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Section C 6. Traffic congestion is a significant urban disamenity in many cities, where urban population and private vehicle ownership are growing rapidly. For instance, every day a large number of commuters travel from Lyon to Paris. There are two ways to make this trip. One way is to drive and the other is to take a bus. Commuting time by car is: C(x) = 15 for a 5 0.1 10 + 50r for a > 0.1 where x is the proportion of commuters taking their car 0 s x s 1. Commuting by bus takes: B(x) = 45 for a s 0.1 30 + 25r for a > 0.1 whatever the number of passengers travelling by bus. The travel time before congestion is 45' minutes by bus and 15' minutes by car. When more than 10% of commuters go by car (x > 0.1) congestion kicks in and the travel time Page 3 of 5 by car and by bus become linear increasing functions of the proportion of commuters taking their cars. The rational for this model is that buses are a only few and do not cause congestion. However, buses have dedicated lanes, and are slowed down less than cars by congestion. a) What is the percentage of commuters using the car that makes them indifferent between bus and car? Sketch the graph of the commuting time for car and bus as a function of the proportion of car-users x, and show graphically the indifference solution that you have found analytically. b) What is the proportion of car users that minimizes the average commuting time (social optimal number of commuters by car)? C) Compare answers in parts (a) and (b). Interpret the difference. How large is the deadweight loss from the externality? d) Imagine now that new bus lines are introduced, and the travel time by bus changes as follows: B(x) = 40 for a 5 0.1 30 + 15x for a > 0.1 How does the indifference number of commuters by car change? How about the social optimal level? Comment on your results. e) The road congestion can lead eventually to an environmental externality, suggest two policy instruments which might be used to reduce both road congestion and pollution. Explain if these measures promote vertical equity or horizontal equity and why