Both Nadia and Samantha are applying to insure their car against theft. Nadia lives in a secure neighborhood, where the probability of theft is 10%. Samantha lives in a lesser secure neighborhood where the probability of theft is 25%. Both Nadia and Samantha own cars worth $10,000, and are willing to pay $100 over expected loss for insurance.
1. How much would Nadia be willing to pay for the insurance?
2. How much would Samantha be willing to pay for the insurance?
3. Suppose the insurance company cannot tell them apart but expects them to be different values and charges them an average premium of $1850. Who is more likely to buy this insurance?
4. Suppose the insurance company cannot tell them apart but expects them to be different values and charges them an average premium of $1850. How much profit would it make?
5. If the insurance company can correctly anticipate the adverse selection, what premiums should it charge??
6. If the insurance company can correctly anticipate the adverse selection, who would be insured?