Question $2(29$ marks total$)$

Suppose a local government is estimating the cost and benefit of adding a new subway station in a neighborhood between two existing stations. The project needs to use $300,000$ kilograms of cements and $400,000$ labor hours. Suppose that the cements were purchased from a local producer that charges a special price of RMB $30$ per kilogram, which is lower than the market price charged by other producers all over the country, RMB $35$ per kilograms. Suppose that the construction workers employed by the project receive a market wage for other construction workers of RMB $40$ per hour, which is lower than the market wage for other types of workers of RMB $50$ per hour. Suppose constructor workers cannot find other types of jobs due to the high technical requirement of such jobs. After the station is built, the maintenance expenses will be RMB $2,000,000$ per year, lasting forever. Meanwhile, the average house price will increase by RMB $125,000$ since the average commute time of each person living in the neighborhood will fall by $30$ minutes per day. Suppose that there are a total of $100$ households living in the neighborhood, that there is one commuter per household, that the average commuter works $5$ days a week and $50$ weeks a year. Moreover, the new station can save $2$ lives each year $($the average number of persons living in the neighborhood and killed on their ways towards the two existing stations before the new station is built$).$ Suppose that each person's life value is measured by the present discounted value $($PDV$)$ of his$/$her life$-$time wages of RMB$100,000$ per year for $40$ years. For example, the PDV of his$/$her wage in the first year should be calculated as $100,\frac{000}{1+r},$ where $r$ is the interest rate. Suppose that the benefits of reduced commuting time and saved lives apply to current and future residents forever. We use an interest rate of $r=5\%$ whenever we need to discount the future value to the present value.

a$)(4$ marks$)$ What are the cash cost and opportunity cost of cements used in this project? What is their difference? Which cost should be used as the material cost of the project in the cost$-$benefit analysis?

b$)(4$ marks$)$ What are the cash cost and opportunity cost of the labor in this project? Explain why. Which cost should be used as the labor cost of the project in the cost$-$benefit analysis?

c$)(2$ marks$)$ How much is the PDV of the maintenance cost?

d$)(2$ marks$)$ What is the total cost of the project over time?

e$)(6$ marks$)$ Use the revealed preference approach to estimate the average value of an hour for a commuter based on the information provided.

f$)(2$ marks$)$ What is the total benefit of time saving from this project?

g$)(5$ marks$)$ What is the total benefit of life saving from this project?

h$)(2$ marks$)$ What is the total benefit of this project over time?