-Steve owns a motorcycle valued at $5,000 and that is his only asset. There is a 5 percent chance that Steve will have an accident within a year. If he does have an accident, his motorcycle is worthless. Steve's utility of wealth curve is shown in the figure above. An insurance company agrees to pay Steve the full value of his motorcycle in case of an accident if he buys the company's insurance policy. The company's operating expenses are $500 per policy. If Steve buys the insurance for $1,000, his expected wealth will be ________, and his expected utility will be ________ than with no insurance.
A) greater; greater
B) greater; less
C) less; greater
D) less; less

Question

-Steve owns a motorcycle valued at $5,000 and that is his only asset. There is a 5 percent chance that Steve will have an accident within a year. If he does have an accident, his motorcycle is worthless. Steve's utility of wealth curve is shown in the figure above. An insurance company agrees to pay Steve the full value of his motorcycle in case of an accident if he buys the company's insurance policy. The company's operating expenses are $500 per policy. If Steve buys the insurance for $1,000, his expected wealth will be ________, and his expected utility will be ________ than with no insurance.
A) greater; greater 
B) greater; less 
C) less; greater 
D) less; less

Quizplus · Accepted Answer

Steve's expected wealth with insurance is $4,000 ($5,000 - $1,000), which is less than his expected wealth without insurance ($4,750). However, his expected utility is greater with insurance because it eliminates the risk of losing the entire $5,000, which is more valuable to him given his risk-averse utility curve.

-Steve Owns a Motorcycle Valued at $5,000 and That Is