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Math Help - Help with rearranging terms

  1. #1
    Junior Member 22upon7's Avatar
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    Help with rearranging terms

    Hi everyone!

    So I have this equation in my economics book:

    1) \alpha A K^{\alpha-1} N^{1-\alpha} = r

    and they simply rearrange the terms to get to this equation:

    2) K = (  \frac{\alpha A}{r} )  ^{\frac{1}{1-\alpha}}   N

    I don't understand how they get from 1) to 2). I managed to get up to this point, but then I don't know what to do next:

    3) K^{\alpha - 1} =   \frac{r}{\alpha A N ^ {1 - \alpha }}

    Any help would be greatly appreciated!
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  2. #2
    MHF Contributor
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    Re: Help with rearranging terms

    Hey 22upon7.

    You have K^(alpha-1) = (r/alpha*A)*N^(alpha-1) Now taking everything to the power (1/(alpha-1) gives

    (K^(alpha-1))^(1/(alpha-1)) = K

    = [(r/alpha*A)*N^(alpha-1)]^(1/alpha-1)

    = N * (r/alpha*A)^(1/(alpha-1))

    = (1/(r/alpha*A))^(1/(1-alpha)) * N since a^(-x) = (1/a)^x and x = alpha - 1 in this case.

    = (A*alpha/r)^(1/(1-alpha)) * N
    Thanks from 22upon7
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  3. #3
    Junior Member 22upon7's Avatar
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    Re: Help with rearranging terms

    Thanks a lot Chiro!

    a^(-x) = (1/a)^x and x = alpha - 1 in this case
    I didn't know about that, I'll have to try and wrap my head around it - shouldn't be too difficult though!
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