An individual has preferences consistent with standard expected utility theory. They have utility function U(x)over wealth x. Starting with initial wealth of $10,000,the person is then faced with two choice problems. The first involves a choice between (A)no gamble and (B)a gamble with an equal chance of winning $1,800 and losing $1,000. The second choice problem,the person first has $1,000 taken away (resulting in the adjustment of the reference point). The choice is then between (C)being given back $1,000 for sure and (D)an equal chance of winning $2,800 or nothing. What can be said about the choices the person would make?

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Quizplus · Accepted Answer

BThe choices a person makes under standard expected utility theory depend on their utility function and the expected utility of each option. Without specific details about the utility function, we can't predict the exact choices. However, we can analyze the consistency of choices based on expected utility principles. Choice A (no gamble) and Choice D (an equal chance of winning $2,800 or nothing) involve different levels of risk and expected outcomes, especially after adjusting the reference point by taking away $1,000. If a person is risk-averse, they might prefer the certainty of Choice A initially but could be inclined towards the gamble in Choice D after losing $1,000, seeking to recover more significantly. This inconsistency can arise due to the change in the reference point and the perceived value of the gamble relative to the new reference point. Choice B (never choosing both A and C) is correct because if a person chooses A (no gamble) initially, it indicates a preference for certainty or a lower risk tolerance. After losing $1,000, choosing C (being given back $1,000 for sure) aligns with this preference for certainty, making it consistent with expected utility theory. Choosing A initially and then C does not inherently involve a contradiction in preferences based on the information given.

An Individual Has Preferences Consistent with Standard Expected Utility Theory