The consumption function or propensity to consume refers to income consumption relationship. It is a “functional relationship between two aggregates viz., total consumption and gross national income.” Symbolically, the relationship is represented as

C= f (Y)

Where,

C = Consumption

Y = Income

f = Function

Thus the consumption function indicates a functional relationship between С and Y, where С is the dependent variable and Y is the independent variable, i.e., С is determined by Y. This relationship isbased on the ceteris paribus (other things being same) assumption, as only income consumption relationship is considered and all possible influences on consumption are held constant.

In fact, consumption function is a schedule of the various amounts of consumption expenditure corresponding to different levels of income. A hypothetical consumption schedule is given in Table 1.

If we take C = 100 + 0.8y, then MPC = 0.8

Here, if Y = 0, C = 100; if Y = 100, C = 180;

if Y = 200, C = 260;

if Y = 300, C = 340 (MPC = In mathematical terms ∆c =0.8 ∆y

C= a + b Y or C = 20 + 0.8Y

Where a>0 and b<1

C= Consumption

a= constant or intercept = 20

Y= income

b= MPC (Marginal prosperity to consume) = 0.8

The above table shows that consumption is an increasing function of income because consumption expenditure increases with increase in income. Here it is shown that when income is zero, people spend out of their past savings on consumption because they must eat in order to live (Autonomous Consumption)

Here, when y = 120, C = 120 (Point B is the diagram)

When y = 180, C = 170, S = 10 (Point S is the diagram)

If Y increases to 360, C = 320, S = 40

In the diagram, income is measured horizontally and consumption is measured vertically. In 45 line at all levels, income and consumption are equal. It is a linear consumption function based on the assumption that consumption changes by the same amount as does income.

Thus the consumption function measures not only the amount spent on consumption but also the amount saved. This is because the propensity to save is merely the propensity not to consume. The 45° line may therefore be regarded as a zero-saving line, and the shape and position of the C curve indicate the division of income between consumption and saving.

### Technical Attributes of the Consumption Function

(i) The Average Propensity to Consume= c /y.

(ii) The Marginal Propensity to Consume = ∆c/ ∆y

(iii) The Average Propensity to Save= s/y

iv) The Marginal Propensity to Save = ∆s/ ∆y

### (1) The Average Propensity to Consume:

The average propensity to consume is the ratio of consumption expenditure to any particular level of income.” Algebraically it may be expressed as under:

APC = C/Y

Where, C= Consumption Y = Income

### (2) The Marginal Propensity to Consume:

The marginal propensity to consume may be defined as the ratio of the change in the consumption to the change in income. Algebraically it may be expressed as under:

MPC = ∆C /∆Y

Where,

ΔC= Change in Consumption

ΔY = Change in Income MPC is positive but less than unity

### (3) The Average Propensity to Save (APS) :

The average propensity to save is the ratio of saving to income.APS is the quotient obtained by dividing the total saving by the total income. In other words, it is the ratio of total savings to total income. It can be expressed algebraically in the form of equation as under

APS = S/Y

Where,

S= Saving

Y=Income

### (4) The Marginal Propensity to Save (MPS) :

Marginal Propensity to Save is the ratio of change in saving to a change in income. MPS is obtained by dividing change in savings by change in income. It can be expressed algebraically as

MPS = ∆S/ ∆Y

ΔS = Change in Saving

ΔY= Change in Income Since

MPC+MPS=1 MPS=1-MPC and MPC = 1 – MPS

Generally the average ie APC is expressed in percentage and the MPC in fraction.