(3) [6 points] Every day 200 sellers consider selling their goods using a trading platform and there are also 200 buyers who come to the platform and want to buy the seller's goods. Each seller has one unit of the good, but different sellers have different qualities of the good. Fifty of them have a unit of the good that is excellent, 50 have a unit that is very-good, 50 have a unit that is fair and 50 have a unit that is poor. Sellers know the quality of their unit of the good; buyers do not know the quality of any particular seller's unit of the good. But buyers do know the numbers of each type of potential seller. The table below provides values for buyers and sellers for each quality of good. 2 Assume that buyers each want at most one unit of the good and are risk neutral - if they don't know which quality of good they are buying they are willing to pay up to its expected value. Assume that any buyers and sellers who do not transact on any day, as well as all who do transact, leave and are replaced the next day by identical buyers and sellers. (a) Find all of the self-fulling expectations equilibria in this market. Show your work. (b) You are the manager of the platform and your objective is to run it to maximize the total amount of money that is paid each day by buyers to sellers (the price times the number of transactions). If multiple prices are possible, and multiple equilibria are possible, you may assume that the price and equilibrium that has the highest amount of payments is what occurs. You know the numbers of each type of seller and the values for buyers and sellers, and unlike buyers you do know each seller's quality. You can't convince buyers of the quality of any seller. However, if you decide to exclude some group of sellers, say all with poor quality or fair quality items, you can convince buyers that you have succeeded in doing this. Do you want to exclude any type of sellers? If so, which one(s) and what is the total amount of money paid per day both before and after your restriction? Show your work