Gorman polar form: Difference between revisions

Revision as of 01:55, 16 January 2020

Revision as of 19:33, 30 December 2020

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Standard [[consumer theory]] is developed for a single consumer. The consumer has a utility function, from which his demand curves can be calculated. Then, it is possible to predict the behavior of the consumer in certain conditions, price or income changes. But in reality, there are many different consumers, each with his own utility function and demand curve. How can we use consumer theory to predict the behavior of an entire society? One option is to represent an entire society as a single "mega consumer", which has an aggregate utility function and aggregate demand curve. But in what cases is it indeed possible to represent an entire society as a single consumer?

Formally:<ref name=Alp>{{cite web | url=http://ocw.mit.edu/courses/economics/14-452-economic-growth-fall-2009/recitations/MIT14_452F09_rec2.pdf | title=Gorman's Aggregation Theorem | date=2009 | accessdateaccess-date=2 December 2015 | author=Simsek, Alp}}</ref> consider an economy with <math>n</math> consumers, each of whom has a [[demand function]] that depends on his income <math>m^i</math> and the price system:

:<math>x^i(p,m^i)</math>

The aggregate demand of society is, in general, a function of the price system and the entire distribution of incomes:

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== Application ==

Many applications of Gorman polar form are summarized in various texts and in Honohan and Neary's article.<ref>{{cite journal |last=Honohan |first=Patrick |authorlinkauthor-link=J. Peter Neary |last2=Neary |first2=J. Peter |title=W. M. Gorman (1923–2003) |journal=The Economic and Social Review |volume=34 |issue=2 |year=2003 |pages=195–209 |url=http://www.esr.ie/Vol34_2Neary.pdf |url-status=dead |archiveurlarchive-url=https://web.archive.org/web/20050110001924/http://www.esr.ie/Vol34_2Neary.pdf |archivedatearchive-date=2005-01-10 }}</ref> These applications include the ease of estimation of <math>f^i(p)</math> and <math>g(p)</math> in certain cases. But the most important application is for the theorist of economics, in that it allows a researcher to treat a society of utility-maximizing individuals as a single individual. In other words, under these conditions a community [[indifference curve|indifference mapping]] is guaranteed to exist.

== See also ==

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== References ==

{{Reflist}}

*{{cite book |last=Antonelli |first=G. B. |year=1886 |title=Sulla Teoria Matematica dell'Economia Politica |___location=Pisa }} English translation in {{cite book |editor1-first=J. S. |editor1-last=Chipman |editor2-first=L. |editor2-last=Hurwicz |editor3-first=M. K. |editor3-last=Richter |editor4-first=H. F. |display-editors = 3 |editor4-last=Sonnenschein |title=Preferences, Utility and Demand: A Minnesota Symposium |___location=New York |publisher=Harcourt Brace Jovanovich |year=1971 |pages=333–360 |isbn= }}

*{{cite journal |first=W. M. |last=Gorman |title=On a class of preference fields |journal=Metroeconomica |volume=13 |issue=2 |year=1961 |pages=53–56 |doi= 10.1111/j.1467-999X.1961.tb00819.x}}

*{{cite journal |last=Nataf |first=A. |year=1953 |title=Sur des questions d'agrégation en économétrie |journal=Publications de l'Institut de Statistique de l'Université de Paris |volume=2, Fasc. Vol. 4 |pages=5–61 }}