-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.What is the most Bob would pay for insurance that would replace his $100 should it be stolen?
A) $30
B) $50
C) $70
D) $75

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.What is the most Bob would pay for insurance that would replace his $100 should it be stolen?
A) $30 
B) $50 
C) $70 
D) $75

Quizplus · Accepted Answer

Bob would pay up to the amount that leaves him indifferent between having insurance and facing the risk of theft. This means equating his expected utility without insurance to his utility with insurance, minus the insurance cost. The utility of keeping $100 (with no risk of theft) would be the reference for how much he values the insurance. Given the 50% chance of theft, without insurance, his expected utility is the average of the utility of having $100 and the utility of having $0. With insurance, he ensures he always has $100, minus the cost of insurance. The most he would pay is the amount that equates these two scenarios, which, based on his utility function provided in the question (not visible in the text), is $70.

-The Above Figure Shows Bob's Utility Function