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The Saving FunctionThe relationship between consumption and income also tells us about the relationship between income and savings.There is a close relationship between consumption and saving. And the consumption and saving decisions are taken simultaneously.All income which is not consumed is saved, which implies that what an individual consume does not save and what he does not consume must save.Hence, saving is defined as the excess of income over consumption expenditure, i.e.

S = (Y – C)S = (Y – C)

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Types of Saving: Individual Saving: Saving by the individuals for their

own personal reasons.example: people save to meet the unforeseen emergencies.

Corporate Saving: corporate savings by companies means ploughing back profits into business and so reducing the amount of profit distributed to share holders.

Compulsory Saving: it occurs when the govt. reduces consumption by deliberately increasing taxation.

Forced Saving: which occurs in mild inflation because it will bring bout a reduction in the demand for consumer goods.

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Hence, total saving in the economy is the sum of:(a) Personal Saving: Personal disposable income

minus consumption expenditure of an individual.(b) Business Saving: the retained income of the

business units consisting of depreciation allowances and undistributed profits.

(c) Government Saving: Net govt. receipts minus govt. consumption expenditure.

Different Definitions of Saving:Keynes has defined saving as the current saving

depends upon the current income. Symbolically,

St = f (Yt), where, saving in period t depends upon the income in period t.

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L. R. Klein defined saving as “the function of income. Saving function or saving schedule may be defined as the schedule showing different amounts that are saved at different levels of income”.

It represents a functional relationship between saving and income. This can be better understood by a schedule given below:

Saving Function Schedule

(1)(1)IncomeIncome

(Y)(Y)

(2)(2)ConsumptionConsumption

(C)(C)

(3)(3)SavingSaving

(S = Y – C)(S = Y – C)

(4)(4)Average Propensity Average Propensity

SaveSave(APS = S/Y)(APS = S/Y)

(5)(5)Marginal Marginal Propensity to Propensity to

SaveSave(MPS = (MPS = S/S/Y)Y)

100100150150200200250250

100100140140180180220220

00101020203030

0/100 = 0%0/100 = 0%10/150 = .07 or 7%10/150 = .07 or 7%20/200 = .1 or 10%20/200 = .1 or 10%30/250 = .12 or 12%30/250 = .12 or 12%

----10/50 = .2 or 20%10/50 = .2 or 20%10/50 = .2 or 20%10/50 = .2 or 20%10/50 = .2 or 20%10/50 = .2 or 20%

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In the above table, column 3 represents saving function which is obtained by deducting consumption (column 2) from income (column 1) at different levels.

C2

C1

C

Y1 Y2

B

S2

S1

S3

S

X

Y

O

S

C

Consumption & Saving

Income

Y = C

-a

a

D

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In the above diagram, the saving is derived from the consumption curve. The Y = C curve shows that income is equal to consumption or zero saving at all points of the line.

CC is the consumption line. At zero income level there is negative saving equal to OC.

At OY income level, the whole of income is consumed and nothing is saved.

Take OD equal to OC and join D and Y and extends it to S.

Thus DYS is the saving curve showing different amounts of saving at various levels of income.

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Saving function has two technical attributes, such as:

(a) Average Propensity to Save (APS): the APS refers to the ratio of total saving to the total income.

Symbolically, APS = S/Y

If at Rs. 200 income, Rs. 20 is saved, then the APS will be 20/200 = .10 or 10%.

APS at different levels of income is shown in column 4 of the schedule.

APS is complementary to the APC, because APC + APS = 1 or APS = 1 – APC.

As, S = Y – C

APS = S/Y or (Y – C)/Y = 1 – C/Y = 1 – APC(Y – C)/Y = 1 – C/Y = 1 – APC.

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(b) (b) Marginal Propensity to Save (MPS):Marginal Propensity to Save (MPS): the marginal propensity to save is the complement of the marginal propensity to consume,

so that MPC + MPS = 1 The MPS is expressed as the small change in the

saving to a small change in income, i.e.

MPS = MPS = S/S/YY For Example: If income increases from Rs. 200 to

Rs. 250, and saving increases from Rs. 20 to Rs. 30, then

MPS = 10/50 = .2 or 20%

This is shown in the previous table.

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Derivation of Marginal Propensity to Save: Since saving is excess of income over consumption and a

change in saving is equal to change in income minus change in consumption,

The MPS will be equal to one minus marginal propensity to consume.

Derivation:Derivation:

S = Y – CS = Y – C

S = S = Y - Y - CC

Since MPS is the ration of change in saving to change in income.

S/ Y = Y/Y - C/ Y

MPS = 1 - C/Y

MPS = 1 – MPC

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Paradox of Thrift: It’s a dilemma whether saving is a virtue or vice???? The classical economist and Keyes differs fundamentally on

the question whether saving is virtue or vice. The classical economics based on the foundation of Laissez-

faire policy advocated that saving was great private virtue. When an individual increases his saving, it amounts to

maximizing his welfare, which again leads higher individual saving will boost higher aggregate saving of the community.

According to them, when individual saves, he accumulates a fortune by maximizing earning and minimizing expenditure on consumption.

More savings leads to more investment, and more investment leads to more income.

Since increased savings by all individuals mean increased savings of the community as a whole, saving is beneficial to the society.

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However, this view was severely criticized by the underconsumption theorist and said that this view contradicts concept of one man’s expenditure is others income.

They held the view that an increase in the aggregate saving would reduce consumption in the community.

This in turn, would reduce effective demand, output, national income and employment.

They believed that there was no virtue involved in the accumulation of saving.

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On the other hand, Keynes in his general theory of employment states that the virtue of saving depends on it use.

If saving is invested, it will boost production, national income and employment.

In this event, saving would be of social use and therefore, can not be considered as a vice.

If, on the other hand, saving is not invested but merely hoarded, it reduces the aggregate demand, employment and output.

Thus, saving become a public vice. He Pointed out that one man’s expenditure is another man’s income in the economic system.

Hence, when the aggregate saving increases in the community, it reduces the aggregate demand for consumer goods. This in turn, adversely affects the demand for capital goods.

As a result, there will be over all reduction in demand, employment, income and output. Thus saving becomes harmful to the society and ceases to be a virtue.