Question

Discuss and show graphically how an increase in consumption at each level of GDP effects saving.

Answer 1

Functional Relationship of Consumption and Saving

The Keynesian consumption function is the conventionally used economic formula to represent the functional association between aggregate consumption and gross national income. Using a simple Keynesian model, a relationship can be established between consumption, saving and national income. The consumption function is given as:

C= a+bY----1

where ‘a’ represents autonomous consumption, which is the subsistence level of consumption required for survival. This component of consumption takes places independent of income(Y) which means that even if Y=0, there will be a consumption of amount ‘a’. On the other hand, ‘b’ is the marginal propensity to consume which shows the change in consumption due to change in 1 unit of income (Y). This also represents the slope of the consumption function and a direct relationship between C and Y results in an upward sloping consumption curve with respect to income (b>0). This means that as income rises, consumption rises.

The saving function(S) is given as:

S= Y-C----2 (derived from Y=C+S).

This equation assumes that income can go either into consumption or into savings. Here too, Y represents income and C consumption.

Substituting equation 1 in equation 2 we get,

S= Y-a-bY or S=-a+(1-b)Y----3 (where (1-b) is greater than 0 but less than 1).

From equation 3, it is clear that when Y=0 with a positive consumption of ‘a’, there is a negative saving equivalent to ‘-a’. [S=Y-C or S=0-a or S=-a].

(1-b) is the marginal propensity to save meaning, the change in saving due to 1 unit change in income (Y). Here too, (1-b) is the slope of the Saving function. Being positive, it shows a direct relationship between Income and Saving. As income rises, savings also increase and thus the saving function is upward sloping.

Graphical Relationship between Consumption and Saving:

Having established these facts, when the level of GDP (or national income) is constant, then an increase in Consumption ‘C’ will automatically lead to a fall in Saving ‘S’. This follows directly from equation 2 where with constant Y, a rise in C implies a fall in S. Since aggregate consumption can also be expressed as aggregate expenditure, in Fig 1(a), aggregate expenditure is plotted on the vertical axis and GDP on the horizontal axis. (this is because aggregate expenditure dependes on GDP). A 45^o line passes through the origin which represents all points for which Aggregate Expenditure=GDP and Saving=0. The aggregate expenditure curve starts from ‘a’ (level of autonomous consumption) and slopes upward, Having plotted these two curves, it is now possible to establish the relationship between consumption and saving. Since saving is the difference between income and consumption, the vertical difference between the 45^o line and C represents saving.

Initially when C>45^o line, Saving is negative (starting from –a in fig 1(b)). At point E, when C cuts the 45^o line, Saving is exactly 0. Then gradually as C rises but goes below the 45^o line, S becomes positive and goes on increasing. This is shaded in pink and as the area in pink increases, it is clear that saving rises at increasing levels of GDP, with rise in consumption.

Thus, it is clear that an increase in consumption at constant levels of GDP decreases savings. However, as GDP increases, savings also gradually increases with increases in consumption, as is shown in figures 1(a) and 1(b).