Suppose half your class would get an A and half would get a B. Students know whether they typically get an A or B, but this is not a certain outcome. A-type students have a 25% chance of getting a B, and B-type students have a 25% of getting an A. It costs $100 to persuade the instructor to raise a B to and A. A-type students are willing to pay $40 to insure they will get and A, B-type students are willing to pay $70 to insure they will get and A.

a) who would buy insurance and at what price in a competitive equilibrium?

b) the insurance company has no idea whether a student is an A-type or B-type student so it looks for signals, if the insurance company recieves no signal it will interpret this as a signal that the student is B-type. Suppose it costs $5 to truthfully signal your type and $10 to falsely signal.What would be the competitive outcome now?

c) Can you change something in the problem that would result in one A-students buying insurance?

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