Suppose insurance companies cannot tell these types of people apart, but know that proportion = .90 of the population is healthy, while 1 = .10 is sick.

(a) Is a pooling equilibrium possible?

Suppose there is a third type of person, who is very sick, and will incur the loss with certainty p = 1.

a) Calculate the most this person would pay for full insurance.

(b) Calculate the actuarial fair price for this type of person.

Suppose there is proportion of very sick people, were is small. There are therefore (1) = .9(1) healthy people, (1)(1) = .1(1 ) sick people, and very sick people.

(a) What will happen in this market as rises from 0?

(b) How large does have to be for the market to start to unravel?

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