Problem 4. (FOR ADDITIONAL POINTS) Each of 150 thousand inhabitants of the N-cit

Question

Problem 4. (FOR ADDITIONAL POINTS) Each of 150 thousand inhabitants of the N-city every morning decides whether to get to work by subway or by car. Inhabitant will get to work in 60 minutes if he will use subway regardless of the number of passengers. Travel time by car, however, is greater as more and more people also have chosen to use it. If n thousand people decided to go by car each of them will spend 10+0.5n minutes on the road. For simplicity, we will assume that the travel time is the only thing that the inhabitant takes into account choosing the form of getting to work. (a) How many people should use cars, so that the total time for all the townspeople to get to work is minimal? Let's call this number of drivers socially optimal. (b) Suppose that each person accurately estimates the number of drivers today, and, independently of others, decides which mode 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 rubles. What is the fee for using a car, so that the number of drivers from (b) is socially optimal?

Explanation / Answer

a)

From the above statemest we can differed that the number of people should be less by the time occurred to enter into that lap . So the required equation would be

150 x 60>= 10 + 0.05n which means n<= 179800 .

b) if no time lag is there and they find drivers on time then the required number should be n = 2800.

c) if 1 min of time is used for 10 rubble then the free time for the incident would be 0.5 minutes for each cases.

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