Question

You own a house worth $400,000 that is located 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, which 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 (i.e., to build the seawall)?

Answer 1

full insurance:

8,000 (without a seawall)

2,000 (with a seawall)

partial insurance for 75%:

6,000 (without a seawall)

1,500(with a seawall)

I will build the seawall if the cost for mainting it are less than the premium difference:

$8,000 - $2,000 = $6,000 per year

If the seawall cost less than this amount is better to build it.

Step-by-step explanation:

the insurance premium is based on the probability of flooding:

without seawall: 1 every 50 years: 1/50 = 0.02 = 2%

with seawall: 1 every 200 years: 1/200 = 0.005 = 0.5%

full insurance:

400,000 x 2% = 8,000 (without a seawall)

400,000 x 0.5% = 2,000 (with a seawall)

partial insurance for 75%:

400,000 x 75% = 300,000

300,000 x 2% = 6,000 (without a seawall)

300,000 x 0.5% = 1,500(with a seawall)

I will build the seawall if the cost for mainting it are less than the premium difference:

$8,000 - $2,000 = $6,000 per year

If the seawall cost less than this amount is better to build it.