Question

If the demand function is $D=150-p^2-3p$, find marginal revenue, average revenuue and elasiticity of demand for price $p=3$.

Answer 1

Elasticity of demand

$D=150-p^2-3p$

$n=\frac{\partial D}{\partial P}\times \frac{P_o}{x_o}$

$P_o=3,x_o=150-9-9=132$

$n=-2p-3\times \frac{3}{132}=-0.204$

MR(marginal revenue)

$=P[1-\frac{1}{n_p}]$

$=3[1+\frac{132}{27}]=17.666$

Average revenue (AR)

$=M\left(\frac{e}{e-1}\right)$

$=17.666\left(\frac{-0.204}{-1.204}\right)=3$