Consider a firm with the production function q = L 1 2 K 1 4 The firm faces a wage rate of w = 20 and a capital rental rate of r = 40. Initially, the firm's capital is fixed at K = 16. (a) Derive the short-run cost function for this firm, C SR(q). Using this, what is the firm's short-run marginal cost function, MCSR(q)? (b) If the firm sells output at a price of p = 60, how much labor will it employ? How much output does it produce? How much profit does it earn? (c) In the long run, what is the firm's cost-minimizing ratio of capital to labor, K/L? (d) What is the long-run cost function, C LR(q)?