Inverse demand function: Difference between revisions

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In [[economics]], an '''inverse demand function''', <math>P = f⁻¹^{-1}(Q)</math>, is a function that maps the quantity of output demanded to the market price (dependent variable) for that output. Quantity demanded, Q, is a 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> Note that the inverse demand function is not the reciprocal of the demand function&mdash;the word "inverse" refers to the mathematical concept of an [[inverse function]].

{{citation style|date=May 2012}}

In [[economics]], an 'inverse demand function', P = f⁻¹(Q), is a function that maps the quantity of output demanded to the market price (dependent variable) for that output. Quantity demanded, Q, is a 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> Note that the inverse demand function is not the reciprocal of the demand function&mdash;the word "inverse" refers to the mathematical concept of an [[inverse function]].

==Definition==

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The inverse demand function is the same as the average revenue function, since P = AR.<ref>Chiang & Wainwright, Fundamental Methods of Mathematical Economics 4th ed. Page 172. McGraw-Hill 2005</ref>

To compute the inverse demand function, simply solve for P from the demand function. For example, if the demand function has the form <math>Q = 240 - 2P</math> then the inverse demand function would be <math>P = 120 - 0.5Q</math>.<ref>Samuelson & Marks, Managerial Economics 4th ed. (Wiley 2003)</ref>

==Applications==