3. Bill rndes the subway at a cost of 75 cents per trip, but would switch if the
ID: 2620279 • Letter: 3
Question
3. Bill rndes the subway at a cost of 75 cents per trip, but would switch if the price were any five minutes longer, but costs only 50 cents. higher. His only alternative is a bus that takes 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 th costs. The fare increase and reduced travel time both take effect in one year an The interest rate is 25 percent (15 points) a. As far costs? d last forever. as Bill is concerned, what are the present values of the project' s benefits and 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.) Part IIL Short Disenceinn Oatinn naExplanation / Answer
a. Bill is willing to pay 25 cents extra to save 5 minutes and his value for each minute of commute time is 5 cents. Now after the proposed renovation and reduction in time - Bill will save 10 minutes valued at 50 cents and his cost will increase by 40 cents. At 10 trips a year, his total benefit from the project will be $ 5 and total cost increase will be $4 . Since these changes are forever, we will calculate the PV using the perpetuity formula:
PV of benefits = 5/25% = $20
PV of costs = 4/25% = $16
Net benefit = $ 4
b. For the city as a whole, with 55000 people who will have same cost & benefits as above, the net present value of the project benefits less cost will be = 55000 * 4 = $ 220000
c. The middle class will be taxed at $1.25 per person or total of (55000 * 1.25) = 68750 which is value lost or reduction for the middle class folks. The poor people value the legal help from this tax at $62500 ony per year, which means that for the city as a whole there is value loss of (68750-62500) = $6250. Hence the cost in this case is more than the benefit
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