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Thread: Supply function firm

  1. #1
    Feb 2009

    Supply function firm

    Hello, I wasn't sure where to put this so I hope it is alright. My problem is the following: I need to determine the supply function of a firm which has the cost function C(y)= 3y^3-6y^2+4y. I know the MC(y) = 9y^2-12y+4 Normally I would solve MC = P and use the ABC formula on 9y^2-12y+(4-p) but I keep getting the wrong answer. I do have a solution manual(the solution is apparently is y(p) = (2/3)+(1/3*sqrt(p)) but it uses the inverse of the MC function but I have no idea why that is being used and how to calculate said inverse because I normally only use the former method and the manual gives no calculations whatsoever. I hope this is clear enough and that someone can help me clear this up. Barbor
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  2. #2
    Sep 2006
    No clue what the context is or what the ABC formula does but sounds like you want y asthe subject of:

    9y^2-12y+4 = p

    $\displaystyle (3y-2)^2 = p$
    $\displaystyle 3y-2=\pm p$
    $\displaystyle y=\frac{\pm p+2}{3}$

    Assuming there's some reason from context that explains why -p isn't allowed; I'll leave that to you.
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