# Marginal Propensity to Save (MPS)

The concept of Marginal Propensity to Save MPS refers to the situation when an increase in the income leads to the increase in the saving. In other words, Marginal Propensity to Save defines that the consumers tend to save more with the increase in income rather than spending it on services or goods.
Marginal propensity to save is also popularly called as MPS. An example can be used to make the concept clear. If a family earns the extra income of one dollar and if 0.45 is the value of marginal propensity to save, then according to the concept of Marginal Propensity to Save, the family will save 45 cents and spend 55 cents out of that one dollar.

The inverse of marginal propensity to save theory is also true. It says that, a decrease in the income will result in the decrease of saving at the same proportion at which the income is decreased.

## Concept of Marginal Prospensity to Save:

The concept of marginal propensity to save is very important in the context of Keynesian economics and is used in the determination of the multiplier value. Mathematically it can be shown that the average propensity to save is described as the ratio of total amount of savings to the total amount of income.
Also, the marginal propensity to save can be enumerated as the ratio between the amounts of saving change and the income change.

When derived mathematically, the marginal propensity to save can be represented as the derivative value of saving calculated with respect to disposable income.

## Mathematical formula for marginal propensity to save:

Marginal Propensity to Save (MPS) = dS/dY
Where S refers to the savings and Y refers to income. The value of MPS always varies from 0 and 1.

The marginal propensity to save holds a relation with the marginal propensity to consume (MPC).

Mathematically, the relation between MPS and MPC can be expressed as :

MPS = 1 – MPC

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