Chapter 2 Garber and Hoel

2-1 How would your typical day be changed without availability of your principal mode of transportation? Consider both personal transportation as well as goods and services that you rely on.

2-3 A bridge has been constructed between the mainland and an island. The total cost (excluding tolls) to travel across the bridge is expressed as C = 50+ 0.5V, where Vis the number of veh/h and C is the cost/vehicle in cents. The demand for travel across the bridge is V=2500-10C.

(a) Determine the volume of traffic across the bridge.

(b) If a toll of 25 cents is added, what is the volume across the bridge?

(c) A tollbooth is to be added, thus reducing the travel time to cross the bridge. The new cost function is C = 50+ 0.2V. Determine the volume of traffic that would cross the bridge.

(d) Determine the toll to yield the highest revenue for demand and supply function in part (a) and the associated demand and revenue.

2-4 A toll bridge carries 10,000 veh/day. The current toll is $3.00/vehicle. Studies have shown that for each increase in toll of 50 cents, the traffic volume will decrease by 1000 veh/day. It is desired to increase the toll to a point where revenue will be maximized.

(a) Write the expression for travel demand on the bridge related to toll increase and current volume.

(b) Determine toll charge to maximize revenues.

(c) Determine traffic in veh/day after toll increase.

(d) Determine total revenue increase with new toll.

2-5 Consideration is being given to increasing the toll on a bridge now carrying 4500 veh/day. The current toll is $1.25/veh. It has been found from past experience that the daily traffic volume will decrease by 400 veh/day for each 25¢ increase in toll. Therefore, if x is the increase in toll in cents/veh, the volume equation for veh/day is V =4500-400 (x/25), and the new toll/veh would be 7 = 125 + x. In order to maximize revenues, what would the new toll charge be per vehicle, and what would the traffic in veh/day be after the toll increase?

2-7 An individual is planning to take an 800-mile trip between two large cities. Three pos- sibilities exist: air, rail, or auto. The person is willing to pay $25 for every hour saved in making the trip. The trip by air costs $600 and travel time is 8 hours, by rail the cost is $450 and travel time is 16 hours, and by auto the cost is $200 and travel time is 20 hours.

(a) Which mode is the best choice?

(b) What factors other than cost might influence the decision regarding which mode to use?

2-13 Consult with the U.S. Department of Transportation website and identify the name and location of highways in your state that are included as part of the National Highway System.

2-16

What do the following acronyms mean?