Question: Suppose there are 100 commuters that use a strip of highway to get to work. They all drive alone and prefer to drive in big cars - it gives them more prestige a makes them feel safer. Bigger cars cost more per mile to operate, however, since their gas mileage is worse. Worse yet, bigger cars cause greater permanent damage to roads.
More specifically, if w is the weight of the car, suppose that a driver's benefits from driving are 4w, while the costs are (3/2)* w2. The external costs, coming in the form of damn to the roads, is (1/3)* w3. Assume age that individuals have utility functions of the form: U = x, where x are the net benefits from driving a car of a give size.
1. What car weight will be chosen by drivers?
2. What is the optimal car weight? If this differs from (a) why?
3. Design atoll system that incentivizes drivers to choose the optimal car weight.