Marginal Propensity to Consume (MPC): Formula, Example, and MPS

“Marginal” means the response to an additional amount of income. In a simple household example, the MPC asks how much consumption changes when disposable income changes. If consumption rises by 60 cents for each additional dollar of disposable income over the period being studied, the MPC for that response is 0.60, or 60%.

Economists often express the concept as the derivative of consumption with respect to income. With observed data or a worked example, a finite-change version is easier to calculate:

MPC = change in consumption ÷ change in income

The Federal Reserve Board’s review of the income-shock literature describes MPC broadly as the derivative of consumption with respect to income. It also shows why a reported MPC depends on what researchers call income, which consumption measure they use, and which response they estimate. The label alone does not supply those choices. See the [Federal Reserve review of consumption responses to income shocks]({source:fedIncomeShocksConsumption}).

An MPC must be tied to a window. An estimate can describe spending during a week, quarter, or longer follow-up period. A household may spend some of an income change promptly, save some, repay debt, or adjust purchases later. “An MPC of 0.60” is incomplete unless the income change, spending measure, population, and response period are also clear.

For a discrete example, compare consumption and income for the same person or group, using the same currency and measurement window. Suppose a hypothetical household has an additional $500 of disposable income over a quarter, and its consumption over that quarter is $300 higher than the comparison path. The calculation is:

MPC = $300 ÷ $500 = 0.60

The result says consumption changed by 60 cents per additional dollar of income in this invented example and over this stated window. The $500 and $300 are illustrative amounts, not a survey result or a typical household response. The calculation also assumes that the measured consumption change is the response being studied; a raw before-and-after difference does not prove that income alone caused it.

When the income change is negative, keep the signs consistent. If income falls by $500 and consumption falls by $300, then ΔC ÷ ΔY is also 0.60. If a source reports a dollar change for one group but a percentage change for another, those ratios are not directly comparable without a common scale and method.

For small changes, an MPC can be understood as a local slope. For larger income shocks, the response may differ across the range. A single ratio therefore summarizes a particular change; it does not establish that the same slope applies to every dollar, household, or time period.

The marginal propensity to save (MPS) compares the change in saving with the change in income. In the same hypothetical two-use model, if the household saves the remaining $200 of its $500 income increase, then:

MPS = $200 ÷ $500 = 0.40

When the model assigns the full income change only to consumption or saving, and both are measured over the same period, MPC + MPS = 1. In that example, 0.60 + 0.40 = 1. This complement is an assumption about the model’s uses of income, not a rule for combining unrelated statistics or different time windows.

Average propensities answer a different question. The average propensity to consume (APC) is total consumption divided by total income; the average propensity to save (APS) is total saving divided by total income. MPC and MPS instead use changes in the numerator and denominator. A household can have a high APC because it spends a large share of its total income while having a different MPC for a new income change.

The distinction is similar to comparing a level with a slope. C ÷ Y describes an average share at a point; ΔC ÷ ΔY describes how consumption moved when income changed. Do not substitute one ratio for the other when interpreting an article or a policy estimate.

In a household model, researchers may study gross income, disposable income after taxes and transfers, or a particular income shock. The denominator must match the question. The U.S. Bureau of Economic Analysis (BEA) defines disposable personal income (DPI) as personal income less personal current taxes, and describes it as income available for spending or saving. That national-account aggregate is not an individual worker’s exact take-home pay. BEA’s [Personal Income and Outlays definitions]({source:beaPersonalIncomeOutlaysDefinitions}) set out the boundary.

Consumption also needs a definition. BEA’s personal consumption expenditures (PCE) measure goods and services purchased by or on behalf of U.S. residents. PCE includes some purchases paid by third parties and some imputed transactions; it is broader than the amount a family observes leaving its bank account. The [NIPA Handbook chapter on PCE]({source:beaNipaPceMethods}) explains its coverage and accounting treatment.

This matters when a reader calculates an aggregate ratio such as ΔPCE ÷ ΔDPI. That ratio describes how two published totals moved together; it is not automatically a household-level MPC or a causal estimate of how a particular income shock changed spending. BEA also defines personal saving as DPI less personal outlays, and personal outlays include PCE, personal interest payments, and personal current transfer payments. Because PCE is only one component of outlays, its change is not mechanically the opposite of the change in BEA personal saving.

Before calculating a real-world ratio, write down the income series, consumption series, population covered, price basis, and period. If the two series have different scopes, frequencies, or revisions, the result may mix measurement differences with behavior.

An extra dollar may not lead to the same consumption change for every household. Relevant circumstances can include liquid savings, debt obligations, access to credit, uncertainty about future income, and whether the income change is expected to continue. These are factors to investigate, not a formula that assigns a fixed MPC to each income or wealth group.

Timing matters too. A temporary payment and a lasting rise in earnings pose different planning questions. Some households may use a temporary change for a purchase or to reduce overdue bills; others may hold it as a buffer. A study that counts spending only in the first month can differ from one that follows purchases for a year, even if both use the word MPC.

The chosen consumption measure can change the result. A study may count only nondurable goods, include services, track total card purchases, or include a broader household expenditure measure. Durable purchases may be lumpy and may be brought forward or delayed. A reported response should be read together with the outcome the researchers actually observed.

The Federal Reserve review organizes the evidence around differences in methods, data, consumption definitions, and income shocks. It is a literature review by its authors, not an official Board estimate or a claim that one value applies to all households. Its page states that FEDS research represents the authors’ views and that conclusions may be preliminary. Those limits are part of the source context, not a reason to treat the MPC as a universal constant.

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A simple ratio of two published series can be descriptive, but it does not isolate a causal effect. Spending and income can change together because of employment, prices, household composition, credit conditions, or other events. An analyst who wants to estimate how an income shock changed consumption needs a comparison that addresses what would likely have happened without that shock.

The Federal Reserve review identifies three broad approaches in the literature: structural economic models, natural experiments that compare affected and comparison groups, and surveys that ask people how they expect to respond to hypothetical changes. Each approach has strengths and limits. A model depends on its assumptions; a natural experiment depends on the event and comparison group; a survey records stated expectations rather than necessarily observed purchases.

The methods may measure different responses. A study can estimate the effect of an anticipated or unexpected change, use gross or disposable income, and observe consumption over different horizons. Its estimated MPC is conditional on those choices. Two estimates that look numerically different may be answering different questions rather than contradicting one another.

For this reason, an MPC estimate is not automatically a forecast for the next payment or a causal law for every household. Use the source’s design and definitions to decide how far the result can be generalized.

MPC and a fiscal multiplier describe different steps. MPC is a household consumption response to an income change. A fiscal multiplier relates an economy-wide output response to a defined policy change and a counterfactual. The first can be an input to a simple spending model; it is not itself the final GDP response.

In an introductory fixed-price model with a constant MPC, no taxes, no imports, no capacity constraint, and no monetary-policy response, repeated rounds of spending produce the formula multiplier = 1 ÷ (1 − MPC). If the hypothetical MPC is 0.60, that model gives 2.5. This is a result of the model’s simplifying assumptions, not a measured multiplier for a real economy or a prediction that a $1 payment raises GDP by $2.50.

Actual analyses must consider which households receive income, how much is spent during the measured window, imports, taxes, saving, supply limits, financing, and policy responses. The existing guide to fiscal multipliers explains why output estimates require a defined impulse, horizon, and counterfactual.

When a headline or paper reports an MPC, check these details before comparing the value:

• Income: Is the change in gross, disposable, labor, transfer, permanent, or temporary income?
• Consumption: Which goods, services, or outlays are counted, and for whom?
• Time: How long after the income change are purchases measured?
• Method: Is the figure a descriptive ratio, an experiment-based estimate, a model result, or a survey response?
• Scope: Which households, country, and period are represented?
• Interpretation: Is the source estimating a causal response, describing co-movement, or illustrating a model?

For the U.S. national-account definitions of DPI and PCE, see the related guide to [personal income and disposable income](/learn/personal-income-vs-disposable-income-vs-personal-outlays-explained). The guide to retail sales versus PCE explains why a single retail series does not cover the whole BEA consumption concept.