There is a large number of commuters who decide to use either their car or the tube. Commuting by train takes 70 minutes whatever the number of commuters taking the train. Commuting by car takes C(x) = 20 + 60x minutes, where x is the proportion of commuters taking their cars, 0 ≤ x ≤ 1.
a. Plot the curves of the commuting time by car and the commuting time by train as a function of the proportion of car users.
b. What is the proportion of commuters who will take their car if everyone is taking her decision freely and independently so as to minimize her own commuting time?
c. What is the proportion of car users that minimizes the total commuting time?
d. Compare this with your answer given in part b. Interpret the difference. How large is the deadweight loss from the externality?
e. Explain how a toll could achieve the ancient allocation of commuters between train and car and be beneficial for everyone.