1 Congestion There is a narrow road connecting a small town to downtown Boston, where commuters each earn $200 per day. Workers in this town all need to get downtown at 9 am. When the road is crowded, congestion makes the drive unpleasant, reducing all drivers' utility by $1 per number of total drivers. So the individual (per person) traffic cost as a function of the total number of drivers (D) is: Cost(D) = D 1. Write out expressions for the total cost, total benefits and social net benefits from commuting in this town as a function of the number of drivers D. Hint: the total cost and befits are the individual costs and benefits times the number of drivers. 2. What number of commuters maximizes social net benefits? What are the social net benefits at this level? 3. Write an expression for individual driver net benefits. If commuters act "rationally" and only think of themselves, how many people will drive to Boston each day? What will social net benefits be from this outcome? 4. If the road were privatized what toll would the new owner set? How many people would commute? Steps to solve: 1. Add a toll (T) to each individual's private decision to use the road. So individuals now enter until their private benefits equal T. 2. Write an expression for D(T), the number of drivers that enter as a function of the toll. 3. After privatization, the road owner's profits become D(T) T. Find the T that maximizes profits.