Question

Elasticity of demand . . .

Answer 1

\[f(p) = \sqrt{50-p}\] ; p=45

Answer 2

I know that\[ E(p) = \frac{ P \times f'(p) }{ f(p) }\]

Answer 3

you may use chain rule to find f', and you have f, and you have P i assume?

Answer 4

i got \[\frac{ -1 }{2 } (50-p)^{-1/2}\] ?

Answer 5

as your f', yes. now sub P= 45, you get f'(P) , and you know f(P) and you know P.

Answer 6

so the denominator is \[\sqrt{5}\] but im not sure about the numorator . . . other than it being 45+(\[\frac{ -1 }{ 2 }(50−p)^{-1/2}\]

Answer 7

you can substitute Point P to f'. in fact that is f'(p) .

Answer 8

Also known as instantaneous rate of change at point P.

Answer 9

so i got 20.23 when i inserted the p but for whatever reason the multiple choice answers for this problem still have the p in them . . . thats why im a little confused

Answer 10

yeah i was wondering if that was a typo you had a capital P on the original question.

Answer 11

if P =/= p then leave capital P, but it is right you sbustittue p to get f'(p) , and f(p)

Answer 12

I'm sorry but I'm still not seeing how any of the options are connected to what we did above

Answer 13

yeah me neither. If we did not substitute p, I get -p/(2(50-p))

Answer 14

but then theres an absolute sign so that nullifies -p, and makes it to p so our answer should be p/(2(50-p))

Answer 15

since numerator is greater than denom, it will be elastic at p = 45, and final answer is last choice.

Answer 16

:) thanks I really appreciate your help!