Derivation of Saving Curve from Consumption Curve

The saving curve is derived from the consumption curve by using the relationship between income, consumption, and saving.

The fundamental equation is: \boxed{S = Y - C}

Where:

• S = Saving
• Y = Income
• C = Consumption

So, saving is the part of income that is not spent on consumption.

As we know that Y = C + S, which means that as consumption and savings together make up income, the consumption curve and saving curve are complementary curves. Therefore, it is possible to derive the saving curve from the consumption curve and the consumption curve from the saving curve. Let us derive the saving curve from the consumption curve. 

For this, first of all, draw a consumption curve CC with OC as autonomous consumption and a 45° line OY representing the income curve as shown in the below graph.

• The point where the consumption curve CC and income curve OY intersect is the break-even point, i.e., Point E.
• At this point consumption is equal to income, and average propensity to consume is one.

At zero income level, OC is the autonomous consumption (\bar{c}), which means that savings (-\bar{c}) at zero income level will be OS. Therefore, the savings curve will start from point S on the negative Y-axis because, at zero level of income, savings are negative. Now the point where the CC curve and OY curve intersects; i.e., point E is the break-even point. It means that at this point C = Y, APC = 1, and Savings = 0. Therefore, the savings curve will intersect the X-axis at point R. Now, join the points S and R and extend it further to get the Saving Curve SS.

Similarly, we can also derive consumption curve from saving curve. The starting point of the consumption curve on the Y-axis will be equal to dissaving at zero income level and the second point on the consumption curve will be the point perpendicular from the point where the saving curve intersects the X-axis.