5. (8pts) Perfect Competition: Bill grows oats. The market supply for oats is Qs = -9 +4P and demand is Qd = 40 3P. Bill's cost function is 26 + 2q + 0.1q2, where q is his output of oats in bushels. a) (4pts) Derive the average variable cost function, the marginal cost function, and the average xed cost function, and graph them on graph paper. b) (2 pts) What is the market price of oats? c) (2 pts) What is Bill's prot-maximizing output of oats? (Use calculus.) What are prots? Use 1'1 = (P AC)q and show in a diagram. d) (2pts) The market for oats is perfectly competitive, and thus the market price must fall to the minimum of average cost for each rm in the long run. Since it is assumed that all rms have the same cost structure, what will be the long-run price of oats? What will be Bill's prots in the long run