A firm has a production function:

q = (KL)1/5

Q2a. (5 marks)

In the short-run, the firm chooses L fixing K = K > 0. Derive the short-run unconditional

(i.e. profit-maximizing) labor demand. Hint: the profit with K = K

is:

p(K L)1/5 wL rK

Q2b. (5 marks)

Show that the short-run unconditional labor demand you derived from Part a is

increasing in K .

Q2c. (5 marks)

With K being flexible in the long-run, find the long-run unconditonal labor demand

and the long-run unconditional capital demand.