2 Pass/Fail? [100 pts] There is a student applying for a job. His type is either A, C, or F (the grade he got in class). If a firm hires a worker of type A, the firm's payoff is 2; if a firm hires a worker of type C, the firm's payoff is 1; and if a firm hires a worker of type F , the firm's payoff is 0. Each type is equally likely (1/3 probability of each). The firm will hire a worker if and only if its expected payoff from hiring the worker is (weakly) greater than k 0. A worker can either disclose her type (grade) or choose "pass-fail" which yields P if her type is A or C and F if her type is F . A worker gets a payoff of 1 if she is hired and 0 if she is not. [25pts] Is there a value of k between 0 and 1 such that there is an equilibrium in which every type elects to be graded "pass-fail?" Explain. [25pts] What is the lowest value of k 0 such that there is an equilibrium in which every type elects to be