Relationship between different propensities (APC, MPC, APS and MPS)

The four different types of propensities are Average Propensity to Consume (APC), Marginal Propensity to Consume (MPC), Average Propensity to Save (APS), and Marginal Propensity to Save (MPS).

Average Propensity to Consume (APC)

It is the ratio of consumption expenditure to the corresponding income level. The formula to determine Average Propensity to Consume (APC) is:

Marginal Propensity to Consume (MPC)

It is the ratio of the change in consumption expenditure to the change in total income. In simple terms, MPC explains the proportion of change income that is spent on consumption. The formula to determine Marginal Propensity to Consume (MPC) is as follows:

Average Propensity to Save (APS)

It is the ratio of saving to the corresponding income level. The formula to determine the Average Propensity to Save (APS) is:

Marginal Propensity to Save (MPS)

It is the ratio of the change in saving to the change in total income. The formula to determine Marginal Propensity to Save (MPS) is:

Relationship between APC and APS

The sum of the Average Propensity to Consume (APC) and Average Propensity to Save (APS) is equal to one.

Proof:

We already know that Y = C + S.

Now dividing both sides by Y, we get

1 = APC + APS $[\because\frac{Y}{Y}=1,~\frac{C}{Y}=APC,~and~\frac{S}{Y}=APS]$

Also, APC + APS = 1 because the income is either used for consumption or for saving.

Relationship between MPC and MPS

The sum of the Marginal Propensity to Consume (MPC) and Marginal Propensity to Save (MPS) is equal to one.

Proof:

We already know that $\Delta{Y}=\Delta{C}+\Delta{S}$

Now dividing both sides by $\Delta{Y}$ , we get

\frac{\Delta{Y}}{\Delta{Y}}=\frac{\Delta{C}}{\Delta{Y}}+\frac{\Delta{S}}{\Delta{Y}}

1 = MPC + MPS $\because\frac{\Delta{Y}}{\Delta{Y}}=1,~\frac{\Delta{C}}{\Delta{Y}}=MPC,~and~\frac{\Delta{S}}{\Delta{Y}}=MPS$

Also, MPC + MPS = 1 because total increment in income is either used for consumption or for saving.

Example:

The inter-relationships between APC, MPC, APS, and MPS can be understood with the help of the following schedule.

$\Delta{C}$

Values of APC, APS, MPC, and MPS

The value of MPC and MPS lies between 0 and 1. Whereas, the value of APC can be more than 1 and APS can be less than 1.

Where,

$\bar{c}$ = Autonomous Consumption

C = Consumption

Y = National Income

$\Delta{S}$ = Change in Savings

$\Delta{C}$ = Change in Consumption

$\Delta{Y}$ = Change in National Income