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# 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.[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]

## 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 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. One of the key assumptions of Keynesian economics is that this parameter is positive but smaller than one, i.e. ${\displaystyle b\in (0,1)}$.[5]

Keynes also took note of the tendency for the marginal propensity to consume to decrease as income increases, i.e. ${\displaystyle \partial ^{2}C/\partial Y_{d}^{2}<0}$.[6] 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,[7] Franco Modigliani and Richard Brumberg's (1954) life-cycle hypothesis, and Milton Friedman's (1957) permanent income hypothesis.[8]

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.[9]

## Notes

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.
5. ^ Keynes, John M. (1936). The General Theory of Employment, Interest and Money. New York: Harcourt Brace Jovanovich. p. 96. The fundamental psychological law ... is that men [and women] are disposed, as a rule and on average, to increase their consumption as their income increases, but not as much as the increase in their income.
6. ^ Keynes, John M. (1936). The General Theory of Employment, Interest and Money. New York: Harcourt Brace Jovanovich. The marginal propensity to consume is not constant for all levels of employment, and it is probable that there will be, as a rule, a tendency for it to diminish as employment increases; when real income increases, that is to say, the community will wish to consume a gradually diminishing proportion of it.
7. ^ Duesenberry, J. S. (1949). Income, Saving and the Theory of Consumer Behavior.
8. ^ Friedman, M. (1957). A Theory of the Consumption Function.
9. ^ d’Orlando, F.; Sanfilippo, E. (2010). "Behavioral foundations for the Keynesian consumption function" (PDF). Journal of Economic Psychology. 31 (6): 1035. doi:10.1016/j.joep.2010.09.004.