Marginal Propensity to Save (MPS) Calculator
Enter the increase in disposable income and the increase in saving to see the MPS from ΔS ÷ ΔYd, with the MPC, the multiplier and the saved share.
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Marginal Propensity to Save (MPS) Calculator
Our Marginal Propensity to Save (MPS) Calculator shows how much of an extra unit of income is put aside instead of spent. Type the increase in disposable income and the increase in saving, and it returns the MPS with the working. Under the result you get the marginal propensity to consume, the simple multiplier (1 ÷ MPS), the saved share as a percent, the extra spending, and a bar that splits the extra income into saved and spent. It is built for economics students working through saving function problems, teachers writing multiplier examples, and anyone who wants to see how much of a pay rise or tax refund ends up as saving.
Quick answer
The marginal propensity to save is MPS = ΔS ÷ ΔYd. Divide the increase in saving by the increase in disposable income. If saving rises by 1,600 when disposable income rises by 4,000, the MPS is 1,600 ÷ 4,000 = 0.4.
- ΔS: the change in saving.
- ΔYd: the change in disposable income (income after taxes).
- MPS of 0.4: 40 cents of each extra dollar is saved and 60 cents is spent.
- MPS + MPC = 1, and the simple multiplier is 1 ÷ MPS.
What Is the Marginal Propensity to Save?
The marginal propensity to save (MPS) is the fraction of an increase in disposable income that a household, or a whole economy, saves. Saving here means every part of the extra income that is not spent on goods and services: money left in the bank, paid into a pension or used to pay down debt. An MPS of 0.4 means 0.40 of each extra 1 of income is saved.
In Keynesian economics saving is a leakage. Income that is saved is not passed on to another person as spending, so the MPS decides how fast a first round of new spending fades out. That is why the MPS sits in the denominator of the simple multiplier.
MPS Formula
- MPS: the marginal propensity to save, a number with no unit.
- ΔS: the change in saving, new saving minus old saving.
- ΔYd: the change in disposable income, new income minus old income.
Measure both changes over the same period and in the same currency. The change in income cannot be 0, because the formula divides by it. Multiply the MPS by 100 to read it as a percent: 0.4 means 40% of the extra income is saved.
How to Calculate MPS
A worker gets a pay rise that lifts disposable income by 4,000 a year. Over the same year the amount saved rises by 1,600:
MPS = 1,600 ÷ 4,000
MPS = 0.4
- Find the increase in disposable income. New income minus old income: 4,000.
- Find the increase in saving. New saving minus old saving: 1,600.
- Divide the saving increase by the income increase. 1,600 ÷ 4,000 = 0.4.
The MPS is 0.4. Two fifths of the pay rise was saved, and the other 4,000 − 1,600 = 2,400 was spent.
Finding ΔS and ΔYd From Before and After Figures
Problems often give income and saving at two points in time instead of the changes. Subtract first, then divide. Suppose disposable income goes from 30,000 to 36,000 and saving goes from 3,000 to 4,500:
ΔYd = 36,000 − 30,000 = 6,000
MPS = 1,500 ÷ 6,000 = 0.25
Enter 6,000 and 1,500 in the calculator. If you only know spending, find saving first with saving = disposable income − consumer spending.
MPS and MPC
Extra disposable income has only two uses in this model: it is saved or it is spent. So the MPS and the marginal propensity to consume (MPC) are two sides of the same split:
MPC = 1 − 0.4 = 0.6
The calculator shows the MPC as the first row under the result. If you have the change in spending instead of the change in saving, start from our MPC Calculator.
The Saving Function: S = −C₀ + MPS × Yd
The MPS is the slope of the saving function, the line that links total saving to disposable income:
- S: total saving.
- C₀: autonomous spending, the amount spent even at an income of 0. It enters with a minus sign because it has to come out of past savings or borrowing.
- MPS × Yd: the saving that grows with income.
With autonomous spending of 3,000, an MPS of 0.4 and disposable income of 20,000:
S = −3,000 + 8,000 = 5,000
Saving is 0 at the break-even income, where the line crosses the axis:
= 3,000 ÷ 0.4 = 7,500
Below 7,500 the household dissaves: it spends more than it earns.
MPS vs APS
The average propensity to save (APS) is total saving divided by total disposable income, S ÷ Yd. The MPS measures the change, the APS measures the level:
APS = 5,000 ÷ 20,000 = 0.25
The table uses S = −3,000 + 0.4 × Yd. The MPS is 0.4 in every row, while the APS starts below 0 and climbs toward the MPS as income grows:
| Yd | S | APS |
|---|---|---|
| 5,000 | −1,000 | −0.2 |
| 7,500 | 0 | 0 |
| 10,000 | 1,000 | 0.1 |
| 20,000 | 5,000 | 0.25 |
| 60,000 | 21,000 | 0.35 |
A published household or personal saving rate is an average rate, so it is closer to the APS than to the MPS.
MPS and the Multiplier
Each time income is passed on, a share equal to the MPS leaks into saving and the rest is spent again. With an MPS of 0.4, new spending of 1,000 leads to 600 of spending in the second round and 360 in the third, while 400 and then 240 are saved. Adding up all the rounds gives the simple multiplier:
Multiplier = 1 ÷ 0.4 = 2.5
| MPS | Multiplier | From 1,000 |
|---|---|---|
| 0.1 | 10 | 10,000 |
| 0.2 | 5 | 5,000 |
| 0.25 | 4 | 4,000 |
| 0.4 | 2.5 | 2,500 |
| 0.5 | 2 | 2,000 |
The last column is the total rise in income from 1,000 of new spending. The smaller the MPS, the larger the multiplier. See our Spending Multiplier Calculator to work from the multiplier side.
Saving Is One of Three Leakages
In an economy with a government and foreign trade, extra income also leaks out as taxes and as spending on imports. Each leakage has its own marginal rate: the marginal propensity to tax (MPT) and the marginal propensity to import (MPM). The multiplier then divides by all three:
1 ÷ (0.2 + 0.15 + 0.15) = 2
With saving as the only leakage the multiplier would be 1 ÷ 0.2 = 5. Adding taxes and imports cuts it to 2, which is why multipliers measured in real economies are much smaller than the simple formula suggests.
The Paradox of Thrift
Saving more is sensible for one household, but if everyone raises their MPS at once, total spending falls and so does total income. In the simple model, 1,000 of investment supports income of 1,000 ÷ MPS:
| MPS | Income | Saving |
|---|---|---|
| 0.2 | 5,000 | 1,000 |
| 0.25 | 4,000 | 1,000 |
When the MPS rises from 0.2 to 0.25, income drops from 5,000 to 4,000, and total saving stays at 1,000 (0.25 × 4,000). People save a larger share of a smaller income and end up with no more saving in total. Keynes called this the paradox of thrift. It applies mainly when the economy has spare capacity.
How to Read the MPS
| MPS | Meaning |
|---|---|
| 0 | None of the extra income is saved. All of it is spent. |
| 0 to 1 | Part is saved and part is spent. This is the normal case. |
| 1 | All of the extra income is saved. |
| Above 1 | Saving rose by more than income, so spending fell. |
The MPS tends to be higher for households with higher incomes, for one-off windfalls and in uncertain times, when people build a buffer. It tends to be lower where budgets are tight and extra income goes on needs.
MPS Examples
| ΔYd | ΔS | MPS |
|---|---|---|
| 750 | 75 | 0.1 |
| 10,000 | 1,500 | 0.15 |
| 1,200 | 300 | 0.25 |
| 3,000 | 1,000 | ≈ 0.3333 |
| 4,000 | 1,600 | 0.4 |
A tax refund. A household receives a refund of 900 and puts 270 of it into savings:
The other 900 − 270 = 630 is spent, so the MPC is 0.7.
A whole economy. National disposable income rises by 2,500 (in billions) and total saving rises by 500, so MPS = 500 ÷ 2,500 = 0.2 and the simple multiplier is 1 ÷ 0.2 = 5.
Key Terms
- Saving
- Disposable income that is not spent on consumption, written S.
- Disposable income
- Income after taxes and transfers, written Yd. Our Disposable Income Calculator finds it.
- Dissaving
- Spending more than income by drawing on savings or borrowing. Saving is negative.
- APS
- Average propensity to save, total saving divided by total disposable income.
- Leakage
- Income that is not passed on as spending at home: saving, taxes and imports.
- MPC
- Marginal propensity to consume, the share of extra income that is spent. MPC = 1 − MPS.
How to Use the Marginal Propensity to Save (MPS) Calculator
- Enter the increase in disposable income. Type how much disposable income went up, such as 4,000.
- Enter the increase in saving. Type how much saving went up over the same period, such as 1,600.
- Read and copy the result. The MPS appears as you type, with the working, the MPC, the multiplier, the saved share and a bar showing the saved and spent parts. Press Copy to copy it, or Clear or Esc to start again.
Example: income rises by 1,200 and saving rises by 300. The MPS is 300 ÷ 1,200 = 0.25.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is the marginal propensity to save?
The marginal propensity to save (MPS) is the fraction of an increase in disposable income that is saved instead of spent. An MPS of 0.4 means 0.40 of each extra 1 of income is saved.
What is the MPS formula?
MPS = ΔS ÷ ΔYd. Divide the change in saving by the change in disposable income. If saving rises by 1,600 when disposable income rises by 4,000, MPS = 1,600 ÷ 4,000 = 0.4.
How do you find MPS from MPC?
Subtract the MPC from 1, because extra income is either spent or saved. If the MPC is 0.6, the MPS is 1 − 0.6 = 0.4.
How does the MPS set the multiplier?
The simple multiplier is 1 ÷ MPS. An MPS of 0.4 gives a multiplier of 2.5 and an MPS of 0.2 gives 5. A smaller MPS means less income leaks into saving each round, so the multiplier is larger.
What is the difference between MPS and APS?
The MPS is the change in saving divided by the change in disposable income. The APS is total saving divided by total disposable income. With saving of 5,000 out of income of 20,000 the APS is 0.25, even if the MPS is 0.4.
Can the MPS be greater than 1 or negative?
In standard models the MPS lies between 0 and 1. It is above 1 if saving rises by more than income, which means spending fell. It would be negative if saving fell while income rose. This calculator takes increases only, so it does not return a negative MPS.
What is the saving function?
The saving function is S = −C₀ + MPS × Yd. Total saving equals the MPS times disposable income, minus autonomous spending. With C₀ = 3,000, MPS = 0.4 and Yd = 20,000, S = 5,000.
What is the paradox of thrift?
It is the idea that if everyone tries to save a larger share of income at the same time, total spending and income fall, so total saving may not rise at all.
Is the MPS Calculator free?
Yes. It is free to use, with no sign-up and no limit on how many times you use it.
Sources
- Wikipedia. Marginal propensity to save.
- Wikipedia. Average propensity to save.
- Wikipedia. Multiplier (economics).
- Wikipedia. Paradox of thrift.
- OpenStax. Principles of Macroeconomics 3e, Appendix B The Expenditure-Output Model.
- Corporate Finance Institute. Marginal Propensity to Save.
- U.S. Bureau of Economic Analysis. Personal Saving Rate.
Try our MPS Calculator to see how much of an extra unit of income is saved and how much is spent.