A city government has hired a private rm to build a new bridge in the city at a cost of $120M. The bridge has just

A city government has hired a private firm to build a new bridge in the city at a cost of $120M. The bridge has just been completed and opened. If no toll is charged, then 25,000 vehicles (total) cross the bridge during rush hours on a normal weekday. There are rush hours 5 days per week, 51 weeks per year. The maintenance cost imposed by an additional vehicle crossing the bridge is very close to 0. But every crossing by a vehicle creates an externality. If q thousand vehicles cross the bridge during rush hours, then the marginal damage (the cost imposed on others by an additional vehicle crossing during rush hours) is q/20 dollars. Thus if 10 thousand vehicles cross, then the marginal damage (damage from another crossing) is 10/20 = 1/2 dollar. Assume that the demand for crossings during rush hours is linear with a choke price of $5. In the problems that follow, “efficient” means maximizing total surplus.

a. Explain the meaning of a choke price of $5.

b. Find the equation of the demand curve for crossings during rush hours. Hint: Find the prices and quantities associated with two points on the demand curve and use them to find the slope of the curve.

c. What is the most important externality that might account for most of the marginal damage from an additional crossing of the bridge? Assume that having the bridge built does not increase the total amount of driving in the city.

d. Given the information above, what would the marginal damage from an additional crossing during rush hours equal if there were no toll? Be as specific as possible. Use information discussed in class to explain how the externality or externalities you described in part c might cause this amount of marginal damage from a crossing over a bridge in a real U.S. city.

e. Market economies have several ways of reducing inefficiency due to externalities (with or without government intervention). List three different ways city residents could reduce the inefficiency from the main externality connected with use of the bridge. Compare how effective the different ways are likely to be in reducing the inefficiency that the main externality in part c could cause.

f. What is the efficient number of crossings of the bridge during rush hours? What toll could the government charge for a crossing in order to have an efficient number of crossings? Assume that the toll can be charged electronically without affecting the flow of traffic on the bridge. Draw a graph of the demand curve for crossings and the marginal damage curve and show the efficient toll and the resulting number of crossings.

g. The height of the demand curve represents the maximum willingness to pay for an additional crossing, given the number of other crossings. A driver considering making that crossing takes into account the q other crossings and any congestion they cause. Does this imply that we are double counting the congestion cost if we include it in marginal damage and subtract it when we calculate total surplus? Explain.

h. Suppose that the firm that built the bridge owned and operated it and charged a single toll, the same to all vehicles crossing during rush hours. What toll would maximize the firm’s profit? How many vehicles would cross during rush hours if that toll were charged? Compare this number to the efficient number of crossings in part e.

i. Suppose that the demand for crossings of the bridge at times other than rush hours is linear, with a choke price of $4. If no toll were charged, there would be 10,000 crossings per day at times other than rush hours. These crossings, spread over a longer period than the rush hour crossings, have negligible marginal damage. If we treat their marginal damage as 0, what is the efficient total number of crossings over the bridge at times other than rush hour? What is the toll the government should charge at times other than rush hour in order to maximize total surplus?

j. Suppose that the firm could have borrowed $120M, built the bridge, and owned and operated it itself. The firm would have paid back the loan plus interest by paying 7% of the loan per year for the lifetime of the bridge. The firm would also have had costs of $3M per year for managing, maintaining and insuring the bridge. Still, it could have made a profit if it charged tolls at all times. What is the most profit it could have made per year from building and operating the bridge?

k. Suppose that the government charged a $1 toll per crossing during rush hours and no toll at any other time. If we calculate the government’s profit the way we do the private firm’s profit (with the same costs as the private firm must pay), the government would make a loss from the bridge. Does this imply that total surplus would be higher if the private firm owned and operated the bridge instead of the government? Explain. Could the government have increased the total surplus by charging a toll outside rush hours? Show that your answers are correct.