One hundred commuters need to use a strip of highway to get to work. They all drive alone and prefer to drive big cars—it gives them more prestige and makes them feel safer. Bigger cars cost more per mile to operate, since their gas mileage is lower. Worse yet, bigger cars cause greater permanent damage to roads.

The weight of the car is w. Suppose that the benefits from driving are 4w, while the costs are (3/2)w2. The damage to roads is (1/3)w3. Assume that individuals have utility functions of the form U = x, where x is the net benefits from driving a car of a given size.

a. What car weight will be chosen by drivers?

b. What is the optimal car weight? If this differs from a, why?

c. Can you design a toll system that causes drivers to choose the optimal car weight? If so, then how would such a system work?