3. [16 marks) Consider an open-access highway of fixed length and capacity, which is non- rival only for sufciently low traffic volumes. Assume the highway is used exclusively by identical commuters who make either one or zero daily round trips on the highway, depending on whether they obtain a not benet from taking a round trip. Assuming there is one commuter per vehicle, the daily number of round trips, vehicles and commuters on the highway are equal. A commuter's travel time per round trip is given by 1 if v S v,- _ 6' TIE\") _ (vi) if v > 19,; in hours, where v 32 0 is trafc volume on the highway in number of vehicles per day, 17,: > D is the critical trafc volume at which congestion sets in and 6 > D is a congestion parameter. Due to foregone opportunities, fuel consumption, vehicular wear and tear etc., using the highway costs a commuter c > 0 dollars per hour of travel. Therefore, a commuter's total cost of using the highway is C(17) = cT(v) dollars per round trip when the trafc volume is 17. With the highway providing access to employment, the benet to a commuter of using the highway is b dollars per round trip, where it is assumed that b > c [i.e. that using the highway is worthwhile to a commuter if congestion is absent or insufficiently high]. Let FE and v* denote the equilibrium and efcient trafc volumes, respectively. a. Derive the solution for v3 in terms of the model's parameters, and verify that v.5