Propensity to Save: Saving Function
Propensity to save or saving function is the counterpart of the consumption function. Saving function shows relation between the level of saving and the level of income. Keynesian economics regards saving as a function of income. The higher is the level of income, the higher will be the amount of saving.
Question: Using appropriate diagram explain the concept of saving function.
Saving Function:
- Saving function defines the functional relationship between saving and income.
- Saving is the function of income
S = f (Y)
Y = S + C
S = Y – C
Where, S = aggregate saving
Y = income
C = aggregate consumption expenditure
- The part of income which is not consumed is saved and the part of income which is not saved is used as 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.
- Saving function can be explained by two concepts :
1. Average Propensity to Save
2. Marginal Propensity to save
1. Average Propensity to Save (APS) :
- Average propensity to save refers to the proportion of income that households want to save.
- It is derived by dividing total desired saving with total income. It defines the relationship between saving and total income.
APS = S / Y
Where, APS = average propensity to save
S = total desired saving of the households
Y = total aggregate income
2. Marginal Propensity to Save:
- Marginal propensity to save relates the change in total desired saving to the change in income that brought it about.
- It is the proportion of additional unit of income saved (not spent on consumption).
- MPS is the ratio of change in total desired saving to change in total income.
- Symbolically, MPS = ∆S / ∆Y
Where, ∆S = change in total desired saving
∆ Y = change in income
- MPS is also the slope of Saving curve.
- MPS is assumed to be constant, that is why the saving curve is a straight line curve, with constant slope.
Properties of Saving Function:
Consumption and Saving Function
1. Consumption expenditure exist when there is no income. There is a minimum consumption expenditure even at zero level, this gives rise to equal amount of dissavings or negative savings.
2. Thus, the saving line – S starts from negative intercept of Y – axis.
3. Saving line is upward sloping indicating that the higher income level leads to higher amount of saving.
4. At low income level saving is negative ( C > Y) , at high income saving is positive (C < Y) and at break even point saving is zero (C = Y) .
5. Sloping of S – line indicates the marginal propensity to save. It is clear from the saving line S that its slope is positive but less than 1. This indicates that MPS is greater than zero, but less than unity at all levels of income i.e., MPS is positive. Means, the value of MPS loes between 0 and 1 ( 0 < s < 1).
6. The linear consumption function is expressed as
C = ( a + c Y)
Where, C = aggregate consumption expenditure
a = autonomous consumption expenditure
c = marginal propensity to consume
Y = income
Relationship between Consumption and Saving Function:
Question : What is the relation between APC and APS ?
Question: What is the relationship between MPc and MPS ?
Question : Explain the sum total of c and s is equal to 1.
Answer: There is a simple relationship between consumption and saving functions.
APC and APS must add to unity and MPC and MPS must add to unity or c + s = 1
Explanation:
We know that the income is either spent or consumed thus,
Y = C + S
Dividing above equation by Y
Y/ Y = C / Y + S / Y
1 = APC + APS ……..( since C/Y= APC and S/Y = APS)
Therefore, APC = 1 – APS
and APS = 1 – APC
Similarly additional income is used either increasing consumption or in increasing saving, i.e.,
∆C + ∆S = ∆ Y
Dividing above equation by ∆Y
∆C/∆Y + ∆S /∆Y = ∆Y/∆Y
Or MPC + MPS = 1
Or c + s = 1 ……. (Since MPC =c and MPS = s)
Therefore, MPC = 1 – MPC
And. MPS = 1 – MPC
Derivation of Saving Function:
Propensity to save curve can be derived from the propensity to consume curve.
- The 45° income line (Y line) passing through the origin, indicates that whatever is the level of income, the aggregate consumption plus saving are equal to income at all level means, Y = (C + S).
Consumption and Saving Function
- Thus, saving function can be derived from consumption function ( as S = Y – C) by the difference of income and consumption expenditure.
- Graphically, saving is vertical difference between 45° line and consumption line (C).
- Saving function can be derived from the difference between 45° line (Y) and consumption line (C).
- As the income increases, the difference between consumption and income also increases.
- At higher level of income Y > C thus, S = Y – C , so saving is positive.
- At lower level of income C > Y thus, the saving is negative, it is called dissavings.
- At zero level of income, consumption is equal to intercept ‘a’ therefore saving is negative intercept ‘-a’.
- At point E when Y = C, thus C = 0.
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