Suppose a society contains two individuals. Joe, who smokes, and Tanya, who does not. They each have the same utility function U(C)=ln(C). If they are healthy, they will each get to consume their income of $15,000. If they need medical attention, they will have to spend $10,000, leaving them $5,000 for conumption. Smokers have a 12% chance of needing medical attention, and nonsmokers have a 2%chance.
An insurance company is willing to insure Joe and Tanya. The twist here is that the insurance company offers two different kinds of policies. One policy is called the "low deductible," (L) for which theinsurance company will pay any medical costs over $3,000. The other is a "high deductible," (H) for which the insurance company will pay any medical costs over $8000.
How do I take into account these deductibles when calculating the actuarially fair premium for example? How is the setup?