1. Aaron has an initial wealth of $10,000. There is probability 0.02 that an accident will...
1. Aaron has an initial wealth of $10,000. There is probability 0.02 that an accident will occur, which will cause him a loss of $3,600. Aaron's utility function is ?(?) = √?. Calculate his risk premium, and compare it to the expected value of the loss.
Homework Answers
Initial wealth is 10000.
Wealth after loss is 10000 - 3600 = 6400.
Expected loss = 0.02*3600 = 72.
Utility at current status of wealth = U = 10000^0.5 = 100.
Expected wealth = 0.98*10000 + 0.02*6400 = 9928.
Expected utility under loss = 0.98*(10000^0.5) + 0.02*(6400^0.5) = 99.60.
This implies that certainty equivalence would be 99.60 = (I)^0.5 or I = 9920.16.
Risk premium = Expected wealth – CE = 9928 – 9920.16 = 7.84.
Hence, expected loss is 72 while risk premium is 7.84.
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