LINEAR CONSUMPTION FUNCTION

A linear consumption function is generally expressed as

C = f (Y) = a + bY (a > 0, 0 < b < 1)

This equation indicates that consumption is a linear function of income. ‘a’ and ‘b’ are the two parameters of this equation. An economy spends some minimum expenditure ‘a’ on  consumption (C), may be out of their past savings, even when the level of income (Y) is zero. o this, proportion ‘b’ of additional income is added up, as and when income of the economy rises. As consumption cannot increase by an amount more than the increase in income, ‘b’ always lies between 0 and 1. Thus, the consumption rises by a lesser absolute amount than the increase in income.
  
The relationship between the level of consumption and the level of income can be explained with the help of the following, example. Suppose, consumption of a country at zero level of income is Rs. 30 crores. Further, let us assume that the country consumes 80% of the every additional income. The consumption function of the country would be C = 30 + 0.80 Y. Now, we can easily find amounts of consumption expenditure corresponding to different levels of national income. When the national income rises to Rs. 200 crores, its consumption expenditure would be (30 + 0.80 * 200) or Rs. 190 crores and so on. Table 3.3 provides consumption expenditure of the country corresponding to various levels of national income.

                                           Table 3.3: Consumption Function Schedule C = a + bY



This consumption function is depicted in Figure 3.1. The consumption is plotted on the vertical axis and the income on the horizontal axis. In this graph, the intercept on Y-axis represents consumption corresponding to zero level of income. That is, if Y  =  0,   C  =  ‘a’ . Here, ‘a’ is called autonomous consumption, a consumption which does not depend upon the level of income. The linear form of the consumption function indicates same slope ( b = ΔC/ΔY )  throughout the curve. Thus,  MPC is constant on this consumption function. Since the MPC shows how consumption expenditure of individuals is stimulated by the additional income they earn, the second part of this consumption function ‘bY’  or  ΔC/ΔY *  Y  or MPC * Y is the induced consumption.

Thus, the formula for consumption function is

C   = a + bY      (‘b’ is MPC)
     = Autonomous Consumption + Induced Consumption


 
In this linear consumption function, APC is falling, as the level of income rises. For example, in Figure 3.2, APC for OY1 level of income is A1Y1/OY1 or the slope of the ray OA1 Similarly, APC at point A2 is A2Y2/OY2 or the slope of the ray OA2; at point A3, APC is A3 Y3/OY3 or the slope of the ray OA3. It may be observed that the slope of OA3 is less than that of OA2, which is still less than that of OA1. Likewise, the slope of the ray from the origin to any point on the consumption line CC declines as one move rightwards on CC curve.

Thus, APC is declining in the case of linear consumption function, with positive intercept  on the Y-axis, while MPC is constant and smaller than APC for all levels of income (see Table 3.3 and Figures 3.1, 3.2). This type of consumption function shows a non-proportional income  consumption relationship, which is generally observed in the short Keynes is concerned primarily with  the MPC, as his analysis pertains to the short run, while the APC is useful in the long-run analysis. The value of MPC is assumed to be positive and less than unity  (0 < MPC <1) by Keynes. This means that when income rises, the whole of it is not spent on consumption. On the contrary, with fall in the level of income, consumption expenditure does  not decline in the same proportion and never becomes zero. It has practical significance in the sense that it explains the theoretical possibility of over production or under employment equilibrium. The economic significance of the MPC lies in filling the gap between income and consumption through planned investment to maintain the desired level of income.


If, however, the linear consumption function passes through the origin, the APC and the MPC are equal and constant. In this situation, the slope of the consumption line OC indicating the MPC and the slope of the ray from the origin to any point on the consumption curve indicating APC will be the same (see Figure 3.3).


In such a consumption function, consumers spend the same proportion of their income. Such consumption function can be written as C = bY, where ‘b’ is the slope (ΔC/ΔY) of the consumption function.
        
                             APC  =  C/Y = bY/Y = b

Both APC and MPC in this case are equal to ‘b’. For this consumption function, saving (S) as well as consumption (C) are zero at the zero level of income. As the income rises, the consumption rises at a constant rate.

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