Question

The demand function of a commodity at a sales price p is given by: D(p) = 700/p − 250 p^2−0.002p Find the elasticity of demand and the price of unit elasticity(meaning what is p when |E(p)| = 1).

Answer 1

$\frac{dD(p)}{dp}= -700p^{-2}-500p-0.002\\ \text{which is the elasticity of demand}\\ \text{The price of unit}.\\ E(p)= -700p^{-2}-500p-0.002\\ E(p)=1, \\ 1=-700p^{-2}-500p-0.002\\ \text{multiply both sides by} p^2 \text{and collect like terms}\\ 500p^3+1.002p^2+700=0\\$