Find equation for which demand is elastic if the price-demand equation x=f(p)= sq. rt. (2700-3p^2). [Be sure to find the domain first.]  

1 Answer

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should remember that the equation that represents the elasticity of demand is:`E= (p/Q)*(dQ)/(dp)`

Supposing that the equation of demand is `Q = sqrt(2700 - 3p^2), ` you need to differentiate the demand function with respect to p such that:

`(dQ)/(dp) = ((2700 - 3p^2)')/(2sqrt(2700 - 3p^2))`

`(dQ)/(dp) = (-6p)/(2sqrt(2700 - 3p^2))`

`(dQ)/(dp) = (-3p)/(sqrt(2700 - 3p^2))`

Notice that `(sqrt(2700 - 3p^2))!=0` , hence `2700 - 3p^2!=0` .

You need to find what are the values of p that cancel denominator such that:

`2700 - 3p^2 = 0 =gt - 3p^2 = -2700`

`p^2 = 900 =gt p_(1,2) = +-sqrt(900)`

`p = +-30`

You need to keep only the positive value for the price p, such that p=30.

Hence, evaluating the equation of elastic demand yields `(dQ)/(dp) = (-3p)/(sqrt(2700 - 3p^2))`  over the restrictive domain `(0,30)U(30,oo).`