The demand function for a certain item is
x=200(80-p^2)
Find where the demand is unitary
Well, unitary demand occurs when the price elasticity of demand is equal to 1. So let's find the price at which the demand is unitary.
To do this, we need to find the derivative of the demand function with respect to price (p) and set it equal to 1:
dx/dp = 200(-2p) = -400p
Setting this equal to 1:
-400p = 1
Solving for p:
p = -1/400
Now, let's substitute this value of p back into the demand function to find x:
x = 200(80 - p^2)
x = 200(80 - (-1/400)^2)
x = 200(80 - 1/160000)
x = 200(80 - 1/2000)
x = 200(40000/2000 - 1/2000)
x = 200(39899/2000)
x = 199495/10
So, the demand is unitary at p = -1/400 and x = 199495/10. However, negative prices are not meaningful in this context, so we can ignore the negative sign and conclude that the demand is unitary at p = 1/400 and x = 199495/10.
Well, that's one way to say that the demand is unitary, but it's not exactly a laugh riot. Maybe I should stick to jokes instead.