A firm's cost function is TCi = a + bqi + c qi2, where a, b and c are positive constants a. Find its marginal cost function, and show that MC is increasing for all q. b. Find its average total cost function. Now, prove that at the quantity that minimizes ATC, MC = ATC. c. Suppose TCi = 1000 + 20 qi + .1 qi2 Find the firm's short run supply function, qi(P). If there are 3 identical firms in this market, what is the market supply function? If demand is Qd = 1000 15 P, what is the short run equilibrium price? What is each firm's profit or loss? What is the industry's consumer surplus? Is this market in long-run equilibrium? How can you tell? d. In the long run, what is each firm's optimal quantity? What is the long-run equilibrium price? How many firms will exist in the long run?