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.

Question

Shaira Pearl Mesina · Accepted Answer

Final Answer : C, Explanation :  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.

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