# Find the elasticity of , E(p) for the demand function q = 4000 - 40p^2 and determine if demand is elastic or inelastic at p= 5 calculus

The price elasticity of demand is given by the percentage change in demand for a percentage change in supply. If the expression for demand (q) in terms of the price (p) is given by q = 4000 - 40*p^2, the price elasticity is E(p) = given by `((dq)/q)/((dp)/p)`

`q = 4000 - 40*p^2`

`dq = -80*p dp`

`((dq)/q)/((dp)/p)`

=> `((-80*p dp)/(4000 - 40*p^2))/((dp)/p)`

=> `(-80*p dp *p)/((4000 - 40*p^2)*dp)`

=> `(-80*p*p)/(4000 - 40*p^2)`

=> `(-80p^2)/(4000 - 40p^2)`

At p = 5, the value of ` E(p) = -2/3 = -0.66`

As the elasticity is less than 1 at p = 5, the demand is inelastic.

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