MPC Calculator

What do you do with the next hundred?

Imagine your pay goes up by a hundred next month. What happens to it?

Some of it gets spent. Some of it does not. The split between those two is the whole of this calculation.

Marginal propensity to consume is the fraction of extra income that gets spent rather than saved. An MPC of 0.8 means eighty of every hundred goes straight back out again.

It sounds like a small piece of household trivia. It is one of the most consequential numbers in economics, because when a government decides whether a tax cut or a stimulus payment will do anything, this is the number the answer hangs on.

Four inputs here, two outputs. The arithmetic is a division. What it feeds into is not.

Four boxes

1. Increase in disposable income. How much extra came in, after tax.
2. Increase in consumer spending. How much of that extra went out.
3. Autonomous consumer spending. What gets spent even when income is zero. More on this below, because it is the odd one.
4. Disposable income. Total income after tax, not the increase.

You get back two things: the MPC itself, and total consumer spending.

The second and fourth boxes trip people up, so read them twice. Boxes one and two are about the change. Box four is about the level. If you type your whole salary into box one you will get an MPC that describes nothing.

One rule the tool enforces: spending must increase by less than income did. Try to spend more than you gained and it stops you, which is the right call for a measure that is meant to be a fraction.

Two formulas, and one of them is a straight line

The first is the MPC itself:

MPC = change in spending ÷ change in income

Spend 800 of an extra 1,000 and your MPC is 0.8. That is it.

The second builds the consumption function:

Consumer spending = autonomous spending + (MPC × disposable income)

Look at the shape of that. A fixed amount, plus a constant fraction of income. It is the equation of a straight line, with autonomous spending as the intercept and MPC as the slope.

Which is why MPC matters so much to anyone modelling an economy. It is not a description of one household on one day. It is the slope of a line that says how spending responds to income, at any income.

And there is a twin worth knowing. Whatever is not spent is saved, so:

MPS = 1 - MPC

Marginal propensity to save. An MPC of 0.8 means an MPS of 0.2. The two always add to one, because extra income has only two places to go.

A raise of a thousand

Disposable income goes up by 1,000. Spending goes up by 800. Autonomous spending is 200, and total disposable income is 2,000.

MPC = 800 ÷ 1,000 = 0.80

Consumer spending = 200 + (0.80 × 2,000) = 1,800

So this household spends 1,800 of its 2,000 and saves 200.

A few more, to see the range:

Notice that MPC always lands between 0 and 1. Spend none of the extra and it is 0. Spend all of it and it is 1. There is nowhere else for it to go.

Why economists care so much about this one number

Here is the part that turns a household ratio into a policy lever.

When you spend money, it does not vanish. It becomes somebody else's income. And that person then spends a fraction of it, which becomes a third person's income, and so on.

The chain does not go on forever, because a slice leaks out to savings at every step. But it goes on long enough to matter, and where it stops is set entirely by the MPC:

Spending multiplier = 1 ÷ (1 - MPC)

Watch what happens as the MPC climbs:

Read the last two rows again. Going from an MPC of 0.9 to 0.95 doubles the multiplier. A five point change in one household ratio, and the effect of a stimulus doubles.

That is why governments handing out money care enormously about who receives it, and it is why the question of whether people will spend or save a payment is not an academic one.

A caution before you take that table too seriously. It assumes every round of spending stays inside the economy, and in reality a chunk leaks out to imports and to tax at every step. Real world multipliers come out well below the textbook figures, and the argument about how far below has been running for the better part of a century.

The spending that happens even at zero income

The third box asks for autonomous consumer spending, and people usually stare at it for a moment. What is spending that does not depend on income?

It is what you spend when you earn nothing.

Because you still eat. You still pay for shelter. Your income can go to zero and your spending cannot, and the gap gets covered by savings, by borrowing, or by family.

In the formula it is the intercept, the amount that stays even when income is zero. On our example, autonomous spending is 200, so a household with no income at all still spends 200 and is 200 in the hole.

That gives you a genuinely useful figure. The income at which spending exactly equals earnings:

Break-even income = autonomous spending ÷ (1 - MPC)

With autonomous spending of 200 and an MPC of 0.8, that is 200 ÷ 0.2 = 1,000.

Below 1,000 this household spends more than it earns. Above it, it saves. Exactly at it, it breaks even.

Which is a much more concrete way to think about a household's finances than any ratio, and it falls straight out of two numbers you already entered.

Not everybody has the same MPC

The single most reliable finding about MPC is that it is not the same for everyone, and it varies in a predictable direction.

Households on lower incomes tend to have a higher MPC. Give a household that is already short of money an extra hundred and close to all of it gets spent, because there is a list of things waiting for it.

Households on higher incomes tend to have a lower MPC. The extra hundred arrives on top of an income that already covers everything needed, so a larger share goes into savings or investments.

That is not a moral observation. It is what happens when necessities take up a fixed slice of a small income and a tiny slice of a large one.

But here is the thing. If you accept both that MPC is higher at lower incomes and that the multiplier rises steeply with MPC, then where a payment lands changes how much it does. The same money handed to different households produces a different effect on total spending, and the difference is not marginal.

That single observation sits underneath a very large share of the argument about how stimulus should be designed.

Where the number stops being reliable

Four things this calculation quietly assumes.

That the change is permanent. People treat a one-off windfall very differently from a permanent raise. A bonus tends to get saved or spent on something one-off, while a salary increase changes ongoing habits. Same amount, different MPC, and this cannot tell them apart.

That the MPC is constant. The consumption function draws a straight line, which assumes the same fraction is spent at every income level. In reality the fraction falls as income rises, so the line is really a curve and the straight version is an approximation over a modest range.

That you can measure the spending change cleanly. This is harder than it sounds. Household spending moves for a dozen reasons at once, and separating out the part caused by an income change is the whole difficulty of measuring MPC in practice.

That the two changes are the same period. Income arriving in one month and being spent over the following six is common, and comparing a monthly income change against a monthly spending change will understate the MPC badly.

So treat the output as a description of the numbers you supplied rather than a measurement of a household. The formula is exact. What it is exact about is what you typed.

This is an educational calculation rather than financial advice.

Questions people ask

What is marginal propensity to consume?

The fraction of extra income that gets spent rather than saved. Spend 800 of an extra 1,000 and the MPC is 0.8.

How is it calculated?

Divide the change in consumer spending by the change in disposable income. Both must be changes, not totals.

Can MPC be above 1?

Not as a fraction of extra income, which is why the tool requires spending to rise by less than income. Sustained spending above income means borrowing or running down savings rather than a propensity above one.

What is marginal propensity to save?

One minus the MPC. Extra income has two places to go, so the two always add to one. An MPC of 0.8 means an MPS of 0.2.

What counts as autonomous spending?

What you would spend even with no income at all. Food, shelter, the unavoidable minimum, covered from savings or borrowing. It is the intercept of the consumption line.

What is the spending multiplier?

One divided by one minus MPC. At an MPC of 0.8 it is 5, meaning 100 of new spending eventually generates 500 of income as it circulates. Real world multipliers are lower, because spending leaks out to imports and tax.

How do I find my break-even income?

Divide autonomous spending by one minus MPC. With 200 of autonomous spending and an MPC of 0.8, you break even at 1,000.

Does MPC differ between households?

Considerably, and predictably. Lower income households tend to spend a larger share of extra income, because there is more waiting for it. That is why the design of a stimulus payment matters as much as its size.

References

The marginal propensity to consume, the consumption function expressing spending as autonomous consumption plus a constant fraction of disposable income, and the resulting spending multiplier of one divided by one minus the marginal propensity to consume, are standard results in macroeconomic theory. The measurement of disposable personal income and personal consumption expenditures, from which the ratio is calculated in practice, follows the national accounts published by the US Bureau of Economic Analysis. The point that money creation and household spending interact with monetary policy, and that the circulation of spending is constrained in practice, is discussed in the Bank of England's Quarterly Bulletin.

1. United States Bureau of Economic Analysis, Personal Income and Outlays, National Income and Product Accounts. https://www.bea.gov/data/income-saving/personal-income
2. McLeay, M., Radia, A., and Thomas, R. (2014). Money Creation in the Modern Economy. Bank of England Quarterly Bulletin, 54(1), 14 to 27. https://www.bankofengland.co.uk/quarterly-bulletin/2014/q1/money-creation-in-the-modern-economy
3. Federal Reserve Bank of St. Louis, FRED Economic Data: Disposable Personal Income and Personal Consumption Expenditures. https://fred.stlouisfed.org/series/DSPIC96