CATALOG 17 Thin paper in prepared for staff-wV P 7 6 one andis not for publication.

* w S S > f-TlDview expreseedr those ofthe author and not necessarilythose of the Bank,

IlINTATIONAL BANK FOR RECONSTRUCTION AND DEVEPCEIT

INTERATIONAL DEVELOFMTJ ASSOCIATION

SECTORA LEc lonomics Department Working Paper No. 76.NTERNATn1ONAL WRA 76

FOR

RECONSTRUCIIC)N AN'D DEVELOPMENT

JUN 2 41986The Economics of Rail Line Closure

Kay 22, 1970

The paper discusses how to determine whichsections of a rail system to close and when. Thesedecisions are analyzed for both the economic (netsocial bencfits) and financial (railway companylsgains) objectives, when either exogenous trafficprojections or traffic demand curves are available.The issue of government subsidization of rail erviceis also discussed. Etamples and procedures foicomputing costs and optimum timing are included amongthe annexes.

The approach of the paper is essentially theoret-ical. Further work is envisaged on actual case studiesto develop pragmatic solutions for the line closureproblem.

The author, associate professor of economics atthe State University of Neo York College at Oneonta,is grateful for the comments, criticisms and construc-tive suggestions of Wf. Jan de Weille and for thecoments of other colleagues. He wishes to thankMessrs. de Weille and H.O. van der Tak for makinghis work at the Bank highly interesting arnd enjoyable.He aloo appreciates the assistance of Miss S. Snell,who edited the paper, and of &as. B. Easter and Mias J.Iasaire, who typed it.

Sector and Projects Studiss DivisionPrepared by: Ranjit K. Sau (Consultant)

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TMe ftonomics of Rail Line Closure

TAMB 0 GA1TENTS

10 Introduction: Therms Scope, and Outline 1

IL ProJect Alternatives and Cosat 7

D Determination of Alternatives 7

1. Rail operating Alternatives 72. Substitute Service Alternatives 9

B. Types of Coaet and the Principle of Avoidable Coot. 10C. Su_mry 1B

lI1. Economic Analysis, Traffic Volume Oiven 16

A. The General Method 16B. The Doiteux Effect 18C. Suiury 19

IV. Ebonomic Analysis, Demand Ptnction for Tr&isportation Given 21

A. The General Method 21

1 The Concept of Social Surplus 212. Some Typical Cases 23

B. Case A: Rail vs. Now Highway, PerfectSubstitutability 25

C. Case B: Rail vs. Now Highway, ImperfectSubstitutability 28

D. Case C: Rail vs. Highway IEprovement 29F. The Role of Cost-Benefit Analysis 32P. ProJect Selection and Optimun Timing 330. &uuary and Conclusions 35

V. Financial Analysis 37

A. Traffic Volume and Rbevenue Oiven 37B. Demand for Transportation Given 40C. Summary and Conclusions 43

VI. Pricing, Deficit, and Subsidy 44

VII. Suary and Conclusions 7

ANBEIM

I. Choice BetweeD Dleselization and Electrification

II. Cocputation of Coate

IIr Dynamic Cost Minimisation and the Optimum Timing of Substitution

eV. The Optimm Timing of Substitution: lcmples from Argentina andSpain

V. Conaumra' Iarplus Measurement for Close Substitutes

VI, Marginal Cost Pricing and the Theory of Second Beat

VII. Cost-henefit Analysist An Rample

LIST OF TAMES

Page No.

Table 2.1: Long-Run Coltas An nliustration 11Table 2.2: menoes in Four Private Danish Railways 13Table 5-.l Railway Closuret Year-by-Year Renue, Cost

and Profit 40

Table 6.1: Price Change Required to Achieve Change inTbtal Revenue 45

Table II-l: Suary Eetisates of Long-Run Marginal Costsin the U.S. Railways Annex ir, 6

Table IV-1: Argentina: Optimum Timing of HighwaySubstitution Annex rV, 2

Table IV-2: Spain: Estimated Costs for Railway andHighway Passenger Services betweenQuintanar and Villacanas Annex IV, 6

Table VII-lt Cost-Benefit Analysis of Withdrawal ofSheffield-Barnaley Service Annex VII, I

LIST OF FIGWRES

Figure 4.1t Consumera' and Producers' Surplus 22Figure 4.2: Demand for Transport and Long-Run Marginal Costs 25Figure 4.3: Demand for Transport and Short-Run Marginal Costs 27Figure 4.4: Demand for Existing Rail and New Highway

Services and Long-Run Marginal Coats 29Figure 4.5: Demand for Eisting Rail and Existi. g Road

Services and Long-Run Marginal Costs 31Figure 4.6: Demand for Road Service Alternative V and

Long-Run Marginal Coots 31Figure 5.1: Railway Revenue and Cost Over Time 38Figure 5.2: Railway Marginal Revenue and Long-Run Marginal

Cost

Page No.

Figure 5.3s Railway Mcrginal Revenue and Short-RunMarginal Coat 41

Figure V-1: Demand for Road and Rail, Case A Annex V, 3Figure V-2: Denand for Road and Rail, Case B Annex V. 3Figure V-3: Dea nd for Road and Rail, Case C Annex V, 3

I. INTRODUCTION: THEME, SCOPE, AND OUTLINE

1. An adequate transport system is usually a prerequisite if not

a gruarantee of economic growth. Since transport is highly expensive,

frequently accuunting for as much as 15 to 30 percent of public investment,

it is of considerable importance that the resources engaged are optimally

utilized. This requires a continuous review of the transport network.

Should a new railway line be built? Should it use diesel or electric

power? Sthould an existing railway line be replaced by a road improvement

project? Should a port be further developed? These and related questions

need periodically to be posed, analyzed, and resolved.

2. We are concerned in this paper with one aspect of this broad issuet2/

for any existing rail line carrying passenger and freight traffic, is the

service it provides justifiwd? If so, for how long? When and under what

conditions would it be more economical to partially or fully replace the1 ~~~~~3/.

line with an alternative mode or transport (a road)? If the decision in-

volves a budget deficit, should the government provide a subsidy? These are

the basic themes of this paper.

V Hans A. Adler, Sector and ProJect Planning in Transportation, World BankOccasional Paper No. 4 (1967), p. 5.

/ Throughout this paper we shall assume that the railway line under reviewcarries both passenger and freight traffic. If in a certain case, itcarries only one kind of traffic -- only passenRer, or freight -- thesituati.on is much simpler and the logic of our analysis still holds.

2( For convenience, we shall take road as the only alternative to rail.These questions are usually raised in connection with so-called "branchlines". But, the label of "branch line" is often applied to sectionswhich are, economically speaking, no different from "mainline" sections.This is clear in the cases of Talora-Kigoma and Tabona-Mwanza sections ofthe East African Railways, the former be.iig classed as the official main-line and the latter as a branch line despite its heavier traffic densities.See: The Economist Intelligence Unit, and Freeman, Fox, Wilbur Smith andAssociates, East Africa Transport Study: Draft Report, London, 1969, Vol.V, p. 285. Terminology should not obscure the true nature of the problem.These questions should be raised for any railway section whose viability isin doubts, no matter whether or not it is officially called a "branch line".

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3. ihy does an existing railway line, presumably thought to be viable

during its construction, lose its Viability over the course of time? The

reasons include loas of rail traffic to road, construction of lines in areas

which subsequently failed to develop, construction of lines to develop re-

sources which were eventually exhausted, and suustandard construction of lines.

In Australia, the decline of ports outside the capital cities it an additional

reason.

ii. AA conmm feature of uneconomic railway lines is a reldtively light

volume of traffic. Rail is characteristically suited to handle a large volume

of traffic and long-distance traffic; when traffic density is low, the viability

of the line is open to question whether i-t is officially a branch line or not.

One rule of thumb to identify uneconomic railway sections is to consider, first,

the annual traffic density in gross tons-kms.per rail km. covering both pas-

senger and freight services, Since this index may occasionally underestimate

the importance of the section's relation to the rail system as a whole, the

second index is the annual figure of traffic originating in the section. How-

ever, it is impossible to suggest any precise numerical cutoff points which3/

would be valid for all countries and at all times.

LJ See ibid., p. h73. "In order to keep construction costs to a minimun theState xo vernrmnt Railways sometimes were forced to build branch lines withonly lightweigh.t rails and a minimum of ballast. Although these linesgenerally served thsir purpose, in later years their substandard conditionusually gave rise to high maintenance costs and imposed serious operatingrestrictions on trains using the lines."

/ See O.R. Webb, "The Closure of Uneconomic Rail Lines in Australia,"Economic Recor5, December 1963, pp. h68-76.

f In Argentlna, for example, any railway section which did not have a grosston density of at least one million tons per year (excluding the weight oflocomotives) or which did not show originated traffic equal to at least 500tore per km.. o. line was conaidered subject.to study. As a result, .40 per-cent of Argentina's railway lines an of 1958-59 was brought under a criticalexamination. Ministry of Public Works and-Services, Transportation PlanningOroup, A Long-Range Transpo,tation Plan for Argentina, Buenos Aires, 1962,Appendix Ill, pp. _y-30.

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5. In countries such as Australia, Britain, Canada, Finlands

Ireland, Japan, Sweden and the U.S.A., the withdrawal of railway serviceo

In favor of road services has been confined mainly to lines with light,. . - 1/

traffic density. The chiet test of railway line closure in most of these

countries has been "that by so doing there would be a financial betterment

to the raibvaZ7 Administration itself." Because traffic flow may be very

unevenly distributed over the tranaport network, reduction in service on

lightly-traveled lines can produce such savings. The Beeching Report, for

instances, points out tlit in 1963 one-third of the route mileage of the

British Railways carried only one percent of the total passenger miles;.

one-third of the mileage carried only one percent of the freight ton-miles.

Similarly, one-third of the railway stations produced less than one percent

of the total passenger revenue; one half of the stations produces only two2,/ l&

percent. The Report finds tk,dt the withdrawal of services frem part of

the light-traffic routes would result in a net saving of more than E 18

million per year.

See A.W. Burges and J.W. Channon, The Riverhurst Region of Saskatchewan,Montreal: Canada Department of Agriculture; J.W. Channon, D. Zasada, andR.T. Miller, The Boissevain Region of Manitoba, Montreal: Canada Depart-ment of Agriculture; John F. Due, "An Empirical Study of AbandonmentDecisions," Journal of Finance, XIV, September, 1959, 3, pp. 361-72;D. ilerlihy, "Substitution of Road Services for Rail (Freight and Passenger),"Monthly Bulletin of the International Railway Congress Association, XLII,October, 1965, pp. 607-42; and Webb, op.cit.

2/ D. Herlihy, "Substitution of Road Services for Rail (Freight and Passenger),"Monthly Bulletin of the International Railways Congress Association, XIIII,December, 1966, 12, p. 1621.

/ British Railways Board, The Reshaping of the British Railways, (TheBeeching Report), London: H.M. Stationery Office, 1963, Part 1, pp. 10-11.

hi This, however, does not necessarily mean that the closure of that one-thirdof the route mileage would affect only one percent of passenger traffic,or freight traffic of the railway system.

i The Reshaping of the British Railways, Part 1, pp. 18-19.

6. - In Some instances, investigations of rail line closure go beyond

the relatively n±row limits of the railway's direct financial benefit. In

a transportation study in Argentina, for example, where the relative coits

of the substitute higb%.y service were alo taken into account, it was found

that about one-third of the railway network was ufeconomic and should be

abandoned, and that an additional one-tenth needed further vtudr witl an eye

to possible later abandonment.i'

7. Thfe iagnitude of the problem of uneconomic railway Ui rs cja be of

co ls.able i*ort ncO, as in the countries mentioned so far, ivtl* lb

other countries it may be relatively insignificint, ts in Korea./

8. In this paper, we shall study the problem with refererce to two

alternative objectites, namely, profit maximization (or loss minimization)

within the railway syste, and the maximization of het soial benefits. Fbr

the first objective, only those costs and revehues directly relevant to the

railwy system itself are included, and profit is defined as the difference

between revenue and cost. Costs are reckoned usihg the market pricec sf the

inputs and revenues at their nosinal value. Fot tbo second objeettive all

costs and all bonefita to society ab a whole are relevant; cost are calculated

using shadow prices of the inputs and behefits are seasured on an economy-

wide basis. These two objectives are sometimes r"ferred to as the financial

objective and the economic objective, respectivelyY

Adler, o. cit., p. 7./ See Ministry of Trancportation, bpublic of Kotea, Korea Trangportation

Survey. Vol. nv, December, 1966./ See Adler, op clt., pp. 33-60; and also LLM.D. Little and James A. Miwrlees,

Manual on Industrial Project Analysis in Developing Countries, Vol. II,Paris: O.E.C.D., 1969. The mechanics of calculation are the same for bothobjectives. Coats and revenues (benefits) occurring at different pointsof time are made comparable by discounting (present value calculation).

stWP msttll dj.uiu'jM'aish between two lYPes of cases in our analysis.

In one case, thie total (all modes) traffic v6lume in exogenoiisly projected

on the br d of expected economic.Wowth and the pattern of induatrial location. The

problem then bjils down to minimizing transportation costs. In the other

case, the traCfic volume is not given but is deriveA f"cm the known demand function

for 'ransport services. Under such circumstances, the problem is no longer

one of simple cost minimi7.ation, but of profit or net social benefit maxi-

uilzation.

10. Replacement of rail by highway service is not always a simple

matter of economics. It may involve change in the pattern of cnmmunity

life in the affected area; it may require redistribution of authority2/

auong governme:L ministries, and it may cause some inconvenience in the

t.rnnslLion from riil to road. In short, It is both a socio-political and

economic matter. Let it be clearly understood that we are presently con-

ccmned with only the economic aspect of the problem, and excluding fiscal

questiots at that. We shall not deal with financing of possible railway

deficits (local vs. general taxation).

1]. Our plan of study is as follows. Chapter II emphasizes careful

*xamination of all possible cost reductions and improvements of rail

se.r¢1ce, and carorul analysis of all the rail and substitute highway service

alterr.itives. This chapLer also introduces the cost concepts to be used

uubsequently.

I For axample, some believe that the closure of branch rail lines in theprairies of Ca-nada would reduce most prairie communities to "ghost towns".

-For an opposing view supported 'oy factor analysis and multiple regressionanalysis, see Gerald llodge," Branch Line Abandonment: Death Knell forPrairie Towns," Canadian Journal of Agricultural Economics, February '968,p S4-70'.

/ Scoo D. Herlihy, "Substitution of Road Service ft'r Rail (Freight and Passen-ger)", Morit.-ily Bulletin of the International Railway Congress Association,June 199 pp6.-n 1120-1135' '.~''~ - ''

12. Chapters III and IV are concerned with the cnalysis of the pro-

blem when the objective is to maximize net social benefits or social sir-

plus (economic analysis). Chapter III examines the case in wihich the traffic

volume is exogenously given; the foliowing chapter, the case in whilch .lemand

curves for transportation are given.

130 Chapter V presents a firaniicial analysis of the two cast s of Chapters

III and IV. In Chapter V, the objectivte is to manximize railway 1rofit (mini-

mize loss). Chapter VI briefly notes the importince or pricinl: olicy in

relation to optimal investment plannuing. In the main, it deals *;ith tne

question of.government subsidy of railway deficit. Chapter VII pre:ie:t.s a

summary of the tect, and its main conclusions. Tuie anntexes are devote.t to

mathematical analysis., elaboration of some concepts used in the text,

exaW1.% and a discussion of the marglnal cost pricing rule anti the theory

of second best.

i.. iThe method of optimization developed in Chapter III and Annex III

minimizes estimated costs, while that in the beginniiing or Chapter V minimiz.es

loss (maximizes profits) w414 certain circu.m- L-iwes. We believe these two

methods are fairly operational,,considering the data usually available to a

project evaluator. The methods preseatad elsewhere in this sLudy are

basically applications of cost-benefit analysis, and are as practical as otlher

cost-benefit tecluniques.

-7-

11. PROJECT ALTMINATIVES ANfl COSTS

-l. This chapter explores the possibilities of reducing railway

operating costs to improve the viability of service offered. All

feasible rationelization or rail service needs to be exasained and ali

alternaLives prepared,before raising, the issue of substitution b7 road

service. Options other than continuing present service and closure

are open: it may be worthwhilts ^°or example, to operate at a certain

scale, for only certain types of traffic, on a certain schedule, and to

reorda1iize the personnel. Considerable economies may be achieved fromV

such operational rationalization. The next step is to estimate costs

for each alternative, a topic also covc in this chapter.

A. Determination of Alternatives

1. Rail Op*rating Alternatives

2. A fundamental principle of efficient resource allocation is that

output should be produced at minimum total costs. However, the valuation

of outpit. for transportation service is problematic because transport

users zonsider speed, comfort, reliability, and scheduling in addition to

prie!e. Any measure which aftecto t;..se elements is likely to influence

both the demand ror and the costs of transportation. In principle, there-

fore, closure of even the tiniest station in a light t-iffic line requires

I/ On the light-trafric Central Wales line, ror instance, seven stations wereused by fewer than five passengers per week. It was suggested that operatingeconomiies could be achieved by closing some stations, reducing the number ofcalls made by train3 at others, -And reducing the number of journeys per day ineach direction from fe- to three. See G. Clayton and O.H. Rees, The EconomicFroblems or Pural Transport in Wales, Cardiff: University of Waies Press, 196?,;nnd also P.K. Else and M. Howe, "Cost-Benefit Analysis and the Withdrawal ofRailway Services," Journa' of Transport Economics and Policy, May 1969, pp. 186-187. In some Western European countries, a number or rail stations have beenclosed in order to improve the financial position of the railways,from 20 to 50percent during 1955-65. See D. Herlihy, op.cit., p. 1133.

an boratebcot C08t nfit analysis0 In practice9 however, such issues

cau be settled with simpler analysesD consider.ng the order of magnitude

of the costs and benefits involved.

3 SMost operating alternatives resn be broadly cl.nasified into two grotupqg

those which produce more or lose the oaae benefits to transport users but involve

different time patterns of costs for the railway, and thoee which have different

user benefits and lifZerent time patterns of railway costs. The .hoice between

dieselisation or electrification of r'ailway is one example of the foraer, Trans-

port users may be indifferent as long as they get the same kind c'f service. But

thea. two types of projects require different capital expenditures, and maintenance

and operating expe08ne0 For the technique of finding an optimal solution in such

a case, see Annex ID wChoice Between Dieselisation qnd Electrification."

14. A mmre co"lez example rorld be a proposal to switch from

scheduled freight sewvice betwem pointo A and B to on-demand service because

the traffic is so liUght that trains usually carry small, uneconomic loads.

We assume that the probability distribution of wrival ef goods at each

station to be oarrie e to the other la gLven and to indeperdent of train

schduling,5 that oasto of waiting tim et tha-ortginating station are Iknown,

and that runnrig tia betwee A and B La indepandent of train size but

operating costs (fuel, wagons, maintenance, etc.) ver with size. Uder

such cireumstances, queuing theory can be used to find a schedule that PflnLO

minese total costs user' costs and railway costs.

5. 7Ae problem bec;ees more ctuplex whean the probability distrl.bution

of originatig tra.iC is a-function of the frequency and dependability of

I/ For an introduction to queuing models, LIA their application toscheduling problemj, see C.W. Churchman, R.L. Ackoff and E.L. Arnotf.,Introduction to Operations Research, Neo Torks John Wiley, 1957,Chapter 14h, 15 and 16. Our problem is more cc.tlicated than mosttextbook applications of the queuing theory sinceit involves twovaytraffic.

.tru:g snu*e'rI.widtl.y mmy dl v.trt, parL Olr thimi trnftle to nn alternative mode.

To Soinix extiniL, itdt i s etii bo' I tacorporated into tihe model by introducing

cus Uuner impatietltco. Ir Some trafCic dries up as a result of the switch

from tile existing schedule to on-demand service, there is a loss of benefit

wltici is difficult to predict. If traffic does not dry up but is simply

diverted from rail to another mode, the on-demand schedule can in principle

be worked out by minimi7ing the total costs of rail and diverted traffic.

If this total cost is less than that of the existing service, it is worthwhile

to switch to cn-demand service. In effect, one schedule is being replaced by

-another to redluce costs.

The second kind of operating alternatives, involving changes in

both user benefits and railway costs, arises more frequently. For example,

faster and more coxfortable rail service could draw more traffic, but it

may also raise costs. Under these circumstances, the correct method is to

line up all feasible, mutually exclusive rail service alternatives and then

choose the one with thie largest net benefits, i.e., the highest present

value of benefits minus costs.

2. Substitute Service Alternatives

7. The rail service alternatives should be compared with the substi-

tute road Service alternatives. If a highway network parallel to the rail

1lne alrcady exists, alternatives such as bus service for passengers are

po.sible. However, if a highway must be built to replace the rail service,

1/ See Philip H. Morse, Quaues, Inventories and Maintenance, New York:John Wiley, 1958, especially pp. 24-28.

'/ See Chapter IV. See also Ronald N. McKean, Efficiency in GovernmentIrouglh Systems Aralysis, New York: John Wiley, 1958.8

1/ For Ule Villarnnas-Quintanar rail line in Spain, two alternative plansO :ub:sLUxite passenger service on the adjacent highway were considered.See Annex IV, "The Optimum Timing of Substitution, Examplea fromArgenti n and Spain".

broader alternatives exist. The route has to be chosens- variotut typen

of highway will be possible (two-lane, three-lane, four-lane, divided)

each with differen' standards of surface, gradient, aligntment, and so on.

The planning authority should have enough experience to weed out clearly

unsuitable plans, suchl as a four-lane di.vided higlway with a low-grade surface

(if the volume of traffic justifies the one it must. rule out the other).

The problem is therefore to choose the best Or several practicable plnOs.

B. M es of Costs and the Principlc of Avoidable Covt.s

8. For subseqluent analysis we slhall need information on three types

of costs, namely, -long-ruw average cost (Clhapters III and V) atid sliort-rwi

and long-run marginal costs (Chapters IV and VI), Ey long, rup, we mean

a period of time long enough to permit variation in input; correspondingly,

the short run means a span or time during which broadly spe aking, t:e

plant is fixed and production can be%increasod only by incurrinw! operating

expenses. In the short-run, major investmient is ruled out rjr techidcal

or other reasons..

9. In practice, it may be difficult to identify the costs aLtrihu-

table to a particular line or a certain section of the railway systen. To

avoid difficulty, we use the following principle: reckon 311 cost.q whicli

can be avoided by not carrying trarfic on the railway secthon under review,

whether these costs are incurred on this line or elsewhere in thte system.

This principle holds for estimating the costs of highway service as well.

M See David M. Winch, The Economics of Highway Planning, Torontos Jniversityof Toronto Press, 196>3, pp. 44-L5.

For exaple, muppose that the present value of the investment, maintenance,

and operating casts of producing one unit of output per year over an

extended period ia $900. This is equivalent to the present value of an

infinite stream of $90 per year at an interest rate of 10 percent., Though

the actual cast stream may fluctuates it is equivalent to a constant stream

of $90 per year (See Anmex !I,'CoupItation o^ Cotst,). Similarly, suppose

that the cost streams of producing t-o units annually is equivalent to a

constant stream of $112 per year, $138 for three units, and so forth (see

Table 2.1, columns (1)' and (2y). The. long-run average cost is defined as

the ratio of long-run total cost per period to the level of output per

period (Table 2.1, oolumn (4)). The marginal cost is, by definition, the

additional cost of producing one 'sore unit of output. It is simply the

difference between tUe cost of n units and that of (n-l) units (Col. 3).

Because short- and long-run total coats may be different, short- and long-

run lrginal costs may be different.

Table 2.1: Long-Run Costs: An Illustration

inpu Long-!Run Costs($

Physical Total Marginal Averageunits (2)/(1)

(1) ~~~~(2) (3) (4)-

1 90 902 112 22 563 138 26 l,64 168 30- 42

.5 202 34 40.46 2140 38 140.7 202 42 40.38 328 46 419 378 50 42

10 432 514 143.14

1 See Jacques Lesourne, Economic Analzsis and Industrial Management,Englew oN.J.s PrentThe Hall, 1963, Ch. 10.

- 12 -

10 The calculation of coats is complicated when more thall one

product is produced. The railway provides two servicess.passenger and

freight. Cost of inputs which are used for both (railway tracks) may not

be avoidable even if the output of one product is discontinued. In thisIl

case, the allocation of joint costs between services is irrelevant and

urnnecessary. We may note that all joint costs are non=avoidable costs,

if only one of the activitles is suuspended. llowever, not all nc,-avoidable

costs are joint costs. The pension payment to a retired freljht train

operator, for example, is a non-avoidable cost, but not a *joint :o.;t of

freight and passenger services.

11. It is important to distinguish between operating costz given joint

service and those of one service operating alone. Estimated opcxating expenses

of freight and passenger traffic in four railway ststems of Denn.%rk are giveii2/

in Table 2.2. For instance, in system A, the to-.nl operatinti e.xpenses are

483 thousand crowns, while the savings of such costs by discottiilnning elther

passenger or freight service individually are given by 20316 and 156.73/

thousand crowns, respecLively. These are, in essence, avoidable ctts.

_ The Economist Intelligence Unit et.al., op.cit., has distributed Jointcosts arbitrarily between freight and passenger traffic. Such cost esti-mates are not valid for the purpose of decidinjg about partial. railwayline closure.

2/ This table considers only operating expenses and does not includ.^ anyavoidable capital or maintenance costs.

3/ These are called "subtractional costs", or "construction costs" as dis-tinct from "expansion cost". See J.1. Dreze, "Some Postwar CotiLributions.of French Economists to Theory and Public Policy," knerican ieonomic!Review,June 196n Supplement, pp. 8-10; and Lesourne, op.cit., anid J.SMobrg, Costs and Revenue Analyses, Profitability Estim:ates, Bu.tgetargPlannings Stockholms Swedish State Railways, 1967, p)p. 20-2^.

But if either the passenger or freight service is operated alone, the

operating costs would be 326,3 and 279014 thousand crowns respectively.

Whis banic asymmetry has to be kept in mind.

Table 2.2, NxPensen in Four Private Danish Rail'ays(in thousands of CroyDs)

Savings in Operat,ing Operating CostsRailvay Costs by When the Railway Total-Operating Costs

Discontinuing is Operated Only forPassenger Freight Passenger Freight (2) <. (5) (3) TM14Service Service Service Service

A 203.6 156.7 326.3 279.4 41a0B 1142.8 129.5 262.6 2149.3 392. 'C 95.5 113.7 170.6 188.8 284.3D 55.6 147.6 136.1 128.1 183.7

Total 1497.5 1447.5 895.6 845.6 l1343.1Average 124.l4 111.9 223.9 211.4 336.0

Source: Sjoberg,, Op.cit., pp. 21-22.

12. The nature Of avoidable coats also depends on the time horizon.

A comparison of avoidable costs with the estimated revenues (benefits) in

the short-run (say five years) or in the long-run (say, fifty years) is

not in itsrlf necessarily a good basis for closure decisionso As an illus-

tration we take two caaes from the British Railwayso In 1951, the British

Transport Commission recorded that costs would include the actual expendit-

ures incurred, or to be incv-red in the long run,to maintain and operate

the apparatus required for a given level of services and treffic. In keep-

ing witlh this approach, the cost calculations presented at the Lewes-East

Orinstead inquiry included reneval charges for all capital assets involved,

though some would not have needed replacement until many years after the

inqulry. The other extreme -- very short time horizon -- is illustrated

- 14 -

by the St. Ives-Kettering case, where in estimating avoidable costs, a bridgeI/

with a technical life of possibly 100 years was written off in five years.

These two cases pursued the wrong question. The appropriate question for

the profit maximization (or loss minimization) criterion is not whether a

railway service will cover its costs if run for a specific nwnber of years,

say, five or firty, but whether there is any period of time for 4rhich tle

avoidable costs can be covered by the estimated extra revenue.

13. Therefore, all costs have to be calculated keeping in Aiew

the time horizon for alternative, combinations of the railway serrices. We

need to know, for example, the costs of passenger traffic when freight traffic

is to remain at a certain given level per unit of time; tie costs of

passenger traffic when freight traffic is to be discontinued; the

costs of freight traffic when passenger traffic remains at a cer;ain given

level per unit of time; the costG of freight traffic when passenger traffic

is to be terminated, and the costs of selected items of freight traffic under

other assumptions about other traffic etc. The highway costs also have to

be computed under similar- assumptions. Thus, a number of cost estimates are

necessary if partial closure of the rail service is under consideration. If

only complete closure is being considered, we compute the aggregate costs of

freight and passenger traffic.

C. Swmmary

14. The railway plant which has been inherited from the past may or

may not be optimal in view of expected future traffic flow. There may

exist scope for rationalization of the railway operation. The first step is

to review the present position and prepare practical alaternatives to preser",

service. They should be compared with similar alternatives for substitute

/ See M. Howe and G. Htills, "The Withdrawal of Railway Services, "Economic Jour-nal, June 1960; Britishl Transport Commission, Annual Report for 1951, andChapter V of this paper.

- 15 -

road service. For each alternative, three kinds of coats have to be

calculated& long-run average coat, and ahort- and long-run marginal

cotat, as defined above.

III. Economic Analysis, Traffic Volume Given

A. The Oeneral Method

1e The principle of selection among alternatives with equivalent

benefits and benefit patterns is to choose the alternative with the least

(discounted) cost. In this chapter we shall apply this principle to

determine the optimal timing of replacing rail by highway sery.4ce under

the assmption that the volume of traffic in given. ihen rail and highway

services are perfectly equivalent (transport users are indiffezent betamen

the two if the same price is charged for traffic between any p ints A and B

on the line), and either the price is given or the demand curve is perfectly

inelastic, then the total volume of rail and road traffic is known, regard-

lese of whether and when the railway line is replaced by the highway. A

perfectly inelastic demand curve implies an infinitely large consumers'

surplus at any finite price; thus, at any cost short of infinity, the transport

project is econoiically justifiable. This-asa at ion, although admittedly

rather heroic, is frequently made in transportation studies.- In the next

chapter, we deal with the optimal timing of rail replacement in the case when

the aasuaption of perfectly inelastic demand does not hold.

In the Argentina transportation study, for eample, the traffic forecastis made on the basis of the anticipated economic growth and industriallocation; the question of replacing certain railway lines is solved byminimizing the transport cost of the projected traffic. Essentiallythe sae procedure har been followed in the Spanish Railway Studyt foreach of tUwee alternative growth rates for future traffic, the costs ofthe railway operation vis-a-vis those of the substitute highway servicesare examined. See Hiniatry of Public Wbrks and Services, TransportationPlanning Group, A Long Range Transportation Plan for Argentina, EbenosAires, 1962, Appendix I: and Ralph F. Rechel, Spanish State Railway StudyProaram for Discontinuance of Services on Light Traffic Railway Line:Interim Report Illustrattng Appropriate Methcds of Econinic and FtnancialAnalysis, Washington, D.C.: August 1966, p. 8.

- 17 -

2. When the railway line is replaced by highway, two .YPpon of

highway cota are incurred, (i) capital expenditure for construction

or improvemant of she highway, and (ii) maintenance and operating

expnsea on account of the traffic now diverted from rail to road. For

siplicity1 let us anause that the required capital expenditure for the

highway remains unchanged by timing, i.e., no matter in which year the

construction or improvement is initiated. For each additional year the

railway service is allowed to opera.e, there is a "gain" consisting in

savings on the capital charge for the postponed capital expenditure of

the highway and on operating and maintenance costs of road service, On

the other hand, there la a "loss" consisting in the costs incurred- to

operate and maintain the railway service for a year. Eventually the

lose in postponement of the highway program by one more year will exceed

the gain. This is the optimal time to replace rail service by highway

service.

3. The determination of the optimal time to replace the railway

service can be broken into two stepa. Firstly, copa'e the long-run

average coat of the railway service with that of the substitute highway

service. If the former is leoss than the latter, the railway service

If, for example, the required capital expenditure for the highway is$10,000, the ht#hway operating and maintenance costs per year, $100,and the railway operating and maintenance cost per year, -$250, then if therailway service continues fr one more year, the cost is $250. By thesame token, we have postponed a capital expenditure of $10,000, whichwould earn $500 in a year at an interest rate of 5 percent. Thus wegain $500 in capital charges and $100 in road maintenance and operatingexpenses. So the "loss" is $250 but the "gain" is $600, as a result ofpostponing the replacement of the railway by a highway for a year.Strictly speaking, this formulation is only valid for a constant flow oftraffic year i,, year out, and does not allow for (di)economies of scale.Mbre generally, one should compare the aggregate present value of totallong run costs (i.e. operating, maintenance and investnet coata) requizredto serve future traffic deandae permanently i either rail or road.

.should continue. If tha former is larger, soone o later, highway

service should replace the e£ating railway service. Secondly, to

tbrmine the rrocks. optAm timing,D detrmine at whiat point the "lossQ

In the postponement of the highway program by one more-year tends to

exood the "gain" therefro. Three formlas for ceiputing thiae tim are

given in OAn L IIC WNWIes fran Argentina aud Uein We given in Ann=e N 0

D. The Boiteux Effeot

1Investent p6licy, operating and maintennce policy, &-A the

optiml timing of replacing rail service are inter'e.ad. As Marcel

Doitenu witesp in connection with certain local railroad lines in Frances

%U1 a decision1 reached concerning the retiremet date ofan unprofitable line, the line will be maintained normallyand its eliination will never soem justified. After all alie kept in proper order can 0o.carry on for quite some timeunder its old momontia, and can operate at a profit forseveral years at minimm expense (often for leas than thetotal cost of operating a highway transport service)o Iltus upcsep on the other hand, that It has been decided somefiftee years ago to set the dates at whoh deficit linsawo1d be sucoessively abandoned, and that these lines-had beoAmanaged accordingly. We should find in 1952 that a linescheduled for retirement in 195l4 can still be operated for twoor three yars ithout prohibitive costs, but that, beyondthat tima, its maintenance wvoud involve such expendituresthat nobody would dwwn for a moment the Advastae ofreplalng it forthwith with a higway rvice." g

The point is that operating and maintenance ozpes dipend largely on

retiremnt polir, WA Vice arsa. In view of this interdependence, asone-

times referred to as the Doiteut effectY'tle general procedure of dynamic

V Qwoted by Pierre Hasee, Ttima Inveent D.cisian New Yorkt Pv4ntice-Hall, 1962, p. 48.

/ Ibd., pp. 149-59,

° 19-

cost minlnhatioa in as follwa. Designate an arbitrary tim period 0

when the rallmy service would be replaced by road serviceO Obaerv_=

Ing the quality and safety requirements of railway operation, determine

the time pattern of investment and maintenance expenses entailed by

continuing service such that the present value of such costa less the

salvage value of. the disposable assets at period 0 is a minimu. To thisp

add capital, maintenance' and op. .atlng expenses of highway service

fram period 0 to 8 finite or infinite tim horison,, as desired. The

minimum total discounted costs will vary with the choice of 0. the

optimum tiing i that 0 for wich total discounted costs are minimized.

Co Summary

50 If the volume of. traffic per unit of time is given from projections

and the problem is to minimise the transport cost, compare the long-run

average cost of carrying the traffic on the ezisting railva line with the

corresponding long-run average cost of highwa service.a' If the former io

less, the railway service need not be replaced by a highway service; if

greater, it should be replaced.

6. To determine the optimum timing of replacement, take a arbitrary

time period 0 when the railway service is assumed to be discontinued. Cam-

pute the minimum costs of carrying the traffic by rail up to period 0 with

the knowledge that rail service will then be terminated; add the highway

transport costa from period 0 to the time horison. The total cost t husl

computed is a function of 0. Chooae 0 such that these total costs are

minilsed with reference to 0. The computation of the optimal 0 is much

I/ k assme that highway width, curvature, gradient, pavement, and otherdesign components have been chosen to minimize cost and that the resultinghighway cost streams are given.Se Soe also footnote 2 on page 17.

ifd i t Is £uwther assumed that rail operating fland iwaintenatiie

coto opa) izdqp@4t of the time at t5hich the rail service is Lermina-

t(dB tha amounts to igoring the so-called Boitoux effect. Formulas

W e&ulcultitg. aptimta 0 for this iiplification are given in Anniex III

- 21 -

IT0 Etonomic Analysis, Demand function for gAnportjLinn Given

lo - In the previous chapter the optimum timing problem came dom

to minimizing total transport costs given the total volume of rail and road

traffic. The approach of this chapter is more general, since the volume

of traffic is not taken asgtven but as a function of price and of whether

rail or highway service is being used. Furthermore, the objective is not

just to minimise transport costs, but to maximize social surpluns defined

as the difference between the social :.enefits and social costs in the

familiar language of cost-benefit analysis.

A. The General Method

o. The Concept of Social Suprlus

2. Benefits recei.-ed by transport users are fully reflected in the

demand curve for transportation. If in Fig. 4.1 the price of rail journey

per mile is set at P and ',he volume of traffic is X. then the Ith marginal

unit of traffic is deriving benefits from the railway to the extent of P

dollars- benefits to intra-marginal traffic (at each point from 0 to X)

are higher (from A to P). The total benefits are given by the area under

the demand curve from the origin to the point X, or the area OABI in Fig. 4.1.

22 -

ENEs Zawl2 Consumers' and Producerst Su21lus

Price

Nile

CGot A ,OIk.Ufl i. ;e.rp1u::

D

0~~~~~~~.00

1H '; Lku*iwa.d for traiiwporLatioi

° Vol I .h-

Since the price Per unit is-Pe the total awunt paid by traffic X is OM.

Area APB, or OAM Rinus OPU, is called consuasre' urplus.

3. Parallel to the notion of consumers' aurp;us is that of pducersl

surplus. If for traffic output OX the *erags cost of production is CX, tho

producer earns a surplus to the extent of BC per unit,, Or a total surplus

of CDPY) Alternatively, if the average cost is C'Z, the producera' surplus

s negativet and wanti to area BC'D'P0

N Note that if ML ia the marginal coat curve, the total cost of outputO i given by the area OtL Thu ODC - OMI; and BCDPP NW.

- 23 -

h. Whether producers' aurplus is positive or negatives the

relevant quantity In consusers' surplus plus producers' surplua, called

the social surplus. With a decreasing demand curve, as in Fig. 4.1,

consumers' surplus iS always positive within the relevant price range,

but producers' suqpub may be positive or negative depending upon the price

and the average cost of production. In any case, a project ia justified

if the sum of the consumers' and producers' surpluses is positive, because

this implies that the total social benefits received from the project

exceed total costs. In principle, the recipients of benefits could copen-

sate those to whom costs accrue and still be better off. A Ljrollary to

this is that the price should be equal to the short run marg. aal cost of

production.'

2. Some Typical Cases

5. Initially, we assume that only rail service exists and that - now

highway would have to be constructed to provide alternative service. Under

these circumstances, the first case we consider is based on the assumption

that the railway service and the alternative highway service are perfect

substitutes, in the sense that the demand curve for transportation remains

the same irrespective of whether rail service or road service is available.

mhe quantity demanded -- the actual volume of traffic -- depends upon the

price charged. In the second case, the rail and highway services are not

perfect substitutes and can no longer be treated as identical comodities.

Then we examine the case in which road and rail coexist and the issue is

road improvement rather than road construction. After the discussion on

cost-benefit analysis, we will briefly present methods of project selection

1/ See Chapter VI and Annex VI.

-24-

conoerbi3 with optlmm timing.

6. Our strategy is to reduce the problem to choosinl iimoig a set

of mutually exclusive projects. Although it is not analytically diffl-

cult to include complex projects involving both rail and road (for

example, faster train service with rewer utops for long-distance traffie

combined with bus aerirce for short-distance traffic), for the :ake of

simplicity of presentation, we limit ourselves to simple projecis S

involving either rail or road. In view of tle discussion in Chipter II,

we first line up the alternativz projects, beginning with passtnger

service alone. Let present rail passenger service be denoted by VO, inld

let two alternatida rail passenger services be denoted by V and V,,

respectively. Similarly, let two substitute road services be c.;led

V3 and V4 . We want to choose among these five mutually exclusive project;.

7. The procedure we follow is to examinc four proposed passenger

service projects, with reference to their respective social surpluses per

period in the long run. Whichover has the largest social surplus is

then compared to VO, the present rail service. A similar exercise is

carried out for freight traffic alone. This constitutes a revie.w of all

partial closure alternatives. Then we examine all the proposed alternatives

of rail and road services for passenger and freight traffic together,

covering the complete closure possibilities. The project selected is the

one with the maximum maximorum of social surplus.. It may involve partial or

complete closure of the railway services, with or withouL the substitute

road sei7ice. If all rail and road alternatives have negative social

surpluses, the. rail services should be terminated witlhout providing zany

sub3titute road service.

8. The next issue is to determine the optimum timing of the swith-*5+ the r.e:' isr:< iStoHer z !'- ,,: >-.!

aier. The optimization method developed in detsil below assumes that

some variant of the substitute road service has been found to be the best of

'.he alternatives, for passenger service alone, freight alone, or for pas-

s20iijer X d freii,ht toFelher, as the case may be. This road project is then

.compalred with the oxisting rail project.

B. Case A: Rail vs. New Ifiglhway, Perfect Substitutability

0in Fi. ia.4, DD itn the demand curve for transport per unit of

timo, whetlier it is rail or road service. For instance, if the price

c:harl,ed is OC per ton, 00 tons of traffic move between two given points

per period. 1MCR is the long-run iarginal cost curve for railway service,

while WM3I is .h0it ror the highway service. The social surplus is maximized

ir price'is equated to the marginal cost. So the'social surplus with the

railway servicc is givean by area DAF per period; and that with the highway

vervic. ls Iriven by area DBE per per3.od. The terminati.on of rail service should

-be com::idered if aitd only W' area DAF' is less thinr area DBE; otherwise, rail

bervies. ;;I0oulId con 'iniu,)

Figure 4.2: Denand For Tranaport.and Long-lhun Marginal lost

Prioc

Mile.'nuidmd t A Demnnd for Transport

C WC R

O Traffica H D Volume

1/ See also footnote 2, page 17. Strictly speaking, the comparison shouldbe between the aggregate present value of the sequence of (annual) social-surpluses it future traffic demands are served permanently either by- _ ....

26 -

10. Unleas the demand curve io perfectly inelastic (a vertical line)

or the cost ourves are perfectly elastic (horisontal lines), then the long-

run marginal coats of rail and highway services at any specific volume of

output, taken alone, are irrelevant to the closure decision. If the rail

service is tn operation, the equilibrium volume of traffic in Fig. 4.2

would be CB, at uhioh FH is the marginal coat. At this trafflz level, the

marginal cost of alternative road service is given by HJ, which is greater

than the margial coAt of rail service by FJ, Alternatively, i the

road service is in qperation, the marginal cost of road service at the

equilibrium traffic level 00 is still more than that of the alternative

rail ,ervice. hose facta do not necessarily meen that rail se-vice should

not be replaced. The social surplus generated n equilibrium tr a transport

service is the sole criterion; the marginal cost alone is not an indicator

of that mount.

11. To continue vith our eszmple, if the social surplus with rail is

leos than that with the highway, then the latter should replace the ratlay

service. How, then, in the replacement time determined? In general,, if the

highiay program in postponed for an additional years the "loss" is given by

area DERe. The gain in the social surplus generated by continuing the rail-

way service for one more year. Thus for every successive year of poatpone-

ment, the correspondig marginal gains and marginal losses should be com-

pared. The time for replacement is at hand when the two are equal.

12. More specifically, once the demand and cost curves ahow that rail

service will be discontinued sooner or laters major railway inveatment is

ruled out. The loiteux effect states that operating, maintenance, and

/ See also footnote 1, page 25.

eVut;ib'Unt. policy d.'pend:, upon the anLiu.p:at.ed date of retirement of the

rvi'ee. Iliere1'Ioret we' dlesignato :n arbl t.rary time per{dl p for rail

::ervire closurt: auid work out thie implied operating, maintenance, and

te.luipment pol'cy. For iriy given 0, we can compute the short-run marginal

Cost curves of the rail service for periods T-1,. .. , 06 denoted respectively

.by alc: , SKCR,a, *-s HC'0 in Fig. h.3. The short-run marginal cost

euirves presumably shirt upward over time, since, in the absence of any

major investment, produetion is based on progressively older and more

det4eriorat.ed plAnt alnd equipment. Since price is equal to short-run

nreitial. cost in every period, the price also tends to rise, traffic to

fall, and the'social surplus to shrink.

ll. If the socinl surplus from the,railway at the designated 0 is

QNiual to nrea DBE, then that is the optimum 0 to discontinue rail service:

SMCR will ble fprenter thian S14CR0 and the social surplus from the rail

servtc 1in 0 e 1 will bt! less than thaL Crom the alternative highway service.

Figlr,' 4.3: Demand for Transport andShort-Rtu Marginal Costs

D

PricePerMile;and _ \4CH

CostsbMCR

0+N. ~~~~~~~~MACRO

/ SMOR 2, ,SMCR.,

Traffic0 Volume

D'

- 28 °

Ifs howevers the social surplus from the railway service at t.he desigi al.tt

0 is greater or less than area DBE, the exercise muist be repe.Led using 3

larger or smaller value for J, respectively. Throu;h uucceusi.ve i teratioitls,

the optimum p can be found. This is the algorithn of finding the op'.imini

when the objective is to maximize social surplus.

14 Thhe validity of this procedure is contingent upon tthe 3as;tmlpt.ion

that price in actiaally equal to the short-run margInal cost; if a ditile'rent.1/

pricing policy i followed, the analysis loses some of its significance.

However, given any pricing policy and its objective, a simill.r anaLlyt10.1 l

process can be worked out. For examplo, I f price is ouiuLted t.o aver:at!e co:;t.

in order to matimize only coinsumer surplus while keepin; Lh.. Lr:answport. bud.'&.

in balance, our aodel needs only one modirications replace m.rginal cosL

curves with corresponding average cost curves. Ir thhe objet.Liv Is t-o maxi-

mize profit, the exercise can be carried out, witii mtrarginal rteonue ant marginaI

cost curves.

C. Case B: Rail vs. New Highway, Imperfect Substitutability

15. Now we examine the case of nora-ideritical dm.imliI curves for rail and road

services. Let DD' be the demand curve for rail service a3d dd' the demand

curve for the alternative highway service in Fig. 4l&.. Again, IMCt atl4 I14CH

V For a forceful reasoning in favor of slhort-run marginal cost pricing intransport, see A.A. Walters, The Economics of Road User Clarges, WorldBank Staff Occasional Papers No. 5, 1968.

2/ See C.D. Poster, The Transport Problem, Londont Blackie, 1963,Chapter IV.

3/ See Chapter V of this paper.

° 29 -

are the two long-run marginal cost curves for railway and highway respectively;

hence DAF and dBE are the social surpluses generated by rail and road.

Figure 4 4a Demand for Existing Rail and New HighwayServices and Long-Run Narginal Costs

DPriceper 1le.and Cost

d

B X

:C~~~~~~~~~~~~JC

Traffic Volume

0 OH D' de

As before, rail service should ultimately be withdrawn if and only if area

DAF in less than area dBE,IV and the optimum timing of withdrawal is deter-

mined by following a similar procedure as described in connection with

Pig. 4.s. If area DA is not less than area dBE, the railway service should

continue.

D. Case C- Rail vs. Highway Improvement

16. In cases A and B, we assumed that a substitite highway would have

to be built. If, however, a highway adjacent to the railway line already

exista, rail !'ne closure may require only improvement of the highway to

carry the higher volume of traffic. The basic principles of our analysis

still hold, but the method of computation is somewhat different. If, for

I/ See also footnote 1, page 25.

-30 -

example, the existing equilibrium is as in Fig. Ih.5, the toLal social

surplus in equUiibrium is given by DAP plus dEE. Note that when bo:h

rail and road se?vice are available, consumers reveal a preference for

rail service to the extent of OR. If rail service is withdiriwn and only

existing road service is supplied, consumers may be worse otf. Ir. aiiy

case, we smphasize again that we are seeking Lo maximize social siu!plus.

17. An mentioned in Chapter II, a number of road service alI,ernatLiv:;

may exist, diffeeing in speed, comfort, scheduling, and other res;xcte2/

frb. existing road service. Let V in Fig. i.6 be the road service with Ciexgreatest social surplus of all road and rail alternatives being considered

as replacements for Ute existing road and rail services in Fig. .<. In

Fig. 4.6, HI' is the deand curve for V., IMCrU its long-run margi Al :o:tL

curvel thus, the social surplus generated by Vx i; given by t'CL. Botli the

existing rail service and the existing road service should be terminatM1 In

favor of road alternatiwe Vx if and only iC IIKL in Fig. 4.6 is treater tlha

tha sun of DAY and dBE in Fig. .i. If this is the case, the optimum timinj,

of withdrawal l1as to be worked out followin,v a procedure aruilagous to ttut

described in connection with Fig. h.3.

1/ When road and rail aervice are taken as close but. not perrect substittit.cs.their demand curves are interdependent and Lhe measurement of col'timers'surplus for both together is somewhiat difficult. It can be shiown tlita thedemand curves in Fig. 4.S slihitly underesti.nate thie true consauers,' bur-plus derived jointly from road and rail combined. TD simplify thea exposi 'ion,the discussion in the text assumes that the underesatirtlon is negligible.See Annex V, "Conow_r' Surplus Measurement for Close Substitutes.',

g For example, the Villacanas-Quintanar section or the Spanian railway syetenhas an adjacent, well-developed Iilghway. At least two alternative variant'.of the passenger service on the existing hdghway lave been conside.red as sub-atitutes for the rail service. See Annex IV, "The Optimum Tiuitug ofSubstitution: Case Studies From Argentina and Spain".

' bee also footnote 1, pogp 25.

- 31

?igie I.S:Deinand ror-Existring Ratl andExisting Road Services and Long

'ilKc( - Price~~~jiiJ D ~~~~~~~and d

Coo L Cost.C() Raill (b) Road

A

P p ~~~~.AMTCR

I ..

0 R D ~~~~ ~~~~0 S dwTrafftic TrafficVolume Volume

Figure 4.c: Demand for Road Service Alternativeand Long-Run Margin7a Cost

I?riceanzd

01ft f~~raffic

Volume

- 32 -

180 ~T analysis can got somewhat more coplicatoti if we recogni-.:e

that demand omvon may not remain stable over time but mway shirtD

depending upon the price cha,rged for and the economic devlopmsnL iuiAtaced

by the new transpotation serwice Also, ir thlo c3se for a hirgWaY ALrkds

on Its mrit as a stimulus to rapid economic development, Ute otmutis Lirmie

to replace rail service by road should be advanced, accordingl.y.

B. The Roq3e of Cort-BenelPit Analysis

190 In cbbt-benefit terms, a project is wortlwhile if tlhe benefitb,

to homever tho may Oascrue, are in excess of the estimated costs. Am

w1 have seen. aboveS,the area under tha demand curve measures tie total betie-

fits received bp tho consumer of a transport service, while thie area under

the marginal mot cwve represents the estimate total 0osts. 'de call the

difference betwen these two areas the social surplus. The social surplus

is therefore a met-benefit criwiioo0 Why then have we so far used the

soial surplus viather than the more usual cost-benefit? The fundamental

reason is that the former underlinos the importancle of pricing policy. To

quote Prest and Turvey,

"The pricing policy adopted will atfect project outputs, andhence project costs. Tblls orl a motorway, for linstance,will affect the volifs of trafric, Andt thlisi may affect theapropriate width at which it should be constructedM. Tiusbenetts and costs are not independent of pricing policy." ^/

The literature on cost-benefit analysis is voluiidnous. Fior a cpre-hensive review of the technique, see A.R. Prest and R. Turvey, "Cost-Benefit Analysis A Survey," Surveys of Econoirtc Theory, Vol. III$londons Macmillan, 1966, pp. 155=207. For costbenefit analysis oftransport projects in particular, see C.D. Foster and ?1.E. Beesley,"stimating the Social Benefits of Constructixig an Undergrowdl Railwayin London," Journal of the Royal Statistical Society Ser4es A, Vol.126, 1963, pp. U6-76; and P.K. Else and H. Howe, op.clt.

2/ O22ci .. p. 171. See also Chnpter VI, "Pricing, De=ict, and Subsidyr,ArIAnnex VI,, "Mrginal Cost Pricing and the Theory of Second Beatv" inthis papelo

_ 33 -

'Once pricing policgy -i tven, the size or the transport projecttad the

volume of traffit are determined. Once the volume of traffic is tiius

de.leruiti:d, it does not. matter whether the analysis is carried out in

Lerms or social surplus or cost-benefit; they are identica".

wO. 'his 'observation should be qualified. If the planning authority

or a country 'as a multiplicity of objectives such as "better" income

distribut,ion and balanced regional development, benefits may not aU be

eLually valuable.j Different weights may ha-ve to be attached to benefits

accruing to certain sections or the population in certain regions. Cost-

bene&iM analsis is evidently more flexible and operationally more suitable

th3n tle straightforward social surplus analysis as outlined above in ac-

countLng for such factors. With cost-benefit the timing of the railway

serviee withdrawal can be determined to maximize net social benefit. A set

ok cost-benefit analyses has to be done for rail service replacement by the

optimum higway service in year t n 1, 2, 3,. e.The optimun year is the

year in whdch the net social benefits are maximized from the present to the

enld oC Lhe time horizoni. An ex le of cost-benefit analysis for rail

service withdrawal is I.Lven in Annex VII.

P. Project Selection and Optirmum Timing

:'1. So far we have been concerned primarily witl a single railway section.

Wlhen a itumber of railway sectionr are subjected to analysis, we may come up

wilAi .i list or investment projects, some involving investment in railway

service ani others in road service. Since investible resources are limited,

priorities have to be assigned to these projects as in all economic plan-

nlrn. We mention two attetpts to cope 'with this problem. Peter Steiner and

1! For ; lucidi diseussion, see Stephen A. Marglin, Public Investment Criteria,Canbridges M.IeT. Press, 1967.

Stephen NargUn have developed programing models for choosing among

alternative public investment projecta, &ubject to a budget constranit.

KarILin's model is dynamic in the sense that it tnkes Into aecount

biuget conatraints over a number or years, and determinee accordingly the

optim tim sequence of projects. But these mo.1.'ls rcquirc an nmount. or

date which my not be readily available to an evaluator of rail and road

projects.

22. Another method of selecting projects at the sector lovel -dlIicli

are cormiute1t vd.th national planninrg has been suggested by A.K. Sen.

it cals for three sets of data, namely, (a) the objectives and their

relative Weightes (b) the rate of discount, and (c) the shadow prices of

ajo,r inputs uch as labor. and foreign exchanmeto be provided to the

project evaluator at the sector level by the national economic planners.

The project evaluator, using social surplus (cost-benefit) anslysiss draws

up a Uist )of projects and their tlme sequence. The national plajuier now

colQares the total demand for.resources in the crAntry with the availability

of resources. If the demand is higher, for instance, he would ralse Uhe

discount rate and shadow prices'. Iext the project evaluator at the sector

level would repeat his calculations using the new dat-a, producing, a new

list of projects in time sequence. The national planner again compares

the resource requirements of these projecLu wit.h the available :upply. It

can be proved that under certain assumptioiw t1is I Lerativo procose

/ See Peter 0. Steiner, "Choosing Among Alternative Public Ittvesta.ente inthe Water Resource Field," Americant Econiomic Review, December 10-v4; andStephen A. Marglin, Approaches to Dynamic Investment Planning, AmsterdamsNorth Holland, 1963.

/ "The Role of Policy Makers in ?roject Formulat.Ion and Evaluationl,"Industrialization and Productivity Bulletin, (13), pp. 23-2i6.

35

.converges on an optimum solution. It is therefore suggested that the

pro,'ect evaluator prepare lists -.f projects and their time sequence

corresponding to a set of reasonable alternative discount rates and shadow

prices of labor and foreitsn exchange, etc. The national planner then would

:loclC. t.liat lisL wdic;h is consistent with the overall resource availability

avow and It the years aliend.

O. Summary and Conclusions

..- itWhen Uie trarl'ic voltune is not given as a datun, but the demand

ctWvt':; ror UMoo rallway servtce and for a reasonably comparable highway

service.are given, Ute *qtiestiorn as to whlether and When the rail service

silouldt be wi Uldrawn. in ravor of road service is relatively complex to

rezvolv.e. Assumiit} Utat l.he objiective is to maximize the social surplus,

detrined as the sumn or connmimers' and producers, surpluses, from which it

rollow; Utat price should be equated to m.irginal cost of production, the

proble.: at h: and can be rasolved in the following way. ?irst, from the

L1,'0,1.1j Cu1rveVS nnlid lo;r.-rnu m:ar.inaj cost curves, determine the social

.iar;nl,: ,er period genhir.aLed by thc railway service and by the alternative

ldi wIaway oervico. Ir tJike long-rum :ocial surplus of rail service per period

;:: lT.e: M.in .;i13at of hi'ihway, thre rail service shiould be withdrawn in due

.:our!e.-/ Optiwal Lining of withdrawal is to be determined by comparing the

n.ar;;,lvi ganr of posLponomi'nt witX the corresponding marginal loss. Con-

w^rSely, ir tle lon,g-riui surplus of railway per period is greater than tha:.

arL hirglway, tbe rail service should be allowed to continua.-

L/T'M s is essentially "two-level planning." For rigorous mathematical dis-cussions and applicat ions, see J. Kornai and T. Liptak, "Two-levelPlakutinge," EcononoLriv;a, January 1965; 0. Dantzig and P. Wolfe,I'Dveompaos.i .ionr Principi. as for Linear Programs," Operations Research, 1960;rnit J.K. SeiniupLa and Karl A. Fox, Optimization Techniques irn Quantitativerfl111il a .T.m4't2., AW.s1Aer'am: North-HMland, 1969.

2/See also footnote 1, pag, 25.

24. Cost-benefit analysis is essentially tihe biane au .;ornial taurplhs

ysia? HowevOetV if there is a multiplic]ty or objeetiive:i, t.he rormer

lu jperationally more flexibl.e ror takdng them into accounL.

25. In order to promote consistency with overall nattonal plannigly,

Uh project evaluator at the sector level should evaluaLe the pro,j.oel-s

mnd determine t!eir time sequence for reasoiublw alternative a.tLs of MiL;-

zount rate and shadow prices of major inputs auch as labor andr foreigni

xchange.

37 _

V.- FIkACIAL ANALYSIS

1 i. In the precedi;ag two chapters, the basic objective was maxi-

m.?7ation of social surplus for a given volume of traffic and for given

deman.l curves. Now we shall consider the rinancial objective, namely,

m.ximniiat.ion of tlhe railway prorit (miniini.ation of the railway loss).

Thi.- dantie itn objective is reflected in estimation of costs. With the

til.ii.ial objective, costs are rec'koned at market prices (including taxes

anld oub:iAdiert); only thoue costs are taicen into account which are incur-

redl by the railwaty itserlf. Secondly, for computing profit, only the

revetule earned by the railway is relevant. We shall distinguish two

l'se&:: (i) volionc or traffic and expected future revenue are assumed

La be kuoiwii, (ii) tle de.ndnd curve for transportation is known.

A. Tr:al''ie Volume and Revenule Given

ItC li a certMin railway section the expected volume of traffic

i ;t:lt' yo:irs aheatd h. kuowti, c,ii thie basis of past experience or otherwise,

i..; t'.! -Ae to be char.!or' is also kinown, then one can calculate the dis-

Ooiintk-.t preotmit. valule oi' totail earnings corresponding to the closure of

t.ho r..i iw.y sorevie. in yoo 0 0, 1, , 3, ... . In Fig. 5.1, curve OR

Ptro-t> -. - th.lieve dis-oinot.tdt present values. If Ute railway service is

lo:cvd iti year 0 = T', for iristaxice, tiac present value of total earnings

;iLtribul.-able Lo L4db see Lion Crown now Lo year T' is given by PT .' The

eurve OR tilses. at a docreasinR rate because annual revenue does not rise

fait. onou.ugh to overcome Lihe effect or the discount. Onie may also calcu-

Lit.e t.hie preeu1t, valuev or the total costs from now to year 0 if the rail-

w:ay S'rvice were to be closed In 0. In Fig. 5.1, CC is a curve of such

Vort s. If tlt.? ziervice is continued only up to period T', for instance, and

t,Iut', .. I'rl.duIated, the present value of the total costs is given by QT'. Thus

- 38 o

7.gure t.15 Atailw&y Revenue and Cost Over Time

C' (Cost)-E (Cout)

unulative /resent I

uJlue of .'1/evenuend Cost

T T X T ! , . __ ._ _ 11 'ime

/ l' , lII .I .

0. tI

with tVe revenue curve OR and cost curve CC , the prJesent value of the

prorit earned by operating the service up to year T and then closing

IL astunts to PQ. Similarly, tie profit for 1 - T is UV.

With these two curves, the rail service-is unprofitable up to

yeaP t.. It would be proritable to close the service some time between

years t and t'. The optimum time to discontinue the service is the time at

whichi piresent value of profit is at a maximum, or year T. In year T, the

mi^rginzd gain of postpoidng the discontinuance by one year is equal to the

nuar,:inal loss in the selise tlat th6 slope of curve OR is equal to that of

CC' .

t4. If tUe cost curve never croosse below the revenue curve, the

t.ermlniLion or rail StirviCte would niever yield a positive profit, as for

co::t. 'Urv Ei Iand revenuze curve OR. II' rail service is abandoned imrne-

dti9t.'ly. the loss would :mioaunt to OE. Loss could be minimized by continuing

the service to year T', when Llie tangent.s to EE and OR are parallel.

At ternitively, the cost curve may lie below the revenue curve beyond aome

PoInt. iu t.ime. In thlie case it may be profitable to continue service

indeth 1 adtely beyond that Point, even though it is unprofitable up to then.

The curve:; show us thiat even though a rail service is commercially

ut1ipt;14itablTeh ow and i:; likely to be so in the next few years, it does

not. ocatt.:isnrily fo]low 1.hat profil . can be maximized or loss minimized by

14'rinninating thle service itiniediately. Wt? r.ijst consider the alternatives

t%1'f1 }:it. it now, nex1. year, and inany years into the future and calcu-

1 t-.e ;ro-s;ent values or rovexilics, and cos s, and profit as sunmarized in

r.,iti 1 le ir tile P's in columi (4) are all negative, the optimum year

Table 5.1t Railway Closure.: Year-by-YearRevenue, Co t and Proi'i l

Present Value ofof Cumulative Cumulative Net

Clostng Revenues Costs Prorit(2) (3) N(L1 AiL) (3) _

O (Now) R0MG .C P0

1 R, C, .lP

2 R2 C2 P2

3 3 34 % c 4 P4

5 R5 C5 P5

of discontinuing the uervlce is that year when P it lowust. If scme of tht'

P's are poaitive, it may be piofitable to continue service for some years,

although it may be unprofitable at present and 1ia the near CuLure. TMhe

optimum year for closure is that year in whiclh P has the highest value.

B. Demand for Transportation Given

6. 'When the denand curve is given, the analysis is somewhat more

complicated. The procedure is formally very similar to th.%t giver in the

preceding chapter using social surplus maximization. First, the *tuestions

should the lin, be diacontinued? In Fig. 5,2 let JiM be the curve of

marginal revanue, definad an the increment in total reverue resulting from

production and sale of one additional unit. :NCR ia tie long-run marginal

R Fbr more on marginal revenue, see P.A. SamLue1.10i1, &Ltovonlcs; ax zUtNew York: McGraw-HiU 1964, pp. 478-80.

Flgure 5.i: Railwva Marginal Revenue and Lonllr-Run* . - riIrginal Cot;L

R

Rovemt?IIE.itdE

I14CR

-A

0 L R TrafficVolume

Fifnire t Ra1: R hilw3y Mar -inal Revenue and Short-RunMarginal Cost

;.tki

\ \ ' ~ ~~~ SMCR,; \ ~~/

Os I X -% / , sMr,\s~~~~~~~~sc

\. ~~\ . t

\ - bS ~~ /

s . .SK. /s_ -__- .-- _

S.'R

. \~~~~~~~~~~~~~~~S

0 R Vraf ficVolume

cost curve. Profit is maximized at the output at whichl t Ue marl.1tuil .toi L

curve intersects the marginal revenue curve. Thu:;, are,t RA I., tleu protii 1.

per period in the long run, ecuilibriumn output being OL. Arter compiittin

the profit for each alternaUive rail service, choo:se tie alte-rntive

yielding the highest profit. If no alternatilve, Including, the present- onr.,

shows profit in the long run, presfent rail service tihould b.!

7 Second, tho questions ir the line is Io be, closedl, wlien?

Suppose rail service is Len Ltatlly to be dlo-con.inued Itn an arbi:-.r;ri1y

chosen year 0. No further major rai3 Jnve.!aient. uifl be inade. C.oimpiit.

the short-run marginal cost curves: SKCR1 , SICR., S1IRC3, ... , SIRC0 for

yearbl1, 2, 3, c.oo 0s respectiyely. Since production is using progres-

sively older and more deteroriated plant and equipment, maisntenanze aln:

operating expenses will increase over time. 'The.short-run marginal coat

curve will therefore shift upward as slhown in Fig. ';.3. Accordirgly, the

amount of profit per period falls over time. If' bhe pre-dotert'iineJ 0 is

such that profit in year p is exactly .ero, then hius is the optimum 0

and the rail service should be closed in that year. If prorit in year 0

turns out to be negative, repeat the exercise wi Lh a smialler value of 0;

alternatively, if profit in year 0 is positive, try a higher valute of 0

This iterative procedure will convcrgo on tlhe optimum 0.

1sh3 -

C'. Swaruary and Conclusions

eWhe obJective is to maximize railway profit (minimize 1088).

;\'tts are to be reckoned at market prices (including taxes and subsidies);

only those costs are taken into account which are incurred by the railway

in providlng the rail service under review. For computing profits only

Uwc revenue earned by the railway system is relevant.

9. If uhe volume or traffic and tle corresponding revenue per year

expected in future are Inown, it is relatively oasy to determine whether

and when the rail service should be discontinued. Calculate the present

*-;lue of total profit derived from continuing the service up to year 0,0, ;, s, , ... . 'flie result is a list of profits to be earned, and/or

lo,v:.; t.o be Liucurred. hlat value of 0 is optimum for which profit is

hi~~ rie:1, or tlhe loss lowest.

lo. If, instead, the demand curve-is given, the analysis is somewhat

nrtIe icomplicated. Etouililrium output is dtetermined by the intersection of

the mart,Lnal cost and marginal revenue curve; the area between these two

eurvef measures the pro(it per period. The rail service alternative for

hi1lil profit is greatest is the optimum. Ir no variant, including present

servio.'.yields profiL iii the lonty rtn, the present service should be ternti-

na ted. The method of determining the optimal time for the termination is

forma]ly aimilalr to tle.t one presenIed in the preceding chapter but uses the

nuirgi n:il revenflue curve insLead of the Iransportation demand curve.

VI. PRICING, DEFICIT, AND .SITBSIDY

1. In a classic paper, Foster and &t!esley eatimate a posltive. dis-

counted present value of the proposed Victoria Line in Londons. it a

5 percent discount rate, social benerits minus all social costs would

amount to L65 million; at 6 percent to E39 tillion; nnd at 8 percent. rip'`.million. Then they examine t;e implications of alternative methods or

financing the investment. In their words,

*There is a serious problem now: ... to finance the Victorialine in the traditional manner would cause serious sociallosses... A high proportion of social benefits (up to between1.l and 61 per cent) would be lost if the Victoria Line werefinanced in the traditional way by a flat-ratc percentageincrease in fares." I/

This example clearly underlines thc relationshilp btwven pricing, and

optimal investment. This is a highly con4i1ex vubject, dealL wit's extenuivel1y

in the literaturo. We do noL propose to eo Into it here in a compre-

hensive way and shall only touch on cerl.ain a5p.w t-..

2. In course of exalining the unprofitable railway lines of the Bri tish

Railways, the Beeching Report considered the merits of redt:einn t.he fare to

attract more traffic and of increasing the fare. In theory, the amount at

price change required to make the railway service financially viable may rot

in fact be feasible. Let P stand for pri cc and Q tor quantity deminded. Tne

elasticity of demand, d, is defined as: e - d loV.1/dlog P. Therefore, J log

Q a e. d log P. Now, totpl revenue is P.Q. So dlog P.Q - d log P + diog , J

(1 e) d log P. If the elasticity of demand is -l.5, a 10 percent fall in

lJ N.E. Beesley and C.D. Foster, "The Victoria Lines Social Benefit sn.'Finances," Journal ot' the Royal Statistical Society, Series A, 19 b5o,pp. 67 and tSO.

2/ See, for example, R. Turvey (ed.), Public Ent&eprise, Penruin, 1968., British Railways Board, op.cit.,Part l, p. 18.

price li reauired to inoreree revenue by only half as mruc;h, while it induces

=. 'St pe-cent. rise in traffic. If the clasticity of demand is -2, a 10 percent

reduction or rrice results in an increase of revenue by the same percent, but

treaific voltme rises by twice as much. Such relationships between price change

and total revenue are given in Table 6S.1 for three values of the elasticity

'of demand,

Table 6.1: Price Change Required to Achieve* - Change in ToLal Revenue

" ' ' (percentage)Change in Price

Clhallne in- el e -.0.8 e = -1.5 e - -2.0

20 +1O0! lo ~ ~ ~ ~ ~ ~ ~ ;O 20 So_ }t} _ t7t) +~~~ ~ ~~100 .,50

The more fundnaentnl kluestion is whethier railway p.ricing policy

;-::lJl b.1 dari;:nd sol.'.y to iniprov- the financial position of the railway

~.t:l. ~.1:; tile casc ol' the Victoria Line, price change significantly

: s; Ee ::oc ial. bene 'it,s.

!1. If we 'Lkc ns :diven tlih margirL2l cost pricing rule, the railway

m:ny r.:tc, btadreL deCicit. Cor the rollowiing reasons.

(1) If the r:jilway exhibits increasin.- returns to scale,-ar,t nal cost. would bi ltss than averagc cost. 1/

(il) Since tite econiomic cats are calculated in terms of theslhndow prircen of capital, labor and foreign exchanges,the financial costs may be greater than economic costs.

Pareont.hetica:l.ly, we m;ention here that French econoiists Allais, Boiteux,*:lJU i)breu have sugges:teod Lhat all prices slhould bte proportional to

ri,gtrnal costs irreroective oa' dendnd elasticities. The factor of pro--x tt.i i,on;i t ;would be :o cho::en as to bring about 8j break-even situation.Se.e Droee, op.clL., pp. 27-14. Foster suggests average cost pricing-. 0i'l .O111A coM:F4tiuole.ly maxin,ize. eisiist,T r surplus subject to the conditionor 1%l .vn'itij bm.i,t-o'. Po:s.er, op.4!t.., Chnpter IV.

(iii) For poutical or other reasons, the government asydecide to operate certain railway services which,on econic grounds, should be closed.

If deficit arises for the third ?easonq the governmt will pay for the

deficit1, one wy or another. But if a deficit is expected for ithler of

the first two reasons, should the govarnment subsidize the sevice?

50 . SfWbile the resources at the disposal of the goverrment are limited,

claims on them are practically wxlimited. When the goverrment raises revenue

by taxation, it displaces private investment to scme extent. Whether

governm t funds thus collected should be spent on meeting deficits of aY

certain railway sector raises complex questions. As long as the goverrment

nget is limited and there is an opportunity cost of public fuds, the issue

of subsidizing a rail deficit cannot, in principle, be resolved in isolation

y the project evaluator at the sector level. What the evaluator can and

hould do is uws ensitivity analysis to prepare alternative lists of projects

orresponding to reaeonable, alternative sets of shadow prices of capital,2/

abor, and foreign exchange. Then the national plarner1 keeping in view

he overall resource availability and requirements, would determine which list

f projects is consistent with the national plan. Any projects on the list

equiring subsidy should be funded,

0 IHowever, if the objectives of national economic policy and the

hadow prices of capita), labor, and foreign' exchange are given and the net

ocial benefits of the railway service turn out to be positive,, the service

hould be subsidized, or the project should not be undertaken at all.

t The British Oovernment'W White Paper on transport policys, for instance, statesthat, in deciding whether to provide financial assistance to socially desir-able but unremunerative railway services, "the Minister will weigh the cost ofretaining the service - in terms of the amount which wiU have to be paid -against the social and economic benefits it will bring". See Ministry ofTransport and British Rilways Board, Railway Policy,Cmnd. 3439, London: Hi.MStationery Office, November 1967, para. V3.See Chapter IV, Section F, "Project Selection and Optimum Timing," in thispaper.

VII. SMARY AD CONCLUSIONS

1. We begin with a rail service which is apparently unprofitable or

uneconomic compared to alternative transport service such as road. Should

rail service be replaced by a highway service? If so, when? If it is not

to be replaced, should any deficit which ariaes be subsidized by the govern-

ment?

2. We consider two alternative objectives, namely, social surplus

maximization, and profit maximization or loss minimization of the railways.

3. Closure or continuation of present service are not the only two

options available to the railway line. The line may be partially closed,

or closed only to a certain kind of traffic. It may be operated on a dif-

ferent scale, on a different schedule, and with a different operational

system. In other words, it may be rationalized in a number of ways, several

of which should be worked out with an eye to future traffic. These operating

variants of the rail service should be matched with alternatives for the

substitute road service. The method cf comparison is given below.

4. Consider first the case where total future traffic is given. The

problem is simply to minimize transport costs and compare the long-run

average cost of rail service with that of road service. If the former is

larger, the rail service should be replaced at some point, if not, it should

carry on. If the rail service should be terminated, the optimum timing can

be worked out as follows. For an arbitrary date of closure, 0, optimize

maintenance and operating policy. Now calculate the present value of the

costs up to 0, and those of-highway service thereafter. Obviously the

total costs, thus comprted, ia a fbnction of 0. The optimum 0 is that for

which total cost is minimized with reference to 0. This is the general

principle of dynamic cost minimization. The computatico of the optimum 0

° 4B °

Is much easier under certain simplifying assumptions; three simple formulas

for 0 have been derived (See Annex III).

.5. XNxt, consider a more general but more complex case where the

traffic volume In not given but the deand curve for transport (rail and road)

* service is. For the moment, assume that the rail and road services are perfeci

substitutes in the seons that the demand curve to independent of whether and

when rail service is-replaced by road service. (We also examine the case when

,rail and road are not perfect substitutes). Also assume that the objective

is to Us=Xise the social surplus, defined as the sum of consumers' aurpluses

and producers' surpluses.

6. Now. take the demand curve and the long-run marginal coat curve of

railway. She social surplus in mxiiaised when the price is equated to the

marginal cost. The long-run social surplus generated by the raii service

per period has to be compared with that generated by the alternative road

service. If the former is greater than the latter, the rail service should

continue.. ;; the former is less, the rail service shorld be terminated sooner

or later in favor of its substitute. If so, when? Again, take an arbitrary

time period 0 when the rail service is assumed to be replaced. Given the

demand curve and the short-run sarginal cost curves for every periLod up to 0,

the social surplus generated by the rail service can be computed. The short-

run marginal cost curves for rail would shift up over time because, in the

absence of major investaent, the operating and msintenance coats would increase

an the existing plant and equipment ages. If the social surplus in period 0

generated by the rail service is more than the social surplus derived from

the demand curve and the long-run marginal cost curve of the road service,

~~~~~~~~~~~ 1.

take a higher value of 0 and repeat the above process. The optimum 0 in

reached when the social surplus of the rail service in period 0 1s approzimatel3'

equal to that of the road s3rvice.

7. ~ XNowadays, coat-benefit analysis is a familiar exercise in trans-

port. This analysis is equivalent to the social surplus analysisBas given

above under the assuMption that there is only one objective, namely, aaxi-

misation of the net benefits - social benefits Minus social costs --

without regard to whom they accrue. However, cost-benefit analysis is a more

powerful tool in the sense that a multiplicity of objectives, such as more

equitable income distribution, and a multiplicity of constraints, such as

savings and balance-of-payments, can be directly taken into account.

B.8. In any event, since resources are limited, there is a need to

assign priorities to the investments in the railWay sections of a system

which emerge from the above-mentioned social surplus analysis. With this

encd in view, the project evaluator should conduct a sensitivity analysis

by tak.ng reasonable, alternative sets of shadow p:ricee of capital, labor and

toreign exchaJge. The highest priority is assigned to that project which

both has the largest social surolus and also survives all or most of the

iensitivity analysis.

Next we consider the objective of improving the finascial position

zf the railway system alone. If tba volume of traffic and the expected

rutur3 revenue are known, the optimum year of discontinuing the service has

to be worked out which maximizes the railway profit or minimizeo the loss. This

method is relatively 8 1 If the traffic depends upon the price charged

and the d_nd curve io knows, the profit maximizing volum of Uraffic in

the long run is determined by equating the marginal reven and the long-run

marginal cost. Sho profit for each of the alternative variants of the rail

servce can thus be ooWuted. And that vriant is chosen which yields the

largest *mmunt of profit. If no vriant is profitable9 ihe service should

be discontinued. .e alVritbJ for finding the optimal ti.. is analogous

to that used in -w ocuOic analysis.

100 FinaL>D m eked whether the goveriment should subsidise rail°

uW deficits. I o ses the gowroDt decides for political or other

reasons to retain a rallwq service against economic considerations, it is

in effect taking the responsibility of subsidizing it in sone for* or

other. However, deficit may arise alao because long-run marginal coot is

lose than long-run avcrage cost. As long as the govermient budget is lim iod

in quantity and thbre is an opportunity cost of raising government funds,

the question of spbsidising the deficit of a railWa service cannot be re-

solved in iolatioo. It requiresa. broader analytical framework. However,

given the objectives of national economic policy and their relative weights,

and the shadow prices -of capital, labor and foreign .mhange, if the railway

project has a positive net present ralue in ter -of the cost-bonefit analysis

the govermusat should subuidiie the deficit it any; otherwise the project should

not be undertakeo at all acd the subsidy issue does not arise,

A.AANX I

(NMICM M1W.1-:4 DISELIATIUON A*'J & PR2IFItATION

1. The principle of choice between dieselisation and electrification ofa railway service is to accept the alternative with the minimum presentvalue of total costs,- from a class of alternatives equivalent in the ensethat the magnitudes and time patterns of their benefits are similar.- Let:

K, K' capital cvpqnditures for dieselization anbdielectrification, respectively;

A, A' annual operating and maintenance expenses for thetwo projects, respectively;

T, T probable life-spans of plans and equipment for thetwo projects, respectively; and

i = Lhe consLant rate of discount.

Thc present value of Lhe costs of dieselisation appears to be:

T-(1) .=K4A ,J -it

* C = K + A J e dt

L,ikewise, the present value of the costs of electrification is:T/* -it

(2) C' Ks + A e dt* 0

2. 1 Lis ziecessar7 So correc t for. the tnequal life-spans of plant andeqculp:riln.. ;b simply suppose each is indefinitely renewed at the end of itsecron tic life. Thus, for diieselization we get:

l;' Scc llarcel Roiteux, "The Choice of Plant and Equipment for the Productionof i'ectrie '.nergy,", in Janes it. Nelson (ed.), Itarginal (st Pricing inI'raMtice, 1ux:1ewood Cliffs, :.,.: Prentice-Hal', 1964, pp. 199-208J.

~AiJiEX ?r -1 1 r- -?oltC 1 -Pace2 2

.- ItF 2T -it -3 it1. >,, ., . oiT - 2T

d a + KG dt * Ke A T a dt .] [ [ .~~~~~~~~2T2

(original p3.ant and equipment) (firs. replacemment) (seconid replacemziit)

ors

Co K a A7a dt

-whore a reprsesits the rate of replacement annuity at. coIzwuid interest i forT years. This expression can be rewritten as folos:

(3) c - K a ( A) A

ilarly, the total discounted coats of the electrification project, is given by:

(4) CI K I * (a' K * l)/i

where a' is the rate of replacement annuity at compound interest i for T' years.The choice depends on whether C or C' is greater.

3, If we wish to ealculate the cost per period from (3) and (4), Lheprocedure is as followss Let Y denote the Cost or dieselization

C Z /e dt Y/i

or9 in view of (3~we gets

Simlarly, the cost of electrification per period, denoted by Y', is given bys

(6) Y° o(iKa) +Al

ANNEX IPage 3

^s. If, however, instead of indefinite renev'al, a finite time horizonis envisaged, further corrections are necessary in the total cost calculationto take into account the salvage value of the plant and equipment at theend of the specified time period. Also, in the above exercise, we assumethat Wto economic life of plant and equipment and its maintenance expenses arefixed. There mny exist scope for choice: the life of the equipment maydepend upon the maintenance and operaking policy.l/

This example of choice between two kinds of equivalent projects isintended to establish one principle: 'lf the benefits are the same but coststreans are different, choose the alternative which has the lowest discountedCos;ts.

/ For a. discussion of a rarkge of other issues relative to replacement, seeD. W. .Jorgenson, .1. .1. McCall, aid R. Radner, Optimal Replacement PolicY,Otica,;o: aind McNally, 1967. Sce also flasse, op. cit., Ch. II.

ANNEX II

'WNPUTATION OF CLSTS

A-. "Long-Rum Average Lbst.

1. ''For any given volume of traffic, tho time stream of costs is uneven;it is particularly high When a major capital expenditure takes place.Let C denote,the expenditure at time period,t, under the assumption that,a certain level and quality of transport service per unit of tire must beprovided indefinitely. The present value of the cost stream.at the discountrate i, denoted by C, is as follows:

--it(1)- CH- C e dt

> 0, ~t

irom the total C, we need to derive the amount of costs per period, denoted by*Y. Dy definition,

C''~. ,'/e ,,dt Y/i0.-

.C sr A'Xz-

or, in view ofr l),

-it() Y i Ct e dit

If the volume of traffic per period is Q, the average 'cost of traffic perperiod Is simply Y/Q.

2. Jt is easier to understand (2) if it is assumed that in order to sustainindefinltely the given volume of traffic we have to incur now a capitalexpenditure of K, with an economic life or T years, and operating and maintenanceexpenses of A per period. rhen it becomes clear that Y of (2) here isfOnTtV.,Y identical with Y of (5) in Annex I.

B. Short-Run Marginal Cost.

.3. The estimation of short-run marginal Cost of rail service has given riseto an anusing story kIown as the "Passenger to Calais Paradox" of Gabriel Dessus.l'

1/ Gabriel Dessus, "rhe General Principle of Rste-Fixing in Public Utilities",in .J. R. !Nelson (ed.), op. cit, pp. 42-44; Lesourne, op. cit., pp. 275-277; andWalters, Op. Cit.

ANNEX IIPage 2

Suppose that a passenger gets to the Station Paris-ioord just in time to boardthe Calais-bound train. If unoccupied seats are available, the cost of

.. transporting this passenger is, in practice, nil.- But if it is necessaryto put an additional coach, run an extra train, lay a now wrack, or widen the Chati-tilly bridge, the cost of moving this last passenger mouwts with astonishingrapidity. How, in a situation like this, do we estimate marginal cost oftranBport? The indivisibility of inputs of railway service and the unforeseennabure of passenger demand are at the root of this paradox.

4. Let us assume that the number of Calais passengers who travel each dayfrom Paris-Nord reiains unchanged, and let us focus our attention on thediscontinuity of the coach factor. Suppose that a coach has a seating capacityof eighty passeogers, and that as long as a coach is not full, the transportcost of an extra passenger is nil. khen the coach is full, the cost of anadditional pasoeoger is indetezminate, since the possibility of accomodatingan eighty-first traveller has been ruled out ex hypothesi.

5. Pbr a given number of ooaches, a passenger's marginal cost relative tocoaches will be nil or indeterminate, depending on whether the coaches are Lullor not. However, the number of coachcs to be utilized is itself a variableto be determired by marginal considerations: it must be such that the proceedsfrom fares remunerate the coaches in service at their marginal cost of production.Consequently, the problem of determining the number of coaches to be run hasto be considered not in terms of one additional passenger per day, but in termsof a group of eighty additional passengers per day. It is in this maiuier thatthe indeterminacy of marginal transport cost relative to coaches is circumvented:its magnitude is equal to the eightieth part of the marginal coach's dailyrimzinmg cost.

6. However, it is possible that-the demand for passenger service is randomin nature amd does not necessarily come in nultiples of eighty, so the lastcoach will not be full and the cost of transporting a further passenger willbe nil. thder such circuzwtances, the railway's planning has to be based on acertain number of expected passe nfrs, with provision of "spare capacity" toaccouodate unforeseen passengers.-

7. The short run, however, is defined as that span of time within which nomajor investment in plant and equipment is feasible, technically orotherwise. In the shortrun, therefore, the capacity of plant is by definitionmore or less fixed. Whether minor replacement of equipment,which is allowed,in worthwhile depends on the length of the period.

V See Walters, loc. cit., and Lesourne, op. cit., pp. 284-289.

ANNEX II

: 8..".Assume that the duration of the short run is precisely given, and thatproduction is scheduled to increase by dQ from its present level. If dCt isthe -additional amount of expenses (for maintenance, operation, and replacementif called for) in period t, then the present value of the additional costs,

.deitoted by d C, is given by:

-it*-(3) -d Ca (dCt dt

where 0 is the period marking the end of the short run. From dC we cancalculate the marginal cost per period, denoted by y. ay definition,

(4i) d C y| e dt

or, in view of (3) and (14),O 0.

-it -1#t .y - iJ (d Ct) e dt(- e )

The y of (5) is the short-run marginal cost per period; it represents theavoidable additional costs reckoned on a per period basis.

C. Long-Rum Marginal Cost.

9. The definition of the long-run marginal cost ib similar to that of short-run marginal cost, except that d C now includes capital expenditures as well,-and 0 is replaced by X, in equatiAns (3), (4), and (5).1

10. While the empirical estimation of railway costs has a long history, nomethod has yet been fully developed and tested for estimating relevant 4raneportcosts in the context of railway closure decision. ?I re are, broadly speakine,three methods of estimating long-run marginal cost, accounting, statistioal

1 / See Tesourne, op. cit., pp. 271-272; and also R. Turvey, 'Marginal Cost, nEconomlc Journal, June 1969, pp. 282-299.

Z/ ie methods are also applicable for estimating short-run marginal cost;see Lesourne, op. cit., pp. 292-313.

:-ANHEI IlPage 4

1/analysis, and direct technical analysis. I¶e first method is used forcost eoisation in the Spanish railways study./ and the East Africa Transport

itudlya3 ile tje second method has been used in connection with tUe ll.S.rdilwar ssa8.16-

1l. 5 The Est Africa Transport Study computes essentially the averaCe costwhlch differs from marginal coat in nature and maganitude. Wb have aireadjrseen in Chapter II that the basic framwoork of cost estimation this study-w eo is sinwhat irrelevant to the problem we have posed. The method usedin the Spanish Railways study is much more reasoxiable, sinLce it considers onlyavoidable oosts; nonetheless, it does not calculate the long-term zaarLinalcost of transport as we have defined above. This calculation would be

possible using the cost data given in the report, since the sets or cost dataare related to alternative levels of traffic (high, medium and low forecasts).

12. In the U.S. railway study, the method of statistical analysis forestimating marginal cost of railway transport is quite sophisticated, but againrather irrelevant to our purpose. The results, suznarized in Table 1I-1,have been derived by the method of least squanres multiple regression, withc1tes-section data (1947-50 averages and 1952-55 averages) from all Class IUnited States railway systems with over 3,000 mdles of total track, except theNew York Central and the Pennsylvania Rsilroad. ibr example, 1947-,0 maintenanceof way and structure expenses have been computed by:

(6) z - 3,5 4 0,801 + 714 St + 0.000284 Q + 0.000772 Qp R2 - 0.9321

(372) (0.000069) (0.000415)

where B represents an expense account, S a size measure, and Q a traffic variable,nd the subscripto denote the followlng sub-categories:

w - maintanance-of-way expenses;t - track amleage;f - gross ton miles of freight traffic;

and p - gross ton mdles of paosentger traffic$'

k For an approximate example of the direct te-hnical analysis for railwaymarginal cost, see Sjoberg, oM. cit., pp. 42-55oNechel, op. cit.

/ maThe boonoitTIntelligence Uhit et. al.,op cit.J. R. iAyer, M. J. Deck, J. Stenason, and C. -Zick, The ftonomics ofOoetition in the Transport-ation IndustrIes, Cambridge: HarvZrd University

Press, 1959.D Ibid, pp. 277-278.

ANNEX IIPage 5

Tie figures in parentheses below the parameters are standard errors ofestimates; if a probability model is appropriate, the parameters areconsidered significant if the- parameters exceed their standard errors bya factor of 1.6 to 2.0.

13. A major statistical objection against this kind of estimation oflonr-run marginal cost is that the presence of multi-collinearity betweenfreight and passenger traffic tends to reduce the economic significance ofindividual parameters. B3esides, in view of possible multicollinearity,the high correlation may be spurious. For puruposes of predicting total ythese phenomena are not harmful, as long as the spurious- relationship isunifonm. But they invalidate the method for measuring marginal costs offreight traffic and passenger traffic separately. In any case, for ourpurposes, the parameters do not signify avoidable costs, in the sense that(6) may not hold at all if one of the services is closed altogether. Further-more, one has to be prepared for getting absurd results. For example, theequation for 1947-5D joint equipment repair costs turned out to be:

2(7) E D $265,600 + $0.000113 Q - $0.000109 Q R - 0.76

jer f P(0.0000236) (0.0000951)

where the subscript jer on the e perse variable indiczit.esthat joint equipmentrepair costs are beinG analyzed.- The parameter of the passenger variablehas the wrong sigl. Witih that variable eliminated, the cost function wasmodified to the following:

(3) E $35;1,100 + $0.0000889 Q R2 - .76jer f

(0.0000108)

Obviously, the elirination of the passenger service makes very little differenceto the aialysis; neither Ute multiple correlation nor the freight variablecoefficient are modified substantially.

14. This kind of analysis of marginal cost, therefore, is not uBeful in- thecontext of railway line appraisal, because the individual coefficients do notlhave the kind of economic significarnce which is relevant here. The authorsor the tl. S. study, after all, had a different purpose in mind. How, then,should Ute long run marginal cost be computed? The planning authority must

Ltc/ Tbid, pp. 299-300.

A:X II

Table 11-1, Sw9z7y Estimates of Long-Run marginal Coate in the U.S. RallwaYs

(Per gross-ton-mile; U. S. cents at current prices)

.9hl-50 1952-55No. - ~ Costs Freight Passenger Freight Passenger

(1) Train, ation, yard, traffic,and general elpenSes 0.8721 4.2330 1.700 1l. A

(2) User cost portion of maintenance

cost 0.6900 1.4100 0.910 1.53(3) Variable portion of depreciation

expanses 0.2120 0.9760 0.216 1.00(4) Marginal operating Costas

(1) + (2) + (3) , 1.7741 6.6190 2.626 7.03(5) Variable portion of capit1l- coate* 0.4011 1.4079 0.445 _ __4

(6) Total long run marginaloperating and capital

costs: (L4 + (5) 2.1752 d.0269 3.271 3.51

* At 0% interest rate.

Note: For pricing decisions, these cost figures need several modi±icarions.

First, some sort of conversion between gross ton miles and revenueton miles is needed. Secondly, these figures should be price correctedto bring them up to current levels. Thirdly, these estimates are

"typical" figures applying to freight and passenger mnvements of anaverage or ordinary kind. Adjustments should be made for qualitydifferences in the service rendered. See Meyer et. al., pp. 61-o3.

Source: Mieyer et. al., op. cit., p. 62.

.ANNEX IIPage 7

make estdintes of the time stream of avoidable capital expendituresand of mnintenance and operating expenses for alternative volumes oftraffic, and then calculate the marginal cost from an equation such as(5), replacing 0 by aD The Validity of such an estinate of the long.run marGinal cost, of course, depends entirely on the validity of theoriginal estimates of expenditures, expenses, and the discount rate.

ANNEX III.

MYItAMIC COT' MTNIMIZATION AND THE orImuim TIMINU OF SUBSTITUTION

1. .I thU volume of traffic is given and rail and road services areequivalent, the relevant indicator is the long-run average cost. IfIt is lower for rail than for road, the question of replacing rail servicedoes not arise. II long-nun average cost for road is lower, riil serviceshould be replaced. Then the question of timing arises.

2. For existin- railway facilities, slated to be replaced, let m be theannual operating and maintenaice expenses of the railway service in R thebase year. :aJor rallway investment now or in future is ruled out. yz,derUhcsc eircumstances, suppose that mu rises at the rate of -per year.;YFur thermore, let S be the amount tf costs which would be saved in therailway system as a kwhole, plus the current salvage value of the equipmentof the rail.Wy service under review, and suppose S falls at the rate of fper period of time as long as the closure decisionRis postponed.

3. Also, let IC be tie. required capital expenditure for the highway, to beincurred in the pe#iod when the railway service is replaced and repeated every7- years thereafter. rhus, / is the lifespan of highway plant. Let mH betie annual operating and maintenance expenses for the highway service.

iie., the present value of the cost of operating the rail serviceun to, and not beyond, 3ear 0,and replacing it by road service in that yearis -ivei by:

C ml e3 1-i)tdt - S e-(f+±) 0 1 e it dt

-i0 -i(0 +7) . +2:;)

+ Krf e +K e H + e j O * | or

mn .'f (g-i)P 1' -(0+i)O m -iP(1) C a1 S e. - S H e

g-i J + R i

-10 a K -i0+ KH e + _H H e

i

wcere -a. is the constant replacemenit annuity at compound intbrest i, the lifesp'an o°l Kl being2' years. Obviously, C in (1) is a function of 0.

/ ThIUs we are assuminow'there is no Boiteux Effect, described in Chapter III.

-AENBI IIIRig& 2

5. NW, choose 0 uc that C is zrAninized- TIds requires the fllowit g:

(2) a *m + K (i +a) (f + i) S . ,, N t R

te solution for 0 i given in the figure below.

go

- / _ - -- - a + 1 (i + a)H tl H

-f0H R H)j 'a-

I_ I. 'im

6. If S is negligible, (2) reduces tota.3 ~ ~ ~ R * Kg (1 + a)

(3 o a..1 logo* ~ (i.ai* 'R

It S is ignored when in fact it is not a negligible majnLitudc, the optimaltime ORwould be overestimted by (3) Statement (3) also inUlies thatif R is greater than H + K (i + a ), the optimal 0 is negatv, i.e., thereplaceent of the railway service byV road service is overdue.-

2/ Such instances can be found in certain railway sections of Argentina,vuder certain wiptions. See Annex IV.

AN.1EX III

7. If f is zero, i.e., if the salvage value of the railway equipmentdoes not fall with the phsneage of time, (2) becomesz

- - x + i (1 +~~ a )-i S(Ii) ~ .- L log i H H (4) pa 1 1°e -L

R

UO Tn summary, if it turns out that the long-run average cost of railwr7servicc is more than that of the alterniaLive highway service for a givenwlune of projected traffic, the for mer service should give way to the latter.UnWer certaLi siiqlilpyiiw assumptions the optimal timing of the switch-overcan be calculated witit (2), (3), or (4).

ANINEX IV

THE OPTIMUT1 TIIfli\'G OF SUBSTITUTION: EUMUS FRCQ

ALVEMTIIIA AU]D SPAIN

1. dhis annex relate's to the econanic analysis wnen traffic volume is given(Chalter III) and to. Annex III, "Irnamic Cost Ilinimization and the Optimal*',iming of Substitution. r To principle, costs should be calculated at shadowplrices of the inputs; but in the following cases market prices have been used.

FIFTEEN EAMPLES FROM THE AROENTINA TRANSPORTATION STUDW

2. Table IV-1 gives relevant data for fifteen selected railway sectorsof the Argentina railway systemi. Traffic on these lines has been projecLedon the basis of the anticipated pattern of economic growth and industriallocation. 'he problem is to minimize transport costs, given the trafficforeca,31. The substitute highway is assumed to be equivalent to the railwayin the sense that the volume of traffic is not expected to be sensitive tothe mode of transport. The required capital expenditure and operating and

maintenance expenses of the higshway service are ala given in Table IV-l.

3. The fifteen railway sections of Table IV-1 fall into five categories,defined by the relations between annual operating and maintenaace expensesof rail and highway (m and m , respectively) and betwein the capitalexnenditures (KR + KH It H

Sections (1) - (5): H< m , K>K m-O

(6)-- (10):mH < m^ K >K. > 0

(11) - (12):mi <im , O<K <KH R RH

(13): n > m, K ,C( :>0H it It H

(lO4- (15):mH> m ,O< K < KH ll R H.

1/ Ilinistry of Public Works and Services, Transportation Planning Group,

A LonG Range Traisportation Plan for Argentina, Buenos Aires, 1962.

*T gm I'm xmM ll*sta-6 geo.i'm Po qiG N p£Mu ()C)in,'.gme ep jefl n '() umIut ai Cm nro. * (j. %) _ lowo e % wd t sW _in st,mau to*ion p em weso ittqn*s. * (a * Po * V3 -AM £mueu 1 a 'mpsu *eu Oa el q eqt e msamm AflUa iTs tqJ" SU- on O ° 1 I*U isoj ') ( (9) _p SPWU

9"SK ftL(C CUTI LVeB 0T1 oirs¶ o`MrC6 6'C e u SdM~ UO*M w99'1t 1S 91 W: 9't 95S*(C gO-og o0aU1 (%-9g% qp-

dgiA9 wAgse 0g6. W 969 LC 00090 (109S US S15', (0 11

8& "WI L 0 W L go 0 9T (CV9 t t - . a8

O II _ "I 160 1S9: 9S-S IST-e S9 -S ((9 1 001 tIISTtfMIILO'"mt ITT * - h ae SWOtt- 01r16 (61 c L90-l WKS*fl 0o09t 9f-5c m3q *r* T Y "WI ILS*( LOV1 l i tW6m 0"9 ILT4,1o Mot q Ce meto *9 I 2 WI - S 6gl UC- 9S9*, IWO! SL! 9tOm usSS im-

u1 9q 99OwSdS {If- L* I a 11 A S L't 191 -t ooau l9n 1st1St t"Loo 000-56 &SUtI ald) wd 'V-Isw w* 1 "WI _ 1L dICT U t'l 9t- 6S-W f5t91 0C9-10 09l9 g,9U L* 9* tIo M's WI's 990 96-01 - w-U -o" ragtag m 'S* Wo !mA W.C0 T° L °- tLC "

t'* (360 W.S * ssn (36.0 ara w 59(1t- OW urtri s of t'01 0(L*o MITK 9(1 OtLO SL8L - YI-CS VPmwu!I t a

U6> "@0 999£ - U-S wo S: ° Su-0awlem" Sr ttn() (0.) ) () 1) (9) (5) (q) (C) (a) C:).. ~~~~~~~~~~~ . . ( ,. l)3. . 3 ,A)_ 3 C.w.U _ , _VI 7,K_i uK ae ii in

4mt Jo *almus u b j.P_) l . )- t- *RU IS0 -tflqt J@ Dol .eWlTKq'0~~~~~~~~'e __~ze I'WTU slxa-x . t.e b

1111110110111 TnidT

(see uIf) . 8 6 0 2

mwsuew-nuu -_ ae~ _mi~ _t etq

ANNEX IVPage 3

The first five sections are exaMples of how economies of operating andmai:ntenance costs can be.achieved by switching to road service requiringno additional capital expenditure. In snch caees, rail service should bereplaced by.highway service immediately.

4. Fbr the next five sections, both operating and raintenance costsand capital expenditures are higher for rail than for road. However, theeconomic life of railway investb2nt is assumed to be 30 years while that ofhighway investment is 25 years.- Since K is the capital expenditure, m

R Rannual operating and maintenance expenses, and a1 the constant replacementannuity at. compound interest i for. K with a lifA span of 30 years, the

I.long-run total cost per period is (mR + (i + aR) KR)i which is the total ofoperating and maintenance costs, and interest and capitalcharges per unit of time. If this amount is divided by the volume of traffic,we get long-run average cost of railway service. Cbrrespondingly, the long-run total cost per period for highway service is (m + (i + a ) K ).

B H H

5. A comparison of Columns (4) and (5) for sections (6) - (10) revealsthat in all cases the long-run average cost of railway is higher than thecorresponding highway cost. These railway sectors, therefore, should bereplaced by highway. What should the timing be? While the Argentina reportsuggests a time-table. for the replSement of railway services by highwayservices, it seems to be arbitrary'.. If it is based on the highway cost-benefit analysis,2/ the methodology is incorrect, since it does not take intoaccount relative costs of the two transport modes.

6. Applying our method, let us suppose that the railway operating andmaintenance costs in 1960 as given in column (8) rises thereafter at a certainrate. Ignoring the possible salvage value of the railway plant, we can useequation (4). for.sections (6) - (10) leads to the conclusion that the optim,um0 is negative; in other words, the renlacement of the railway service by ahit-hway service is overdue. As for sections (U1) and (12) columns (4) and (5)-show that the long-run average rail cost is higher than the long-run averagero.ad cost. By the same reasoningl as above, the railway line should have been'discontinued long ago in favor of equivalent road service. The last three

1/ rlinistry of Public Works and Services, op. cit., Appendix II. p. 68.Z/ See op. cit., Appendix III, p. 95.3/ R1eported in Appendix II, pp. 67-70.

ANNE IVP~g 4

rauq line1 ahould not be discontinued at aUl becase the long-runaverage cost of rail is lover than that of road.

1/A CaBS Study from the Spuiiah i1lwwy Syeted

7. T fifteen railws sectors of the Argentina railwivs were consideredfor cocplete closure. A distinguishing feature of the analysis of Spanishrailway sections is that the sections are being considered for partialclosure, namely, discontinuance of passenger service keeping freight serviceintact.

B. The Villacanas-Quintanar rail line in Spain is a stub end braR'lhiline, 25 km. in length, extending east from a Junction point 1?1 k-m. :'nof Madrid on the main line to Andalucia (see figure). Villacann:s is LieJurction station. Both Vie branch line and thet main line are parallei'Jby paved highways over their entire 1Lngth, and Quinta:nr. t.ne ternmilis orthe line, lies on National Highway 301. Quintanar and t-wo interim. %t3ti3tA:on the line receive regularly scheduled bus service direct to Madrid. whcreasrail passengers going to Madrid Fmust change trains at Villacanas. 2/

Madrid

Ibad

- - - - Rail\

1 Ralph E. Rechel, SPanish State Railway Study Progra! for DiscontLinuanceof Services on Light TraTfic ;Iailway Lines: 'ntcrim .Seport Illustratin4APpropriate Nlethods of Economic aid Financial Analysis. Washinl:;Wn ,. X,Augstut l90o.

2/ lbchel, 2C. cit., p. 3.

ANNEX IV

9. rIo alteniaLive plans of highway passenger service to replacethe Villacanas-Quintanar rail service are being considered. Alternative Ais a straight substitution of bus for the present rail passenger servicebetween Villacanas and Quintanar; all passengers going to or coming frompoints beyond Villacanas would transfer to or from mainline trains as atpresent. Alternative B, on the other hand, provides a separate andcontinuous through bus service from Quintanar to Madrid and other pointsnorth of Villacanas in addition to the services within the study line.The costs of the Alternative B through bus service to Madrid have beenlallocated between the within-the-line portion of the trip and theVillacanas-iTadrid portion. This allows comparisons of the total costsof the services movinz- within the line, and identification of theincremental costs of introducing through service from Villacanas to Madrid.

10. rhe estimated annual operatin- costs and reqr9 red capital investmentfor Uhc Quintanar to Villacanas railway passenger Corvice from 1965 through19 90 are given in Table IV-2. The table also rives the correspondinehighway costs for Alternative A alone. 'his is a very clear case: rail

.costs. dominates road costs 'in every year through 1990. with two insignificantexceptions (1975 atid 1!d5). There is no possibility of any asin bypostpo1nin- the switchover from rail to road; the optimal timne is alreadyoverdue.

11. Int order to decide between Alternatives A and B of the road service,tiheir respective cost streams would have to be compared, which we have noteonie. In aiy evet, 'tte road services between Quintanar and Villacanasas proposed in Alternatives A and T3 are qualitatively different and mayhave different demanid curves. rhis is a separate matter which has beentrented in Ciapter IV above.

ANN= IVPA- 6

TR.I-Zs SainsptSald 0 t o ir l ad aW!PAm!iMer Srvic.

B.mQuintuanr and Villaoa sa

~(x4211cn pesetam)-

Itil Wghva.yOperting Capta TotiLl oeting -djiital Total

row - Int eetmentt Outl1

* 1>965 be5981 i4598 1.570 2.710 4.2dO1966 4;677! 4.677 1.802 .1.355 3.1571967 4.677 4.677 1.802 1.8021968 4.677 ..677 1.932 1.355 3.287U969 4e.71,5 4..745 2.163 2.163

1970 4.715 4-.745 9,248 2.24d197 4.B21 4.821 -2,246 '2.24J1972 4.821 7.650 12.471 2,479 2.4791973 4.82. 4.821 M4?9 2.4791914 5.180 7.6go 12.830 L609 1.355 3.964

n75 5.180 5.180 2,609 2.70o 5,311976 5.180 5.180 2.840 1.355 4.1951977 5.180 5.180 I81-0 2.8401978 5.18A 5.1S 0 M.640 1.355 4.195179 5.256 5.256 2.927 2.927

190 5.256 5.256 2.92? 2.9271961 5.256 5.256 2.927 2.9271982 5.256 5.256 2.927 2.927183 5.256 5.256 3.013 3.0131984 5.256 5.256 3.013 i.355 4.368

1965 5.256 5.256 3.013 2.710 5.723196 5.256 5.256 3.013 1.355 4.3681987 5.333 5.333 -3.013 3.0131988 5.333 5.333 3.288 2.710 5.99i198 5.333 5.333 3.288 3.2dB1990 5.333 5.333 3.2d8 3.288

TOAL lZ7.nk 3§.300 ]12.4 67.528 17.5 !;.143

?4toa: ThesO figures relate to the "high" traffic forocast for Altoriabive A, whe-is a straight substitution of buws for the przi3ant rail servico, as disrlc8tfrom Alumative B, in iidh provision is wAs for a thUuelu servico fromQuintanar to Madrid and other poiiits norts of Villa aCLs, as well as therequired nervice within the study lille.

Okmrce: 3;whel, ou. cit.

ANN E V

CONsM1MS' SURPLUS MEASUREX4NT FOR CLOSE SUETITUTE;

l. | Let there be n consumers (i - 1. 2, ... , n) who buy two substitutegoods, say, road (x) and rail (y). Consider consumer J. His utilityfunction is: uj u uj(xj, yj zj) where % is the generalized comnwdity"money'Z which stands for all other cpmwodities. (Hereafter, for conveniencewe shall omit subscript J.) The prices are respectively p, q, and 1.Consumer J maximizes his utility function subject to the budget constraint,Py the Kuhn-Tucker theorem, the necessary conditions are:

(1) (iu/ x)/pR S for x 0

(2) (cu/ d`y)/qr -A) for y O

(3) (Jfu/ ) z > 0 by assumption

where is the Lagrange myltiplier.

2. E:ementary theory of consumer's behavior assumes that the consumerbuys a positive amount of each and every commodity, mainly because the usualwethod of calculus cannot cope with corner solutions.l/However, followingthe contributions of Kuhn, Tucker, and Arrow in 1950,- the-theory has nowbeen generalized.

3. For every consumer, conditions (1)-(3) hold. Accordingly, we canconstruct the int.erdependent market demand curves for road and rail by--lateral summation of individual demand curves. Let road and -ail servicesbe supplied at their respective marginal costs. While this is not essential,it only makes the road-rail model determinate. Referring to (1)-(3), threecases can be distinguished.

4. Case A. All consumers can be divided into two exclusive groups.'lhe consumers in one group consume- road only, but no rail (x >, 0; y 0);while in the other they consume rail only, but no road (x - 0 y:> 0).The market demand curves are given in Fig. V-1, where p* and q4 are the

1/ If.W. Kuhn and A.W. Tucker, "Non-Linear Programming" in Jerzy Newman (ed.),Proceedings of the Žecond Berkel.ey Symposium on Mathematical Statistics andProbability, Berkeley, 1950, 01-92; and K.J. Arrow, "An &tension of theRasic Theorems of Classical Welfare Economics". ibid. 507-32.

ANNEX VPage 2

euilibrium priiOSe In other wordas, DDO is drawn on the assumption thatrail price L q ; similarly, dd' is drawn aassuming that road price s p"In this sense, DD and dd' vil be referred -to as demand curve "in 'qui-librium. Consmers' surplus from road is Dp*E, and that from rail isdqo*e. The total consumers' surplus froa road and rail together for consuersas a group is given by P*E -o dee

Case B. In this case both x and y are positive for each and everyconuir. mTat is, everyone conms both road and rail (see Fig. V-2).The consmrs' surplus from road only is Dp*F and that from rail only isd4*e. To find total consumers' surplus, suppose that road is withdrawnand the consumers are paid in money to the extent of DpE as compensationfor their lost consursl surplus. Since road is withdrawn, the marginalutility of rail wl rise; according,?, dd' shifts up to aa'. Now thecon-onral surplus from rail is aa'eq , which is larger than dq*e.. S thetotal oonsumer3' surplus from roAd and rail-together is Dp*E + aaleq*.

60 lAlternatively, we could suppose that the rail service is wiihdrawnand the conumers are compensated in money to the extent of dq*e. In theabsence of rail, the marginal utility of road rises; DE shifts up to MA.So the total consumer surplus is liven by dqe e 4A' Ee It can be shownthat DP*E e aaleq* dq*e + AAIE'O

7C EB contrast, note that in Case A, if road service is withdrawnthe marginal utility of rail does not shift up (Fig. V-la), because therail consumers do not buy road in the first place. Similarly, the marginaluitity' of road, DE, is unaffected if rail is withdrawn, because roadconsumers do not buy rail anyway. Under the-conditions of case A, therefore,)p*E * des is the correct measure of total consumers' surplus of road and

rail together.

80 Case C. This case lies in between the two above extremeso Htresome consumers buy road only, but no rail; some buy rail only, but no road;the remaining consumers buy both road and rail (see Fig. V-3). Let D'3 bethe demand curve for road of those consumers who buy road only, and let DCbe that for rail of those who buy road and rail. Demand curve DD' is derivedby lateral suzation of DB and DC. Similarly, db is the demand curve oftboae consumers who buy rail only, while dc is that of those who buy bothrail and road. As ia Case A, the total consumers' surplus of pure road-asers and rail-users- is given by DP*F o dq*f. Next, employing the metliodof Case Bs, we can find the total consmers' surplus from road and rail forthose consumers who buy both; it is given by Dp G o higq*, which is equivalentto dq*g + HIGoe So in Case C, the total consumers' surplus from road andrail.for consuamrs as a group is given by Dp*g + dq*e + higd, or,, Dp*E +dee + HIaD.

9. In sumary, the measureaent of the consumers' surplus of two substitutegoods with many consmers is complicated. In the simplest case, when everyconsumer buys either rail or road and none buys both, total consumers' surplus

ANN V"

D ~ ~ N '

V-la ~Roadw ~~V-18 Vlb

Figure V-1: Demand for Road and Rail, Case A

A

D l Atd \ aa~~~~~~~a

- -. ~ ~ ~~~~~~~~ -~ i \ -, 0 <d

I ~~~~D'

*:, 4 __.::_., ORoad . Rail

V-2a ? V-2b

Figure V-2:. Demand for Road and Rail, Case B

h

P ~~~~~~~~~~~d

G~~~~~~~~~~~ qi f

Road RailV-3a V-3b

Figure V-1: Demand for Road and Rail, Case C

Amnex V

figs both'road and rail Is s-ily the ddttdion of the W.rjhll triuglesgnder the dein curwes win e i1ibrium"o DIweYe, %fttw tale clse9

or Came B or C as ^omted, s more relistic is an eq4rical questionand cannot be settled a yurior. In*y event, if sap consuwera buy roadas well as rail, the s of the above-mentioned Marshall triangles under-estimtes total cons rsl' surplus from road and ral together. TosiWllfy the ition, the discupion it CeWt.r IV asses that theextent of uch uadwrestlution is negligible. This as mtion need not,be ais correct; udinever neceusary, total conmre surplus ashould beiwasuad sbqu in Ca B and Co

AN.JE VI

-VX.XAT, LIST !';r u AD WE' rTv:iy OF SEO)ND 8ESr

1.- In a frictionless competitive economy, the ?areto optimum requiresthat the price of every product be equated to its short-ru marginal cost. / Thesame rule has been recommended for the transport sector._ &.Bt real

,economies are not frictionless competitive systems; there are distortions,such as external econonies, nonopoly elements, lack of certainty, etc.If Iti most sectors of tne economy, the price-equals-marginal-cost ruleis inot observed, should it Ji followed by rail or road transport? This isthe problem of second best.Y

2. The factors which may justify pricing transport services above orbelow marginal cost in the interest of efficient resource allocation areas follows. The reascns for pricing in excess over marginal cost are:

a) important close substitutes sell at prices significantly,above max-,ihal cost, or generate large external economies;

b)- products for which transport is a major input sell at pricessignificantly belofi marginal cost or involve large externaldiseconomies;

c) important close complements sell at prices significantlyI below marginal cost or generate large external diseconomies; andd) major inputs of the transport industry are bought at prices

sig;ificantly below marginal cost or involve large externaldiseconomies.

The reasons for pricing transport service below marginal cost can be inferredfrom the above.41

1/ See Turvey (ed.), Public Ehterprise.2/ See Ilaurice Allais ando-thers)jOtions in fransport Tariff Policy,

BIrussels: EEC, 1965. Also cf.: ,Efficiency in the allocation ofresources and economic activity requires that the road authority levycharges aL marginal cost", quoted from Walters, op. cit., p. 97.

/ .bor the theory of second best, see R. (. Lipsey and K. Lancaster,"The General Theory of Second Best," Review of Economic Studies, 1956-57,pp. 11-32; D. A.. !)avis and A. a. Whinston, "Welfare Economics and theTheory of the Second Best," :ieview of Economic Studies, 1965, pp. 1-14; andIURnjit K'. Sau, I'Monopoly, General Equilibrium, and the Theory of Secosilest," Australian Economic Papers (forthcoming).

4/ See l{. Turvey, uptinal Pricing and Investment in Electricity Supply, London:196d, pp. 88-8a.

ANNEX VI

Uhilo it ma be desirable to adjust tranaport pricing to allow fortbase non-optimalities, it would, in maq cases, be better to tackle themdirectly. It is better to aim for- the beat rather than adjustii to thesecond bout. This approach has the subsidiary merit of simplicity , siniceit rquire less data from those responsible for transport pricinL.l/Of course, where the above-mentioned distortions are not directly alterable,dgpart2es from marginal-coat pricing in transporL are cafed for. Sinceauch departures may take various forms, they are not covered by thisgeneral discussion. -

Ibid. Also cf., "The most noticeable feature of the results, for atW onew7ois concerned with trying to formulate oractical pricing; policies, is their

coplexities, and the fact that their informational requiremonLs are unlikeZ3to be met.,' R. Rees, "Second-Best Rules for Public Enterprise Pricing:,"Bconomica, August 1968, p. 270.

ANNk:X VIT

COSt-BENEFIT ANALYSIS: AN EXAMNLE

1'.. In this annex, we present an example of cost-benefit analyais*as applied to the witldrawal of railway services.l/

2. The Sheffield-3arnsley route of the British Railways is 15 miles-on. and is ,provided with local passenger service approximately everyhour In each direction. The places on this route are fairly well suppliedwith alternative transport facilities; the'railways play a relativelysmall part in providlng local transport in-the area. It is esiAmated that,of commuters from outside Sheffield arriving in the city before 9 A.M.,appro2dmatel.- 3 percent travel by train, 45 percent by bus, and 52 percentby car. 4'1onetheless, the Sheffield-Barnsley railway service carries anappreciable volume of passengers, including comuters into Sheffield, andit appears,to be the busiest local serviceAin.the area. 2V

3.' The main social costs arising frok,,, the vithdrawal of the passengerservice have been divided into three cateaories:-

(a) those arising from journeys diverted to otherforms oS transport, namdly] bus and private car;

(b) those arising from journeys no longer made; and(c) those affecting the rest Of the comunnity.

*'rFree alternative assumptions are made about the distribution of the displacedrail traffic:.

Assunptions

Pro portions "bf Journey (percent) I II III

1. Diverted to bus 33.3 5 582. Diverted to private car 33.3 . _ 22 223. 'o longer made 33.3 33 20

100.0 _T_

4. Whether the traffic diverted to bus would caIl for additional investmentia bus and highway capacity depends on how much of the diverted traffic takes

,place duringz peak hours and on exsiting capacity limits. Accordingly, annual

Li Else and Howe, op. cit., pp. 17S-19 4 . Also see A. R. Prest and it. Turvey,"oslst-%enefit Analysis: A Survey," Economic Journal, 1965, pp. 683-735.

2/ Else and Howe, op. cit, p. 180.

ANMEX VII

.cpital cost of additional vehicles (and highww eLuenditurs, if necessaxy),-and their operating costs are to be taken into account. In addition, tilewxtra time which passengers have to spend on bus journey must bo reckoiied4tMi.Beealey suggests accounting this time at 40 percent of ani estimatedaverage earning rate for the persons concerned.l/

Pb For traffic divertcd to private car, it is assumed tJat the car3used would already be owned by the rail passeucers concerned. Heuice,only additional runwnin cost of cars, as well as tiw extra time o' jiouricyrequired during peak hours, is to be taken into account.

6 Jourmeys no longer moad represent a social loss of consumer.'surplus. In the locality under study, bus and train fares are more or less¢comparable. If a journey is no longer made, the reason mus; be that bustakcq more time; this additional time can be valued in monetary terirs.Asuudng that the relevant part of the demand curve is approximactely linear,it can be shouo that the average social loss of consuixrs' surplus equalshalf the additional cost (i.e. half the value of additional jouniey Lime)of bus travel for each journey.

Social costa ill also be increased by the cost of the additionalcongestion during peak hours to vehicles already o( the road.

80 The four sources of social costs ar quantified in Table VII-1.The benefits are considered to be mainly the resources preseotly used t:ioperating the serice which would be saved if the service is vi Wdragi.These do not include any savings in track and slal in;g costs, sinceIt is assumed that the tracks would still be required for the area'sconsiderable freight traffic. 2

9. Table VII-lindicates that the railway service should be withdrawnunder assumptions I and II, but nDtained under assumption III. :3upposeassumption III is accepted. bes it follow then thaL the railway serviceshould continue? If so, then should the government subsidize the servicein case it involves financial loss? Under assumption IIE -the social, costof withdrawal of the railway service is more than the corresponzding socialbenefit. If the cost and benefit have been properly measured, witidrawalof service would not be an inprovement, and the service Justifics govcrt:meilt.subsidvy should it incurr finanicial loss.

I/ It. E 3eesley, I"The Value of Tinm Spent in Travelling: Som.e ..ewEvidence," Econmiica, N. S., Vol. 32 (196P,, pp. l7-1 6 5.

2/ Else and Howe, on cit.p p. 1(16. .Vote that this viewpoint is insharp contrast t3fiiat of tne 9at African 1yansport Stud"'.

ANNEX VII

rA:hL. VII-1: Cost-Benefit orSvice

(In thousand pounds sterlisi per year, based on 1966 volumeof trarfic).

Asaumption Assumption Assuz4itionI II III

1. Traffic divertcd to buses:(a) cost of addiLional bus journey 6.540 9.810 19.620(h) value of additionel journey time 15.750 21.330 28.990

Total 22.300 31.10 W.610

2. Traffic diverted to private car:(a) Running cost of vehicles 25.040 25.040 25.040

(b) Value c additional jouruey-time 1.590 1.050 1.050

. Aita1 2L). 630 _ _.0_90 __09i

3. Traffic lost:Value of benefits foregone 11.150 11.140 5.5140

4. toneestion Lost of other road users 8.070 8.920 .11 420

*rot tl social costs: -I + 2 + 3 +L4 68.150 77.290 91.960

trot-a social benefits(excluding aly savings in trackand signalling cost ) & 80.000 80.000 80.000

.3Il'rce: ;Lsc and i{owc, op. cit., p. 183.

10.. The proper valuaticn of the costs ad benefits of a project,especiaD in a deveping econww, requies that at least Utree setsof basic data be supplied to the project evaluator by tho top-levelpolicy-makers: (a) the objectives of the national economic policy anidtheir relative weightm, (b) the rate discotuit, and (c) the liadowprices of labor and foreign gxge.Y

1/ Seo- A. K. Son, "The IDle of Policy-aJmrs in Project 1ulbrmiatiosn andBirLuation, Industrialization and 'roductivitx 3ulletin, Vol. 13,pp. 25-36.