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.
The Spending Multiplier formula
Calculator
Enter the MPC and the change in spending to get the multiplier and the resulting change in GDP.
Fraction of each extra dollar of income that households spend.
The initial injection, for example new government spending or investment.
Every $1 of new spending ends up raising GDP by 5 dollars, so $10B of spending raises GDP by $50B before crowding out.
- MPS
- 0.2
- Change in GDP
- $50B
MPS = 1 minus MPC, the share of each extra dollar that leaks into saving.
How to calculate Spending Multiplier, step by step
- 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: Spending Multiplier
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).
Watching the chain actually converge
The multiplier is not a rule to memorise, it is the sum of a chain, and doing one chain by hand makes every later question easier.
Take an MPC of 0.8 and $100 billion of new government spending. That $100 billion is somebody's income. They spend 80% of it, so $80 billion becomes the next person's income. They spend 80% of THAT, so $64 billion moves on, then $51.2 billion, then $40.96 billion.
After five rounds the cumulative total is $336 billion and still climbing. The rounds never quite stop, but they shrink geometrically, and the sum converges on 100 ÷ (1 − 0.8) = $500 billion.
That is where 1 ÷ MPS comes from. It is a shortcut for adding an infinite series, not a separate fact, and seeing it converge is what makes the size of the MPS feel important rather than arbitrary.
Why the real multiplier is smaller than the formula
The 1 ÷ MPS version assumes the only thing stopping a dollar circulating is saving. Two other leakages are real.
Taxes take a share of every round of income before it can be respent, and spending on imports sends part of each round to a foreign producer rather than a domestic one. Including them, the multiplier is 1 ÷ (MPS + MPT + MPM). Every extra term sits in the denominator, so each one pulls the answer down.
AP questions almost always hand you the simple version, so compute 1 ÷ MPS unless a tax or import propensity is given. The leakages are the reason to write "up to" in front of a multiplier answer: the formula gives a ceiling on the effect, not a prediction of it.
There is also a timing point worth a sentence in an essay. The rounds take real time, so the full effect arrives over quarters rather than immediately, which is part of why fiscal policy is criticised for acting slowly.
Spending Multiplier questions
What is the spending multiplier formula?
Spending multiplier = 1 ÷ (1 - MPC), which also equals 1 ÷ MPS. Multiply it by the initial change in spending: ΔGDP = multiplier × Δspending. Example: MPC = 0.8 gives 1 ÷ 0.2 = 5.
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.
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