MPC Calculator

What marginal means here

Marginal propensity to consume measures what a household does with the next dollar it earns, not with the dollars it already had. A family earning 60,000 dollars a year might spend 54,000 of it. That average tells you their standard of living. It says nothing about what happens when a raise arrives.

Hand them 5,000 extra dollars and they might spend 4,000 and save 1,000. The share spent, 4,000 out of 5,000, is the marginal propensity to consume. Economists shorten it to MPC, and it is one of the small numbers with large consequences: OpenStax's expenditure-output model builds an entire theory of national income on it.

The word marginal does the work. It always means the change, never the level. Spending 54,000 out of 60,000 is an average of 0.90. Spending 4,000 out of a 5,000 raise is a marginal rate of 0.80. The two can move in opposite directions, and only the marginal one predicts what a stimulus check or a tax cut will do.

The MPC formula

The formula is a ratio of two changes: MPC = change in spending / change in income. Take spending after the income change, subtract spending before it, and divide by the income change that caused it. The result is a share between 0 and 1 for most households, where 0.50 means half of every extra dollar gets spent and 0.90 means nine tenths does.

The mirror image is the marginal propensity to save, or MPS. Whatever slice of the extra dollar is not spent is saved, so MPS = 1 - MPC, and the two always sum to 1. MIT's open microeconomics course uses that identity throughout its consumption chapters.

The last two columns introduce the multiplier, covered in its own section below. The short version: money spent becomes someone else's income, and that person spends a share of it too, so the original dollar keeps echoing through the economy until the saved slivers eat it up.

Worked example: the 5,000 dollar raise

Start with the numbers in the calculator's default fields. Income before the raise is 40,000 dollars a year and spending is 36,000. After the raise, income is 45,000 and spending is 40,000. The income change is 45,000 - 40,000 = 5,000. The spending change is 40,000 - 36,000 = 4,000. MPC is 4,000 / 5,000 = 0.80, so four fifths of each extra dollar went to consumption and MPS is 0.20.

Now trace where the spending goes. The 4,000 of new consumption becomes income for other people, who spend 80% of it, which becomes income for a third group, and so on. Each round is 0.8 times the one before it.

The rounds shrink toward zero, and the grand total is the first round divided by the amount leaked into saving each cycle: 4,000 / 0.20 = 20,000. Add the original 5,000 of income and the raise supports 25,000 dollars of economic activity, five times its face value.

Average and marginal are different animals

Households that earn little spend most of what they make, and households that earn a lot bank most of what they make. Both statements are about averages. Marginal asks a different question: what happens to spending when income moves by one step?

Run the same family through the calculator twice. Before the raise, average spending is 36,000 / 40,000 = 0.90 of income. After it, 40,000 / 45,000 = 0.89. The average fell even though the family is spending more money in total, because the raise was handled at a marginal rate of 0.80, below the old average.

That is the normal shape of a consumption function. The average stays above the marginal rate as long as the household saves something at every income level, and it slides toward the marginal rate as income grows. Anyone quoting "households spend 90 cents of each dollar" from an average and applying it to a tax rebate is making the classic mistake this table is built to expose.

Why the multiplier is 1 / (1 - MPC)

Each round of spending is the previous round times MPC, so the total is a geometric series: 4,000 + 4,000 x 0.8 + 4,000 x 0.64 and so on. A series whose ratio is 0.8 sums to its first term divided by (1 - 0.8). The first term is the original spending change, so the whole chain equals the initial change times 1 / (1 - MPC). At MPC 0.80 that factor is 5.

The formula explains the table above without any iteration. Spending of 4,000 times 5 is 20,000 of downstream activity. At MPC 0.50 the same spending would echo only twice as far, 4,000 / 0.5 = 8,000, because half of every round leaks into savings accounts instead of cash registers.

Real economies leak faster than the classroom model. Taxes take a slice of each round, imports send another slice to foreign producers, and firms may meet demand from inventory rather than new output. Forecasters who track fiscal stimulus therefore use multipliers well under 5 for the United States, and they treat the 1 / (1 - MPC) figure as a ceiling for a closed economy with no government. The direction is right even when the size is not: a higher MPC means a bigger echo, always.

What MPC does and does not predict

The concept earns its keep in policy arithmetic. A 1,200 dollar stimulus check with a recipient MPC of 0.80 puts 960 dollars into the economy in round one and supports 1,200 x 5 = 6,000 dollars of total demand in the simple model. The same check with an MPC of 0.50 supports 2,400 dollars. Whether a program is worth its cost depends heavily on who receives it, which is why the targeting of checks and rebates gets argued about as much as their size.

The income measure matters as much as the spending measure. MPC is defined against disposable income, the money left after taxes, so compare a gross raise against a net one and the ratio comes out wrong. Timing matters too: a year of income change measured against a month of spending change produces a number that means nothing.

What MPC cannot do is promise the future. A household's marginal rate depends on whether the income change looks permanent, on debts coming due, and on confidence. BEA's personal income and outlays data shows national saving rates swinging by several points within a single year, which is more than enough movement to wreck any forecast built on a fixed MPC.

Reading your own number

Plug in two pay stubs and two months of card statements and the calculator gives a personal MPC. A few habits make the number mean something. Use take-home pay, not gross. Use comparable periods, ideally the same month in different years, so bonuses and holidays do not distort the comparison. And strip out one-time purchases: the year the roof was replaced is not evidence about spending habits.

The result lands where you would expect. Households living paycheck to paycheck post MPC values near 1, because an extra dollar has nowhere to go but the register. Households with full emergency funds post values near 0.5 or lower, because an extra dollar is invisible to the budget. Neither number is a virtue or a flaw; they are descriptions of slack.

The useful reading is the trend. If your MPC drifts upward over the years while income rises, lifestyle is growing faster than the balance sheet, and the saving rate is eroding from the margins where it is hardest to see. The number to aim at is not a target MPC but a stable or falling one.

What the calculator returns

Enter income before and after an income change, spending before and after, and optionally an amount of extra income to trace through the multiplier. The tool returns the MPC, the MPS, the spending multiplier, the dollar change in consumption, and the total spending the traced income would support in the simple model.

It also reports the average share of income spent before and after, so the gap between average and marginal is visible instead of hidden. If spending rises by more than income does, the MPC comes out above 1, which usually means the household borrowed or drew down savings, and the tool flags it rather than refusing the input.

The multiplier output carries the classroom assumption of no taxes and no imports, which is stated on the page rather than buried. Treat it as the size of the echo in a sealed system, not as a forecast for the United States economy.