# Math Help - Finding Eqn of a Line Given Slope

1. ## 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!

2. I dont know anything about the slopes or economics or anything like that, but I can tell you that
$\int { - \frac{{2^{\frac{1}
{2}} n^{ - \frac{1}
{2}} }}
{2}{\text{ }}} dn = \int {\frac{{ - \sqrt 2 }}
{{2\sqrt n }}} {\text{ }}dn = \frac{{ - \sqrt 2 }}
{2}\int {\frac{1}
{{\sqrt n }}{\text{ }}dn} = - \frac{{\sqrt 2 }}
{2}\left( {2\sqrt n } \right) = - \sqrt {2n}
$

Your integration was perfect except for the negative sign getting lost somewhere.

3. 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!