Evening exam solutions

There is nothing wrong with taking one but not two

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Unformatted text preview: tion 4. (5 minutes) People with positively correlated losses do not benefit from pooling risk. False. As long as they are not perfectly positively correlated, they still benefit from pooling risk. Question 5. (5 minutes) Samuelson's result discussed in class shows that anyone who prefers to take a bet once must necessarily like to take the same bet twice. False. Samuelson’s result indicates that if you are not willing to bet once, you must not be willing to bet twice. There is nothing wrong with taking one but not two bets.  ­ 1  ­ Question 6. (5 minutes) A risk averse person with a constant coefficient of relative risk aversion necessarily has an increasing coefficient of absolute risk aversion. False. The person must have a decreasing coefficient of absolute risk aversion. There are two different ways to justify the answer. a) If someone has a constant coefficient of relative risk aversion, then Wu ''(W ) Ru (W ) = ! = C where C is a positive constant. u '(W ) Therefore, the coefficient of absolute risk aversion is u ''(W ) C Au (W ) = ! = , which is a decreasing function of W. u '(W ) W Question 7. (5 minutes) Suppose gambles A and B have the same mean. If A has a higher variance than B, then B second order stochastically dominates A. False. The fact that A and B have the same mean and that A has a higher variance is not a sufficient condition to claim that A is a mean preserving spread of B. Second order stochastic dominance requires everyone with a concave utility function to prefer one lottery to the other. As we’ve seen in class, some lotteries with the same mean and a higher variance are preferred by some concave utility functions. Therefore, just looking comparing the variances of A and B is not...
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