Suppose the firm has a production function of the form f(k,l,m)=(klm)^1/4 and faces input prices (1,2,8) for (k,l,m) respectively.
a) What is the firm's cost function? What is their supply function? How much capital k does the firm use to produce q=4?
b) Now suppose that the firm's capital is fixed at k=16? What is the firm's short-run average cost function?
c) What is the short-run cost function when k=40?