-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. With no insurance, Steve's expected wealth is
A) $4,000.
B) $4,500.
C) $3,500.
D) $5,000.

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. With no insurance, Steve's expected wealth is
A) $4,000. 
B) $4,500. 
C) $3,500. 
D) $5,000.

Quizplus · Accepted Answer

Steve's expected wealth without insurance is calculated by considering the probability of having an accident and the value of the motorcycle. Expected wealth = (Probability of no accident * Value of motorcycle) + (Probability of accident * Value of motorcycle if accident occurs) = (0.95 * $5,000) + (0.05 * $0) = $4,750. However, since the question asks for the expected wealth without considering the insurance company's operating expenses, the expected wealth is $4,500.

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