1 - Purdue University



|CE361 Introduction to Transportation Engineering |Posted: Sun. 16 November 2008 |

|Homework 10 Solutions |Due: Mon. 24 November 2008 |

PUBLIC MASS TRANSPORTATION

1. Transit ridership forecasts. Average daily ridership for the Mythaca Bus Company is 12,700. The base fare is $1.00. The MBC staff is recommending that the base fare be raised to $1.25. The most recent fare change was from $0.75 to $1.00 in 2002. After that fare increase, average daily ridership dropped from 9305 to 8243. Since then, the average daily ridership has grown gradually to its current level.

A. (10 points) Elasticity of demand with respect to fare. Using the shrinkage ratio equation, calculate the fare elasticity in Year 2002. Was the demand elastic or inelastic in Year 2002?

(10.14) [pic]= -0.3424

Revenue before: P0 * Q0 = $0.75 * 9305 = $6978.75

Revenue after: P1 * Q1 = $1.00 * 8243 = $8243.

Revenue increased, so demand was inelastic.

B. (10 points) What will average daily ridership be if the current base fare is raised to $1.25, assuming the Year 2002 fare elasticity applies? How will fare revenues change as a result of the fare increase?

(10.14) [pic]=-0.3424;

(Q1–12,700) = -1087.11; Q1 = 11,613.

Revenue before: $1.00 * 12,700 = $12,700.

Revenue after: $1.25 * 11,613 = $14,516.

C. (5 points) If the Board members do not want the average daily ridership to drop below 10,000, what is the maximum possible value (to the next lower $0.01) of the new base fare?

(10.14) [pic]=-0.3424;

(P1 – 1.00) = 0.6209; P1 = $1.6209 ( $1.62

D. (10 points) Service elasticity. What if a change in service is proposed, instead of a fare increase? In a city similar to Mythaca, average daily ridership dropped from 8262 to 7408 last year after bus schedule frequency went from four times per hour to twice per hour.

• Calculate the elasticity of demand with respect to frequency for that “similar city”.

(10.16) [pic]= 0.2067

• Calculate the elasticity of demand with respect to headway for that “similar city”.

(10.16) [pic]= -0.1034

E. (10 points) If MBC were to reduce its service from four times per hour to twice per hour, and if the service elasticity from the “similar city” applies, what would be the average daily ridership in Mythaca? If the current MBC operating costs are $48,200 per day, compute MBC’s farebox recovery ratio before and after the proposed service change. Assume that every one percent reduction in service causes a one-half percent reduction in operating costs.

Frequency-based calc: [pic]= 0.2067;

Q1 – 12,700 = -1312.54; Q1 = 11,387.

Headway-based calc: [pic]= -0.1034;

Q1 – 12,700 = -1313.18; Q1 = 11,387.

Recovery ratio before: [pic]= 0.263

Service is reduced by 50 percent, so operating costs decrease by 25 percent – from $48,200 per day down to $36,150.

Recovery ratio after: [pic]= 0.315

F. (10 points) Cross elasticity. Gasoline prices rose from $2.95/gal in July 2007 to $4.10/gal in July 2008. CityBus ridership in July 2008 was 238,818. Go to , About CityBus, Ridership Reports, Riders by Fare Classification to find Farebox Boardings for July 2007. Calculate the cross elasticity of transit demand with respect to gasoline price.

Farebox boardings in July 2007 were 143,987. Between July 2007 and July 2008, gasoline price increased 39.0 percent, while CityBus ridership increased 65.9 percent. Assuming no other factors were involved, use (10.14) to calculate cross elasticity. [pic]= +1.69.

2. Transit performance measures. Go to dot and click on “Modes of Transportation”, “Transit”, then Indiana Public Transit Annual Reports. Using the 2006 Indiana Public Transit Annual Report, …

A. (10 points) Update the Lafayette row in FTE Table 10.4.

Use entries appearing on pages 86-87 of the 2006 Annual Report.

| |Peak |TVM |Ridership |Cost/mi |Cost/trip |Recovery |%Labor |

| |Vehs | | | | | | |

|Lafayette |44 |1,368,050 |2,153,333 |3.13 |2.01 |0.23 |74 |

|1999 | | | | | | | |

|Lafayette |58 |1,683,866 |4,353,181 |4.45* |1.72** |0.24*** |73**** |

|2006 | | | | | | | |

* Checked entry with Total Operating Expense $7,488,985 / TVM 1,683,866 = 4.45.

** Checked entry with Total Operating Expense $7,488,985 / Ridership 4,353,181 = 1.72

*** Checked entry with Fare Revenue $1,801,594 / Total Operating Expense $7,488,985 = 0.24

**** Labor costs = Operator Salaries/Wages $2,663,296 + Other Salaries/Wages $ 1,411,471 + Fringe $ 1,402,071 = $5,476,838.

Labor costs $5,476,838 / Total Operating Expense $7,488,985 = 0.73.

B. (5 points) Compute the fuel consumption rate (mi/gal) of vehicles in the Lafayette fleet.

Page 86 of the 2006 Annual Report: Fuel consumption (gal) = 414,440.

mpg = TVM 1,683,866 / 414,440 gal = 4.06

3. (15 points) Life-cycle cost calculations. Repeat the analysis in FTE Table 10.6, but with the following changes: A hybrid bus replaces Tornado as Bus 1. The Hybrid has a purchase price of $361,140, fuel use of 5.3 mpg, and annual maintenance costs of $9988. Fuel $/gal = 2.814 for both buses. Which bus has the lower LCC?

The Fuel 1 and Fuel 2 columns in FTE Table 10.6 change. So do the purchase price, mpg, and maintenance costs for the first bus (now Hybrid). Both LCC(1) and LCC(2) increase, but still LCC(1) > LCC(2). The Typhoon diesel has a lower Life-Cycle Cost than the Hybrid over 12 years.

| |Hybrid | |Typhoon |

| |fuel $/gal | $ 2.81 | | |fuel $/gal | $ 2.81 | |

| |mpg |5.3 | | |mpg |4.1 | |

| |fuel cost/mi | $ 0.531 | | |fuel cost/mi | $ 0.686 | |

| |bus-mi/yr |46,000 | | |bus-mi/yr |46,000 | |

| |fuel cost/yr | $ 24,423 | | |fuel cost/yr | $ 31,572 | |

| |Driver $/hr |$19.10 | | |Driver $/hr |$19.10 | |

| |bus mph |12.0 | | |bus mph |12.0 | |

| |Driver $/yr |$73,217 | | |Driver $/yr |$73,217 | |

| |Maint $/yr |$9,988 | | |Maint $/yr |$7,372 | |

| |discount rate |4.5% | | |discount rate |4.5% | |

| |"inflation" |0% | | |"inflation" |0% | |

| |LCC(1) | $1,342,555 | | $ 86,412 |LCC(2) | $1,256,143 | |

| | | | | | | | |

|Yr |Purch 1 |Fuel 1 |Maint 1 |Driver |Purch 2 |Fuel 2 |Maint 2 |

|PW | $ 361,140 | $ 222,707 | $91,076 | $667,632 | $ 233,400 | $ 287,889 | $67,222 |

|1 | | $ 23,372 | $ 9,558 | $ 70,064 | | $ 30,212 | $ 7,055 |

|2 | | $ 22,365 | $ 9,146 | $ 67,047 | | $ 28,911 | $ 6,751 |

|3 | | $ 21,402 | $ 8,752 | $ 64,160 | | $ 27,666 | $ 6,460 |

|4 | | $ 20,481 | $ 8,376 | $ 61,397 | | $ 26,475 | $ 6,182 |

|5 | | $ 19,599 | $ 8,015 | $ 58,753 | | $ 25,335 | $ 5,916 |

|6 | | $ 18,755 | $ 7,670 | $ 56,223 | | $ 24,244 | $ 5,661 |

|7 | | $ 17,947 | $ 7,339 | $ 53,802 | | $ 23,200 | $ 5,417 |

|8 | | $ 17,174 | $ 7,023 | $ 51,485 | | $ 22,201 | $ 5,184 |

|9 | | $ 16,435 | $ 6,721 | $ 49,268 | | $ 21,245 | $ 4,961 |

|10 | | $ 15,727 | $ 6,432 | $ 47,146 | | $ 20,330 | $ 4,747 |

|11 | | $ 15,050 | $ 6,155 | $ 45,116 | | $ 19,454 | $ 4,543 |

|12 | | $ 14,402 | $ 5,890 | $ 43,173 | | $ 18,617 | $ 4,347 |

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