Consider again the example of grade insurance. Suppose students know whether they are typically A, B,C, D or F students, with A students having a 75% chance of getting an A and a 25%chance of getting a B; with B, C and D students having a 25% chance of getting a grade above their usual, a 50% chance of getting their usual grade and a 25% chance of getting a grade below their usual; and with F students having a 25%chance of getting a D and a 75% chance of getting an F. Assume the same bell-shaped grade distribution as in the text—i.e. in the absence of grade insurance, 10% of grades are A’s, 25% are B’s, 30% are C’s, 25% are D’s and 10% are F’s.
A. Suppose, as in the text, that grade insurance companies operate in a competitive market and incur a cost c for every level of grade that is changed for those holding an insurance policy. And suppose that A through D students are willing to pay 1.5c to ensure they get their usual grade and 0.5c for each grade level above the usual; F students are willing to pay 2c to get a D and 0.5c for each grade level above that.
(a) Suppose first that your instructor allows me only to sell A insurance in your classroom. Will I be able to sell any?
(b) Suppose next that your professor only allowed me to sell B insurance. Would I be able to sell any?
(c) What if I were only allowed to sell C or only D insurance?
(d) If they were the only policies offered, could policies A and D attract customers in a competitive equilibrium at the same time? In equilibrium, who would buy which policy? (Hint: Only C, D and F students buy insurance in equilibrium.)
(e) If they were the only policies offered, could policies A and C attract customers in a competitive equilibrium at the same time? (Hint: The answer is no.)
(f) If they were the only policies offered, could policies B and D attract customers in a competitive equilibrium at the same time? (Hint: The answer is again no.)
(g) Without doing any further analysis, do you think it is possible to have an equilibrium in
Which more than 2 insurance policies could attract customers?
(h) Are any of the equilibria you identified efficient? (Hint: Consider the marginal cost and marginal benefit of each level of insurance above insuring that each student gets his/her typical grade.)
B. In A(c), you identified a particular equilibrium in which A and D insurance are sold— when it was not possible to sell just A insurance.
(a) How is this conceptually similar to the self-selecting separating equilibrium we introduced in Section B of the text?
(b) How is it different?