Jack has two options next year, Job A and Job B. The earnings in the two jobs differ and are random. In Job A, earnings will be $25 with probability 1/2, $36 with probability 1/6, or $81 with probability 1/3. In Job B, earnings will be $36 with probability 2/3 or $64 with probability 1/3. If Jack has preferences over earnings given by u(e) = √e, where e denotes actual earnings, which job should he take and why? b. Calculate the Certainty Equivalents and risk premiums for Jack for both Job A and Job B.
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- Suppose the Economics Department has a graduation party for its students but as a final test they must show they have learned something about trade. Students in group A are given food (F) when they walk in, and students in group B are given a drink (D). Refer to Scenario 1. Suppose that all members of both groups have identical preferences where food and drink provide utility U = FαDβ. The exchange would be such that (a) both would be guaranteed to be better off than when they entered.(b) both would be guaranteed to be at least as well off as when they entered. (c) students in group A would end up with more utility. (d) students in group B would end up with more utility.Suppose that after the 2020 presidential election there are three races that are too close to call: Wisconsin,Michigan, and Pennsylvania. In order to become president, a candidate must receive 270 electoral votes ormore. Wisconsin has 10 electoral votes, Michigan has 16, and Pennsylvania has 20. Suppose that in theother decided races, Democrats have 259 electoral votes and Republicans have 233. The Democrat has an80% chance of winning Wisconsin, a 50% chance of winning Michigan, and a 10% chance of winningPennsylvania. A statistician defines a random variableXto be +1 if the Democrat wins,−1 if theRepublican wins, and 0 if neither candidate reaches 270 electoral votes. Find the probability densityfunction ofX. (Hint: Make this easier by figuring out the scenario in which the Republican wins or there isa tie!)If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using MAXIMAX CRITERION? D1 D2 D3 D4 What decision alternative will he choose if using MAXIMIN CRITERION? D1 D2 D3 D4 What about MINIMAX REGRET CRITERION? D1 D2 D3 D4 What decision would he make if using criterion of realism at alpha 0.6 is used? D1 D2 D3 D4
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