Gary likes to gamble. Donna offers to bet him $70 on the outcome of a boat race. If Gary's boat wins, Donna would give him $70. If Gary's boat does not win, Gary would give her $70. Gary's utility function is U(c₁, c₂, p₁, p₂) = p₁c²₁+ p₂c²₁, where p₁ and p₂ are the probabilities of events 1 and 2 and where c₁ and c₂ are his consumption 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 .3.

Question

Quizplus · Accepted Answer

To evaluate the expected utility, Gary needs to calculate the expected value of his utility function. Let x be the amount of money he wins from the bet, which can take two values: $70 (if his boat wins) and -$70 (if his boat loses). Then:

EU = 0.3*U($80 + $70) + 0.7*U($80 - $70)

Since his utility function is increasing in income, he would prefer to win the bet and have $150 (if his boat wins) than to lose the bet and have only $10 (if his boat loses). Therefore, U($80 + $70) > U($80 - $70), which implies that EU > U($80). In other words, taking the bet would increase his expected utility.

Gary Likes to Gamble