Keynes income and consumption relationship:

Keynes made it apparent that there is a direct association among income and consumption. Propensity or consumption function to consume is the ratio that evaluates the functional relationship among income and consumption. In mathematical form the association can be stated as,

C = a + b y …. (1)
C = 4 + .8Y.... (2)

Therefore a consumption function is usually explained in terms of the linear equation Y = a + bY where the constant ‘a’ is the amount of independent consumption and slope (b) is MPC. The rate of change in expenditure due to change in income based on the MPC. Equation (2) simply states that consumption (C) based on income(Y). The + sign points out that as income raises, apparently consumption will also raise. However the rate of raise in consumption will be slight less than that of the rate of increase in income. It is since some unspent portion of the income will be saved. This aspect is made clear in the Keynes law of consumption. He indicates, “The psychology of the community is such that whenever real income is raised, aggregate consumption is increased, though not so much as income”. Keynes as well made it apparent that in the short run, the consumption function is stable as consumption habits of the people are much more or less stable in short period.

All such points or the income-consumption relationship can also be stated in figure above. The vertical axis exhibits the spending on consumption pointed by C and the horizontal axis exhibits income or output indicated by Y. The straight line consumption function CC is stated in terms of equation C = 4 + .8Y.

The consumption curve CC is a short run curve. In this situation consumption occurs even whenever income is zero. In equation (2) 4 is the level of primary consumption whenever income is zero and it is not affected by the income. Even if income is zero, people spend certain minimum level either by gift or borrowing. This consumption that is not associated to income is termed as autonomous consumption. That is the reason why curve C begins from 4 on vertical axis.

In equation (2) .8 points out that 80 % of additional income is spent on consumption and it is termed as marginal propensity to consume (i.e., MPC). Therefore MPC is the ratio of change in consumption to change in income. In another words, MPC is the rate of change in propensity to consume.

MPC = Change in consumption/ Change in income

Or MPC = ΔC/ΔY

Here, 
ΔC: Change in consumption and
ΔY: Change in income

The slope of consumption function or another straight line is evaluated by dividing the vertical change by horizontal change. The symbol A symbolizes a change. Or slope can as well be computed as:

Slope = Vertical change/ Horizontal change

The tendency to consume is supposed to be stable in short run. So, out of the given income how much will be spent based on the slope of the curve.

In this situation, .8 points out that out of every additional income earned 80% will be spent for consumption by keeping the rest for saving. In brief, consumption function associates the amount of consumption to the level of income. Therefore consumption of an economy based on the level of income. Whenever the income of an economy mounts, consumption too rises and vice-versa. Assume that people spend more in an economy in relation to their income; and their MPC will be much more.

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