Problem: Consider a state in which automobile drivers are divided equally into two types of drivers: careful and reckless. The average annual auto-insurance claim is $400 for a careful driver and $1,200 for a reckless driver. Suppose that the state adopts an insurance system under which all drivers are placed in a common pool and allocated to insurance companies randomly. An insurance company cannot refuse coverage to any consumer it is assigned, but a consumer who is unhappy with the insurance company has the option of being reassigned (randomly) to another. By law, each insurance company must charge the same price to all its customers (i.e. no price discrimination). Assume that the insurance market is perfectly competitive and that claims represent all the costs associated with provision of insurance. Predict the minimum price of auto insurance under two alternative policy scenarios given below. Show all of your work and explain your answers.
A. Auto insurance is mandatory
B. Auto insurance is voluntary