Consider a lottery L consisting of getting 0 with probability 1/3 and getting 9 with probability...

 

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Consider a lottery L consisting of getting 0 with probability 1/3 and getting 9 with probability 2/3. Hence, L = (0, 1/3; 9, 2/3). It is clear from this that the expected payout from this lottery is EL 1/3 x 0 + 2/3 x 9 = 6. Consider four individuals a, b, c and d characterised by their utility function for money given by Ua(x) = x U(x) = log(x+1) === 100 Uc(x) = 100- x+1 1 Ua(x) = 1- x+1 Here "log" stands for the 10-base logarithm. + For each of these four individuals you are asked to compute the following quantifiers regarding the lottery L: (a) The expected utility of the lottery L. (b) The certainty equivalent of the lottery L. (c) The risk premium attached to the lottery L. Show your computations for each of these quantifiers and for each of the four individuals. Consider a lottery L consisting of getting 0 with probability 1/3 and getting 9 with probability 2/3. Hence, L = (0, 1/3; 9, 2/3). It is clear from this that the expected payout from this lottery is EL 1/3 x 0 + 2/3 x 9 = 6. Consider four individuals a, b, c and d characterised by their utility function for money given by Ua(x) = x U(x) = log(x+1) === 100 Uc(x) = 100- x+1 1 Ua(x) = 1- x+1 Here "log" stands for the 10-base logarithm. + For each of these four individuals you are asked to compute the following quantifiers regarding the lottery L: (a) The expected utility of the lottery L. (b) The certainty equivalent of the lottery L. (c) The risk premium attached to the lottery L. Show your computations for each of these quantifiers and for each of the four individuals.