Question

40. The demand equation for a product is given by P = 30 – 0.1Q2
i) Write an equation for the point elasticity as a function of quantity.
ii) At what price is demand unitary elastic?

Answer 1

i)$Qp=\sqrt{\frac{P-30}{0.1}}$

$Ep=Q'p\frac{P}{Q}$

$Ep=(\sqrt{\frac{P-30}{0.1}})'\frac{P}{\sqrt{\frac{P-30}{0.1}}}=(2\sqrt{\frac{P-30}{0.1}})^{-1}(\frac{P}{\sqrt{\frac{P-30}{0.1}}})=\frac{P}{2P-30}$

$Ep=$

ii) Ep=1

$1=\frac{P}{2P-30}$

P=30