Let there be two factors (inputs), L and K, (,) + 2 , with factor prices w and r, respectively, (, ) ++ 2 . Let the firm's production function be = where , > 0.

a. Find the long run total cost function (, , ). (10)

b. Let capital be fixed at = in the short run. Find the short run total cost function (, , ; = ). (6)

c. Let p be the price of y. If this is a competitive firm, find how much would it produce in the short run. (6)