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Math Help - Cost Minimization function with exponent

  1. #1
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    Cost Minimization function with exponent

    OK, so the equation is:

    X = K^.25 L^.75, w = 2, r = 4

    I know that:

    Marginal Product of Labour/Marginal product of Kapital = w/r

    So I take the derivative with regards to "l" on top and do the same with respect to "k" on bottom and get...

    (3/4K^.25 L^-0.25)/(1/4K^-0.75 L^0.25) = 2/4

    The 4's on bottom negate each other...and we know that the negative exponent flips to the other side of the dividing line, which gives us:

    3K/L = 1/2

    Cross multiply, survey says...

    6K = L

    Now, I know I have to plug this back into the original equation (ie. for every "L" there is 6"k")...when I do that, I get

    X = K^0.25 6K^0.75

    My question is where do I go from here, and did I do the math right?

    Ibrox
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  2. #2
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    Yes, you did!

    X = K^.25 6K^.75 (The same base so you adds the exponents)

    X = 6K or X = L.
    Last edited by Prof Paulo; October 18th 2009 at 07:42 AM.
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  3. #3
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    I thought the 6K^0.75 kicks in first before I add the exponents up
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  4. #4
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    Talking

    Quote Originally Posted by ibrox View Post
    OK, so the equation is:

    X = K^.25 L^.75, w = 2, r = 4

    I know that:

    Marginal Product of Labour/Marginal product of Kapital = w/r

    So I take the derivative with regards to "l" on top and do the same with respect to "k" on bottom...
    From what you've posted, K (or k?) is "on top", so I'm not sure what you mean by "to 'k' on bottom"...? Also, you posted this to "pre-algebra", but then refer to taking derivatives (from post-algebra calculus)...?

    How do X, K, L, w, r, l, and k relate? With respect to what are you differentiating? What are you differentiating? What are the necessary formulas and relations? What are you trying to accomplish?

    Please be complete. Thank you!
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