Saving function equation. As saving function is corollary of consumption function, we can derive the correspondine savine function from consumption function equation, straight C space equals space straight C with bar on top space plus space bY by substituting it in the equation S = Y – C as shown below.
straight S space equals space straight Y space minus space straight C
space space space space equals space straight Y space minus space left parenthesis straight C with bar on top space plus space bY right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis because space straight C space equals space straight C with bar on top space plus space bY right parenthesis
space space space space space equals space straight Y space minus space space straight C with bar on top space minus space bY

box enclose straight S space equals space minus straight C with bar on top space plus left parenthesis 1 minus straight b right parenthesis straight Y end enclose

where straight C with bar on top space equals spaceAutonomous consumption left parenthesis negative straight C with bar on top represents dissaving which is needed to finance autonomous consumption when income is zero. Clearly at zero level of income, amount of Autonomous Consumption = Amount of dissaving. (This indicates withdrawl from past savings or borrowing) b = MPC (So that 1 – b represents MPS. Since b is less than 1, therefore, MPS 1 – b is positive.)
Y = Income.
For example, the saving equation S = – 30 + (1 – 0.75) means -30 is dissaving (or autonomous saving that needs to take place to finance autonomous consumption). As income increases, 0.25 (= 1 - 0.75) or 25% of additional income is saved.