题目如下,谢谢帮忙拉

This exercise is a direct application of what we have seen in class about differential
information to insurance theory.
Individuals have an income of 2 units, but can lose 1 unit in a bad state. They
take out variable insurance 0 < x < 1 for an ex ante premium of xp which returns x
in the bad state. They maximize expected (probability-weighted) utility. Their ex
post utility is described by the natural logarithm of ex-post consumption C: ln(C).
The probability of loss is pl = 1/3 for low-risk and ph = 0.5 for high risk
individuals. Suppose that insurance companies are competitive and can distinguish
these types (they know exactly the type of the consumer). As a consequence, they
offer the fair premia 1/3 to low risk individuals and 0.5 to high risk individuals.
(1) How much insurance do these types buy at these rates?
(2) How do their insured utility levels compare with their uninsured expectations?
(3) Assume now that insurers cannot distinguish the two risk types. First
explain the consequences for the insurer in term of pricing, and why fair
pricing is no longer possible.
(4) An insurer offers to every agent a contract with a premium 0.5 allowing the
high risk types to fully insure. What do the low risk types do when faced
with this premium rate?

[此贴子已经被作者于2009-5-12 22:46:00编辑过]