Inverse demand function: Difference between revisions

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In [[economics]], an '''inverse demand function''' is the the mathematical relationship that expresses price as a [[inversefunction (mathematics)|function]] of aquantity '''demanddemanded function'''.(is Theis inversetherefore demandalso function views priceknown as a function'''price of quantityfunction''').<ref>{{Cite book|title=Intermediate microeconomics : with calculus|last=R.|first=Varian, Hal|date = 7 April 2014|isbn=9780393123982|edition= First|___location=New York|pages=115|oclc=884922812}}</ref>

Historically, the economists first expressed the price of a good as a function of demand (holding the other economic variables, like income, constant), and plotted the price-demand relationship with demand on the x (horizontal) axis (the [[demand curve]]). Later the additional variables, like prices of other goods, came into analysis, and it became more convenient to express the demand as a [[multivariate function]] (the '''demand function'''):

Quantity demanded, ''Q'', is a function <math>f</math> (the demand function) of price; the inverse demand function treats price as a function of quantity demanded, and is also called the price function:<ref>Samuelson, W and Marks, S Managerial Economics 4th ed. page 35. Wiley 2003.</ref>

<math>{demand} = f({price}, {income}, ...)</math>, so the original demand curve now depicts the ''inverse'' demand function <math>P = f^{-1}(Q)</math> of price with extra variables fixed.<ref>{{cite web |last1=Karaivanov |first1=Alexander |title=The demand function and the demand curve |url=https://www.sfu.ca/~akaraiva/demfun.pdf |website=sfu.ca |publisher=[[Simon Fraser University]] |access-date=29 August 2023}}</ref>

:<math>P = f^{-1}(Q).</math>

The inverse demand function forms the [[demand curve]]. The function appears in this form because economists place the independent variable on the y-axis and the dependent variable on the x-axis.

==Definition==