The transit pricing evaluation model: A tool for exploring fare policy options

0191-!Mi’lR?104031!-IIU)3.0010

Tranrpn Rrr...4 Vol. 16A. Ho 4. pp 313-323. 1981 Pnnkd m Grenl Bnlam

Pergamon Press Ltd

THE TRANSIT PRICING EVALUATION MODEL: A TOOL FOR EXPLORING FARE POLICY OPTIONS ROBERT CERVERO Department

of City and Regional Planning. University

of California,

Berkeley, CA 94720, U.S.A.

(Received 19 Augusf 1981) Ah&net-A model is presented for probing a range of impacts which could be expected when instituting a new transit pricing system. The model weights on-board ridership survey responses based upon disaggregated fare elasticity estimates. In addition to forecasting the potential ridership and fiscal consequences of a new fare structure. the model incorporates revenue and cost data on specific users’ trips to estimate changes in farebox

recovery as well as effects on efficiency and equity. This paper describes the working components of the model followed by a demonstration of its use. Empl,oring fare, cost, and trip-making data from the Southern California Rapid Transit District, the system’s current prlcmg practices are examined. Long distance users were found to pay disproportionately low fares in relation to the cost of their trips, while very short riders were generally overcharged for their tries. A distance-based pricinr! scenario is then designed and tested with respect to its ability to remedy some of thd problems associatedwith

iat fares.

LNTRODUCTIOK

The planned phase out of U.S. Federal operating assistance means that alternative revenues will have to be found if current levels of service are to be maintained. The farebox represents the most obvious revenue source for replacing withdrawn Federal dollars. Clearly, higher future transit fares can be expected almost universally. However, it’s also likely that transit managers will increasingly turn to more innovative pricing arrangements which capture some of the differential costs of providing services. More finely graduated distance-based pricing and peak/off-peak fare differentials, in particular, will likely gain in popularity during the eighties. The ability to accurately estimate the impacts of alternative fare proposals certainly deserves a place among the transit planner’s repertiore of skills. Not only is it necessary to examine the likely ridership and fiscal consequences of a fare change, but one must also be able to identify who will gain and who will lose in the process. Recent studies have indicated that today’s transit pricing structures tend to be grossly inequitable, with shortdistance, off-peak users typically cross-subsidizing the often more afluent long distance, rush hour commuter (Cervero, 1981; Pucher, 1981). Minimizing the maldistributive impacts of any fare change is particularly important in view of transit’s social role in providing mobility opportunities to disadvantaged groups. This paper presents a working model, coined the Transit Pricing Evaluation Model (TPEM), which was designed for forecasting the full range of impacts which could be anticipated with a fare change. The model is akin to that developed by Ballou and Mohan (1981), with the notable exception that TPEM was designed primarily for examining structural changes in transit pricing. Moreover, demand is estimated as a non-linear function of price changes, and cost estimates (including those associated with new fare collection systems) serve as an integral component of the analysis. The model is partiTRCA)

Vol.

16, No.

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cularly suited to examining the possible efficiency and equity repercussions of alternative fare policies. MODEL FEATURES

TPEM was originally developed for assessing the likely consequences of various fare scenarios proposed for three California transit properties (see Cervero et 01. 1980). A fairly disaggregate model structure was adopted so that distributional impacts could be assessed at the individual passenger level. Accordingly, actual patronage information, such as that collected from on-board surveys, constitutes the most important data inputs into the model. In particular, date on passengers’ fare payment, trip length, time period of travel, and demographic characteristics are essential to the analysis. In addition to estimating the likely revenue and ridership effects of a fare change, efficiency and equity consequences are also assessed. In broad terms, efficiency relates to the ability of a price structure to capture the marginal cost of serving specific trips while equity is concerned with how disparities between trip costs and trip fares are distributed among various socioeconomic groups. The criterion variable employed by TPEM in evaluating both efficiency and equity is essentially a farebox recovery ratio disaggregated at the level of the individual user (i.e. a ratio of what share of a given user’s trip costs are met through the farebox). This can be measured for individual passengers by taking a ratio between the fare revenue paid for a particular trip and the estimated cost of serving that trip. The cost of a single journey can be estimated by dividing the daily cost of serving all trips on a particular route by the total daily passengers on that route. However, an even smaller unit cost can be acquired by indexing a route’s daily cost by passenger-miles, thus providing a detailed estimate of the average expense incurred in serving each mileage increment of travel on the route. This becomes a reasonable proxy for measuring marginal or “incremental”

ROBERT CERVERO

!I4

costs in that distance increments provide the most pragmatic yardsticks for gauging relative cost differences among trips. In order to make fare data comparable to cost data, it’s necessary to index fare revenue on the basis of passenger-miles as well. Thus, the actual criterion variable used in TPEM is a ratio of revenue and cost passenger-mile (hereafter abbreviated per RPM/CPM). Taking the fare paid by a passenger and dividing it by the length of his or her trip. then, yields RPM for the trip: when ratioed to the cost per passengermile (CPM) associated with the particular route of travel. an approximate index of the trip’s farebox recovery ratio (or RPM/CPM) is produced. TPEM evaluates efficiency by comparing the mean RPM/CPM estimates generated for various categories of trip distance and time-of-day. For example, an efficient fare structure would return comparable shares of costs through the farebox for short as well as long trips and for peak and off-peak journey alike (holding the systemwide subsidy level for all trips constant); in other words, the mean RPM/CPM estimate for all trips under a mile would be similar to that for all trips exceeding, say, 25 miles. In a similar sense, the model assesses equity by comparing the mean RPM/CPM among various categories of socioeconomic status. Thus, based on the income, ethnic, auto ownership, etc. responses from on-board surveys, differences in mean RPM/CPM levels among demographic groups can be used in examining equity impacts. Figure I summarizes the key elements of TPEXI in a step-wise fashion. The model initially calls for the analyst to specify an alternative to a system’s current pricing policy. This is typically done as a response to certain deficiencies which exist. such as insufficient farebox returns or gross price inequities. So. fares associated with specific trip distances, time periods. etc. are delineated at this step. Data from on-board surveys are then used to drive the model. Survey data provide an initial index for estimating ridership responses to a fare change. Using disaggregate fare elasticity estimates, data

Based on Pro posalr Analysis of the Lkflclencles CUT- rent Efflclency In Price F”lll ,” and _._.-I

1 i I

cases (records) are then weighted according to the sensitivity of specific user groups to price changes. Adjusting each survey record to reflect an individual passenger’s relative “frequency of use” under the fare policy of interest, overall revenue and ridership impacts can then be estimated by aggregating the adjusted sample. By merging cost and revenue data which account for both changes in fare levels and collection costs, a pricing option can be further analyzed with respect to its efficiency and equity repercussions. It’s perhaps appropriate at this point to mention what the model doesn’t do. The intent of TPEM is only to estimate the direct fiscal, ridership, and equity impacts of a fare change, and not to derive a socially optimal fare for a particular transit operation. The model assumes that an appropriate fare has already been determined by a responsible policy body, reflecting a community’s views on the external benefits and social role of public transportation. Furthermore, it assumes that other factors which influence ridership-such as travel speeds, safety, schedule adherence, etc.-remain the same after a fare change. Thus, TPEM examines the impact of a new fare independently of any other improvements. In sum, it serves principally as a tool for estimating the “after” effects of a fare change within a fairly short range context and isolated from any service or operational improvements. The remainder of this paper traces through the flowchart shown in Fig. I in greater detail. The paper concludes with a demonstration of how TPEM might be used to examine a fare proposal.

.ANALYSlSOF RIDERSHIP AND REVENUE IMPACTS

In forecasting the likely ridership and fiscal effects of a fare proposal, TPEM weights individual responses based on the fare elasticity estimate associated with each user’s trip. entire

Additional

Adjustmnt

3at.a

and

Inputs:

Cost

Weighted

responses

sample

to estimate

of

are

then

the overall

aggregated patronage

over

RevenuL

Data:

$%k;

nean

RPH/CPI(

Estimates of New Fare IPolicy Proposal and and Evaluate Effi ciency

[ValUeS

Fig. I. Siepuisc >urnrnarL of thr tranjlt pncing evaluation model.

the

response

I

The transit pricing evaluation

to a fare change. Fare elasticities represent the key link in the analysis since estimates of ridership impacts are only as good as the elasticity assumptions used to derive them.

315

model

The midpoint index expresses change in relation to the arithmetic average of the “before” and “after” price and ridership level. A final non-linear measure in arc elasticity Kemp 0974a) defines it as:

log Qta- log Qo “O=logPb-logP,. Formally, fare elasticity can be defined as the proportional change in transit demand resulting from a proportional change in price. Estimates between 0 and - 1 mean that the proportional change in ridership is less than the proportional change in fare (i.e. inelastic demand). Anything less than - I. on the other hand, indicates eiastic demand. With few exceptions, past studies have shown transit ridership to be relatively insensitive to price changes, with elasticities typically within the range of -0.1 to -0.5 (see, for example, Lago et al., 1981). Several alternative approaches are found in the transportation literature for computing fare elasticities. The most theoretically satisfying measure is the poinf elasticity, defined as:

where Q represents ridership and P represents price. Point elasticity expresses the slope of a transit system’s demand curve at any single tangent. The measure assumes, however, that a mathematical relationship can be established between Q and P based on some expression of transit users’ marginal utilities for travel. In practice, the scarcity of longitudinal data has hampered the computation of this measure. Also, attempts to capture price-demand relationships longitudinally have proven difficult due to the compounding effects of other variables over time, including changes in service levels, exogenous factors, and secular growth. As an alternative to causal demand models, elasticity can be measured on the basis of only two observationsridership before and after a fare change. The simplest approach is to draw a line between data points and compute a constant elasticity slope. Grey (1975) call this measure a line elasticiry, defined as: ?I=

HQ.- Qb)/Qbl+KP, - Pb)/Pbl

(2)

where subscripts b and a refer to the respective ridership and price before and after a fare change. This approach assumes a linear demand curve and measures elasticity in terms of initial ridership and price. It also assumes symmetry-demand changes at a similar rate regardless of whether prices increase or decrease. Intuitively, the line measure seems inconsistent with the industry’s prevailing view that transit’s demand curve is non-linear. Two other elasticity indices respond to this criticism of the line measure. Grey offers a midpoint elasticiry index which establishes a hyperbolic-type relationship between any two points of fare and ridership change. He defines it as: Pt, - Pa Oh - Q. ‘7m=l/2(Q,+Qb)i1/2(~b+~,).

(3)

(4)

Using common logarithms of Q and P, it also establishes a hyperbolic relationship between any two observations of price change. Choosing a fare elasticity measure As mentioned earlier, the unavailability of longitudinal data suitable for demand modeling often precludes the estimation of point elasticities. Which alternative concept, then, is most appropriate for measuring elasticity from “before” and “after” data points-line, midpoint, or arc? With very small changes in fare, all of the approaches provide a close approximation to point elasticities (i.e. as the limit of a change in price approaches zero, a change in demand will be the same regardless of the shape of the curve at a particular point). As fare changes become larger, however, the ridership effects attributable to the three alternate concepts differ considerably. The sensitivities of the three approaches to various price changes can be compared. Given a fixed elasticity estimate, a current price and ridership level, and a proposed new fare, future demand can be easily projected. Equations (j)-(7) present the appropriate formulae for computing future ridership (Q.) using the line, midpoint. and arc concepts respectively.

Q Ptmldpnt)

=(]-qlm)QbPb+(l+qm)QbPa (I+ tl,Pb + (1 - q,)P,

(6)

Qq,,c, = antilog It), log PO- ?.log Pb + log QbI. (7) Setting 7 = -0.3, P,, = 50 4, and Qb = 100 passengers, the effects of each elasticity measure on future demand projections (Q,,) were computed for a range of hypothetical future fares (P,). Results are summarized in Fig. The figure shows that the rate at which ridership changes from the origin (Pb, Qb) varies among the elasticity concepts. Differences also depend on whether the hypothesized new fare (P.) is an increase or decrease from SOcents (Pb). The line approach yields a constant elasticity throughout the range of possible fare changes. Compared with the other measures, it generates sharp ridership losses with large increases in fare. The midpoint and arc approaches, in contrast, produce demand curves which are convex to the origin. As prices deviate more from the origin (Pb), the demand curve approaches the axes (P, and QO) asymptotically under both measures. The estimated ridership effect of any pricing proposal is obviously quite sensitive to the particular elasticity

316

ROBERTCERVERO

notes : = Price

‘b

before fare change

:

Price after

=

RIdership

before fare change

Oa

:

Ridwshro

after

7

=

Fare elosticfity

pa ‘b

fore

change

fare

change

?I 60-

70

80

90

100

II0

120

130

I 140

Qa

Fig. 2. Demand relationships for alternative elasticity estimates (for n = - 0.3, Pb = 50, and Qb= 100).

concept employed. Grey (1975, p. 79) remarks that the choice between approaches “should be governed primarily by which is likely to give the best approximation to the true demand curve over the range of price changes being considered (emphasis added).” It follows that whenever large price changes are being considered, demand curves in Fig. 2 should be contrasted on the basis of price extremes. We can turn to previous studies to gain some insight into what shape transit systems’ demand curves usually take as a function of price. Past demand models have consistently produced loglinear relationships between fares and ridership, similar in shape to the arc and midpoint curves (see e.g. Frenkena, 1978; Kemp, 1974b; McFadden, 1974: Nelson, 1972; and Schmenner, 1976). Thus, whenever large fare changes are being contemplated, the line approach seems the least appropriate elasticity measure. However, which of the other two approaches theoretically most closely approximates the point measure-midpoint or arc? Several empirical findings shed light on this question. Kemp (1974a) and Donnelly (1975) found ridership responses to fare increases (forward elasticities) to be higher than from fare decreases (backward elasticities). For Atlanta’s and San Diego’s fare hikes and fare reductions, for example, Kemp computed forward elasticities in the neighbourhood of - 0.50 to - 0.55 and backward elasticities ranging from -0.20 to -0.40. Figure 2 indicates that the arc measure produces slightly higher ridership losses from fare increases than does the midpoint measures, and slightly larger ridership gains from fare decreases. Thus, the arc measure tends to be a little more elastic than the midpoint. It also more closely reflects the findings of Kemp, Donnelly and others regarding the patronage impacts of fare increases. Given the trend toward higher rather than lower fares, the arc measure was adopted for TPEM because it more closely matches empirical evidence and it also provides more of

a worst-case view of the possible ridership impact of fare increases. Ridership and revenue computations TPEM uses the structural form of eqn (7) to estimate each passenger’s “ frequency of use” (Qa,) on the basis of the new fare (P,,) associated with his or her trip. For modeling purpose, eqn (7) can be reexpressed to reflect the unique response of each sample passenger i: Qui= antilog (vi log P,, - vi log Phi- log Qb,) (7a) where: Q0 = relative “frequency of use” after fare change Qt, = relative “frequency of use” before fare change P, = price after fare change P,, = price before fare change i = individual passenger (survey response) ni = arc elasticity associated with passenger i’s trip. This equation projects future usage on the basis of disaggregate arc elasticities associated with the trip of passenger i. (Preferably. elasticities disaggregated and cross-tabulated in terms of distance, time-of-day, and user socioeconomic characteristics are employed.) Since each record from an on-board survey typically represents a single passenger, eqn 7a can be written in terms of a weight ( MT,) by setting Qh, equal to I: WT = antilog (q,) log P,,, - 7, log P,,) where Wr, = ridership response weight for new fare icy.

18) pol-

!li

The transit pricing evaluation model

where

C = cost of rider i’s trip on route j during time period k (including additional coliection costs) under ne* fare policy PM = passenger-miles traveled h! rider i j = route surveyed k = time period i = individual passenger n, = number of routes surveyed n, = number of time periods n, = weighted sample size for route r and time f.

PCRZD= percent change in system ridership under new fare policy n = initial sample size from on-board survey. The revenue impact of a new pricing policy are next computed as the product of the proportional change in ridership and the proportional change in average fare:

TPEM then analyzes a fare proposal’s efficiency and equity impacts by contrasting RPM/CPM differences among categories of trip distance. time-of-day. and user demographics. Together, these criteria provide a full picture of a proposed fare policy’s possible range of economic and distributional consequences.

TPEM then measures aggregate ridership impacts of a new fare policy in terms of the percent change in initial patronage (PCRID) by summing over all observations: 2 [antilog (qi log Pai PCRID = 100 ,=, 1

l)i 1%

pbi)l

n

-n i

(9)

CASE STUDY OF TPEM

PCREV = 100.

where PCREV = percent change in system revenue under new fare policy. As revealed by the equation, new fare systems can be expected to generate higher revenue returns whenever price increases are relatively greater than patronage losses. ANALYSIS OF EFFtClENCY

Ah’D EQUITY IMPACTS

TPEM evaluates the potential efficiency and distributional consequences of a fare proposal by analyzing changes in RPM/CPM among various categories of users’ trip distance, time-of-day, and socioeconomic status. New fares are initially assigned to sampled users based on the proposed pricing structure. Under a distance-based proposal, for example, each sampled passenger’s new fare would be estimated by multiplying the updated price rate times his or her trip length. Trip costs for each route are also adjusted to reflect the additional collection and administrative expenses associated with the fare proposal. In addition, estimates of passengermiles change at the rate of the weighted increase in ridership, meaning that cost per passenger-mile estimates also change for each bus route and time period under study. Combining these data, the mean RPM/CPM (i.e. systemwide farebox recovery) of a fare proposal can be computed from eqn 11:

where R = price paid by rider i under new fare policy

TPEM was first employed in evaluating several fare scenarios written for three California transit properties. pricing One of the scenarios. a distance-based arrangement tested for the Southern California Rapid Transit District (SCRTD) serving the Los Angeles metropolitan region. is presented in this section. Prior to testing alternative SCRTD fare programs, the system’s fare policy at the time of the research was examined. During fiscal year 1978-79, the period from which the most recent patronage and cost data were available, SCRTD priced basic services at a uniform rate of 45 cents per ride. SCRTD’s predominately flat fare structure was supplemented by distance-based pricing on only a few freeway express services. The system also offered an assortment of prepaid pass programs as well as special elderly and youth discount programs. Initially, patronage responses to an on-board survey administered on thirty representative SCRTD routes during the spring of 1979 were gathered for the study. Proportional random sampling produced over 10,000 data cases which were then weighted to eliminate any undersampling of elderly, minority, and short-haul patrons. From the survey, each sampled user’s revenue per passenger-mile (RPM) was computed by dividing fare payment by trip length. In cases where patrons boarded with passes, cash fare equivalents were estimated based upon known usage rates per month for the particular pass type. Estimating the cost per passenger-mile associated with each trip proved to be much more difficult (see Cervero, et al. 1980, for a detailed discussion of the cost allocation methodology). Initially, a model was developed which allocated systemwide operating costs among bus routes based primarily on a route’s vehicle miles and hours of service. Referred to as the “unit cost” method, this allocation approach was used to estimate daily operating expenses of the thirty bus routes under study. The models were then respecified using more detailed data from SCRTD’s individual operating divisions in an attempt to capture unique cost characteristics of different service types (i.e. express vs local) and operating environments (i.e. suburban vs central city) (see

318

ROBERT CERVERO

was 0.66, and the rates continued to decline with distance, reaching a value of 0.06 for journeys beyond 25 miles. Since trips under one mile accounted for 10% of SCRTD’s total journeys, a enormous cost burden was being shouldered by a significant minority of riders. The breakdown of recovery ratios by time-of-day clearly revealed that off-peak users cross-subsidized their rush hour counterparts. Figure 4 indicates that midday services, which accommodated approximately 45% of SCRTD’s daily trips, yielded the best returns on costs, while peak services appeared the least cost-efficient. In terms of equity, the results were mixed (Table I). Surprisingly, the net transfer effect of SCRTD’s fares was found to be mildly progressive, although the relationship was statistically insignificant. With regards to riders’ “vehicle availability” status, those without access to an auto were found to cross-subsidize users with other travel options only to a small extent. In general, crosssubsidization also hurt those who were college-age. female, and making medical trips. On the whole, the fare penalties imposed on these groups were quite modest, however. In sum, SCRTD’s flat fare structure was found to be largely inefficient, with long distance and peak period users paying extraordinarily low fares for their services. From a distributional standpoint, the incidence of crosssubsidization did not appear regressive; however, those traditionally thought to be most dependent upon transit were found to Lose more under current pricing than other user groups, though the overall transfer effect tended to be modest.

Cherwony, 1977 and Dierks, 1975, for further discussions on this approach). Thus, cost formulae applied to routes operating in lower density areas under relatively free flow conditions differed from those used in estimating costs of inner city, congested services. Each route’s estimated daily costs were next factored into peak and offpeak components using an allocation procedure which accounted for time-of-day differences in rates of labor productivity and capital depreciation (see Cherwony and Mundle, 1978, and Levinson, 1978 for discussions on these adjustments). This refinement served to attribute the cost impacts of restrictive labor contracts (which prohibit the hiring of parttime workers, split-shift duties, etc.) and the overall scale of transit infrastructure primarily to peak users. Cost per passenger-mile estimates were then computed for each of SCRTD’s routes under study by time-of-day. Among the thirty routes examined, the mean CPM during the peak period was 17.61 with a standard deviation of 16.6 e while the mean off-peak CPM was 14.6~ with a standard deviation of 23.512.It’s apparent that the cost models employed effectively captured the differences in unit costs among bus routes and time periods, particularly given the wide variance in estimates. Based on a particular sampled user’s route and time period of travel, then, the CPM estimated for his or her trip was merged with the fare data to produce the RPM/CPM index. This process essentially allowed SCRTD’s systemwide farebox recovery ratio of 0.46 to be factored among its patrons, accounting for differences in passengers’ fares. trip costs, and travel characteristics. The analysis of RPM/CPM differences among the twelve trip distance categories shown in Fig. 3 revealed tremendous disparities in fare payment. Those riding less than a mile appeared to cover a far greater share of their costs than other users. The under one mile group generated a revenue-to-cost ratio of 2.22. By comparison. the farebox recovery rates for the one to two mile group

Testing a distance based pricing sceranio One of the scenarios proposed in response to SCRTD’s flat fare deficiencies involved pricing services as pure linear functions of distance. This scenario called for pricing all services at a base fare of IO&.with Se per

2.5

2.0 -

f =: f PI

i .s 11

1.0 -

Average

Farebox

0.5 - _ __

il

~____

System Recovery Ratio equals 0.463

_-_____-_____-____-_-_______________-_ i;-,

~.f---jl---lr-lfy-l~i

I

oCl

l-2

2-3

3-4

4-6

6-8 TRIP

Fig.

3. Comparison

of

E-10

?ENCTH

SCRTD’s RPM/CPM

IO-12

12-15

IS-20

imiles)

estimates

by trip

distance

categories.

20-25

‘25

The transit pricing evaluation

model

319

0.6

.7 .6 Farcbox

.5 f Y

System Average Recovery Ratio

0.463

equals

._ ---

_ -

_-

.4

B .3 .2 .1 0

1 AI4 Peak

(6-9

An)

-

Hidday (VA-3PI

PM Peak

(3-6

TIME

PM)

Evening

(I

(6-l 1 PM)

IP-6A)

PERIOD

Fig. 4. Comparison of SCRTD’s RPM/CPM estimates by time period.

Table 1. Equity impacts of Scrtd’s current fare structure Group RF’M/CF’H: .524

.407

.43? .371

.560 .492

.460 .429 .445

.602

.460 .477

.402 .440

.6OB .434 .559 .460 .41B

.369 .191

.449 .461 1.044 .463

ROBERT CERVERO

320

mile surcharges for journeys beyond one mile. except for students and elderly passengers who would pay distance increments of 6k and 4&per mile respectively. A regular user traveiing 8 miles would therefore pay around 70h, while a 25 mile journey would run over $2. Although a stage or zonal structure with surcharges of IO-15b per step might prove politically more feasible. this particular scenario was tested principally for the purpose of equalizing fares in relation to trip costs for all SCRTD users. In employing TPEM to evaluate this scenario, two additional data inputs were required. One, fare elasticities were specified for particular types of trips by using a systemwide long run elasticity estimate of - 0.1, and adjusting it to reflect the sensitivity of specific user groups to fare changes. The range of elasticity estimates shown in Table 2 were estimated using findings from past empirical studies which found short-distance, older, higher-income, and male trip-makers to be somewhat more price-sensitive than the average user (see Kemp, 1973, Pratt et al. 1977 and Lago and Mayworm, 1981). Though sensitivity testing on low to high ranges of elasticity estimates was employed in the original modeling of scenarios, the findings presented in this paper are based solely on mid-range estimates of long run responses to fare changes (i.e. 6-12 months following fare revisions). In addition, fare collection costs associated with more complex, graduated pricing were projected and incorporated into the model. The scenario assumed that finely graduated fares would require that a ticket issuing machine plus two cancellers be installed aboard most of SC’RTD’s 2600 vehicles. In addition, automats installed at key loading points on all of SCRTD’s routes were assumed. Finally, a corps of roving inspectors was assumed for enforcing the graduated system. Other incidental costs which could be expected include those related to maintenance. operations, fare handling, and

I

5,000-9.999 :o.ooo-19.999 20.000

k

and

Over

retrofitting vehicles. Table 3 presents the combined annual depreciation and operating cost estimates of operationalizing a finely graduated fare system on the SCRTD system. Such pricing could be expected to raise SCRTD’s current fare collection costs by over 700%, while increasing the system’s total annual operating cost by 2.4%. Accordingly, the CPM estimate of each bus route was increased by a factor of 1.024 under this scenario to incorporate the transactive cost of instituting graduated pricing. TPEM employed eqns 9 through 11 in estimating the ridership and revenue impacts of this scerario. Table 4 reveals that overall ridership levels would probably remain virtually unchanged while revenue income could be expected to increase by over 11%. This fare arrangement could also be expected to raise the system’s overall recovery rate to .50%, a growth of almost 9%. It’s apparent from Fig. 5 that pure distance-based pricing could virtually eliminate SCRTD’s current fare disparities. In fact, no cross-subsidization is discernable among distance groups: long-haul journeys appear as financially productive as short distance ones. Under this scenario, the RPM/CPM ratio of trips under one mile could be expected to fall by 275% while the recovery rate for journeys exceeding 25 miles would likely increase over 700%. Finally, a pure distance based pricing arrangement could be effective in neutralizing current RPM/CPM differences among time periods as well as among socioeconomic classes of riders (Table 5’1. In particular, graduated fares would appear advantageous to SCRTD’s female and medical trip users. In sum, these modeling results suggest that a more differentiated price structure could correct many of the problems linked with SCRTD’s flat fare structure. Fares finely graduated by distance provide a means of approximating marginal cost pricing. Distance pricing also

Table !. SCNII disaggregatefare elasticity estimates .-___

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321

The transit pricing evaluation model Table 3. SCROD collection cost estimates for graduateddistance-based pricingscenario COST ESTIMATES

COLLECTION COST COMPONENTS

On-Board Ticket Dispensers and Cancellers Q $8500 per vehicle (including farebox costs) ................... ....

........

$17,000,000

Curbside Automats Q $10000 each ......... ............... . ........ 16.000.000 Total Capital Costs ..................................... ........ 33,000,000 ife .... Annual Depreciation Q 8: interest and 15-20 year service 1, Annual Inspector Cost Q $17000 per Inspector ... .........

........

1.700,000

Other Annual Operating and Maintenance Costs Q 25% of Capital Depreciation ....................................

903,930

Projected Total Annual Collection Cost ...........................

6,219,180

Current Total Annual Collection Cost .............................

980,000

Difference Between Projected and Current Costs ...................

5.239.180

Difference as Percent of Total System Cost .......................

2.40%

Table 4. Estimated

ridership and revenue impacts of graduated distance-based

SCROD pricingscenario

X Change in System Ridership ................................

+0.1

% Change in System Revenue Income ...........................

+11.3

Mean RPM/CPM (i.e.,

system farebox recovery ratio) ..........

% Change in Farebox Recovery Ratio ..........................

seems to offer some equity benefits: by setting fares in line with the incremental costs of serving users’ trips, those most in need of transit appear to gain. In addition, graduated fares could improve the system’s overall financial picture by generating much-needed additional income. Moreover, the ridership impacts of finely differentiated fares would probably be minimal: patronage losses due to higher long-haul prices would generally be counter-balanced by gains in short distance usage. Ignoring questions regarding user acceptance, automated fare collection technology would appear to be a cost-effective investment in SCRTD’s case in that the system’s overall farebox recovery ratio could be expected to reach fifty percent. Collectively, these findings augur well for distance-based pricing as a preferred fare policy. sumhlARYREMARKs

With transit officials increasingly looking to the farebox to solve their financial problems, a better understanding of the full consequences of instituting a new fare system is essential. An analytical model was presented for exploring the likely effects of fare changes on efficiency, equity, ridership, and revenue productivity. The model analyzes a fare strategy by weighting sample cases from passenger surveys based on disaggregate arc price elasticity estimates. Incorporating the additional costs of collecting graduated fares into the analysis, the model can be used to examine changes in the average farebox recovery ratio of different types of trips and services. The Transit Pricing Evaluation Model was employed TR(A) Vol.16,No.4-F

3,615.250

.50 +8.7

in examining SCRTD’s current pricing structure as a prelude to the design of a remedial fare scenario. SCRTDs predominately Aat fare structure was found to embody considerable inefficiencies, particularly with respect to its ability to capture the cost of serving long distance trips. SCRTD’s short distance users were found to pay on the order of twelve times as much per mile of service as the average rider. Price disparities were also quite prevalent between peak and base periods. Overall, the redistributive consequences of SCRTD’s current fare practices appeared to work against those who are traditionally most dependent upon transit. A finely graduated pricing scenario was designed in response to current deficiencies and tested using TPEM. This arrangement could be expected to reduce inequities and improve the system’s financial performance while essentially retaining current patronage levels. Local decision-makers, however, must balance these goals against those related to passenger convenience and fare simplification. Given the inherent conflicts among various pricing objectives, it’s imperative that the relative advantages and disadvantages of alternative pricing approaches be confronted through informed public discussions. TPEM is intended to serve as an information tool in assisting transit managers probe the policy implications of different fare options. As such, it’s only an aid to constructive policy-making and cannot begin to replace managerial judgement and experience in transit pricing decision-making. Through interactive computer facilities, the model can be used for sensitivity testing as well as quick response analysis. Many standard software pack-

ROBERT CERVERO

System Average Farebox Recovery Ratio equals 0.501

I

l-2

2-3

3-4

4-6

6-8

8-10

10-12

12-15

20-25

15-20

25

TRIP LENGTH (miles)

Fig. S. Comparison of SCRTD’s RPM/CPM estimates by trip distance categories under the graduated pricing scenario.

Table 5. Efficiency and equity impacts of graduated distance-based SCRTD pricing scenario

RPM/CPM For: Current Pricing

Graduated Pricing

% Change

Time Period: Base

.55

.5a

+

Peak

.37

.42

+ 14

5

Annual Family Income: ~$15,000

.45

.50

+

11

.4a

.50

+

A

None

.47

.51

+

9

i

.45

.50

+

11

~$15,000 Vehicles Available:

Language Back-: English-Speaking

.46

.49

+

7

Spanisn-Speaking

.48

.52

+

3

.JS

30

.44

.50

Youth

.50

.46

College

.56

.55

!diddle

.42

.3l

Senior

.19

.31

i;ork

.45

.49

+

3

Non-iork

.46

.50

*

1.04

.66

.46

.50

Gender: ~__ Femaie flale age Group:

Trip Tipe_:

Yedic31

3 58

*

u

The transit pricing evaluation model ages are available which can be used in designing real

time graphic displays of TPEM'soutput. Such capabilities could prove useful in policy meetings and public hearings on fare changes as well as part of a transit agency’s on-going financial planning efforts. REFERENCES Ballou D. B. and Mohan L. (1981).A decision model for evaluating transit pricing policies. Irons Res. 15A. 125-138. Cervero R. (1981)Efficiency and equity impacts of current transit fare policies. Trans. Res. Rec. 799,7-15. Cervero R. B., Wachs M., Berlin R. and Gephart R. (1980) Efficiency and Equity implications of alternative transit fare policies. Urban Mass Transportation Administration, Washington, D.C. Cherwony W. (1977) Cost Centers: A new aporoach to transit .. performance. Transit 1. 3, 70-80. Cherwonv W. and Mundle S. (19781.Peak-base cost allocation models. Tram Res. Rec. 633.52-56. Dierks P. A. (1975). Financing Urban Mass Transportation: A Study of Alternative Methods to Allocate Operating Deficits. Ph. D. dissertation. University of Washington. Donnelly E. (1975). Preference elasticities of fare changes by demographic groups. Trans. Res. Rec. 589, 30-32. Frankena M. (1978). The Demand for Urban Bus Transit in Canada. J. Trans. Ecan. Policy. 12, 28&303. Grey A. (1975). Urban Fare Policy. Saxon House, Heath, Ltd. Westmead. England.

323

Kemp M. (1973). Some evidence of transit demand elasticities. Transpn.2. 27-38. Kemp M. (1974a) What are we learning from experiences with reduced transit fares? The Urban Institute, Washington, DC. Kemp M. (1974b). Transit improvements in Atlanta-the effects of fare and service changes. The Urban Institute, Washington, D.C. (1981). Lago A. M. and Mayworm P. D. (1981)Transit fare elasticities by fare structure elements and ridership submarkets. Transit 1. 7, S-14. Lago A. M., Mayworm P. and McEnroe, J. M. (1981). Further evidence on aggregate and disaggregate transit fare elasticities. Trans. Res. Rec. 799,42-47. Levinson H. S. (1978) Peak-Off Peak Revenue and Cost Allocation Model. Trans. Res. Rec. 633, 29-33. McFadden B. (1974)The measurement of urban travel demand. J. Public Econ. 3, 303-328. Nelson G. (1972)An econometric model of urban bus operation. Institute of Defense, Washington, D.C. Pratt R. M., Pederson N. J. and Mather J. J. (1977) Traveler response to transportation system changes: A handbook for transportation planners. Urban Mass Transportation Administration, Washington, D.C. Pucher 1. (1981)Equity in transit finance. J. American Planning Assoc. 47, 387-407. Schemenner R. (1976) The demand for urban bus transit: A route-by-route analysis. 1. Trans. Econ. and Policy. 10.68-86.