Suppose you decide to start a new company to insure homeowners against flooding. During heavy rains, many people's basements flood, and this can cause a lot of damage and cost a lot of money to repair.

For simplicity, assume that:

• The average new house costs $300,000.
• The probability that any house will flood in a given year is 1.7%.
• If flooded, the average homeowner will incur $12,000 of expenses that you would reimburse.
• In addition to the cost of reimbursing the customer, should their home flood, your company also incurs an administrative cost of $50 per customer insured (regardless of if they file a claim or not.)

You do market research and discover that all homeowners break down into one of three groups based on their feelings about the risk of flooding:

• 30% are risk neutral.
• 55% are risk averse. They are willing to pay a premium up to (and including) 25% more than their expected cost of flooding.
• 15% are extremely risk-averse. They are willing to pay a premium up to (and including) 45% more than their expected cost of flooding.

(A)[3 points] Assume that you can tell what type of customer anyone is before they buy your insurance. You can also charge each customer a different premium.

• What premium would you charge to the risk-neutral homeowners? Is it worth serving them?
• What premium would you charge to the risk-averse homeowners? Is it worth serving them?
• What premium would you charge to the extremely risk-averse homeowners? Is it worth serving them?

(B)[3 points] In reality you cannot tell what someone's risk aversion level is when they buy your insurance. Thus, you have to set a single premium. What premium should you set and who will buy your insurance?