The price for one unit of capital is
and the price for one unit of labor is
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?
Step 1: Formulating the minimization problem.
Step 2: Lagrange function.
Step 3: First order conditions.
Step 4: Solve the system of equations for
Equating Equations (1) and (2) after solving for
Substituting this in the optimization constraint gives:
The minimal costs can be obtained by substituting the optimal factor combination in the objective function: