Find (a) the elasticity of demand and (b) the range of prices for which the demand is elastic (E , -1). f(p) = 200(30 - p)

Question

anonymous · Answer

@abb0t  an u help?

abb0t · Answer

Is this econ?

anonymous · Answer

calculus my teacher said to use this  E = p ⁄ f(p) * f'(p) and f(p) = 200(30 - p).

abb0t · Answer

So you're being asked to find the derivative (change in elasticity) right?

anonymous · Answer

this is what i did before  and she said to correct it 

p = 10 f(10) = 4000
p = f(20) = 2000
then the elasticity is 
4000 – 2000 over 4000 + 2000/ 10 – 20 over 10 + 20 = 1/3 over -1/3 
So the elasticity is -1

anonymous · Answer

yes

abb0t · Answer

Can you rewrite the formula using latex, I see you used some type of chain rule or product rule there. Because if you take the derivative of what I see, all you get is 6000-200  = 5800 and you can't evaluate a constant from E <p < -1

anonymous · Answer

okay and how would i rewrite it?

abb0t · Answer

use the equation editor option on the bottom of the text box

anonymous · Answer

ok

anonymous · Answer

$$f(p) = 200(30 - p) $$

anonymous · Answer

$$  E = p ⁄ f(p) * f'(p) and f(p) = 200(30 - p)$$

abb0t · Answer

hmmm..strange question. LOL. It's not the math that im not understanding, it's the application of is. 

But I think that you're being asked to find "E" in which case you have: $$E = \frac{ p }{ (6000-200p) \times 5800 }$$

anonymous · Answer

okay hold on let me show you a video of it

abb0t · Answer

The 5800 is simply the derivative of the function, f(p)

anonymous · Answer

https://ss01.ecotoh.net/vportal/VideoPlayer.jsp?ccsid=C-316dcc8e-c2c4-4f0f-b57f-873ceacfad1c:1#

abb0t · Answer

OHHHHHHHHHH I see what they did there. That's a good video, very similar to your question. What are you having trouble understanding?

anonymous · Answer

How to use that formula my teacher game me and also I'm not seeing how i did it wrong from the beginning?

abb0t · Answer

it says that revenue is $ p \times f(p)$  whcih in your case is $p (6000-200p) = 6000p-200p^2$

abb0t · Answer

take the derivative of that.

anonymous · Answer

the derivative of all of 600p - 200p^2

anonymous · Answer

i get 600 - 400p

abb0t · Answer

@Mertsj

anonymous · Answer

oh my bad its 6000

anonymous · Answer

i get -400(p - 15)