Inverse demand function: Difference between revisions

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==Definition==

Market demand is determined by price, y=f(x)

In mathematical terms, if the [[demand curve|demand function]] is Q = f(P), then the inverse demand function is P = f⁻¹(Q),. whoseThe value P in the inverse demand function is the highest price that could be charged and still generate the quantity demanded Q.<ref>Varian, H.R (2006) Intermediate Microeconomics, Seventh Edition, W.W Norton & Company: London</ref> This is to say that the inverse demand function is the [[demand curve|demand function]] with the axes switched. This is useful because economists typically place price ('''P''') on the vertical axis and quantity ('''Q''') on the horizontal axis in supply-and-demand diagrams, so it is the inverse demand function that depicts the graphed demand curve in the way the reader expects to see.

Price can also be determined by demand, x=f(y), this is the inverse demand function (price reaction and demand)

In mathematical terms, if the [[demand curve|demand function]] is f(P), then the inverse demand function is f⁻¹(Q), whose value is the highest price that could be charged and still generate the quantity demanded Q.<ref>Varian, H.R (2006) Intermediate Microeconomics, Seventh Edition, W.W Norton & Company: London</ref> This is to say that the inverse demand function is the [[demand curve|demand function]] with the axes switched. This is useful because economists typically place price ('''P''') on the vertical axis and quantity ('''Q''') on the horizontal axis.

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> Note that although price is the dependent variable in the inverse demand function, it is still the case that the equation represents how the price determines the quantity demanded, not the reverse.

==Applications==