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Math Help - How to rewrite an infinite product of a production function.

  1. #1
    Newbie
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    Oct 2012
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    L.A.
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    How to rewrite an infinite product of a production function.

    Hi! Well I've been struggling with this equation (production function):

    \prod_{i=1}^n x_i^{a_i} = f(x) = y

    I need to find Xi in order to subtitute it in the equation (because I have to find the "cost function" of that production function) (pd: I've concluded that the following is the "cost function" i need to minimize):

     g(y,w) = \sum_{i=1}^n w_i x_i

    So I need to know how to deal with the product.

    Thanks for your answers.
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  2. #2
    MHF Contributor
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    Re: How to rewrite an infinite product of a production function.

    Hey Alm22.

    Have you considered the log of f(x) or log(y)?

    Minimizing the log of something is equivalent to minimizing that something.
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