# Consumption function Graphical representation of the consumption function, where a is autonomous consumption (affected by interest rates, consumer expectations, etc.), b is the marginal propensity to consume and Yd is disposable income.

In economics, the consumption function describes a relationship between consumption and disposable income. The concept is believed to have been introduced into macroeconomics by John Maynard Keynes in 1936, who used it to develop the notion of a government spending multiplier.

## Details

Its simplest form is the linear consumption function used frequently in simple Keynesian models:

$C=a+b\cdot Y_{d}$ where $a$ is the autonomous consumption that is independent of disposable income; in other words, consumption when income is zero. The term $b\cdot Y_{d}$ is the induced consumption that is influenced by the economy's income level $Y_{d}$ . The parameter $b$ is known as the marginal propensity to consume, i.e. the increase in consumption due to an incremental increase in disposable income, since $\partial C/\partial Y_{d}=b$ . Geometrically, $b$ is the slope of the consumption function. One of the key assumptions of Keynesian economics is that this parameter is positive but smaller than one, i.e. $b\in (0,1)$ .

Keynes also took note of the tendency for the marginal propensity to consume to decrease as income increases, i.e. $\partial ^{2}C/\partial Y_{d}^{2}<0$ . If this assumption is to be used, it would result in a nonlinear consumption function with a diminishing slope. Further theories on the shape of the consumption function include James Duesenberry's (1949) relative consumption expenditure, Franco Modigliani and Richard Brumberg's (1954) life-cycle hypothesis, and Milton Friedman's (1957) permanent income hypothesis.

Some new theoretical works following Duesenberry's and based in behavioral economics suggest that a number of behavioural principles can be taken as microeconomic foundations for a behaviorally-based aggregate consumption function.