Question

Adverse Selection: Suppose Snake Farm insurance provides fire insurance coverage to 10,000 homeowners in California. Based on historical data, Snake Farm’s expert statisticians (a.k.a actuaries) have calculated that in a given year on average 100 of Snake Farms customers will lose their homes due to a fire. The historical data also shows that the average cost of replacing a house is $100,000.

1. Assuming that Snake Farm’s must charge the same insurance premium to all its customers, how much will Snake Farm charge its customers per year if it wants to break even? (show your work)

1. What if 50% of Snake Farm’s customers own “fire safe” homes, which reduce (but do not eliminate) the chance that their home will be destroyed by fire. The historical statistics reveal that of the 100 homes that burn down per year, only 10 of them are “fire safe” homes. These “fire safe” homeowners are not willing to pay more than a $500 insurance

Answer 1

We are given that fire insurance coverage is provided to 10,000 homeowners in California. Based on historical data, we know that in a given year, on an average, 100 of Snake Farm's customers lose their homes to fire. Average cost of replacing a house is $100,000. So the total cost that Snake Farm will incur woulld be 100*100,000 = $10,000,000. For Snake Farm to break even, it must charge $10,000,000/10,000 = $1,000 premium from each of the 10,000 households under insurance coverage each year.

If 50% of them own fire safe homes, they will only pay $500 insurance premium per year. This means the premium from these 5000 households will be 5000*$500 = $2,500,000. The total cost would now be 90*$10,000 = $9,000,000 (Only 10 out of those burned were fire safe, leaving the 90 vulnerable). The Snake Farm then must recover the remaining $6,500,000 from the remaining 5000 households which do not have fire safe homes. Thus, the premium to be charged from them would be $6,500,000/5000 = $1,300 per year.