Spending Multiplier Calculator (MPC, taxes & imports → change in GDP)

Understanding the spending multiplier calculator — concept and principle

The spending multiplier tells you how much total output (GDP) changes when government spending, investment or exports change by one unit. This calculator computes the multiplier with taxes and imports, the simple textbook multiplier and the tax multiplier.

Half of each new round leaks to saving, taxes and imports, so 100 of extra spending raises GDP by about 200, not 500.

How it is calculated

Simple multiplier = 1 ÷ (1 − MPC).
With a proportional tax rate t and a marginal propensity to import MPI: multiplier = 1 ÷ (1 − [MPC × (1 − t) − MPI]).
Change in GDP = multiplier × change in spending.
Leakage per round = 1 − [MPC × (1 − t) − MPI] (saving + tax + imports).
Tax multiplier (simple model) = −MPC ÷ (1 − MPC).

The principle

New spending becomes someone's income. They pay part in tax, save part, spend part on imports and spend the rest on domestic goods, which becomes another person's income, and so on. Each round is smaller, and the total forms a geometric series whose sum is 1 ÷ leakage. The more that leaks out each round, the smaller the multiplier. A tax cut has a smaller effect than the same amount of spending in this model because people save part of the tax cut before spending it.

Worked example

Default inputs: MPC 0.8, tax rate 25%, MPI 0.1, change in spending 100.

Spending kept per round = 0.8 × 0.75 − 0.1 = 0.5; leakage = 50%.
Multiplier = 1 ÷ 0.5 = 2.
Change in GDP = 2 × 100 = 200.
Simple multiplier = 1 ÷ 0.2 = 5, which would give 500.
Tax multiplier = −0.8 ÷ 0.2 = −4; MPS = 0.2.

Each point is the calculator re-run with only “Tax rate on extra income (%)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Tax rate on extra income (%)	Spending multiplier
6.25	2.86
12.5	2.5
18.8	2.22
25	2
31.2	1.82
37.5	1.67
50	1.43

How to read the result

The gap between 5 and 2 shows how much taxes and imports dampen the effect. Real-world multipliers are usually smaller still, because the model assumes spare capacity, fixed prices and unchanged interest rates. When the economy is near full capacity, extra spending tends to raise prices rather than output.

Common mistakes

Using the simple multiplier as a forecast.
Ignoring imports, which are large for small open economies.
Forgetting that monetary policy may offset fiscal changes.
Mixing up the spending and tax multipliers.

Keep in mind: This is a simplified Keynesian model. Actual effects depend on the state of the economy and policy responses. For learning, not forecasts.

Frequently asked questions

What is the formula for the spending multiplier?

1 ÷ (1 − MPC) in the simple model; with taxes and imports, 1 ÷ (1 − [MPC × (1 − t) − MPI]).

Why is the tax multiplier smaller than the spending multiplier?

Part of a tax cut is saved before it is spent, so the first round of spending is smaller.

Are real multipliers this large?

Empirical estimates are usually smaller than textbook values and vary with economic conditions.

Sources: Keynes, J. M. (1936). The General Theory of Employment, Interest and Money · Mankiw, N. G., Macroeconomics (Keynesian cross and multipliers)

Checked 9 Nov 2026. Spending multiplier = 1 ÷ (1 − MPC), example MPC 0.7 → 3.33: T. Brown & C. Foreman, “UH Macroeconomics 2022” (revised OpenStax text, CC BY 4.0), chapter “The Expenditure-Output Model”. Multiplier with proportional taxes and imports and the lump-sum tax multiplier: standard Keynesian expenditure-model formulas.

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