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MIT1_201JF08_final07

# MIT1_201JF08_final07 - 1.201 11.545 ESD.210 Introduction to...

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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!

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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 10 5 ), 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, P L is the price of labor (in \$ per hour), P F is the price of fuel (in \$ per gallon), P M 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 2
US 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

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