# Question: Bill rides the subway at a cost of 75 cents

Bill rides the subway at a cost of 75 cents per trip, but would switch if the price were any higher. His only alternative is a bus that takes five minutes longer, but costs only 50 cents. He makes 10 trips per year. The city is considering renovations of the subway system that would reduce the trip by 10 minutes, but fares would rise by 40 cents per trip to cover the costs. The fare increase and reduced travel time both take effect in one year and last forever. The interest rate is 25 percent.
a. As far as Bill is concerned, what are the present values of the project’s benefits and costs?
b. The city’s population consists of 55,000 middle- class people, all of whom are identical to Bill, and 5,000 poor people. Poor people are either unemployed or have jobs close to their homes, so they do not use any form of public transportation. What are the total benefits and costs of the project for the city as a whole? What is the net present value of the project?
c. Some members of the city council propose an alternative project that consists of an immediate tax of \$ 1.25 per middle- class person to provide “free” legal services for the poor in both of the following two years. The legal services are valued by the poor at a total of \$ 62,500 per year. (Assume this amount is received at the end of each of the two years.) What is the present value of the project?
d. If the city must choose between the subway project and the legal services project, which should it select?
e. What is the “distributional weight” of each dollar received by a poor person that would make the present values of the two projects just equal? That is, how much must each dollar of income to a poor person be weighted relative to that of a middle- class person? Interpret your answer..

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