Editing Consumption function

{{Short description|Economic model relating consumption and disposable income}}
{{Distinguish|demand function}}
[[File:Consumption Function.png|thumb|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 (economics)|consumption]] and [[Disposable and discretionary income|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 (mathematics)|function]] that [[Map (mathematics)|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>{{cite book |first=John |last=Lindauer |author-link=John Lindauer |title=Macroeconomics |location=New York |publisher=John Wiley & Sons |edition=Third |year=1976 |isbn=0-471-53572-9 |pages=40–43 }}</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 [[Fiscal multiplier|government spending multiplier]].<ref>{{cite book |last1=Hall |first1=Robert E. |author-link=Robert Hall (economist) |last2=Taylor |first2=John B. |author2-link=John B. Taylor |chapter=Consumption and Income |pages=63–67 |title=Macroeconomics: Theory, Performance, and Policy |location=New York |publisher=W. W. Norton |year=1986 |isbn=0-393-95398-X }}</ref>

==Details==
Its simplest form is the ''linear consumption function'' used frequently in simple [[Keynesian economics|Keynesian models]]:<ref>{{cite book |first=David |last=Colander |author-link=David Colander |title=Macroeconomics: Theory and Policy |location=Glenview |publisher=Scott, Foresman and Co. |year=1986 |isbn=0-673-16648-1 |pages=[https://archive.org/details/macroeconomicsth0000cola/page/94 94]–97 |url=https://archive.org/details/macroeconomicsth0000cola |url-access=registration }}</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 fact|stylized facts]]:<ref>{{Cite book |last=Mankiw |first=N. Gregory |url=https://www.worldcat.org/oclc/1289514240 |title=Macroeconomics |date=2022 |isbn=978-1-319-26390-4 |edition=11 |location=New York |at=20-1 What Determines Consumer Spending? |oclc=1289514240}}</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">{{cite book |last=Keynes |first=John M. |title=[[The General Theory of Employment, Interest and Money]] |publisher=Harcourt Brace Jovanovich |year=1936 |location=New York |at=Section 3.8.2 |quote=There are not many people who will alter their way of living because the rate of interest has fallen from 5 to 4 per cent, if their aggregate income is the same as before... the short-period influence of the rate of interest on individual spending out of a given income is secondary and relatively unimportant, except, perhaps, where unusually large changes are in question.}}</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 [[Microfoundations|microfoundation]] approach to the macroeconomics of saving.<ref>{{Cite journal |last=Solow |first=Robert M. |date=2004 |title=Introduction: The Tobin Approach to Monetary Economics |url=http://dx.doi.org/10.1353/mcb.2004.0067 |journal=Journal of Money, Credit, and Banking |volume=36 |issue=4 |pages=657–663 |doi=10.1353/mcb.2004.0067 |s2cid=154008365 |issn=1538-4616 |quote=... recall Keynes’s argument that the marginal propensity to consume should be between zero and one, or his discussion about whether the marginal efficiency of investment should be sensitive to current output or should depend primarily on “the state of long-term expectations.” Those are microfoundations.|url-access=subscription }}</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>{{Cite book|title=[[The General Theory of Employment, Interest and Money]]|last=Keynes|first=John M.|publisher=Harcourt Brace Jovanovich|year=1936|location=New York|quote=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.}}</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>{{cite book |last=Duesenberry |first=J. S. |year=1949 |title=Income, Saving and the Theory of Consumer Behavior |url=https://archive.org/details/in.ernet.dli.2015.84155 }}</ref> [[Franco Modigliani]] and Richard Brumberg's (1954) [[life-cycle hypothesis]], and [[Milton Friedman]]'s (1957) [[permanent income hypothesis]].<ref>{{cite book |last=Friedman |first=M. |year=1957 |title=A Theory of the Consumption Function }}</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>{{Cite journal | doi = 10.1016/j.joep.2010.09.004| title = Behavioral foundations for the Keynesian consumption function| journal = Journal of Economic Psychology| volume = 31| issue = 6| pages = 1035| year = 2010| last1 = d’Orlando | first1 = F. | last2 = Sanfilippo | first2 = E. | url = http://dipeg-wpe.unicas.it/dipse/files/wp200805.pdf}}</ref>

==See also==
* [[Aggregate demand]]
*[[Absolute income hypothesis]]
* [[Life cycle hypothesis]]
* [[Measures of national income and output]]
* [[Permanent income hypothesis]]

==Notes==
{{Reflist}}

==Further reading==
* {{cite book |first=J. Carl |last=Poindexter |chapter=The Consumption Function |title=Macroeconomics |location=Hinsdale |publisher=Dryden Press |year=1976 |isbn=0-03-089419-0 |pages=113–141 |chapter-url=https://books.google.com/books?id=TLS7AAAAIAAJ&pg=PA113 }} ''(Undergraduate level discussion of the subject.)''
* {{cite book |first=Thomas J. |last=Sargent |author-link=Thomas J. Sargent |chapter=The Consumption Function |title=Macroeconomic Theory |location=New York |publisher=Academic Press |year=1979 |isbn=0-12-619750-4 |pages=298–323 |chapter-url=https://books.google.com/books?id=X6u7AAAAIAAJ&pg=PA298 }} ''(Graduate level discussion of the subject.)''

==External links==
* [http://www.economic-truth.co.uk/content-essays/bsc/keynesconsumption.pdf An essay examining the strengths and weaknesses of Keynes's theory of consumption]

{{Consumption}}
{{Consumer behaviour}}
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[[Category:Consumption (macroeconomics)]]