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ISyE 4803b Homework 9
1.
In class we discussed the notion of adverse selection for purchasing trucking
services.
The following example (taken from
Managerial Economics
by Allen et
al) illustrates the idea for insurance.
Suppose there are two categories of drivers:
high and low risk.
Each policyholder has an initial wealth of $125, but a loss can
reduce the wealth to $25; that is, drivers can lose $100 of their wealth should the
loss occur.
For highrisk drivers the probability of loss is 0.75 and for low risk
drivers the probability is 0.25.
In addition, assume that a driver’s utility is equal
to the square root of their wealth (this would be the case if a driver were risk
averse).
Answer the following:
a.
Determine the competitive premiums for the insurer (i.e., the premium
based on expected losses) for each group.
b.
Find the utilities with and without insurance for each group.
c.
Now suppose that the insurer can’t distinguish between high and low
risk drivers.
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 Spring '08
 Staff

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