Assuming that price of labor (L) and capital (K) are 12 and 3, respectively. One manufacturing company is facing production function given as Q = LK .
(1) What will be the input combination based on the aforementioned information to minimize the cost? Support your answer by using mathematical cost minimization and explain in verbal.
(2) By using the answer from (1), derive demand function for both labor and capital.
(3) Based on your answer from (2), derive your total cost function.
(4) Based on your total cost function, derive the average total cost.
(5) Now, you know that the company has limited budget of 600. What will be the cost minimizing input of labor and capital?
(6) If the price of capital increased double, what will be the optimal labor and capital to maintain same output from (5)?