Gwen, who obeys the axioms of expected utility theory, is faced with four possible outcomes: A,...

Transcribed Image Text:

Gwen, who obeys the axioms of expected utility theory, is faced with four possible outcomes: A, B, C and D. Her ranking of these outcomes is A> B>C> D. Gwen is indifferent between the certainty of B and a lottery where there is a 25% probability of A and a 75% probability of D. She is also indifferent between the certainty of C and a lottery where there is a 20% probability of B and a 80% probability of D. (a) Construct a von Neumann-Morgenstern utility function that reflects these preferences and is such that the largest utility is 80 and the smallest utility is 20. (b) How does Gwen rank the lotteries L = ACD 23/1/20 (c) For what value of p is Gwen indifferent between L = (d) Normalize the utility function of part (a). and M = B ACD C с 2) and N=(B₂₁1C₂) ² P 1-p 13 1 ? Gwen, who obeys the axioms of expected utility theory, is faced with four possible outcomes: A, B, C and D. Her ranking of these outcomes is A> B>C> D. Gwen is indifferent between the certainty of B and a lottery where there is a 25% probability of A and a 75% probability of D. She is also indifferent between the certainty of C and a lottery where there is a 20% probability of B and a 80% probability of D. (a) Construct a von Neumann-Morgenstern utility function that reflects these preferences and is such that the largest utility is 80 and the smallest utility is 20. (b) How does Gwen rank the lotteries L = ACD 23/1/20 (c) For what value of p is Gwen indifferent between L = (d) Normalize the utility function of part (a). and M = B ACD C с 2) and N=(B₂₁1C₂) ² P 1-p 13 1 ?

Answer rating: 100% (QA)

To construct the von NeumannMorgenstern utility function lets denote the utility of each outcome as follows UA uA UB uB UC uC UD uD We know Gwens preferences A B C D which translates to uA uB uC uD a ... View the full answer