Elasticity of Demand problem help

[hallie]

Hi, I know this may seem like a dumb question, but I just can't seem to get by one part of each elasticity of demand problem I come across. For example:

Use the​ price-demand equation below to find​ E(p), the elasticity of demand.
x=f(p)=20,000-550p

I know that E(p)=pf'(p)/f(p), so in this problem that would get me E(p)=p(-550)/20,000-550p, but after that, I am unsure of how to divide the equation in order to simplify it.
I know the answer is E(p)=11p-/400-11p, but if anyone could tell me how to divide/simplify the equation in order to get to that answer, I would be extremely grateful.

Thank you!

 

[MarkFL]

Okay, it looks like you have derived:

$$E(p)=\frac{-550p}{20000-550p}$$

Now if we divide the numerator and denominator by -50, we obtain:

$$E(p)=\frac{11p}{11p-400}$$

Does this make sense?

 

[hallie]

Where do you get the -50 from?

 

[MarkFL]

Where do you get the -50 from?

Since there is a minus sign on one of the terms in the denominator and a minus sign on the numerator, if we divide by a negative number, then we will only have 1 minus sign in the denominator. I prefer the form:

$$\frac{a}{b-c}$$

over:

$$\frac{-a}{c-b}$$

Even though they are equivalent, I like fewer negatives. Then if we look at 550 and 20000, we see that 50 is the GCD, so dividing each term by -50 will result in the simplest terms in the form with fewer negative signs. :)

 

[hallie]

Since there is a minus sign on one of the terms in the denominator and a minus sign on the numerator, if we divide by a negative number, then we will only have 1 minus sign in the denominator. I prefer the form:

$$\frac{a}{b-c}$$

over:

$$\frac{-a}{c-b}$$

Even though they are equivalent, I like fewer negatives. Then if we look at 550 and 20000, we see that 50 is the GCD, so dividing each term by -50 will result in the simplest terms in the form with fewer negative signs. :)

Perfect! Thank you so much for this explanation! :)