2) 100 commuters 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 worse. Worse yet, bigger cars cause greater permanent damage to roads. More specifically, if w is the weight of the car, suppose that the benefits from driving are 5w, while the costs are (1/2)*w. The damage to roads is (2/3)*w. Assume that individuals have utility functions of the form: U = x, where x are the net benefits from driving a car of a given size. i) What car weight will be chosen by drivers? 11 ) What is the optimal car weight? If this differs from (a), why? iii Can you design a toll system which causes drivers to choose the optimal car weight? b) Suppose that tastes change and drivers no longer care about their car weight. They are now only interested in minimizing the costs of driving. The costs of driving in the absence of government regulation are a function of the number of axles on a car - the gas costs per 100 miles driven is (1/6)*A', where A is the number of axles. The government reestimates the damage to roads from driving and finds that damage is reduced by having more axles on a car. If a car has A axles, the damage to the road per 100 miles driven is 20/A. Using more gas on the many axle cars also causes more pollution, so that the total pollution for a 100 mile trip is (1/3)* A2. (i) What is the socially optimal number of axles? (ii) How can the government enforce this social optimum