A firm has a fixed proportion production function

q = (min{K, L})1/3

Q5a. (5 marks)

Find the long-run conditional labor demand. Hint: it solves the long-run cost

minimization problem.

Q5b. (5 marks)

Draw the isoquant of this production function and the isocost lines, indicating the

optimum.

Q5c. (5 marks)

Prove that why profit maximization must imply cost minimization.