Saving is that part of income which is not spent on current consumption. The relationship between saving and income is called a saving function.
Simply put, saving function (or propensity to save) relates the level of saving to the level of income. It is the desire or tendency of the households to save at a given level of income. Thus, saving (S) is a function (f) of income (Y).
S = f (Y)
Relationship between Income and Saving:
There is a direct relationship between income and saving, i.e., if income increases, saving also increases but by less than the increase in income. It means as income increases, the proportion of income saved increases (because the proportion of income consumed decreases).
At a lower level of income, saving is negative. In the initial stages when there is a very low level of income, consumption expenditure is more than income leading to negative saving.