Assume the following production function: q = = vl, i.e. no capital equipment, just labor (measured in hours). The firm is a price-taker both for its output (which it sells at price P per unit) and its workers (which it pays the prevailing wage rate of w per hour). a. Derive this firm's total cost function. b. Derive the firm's profit function. c. What is the firm's supply function q(P,w) for its finished output? d. What is the firm's labor-demand function /(P,w)? e. Describe intuitively why these functions have the form they do