(50pts) Suppose that there are three roommates who have to decide whether or not to acquire a TV that costs $300. Person A and B are willing to pay $80 each to have the TV present, while person C is willing to pay $150. The willingness-to-pay is one's private information. a. (10pts) Determine whether acquiring a TV is efficient or not. Explain. b. (10pts) Discuss if every person has an incentive to contribute $100. Explain. c. (30pts) Provide a Groves-Clarke mechanism to achieve an efficient outcome. Especially, explain who the pivotal person(s) is and calculate the tax for the pivotal person(s). Explain why person A and C have no incentive to misreport their willingness-to-pay