Sally Kink is an expected utility maximizer with utility function pu(c₁)+ (1 - p)u(c₂), where for any x

Question

Sally Kink is an expected utility maximizer with utility function pu(c₁)+ (1 - p)u(c₂), where for any x < $3,000, u(x)= 2x, and for x greater than or equal to $3,000, u(x)= 3,0001 + x. A)Sally will be risk averse if her income is less than $3,000 but risk loving if her income is more than $3,000. B)Sally will be risk neutral if her income is less than $3,000 and risk averse if her income is more than $3,000. C)For bets that involve no chance of her wealth exceeding $3,000, Sally will take any bet that has a positive expected net payoff. D)Sally will never take a bet if there is a chance that it leaves her with wealth less than $6,000. E)None of the above are true.

Quizplus · Accepted Answer

Sally's utility function changes at the $3,000 mark, indicating different attitudes towards risk below and above this threshold. For amounts less than $3,000, her utility is linear (u(x) = 2x), which suggests risk neutrality—she values each additional dollar equally and will accept any bet with a positive expected value. The question does not provide enough information to accurately assess her behavior for wealth levels above $3,000, as the utility function provided seems to be incorrectly formatted or incomplete. However, the statement in option C is correct based on the utility function's behavior for wealth less than $3,000.

Sally Kink Is an Expected Utility Maximizer with Utility Function