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  1. MHB Apprentice

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    #1
    If i'm given a firm's production function of

    $ \displaystyle Y=zK^{\alpha}{N}^{1-\alpha}$

    Then assuming $ \displaystyle K$ is fixed and cost free, we can get our profit maximzation problem of

    $ \displaystyle \max_{{N}}zF(K^{\alpha}{N}^{1-\alpha})-wN$

    To find the optimality condition, $ \displaystyle {MP}_{N}=w$ , I take the partial derivative and find

    $ \displaystyle z{F}_{N}=z(1-\alpha){K}^{\alpha}{N}^{-\alpha}=w$

    Here is where i'm stuck.

    I need to show that the optimality condition can be written as $ \displaystyle \alpha=1-\frac{wN}{Y}$

    Any help would be appreciated.

    Thank you,

    Gin

  2. MHB Apprentice

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    #2
    Quote Originally Posted by Ginnee View Post
    If i'm given a firm's production function of

    $ \displaystyle Y=zK^{\alpha}{N}^{1-\alpha}$

    Then assuming $ \displaystyle K$ is fixed and cost free, we can get our profit maximzation problem of

    $ \displaystyle \max_{{N}}zF(K^{\alpha}{N}^{1-\alpha})-wN$

    To find the optimality condition, $ \displaystyle {MP}_{N}=w$ , I take the partial derivative and find

    $ \displaystyle z{F}_{N}=z(1-\alpha){K}^{\alpha}{N}^{-\alpha}=w$

    Here is where i'm stuck.

    I need to show that the optimality condition can be written as $ \displaystyle \alpha=1-\frac{wN}{Y}$

    Any help would be appreciated.

    Thank you,

    Gin
    Dont get the notation. What is z and F and also F with a subscript N

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