LS 145 Disc_Week 9_Handout_Solved

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University of California, Berkeley *

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Feb 20, 2024

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LS 145 Discussion Section, Fall 2023, Week 9 Quiz 10 Review GSI: Cristina Violante 1 Cristina owns a Prius. There is a 2% chance that the catalytic converter on the Prius will get stolen within the next year, in which case the cost of replacement will be a total of $4000. 1. What is Cristina’s expected monetary loss? EMV = p 1 O 1 (+ p 2 O 2 + p 3 O 3 + p 4 O 4 … ) EMV = .02 * 4000 EMV = $80 2. Will an insurance company charge Cristina more or less than the EML as an insurance premium to cover this kind of loss? Insurance companies charge more than EML so that they can make a profit. 3. Why might Cristina spend $100 as an insurance premium to get this kind of coverage, even if the EML is less? Cristina might spend more on insurance because she is risk adverse . (See question 5, below.) 4. If Cristina pays $105 for the insurance, what is her risk premium? Risk premium = Insurance premium - EML Risk premium = $105 - $80 Risk premium = $25 5. If Cristina pays $105 for the insurance, it’s because: (a) Losing $105 causes her greater disutility than the expectation of having a 2% chance of losing $4000. (b) The expectation of having a 2% chance of losing $4000 causes her greater disutility than certainly losing $105. Þ (b) is the correct answer. This is the definition of risk aversion. Cristina would rather certainly have to pay $105, than possibly have to pay $4000, even if the chances of having to pay $4000 are very low.

LS 145 Discussion Section, Fall 2023, Week 9 Quiz 10 Review GSI: Cristina Violante 2 6. If Geico wants Cristina to pay $160 for the insurance and she refuses, what does that tell us about her risk premium? This tells us that Cristina’s risk premium is less than $80 ($160 - $80). At that point, she would rather run the risk of having to possibly pay $4000 in the event that her catalytic converter is stolen. 7. Why is the insurance company willing to sell Cristina this insurance? How is this profitable for them? The law of large numbers allows the insurance company to be able to make a profit by having a large number of insurance contracts with many customers. So, even if they end up having to cover the loss of Cristina’s catalytic converter, they will still, on the whole, make a profit, because there are many other customers who are also paying premiums to the insurance company and did not need any disbursements from the company to cover losses. 8. Identify either a moral hazard or an adverse selection problem to do with my possible behavior and the decision to seek insurance coverage for my catalytic converter. How might the insurance company mitigate the problem? There are many possible issues. One problem of moral hazard is that, after getting insurance that covers the loss of her catalytic converter, Cristina starts parking her car overnight on the street in an area in which this theft is common, instead of in a locked garage. The insurance company can mitigate this by, for example, the use of co-insurance or a deductible, which would require Cristina to pay for part of the loss. This disincentivizes her from parking on the street when a safer alternative is available. One problem of adverse selection is that the insurance company might not be able to know in advance whether the risk of her catalytic converter getting stolen is high or low, and so they would not know what her EML is and how high of a premium to charge her. They mitigate against this by asking Cristina her address before giving her insurance, and using the address to calculate the statistical likelihood of theft.

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