An individual owns a car that is worth $20,000, and is considering buying insurance. However, the only insurance which is available has a maximum coverage of $15,000, i.e. the policy will pay only $15,000 if the car suffers a total loss in an accident. The price of the policy is $1,800. There is a 10% chance of having an accident in which the car is a total loss. The focus here is to calculate the expected values with and without insurance. It is not necessary to calculate the variance and standard deviation, as it is obvious that there is less risk with insurance.

(a) Will a risk-averse individual buy the insurance? Show your work and explain.

(b) Will a risk-neutral individual buy the insurance? Show your work and explain.

(c) Will a risk-loving individual buy the insurance? Show your work and explain.

(d) How would your answer to (a)-(c) change if the policy paid $20,000 if the car was a total loss? Explain.