Just roughly give it a try but please do not copy some says wikipedia

An insurance company offers auto insurance policy of $1,000,000 to car owner-drivers. In case of car accident, the insurance company will simply compensate the insured with the insurance amount of $1 million. The insurance company believes that there are only two kinds of drivers, high-risk and low-risk. The distribution of the driver population is as follows: Low Risk Driver Population Population Proportion Probability of Accident 70% 5% High Risk 30% 8% (a) Suppose the car owners know exactly which risk class they belong to. But the insurance company does NOT know this information. Car owners would NOT want to pay insurance premium higher than for their own risk class. Insurance company does NOT want to charge a premium lower than that reflected by the true risk class. What is the equilibrium for this insurance market? (5 points) (b) Now suppose the insurance company is offering the $1 million auto insurance policy with different deductibles for the car owners to choose. The deductibles are expressed as a percentage of the insurance amount. If there is no insurance claim at the end of the insurance period, the only cost to the car owner is the pure premium. In order to protect its profit margin, the insurance company wants to limit its expected loss to $0. Will this work? If yes, determine a possible set of deductibles (au, ) such that they will induce the car owners to truly reveal their own risk class. (al is the deductible for low-risk drivers and dy for high-risk drivers.) (20 points) (c) Based on your analysis is (b), what are the effects of asymmetric information on the insurance cost to the low- and high-risk drivers? (5 points) An insurance company offers auto insurance policy of $1,000,000 to car owner-drivers. In case of car accident, the insurance company will simply compensate the insured with the insurance amount of $1 million. The insurance company believes that there are only two kinds of drivers, high-risk and low-risk. The distribution of the driver population is as follows: Low Risk Driver Population Population Proportion Probability of Accident 70% 5% High Risk 30% 8% (a) Suppose the car owners know exactly which risk class they belong to. But the insurance company does NOT know this information. Car owners would NOT want to pay insurance premium higher than for their own risk class. Insurance company does NOT want to charge a premium lower than that reflected by the true risk class. What is the equilibrium for this insurance market? (5 points) (b) Now suppose the insurance company is offering the $1 million auto insurance policy with different deductibles for the car owners to choose. The deductibles are expressed as a percentage of the insurance amount. If there is no insurance claim at the end of the insurance period, the only cost to the car owner is the pure premium. In order to protect its profit margin, the insurance company wants to limit its expected loss to $0. Will this work? If yes, determine a possible set of deductibles (au, ) such that they will induce the car owners to truly reveal their own risk class. (al is the deductible for low-risk drivers and dy for high-risk drivers.) (20 points) (c) Based on your analysis is (b), what are the effects of asymmetric information on the insurance cost to the low- and high-risk drivers? (5 points)