# Consumption Function

The consumption function or propensity to consume shows the “functional relationship between total consumption and the national income.” Symbolically, the relationship is represented as C = f (Y), where C is consumption, Y is income, and f is the functional relationship. C is the dependent variable of Y and Y is the independent variable. This relationship is based on this assumption that “all possible influences on consumption” are held constant.

Consumption function is the whole schedule which describes the amounts of consumption at various levels of income. The schedule of consumption function shows that when income rises, consumption also rises but not as much as the income. The reason behind it is that a part of the increment in income is saved.

## PROPERTIES OF THE CONSUMPTION FUNCTION

The consumption function has two technical attributes or properties:

### The Average propensity to Consume:

The average propensity to consume may be defined as the ratio of consumption expenditure to a particular level of income. We can get it by dividing consumption expenditure by income, or APC = C/Y.

It is expressed as the percentage or proportion of income consumed.

The APC declines as income increases because the proportion of income spent on consumption decreases and a part of the increment in income is saved.

• APC can be more than one as long as consumption is more than national income, APC>1.
• At break-even point, APC=1.
• When consumption is less than income, APC<1
• APC can never be zero.
• APC falls with the increase in income. Diagrammatically, the average propensity to consume is any one point on the C1 curve. Point P measures the APC of the C1 curve which is OC /OY. The flattening of the C1 curve to the right shows declining APC.

### The Marginal Propensity to Consume:

The marginal propensity to consume may be defined as the ratio of the change in consumption to the change in income. It shows the rate of change in the average propensity to consume as income changes. It can be found by dividing change in consumption by a change in income, or MPC = ∆C/∆Y. The MPC is constant at all levels of income in the linear consumption function.  According to some economists, marginal propensity to consume declines with the increase in income, when consumption function is non-linear whose slope declines as income rises.

Marginal propensity to consume is neither zero nor equal to one.

It varies between zero and unity. The MPC is less than the average propensity to consume (APC), that is, ∆C/∆Y < C / Y. Diagrammatically, the marginal propensity to consume is measured by the slope of the C curve. This is shown in the diagram by NQ/PQ where NQ is change in consumption (∆C) and PQ is change in income (∆Y) or C1C2 /Y1Y2.

### Consumption Function Schedule

 Income [Y] In lakhs Consumption[C] In lakhs Average propensity to consume APC = C/Y Marginal propensity to consume MPC =C/∆Y 0 40 —- —- 100 120 120/100=1.2 80/100=.8 200 200 200/200=1 80/100=.8 300 280 280/300=.93 80/100=.8 400 360 360/400=.9 80/100=.8 500 440 440/500=.88 80/100=.8

The above table shows that consumption is an increasing function of income because consumption expenditure increases with increase in income. It shows that when income is zero, even then, there is a consumption, people spend out of their past savings on consumption. When income is generated in the economy to the extent of Rs 100 lakhs, it is not sufficient to meet the consumption expenditure of the community so that the consumption expenditure is still above the income amounting 120 lakhs (Rs 20 lakhs are dis-saved). When both consumption expenditure and income equal Rs 200 lakhs, it is the basic consumption level. After this, income is shown to increase by 100 lakhs and consumption by 80 lakhs. This is showing a stable consumption function during the short-run as assumed by Keynes.

In a specific form, Keynesian linear consumption function can be written as:

C = a + bY

where C is the consumption expenditure by households. This consists of two components autonomous consumption[a] and induced consumption (bY).  ‘a’ is an intercept showing consumption at the zero level of income, and ‘b’ stands for MPC = ∆C/∆Y

Autonomous consumption is denoted by  and shows the consumption which is independent of income.

Or we can write linear consumption function as:

C = c̅ + bY

autonomous consumption takes place even when income is zero as people spend out of their past savings on consumption because they must eat in order to live. The induced component of consumption, bY shows the dependency of consumption on income. Induced consumption is an increasing function of income because consumption expenditure increases with increase in income.

Mathematically, we can find out the consumption at the various level of income when autonomous consumption and MPC is given.

‘a ‘is the autonomous consumption which is 40 lakhs

‘b’ is the MPC which is .8 at all level of income in the above table.

‘Y’ is the level of income on which the consumption is to be calculated.

When income is 100 lakhs, then,

C = a + bY

C = 40 + .8

C= 40+80

C=120 lakh

When income is 100 lakhs, then consumption is 120 lakhs.

When income is 200 lakhs, then,

C = a + bY

C = 40 + .8

C = 40+160

C = 200

Thus, you can find out the consumption at various level of income with the help of this equation. This diagram illustrates the consumption function diagrammatically. In the diagram, income is measured horizontally and consumption is measured vertically. 45° is the income-line. The C curve is a linear consumption function based on the assumption that consumption changes by the same amount (Rs 80 lakhs). Its upward slope to the right indicates that consumption is an increasing function of income. B is the break-even point where OY1 = OC1. When income rises to OY2, consumption also increases to OC2, but the increase in consumption is less than the increase in income, C1C2 < Y1Y2. Below break-even point, there is a dissaving as income is less than consumption [showing through yellow portion]. The portion of income not consumed is saved as shown by purple shaded area. Thus, consumption function measures not only the amount spent on consumption but also the amount saved.

### Propositions of the Law

This law has three related propositions:

• When income increases, consumption expenditure also increases but not as much as income increases. Because our wants are satisfied side by side with the increase in income, and the need to spend more on consumer goods diminishes. the consumption expenditure never falls with the increase in income. It increases with increase in income but less than proportionately.
• The increased income will be divided in some proportion between consumption expenditure and saving. As the whole of increased income is not spent on consumption, the remaining is saved
• Increase in income always leads to an increase in both consumption and saving.

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