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R.port No. EC-160

FILE Copy

This report may not be published nor may it be quoted as representing the view of

the Bank and its affiliated organizations. They do not accept responsibility for its

accuracy or completeness.

I~rrERNATIONAL BANK FOR RECONSTRUCTION AND DEVELOPMENT

L.'\j7ERNATIONAL DEVELOP~lENT ASSOCIATION

THE ECONOMIC BENEFITS

OF ROAD fRANSPORT PROJECTS

March 18, 1968

Economics Department Prepared by: Herman C-. van der Tak

Anandarup Ray ..

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PREFACE

This paper is related in nature and intent to the 8SSlV" on The Evaluation of Agricultural Projects: A Study of Solie .Economic and Financial Aspects, issued some years ago, Whict\ was an introductory survey of conceptual and netbodological probl.ems arising in this field. It attempts to provide a brief exposition of some of these problems which arise in the economic analysis of road projects. It aims at pro­viding a better conceptual fram~ork by discu.~sing some of the issues which appe~ most often to give rise to misunderstanding and dispute, particularly in the measurement of benefits said to result from an in­crease in traffic induced by a roadiq>rovement. The paper is clearly not exhaustive nor does it cover the many questions arising in filling out the framework with appropriate numbers. !tor IOOre detailed discussion of those issues the n~ader is referred to other studies.

The authors gratefully acknowledge t.1le stiinulat,ing COJJDents on an earlier draft from their colleagues in the Transportation Division of the Projects Department. Discussions with lir. Jan de Weilie and I-'.r. Shl.omo Reutlinger, of the Investmen't Planning DiviSion, have been very helpfuJ. in preparing the paper. However, the customary disclaimer applies, as with all stcU'f papers in this series: the authors alone are responsibl.e for the views expressed.

This paper is a by-product of the continuing work: in the Econo­mics Department on problems of sector and project analysis. Earlier studies given circulation outside the Bank include The Evaluation of Agricul tural Projects: A Stu of Some Economic and financial Asrects

c- __ ~ lay, , e conom:l.C A;ec~ of - ater Utilization l.D .

Irrigation Projects (EC-lj2, January, 1965), On Estimating the 'Econo­mic COst of capit81 (with special. :reference to developing countries) (EC-138, October 21, 1965), An Economic Be praisal of a Road Project: The First Iranian Road Loan of 19 9 IRN-227 (Ec-1L7, September 20, 1966), The Economic Choice between droelectric and Thermal;. Power Develo ments World Bank staff Occasio Papers Number One, 19 , Quantification of

Road User Savings (World Bank Staff Occasional Papers Number Two, 1966), A Cost-Benefit A roach to Educational PI in Develo in Countries

EC-1 7, Decembe r 20, 19 7 , and. The Economics 0 Road User (harges EG-l58, January il, 1968).

Andrew M. Kamarck Director

Economics Department

PREFACE

1 .. The General Setting . . . . . .. . . .. . . . . . . Types of Road Project • • • • • • • • • c • • • • •

J.finimum (bst Gases Cost Saving Cases .. Development cases ..

.. . . • • e • • • • • •

e _ • • · . . . . . . .. .. . .. . .

Types of Traffic Growth .. • • .. . . .. · . . Cost and Cost Savings .. .. •• • • · . . . · . .. . .. Beneri ts frol1l Induced Traffic .. .. . . ..

2. Simpl,3 Two-Regional Model .. • .. • .. .. . · . .. . . .. . Equivalent Measures of the Benefi ts .. · . . . .

3. Impact on a Third Region .. • · . . . . 4. GDc;zestion - Rising Transport Costs · . . . . . . 5. The Beneri ts of Diverted Traffic . . . . . ..

Pace No.

1

1

2 3 4

4 6 9

9

14

17

19

22

Road and Hail as Perfect Substitutes It • .. .. .. 23 Imperfect SOOst! tutes, Rail Prices Constant • • • (I 26 Imperfect Substitutes, Rail Prices Cllange .. .. • ... 21

6. Effects of Market Imperfections .. .. • . . . . . . . . 1 . Transport Surplus, Secondary Benef! ts and Double-

(JoWl ting .. .. .. • .. • • .. .. .. .. .. • .. • ..

Transport Beneri ts and Income Cllanges • . . . . . . Further ~pe rcussions .... • .. .. . .. . .

8. Conclusions •• . . . . . . . . . . . . .. ..

APPENDICES A and B

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33

34 35

36

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THE EOONOMIC BENEF1TS OF mAP TRANSFURT PIDJECTS

1. The economic eValuation of an~ ?roject requires an assessment of the cost am benefi tstreams of the investment, as compared with al ter­nati ves. This involves some basic,~ but well-established teclmiques of discounttng costs and be ne fi ts in future years to their "present value"

• in the reference year - usually that in which the capi tal outlq- begins. These teclmiques, and the standard investment criteria, are here taken for granted.!.! This paper mainly focuses on some of the conceptual and methodological problems ariSing in the assessment of the benefits of road proJects. I t only provides a framework: for more extensive treatment of some of the issues, and of the problems of filling it out with figures, the reader may consult the references given below.

2. Many of t..he problems in analyzing the costs and bene!i ts of transport projects are similar to those encountered in other sectors. Nevertheless, practical difficulties differ with the sector and type of project considered. It is useful, therefore, as a preliminary to more detailed discussions of these probler~, and of possible methods of solu­tion, to broadly classify transport projects by the type of pI~blem which they present. As with all attempts at claSSification, some violence will. be done to reality: various types will tend to overlap in real life. Yet, a differentiation by type of project and problem is u:seful as some styliz­ing of the problem is likely to be necessa!j" in order to make possible approximate but workable solutions. This means, of course, that in certain condi tions sone aspects of the problems are strE=ssed as being of primary importance and that others are either ignored or taken as given.

1. The General Setting

Types of Road Project

3. A broad distinction m~ be made bet~een transport projects in-vol ving cost comparisons and those invel ving comparisons of the costs and benefi ts. In the forner, the growth of demand for transport over time is taken as given. The problem is then either to minimize total cost of transport required to meet the expected demand ("minimum cost cases"), or to compare the cost of improving roads wi th the resulting savings in operat­ing costs for the given volwnes of traffic ("cost saving cases!;). In the other broad category of cases, the road improvement, by making reductions in transport costs poSSible, is considered to have a substantial stimulat­ing effect on the growth of output and trade which will, in turn, create more traffic on the road. The beneri ts from the additional. transport expected to develop in these cases are then the dominant factors in the

!/ This applies also to the problem of optimum timing of investments, which tends to be neglected in the usual discussion and practice of project appraisal; see on this subject, Jan de Weille, The Optimum Timing of Investments, lBRD, Economics .~partment (forthcoming).

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econoBia eyaluation ot the iDftst.-nt ("d8~o~nt c.-es"). In,JNall ty J

of COurM, tM eli.tinction geta blurred: ~ projects not 0Dl.y lowr the cost. ot tranaport that would have taken place 1IIJ1Vq, but also iDduce new trallllport. Nevertheless J for both ~ica1. and practical purposes, it ~ otten be justified to concentrate on one predominant aspect waile ignoring otherlllt 80118 brief commants tollow on each ot the t1J)8s of cues distiDguiabed heN.

4. Hi n1 ••.. Cost CUes. One exaple mq be tile provision ot trans-port to the coast lor the output o£ an :tsolated plantation. The road to be constructed is only to serve the plantation. The deMDd for transport depends directq on the demand. for th,e ~output ot the plantatiOD~ usUllling that the latter is not (vi thin a reasonable range) significantly influenced by transport coste. 'lbe question is to detera:Lne the cheapest vq of cu-rying giY8n quantities ot ~utput from the plantation to the port. In such cu.s, givan the demand forecast, it is siDl>l.y a question ot min:tmiz­iDg the present value awn ot ~api tal. investment in the road, its future Jl8inteDance costs, and futu.~ operating costs of the vehicles using the road.

5. A soDl81lb.a.t less orthodox but not iDtrequent exuple i8 that of • penetration road to open up a previously isolated area tor economic developmnt. Such roads are otten conaidered pna. exuples of devalop­~t cues, with the primary benefits being tbe expected increases in net agricultural output. In lII8lly such projects, ho1Iever, the road is oDly a part of the total. investJEnt necess&l7 for agricultural. developl8nt to take place. Other investments DIQ' in\.1)lve land clearance and settle.nt, irrigation fac!l! ties J the provision of fertilizers, marketing and c:redi t facilities, etc. It would appear best in most of these cues to consider the projects (or "programsn ) as primari17 agricultural. and to d,eterZ.ne

. the economic _rit of the road as oDl3 one item in the 'package' of invaat­.nts necessary to produce the expected increase in agncw. tural output. In such cases it is: urrwarranted to t17 to calculate a return on the road in.,...tMnt per .. J the bene!i ta DlWIt be related. to the total. 'package'. Anal.1'aia of nah %'OM projocte ia then reduced to tile easier problem. of lIOrJc:iq out tbe cbeapeat transport facilities required to .et the fONcut deUDd ot output fro. tbe area aDd ita iJIIport require.nt.. The advantage ot this IIpproac:h ie that it focuses attenticn on the crucial "coDlple_ntal7''' invast.-nta aDd other factors in agriculture which ultillatel1' determine. the outco. of the project, and lIhich taDd to be lightl.T treated in tile develop­_n.t ~.t IIpproach. It avoids the daupr of exaae~ted e~ci~ti0D8 ot great devaloplllBnta - otten l)ased on hiatorical. analogies - sillply fro. open-ing up the area by- a new road •. !! .

!I fbis is not to deD1' J of course, that in SOM cu.. the _1'8 provision ot penetration roads have had large d~\~l~nt etfecta. The uplana­tiona lie in a aixture ot pJvaical, cultural, ecoDOllic, political, etc. factors and appl¥ mat to feeder roade into alread1' settled areas; see below, para. 22 ft.

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6. In the anal.1'aia of all auch projects the demand tor tranaport, in tems of volume, type,.~riodicity and required speed, is taken as gi van. The estimates of demand are deri vad fro. outside data, 1M.pendent of the particular transport inftstiEnt choaell. lbe problea is to find tile JIIOst efficient solution to meeting this given transport need b7 m1":1 aizing its costa. The beneti ta from transport do not enter into the problea at all. The analysis is analogous to that of power projects, 'llbere 1 t 1s usual.l7 assumed that the need for po_r is given and 1s indepeadeDt ot ita "value", aDd the task is to .et this given demand at the lowst possible cost.

1. Although in practice fiJding the minimum cost project mq invol va comparisons of different modes of transport, thia paper is ma1nl.1' concerned with road transport.l/ The task then becomes one ot deciding vhich standard ot road should be built, assuming that the 1i1Pea ot vehicle likely' to be used on the road are given. The atandard of road chosen, havaver, involves exalDi nation of the • trade-otfa' betvaen higher or lowr ini tial in'98stant vi th lower or higher future road maintenance coata and vehicle operating coats. The DLinimum coat solution is one ot detem1.D.ing the lowest total. present value of inftatment, road mainteDance and. fthicle operating costs to .at the demand required.

8. Cost Saving Cases. He~ the issue ia whether improvement of an already existing road is vortlnrhile on account ot tbe expected aavinga in tuture fthicle operating costs and in road JI&in'tenance costa. Once again, it 1a assu.d that the iuprove_nt 1IOuld not af'tec.t the projected volume (or destination ot transport). Measuring the real co~t advantages .,. be complicated, howver, by possible diversion of traffic .troll one lmde ot transport, or trom one route, to another. This type of project also shows the tamiliar features of a choice or • trade-off' between larger investments now in order to save on operating (or maintenance) costs later, and lower initial costs but bighe:r costs in later 18ars. Such problems are forma.l.ly siJIUar to those encountered 1Ihen comparing bydroelelctric projects with altemative developments of therul. power.

9. The basis ot comparison should be the relationship ot beneti ts to costs "vi. til and vi thout" the improvement not to "beto~ and atter" the improvement. n..e expected normal increase in traffic volw. m&1' raise unt·~ operating costs tor all whicles above the existing leftl becaWie ot increasing congestion and/or the deterioration ot the surtace ot the exist­ing road 1Ihich can only be avoided by increasing maintenance expenditures.

Y It is appreciated that in practice compNi.sons of road with, aB¥, rail costa are complicated by difterencea in speed, convenience, risks ot losses through time, breakage or puterap, for ~Dlllple. That 1s, a ton-laa is not a homogeneous uni t in the sanae ,".hat a laIh is a kwh. A full anal3sia would involve considerations ot dis­t~bution and inftDto17 costs, ot interest coats of atoclers, etc.

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If these greater maintenance e~nditures are not made the effect may well be 'not only to bring forward in time the expected reconstruction date of the ro ad but also to increase the absolute amount of physical reconstruction required, i.e., not only of the surface but also the base of the road. Vehicle operating costs on the new road, therefore ,should not be compared with the existing level of operating costs but with Q,

graduallY" or possibly abruptlY, worsening situation in the absence of the new facility. The frequent practice of comparing "before and after" understates the benefits.!/

10. Development Cases. In these cases the constructton or improve-ment of the road is expected to have a significant influence on the future volume of transport. That is, by lowering transport costs between two regions a stimulating impact on trade between them is expected. Because of competi tion in trucking, lower costs are assumed to be passed on to the u:Jers of transport and to provide an incentive to fanners and businessmen to expand output in response to the wideniDg of the market.

11. In these cases the volume of transport is not taken as given but ia i tsel! a function of the level of transport costs resulting from the proposed investment in a new or improved road. The estimated demand for transport is not independent of the project, as with the earlier cost comparison cases; the analysis asswnes that the project itself will create transport that otherwise would not come about. The analysis of the project is therefore no longer concerned only with comparing alternative costs of meeting the requirements for a given (projected) volume of transport, but takes into account also the benefits to the economy which are reflected in the additional volUJ'iM! of transport taking place ..

Types of Traffic Growth

12. It may be useful at this point to relate the type of transport projects distinguished above to the customar.y classification of types of traffic growth.,g,/

(a) Normal traffic growth, i.e., the increase in traffic that would take place even wi thout improvement of the road.

!I Nevertheless, it is acceptod that assessing costs I:wi thout" the project may involve substan.tial speculation while the evidence as to costs "before and. atter" ~ be obtainable from recent similar improvements in the particular country. What can be concluded, however, is that if a pTOject is justified on a "before and after" calculation it is more than justified on a "wi th and wi thoutn cal­culationj see alao para. 41, footnote 2.

~/ Terminology is not altogether standardized. Di'V8rted and attracted traffic are used interchangeably. }bre important, so. authors refer to traffic diverted from other modes of transportation or from other conveyances on the same route as \"generated" traffic. This considers the question from the point of view of traffic on a particular road, rather than transport as a whole.

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(b) Induced traffic growth~ i .. e., all other increases in trarric resulting trom the' road iJlprove_nt. This JnQ' be fUrther sub-divided, for so_ purposes, into:

(i) Diverted traffiC, 1.e., traffic diverted to the new or ilproved road fro.. other road routes to the same destination; from other modes of transportation on the 881118 route (railWQ'8, vater, etc.), or from other connymce8 on the same road route (passenger tripe prenousq ucle by bus but nov made by private car).

(1i) Generated (or d.evelopent) traffic, i ••• , traffic in coamodities preTioualT sold loc~ but nov tranaported ooyer the road to places vbex. a better price can be obtained; or the traffic in comodi ties prenouaq s~ld else-1Ib.ere atter traaaport but DOV sold at better prices at different locations served by the new or illproved road; or traffic resulting fro. an expansion of output or sales 'becauae of the lower transport costs brought about by new or improved facilities; and pusenger trips DOW made which, becauseot pooranc:l expeD8ive traDS­port, previously either did not take place at ":~.l or were to other destinatioDS.

13. It should be Doted that "diftlWiOD" is here defined as a shift between various P088ibili ties of rea.ching the s .. destination. Generated traff'ic, however, may also involve diversion in the sense ot a shift troll one destination to another. In either cue traffic on the old road, rail, water or air f'acili.ty is reduced, and, as a reaul t, operating coste on these may be less because of raduced congestion. Furtb.eraore, it is cl.ear that generated (deftlo~t) traffic DOt oDl7 create. add1:t1cmaJ. traD8pOrt on the new road, but..,. alao suppress transport that otbe1'V1a. would baft taken place elsewhere.

14. '!here is no sillple relation between the different t1J)8S of tra.£fic growth and the t1)les or project distinguished above. Tbe dUraNnce. are, ot course, in the form ot the analysis rather than in the projects. Minimum cost projects, such as transport tor a new iron ore Dd.ne or a peD8-tration road, typically involve development traffic aince there will be DO

transport Without the project. For anaJTt;ical purposes, hcnIeftr, it 1. aasUJ8d that the projected transport, vol .. s are given, 1DdepeDclent of'

.; traf'fic coata, and attention ia locused OD Id.n1Id.s1Dg costs ot tbis trans­port; tiftll tIlese JtJ DillUll costa ...., possibl1" be prohibi t1 ve17 hip in tbat the urket price ot the goode (including transport coata) ia too bip tor tbem to be sold coapeti ti"17. Coat aaviDg projects relate clearq to "no1Wl.l traffic" and, .. discU8sed belo., rather more Ulb1guoul1' to: diftrted traffic. III deftl~t cues tbe clellaDd tor traD8pOrt, mel the beDeftu

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derived from it, are not taken as given but are regarded as being dependent upon the road improvement. '!bese questions obviously arise with develop ... ment traffic. This relationship occurs also with eli varted traffic.

Cost and Cost Savings

15. The economic eValuation of all types of projects requires esti­mates of costs. The total. analysis ma.y, in so_ cases, consist solely of a comparison of costs, i.e., the minimum cost projects. The same is true for cost saVing cases, although conventionally the savings in operating (and maintenance) costs on normal traffic resulting from the project 'are described as its "benefi ta". In such cases 'cost savings' alone play a role in the analysis; the problem of the "benefits" from transport does not arise. It is only in development and relevant mixed cases that the analysis considers both costs and benefits, in the latter sense. The re­mainder of this section discusses briefly the various costs involved in road transport projac·cs. Subsequent sections deal more extensively with the evaluation of benefits fl-om induced traf:fic, as described in para. 12 (b) above.

16. Costs may be conveniently broken down into the following major categories:

(a) Investment costs of roads;

(b) Maintenance costs of roads;

(c) Road user costs; and

(d) Other cost factors associated with transport (e.g., accidents, produce damage or losses).

Estimating these costs meets with various difficulties, relating ill part to the problem of assessing the physical inputs in different types of roads, vehicles and operating condi tions, and in part to their valuation.11 Invest­ment and maintenance costs are, in pnnciple, relatively simple to-estimate, although the errors, in practice, may be substantial.,gl More comparative data

!I In making an economic evaluation of a transport project, costs and benefits should be evaluated in tenns of their true value to the econoD\V which, for various reasons, may not be properly reflected in actual prices. This may require, for example, adjustments for exchange rate distortions, 0; to 'net out' for taxes on fuel, etc. On the ques-tion of use o,f. shadow prices in transport; analysis, see J e. g., Hans A. Adle r, Sector and Project Planning in Transportation, World Bank staff Occasional Papers Nwnber Four, Th~ Johns Hopkins Press, 1961. .

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on typical construction and mainteD4Rce coats aDd. on construction periods, tor d:l.f't,r8nt types ot roads end conditions would se •• help­tul. in keeping such estimatingerrora to a Jd.niaabll.

17 • 'Estimating road user coata in difterent coiuli tions ot surface, gradient, curves, e~Atd and traffic congestion is Jlk)r. cOlllplex.A good deal of research effort bas gone into trying to assesa the eftecta of some of these factors on au.ch direct vehicle operating cost ita_ as fuel cOM'Ilq)tion, tire wear, vehicle uintenanee and repairs as _11 u on vehicle utilization and thus on the coat of drivere and the !1epreciation and interest cost of vehicles. Thia l'esearcq !hu y.l.elded a lil88S of techni­cal. coefficients indicating difterence, in riilicle operating costa reeul ting from dUferent ld.nda ot road. ~,. 11"""-' ,",f.f~~o., depend, of course, not only on these coefficiente but a1Io Qft 41fteianae. in tbe valuation plac\Jd on, •• g., fuel, vehicle and dr1ftl"_ tt., etc. B7 colibiDiDg the.e various ele_nta, efforts haft been JUde to arrive at moN objective measures of road uti,er costs on different roads and ot the savings that DIIV' be expected from road improvement. Such estL_tea of road user savings are a en.cia]. part of the economic an&qsis of most road- projects.l/ Howver, because of the difficulties of classification ot roads and vehicles they are necessari~ rough approximations which JDq' not accurately descrIbe any particw..r case. Practical measures of the costs of congestion arxl the savings resulting frnm its elimination i·n different circumstances are even less satistactory. Y 18. In addition to ro&d user costs in the uauall.y accepted sense tbere are other costs directly associated vi. th transport conditions. Higher speeds shor1;en the time spent by goods and passengers (including "s.elf­driving passengers") in transit. There does not appear to be any agreed basis as to estimating the actual. value to be put on time savings ot persons travelling Whilst at work, or to or from work, or for pleasure. On-the-job time savings are uauall.y geared to the value of a passenger's time as re­flected in his saJ.ary. There does not seem to be any deJlK)ll8trable evidence as to whether this is an appropriate basis ot' valuing ~ savings in travel for other pwrposes. It iq»lies that people are only interested in arriving, somewhere, and not at all in getting there.3/ Sightseeing is one clear - ,

!/ See, Jan de Weille, Quantification of Road User Savings, Wo~1d Bank $taff Occasional Papers Number Two, The Johns Hopldrus Press, 1966,

. and literature cited therein. See also, e.g., Lionel Odier, The Economic Beneti ts of lbad Construction and Improvements J Bureau­Central d' Etudes pour les Equipe_nts diOutre-lIIBr, Paris (no date).,

Y For a brief survey ot some evidence, see, Alan A. Walters, The F"cono­mica ot !Gad User Charges, EC-l$8, IBRD, January 11, 1968.

1/ Quite apart from the fact that equating the value of one hour of leisure with hourl1" eamings is rather heroic. On V&U8 of time savings, see, H.Jtbhring and M. Hanritz, Highwvnefi~ an~i-cal. FraJileVork, Evanston, Ill., 1962, and H. E. sley, e V~ T~ Spent in Traftlling: So_ New Evidence, Economica, MaT 1965.

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illustration to the contrary. The amount people are willing to pay for greater speed on, e.g., a toll road, may give some direct indication, if' corrected for such factors 88 convenience and safety. A shorter tr~si t time for goods (and more reliable delivery) tends to make possible smaller inventories and lOEr storage costs. Li ttl-e appears to be known, hOliever!) about the quantitative importance of such savings on working capital and warehouses in various conditions.l/ For perishables - dair,y products, frui t and vegetables - speed of deli very ~ substantially cut down on wastage, or expand the possible market horizon.

19. More generally, and apart from speed effects, damage to goods during transport .., differ greatly depending on the state of the roads and the nature of the goods being transported which JDq' require different packing cos'lis to prevent damage. This is, of course, relevant only for more fragile conwnodi ties. Accident rates and consequent;pe.rsonal injury and material daage also vary wi til roat and traffic conditions.

20. These associated costs mainly concern the shippers or passengers, rather than the truckers. (Accidents affect, of' course, both). In making , cost conparisons they should, in principle, be taken into account as far as possible. Otherwise the cost conparisons ~ be distorted by differences in the "qu.a1.itY'~ of the transport services provided. Alternatively, trans­port of different quality may be looked upc.'1r! as separate services J each with its own value to transport users.2/ This applies even JOOI'e to dif­ferences in comfort or convenience. -

21. These different cost components are not equally important in al.l cases. It has been suggested,)/ for example, that in most uJlder­developed co~'tries the savings in-direct vehicle operating costs predominate and time savings are less important, in contrast to the industrial COWl tries where the cost of congestion is stressed. This view is based on the nature of the improvements being made: i.e.: in the underdeveloped countries significant aJIIOWlts or road inve's'tEnt are to improV3 road surfaces, lead­ing to less vehicle wear and tear (and possibly road maintenance outlays), whereas in the developed countries investments are more likely to be for greater-capaci ty and higher-speeds, thus leading mainly to time savings. For Jll)st inter-city road projects in developing cOl.Ultr';!,es it would appear a good approach to rely :for transport cost savings mainly on vehicle operating costs (am road r4ai.ntenance outlays) J and to take account or such elements

Y On inventories, see Meyer, Peck, Stenaaon and Zwick, The Economics or CoJ!!)etition in the Transportation Industries, Cambridge, 1959, pp. 190-192 and 348-353.

~ A reduction in associated costs ~ be treated either as a cost reduction for tQe s~pper; or, if transport rates reain the same J

as caUSing an equivalent shift upward in the demand curve for trans­port. See also below, para. 47 ff.

I

JI See, E. K. Hawkins, "Investment in Hoads in Underdeveloped Countries," Bulletin of Oxfo:ro Univers:_ty Institute of Statistics, IIJovember 1960.

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as inventori savings" damage reduction and iq>rovementa in comfort, -only when they are demnstrably siE;nificant. Further research work on the quantification of these aspects, to get a clearer idea of their relative importance in various circumstances, liOuld seem desirable.

Benefi ts from Induced Traffic

22. In the previous sub-section we touched on the road user savings benefits from a road lDproveJll8l'l.t, i.e., the ct)st savings on nonnal. traffic. We tum now to the principal concem in tbis paper; the eValuation of the benefi ts from induced tra:Cfic. What are the beneli ts from an increase in transport resulting trom·a road improvement? A simple approach would measure the gross benefi ts of induced traffic by its market val~ to trans­port users, as _asured by the product of the additional. volume (e.g., t.on lan., tons, or vehicle jO'Q,meys) and thecC)rresponding unit price of the transport concemed. This would be quite justified if the increase in transport were small, or if the demand for the particular transport services were perfectly elastic. Unfortunately J in practice, these condi tiona are in many cases not met. Improvements J and the resu.l ting increase in tra.t'fic, are often not small, either 'because of inherent indi vis1bili ties or because discrete changes &.n;l made rather than "marginal" adjustDtnts, and' demand for transport services cannot normally be considered perfectly elastic. In that case "revenue ll from induced traffic is not an adequate measure of its gross benefits;addi·tion~J. "surplus" should aJ.so be taken into account. Evaluation of benefits from "j~hduced traffic in tenns of consumer (and producer) surplus will be discussed at some length below.

23. The next section considers the tenefi ts from development tlraffj.c, and the underlying factors determining their importance; to illustrate the argument,; it uses a simple model of transport improvement between two regions. This is followed by a section discussing the complications arising when a third region is affected. A later section considers whetber the conclusions alter when transport costs are increasing for larger volumes of traffic because of congestion. The neasurement of bene!i ts on diverted traffic is dealt with next, follolied by a discussion of the effects of various market imperfections on tha benefits of a road improvement. A final section comments on th.e relation bet-ween various measurements of surplus, so-called secondary benefits, and the risk of possible double-counting of benefits.

2. A Simple Two-Regional Model

24. The factors determining the gross valt:.e of the additional trans-port induced by lower transportation costa may be illustrated by a simple example. Sq' a poor road between a "region" and the "center" is improved, and transport costs of the shipper are reducerl,. The volume of transport of a c01lll1lOdi ty between the center and the region depends on the price differenti·al. existing between the center ;and the region, and on the price elastici ties of supply and demand in both the region and the centel'. }t'or ease of exposition, the price differential between regions and center is assumed to consist solely of transport costs; other distribution costs and profits are ignored. With lowr transport costs on the new road,

- 10 -,

FIGURE I ~--------------------------------------------------------------------------------------------,

I _ ~

Price of Commodity

PA

o

Region A

'1 '.'

Output of Commodity

Price of Commc::o)'

Ps

o

Reoion B

58

Output of . Commodity

•

- 11 -

transport lfi.J.~ tend to crow mtil for each colllllkHli ty the price differen­tial between region and center is llL-rowed to the DeW unit transport cost 1;0 the shipper.!! Part of the increase in the YOIUIIB of tramsport (the "production allocation effect") may involn higher output in the region for sale in the center, stimulated by lcrt.48r t.t-8118port costs and higher net producers' prices. Another part (the ItcoDSUDption aJ.l.ocation effectn )

~ reflect greater shipEnts of coJDOdi ties fOl,.rl¥ produced and con­sw.d in the region but 1Ihich are nov, 00 a~co1Dlt of the reduction i.n transport costs, more prof! tabl,y exported to the center. ADd, .i1l1] arly, of course, for traffic in the opposite direction.

25. The relative quantitative importance of these two components of generated traffic depends on the price elasticities of supp~ and demand of the coJaOdit)" (;;:·oncemecl.2/ For traffic from tbe region to tbe center, for exuple, the "1'8 inelastic is deand in the region, the less important will be the C(on8lD1ption allocation etfect; the increase in local. prices in the region wen supplies are diverted to the center will choke otf the growth of this traf'fic. Similarl1', inelastic supply' in the region, i.e .. , rapidly rising costs with. expanded output, will tend to limit the produc-tion allocation effect.)/ Inelastic supply and demand in the center, on the other hand, lilli ts the scope for total development traf'fic generated by the projectJ as 8ft1l a aall increase in supply from the regioD vill dep:ress the price in the center, thus cutting off additional developEllt traffic.l!I

26. A bit of geometry will help the discussion. In Figure I, region A is the 1tblportingll region, or the "center", and region B "export.sll ; wi thout arq trade or transport, the price in A is higher than in B. If transport costs (9AB) are less thaD the price differential vi tbout trade, trade and transport between A and B vill take place.2!

Y Or simply the new transport rates, if distance has not been shortened, and n associated costs" (of damage, etc.) have not been reduced. Cost reductions which do not benefit the shipper through lowr rates or loliBr rr associated" costa CatUlot, of course, develop or generate traffic directJ.y, but ma.y do so via an 'inco_ effect' by lIhich the recipient of the savings consumes .,re transport.

Y This is true if the cross elasticities are small enough to be ignored.

1/ Supply elasticities, of course, are in tum related to physical and human resource availabUi ties, inBti tutional factors, etc e

41 For complications on account of a third region, see below, para. 31a. ft.

5/ In the notation used in this paper, superscript 0 alvqs refers to the initial situation. Superscript 1 re£em to the new situation. Indivi­dual. subscripts A, B and C relate the variables to the regiou. When two subscripts occur, such as TAB' 9AB the variables reter to'two regioWl simul taDeousl,y, e. g., the volU1118 ot ~rade, T, between A and B is TAB.

- 12 -

27 • Suppoae, for exup1e, that vi til the old rold the prices _re ~ and 11, the difference between thea being equal to the transport coat at.· !ben &1, &)lIOuld be the left1s o~ production in A and B, reapec­tive~, and nt, L1 would be the levela of conaumption in A aoii B, NS­

pectiYel¥. AB· (Ii - Si> • °xt would be th\" yol")~_ @t excesa de.and (or fliIIportAfI> in A. SiIIi.l. arly , EF • (&1 - ~~) • ox.: would be tile exceas aupply {and flelq)orta" > in B. AB, of course, 'iIOuld equal EF. With tile nev road, transport cost is reduced to, s87, 9b, corresponding to the n~v level of prices Pi and pl. As a result, iIIporta of A become CD and exports fro. B beco. GR, viUl CD • GP'. The increue of COD8U11pt!on in A ia gnater tban tile fall in conslDIption in B. The increase in production in B is greater tb~::n the fall in production in A. 'lb. total increase in trade (and trarusport) equals DI + JC • HI{ + LG. Clearly, the greater the elastic! ty of output in region B, the greater v11l be the production alloca­tion effect in generating tratfic; and the more elastic is demand in the region, the greater will be the consumption allocation effect.

28. One can easily show the relation betveeD the demand and supply relationships in the t1Io regions and the ordinarr dew.ad cum tor tr8IUI­~. We shall uau.e for the tt. being that tbe road 1a the onl.y link between the tva regions. The transport deDl8Dd. curve corresponding to the condi tiona in Fig. I i8 shown in Fig. II below. 'JY, in Fig. II, is the transport cost at which there is no transport. That i8, OY 1s the level at which transport costa become prohibi ti ve· and' no trade takes place. 01, on the other hand, ia tbe volu. of trade when traneport costs are zero. The volu.e of transpr)rt at coat 9L 1s TL (AB in Fig. I). The volUE increases to TIa (DC in Fig. I) vhen transport cost falls to 9fa. The slope of the demand. curve for transport depends, of course, on the slopes of the dell8Dd and supply curves of the coJlllllOdity in A and B. The slope

is gi.,..n b7 LIf A' were L is the difference between the slope(1$ of the deJl8Dd and supply curves in A, and M is the ~fterence between the slopes of the demand and .up~ curves in B.L!

!I The relationship ~ be presented more concisely if the demand .and supply curves in A are transformed into the excess demand curve shoving how much demand exceedB supply for any given price; and, similarly, for the excess supply curve in B. From these curves one can read off directly how much will be transported (traded) for any particular level of transport.

•

Coat ot trauaport be .... A ad B

o

-13-

Fipn II

X TAB Volu. ot trade and trauport betwen A Ed B

29. . !he elasticiv of deUDd tor transport; depeDds .1Idl.ar.17 on tIae difterence between tile elasticities ot tbe d_ad ad SUPPlT cum. tor co"'d1:t~· in A aDd :in B. ibe ditferences are obtained, bneftr, atter wightiDg the elutici t7 of deand in A by' VA.' i. e., the proportion of A'. cou..,tion to A'. iIIporta; aDd the eluticit"7 of .~in A b7 VA' i ••• , the pmportion o~ A'. production to A'. iIIporte. 81 a1 ] arq, tor B. 'lbu8, let 118 wr1 'bI:

1Ihere

au.cl B(DA), B(Ds) aN the elutic1 tie. of demand in A aad B; ad I(SA)' E(SB) are tile elasticities ot SUPPlT in A aad B. Tben the eluticit7 of de.aDd tor transport iro. B to A, B(TAS), is giftD b7 y:

(1) . B('l'AD) • 8AD PJ..~ Pal (0

11 See Jppend1y A, pAru.'.3-6, ~or cI ... l:ftti~.

-lJ,-

JO. ,... Aau1a .. it 1. obviou that the ela.sticit7 of deand tor ~~ ttti1 l;i iNatel', tM gNater are the elasticities ot demand aDd. .upp17 tor .... DoilllDdiv in both regicma (in absolute values). Also, the INa ..... r il +.be IiilNDt ot trade relative to regional production and cODliUllption. 1'.b.r.:',1.r will be the elast:icit7 of the transport; demand. These N8111 ta aN lm18ibl. and in line vi til what ODe wuld have expected. In specla1 ~_., the tbnwla is turther sillplitied. For 8x..,le, lIhen the elastic! tt of 'UPP17 in region B 18 intini te, the tormula reduces !/ tol

(2)

Equivalent Me_un. ct the Benefits

31. '!he benefiu troll the reduction in the transport coat...,. be _asurad in two equiYalent vqa. The total. uet gain in consumers' and producere • aurplue8 in A and B is gi ftIl by the 8UIIl ot the areas ABeD and EroH in Fil. II COD&1UMr8 gain in the "center" A, 1Ihile in the ex­porting area B producers reap the beDetits. ABCD represents the net gain in consw.rs I surplus in A aDd EFQH represents the net gain in producers' surplus in B. It can. easil,y' be shown that :this total. beneti t ABCD + EFGH is exact17 equal. to RSiU in Fig. II, i.e., ~e inCN&Se in consumer surplus under the transport demand cu.rve.2/ The road. user 8arings on the normal volus. ot traffic '1'is are RSUV • TiB. A8ABJ aDd the development benefits are SVW a ~6TAB.A9AB.

32. '!he size ot the develop_nt beneli ts depends, ot course, on the elastici ty ot the demand tor transport. Specitical.ly J the development benetita (Y) are given JI by:

(3) y:. - ~ RS E(TAB) > 0, where

R is the road user savings on uonnal traffic ;. T~B 419ABJ

S ia tIw Nlati .. , Nciuction in unit transport costs -:iB ; aDd 1('liAl) ii, .. 'before, the elasticity of demand and ii neiatift_

11 This can eas117 be seen by- letting m tend to infinity in equation (1).

Y ABCD + EFGH •. .ABJ! + (ADI + &TC) + REF + (HKE + LGF) • (ABJI + ILIF) + AD! + BJC) + ~\lKE + LGF)

• ~P: - Pi> + (P~ - 11» 'l1B +( tB - TXa) COPA+ 4P~ 2 L -

• A8T~ + .4T • ..t.8J,B.

JI Y -.area SW - ~~9AB4TAB - - ~e;;t.TAB.E(TAB)· - ~ RoS.E(TAB)·

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It follows that:

(4) y R • - ~ SE(TAB) > 0, i.e. J

ths development benef'its will be larger in relation to road user savings, the larger is the reduction in transport cost relative to the initial.

• transport cost and the larger ia the elastic! ty of demand for transport.

JJ. The changes in the elasticity of demand f'or transport and in the relative importaDce of development benefits:are illustrated with the following sets ot lvPothetical data.l/ The elasticity of demand for transport is given by equation (1) (para.. 29), ~ the relative illpOrtance of development bene.f'its by equation (4) (para. 32). Column (1) corresponds to the case where overall production does not cbaDge since the supply elastici ties are zero. There is only a reallocation of' demand. Co1wnn (2) corresponds to the cue v1:tbout reallocation ot daand (aince demand elasticities are zero), but with a reallocation of production following the change in the transport cost. The different values of the elastic! ty of trausport demand and the imporf.ance of' development benefi ta in colUJlllS (1) and (2) are the results of thE! difference in the initial prices. Q)lumns (3) and (4) are identical except tor the value of E(DA); a compari­son shows that E(TAB) is greater vben E(D!.) is greater. Columns (3) and (5) are identical except tor the value of E(SA) j a coq>arison ot columns (3) and (5) reveals that E(TAB) is greater when E(SA) is greater. Similar­ly, it can be 81»1111 that E(T AB) is larger the larger is ei tber E( Ds) or E(Sa).. The ratio of development benefits to road user savings i varies, of course, with the elasticity ot transport demand E(TAB). It is alao proportional to the percentage cbaDge in transport cost; lIhich is 33% in our example. A smaller ( or larger) reduction lIOuld change i accordingly.

Elasticities (1) (2) (3) (4) (S) Demand in A E( D.l) -1 0 -1 -2 -1 Supply in A E(SA) 0 1 1 1 2 Demand in B E(Ds) -1 0 -1 -1 -1 Supply in B E(80) 0 1 1 1 1

Weights Consumption/exports in A Production/imports in A Consumption/exports in B Production/exports in B

Transport Costs Initial New Change

Prices Initial in A Initial in B

Results Elasticity ot transport

d_nd E(TAB) Batio of deftlop_nt bene- y 1'i ts to road user savings R

~ 2 )

( 1 :-> ~ 2 ) , <- J .~-~

tE J ._-_._.--. )

~ - 2 -----~ < 1 --~

-E 4 ~ .'

< 1 ~

-1.2 -o~682 -1.9 -3 .. ·2.5

0.2 0.113 0.316 0.5 ,4174

i , !

Price of Commodity

PAl

PA p1

A

o

DA\/SA

Region A

Price

of Commodity

Pel

p1 8 pI

Output of 0 Commodity

FIGURE m

Region B

Pric. of Commodity

Pc

Output of 0 Commodity

Reoion C

Output of Commodity

. ".

• ~ 0\

1 ..,,4

.I .'

•

- 11 -

3. I!p!Ct ona Third Bagion

34. Thus tar _ have cODsidered onlY' the ettects of road i1IIprove~ men t between two regions, vi thout taking into account the fact that a third region 1JIq also be affected. Suppose there is a third region which coq>etes with B ill exporting the coDlOdit7 concemeci to, the center A. ObvloWl17, producers in C are llkely tosutfer a loss if the road between B and A is ~roftd 1Ih1le transport costa betneD C and A (eAC) remain the s_: tbe cOlllp8titift position of C has worsened.

35. This is illustrated in. Fig. III. Befo~ tile road betwen A am B is iDIp~ved, B exports GH to A, and C exports MN to A.l! GH + MN- AS is A'S. total. iJIports. '!be t:taD:,ort cost between A and B is &is - po - Pft' and, between A and C is VAC • P A - P~. The transport cost betwen A· and C, 9AC' is assumed to remain unchanged at 9AC • "AC. When the road betwen A and B is improved, 9AB falls to ~ a 1. -~. Since 9AC does not change,

VAC = ~ -~. As a result, PA and Pc fall, but PB rises. Con8llJllers benefit in A and C and producers benefit in B. Trade and transport between A and B increases and that between A 8nd C decreases. Total trade and transport increases from AB to CD. The changes in transport, and the bene­ti ts from lover transport costs, depend again on the demand and supply elasticities for the commodity in the ~~e regions.

36. For transport bet_en B and A, the demand curve can be drawn corresponding to the conditions of Fig. III above. Y Assuming that 9AC is constant, the relationship between TAB and QAB is shown as below

M{L+·N) . in fig. I V. The slope of this curve is L + M + N'· lihen L, M and N are

the difference between the slopes of the demand and supply curves in A, B and C respectively.¥ ' .

Footnote !I from page 15:

We have the following restrictions on the weights: VA-WA-l

WB- VB - 1

VA~l

VB~O

Y We aBswae that there is no road, or trade, between B and C.

Y This demand curve is drawn on the assumption that C is an exporter to A and reaina 80. In order to guarantee that C is alwlqS an exporter a special u8U11ption is required. This is elaborated upon in Appendix A,. para. 8.

J! For explanation, see Appendix A, para. 13.

-18-

Figure IV

TAB Vol .. ot trade and trans­port betwen A and B

37 • The elastic! ty ot demand £o~ transport betwen B and A can be .~re8sed again in tara ot the dfUerencea in elaUei ties otsupply and demand ot the eo.aoclity in the three regioDs:l/ -

(S)

where 1 and II are detined as betore, 'T ia total. iIIporta ot A, TAB 1s exports ot B and TAe is exports ot Cj and n • VcE(Dc) - WeE(Se)' with

Dc '. S,. Va • 5 D and We· s:-:=-n:. In this cue also, the higher are the c - c C 1 C individual deUDcl and supply elutiei ties, tbe hisber 18 the elutici ty ot demand tor traDaport. S1ld.larly, the le.. ia the clepeDdenee on trade in the regiona, the higher will be the eluticit7 ot deaQd tor transport •.

38. The beneti ts tro. lo ... r transport coata can aaaiD be ... urad in two equivalent vqs, e1 ther u the SUlll ot tbe chaDps in proclucera' aDd consumers' surpluses, in Fig. III,or uthe increase in the area under the deJllUld cum tor traneport beWeen A and B in Fig. IV. The eOD­sumers gain in A ~ C ,aDd lose in B, vh1J.e the pro<lucel'8 loa. in A and C and gain inB. Bet,rrlng to Fig. III, net gain equal. [ABCD + HIJQ - MNQIU

!I For derivation, see Appendix A, para. 13.

•

- 19 -

which is exactly equal to the area RSUW in Fig. 'IV./1 The 108e in the competing region C is tul.l7 refiected in the demaDdcurve tor tranaport between A and B. Total beneti ta are, as betore, the sum ot road WIer savings (RSUV • ThA9AB) .aDd deY81~t benetita (sw - .~TAB~8AB).

Equation (3) again yields the sise ot the developll8nt beDetits. We CaD

judp the relative iJIportance ot develo~nt benetita, as betoN, by

using equation (4), viz., i · ~ SE(TAB)·

4. Congestion - Rie.ing Transport Costa

39. Thus tar _ have aaew.d that both betore and after the road iDlprove_nt the coet ot transport vas COll8taDt over the range ot traffic considered. In MD1', it not .oet, c ... s in de .... loping countriee thie is probab17 a good approx1Jlation. A stylised picture ot Tehicl. operating coste on a given road tor ditterent Tol1m88 ot trattic aho1f8 a IIOre or less horizontal. "pant up to the point _ere cODgeetion begiDa; then a curve upva.rd over the range where congestion increases, and tiDally a vertical sepant when "full capaci t7" ot the road 18 reached. In the more usual. case, in developing countries, vbere road inveat.nts tend. to be needed not so much because ot congestion on existing roads, but ratber to lower vehicle operating costs even though existing facilities have not yet reached a capacity restraint, the horizontal. aection of the curve is the most relevant one. }Gad iJDproveDBnt shifts this horizontal cost curve downward, with the results discussed above. We shall now briefly consider whether congestion and rising costs change the argument.

40. If vehicle operating costs on the improved road are rising vi th additional. transport,2/ the analysis is essentially the same as before. The net benefits from the road improve_nt are again _asured

!/ Net gain in producer surplus in B is JIHG -, ~PB (toAB + Tia>.

Net gain in consumer surplus in A is ABeD :I ~b.PA (TO + Tl>,

or, since T -, TAB + TAC'

ABCD • J,j.o..PA [(T~ + ria> + (~C + ric»' As 6P A :I 6 Pc (transport costs between A and C are constant),

the net loss of producer surplus in C • ~AP A (TAc + riC).

Total net gain in A, B and C is therefore .

~ ~A +APB) (T~ + TiB) :I ~6QAB(~ + Tia)

which exactly equals the area RSUW, i.e., the change in the area under the demand curve for transport between A and. B.

g,/ Road improve_nt is likely to result not olll7 in lower user costs but alao in greater capacity because ot higher possible speeds. This tends to extend. tbe horizontal section ot the cost curve. On the other band, if deJUnd tor tr~ort is very elastic, road improve_nt might result 'in congestion througb induced traffic.

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by the increase in the area under the der.;~~ curve tor transport.!! The only clitterence is that nov this involve. the producer surplus of the transport 1nduatry. As Fig. V sbows, the area PQCA measures tne net beneti ts troll the road iJprove.nt. This area takes. into account not only the road user aavinas, and the developlll8nt benefits as before, but also the change in producers I surplus accruing to the transport industry serving the route tromB to A.

Figure V

Transport cost D between A

F L-----~~

D

> o TAB VolUme of transport be tween A and B

41. In Fig. V, AFEM is now the road. user savings (T~ ~9 AS) •

AHe is the develop_nt benetits (~6TABA9AB). Both of these are saller

than what they would have been vi th a horizontal transport supply curve J 2/ because the fall in the transport cost (A9AB • AM) is 1es8 than the down-

ward shift in the supply curve (PQ • AB). Road user savings plus develop-ment beneti ts (ACEF) equal, as before, the sum of changes in prod~cers' and consumers' surpluses on the commodity in the :regions affected by the reduction in transport costs (ct. Fig. I or III above). In addition, how ve r, to those benefits of the users of transport, there is a net in­crease in producers' ,urplus to tbe truckers providing transport between

Y Pl"ovided that the supply curve _UUNS the marginal cost of trans­port. It the supply curve refiects the average cost, as it usually doe" in practice J there are further complications which are discussed in para. $7 below.

Y The ettect ot a rising supply c~ ot transport i~giVen in 4ppendix A, Section III.

- 21 -

B and A, 8IIOunting to ECIJ{ .1/ The overall net benetl ts are therefore FAClIt (. PACQ). It is obrloua that the orirall benef11;8 are SlI&ller. thaD they would have been vi th a horizontal tranaport supp~ curve; i. e. J

FACJ.K ./2 and the increase in procluce~ I surplus of the truckers nov absorbs part oTthe former road user savings Imd deftl~nt beneflta. The.,:re inelastic is the supp:q of road _mee I the less important beao. develop­_ot benefits and the share of total benetita accruing to users of transport, and the greater is the share absorbed b7 the transport induatr.1 as producere' surplus (profi ta) •

!I Total change in area under deund curve =- FACE • FAGE + AOO. Los8 in producers I surplus • FAGE. Gain in producers I surplus • PGCQ. Total. net gain • FACE + PGCQ - FAGE = PACQ. But PACQ = PABQ + ACB. And PABQ = FABK. So J we can write PACQ • (PGCQ - FAGE) + FACE • FACE + EClI<.

Hence, ECBK· (PGCQ - FAGE) • net gain in producers' surplus.

Y To be precise, horizontal over the relevant range of potential traffic generation. In the figure below, the fact that without the road improve­ment traffic has grown beyond the point K where costs begin to ·rise,

, and that on the improved road cost would begin to rise again if traffic increases sufficiently beyond F, does not arfect our previous argument. Road user savings are measured by LECBA (or by LECG it the cost curve ia assumed to show average cost), and deve~pm8nt benefits by EFC. It does illustrate, however, the possible error of making "before and after" comparisons (cf. para. 9 above), 1Ihich would measure road user savings on nonual traffic by LEclA, ignoring the rise in (marginal) Wli t cost from OA to OG; and development traffic by EFcl instead of EFe. Thus it would underestimate total benefits by thle "peak" BCFal. (Even if normal. traffic were est:iJaated at LM, and gelnerated traf'flc at MF, there would still be a loss of the benefit peak EtNe).

Cost of transport

G \1

A 1-----_+.:0

1

L~--------~--~~~r_--~---------· 1~>~ , , ()

I , I

, , .~ D

Vo11l1lm of transport

- 22 -

42. Altemati ftly, one aisbt also think ot tbe total beneti ts being cOllpoeed of "road ueer s.Y.l.Dssn FABK aDd "develop_nt benefits" AC2B • ACBj but ~se are not the concepts we have uaed thus tar and are not equivalent to the sua ot chaapa in surplus on production aDd consUllption ot the co..,dity resulting trom lO1l8r transport coste. FABK and AC2B lIOuld han represented the road u_r savings aDd developMnt benetits, reapectivel1', if tne transport suppl,y cu.ne were horizonta.l and the transport de.ndcurve _1'8 adjusted appropriately. '!be slope of the "adjusted" demand curve, through A and C2 instead of G:l. depends, ot course, on the slope or' the transport supply cum, and is giveD by

.b.TAB. 11 Given tbe "adjusted" c:leaand curve tor transport, _asu:rell8nt K - .

of beneti ta fro. a road iJlproft_nt vi tb upward sloping transport supply curve proceeds in .xactl.y the s_ vq .. betore in the lUlcoDgested case.

43.. We bave seen that in t.be cue ot a less than perte~tlT e'utic aupp~ ot transport, the gaiDa conaist not oDl1' ot the producers' aDd. consu.rs' SlJl'Plua.s ari8ing out ot the changes in tbe pattern ot produc­tion and conaumption ot the cOllllOdi tl', but also ot the producers' surplus in the transport; service 1ndustr.y. As the increase in tbe volw. ot trade and tranapol!!r, i8 les. in this cue, the chaDge in the area uncI8r transport de.and curve, retlecting beneti 1;8 elsewhere, will also be less. In tile extra. cue of a perfectly inelastic sUPP17 ot transport between, A and S, the benefit ot a reduction in transport cost will consist only ot an in­crease in rant accruing to the transport serrice inciuatry.

44. If the supply curve of transport between G and A is also posi-tively sloped, then our assumption of' a constant tl'aUl5pOrt cost between C and A will no longer hold. This causes so_ complications, but does not call for any significant changes in our method or in our concluaions. 2/ The only alteration neces8ary is to interpret the delmand curve tor trans-­port betwen A aDd B as a locus of' price-quantity equilibrium poin:~s, since the demand cum i teelr wiU nov shift 111 th changes in the transport cost betwen A aDd C.

s. The Beneti te ot Dl ftrted Traffic

45. We have eDColUltered already 80M tqpe8 ot diftnsion. As a relult ot a road illP.roft.Dt, ~D8 producu,g region gained. at the expense of another in selliJ;ll to a third market, and traffic on the improved lOad was consequentl1' diverted trom another road. We showed that the net bene­tita ot such "diversion" are tul.l7 accoWlted tor in the road user savings

Y Where K· AB in Fi,. v. (AeAB + ~AB~. h beiDg tIJa po81tift slope of the supply' cum. Note tha:i. .lCB • ~TAB.K' and PABQ· T~.K.

~/ For a detailed discussion of this case s.. Appendix A, Section IV.

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plus development benetita as maaaured by the increase in the area under the demand curve for transport on the improved road. Similarly, part of the increase in traffic on the improved road JI81" consiatof a diversion of goode previously tranapo'rted to and sold in another market. In all such casee the J'J8t beDef~ts are _uured bY' the area under the transport de1ll8Dd curve for the improved road, vhi~h in tllm

depends on supply and demand eluticiti8e for the co.odities'concemed in the various regions and ma.rkets iDwlved and the reduction in tz:ana­port costs.ll Thia diversion ot traftic resulting trom changes in production and cOIUIwaption pattems ot a coJlllDOdity when a road il 1m­pro'Yed, is tullY' reflected in tbe cie'YelopJEDt benetits on the new road: 108ae8 due to the possible decline ot traffic elaewhere are already account.ed tor in the demand curve tor transport on the improved road. There is DO need to allow eeparate17 tor 1088es on those other roads.

46. Does this also hold tor "pure" diversion where a cost reduction resul ts in the 8ubsti tution oi~ one route or mode of transport for another in transport from A to B, quite apart from an;y shifts in transport resul t­ing from changes in output and consumption of commodities? Or should the loss of traffic, and surplus, on the railwa.Y or altemative road be treated as an o,frset to the gain in surplus on the iq:.roved road? This question is briefly considered in this section in terms of road/rail coapetition. The problem of eli version of traffic from one road to another is, of course, similar.

Road t,;lI1d Rail as Perfect Substitutes t: __

41. So far we have assUJIIed that the roads are used only for carry­ing a commodity from one region to another, that is, transport services are intenrediate goods and not tinal. consumer goods. If transport ser­vices are regarded in this wq, then road and rail services should be treated as perfect substitutes. Both rail and road provide the same commodity, namely, transportation. Hence, the, cos,t of transportation by road and by rail MU8t be the same. This apparently contradi~ts the fact that rail rates and the eost of travelling by road usually differ. This is not a contradiction, bowver, since in our analysis the transport cost be'tween regions is equated to the price differential between ttle tva regions. Our definition of transport cost, therefore, includes not only rail rates and trucking costs, but &lao all the costs associated with "door-to-door" delivery, interest on goods in transit" breakage, etc. In other words, the total cost of "(ioor-to-cioor". transportation via rail, if both rail and road services are used only for transporting a commoctl ty from one region to another. It 118 regard road and rail services as perfect substitutes, then we can reinterpret the road transport demand curves derived earlier 88 the total demand for transportation. There is

!I With the additional complication, discussed in Section 4 above, that in case of congestion transport coats depend on the volume of traffic.

i,

Price of Transportation

H

I

K

- 0

FIGUREJZI

VOLUME OF TRANSPORT

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no separate demand curve for road (or rail). Then the diversion pro­blem beco_s simply one of detel'llining the ,tllocatioD of total supp:q between two cmapeting suppliers of the same service • With upward sloping sUPP11" cu:rws,!I tile illprove_nt of tile road shifts the aupp17 curve of road services to the right. The area under the demand. cum nll increase, and. the producers' surplus of the truckers will increase; but tbare i8 an (partial.l7) ot.tsett1ng 108s of producers' surplWl.b7 the railVQ's. Total gains ~ nov __ urad by the change in area be\wen the total demand cum and the total supply curve of. transport. This 1. shom in Fig. VI •

48. Sa and Sr. are the aupp:q curves of road and rail services, respectively, before iJapro'YeEJ1t. si is the aupP11" curve of road, after

improvement. Sr. + Sa and s.r. + si are the total sUpply cums betore and. after improvement.2/ DD is the demand for tranaportation services. Initially, total supplY and demand equal. .lE, ot lIhich AC is supplied by road and AB by' rail. Atter illprove.nt, rail traffic decliD88 to DF mel road tratfic. rises to 00. TIle total. producer surplus betore the illlproYe­ment was AIK.LE ot 1Ihich ARB .tor rail and AlC - HIiIlEB tor road. After improvement total producer surplus beco_. Jl{Hllp;1., which is larger than the old surplus AIHlE. The rail surplus clearlY foes d01lIl to lBF < ~j but the new road producer surplus rises to HKHllE F which is greater tban InHlEB. The consumers' gain, o.t course, increases by AD~E, aut..({ the total. net gain consists ot the band IKHllElEl{l. This is esaential.l7 thti same result as the congestion cue discussed ear1ier (paras. ho ff.) eXt:ept that the composite supply' curve for rail plus road. is so.w.t .,ft\l collplu.

49. It should be noticed, in Fig. VI, th.tt:t ~e 10s8 of surplus by' the rail:..'qs is ortset by the gain ot surplus by the remaining rail custo_ra plus ha1i" the gain of custoErs divart\;)d from rail to road. '!be remaining surpluses are gained b,. the consumars and. producers of the road serrices. In other words, it we estimate a "cleJUDd curve" tor road transport alone, i.e., a locus ot roadcost (price)/quantity oq1lilibriUJI points giftn the suppl;y curve tor rail., _ can _asure the h~tits from a road L'lV8st.nt qain as betore by the change in area between the deJl8Dd. and supp:q cums fur road transport. Provided tbat rail rates _aunue tile urgi.na.l coat of the di'Yerted traffic, there i8 tben no need to allow aaparate:Q" tor the loss ot traffic b7 the rai11f818. J/

1/ With horizontal suppl;y curves I 81 ther rail or road would, of course, supp:q tba total demand for trawsportat1on, if' rail and road semces are perfect substitutes. New cheap transport replaces the old. high-cost transport; colipletelyS

y The e~8itioD UIlWES that the suppl3' curves are atra1.ghtllDe, ad ~t old 8DCl D8V aupp13 curves are parallel.

11 This ia, of course, not a '7817 realistic uSWlption. For cOllplica­tiona arising it it 1s dropped, sse section 6 below.

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Il!?!rfect Substitutes, Bail Prices Constant

SO. It rail aDd road are not perfect eubetitutes theY' will have separate demand curves which eaanot s1mp13 be added up tnto. one deund cum tor transport. 1he two de.and· curves v:I.ll be Dtual.q dependent,y when the price ot road services faJ..la, the de~ curve tor rail sb.i1'ta to the lett. Let us aasu., tor the tu. be~, that the price of rail services does not change in response to the decline i.u traffic. 2/ Thus there are no further repercussions of the reduction in road costs beyond the shift in the deJl8Dd for rail. This is shown in Fig. VII below.

CDst and

p

Price~ ot RI----"" trans-port

RJ.

Figure VII

VolU118 of' trauport

Cost and price ot trans-

port PE t---~-----.l..

Volw. of transport

Sl. The daand c~ for !'Qat! senices is dra1In on the U8U111ption that tbe price tor ra;.l ienices is It. The ro84· costs and price decline tro. 11 to Pi and ~ traffic expandi trom Ro to 11. 'lhe shift in the

demaad curV'e tor rail (fro. !fIt toDiDt> reduces rail traffic, at the

Y It the,- are per.tectly independent thare would, ot course, be no eli ftrsion probl.~

Y '!he demaDd for rolad aDd rail, Da ad DL

, are tunction~ of both prices, PR aad PL. Since tbe price of rail services does not chauge vIMm tbe clemaad CJIrV8 .tor rail serric •• ahifta, the ~und curve tor road_rnaea do.. not abitt. The price of ratl services v1ll not chaDge it the supply curve of rail aervices is horlsont~.

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same rail rate ~, troll Lo to Ll • The gain in utilit7 (benetita) is shown by the gain in1conauers surplws under the deund curve tor road services (area PiPRBl).1/ 'lhe reduction in the area under the rail demand curve is irrelevant.2/3/ This is further discussed in Appendix B, Section I. - - !

I!p!rtect Substitutes, Bail Pricea ChaDle

52. When both the price ot road and ot rail, PR and PL' varr, then both the demaDd c~s, ~ and DL, shift toll.ov.i.ng a cbaDge in road traDBport cost. It is then no longer possible to _asure cODSu.tra'. surplus in the sa. -117 as in the previous paragraph. Coliputation of the consumers I surplus in this c_ 1s discussed in Appendix B, Section II. The _thod ot cOlllputatiOD is diag~tical.l7 mom below in Fig. VIII.

Cost Pi ~ce AKR ot trans' -.

Road -port

P~~---tI!

Figure VIII

Q:)st and H price of trans­port.

Rail -

P~t------~

D DR ~----~~--------~~----~ o ~ Volume of

transport

o VOlUM ot tran"~rt

11 The assumption that rail and road services are not perfect substi­tutes implies that these services are now being treated as consumer goods • Hence, the change in the area under the· demand :for road may be referred to as a change in consumers I surplus.

Y This proposition is proved in Appendix B. For a discussion o:f this ProPOSi. tion., see: I. M. D. Little, A Critile of Welfare Economics 2nd ed., Oxford University Press, pp. 175-17 ; and E. J. Mish8D, "A' Survey of Welfare Economics," in Surveys of Economi,c Theory,Vo1.I Macmillan, 1965, p. 200.' ,

J.! ~ere ma.v, otcours.~,be !- gain also in producer suzplus on the road, ~f the road supply curve 18 s10ping upward. .

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53. The road demand curve DR is drawn on the assumption that rail

does not exist (XL ::I O)y. At the road price pi, demand for road ser­vices is then OD =~. The rail demand curve Dt is drawn, in turn, on the assumption that OD road services are supplied at price P~; at price

P~ for rail, OG of rail services is then demanded. The consumers' willing­

ness to pay for on ai' road plus on oj' rail is given by AOOe + HOGF. Similarly, willingness to pay can be worked out in principle for other combinations of rail and road services and then compared to th.e previous one. Once we know the' change in the willingness to pay we can also com­pute the change in consumer surplus. '!'his is because the consumers I surplus is simply the total willlngness to pay minus the cost incurred by the consumers.

6. Effects of Market Imperfect.ions

54. The discussion so far has assumed that transport costs are the only reason for a price differential. between two regions. All other dis­tribution costs were; ignored or implicitly assumed to be zero. Further­zr.ore, transport rates charged to shippers were assumed to be based on marginal. costs. to the economy and to reflect the marginal value of the transport services to the economy. In that case our previous conclusions follow. However., other distribution costs are not negligible. In many cases transport rates are higher than the marginal cost to the economy because of monopolistic rate setting, cross-subsidization between different routes and products, government interventions J road user charges, etc.; and restrictions on 'f:,ransport, coupled with rate control, or a monopolistic distribution system, may l.iake its marginal value exceed the rate charged. In this section we briefly consider whether such market imperfections call for any change in our p~vious conclusions.

55. We mentioned above that, for various reasons, transport rates might be . above marginal. costs, and the volume of transport therefore less than in the conditions assumed thus far. A road improvement results then in less road user savings, tJecause of the smaller volume of normal traffic, but the induced benefits ~ not necessarilY smaller than before. This depends on whether the lower costs are passed on in lower rates. If they are not at all, there are, of course, no induced traffic and benefits. On the other hand, lower transport costs might be a factor in breaking a transport monopoly and lead to a more than proportional. lowering of trans­port rates. In th2t.. case the induced benefi ts would be larger and the road user savings smaller than in the standard cases discussed earlier.

Y The special. demand curve DR( XL :a 0) is not ~ be confused with the

ordinary demand curve Da(PL • P~) used in Fig. VII. DR(lL:II: 0) will'

be to the right of DR( PL • p£) ,.

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56. This is illustrated in Fig. IX below: before the improvement, unit costs are OD but rates charged are OF, so that the volume of traffic is FG <DC. The road improve_nt reduces cost to OA. According to the earlier argument, road user savings would h8.ve been ABeD and the induced benefits BEC. Howver, if transport rates before the improve_nt are at the level OF, rather than OD, the road. user savings are o~ ABlClD. The induced benefits will depend on the extent to which rates decline .as a result o.t the road improvement. If they do not at all, induced benefits will be zero. If the rates were to decline to level OA, the induced benefits would be Bl in, lIhich is obviously much larger than the nnormal" induced benefits BEC. Little can be said in general about the most likely outcOIlf!.

Figure IX

\ \

Cost and F price of transport D

A

I

t , t

o Volume of transport

57 • Taxes (ad valorem) on operating costs of vehicles have similar effects. In Fig. X, below, road user costs including tax are OA before and OB after improve_nt; the tax component is given by AAI and BBI, respectively. ABeD refiects the increase in consumers' surplus accru­ing to road users wen the road is improved. In this case, however, a ne t change in tax revenue is likely. These losses (gains) of tax revenue, reflecting equivalent losses (gains) of utility elsewhere, must be deducted from (added to) the gain in consumers' surplus ABCD. The net change in tax revenue consists of two parts: loss of revenue on the normal. VOlUE of traffic, measured by ARSD !I, and a gain of

!I ARSD - AAlnlD - RAlfs • AAlnlD - BBIK1K. AAlnlD and aal-K1K are tax revenue on normal' traffic before and after improvement, and AAI DlD > BalK IK s~ce jJ).:> sal. (The tax rates remain the same: AAI Bal AO =00' end AO > BO).

- )0 -

revenue on the induced traffic, measured by KKl:LC. Total benefits" thus .aDlDWlt to RllCS, i. e., road user savings excluding the tax element for normal traf'fic, plus Il{lLC, i.e., the conau.rs I surplus on the induced traffic (KCD) with the corresponding tax contribution (KKlLC). The imposi tiOD of ad valorem taxes on the vehicle operating costs thus tends to enhance the importance of the induced benefits relative to the road user savings.

Cost and price of transport

B

Figure X

o Volume" of transport

58. In these examples transport rates are above marginal costs j the rates mQ" also pe below the marginal costs. In the earlier dis­cussion of congest.i,on we assumed that the supply' curve was· based on marginal 80cial costs, i. e., ~Ag:inal costs to the economy. Suppose nov, more realistically', that the supply curve renects average costs,' i.e., the congestion costs ot an additional truck to road users other than itself 'are not accounted for 'in the private road user costs. In that case the supply curve, SOSO in Fig. n, will be below the marginal­social-cost curve McO on which our earlier argument was based. Conse­quently, the volume of normal traffic will now be larger (Or» OXO). Road user savings will, theref~re, be large~~ rsl~lA~ SOslBA. The increase in traffic is now yOy instead ot r'X. TIle oeneti ts ~t this induced traftic are ~ 81DD of the gain PBl C OD the traffic yOX, anet the loss CRQ on the _XC!SS traffic xlylL!_ The net benefits on the, increase in tratfic toy are J therefore, obviously smaller than that on

!I "Roed User Savings" and "Development Benefits" are here defined as in paragraph 42 above.

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t>Xl, as PBl C - CQR ~ ABC. Total benefi ts are nov S°slBlAl + PBI C - CQR • SOSlCA + AAip - 'CQ~ In other words, as cC?q>ared with tbe earlier ~aae8 where rates equalled the marginal social costs, there is a gain of AAlP (because there is no longer a loss on the old excess traffic -fJyO) aDd a 108s of CQR on the new excess tratfic Xlyl. A8 ~R > APAl , the not etfect of an average-coat supply curve is to reduce the benefits from a road improvement.

Cost and price of transport

o

Figure n

D

.-

Volume of 't,ransport

59. Thus far we discussed the effects on the bene!! ts from a road. investment of a divergence between transport rates and marginal costs to the econoDG". Similar resul ts follow, of course, if transport rates diverge from the . marginal values of tranUl0rt. Scarei ty of trans­port facilities combined with rate control res ts in private values exceeding rates. Or the private value of transport mq be below its value to the econollQ" be~ause the demand. of shippers is arfected by a monopolistic structure of marketing, or government control of the COIlllDO­

eli ty' concerned. In other lIOrdS J such distortions mq keep the price differential between region and center, in the terminology used here, above the margin&1. cost ot transport plus distribution. 'Ibis ~ also happen when shippers are ignorant of the potentially existing maZ'ket possibili',ies. In all such cases road user savings on normal tr&tfic will be smaller than they otherwise would have been, and the developaent benefi ts may be ei tiler smaller or larger depending on the effect, if any J

of the road improveJll8nt on the I118gni tude of the market imperfectio:ns.

60.. To illustrate, in Fig. XII below, OP and OQ are unit costs ot transport and rates charged lly truckers, before and after improvement. DsDs is the. demand curve for traD8pOrt vi thout restraints on tranfJPort or

... 32 -

JIOnopoly teatures in distribution. In that case, as in our standard example in earlier sections, road 'WIer savings 1IOuld be PQRS, and the developD8nt beneti ts . SM. Hoveftr, it tor whatever reason the V01UM

ot . transport is restricted to OK • PSJ., road user savings U'8 only PQRJ. SJ.. For a Tolu. OK, the marginal value ot transport ; ~;J the econo-lQ' is KG and its aargiDal cost is ISl (uslDliDg constant costs). The sise ot develop_nt benetits depends on _at happens to the gap GSJ. when transport costa tall to KRl • If' the road. iJlprove_nt only' videns tbe gap between the cost ot transport and its value to the econoll1' from GS]. to GRI' and is tull.y absorbed in higher prot! ta to middle_n, or govem­men t revenue, or wind.faJ.ls for the lucky tev who manage to get hold of' transport, there will be no develop_nt benetits at all. At the other extreme, development benefits migbt be as D1Ucb as GRJ.T if the road. improve­ment led also to a radical improvement o£ the market for transport or distribution. Even if the gap between marginal social costs and values were simply maintained at its existing level (i.e., GS]. • ~~) the development benefits GRj,~r'l would be mucb larger tban in our standard cue (Sm). It is clear then that caution is required in using the standard _aaure-.n"ta of the benefits from a road illiprove_nt.

Cost and price of transport

pr----------------+----~------~ Qr---------~~~--~----~~

o I

HI Volume of transport

61. 1his is also relevant tor. traf'tic eli ftrtedtroa rail', or from an alternative road. In the discussion of traffic diversion from rail to road, - 88suaed that the rail rates reflect marginal costa ot the diverted traffic. It, tor eXUlple, there is a gOYemErlt tax on rail services, then the contraction ot the volw. ot rail serrice. Will lover government revenue. This loss of tax revenue -.v const! tute a loss of' utili V • Provicled thiS loss is a smal.l. tra<;tion of the total revenue and governil8nt e~nditure produces the SaM utility at the .argin as any other expenditure, the loss of tax revenue can be regarded as a loss ot utility. -In that case,

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we auat adjUst our previous net beneti t calculations bY' allowing tor this loss or tax revenue. !I 62. The same problem arises for any other divergence between rail rates and marginal. costs. If rates exceed the arginal cos.ta tor the diverted rail traffic, there is a loss on rail traffic that should be deducted from the benefita on road traffic as __ urad bY' the c:hanp in area under the road d..ant1 curve. Oon'fttrae17, it the marginal. coats ot the eli verted rail traftic exceed the rates, then is an addi t1cmal gain that should be taken into account. In practice both cases are 11kel1 to occur, depending on such factors as the rate structure of the ra:l.lvqs, whether the divergence of traffic leads to closing ot the line or i1ivolves aall savings in operating costs, etc. In fev cu.s would it s ••• sate to ignore these ettecta.

63. In paragraph 56 above, we discussed the meuure_nt ot benefits from an improve_nt of a congested road if we uaume, realisticallY', that .the supply curve tor road transport is based on average social costs and ignores the congestion costs ot an additional truck to other road users. In that cue, marginal social costa of road transport exceed the average costa on whieh road. users base their decisions to use the road. If a road iapl'OveDl8nt diverts traffic from congested roads, tbe reduction ini congestion on these roads gi '9'8S then riae to add! tional beneti til _aeun.td by the artJa between the -.rginal and average social. cost curves for the . di varted valUE ot traftic. Whether this correctiQn is important depends. of course, on the extent of congestion on roads from which traftic is diverted and on the size ot the associated congestion costs.

64. Th. foregoing discussion baa 81Iply demonstrated that market imperfections give rise to substantial qualifications to our earlier conclusions conceming the Masuremant ot tbe benetits trom a rom iJlprove­mente It alao illustrates that generalizations are more difficult it allowance is made tor these complications. Too web depends on the con­ditions goveming aDif particular case. It is clear, however, that the reader should be v&ry' ot 8lfT .chanical application ot the sillple tomulas gi van in sections 2, 3 and 4 ot this paper.

7 OJ Traaaport Surplus, Secondary Benetits aDd Double-Countiy

65. We have discussed at so_ length the _asuremant ot benetits from a road investment and their relation to changes in production and cOD8Ullption ot the coJlllOdit7 transported. We noted that the chauga in

!I Similar ettects ..., occur between different markets - the cue discusaed in section 3 - and give rise to offsetting 10sae8 in the third region that are not taken into acCOWlt in the demand cum tor transport between A and B. In other vords, 8uch lo_a should be apeciticaJ.:q allowcl tor in .uur1ng the net beneti te ot develop­-.:at t.rattic.

"

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the area between the ~elUlld and supply curves tor transport on the ilIprowd road is, in general, a full __ ure of the benefits.!! Market imperfections Ii va rille to important. qualifications, but otherwise there i8 no reason to taD irito account any' turtbar gains or losses elsewhere in the econolV'. As it is somet:LJies argued that various "secondar:r benetits" should be taken into account, in addition to these direct transport benetita, it JIJIq be worthwhile to add SOIll8 further comments on this question.

Tr!ll!Port Banetl ta and Income Changes

66. ~nsider the cost savings on nomal traffic resulting from a road improve_nt. These JfJi!,y, ot 90urse, accrue, as _ have seen, to the truckers, the shippers, or the producers ot the transported cOllllllOdity in the form of higher pn)tits, land rents and wages, or to the consumers in tbe form ot lover prices. SiJlilar~, the benetita trom induced traffic IIQ'be ninected in higher profits to shippers, higher land ,rents or other factor incomes or loar consumer prices. ']hey are not only eamed in the immediate area served by the road, but ~ accrue to beneficiaries else­where insofar as they nov find it profitable to use the better road and expand output and trade. At the same time, as discussed abaft» there are likely to be losses for producers in the competing area, or on competing routes or modes ot transport. Our argument has been that in JII8D7 conditions all the repercussions are reflected in the demand curve for transport on the improved road, and. that a full measure ot the benefits can be obtained by taking account only ot the increases in the area below the dellaDd curve for transport on the road concerned and the accompanying changes in producers I surplus of tbe tran~ort industry, it any ,earned on the road. (We also noted, it is worth ~peat.ing, that in case8 with market imperfections in transportation or distribution affecting competing regions or DIOdes of . transport there .lUl' be Qther losses to be allO'll8d tor). What needs emp~iz­ing here, however, 1. that there are JII&IV' difterent but equivalent Wll38 of measuring the benefits 'from transport; either on the leval ot the supply and demand for transport, or of the ultimate beneficiaries of better trans­port .ervices. Those measures are altematlves, however. The)" should not be added together. One should not first MUure the road user savings and then add the higher pJlOfi ts ot the truckers; or _aure the surplus on increased transport, and then add the value ot increased agricultural output, or land rents, etc. To do so is plainly double-counting.£1

!I So_ reinterpretations of the "demand curve" .... 1'8 necessary; and the :_uure IIq break dOVD if demand cums tor competing modea an "parate, i.e., it rail and road are "CODSUJIIJr goods· (cit. paras. S2, >3 above). .

Y See tor a useful discussion of the relation bet_en difterent mea­suree ot transport beneti ts, Clell G. Harral, . Preparation and Appraisal of Transport Projects, The Brookings Institution, Washing­ton, D.C., October 1965, p .• 5i ff. (mmeo •. )

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67. This should not be misunderstood. It is not argued, of course, that knowledge ot the repercussions tor the producers and consumers ot transport services and cODlDOdi ties in the area ot the improved road. and elsewhere are not important. On the contrarT, as we have seen, the inter­re~ation of these demand ard supply factors of competing regionS and transport determines the extent ot induced traffic. Develop_nt traffic, in sections 2 and .3, was derived trom delUDd anq supply' in various regions for the commodity transported. The effects of a rising transport supply' curve (section 4) J and of diversion (section S), were discussed in terms of interactions between commodity production and co~sumption and transport condi tions, and between supply of transport by' different modes. In some cases, the analysis of transport benefits DUq bear even more heavilJr on "interrelated packages". It might be convenient to bypass the problem of deriving a demand function for transport by ,focusing directly on the agri­cultural effects. This is the customar,y solution in irrigation projects when faced with similar problems conceming the evaluation of water. FOr transport projects, however, this approach appears to offer less promise, at least for trunk roads. Direct measurement of agricul. tural effects may be useful for the analysis of the benefits from feeder roads.!!

Further Repercussions

68. Whoever receives the immediate ben~fi ts resUlting from the road improvement, the increases in income are passed on, directly or indirectly, in expenditure for consumption or investment, with subse-quent further adjustments in output and income. Part of the income from cost savings may be invested, for example, in additional. transport; other parts are spent on expansion of agriculture, or industry, etc., or on higher consumption, leading to further repercussions and adjustments. These effects on output a~d income are not necessarilY in tha region served by the road, but tDJq be felt elsewhere in the econoD\Y. Again as a result, some people gain and others lose. Many different repercussion patterns are possib2..s - depending also orl' the distr.1bution of the original cost savings, or benefits from induced transport, between truck~rs, shippers, etc. - with many different effects on output and income distribution. All of them, however, reflect various uses made of the direct benefits (or adjustments to losses). CoWlting again as benefits these second8l7 increases in value of output and/or transport :resulting' trom the primary benefits amounts to double-counting •.

Y For penetration roads, it was suggested above (para. 5), the major problem is probably the agricultural development scheme; the road aspects are then better treated as a minimum cost problem, thua avoiding the measurement of transport development benefits.

- 36 -

69. These repercussions on income and output, beyond the direct benefits from road user. savings and induced transport, are not relevant for benefit-cost analysis adming at optimization of resource allocation. A (pure) cost-saving road project, lor example, without economic justi­fication in terms ot direct savings benelits cannot be made neconomic" by including such indirect eftects. Including proti table and unprofi t­able elements into one investment package with a satisfactory economic return does not make the unprofitable components econo3llcally justified. As a practical. consideration, moreover, it is not clear whether, and at what point, further n tertiaryn elfects should be cut off. The repercus­sions of the project do not peter out; they do not constitute a multiplier process with leakages putting a definite limit to the magnitude of total repercussions. The problem here concerns al temati ve resource allocation patterns, not an increase in aggregate demand. If the latter were the problem, pumping in more purchasing power by budgetary or monetary means would be the simple answer. To take account of all repercussions and . interrelationships would requil"8 detailed conq:>arison of complete al terna­tive investment programs and pattenls of development. This is hardly a practicable task, and defeats the ver.y purpose of project analysis, i.e., decentralized decision-making.!!

8. Conclusion

70. 'lb. conclusion of sections 2 and 3 of this paper is that 8JJ. benefi ts from a road investment are accurately measured by the change in the area under the demand curve ior transport between the regions connected by the road. This 'conclusion depended on the assumptions that the trans­port services are only valued as intermediate goods and that there is no change in the surplus ot the producers of the road services as a result of the road improvement. The extension of the measure necessary when there is a change in thE.~ surplus of the truckers, because of an upward­sloping supply curve of transport on the new road, haa been discussed in section h. An upward-sloping supply curve of transport lor the competing region, however, requires only SODe reinterpretation of the demand curve. Competing modes of transport on the same route cause further complications (section 5). If we·~ as~ume that both modes of transport supply per­fectly substitutable transport services whiCh are only used to transport commodi ties from one region to another, a sui table :reinterpretation of the "demand curven for road transport, maintai.n~ the previous measure of the benefits. When road services and the services of a competing mode of transport such as rail are not perfect substitutes, but are final consumer goods with separate deJQ8lld curves, the net ~hange in the consumer s'Q.rplus is measured by the demand curve for road transport, provided the price of

Y In principle J the secondary etfects are renected in the (shadow) prices of inpute 8Qd o~tputs of the transport serVice, and in the projections of demand for transport.

- 37 -

the competing service does not change in response to changes in the road transport costs. If it does change, howver, the nonnal. computa­tion of the change 'in the consumer surplus does break dow. .And, as discussed in section 6, market imperfections necessitate important qualifications in the earlier measure us~d; in particular, they ma..v require explicitly taking account of repercussions of road inveatDenta on the surpluses from coq>eting routes or modes.

71. We have looked at the increase in the area between the demand and supply curves for transport as a sum of two parts: the road user savings plus induced benefits. Road user savings accrue to the initial volume of traffic, i. e. , only those who use the road at the initial trans­port cost will realize the cost savings due to the fall in the transport cost. Hence, to calculate the road user saVings we need to know the volume of. traffic without improvement and the change in the tranapo~ cost brought about by the road improvement. However, in order to cal.eulate the induced benefits of diverted and development traffic we have to estimate not only the fall in the transport cost but also the volume of tra:Cfic induced by the lower transport cost. Induced benefits can often be an important component of the benefits of a road improvement. The higher the elasticity of demand for transport, and the higher the fall in the transport cost, the more important will d~velopment benefits be. If we have data on different volumes of traffic and the associated levels of transport cost we can estimate the elasticity of the transport demand curve (or the slope, if the curve is linear). If we lack such data we could still estimate the elasticity of the development component (but not the di verted traffic component) of the demand for transport by estimating the underlying elasticities of de~BDd atld supply of the t~ans­po~d commodity in the trading regions.

72. The quanti ties mentioned in the previous paragraph are, however, frequently difficult to measure, particularly in underdeve1.oped cOlUltries. For example, cost ',,-avings of road. users can seldom be directly measured, al though rate changes m.&\V possibly give some indication. General lmowledge of the effect of'specific road improvements on road user costs, adjusted to local conditions, is a more satisfactory approach to thieproblem.l/ The surplus on induced traffic presents greater problems. Even conceptua.lly, as discussed in this paper, there are complications if market imperfections in transport and distribution are significant. In practice, the problem is likely to be worse. The growth of traffic, and its breakdown between normal and induced traffic, is difficult to estimate. The simple measures of benefits from induced traffic. based on changes in transport costs used in the earlier sections above, are infrequently, it would appear, a aatis': factory guide to the surplus on induced traffic. The difficulties beco~

!I See de Wei11e, ~. ~.

- 36 -

even greater it a diftrpllce betwen arginal social cost aDd benetits ot tranaport 1'ro. collp8t1ng 8OW~8 ot aupp:q, or by a cOllp8ting mde, uke8 it MC88_ary, as noted earlier, to aka an e8timate ot the 10s8es suffered by, sq, the region or railvq froll lIbich traffic is eli verted.

73. It is clear, then, that conceptual. clarity is a neceS88l7, but not 8ufficient condition tor plausible eet.baation ot tbe benefits of' a road 1mproveMnt. The practical. d1fficul.ties of estimation are obviously great. In some cases there mq be good reasons tor thinking that the road user sarings, which can probably be measured with somnhat greater confidence, are the bulk ot the eatiJaate. But this is certainl.y no general rule. Tbe develJ)p_nt ben.tits ..., be quite iDportant - in fact, the 1IIOSt releyant part tor so_ road improw.nta. In cases 1Ihere cm.ngea in transport costa gift a good indication ot the height ot the "de'V81op­_nt triangle", the main issue i8 the volU18 of induced tnl.ttic, in rela­tion to normal traftic. But in cases where the distortions in transport or distribution are serious, as DV' often be the case - a reasonable est.1aate ot the benef'i ts trom development and eli vertec! traftic and possible offsetting losses elsewhere c8IUlot be made vi thout considering explicitly the cOllplicationa considered at some length in this paper. It should. be admitted that in the present state of our knowledge, estimating the bene­ti ta ot road in~~8tmenta is an art as 11811 88 a science.

APPENDIX A (to Sections 2, 3 ~d 4)

I. Two-Hegional Case

1.. The an&:qsis in Sec:i;,ion'2 is deri:ved troll a simple linear model. We shall describe the .,del in this section. We 88SliM tbat in the absence, ot ~ ~nde between region J. and region B, the price ot the cOJa)dity v11l be higher in A than in B. '!'be' IIi.nbmJI pl'Ohibi-

, tift trausport c""t which will p!e'VeD.'t 8DT .,ftJII!BD't of thEt co~diV bet1leen the tvo regions equals this price difference. ,As the transport cost is loweredj the price in A vill fall 8Dd the' price in B vill rise. Buti unless the transport cost' f'LUS to zero (free trade), the ,pr1~e in J. Will aJ.1I87S be greater tban the price in B~ This .aDS, ot course, tbat A v111 alvqs remain an iaporter from E.. 'l'be iJlprov_nt of the ~ad between A mel B will reduce' the transpc,rt cost and. establish a new lover price difrerence ~tveen A and B. . Since ve have equated the price dille renee to the transport C~8t it i8 at once clear tbat our definition ot tJw traDSport cost is broader than usual. The coat of transportation is the cost ot "cioor-to-c:loor'1 delivery. The coat of transportation on the road is only a part, although probably the moRt iJIportant part, ot the transport cost as we have'defined it. '

2. The model used in Section 2 is:

1. DA • aA + bA PA

,2. SA - e(A +.'1 A P A .

3. DB :;a aB

+ bB

PB

h. SB -a(B + PB PB

5. D -t. D + A B SA+ SB

6. PA D PB • 9AB

Notations:

D • DeJaDd

S • Supply

P - Price

gAB- Transport cost betwen J. and B

> u( A

Appendix A -. Page 2 -

Notations (cont'd)

With no trade;, PA '> PB, i.e., ~ "I > -.

M

3. The above' sysf,em can be solved to yield

1. A B .

H + I + M Q ' - .::> PA =- 0

L+M L + M AB

A,B.., H + I L > PB

:II - r-:;M 9AB 0 L+M B.

A.B~ LI-HM + LM 9 ~ 0 • L+M L + M AS

9.

A.BJi • A,B~ A

10.

where ~~ "

PA - equilibrium price in A in the 'tlIo-regio.p (AB) case.

A,B P B • equilibrium price in B in the two-region (AB) case.

and, ,-.J) - _ X • D- S :lilT A A A AB

equilibrium values -.S _ _ x---S-n-T -~ B B AD

A,B A,B Since, ~ volwae of trade. TAB • if- ~,the

transport demand cum is given by

LI-HM LM 11. Tn" " • " + 9AB, and is sh01lll below in

L+M L+M Fig. I ~orre8pond1D1 to Fig. II in tbetext.

liM - lL 1M

Appendix A - page 3 ...

Figure I

LM L + M < 0

Ll - HM L+M

5. The slope of the curve is, from equation (ll), LM M ... Now, , L +

=-----

1 =-PA

= L t were L is as def'ined in the text (para. 29). P

A

The quantities PA, DA, SAj Vt' ~ ... re£er to the equi1ibriummagnitudes corresponding t~ the point a vh1Ch the elastici ty is to be taken. !hey shQuJ.d have been marked nth an appropriate superscript to indicate this. We have not done so tor the sake ot uotational. simplicity. Similar17,

M ~ f- m, where m is 88 defined in tbe text (para. 29). B .

6. The price elasticity of the transport demand curve is given bY' 9AB LM -- -- = E(TAB). Substituting tor L andM, aDd DOting" that DA - SA • Sa ~. Ds, ~ L+K' ,

we'get the equation (1) in the text (para. 29).

<'

. ~ . ..".. ,

~ ,

11. Three-Blsional CUe

7. . The model used in Section 3 in the text, i8 given. by-equations' 1-4 ot the, previous JiIOde~,' combined with the . tolloviDg .quations:

Sit DC • ·c + ~r!c be " 0

6. s • "<c + fJc!c tSc > 0 ac > d.,

c C

7. DA + D' B + DC • SA + Sa' + Sc

8. rA • PB + 9.lB 9AB ~o

9. PA - Pc + 9AC 9AC ~o

(be - de> • N < 0

i H J I We ,US\1Jll8 that J wi tbout any tnde, P A > . Pc > PB, ••• , - ::> - > -. A 'L N M

8. Since _ are interested onl7 in the cue where C is an exporter to A, _ shall JUice an uaUlllption which will ensure this. This assUmption will guaran~ that C enters trading as an. eltpOrte~ to A aDd remains ~ exporter. This 888WDption is:

A,B I . J H + I' •• _ ~ • • _ J. QAC iJAC PA N t + M "

9.18· 0

.liB \ libere, PA,' . 'is the value ot PA ~en 'there ia tr~e between A and 9' '·0 :A.B

B only'" ~tbout 8D7 t~8pOrt cost' be~en .land 'B. i is ~e value of Pc that WOuld rule if C did not enter trading.' In othervoiUe, _ asSUJE that the traD8pOrtc~~t 8£,C' be~n A' and CJ ra-.ins constant at a level gi.,.o by-the difterence bi\Wen tile tNe· trade price in A (without, partici­pation b,. C) and the isolation price in C. This is a sufficient c'ond! tion, not, a neceas.ar.r one.. T. nece88aJ7 condition is weaker. But this assUmp­tion aiJlpliti •• " the analJ'8ia wi tboutcbangiDg . the basic conclusions •

.",

9.

Appendix A - Page S ..:

- . Ii + I J "The 'solutions ate, using CilAC D L + M - N '

10.

ll.

12.

13.

- H + I M PA • L + M + L + K + N 9AB

'p' • H + I _ (L + N) 9 B L+ML+M+N AB

,-- J P .­C . N

+ . M 9 L+M+N AB

-D IL - 11M LM + L + M + N QAB X =

A L+M ~ 0

14. xD= HM-IL _ 9 M(L + N) < 0 B ABL+M+N L+M

15. xD= MN 'N QAB <. 0 c L+M+

Volume of trade, -3 -.:S '"ID T = TAB + T AC = XA + X = C A

10. From this ll'~del, we· can derive relationships between TAB and

QAB' TAG and QAB' and TAB + T AC = T and 9AB• The relatio:nship be_en

QAB and TAC(- X~) is shown below in Fig. II. This is derived from equation

. . (HM - IL) (L + M + N) (15) ~ve, not1l1g that at the. level 9AB ::I (..U = M(L + N) (L + M) , TAe

equals T since .trade between A and B disappears {TAB ::I o}.

. w

Figure II

N(IL - liM) (L + N) (L + M)

~ (HM·- IL) ~L + K + X) • . MtL + » (t + M)

Appendix A - Page 6 -

11. The relationship between TAB and 9AB, the ona used in the

text (para. 36) is given by equation (14) above. This is' shown below, in Fig. III.

UJ

Figure III

LM+MN L + M + N

IL - HM L + M

12. The relationship between T and 9AB is shown belo,. in Fig. IV.-

w

Figure IV

!i(IL - HM) (1\ N) (L + M)

LI .. 11M L+M

L+M+N

T a TAB + TAC

Appendix A - Page 7 -

13. The elasticity of the curve in Fig. III is derived. ana].ogous.J,Y M(L + N~ . to the previous case. The slope' 1s given by L + M + ~, tromequat1on

. . 9AB M(L + N) .' . (14) above. We have, E(TAB) = T · L + M + N. We have 'seen, tIl.at tAB' n

L = *, }t = p;. N can be shown to be equal to 1': where n is as defined ABc

in the text (para. 37). Substituting for L, M, N, 118 get the equation (S) .in the text (para. 37).' This e~re8.ion is, however, ~re complicated than the one in equation (1) (para. 29). The reason 1s simply that, in the case of equation (1), DA - SA • SB -':oa,. and hence, i twas possible to achieve a reduction to a simpler form.

III. Hieing Transport Cost

14. Q "'" was used as a parameter in both the Two-leglonal ~d the Thr(~e-RegioAi:J. model. We JII83' consider QAB as an endogenous var.iab1e by .adding an equation for the transport supply' urve.

15. Let this equation be:

TAB :& g + h9 AB' h > O.

Using this in the first model (Appendix A, Sec iiion I) we get, USing equa­tions (6) and (8):

,.J geL + M) - (LI - HM) Q AB = LX - h(L + M)

as the equilibrium value of QAB. Using the equations in the second mOdel (Appendix A, Section II) we get, using equat,ions (8) and (11): .

-' geL + M) - (LI - HM) 9· = •

AB M(L + N) - h(L + M + N) L + M + N

L + N

as the equilibrium value of QAB. Using these values of 8AB ,we can eliminate QAB from the equations (7-10) (Section I) and equations (10-15) in (Section -II) getting new equilibrium values of the variables concemeci. Shifts. in the transpo~ supply' curve will be represented bY' changes in the value of the parameter g.

IV. Variation in the Transport Coat betwen A aDd C. QAC

16. We have mentioned in paragraph 44 o£ the text that neither our conclusions, nor our method need be signl£icantly modified it we relax the assumption that the transport cost between A and 0, ~AC' is constant. We wish to show why this is true in this section.

Appendix A - Page 8 -

17.. Constancy of the transport cost, QAO, can be justified by assuming that the supply curve of transport services between A and C is infinitely elastic - hOrizontal, at least in the 19levant range. However, if the supply curve is positively sloped tJum 9AC will fall wen the demand for· transport between A and C falls.' That is, wen . QAB falls due to a road . improvement, 9AC will tall too. This fall in QAC will shift the demand curve for transport betwen A and B ~ the

left causing a further fall ill 9,lB it the supply cum of transport between A and B is also positively sloped. In the new equilibrium, after the interactions end we will have a lower 9AB, a lower 9AG. a lower TAC and probably a higher TAB. This is illustrated below in Fig. V.

QAC

Trans­port cost 1 betwee DC A and

Q AC Q i--oIp-;op.--ofC

9ic T I---~""

o

Figure V

QAB Trans­port cost between n! A and B :-B

o QAB V~~--~

81 AS Z

Transport between A and C, TAC

Zl a.-----::::I"'Ii

o Transport between A and B, TAB

18. In Fig. V above, (9ia, 'AC' TXc' ~) is the set or values in initial equilibriWil. Sia, the s.upply curve ,between A and B, ·falls to

siB due to the improvement ot the road between ,A and B. (eis, eic' Tic' Tis) is the set of values in the new equilibrium. Both the demand curves have shifted to the lett. 9 AD and 9 AC are lower than before. The traffic between A and C has also fallen. We have assumed here that traffic between 'A and B has increased. We might similarly conceptualize a series of shifts in S AB

Appendix A - Page 9 -

giving rise to a" series ot new eq1.ti.librium pOints. The locus ot all the equilibriuill values of QAB is LL, as drawn in ~g. V above. LL could be positively or negatively sloped, or be vertical, "depending on the specific forms g1 van to the d.eund and supply functions. The locus ot the equilibrium values of QAO, on tbe other hAand is the supplY curve SAC' since SAC dOes not shift (the road between A aDd C is not improved).

19. We can d.evi__asures of' the surpluaes enjoyed b7 .the COD8U1118r8 and producers ot the cOJlllllOdit:y in terms of Fig.-V, exactly as before (footnote 1, para. 31 and footnote 1, para. 38). Referring to Fige III in the text, the net gain from the point of view of CODSUMr8 aDd producers of the cODllDOdity- is given bY':

Net ge.in • ~PA [TiB ~ -ria + ~c + rlJ . + ~B [T1s + ~]-~c ~~c + ~c]

The term ~PA [Tia + ria + ~c + TlJ is the uet gain in C.ODSu.rs. -11 surplus in region~ (area ABCD in Ffg. III). The tem ~B [TIB + ~ is the net gain in procl\\Cers surplus in region B (area JIGH in Fig. III) and the term ~P C ~AC + TIJ is the loss of producers I surplus in region

C (area MNQR in Fig.III). In this case, ,. have o.PA + APB • ~9AB and .

.6..P A -.6P C a 6QAC• Hence, the net .gain can be written as:

Net gain • ~A9AB [t'AB' + ~J + ~b9AC [T:C + ~c] Looking at Fig. V above, we can see that

area QSUT - . area QRUT + area RSU

• ~QAC [T~c + TiJ and

area VWXZ • area WWYZ + area WIY

• ~~ABAT~ + ria We have thus obtained measures of the net beneti t in tel'lll8 ot the dell8lld and supply tunctions ot transport between A and B and between A aDd C.

20. We sa bet ore that, with constant 9.A.C~ the net gain i8 entirely . refiected by the change in area under the deJllllld curve tor transport be_an A and B. A little reflection will show that in the present cu.; where "AC depends on the volw. of transport T AC' the net gain is aillUar17 .1Knm b7

Appendix A - PaP 10 '-

tb8 chaDp in the area UDder the locULI LL, i.e., 1»7 ana WU. Dle reason i8 that the producers of tt. transport •• rvice betwean.1. and C have lo.t a surplus ~t17 equal to QSU'l'. Taking this .losa ot· produce.rs ' s-qrplusinto account .. are left with the area VWXZ astbe net gain. '!he only differpce in this case is that the net gain i8 nov meaaured by the chauge in the area under the locus LL (VWXZ) ,wereu betore 1 to.... . chaDge in the area uDder the non-shifting demand curve (other prices being Qonstant) for transport .betwen A. and B. ibis calls for only a minor 'reint.rpretation ot the statement that "the net gain is measured b7 the change in the area under the demand curve for' transport between A and Bit.

21. Ot course. in order to measure total uat gain it i8 clear from . Fig. V above, that _ still have to account for the change in the surplus of the producers of the transport services betwen A and B. VWXZ has to be corrected by tne net increase ot producers' surplus (Z~xrl). But this case haa been t~ diacusaed'in Section 4 under. the ti tJ.e n Congestion" • TheM i. nothins to add to that dillCussioD here except to _D:~ionthat the demand cum has to be m.l)laced by' 1~ locus LL.

22. ~. reader ., "rJ" < ,'IIOnder wlv' the introduction of iJiterreJ.ated . demand functions in this' ,,,,ase does not result in the same kind of proble_

as we faced in the road-rail di wraion problem (paras. ,2, .$3, Section V). The reason is that in SectiOD8 2 aDd 3 (deacribed b7 the models in Sections I and II of this. Appendix) the transport services bet1leen A and B and betwen A and C we1'8 not treated as final consumer goods. The demand for transport port between A and B and between A and C _re derived demands. The trans­port services did not enter into the conSUMr8' utiU ty function direct17. Thus they did not yield any consumers' surpluses by thems~lvesil The chan •• in the surp1us8a ot consumers' and producers ot the oolllllOdity _1'8 :measured by the changes in the area under the deJl8lld curve tor tranaport betweD A and. B. '!his i8 a convenient _uure which saves us trom conDi­d.ring the deUlld and supply cums of the cODllOdi tT directly.

23. In tbI road-rail d1 version case, hGvner, road. and rail _1'8 treated U cODp8t1ng .tiDal conw.r goods which give utility" to the CODSUMrB. ~'he road-rail eli veraillll probla caDDOt be handled in terma of the JDDde18 in Sections I aDd II of this Appendix as theT stand nov. We have to introc1uce separate c1eDl8Dd equations for road and rail services in those models. The models J tIleD, will become three-colllDOdi ty mod8ls instead of being one-co-.odity lIIOdela 88 theT are DOV. In other words, .. shall have to &1.lov for the poasibUi V that, stq J road services 11UV' compete in cODaUlption with not only rail 8erv1ce8 but aleo with the coaaodit)" i tsel! • The c1eund tor the collllllOdi ty will be a function, not only ot ita price but also of the prices ot road and rail services. Howver, when the road aDd ~ail serrices are not related in consUillption to the colllllOdi t7 then ... can use· the _thode discussed in Section 5 1;0 compute changes in consu..ra' surpluses. '.

..

APpENDIx S' ,(to~seotion 5)

. . ,

1.' InS8ction S' (~u.. 50 and, Sl) lie, diac\18s.<i ,th8, rOaa-ra;11· diversionprobl..emon the assumption tha.t ,rail 'prtcea do Qot change in ' r'~spon8e ~ changes in :road~ prlces(I We aaaerted ,at; ~t :tiiII'tb&t, in a 'case,·where 'the prices ot',relate<l colllblit1ea '~ ~onstant, the ", net ,change in' the consumers' surplus due to, a, tw.' in, ~, road pric'e: i8, g~ven ,by the . change in the area under the deund curve to'r road.: * ,ah&U f,"

prowthls proposition'.in this appendix •. Betore' we'do 80 _ sball, 1Mk. a few commen~ regarding the concept of consumers' ~urplus.

2,. The demand curve ot a colllllOd1ty,' Xl, 1s' ,usuaJ.ly drawn with 1'88-pectto changes in the price of that coJllllDdity. ,The pollition ot the' , demand curve, ,is unique17 g1 van if the eoDlllOdity, is not rela~d' to arq, other conned.! ty ori!' the prices ot related comoditiea are held constant, when the price ot the COJlllll)di ty change's. When the, prlc,eot the cOJllftOdi't7 falls and the demand for it'increases, the change in the area under the ' demand curve (its position being uniquely given) ie regarded as the chaDge in consumer surplus. We cannot measure changes in conau.rs" 8urp~uise8 in this way if the prices of related co~tie. are allowed to V8Z7 in response (E$ince' the demand curve for Xl v1ll shif1i its' poiiition). How to measure consumers r surpluses in such a case is the' subject ot the next section. In this section we assume that thec:lemanc:l curve for Xl. baa a unique position (t.ne' prices of related COJnR)di ties do not change).

3. The increase, in consumers' s.urplu8 is a _asure of the increase in welfare or utility enjoyed bY' the conswners 1IheD the price ot the , commodity falls. Our priJnJU'y ~oncem is to measure the change in ut~lity . (for this we must, of course, assume that util~ ty is cardinally measurable). ' . 1be t.,echnique of consumers' surplUs is a tedhnique for _asuring the change in u.tili ty. The use ot this technique is: valid provided certain condi tions are fulfilled. In the course of our proof we sha1,.;l mention the required cond1 tiona. Under certain condi tiona the cODsu.rsurplus teclmique ¢il accurately measure the c~e in utility. ' Again, under certain conditions, the change in the ar~,a under the demand, curve will accurately measure th~ change in consumers I surplus., It all the QOncli tiona hold and if the demand curve is defined appropriately',' then the change' in utili ty will be ~asured bY' the change in the area under the demand curve.

4. Suppose there are n goods ~1~ ••••• , •• ,In .. ~,heir prices are PI, • • • • • • • J Pn.!I WeahalI consider the chaD~ l.D utility when the price of only one coDllllDdi ty, Xl' changes, :the o~r prices,

11 For a discussion of this and related matters, 'S8e P'. samuelsoll, rt CbnataQ.cy ot the Marginal utUt ty ot Income, n Studies in Ha~­tical, Economics and EcOno_trlc8 • (Univerai tY' or Chieqo, 1942).

, .t

,;

: '

"

:p 2' •• • ~ • ••• • 'Pl'l,,~iD8'UIlchaDpd~WheD:~priCl. of ~, Pl' cbaDps, tne. ,~titie.ot tb.,' other c~di;,tie.1I1ll- change, i.e., , 1.2' ~ ., '. ,. ' • " • '~I In'.vUl abaDle. Onlcan iJiIiecli.te17eee.that, -it

\ is a lION .enerU 0'" of the'tQad-rail diversion, problem.· Xl .v be, regarded as road ~rrice~ .12' • • • ., _. .., In',, then~ are ,thequanti~ tie" of all 'the relatecicollDOd1ties, including rail~' "

$. ' Let. I1. I1~ ... ' ...• , pg be tba Wt.lal 'PrlC.IIOf ~n . coDOdi ties. Since onl:J PJ. changes, Pi JP~, .,. • • • • • J pK: is:. the Devset of prices. SiJIilar17, let It, Il, · .. · · · · J Jegbe\the

,initifl ~tit,i.a of tbtf n co~,: dit,ies., Since"all qu8Qtitiescibange, xi, ~, · · .• · · ., X;; i~:.tbe new set or quantities. " -_.,

6. We 'now haft to define a cardinal .utilit7function.(),~alitY illpli •• that _ can quantify the chang_sin utillt7. Let the utility' function be U • 'U(Xlt • • • • • .,In). The initial level of utility , is given b7 UO • u( , •••••••• ~) and the n_ level ot utility . 18 gil8D 1»7 ul • u( ,....... • X!} • W. aleo haft a budget cOMtraint

. D . 1JIp17iDl that the to .one,. expenditure IIWItnbe equal ~ total money

income. The budget. constraint. ,statell t.hat. ~ Pi ~ - '1 • 0, where, I

. is tb8 1IDI187 inco.. Kind_:t sing the utility function subject to the budget

, au conat.rai,nt., 118 get. PiA • ;a~' i • 1 ••••• , n. A. is calledt.he

marginal utili t7 ot ineo- and is .. function of all price" and .,ney incOM. In order to use tbe concept of COll8u.r surplus 118 muat 88S'WD8 that the -.rginalutll.ity of incOll8 is constlnt with respect to change" in all pr1c., .... xc.p1iing one, ,88¥, Pli, and. with respect to changes ,in money inco., I. '

Thus, .. geta

i ~ n

. ' "1. We han , .

, 1

. -f: tt!t :~. :~} dP1 ·

[U81ngthe equali~iea ::A -~ ~. i 1

· J: 1i 1 Pi

. Pl

[ using the bw1get cODBtraint 1 --[

P~

• • -AD where D ia the area·. under tbe ciemaD~":" culTe,be:tween P~ ed· Pi,tor Xl- Our uaUlllptiou.' iJIIpq. that the aU-o~ ae.ad. curre. the 0l"d1.nar7·ctitmIllcl Jurre IIIlCl the Hicka~_atild

"de~." : C~ C.O~icie. '!'hentoN, D [ •... - J~ .. I 1dP1 1".". ie - cbup 111 "" " . ~". .

j

i <I

.' "J j

.. j

·f

I

t , f

i I ! {,

")1

j I i

., , i J

i j I

::1

!

I I

i 1 I

I

ccmaw.r surplus UDder t.be de..ad cum for 11- This _aaurea the total cbaDge in utili t7 in thia cue. Hence, to cOlpute tbe total change in utUit7 _ onl.7 have to take into accoUDt tbe change in -area under the demand cum ot the good who.e price baa fallen.

II. Price of Bail Services Variable

8. In this appeadj x .. sbow how the change in consumers surplus can be MUUNd matbematica.ll3 when the price of rail changes in response to chaDgea in the price ot road. We shall. also ahow a diagra.atic COrleS­pondence to the .. theilatical _uure. Tbia case and the diagram have been discussed in tbe text, paragraphs 50-51.

9. W. haft the joint de.aad hnCtiODS

InYerting th_

XR • F(PR' PL); demand for road services

XL • G( PR,f PL); demand for rail services

PL • I(XR, Xr,); PL • price of rail services

Then the total willingness to P&7 W is a 8UIl ot tbe liDe integrals,

J(x:, ~)

w" • (0, 0)

BT iDd.pmdeDCe ot path,

w" • J~ H(~J 0) dXR + J~ I(~J .~) ~ 10. The equation abow is • matheatical. _aaure ot the consumers' v1l.l1ngaes8 to pq. If.. subtract the DOWlt the CODSUErs· actually P&7 _get the COIlSDen' surplu. The total villlngness to Pa.Y' has been computed for the 8ituatiQD when the prices ot ro~ is ~, the price of rail i8 1'£, tile -quantiv ot road aerrices sold ia ~, and the quantity ot raU services 8Ol.d is ~. If tbeprlce of road falls, we shall get another

•

•

•

•

Appendix B - Pap S -

set ot values, Pi, ·Pi, . xi, xi, in the 11811 equilibriUII. Wi th thi~ new set of values ti8 can again _asUN tbe ld.ll1npess to Pill'. Call the new willingness to pq Wle (W1 - WO), tben, represents the change in the willingness to pq troll the initial situation to the new situation • If CO i.s the cost incurred b7 the consUlll8l'8 in the initial. situation, then the consUDlBra' surplus in the initial situation (SO) is giV8D b7 So • wo _ CO. S1JII:1larll', if' c1 is the coat incurred b7 tb" c~re in the new Situation, the cOIl8 .. ra surplus (sl) in the new situation i8 given by s1 • w1-cl. (81 - SO), then, giftS the change iii the caosaera' surplus. Since it is eUT to know Co aDd ~, ccDlputing the change in cOD~rsl surplus ·is eU7 _en 118 bave computed the willingness to pq in the t1IO situations.

11. The equation

has a simple diagrammatic interpretation. The diagr_tic representa­tion was given in the text and is repeated here, below.

~demand curve tor road A("'deJll8lld curve tor rail

The total villingDess to pq is the sum ot the shaded areas above. The

J~ diagram on the left corresponds to H(IR, 0) cUR and the diagram OD

~ 0

the right correllpOJld8 to J 0 L I (~ xx.) dXL•

12. It is to be noted that the cue treated in Section I ot this appendix, "1'8 the price ot rail services remains constant 1IMD 1'984 pricCJs chaDge, i8 a particular case ot the lIIDJ'8 general cue dealt vi til

AppeDdix B - Page 6 .

here. n. _tJIOCl of thi. section CaD be used &lao to treat the special. cue ot s.cUon I. It ia iIIIportant, hovever, to keep in,JIind the dilteNne. betweeD the definition ot toe de.and cum in Section I, 1Ibere other price. are uaD8d to remain constant, aDd the definit101l8 used in this •• ction.

•

•

j:

1