Answer to Question #100938 in Accounting for Noureddin Allazkah

Question

Suppose that there are only two fishermen, Zach and Jacob, who fish along a certain coast. They would each benefit if lighthouses were built along the coast where they fish. The mar-ginal cost of building each additional lighthouse is $100. The marginal benefit to Zach of each additional lighthouse is 90 – Q, and the marginal benefit to Jacob is 40-Q, where Q equals the number of lighthouses.
a) Explain why we might not expect to find the efficient number of lighthouses along the coast.
b) What is the efficient number of lighthouses? What would be the net benefits to Zach and Jacob if the efficient number were provided?

Answer 1

a) It is not possible to find the efficient number of lighthouses along the coast, because neither Zach nor Jacob would be willing to pay for a lighthouse at along. The marginal cost of building each additional unit of lighthouse is 100, which is greater than the amount of expected marginal benefits received by each one.

b) Total benefit = Sum of marginal benefits=90-Q+40-Q=130-2Q.

The level of an activity where marginal benefit equals to marginal cost, the quantity of lighthouses would be efficient number.

130-2Q=100.

Q=15.

The efficient number of lighthouses is 15.