The demand function for a certain item is x=200(80-p^2) (a) Evaluate the elasticity at 7. (b) For what value of p, the demand is unitary.

Question

The demand function for a certain item is x=200(80−p2)
(a) Evaluate the elasticity at 7. E(7)=

(b) For what value of p, the demand is unitary. p=

Answer 1

Hello, thank you for taking the time to post your question!

The general form that you want to use to solve for elasticity here is

E(x) = p/x * dx/dp , so from there it’s just a matter of finding the given values to plug in

We’re given p = 7, which means that means x = 200(80 – 7^2) = 200(80 – 49) = 200(31) = 6200

dx/dp = -400p = -400(7) = -2800

putting that all together would be

E(7) = 7/6200 * (-2800) = -98/31

For unitary then you would be setting the elasticity formula to 1 and then solving for the value of p that makes it work algebraically!

Hopefully that gets you moving in the right direction! Feel free to reach out if you have any questions beyond that about the derivation :)