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Thread: Maximisation problem / costs: Consider a firm with two inputs K and L...

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    Maximisation problem / costs: Consider a firm with two inputs K and L...

    Consider a firm with two inputs K and L that produce an output Q(K, L). The firmís cost function is

    C(K, L) = K + 2L

    It is required to minimize C(K, L) subject to the constraint Q(K, L) = q where q is a positive real constant. You may assume that the optimization problem has a solution at an interior point of R2+.

    (i) Show that

    [tex]\dfrac{\partial Q}{\partial L} = 2\dfrac{\partial Q}{\partial K}[/tex] holds at the optimal point.

    (ii) Assume that Q(K,L) is homogeneous of degree m. At the optimal point, also assume that ∂Q/∂K = r for some positive real r. Find the constrained minimum value of C(K, L) in terms of m, r and q.

    I am not sure how to do this problem or where to start. Would the set up be something like,

    [tex]L( c, \lambda) = K + 2L + \lambda q[/tex]

    [tex]\dfrac{\partial Q}{\partial L} = 2[/tex]

    [tex]\dfrac{\partial Q}{\partial K} = 1[/tex]

    [tex]\dfrac{\partial Q}{\partial \lambda} = q[/tex]

    How would I find the constrained minimum value?
    Last edited by mmm4444bot; 01-07-2018 at 09:07 PM. Reason: Replaced incorrect LaTex tags; fixed line breaks and typos

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