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# Consumption function

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 Title: Consumption function Author: World Heritage Encyclopedia Language: English Subject: Collection: MacRoeconomics Publisher: World Heritage Encyclopedia Publication Date:

### Consumption function

In economics, the consumption function describes a relationship between consumption and disposable income.[1] Algebraically, this means C = f(Y_{d}) where f \colon \mathbb{R} \to \mathbb{R} is a function that maps levels of disposable income Y_{d}â€”income after government intervention, such as taxes or transfer paymentsâ€”into levels of consumption C. 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.[2] Its simplest form is the linear consumption function used frequently in simple Keynesian models:[3]

C = a + b \times 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 \times Y_{d} is the induced consumption that is influenced by the economy's income level. 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).[4]

Criticism of the simplicity and irreality of this assumption lead to the development of Milton Friedman's permanent income hypothesis, and Richard Brumberg and Franco Modigliani's life-cycle hypothesis. But none of them developed a definitive consumption function. Friedman, although he got the Nobel prize for his book A Theory of the Consumption Function (1957), presented several different definitions of the permanent income in his approach, making it impossible to develop a more sophisticated function. Modigliani and Brumberg tried to develop a better consumption function using the income got in the whole life of consumers, but them and their followers ended in a formulation lacking economic theory and therefore full of proxies that do not account for the complex changes of today's economic systems.

Until recently, the three main existing theories, based on the income dependent Consumption Expenditure Function pointed by Keynes in 1936, were Duesenberry's (1949) relative consumption expenditure,[5] Modigliani and Brumberg's (1954) life-cycle income, and Friedman's (1957) permanent income.[6]

Some new theoretical works are based, following Duesenberry's one, on behavioral economics and suggest that a number of behavioural principles can be taken as microeconomic foundations for a behaviorally-based aggregate consumption function.[7]