Question

Each of 150 thousand people of the N-city every morning decide whether to travel by subway or by car. People 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.

If we assume that 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 the townspeople to get to work is minimal (socially optimal number of drivers).

(b)    Suppose that 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 with such independent decision-making? Will this number of drivers be socially optimal?

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

Answer 1