Saving Function

Saving is the excess of income over consumption during an accounting year. Algebraically, saving (S) is defined as: 

S = Y – C, where Y is income and C is consumption 

Since income is either spent or saved, there is a close relationship between consumption and saving,
i.e. the part of income which is not consumed is saved and the part of income which is not saved is used in the form of consumption expenditure.

Like consumption, saving is an increasing function of the level of income, i.e. 

the amount of saving increases with an increase in the level of income.

Thus, S = f (Y)

Propensity to save

Propensity to save is the ratio between S and Y. 

It shows the level of S with respect to a given level of Y. 

Like propensity to consume, propensity to save also has two aspects:

1) Average propensity to save

2) Marginal propensity to save

Average Propensity to save 

The average propensity to save is the ratio of saving to any particular level of income.

Average Propensity to save = saving / Income 

APS = S / Y 

For example: If income (Y), is Rs. 100 crore and saving (S) is Rs. 40crore, then

APS = S / Y

APS = 40 / 100 = 0.4 or 80 %

This indicates that 40 per cent of the income is saved and 60 percent is spent by way of consumption expenditure in the economy.

Marginal Propensity to save

The marginal propensity to consume is the ratio of change in saving to a change income. 

Marginal Propensity to save = Change in saving / Change in Income 

MPS = ∆S  /  ∆Y 

For example: If income (Y), increases from Rs. 100 crore to Rs. 200 crore and saving (S) increases from Rs. 20 crore to Rs. 80 crore, it means that change in income by Rs. 100 crore has caused a change in saving by Rs. 60 crore.

MPS = ∆S  /  ∆Y

MPS = 80 - 20  /  200 - 100

          = 60 / 100

 = 0.6 

It indicates that 60 percent of the additional income is saved and the remaining 40 percent of the additional income goes to consumption expenditure.

Relationship between APC and APS 

We know that:

APC = C / Y

APS = S / Y

We also know that:

Y = C + S (income is either consumed or saved)

(Dividing both sides of the equation by Y)

Y / Y = C / Y + S / Y

1 = APC + APS

So that, 

APC + APS = 1 

Or, APC = 1 – APS

Or, APS = 1 - APC

Relationship between MPC and MPS

We know that:

MPS = ∆S / ∆Y

MPC = ∆C / ∆Y

We also know that: 

(Additional income is either used in increasing consumption or saving)

 ∆Y = ∆C +∆ S 

(Dividing both sides of the equation by ∆Y)

∆Y / ∆Y = ∆C / ∆Y + ∆S / ∆Y 

1 = MPC + MPS 

So that, 

MPC + MPS = 1 

Or, MPC = 1 – MPS

Or, MPS = 1 – MPC

MPC is generally less than unity and greater than zero. It means that a part of increase in income is consumed and the other part is saved.

So, the aggregate MPC and MPS must be equal to unity. Thus, if half of the increase in income is spent on consumption, the other half must be saved.

So that when MPC = 1/ 2 (half), then MPS = 1/ 2(half) also implying that

MPC + MPS = 1 always.