Consider a production function:

q=(LK)^1.5

• The wage and rental rate of capital are w=5,r=1.
• We consider the short-run, so that K is fixed at K=1

** Part a (5 marks)

Show whether the production function has:

• strictly positive marginal product of labor.
• strictly diminishing marginal product of labor.

** Part b (5 marks)

Find the short-run cost function.

** Part c (5 marks)

Explain whether this cost function in Part b implies whether the profit maximization problem has a well-defined solution (i.e. having a finite optimal output), or if the firm will want to expand indefinitely.