1 Fire Insurance All houses in the city of Macondo are made of wood. A typical Macondo resident values their house at 50, 000. During a severe dry season, it is estimated that there is a probability of 70% that a house would catch fire. When a house burns down, its value falls to 10, 000, since extensive reparations will be needed. Citizens of Macondo, all of which are homeowners, can incur a cost of 2, 000 and paint their houses in fire resistant paint. By doing this, the likelihood of a house burning down falls to 40%. Assume that citizens of Macondo do not have another source of wealth; and their utility is given by u(w) = √ w.

1. What is the expected utility of a resident who does not use the fire resistant paint?

2. What is the expected utility of a resident who uses the fire resistant paint?

3. Given the previous answers, will the residents paint their house?

4. Now consider the possibility of insurance. The insurance plan works as follows: the owner pays a premium equal to 28, 000. In the case the house gets burned, the insurance company pays the house owner 40, 000, that is, the insurance pays the total value of the loss. Which combination of actions (buying insurance or not, and painting the house or not) is the one preferred by the homeowners?

5. The insurance company is thinking about changing the premium to avoid the moral hazard problem. Is there a value of the premium they could charge that would induce homeowners to simultaneously purchase insurance and protect their use from fire with painting?

6. List two ways in which the insurance company could offer a different type of insurance contract that could induce homeowners to be careful, even if they have insurance. Briefly explain the reason why they work (no math is needed).