A firm's production function is q = K^2L where q is the quantity produced, K is the amount of capital used, and L is the amount of labor used. w is the wage rate of labor and r is the rental rate of capital.
(a) In the short run when capital is fixed, how much labor should the firm hire?
(b) In the short run when capital is fixed, what is the short run cost function?
(c) In the long run, how much labor and capital should the firm use?
(d) What are the long run costs?