# 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 shows a relationship between consumption and disposable income.[1][2] It is believed that John Maynard Keynes introduced the idea in macroeconomics in 1936. He used it to develop the idea of a government spending multiplier.[3]

## Details

Its simplest form is the linear consumption function. It is used often in simple Keynesian models:[4]

${\displaystyle C=a+b\times Y_{d}}$

where ${\displaystyle a}$ is the autonomous consumption that is independent of disposable income; in other words, consumption when there is no income. The term ${\displaystyle b\times Y_{d}}$ is the induced consumption that is influenced by the economy's income level. It is generally assumed that there is no correlation or dependence between ${\displaystyle Y_{d}}$ and C.

## References

1. Algebraically, this means ${\displaystyle C=f(Y_{d})}$ where ${\displaystyle f\colon \mathbb {R} ^{+}\to \mathbb {R} ^{+}}$ is a function that maps levels of disposable income ${\displaystyle Y_{d}}$—income after government intervention, such as taxes or transfer payments—into levels of consumption ${\displaystyle C}$.
2. Lindauer, John (1976). Macroeconomics (Third ed.). New York: John Wiley & Sons. pp. 40–43. ISBN 0-471-53572-9.
3. Hall, Robert E.; Taylor, John B. (1986). "Consumption and Income". Macroeconomics: Theory, Performance, and Policy. New York: W. W. Norton. pp. 63–67. ISBN 0-393-95398-X.
4. Colander, David (1986). Macroeconomics: Theory and Policy. Glenview: Scott, Foresman and Co. pp. 94–97. ISBN 0-673-16648-1.