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Math Help - Maximization using Lagrange Multipliers.

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    Maximization using Lagrange Multipliers.

    Hey guys, is anyone able to help me with this question?

    Use Lagrange Multipliers to find expressions for K and L which maximize output given by the production function:

    Q=AK^aL^b (A,a,b are positive constants)

    subject to a cost constraint
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  2. #2
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    Quote Originally Posted by wings1340 View Post
    Hey guys, is anyone able to help me with this question?

    Use Lagrange Multipliers to find expressions for K and L which maximize output given by the production function:

    Q=AK^aL^b (A,a,b are positive constants)

    subject to a cost constraint
    Are we to assume that P_K, P_L, and M are constant also? If so,
    Let [/tex]F(K, L)= AK^aL^b[/tex] and G(K, L)= P_KK+ P_LL.

    The max and/or min occure when \nabla F= \nabla G for some number \nabla. Take the gradients of F and G, put them into that equation, write the equations given by the two components, and find all values K and L that satisfy it. (You do not need to find \nabla. I find that dividing one equation by another is a good strategy since it eliminates \lambda and don't for get that P_KK+ P_LL= M is another equation of K and L.)
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