# home4m - x ≥-5000 and u x = 2 x 5000 if x<-5000(a Find...

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Homework 4 1. Calculate the expected utility of a person who faces a potential loss of L = \$10000 with probability π and has a utility index u ( x ) over money: (a) π = 0 . 01 and u ( x ) = x - x 2 10000 ; (b) π = 0 . 01 and u ( x ) = x if x ≥ - 1000 and u ( x ) = 2 x + 1000 if x < - 1000 (c) π = 0 . 1 and u ( x ) = - 2 - x/ 10000 ; (d) π = 0 . 1 and u ( x ) = log 2 ( x + 20000) 2. Which of the above utility indexes exhibit risk aversion? 3. What is the proﬁt maximizing insurance contract that a monopolist insurance company will oﬀer to each of these customers if it knows both π and the utility index u ? 4. Consider a driver who gets into an accident with probability 0 . 01 if he drives cautiously, and with probability 0 . 05 if he drives recklessly. He gets an extra utility of g = 100 from driving recklessly. The monetary loss in the case of an accident is L = \$10000. The utility index is u ( x ) = x if
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Unformatted text preview: x ≥ -5000 and u ( x ) = 2 x + 5000 if x <-5000. (a) Find the insurance contract that the monopolist risk-neutral company will oﬀer this driver if there is no moral hazard (for example the company can enforce the customers to drive carefully). (b) What happens if the company oﬀers the same contract when moral hazard is possible? What is the minimal price that the company can charge for a contract with a zero deductible under moral hazard? (c) What is the proﬁt maximizing contract for the monopolist risk-neutral company under moral hazard? (d) What is the loss in the average proﬁt for the company that results from moral hazard? 5. Can you repeat these steps if the utility index is u ( x ) = log( x + 20000)?...
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