P8 - ECO 310 Fall 2008 Problem Set 8 Uncertainty Due in...

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ECO 310, Fall 2008 Problem Set 8: Uncertainty Due in class on December 9 Question 1 Satoru is an expected utility maximizer with von Neumann-Morgenstern index U ( W ). He is offered 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 indifferent 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 suffer 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 suffer the disaster and nothing if you do not.
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