Question
A firm has the following production function:
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 430 units.
How high are in this case the minimal costs?
Solution
Step 1: Formulating the minimization problem.
Step 2: Lagrange function.
Step 3: First order conditions.
Step 4: Solve the system of equations for , , and .
Solving the first two equations for and equating them gives:
Substituting this in the optimization constraint gives:
The minimal costs can be obtained by substituting the optimal factor combination in the objective function:
Given the target output, the minimal costs are .
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)