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Math Help - improper integrals question (consumer surplus)

  1. #1
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    improper integrals question (consumer surplus)



    This is from my economics class lecture. Can someone explain how the last part (in yellow box) is done? How was the answer obtained?

    Since one of the limits of the integration is infinite, this is an improper integral. So, i thought that since [P^(e+1)]/(e+1) approaches infinity when P approaches infinity, the integral diverges and is meaningless.
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  2. #2
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    If  e < -1 , (I'm assuming that  e is not 2.718... ), the result would be correct, but otherwise I'm with you.
    Also, if  P_0 is positive,  e < -1 would be needed to make  CS positive. Should it be ?
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  3. #3
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    Quote Originally Posted by BobP View Post
    If  e < -1 , (I'm assuming that  e is not 2.718... ), the result would be correct, but otherwise I'm with you.
    Also, if  P_0 is positive,  e < -1 would be needed to make  CS positive. Should it be ?
    Thanks! I finally got it. Sorry for omitting important information. I got the screen shot straight from my lecture slides.

    The above is an example in a monopoly market. Thus, e<-1 because a monopoly will choose to operate only in regions in which the market demand curve is elastic.

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