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Math Help - Finding Eqn of a Line Given Slope

  1. #1
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    Finding Eqn of a Line Given Slope

    Hi everyone!

    This is an economics problem, but even if you know nothing about economics, you might be able to help...

    I am given the slope of the PPF to be

    [z(K^0.5)(N^-0.5)]/2, so I know the the negative (-) of the slope of the PPF is the marginal productivity of labour (MPn).

    I also know that z = 1/2 and K = 4

    What I think I need to do to determine the equation for the PPF is to take the antiderivative of the slope. So I subsituted in z and K to get:

    -[(2^0.5)(N^-0.5)]/2

    but here comes the part where I forget my calculus skills. I got

    (2^0.5)(N^0.5) as my final answer but I'm not sure this is right.

    Is the antiderivative of -0.707(N^-0.5) just equal to (2^0.5)(N^0.5)?

    Thanks for your help!
    Lisa

    Sorry about the lack of Math brackets, I tried putting them in initially but it reallllly messed up my equations, so apparently i don't know how to use them!
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  2. #2
    Member
    Joined
    Dec 2007
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    I dont know anything about the slopes or economics or anything like that, but I can tell you that
    \int { - \frac{{2^{\frac{1}<br />
{2}} n^{ - \frac{1}<br />
{2}} }}<br />
{2}{\text{ }}} dn = \int {\frac{{ - \sqrt 2 }}<br />
{{2\sqrt n }}} {\text{ }}dn = \frac{{ - \sqrt 2 }}<br />
{2}\int {\frac{1}<br />
{{\sqrt n }}{\text{ }}dn}  =  - \frac{{\sqrt 2 }}<br />
{2}\left( {2\sqrt n } \right) =  - \sqrt {2n} <br />

    Your integration was perfect except for the negative sign getting lost somewhere.
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  3. #3
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    Feb 2008
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    Thanks! I wasn't confident about my answer, because it seemed off by alot, but that negative sign was the only problem, thanks for pointing that out!
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