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Chapter 16

EC260 Chapter Notes - Chapter 16: Adverse Selection, Life Insurance, Relative Risk


Department
Economics
Course Code
EC260
Professor
Olivia Ozlem Mesta
Chapter
16

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Chapter 16: Adverse Selection
The Market for Lemons
-The term lemon is used to refer to a used car that turns out to have a lot of problems -
used cars with no hidden defects are called gems
-A famous paper by Ackerlof points out that a disproportionate number of lemons turn
up in the used car market - this arises because of the information asymmetry
between buyers and sellers of used cars
-Sellers have more information about the quality of the car they are selling than the
buyer does
-Buyers will not want to pay more than the average price in the market
-Owners of gems are less willing to sell at the average price because they know that
gems are worth more than the average price
-Owners of lemons are eager to sell at the average price because they know that
lemons are worth less than average price
-As a result, most of the used cars on the market become lemons
-This dynamic will continue to drive down the average quality and price in the market
for used cars
-Eventually, the average price will be equal to the value of a lemon because no one
will sell a gem
-This is a case of adverse selection
Adverse Selection in Automobile Insurance
-Insurers are able to categorize drivers according to type of vehicle, location, age, and
gender and using statistics about accident rates this allows them to determine the
expected loss from each customer and charge premium based on this information
-Good drivers pay lower premiums
-Not all drivers within a category should be charged the same premium - this is where
information comes into play:
Perfect Information
-Within the category of insured drivers who are 22 year old male drivers of sedans in
Philadelphia, some are high risk drivers and some are low risk drivers
-We suppose that each driver in this category has a wealth level of 125 that could fall
to 25 as a result of an accident (i.e., loss of 100)
-The high risk drivers have a probability of loss of 0.75, while the low risk drivers have
a probability of loss of 0.25
-The expected loss of the high risk drivers equals 0.75 x 100 = 75
-The expected loss of the low risk drivers equals 0.25 x 100 = 25
-With perfect information, the insurer would be able to distinguish between these two
groups of drivers
-In this case, the high risk group would be charged a premium equal to 75, and the
low risk group would be charged a premium of 25
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-Now if we assume that these drivers are risk averse, we can define their utility of
wealth:
Utility = (Wealth)0.5
-If the low risk group buys insurance, they pay a premium of 25, which makes their
utility of wealth equal to:
Utility with Insurance = (125 - 25)0.5 = 10
-If the low risk drivers decide not to buy insurance, then they have a 0.25 probability of
incurring a loss of 100 (and a 0.75 probability of incurring no loss)
Utility with No Insurance = 0.25(125 - 100)0.5 + 0.75(125)0.5 = 9.635
-So for the low risk drivers, expected utility with insurance is higher and they will
choose to buy the insurance
-We can similarly calculate the expected utility of wealth for the high risk drivers
Asymmetric Information
-What happens to the above analysis when the insurer does not possess perfect
information about the relative risk levels of the drivers in the category?
-Now they are not in a position to charge competitive premiums to low and high risk
drivers
-The insurer will break even by charging an average premium to this group equal to
0.5(25 + 75) = 50
-High risk drivers:
Utility with Insurance = (125 - 50)0.5 = 8.660
Utility with No Insurance = 0.75(125 - 100)0.5 + 0.25(125)0.5 = 6.545
-Clearly the high risk drivers will still buy insurance
-The low risk drivers, however are better off not buying insurance when average
premiums are charged
-This means that the only people who will want to buy insurance are the high risk
drivers and we are back to our market for lemons scenario
-This will lead the insurer to increase the premium to 75 and only high risk drivers will
buy insurance - the low risk drivers are driven out of the market because of adverse
selection
How Can Managers Restore This Market?
-Two ways that managers can help restore the market for insurance are:
1. Increasing information about individual drivers
-Relies on the insurance market being highly competitive
-Insurers will compete with rival firms to get better information
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