MPS Calculator - Marginal Propensity to Save
Enter the change in income and the change in savings to find the Marginal Propensity to Save (MPS). The calculator also derives the Marginal Propensity to Consume (MPC), the Keynesian spending multiplier, and the implied fiscal stimulus impact. You can work forward from income and savings changes, or backward from a known MPS. Results update as you type.
Formula
Worked example
A household's income rises from $50,000 to $60,000 (Delta-Y = $10,000). Their annual savings rise from $5,000 to $8,000 (Delta-S = $3,000). MPS = 3,000 / 10,000 = 0.30. MPC = 1 - 0.30 = 0.70. The spending multiplier = 1 / 0.30 = 3.33. A $10,000 government spending injection at this MPS would produce approximately $33,300 of total economic output.
What is the Marginal Propensity to Save?
The Marginal Propensity to Save (MPS) is a Keynesian economics concept that measures what fraction of each additional dollar of disposable income a household or economy saves rather than spends. It is expressed as a number between 0 and 1, where 0 means all additional income is consumed and 1 means all of it is saved. In practice, most households fall somewhere in between. MPS is closely related to the Marginal Propensity to Consume (MPC): the two always sum to exactly 1, so MPC = 1 - MPS. Understanding MPS is essential for evaluating fiscal policy, because it determines how much of a government spending stimulus gets amplified through the economy via the Keynesian multiplier.
The MPS formula and how to calculate it
MPS is calculated as the change in savings divided by the change in disposable income: MPS = Delta-S / Delta-Y. If a household earns $10,000 more this year and saves $3,000 of that, the MPS is 0.30. Equivalently, if you already know the MPC, MPS = 1 - MPC. From MPS you can immediately derive the Keynesian spending multiplier: k = 1 / MPS. At an MPS of 0.30, k = 3.33, meaning every new dollar of government spending or private investment generates about $3.33 of total GDP through successive rounds of spending.
What affects the MPS?
MPS is not fixed - it varies across income levels, economic conditions, and individual circumstances. Higher-income households typically save a larger fraction of any income increase because their basic consumption needs are already met, a pattern economists call diminishing marginal utility of income. During economic uncertainty, people save more as a precaution, raising the aggregate MPS. Conversely, in boom periods or when credit is easy, MPS tends to fall as consumers spend more. Age and life stage also matter: younger workers often have lower MPS (building careers, raising children), while those approaching retirement typically save more. Cultural norms and financial literacy can also shift the saving rate significantly across countries.
The spending multiplier and fiscal policy
The Keynesian spending multiplier (k = 1 / MPS) describes how an initial injection of spending circulates through the economy. Each time money changes hands, the recipient saves a fraction (MPS) and spends the rest (MPC). This chain repeats, generating a cumulative impact larger than the original injection. At MPS = 0.25, k = 4.0: a $1 billion infrastructure program would eventually generate $4 billion of total output. At MPS = 0.50, k = 2.0 and the effect is smaller. This is why governments prefer to target stimulus at lower-income households who have lower MPS and higher MPC, maximizing the multiplier effect.
The paradox of thrift
While saving is individually beneficial, the economist John Maynard Keynes identified what he called the paradox of thrift: if all households simultaneously decide to save more, aggregate consumption falls, businesses face lower demand, output contracts, incomes drop, and the economy may end up with no more total savings than before. This paradox is central to understanding recessions. When MPS rises sharply across the economy (a "savings surge"), the spending multiplier contracts and fiscal stimulus becomes less effective at restoring output, which is one reason economists watch aggregate saving rates closely during downturns.
MPS by household income group (approximate)
| Income group | Typical MPS range | Spending multiplier range | Saving tendency |
|---|---|---|---|
| Lower income (< $30,000) | 0.02 - 0.08 | 12.5 - 50 | Very low - most income consumed |
| Lower-middle ($30,000-$60,000) | 0.08 - 0.15 | 6.7 - 12.5 | Low |
| Middle ($60,000-$100,000) | 0.10 - 0.20 | 5.0 - 10 | Moderate |
| Upper-middle ($100,000-$200,000) | 0.15 - 0.30 | 3.3 - 6.7 | Moderate to high |
| Upper ($200,000+) | 0.25 - 0.50 | 2.0 - 4 | High - larger share saved |
Empirical estimates from the U.S. Bureau of Economic Analysis and academic studies. Values vary by country, economic cycle, and methodology.
Frequently asked questions
What does MPS = 0.30 mean?
An MPS of 0.30 means a household or economy saves 30 cents out of every additional dollar of disposable income and spends the remaining 70 cents. The MPC would be 0.70, and the Keynesian spending multiplier would be 1 / 0.30 = 3.33.
Can MPS be negative?
In theory, MPS can be negative if a household reduces its savings when income rises, for example by spending more on credit or drawing down existing savings in anticipation of higher future income. In practice, a sustained negative MPS signals dissaving and is rare at the aggregate level, though it can occur temporarily during economic shocks.
What is the relationship between MPS and MPC?
MPS and MPC always sum to 1: MPS + MPC = 1. This is a mathematical identity because any additional dollar of income must be either saved or consumed - there is no third option. If you know one, subtract from 1 to get the other.
How does MPS affect the spending multiplier?
The Keynesian spending multiplier equals 1 / MPS. A higher MPS means a lower multiplier: if households save more of each dollar received, less money circulates through the economy in successive rounds of spending, so the amplification effect is smaller. Conversely, a lower MPS yields a larger multiplier and greater GDP impact per dollar of fiscal stimulus.
Why is MPS higher for wealthier households?
Wealthier households have already satisfied most of their consumption needs. When they receive additional income, they have little left to spend it on beyond what they already buy, so more of it flows into savings. Economists call this diminishing marginal utility of consumption. This is also why targeted fiscal transfers to lower-income households tend to generate a larger multiplier effect.
What is the difference between MPS and the average propensity to save?
The Average Propensity to Save (APS) is total savings divided by total income: APS = S / Y. The Marginal Propensity to Save (MPS) is the change in savings divided by the change in income: MPS = Delta-S / Delta-Y. APS describes the current saving rate on all income; MPS describes the saving rate on the next dollar earned. For policy purposes, MPS is generally more useful because it predicts how households will respond to income changes.