1.201 / 11.545 / ESD.210 Introduction to Transportation Systems Fall 2007 Final Exam Monday, December 17, 2007 • You have 3 hours to complete this exam. • Show all your work to get partial credit. • You are allowed to use your notes from class, as well as any other notes or textbooks. • You can use a calculator. However, laptop computers, mobile phones, and other electronic devices are not allowed. • There are nine questions in this exam. Good luck!Question 1 (14 points) Cost Functions for Public Transit Systems Karlaftis and McCarthy (2002) estimated a translog cost function for US public transit operators. Following is the first-order approximation of that function (Note: A ‘first-order approximation’ does not include interaction terms): where CV represents the total short-run variable costs (in $ millions), Y is the number of vehicle-miles (units of 105), which is a measure of output, N is the number of route miles, which is a measure of network size, K is the number of buses in the operator’s fleet, PL is the price of labor (in $ per hour), PF is the price of fuel (in $ per gallon), PM is the price of materials (in $ per vehicle hour – material costs were calculated by subtracting labor and fuel costs from total costs and then dividing the difference by peak-hour requirements to obtain costs per vehicle hour) The function was estimated using data from 256 US transit systems over the period 1986-1994. The estimation results are shown in Table 1: TABLE 1: Estimation results Coefficient Estimated value 9.27 0.78 -0.03 0.29 0.71 0.14 0.15 Answer the following questions: a. What is the point elasticity of total short-run variable costs with respect to: i. the price of labor (1 point) ii. the price of fuel (1 point) b. Use your answer in (a) to calculate the effect of each of the following on total short-run variable costs: i. a 2% increase in wage rates (1.5 points) ii. a 10% decrease in the price of fuel (1.5 points) c. Compute the economies of density (defined by varying the amount of output over a fixed system) for the transit agencies studied. (3 points) d. Using the same data on which the cost function was estimated, the authors calculated a short-run average cost of $2.96 (per vehicle-mile) and a short-run marginal cost of $2.31 (per vehicle-mile) for 2US transit operators. Is the relationship between these two values consistent with your answer in (c)? Briefly explain your response. (1.5 points) e. Does your answer in (c) imply that most transit agencies are natural monopolies and that public transit (without proper regulation) is a market that lacks competition? Briefly explain your response. (1.5 points) f. Compute the economies of system size (defined by varying output and network size) for the transit agencies studied. (3 points) Question 2 (18 points) Modeling Public Transit Use in a Metropolitan Area Consider a major metropolitan area which has extensive metro and bus networks. The focus of this question is the analysis of travel demand by transit in this city and specifically the choice of mode to travel within the city. For the purposes of this question you may assume that there is a fixed demand matrix (i.e. that demand between origin-destination pairs is not a function of the level-of-service, and so can be assumed to be constant) representing travel by transit between all origin-destination pairs and that the only modes of interest are metro and bus. Answer the following questions: a. What data would you need to estimate a discrete choice binary logit model reflecting an individual’s choices between metro and bus in this city? You may assume that the attributes which affect choice are the in-vehicle time, walk access time, wait time and monetary cost for the best paths between an origin-destination pair by bus and metro. (4 points) b. List any other mode-specific attributes or individual-specific characteristics that you would include in your model. (2 points) c. Based on your responses in (a) and (b), write two utility functions (one for bus and another for metro) that would capture an individual’s well-being from choosing the corresponding mode. (5 points) d. What is the expected sign of each coefficient you included in your model specification in (c)? (2 points) e. Many studies have shown that a minute of in-vehicle travel time on a bus is more onerous than a minute of travel time on metro. Assume you have a mode choice model that incorrectly assumes that these two travel times are equivalent (i.e. it assumes that a minute of travel time on the bus causes the same disutility as a minute of travel time on metro). What are the implications of using such a model to evaluate alternative investments in the public transit system? (5 points) 3Question 3 (12 points) Path-Based Congestion Pricing In the simple network represented in Figure 1, there are two OD pairs: • A-C: There is only one path connecting this pair (which is the direct path). • B-C: There are two paths connecting this pair (the direct path and the one passing through A). t = 1 + 0.2x A C B t = 5 + 0.1x t = 20 + 0.1x FIGURE 1: Simple network with two OD pairs The travel times on each link are represented by the functions shown in Figure 1. In each function, t represents the travel time on the corresponding link (in minutes) and x represents the number of vehicles traveling on that link. Demand on each OD pair is fixed (inelastic) within the study period: • A-C demand = 100 vehicles • B-C demand = 250 vehicles Assume that travel on the A-C OD pair is priced at marginal cost. In other words, the 100 vehicles going from A to C are already paying a toll that makes their ‘perceived’ cost of using the direct link between these two nodes equal to marginal cost. Also assume that people traveling on the A-C OD pair have no other choice than to use the direct link (i.e. they will use that link regardless of the level of flow). Your task here is to find tolls that you could charge on the two paths connecting B and C. Under path-based congestion pricing, each vehicle is charged based on its OD pair. This means that there can be two vehicles traveling on the link connecting A and C and paying different tolls because one originated at A, while the other originated at B. Answer the following