# ps8 - ECO 310 Fall 2007 Problem Set 8 Uncertainty Due in...

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ECO 310, Fall 2007 Problem Set 8: Uncertainty Due in class on December 17 Question 1 Satoru is an expected utility maximizer with von Neumann-Morgenstern index U ( W ). He is ofered the Following gamble: gain \$ h with probability 1 / 2+ π , and lose \$ h with probability 1 / 2 - π , where h and π are small positive numbers. He is indiferent between taking the gamble or not when his initial wealth is \$ W 0 . Give an approximation oF π/h in terms oF absolute risk aversion at W 0 . (Hint: Use the Taylor expansion to the second order.) Question 2 You have initial wealth W 0 dollars. With probability π , you will sufer a disaster that will wipe out this wealth completely; otherwise it will stay the same. You can insure against this loss. Denote by p the premium per dollar oF insurance. This means that iF you buy x dollars oF insurance coverage, you have to pay px dollars right now, and will get x dollars From the insurance company iF you sufer the disaster and nothing iF you do not.

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ps8 - ECO 310 Fall 2007 Problem Set 8 Uncertainty Due in...

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