Marginal revenue

Summary

• The derivative of the revenue function with respect to \(q, R'\left( q \right)\) , is called the marginal revenue ,

\[MR=R'\left( q \right)\]

• Example: price elasticity of demand equal to -1
• \(q=cp^{-1}\) or \(p=cq^{-1}\)
• \(R\left( q \right)=c\) and \(R'\left( q \right)=0\) for all \(q\) .
• Example: linear demand
• \(q\left( p \right)=a-bp\)
• \(R\left( q \right)= \frac{aq}{b}- \frac{q^2}{b}\)

\[MR= \frac{a-2q}{b}\]

• \(MR>0\) if \(q<a/2\) , \(MR=0\) if \(q=a/2\) and \(MR<0\) if \(q>a/2\)