Consumption function

File:Consumption Function.png

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.<ref>Algebraically, this means <math>C = f(Y_{d})</math> where <math>f \colon \mathbb{R}^{+} \to \mathbb{R}^{+}</math> is a function that maps levels of disposable income <math>Y_{d}</math>—income after government intervention, such as taxes or transfer payments—into levels of consumption <math>C</math>.</ref><ref>Template:Cite book</ref> 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.<ref>Template:Cite book</ref>

Details

Its simplest form is the linear consumption function used frequently in simple Keynesian models:<ref>Template:Cite book</ref>

<math>C = a + b \cdot Y_{d}</math>

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

Keynes proposed this model to fit three stylized facts:<ref>Template:Cite book</ref>

• 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.<ref name=":0">Template:Cite book</ref> This fact is modelled by requiring <math>b \in (0,1)</math>.
• People with higher income save a higher proportion of the income. This is modelled by <math>\frac{C}{Y_d}</math> decreasing with <math>Y_d</math>.
• People, when deciding how much to save, are insensitive to the interest rate.<ref name=":0" />

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.<ref>Template:Cite journal</ref>

Keynes also took note of the tendency for the marginal propensity to consume to decrease as income increases, i.e. <math> \partial^{2} C / \partial Y_{d}^{2} < 0</math>.<ref>Template:Cite book</ref> 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,<ref>Template:Cite book</ref> Franco Modigliani and Richard Brumberg's (1954) life-cycle hypothesis, and Milton Friedman's (1957) permanent income hypothesis.<ref>Template:Cite book</ref>

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.<ref>Template:Cite journal</ref>

See also

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

Further reading

• Template:Cite book (Undergraduate level discussion of the subject.)
• Template:Cite book (Graduate level discussion of the subject.)

External links

• An essay examining the strengths and weaknesses of Keynes's theory of consumption