-The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Living with this risk gives Bob the same expected utility as if there was no chance of theft and his wealth was
A) $0.
B) $20.
C) $30.
D) $50.

Question

-The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Living with this risk gives Bob the same expected utility as if there was no chance of theft and his wealth was
A) $0. 
B) $20. 
C) $30. 
D) $50.

Quizplus · Accepted Answer

Bob's expected utility with the risk of theft is a weighted average of his utility with $100 (if not stolen) and $0 (if stolen), each with a 50% probability. The option that gives Bob the same utility without the risk must provide him with a certain outcome that matches this expected utility. Without the specific utility function or further details, we typically infer that the correct answer must be less than $100 due to the risk of losing everything but more than $0, as it represents a compromise between the two extremes. $30 is a plausible choice that reflects a significant reduction from $100 due to risk but still offers some positive utility, aligning with common utility theory principles.

-The Above Figure Shows Bob's Utility Function