Inverse demand function

In <a href="/facts/Economics/HYctA2Dn">economics</a>, an inverse demand function is the mathematical relationship that expresses price as a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> of quantity demanded (it is therefore also known as a price function).
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 <a href="/facts/Demand_curve/lALNI8BX">demand curve</a>). Later the additional variables, like prices of other goods, came into analysis, and it became more convenient to express the demand as a <a href="/facts/Multivariate_function/cyujR2q2">multivariate function</a> (the demand function):

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 {\displaystyle {demand}=f({price},{income},...)}
 
, so the original demand curve now depicts the inverse demand function 
 
 
 
 
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 {\displaystyle {price}=f^{-1}({demand})}
 
 with extra variables fixed.

Inverse demand function open-in-new

Inverse demand function