Asked by Florence Nichole Rogan on Jun 17, 2024
Verified
Sally Kink is an expected utility maximizer with utility function pu(c1) (1 p) u(c2) , where for any x 1,000, u(x) 2x, and for x greater than or equal to 1,000, u(x) 2,000 x.
A) Sally will be risk averse if her income is less than $1,000 but risk loving if her income is more than $1,000.
B) Sally will never take a bet if there is a chance that it leaves her with wealth less than $2,000.
C) Sally will be risk neutral if her income is less than $1,000 and risk averse if her income is more than $1,000.
D) For bets that involve no chance of her wealth exceeding $1,000, Sally will take any bet that has a positive expected net payoff.
E) None of the above.
Expected Utility Function
A mathematical representation of an individual's preference for certain outcomes over others, considering the uncertainty of those outcomes.
Utility Function
A mathematical representation of a consumer’s preference ordering over a choice set, used to describe how consumers allocate their income to maximize their satisfaction.
Risk Neutral
An attitude or preference indicating indifference between choices with uncertain outcomes, focusing instead on the expected values.
- Examine the impact of wealth fluctuations on a person's risk-taking attitudes.
- Deduce the anticipated utility from given scenarios and select the choice that maximizes utility benefits.
Verified Answer
YB
Yarianna BadilloJun 22, 2024
Final Answer :
D
Explanation :
Sally's utility function changes at an income of $1,000, with a linear utility (u(x) = 2x) for income less than $1,000, indicating risk neutrality (since utility is directly proportional to wealth). For bets not exceeding $1,000, she would accept any with a positive expected net payoff, aligning with risk-neutral behavior. Choices A, B, and C misinterpret her utility function's implications on her risk preferences.
Learning Objectives
- Examine the impact of wealth fluctuations on a person's risk-taking attitudes.
- Deduce the anticipated utility from given scenarios and select the choice that maximizes utility benefits.