4. There are ten houses on Pierson Road. Each is worth $400,000. Each homeowner acts as if she were maximizing the expected value of the natural logarithm of her terminal wealth. A new sewer for Pierson Road has been proposed.

If approved, it will be built for free by a cult of sewer builders. If it is built, nine homes will increase in value by $10,000 and the tenth will lose

$80,000 in value because of accidental floods. No one knows which is the tenth and each home is equally likely to be the unlucky one. For the sewer to be built, unanimous approval is required.

a. Is constructing the sewer a potential Pareto improvement?

b. Suppose each homeowner owns her home free and clear and has no other assets.Will the sewer be approved?

c. Suppose each has a $300,000 mortgage.Will it be approved?

d.What institutional arrangements or markets would improve the collective decision making?