How to Calculate the Spending Multiplier
The spending multiplier equals 1 divided by (1 − MPC), or 1 divided by MPS; multiply it by the change in spending to find the change in GDP.
Formula
Spending multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS | ΔGDP = multiplier × Δspending | Tax multiplier = −MPC ÷ MPS
Steps
- 1Find the MPC. The marginal propensity to consume — the fraction of an extra dollar of income that is spent.
- 2Compute the multiplier. 1 ÷ (1 − MPC). Since MPS = 1 − MPC, this also equals 1 ÷ MPS.
- 3Apply it to the spending change. ΔGDP = multiplier × initial change in spending.
Worked example
If MPC = 0.8, the spending multiplier = 1 ÷ (1 − 0.8) = 5. A $10B increase in government spending raises GDP by 5 × $10B = $50B (before crowding out).
Frequently asked questions
Why is the tax multiplier smaller than the spending multiplier?
A tax cut first raises disposable income, and households save part of it (the MPS portion), so only the consumed fraction enters spending initially. Tax multiplier = −MPC ÷ MPS.
What weakens the multiplier in reality?
Crowding out, imports, taxes, and saving all act as leakages that reduce the real-world multiplier below the simple formula.