Both Adam and John are applying to insure their car against theft. Adam lives in a secure neighborhood, where the probability of theft is 10%. John lives in a lesser secure neighborhood where the probability of theft is 25%. Both Adam and John own cars worth $10,000, and are willing to pay $100 over an expected loss for insurance.

How much would Adam be willing to pay for the insurance?

How much would John be willing to pay for the insurance?

• 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?
• 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?

If the company can correctly anticipate the adverse selection, what premiums should it charge?

• If the insurance company can correctly anticipate the adverse selection, who would be insured?