MI PS09 solutions - Solutions for Problem Set#09 1(a If he...

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Solutions for Problem Set #09 1. (a) If he owns the lottery, the individual will have a total wealth of with probability , and of a total wealth of with probability . His expected utility from it is If he sold can sold the lottery at a price , the minimum price he can accept for selling is determined in following formula (1) (b) If he does not own the lottery, the maximum price he is willing to pay to buy one, , is determined in following equation (2) (2) (c) If the individual is risk neutral, then the utility function would be linear. In this case, the buying and selling price would be same. But when he is risk averse with concave utility function or risk loving with convex utility function, then buying and selling price would be different. (d) Probability is also needed to calculate the selling and buying prices. Suppose , and substitute it with other parameters into equation (1) and (2), From them, we can solve out the selling and buying prices as 2. Utility function is (a) ; (b) The certainty equivalent for this gamble, , is determined in following equation We can solve . Since the expected value of the gamble is , so the risk premium for this gamble is (c) Similarly, the certainty equivalent for this new gamble is determined by And we can solve out , so the risk premium for this gamble is 3. (a) As we calculated in problem 2, for this utility function, (b) Without the insurance, Mr. T’s expected utility is With the insurance, his expected utility would be
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, so Mr. T should buy that insurance plan.
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