How to Calculate MPC and MPS
MPC = change in consumption ÷ change in income; MPS = change in saving ÷ change in income. MPC + MPS always equals 1.
The MPC & MPS formula
Worked example: MPC & MPS
Income rises by $500 and consumption rises by $400: MPC = 400 ÷ 500 = 0.8 and MPS = 100 ÷ 500 = 0.2 (they sum to 1). That MPS gives a spending multiplier of 1 ÷ 0.2 = 5.
Calculator
Enter the change in income and the change in consumption to get MPC, MPS, and the spending multiplier.
The extra income households receive.
How much of that extra income gets spent. The rest is saved.
Households spend 80% of each extra dollar and save 20%, which gives a spending multiplier of 5.
- Change in saving
- $100
- MPS
- 0.2
- MPC + MPS
- 1
- Spending multiplier (1 ÷ MPS)
- 5
Whatever is not spent out of the extra income is saved.
Every extra dollar is either spent or saved, so this always comes to 1.
How to calculate MPC & MPS, step by step
- 1Find the change in income. ΔY, the extra disposable income households receive.
- 2Find the change in consumption. ΔC, how much of that extra income is spent. MPC = ΔC ÷ ΔY.
- 3Find the change in saving. ΔS = ΔY − ΔC, so MPS = ΔS ÷ ΔY. You can also just compute MPS = 1 − MPC.
- 4Check they sum to 1. Every extra dollar is either spent or saved, so MPC + MPS = 1 always.
Use disposable income, not income
The denominator is income after tax. Questions that give a gross income figure and a tax rate expect you to net the tax out first, and using the gross figure understates the MPC every time.
Suppose gross income rises by $1,000 against a 20% tax rate and consumption rises by $600. Disposable income rose by $800, not $1,000, so the MPC is 600 ÷ 800 = 0.75. Divide by the gross $1,000 instead and you get 0.6, which then produces a spending multiplier of 2.5 rather than 4. One skipped step nearly halves the final answer.
What the MPC actually controls
The MPC matters because every multiplier on the fiscal side is built from it. MPS is 1 − MPC, the spending multiplier is 1 ÷ MPS, and the tax multiplier is −MPC ÷ MPS.
At an MPC of 0.75 those come to an MPS of 0.25, a spending multiplier of 4 and a tax multiplier of −3. So $100 billion of government purchases supports up to $400 billion of extra real GDP, while a $100 billion tax cut supports up to $300 billion. Add the two multipliers together and you get 4 + (−3) = 1, the balanced budget multiplier: raising spending and taxes by the same amount still lifts GDP, by exactly that amount.
The sensitivity is worth feeling. Move the MPC from 0.75 to 0.8 and the spending multiplier goes from 4 to 5, a quarter more output from the same policy. Small changes in the fraction people spend produce large changes in what fiscal policy achieves, which is why the figure is estimated so carefully.
Why the real multiplier comes in lower
The 1 ÷ MPS formula assumes the only thing that stops a dollar circulating is saving. Two other leakages are real and both shrink the effect.
Taxes take a cut of every round of income before it can be respent, and spending on imports sends part of each round abroad rather than to a domestic producer. Including them, the multiplier is 1 ÷ (MPS + MPT + MPM), where MPT and MPM are the marginal propensities to tax and to import. Every one of those terms sits in the denominator, so each additional leakage pulls the multiplier down.
AP questions almost always give you the simple version, so compute 1 ÷ MPS unless the question hands you a tax or import propensity. The extra terms are the reason to write "up to" in front of a multiplier answer rather than stating it as what will certainly happen.
MPC & MPS questions
What is the MPC formula?
MPC = ΔC ÷ ΔY, the change in consumption divided by the change in disposable income. It is the fraction of each extra dollar that households spend, and MPS = 1 − MPC is the fraction they save. If income rises by $500 and consumption rises by $400, MPC = 400 ÷ 500 = 0.8.
Why do MPC and MPS have to add to 1?
Each extra dollar of disposable income can only go two places, consumption or saving, so the fractions spent and saved must sum to exactly 1.
How do MPC and MPS connect to the multipliers?
Spending multiplier = 1 ÷ MPS and tax multiplier = −MPC ÷ MPS. A higher MPC means more re-spending each round and therefore bigger multipliers.
What is the difference between MPC and APC?
MPC is marginal: it uses the CHANGE in consumption over the CHANGE in income. APC is average: total consumption divided by total income. A household spending $18,000 out of $20,000 has an APC of 0.9 whatever its MPC happens to be.
Why is the tax multiplier smaller than the spending multiplier?
A dollar of government spending enters the economy in full. A dollar of tax cut lands in a household's pocket first, and only the MPC fraction of it gets spent, so the first round is smaller by exactly that fraction. That is why the tax multiplier is the spending multiplier times MPC, with a negative sign.
Can the MPC be greater than 1?
Not out of the extra income alone, since a household cannot spend more than all of an additional dollar of it. Measured consumption can exceed measured income in a period when a household borrows or draws down savings, but that is the average propensity exceeding 1, not the marginal one.
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