Problem 1: [exam id #887] [20 points] Consider a perfectly competitive market composed of many identical firms, each with the following long-run total cost function: C = q - 15q~ + 60q where q represents the firm's output. The market demand curve is given by: Q(P) = 150 - 12P where Q represents industry output. (a) [7 points] Find the long-run equilibrium price (P*), the long-run equilib rium industry output (Q*), the long-run equilibrium firm output (q*), and the long-run equilibrium number of firms (n*). Please show your work. (b) [13 points] Suppose the number of firms remains at n* (solved in (a)), but in the short run each firm has the following short-run total cost function, SRTC(q) = q2 -6q+300. Further, suppose demand decreases to Q( P) = 324- 18P. Find the short-run equilibrium price (P), the short-run equilibrium industry output (Q), and the short-run equilibrium firm output (q). What are each firm's short-run profits? What will happen to the number of firms in the long run