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 < $2,000, u(x)= 2x, and for x greater than or equal to $2,000, u(x)= 2,000 + x. A)For bets that involve no chance of her wealth exceeding $2,000, Sally will take any bet that has a positive expected net payoff. B)Sally will be risk averse if her income is less than $2,000 but risk loving if her income is more than $2,000. C)Sally will be risk neutral if her income is less than $2,000 and risk averse if her income is more than $2,000. D)Sally will never take a bet if there is a chance that it leaves her with wealth less than $4,000. E)None of the above are true.

Quizplus · Accepted Answer

According to Sally's utility function, her utility is a function of her expected net payoff. Therefore, she will take any bet that has a positive expected net payoff, regardless of her wealth level. Choice B is incorrect because Sally is actually risk averse for any level of income, as her utility function exhibits diminishing marginal utility. Choice C is incorrect for the same reason. Choice D is incorrect because Sally's utility function only depends on her wealth level, not on how she arrived at that wealth level (i.e. whether through a bet or not).

Sally Kink Is an Expected Utility Maximizer with Utility Function