NBSIR 78-1462

Elasticity of Transit Demand

With Respect to Price: A Case

Study

Ralph E. Schofer

Center for Applied Mathematics

National Engineering Laboratory

Washington, D C. 20234

March 1978

Technical Report to: The Office of Service and Methods and Demonstrations

Urban Mass Transportation Administration

U.S. Department of Transportation

NBSIR 78-1462

ELASTICITY OF TRANSIT DEMAND

WITH RESPECT TO PRICE: A CASE

STUDY

Ralph E. Schofer

Center for Applied Mathematics

National Engineering Laboratory

Washington, D.C. 20234

March 1978

Technical Report to: The Office of Service and Methods and Demonstrations

Urban Mass Transportation Administration

U.S. Department of Transportation

U S. DEPARTMENT OF COMMERCE. Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Saruch, Assistant Secretary for Science and Technology

NATIONAL SUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Pag

I. Introduction 1 II. Description and Characteristics of the Study Area 3

III. Data Acquisition and Refinement j

IV. Method of Analysis 15

A. Elasticity of Peak-Period Transit Patronage with Respect

to Price 15

B. Shifts in Transit Demand from Peak to Off-Peak Periods 17

C. Shifts in Automobile Usage IT

V. Results l8

A. Elasticity of Peak-Period Transit Demand 18

B. Shifts from Peak to Off-Peak Transit Usage 22

C. Shifts of Peak-Period Commuters from Bus to Auto Mode 22

VI. Conclusions 28

VII. List of References 30

Appendix A. Supplemental Data Sources 31

Appendix B. Northern Virginia Census Tracts: Populations and Incomes 32

Appendix C . Northern Virginia Bus Fares . 3

6

Appendix D. Illustrative Calculation of Approximate Elasticities 38
LIST OF TABLES

Page

1. Bus Route Operating Characteristics, AM Inbound. Peak Period h

2. Average Weekday Bus Patronage, Shirley Highway 10

3. New Bus Service Added between August and October 197^ 10

k. Estimated Average Weekday Bus Patronage 11

5. Range of Seasonal Patronage Variation Factors 12

6. Estimated Average Passenger Fares by Transit Route Ik

7. Peak-Period Transit Elasticity Estimates 19

8. Summary of Peak-Period Elasticity by Type of Service 20

9. Comparison of Peak-Period Transit Elasticities with Those

from Other Studies 21

10. Distribution of Auto Persons by Carpool Size, Shirley Highway,

6:30-9AM Peak Period Inbound 23

11. Estimated 197^ Population and Median Income in Census Tracts

Adjacent to the Shirley Highway Bus Lines 3^

12. Estimated 197^+ Population and Median Income in Census Tracts

Adjacent to the Lee Highway Bus Lines 35
LIST OF FIGURES

Page

1. Location of Northern Virginia Bus Routes 8

2. Distribution of 6:30-9AM Peak-Period Inbound Shirley Highway

Auto Persons by Carpool Size Before and After Transit Fare Increase.

All Shirley Highway Lanes 26

3. Distribution of 6:30-9AM Peak-Period Inbound Shirley Highway

Auto Persons Using Express Lane by Carpool Size Before and After

Transit Fare Increase. Express Lane Autos Only 27

4. Northern Virginia Census Tracts, 1970 33

5. WMATA Fare Zones (Appendix C) 37
ABSTRACT

This report describes the methodology and the results of an empirical

study of peak-period transit demand elasticity with respect to price

(fare). The results suggest applying different pricing policies to different types of transit service.

Field observations were structured to capture the reactions of morning

(inbound) commuters to a peak-period fare increase introduced on September 1, 1975. The study is limited to bus and automobile travelers on the Shirley Highway and to bus passengers on the Lee Highway, both in

Northern Virginia. The Shirley buses provide express service on exclusive freeway lanes, whereas the Lee Highway buses provide traditional

service on a signalized radial arterial. Typical fares ranged from

$.60 to $.90 before the increase and from $.75 to $1.20 afterwards, re- sulting in increases of between 20 and 33 percent. Demand for service

on the Shirley Highway Express buses proved less elastic (-0.301 to

-0.21+3) than that for the traditional Lee Highway bus service (-O. 8 U 3 to

-0.671). There was little evidence of passengers on either service

shifting travel outside the peak periods to avoid higher fares. The fare

increase had no effect on auto travel.

Key Words: Elasticity; elasticity of transit demand; pricing; transit

planning; transit pricing; transportation economics
I. Introduction

The board of directors of the Washington Metropolitan Area Transit Authority (METRO), after holding public hearings, raised "peak-period" bus

fares on September 1, 1975. These fare increases applied only to the

peak-period operations (6:30-9:30 a.m. and 3:30-6:00 p.m.); off-peak

fares were not changed. The previous fares had been in effect for sev- eral years.

This pricing change provided an excellent research opportunity to study

commuter reactions to fare increases. When confronted by a peak-period

price increase, bus commuters have several options available: they may

pay the increased fare and continue to commute by bus; shift their mode

of commuting from bus to car or carpool; shift intertemporally from peak

to off-peak commuting; or cease commuting.

The purpose of this study is to quantify these reactions for subsequent

use in predicting the consequences of proposed peak-period transit fare

increases

.

The objectives of the research are fourfold:

• to observe and report the elasticity of peak-period transit

demand with respect to price (fare)

• to identify and quantify the impact of a peak-period transit

fare increase on auto usage and car pools

• to determine whether a peak-period transit fare increase caused

any measurable shift in passenger usage from peak to off-peak

times

• to compare the elasticities observed on the Shirley Express

Buses with those observed on conventional bus service in the same metropolitan area, and to determine if elasticities observed for these two qualities of transit service are significantly different

.

This report is organized as follows. The study area and its characteristics are described in Section II below. Procedures for data acquisition and refinements are presented in Section III, while the method of

analysis employed is discussed in Section IV. Study results are presented in Section V, and conclusions in Section VI. Section VII is a list of references. This is followed by Appendices containing further

references, data sources, special computations, and other supportive information.

The study was structured and implemented on extremely short notice. It

could not have been completed to yield useful results without the coop-
eration and support of many individuals £n a number of organizations

within the Washington Metropolitan Area.

Significant contributions were provided by the following individuals:

Ronald J. Fisher, Bert Arrillaga, and Vincenzo Milione of the Urban Mass

Transportation Administration (UMTA) , U.S. Department of Transportation,

Washington, D.C.; Franklin F. Goodyear and Kenneth A. Brown, Metropolitan Washington Council of Governments, Washington, D.C.; Michael A.

Bresnahan, M. F. Hewitt, and G. Perrie Nutwell, METRO, Washington, D.C.;

Nathan Avins, and Abdul Sleemi, Department of Highways and Traffic, District of Columbia Government, Washington, D.C.; Robert H. Watkins, Principal, Rock Creek Associates, Washington, D.C.; James M. McLynn, Principal, DTM Inc., Bethesda, MD; Dr. Karla L. Hoffman, Eric Howe, and

Cheng Ming Huang, National Bureau of Standards, Gaithersburg, MD; and

John H. Mitton. Transportation Consultant, Washington, D.C.

2
II. Description and Characteristics of the Study Area

Historically, Northern Virginia has been a bedroom community for families

of employees working in downtown Washington, D.C. Over the years, large

employment centers have also developed within Northern Virginia itself,

beginning with the Pentagon in the early 19U0's and continuing with the

Central Intelligence Agency in Langley, and later with massive office

building developments in both Rosslyn and Crystal City.

This study quantifies the reactions of commuters living in the Northern

Virginia suburbs who use bus service on Shirley Highway or Lee Highway,

when confronted with an increase in peak period fares. Observations

were made within the Shirley Highway and the Lee Highway Corridors, both

of which are major radial traffic arteries carrying large volumes of

automobile and bus transit commuters.

The Shirley Highway is a recently reconstructed radial freeway connecting

the southwestern parts of Northern Virginia suburbs with employment cen- ters at the Pentagon, and in Crystal City and downtown Washington. During

peak commuter travel periods, an exclusive lane serves bus vehicles as well as car pools of four or more persons. Three regular lanes in each

direction are available to serve other traffic.

The Lee Highway is a multi-lane signalized radial arterial connecting

the northwestern parts of Northern Virginia suburbs with employment

centers in Rosslyn and downtown Washington. As an uncontrolled access facility, Lee Highway serves the needs of local as well as through traffic. Observing and analyzing patronage on these lines permits a comparison of fare elasticities for two levels of bus service—the express

service operated on the Shirley Highway, and the conventional bus service

operated as the Route 2 and Route 3 lines on Lee Highway,.

The census tracts which comprise the Shirley Highway Corridor and the

Lee Highway Corridor are indicated in Figure b in Appendix B. Tables 11

and 12 in Appendix B list estimated 197^ median family income for census tracts adjacent to the Shirley Highway and the Lee Highway. The median

income in the Lee Highway Corridor ($21,180) is higher than that in the

Shirley Highway Corridor ($20,036). This may not be true for bus patrons, however. Median family incomes in census tracts adjacent to the

Lee Highway bus lines could be weighted towards higher income values by

the McLean residential area, whose southern border the lines traverse;

the residents of these very high income areas may not, in general, com- mute by bus. On the other hand, the bottom quarter of the census-tract

median family incomes in the Shirley Highway Corridor are notably lower

than those for the Lee Highway Corridor.

Selected operating characteristics of the bus service observed in this

study are given in Table 1.

3
TABLE

1:

BUS

ROUTE

OPERATING

CHARACTERISTICS,

A.M.

INBOUND

PEAK

PERIOD oZMH 00 '•d- 30

<; c/3 c2 h w Fd >« X

MD

rH i i <r <r 13

Ea Ed co O piH

03 03g

Fd

C/3 iJ

a* H LO 30

cq

m

X Fd CM

12. i i 71

m

O

rH

<5H

35 cn 30 <r 0 OM 3 X O H

Fa"

13. i i <r

m rHrH CO

wwP —-

00

—

w CO CO rH 30 • • • 0 a ca CP O 03 03 o 03 ro 03 Z M r>- i—

uo

O pi CM o H oz Fa

X

M

O in 30

H • • • . <$ Z Ed 30 o r-. X CM O O X rH 30 X Fd M

P-i

H

O Pi

CM

O * * X

X

03 P-i CP EC

X 30 30 0- w * • • • 03 <C < O * Fd 00 rH o cn ON

EE> 00 #* rH

m rH

pp Pi rH P eg

g

X

O

03 Fa Ed

03 \

Fd 03 o * 03 30 NO rx

Pi

W •*

g

M • • P-i g o \r 03 X 00 X o CO cn r\ * rH rH 30 rH

Fd P rH as Fd

X

>L >2

<C <3 #» oo 3 Z 00 00 m 00

34 Ed CP * • • • O Fd •» 33 X rH 30 o 00 M pi <3 * * rH <r rH

Fd Fa 00 Fd 03 >* X Ed Fd >

(H

•* 03

»—3 M 9\ z 30 CM co

Pi 03 CP •* * a • • M 33 Ok EH g 03 X rH m o CO 00

<3 * <* #\ <* rH CO

03

U Fd o Cd Xw

a

CO /““N 03 • CO •

CJ •H rH rH 03 M d •H AJ • • H H g 3 Ed

rH 03 3 P-I Pi H <U ^ * a) -h a) Ed Pi 4-i 03 X a) g hi Fd 3 co CO s w 3 3 CO X T3 H o a) 0) CO CO O E3 O 0> 0) 03 5 O Pi rH rH £o CO 0) Pi -H pi a) S 03 z < •H •H 03 QJ rH 3 1 ex

c2 CO £ g s d -H cn QJ 0)C 03 C/3 Fd <3 3 CO o. g 3 E 3 -H C H EG CP FE 4-1 CO X CP -H CP g O 03 ED U O 3 Fd rH H <13 AJ O X u 03 x rH rH rH 3

Pi P ctt P u ex ^ AJ Ctf fH Cd rH *H

H

O

H 5 d> ai

X o o S <u S 03g 03 Pi 03 Pi i 00 P Fd *H H 1 > d d

EDH 0) 3 E AJ 03 03 03 0)

d CD CO CP a cu 3 C 03 O C d G > 03 > E3 CO O P Z O Pi a> OH O O FX O CO CP . rH CM oo -3- in 30

A

slash

</)

indicates a

peak-period

variant

of

the

route’s

service;

this

generally

supplements

(not

replaces)

the

regular

service

during

tTie

route’s

peak-period.

Some

local

mileage

of

these

bus

routes

is

traversed

at

expressway-like

speeds.

This

is

included

in

the

figures

of

row

2.,

"Number

of

Miles

on

Expressway".
Prior to the September 1, 1975 fare increase, bus fares in both the

Shirley Highway and the Lee Highway Corridors had been stable for a long time. The Shirley Highway Corridor bus service (Routes 7, 8, 17,

18, 20, and 27) was originally operated by the Alexandria, Bancroft, and

Washington (A.B.&W.) Bus Co. This company last increased fares in July

1970. The Lee Highway Corridor bus service (Routes 2 and 3) was originally operated by the Washington, Virginia, and Maryland (W.V.&M.) Bus

Company. This company last increased fares in October 1969. All privately-owned, Washington, D.C. metropolitan area commuter bus companies

were consolidated under public ownership within METRO in January 1973.

METRO analyses indicated that A.B.&W. bus fares were higher than comparable W.V.&M. bus fares, and so in July 1973 METRO reduced A.B.&W. fares

slightly to make them compatible with W.V.&M. fares.

Before the September 1, 1975 fare increase, typical bus fares from

Northern Virginia to downtown Washington ranged from $.60 to $.90. After

the fare increase, these fares ranged from $.75 to $1.20. The fare increase varied from 20 to 33 percent, increasing with length of trip.

Northern Virginia bus fares before and after the September 1, 1975 fare

increase are described in Appendix C, pg. 36. Fare zones are, shown in

Figure 5, pg. 37-

Two characteristics of the study situation complicate interpretation of

the empirical results. The particular date (September l) selected for

the fare increase to become effective was not ideal from the standpoint

of studying price elasticity: significant changes in travel patterns

normally occur at the end of the summer when people return from vaca- tions and autumn school terms begin. Thus it was necessary to adjust

observed modal travel demands carefully for monthly (seasonal) variation,

prior to studying the interrelationship of price and patronage. Additional ambiguity can be attributed to the rapid growth of Northern Virginia: new apartment and office buildings are opening continually.

Since this study dealt with bus patronage by route during intervals of

time stretching over two months, it is likely that some data were affected by changes in demand unrelated to price. Although obviously incorrect data points were eliminated (see Section V below) and the aggregate elasticities were probably not overly affected, there is no way

be certain that the demand changes used in the calculations are solely

the result of -fare increases.

The observational phase of the study consisted of observing and recording

bus patronage on selected bus routes in the two corridors, both before

the fare increase, and then long enough afterwards to expect patronage

patterns to have stabilized. During the same observation periods, auto

vehicle volumes and auto occupancies were recorded at a previously es- tablished screenline on the Shirley Highway. (Auto vehicles and auto

^See references [l] and [2] in Section VII.

2

See Figure 1, pg. 8, and [3], pg. 99*

5
passengers were not counted on Lee Highway. ) After adjustments were

made in passenger and vehicle flows to account for seasonal variation,

the effects of the fare increase on patronage and travel patterns were

analyzed, and measures of elasticity were estimated. This outline of

procedures is elaborated in Sections III and IV.

6
Ill . Data Acquisition and Refinement

As stated earlier, the purpose of this study is to quantify intermodal

and intertemporal changes in commuting patterns resulting from an in- crease in peak-period transit fares. In general, data collection procedures were as follows: bus patronage was observed, both before and

after the fare increase, on selected routes in the Shirley Highway cor- ridor and the Lee Highway corridor. (Table 6 contains a list of the se- lected bus routes.) During the same period, automobile traffic volumes

were observed on Shirley Highway and recorded by person occupancy classification. Bus patronage was observed during peak and off-peak time

periods, whereas only peak-period Shirley Highway auto traffic was observed and recorded. Adjustment factors were developed to correct for

seasonal variation. Fare data were obtained from METRO and were aggregated. The remainder of this section describes the specific data-gathering techniques employed. Section IV discusses the techniques used in

analyzing the data.

Field data were collected on August 19 and 20 and on October 7 and 8,

1975- (The 19th and the 7th, and the 20th and the 8th, were Tuesdays

and Wednesdays respectively. ) The weather was clear on all four of

these days, which were not contiguous with legal holidays. Mean volumes

for the two "before" days and the two "after" days were used in all subsequent analyses. The former period was immediately prior to the fare

increase, and the latter was believed to be sufficiently long afterward

for patronage patterns to have stabilized.

On Shirley Highway, METRO field personnel recorded the numbers of bus

passengers by route number on all Shirley Highway buses between 6:00 a.m. and 7:00 p.m. as they entered the freeway segment of their trip. Locations where field data were collected are shown in Figure 1. Automobile

usage on Shirley Highway was observed at an established screenline location near 20th Street in Arlington, Virginia. Field personnel recorded

the number of autos by passenger occupancy classification from 6:30 a.m. to 9:00 a.m.

In the Lee Highway corridor, bus patronage was observed on two bus lines

(route numbers 2 and 3) at two locations, shown in Figure 1. These two

bus lines, serving North Arlington and Falls Church, Virginia, were observed between 6:00 a.m. and 7:00 p.m. on the aforementioned dates.

Since seasonal variation in traffic flows between August and October is

significant, it was necessary to correct for this factor before quantifying the effects of the fare increase. Data to compensate for seasonal

variation in transit demand were obtained from METRO. Seasonal variation

data were available for the Shirley Highway for both bus patronage and

automobile traffic. Comparable data for the Lee Highway were not available and had to be deduced from a broader data set. Separate seasonal

patronage adjustment factors were derived for the Route 18 Shirley Express Buses, the other Shirley Express buses, and the Lee Highway con- ventional buses, as described below. Average weekday bus patronage was

7
P P

•H P P P P

X5 ,P o P &H Ch

cti Ph X o •H

(L) -p i—1 H O < pp t— E p i—1 O w -=t P

<M E r* LA o VP O P p c— CA O Eh Ov CM •H - i—1

CM

Ww Ph -P •H P X! • e E bD p •H > p CO p

PH

— r\ >5 Ph ctf Xi p O •H

-P P O

•H Ph > E z c o CO ctf 'P o p X

<L> rP CD O bO O H P P P <

T) •H -P o -p P p Ch S • Ph P p P P !>> i> K O rP < 8
obtained for August and October 197*+ for the Shirley Highway bus routes,

and is shown in Table 2. Table 3 summarizes the new bus service which

was added between August and October 197*+* Table 4 shows estimates of

average weekday patronage by month for 197*+ for the Arlington and Alexandria Divisions of WMATA.

Formally, the Route 18 Shirley Highway Express Bus seasonal adjustment

factor (the factor by which to multiply August observations to obtain

"corresponding" October figures) is 2551 passengers f 2460 passengers

= 1.04. However, the additional 3 buses on the Route 18 line constituted

a 4Jo service increase which in all likelihood both induced new travel

and diverted some travel from the auto mode, so that the August-toOctober change in Table 2 does not reflect only seasonal variation. The

actual seasonal variation is thought to lie between 1.00 and 1.04.

Similarly, for the Shirley express bus service other than the Route 18

line, the apparent relationship between August and October demand is

11155 passengers t 10255 passengers = 1.088. However, the additional

10 buses during the peak-period resulted in a similar service increase

which in all likelihood both induced new travel and diverted some travel

from the auto mode. Thus the calculated 1.088 probably does not reflect

only the seasonal variation. The actual seasonal variation is thought

to lie between 1.05 and 1 . 09 .

Data for estimating seasonal variation for the Lee Highway bus lines

were obtained from Table 4 since line-specific information was not available. On a Division-wide basis for 1974, the apparent relationship between August and October demand is 31*015 passengers v 28,697 passengers

= 1.08, for the Arlington Division which includes the Lee Highway Bus

lines. The comparable relationship for the Alexandria division which

includes the Shirley Bus service is 64,884 passengers t 60,526 passengers = 1.07. Recall that the comparable figure for the Shirley express

bus service other than the Route 18 line, from Table 2, is 1.088. From

these figures the range 1.05 - 1.09 for the seasonal patronage variation

factor, October with respect to August, as determined in the "rest of

the Shirley buses excluding Route 18 service," appears reasonable for

use on the Lee Highway Bus lines as well.

These results are summarized in Table 5 below, which indicates the range

of values for the ratio of October to August peak-period bus patronage

which were selected for use in this research.

Bus routings, service frequencies, travel-time data, and fare and fare- zone data were obtained from schedules, published tariffs, and a largescale system map furnished by METRO. Since passengers boarded the buses

in a number of fare zones prior to observation and recording of patronage, it was necessary to estimate an average fare "before" and an average

fare "after" the fare increase.

9
TABLE 2: AVERAGE WEEKDAY BUS PATRONAGE, SHIRLEY HIGHWAY1

Bus Service August 1974 October 1974

Route 18 Shirley Highway Express Buses 2,460 passengers 2,551 passengers

Shirley Highway Express Buses except 10,255 11,155

Route 18

TABLE 3: NEW BUS SERVICE ADDED BETWEEN

AUGUST AND OCTOBER 1974 1

Bus Route Designation

16G2

18H

27B

29Z

Number of Bus Trips

3 in AM Peak Period, 3 in PM Peak Period

3 in AM Peak Period* 3 in PM Peak Period

3 in AM Peak Period, 3 in PM Peak Period

4 in AM Peak Period,

4

in PM Peak Period

Source: telephone communication with John Fularz, Office of Planning, METRO.

2These two bus routes do not figure in the main study, but their 197^ patronage

data were combined with those of other Shirley Highway bus routes in estimating

seasonal adjustment factors.

10
TABLE k: ESTIMATED AVERAGE WEEKDAY BUS PATRONAGE1

Year Division

1974 Arlington

I97 U Alexandria

August October

28,697 31,015

60,526 64,844

Notes for TABLE 4

1. Virginia divisions of METRO did not carry significant numbers of

public school students, so the impact of school trips was neglibible.

2. METRO developed these daily patronage estimates by recording daily

deposits of fares collected by operating Division; estimating ave- rage fares by Division; and dividing (daily) fare deposits by the

estimated average fare.

3. The Arlington Division is the former W. V. & M. Bus Co. The Lee

Highway Routes are a part of this division. The Alexandria Division

is the former A. B. & W. Bus Co. The Shirley Highway Express-Bus

Routes are a part of this division.

Source: telephone communication with John Fularz, Office of Planning, METRO.

11
TABLE 5: RANGE OF SEASONAL PATRONAGE VARIATION FACTORS USED

Bus Service

Ratio of October to August Peak

Period Bus Patronage

Lower Bound Upper Bound

Route 18 Shirley Highway

Express Buses

1.0 1.04

Shirley Highway Express

Buses except Route 18 1.05 1.09

Lee Highway Bus Lines 2 & 3 1.05 1.09

12
Individual bus lines and established fare-zone boundaries were located

on a large-scale map of the existing street system. Based on the distribution of destinations on individual bus lines (e.g. those along

Route 18), and the path length and relative intensity of development

within each of the fare zones traversed prior to observation of patronage, a high estimate and a low estimate were obtained for the average

fare paid on each route, both before the fare increase and after the

fare increase occurred. For most bus lines a "best" judgemental estimate of the average fare "before" and "after" the fare increase was also made. Thus the fare data by bus line could be arrayed as follows:

(illustrative figures):

Before Fare Increase After Fare Increase

Lowest Fare Estimate $.70 $ -90

Highest Fare Estimate .90 1.05

"Best judgemental" Estimate .71 .93

Subsequent elasticity computations (see Section IV-(a)) involve only

relative (i.e., percentage) fare increases; the "high" estimate of the

relative fare increase would be selected in this illustrative example

as the larger of

.90-. TO 1.05-.90

•TO

°r .90

and similarly for the "low" estimate.

This choice, avoiding the "super-high" extreme of (l.05-.70)/.70, in

effect assumes that the distribution of passengers by origin/destination

fare zones did not change significantly after the fare increase. The

estimated fares paid by passengers observed at the counting locations

are presented in Table 6.

13
TABLE

6:

ESTIMATED

AVERAGE

PASSENGER

FARES

BY

TRANSIT

ROUTE

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Os CM * * r 3 3

(U 4J

Cxi ^ #s

w *• * o °z

O co

X 3 z X CO r 0s 0S 0S o * • * CQ - W H H >

os oa •> pa •>

O •>X . , s X X CO * rs 0s #» 0s w

(X » 0S * < * w « Cm pH C-{ H < * * < •> #i 00 

o r*v Q

pa

r"-

O 3 00 3 rH Os •“* z x CM CM cn CM

m z

lU
IV. Method of Analysis

This section describes the method used to quantify the impact of the increase in the peak-period bus fare upon: (a) peak transit patronage

for express transit service (on Shirley Highway) and for conventional

transit service (on Lee Highway); (b) off-peak transit demand; and (c)

auto usage and carpools.

(a) Elasticity of Peak-Period Transit Patronage with Respect to

Price.

The changes in transit demand with respect to increase in price will be

described by the use of demand elasticities. The elasticity of transit

demand with respect to fare (price) is the proportional change in demand

divided by the proportional change in price; i.e.

P. dQ.

e = dQ./Q

i

* dP /P. = ^ . (1)

1 1

Q. = F. (P.

)

l i i

where e. is the elasticity for the i^*

1 route, P. is the fare, and Q. is

the demand function. It is well-known that if e.>(-l) then a small increase in P. will increase gross revenue, P.Q., and if e.<(-l), a small

increase in P^ will decrease gross revenue.

In this study, data were not sufficient to estimate the functions Q.=

F.(P.), so it was necessary to choose an approximation to Equation tl).

Among many possible approximations, the following were chosen:

e

.

l

§. =

4 ~ V«11

Ap

i /pil

’ (2)

£nQ

i2-toQii

(3)

S,nP . „-£nP .

,

i2 il

Here subscripts "l" and "2" refer to "before" and "after" respectively,

while AQ. = Q. n-Q., and AP. = P. 0-P._, . The ratio has been called the

l i2 il l i2 ii l shrinkage ratio ana is a measure frequently used by transit operators

in the United States to forecast the impact of a price change on revenues and patronage. The shrinkage ratio describes the relative change

in patronage with changed fares. The ratio e. , which is also frequently

employed, is known as the arc elasticity of demand with respect to fares.

*"See [ 9 ], pg. 2-1+ and [6], pg. 26-28.

15
For very small fare changes, §. will he very close to For larger

changes, the arc elasticity §. will he larger than £ for fare increases

and smaller for fare decreases. Both measures are defined so that price

elasticities are negative for typical demand schedules.

In this research, demand has heen measured in transit passenger trips.

Demand could also have heen quantified, at least conceptually, in terms

of passenger miles. For demand elasticity measurements on the Shirley

Highway buses where trip length is relatively constant, the choice of

demand measure would have less impact than for the Lee Highway buses

where passenger-trip length is much more variable.

Equation (2) follows from Equation (l) by replacing differentials with

finite differences; Equation (3) follows in the same manner after Equation (l) is rewritten in the equivalent form e. = d( JlnQ. )/d(£nP. )

. Sample calculations are given in Appendix D.

As noted, one goal of this study was to compare the elasticity of express

bus service (operating on the Shirley Highway) with that of conventional

bus service (operating on the Lee Highway). It was therefore necessary

to aggregate separately the individual elasticities of the bus routes

traversing the Shirley Highway, and those traversing the Lee Highway.

Unfortunately, there is no uniquely "correct" formula for such aggregate

elasticities. The particular formula used , refers to the quantities

Q = total demand = EQ^

R = total revenue = ER. = EP.Q.

x 11

and is given by

e = R dQ/[Q dR - R dQ].

Relative to the ’’composite price"

P = E(Q./Q)P.

obtained as the demand-weighted average of the fares on the individual

lines, this formula has the advantage that the customary equations em- ploying elasticities to predict the consequences of price changes, namely,

dQ = e(Q/P)dP , dR = (l+e)Q dP,

remain valid. On the other hand, the aggregation method given by Equation (1*) lacks the theoretically desireable "consistency principle" that

when all e^ have the same value, e should also have this value.

1

Suggested by J. M. McLynn.

1

6
The shrinkage- factor and arc-elasticity approximations obtained from (U) are

(5)

( 6 )

The summations were taken only over routes exhibiting negative elasticities. As discussed in section (b) , positive elasticities were attributed to exogenous changes unrelated to the fare increase.

(b) Shifts in Transit Demand from Peak to Off-Peak Periods

Chi-square tests were used to determine whether there was a significant

shift from peak to off-peak transit usage. One-tailed Chi-square tests

were performed both on individual bus routes and in combinations com- prising (l) the total Shirley Highway express buses and (2) the Lee Highway conventional bus service.

The choice of a one-tailed test over a two-tailed one (for a change in

the pattern of utilization) may be questioned. After all, economic

theory admits the existence of the "Giffen effect," where an increase in

peak bus fares might increase the demand for peak bus service. With

some trepidation, we adhere in this study to the customary assumption

that transit price elasticities are negative. Thus, if the increase in

the peak fare of a route corresponded to an increase in peak patronage

(relative to off-peak), this was attributed to the exogenous forces

discussed earlier in Section II.

(c) Shifts in Automobile Usage

Chi-square tests were performed to see whether there was a significant

increase in use of autos or carpools relative to bus service. As in

section (b), these were one-tailed tests. As discussed in section III,

the data used applied to the Shirley corridor alone, since data on auto

usage were not collected along the Lee Highway.

§ = R^Q/^AR-RjAQ],

5 = [ R

1

2Q

il

An (Q

i 2 /Qii )]

v[Q

1

ERil£n(R

i 2

/R. 1 )-R

1IQ

il £n(Qi 2 /Qil )].

See [7], page 115. The Giffen effect occurs when an increase in the

price of a good, all other prices held fixed, results in an increase in

the demand for that good. In some situations this is consistent with

utility-maximizing behavior by consumers.

17
V. Results

A. Elasticity of Peak-Period Transit Demand

The elasticities of demand estimated for individual routes are shown in

Table 7*

As discussed in Section III, reasonable extrema of both seasonal variation factors and the increase in average bus-route fares were selected

to bound a plausible range for each variable. A "best judgemental estimate" of the average fare change was also prepared, and an associated

estimate of elasticities made. One would naturally expect observed

elasticities with respect to demand to carry a negative sign, since

patronage should decrease with increase in fare. However, in this study

the data for some bus routes which operate on the Shirley Highway indicated positive elasticities; several bus routes exhibited elasticities

whose signs change from positive to negative within the bounds of seasonal

adjustment factor extremes. As note^. earlier, we do not believe these

were instances of the Giffen effect; it seems more likely that the in- creases were caused or brought ^bout by other variables which were not

"tracked" during this research. Such variables might include changes

in employment centers, and/or the opening of large apartment house

facilities. The positive elasticities were assumed to be caused by

"experimental error", and are not reported by bus route nor considered

in preparing aggregate elasticities.

The aggregate elasticities for the Shirley Corridor and the Lee Corridor

routes are indicated in Table 8. The estimated arc elasticity for the

Shirley express bus service (ranging from -.301 up to -.21*3) is substantially different from that for the conventional Lee Highway bus service

(which ranges between -.81*3 and -. 671 ). This result tends to support the

hypothesis that elasticities of transit demand with respect to price are smaller for premium-type express bus service than for conventional bus

service.

Table 9 permits a comparison of the findings of this study with peakperiod transit elasticities estimated in other studies.

^See footnote 1 , pg. 17 . 2Other studies of transit elasticities have also reported occasional instances where positive elasticities have been observed. For an example

see Section VII of [ 11 ] , Table 7, page 5 . See [10] for one researcher's hypothesized distribution of shrinkage

ratios by type of service offered.

18
I

CO

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axa

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•H •H •H •H •HX

w

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X CU

C/3 00 03 00 03 00 03 00 03 00 03 00X 03 00

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•H

X

X

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X •H CO COX

CJX

O

X

a

X cj

X 0 X 0 X 3 CJX

l-l

X

X

X

XXX

X

X

X

X

X CO

X

X < CO < CO < CO C CO < CO < CO X <3 co oX X 0s #* X X * — z Z CO 3 X z N

Eh 0s

M 0S

r 0 X

O

w TO

Eh * Z X

r 0s 0 w cu * co * >4 0S C3 X O X > W 0 w "

0s 0s 0 CO 0 X X* 03 CO CQ X w cu 0

CQ 0s CQ rc

r #» 03

H z 0s 3 O CO <3 S X « X 0 C < r" r 00 0 0 Eh

r%. s 00 co

X

X rH

X CM CM

X co

19

2F,M,T

Arc

Elasticity

-1.189

-1.153

-1.324

-1.707

Shrinkage

Factor

-0.869

-1.159

-0.950

-1.267

3K,V

Arc

Elasticity

-0.673

-0.817

-0.792

-0.963

Shrinkage

Factor

-0.520

-0.650

-0.602

-0.752
TABLE 8: SUMMARY OF PEAK-PERIOD ELASTICITY

BY TYPE OF SERVICE

Low High

Seasonal Normalization Seasonal Normalization

HIGH EST. LOW EST. BEST EST. HIGH EST. LOW EST. BEST EST.

OF % FARE OF % FARE OF % FARE OF % FARE OF % FARE OF % FARE

INCREASE INCREASE INCREASE INCREASE INCREASE INCREASE

[IRLEY HIGHWAY EXPRESS BUSES

c Elasticity -.301 -.290 -.298 -.289 -.21*3 -.21*9

irinkage Factor -.266 -.253 -.263 -.258 -.n211 -.217

:e highway bus TRADITIONAL SERVICE

c Elasticity -.671 -.712 -.679 -.795 -.81*3 -.801*

irinkage Factor -.622 - .656 -.627 -.75^ -.795 -.760

20
TABLE 9: COMPARISON OF PEAK-PERIOD TRANSIT ELASTICITIES'

WITH THOSE FROM OTHER STUDIES

Observed Peak- Period

Arc Elasticity of Demand

with Respect to Price (Fare) Comments

-0.2 Urban buses, London, England, cl973. See

[9]

,

Section 6.1. '

-0.27 Stevenage Superbus Experiment, Great Britain,

cl973. See ’[9], Section 6.1.

-0.27 Urban buses , London, England, 1969. See

'Section VII, [9], Section 12.1.

-0.51 Urban buses, Chicago , 1969. See [12],

page 140.

-0.12 N.Y.C. Subway 1966 Fare Increase. See

f 11 ] , page 5 and Appendix- D.

-0.29 Shirley Highway Autumn 197*+ Data. Crosssectional model-derived elasticity (Model

II) calculated at the means of all variables,

See [13], pg. III-20.

-0.27 Shirley Highway Data collected "before"

and "after" 1975 fare increase. (Mean

value of "Best" estimates of % fare increase

for "Low" and for "High" seasonal normalization factors.)

-0.7*+ Lee Highway Data collected "before" and

"after" 1975 fare increase. (Mean value

of "Best" estimates of % fare increase for

"Low" and "High" seasonal normalization

factors .

)

21
Examination of the limited set of peak-period price elasticities estimated in other city studies seems to support the hypothesis that demand

elasticities vary with the type of transit service offered. Demand for

conventional bus transit service operating over arterial streets, as in

the first four studies , tends to be more elastic than demand for premium

rapid rail service operating on a separate right-of-way, such as in the

fifth study.

On the other hand, there are much more limited travel options to and from

the financial district of New York City (the scene of the fifth study).

It should be noted that the first three studies were all made at least

five years ago in Great Britain, where travel options might also have

been more limited than in the United States. Thus these results might

not be comparable with observations in the U.S.

The sixth estimate was calculated by evaluating a closed- form theoretical

expression for elasticity using mean values of data collected in a sur- vey of Shirley Highway Corridor travelers in the autumn of 197^* This

particular mathematical formula predicting elasticity was obtained fjom one variant of J. M. McLynn's "fully competitive mode choice model".

The close agreement of the theoretically-derived elasticity evaluated

with 197^ data, with the (independent) empirical estimate from data

before and after the 1975 price-increase, lends support to the validity

of both results.

B. Shifts from Peak to Off-Peak Transit Usage

There was little evidence of a shift from peak to off-peak use of bus

services. Of the fourteen bus routes which were analyzed, only two

showed a shift significant at the five percent level upon application of

the Chi-Square test. These were routes 2M and 2T (westbound) and 2F, 2M,

and 2T (eastbound) in the Lee Highway corridor. Since the 2 route offered the slowest service of all routes studied, we may speculate that

individuals using these routes (prior to the change in fare) had more

intertemporal flexibility than is the norm.

Three combinations of bus routes were tested for intertemporal shifts:

all routes in the Shirley corridor; all routes in the Lee Highway corridor; and all routes together. None of these aggregates showed a shift

from peak to off-peak usage at the 5% level of significance.

C. Shifts of Peak-Period Commuters from Bus to Auto Mode

In addition to the above tests for intertemporal shifts of commuters,

analyses were made to detect shifts in travel mode. The distributions of

inbound peak-period commuters using the Shirley Highway, by vehicle oc- cupancy and by mode, are indicated in Table 10. Application of the Chi

Square test to these modal data indicates there was no significant shift

from bus to auto after the fare increase.

1

See [13] Chapter III

.

22
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SHIRLEY HIGHWAY

BUS

PASSENGERS

139 ^

persons

14675

persons
NOTES:

These

data

were

collected

at

the

Shirley

Highway

Screenline

Station

near

20th

Street

in

Arlington,

VA.

CO

coqj

jh -u Cl •H X CJ qj •H

J-I 0) CO X CO u rH

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qj CO 3 E

-C 3 cO

O

c— 30 rH CJ

2k
Since there was no significant shift of commuters from the bus to the

auto mode after the fare increase, the impact of the fare increase on the carpool mode would be expected to be negligible. Surpri singly, the

number of persons per ear increased slightly, from I.58 persons per car before the fare increase to I .67 persons per car after. Figure 2

shows the distribution of peak-period auto person travelers by size of

carpool for all inbound Shirley Highway Lanes. Although these data are

not seasonally adjusted, there is a substantial decrease in two and

three-person carpools and a substantial increase in four, five and sixperson carpools. With substantially the same number of auto person com- muters before and after the fare increase, this suggests a slight drop

in the number of auto vehicles using the Shirley Highway. This actually was the case, with 12648 autos before and 124-79 autos after the fare

increase traveling inbound during the 6:30-9AM peak period. Had these

data been seasonally adjusted, the modified figure for this decline

would have been greater.

Figure 3 shows the distribution by carpool size of peak-period auto

person travelers using the Shirley Highway express lane. Again one observes a dramatic increase in the number of four, five, and six-person

carpools. There was also a substantial increase in the number of automobiles using the Shirley Highway express lane during the peak-period,

from 901 vehicles before the transit fare increase to 1566 vehicles

after. On the regular Shirley Highway lanes, the number of automobiles

traveling inbound during the peak period dropped, from 11,747 vehicles

before to 10^913 after the transit fare increase.

The change in the distribution of travelers among the various sizes of

car pools is probably totally unrelated to the transit fare increase,

instead resulting from commuters returning from vacations and joining or rejoining carpools.

It should also be noted that the Shirley Highway Corridor is not a totally isolated corridor. There are several alternative highway routings,

and even alternative bus routes for some commuters within the corridor.

However, since disruption to commutation by external phenomena such as construction was minimal during the periods of observation, it is believed that the observations utilized herein truly reflect conditions

within the study area at the time.

25
o

<

n

FIGURE- 4- DISTRIBUTION Op 6:30j-9AM PEAK-PERIOD INBOUND SHIRLEY HIGHWAY

AUTO- PERSONS &Y CARPOOL SIZE BEFORE AND AFTER TRANSIT FARE- INCREASE!. ALLlSHIRLEY HIGHWAY LANES

LEGEND

After i r : 2-day (8i, 9 , Oct.. 1975)

Mean, Peak-Period Auto Persons . i

Before -2-day <-±9y m- Aug.: 1975)-

Mean, Peak-Pferiod Auto

Persons. Ray Data^ Not

1 2 3 4 5 6>7 ALL

26
NUMBER

OF

6:30-9AM

PEAK

PERIOD

INBOUND

AUTO

PERSONS

(DRIVERS

&

PASSENGERS)

(.;

.

|,t,i

i

•,

OIVISIOV

<0

!H|

.I'll

1000

2000

3000

—1

•pjrr.ii

i £F_ ^

|

1

i ;

DI 5TRTETT noN o' 7 6; 30'^9AM peak-pe (10 b i: ABOUND SHIRL EY HIG1IWAY A JTO

P-ER IONS Ml 5XNG--E CPRESS- 1ANES BY CA (pnm. vTZf. R F.FORF ikCR ease. EXPRE ;s LAN : AUTO ; ONLY

1 '

j i

1

•

]

1

j i

i

1

I — r

:

!

,

-

:

: j S*ee Figure 2 . or Legend

Js

c

j i

i

s 1 c

>

J 5

j

!

j

. -

i

• • : 5

!

:

: 1

:

• N

! 5

•

j j

1

|

J

:

:

c

c

1

i \

1 4 5 6 2 7 CARPOOL SIZE INCLUDING DRIVER

27
VI. Conclusions

This study, which was conducted in Northern Virginia, began with four

objectives: To observe and report on the elasticity of peak-period

transit demand with respect to price; to identify and quantify the impact of a peak-period transit fare increase on auto usage and carpooling;

to determine whether a peak-period transit fare increase caused any

measurable shift in passenger usage from peak to off-peak times; and to

compare the elasticities observed on the Shirley Express Buses with

those observed on conventional bus service in the same metropolitan

area and determine if elasticities observed for these two qualities of

transit service are significantly different.

These objectives have been fulfilled.

Peak period arc elasticities were determined as follows:

Shirley Highway Express Buses -0.301 to -0.21+3

Lee Highway Conventional Buses -0.81+3 to -0.671

Comparable shrinkage ratios are as follows:

Shirley Highway Express Buses -0.266 to -0.211

Lee Highway Traditional Buses -0.795 to -0.622

In both instances, values for the Shirley Highway Express Bus service

are considerably different from those for the conventional bus service

operating on the Lee Highway.

No noticeable impact of the transit fare increase on the number of

travelers by auto was observed. The seasonally unadjusted (raw) numbers

for peak period inbound auto persons traveling on the Shirley Highway

were 19,950 persons in August, and 20,902 in October after the transit

fare increase. Application of a seasonal adjustment would likely indicate a decrease in auto person trips after the transit fare increase.

At the same time, an overall increase in vehicle occupancy was observed

on the Shirley Highway: from I .58 persons per vehicle before the transit

fare increase to 1.67 persons per vehicle after the increase. This in- crease in persons per car came from other auto passengers, since the total number of inbound autos traveling on the Shirley Highway during the

peak-period dropped from 12,61+8 vehicles before the transit fare increase

to 12,U79 after the increase. These data again are not seasonally adjusted. The decrease in auto vehicle trips would be more pronounced had

seasonal adjustments been applied. The increase in vehicle occupancy

was probably caused by the return of workers from vacation.

There was little evidence of a pronounced shift from peak to off-peakperiod after the peak-period transit fare increase. Of the fourteen

bus routes which were analyzed, only the Route 2M and 2T westbound and

the 2F, 2M, and 2T eastbound operating over the Lee Highway showed a

28
significant shift at the 5% level of significance. Three combinations

of bus routes were studied for intertemporal shifts: all Express Buses

operating on the Shirley Highway; all bus routes operating on the Lee

Highway; and all bus routes combined. None of these combinations indicated a significant shift to off-peak usage.

The overall impact of the peak-period fare change (an increase ranging

from 20l to 33I) is quite minimal. This is to be expected. The last

fare increases on the bus lines investigated in this study were instituted at the beginning of the decade. During this same period gasoline

and oil costs increased by approximately 62%, according to a recent

edition of the Survey of Current Business (U.S. Department of Commerce).

Thus even with a peak-period fare increase of from 20 to 33%, transit

fares remained a great bargain in transportation.

The differences in the elasticities exhibited by the two types of bus

service considered in this study - express buses operating on exclusive

freeway lanes, and conventional bus service operating on a signalized

radial arterial street - tend to confirm that different segments of the

public transit market have different elasticities. Translating this

into rudimentary pricing policy, one might consider raising fares more

on premium transportation services than on traditional services. This

would tend to relate user charges more systematically to the services

received. As long as the aggregate transit demand elasticity with re- spect to fare remains greater than -1, the net increase in revenues due

to higher fares will exceed the net loss in revenues attributable to

lost patronage.

Additional studies should be directed at a comparison of peak-period and

off-peak-period transit elasticities. These results will provide a factual basis for development of a comprehensive transit fare policy.

Difficulties were encountered in this study in determining values for

(route) average fares and for seasonal variation factors, and in identifying exogeneous phenomena which affected transit patterns. These

data problems could have been avoided at high cost, by interviewing individual travelers and keeping track of these travelers (and identifying

new ones) before and after the transit fare increase. This would have

yielded a more precise estimate of transit elasticity with respect to

price. However, it would be of little use to a transit operator con- sidering the revenue impacts of a possible fare increase, since he is

not likely to spend the money necessary to collect the data on his system that would be needed to apply such results with comparable precision.

1

See [10].

29
VII. List of References

1. Charles River Associates, Cambridge, Mass., Measurement of the Effects of

Transportation Changes , prepared for Urban Mass Transportation Administration, U. S. Department of Transportation, August 1972.

2. Campbell, D. T. , and Stanley, J. C., Experimental and Quasi-Experimental Designs for Research , Rand McNally, Chicago, 1966.

3. The National Bureau of Standards, The Evaluation of the Shirley Highway Express-Bus-on- Freeway Demonstration Project/Final Report , US Dept,

of Commerce, Washington, DC, 1975. (National Technical Information

Service PB 247 637)

4. Tarshis, Lorie, Modern Economics, an Introduction , Houghton Mifflin

Company, Boston, MA, 1967.

5. Schmidt, H. E. and Campbell, M. E., Traffic Estimation , the Eno Foundation,

Saugatuck, CT, 1957.

6. Kemp, Michael A., "Some Evidence of Transit Demand Elasticities" , the

Urban Institute, Washington, DC, 1973.

7. Samuelson, Paul A., Foundations of Economic Analysis , Harvard University

Press, Cambridge, MA, 1947.

8. Kemp, Michael A., "The Empirical Investigation of Transit Demand" , Working Paper 708-53, the Urban Institute, Washington, DC, Nov. 1971.

9. Bly, P. H., "The Effect of Fares on Bus Patronage", Report No. 733,

Transport and Road Research Laboratory, Crowthorne, Berkshire,

England, 1976.

10. Ficarra, John T., "The Fare Increase: An Opportunity to Define Markets"

Pas senger Transport , Vol. 34, No. 20, p. 4, Washington, DC, May 14, 1976^

11. Lassow, William, 'Effect of the Fare Increase of July 1966 on the Number

of Passengers Carried on the New York City Transit System," Highway

Research Record . No. 213, Washington, DC-, 1968.

12. Talvitie, Antti, "A Direct Demand Model for Downtown Work Trips,"

Transportation , Vol. 2, No. 2, pp . 121-152, July 1973.

13.

Field, John, Refinement and Extension of the Fully Competitive Mode

Choice Model, Final Report to the National Bureau of Standards, U.S.

Dept, of Commerce, Contract No. 5-35779, by DTM, Inc. Bethesda, MD, 1977.

30
A. BUS SCHEDULES:

Appendix A: Supplemental Data Sources

Published by the Washington Metropolitan Area

defining service immediately before and after the 1975 for the following routes:

Transit Authority (WMATA)

,

fare increase of September

(1) Route 1 (2) Routes 1, 3, 20 & 25

(3) Routes 1, 2, 3, 4, 20 & 24

(4) Route 2 (5) Route 3

(6) Route 3Z

(7) Route 4

(8) Route 5 & 25

(9) Route 5-X

(10) Route 6

(11) Route 7 (12) Route 8

(13) Route 16

(14) Route 17

(15) Route 18

(16) Route 19G, Y

(17) Route 20E

(18) Route 27

(19) Route 28G

(20) Route 29

(21) Route 29Z

B

.

MAPS

1. From Here to There by Metrobus, January 1, 1976, published by the Washington Metropolitan Area Transit Authority (WMATA)

.

2. Northern Virginia Metropolitan Area 1976-77, published by the American

Automobile Association (AAA).

C. OTHER WMATA PUBLICATIONS:

Operators Guide. Fares-Fare Zones & Proper Issuance & Acceptance of Transfers

effective Sept. 1, 1975, Washington Metropolitan Area Transit Authority (WMATA).

Tariff of the Washington Metropolitan Area Transit Authority on Metrobus

Lines within the Washington Metropolitan Area including Intrastate and Interstate operations, effective Sept. 1, 1975. Regular Route Tariff Number 2 issued

by Jackson Graham, General Manager, WMATA.
Appendix B

Tracts, ]

i

32

TABLE 11

Estimated1 1974 Population and Median Income in Census Tracts Adjacent to

Shirley Highway Bus Lines

Tract Number Population 2 Median Income Measure Ranking

4064 5594 $24125 7

4055 3908 20032 15

4054 2399 24833 4

1*053 6 ll 8 12293 25

4043 1917 13361 22

4042 15385 24233 6

4040 5564 21523 12

4039 3066 23310 8

4038 9045 22715 10

4036 2906 14336 20

4035 6154 13629 21

4034 7115 21221 13

4033 1429 26949 1 4023 6611 21809 11

4021 3419 17194 19

4020 2036 22796 9

4015 2535 20719 14

4014 3310 25991 3 2015 3511 11417 26

2010 3727 9025 28

2009 4321 24431 -j 5 2008 5765 l844l~5 16

2006 3951 17373 18

2005 5364 8760 29

2004 6011 8591. 30

2003 9563 18057^ 17

2002 4594 26532_ 2 2001 10929 9683^ 27

1030 2529 13119 23

1029 5940 12944 24

Unweighted average income = $18,315-

Median = $20,036.

International Data Development Corporation, "Estimates of Population and Income for

Tracts in Washington, D.C. SMSA( 1974 ) " , National Technical Information Service Document

PB 2U5 331-

2

Income measure treats unrelated individuals in a household as separate units, but

combines the incomes of family members.

Population and income estimates were given for subareas making up each of census

tracts 2001, 2003, and 2008. In these cases, the tract median income was approximated

by averaging the median incomes of the subareas comprising the census tract* weighted

by the estimated populations of the subareas.

34
TABLE 12

Estimated1 1974 Population and Median Income in Census Tracts Adjacent to

Lee Highway Bus Lines

Census Tract Number Population Median Income Measure Ranking

5002 6125 $15555 27

5001 3036 20964 18

UlOl 5717 26800 4 4099 9363 23115 11

4098 3238 20348 20

4097 2730 26241 7 4096 3934 27317 3 4093 4964 27462 2 4092 23610 21398 15

4091 4983 21247 16

4090 2457 18186 24

4089 450 18421 22

4087 1326 26666 5 4086 7040 18642 21

4079 3261 28379 1 4078 5268 26658 6

4075 6797 15935 25

4074 5369 15460 28

4073 7131 26155 8

4072 4156 15947 19

4071 4758 15633 26

4070 4091 10638 33

4069 6649 10868 32

4068 10685 21112 17

4067 5145 12018 31

4o66 2427 21517 14

4o46 2320 22632 12

4045 2628 18200 23

3112 2670 24118 10

3111 4684 13478 30

3110 3293 21533 13

3109 4548 24906 9

3108 4643 13804 29

Unweighted average income = $20,344

Median = $21,l80.

International Data Development Corporation, "Estimates of Population and Income for

Tracts in Washington, D.C. SMSA(l974)", National Technical Information Service Document

PB-21+5-331.

Income measure treats unrelated individuals in a household as separate units, but

combines the incomes of family members.

35
Appendix C: Northern Virginia Bus Fares

A. PEAK-PERIOD INTERSTATE FARES BETWEEN VIRGINIA ZONES AND DOWNTOWN

WASHINGTON, DC :

Old Zone

Number

New Zone

Number Before

1 Sept. 75

Fare

After

1 Sept. 75

Trips within one zone Trips crossing one zone boundary

Trips crossing two zone boundaries

Trips crossing three zone boundarj.es

Trips crossing four zone boundaries

Trips crossing five zone boundaries

$ .50 $ .60

.60 .75

.70 .90

.80 1.05

.90 1.20

$1.00 $1.20

AND AMONG VIRGINIA ZONES :

Fare

Before After

1 Sept. 75 1 Sept. 75

$ .40 $ .50

.50 .65

.60 .80

.70 .95

.80 1.10

$ .90 $1.10

C. OFF-PEAK FARES :

Prior to September 1, 1975, there was no distinction between peak fares

and off-peak fares. The fares indicated in A and B above as "Before

1 Sept. 1975" applied, based solely upon origin and destination of trip.

After September 1, 1975, zones are no longer applicable to the determination of off-peak fares:

All intrastate off-peak trip fares are $.40

All interstate off-peak trip fares are $.60

Note

The peak period is defined in the tariff and on the published transit

schedules as 6:30 am - 9:00 am and 3:30 pm - 6:00 pm weekdays. All other

times are considered as off-peak travel periods.

D. WMATA FARE ZONES:

See Figure 5 on next page.

36
\

\

FIGURE 5 WMATA FARE ZONES

3 n
Appendix D: Illustrative Calculation of Approximate Elasticities

We illustrate the calculation of approximate elasticities using data

observed before/after the 1966 fare increase from 15c to 20c in the New

York City subway system.

Table 7 of [11], page 5- gives

Decline in turnstile registration from financial district

stations in period 4 p.m. - 7 p.m. = 3.4%.

So: ^

= - 3 . b% , q

2

/ Qi = 0.966

Also: AP

P

5C

= 33%

15C

For shrinkage factor:

, P

2 /P = 1.333.

. =

A_q , AP _

-. 034

e Q

7 P .33

For arc elasticity (see Equation 7 of [9],

e = £n(Q

2 /Q

1 )/£n(P2 /P

1

)

= 0-966 =

£n 1.333

= -0.103

page 15)

38
4BS- 1 I4A (HE V 7-7 11

U S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBI.K ATION OR REPORT NO. 78-1462 (DOT)

2. Ciov’t Accession

No.

3. Recipient’s Accession No.

4. UTLE AND SUBTITLE 5. Publication Hate Elasticity of Transit Demand with Respect to Price:

A Case Study 6. Performing Organization ( ode

7. AUTHOR(S) Ralph E. Schofer 8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON. D.C. 20234

10. Project/Task/Work Unit No. 2050404

11. Contract/Grant No. DOT-AT-40018

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Office of Service Methods and Demonstrations

Urban Mass Transportation Administration

U.S. Department of Transportation, Transport Bldg,

2100 2nd St., SW, Washington. DC 20590

13. Type of Report & Period Covered

Final

14. Spon soring Agency Code

15. SUPPLEMENTARY NOTES

To be published in outside journal.

16. ABSTRACT (A 200-word or tess (actual summary o( most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This report describes the methodology and the results of an empirical

study of peak-period transit demand elasticity with respect to price (fare).'

Field observations were structured to capture the reactions of morning (inbound) commuters to a peak-period fare increase introduced on September 1,

1975. The study is limited to bus and automobile travelers on the Shirley

Highway and bus passengers on the Lee Highway, both in Northern Virginia.

The Shirley buses provide express service on exclusive freeway lanes, whereas

the Lee Highway buses provide traditional service on a signalized radial

arterial. Various impacts are identified, quantified and compared.

Demand for service on the Shirley Highway Express buses is less elastic

(“ 0*274 to —0.218) than that for the traditional Lee Highway bus service

(“0.535 to -0.273). There was little evidence of passengers on either service

shifting travel outside the peak-periods to avoid higher fares. The fare

increase had no effect on auto travel. These results suggest applying different pricing policies to different types of transit service.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Elasticity; elasticity of transit demand; pricing; transit planning;

transit pricing

18. AVAILABILITY [xH Uni imited

[ For Official Distribution. Do Not Release to NTIS

[

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