You own a house worth $500,000 on a river. If the river floods moderately, the house will be completely destroyed. This happens about once every 80 years. If you build a seawall, the river would have to flood heavily to destroy your house, and this only happens about once every 250 years. What would be the annual premium for an insurance policy that offers full insurance? For a policy that only pays 80% of the home value? What are your expected costs with and without a seawall?

****USE THIS EXAMPLE TO FIND YOUR ANSWER TO THE ABOVE QUESTION****

You own a house worth $400,000 on a river. If the river floods moderately, the house will be completely destroyed. This happens about once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, and this only happens about once every 200 years. What would be the annual premium for an insurance policy that offers full insurance? For a policy that only pays 75% of the home value? What are your expected costs with and without a seawall? Do the different policies provide an incentive to be safer (build the seawall)?

Do the different policies provide an incentive to be safer (build the seawall)?

Solution: With full insurance:

Without a seawall, the expected loss is

400,000 0.02 = 8,000

With a seawall, the expected loss is

400,000 0.005 = 2,000

The insurance company will charge the expected loss as a premium. Your expected cost under either scenario each year is the premium.

With partial insurance:

Without a seawall, the expected loss is

300,000 0.02 = 6,000

With a seawall, the expected loss is

300,000 0.005 = 1,500

The insurance company will charge the expected loss as a premium. Your expected cost each year is:

Without a seawall:

[0.02 (300,000 - 400,000) + 0.98 (0)] - 6,000 = -8,000

With a seawall:

[0.005 (300,000 - 400,000) + 0.98 (0)] - 1,500 = -2,000

Unfortunately, neither insurance policy is better or worse. Although the premiums under the partial insurance policy are lower, the expected cost each year is the same as with full insurance. In either scenario, you will build the seawall if the annual cost of building and maintaining a seawall is less than $6,000/year.