Each round saves the MPS share of what it receives; cumulative saving approaches the full $100 injected.
Round
Received
Saved
Cumulative saved
1
$100.00
$32.00
$32.00
2
$68.00
$21.76
$53.76
3
$46.24
$14.80
$68.56
4
$31.44
$10.06
$78.62
5
$21.38
$6.84
$85.46
6
$14.54
$4.65
$90.11
7
$9.89
$3.16
$93.28
8
$6.72
$2.15
$95.43
All rounds
$312.50
$100.00
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What it calculates: Marginal propensity to save (MPS), Marginal propensity to consume (MPC), Spending multiplier, Saved from a $100 first round.
Updated 22 September 2026 · Transparent assumptions
Saving up $3,200 on $10,000 of extra income is an MPS of 0.32
The marginal propensity to save is the share of an extra dollar of income that is saved: the change in saving divided by the change in income. A household whose income rises from $40,000 to $50,000 and whose saving rises from $4,800 to $8,000 has an MPS of 3,200 ÷ 10,000 = 0.32.
MPS = ΔS ÷ ΔY = 1 − MPC
Because an extra dollar is either spent or saved, the MPS is 1 − MPC. This household’s MPC is 0.68, measured from the same two years of spending: $35,200 and then $42,000.
Worked example
ΔS = 8,000 − 4,800 = 3,200
ΔY = 50,000 − 40,000 = 10,000
MPS = 3,200 ÷ 10,000
MPS = 0.32
Every round leaks 32% into saving, which is why the multiplier stops at 3.125
In the simple Keynesian model saving is the only thing that removes money from the spending stream. A $100 injection is spent in full, then 68% of it is re-spent while 32% is saved, then 68% of that, and so on. Each round is smaller because of the saving leak, and the total of all rounds is 100 ÷ 0.32 = $312.50.
k = 1 ÷ MPS
Looked at from the saving side, the rounds do something striking: the saving they generate adds up to the whole $100. The injection keeps circulating until exactly as much has been saved as was injected, which is the multiplier’s way of arriving at the equilibrium condition that saving equals investment.
The leak, round by round
Round 1: $100 spent, $32.00 saved
Round 2: $68.00 spent, $21.76 saved
Round 3: $46.24 spent, $14.80 saved
All rounds: $312.50 spent, $100 saved
Add a 20% tax and a 15% import share and the multiplier falls from 3.1 to about 1.7
Real economies leak in three places. Income tax takes a share before it can be spent, imports send spending abroad, and saving removes what is left. In a model with a proportional tax t and a marginal propensity to import m, the multiplier is 1 ÷ (1 − MPC(1 − t) + m). With an MPC of 0.68, t = 0.2 and m = 0.15, that is 1 ÷ (1 − 0.544 + 0.15) = 1.65.
k = 1 ÷ (1 − MPC(1 − t) + m)
UK A-level courses bundle the three leaks into a single marginal propensity to withdraw, MPW = MPS + MPT + MPM, with the multiplier 1 ÷ MPW. The MPS on its own gives the largest multiplier the model can produce; every other leak makes it smaller.
Uncertainty raises the share of extra income people save
Households save more of each extra dollar when the future looks risky — the precautionary motive. Job losses around them, falling house prices or tighter credit all push the MPS up, which lowers the multiplier just when a government would most like it to be large. The personal saving rate’s leap to a record 31.8% in April 2020 is the extreme case of the same behaviour.
This is one reason stimulus aimed at households with little cash tends to work better than stimulus spread evenly: those households have the lowest MPS, so less of each dollar leaks out in the first round.
A high MPS weakens demand in a slump but funds investment at full employment
Whether a high MPS is good news depends on the state of the economy. With idle capacity, extra saving means less demand, lower output and — by the paradox of thrift — no more total saving than before. At full employment the extra saving can fund investment instead, raising the capital stock and future output.
Growth models built on saving, from Harrod–Domar to Solow, work in the second setting. The average propensity to save calculator shows the Harrod–Domar arithmetic; the MPS here is the short-run, demand-side view of the same household choice.
Three ways an MPS calculation goes wrong
Each of these produces a number that looks plausible and is wrong.
Using levels instead of changes. S ÷ Y is the average propensity; the MPS needs ΔS ÷ ΔY.
Using account balances. Saving is the flow of unspent income over the period, not the balance in a savings account.
Applying 1 ÷ MPS to an open economy with taxes. It is the saving-only upper bound; taxes and imports make the true multiplier smaller.
Frequently Asked Questions
How do you calculate the marginal propensity to save?
Divide the change in saving by the change in income: MPS = ΔS ÷ ΔY. If income rises by $10,000 and saving by $3,200, the MPS is 0.32. Equivalently, MPS = 1 − MPC.
What is the relationship between MPS and the multiplier?
In the simple model the spending multiplier is 1 ÷ MPS. An MPS of 0.25 gives a multiplier of 4; an MPS of 0.5 gives 2. A larger share saved means a smaller multiplier.
Is a high MPS good or bad for the economy?
It depends on conditions. With unemployment and idle capacity, a high MPS weakens demand and output. At full employment, higher saving can fund investment and raise future output.
What is the marginal propensity to withdraw?
A term used in UK courses for all leakages together: MPW = MPS + MPT + MPM (saving, tax and imports). The multiplier is then 1 ÷ MPW.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Results are estimates for planning and analysis based on the figures you enter. They are not accounting, tax, or financial advice — verify with your own records and a qualified professional before making decisions.
Sudha, J. (2026, September 22). Marginal Propensity to Save Calculator. Calculator Matters. https://calculatormatters.com/economics/marginal-propensity-to-save-calculator/
MLA
Sudha, Jay. "Marginal Propensity to Save Calculator." Calculator Matters, 22 Sept. 2026, https://calculatormatters.com/economics/marginal-propensity-to-save-calculator/.