Afternoon Exam solutions

# Justify actuarially fair prices are equal to the

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Unformatted text preview: aul’s total wealth at 2% is: 1% ! 90, 000 + 1% ! 360, 000 = 225, 000 2% c. (4 minutes) What is Paul's coefficient of relative risk aversion? Justify. d. (8 minutes) Suppose an insurance company offers a policy that reimburses Paul for the total loss if the earthquake happens. The policy costs \$C. What is the highest price \$C that Paul would be willing to pay for this policy? (Include the calculations in the answer). Expected utility for Paul’s total wealth without insurance:  ­ 3  ­ Paul would be willing to pay \$C for the insurance coverage as long as his utility under full insurance is greater than the expected utility without insurance: Therefore: e. (4 minutes) Is the highest price that Paul would be willing to pay for this policy smaller, equal to, or greater than the actuarially fair price? Justify. Actuarially fair prices are equal to the expected indemnity payments received from the insurance company: Pfair = 0.01 ! (300, 000 &quot; 30, 000 ) = 2, 700 The highest price Paul’s willing to pay, 3,591, is higher than the actuarially fair premium Pfair. This is because Paul is risk averse (u’’&lt;0). Risk averse individuals are willing to pay a premium higher than the actuarially fair premium to buy full insurance when that’s the only insurance option available. f. (4 minutes) Now suppose the insurance company allows Paul to buy as many insurance policies as he wants but charges a positive load in each policy. Should Paul fully insure? Justify. No. Mossin’s Theorem shows that when the load of the policy is positive, risk averse individuals should no longer purchase full insurance.  ­ 4  ­ Part III: Qualitative Question Question 9. (17 minutes) In 1948, Milton Friedman and Leonard Savage suggested that individuals...
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## This note was uploaded on 02/03/2014 for the course INSR 205 taught by Professor Kent/smetters/nini during the Spring '09 term at UPenn.

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