Problem Set 2
Public Finance – 3319
John just purchased a new car today and paid $40K for it. He needs to go to
Ottawa tonight but there is a weather warning that roads are full of black ice and
dangerous to drive. The dealer can only issue a mandatory liability insurance
that covers only damages to other cars and persons but not the John’s car. He
knows that there is a 90% chance that he will not have an accident. But if it
happens he will lose his car. Suppose that it’s late and all insurance brokers are
closed, all flights are full, and he missed the last bus. Canceling the trip will cost
him $4,000. He is just thinking the best possible action. Since you are his best
friend taking Public Finance at SMU, he calls you to get your opinion.
a) Using your own utility function and calculating expected utilities, how
would you advise him? Justify your answer with numbers.
b) Would you change your answer if the probability of no-accident were
c) What amount of cost would change your answer in (a)? Explain your
answer by calculating CEW.
There are two groups of people: street racers (SR) and low riders (LR). SRs have
10% chance that they will have an accident in the next 12 months. The same is
true with 1% chance for LR. If an accident happens, both lose the car they own
(in insurance jargon it’s called “total”). They have an identical utility
function (𝑈 = √𝐶) and a car, which is worth $40K.
a) Calculate the maximum premium that each group would be willing to pay
for an insurance coverage.
b) Calculate the premium (Pact = $ amount of loss if accident happens X
probability that an accident happens) that insurance company would
c) Calculate the consumer surplus (the increase in their well-being
measured by U) for both groups if they buy the insurance coverage at the
price that the insurance company charges.
d) Explain how insurance company would know who is who, in other words
how it distinguishes SRs from LRs.
e) Is there any incentive for SR to lie about their true risk profile? If they
(SRs) say (lie) they are LRs, how much increase they experience in their
well-being measured by U?
f) This is called asymmetric information: the information that is known by
one side is not fully known by the other side. Show the insurance
company’s profit if the company ignores the asymmetric information and
believes that the information risk holders reveal about their risk profiles
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