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note11 - Microeconomic Theory Econ 101A Fall 2008 GSI Eva...

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Microeconomic Theory Econ 101A Fall 2008 GSI: Eva Vivalt Section Notes 12: Adverse Selection and Moral Hazard 1 Adverse Selection Let’s take the previous example: The consumer begins with income of y 0 . The consumer has probability p > 0 of getting into an accident which will cause the consumer to incur a loss of income of L . With probability 1-p there won’t be an accident. An insurance contract is available which has a payout of - πC if no accident occurs and a payout of C - πC if an accident happens. – except now there are two types of individuals with different probabilities of having an accident. We assume that the individuals have the exact same expected utility function which implies that they have the same degree of risk aversion. The low type has an accident with probability p L and the high type has an accident with probability p H , where p L < p H . 1.1 Efficient Solution: Perfect Monitoring First, we consider the case in which insurance firms can tell which type of consumer they are facing. This assumption is sometimes referred to as “perfect monitoring”. In this case, the insurance agency will set a premium for the low type, π L = p L , and a different premium for the high type π H = p H . Note that this implies that for the low type: u 0 ( y 0 - π L C ) u 0 ( y 0 - L + C - π L C ) = p L 1 - p L π L 1 - π L = 1 Which means that x 1 = x 2 for the low type, i.e. they insure fully. Similarly, for the high type:
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