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Suppose you did a long-run profit-maximization problem, and the solution is (?∗,?1 ∗,?2 ∗) = (10,5,6)....

Suppose you did a long-run profit-maximization problem, and the solution is (?∗,?1 ∗,?2 ∗) = (10,5,6). Now you are doing a cost-minimization problem with output level 10. What are the cost-minimizing levels of ?1⁡and⁡?2?

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Answer #1

The dual approach of cost minimization, minimize the cost subject to output constraint and maximize the profit subject to cost constraint.

Therefore, profit maximize when units produced (y) is 10 units with the help of 5 units of x1 and 6 units of x2.

Then the cost minimizing inputs required to produce 10 units of output would be 5 units of x1 and 6 units of x2.

The cost minimizing levels of x1 and x2 are 5 and 6 respectively.

Answer: x1=5 units, x2 = 6 units.

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