Saving Function, propensity to save

 

SAVING FUNCTION

Saving is that part of income which is not consumed because disposable income is either consumed or saved.

Thus, Y = C + S

S = Y – C

where Y = Disposable income, C = Consumption, S = Saving

Saving is also a function of income. S = f (Y)

Saving function or propensity to save shows the savings of households at a given level of income during a given period of time.

Alternately, it shows the different levels of saving at different levels of income in an economy.

PROPERTIES OF THE SAVING FUNCTION

The propensity to save is of two types:

1- The average propensity to save

2- The marginal propen­sity to save

The average propensity to save: Average propensity to save is the proportion of disposable income that is saved. It shows us about the proportion of each income level that people will save i.e., they will not spend on consumption.

Mathematically APS= S/Y

Where S= Savings and Y= Disposable Income

APS rises with increase in income because the proportion of income saved keeps on increasing. APS can be negative or Zero. At income levels which are lower than the break-even point, APS can be negative as there will be dis-savings to satisfy consumption needs which is known as autonomous consumption in the economy. At the break-even point where consumption expenditure is equal to income, APS is zero. but it can never be 1 or more than 1 as saving can never be equal to or more than national income.

Marginal Propensity to Save (MPS): The marginal propensity to save indicates to the change in savings induced by a change in the disposable income.

Thus, MPS = ΔS/ΔY

Generally, value of MPS varies between O and 1. Value of MPS remains constant throughout in the linear saving function.

The APS relates total saving to total income while the MPS relates a change in saving to a change in income.

Saving Schedule

Income [Y] In lakhs	Consumption[C] In lakhs	Saving [S] S=Y-C In lakhs	Average propensity to save APS = S/Y	Marginal propensity to save MPS =∆S/∆Y
0	40	-40	----	----
100	120	-20	-0.2	0.2
200	200	0	0	0.2
300	280	20	20/300=.067	0.2
400	360	40	40/400=.1	0.2
500	440	60	60/500=.12	0.2

In the above diagram, national income is measured on the X-axis and saving is measured on the Y-axis. Saving curve slope starts from the S on Y-axis indicating that there is negative saving equal to autonomous consumption. When income is zero or very low, people dissave to satisfy their consumption needs. 

This is shown by

When income equals consumption expenditure, then savings are zero at R point. This is known as break-even point. As income increases further after the break-even point, savings also increase but by less than proportionately. The S curve is linear (straight line) because the rise in income and savings is at constant rates [Rs 100 lakhs and Rs 20 lakhs respectively].

Relationship between Average propensity to consume [APC] and average propensity to save[APS]

the sum of average propensity to consume and average propensity to save is equal to one because income is either used for consumption or for savings.

Symbolically, APC + APS = 1

As,

Y=C+S Dividing both sides by Y, we get

Relationship between marginal propensity to consume [MPC] and marginal propensity to save[MPS] 

Since the additional income is either consumed or saved, the sum of marginal propensity to consume and marginal propensity to save is equal to one. MPC + MPS = 1

where S indicates to the savings.  ‘-a’ is an intercept showing at the zero level of income, and ‘1-b’ stands for MPS = 1-MPC and ‘Y’ indicates level of income at which savings has to be calculated.

Or we can write linear saving function as:

Thus, saving function indicates that the whole of increased income is not spent on consumption, the remaining is saved.

Second, increase in income always leads to an increase in both consumption and saving.

Dr. Swati Gupta

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