Suppose that school teachers in New Haven, CT who ride bicycles for recreation or exercise face...

Suppose that school teachers in New Haven, CT who ride bicycles for recreation or exercise face a greater risk of having their bike stolen than professional bicycle messengers. Specifically, there is an 80% chance that a teacher will lose a $2,000

bicycle during a given year but only a 20% chance that a messenger will lose a bicycle. Assume that an equal number teacher and messengers own bicycles in New Haven.

a.If an insurance company cannot tell a teacher from a messenger, it must
therefore charge the same premium to everyone. What will the actuarially fair insurance premium be if both teachers and messengers buy insurance policies?

b.Let us say that teachers and messengers both have the logarithmic utility functions u(C) = log C, and they both earn $20,000 a year, and they care about their total wealth (earnings and the $2,000 value of the bicycle). Will the teachers and messengers purchase bicycle insurance at the premium found in part a.? Explain.

c.Given the answer to part b., does the insurance company make any profits or incur any losses? If the insurance company does not break even, what should the premium be for a fair policy? Would the new premium cause teachers and messengers to change their decision about purchasing insurance?

d.Suppose now that the insurance company can observe the “type” of the customer. Would the answers to parts a. and b. change?

Expert Solution

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Rahul Sunny answered 2 years ago

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