Question

Your house is worth $400,000 and you have $300,000 in a savings account. There is a 1 percent chance of a fire in your house. If the fire occurs, there will be $300,000 in damages to your house.

a. Suppose you do not have fire insurance. If the fire occurs, you will have to pay $300,000 to repair your house. What is the expected value of your wealth (including both the value of your home and your savings account) at the end of the year?

b. We will say that an insurance policy is fair insurance if the premium for the policy equals the expected value of the claims the insurance company will have to pay. An insurance company offers you a fire insurance policy. If a fire occurs, it will pay to repair your home. The premium for the policy is $3,000. Has the insurance company offered you fair insurance?

c. If you are risk averse, would you buy this insurance policy? Defend your answer.

Answer 1

a. If there is no fire, total value =Value of Home + Amount in Savings Account = $400,000 + $300,000 = $700,000

If there is a fire, there will be damages and $300,000 needs to be paid out. It is assumed that once repairs are done, all damaged will be taken care of. So Value of house remains same but there is no money left in savings account.

So total value in case of a fire = $400,000

Expected Value at end of year = 0.99*$700,000 + 0.01 * 400,000 = $697,000

b. Loss in case of fire = $300,000

Probability of Fire = 1%

So expected loss = 1% * 300,000 + 99% *0 = $3,000

So if the insurance is offered for $3000, it is a fair price to pay.

c. If I am risk averse, then I will buy the insurance since the insurance is fairly priced. As I am risk averse, I will be looking to minimize my loss. Buying the insurance means that in case there is a fire, I do not lose anything. If there is no fire, I lose only $3000 which is negligible compared to the damages in case of fire.

So as a risk averse person, I will always buy the insurance.

As a consumer, I will seek to equalize the marginal utility of wealth across various scenarios. To maintain the same level of wealth in different scenarios, I will look forward to costlessly transfer the value across scenarios which can be done with the help of a fair priced insurance.