Population -150 thousand.Every morning they decide how to travel. They get to work in 60 minutes by subway regardless of the number of passengers. Travel time by car is greater as more people use it. If n thousand people decided to go by car each of them would spend 10+0.5n minutes on the road. When choosing a means of transport, people only consider the travel time.

(a)     How many people should use cars, so that the total time for all people to get to work is minimal (socially optimal number of drivers).

(b)    If each person accurately estimates the number of drivers today, and, independently of others, decides which means of transport to use. How many people will go by car? Will this number be socially optimal?

(c)   Each person estimates 1 minute of his time at $10. What is the fee for using a car, so that the number of drivers from (b) is socially optimal?