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 < 8,000, u(x)= 2x, and for x greater than or equal to 8,000, u(x)= 16,000 + x. A)Sally will never take a bet if there is a chance that it leaves her with wealth less than $16,000. B)Sally will be risk neutral if her income is less than $8,000 and risk averse if her income is more than $8,000. C)Sally will be risk averse if her income is less than $8,000 but risk loving if her income is more than $8,000. D)For bets that involve no chance of her wealth exceeding $8,000, Sally will take any bet that has a positive expected net payoff. E)None of the above.

Quizplus · Accepted Answer

Sally's utility function changes at $8,000, from a linear form (2x for x < 8,000) indicating risk neutrality, to a form with diminishing marginal utility for x ≥ 8,000, indicating risk aversion. For wealth levels below $8,000, since her utility function is linear (2x), she values each additional dollar equally, which is characteristic of risk neutrality. Therefore, she will accept any bet with a positive expected net payoff if it does not risk her wealth exceeding $8,000, as her utility in this range does not diminish with increasing wealth.

Sally Kink Is an Expected Utility Maximizer with Utility Function