6. A law firm hires a now associate and (initially) puts her in charge of filing paperwork. It is common knowledge that the associate is talented with probability 0.6 and not talented with probability 0.4, and the associate observes her type directly, Filing paperwork for t hours per day costs the associate t if she is talented and 2t if she is not. The firm observes t and then makes the decision to either make her partner or fire her ('up or out"). The payoff for the associate of being fired is zero minus the cost of paperwork, and the payoff of being made partner is 10 minus the cost of paperwork. The payoff for the firm does not depend on the paperwork; it is 0 for firing her in any event, 5 for making a talented lawyer a partner, and -20 for making her partner if she is not talented. Let /4, represent the firm's updated belief that the associate is talented given she puts in t hours of work per day. a. Describe the unique outcome (t, partner or fire) of all pooling PBE for this game along with the belief on the equilibrium path. Then describe more generally what the beliefs have to be off the equilibrium path. b. In any separating PBE, if the associate isn't talented, how many hours of paperwork t does she do per day? What are the range of possible values for t for the talented associate that can be supported in a separating PBE? d. Find the unique PBE that survives the intuitive criterion (equilibrium dominance). Is it separating or pooling? 7. A seller sells a good to a prospective buyer. The buyer values the good at 69, where # is