Public Mass Transportation

CE361 Introduction to Transportation Engineering Posted: Fri. 10 November 2006 Homework 10 Solutions Due: Mon. 20 November 2006

PUBLIC MASS TRANSPORTATION

1. Transit ridership forecasts. Average daily ridership for the Mythaca Bus Company is 10,253. The base fare is $1.00. The MBC staff is recommending that the base fare be raised to $1.50. The most recent fare change was from $0.75 to $1.00 in 2001. After that fare increase, average daily ridership dropped from 9251 to 8241. Since then, the average daily ridership has grown gradually to 10,253. A. (10 points) Elasticity of demand with respect to fare. Using the shrinkage ratio equation, calculate the fare elasticity in Year 2001. Was the demand elastic or inelastic in Year 2001?  Q  Q   1 0    %  Q  Q0  (Q1  Q0 )P0 (8241 9251)*0.75 (10.14) shr      0.328 %  P  P  P  (P  P )Q (1.00  0.75)*9251  1 0  1 0 0    P0 

Revenue before: P0 * Q0 = $0.75 * 9251 = $6938.25

Revenue after: P1 * Q1 = $1.00 * 8241 = $8241. Revenue increased, so demand was inelastic. B. (10 points) What will average daily ridership be if the current base fare is raised to $1.50, assuming the Year 2001 fare elasticity applies? How will fare revenues change as a result of the fare increase? (Q1  Q0 )P0 (Q1 10,253)*1.00 (10.14) shr    0.328 ; (Q – 10,253) = -1681; (P1  P0 )Q0 (1.50 1.00)*10,253 1

Q1 = 8572. Revenue before: $1.00 * 10,253 = $10,253. Revenue after: $1.50 * 8572 = $12,858. C. (5 points) If the Board members do not want the average daily ridership to drop below 9000, what is the maximum possible value (to the next lower $0.01) of the new base fare? (Q1  Q0 )P0 (9000 10,253)*1.00 (10.14) shr    0.328 ; (P1 – 1.00) = 0.373; (P1  P0 )Q0 (P1 1.00)*10,253

P1 = $1.373  $1.37 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 8722 to 7150 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”.  Q  Q   1 0    %  Q  Q0  (Q1  Q0 )S0 (7150  8722)*4 (10.16) shr     = 0.360 %  S  S  S  (S  S )Q (2  4)*8722  1 0  1 0 0    S0   Calculate the elasticity of demand with respect to headway for that “similar city”. (Q1  Q0 )S0 (7150 8722)*15 (10.16) shr   = -0.180 (S1  S0 )Q0 (30 15)*8722 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 $42,000 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. (Q1  Q0 )S0 (Q1 10,253)*4 Frequency-based calc: shr    0.360 ; Q – 10,253 = (S1  S0 )Q0 (2  4)*10,253 1 -1845.54; Q1 = 8407. (Q1  Q0 )S0 (Q1 10,253)*15 Headway-based calc: shr    0.180 ; (S1  S0 )Q0 (30 15)*10,253

Q1 – 10,253 = -1845.54; Q1 = 8407. Re venue before $1.00*10,253  Recovery ratio before: Oper cos ts before $42,000 = 0.244 Service is reduced by 50 percent, so operating costs decrease by 25 percent -- $42,000 per day down to $31,500. Re venue after $1.00*8407  Recovery ratio after: Oper cos ts after 0.75*$42,000 = 0.267

2. Transit performance measures. Go to www.in.gov/dot and click on “Modes of Transportation”, then Indiana Public Transit Annual Reports. Using the 2005 Indiana Public Transit Annual Report, … A. (10 points) Update the Lafayette row in FTE Table 10.4. Use entries appearing on pages 82-83 of the 2005 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 1,689,272 4,301,043 4.30 1.69 0.29* 73** 2005 * 1.00 – Operating subsidy ratio = 1.00 – 0.71 = 0.29 ** Labor costs = Operator Salaries/Wages $2,604,124 + Other Salaries/Wages $1,376,105 +Fringe $1,347,108 = $5,327,337. Total $5,327,337 Operating Expense = $7,261,346. %Labor = $7,261,346 = 0.734 B. (5 points) Compute the fuel consumption rate (mi/gal) of vehicles in the Lafayette fleet. Page 82 of the 2005 Annual Report: Fuel consumption (gal) = 423,494. TVM 1,689,272  Mpg = gal 423,494 = 3.99

3. (15 points) Life-cycle cost calculations. Repeat the analysis in FTE Table 10.6, but with fuel $/gal = 2.0812. Only the Fuel 1 and Fuel 2 columns in FTE Table 10.6 change. Both LCC(1) and LCC(2) increase, but it is still the case that LCC(1) > LCC(2). The Typhoon still has a lower Life-Cycle Cost.

Tornado Typhoon fuel $/gal $2.0812 fuel $/gal $2.0812 mpg 4.7 mpg 4.1 fuel cost/mi $0.443 fuel cost/mi $0.508 bus-mi/yr 46,000 bus-mi/yr 46,000 fuel cost/yr $20,369 fuel cost/yr $23,350 Driver $/hr $19.10 Driver $/hr $19.10 bus mph 12.0 bus mph 12.0 Driver $/hr $73,217 Driver $/hr $73,217 Maint $/yr $9,797 Maint $/yr $7,372 discount discount rate 4.5% rate 4.5% "inflation" 0% "inflation" 0% $1,181,17 LCC(1) $1,201,075 $19,901 LCC(2) 4

Yr Purch 1 Fuel 1 Maint 1 Driver Purch 2 Fuel 2 Maint 2 PW $258,370 $185,738 $89,335 $667,632 $ 233,400 $212,919 $67,222 1 $19,492 $9,375 $70,064 $ 22,345 $ 7,055 2 $18,653 $8,971 $67,047 $21,382 $6,751 3 $17,849 $8,585 $64,160 $20,462 $6,460 4 $17,081 $8,215 $61,397 $19,580 $6,182 5 $16,345 $7,862 $58,753 $18,737 $5,916 6 $15,641 $7,523 $56,223 $17,930 $5,661 7 $14,968 $7,199 $53,802 $17,158 $5,417 8 $14,323 $6,889 $51,485 $16,419 $5,184 9 $13,707 $6,592 $49,268 $15,712 $4,961 10 $13,116 $6,309 $47,146 $15,036 $4,747 11 $12,551 $6,037 $45,116 $14,388 $4,543 12 $12,011 $5,777 $43,173 $13,769 $4,347