CE 434 – PUBLIC TRANSPORTATION ASSIGNMENT 3: DEMAND FORECASTING DUE DATE: 2/26/24 1) Supply and Demand Analysis (30 Points) You work as a Big City Transit Authority (BCTA) transport economist. BCTA is designing a new airport flyer transit route to get people directly between the city center hotels and the local airport. Two different alternatives are being considered: a) a light rail system and b) an express bus. The demand for transit service (in passengers per run) can be described as follows: 𝑉 = 3000 − 120𝐶. The cost function for each system (in dollars) can be described as follows: 𝐶 = 10 0. 5𝑉 for the express bus, 𝐶 = 15 0. 2𝑉 for the light rail system. Assume there are 15-minute headways (i.e., time between two consecutive runs) for both alternatives. Provide a graphical illustration of the supply and demand functions and determine the equilibrium demand and price for both transit alternatives. Which system will generate the greatest number of hourly riders? How many per hour? (Round up to the nearest integer). 2) Transit Price Elasticities (35 Points) 2.1. Fare-free Tuesday (14 Points) City bus is planning a fare-free day on the first Tuesday in March. This means that the usual $1 cash fare will not be charged that day. Using a fare elasticity of -0.30 and a typical March weekday “cash” (non-pass) ridership of 1,400 passengers, calculate: a) How many non-pass riders can the bus company expect on that Tuesday in March? (7 Points) b) What is the difference between the typical March weekday demand and the demand expected during the fare-free day? Do you think your estimation is accurate? (Please explain why.) (7 Points) 2.2. Using elasticities for decision-making (21 points) Two years ago, a bus system carried 5,964 cash-paying riders when the cash fare was $0.50. Last year, after a cash fare increase to $0.75, the cash-paying ridership fell to 4,711. a) What is the demand elasticity of cash-paying riders with respect to fare? (6 Points) b) Calculate the fare revenues for each year. (5 Points) c) Is the transit demand elastic or inelastic with respect to fare? Explain on what you based your conclusion. (5 Points) d) Some members of the transit agency’s Board of Directors say they want to restore the old $0.50 cash fare next year. Estimate cash-paying ridership next year at the lower fare to provide a recommendation to the Board. (5 Points) 3) Mode Choice Estimation (35 Points) 3.1. Choosing between two modes (18 Points) Assuming a binary logit model and given the following information about the utility function, please answer the following questions: 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝑈𝑘 = 𝐴𝑘 − 0. 05𝑇𝑎 − 0. 04𝑇𝑤 − 0. 03𝑇𝑟 − 0. 014𝐶 Variable 𝑇𝑎 = 𝑎𝑐𝑐𝑒𝑠𝑠 𝑡𝑖𝑚𝑒 (. ) Private auto 5 Mass Transit 10 𝑇𝑤 = 𝑤𝑎𝑖𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒(. ) 0 15 𝑇𝑟 = 𝑟𝑖𝑑𝑖𝑛𝑔 𝑡𝑖𝑚𝑒(𝑚𝑖𝑛.) 25 40 𝐶 = 𝑜𝑢𝑡 − 𝑜𝑓 − 𝑝𝑜𝑐𝑘𝑒𝑡 𝑐𝑜𝑠𝑡 (𝑐𝑒𝑛𝑡𝑠) 𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝐴𝑘 150 -0.01 100 -0.07 a) Briefly explain why all coefficients of the variables in the utility function are negative numbers. (6 Point) b) Determine the share of persons-trips by each of two modes (private auto and mass transit). (6 Points) c) If a 1,000 people are planning to travel between two areas and the above model is a good approximation of their behavior, calculate how many people are expected to use mass transit. (6 Points) 3.2. Choosing among four modes (17 Points) A total of 1,200 residents of a suburban town are traveling to work in a nearby large city. The residents have four mode choices as represented in the utility functions bellow: 𝑈𝐷𝐴 = 0. 8 − 𝑇𝐷𝐴 − 0. 25𝐶𝐷𝐴 𝑈𝑅𝑆 = 0. 2 − 𝑇𝑅𝑆 − 0. 25𝐶𝑅𝑆 𝑈𝐸𝐵 =− 0. 2 − 𝑇𝐸𝐵 − 0. 25𝐶𝐸𝐵 𝑈𝐶𝑅 =− 𝑇𝐶𝑅 − 0. 25𝐶𝐶𝑅 Where DA= drive alone, RS= carpool or vanpool, EB=Express bus service, and CR=Commuter Rail. T is the total travel time (hrs) and C is the out-of-pocket cost ($). For each of these modes, the average trip characteristics for the 1,200 residents are given below. DA RS EB CR Time (hours) 0.9 1.0 1.3 1.2 Cost (dollars) 7.50 3.50 4.00 5.00 a) How many will likely choose to carpool or vanpool? (5 Point) b) How might the utility function be structured to more effectively represent the differences in modal attributes? (6 Points) c) How might the utility functions be structured to better reflect changing demographic patterns in the U.S.? (6 Points)