This document discusses how to derive a saving function from a consumption function and how to derive a saving curve from a consumption curve. It explains that saving (S) equals income (Y) minus consumption (C). It also shows that the saving function can be derived as S = (-c̅) + (1 - b)Y, where -c̅ is dissaving and (1 - b) is the marginal propensity to save. Additionally, it demonstrates how to plot the saving curve by drawing a straight line from the starting point of savings to where the consumption curve intersects the 45-degree line, where savings are zero.
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
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 ‘breakeven
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
S1 (=OC1 distance), this is the starting point of
saving curve, at Oϒ1 or E1, savings are zero as C =
ϒ (correspondingly in Panel A).
• We may derive straight line saving function by
joining S1 and E1, and extending the curve further.