You are the Dean of the Faculty at St. Anford University. You hire Assistant Professors for a probationary period of 7 years, after which they come up for tenure and are either promoted and gain a job for life or turned down, in which case they must find another job elsewhere. Your Assistant Professors come in two types, Good and Brilliant. Any types worse than Good have already been weeded out in the hiring process, but you cannot directly distinguish between Good and Brilliant types. Each individual Assistant Professor knows whether he or she is Brilliant or merely Good. You would like to tenure only the Brilliant types. The payoff from a tenured career at St. Anford is $2 million; think of this as the expected discounted present value of salaries, consulting fees, and book royalties, plus the monetary equivalent of the pride and joy that the faculty member and his or her family would get from being tenured at St. An ford. Anyone denied tenure at St. An ford will get a faculty position at Boondocks College, and the present value of that career is $0.5 million. Your faculty can do research and publish the findings. But each publication requires effort and time and causes strain on the family; all these are costly to the faculty member. The monetary equivalent of this cost is $30,000 per publication for a Brilliant Assistant Professor and $60,000 per publication for a Good one. You can set a minimum number, N, of publications that an Assistant Professor must produce in order to achieve tenure.
(a) Without doing any math, describe, as completely as you can, what would happen in a separating equilibrium to this game.
(b) There are two potential types of pooling outcomes to this game. Without doing any math, describe what they would look like, as completely as you can.
(c) Now please go ahead and do some math. What is the set of possible N that will accomplish your goal of screening the Brilliant professors out from the merely Good ones?