A firm is looking to hire an employee. Candidates for this job can be of two types: they can be the lazy type or the ambitious type. Candidates may choose to get a college degree or decide not to get a college degree. It is mentally costly for the candidate to obtain a college degree (there is clearly a monetary cost of going to college, but we are ignoring that part in this question.) A candidates type is private information. But the firm knows whether the candidate has a college degree or not. The cost of attending college depends on the candidate's type. Lazy types find doing homeworks, attending lectures, taking exams more costly than ambitious types so getting a college degree is more costly to them. Specifically, candidates' costs of getting a college degree are 

The candidate's payoff is the benefit of the job minus the cost of going to college. The candidate receives a benefit of 130 regardless of his type if the firm offers him the job or 70 if it does not. For example, if a lazy candidate decide to not have a degree and he is offered a job he receives a payoff of 130 - 50 = 80 and if a ambitious person has a college degree and he does not get the job he receives a payoff of 70 - 80 = -10. Before the firm meets a candidate, it believes the probability he is lazy is .75 and the probability he is ambitious is .25. The firm will receive a payoff of 100 if it hires an ambitious person, 25 if it hires a lazy person, and 60 if it hires no one. 120 30 80 

a) Does this game have a pooling equilibrium? Why or why not? Defend your answer care- fully and show every step of your calculations. 

b) Does this game have a separating equilibrium? Why or why not? Defend your answer carefully and show every step of your calculations.

Does not have a college degree Has a college degree Lazy 50 120 Ambitious 30 80