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# Expected Utility

(See attached file for full problem descriptions)

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1. Sam's utility function...
2. Use standard economic reasoning...
3. How does a class action differ...
4. Suppose a potential injurer...
5. Suppose that when injurers are sued...
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#### Solution Preview

Q1.
a) Yes. The utility function of a risk averse person is convex. The utility function x^0.5 is convex. Hence he is risk averse.
b) Expected wealth = current wealth + expected wealth of suing event
The suing event has following outcomes:
Outcome Probability Payoff
Win 0.6 -50
Loose 0.40 - 130 or -150 with probability 0.5

=1000 + 0.6*(-50)+0.4*(0.6*(-130)+0.5*(-150))
=914

Expected Utility = 0.6*(1000-50)^0.5+0.4*(0.5*(1000-150)^0.5+ 0.5*(1000-130)^0.5)
=30.22
c) The maximum he is willing to pay to avoid trial is the amount which will bring his utility from the wealth equal to that under trial.
Let x is the amount then we have:
(1000-x)^0.5=30.22
Solving we get x=86.55

Q2:
In insurance market insurance companies sell insurance products, which take care of the individual risks against payment of small premium. For example, suppose the risk of fire is 5% for an individual. In case fire does not occur the wealth of the individual remains same. But if the fire occurs, his entire wealth is gone. So although the risk may be small the consequence of risk is devastating. Insurance companies pool these risks and spread the amount of loss to the all policyholders. For example, say 100 people take the fire insurance each with 5% risk of fire. So it is expected that 5 people will face the fire in this year. If they do not insure that 5 people will loose all their wealth. As individuals are risk averse they do not want to take the risk. The insurance company charges a small premium from all the 100 individuals and payoff the insured sum in case there is fire. So by pooling the premium from ...

#### Solution Summary

Expected Utility is determined. The standard economic reasoning is discussed.

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