Question : The city of San Diego is deciding whether or not to convert a local park into a parking garage. The park only benefits residents of Bird Rock, and the parking garage would similarly only benefit Bird Rock residents. Bird Rock residents would happily pay $15 in order to park all day. The new garage would have 200 spots, and would cost $1,000,000 to build.
Assume the garage would take a year to build, but then would be open every day of the year in the following years. The maintenance costs would be $10,000 per year, starting in the year after it is built. Assume a social discount rate of 5 percent for this problem.
Of the 2000 residents of Bird Rock, half live 2 minutes away from the park and half live 10 minutes from the park. From a survey, the city of San Diego finds that individuals who live 2 minutes from the park visit the park almost daily (300 times a year). Individuals who live 10 minutes from the park visit about once a week (60 times per year). Bird Rock residents value travel time at 50 cents a minute. There are no costs of maintaining the park.
To solve this problem, it will be helpful to know that: \sum K^{t}A=A/(1-K) if k?(0,1), where t=0 indicates the first period and A is a parameter representing a constant amount.
a. What is the net present value of the parking garage? (Consider only the costs and benefits of providing the parking garage, not the costs of "not providing" the park.)
b. Assume that the two observations (cost per visit and number of visits for residents who live 2 and 10 minutes away) correspond to two points of the same linear demand curve for local park visits. Use the two observations to derive a demand curve for visits to the local park. (Don't forget to count the time costs coming and going to the park.)
c. What is the annual consumer surplus for residents who are 2 minutes away? What is the annual consumer surplus for residents who are 10 minutes away? What is the net present value of the park to residents?
d. Should the parking garage be built? Why or why not?