Assume that an industry consists of 10 000 identical firms and it is a perfectly competitive market. Firms sellits product at a price of $30 per unit. The industry's demand curve is Q =400 -10P. A firm'scost function given asTC =100 +8Q +4Q2.

a. What are the demandand Marginal revenue curvesfor a typicalfirm in this market? Explain. Determine the firm's profit-maximizing level of output. Compute its profit. Identify whether it is operating in short run or long run.

b. Prove that the point of minimum average cost is Qmin = 10. If not, explain why and find min. ATC. What is efficient scale here?

c. Suppose now this firm is monopolistically competitive firm. Compute its profit in the short run and long run.

d. Which firm does produce more in the short run?long run? Why?