The relationship between income and consumption also tells us what kind of relationship exists between income and saving. So, the saving function may be derived with the aid of the consumption function.

Saving function expresses the relationship between the level of disposable income and the amount of desired saving in an economy.

In our simple model with no government and no foreign trade sectors, income equals by definition, consumption plus saving:

Y = C + S

We known from the consumption function that C is equal to ά + By.
Therefore, after substitution, we get

                Y = ά + By + S
or            -S = ά-Y + By
or            -S = ά – (1-b) Y
or              S = -ά + (1-b) Y

Thus, the saving function is

where – ά the Y- intercept and (1-b) is the slope.

The saving function shows  that saving changes as income changes. If the changes in saving is denoted as ΔS and the change in income as ΔY, the ratio of the change in saving to the change in income ΔS/ ΔY is 1-b. i.e, the slope of the saving function. This relationship is called the marginal propensity to save (MPS). Since ‘b’ represents the MPC, the MPS is 1-MPC. It implies that the MPS is between 0 and 1, provided that the MPC, is between 0 and 1.

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