Meaning of Consumption Function

Consumption is defined as an act of spending income on buying goods and services to satisfy current wants. In other words, it refers to the expenditure on the consumption of final goods made by the household at a given level of income. Consumption function or propensity to consume refers to the general relationship between two aggregate, i.e. income and consumption.
Meaning and concept of consumption function were defined by different economists. In short, consumption function establishes a functional relationship between income (as an independent variable) and consumption (as dependent variable). It also shows how consumption varies with given changes in income. But, the propensity to consume shows the schedule showing the various amount of consumption corresponding to different levels of income.
Algebraically, it can be written as,
C= f(Y)
where, C = consumption, f = function and Y = income.

Linear Consumption Function

If the slope of the consumption curve remains constant throughout its length, it is said to be linear consumption function. In other words, if both disposable income and consumption change at a constant rate, consumption function will be linear.
Mathematically, it can be written as:
C = a +bYd
where,
C=Consumption expenditure,
a = Y-intercept of autonomous consumption,
b = Marginal propensity to consume or slope of consumption curve or rate of change in induced consumption with respect to change in income.
Yd = Disposable income.
If we have information about autonomous consumption (a) and the marginal propensity to consume (b), the consumption expenditure for different levels of income can be calculated by using the equation of consumption function, i.e.
C= a+bYd