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  1. MHB Apprentice

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    #1
    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 accross. 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!

  2. Pessimist Singularitarian
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    #2
    Okay, it looks like you have derived:

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

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

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

    Does this make sense?

  3. MHB Apprentice

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    #3 Thread Author
    Where do you get the -50 from?

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    #4
    Quote Originally Posted by hallie View Post
    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:

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

    over:

    $ \displaystyle \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.

  5. MHB Apprentice

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    #5 Thread Author
    Quote Originally Posted by MarkFL View Post
    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:

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

    over:

    $ \displaystyle \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!

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