Q3. (Road Pricing) Suppose that the government would like to discourage certain percentage of private drivers from using their cars. Assume the following.

(i) Currently, there are 1000 drivers. They all drive round-trip each day.

(ii) Average driving time per one-way trip as a function of the number of drivers is

given in Table 1.

(iii) The distribution of monthly income for the current drivers is given in Table 2.

(iv) The opportunity costs of driving per hour = 50% hourly salary during work.

(v) Each driver in Table 2 works 160 hours per month.

(vi) Choice of transport mode is only based on time and cost.

(vii) Gas price and public transportation fare are ignored.

(viii) Drivers only care about traveling time when deciding whether to drive.

(ix) All drivers currently (i.e., before the congestion tax is imposed) save 10 minutes

one-way by driving instead of taking public transportation.

(x) If 25% of drivers stop driving, they will use subway. But that will cause more

congestion in subway and the travel time in subway will increase by 3 minutes.

Table 1. Number of drivers and average driving time.

Number of drivers	Average driving time per one-way trip (minutes)
250	15
300	15
500	20
750	30
950	40
1000	45

Table 2. Income distribution of the drivers.

Monthly income ($)	Percentage of the current drivers (%)
< 1,000	10
1,000 1,999	15
2,000 2,999	25
3,000 3,999	25
4,000 4,999	15
5,000 7,000	10

a. Given the above information, if the government wants to use a congestion tax to achieve its goal of discouraging 25% of drivers, what is the level of congestion tax (assume that the government can only set one congestion tax level for all drivers)? Explain your answer carefully (5 points)

b. Given the level of congestion tax that you set in part (a), how much benefit per day would the income group of $5,000-$7,000 receive after the tax is imposed? Explain your answer carefully. (5 points)