Non Linear Consumption Function

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In real life, the marginal propensity to consume does not remain constant at all levels of income. It is possible that the MPC of an economy may decline as the level of its income increases. This happens because when basic needs are satisfied, an increase in income will reduce MPC and increase MPS. In such a case, the consumption function curve becomes non-linear. The slope of this curve declines, as the level of income rises. The economists have justified this shape of the consumption curve on the basis of empirical studies.

Figure 3.4 shows a non-linear consumption function. It is clear from this figure that there is some consumption expenditure even when income is zero. We observe in the figure that the increase in consumption declines in response to a constant increase in income. In Figure 3.4, ΔY1, ΔY2, ΔY3, and ΔY4 represent equal increments in income. But, the corresponding increments in consumption  ΔC1, ΔC2, ΔC3, and ΔC4   become smaller and smaller. Therefore, their ratios ΔC1/ΔY1, ΔC2/ ΔY2, ΔC3/ΔY3 and ΔC4/ΔY4 indicate declining slope of the consumption curve. The continually declining slope implies diminishing marginal propensity to consume. Therefore, when consumption fails to increase at a stable rate in response to rise in income, the consumption  curve becomes non-linear.   
Diminishing Propensity to Consume

In Figure 3.5, ‘A’ is a point on the non-linear consumption function curve CC. At OY level of income, the amount of consumption if AY. The ratio AY/OY gives the value of APC at point ‘A’, which is nothing but the slope of the ray OA from the origin ‘O’ to point ‘A’ on the consumption curve. On the other hand, the MPC at point ‘A’ is given by the slope of the tangent AB at this point, that is AY/BY. Clearly the slope of AB (i.e..AY/BY) is smaller than the slope of OA (i.e.. AY/OY), as OY < BY. So, MPC is smaller than APC. Further, at point ‘D’ on the curve, APC is given by the slope of the ray OD. It is obvious that the slope of OD is less than the slope of OA. Therefore, for non-linear consumption curve, both APC and MPC decline continuously and MPC is lower than APC for all levels of income. Also the rate of decline in the APC is smaller than in the MPC. Such changes are only possible during cyclical fluctuations.
APC and MPC in Non Linear Consumption Function
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