Evening exam solutions

# This is because peter is risk averse and as we have

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Unformatted text preview: , constant, or decreasing? Justify. 1 − u' ' (W ) 1 Au (W ) = − = − 4W W = , which is decreasing. 1 u' (W ) 2W 2W d. (8 minutes) Suppose an insurance company offers a policy that reimburses Peter for the total loss if the earthquake happens. The policy costs \$C. What is the highest price \$C that he would be willing to pay for this policy? (Include the calculations in the answer). 2 98 1, 000, 000 − C = 490, 000 + 1, 000, 000 100 100 2 × 700 98 × 1, 000 ∴ 1, 000, 000 − C = + 100 100 2 2 ∴1, 000, 000 − C = (994 ) ∴ C = 1, 000, 000 − (994 ) = 11, 964 . ( € € € ) ( ) € €  ­ 3  ­ e. (4 minutes) Is the highest price that Peter would be willing to pay for this policy smaller, equal to, or greater than the actuarially fair price? Justify. The actuarially fair price is 2%×(750,000 240,000)=10,200. This is lower than the highest price Peter would pay. This is because Peter is risk averse and, as we have seen, risk averse individuals are willing to pay an amount lower than the actuarially fair price to buy full insurance when there is only the option of either full coverage on no coverage at all. f. (4 minutes) Now suppose the insurance company allows Peter to buy as many insurance policies as he wants but charges a positive load in each policy. Should he fully insure? Justify. No. By Mossin’s theorem he should not fully insure when each policy has a positive load.  ­ 4  ­ Part III: Qualitative Questions Question 9. (12 minutes) In 1948, Milton Friedman and Leonard Savage suggested that individuals are risk averse for wealth values below a certain level and risk seeking for wealth values above this level. a. (6 minutes) Draw the Bernoulli utility function of the individuals described above in a graph with...
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