total is already 2,231.56, about 89% of the full 2,500.

Spending Multiplier by MPC

The multiplier grows quickly as the MPC gets close to 1. Moving the MPC from 0.8 to 0.9 doubles the multiplier from 5 to 10. If you need to work out the MPC first, use our MPC Calculator, or start from saving with the MPS Calculator.

Spending Multiplier vs Tax Multiplier

A tax cut also raises output, but by less than the same amount of spending. Households save part of a tax cut before any of it is spent, so the first round is smaller. The tax multiplier is:

The minus sign means taxes and output move in opposite directions. With an MPC of 0.8:

The last row is the balanced budget multiplier. Spending and taxes rise together, the two effects partly cancel (5 − 4 = 1), and output rises by exactly the amount spent. The calculator shows the tax multiplier as a row under the result.

How Much Spending Closes an Output Gap?

The formula also runs backwards. If you know how far output is below its potential, divide the gap by the multiplier to find the spending needed to close it:

With an MPC of 0.8, a gap of 2,000 needs 400 of new spending. Closing the same gap with a tax cut takes more, 2,000 ÷ 4 = 500, because the tax multiplier is smaller.

Spending Cuts Work in Reverse

The multiplier applies to falls in spending as well. Suppose firms cut investment by 300 and the MPC is 0.75:

Output falls by 1,200: the first 300, plus 900 of lost spending by the people whose income dropped. Enter a negative change in spending, such as -300, to see this in the calculator.

Why Real Multipliers Are Smaller

The simple formula assumes saving is the only place extra income can go. In a real economy part of each round is also taken in tax and part is spent on imports. With an income tax rate t, the multiplier becomes:

A tax rate of 25% halves the multiplier from 5 to 2.5. Adding a marginal propensity to import of 0.1 lowers it again:

• Crowding out: government borrowing can push up interest rates and reduce private investment.
• Spare capacity: if the economy is already at full output, extra spending raises prices more than output.
• Time: the rounds take months or years to play out, and the formula gives only the final total.
• Expectations: households may save more if they expect higher taxes later.

For these reasons, measured fiscal multipliers are usually far below the values the simple formula gives. Treat the result as a classroom model, not a forecast.

Spending Multiplier Examples

A road project. A government spends 120 million on roads and the MPC is 0.75:

Starting from the MPS. Households save 0.1 of extra income, so the MPC is 1 − 0.1 = 0.9 and the multiplier is 1 ÷ 0.1 = 10. New spending of 250 would raise output by 2,500.

A lower MPC. With an MPC of 0.6 the multiplier is 1 ÷ 0.4 = 2.5, so export sales of 1,000 raise output by 2,500.

A result that does not end. With an MPC of 0.7 the multiplier is 1 ÷ 0.3, which is about 3.3333. The calculator marks rounded results with ≈.

Key Terms

Injection

New spending that enters the economy: government spending, investment or exports.

Induced spending

The extra consumer spending caused by the rise in income, on top of the injection.

MPC

Marginal propensity to consume, the share of extra income that is spent.

MPS

Marginal propensity to save, the share of extra income that is saved. MPS = 1 − MPC.

Tax multiplier

The change in output per unit change in taxes, −MPC ÷ MPS.

Output gap

The difference between actual output and the output the economy could produce.

How to Use the Spending Multiplier Calculator

1. Enter the MPC. Type the marginal propensity to consume as a decimal from 0 to under 1, such as 0.8.
2. Add a change in spending (optional). Type the first change in spending, such as 500, to also see the total change in output. Use a minus sign for a spending cut.
3. Read and copy the result. The multiplier appears as you type, with the working, the MPS, the tax multiplier and a bar showing the initial and induced parts. Press Copy to copy it, or Clear or Esc to start again.

Example: an MPC of 0.75 gives a multiplier of 1 ÷ (1 − 0.75) = 4. New spending of 120 raises output by 480.

Who Can Use This Calculator?

Frequently Asked Questions (FAQs)

Sources

• Wikipedia. Fiscal multiplier.
• Wikipedia. Multiplier (economics).
• Wikipedia. Marginal propensity to consume.
• Wikipedia. Balanced budget (balanced budget multiplier).
• Wikipedia. Crowding out (economics).
• OpenStax. Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model.
• Corporate Finance Institute. Fiscal Multiplier.
• WallStreetMojo. Multiplier Formula.