Suppose Ordinarily Half Your Class Would Get an a and Half

Essay

Suppose ordinarily half your class would get an A and half would get a B, with A students having a 25% chance of getting an A and B students having a 25% of getting an A.It costs $100 to persuade the instructor to raise a B grade to an A.A student is willing to pay $40 to insure she will get her usual grade and $70 to insure she will get a higher grade than usual.
a.Who would buy insurance and at what price in a competitive equilibrium?
b.Suppose it costs $5 to truthfully signal your type and $10 to falsely signal what type of student you are, and if an insurance company receives no signal, it will interpret this as a signal that you are a B student.What would be the competitive outcome now?
c.Suppose a new teacher comes in -- and this teacher is willing to change a grade for just $60.How does your answer to (a) change?
d.How would your answer to (b) change?
e.Can you change something in the problem that would result in only A-students buying insurance?