Consumption function

Not to be confused with demand function.

In economics, the consumption function describes a relationship between consumption and disposable income.^[1][2] 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.^[3]

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

Details

Its simplest form is the linear consumption function used frequently in simple Keynesian models:^[4]

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

where ${\displaystyle a}$ is the autonomous consumption that is independent of disposable income; in other words, consumption when disposable income is zero. The term ${\displaystyle b\cdot Y_{d}}$ is the induced consumption that is influenced by the economy's income level ${\displaystyle Y_{d}}$. The parameter ${\displaystyle b}$ is known as the marginal propensity to consume, i.e. the increase in consumption due to an incremental increase in disposable income, since ${\displaystyle \partial C/\partial Y_{d}=b}$. Geometrically, ${\displaystyle b}$ is the slope of the consumption function.

Keynes proposed this model to fit three stylized facts:^[5]

• People typically spend a part, but not all of their income on consumption, and they save the rest. They typically do not borrow money to spend, or borrow money to save.^[6] This fact is modelled by requiring ${\displaystyle b\in (0,1)}$.
• People with higher income save a higher proportion of the income. This is modelled by ${\displaystyle {\frac {C}{Y_{d}}}}$ decreasing with ${\displaystyle Y_{d}}$.
• People, when deciding how much to save, are insensitive to the interest rate.^[6]

By basing his model in how typical households decide how much to save and spend, Keynes was informally using a microfoundation approach to the macroeconomics of saving.^[7]

Keynes also took note of the tendency for the marginal propensity to consume to decrease as income increases, i.e. ${\displaystyle \partial ^{2}C/\partial Y_{d}^{2}<0}$.^[8] 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,^[9] Franco Modigliani and Richard Brumberg's (1954) life-cycle hypothesis, and Milton Friedman's (1957) permanent income hypothesis.^[10]

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.^[11]

See also

• Aggregate demand
• Absolute income hypothesis
• Life cycle hypothesis
• Measures of national income and output
• Permanent income hypothesis