 # How to Calculate Marginal Propensity to Save

| Updated Aug 31, 2019

Marginal propensity to save (MPS) describes the share of additional income that a consumer saves. That means it describes the percentage of additional income they spend on saving instead of buying goods or services. Thus, marginal propensity to save can be calculated as the change in saving (ΔS) divided by the change in income (ΔY). That can be expressed using the following formula:

MPS = ΔS / ΔY

Please note that MPS is also the inverse of the marginal propensity to consume. However, in the following paragraphs, we will focus on the formula above and analyze it to learn how to calculate marginal propensity to save step-by-step.

## 1) Find the Change in Income (ΔY)

The first step to calculate MPS is to find the change in income (ΔY). Note that the Δ sign stands for the Greek letter delta. This letter is commonly used as a mathematical symbol for the difference between two distinct values. Thus, the change in income describes the difference in an individual’s level of income between a certain point in the past (Y0) and a more recent point in time (Y1). That means, to find the change in income, we have to subtract Y0 from Y1.

To illustrate this, let’s say you have a friend called Johnathan, who works at a fast-food restaurant as a cashier. At this position, he earns a salary of USD 20,000 per year. However, because Jonathan is such a disciplined and hard-working employee, he’s promoted to Floor Manager. That means he gets more responsibility and a higher salary. His new salary as Floor Manager is USD 36,000 per year. As a result, the change in Jonathan’s income amounts to USD 16,000 (i.e., 36,000 – 20,000).

## 2) Find the Change in Saving (ΔS)

Now that we know the change in income, we have to find the change in saving (ΔS). Just like before, that means we are trying to find the change in the level of saving between two separate points in time (i.e., S0 and S1). Particularly, we are looking to find the change in saving before and after the change in income described above. This allows us to find out how much of the additional income is spent on saving.

Going back to our example, let’s say that Jonathan was able to save USD 4,000 out of his USD 20’000 salary every year. That includes money in his savings account as well as other investments such as a Roth IRA or 401(k). After his promotion, John puts more money in his savings account and 401(k), so that he will be able to retire earlier when he gets old. That means his saving increases to USD 12,000, and the change in saving is USD 8,000 (i.e., 12,000 – 4,000).

## 3) Divide Change in Saving by Change in Income

Once we know both the change in income and the change in saving, we can finally calculate the marginal propensity to save by dividing the change in saving by the change in income. Please note that the value of the MPS will always lie within a range of 0 to 1. If none of the additional income is saved, ΔS is 0, which results in an MPS of 0. Similarly, if all extra income is spent on saving, ΔS is equal to ΔY, which results in an MPS of 1.

To illustrate this, let’s calculate Jonathan’s MPS. We know that the change in income is USD 16,000, and the change in saving is USD 8,000. That means, his marginal propensity to save is 0.5 (i.e., 8,000/16,000). Or in other words, Jonathan spends 50% of his additional income on saving. By contrast, if he decided to save all of his additional income, his MPS would be 16,000/16,000, which is equal to 1. Similarly, if he decided to save none of the additional income but spend it all on consumption, his MPS would be 0/16,000, which is equal to 0.

## In a Nutshell

Marginal propensity to save (MPS) describes the share of additional income that a consumer spends on saving. It is the inverse of marginal propensity to consume, which can be calculated as the change in saving (ΔS) divided by the change in income (ΔY). The value of MPS will always lie within a range of 0 to 1. If all of the additional income is saved, MPS is 1, because ΔS is equal to ΔY. Similarly, if none of the additional income is saved, MPS is 0, because ΔS is 0.