Gr xiib & c -eco- ch-4-s4

Derivation of Saving Function

2. Income Determination
Grade XII
Economics

3. Learning Objectives
•To understand the derivation of saving
function from consumption function
•To understand the derivation of saving curve
from consumption curve
•To calculate MPS and APS

4. Consumption and Saving Schedule

5. Saving Function
•Symbolically, saving is expressed as follows:
•S = ϒ – C
•(S = saving; ϒ = income; C = consumption )
•Saving is also a function of income.
•Symbolically, saving function is expressed as
follows:
•S = f(ϒ)
•(S = aggregate saving; ϒ = income; f =
function)

6. Derivation of Saving Function
•Saving function explains the relationship between
national income and aggregate savings and it can be
derived from the consumption function.
•We know that S = ϒ – C and C = c̅ + bY
•∴ S = ϒ – {c̅ + bY}
•S = ϒ – c̅ – bY
•S = (–)c̅ + (1 – b) Y
•where, S = saving;
•(–)c̅ = dissavings
•(1 – b) = MPS;
•ϒ = given level of income.

7. Derivation of Saving Curve from
Consumption Curve
•The straight line saving curve can be drawn using a
straight line consumption curve and the 45° line.
•In the diagrams there are two Panels, A and B,
showing the derivation. In Panel A, consumption is
represented on the Y axis while in Panel B, savings is
represented on the Y axis. Income is represented on
the X axis in both. 45° line in Panel A represents all
the points where consumption and income are equal.
•In Panel A, Consumption Curve starts from Y-intercept
at point C (autonomous consumption) and intersects
45° line at point E, which is known as the ‘break even
point’ where C = ϒ or S = 0.

8. Derivation of Saving Curve from
Consumption Curve
•At this point, the value of APC will be one (unity).
•At any level of income to the left of E; C > ϒ,
leading to negative savings , whereas at any point
to the right of E, we have C < ϒ leading to positive
savings.
•At origin, in Panel B, savings are at
S
1 (=OC
1 distance), this is the starting point of
saving curve, at Oϒ
1 or E
1, savings are zero as C =
ϒ (correspondingly in Panel A).
•We may derive straight line saving function by
joining S
1 and E
1, and extending the curve further.

9. Derivation of Saving Curve from
Consumption Curve

11. Complete the Table
Income Consumption MPS APS
0 80 ___ ___
100 140 0.4 ……..
200 ….. …… 0
…… 240 …… 0.20
…… 260 0.8 0.35

12. Solution
Y C S Δ S ΔY MPS APS
0 80 -80 ____ ____ ____ ____
100 140 -40 40 100 0.4 -0.4
200 200 0 -40 100 -0.4 0
300 240 60 60 100 0.6 0.20
400 260 140 80 100 0.8 0.35

13. Review
•How do we derive saving curve from
consumption curve?

14. Recapitulation
•Consumption function can be derived from
saving function
•Consumption curve can be derived from
saving curve.

15. Thank
You