thats the question

Quantitative Question: A firm has average costs given by: AC = 400/Q + 50. (a) (6 points) Based on just the information about AC, is this firm a natural monopoly? Briefly describe why or why not. (b) (8 points) Suppose that inverse demand is given by P = 90 - Q. What linear price will maximize welfare while allowing the firm at least zero economic profit? How much will be sold by the natural monopoly? (c) (4 points) Suppose that the natural monopoly sells to two different groups of consumers. If the regulator wants to use Ramsey pricing, what would need to be true about the two groups of consumers? (d) (4 points) If the regulator used Ramsey pricing, explain whether welfare, producer surplus and consumer surplus for the two groups would rise, fall or stay the same as in part (b)? (e) (6 points) Suppose the firm can make an investment to lower its fixed costs. The investment costs $25 but lowers fixed costs by $50. Explain whether: (1) the regulator would want the firm to make the investment, and (2) whether the firm would be likely to make the investment under cost-plus and fixed-price regulation