A firm hires two kinds of workers, alphas and betas. The population at large has equal number of alphas and betas. One cannot tell a beta from an alpha by looking at her, but an alpha will produce $3,000 worth of output per month and a beta will produce $2,500 worth of output in a month. The firm decides to distinguish alphas from betas by hiring a university professor to give them an examination. A worker will be paid $3,000 if she gets at least 60 answers right and $2,500 otherwise. For each question that they get right on the exam, alphas have to spend 1/2 hour studying and betas have to spend 1 hour. For either type, an hour's studying is as bad as giving up $20 of income per month.

[a] Does this scheme lead to a pooling or a separating equilibrium? (i.e. will the firm be able to distinguish types?)

[b] What will be the equilibrium number of correct exam answers for each type?