Find the elasticity of demand function as a function of p. x=800(p+2)2

Question

Find the elasticity of demand function as a function of p.

x=800(p+2)2

Answer 1

x=800(p+2)^2

price elasticity of demand is the percentage change in x divided by the percentage change in p. point price elasticity of demand is the derivative, dx/dp times p/x. (dx/x)/(dp/p) = the limit of the percentage change in x over percentage change in p, as the change approaches zero.

dx/dp = x' = 1600(p+2) = 1600p+ 3200

(dx/dp)(p/x) = (1600p^2 +3200p)/x