22.1 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; that is, 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 insure 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?