Suppose there are two kinds of people in society who are equally represented —those with 20% chance of developing diabetes next year, and those with 2% chance of developing diabetes next year. Individuals know their own risks but the insurers cannot discern this information (so they can’t charge different prices to different people). Purchasing health insurance is voluntary in this society. Diabetes costs $12,000 to treat. If you are an insurer who will offer a full coverage policy (i.e. you will pay $12,000 on behalf of your customer if diabetes happens), what should you set as your premium, and why?
Please explain the difficulty you face as an insurer in figuring out the optimal premiums to charge in this situation.