Road Damage Question

Could you help me with the following question?

Problem II. Road Damage (15 points) (Q16 of ch.5 of the textbook.) One hundred com- muters need to 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 and makes them feel safer. Bigger cars cost more per mile to operate, however, 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 12w, while the costs are 3w'. The damage to roads is 2w. Assume that individuals have utility functions of the form U = r, where r are the net benefits from driving a car of a given size. 1. What car weight will be chosen by drivers? (5 pts) 2. What is the optimal car weight? If this differs from (1), why does it? (5 pts) 3. Can you design a toll system that causes drivers to choose the optimal car weight? If so, how would such a system work? (e.g. how might the toll depend on the car)? (5 pts)