As in the case of a straight line consumption function, the straight line saving function can be described as a sum of saving at zero level of income (which is equal to intercept OS on the - Y-axis) plus the fraction of income saved (MPS) at a given positive level of income. Since, at zero income level, consumption expenditure is positive (as given by autonomous consumption level 'a'), saving at the zero income level must be '-a' because any expenditure at zero income would mean an equivalent amount of negative saving. Further, at the given income level Y, amount of saving is given by income minus consumption, i.e.,
Y – bY
or (1-b)Y
Since b shows fraction of income consumed, therefore (i-b) shows fraction of income not consumed or saved. Thus, the equation for saving is
S = -a + (1-b)Y.
This equation for a linear saving function can be found from the equation for linear consumption function as follows:
C = a + bY
and S = Y – C
= Y – (a+ bY)
= Y – a-bY
= -a + Y –bY
= -a + (1-b)Y
Since (1-b) is the marginal propensity to save which is denoted by 's', we can write the equation as
S = -a +sY
