Job Analysis
MS 405 Assignment #3
1- In an experiment subjects are given between the two gambles: Gamble 1: A: $2500 with probability 0.33 $2400 with probability 0.66 $0 with probability 0.01 Gamble 2: C: $2500 with probability 0.33 $0 with probability 0.67
B:
$2400 with certainty
D:
$2400 with probability 0.34 $0 with probability 0.67
Suppose that a person is an expected utility maximizer. Set the utility scale so that u($0) = 0 and u($2500)=1. Denote u($2400) by x. a) Which one would you prefer, A or B? C or D? (Without any calculations!) b) For what values of x would a person choose option A? For what values would a person choose option B? c) For what values of x would a person choose option C? For what values would a person choose option D? d) Comment on your preferences stated in part a. Are there any paradoxes? 2- Professional tennis has become a big business with big prizes. There frequently is a large disparity between the prize for the winner and that for the runner-up; For example, the former may receive $100,000; the latter $32,000. In 1983, Michael Mewshaw asserted that finalists often make secret deals before match to divide the pot; that is they agreed that both winner and loser would get ($100,000+32,000)/2= $66,000. This practice, known as splitting, was particularly likely to occur, he said, “in special events and exhibitions, and on the [World Championship Tennis] circuit, all of which tended to have huge prize-money differences.” If a player has the following utility function and believes that he has a 50-50 chance of winning, will he be willing to split?
3- An alternative has a probability 0.6 of winning $25,000, 0.2 of winning $1,000, and 0.2 of losing $50,000. a) Determine the expected profit for this alternative. b) Determine the certainty equivalent for the alternative using the utility function , where x is in thousands of dollars. c) What is the risk tolerance of the decision maker who has the utility function presented in part b.
1- In an experiment subjects are given between the two gambles: Gamble 1: A: $2500 with probability 0.33 $2400 with probability 0.66 $0 with probability 0.01 Gamble 2: C: $2500 with probability 0.33 $0 with probability 0.67
B:
$2400 with certainty
D:
$2400 with probability 0.34 $0 with probability 0.67
Suppose that a person is an expected utility maximizer. Set the utility scale so that u($0) = 0 and u($2500)=1. Denote u($2400) by x. a) Which one would you prefer, A or B? C or D? (Without any calculations!) b) For what values of x would a person choose option A? For what values would a person choose option B? c) For what values of x would a person choose option C? For what values would a person choose option D? d) Comment on your preferences stated in part a. Are there any paradoxes? 2- Professional tennis has become a big business with big prizes. There frequently is a large disparity between the prize for the winner and that for the runner-up; For example, the former may receive $100,000; the latter $32,000. In 1983, Michael Mewshaw asserted that finalists often make secret deals before match to divide the pot; that is they agreed that both winner and loser would get ($100,000+32,000)/2= $66,000. This practice, known as splitting, was particularly likely to occur, he said, “in special events and exhibitions, and on the [World Championship Tennis] circuit, all of which tended to have huge prize-money differences.” If a player has the following utility function and believes that he has a 50-50 chance of winning, will he be willing to split?
3- An alternative has a probability 0.6 of winning $25,000, 0.2 of winning $1,000, and 0.2 of losing $50,000. a) Determine the expected profit for this alternative. b) Determine the certainty equivalent for the alternative using the utility function , where x is in thousands of dollars. c) What is the risk tolerance of the decision maker who has the utility function presented in part b.