2. Suppose there are two players: a Worker (W) and a Firm (F'). W has private information about their own level of ability. F' knows that with probability p, W is high ability type (H), and with probability (1 p), W is low ability type (L). After W observes their own type (a draw by nature), they decide whether to get a degree (play E) or not (play N). F observes W's education, but not their type. F' then decides whether to employ W in a managerial job (M), or a clerical job (C). The payoffs are as follows: if F' employs a worker of type H in a managerial job, it obtains a payoff equal to 10; if F' employs a worker of type L in a managerial job, it obtains payoff equal to 0; if F' employs a worker in a clerical job, it obtains a payoff equal to 4 regardless of the type of W. A worker of either type obtains a payoff of 10 in a managerial job, and 4 in a clerical job. The cost of education differs, however. For an H-type worker the cost of doing a degree is , whereas for an L-type worker it is 3c. We present the game in extensive form in the following figure: 10, 10 10c; 10 H F o Wi _ F ; q) 4.4 C i(p) (). C 4c 4 ; | High| | ' 10,0 | Low 1 = | 10 3,0 (1 p) (1 - q); _ N . B 44 C 43c,4 (a) Assume p = L. For which values of c is there a separating equilibrium in which the high-ability worker selects E and the low-ability worker selects N7 (6 marks) (b) Now suppose p = 110 and = 2. Under these assumptions, can an outcome in which both types of worker selects N be supported in a perfect Baysian equilibrium? (6 marks) (Continued overleaf) :C2020 (c) Now suppose p = % and = 3. Is it possible for both types to select E in a pooling equilibrium? (6 marks)