Finance questions

Each driver has cash in the amount of $600 and owns a car worth $2,000 (thus initial wealth W 0 = $2, 600 for all drivers). However, drivers have different probabilities of crashing their cars; some are high risk (pH= 30%), some are medium risk (pM= 20%), and others are low risk (pL= 10%). There are only two states of the world, crash and no crash. In the crash state, drivers suffer a total loss; i.e., cars become worthless whenever crashes occur. Insurance is available, although it is not compulsory. Thus, drivers insure themselves only if the expected utility of being insured exceeds the expected utility of going without insurance. While insurers know that there are equal numbers of high, medium, and low risk drivers, there is asymmetric information; specifically, insurers cannot identify which drivers are high, medium, and low risk