Gary likes to gamble. Donna offers to bet him $54 on the outcome of a boat race. If Gary's boat wins, Donna would give him $54. If Gary's boat does not win, Gary would give her $54. Gary's utility function is p₁x² +p2x², where p₁ and på are the probabilities of events 1 and 2 and where x₁ and X2 are his wealth if events 1 and 2 occur respectively. Gary's total wealth is currently only $80 and he believes that the probability that he will win the race is 0.4. Which of the following is correct? (please submit the number corresponding to the correct answer).

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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Gary likes to gamble. Donna offers to bet him $54 on the outcome of a boat race. If Gary's boat
wins, Donna would give him $54. If Gary's boat does not win, Gary would give her $54. Gary's utility
function is p1 x + p2x3, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and
X2 are his wealth if events 1 and 2 occur respectively. Gary's total wealth is currently only $80 and he
believes that the probability that he will win the race is 0.4.
Which of the following is correct? (please submit the number corresponding to the correct answer).
1. Taking the bet would reduce his expected utility.
2. Taking the bet would leave his expected utility unchanged.
3. Taking the bet would increase his expected utility.
4. There is not enough information to determine whether taking the bet would increase or decrease
his expected utility.
5. The information given in the problem is self-contradictory.
Transcribed Image Text:Gary likes to gamble. Donna offers to bet him $54 on the outcome of a boat race. If Gary's boat wins, Donna would give him $54. If Gary's boat does not win, Gary would give her $54. Gary's utility function is p1 x + p2x3, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and X2 are his wealth if events 1 and 2 occur respectively. Gary's total wealth is currently only $80 and he believes that the probability that he will win the race is 0.4. Which of the following is correct? (please submit the number corresponding to the correct answer). 1. Taking the bet would reduce his expected utility. 2. Taking the bet would leave his expected utility unchanged. 3. Taking the bet would increase his expected utility. 4. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. 5. The information given in the problem is self-contradictory.
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