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The aggregate volume of saving in an economy comprises of (a) personal saving (personal disposal income minus personal consumption expenditure), (b) gross business saving (the retained income of the business units consisting of depreciation allowances and undistributed profits), and (c) government savings (consisting of net government receipts minus government consumption expenditure).

Unlike the classical thinkers, Keynes made saving a function of income. According to Keynes, the relationship between saving and interest is not highly significant. Some people especially the poor may not be able to save even at a very high rate of interest, while some (the rich people may save even at a low of interest on account of their surplus income). Thus, the main determinant of saving (like consumption) is the level of income. The higher is the level of income, the higher will be the volume of saving and vice-versa. Since income saved is nothing but income not consumed, the relationship between income and consumption under the consumption function can be used to explain and derive income – saving relationship for the saving function.
Derivation of Saving Function
                              Fig. 3.6: Derivation of Saving Function

Figure 3.6 shows the relationship between the saving and the consumption. In this figure, income (Y) is shown on the horizontal axis and the vertical axis represents consumption (C) and saving (S). The 45o line passing through the origin is equidistant from X as well as Y- axis.This line, may be called as guide line or Y= C+S line. It suggests that whatever be the level of income, the aggregate consumption expenditure plus saving is equal to income. This 45 degree quality line can be obtained by plotting points corresponding to equal values on each axis.Same scale has been used on both the axis of the diagram. The difference between the 45 degree line (C+S line) and the consumption line (C line) represents saving. Graphically, saving is the vertical distance between the 45 degree line and the consumption function. The saving is positive, when the income (the equality line) is higher than the consumption and negative when income is lower than consumption. In this figure, for the income level smaller than OYo (say,OY1), the consumption expenditure exceeds the income, the saving is negative. Further, when the income level is zero, the consumption equals ‘a’. Hence, saving equals ‘-a’ obtained by subtracting C = a from Y= 0. Negative saving or dissaving arises, when individuals consume more than their income. In Figure 3.6, the negative saving is shown below the horizontal axis in lower portion of the diagram. Beyond OYo level of income, consumption expenditure is smaller than income and so saving is positive. The positive saving is shown above the horizontal axis in Figure 3.6. Corresponding to OYo level of income, the consumption function intersects the 45o equality line. At this level of income, the consumption expenditure is exactly equal to the income. Therefore, the saving at this level of income  is zero. Similarly, other points on the saving function can be obtained by considering different levels of income.

As the consumption function is linear, the saving function is also linear. Now the formula for the saving function can be derived from that of the consumption function. We know that

S = Y – C (since Y = C+S)
   = Y - (a + b Y )  =  -a + (1-b) Y    [ 0< (1-b)<1]

‘-a’ is the intercept of the saving function on the Y-axis. Further (1-b) is 1-MPC or MPS. It is the slope of the saving function, measured by the ratio of the change in the saving  (ΔS) to the change in the income (ΔY). The saving function, thus indicates that the amount of saving will be equal to the amount of dissaving an economy will need at the zero level of income to support a minimum amount of consumption spending (-a) plus some proportion (1-b) of the actual national income.

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