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Suppose you are the owner of a health insurance company. In exchange for a premium, you pay the medical expenses for two types of customers: smokers and non-smokers. Over the course of a year, 50% of smokers incur medical bills of $600 and 20% of non-smokers incur medical bills of $120. Finally, suppose that the world consists of 50 smokers and 50 non-smokers.
a. If you can determine who is a smoker and who is a non-smoker (Symmetric Information), what is the minimum premium you should charge smokers and non-smokers?
b. Now assume you do not know which of the customers are smokers and which are non-smokers. If you can only charge a single premium, what premium do you charge to all of your policy holders?
c. What is your profit from charging the premium found in part b? What happens to the smokers and non-smokers in this market?
d. What premium must you charge in order to break-even?

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