Mathematics

From the equation:

${\displaystyle Y=C+S}$

APS is calculated from the amount of savings as a fraction of income.

${\displaystyle APS={\frac {S}{Y}}}$

APS can be calculated as total savings divided by the income level for which we want to determine the average propensity to save.

Example 1: The income level is 90 and total savings for that level is 25, then we will get 25/90 as the APS.

Average propensity to save can not be greater than or equal to 1, but APS can be negative, if income is zero and consumption has a positive value.

Example 2: The income is 0 and consumption is 20, so the APS value will be -0.2. ^[1]

Average propensity to save is decreasing

As is a fraction of income, an increase in income would make the proportion of saving lower. Also income rises faster than savings so APS tens to decrease as income increase.

Marginal propensity to save (MPS)

Marginal propensity to save is the proportion of an increase in income devoted to savings. Mathematically, the ${\displaystyle {\mathit {MPS}}}$ function is expressed as the derivative of the savings function ${\displaystyle S}$ with respect to disposable income ${\displaystyle Y}$, i.e., the instantaneous slope of the ${\displaystyle S}$-${\displaystyle Y}$ curve.

${\displaystyle {\mathit {MPS}}={\frac {dS}{dY}}}$

or, approximately,

${\displaystyle {\mathit {MPS}}={\frac {\Delta S}{\Delta Y}}}$, where ${\displaystyle \Delta S}$ is the change in savings, and ${\displaystyle \Delta Y}$ is the change in disposable income that produced the consumption.