You produce children's toys and are shopping for product liability insurance. You have conducted very thorough engineering and lab tests of your toys and have calculated hazard rates from toy breakage, incidents from how children interact with them, etc. You have determined that there is a 0.02% chance of a "major" incident occurring with one of your toys in the next year, defined as an incident resulting in $1m in damages.

1. Based on these facts, what is the premium you expect to pay for actuarily fair insurance?
2. After shopping around, you are offered a few premiums that are higher than you expect. Insurers define "major" events the same way but disagree on the probability of one of your toys causing a major event in the next year. (They claim this probability is higher.)

• Why might prospective insurers assume a higher probability of a major event?
• What can you do to try to resolve the difference in understanding of this probability? List and describe two.

3. If instead prospective insurers cite the same definition of a "major" event and the probability of it occurring in the next year, why might they be asking for premiums higher than the actuarily fair rate (aside from market power)? What is a solution to this issue?