EQUATION OF CONSUMPTION CURVE

Consumption curve can be put into two parts:

When income is zero, there is some consumption, which is known as autonomous consumption.

When income increases, consumption also increases but the rate of increase in income is more than that of increasing consumption and this rate depends upon MPC. The consumption pictures influenced by income is known as induced consumption, which can be estimated by multiplying MPC by income. i.e. b(Y)

Therefore, consumption can be represented as:

C= C̅+b(Y)

Where

C̅=Autonomous consumption

C= consumption, 

b= MPC

Y= Income

EQUATION OF SAVING FUNCTION

With the help of linear consumption function situations, we can derive the equation of the linear saving function.

We know, Y=S+C

                 S=Y-C………………(1)

And         C=C̅+b(Y)………….(2)

Putting the value of C in equation 1 we get.

S=Y-(C̅+b(Y))

S=Y-C̅-b(Y)

S= -C̅+Y-b(Y)

S=-C̅+Y(1-b)

Where,

S=savings

C̅=amount of dissaving’s at 0 levels of income.

Y= total income

1 – b = 1 – MPC = MPS

Derivation of Saving Curve from Consumption Curve

Let us understand how we derive the saving curve from the consumption curve:

At zero level of income, autonomous consumption is OC, which means that savings will be OS and hence saving curve will start from the point as on the negative y-axis.

Consumption curve intersects income curve at. Which means it is break-even point where consumption is equal to income, and savings are zero. Therefore, at this particular point saving curve will intersect the x-axis at point r. By joining points S and R and extending it further, we get the saving curve SS.