Exam 1

  1. Question

    A firm has the following production function:
    F(K,L)=K L3 .

    The price for one unit of capital is pK =20 and the price for one unit of labor is pL =11. Minimize the costs of the firm considering its production function and given a target production output of 730 units.
    How high are in this case the minimal costs?

    Solution

    Step 1: Formulating the minimization problem.
    minK,L C(K,L) = pK K+ pL L = 20K+11L subject to: F(K,L)=Q K L3 =730

    Step 2: Lagrange function.
    L(K,L,λ) = C(K,L)-λ(F(K,L)-Q) = 20K+11L-λ(K L3 -730)

    Step 3: First order conditions.
    L K = 20-λ L3 =0       (1) L L = 11-3λK L3-1 =0       (2) L λ = -(K L3 -730)=0       (3)

    Step 4: Solve the system of equations for K, L, and λ.
    Equating Equations (1) and (2) after solving for λ gives:
    20 L3 = 11 3K L3-1 K = 11 3·20 · L3-(3-1) K = 11 60 ·L

    Substituting this in the optimization constraint gives:
    K L3 = 730 ( 11 60 ·L) L3 = 730 11 60 L4 = 730 L = ( 60 11 ·730) 1 4 =7.94365468  7.94 K = 11 60 ·L=1.45633669  1.46

    The minimal costs can be obtained by substituting the optimal factor combination in the objective function:
    C(K,L) = 20K+11L = 29.126734+87.380201 = 116.506935116.51

    Given the target output, the minimal costs are 116.51.
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