[Market Signaling]

The admissions committee at Hogwarts School of Witchcraft and Wizardry is evaluating sorcerer candidates. the school's tradition dictates that accepted pupils get a stipend that reflects the committee's assessment of how many magic tricks they can perform. there are two types of pupils in equal numbers. good pupils can perform 10 magic tricks, while bad pupils can perform only 2 magic tricks. good pupils are also superior to their bad counterparts in one other aspect: they are better at flying a broom. all pupils dislike flying a broom, but it is less unpleasant the more skilled you are. denote the stipend by s and the hours spent flying a broom by b. the utility of the two types of pupils looks as follows:

Utility function of Good Pupil: U_G = s - 0.5b

Utility function of Bad Pupil: U_B = s - 2b.

1. suppose the admissions committee can tell if a candidate is a Good pupil or a Bad pupil. how much broom flying does each candidate do? what is the stipend of each candidate?
2. suppose the committee is unable to tell if a candidate is a Good pupil or a Bad pupil, and there are no brooms available. what stipends will each candidate be paid?
3. suppose the committee is unable to tell if a candidate is a Good Pupil or a Bad Pupil and there are broom available. how much broom flying will each candidate do? what stipends will they be paid?
4. In the absence of brooms, does the information asymmetry make the Good pupils better or worse off? How about the Bad pupils?
5. With brooms avialable, does this information asymmetry make the good pupils better or worse off? how about the bad pupils?