Economic fundamentals of road pricing: a diagrammatic analysis

Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized ___ IS (070 Pollcy Research WORKING PAPERS L Transport Infrastructure andUrbanDevelopment Department TheWorldBank December 1992 WPS1070 EconomicFundamentals of RoadPricing A DiagrammaticAnalysis Public Disclosure Authorized TimothyD. Hau Most economists agree that road pricing benefits society by curtailingcongestion.Efficiencyanalysisdemonstrateswhy the public rejectscongestionpricing.A dedicatedroad or transport fund is moreviablewhentheroad usersarechargednotonly for the damagecaused by heavyvehiclesbut also for congestion. PolicyRearchWoding PapsdismLataeth rmdingsofwoiprogrcsatncountgethccxchangeofideaunangB nkstaffand til othas iMacenedin de-volopnelttssues.Thempapcgscary thenanm of dieautho, reflactealy theirviews,znd shel be usedand citedaccordingly.hefindn.inu cprcsttion, andconduws aretheauthoz' own Tley shouldnoto atttbutedtotheWeWd Bank, its Boardof Directos,its managment,oranyof itsmembercounties. PolicyResearchl Transport| WPS1070 This paper- a productof the TransportDivision,Infrastructureand UrbanDevelopmentDepartment'is partof a largereffortin the departmentto evaluateoptionsforchargingfor roaduse. Copiesof thepaper areavailablefreefromthe WorldBank, 1818H StreetNW,Washington,DC20433.PleasecontactJennifer Francis,room S 10-063,extension31005or 35205(December1992,96 pages). Hau presentsa conceptualframeworkfor road pricingbased on a rigorousdiagrammatic- but nonmathematical- frameworkderivedfrom first (economic)principles.His analysisof traditionalargumentsabout road pricingshows whyimplementingcongestionpricing as practiced in the past has encounteredobstacles. Partly,it is becauseboth types of road usersthe tolled and the tolled off (thosewho avoidthe road to shun a toll) - are shown to be worseoff under a constantvalue of time, exceptfor the government.And whendifferencesin time valuationare taken into account,primarilythose with very high time valuesare better off. Unless congestiontoll revenuesareearmarkedand travelersperceivethat the moneyis channeled backin reducedtaxes,lower user charges,or improvedtransportservices,neither the tolled nor the tolled off will supportroad pricing.Only where thcre is hypercongestionis everyone better ofi with congestionpricing. In the absenceof scale economiesor diseconomies,the level of economicprofitstoll revenuecollectionsless a road's fixedand non-use-relatedcosts- servesas a surrogate market mechanismindicatingthat a road should be expandedor downsized.The decisionto let roads deteriorateover time is iiself an act of d;sinvestment. Hau showsthat if a road authoritylevies economicallyefficient chargesfor congestion,it is possibleto make moneyon a road. Roadscan be profitablein urban areas in the long run becauseland rents are high; congestiontolls reflectthe associatedhigh opportunitycosts. On urban roads with indivisibilitiesand diseconomiesof scale,efficientpricingmay curtailthe extent of profitableundertakings.On ruralroads with indivisibilitiesand economiesof scale, marginalcost pricing can produceshortrun profits.Economicefficiencyis enhancedby pursuingoptimalpricingin the short run and optimalinvestmentin capacityin the long run. The rule is to implementshort-runmarginalcost pricingwhilevaryingroad capacityover the long run. Insightsby Newbery,Small,and Winstonaboutthe economicimplicationsof the extensive damage that heavyvehiclescause to roads enrich the basicMohringmodel. Chargingfor both the externaland variablecost of road damage,by assigninga fee basedon vehicle weightper axle, can help coverdeficits arising from road congestion. Evenif a road networkis broadlycharacterized by increasingreturns to scale in building and strengtheningroads,the deficitcould be closedby diseconomiesof scope.A road networkthat accommodatesboth cars and trucks costsmore than the sum of an autos-onlyand a (smaller)trucks-onlyroad system.So the surplus associatedwith diseconomiesof scope offsets the potentialloss associatedwith scale-specific economies.A dedicatedroad or transportfund is all the moreviable becauseroad users are chargednot only for the damagecausedby trucks and heavyvehiclesbut also for congestion. T'he Policy Research Working PaperSeries disseminates the fidings of workbyder way in teBank. An objective of the seDies is to get these findings out quickly, even if presentations are less than ftuly polished. 'Me fndings, interpretations, and conclusionlsin these papers do not necessarily represent of ficial Bank policy. Produced by the Policy Research DissemiinationCenter Economic Fundamentals of Road Pricing: A Diagrammatic Analysis by TimothyD. Hau Tansport Division Infiratructureand UrbanDevelopmentDepartment The WorldBank Economic Fundamentals of Road Pricing: A Diagrammatic Analysis by Timothy D. Hau CONTENTS ACKNO.lEDGvMENn ABSTRACT iv .............. ........................................ v , .................................. I. CoNCEnUAL GiDELES H. PuBLIC/PiVATE OWNERSP OF RoAS CAusE OF CONGeBsTION: HI. - THE CLASSICAL CASE(IN TH SHORT OF RoAD CONGESTION FOuNDATIONS R.UN) DEI@D ANDAM SUPPLY..................................... V. VERYCONoEsTEDRoA VI. THL WELFAE VI. THE EFFEC ON TH TOLLD, TH ToED AMDBorLNEcKS PACTOF RoAD PRicIN Policy nIplications IX. ... .......4 ............................................... IV. V 3 8 10 ...................... 12 13 ......................... OFF AND THEUNTOLLD ...... . 13 17 . ...... 18 L. SHORTRUN EQULMRIUM ................................... CONVERGENCE TOWARDS LONG-RUN EQUILBRUM RiIU.Ns ............................................. NvsT .. .. UNDER CONSTANT 20 ............................... * *.. 22 X. Op*M>L Xl. LoNo-RUN VS. SHORT-RUN MARGNAL COSTPRICING.................. XI. INDiDUAlS' Tm TRADE-OFFBETWEEN xm. 28 FnsT-BEsT OPTMAL PRICINGAND INvSTmEN RULES................ Empnjri1Considerations. .................................. 28 AND EASURYAccouNTs 24 ... ....25 The First Rule -- The Optimal Pricing Rule ........................ The Second Rule -- The Optimal Capacity Rule ..................... Perspective on the Result ......... 28 29 29 XlV. RELAXATION OFASSUMPTIONS ................................ 31 31 .. 1) Differences in Time Valuation 2) Demand Variability and Peak-Load Pricing ...................... 32 4................... .................. 3) Indivisibilities Optimal Pricing and Investment with Indivisibilities: An Example ... . 35 4) Returns to Scale ...... ...................... 37 A. Economies of Scale and RuraRoads ..................... 38 B. Diseconomies of Scale and Urban Roads ................... 39 C. Diseconomies of Scale and ndivisibilities ....... ........... 41 42 .......... D. Economies of Scale and Indivisibilities .......... E. The Extent of Indivisibilities vs. Divisibility and Their Effects on 44 Scale (Dis)economies ............................ 45 ...... F. Empirical Evidence on the Scale Economy Issue ........ G. Recent Results on Cost Recovery ....................... 47 51 .. 5) Vanability of Road Thickness The first rde -- the optimal pricirg rule ..................... 52 The second rule -- the optimal capacity;,xle................... 52 The third rle -- the optimal durability rue ................... 52 53 ............... Economies of Scope vs. Diseconomies of Scope. XVh. SUMMAY AMDCONCLUSIONS ................................ A. The Role of a Road Fund ................................ B. The Role of a Transport Fund .. 56 61 62 . . .................... . APPElDMI: ................... Measurement of the Welfare Impactof Road Pricing .................. 65 65 FIGuE .................................................. 71 REFRENCES ............................................... 89 LIT OF FIGURS Figure 1 Derivation of a Travel Time-Flow Curve of an Urban Highway .73 Figure 2 Derivation of the Marginal Cost Curve and Congestion Tol .... Figure 2(a) 'Dynamic' Phenomenon of Traffic Growth: The Relaxation Effect Figure 3 74 ... Welfare Impact due to the Itroduction of Road Pricing in the Peak Period: Short-Run Marginal Cost Pricing 75 .76 Figure 3(a) Figure 4 Figure 5 Figure 6 Figure 7(a) Figure 7(b) Welfare Impact due to the Introductionof Road Pricing in the Peak Period: Short-RunMarginal Cost Pricing 'Hypercongestion' Case ......... ................... 77 Effect of the Introductionof Road Pricing in the Peak Period on the Off-PeakPeriod . .................. 78 Introducingthe (Short-RunAverage) Fixed Cost, SRAFC, of a Road, Short-RunOptimalToll with EconomicProfit .... Long-RunEquilibriumof an OptimallyDesignedRoad with Both OptimalPricing and OptimalInvestment ............. 79 .. 80 ConstantReturns to Scale with Road Divisibility: Doubling OptimalRoad Capacity, K, and Traffic, Q, Result in Doubling Fixed Cost, Variable Cost and Total Cost (FC, VC, TC) and Toll Revenues (t*- Q*) .... ...... 81 The Relationshipbetween Short-RunAverage Total Cost and Long-Run Average Total Cost and Marginal Cost with Perfect Road Divisibility and Constant Returns to Scale .... ..... 81 Figure 8(a) Road lndivisibilitiesunder Constant Retums .................. Figure 8(b) Optimal Pricing and Investmentwith Indivisibilities: Expansionfrom a 2-Lane Road to 4-Lane Road .... Figure 9 .... Economiesand Diseconomiesof Scale in the Provision of Road Capacity with the Growth of Travel Demand .... 82 .......... ........ Figure 10 Doubling the Number of Streets - Road Capacity -- Results in Quadruplingthe Number of Intersectionsand Traffic Lights and DoublingWaiting Time .84 Figure 10(a) Original Scenario-Existing Street Configuration .84 Figure 10(b) Final Scenario - Number of Streets are Doubled .84 Figure 11 Diseconomiesof Scale: Urban Road Network with Perfect Divisibility .... 82 83 85 .. Figure 12 Economiesof Scale: Rural Roads with Perfect Divisibility . .86 Figure 13 Dereasing Returs to Scale and Extent of Indivisibilities . .87 Figure 14 Increasig Returns to Scale and Extent of Indivisibilities. 87 ACKNOWLEDEMENTS A rudimentaryversionof this resech paper was pented at the 2nd InternationalConferenceon Privatizationand Deegulaton, Tampere,Finland,June 16-20, 1991. Part of the findingsof this researckwaspresentedat the 6th WorldConferenceon TransportResearch,Lyon, France,June29 July 3, 1992;Seminaiiode TarificacionVial1992(RoadPricingSeminar),sponsoredby theMinistr* of Trnsport, Santiago,Chile,July 20-21, 1992;the Symposiumon RoadPricing, sponsoredby the SwedishNationalRoad Adminisation and the Departmentof RegionalPlanning,RoyalInstituteof Technology,Sigtuna, Sweden, November9-10, 1992; and the Southwest CongestionPricing Conference,sponsoredby the Universityof Houston's Center for Publih Policy and Citzens AdvocatingReponsibl Tansportation, Houston, Te.as, January 4-5, 1993. Commentsby participantsat theseplacesare gratefullyacknowledged.I have benefittedfrom the discussionsand commentsof manypeopleon the controversalsubjectof road pricingand I take this opportunityto thankWilliam.Vickrey,MichaelBeedey,KiranBhatt,RichardBird,AndrewEvans,StephenGlaister, PhilGoodwin,JoseG6mez-Bdflz,Chris Hendrckson,PeterJ. Hills,JakeJacoby,JanJansson,Peter Jones,TheodoreKeeler,DamienKulash,Odd Larsen,HenningIauridsen, DouglassB. Lee, Peter Mackie,AnthonyMay, RobertMcGillivray,HerbertMohring,Richw-dMusgave, YewKwangNg, Esko Niskanen,Tae Oum, FaridehRamjerdi,GabnielRoth, KennethSmall, Antti Talvitie,Tom Tietenberg,Burkhardvon Rabeaauand Sir AlanWalters. I am also gratefulto WorldBank staff, includingEsra Bennathan,PhilipBlackshaw,JoseCarbajo,AnthonyChurchill,ShantaDevarajan,Asif Faiz,JeffreyGutman,ClellHarral,Ian Heggie,ChrisHoban,GregoryIngram, FridaJohansen,Kyu Sik Lee, WilliamMcCleary, WilliamPaterson, Richard Scurfield, Zmarak Shalii and Larry Summers. Supportsevices from Marat Callan,Pam Cook, Barbar Gregory,BeatriceSito and Gabriella St_imetz are gratefullyackmowledged. Theseacknowledgements do not meanthat they sharein the viewsexpressedin this paper. I alone etainfull responsibilityfor its contents. TimothyD. Hau v - ABSTRACT EconomicFundamentalsof Road Pricing: A DiagrammaticAnalysis by Timothy D. Hau This paper presents a conceptual framework for road pricing based on a rigorous diagrammatic -- but non-mathematical-- framework derived from first (economic)principles. It throws light on congestion pricing systems and issues surrounding short-run and long-nm marginal cost priing, scale economies and diseconomies,indivisibilities,road durability, the peak-loadproblem in urban transport and the financial viability of the public provision of road services. The paper integrates the ideas of Mohring, Strotz, Vickrey, Walters, Keeler, Small, Winston and Newberyinto a single analytical framework. Analysisof the traditionalroad pricing argumentsdemonstrateswhy congestionpricing as practiced in the past has understandablyencountered obstacles to implementation. This is partly because both types of road users, the tolled and the tolledoff (those who avoid a road in order to shun the toll), are shown to be worse off - with the exception of the governL -nt under a constantvalue of time. Even if differencesin time valuation are taken into account, it is still essentially the case that primarily those with very high time values are made better off. Unless congestion toll revenues are earmarked and travellers perceive that the money is channeledback in the form of reduced taxes, lower user chargesor improvedtransport services, neither the priced nor the pnced off would support road pricing. It is only in the case of hypercongestioncan congestionpricing be shown to make everyone better off. In the absence of scale economies or diseconomies,the level of economic profits, i.e., toll revenue collectionsless the fixed and non-use related costs of a road, serves as a surrogate market mechanismindicatingthat a road ought to be expandedor downsized. The decision to let roads deteriorate over time in and of itself is an act of disinvestment. Further, it is shown graphically that if a road authority were to efficiently charge for congestion, it is possible to make money on the road. Profitable roads arise in urban areas in the long run because land rents are high and congestion tolls reflect the high opportunitycosts. Yet, efficient pricing in the presence of both indivisibilitiesand diseconomiesof scale in urban roads may curtail the xent of profitable undertakings,whereas pursuing marginal cost pricing under the restrictive - vi - and scaleeconomiesin rural roadscou d resultin profitsin the conditionsof bothindivisibilities shortrun. Economicefficiencywouldbe enhancedif optimalpricingwerepursuedin the short run and optin'l investmentin capacitywere pursuedin the longrun. The rule is thereforeto implementshort-runmarginalcost pricingwhilevaryingroad capacityover the long run. Recentextensionsby Newbery,Smalland Wimstonhave enrichedthe basic Mohrng by incorpomtingthe fact that heavy vehicles modelthat this paperdevelopsdiagrammatically are responsiblefor extensiveroad damages. Chargingfor both the extemaland variablecost of road damageson a vehicleweightper axle basis can help cover the deficitthat may arise from congestiontolling. Evenif a roadnetworkis broadlycharacterizedby increasingreturns the deficitcouldbe closedby diseconomies to scalein roadconstruction'suseand strengthening, of scope. The existenceof scopediseconomiesin highwaysmeansthat a road networkthat both loadingand trafficvolume,as founduniversally,costs morethan the sum accommodates of an autos-onlyand a (smaller)trucks-oniyroad system. Hence, the surplusassociatedwith economies. The of scopeoffsetsthe potentiallossassociatedwith scale-specific diseconomies viabilityof a dedicatedroador transportfundis enhancedby the fact that the roadpavementis chargedin twodimensions:oncewhentrafficflowcreatescongestionand anotherwhentraffic loadingscauseroad damages. EconomicFundamentalsof Road Pricing: A DiagrammatiAnalysis 1. is major conurbationsof both developedand developingcountries, congestionis inctssantduring the peak periodsand oftentimesthe interpeak.Y/Yet the traditionalmethods of effectivelycurtailingcongestionare few, and their usefulnesslimited. On the supplyside, the expansionand improvementof roadsis restrictedby increasinglytight fiscaland physical onstraints. On the demand side, however,the problemcan be addressedby pricing or regulation. This paperuses the pricing(or market-based) approachto grapplewithcongesrion 31 The aim of road pricing is becauseof its inherentflexibilityand powerof discrimination to internalizethe externalitiesgeneratedby roaduse. My focushereis on removingtheexternal effects caused by motorists by charging for congestionand road damage externalities. Congestionis recognizedas an importanttype of externalityfrom vehicle usage in both developedand developingcountriesin thatit representsa large shareof totalesumatedroaduse costs (Newbery(1988bc,1990)and Newbery,Hughes,Patersonand Bennathan(1988).I 2. Thisresearchbeginswitha seriesof twopaperson roadpricingin theoryand practice. The first paper presentsa conceptualframeworkfor road pricing. It gives an interpretative abridgmentof the literatureon the theoryof optimalpricing,investmentand durabilityof roads By the tum of the centuy, mory o tan four-fifthsof the world's most heavily-ppulted agglomeratonsare proect to be in tho developing wodd(WorldBank(1991),p. 3 andp. 22). ZI Thoregulaoy approachon quanity- the so-calledcommandand controlmeasures- suffersfromits inability to provide correct market sipals to inducethe most efficient trips to be undertaken. In contrast to priing incentives,it gfferatesvirbtallyno revenuesfor thepublicsector(seePozdena,Schmidt,andMartin(1990)). 3/ The totalcostof undetkWnga trip- both 'private'and 'social' - involves: 1) congestion(whichis bomeby roadusers);2) pavementwear(whichis coveredby theroadauthority);3) air and noisepollution;and 4) costs of accidents(bothof whichare bomeby societyat large);in additionto 5) vebieleoperatingcosts. 'Social cost' (i.e., bothinta andextenal costs)hereare distinguished from 'pivate costs'(i.e., intanal costs),the ltter of whichareself-financd. Thosetaveller-borneinteral costsinclude:1) vehicleopeating costsas weol as2) tim costsand delayin conested traffic(Newbery'sdefinitionof roadusecostsrefersonlyto theextel cost.) This paperdealsmainlywith the marginalcost pricig of congestionand pavementwear chargesas opposedto margial socialcost picig, whichis definedto include- in additionto privatecosts - all th arnal costsof coagwestion, air polluton,noisepollution,accidents,rod damagesand externalities.Hence, stictly speing, 'congestion pricing'referssolelyto thepricingof congestionextenalitywhereas'roadpricing' refersmoregenally to thepriing of al externalitiesfrommobilesources. - 2- based on the works of Herbert Mohring, Robert Strotz, WilliamVickrey, Alan Walters, TheodoreKeeler, Kenneth Small, Clifford Winston and David Nowbery.4/ It aims to integratetheir ideasand principlesinto a singleanalyticalframework. I am convincedthat the presentation of a rigorousand unified diagrammatic -- but non-mathematical-- framework derivedfromfirst economicprinciplescastsimportantlighten congestionpricingsystemsand on issues surroundingshort-runand long-runmarginalcost pricing, scale economiesand indivisibilities, the poak-loadproblemin urbantransport,optimalroaddurability, diseconomies, financialviability and cost recoveryin the publicprovisionof road services. Whilethereare severalautomaticroad user chargingand electronictoll collectionsystemsin use in parts of Norway,Italy,France,and the UnitedStates,as wellas billsin parliamentto implementvarious formsof road pricingin Santiagoand Stockholm,one congestionpricingsystemis currently operating(Hau (1992)). That is Singapore'sArea LicensingScheme,which is now in the processof beingconvertedinto the ElectronicRoadPricingSystem,to be operationalin 1995 (see Watsonand Holland(1976, 1978),Behbehani,Pendakurand Armstrong-Wright (1984)). Even so, the chargingof vehiclesby daylighthours in Trondheim,Norway (with further differentialpricingfor electronictag users)since1991couldbe regardedas a rudimentaryform of congestionpricing. Recent technologicalbreakthroughsin automaticroad user charginghave brought 3. electronicroad pricingnmuch closer to reality. Thus, the secondpaper (Hau (1992))in this researchpresentsa taxonomyof alternativetechnologiesof congestionpricing. It drops the crucialassumptionthat the implementation of short-runmarginalcost pricingis costless(Hau (1990)). In particular,it comparesand contraststhe methodsof manualversus electronic chargingschemes. Electronicapproachesare analyzedprogressivelyby discussingfirst, the whichincorporaterecenttechnological increasinglypopularelectronictollcollectionmechanisms advances *n automatic vehicle identification- commonlyknown as AVI - as well as smart cards. The ariateness and applicabilityof electronictoll collectionmechanismsto I owe much intellcul debt to theseauthorsandI am very gratefil for the opportunityof discussingmy work with severalof them -3electronicroadpricingare thendealtwith. Thecompanionpaperalso analyze% therelativecost° effectivenessof each technologyand performsbenefit-costanalysiswhere data permits. The for relievingcongestionare discussedandpolicy implicationsof usingeachof themetechnologies are drawn. recommendations I. CoNcEPTuAL GuIDELNS 4. Rising real incomesresult in increasedaspirationsfor the ownershipof private automobiles.Barringmajorrestraintmeasures,an increasingnumberof motorvehiclesmeans that travel demandswellsconcomitantly.Becausemunicipalitiesare findingit increasingly the rateof growthof trvel demand difficultto financenewroadconstructionandimprovements, outstripsthe growthof road capacity(Hau (1988)). Transportplanners,with limitedoptions available,find it very difficultto combateffectivelymountingtrafficproblemsin the face of increasingurbanization.Theresultingtrafficexplosionis an illustrationof Parkinson'sLaw or Downs'law of peak-hourexpresswaycongestion,in whichcommutertrafficascendsrapidlyto the level of new capaity in urbanareas (Downs(1962),Mohring(1965)). Trafficengineers have long been familiarwith this "fundamentallaw of highwaycongestion"in whichlatent demandexpandsto fill the gap createdwheneverhighwaycapacityis improved(Small,Winston and Evans (1989),p. 85). In this section,I set up the conceptualguidelinesthat allow authoritiesto curtailtrafficcongestionin an efficaciousmannerat the sametime as satisfying the WorldBank'sgeneralguidelinesfor publicsectorprojectsandurbantransportpolicy(World Bank's OperationalManualStatementNo. 2.25 (1977),WorldBank'sUrbanTransportPolicy Paper(1986),and Juliusand Alicbusan(1989)). 5. In a nutshell,the essentialprinciplesinclude: 1) implementingshort-runmarginalcost pricing(short-runefficiency)to generate maximumnet benefits for society: efficiencypricirg; 2) undeaking investmentin infrastructurewheneverthe additionalbenefitsexceed the costs (long-ran efficiency)to societyof doing so: econonuc iabilty; -43) 4) investingin transportserviceswhen benefitsexceed costs; promotingpublic transportservicesespeciallywhenrevenuesexceedcosts: financialviability; maintaining'fairness'amongbeneficiaries,for example,via benefittaxationequity -- wherepossible;and 5) usingpricingandcostrecoverypoliciesto improvethe efficiencyof managingthe public sector - cost-effectveness and managerialefficiency- if possible. H. OFRoADs OWNERSHP PUBLIC/PRIVATE CAuSEOFCONGESTION: Roadswhichare infrequentlyutilizedpossessthe characteristicof nonrivalconsumption 6. amongusersand are traditionalexamplesof publicgoods. Joint consumptionmeansthat roads yield services that are simultaneouslyenjoyedby more than one user, withoutsubstantial detrimentto the satisfactionof others. If roads are totallynonrivalrous,then neoclassical economicprinciplesdictatethat roadsoughtto be providedfor by the publicsectorand financed from generalrevenuetaxation(andperhapsland valuetaxation),fully takinginto accountthe socia opportunitycostofpublicfunds. Onthe otherhand,roadswhichare heavilyutilizedhave the nature of rival consumptionamongusers and are called congestedpublic goods. These varisble-usecongestedpublicfacilitiesthen approximateto varyingdegreesthe rival natureof privategoods. Privategoodsare of courseprovidedcontingentuponpayment,excludingthose whoare notwillingto pay for them. Alas, withfree accessto roads,peopleare not banredfrom the use of scarceservices,resultingin overuse. Hencemarketfailuredue to nonexcludabiliy cals for governmentalinterventionin the form of better designedroad user charges and motivatingcharges which correct for externalities. (the failure of the voluntarypricing is referredto as the 'free-riderproblem'in thepublicfinance mechanismdue to nonexcludability literature(Boadwayand Wlldasin(1984),Chapter3)). Note that it is the traditionalinability to exclude motorsts from the use of crowded streets that is die cause of market failure. However,when refinementsin automaticvehicleidentficationtechnologybecomeeven more cost-effective,automaticroad user chargingmeansthat marketfailureis somewhatovercome. Thisis becausepriccsare thenableto reflectboththe intensityof demandand the trueeconomic and preferencerevelationwouldthen be cost of road use. The problemsof nonexcludability -5 - virtualy eliminatedand the advantagesof price incentivesreaped. Thus the standardpublic financetext (see,for example,Musgraveand Musgrave(1989,Chapter4)) arguesthat both the - or rather, costly characteristicof publicgoodsand the nonexcludability nonrval consumption excludability-- of congestedpublicgoodsare causesof marketfailure,callingfor government intervention.Hence,roadswhichpossessthe attributeof congestedpublicgoods, and thushave a partally rival consumptioncharacteristic,oughtto be treatedby the relevantgovernmental authoritiesas mixedor impurepublicgoods,if not privateor clubgoods (Buchanan(1965)). 7. The foregoingdiscussionleads naturallyto the transporteconomist'sdefinitionof congestion. That is, as more and more vehiclesjoin a traffic stream,the travel times of all motoristsmaking trips are raised, resulting in delay to all. In essence, the congestion phenomenonis one of excessdemand,givena fixedroad network. Yet the fundamentalreasonwhy congestionoccursso ubiquitouslyis becauseproperty 8. nghts are not clearlydelineated,yieldingmarketfailure. If roadsare bothprivatelyownedand competitionprevailsin the provisionof roads, usagewouldbe (Pareto)optimalin the absence of scaleeconomies(Knight'sconjecture(1924))Y If roads are not privatelyowned,access to and usageof roads are effectivelyfree to the traveller,resultingin excessiveuse of those roadswhere taffic is heavyenoughto producesignificantadverseinteractionamongvehicles. 5/ Weknowthatcomption rsuls in conomcefficiency.in thecontextof roads,ownersmaxim thereturn between wherethedifference marinalcostofproduction, to thir landbysettingdo pic equato theshort-nm the short-n maginadcost adthe averg vaiable cost represa the quasi-entto the fixedfactorof produon. CM notio of qi-ent is discussedin footnote29.) Thisis theanalogto societymimickingthe ladowner' no maximizg behaviorby chari the optimal(Pigouvian)toil- the decetalized competitive n in SectionVm and theproofof this cost d averg variablecost (seedio divergencebeweenmaI returs is dealtwithby the conecturein Vwkrey(1968)).Kniht furter arguesthat thecaseof increasing maket alowingany one gentto rmin boind to exhaustscaleeconomies(seeWaltors'(1954)interpretation ofKnight'scojectu (1924),whichdoesnotaccordwithmyintpretaion here). I arguethatthegovernment pricing. monopoly is leftwi therol of beingtheaget tt char the congetiontoll, in order to .Jfevent costsof publicownership reqirments andtransaction Afterall, it is uncla a pori thatthebiformational wouldexceedthe socil cost (sch as rn-sekig) of reguatig prvate ownersip. In otherword, it is debatale whethr gove _ment failureis neemily gter than marketfailure,especiallyin developing countios. Forinstae thogovenmet'spowerof eminentdomainoverpublicprojectsmayreduceits land rent acquisition androadcadmact cost whers thecommonpropertynatur of roadswouldencourage dissiain -6(rhe overcrowdingoccurs despitethe fact that motoristsalreadyhave to pay fuel taxesand feesandpurchasetaxesfor owninga vehicle,whichcan be regardedas entry registration/license fees only.)V On the other hand,it is unlikelythat privateownershipof roads would yielda perfectlycompetitivemarket structurebecausealternativeroutes are in general not perfect substitutes.Hence,thoseroadownersmightexploittheirlocationalattributesand monopolistic prerogativesby raisingchargesabove marginalcost. In addition,incentiveswouldarise for collusion. Thus competitionwouldat best be imperfectin the case of road provisionwhere lumpinessis found. The relevantcomparison,basedon efficiencyconsideration,is the welfare cost associatedwith governmentinterventionvis-a-visthe dead-weightloss associatedwith the monopolisticor oligopolisticpricing practicesof private ownership. In addition, it seems reasonable to argue that there are other grounds - such as equity - for regarding landowners' super-normalprofits, or collusivetendencies,as undesirable. In practice,virtuallyall roads belongto the governmentand not to privateowners. Because of free-accessroads, one should not be surprised to be confrontedwith the pervasivenessof congestion.This is the commonpropertyresourceproblem,whichyieldsan 2 / One might ask whether or not some congestion-prone roads ought to be externality. privatizedto internalizethe externality.Thekey factoris whether(sufficient)competitioncould 9. be madeto prevailto ensure,in the absenceof regulatoryrestraints,that theseroads are not overpriced. A testablehypothesisin contestablemarketstheory is to check whether the fi/ The fueltaxeswhichmotoristspay are generallyusedto contibuteto: 1) the maitenanceand operating(and in part the investment)costs of roads, 2) debtserviceon highwaybonds, and/or3) generaltax revenues. of howfueltaxrevenuesare disposedof, the mainproblemof the uniformfueltax is its inability (Independent of a fueltax, first registationtaxesand to varyby timeand placeof use (see Hau(1992)).)Thecombination a two-partor multi-parttaiff. annuallicensefees canbe regardedas, to a roughorder of approximation, 2/ and enforceable,privatebargainingwouldinternalize exchangeable As longas propertyrightsarewell-defined, all 'extenalities'and yieldan efficientallocationof resourcesindependentof who is heldliablefor creatn externaleffectsin thefirst place(Cosae(1960,1988)).SinceCoae's so-calledtheoremholdsonlyif the costS of transactionsare nil and incomeeffectsarenegligible,it appliesmainlyto thecaseof smallnumbers.With externalities,I arguethat the largenumbersof peopleaffectedcleadyresultin congestionand mobile-source largetrnsactionscosts,and hencemarketfailure,beckoninggovenmentitervention. Further,Cooter(1982) arguesthatCoae doesnot distnguishbetweenzerotansactionscostsand zerobargainingcosts,and thatthe generait of the CoaseTheoom is oveted. -7conditionof potentialcompetitionand not actualcompetitionis satisfied(Baumol,Panzarand Willig(1982,Chapter 1)). One surmisesthat it may be difficultto assumethat it wouldbe effectivein practice,especiallyin the case of roads whereirreversibilityand lumpinessexists (BaumolandLee (1991)). Also,noncomparability mayoccurbecausea competitorwouldfind it difficultto duplicatea road on the same alignmentand would likely settle for inferior alignment.Economicefficiencycouldbe enhancedin somecasesif therewerea mixtureof both privateandpublicroads,sincetheexistenceofpublicly-providedfireeways mightlimitthe degree to whichthose who use privateexpresswayswouldbe chargedmonopolyprices. Similarly, privatetoll roads could serve to over-zealousgovemmentsfrom overchargingon public toll roads.A/ 10. In short, the congestedpublicgoodnatureof roads suggeststhat thesefacilitiesshould be treatedmore like club goods or privategoods,yet the status quo appearsto suggestthat publicownershipof roads is insdtutionallypreferable. If so, municipalities oughtto simulate the worldngsof a competitive,privatefirm and industryby settingcongestiontolls on public roads to internalizethe congestionexternality. This thereby deals with the problemsof nonexcludability and preferencerevelationexploredearlier. If a privateownershiparrangement is deemedbeneficialat times,the governmentcouldexerciseits powerof eminentdomainin reverseby alteringthe structureofpropertynghts of the relevantfacilitiesfrompublictoprivate ones. Thiscouldbe done,for example,by auctioningoff govenmment landto the highestbidder (and simultaneouslyreducing general taxes and/or providing more public goods), or, alternatively,by designatingthe competitiveprovisionof highwayservicesto corporationsor privatecontractorsvia 'franchisebidding"(Mills(1981)). I haveargued,on bothefficiencyand equity grounds- followingour conceptualguidelines- thatthe facility's ownershiparrangement 8/ Note tbata relativelyuncongeatedtoil road would yield inefficint tc offto alternativepublicroadswhichar eady congted. SooJohan for a discussionof tollrads and roadprivadition. allocatiaoif its effectis to plice traffic (1989)and CatlingandRoth (1987) -8- ought to reside with the government,with the proviso of setting cost-effectivecongestion tolls.2 / I next showhow a congestiontoll can be derivedfrom a transportationengineering speed-flowcurve. In the proces, the equivalenceof efficientcongestiontollingand the shortrun marginalcost pricingof vehicleflowis established. IIm. FOUNDATIONS OFROADCONGESTION - THECLASSICAL CASE(INTMESHORTRUN) 11. Road congestionis well foundedin the economicsand transportationengineering literature(Dupuit(1844, 1849),Pigou(1920)and Waltes (1961a, 1961b)).p It beginsby consideringa rpresentativedriver cruisingunderlow traffic conditionsalonga given stretch of urbanroad withfixedbeginningand end points. Therepresentativedriver wouldbe able to achievea meanfree speedthat balancesthe benefitsto him of a fastertrip againstthe costs to him of higherenergyrequirementsand a greaterrisk of an accident. CeterLs paribus, as other vehiclesenter the road thereafter,densityincreases,speeddrops and travel time (or delay) lengthens(andaccidentprobabilityrises). Thecausalityis as follows:trafficdensitydetermines speedand not vice versa. Paalleling the theoryof fluid dynamics,tffic flowis the product of density, in vehiclesper kllometer,and speed, in kilometersper hour. Note that the rectangular area in Fig. l(a) - the speed-concentrationreationship - is equivalent to traffic flow,expressedin vehiclesper hour(seeGerloughand Huber(1975,Fig. 4.12) andMay(1990, Chapters7, 10), for example). Hence,taffic flowis the productof trafficdensityand speed, with trafficflow attaininga maximumat F" with speedat S' in Fig. l(b) - the speed-flow relationship(seeHaight's(1963)'fundamentaldiagramof road traffic' - a flow-densitycurve- 2/ WhiloI am convncd of to advutos of _arkt hoes, I bhwesornisreevatons abouttdir extnt. For eample, sono have arued dot may 1sowlem shul be prvided for by the mt, and aso that tansport infrastructursoud ao be pivavtd (Raoth (1987,aptr 6) nd Cating and Roth(1987)). It is difficultto sme,in to abso of raod divisibility and competitivefoae, howmainal costpricingwouldbe pursuedand_maaed by pnvat toadowws Frm a publicchoicoperpctvo, the uno argumnt couldbe reversodand applihdwithprepc to govemmta authores. This explain whyI arue hat perps a mixed systemof public/pivateo wouldbe ableto nap thedteh of both. IQ/ WhileWale (1968,pp. 31-34,aC._ 3 Annex)diaees aptma investnt, hiswork emphasietheshort run cdaacterof roadping. Mb alpproh tk intspais to lhihlihtboth the bort-and-g-ru natm of die congestio probm in ordw to explore de issue of coat rcovery. -9 - - and similarfiguresin Monison(1986)). (Toutedmaximumflowfiguresof the 'capacity'for a typicalexpresswayare about 1800-2000vehiclesper lane-hourat 50-55kilometersper hour (30-35mph) (see Gerloughand Huber (1975,Chapter4) and any HighwayCapacityManual, for example,TransportationResearchBoard(1985, Chapters2-3));w 12. Givena fixeddistanceof saya kilometerof road,the trafficengineer'sspeed-flowcurve can be straightforwardly convertedto a traveltime-flowcurveas traveltime is the reciprocal of speed,withvehicles-kilometer per lane-kilometer-hour on the horizontalaxis (see Fig. l(c)). Usinga constantvalueof timeas a shadowpricefor the representativedriver,tr,--eltimeis then convertedto a moneybasiswhichyieldstimecost, calledthe averagevariablecost, AVC (see Fig. 2). Lowtrafficvolumecorrespondswithrelativelyhighspeed,so fuelcost wouldbe high. Withhigh trafficflowand lowspeed,however,fuelcostwouldalsobe kepthighbecauseof fuel causedby the alternateaccelerationand decelerationassociatedwithdensetraffic. inefficiencies Thesetwo factorsroughlycancelone anotherout, leadingto the plausibleassumptionthat the costsof opeating an automobile(whichincludefuel, oil, maintenanceand depreciationcosts) are approximatelyindependentof the level of taffic flow (Mohring(1976, Chapter 3), AASHO's(1960)'RedBook'). A fixedmoneycost for the vehicleoperatingcostcan therefore be added to the time cost portion to form the generalizedcost - an accpted constructof transport economists(Nash (1976) and Button (1982)). Similarly, the road's variable maintenancecost, whichis assumedto be proportionalto the traffic level, followingWalters (1968,p. 24), can be added up also (see Fig. 2). 1 / So it is the time cost elementthat is portionof the AVC curve. The AVCcurve climbs mainlyresponsiblefor the upward-sloping upwardsbecausesignificantnegativeinteractionsoccur beforetrafficreachesmaximumbasic capacity,Q; it is variablein the sensethat as trffic flow, Q, is inased, congestiondelay JJ 12/ Economists' notionof 'cpcity' is whever congeio dday bogins,whichis considerably lesst traffic engineer'concepLFurte, vehiculaflowis sometimes normaizedby thecapacity of a crtain roadto yield a 'volun_eocapacityq ratio. upverticalywiththevehicle openg costandvaiableroad Hencethemargi co curve,MC,whensummed maintenance cot, yieldsa anlad mginal os curve,MC. Thesm notaions pplyto theaveragevariable co curve. - 10- r (contrary to the engineering actually sets in rapidly at substantiallybelow the traffic level Q01 notion of a constantaverage variable cost curve extendingup to the point Qu i FP). After the engineering or basic capacity, Q"" is reached, AVC becomes an 'inverse supply' curve. Note that the standard supplycurve is nonexistentin the context of roads.ia/ IV. DEMANDANDSUPPLY 13. The 'supply' side can be made to be congruent with the demand side when a conventionaldemand curve is specifiedto depend on the travel cost (price)facing a traveller for a single trip. When an initial demand function, Q",intersectsthe AVC curve at point U (Fig. 2), a (stable) equilibrium is said to exist at Q°. This is an equilibrium point because travellers' willingness-to-paycurve, i.e., the inverse demand function, equals the average variable cost curve -- the function upon which travellers base their travel decisionc.. After a small excursion of the demand in the neighborhood of the equilibriumpoint, unfettered use results in a return to the observed traffic level, Q°, hence the equilibriumis considered stable. 14. Basic price theory says that whenever the average variable cost rises, it means the marginal cost curve lies above it.15/ The vertical differencebetween the two cost curves is 13/ The solid portion of the speed-flowcurve and travel time-flowcurves in Figs. 1 and 2 denote the 'normal' part of the curves. The non-soLidbackward-bendingportion of the cost curve (Fig. 2) meanstat time cost increases becausetraffic flow is reducedafter the gineering capacityis reached. The backward-bendingcurve, far from being fictitious,has been substantiatedin the litrature (Gerloughand Huber (1975, Chapter 4), Keeler, Smal and Associates(1975, Fig. 1)). Schiff(1991) explores this backward-bendingcase. 14/ The demand fimction,Qd, is an observed, constant-money-incomeMarshalliandmand curve, with the usual regularity conditions. It approximatesthe exact Hicksian demand curve, which yields the true reflection of willingness-to-payand marginalbenefit. Formally,at equilibriumGC(Q) = Q'P), and Q"(GC(QO)) = Q°,where GC is the generalizedcost. Since GC is simplya tra tion of AVC, the interpretationof one is synonymous with the other. 15/ Marginal cost is obtainedas fTollows:MC * AC(Q)/AQ = AVC(Q) + Q *AAVC(Q)/AQ = AVC(Q) *(1 + e) where C(Q) is the cost function, e is the elasticityof the AVC curve, i.e., the rate at which time cost rises with respectto a one percent rise in traffic flow (Walters (1961)). The first term composesof only time cost and the second term is the marginal(external)congestioncost, set equal to the congestiontoll. Marginal cost pricing of a trip, P, is achievedby setdng P = MC. This is known as the first-bestoptimal pricing rule: our first optimalityrule. (Note that AVC dependsparametricallyon the capacitylevel K, and can be expressed - 11 - the marginal (external)congestioncost - the additionaldelay that one driver imposeson the rest -- which is not taken into account by the last driver who joins the traffic stream. In fact, since each driver chooses whether or not to travel according to the AVC curve -- being the decision curve -- he or she totally ignores the resulting external congestion cost imposed on felow motorists. We thus have the optimal point Y at which the marginal cost curve intersects the (peak) demand curve in Fig. 2. In other words, Q' is the associatedoptimaloutput in the sense that the generalizedcost which includes extemal congestioncost and other variable costs (i.e., constant (unit) operating cost of a vehicle and variable maintenancecost of a road), is equated to the price. The congestioncost is the additionaltime cost that a motorist imposeson others, calculatedby taking the incrementin average time cost caused by the added trips and multiplied by the number of vehicles in the traffic stream. The Pigouvian tax applied to roads is that optimal toll which closes the wedge betweenthe marginalcost and average variable cost curves by emitting the correct signal wrd creatingappropriate (dis)incentives. 15. This Pigouvian toll-tax is equal to the marginal external congestion cost. It is also known as the net-benefitmaximizing,economicaUyefficient, (Pareto)optimaland marginalcost toll. (If one prefers, it can be regarded in graphic terms as a sin tax, even though it has not yet included the cost of environmentaland other externalities.) Hence the marginal cost pricing of trips in the short run (given that a road is fixed) yields a first-best Pareto optimal allocationof resources. The optimal road user charge is then comprised of a congestion toll and another componentwhich covers the variable road maintenancecost (see Fig. 2's legend). as AVC (Q, K). WithoutloSSof generality,the inclusionof the averge vehicleoperating cost and variableroad maintenanccost-both beingconstant with respect to taffic -simply alters both the left-hand side and the right-hand side by the same amount). Implementingmarginal cost pricing in this case means pricing the difference betweenmarginalcost and the average variablecost of a trip, plus a componentwhich coversthe cost which the motoristimposeson the community(see Fig. 2's legend). We shall return to an intuitivediscussion of this subtle but importantdistinction. Note further that marginalcost rises asymptoticallyto the engineering capacity level of Q and is undefinedfor the AVC curve at points beyond V. - 12 V. VERYCONGESTED RoAS ANDBoTrLENEcKs 16. Observethat at the equilibriumpointU in Fig. 2, the resultantthroughputis significantly less than the road's maximal flow capacity of point V. The 'ackward-bending 'supply curve' exists because a one percent increase in density results in more than a one percent decrease in speed when very dense traffic is reached. (That point X is a stable equilibriumpoint can be seen intuitively by perturbing the price level while point w is unstable in that any disturbance will result in a movementto U or X.) The point here is that quite a few cities, for example, Bangkok, Budapest, Buenos Aires, Hong Kong, Jakarta, Medico City, Santiago, Sao Paulo, Seoul, Singapore and Taipei are faced with extremely congested situations such as point X, cerainly during peak of the peak. 17. Consider the dynamicphenomenonof traffic growth as shownin Fig. 2 (a). Suppose the initial demand curve intersectsthe average vanable cost curve at point 1. As traffic grows, the observed number of vehicles per lane-hour increases from point 1 to 2 to 3 (which is identicalto point U of Fig. 2). A further increase in demand beyond point 4 would result in a discontinuousjump to the backward-bendingpart of the unit variable cost curve at point 5. Intuitively, traffic congestionworsens rapidly and 'jams up' all of a sudden at times. After a while at this point, travel demand would start to slack off to points 6 and 7 (which is identical to point X of Fig. 2). Note that traffic would be movingat a snail's pace as queuing develops. This corresponds diagrammaticallyto the positive sloping part - as opposed to the relatively smooth trffic of the 'normal' downwardsloping portion - of the speed-flowcurve, Fig. l(b). As travel demand continuesto diminish towards the end of a rush hour, say, the traffic level would touch point 2 briefly but would then end up at point 8. Thereafter, further slackeningof demand results in traffic retumningto the upward sloping portion of the unit cost curve at point 1, say. This is known as a relaxation phenomenon in an engineering and physics context. Therefore, the points between 4 and 8, such as the equilibriumpoint W, are never reached in realityl 1 We concludethat it is precisely the daily recufrent peaking characteristicof travel 16/ In othercontextssuchas Waltms(1987),pointW is desuibedu an unstableequiIibriumL - 13 demandthat calls for innovativesolutions. That the trffic level at those nsh hour periods seems to be near gridlock -- an illustrationof 'hypercongtion' - is too important a case to be ignored(Walters(1987)). VI. TBEWELFARE IMPACTOF ROAD PRICING 18. Thepurposeof this sectionis to highlightoneof the mainpointsof thispaper,the proof of whichis relegatedto theappendix.Economistsknowthatroadpricingresultsin improvement in welfareto society,yetpoliticiansandthepublicalmostunanimously regardit withskepdcism. Why? To economists,the increasein welfarecomesabout becauseof the impositionof an externality-corrective(toll-)tax. Yet, for those motorists remainingon the road, the congestion toll is similar to a tax increase. Under conditionsof 'normal' traffic (or non-hypercongested situations),note that the toll-taxpaid by the motoristexceedsthe valuationof time savings resultingfrom road pricingon average,so that the 'tolled' is worse off.1 Those who are pricedoff the roadto an inferiormodeor timeof travelin orderto avoidpayingthetoll are also worseoff, whilethosewho remainon otherindirecdyimpactedroads are eitherworse off, if congestionarisesthere, orjust as welloff, if thereis no resultingcongestion.It tums out that the government,in collectingtoll revenues,becomesthe mainparty that is betteroff. S ON THETOLLED,TH TOLLEDOFF AD TH UNTOLLED VII. THB EFF 19. In the appendix,I establish the propositionthat marginal cost pricing of trips maximizes the net benefit to society in the sense that a Pareto-efficientsituation is attained, that is, no one can be made better off without making someoneelse worse off. The quantity approach (the 'American' approach)yields the welfaregain due to road pricing of area I (shown by the trangle UYZ in Fig. 3). The equivalent area, e+f-d, is the welfare gain using the change in total benefits and costs approach (the 'Britsh' approach). The latter area is the cost saving of area iZ/ Mm 'toiled,the toled off, ad td u-toiled' an cnn coinedby Zeds ad Call (1964). My approach difl_tiatee f*omboth Zettoland Carl and Woldad Hamidckacs (1984,pp. 114-116)in thatI applythe standardnoesoai methodof wdfre onalym ystheappdix to detivemy reaut and policyimplications. - 14 - e+f+g+k less the lossof the usevalueof area g+k+d. We notethat there are two groupsof travellersthat are clearly adverselyaffectedby road priing: the tolled and the tolled off. Briefly,the Britishapproachto the calculationof welfaregain says that those who remainon theroadafterroadpricingis introducedincura costby makinga tollpaymentof the rectangular area b+c+e+f. On the otherhand,the travellerbenefitsin the form of reducedtraveltime-'forcibly'induced-- and the resultanttimesavingsis the smallerrectangulararea e+f. Hence the consumer-traveller wouldregardthis exchangeas not gettinggoodvaluefor moneybecause the travelleris still facedwitha net paymentof area b+c relativeto the no toll situation: this area is his loss of consumer'ssurplus. Despitesucha trade, the travellerwouldundertakethe stillexceedsthe price. trip becausehis willingness-to-pay 20. Theotheridentifiablegroupincludesall thosemarginaluserswhosewillingnessto pay is not high enoughand henceare tolledoff the road. As a group, their loss in valuation,the verticaltrapezoidalarea d+g+k, exceedstheir savingin time cost of the area g+k by the (welfare)lossin consumer'ssurplusof area d. Soboth groupsare necessarilyworseoff vis-avis the originalsituation. This is shownto be true despitean argumentthat those whoremain benefitfrom reducedtime cost! Theydo benefitfrom reducedtravel time, but they have to exchangemoneyfor time. In addition,the "tolledon" is eitherjust as well off, or worse off, dependingon whetheror not congestionarises. So it appearsthat, a move from a Pareto inferiorpositionto a Paretooptimalstateleaveseveryoneworseoff! How couldthis happen? It comesabout becausewe have not yet accountedfor one agent: the government. The toll revenuecollectedby the governmentis consideredan actualgainto societyin that it is counted onceonly. Indeed,it mayhave a greatervaluethan the dollaramountitselfif it replacesother (income)revenuesourceswithan excessburden. 21. Supposethe tollrevenueis collectedand thenputaside. An 'efficient'amountof traffic and congestionwouldstill exist on the road in question,yet society- an aggregationof both gainersand losers- wouldbe definitelyworseoff. Unlessthe publicin general,or roadusers II/ It isas if a blakmie - thegovernmt - ca ou pat of t motoris'sconsumerssuplus. - 15 - in particular,can partake in the tax proceedseither in the provisionof public goods and/or reductionin tax revenues,theywill definitelybe worseoff from this impositionof an 'optimal' congestiontoll. If fundsare not channeledback to road users, the government,or the rest of society, gains, but only at the expenseof those faced with road pricing. However, because of the nature of the Pigouviantax, which possessesan asymmetricprice signal, generatorsof externalitiesare taxedbut thoseaffectedby the externalityare not supposedto be. compensated.This is a requirementof optimalityin the case of bothpublicand privategoodtype externality-corrective taxes(Baumoland Oates(1988, Chapter4))?Ql 22. Twochoicesto thosewhoare tolledoff theroad are to usethe roadduringthe off-peak periodor switchoverto publictransportduringthe peak. The analysisis similar in spiritfor both classes, so I will illustrateit for the off-peakperiod, for simplicity,followingthe same notationusedthus far. Substitutionof traveldemandfrom peak to off-peakhas the effectof shiftingthe off-peakdemandcurve to the right, from Q 0,, to Qdqt(Fig. 4). It is easy, as is sometimesdone, to regard the area m as an additional'benefit'. This procedureis incorrect becausethe area boundedby the demandcurvesin the substitutedoff-peakperiodis in fact a pseudo-benefitand is alreadyaccountedfor by the welfaregain to road pricingin the peak period, i.e., the triangulararea 1, in Fig. 3 (Mishan(1988,Chapter8)). Intuitively,sincethere are no changesin consumer'sor producer'ssurpluses,thereare no net changesin benefitsor costs: the additionaltripsmadeduringtheoff-peakperiodare entirelyself-financing in the short run. If congestionwere to set in during an off-peakperiodwith relativelymediumlevelsof congestion,say, duringthe inter-peak,efficiencysuggeststhat anothercongestiontoll level be set to internalizethecongestionexternality.In thisway,trafficwillsettleto anotherequilibrium 1/ The SmeedReport of 1964 and others effectivelyasswne away the problem by stating tbat the congestiontoll revenues will be retuned to the popuaion in a lump sum nondistorionary manner. 2QI Note tat Baumol& Oates (1988, 2nd edition, Chapter4) correcs the mistake made in the earlier edition(1975, 1st ed., Chapter 3), which says that only the victimsof private good-ype externalitiesought to be compensated for after the impositionof a Pigouvian tax. This result is contray to acceptednotions of justice. However, Baumol and Oates (1988, pp. 236-240)point out that if the tax revenueswere funelled bacwkeabwrcy, then ther would perhaps be only insignificantdivergencesfiom Paeto optimality. The idea is that wedth effects an consmption ought to be minimized. - 16 - level witha smallercongestiontoll in the inter-peakpeiod. 'Ais is the idea behindpeak-load or differentialpdcing. A dynamicprocesstakesplaceamongthe peak and inter-peakperiods untilan equilibriumis settledupon. Propercost-benefitanalysisrequires at the changesin net benefits be calculatedonly in the periods which encounterchanges in travel time due to congestionor decongestion.Wit}.a two marketmodel, the welfareeffectsof road pricingin thepeakperiodare simplyrepeatedin the inter-peakperiodwhenevercongestionis encountered. 23. It turns out that there is a case often overlookedin which everyone, includingthe government,can be shownto be betteroff. Thisis the caseof 'hypercongestion',wheredensity is beyondthe pointof maximumflow. Here the trafficdensityis so high thatboth trafficflow and speeddiminish,withthe generalizedcost POand trafficQ0 occurringat pointA (Fig.3(a)). (Eventhoughit violateseconomicrationalityto end up at sucha pointA, this typeof trafficjam doesin facttranspirefairlyregularly,thoughlimitedto peak periodssuchas peak-of-the-peak.) Theimplementatonof a marginalcost tollwouldresultin travellersrevertingto thenormalnonhypercongestedportion of the speed-flowcurve (such as may be observeddownstreamof a bottleneck),whichcorrespondsto the lowerbranchof the AVC curveat pointC in Fig. 3 (a). In addition, the travellershave to pay a unit toll paymentof distanceBC, resultingin a genemlizedcostto the motoristof P', whichis still lower thanP0. Becauseof the pricedecrease from PI to P', trafficthereforeincreasesfromQ to Q' correspondingly.In this case, literally everyoneis made better off: the tolled, what I call the "tolled on," and the government.3 1 If the speed-flowcurve is as depictedin Fig. 1 (b), then hypercongestion appearsmoreoften than is commonlyrealized: it occurswheneverspeeddropsto half (approximately 60%)of the maximumspeedlimit. 2/ It can alsobe shown,usingte techniqueof wdlfr, anDaysiselaborated in the appendix,tbat net ai fitto societyfrom such a ntional move is equal to area o+p+q+r+a+t+u+v (- ar o+p+q+r+a+t+w+x). - 17 Policy ImDlicatios: 24. Ever sincethe Frenchengineer,JulesDupuit(1844),introducedthe powerfiulconcept of consumer'ssurplusto analyzeissuesof the efficientpricingof (toll)roads, economistshave embracedthat notion,extendingand deepeningknowledgein that area. Efficiencyanalysis carefullyshownhere indicatesthat societywouldunequivocally gain from road pncing. The questionthat arises naturallyis why road pricing, with one single exceptionworldwide,has failedin the sixties,seventiesand eightiesto get off the ground. I show,using the analytical frameworkdevelopedabove, that road pricingas sold in the past is most likely doomedto politicalfailure. Thisis becausealmostall motorists,includingboththe oneswhoare tolledand tolled off, find that they are invariablyworse off as a result, except in the case of hypercongestion(see footnotefor qualification). The sole unmistakablegainer is the government. If road users do not perceiveor are not persuadedthat they benefitfrom the government'snewly collectedrevenuesin the form of provisionof transportservicesand worthwhilepublicexpendituresor receivetransfersin the formof reducedgeneraltaxpayments, albeitindirectly,it is highlyunlikelythatthesegroupswouldacquiesceto thepricingof existing roads. Cooperationwouldbe morelikelyif they are guaranteeda reductionin motorvehiclerelatedtaxessuchas importduties,first registrationtaxes,annuallicensefees and/orfueltaxes. In particular, the replacementof - rather than an additionto - existing vehicle-relatedtaxes by cost-effective congestiontollswouldespeciallybe welcomeby road users. 25. A naturalquestionthenis as follows:is therea theoreticalargumentfor dedicatedfunds or earmarkingso that societyas a wholewouldbenefitfrom theimplementation of roadpricing? Restatedanotherway, is there a way in which road users can act as beneficiariesand be 22/ Thepolicyimplications discud beroa basedon theassumptionof costat vduo of tme - the as_mpm used by Walteosand othr n derivingthe avegp variable coat curvo(see sectionXIV,subsaecon , below). My reuk that roadpcing makeseveayonewor off exceptthegovenmnt is meantin an averg sune. People'stim valuations differin reaity, so thatthis resultis modifiedto say that oly thosewith fairlyhg valuationof time wouldbe betteroff, and eveyone elsostill worseoff. Te conditionis that the weighted valuationassciated witht timesavimgs rectagle of areae+f mustexceedtheirtotal mony 'ayment of ae b+c+e+f basedon a weightedcongestiontoll. Otrwis, eventhos whoremainon the toiledroadwold continueto pay but would actuallybe worse off relativo to theirstatus quo. - 18 indirectly'compensatedfor' the paymentof tolls by satisfyinga commonlyacceptednotionof fairness,whilecarefullyskirtingthe first-bestpricingrule? I thinkthat the answeris 'yes', althoughnot entirelywithoutqualifications. VI. SHORTRuN EQUILIRIUM Thepropositionthat optimalpricingof and investmentin a highwaysystemparallelsthe 26. industryof a textbookcommoditywas shortand longrunequilibriumconditionsof a competitive first shownby HerbertMohring(Mohringand Harwitz(1962),(Mohring(1965, 1976)).3/ Economicanalysisof transportproblemsis simplifiedconsiderablyby explicitlyrecognizingthe he purchasesfactorinputs travelleras both consumerand producer,and as producer-traveller approachis advancedboth cogently suchas traveltimefrom himself. This short-run/long-run economistssuchas Keeler,Small, andlucidlyby Mohringand usedby establishedtransportation Kraus,Glaister,Morrison,Winstonand Oum. In the short run, some inputs for producinga textbookcommodityare regardedas 27. Under competition,an economicallyefficientoutput level is achievedwhen the fixed. price equals the short-run marginalcost of producingthat good. A market-determined competitiveproducerpurchasesvariableinputsby hiringlaborand procuringraw materials,in additionto investingin a fixedinput,capital. Thereafter,the firm combinesthe inputsvia the productionprocessand createscommoditiesto be sold to a consumer. In other words, the produceruses the revenuewhichhe obtainsfrom sellingthe goodat the givenprice to pay for the variableinputsof laborand rawmaterials,plus the fixedinputin the form of quasi-renton the capitalequipment,normallyregardedas the accountingprofit. Thegraphsfor the textbook commodityare similarto (but not exactlythe sameas) the caseof roadsconsideredin Figures ZV 4/ (1985). See surveyby Winston Mhm standarddefinitionof shortrun is a situaion in which someproductive inputs are regarded as fixed, and hencecetaincostswouldbe fixed. However,thedefinitonof longrunrefersto a sitationin whichall npUtS vary. In the roadcontext,thedurationof thelongrundependson therateat which,say,thesizeof a roadand hence the basicor enginering capacity,can be varied. - 2 and 3.2/ 19 - In transport, the short-run marginal cost of a trip, which we derived rigorously from an engineering speed-flowcurve, is to be set equal to the 'price' of a trip. Recall that transport is unusual in that the traveller is both a producer and a consumer. Analogousto the paallel case of a textbook commodity, the road user, when undertaldng a trip, supplies some of his own variable inputs, which include vehicle operating cost and time cost. We have seen that the competitivelevel of trips exceeds the efficient quantityin the presence of congestion. Hence, becausethe quasi-rentof a highwayfacilitywould be dissipateddue to free competition, an optimaltoll shouldbe imposed to capture this quasi-rent. Clearly, even though the dictum of short-run marginal cost pricing prevails in both cases, the optimal toll does not equal the short-run marginal cost of producing an output but is equivalent to the difference between marginal cost and average variable cost. This is a subtle but important distinction between transport and widgets. 28. The optimal toll is the efficient charge referred to in Mohring and Harwitz's (1962) mathematicalstatementof this problem and Newbery's (1989) Proposition 1. The optimal user charge is then the optimal toll plus another component required to cover the variable maintenancecost of a road discussedin Walters' (1968, p.2 4) and Newbery's (1989)Proposition 2 (see Fig. 2's legend).X/ As discussed before, to focus our efforts here, the optimal user charge shouldultimatelyinclude air, noisepollution, accidentcostand road damageexternalities. 29. Walters (1968, Chapter 2) defines the term 'user charge' as the money charge that governmentalauthoritieslevy on travellers for the congestioncost they impose on others and for the variable maintenancecost of the road incurred due to their use of that road. In the absence of congestion, the user charge coversthe unit road maintenancecost componentonly and would be independentof the traffic level. Walters (1968, Chapter 4) then coins the term -economic 251 With sandard goods,both dh short run nmrginaland averagevariablecost curves canldeclineand swing upwards,whers I haveshownthatboththe shortrun marginalandaveragevariablecost curvesi transpt newc declinebut only rs upwards. 2I Moreprecisely, Newbery's (1989) Propositions1 and 2 include theinvariatemaintenace cost due to weathr. - 20- user charge (EUC)"to be equivalentto the generalizedcost conceptor user price employed here. Thislatterusagemightleadto a possiblemisunderstanding aboutthe demandand supply side or even double-countingand is the-eforeavoidedhere. 30. To recapitulate,shortrun equilibriumin transportoccurswhenthe government,in the form of a highwayagency,behavesin an optimizingfashionjust as a privatecompetitivefirm wouldwere it possibleto organizethe industryin a competitivefashion. The optimaluser charge shouldnot be set equal to the price but wothe differencebetweenthe marginalcost and the averagevariablecost of a trip. IX. RETURS LONG-RUN EQunITMBR UNDER CONSTANT CONVRGENCE TOWARDS 31. So far we have confinedourselvesto short-runequilibrium.The fixedcost component has been deliberatelyleft out of the analysisof the marginalcost of a trip.= The motorist is obliviousto the capitalcost of a road, and his behavioris independentof it. However,from the highwayagency'splanningpointof view,the capitalcost of a roadis very muchtakeninto account. Oncea highwayis built, however,it is regardedas sunk. The sunk cost of a road, onceincurred,is irrelevantto a planner: onlycurrentand futurecosts,not historicalcost, serve as a correctguide to planningfutureinvestment. Sincethe variableroad maintenancecost is assumedto be constant,the marginalcost of a trip thus remainsthe same. 32. In the long run, however,a highwayagencycan vary the fixed capital input by expresswayexpansion,if theinvestmentis deemedjustifiable. On theotherhand,if a rural road has been built as a result of past planningerrors, it can be allowed to deteriorateor be downgraded(or be evenauctionedoft. Expandinga roaduntilthe additionalbenefitequalsthe additionalcost of buildingit wouldyieldmaximalnetbenefitto the community.Howmightthis be done withoutresortg to a full-scalecost-benefitstudy? Z1/ of outay necessaryto str production. Ih fid costof a firmis definedto be Xt minum amount - 21 - To see how this might be done, we introducethe fixed cost, i.e., the cost of 33. construction,togetherwith the 'invariate' maintenance,depreciationand operatingcosts of a road that are incunredby a governmentalauthorityin Figure5.W1 We thenconvertthe entire fixedcost into the cost per time periodof a unit of capitalfor utilizingthe flow of highway with the averagevariablecostof a trip services. Thisis donein order to makeit commensurate discussedthus far. The summationof the short-runaveragefixedcost and the averagevariable cost curve yieldsthe averagetotal cost curve. Chargingthe optimaltoll of the distancet' in Figure 5 seems to be more than sufficientto cover the short-runaverage fixed cost of the facility. In this case,the optimaltoil, t', exceedsthe short-runaveragefixedcostof the facility, SRAFC', by the unit profitdifferenceof u'. In general,there is no a priori reasonwhy toll revenuecollectionsbasedon short-runmargnal cost pricingcannotcover the non-use-related costsof a givenhighwayfacility. 34. In the caseof a textbookcommodity,wheneverthe quasi-rentbeingearnedby a firm's existing capital equipmentexceeds its cost, there is an incentive to expand production. Ultimately,the quasi-rentearned by the existingcapitalequipmentwouldthen be equal to its (fixed)cost.2 Puttingit anotherway, upon seeingthe existenceof economicprofits, other firms enter the industryalso, shiftingthe industry supply outward, increasingoutput and loweringprice as a result. Theunrestrictedmobilityof resourcesand theentryand exitof firms serveas the instument by whichprofitswouldbe competedaway in due course. Whencapital is freely varying, long-run equilibriumis reached when zero economic profit occurs. Equivalentlysated, the quasi-rentearnedon the firm's capitalequipmentequalsits cost, i.e., 71/ aI/ hmtwm lnvarlaw, ie., non-taffiC rlated nit c cot is found in Walftr (1968, p. 23). to a firm is the acounti profitsp1w interestexpens on borrowedfiuds, if any. The e quasim-reit acomting profitis the finr's totalrevu lesaits contwua costs, includinginterestexpse on borrowed fiuds, wags to labor, cost of vw maters, and rentalcoatof leasedbuildings. Accountingprofitless the madmtrun of the owner-mupli.dma_s i t oconomicprofit Altenaively, th qua-rent on imvest capit is te total evau lm the variabb costs, La., includingwages, cost of raw mateials and rental cost, but ewludig interet expens an borrowedfunds. Totalreve lesototal vaiable and fixedcost yields economicprofits. Tbefixedcost of investedcapitalincludestih entireopportunitycostof capital,regardless of wheter funds bonowedor not. (Seete thiWfootnoteof Appendix(footnote71)andMoaring(1976,pp. 8-11)). I am gratful to HEbrt Mahringfor clarifyingthesepoints. - 22 - This conditionholds the marketreturn of the cost of reproducingthe investedcapital. underconstantreturnsto scale, wherea proportionateincreasein all inputsis compatiblewith the sameproportionateincreasein outputs. Givenfixedfactorprices, total cost also doubles, so marginalcost remainsconstantin the longrun. Witha slightbut crucialmodification,this analysiscarries over to the case of roads. When the quasi-rentof the existingcapitalstock exceedsthe normalmarket return on the cost of reproducingthe investedcapital plus the highwayfacility'sinvariatemaintenanceand depreciationcosts, new investmentis expectedto find its way in that road segmentof the highwayindustryif the appropriateprice signalsare given. Equivalently,in the longrun, if toll revenues- whichrecoverquasi-rentsthroughout timeperiods- exceedthe entirefixedcostof the existingfacility,the highwayauthoritywoull have the appropriateincentiveto expanda stretchof that road until aU economicprofits are erodedaway. As we have seenin the caseof roads,the variablecost is composedof the userself-financing.Thenon-userelatedcostsare then suppliedtimeandoperatingcostsand are fuUly financedseparatelyby the road agencyvia tollrevenuecollections.In this way, full costsare coveredand thereis no need to raise chargeswhenthere are constantretums to scale. X. OPrwAL INVSTMNT In the long run, toll revenues would then exactly cover the amorized cost of 35. construction,invaniatemaintenanceand depreciationcosts of roads - a powerfulresult first shownby Mohringand Harwitz(1962,Chapter2) and Mohring(1965)- underthe technical conditionsof constantreturnsto scalein roadconstruction,maintenanceand roaduse. Constant returnsto scale intuitivelymeansthat the cost of buildingand maintainingan expresswayis proportionalto the capacity. Constantreturnsto road use yields an intuitiveinterpretation: traveltime dependssolelyon the volume-cacity ratio. If the engineenngcapacityand the QI of it elsewhere,hencethecost is themaket The(opportunity) cost of a resourceusedhereis thehighestreatun returnon reproduction costand not historicalcost. - 23 - traffic flow were doubled,unit travel times wouldremainthe same.#'1 The final long-run equilibriumis shownin Fig. 6. By faithfullypursuingthe policyof marginalcost pricingof a trip by charginga congestiontol - the differencebetweenthe marginalcost and the unit variable(time)cost -- and by expandingor appropriatelyreducingthe capacityof the road until there is zero economicprofit, the output (of vehicle-kilometers per lane-kmper hour) is consideredoptimal. At a momentin timefor an existingroad, outputis optimalin the sense that, giventhe marginal-costprice, the efficientlevel of trips is achieved. Undertakingeither moreor less trips wouldinvolveloweringthe net benefitto the community. In the long run, outputwouldbe 'doubly' optimalif it is the efficientlevel of trips for that link of road which has been optimallybuilt. Diagrammatically, not onlydoesthe implementation of a congestion toll internalizethe externalcongestioncost, it can be seen that the toll covers the short-run averagefixedcost of the road in a stationarystate. Recallthat for homogeneoustraffic the averagefixedcost of a roadis simplydefinedto be the differencebetweenthe averagetotalcost and the averagevariablecost. Clearly,collectinga unit toll wouldcover the entire average fixedcost of the road andyieldzeroprofitonlybecausethe existenceof economicprofitor loss servesas a quasi-marketmechanismin the investmentdecisionof whetherto expandor contract the highwaycapacity. With zero profit, the minimumpoint of a short-runaveragetotal cost curveis obtained. For any givenlevelof output,the minimumtotalcostof yieldingthis output wouldbe obtainedonly if the optimalinvestmentlevel in capacityhad been chosen. Looldng at it the otherway, the optimumsizeof a roadis obtainedby drawinga locusof all the minima of the varous short-runaverage total cost curves of different sizes (and capital costs) of 3I/ i 1) the capital and invariatemaintenancecost of highwaycapacity,KC, is directlypreportional to tbe engineeringcapacity,K, i.e., KC (K) = aK, wher a is a constant,dhenthereexistsconstat trns to scale in highwayconstruction(and invarateroad _mnce). (In mtematical jargon, KC is homogeneous of degroeone in capacity.) The engiering capacityis measiredby lane-widthand is treatedas a continuous variable.Further,tf2)(a)trafficcanbe expressedin termsof a homogeneousunit,Q,in vehicleper lne-hour, and thetimecostfunctionAVC(Q,K)dependsdirecdyon e trafficflowbut is invetselyrelatedto thecapacity and (b){(doublingbothhighwaycapacityand trafficflowresut in thetraveltimeof a tt4premain the same, thenthereexistsconstantreturnsto roaduse. (Ma cally, theAVCfuncticnis homogeneous ofdegreezero in trafficvolumeand capacity.) Withconstantretrns to road uw, AVC(Q,K)can be formallyrewrittenas AVC(QIK),whereQ/Kis thevolume-capacity ratio. Sinceunitvehicleopeatingandvariableroadmaintenace costs are both indepdent of the level of output,and capitalcost, KC, is proportionalto lane expansion, ATC(Q,K)= ATC(Q/K) holdsalso. Thesetwotechnicalconditions arecrucialto Morng andHaMritz's(1962, pp. 85-90)so-calledtheoremand to Keele and Small's(1977)extsion of Mohring'stheorem. - 24 - highwaysand choosingthat particularsize of the road associatedwith the point where the demandcurve intersectsits marginalcost curve. We do this becausethe demand reflects motorists'maximumwillingness-to-pay and hencethe incrementalbenefitof the last trip. Since the minimumpointsof the short-runaveragetotalcosts underconstantreturnsare of the same height,the long-runaveragetotal cost is a horizontalline tangentto all the minima. With the long-runaveragetotalcost beingconstant,so also is the long-runmarginalcost. Hence, it is only at the minimumSRATC point that long-rn margin cost pricing holds. LoNG-RuN VS. SHORT-RUNMARGINALCOSTPICINGRI X. 36. Intuitively,the long-runmarginalcost of producinga trip yields the total cost of undertakinga trp to the communitywhen all fixed and variable inputs can be varied continuously in thelongrun. Proponentsof long-mnmarginalcostpricingarguethatthe market return to capitalinvestmentwouldpresumablybe fullycovered. Yet the equivalenceof shortun and long-runmarginalcost pricingholdsonlyin certaincases,includingthe static demand and singleperiodcase consideredhere. As shownin Fig. 6, long-runmarginalcost pricing wouldcover aUthe variablecosts,includingtimecost, vehicleoperatig cost and variableroad maintenancecost,phw the fixedconstruction,invariatemaintenance,depreciationand opeating costs of the road. In fact, short-runmarinal cost pricingcoversthe entirecapitalcost of the facilityjust as muchas long-runmarginalcost pricingdoes, as can be seendiagrammaticalyin Fig. 6. After all, both the short-runand long-runmarginaland averagecostsare equalin the long mn, with both sets of cost curves intersectingthe demandcurve at the same point. However,if a road is not optimallyconstucted but underbuilt,then long-runmarginalcost pricing would bendout too low a price signal, therebyexacerbatdngcongestion. Short-run marginalcost pricing,on the otherhand,wouldgive the corect signalof higherwllingness-to321 Pro (1969,p.8), Water (1968,p.33),BDunahnsad Waltn (1979,p.33)and Bird(1976,pp.33 -3 9 ) argue for ihort-runrq maurl coatpricng whbwruothes arguef1r loun murgnaslcomtpncins. Sincethe msueof long-rmvs. shost-mu maqprnl cot pncnighas beanwithu for SmO tinum, a claification in order (swetfe ntw debatebeiwehmJordan (1983a, 1983b, 1985) ad Vwikoy (198S)). Vikry poinls out tht th concept of log-nm maurginlcoatbeoome.obfuscated wbh swvealdemandpriods, e.g., peak, mitepeakand off-peak, occurdiunmaUy, givandlocameof a an sportaionbifrstrucur dot hs aleudy beanconstructed - 25 pay and also yield positivetoll revenuesand economicprofits as a by-product. Short-run marginalcost pricingis the rule to use wheneverlong-runequilibriumis not reached(and of course when it is). Lookingat it anotherway, if short-runmarginalcost is below long-run marginalcost at the currentoutput,it meansthat the road has been overbuilt. But, of course, this does not mean that the size of the expresswayshould be or indeed can be varied wheneverdemandfluctuatesdaily. Rather,it meansthat the price oughtto be instantaneously variedaccordingto demandpatternsusingshort-runmarginalcost pricing. 37. Indeed,ProfessorWfIliamVickreyhasemphatically arguedthat therecan be no solution to the urbantransportationproblemwithoutpeak-loadpricing. Proper time-of-daypricingcan be implemented only usingshort-runmarginalcost. (Weshallexplorethispoint furtherin the sectionon demandvariability.)Pursuingshort-runmarginalcost pricingperiodby periodby varyingroadcapacityincrementallyovertimewouldnot onlyguaranteethe best useof society's resourcesbut wouldalso enableroadagenciesto recoverall costs- as an incidentalby-product - in the long run. It is thereforerecommended that short-runmarginalcost pricingbe used definedwhenevercyclical sincethe conceptof long-runmargnalcost cannotbe unambiguously vaiatons in demandare involved. XII. TRADE-OFF BETWEEN INDBVDUALS' TIM ANDTREASURY AccouNTs 38. Anotherway of obtainingthe optimalinvestmentlevel for roads is to answer the followingquestion: what is the minimumcost to the communityof road building,takinginto accountboththe highwayagency'sdesireto minimizethe fixedcost of capitalfacilitiesand the travellingpublic's desire to save time' By minimizingthe total cost - the sum of these two costs: the variable (time) cost of trip make and the fixed cost of the governmental authority- a twade-off is foundbetweenindividuals'time and the teasury's accounts. Given a non-optimalcapitalstock (K') assodatedwitha particularhighway,as in the previousgraph, 3/ Solvingthoproblem of codtmininiutios the community. quivalet to solviugtbeproblemof maximiton of net benefitto - 26 - Fig. 5, it can be seen that the leastcost for the communityinvolveshavinga road that is too small, for the level of demanddepicted. Expandingthe capacityof the road may reduce the user's trip cost evaluatedat a giventraffic level. Long-runequilibriumis reachedwhen the minimumpoint of the short-runaveragetotal cost curve (equalsthe short-runmarginalcost curve)intersectsthe demandcurve. For the governmentalauthority,road capacityis a choice variable. By increasingits size, the volume-capacity ratio dropsin the shortrun, and so does time cost. However,the cost of road capacityincreases. Intuitively,the highwayagency continuesto expandthe road until the marginalbenefitfrom savingusers' time costs is just offset by the marginalcost of one unit of capacity. It is at the output, Q* with an optimallybuiltroadK*, in Fig. 6 that the valuationof the last trip takenjust equalsits marginal cost, thatis, the incrementalcost of the trip to others,the motorist'sowntimecost in congested traffic, plus the vehicle operatingcost and the road maintenancecost.3' The highway agency,by settingan optimalroad user charge whichis equal to the congestiontoll and the variableroadmaintenancecost component,wouldbe able to inducethe motoristto travelup to the pointwherethe price of a trip equalsits short-runmarginalcost. By pursuingthis pricing policyfor each stretchof road, the use of a non-optimal,existinghighwaynetworkwouldbe optimized.Further,by expandinghighwaycapacityup to the pointwherethe quasi-rentof each capitalfacilityjust coversthe costof reproducingit, withzero (economic)profitremaining,the net benefitto the communitywouldbe maximized.Bysymmety, abandoningor downgrading roads is necessarywhen economiclosses occur. The decisionof not maintainingroads is tantamountto the act of disinvestingroads. AII D1/ Formally,givena particularlevelof output,thecost-iniming autority wouldexpandtheroadup to thepoiat wherethe marginalvaluationin timesavingsdue to a unitincreasein capacity, - Q *AAVC(Q,K)/IK,equals to the marginalcostof a unitof capacity,R. R is therentalcostper timeperiodof capacity,whichincludesthe invariatemaintenance and otheropeting costsof a road, depreciation andimputedintereston investedcapital. The negativesignwouldoffsetthe inverserelationahip of AVCand K, yieldinga positivemagnitudefor the entireterm. Alternatively, theroadis to be expandedup to thepointwherethemarginalextenal congestioncost just offsetsthemarginalcostof investment in capacity.Thisis thesecondoptimality le: theoptimalinvestmt in capacitynle. Thesuperscript* symbolindicatesthatthatvariableis optimized. - 27 39. Henceforth,to simplifyboth our discussionand the diagrams, we ignore the individual's vehicle operating cost and the variable road maintenancecost since they are self-financing.2/ Note that our conclusions thus far hold under the assumption of constant returns to scale and perfect divisibilityof roads. Consider a three-lane road with capacity K3 in Fig. 7(a), where output is now measured in vehicles per hour.=/ Since the highway authority has efficiently priced the road by setting the congestiontoll t3 * and optimaly built the road by investingat K3*, it can be seen that the toll revenue covers the fixed cost of the road. So far we have simply translated Fig. 6 into Fig. 7(a) with the costs borne by motorists convenientlyleft out but not forgotten. Assume that both traffic volume and road width, i.e., the number of lanes, are doubled and that the inputs to each of the componentcosts under constant returns are doubled, then i) the fixedcosts of construction, maintenanceand depreciation,ii) the variable time costs, and fii) the total costs are all doubled.38/ Intuitively, the geometric doubling of the rectangularareas of road constructionand maintenancecosts is synonymouswith the condition of zero economies of scale (given fixed input prices) in road construction and invariate maintenance. Similarly, the horizontal doubling of the rectangular areas of the time costs suppliedby individualusers is akin to the technicalconditionof zero economies of scale in road use. 36/ I have tbereforegroupedthe non-trafficrelated ma_itc and operting costs as part of dte short-runaverage fixedcoat curve. Bear il mindthat the variableroad maitenance cost (not drawnin Fig. 7(a)) is being recoveredby a separateroad user charge componentas shownin Fig. 2. With the condition of zero economies of scalein totalroad mainltnce, the total mintenancecostis thusexactlydoubled. Also,economicprofits fromnowon willbe refenredto as 'profits'. n/ Threelane roadsare foundin Australiawheretheyare referredto as, 'two-and-a-half lane roads' by Hoban (1987). Lg/ Thestringentassumptionof a roadbeingfinelydivisiblewillbe relaxedand indivisibilities introducedlateron. - XH. 28 - FIRST-BBST OPTIMAL PRICING AM INVESIMNTRuLE Empda Considerations: 40. Byestimatngbehavioraltraveldemandfunctionsusingstate-of-the-art logitmodechoice models,one couldobtainempiricalesdmatesof marginalvaluationof time (as a functionof incomelevels)(Hau (1986)). When combinedwith a fine-grained,parametrictransportation corridorsupplymodelof the San FranciscoBay Area (Talvitieand Associates(1978)),multimarketdemandand supplycouldbe equilibratedand cost-benefitanalysisof alternativepolicies performed(Hau (1987)). Heuristically,the adjustmentprocesstowardsthe finalequilibium parallelsthatof the cobwebequilibriummodelof adjustment.Optimaltollsand welfaregains and losses could thus be simulatedwith apprpriat specificationof the marginaltravel time function. The resultsobtainedare for a short-runequilibrummodelof demandand supply. 41. Even with poor data, one could make some progress in empiricalwork. Given an estimateof a speed-flowcurve and the correspondingtravel-timeflow curve, we know how theseengineeringcurves can be convertedto a short-runaveragevariablecost curveof a trip, usingan estimateof the valueof time. A 'supply' elasticityestimatetogetherwitha value for unit variable cost would yield a one-to-onecoaepondence betweenthe short-runaverage variablecost and the marginalcost (see footnote15 for formula). A rmughestimateof the demand elasticity and the traffic level of a particular road would yield a first order approximation of the propercongestiontoll. Now,in order to maximizeaggregatenet benefit, two operatingrules shouldbe followedby the roadauthority. TheFirst Rule - The OptimalPridng Rule: For eachstretchof road, short-runmarginalcost pricingis fulfilledby settinga toll at the excess of short-runmarginalcost over short-nm averagevariablecost. The intuitionis that this congestiontoll wouldserve to internalizethe congestioncost that a driver imposeson others. In addition,the motoristis chargedanother componentwhich covers the variablemaintenanceand opeating costs of a road which he imposeson the road authority. Thus the publicauthority'simpositionof an optimalroad user -29 chargewouldcoverboththe extrnal costof congestionas wellas thevariableroadmaintenance and operatingcosts. The SecondRule - The OptimalCapacit Rule: Underconstantreturnsto scaleand optimal pricing, whenevereconomicprofit is foundin the operton of one road link, the procedure wouldbe to expandthe capacityof that stretchof road. Theexistenceof a loss undershort-run marginalcostpricingsuggeststhatthe roadhasbeenoverbuilt. By alteringthe capacityof each road in the long run accordingto the quasi-marketsignal of profits and losses, the entire highwaynetwork'sinvestmentlevelin capacitywouldbe aptimized,withthe fixedcost of each road covered. Alternatively,the road authority,by tradingits direct resourcecosts against individuals'traveltime, followsthe rule of settingthe marginaltraveltimesavingsequalto the matginal cost of investment for an additional unit of capacity. The capacity of a road is expandeduntil the marginalcapitalcost equalsthe marginal(external)congesdoncost. erWpective on the Result: 42. What we havedescibed is the long-runequilibriumof an optimallydesignedcapacity of a road network under constantren. If the road authoritywere: 1) to pursue the efficiency-enhancing policy of pricingaccordingto the margnal cost of a trip, and 2) to minimizethe sum of the directresourcecostsof providinga road and thevalueof user-supplied travel time inputs,then the road wouldbe both efficientlyutlized and optimallyexpanded. Noticethat the optimallydesignedroadhas a positiveamountof externalcongestioncost. This results from the road agency's desire to minimizeboth the sum of the direct cost of the investmentin capacityand individualdrivers' travel time cost. In our simple framework, congestiondelay wouldnever be entirelyabsent,contraryto what environmentalists and road userswouldprefer,becauseachievingzerocongeson is verycosty to the community.in other words,an optimalamountof congestionextenalityis a validconcept,just as an optimalamount of pollutionhas longbeenrecognizedin the envinmental economicsliterature. Whatif there is no congestionon a particularroad? Zero congestionmeansthat that stretchof road hasbeen overbuilt(or pricednon-optimally) and shouldperhapsbe downgradedor even abandoned. If - 30 excesscapacityoccursall the time, the road possessesthe non-rivalconsumptioncharacteristic of a pure publicgood. Thenwe are facedsquarelywiththe standardtaskof provisionof public goods. If resourcesare plentiful,financingthe shortfallvia generalrevenuetaxationhas been theconventionaldictum. Similarly,if publicresourcesare scarce,theopportunitycost of public funds must be accountedfor.& If lump sum taxationis infeasibleand resources are severelyinadequatebecauseof politicalconstraints,then it is possiblefor one to considerthe feasibilityof financingvia Ramseypricing.0 If it is uncertainwhether the (marginal) deadweightlossesfromgeneralrevenuefinancingexceedthoseobtainedfromRamseytaxation, financialand otherconsiderationssuchas equitymay then have to be appealedto in order to justifythe potentialuse of Ramseypricingin the roadsector. 43. Bycontrast,a roadwouldpossessthe.ival consumptioncharacteristicof a privategood whenexcessdemandoccurs. Hencea congestedroad is also regardedas a congestedvariableuse publicfacility. Becauseof this mixedgood nature,and basedon the theoryderivedhere from first principles,the provisionof road servicesought to reside with the public sector. UndertL ;onditionof constantreturns,the optimaltollrevenue,whichcapturesthe quasi-rent earnedfromthe investedcapital,wouldcoverthe entirefixedcost of the road in the longrun. No residualor overheadcost need be allocated. If profit exists, then it is becausethere is insufficientroad capacity(or pricingat a levelabovemarginalcost). The roadis thereforenot 9/ 40I In the comion paper (Hau (1991)), I present calclatios of the opporunity cost of finacing alternative chang mechianms. FrankRamsey's(1927)inverseelasticityformulaunderthe case of independentdemandswas discoveredin rens to Pigou's question of how to set tax rates in order to minimize the welfare losses associatedwith meeftinga tax revenuerequirem Theproblemof the choiceof optimaltax rateswhichare subjectto a revenueconshaintis formallyequivalentto thatof the settingof optimalpriceswhichare budget-constrained. Ramseyprcing in thepresenceof axtalities reqires thatit be computedon thebasisof maginal costand a facdonof themarginalextemd cost (OumandTrethaway(1988)). Clearly,in thepresenceof leakages,nonexcludability andpartid rivalryin consumption, the uirements for theimplemtaton of Ramseypricingare considerablymmrestingent than those of pursuingmarginalcost pricing. On conceptual,empiricaland implementation grounds,marginalcost pricingis superiorto eventhe simplestform of Ramseypricing:the inveneelasticitynrle. Thecomputatonof Ramseyprices,for instance,requirestheestimationof margial cost as a prerequisiteand thedetermination of revenuetargets. Despiteall theproblemswithwhichRamseypricing is fraught,researchintothis itring issuois potentially useful. Afterall, increasinglytightfiscalconstains, countrieswilldemandalteative fundingmachaims. - 31 - in long-runequilibrium.Theexistenceof profitservesas a surrogatemarketsignalto expand capacity. Themottois as follows: "If a road makesmoney(i.e., economicprofit), expandit, elsenot." Similarly,if a roadloses money,it suggeststhat plannersmadethe wrongdecision or were given over-opdimistic forecastsof traveldemand. In that case, marginalcost pricing is still to be adheredto, with the congestiontoll set closeto nil. A user chargecomponentis still neededto coverthe variableroad maintenancecost. Thusit may even be worthwhileto abandona money-losingroad and save on any annualinvariatemaintenancecosts that might arise. Efficientpricing, financialviabilityand cost recoveryare thereforeentirelyconsistent with one anotherunderconstantreturnsto scalein long-runequilibrium. XNV. RELAXAnON OFAssuMPTIONs 44. The above discussionassumesthat the governmentaims to maximizewelfareof the communityby simulatingthe workingsof a competitiveindustryand pricinghighwayservices at marginalcost. Thereare a few majorassumptionsthat needto be relaxed: 1) constantvalue of time, 2) staticdemand,3) perfextdivisibility,4) constantreturnsto scaleand 5) variability of road thickness. We considerthe relaxationof eachassumptionin turn. 1) Differencesin Time Valtion 45. The traditionalpresentationof roadpricingand my ensuingcritiqueassumea constant 1 value of time (Walters(1961a))A' The diagrammaticanalysisin Figs. 2 and 3 implicitly assumesthat every driver is identicaland maintainsthe sametime valuation. What happens when there are heterogeneousmotorists, with different time valuation and tastes? A mathematical proofthat generalizesthe aboveresultfor homogeneousdriversto heterogeneous oneswithdifferentvaluesof timeis shownby Mohring((1975),(1976,Chapter4 Appendix) and Strotz(1964a,1964b),but theintuitionbehindit is not difficult.Insteadof the optimaltoll 41/ In his pionering work on road pricing, Walters (1961) (and authors thereafter) assues that traffic is homogeneous,with all vehiclesand drivers being the same, with the resultantidenticalvaluationof time for all. - 32 - driver's valueof ime, the timevalueis nowa weightedaverage beingbasedon a representative of the differentmotorists'valuationof time, weightedby the numberof trips taken by those motoristswho actuallyuse the facility. If a traveller'stimevalueand the numberof trips are closeto the average,he willpay the averagetoll payment. If anothermotorist'stime valueis higher [lower]than average, he would be willingto pay more (lessi than the average toll payment for taking a trip. He thus would be willing to, though begrudgingly,pay the difference.The congestiontoll, P' - P", in Fig. 3 thencan be labeled the wighted congestion averagevaluationof time. toll, and the constantvalueof timeis re-interpretedas the weighted For a trip witha sufficientlyhigherthanaveragetimevalue,the timesavingof a trip, (P - PI% can be even higherthan the weightedcongestiontoll, P' - P", thus makingthe motoristbetter off. On the otherhand, for a (shopping)trip havinga lowertimevaluation,the user still has to makethe averagepaymentand thereforewouldbe madeworseoff. Nevertheless,theyboth remainon the tolledroad, as opposedto beingtolledoff, becausetheirindividualtrips' marginal still exceedsthe generalizedcost of their respective valuationor maximumwillingness-to-pay journeys. The use of alternativevaluesof time wouldrelax the pointI madeearlierthat road pricingwouldmakeaUlgroupsexceptthe governmentworseeff. By relaxingthe assumption of a constantvalueof timefor everyone,thosepeoplewithhigh valuesof time wouldbe made betteroff at the expenseof thosewithlow valuesof time. Thisintuitiveanalysisassumesthat everyoneis facedwiththe sametoll, as in the workingsof a competitiveeconomy,and that a perfectly discriminatingmonopolisticauthority is non-existent. We concludethata singletransportationfacilitywithdifferencesin valuesof timewould 46. not alter fundamentally our derivedresult, uing the standardassumptonof constantreturns. Again,with efficientpnrcng, financialviabilityand full cost recoveryare achievable. 2) DemandVariabilit and Peak-LoadPricing 47. We havein fact consideredthe caseof variabledemands,Iwr ala, whenwe discussed the welfareimpactof roadpricingon the peak and the off-peakperiods. Thereit was shown thata congestiontoll is neededduringthe peak whenthereis excessdemandbut not duringthe - 33 - off-peakwhen thereis excesscapacity. Noticethat becausethereis free-flowingtrafficin the off-peak,no tollingis requiredbecauseno externalcost of congestionis generated. Therefore no quasi-rentis beingearnedon the investedcapitaland onlythe variablecostsare paid for by the traveller. On the other hand, during the peak period, a positive quasi-rentis earned. (Supposefurtherthat there is an inter-peakperiod, somequasi-rentsare also generated.) With highwaycapitalstockremainingunchanged,the systematic,diurnalnatureof traveldemand(as opposedto the static,invariantdemandcase)meansthat the sumof quasi-rents(ratherthanjust the quasi-rentfrom the singularpeakperioditself)of the investedcapitalshouldbe compared withthe cost of the highwayfacility. In otherwords,whenall the quasi-rentsover the entire demandcycle are summedup and comparedwith the capitalcost, expansionof the highwayis eitherwarrantedor not, underconstantreturns. Thesameconclusionsobtainedthus far again hold.F 48. P intereting implicationis that the entirecapitalcost of the highwayis 'allocatedto' and bome by peak travelers, mainlynsh-hour commuters. This surprisingresult may seem 'inequitable',yet it is perfectlyconsistentwith efficiencyanalysis. After all, it is peak users themselvesthatcreatecongestionand theythatdemandthe useof heavilycongestedexpressways whichrequiremassiveinfrastructuredevelopments.Withoutthem,the optimalsizeof the road wouldbe considerablysmaller. The result of allocatingall capitalcosts to users of the peak periodhas long been recognizedin the literatureon the pricingof publicutilitiesa la Boiteux (1960). Followingour earlier example,the extent to which there is anotherperiod - the interpeakor shoulderperiod - with even a modestamountof congestion,would allow for differentialpricingand thus the allocationof somecapitalcosts to these interpeaktravellers. Theoptimalinvestmentrule is then to expanda road untilthe sum of the quasi-rentsover the demand cycle equals the entire capital cost of the facility under constant returns. By inplementingpeak-loadpricing and altering the investmentlevel of the highwayfacility, dependingon whetherprofitsare positiveor negative,the highwaynetworkis againoptimized. 4/ Theouputvuiableneedsto be rodefinedas vehiclespe lanepercycle,withthecyclebeingthedurton of a particularchugin period. - 34 - Hence,theconsideration of demandvariabilityandpeak-loadpricingwouldnot changethe status of our conclusions,in the presenceof differencesin valuationof time. The fact that the fluctuatingdemandsover the variouspeak, off-peakand inter-peakperiodsof a demandcycle are linkedby a fixedcapitalfacilityand the observationthat the consumptionof trips must be satisfiedby the productionof trips duringthat particulartimeperiodcombineto yielda simple modificationof our result. Pricing,financialviabilityand cost recoveryare again consistent withone another. 49. Keeler and Small (1977) show rigorouslyhow the Mohring-Harwitzframework developedhere is extendedto the case of variabledemandsusing peak-loadpricingin the presenceof independentdemandsand no indivisibilities.43By assumingthe demandin each periodin factdependson otherperiods,i.e., the caseof dependentdemands,the derivedresults still go through(Mohring(1970))AY' 3)ndisiaik 50. Whilestillretainingthe assumptionof constantreturns,but accountingfor differences in valuesof time and demandvariability,we proceedto drop the assumptionof a road being finelydivisible. Road construction,in fact, involvessignificantindivisibilitiesthat cannotbe ignored. For example,a roadmustpossessthe minimumwidthfor accommodating a standardsizedautomobileand shouldalso, ideally,be bi-directional.In the perfectlydivisiblecase, the long-runaverage total cost carve which envelopesa continuwmof closely-packedshort-run averagetotalcos; cur. es at theirminimumpointsis madehorizontal. A flat LRMCcurvealso coincideswith the correspondingLRATCcurve (see Fig. 7(b)). Due to the presenceof 431 It is due to the asumptionof independetdems Ihatlong-rn marginalcost pricing(equalsto short-nm margnalcostpricing)stil holdsat eachtimeperiod. Theconceptof long-nmmarginalcost pricingis blurrd in thecaseofjointnessof demand 44/ Usingthe distibutionof currentdemanddistribution as given,whichis synonymous with asumig independent demands,wouldresultin upwardbias in peakperiodsand downwardbias in off-peakpenodsbecauseof the possibilityof substitution (Keelerand Small(1977)). - 35 - indivisibilities, however,the formerlyneatand continuouspatternof theLRMCcurveis broken (Neutze(1966),Kraus (1981b)). The new long-runaveragetotal cost curve is now composed of a seriesof short-runaveragetotalcost curves,whereSRATC 2, SRATC 4 and SRATC 6 denote a two-lane,four-laneand six-laneroad respectively.The long-nmaveragetotalcost curve is a seriesof short-runaveragetotalcost curvesconnectedtogetherin a scalloped-like pattem(see the solid LRATCcurvelabelledABCDEFGin Fig. 8).AV The long-runmarginalcost curve takeson the various short-runmarginalcost curves in the respectiveregions,resultingin a discontinuousshark's tooth-shapedLRMCcurve (see the thick LRMCcurve in Fig. 8(a)). Henceone is alwaysworkingwiththe short-runcurvesthemselvessinceone couldonlyoperate with a capitalfacilitywhichis given. By now, it shouldbe clear that whenevera short-run marginalcost curve rises abovea short-runaveragetotal cost curve,profits can be obtained under short-runmarginalcost pricing. Thus, if demandhappensto intersectthe short-run marginalcost curvesin the regionof Q 2 Q24, Q 4 Q4 and Q6 Q&, and multiplesthereof,then the road makesmoneyin the longrununderconstantreturns. Per contra,to the left of the outputs, Q2, Q%and Q6, namely in the region of °Q2, Q2 4Q4 and Q44Q6 , the road loses money. With a 2-laneroad, as trafficincreases,the road's largefixedcost is spreadover the additionaltraffic, and as congestionsets in, the road beginsto make money. In otherwords, as traveldemand continuesto growalongthe trend,adherenceto short-runmarginalcostpricingsuggeststhatthe road wouldgo throughan unavoidablecyclicalpatternof deficit,surplus,deficit,surplus,etc. Whetheror not one undertaks a road expansionprojectfromtwo to four lanesdependson the magnitudeof the net benefitpie, takinginto accountthe welfaregain and loss triangles. OptimalPricingand InvestmentwithIndivisibilities:An Example 51. Consider the demand as depicted in Fig. 8(b), with the actual considerationof indivisibilities.First, we followthe first-bestpricingrule of tolling the differencebetween 4S/ A similr setof discontinuous curvesis foundin, for example,Bennathan and Walters(1979,Fig.2.2). Note thatthescalloped-like pattern is asymmetric becausetheunitcostcurvesforfourandsixlaneroadsarehorizontal multiples of thoseof the two-laneroad. In otherwords,underconstantretns to scale,the AVCand AFC curves,and henceATCcurvesfan outhorizontally- a mistakethatis quitefrequentlymadein the literature (see, for example,Hayutin(1984,Fig.2.8 and2.16)). - 36 - short-runmarginalcost and short-runaveragevariablecost, t*. This yieldsthe optimaltraffic levelof Q* and a positiveprofit. Withoutthe indivisibilityconstraint,the existenceof profit would indicate that the road is underbuilt. With indivisibilities,the direct one-to-one correspondencebetweeneconomicprofitand roadexpansionis lost. One is thereforeleft with the binarychoiceof, say, expandingthe roadfrom a 2-laneroad to a 4-laneroad. Usingthe welfareapparatusthatwe have developedin the Appendixand Figs. 3 and 4, however,the net benefitof sucha moveis shownto be the sumof the welfaregain of goingfrom Qz to Q**, as indicatedby the triangularareas b+c, and the welfareloss of movingfrom Q* to Qz4,as shownby the triangulararea a. Sucha movewouldclearlybe desirable. Witha 4-laneroad, however,the optimaltoll of t** wouldbe insufficientto cover the fixedcost of this new road, resultingin a shortfall. Thus, even thoughthe movefrom Q* to Q** is a beneficialone, it wouldmeanthatthe roadauthontywouldswitchfroma profitableregimeto a loss regimeafter incurringthe investmentcost. 52. Thus the optimal sequenceof decision-makingis first to establishthe policy of implementingmarginalcost pricingand then to plan future adjustmentsof the road network accordingto exeed futuredemandand establishedpricingpolicies. Whendemandfluctuates, pursuingshort-runmarginalcost pricingat presentwouldmeansettingdifferentprices,or tolls, in responseto expectedcurrentconditions. 53. Suppose the govermmentwere faced with a tight budget constraint. It would understandably thenbe unableto undetak all publicprojectswithpositivenet benefits. If this road authoritywere mainlyconcened aboutcash flowand financialviability,it couldopt not to expanda road, i.e., under-invest,but stll chargea congestiontoll on the built-uptrafficand satisfy economicefficiencyin the short run. This option however would not lead to the maximizationof society'swelfarein the longrun. - 37 * Returmsto Scale 54. The issue of whetherconstantreturns to scale exists or not in road transportis a controversialand imporant one. Uldmately,it can be answeredonly via careful statistical analysis. The availableevidencein road transportationindicatesthat aU three cases exist: decreasing,constantand increasingreturns to scale (see Fig. 9) - paraleling the case of a competitiveprivatefirm and industry- withprofit,zero profitand loss, respectively.(Thisis but a well-knownresult of economictheoryappliedwith slightmodificationto the highway.) It is importantto realizeat the outsetthat the case of scaleeconomies,or increasingreturnsto scale with fixed factorpnces under least cost combinations,is merelya case of insufficient demandwithrespectto the marketsize in the long run - a point thatis sometimesneglected. The implicationis thatif trafficwereto growto a pointwherethe capacityof a roadis reached, congestiondelay wouldset in, and congestiontoll revenuescouldbe collected. After all, the as shownin Fig. 8. Profitsmayoccur short-runmarginalcost curveis alwaysnon-decreasing, despiuethe factthatthe long-runaverageand costcurvemaybe decliningand theconesponding long-mnmarginalcost curve lies below the averagecost curve.46 Then if traffic were to continueto grow as real incomesand auto ownershiprise, concomitantwith expressway expansion,the decreasingretun regionwouldthen be encountered(see Fig. 9). In the case of incresn returnswithperfectdivisibility(wherenaturalmonopolyargumentslie), the longrun marginalcost curve below the long-runaverage total cost curve pulls it downwards, resultingin losses,beckoninggovernmentsubsidization.On the otherhand, if traveldemand is sufficientlyhigh relativeto the engineeringcapacitiesof roads, the money-maldngroad enteprises wouldprovidemuchsought-afterfundswhichcouldbe used to financeefficiently pricedbut money-losingroads - onlyif theseroads yieldpositivenet benefitsto society. We turn nextto a disussion of thetheoryunderlyingthe economiesvs. diseconomies issue,together with perfect divisibilityvs. indivisibilities,and end with a review of the empirical evidenceand recentwork. di/ Thispoiut wM be e_bid laer in Fig. 12 and 13(a). Basically,with paefct or lmostperfect divisibilityand scaleoe_ondes, only losskswill occur,wh with indiviibilies, eithe profitsor losses will mlt depadu athM level of travel demand - 38 A. Economiesof Scale and Rural Roads 55. There is a preponderance of evidence -- geometric, engineering and otherwise - supporting the case that there are significanteconomies of scale in the construction of rural 47' roads (Walters (1968, pp. 180-82),Mohring (1976, pp. 140-42)).- The illustrations below follow Mohring's scale economy analysis using the geometry of transport right-of-way. In particular, a two-lane road requires a minimumof a twelve-feetwidth for each lane and a few feet for shouldersand drainage ditches. What this means is that a non-trivialproportion of the provision of a road's right-of-way involves dead space. These indivisibilities- required to contributeto the buildingof a minimumacceptablestandard suchas a given pavementthickness and road size - help contributeto economiesof scale as the large fixed cost of constructionand invariate maintenancecosts are shared over greater amountsof traffic. Thus doublingthe width of a two-lane road more than doubles its traffic capacity, the so-called 'shoulder-effect' (Hayutin (1984),pp. 106 and 154). Further, we know that the engineeringor basic capacity of a two-lane road is about 2000 vehicles per hour. Since the standard four-lane road has an average engineeringcapacityof 1800- 2000 vehiclesper lane-hour, doublingthe width of a twolane road almost quadruples its capacity (see any Highway Capacity Manual, for example, Transportation Research Board (1985, Tables 2-1 and 2-2), yielding economies of scale associatedwith road use. However, capacity per lane remainsconstant beyond four-laneroads, resulting in zero economiesof road use thereafter. Further, in order to level hilly terrain and/or fill valley for transportationpurposes, the earth movingcosts rise less than proportionately. In fairly flat or rolling country selectedas sites for road building, doubling the width of a two-lane road generallyinvolvesless than doublingthe earth movingcosts. (On steep hillsides, however, the reverse may be true.) Hence, for these three reasons of: 1) the existenceof large fixed costs due to indivisibilities,2) the technologyof road capacity, and 3) the possiblereduction in earth movingcosts, we can claim that there are economiesof scale associated with the construction of a two-lane to a four-laneroad. Nevertheless,despite the fact that typical four-lanehighways 471 of ur*a roads. Meyer,lain andWohl(1965,pp. 200-204)alsofoundsomeevidenceof scaleeconomies However,KeelerandSmal(1977,p. 5) queryMeyer,KainandWohl'sfindings,stadngthattheirresults arein factbasedontheirinitalassumptions. - 39 - possesstwo-thirdsdead spaceand eight-lanehighwayshave onlyhalf the dead space,it is not clear from the geometryof highwayrights-of-waythat economiesof scale in urban highway for the effects constructionexist. Thisis becauseit is ratherdifficultto controleconometrically of urbanizationand separateit from the effectsof size. For example,four-laneroads tend to be builtin ruralareas,whereinterchangesandoverpassesare widelydispersed,andright-of-way costsare low. On the otherhand,six-laneor eight-laneroadsare builtmainlynear metropolitan conurbations,whereexpresswayinterchangesand overpassesare closelyspacedtogether,and landacquisitioncostsare high. In practice,the roadauthoritytendsto tradeoff (andavoid)high right-of-waycosts with increasedtunnellingand flyoverconstructioncosts. Lane expansion from a six-laneto an eight-laneexpresswayat the margin, for example,wouldincreasingly encounteralignmentconstraintsassociatedwith the terrain. (rhese constraintsmightexplain whycapacityper lane is reducedwithsix-to eight-laneexpansion(Mohringand Harwitz(1962, p. 97)).) This argumentis quiteindependentof whetherthe expresswayis locatednear urban areas. Henceall threecasesof returnsto scaleoccur,resultingin theclassic,U-shapedlong-run averagecost curve,parallelingthat of a firm withina competitiveindustryas we have seenin Fig. 9. B. Diseconomiesof Scaleand UrbanRoads 56. The discussionthus far has centeredon economiesof scale to road widthfor single roads, as opposed to a system of roads. Strotz (1964a) conjectures, and Vickrey argues convincingly,that there are considerabledisecononr -- of scale associatedwith an urbanroad networks.48/ The reasoningis basedon the geometryof rc I network. Givena rectangular grid for an urbanroadnetworkspaced2 kilometersapart, as in Fig. 10(a),there are 9 setsof area. Supposethenumber (space-intensive) intersectionsand trafficlightsin a 6 kilometer-wide of streetsis doubledin order to doubleroad capacity,yieldinga grid of a one kilometer-wide spacing(Fig. 10(b)). Quiteapartfromthe possibleincreaseof constructionor landacquisitions Al/ I am extremelygratefil to WilliamVickreyfor pointingout the subtletiesof theseargumets. See Vickrey(1965,pp. 287-288)andMohring(1976,pp. 144-145)alsofor thebasicline of reasoning. - 40 - costs, the numberof intersections- and the requiredland area and tffic lightinstallationsis quadrupledto 36. (If no taffic lightsare installed,eachintersectionrequiresan evencostlier overpassor perhapsevena fullinterchange,a caseconsideredby Mohring(1976,pp. 144-145).) Moreover,despitethe fact that trip lengthremainsunchangedbetweenthe origin, 0, and the destination,D, the numberof trafficlightsencountered,and hencewaitingcosts, wouldthen doublefrom4 to 8 (unlessoverpassesor interchangesare constructed).Either the installation of traffic lights or the buildingof overpassesand interchangeswould serve to bid up the opportunitycost of land (becauseless non-highwayspacewouldbe left for businessor other activity)as wellas to increasesubstantially the sumtotalof the costsof undertakinga trip to the community,resultingin a risinglong-runaveragecostand also a long-runmarginalcost curve. The resultantlong-runequilibriumfor an urbanroad networkin the presenceof diseconomies of scaleis depictedin Fig. 11. Theanalysisof the rlationshipbetweenlong-and short-runcost curvesis similarto the case of constantreurns to scale and is not repeatedhere. However, becausethe long-runaveragecost curve is rising, the short-runaveragetotal cost curve for a two-laneroad, SRATC 2 , is tangentto the long-runaverage cost curve to the right of the minimumSRATC 2 point. Becausethe SRMC 2 lies above the SRATC 2 , SRMC 2 intersectsthe LRMCfrom below. Short-runmarginalcost pricingis equivalentto long-runmarginalcost pricingat the efficientoutputlevelQ2*. Noticethat the optimaltoll, tV*,followsfrompricing at short-runmarginalcost and tollingthe differencebetweenshort-runmarginalcost and shortrun averagevariablecost. The differencebetweenSRATC 2 and SRAVC 2 is, by definition, SRAFC 2 . The optimaltoll, t2*, cLearlyexceedsthe SRAF4 by the unitprofit of 12*, withthe corresponding rectangulararea of profit wa*Q2*. As the urbanroad networkexpandsfrom an existingsingletwo-laneroad to a doubletwo-laneroad, say, substantiallycostlierconstruction, tunnellingand land acquisitioncosts are encountered.10 We have also establishedthat time costsrise becauseof additionalinterons and wait time required. Eitherof the abovetwo factorswouldserveto pushthe SRAFCand SRAVCcurvesup, togetherwiththeSRATCcurve. Justas thecongestiontollfilledin the wedgecausedby the divergenceof short-runmarginaland 49/ raing finai cost of otuctin via tu ig aNd/orflyover.,togetherwith high land r_smptioncod, ae comdmt withthefindiypof Hau(1989)forHongKog. - 41 - averagevariablecost curves,the divergencebetweenlong-runmarginaland averagetotalcost curves serves as an indicatorof the unit profit (or loss). In competitiveequilibrium,all economicprofitsare competedawayin the long run, so the questionsthat followare: in what senseis the case of diseconomiesof scalea 'long-run'concept,and whatis the interpretation of theprofitareasof r2* Q2* and v4* Q 4 * (fordemandcurvesQ24 and Q, respectively)?The existenceof economicprofitsin the longrun is attributableto the rents earnedby an invaluable fixedfactorof production- land.5Q/ Eventhoughboth the SRAFCand the SRAVCcurves reflectthe increasein costsmentionedabove,the existenceof the risingopportuniycost of the fixedfactorof the remainingparcelsof landis stillleft unaccountedfor. Intuitively,just as the driver,in the short run, by imposingexternalcongestioncost on othersdue to his presenceon the road, is chargedfor it, so also shouldthe urbancommunity,in the long run, chargefor the use of scarce urban land in a marketeconomy. Putting it another way, if all factors of production -- includingland - were doubled, so that a scarcity value could be imputed to land, all economicprofitswouldbe competedaway and vanishin the long run. Clearly,the supply of land cannot be doubled,so it is the existenceof land rents which yields (the areas of) economicprofitsin Fig. 11. Noticethat we couldno longeruse of the existenceof profits as a surrogatemarketsignalbecauseof decreasingreturnsto scale. Sincethe urbanroadnetwork is supposedto generatesubstantialsumsof moneybecauseof highland values, relyingsolely on the profitmechanismand incautiouslyinvestingon urbanroadsuntilaUeconomicprofitsare competedaway wouldresultin over-investment in roadcapacity. With diseconomies of scale and divisibility,roads geneate positiveprofits. Performingproper projectappraisalof roads cannotthereforebe circumvented. C. Diseconomies of Scale andIndivisibilities 57. The case of disoconomiesof scalecombinedwith indivisibilitiesis similarin spiritto the analysisof the constantreturnscase with indivisibilitiesin Fig. 8. For instance,at any IQ/ A puristMh agu ttthes rs actullyacornsto lanonesmd thusual udoly profitsbeg zeo sotill holdsi tb po pn of risnglog-nm aveag costs. of longnmsuper- - 42 - momentin time, the regionsto the right of Qz,, and Qg in Fig. 11 wouldyield profits. In the rise of decreasingreturnsto scale, with or withoutindivisibilities,the correctrecourseis to investonlyif the roadprojectin questionpassesa stringentcost-benefittest and onlyif rising costs of roads are comparedto the quasi-rentsgeneratedL the variable demand periods diurnally. In otherwordsshort-runmarginalcost pricing,or congestiontolling,as opposedto long-runmarginalcost pricing, shouldbe implementedfor eachperiodover the demandcycle and the quasi-rentssummedup, regardlessof whetherthe facilityis optimallybuilt. When demandis not knownwithcertainty,probabilisticor expecteddemandcouldbe usedinsteadand all real benefitsand costs over the economiclife and time periods of a project should be properlymeasured,discountedand comparedwiththe capitalcost of implementingthe change. If finelydivisibleprojectsare available,we have seenthat the procedureis to invest untilthe marginal benefit of a project -- in the form of time savings -- equals the marginal cost of abound,then traditionalpublic investment constructingthe capital facility. If indivisibilities criteriausing the net presentvalue criterionor Mishan's(1988, Chapters35-38)normalized intemalrate of return procedurecouldthen be complementedwith the diagrammaticwelfare analysispresentedin this paper. In sucha case,unfortunately,the neatlinkagebetweenprofits and lossesas a 'market' mechanismand guideto investmentis severed. Thusit is possiblefor a projectwith high net benefitto yiew a financialdeficit. As mentionedbefore, if a road authoritywerefacedwitha severefiscalconstraint,thenthe roadagencycouldchooseto underinvest, rather than over-invest,when faced with an all-or-nothingsituationof indivisibilites. Still,it shouldpursuemarginalcostpricingin the shortrun, whilefully takdnginto accountthe opportunitycost of congestiontoll financing(seeHau (1992)). In this way, short-runmarginal costpricingwouldyield botheconomicefficiencyandprofit,eventhoughan optimalinvestment strategywouldgeneratean even higherlevelof net benefitfor the communityin the long run. D. Economiesof Scaleand Indivisibilites Per contra,the aboveanalysisfor the case of decreasingretums to scaleof an urban 58. road networkcarriesover in reverseto the caseof increasingreturnsto scalefor rural roads. Therethe sumtotalof thequasi-rentscapturedvia short-runmarginalcost pricingis insufficient - 43 - to cover the entire fixed cost of a particularrurl road. Scale economiesabound in the constructionof rural roads, so that unit losses,12*and L4*, resultin the case of an optimized two-laneand four-lanerural road, respectively(see Fig. 12). Standardneoclassicalarguments then call for subsidizationout of the public treasuryfor the case of scale economies. The presenceof bothindivisibilities and scaleeconomies:iuld alter the calculationof optimaltolls and subsidiessubstantially(Kraus(1981b)).It turnsout, perhapssurprisingly,that theexistence of indivisibilities servesto improvethe stateof affairsvis-a-visthe governmentbecause,as was shownin the constantand decreasingreturnsto scalecases withindivisibilities,both surpluses and deficitswouldoccuralternately,dependingon the levelof traveldemand. Similarly,in the case of rural roads with both scale economiesand indivisibilities,there are regions(such as those to the right of QO,, and Q4.1.in Fig. 12) where short-runmarginalcost pricingyields profitsratherthanlosses. Thisis because,withindivisibilities, the long-runmarginalcost curve - composed of joined segmentsof the short-run marginal cost curves -- is no longer declining all the waybutpossessesa sawtoothedpattern,alternatelyexceedingits corresponding long-run (andshort-run)averagetotalcost curvesand risingat an even fasterrate. Thus,just as in the caseof constantreturnswithindivisibilities, whenevera SRMCcurveexceedsa SRATCcurve, profitexistsand vice versa. It is thereforequiteconceivableto havea congestedtwo-laneroad whichgeneratesprofitseven when subjectto increasingreturnsto scalefor sufficientlylarge changesin capacity.Theexistenceof lossesdoesnotmeanthatthe roadagencyshouldcut back on the provisionof highwayservices. On the contrary,it merelymeansthat other sourcesof funds ought to be soughtin order to financea worthyproject. The governmentauthority's decisionto cut back servicesjust becauseof losses in such a situationwould yield underinvestmentand possiblystifleeconomicdevelopmentand growthin the longerrun. The neat linkagebetweenroad expendituresand tollrevenueshas disappeared.Again,the passageof a toughcost-benefitcriterionis thena prerequisitefor a projectto result in maximizingsociety's welfare. To repeat,only(fcongestiontoll financingis all thatis soughtby theroadagency,and not optimnlinvestment,is it possble to let a two-laneroad becomecongestedin the face of risingurbanizationand motorization,whiledifferentially pricingit via congestiontolls. In this way, efficientuse of a given road is enhancedvia short-runmarginalcost pricing, but the efficientlevelof road capacityis not beingachievedin the longrun. - 44 E. The Extentof Indivisibilitiesvs. Divsibilty and Their Effectson Scak Qs)=coomies 59. How often do we encountersurplusesin the presenceof scaleeconomiesand deficits in the presenceof diseconomies?Theanswerdependson the extentof thepresenceor absence of indivisibilities.Thereare two viewson this issue. The fist perspectivea la Keeler,SmaU and Starkiearguesthat the aggregateroad networkcouldbe regardedas divisible. The other view, presentedby Walters (1968, Chapter 3) and Kraus (1981b),contendsthat roads are indivisiblebecausethe main measureof highwaycapacityinvolvesthe discreetnessof the numberof lanes. 60. The constructionof a road or an additionallane may not be finelydivisiblein and of itself, but taking the road networkas a whok, a single newly constructedfacilitycan be regardedas an icremental additionto the network,resultingin theapplicabilityof the foregoig marginalanalysis(Keeler,SmaUandAssociates(1975,Chapter2)). Also,oftentimes,varying somedimensionsof road features,otherthanthe numberof lanes, increasesthe capacityof the road network. For example,the lane width, the provisionof auxiliarylanes, horizontaland verticalalignments,and the surfacingof roadshoulderscan all be variedincrementally(Starkie (1982)). Onecouldcharacterizethis viewby treatingthe lane capacityas a continuousvariable rther than a discreteone (Small,Winstonand Evans (1989, p. 103)).If the road authority pursuesthe twinoptimizingrules of pricingand investmentin capacity,then the roadnetwork wouldbe in long-runequilibrium.So withconstantreturnsand a divisibleroadnetwork,roads wouldbreak even. However,someindividualroads wouldmake moneyand somewould lose money. On the whole,if the economiesand diseconomiasof scaleare "probablyroughly offsetting"as MeyerandG6mez-Ibgflez (1981,pp. 191-192)concluded,thenthehighwaybudget wouldbe balanced. Whetheror not scaleeconomiesand diseconomiesare counter-balancing woulddependon the degreeof urbaniation. Withincreasngurbanizaton,profitswouldtend to predominateeven aftercharginglandrentsas a cost. Withindivisibilities,theprofit (or loss) A/ Consnt or even decreang raturns wouldbe satified if two bi-directionalroadwys ae built in proximityto on another. -45 - regimeoccurs about half the time but it is unclearwhat the relativeweightswould be when traveldemandis reasonablyassumedto growover time. 61. Underdecreasingreturnsandperfectdivisibility,we haveshownin Fig. 11 thatprofits alwaysoccur. The essenceof that figureis combinedwithFigs. 13(a)through13(c). Perfect (Fig. 11)and almostperfectdivisibility(Fig. 13(a))andan urbanroadnetworkwouldmeanthat the marginalcost priing of tripswouldalwaysbe profitable. Note that the continuousregime of profit will not be uniformonce a thresholdlevel of indivisibilitiesis reached, resultingin regionswhere losses also occur. If the extent of indivisibilitiesprogressesfrom small but significant(Fig. 13(b))to severe(Fig. 13(c)),the regionswhichyieldpotentiallossesbecome even larger. The symmetrycaries over to the increasingreturns to scale case. Again, the substanceof Fig. 12 is culledandcombinedwithFigs. 14(a)through14(c). Withperfect(Fig. 12)and almostperfectdivisibility(Fig. 14(a))in thepresenceof scaleeconomies,losseswould alwaysoccur. With scale economiesand a 'significant'level of indivisibilities(Fig. 14(b)), smallerregionsof profit wouldbecomeavailablebut woulddisappearwhen approachingthe neighborhood of thelimit(Fig. 14(a)).Nevertheless,evenif one wereto acceptWalters'(1968, Chapter6) argumentthatthereare sgnificantindivisibilities and scaleeconomiesin ruralroads, we have demonstratedthat profits (and losses, of course) would neverthelessarse under congestiontolling. Scaleeconomiesin thepresenceof indivisibilitiesand financialviabilityare notnecessarilyincompatible. F. Empirica Evidenceon the ScaleEconomyIssue 62. Fitchand Associates(1964,p. 131)givesome numericalsupportfor the case of scale diseconomies in the UnitedStates. Walters(1968,pp. 184-185),usingMeyer,Kainand Wohl's (1965,p. 205)data, showsthatthereare diseconomies of scalein the constructionof four-lane, six-laneandeight-laneurba roadsegments.(ByemployingWalters'straightforward approach, Hau (1989)demonstratesthat thereare increasingcostsassocatedwitha sampleof four-lane, five-laneand six-laneroadsin Hong Kong.) Withoutimposingany prior specificationsabout the extentof return to scale - Keelerand Small(1977)find evidenceof constantreturns to - 46 - scalefor a sampleof San FranciscoBay Area roads. Their often cited econometricstudy is importantbecauseof the balancebudgetimplicationfor congestionpricing,a result whichwas also quotedby Newbery(1990).F' By contrast,usingengineeringspecificationsto estimate eachof thecost componentsof an urbanhighwaynetworkmodel,Kraus(1981a)findsthat there are increasingreturns to scale in road constructionin terms of length of freeway and interchangesbut not for overpassesand lengthof arterials. He makesthe crucialobservation that factor prices (such as right-of-wayprices) are to be held constantfor makingrelevant comparisonsof scale- specific(dis)economies.The reciprocalof his best "pseudo-empirical" estimateof returnsto scalein urbanhighwaynetworkcapitalcostsis 0.84, whichtranslatesto the economiesof scale degree of 1.19. Meyer and Gomez-lbgilez (1981, pp. 191-192),in assessingthe availableestimatesin the conflictingliterature,concludethat economiesand diseconomiesof scaleare "probablyroughlyoffsetting." Hayutin(1984),in an unpublished dissertation,refined the Keeler-Smallmodel and applied it to a sampleof U.S. Interstate Highways.By includingbothintercity(or rural)and urbanroutesin her data set, sheestimates that there are clearlyincreasingreturs with respectto the numberof lanes. Her x,aultsbear out Mohring'sscaleeconomyimplicationsof highwaygeometrywith respectto the "shoulder 5I Keelerand Small's(1977)resultis one of the morerigorouseconometricanalysesbearingon the scale economyissue, iDthat theyare ableto separatethe confoundingeffectsof sizeand urbanization.In particular,theyregressedconstuctioncost per lane-mileon the numberof lanesand variousdiscrete variableswhichcapturethe dfes betweenurban, suburbanand rural-suburbanareas. It is the inclusionof thelattervariableswhichenablethemto ecomometrically controlfortheeffectsofexpressway capacityon construction cost. Theselectedsampleof 57 roadswasbasedon all state-miainnedroads for nine San FranciscoBay Area counbes,includingarterials,expresswaysand rural roads. They estimatedboth a non-linearand log-linearspecification,with both yieldingstatisticallyinsigificant stastics for the esfimaeddegreeof homogeneity.Basedon the slightlybetter fit for the log-linear specification,the rturms to scale parmeter of (-)0.0305translatesitself into the cae of ^mildlyincreasingrtuns to scaleof 1 - 0.0305= 0.9695. By taing the reciprocalof theestimaedretwnsto scale puamete, the economiesof scde degreeof 1.0315is obtained. Since 1.03 is staiscally indiinpuisable^ fiom 1, theyconcludethat there is no firm evidencefor scaleeconomiesin road conruction masuredin termsof lanes. Thefr-reachingpolicyramifications of thisresultcouldperbaps be buttesd if therewere calculationsor discussionof the powerof their hypothesistests. This is becausenot beingable to trect a null hypothesisis not necessarilyequivalentto acceptingthe null hypothesis.Onehopesthat the typoII error is relativelysmall. However,to be fairto their important contribution,the powerfunctionfor publishd papersare seldomto be foundin the literaue. -47 effect" More recently, in reassessing the earlier work of Keeler and Small (1977), Small, Wimstonand Evans (1989, Chapter 6) use the result of zero economies (corresponding to the scale economyparameter of 1.00) as well as the mildly increasing returns case of 0.97 (correspondingto the scale economy parameter of 1.03) (see Small (1992, Chapter 3) for a review also). Fully cognizant of the possibilityof the existence of increasing returns to scale in urban highwaytravel a la Kraus, they presented their simulationresults on highway finance based on three encompassingparameters for the degree of scale economy: namely 1.00, 1.03 and 1.19. G. Recent Results on Cost Recovery 63. As part of a major World Bank research project, Newbery (1988abc, 1989, 1990) and Newbery, Hughes, Paterson and Bennathan (1988) extend Mohring's now classic result of highwayfinance by relaxing the assumptionof an infinitelydurablehighwaywhosecapacity can be continuouslyadjusted. It is common knowledgethat pavementswear out after extended use, but it is less well known that the damage of a vehicle on the road pavement is related to the weightper axle, as opposed to the gross vehicle weight per se. Common Practice (Highway ResearchBoard (1962))is to measurethis damagingpower by the numberof equivalentstandard axle loads (ESAL), where one ESAL is equivalentto the load of 18,300 lbs. (8.2 tons or 80 kilo newtons)singleaxle. The AmericanAssociationof State %ighwayand TransportationOfficials' milestoneroad test indicates that the damagingpower ot a vehicle on pavement is proportional 53/ Hayutin(1984,Chapter4) regressedconstuctioninvestmentper mileol the numberof lanesand other variablessimila to thoseused by Keer and Small(1977) (seepreviousfootnote). Further, by including the paved width per lane variable aeoconomies to width measuredin feet. rather than in lanes, result. Hayutin(1984, ChapterS) conludes that the strongereffectof scaPleconomieswith respectto the number of lanes dominates the effect of dmiecomies associatedwith buildingwider footage. In an excellent review of the litentue surroundingthe scale economyiasue, Hayutin(1984, pp. 158-159)observesthat Meyer, Kain and Wohl's (1965, pp. 200-214)conclusion that there are increasing returns to scale in feeway constuction stems fom thdir engeing assumptions about costs, as opposed to actaul estimation. Her stistical results, however, ae surive of their conclusions. My commentregarding the power of the hypotbesistests applies to her study also. - 48 to the fourth power of individual axle loads, acquiring the title of the "fourth-powerlaw. For instance, the rear axle of a 13-tonlight truck with two axles can result in over 300 to 2400 times more pavement damage than that of a large car weighing 2 tons.0 One inescapable conclusion is that almost aU damage is caused by heavy vehicles such as trucks and buses: relatively little is due to automobiles. Recently, Newbery (1988a) characterized another type of externality caled a road damage externality: the emenoal damages imposed upon the pavement by heavy vehicles result in increased vehicle operatingcosts to subsequentmotorsts for the rest of the periodic life cycle of a road. (Thus, the various costs of undertakinga trip mentionedin the introduction of this paper (footnote3) should now be more narrowly defined as eermal costs, namely: 1) marginal exteral congestioncost; 2) road wear cost and damage exteralities (grouped under the rubric of road damage cost); 3) environmentalcosts; and 4) costs due to increased risk of accidents not borne by private parties.),W /AI Formally,thedamagig power(in EASLe)of an axleload,1,in tons,is approximately equalto: (U8.2y), hece we say tht the damagingpoweris proportionalto the fourth powerof the axle load. As a hypotheicaleample, a 24 tontruckwhoseweightis distributedevenlyamong2 axleswouldcausemore than3 timesas muchdamageas thes truckwhoseweightis distributedevenlyamong3 axles:(2/3) -(12V8)'= 3.37S. S/ Mheexampleassumesthatmoreof thoweight-8 tns - is distributedon the rearaxleof thelighttbuck whers a fily loadedautomobile has its weightuniformlydistrbutedamongthe twoaxles. Smalland yag (1988)and Small,WinstonandEvans(1989,Chapter2 Appendix)have recentlydsput the fourth-pwe law and perfimd a statisticaanalysisof AASHO'sroad test data to show that the equivalence factorfor anaxleloadrisessteeplyto dtethirdpower,therebyproposiAg a Zthird-power law instead. Whetherthepowertermis actually3, 3.5 or 4 (asrespectivelyclaimedby Small,Pateron, or engineersconventionally)is not as crucialas the significantmantenanc costsavingsto be made if vehicle damageis efficientlychargedfor. Conceivably, an increasein thepowertermwouldenlargethe small deficittht Small,WinstonandEvansobtainedbychargingforcongesionandroaddamagecosts. I argue tht the chargi of aUextraities includingenvirmentl and acciet costswouldvery likelyclose any rmining ap. 6/ Basedaonempiricalovidenc for the whole oad networkof Tuna, Nwboery,Hughes,Patersonand Beanathan(1988,Table7, 23 andpp.58-59)andNewbery(198&,Table1) deamnstrutthattheextenal urbancogesion costsalon accountfortho 'ovewhelmng fiaciaon(aboutnin4enths or more)of total extenal coss of roaduse (excludig environmea and accdet cost) for autmobilesand ulities. For heavyvehicles,the reverseappear to applyin both Tuniia and Ghana,with road damagecosts doin_ating instead (8e Gronau (1991) also). (Heggie and Fan (1991, Annex 1) argue that some of Newbory'scalcuaos of congestioncostsfor TunisiaarMovertdmates.) Cog restion costsconstitut a argo shae of totalroadcostsfor boththe UnitedKingdom(nine-tens) andthe UnitedStates(one-filfh) in the klon run, whlera road damagecosts a about 3 to 3.5% in the United Kingdomand only 2% in the UnitedStates(Neowbory (1988a),Small,Winstonand Evans(1989),Chapter6). Pollutioncosts - 49 - 64. Newbery's(1988a)"FundamentalTheoremof RoadUser Charges' saysthat if. 1) the maintenancepolicy pursued by a highway authority is condition-responsive,i.e., road maintenanceis carriedout whenevera road'spre-determined roughnesslevelis reached,without being optimaUyset (Paterson(1987));2) the age distributionof roads over the life cycle is uniformlydistributed;3) thereis no trafficgrowth,i.e., trafficflowis constantover time;and 4) all road damageis causedsolelyby vehicles,dten the externalroad damagecost is nil on average (Newbery (1988a), Proposition1). The variable road maintenanceuser charge component,appliedon a per ESALbasis, wiUfullycover the averagecost of repair (Newbery (1988a),Proposition2). Whenvieweddiagrammatically, this resultis analogousto charging for maintenancecost in anotherdimension,as opposedto chargingsolely for the congestive effectof automobileson a per passengercar equivalent(PCE)basis in Fig. 3. Intuitively,the damagingforce of an additionalESALhas the externaleffectof raisingthe vehicleoperatng costsof subsequentvehiclesovertime,just as the externalcongestiveeffectof an additionalcar has on other vehiclesbehind it withina traffic stream. in addition,the indirectimpactof accumulatingmore ESALsis to reach the preset, maximumallowableroughnesslevel of the road earlierthan expected,therebyprecipitatngan overlayand a correspondingloweringof vehicleoperatingcosts. It is uncleara priorlwhichof thesetwo magnitudesdominate.Hence Newbery's(1988a,1989)breakthroughwas to prove, in a varietyof ways, that the additional vehicleoeaing costsattibuted to road damageexnalities just cancelout with the vehicle operatingcost savingswhenaveragingoverroads of differentvintages. 65. In the generalcase, the fundamentaltheoremrelaxesAssumption4) aboveby allowing for roaddamagesthatare independentof use, suchas weather-related deterioration.In thiscase of a condition-responsive maintenance policy,the roaddamageexternalityis no longerzerobut is quantitativelynegligible. While the use-relatedpart of maintenancecosts is chargeable becauseof the road damagecost, the fracdondue to weatheris not allocable. Hence the presenceof weather-related roaddamageresultsin onlypartal recoveryof all maintenance costs appear to account for less tdan o _enhof total road cost in the United State, wheres accident costs ae an te sam=order as extera conWestion coss for the United Kindom. (Newbery(1988b, 1990)). - so - when only charging by road damage costs. Therefore, in order to close the highway budget deficit, Newbery (1989) needs to price for the marginal external congestion cost within a standard long run framework (see Newbery (1988b) also). That is, under the conditions of constantreturns to scale and road use, the efficientcongestiontoll will yield revenues that cover the capital cost of the highway but only the invariant (or non-allocable) portion of road maintenance cost attributable to weather, see Fig.5 for definition of short-run fixed cost (Newbery (1989), Proposition 1). (FollowingMohring (1965), we have seen how this is done in our simple investment rule of comparing optimal toll revenues with fixed costs, be they constructionor maintenancecosts, see Fig. 5 and the surroundingtext.) It then naturally follows that the optimalroad user charge, i.e., the optimalcongestiontoll-cum-roaddamage charge, will then yield revenues that cover the capital cost of the road and the total road maintenancecost in a constant returns world (Newbery (1989), Proposition 2). In other words, the optimal congestion toll covers both the capital cost of the road and the non-allocablefraction of road maintenance, whereas the allocable fraction of road maintenanceis still chargeable to traffic loadings via the average variable road maintenancecost componentper ESAL. This explains why the total expenditureon road maintenanceis fully recoverable. Ifthe same constantreturns conditions and assumptions 1) through 4) again apply, and if we firther accept that 5) heavy vehicles predominantly use the slow lanes and are confined there, then the optimal road user charge will recover the capital cost of the highwayand twice the total maintenancecosts of the road (Newbery (1989), Proposition3). If all heavy vehicles are confinedto the slow lane, then the damage costs are accumulatedin a shorter time span than if they were to be spread out evenly over all lanes. This has the effect of raising the maintenancecost of the slow lane and the effective cost of widening the whole road, since all lanes are typically resurfaced together once the performance service index of the road dips below the trigger point. Cost-benefit analysis of lane expansionto reap time savings suggests that the marginal cost of investmentin capacity would now have to account for both the increased road maintenancecost for road strengthening and the annuitized capital cost on a PCE basis. Tis is a slightly modified version of our earlier optimalinvestmentrule.) Moreover, heavy vehicles are charged for the traffic loadinigsthey create. While stronger roads are cheaper to maintain, investmentin road strengtheningis costly, resulting in costlier upkeep and higher capital cost. The larger fixed - 51 - costs translatethemselves,in the long run, into a requirementfor highercongestioncharges, which heal contributeto an overallbudgetsurplusfor the road authority,despite"massive" (Newbery(1989)).Anotherwayof lookingat thisresult increasingreturnsto roadstrengthening is thatthe congestiontolleffectivelycoversthe road's entirecapitalcost as before, whereasthe maintenancecost is recoveredtwice -- once via the variableroad maintenanceuser charge componentappliedon a PCE basis and the secondtimearoundvia heavyvehiclesper ESAL. Themostseriousdrawbackin the propositionsaboveis the conditionof constantreturns 66. to scale.S7/ We have reviewedthe empiricalevidenceand find that there are increasingas wellas decreasingreturnsto scaleoperatingon differentpartsof theroadnetwork,meaningthat deficitsas well as surpluseswouldmostlikelyco-exist. 5O Mariabili of RoadThickness We are now in a positionto formallyrelax the implicitlyused assumptionof a given road thicknessand to incorporatethe latest work into our model. In Road Work: A New HighwayPricing and InvestmentPolicy, Small, Winston and Evans recently provided a 67. expositionof theirtechnicalextensionof Mohringand Harwitz'slong-runresult comprehensive on highway economicswith optimal durability, within a standard neoclassicalwelfare maximizationframework.a/ Insteadof takingcurrent highwaydesignstandardsas given, 57/ mainnteacestrategyas the Newbey (1988a)regardsthe lackof the pursuitof a condition-responsive and Small's (1977)resultof constnt Neowbey (1989) cites Keeler serious limitadon. Further, most Bay Area roads. Newbery (1990)alsocites a sample of San Francisco to scale, which is based on reuns cicsing retuss lightly demonstates when Kraus reatuns constant Kraus(1981a)asevidencesuwporting (seeprevioussection).Basedon an earlierversionof Newbery(1989),Heggieand Fon(1991)takeissue with manyof Newbery'sassumptions. 58 Newbery(1989),for example,derivesopimal durability(or strenglh,rather)and confinesthe extentof his analysispricipally to the contant reus to scaleworld. By coDtra, Small,Winstonand Evans (1989,Chapter6) explicitlyexplorethe caseof incrasing retuns to scaleof road consruction,as well analysis andarteial - withsensitivity as durability,andpreet simulationreslts of anurbanexpressway problemyield of theiroptimization - witdina long-rn equilibum famewor Ihe firstorderconditions the optimalpricing,investmentanddurabilityrles. - 52 another characteristic of a road -- its thickness - can be varied. A thicker pavement would serve to withstandthe damagingpowerof trucksmoreand therebyprolongthe life of a road. Despite the fact that there are tremendouseconomiesassocated with road durability,the additionalstrengtheningof the road wouldstill substantiallyincreasethe totalinvestmentcost of an overlay. Usingthe standardoptimizationtechniqueof consumer'ssurplusand producer's surplusmaximization,the intuitionof the threeallocationrules derivedare againbasedon the simplenotionof settingmarginalbenefitequalsto marginalcost. Thatis: 1) Thefirst rde - the optimalpricing rie - says that the traveller shouldundertake a trip only up to thepointwherethe incrementalbenefitjust offsetstheincrementalcost to the community. A vehicle'sentry into a transportcorridorresultsin two effects: the congestiveeffectwhich dependson the numberof PCEs,and thedamagingeffectbasedon the numberof ESALs. Thus our optimalpricingrule derivedearlier is adjustedto includean extra component- a road damagecharge- whichbalancesout any short-fall. 2) Thesecond rude- the optimal capacity rde - says that, with a condition-responsive maintenancestrategybuilt in, optimalinvestmentfor highwaycapacityis then to expandthe widthof the roadup to the point wherethe marginalcost of capacityplus maintenancecost is equivalentto the resultanttime savings. 3) Thethirdrile - die optmal durability rie - says thatthe road is optimallystrengthenedby investingup to the pointwherethe marginalcost of durabilityjust equalsthe savingsin vehicle operatingcosts to other motoristsplw the associatedsavingsin maintenancecosts due to a thickerpavement. The two latter rules could be regardedas an investmentrule extendedinto two different dimensions. Thus the three rules of optimalpricing,opimal capacityand optimaldurability yield efficientpricesand trips, as well as the optimalnumberof lanesand inchesof pavement thickness. 68. Thereis evidencethatthere existeconomiesassodatedwithroad strengthening(Small, WinstonandEvans(1989,Chapters2-3),Winston(1991)). By reanalyzingAASHO'sroadtest data withinan economicoptimizationfrmwork, Smalland Winstonreport that the opimal thicknessfor a rigid pavementis an inch and a half higherthan the currentten inch standard, -53 whichfollowsAASHO'sguidelines.Theremarkablefindingis thata mereincreasein thickness of 15% wouldlead to a doublingof pavementlife from 13 to 26 years (Smalland Winston (1986, 1988), SmaUand Zhang (1988). The logical implicationof massiveeconomiesto increasingroad thickness - a fact long known to highway engineers - is losses for the road authority. We thereforeask: is therea theoreticalreasonthat wouldallowus to still adhereto the impeccablemarginalcost pricingprincipleand yet achievethe goal of cost recovery? To answerthis questionwe turn to the notionof diseconomiesof scope. Economiesof Scopevs. Diseconomies of SMcpe 69. Theconditionof constant,increasingor decreasingreturnsto scaleyieldsthe respective resultof breakeven,lossor profit,respectively(see sectionXIV- 4 and Fig. 9). Tbeempirical findingsof returns to scale evaluatedearlier suggestthat decreasingreturns to scale in road constructionin urbanareasmayperhapsoffsetthe increasingreturnsto scalein rual areas, but that the highwaybudgetmay stiUbe in deficitdue to economiesof road strengthening.The answercan only be establishedusingeconometricanalysis. Even if we were to acceptKeeler and Small's(1977)carel findingof constantreturns, wouldit not seemplausibleto arguethat the pavementdeficitdue to significanteconomiesto roaddurbility necessarilyyieldan overall deficitfor the road authority? Theansweris no. 70. Up til now, we have confinedourselvesto the singleproductworldof trafficvolume. But road transportinvolvestwo products: namelytrafficvolumeand loadings,whichcarries us into the literatureof multiproductindustriesand returns (Baileyand Friedlaender(1982)). Theissue is whethera multproductfirm canjoindy manufacturethe variousproductscheaper thanif eachfirm were to producean outputseparately. If it is cheaperto combineoperaions and share in thejoint costs, thereare economiesof scope. The notionof diseconomiesof scope can best be grsped by ilusating the designof a railwaytrack(Kim(1987)). A railroadtrack that is built to withstandthe axle loadingsof freightwouldneedgreaterstrengthand thickness, whichconflictwith the requirementof securinga smoothride for trainpassengers. Ensuring both thicknessand smoothnessof tracksis morecostly,resultingin diseconomies of scope. The - 54 - analogycanriesover to roads, whereit wouldcost more to producea highwaythat is thick enoughto handleheavyvehiclesand yet wideenoughto accommodatethe considerablylarger numberof automobiles.Thus thereare no economiesof scopeeven thoughoneproduct-- the numberof loadings-- is clearlysubjectto increasingreturnsto durability,whereasthe other product - the traffic volume -- is potentiallysubjectto increasing returns to scale due to road construction. In other words, it is the other characteristic of production -- the scope -- that wouldtip the budgetbalanceaway from a deficit(Small,Winstonand Evans (1989),Chapter 6). 71. Automobilescausevirtuallyno roaddamagescomparedwithheavyvehiclesbut trucks are fewer in numberand therefore cause lesser amountof congestion. Hence one could separate, roughly speaking,traffic flow from loadingsby identifyingautomobileswith the formerand truckswiththe latter. Trafficflow,in tum, requiresroad capacitywhereasloadings requireroad strengthening.Theempiricalfindingof "modestbut significant"diseconomiesof scopeby Small, Winstonand Evans (1989, Chapter6) of about 6 to 10% tips the productspecificeconomiesof scale closer to one - the constantreturns case. (The multi-product economiesof scalerangefrom 1.00 to 1.06.) Their bottomline simulationresultsof an urban expresswayand arterialand sensitivityanalysisdemonstratesthat a budgetbalanceand hence cost recoveryare achievable. The shortfallof a few percentof total road costs can still be recoveredby maintainingsomelevelof first registrationfees,annuallicensesand/orfueltaxes. Finally, since all externalitiesought to be internalizedin principle,air, noise pollutionand accidentcosts shouldalso be appropriatelychargedfor (Carbajo(1990)and Cameron(1991)). In this way, the highwaybudgetwouldmostlikelymakea profit (see footnote56). 72. The basicintuitionbehindthis remarkableresultis as follows: becausemostroadsare currentlybuilt to accommodateboth automobilesand heavy vehicles, a neat dichotomyof allocatingpavementwear costs betweenautomobilesand truckscannotbe achieved. Thus 1) the marginalcostpricingof trafficflowrequiresa congestioncharge- whicheffectivelycovers the capitalcost of investmentin the long run - and 2) the marginalcost pricingof pavement wear - associated with the investmentcost of strengtheningthe road -- results in a relatively -S5 steeproad damagecharge. The marginalcost-basedroad user chargescombineto yield the double-chargingof roads, depictingdiseconomiesof scope.nj One logical implicationof the diseconomiesof scopeargumentis that savingscould be reapedfrom buildinga thinner autos-onlyroad system(thesavingsof whichare estimatedto be on the order of 23%by Keeler and Small(1977)). With a universalroad system,roads shouldthen be built or resurfaced durablyon the slow lane only and heavy vehiclesshould be confinedto that lane. (This experimentis beingcarriedout in Californiaand Florida(Small,Winstonand Evans(1989,p. 15)). S9/ Ibe theorecal findingof tho double- ng of roadsis dso deived by Nevwery(1989)for the cae of consantreturnsto scaleandroaduse. However,he neithercitesnor employsspexficailytheconcept of multiproductrtums in his wor - 56 - XV. SUMRY ANDCONCLUSIONS 73. One of the earliestcontributionsto the economicanalysisof road pricingwas from a French engineer,Jules Dupuit (1844). He was the one (and not Alfred Marshall)who introducedthe conceptof consumer'ssurplus-- the comerstoneof the welfareanalysisof any publicproject- and broughtit to bear on the subjectof tollroads. It is a similartack that this paper has taken, in the beliefthat a picturewouldperhapsspeaka thousandwords. I have synthesizedthe dominantthinkingto date on the topicof road pricingby the mainprotagonists and integratedtheminto a consolidated,analyticalframework. 74. Accordingto my analysis of the traditionalroad pricing arguments,it is hardly surprisingthat road pricingas advancedin the past encounteredits share of difficulties. This is becausethe congestiontoll has the effectof a tax (increa) on trip-makers,despitethe fact that it is an externality-corrective tax. The gist of the argumentis as follows: people are againstcongestionpricingbecause: 1) those whoare tolledwouldfacea higherprice relative to a no tax situationon average;§/ 2) those who are priced off the road in order to circumventpayingthe tollare clearlyworseoff as a resultof the 'forced' switchontoa different modeor time of day; and 3) the other road userswho are not tolled-the tolledon - are no betteroff and, indeed,mayevenbe worseoffif congestionis encountered.My appliedwelfre analysisactuallytakesinto accountthe increasein revenueto the governmentand the issueof transferpayment. If eachof the partes is separatedout as: 1) the tolled, 2) the tolledoff, 3) the tolledon, and 4) the government,the groupthat standsto gain the mostis the govemment (andthe untolled- the rest of society),unlessthe tollrevenuesare earmarked. The otherparty thatis primarilybetteroff are thosewithveryhighvaluesof time. Onlyin the hypercongestion case couldaU groupsbe madebetteroff on average. 6Q0 Considora mro alisic siuatiaonwhr theexitence of a uifom fiel tax offtively tdsates ibslf ino a tip pricetat is higher(buotno a high a th peak-perodpnice),and exactlytho sam analysis follows. -57 75. It has been argued that the dispositionof the revenuesof externalitycorrective(toll-) taxes should accrue to the public treasury (Baumol and Oates (1988), p. 29)AY' Conventionalcost-benefitanalysistreatsa dollaras a dollarto whomsoeverit accrues,and also implicitlyassumesthat only consumersderivesatisfactionfrom revenues. Hence, unlesstoll re;'enuesare channeledback throughreduced transportationrelated taxes, user charges or improvedpublicservices,neitherthe tollednor the tolledoff wouldendorseroadpricing. 76. In this paper,I havealso shownstep-by-stephowto implementshort-runmarginalcost pricing in transportfollowingWalters and others. In particular, I have establishedthat implementing the optJmalpricing rule -- the first rule - is equivalentto settingan optimalroad user charge,where: 1) a congestiontoll on the differencebetweenthe marginalcost and the averagevariablecost of a trip is imposed,and 2) the maintenancecost of road use is also charged. Further,I haveshownthatthe processof determiningan optimallypricedandinvested road systemis similar,albeitwitha coupleof importantdifferences,to theprocessof achieving long-runequilibriumof a typicalproductwithina competitiveenvironment,inspiredby the basic Mohring-Harwitzmodel. The issue of short-runvis-a-vislong-runmarginalcost pricing is clarifiedinteralia. For instance,implementingshort-runmarginalcost pricingis equivalentto pursuinglong-nmmarginalcost pricingin a steady-stateworldin the long run. However,only short-runmarginalcost pricingwould be able to capture the peak/off-peaknature of travel demand. In the absenceof scaleeconomies,the optimal capacityrude- the secondrule- says that the existenceof economicprofit, i.e., toll revenuecollectionless the fixed and non-userelatedcostsof a road, wouldserve as a surrogatemarketmechanismindicatingthat the road oughtto be expanded. Puttingit anotherway, the investmentrule says that a road oughtto be expandedto the point wherethe additionalcost of investmentin capacityequalsthe additional savingsin traveltime. In the long run, toil revenueswouldcover the intereston the capital investment,invariatemaintenance,depeciation and operatingcosts of the road. Maximizing society'swelfaredictatesthat one shouldimplementshort-runmargnal cost pricingover the .J/ Thisis beas a Pigouvin taxis onewhichimposea positivepriceon a producerof an externalityand a zro pice on a consum_rof X exterality. - 58 long run by varyingthe sizeof the highwaycapitalstock. In this way, the pursuitof efficient pricingand a self-financing road systemwouldbe compatiblewithone anotherand no residual costneed be covered. In one stroke,the samecongestiontollingmechanismsolvesthe pricingcum-investment problem,satisfyingthe conceptualguidelinesof efficiencypricing, economic and financialviabilityas set out in the introductorysectionof this paper. 77. Relaxingand flushingout majorassumptionsindicatethat the result derivedhere is robust and applicableto: 1) a multiplicityof roads, 2) a road which is subjectto diurnal variationof demandand the peak-loadproblem,and 3) differencesin valuesof time. If constant returnsto scalecan be shownto hold on averagefor a particularcity with severecongestion, it couldpotentiallyaid in greatlysimplifyingthe planningof highwayinvestment.It couldalso be usedas a yardstick,againstwhichscaleeconomiesor diseconomiescouldbe measured. 78. Economicefficiencywouldbe enhancedif marginalcostpricingof a trip were donein the short run and optimalinvestmentin capacitywere pursuedover the long run. I have establishedthat, if governmentalauthoritieswere to charge correctlyfor congestion,it is possiblefor themto make moneyon a road whilesatisfyingeconomicefficiency. Profitable roads arise in heavilyutilizedor urbanareas becauseland rents of real estate are high and congestiontolls reflectthe risingopportunitycosts. Yet, it is possiblethat congestionpricing in the presenceof bothindivisibilities and diseconomies of scalein urbanroadsmay curtailthe extentof profitableundertakings.Similarly,pursuingmarginalcostpricingunderthe restrictive conditionsof both indivisibilities and scaleeconomiesof rural roadscouldalso resultin profits in the short run. Thus far the pointsI have madeare basedon first principles. 79. In the longrun, the simplepricingand investmentmodelimpliesthat the marginalcost pricingof trips coversall the fixedcostsof the roadand the congestiontoll (whichcapturesthe quasi-rent)behavesas if it is a capitalcharge. This analysisalso mea that an optimally investedroad systemis in fact one wherea road shouldnot alwaysbe uncongestedduring the peak period. An optimallycongestedroad is akin to the commonlyacceptednotionof an optimalpollutionlevel in the field of environmentalexternalities. An uncongestedroad for - 59 - every time period of the day would suggest that that road is over-invested,either because of indivisibilities or nonmarginal cost pricing. If a road is indeed overbuilt, abandoning or downsizingit in the long run may be unavoidableon narrow cost-benefit criteria. The act of downgradinglightly used roads in order to save on the costs of maintaininghigher standardsof road pavement is a form of disinvested.u/ Alas, given that almost all existing road systems are non-optimallydesigned and that costs are considered sunk in the short run, the efficient usage of such a network would still call for marginal cost tolls. Any increase above the road user charge should then be regarded as a 'pure tax element' or surcharge, whose contribution to general revenues should perhaps be made on either fiscal or non-economicgrounds. 80. One may ask: startingoff with an overbuilt road system, say, is there a way in which road pricing based on the marginal cost concept can be implementedwithin an institutional context where severe fiscal constraints on public expendituresprevail? To answer this question requires that we go beyond first principles. 81. Recentextensionsa la Newbery-Small-Winston have enrichedthe basic modeldeveloped diagrammaticallyhere by incorporating the fact that heavy vehicles are the cause of road damage. Charging for both the external and variable cost of road damage on a vehicle weight per axle basis would help close the deficit that may arise from congestion tolling. Further, a road needs to be strengthenedto the point where the additionalcost of investingin durabilityjust balances out the incrementalsavings from maintenanceand vehicle operating costs. Thus the third rule - the optimal durability rule - is born. As a natural extension of pricing for externalities,air, noise pollution and accidentcosts ought to be charged for. Surely in this way the highway budget would more likely involve profits than losses if the issue of cost recovery of the sector cannot be ignored. 621 The commonpractceof downgradng roadsis constent with the findngs of road detenorationin developingcountries (Hal andFaiz (1988,p.32)). -6082. Givenpointestimates(or preferably,functionalspecifications) of speed-flows,demands and the value of time, one can estimateand simulatesome of the analyticalresults developed here. Whencombinedwith the associatedoptimalpricingand investmentrules, the efficient l-vel of prices, user charges, speed,volume-pacity ratios, and trips, as well as the optimal numberof lanesand inchesof pavementthicknessescan be obtained. 83. The factthat in the transportcontext,the consumer-producer is botha willing'victim' as well as a 'beneficiary'has policy implications. As 'victims' of congestionexternalities, perhapstravellersoughtto be compensated.Note, however,that Pigouviantoll-taxrevenues are not supposedto be usedto compensate'victims'of extmalities (Baumoland Oates(1988), p. 23). Also, intuitively,motoristswouldbe inducedto drive more becausethe level of compensatorypaymentswould dependon their car usage, so economicefficiencywouldbe violated.In thiscontext,a roadfundwouldbe consistentwithfirst-bestpricingonlyif the funds were usedin an indirectmanner. Travellersare also 'beneficiaries'of road transportby virtue of theirbeingpresenton congestedroads,and theircontributionsto the toll revenuecomponent of 'user charges' reveal their willingnessto pay. In the absenceof lump sum transfers, earmarkingof tollrevenuescouldserveas a usefuldevicein principleto approximatingbenefit axation as a way of satisfyinga commonlyacceptednotionof 'fairness.' Similarly,heavy vehiclesoughtto incurtheir'fair' shareof hety pavementwearfees. Combiningtheseplausible argumentsand our earlierresults of optimalpricingand investmentprinciples,suggeststhat some form of dedicatedfundsis perhapsnecessary- eitherin the form of a road fund or a transportfund- if road pricingis to gain politicalacceptance.w/ 63/ Recet developments in electonic toil collectionand electrnic road picing in Norway,Swedenand Cabridge, (England)pointto the fct thattraveller do not objectto roadpricingwhenthe toilrevemu ar earmakedtor bothroadconstruction andi1provementandor theprovisionof betterpublictnort (Withoptimaltolling,however,highpurchasetaxe and rgsation/licens feesof vehiclesoughtto be reducedto a levelsufficientto coverthe administraveandenforcmet coatsof colection. If the road maintenancct is constmt with reapec to the trffic level,a sppopriat fue tx could perhapsbe usd to aoximate uwe.) Inded, a recentnatonal m8uveyconductedin Englandidicates thit whenpeoplewere asked whetherthey an for or againstroadpricing,about57%sr aainst iL However,whenthe questionwasposedin a differentway: wouldtheybe supportiveof apac*ageapproachto roadpricing,withtherevenuesfrom roadpricingusedonly to fimmcepublictranpoit, 57%of thesamesurveyedpopulationwerein favor - 61 A. The Role of a RoadFund 84. If a road fund were to be set up,compensaion wouldneed to be made sufficiently indirectto satisfyParetoefficiency. Thus the fundsfor road constructionshouldbe usedboth to maintainexistingroadsand to financenewroads,and theprofitsgeneratedfrom urbanroads couldbe used to financethe fixedcapitalcost of worthwhilerural roads in a nondistortionary manner.o To what extentcan the profits collectedfromheavilyusedroads offsetthe losses arisingfrom the constructionof lightlyusedroads? The answerdependson the extent of the interacdonof bothscaleeconomiesand indivisibilities and shouldbe examinedon a countryby countryand case by case basisusingeconometricanalysis. 85. A road fund is attive becauseof the high marginalcost of raising a tax dollar. Moreover,a road fund run by an autonomousauthontywouldincreasethe linkagebetween revenuesand expenditures,currentlylacldngin a politically-based budgetingprocess, thereby improvingmanagerialefificiency.Withoutthe settingup of sucha fund,however,deficitsfrom lightlyusedrural roads (withincreasingreuns to scale)woulddemandsubsidizationfrom the of od pricing rdtr twn against it (Jon (1991), Goodwin (1989)). (May and Gardner's (1990) imulation results also confinm th cas for an integted approach to road pricing, and buttre the alyticalresut preseted he.) Using an eqiirum trvel demandmodel of modal choiceapplied to tie San Fancisco Bay Aea, Smal (1983)concludestt congestionpricing combinedwith the redistnrbutioof toll revenueswouldrudt in benefitsto aUincom groups. As an ilustrion, the OsloToilRing,cumentlyi operatio, chargesprivat cars (lightvehicles)going intothe citycentera tollof 10kronos(approximately US$1.50).Roughly60% of motoristsapt for the subscriberlanesin 1991,whichare opeated viaelectric tollcollection,ratherthanmanually-opeated toil blaes. About80% of the eamarke fiunds r used to fimmceroad consuction and 20% for busways,busesimdtms. Theoptio natureof thosucesfl OsloTollRingraisestheinguing idea that congestiontollingdsouldpedrps be implemeatedan a voluntarybasis: with the choiceof a combination registiton fee/fueltaxbasedan 'averao' usge, or a subscriptionto the useof electronic devices j4/ Thecommonsensenotionof uing the profitsfrom eavilyued roadsto fiance lighly usedroadshas its intelleal rots in AlfredMasal's 'tax andbounty'syaemof pticing: 0no simplepln wouldbe th levyingof a ta by the communityon their own incomes,or on thoproductionof Soodswhichobeythe lawof diminsing retun, and devotingtho taxto a bountyon theproductionof thosegoodswithroad to whichthe law of incrai Mua retum acS sharply. AlfredMasrlA, c o 1920,p. 392 alsoobsvwesdat it is noeoo_y toconider to caotof adminiseringsuh a tax-subsidy systeLm - 62 publictreasury,and wouldthus competefor tax moneyvaluedat a high opportunitycost. By symmetry,surplusesthatacue in heavilyutiliwdurbanareas(withdecreasingreturnsto scale) These welfare losses and premiums would should then be priced at a pre,mwn. presumablyoffset one anotherif viewedwithinthe same (transport)sector - witha nominal value of a dollar being treatedat its face value - so that we are back to the case of pure efficiencyconcerns. 86. Even if a certaincity in a developingcountry,say, is foundto be faced with mainly increasingreturnsto scale, the deficitcouldbe closed,in principle,by appealingto the notion of scope. Meetingthe requirementthat a roadnetworkbe bothlarge enough, of diseconomies in terms of capacity,and strongenoughin termsof pavementthickness,can be quite costly. bothloadingand in highwaysmeanthata roadnetworkthat accommodates Scopediseconomies trafficvolumefounduniversallyis morecostly than the sum of an autos-onlyand a tailored trucks-onlyroad system. Hence,the surplusassociatedwithdiseconomiesof scopeoffsetsthe potentialdeficitsassociatedwith scle-specificeconomiesof road constructionor use. The viabilityof the fundis enhancedby the fact that the maintenancecost of the roadpavementis recoveredtwice: once whentrafficflowcreatescongestion,and the secondtimewhentraffic loadingscause road damage. Thus, the idea of a trust fundadministeredby an independent agencyaccordingto strict cost-benefitprnciples is likey to be feasible. B. The Role of a Transort Fund Alternatively,takingthe transportsectoras a whole,a transportationfind oughtto be 87. set up.i/ If dedicatedfunds are set up in this way, indirect'compensatory'paymentscan be achievedand wouldnot depart far from optimalty. I recommendthis both becausethe 65/ I amindebted to Sir AlanWalus for this inight. f&I Usig an entirelydiffrent o th theon usedhere,Vickrey(1977)establises thoresultthatcities economies to financemasstransitandpublic shoulduselandrenttaxreveues aiing fwomagglomeration ae subjectto increasingremus. Indeed,he arguesforcefillyand provesthe case trnportaion vwhich thatno subsidizingtes fixedcoatswoud be inefficient - 63 problemof highwaycongestionis tied intrinsicallyto the provisionof poor transitalternatives a substantialif not the lion's shareof tripsundertaken and becausepublictransportencompasses in both newly industrializingand developingcountries(Deaton(1987)).R Typically,the bus route and frequencyeconomiesof productionof bus servicesis subjectto consumer-side scale. Hence additionalfunds in the form of user-sidesubsidiesare requiredto meet the financialshortfallarisingfrom the capitalequipment,if bus usageis pricedat marginalcost. Road pricingwouldresult in more crowdedand inferiorpublic transportservicesunlessbus companieswere to offer more bus services(and hencelower generalizedprices)as a supply response. Then 'untolled' public transportusers or captive riders would be made better offWMHere the doublechargingof automobilesvia traffic volumeand heavy vehiclesvia loadingswouldhelp to closethe deficitgap. Increasingby popularrapid masstransitand light rail systems - both of whichare subjectto significantscale economies- also requirecapital funds,the constructionof whichshouldbe basedon economicviability. Unlessa globalview is takenof the congestionproblemand morerationaltime-of-daypricingpracticedin all modes problem pricedmodes),theurbantWansportation (in contrastto tacing individual,non-optimally will continueto be pervasive. Even withoutdedicatedfunds,it is essentialto pursue efficientpricingand stringent benefit-costanalysislink by link and modeby modeon both a volumeand loadingdimension. Thereafter,the results can be presentedfor public scrutiny,therebyimprovingmanageral efficiencyand publicaccountability.Thecompetitivetenderingand privateprovisionof certain 88. transportservicescouldalso serveto enhancemanageralefficiencyin the publicsector. Issues warrantingfurtherinvestigationincludethe corporatizationof certaintransportagencies. 89. Subjectto furtherresearch,the idea of settingup a transportationor road fundand the pursuitof marginalcost pricingin aU its dimensionswouldenableus to satisfythe quinpartite Z/ 68/ Theprovisionof publictraort mentionedin SectionViI, umed to operateunderconstantretms was ued merelya an iliustrativeconvenience but thisassumptiondoesnot resultin lossof generality. Notably,captivebw pasage lowerd. traveltimesm wouldbenefitftomroadpncingif equilibrumtramnsit - 64 - principlesof the WorldBank'sgeneralguideines,as statedat the outsetof this paper, namely to: 1) implementefficiencypricing, 2) meet economicviability,3) meet (to a considerable extent)financialviability,4) achieve(somedegree of) 'fairness' amongbeneficiaries,and 5) attain(somewhat)managerialefficiencyof thepublicauthority.Theconceptionof a fundpasses manyof the criteriafor a 'good' earmarldngarrangementas presentedin McCleary(1991). The implementation of marginalcost pricingin boththe trafficand loadingdimensioncouldbe done withthe adventof recenttechnological breakthroughsin automaticroad user chargingulizing automaticvehicleidentificationand classification,all of whichare subjectto remarkablescale economies(Elau(1992)). Alternatively,less powerfil road pricinginstuments such as area licensing,simplecordonpricingschemesand the monitoringof vehicleand axle loadingvia weigh-inmotionscalescan be used. TimothyD. Hau -65- Appendix Page 1 of 6 APPENDix: Measurementof the WelfareImyactof Road Pricing A brief analysisof the measurementof the welfareimpactof roadpricingwouldhelp 1. explainwhy road pricingis unpopular. We will considerseveralacceptableapproachesto measuringthe net benefitsoffered by the introductionof road pricing on a non-perturbed equilibrium.Eachcastsdifferentlightand insightson thecontroversysurroundingroadpricing. A. OuantityApproach The first approach,whichis more popularin the U.S. literature,is to measurethe 2. so-calledwelfaregainor lossareas(seeKraus,MohringandPinfold(1976),for example).This standardmethodis labelledthe quantityapproachor the 'Amencan'approach(seeFig. 3). The from a reductionin trips from Ql to Q' as a result loss in valuationto the consumer-traveller area of increasingthe generalizedtravelcost to him from P to P' is the verdcal,tWapezoidal d+g+k. The savingin resourcecost to travellersfrom the reductionin traffic,togetherwith the savingof congestionin the formof externalityreduced,is the verticalarea l+d+g+k. The net benefitto societyof the introductionof road pricingis givenby the trangular area 1. Net Benefit Aroach A variantof this approachis the net benefitapproach(see Fig. 3). The net benefitin 3. the case of the optimaltrafficlevelof Q' is typicallya large trangle (thepie area a+b+e+h betweenthe demandfunctionand the marginalcost curve),withthepie tiangle emanatingfrom the point of optimum. Similarly,the net benefitin the case of the non-optimallevel of Q°is givenby the differenceof the pie area a+b+e+h and the small triangulararea 1. The latter area is of coursethe welare cost savedwhenthe trafficlevelis inducedto be loweredfrom Q' to Q'. This variant is intuitivelyappealingas it graphicallyillustratesthat net benefit is Appendix Page 2 of 6 -66 - maximizedwith marginalcost pricing. Any departure from the point Q', either in a positive or negative direction, would slice into this maximal net benefit pie. To the left [or right] of Q', travellers' marginal valuation would exceed [or be less than] the marginal cost. B. Change in Total Benefits and Total Costs Approach The above procedure, and its variant, is an impeccable one. However, there is an alternative intuitive method to calculating the net benefit of introducing road pricing. This 4. approach is widely used in the British literature (Ministryof Transport (1964), Tanner (1963, p. 318); Gwilliamand Mackie (1975, pp. 105-106),Thomson (1970)and Thomson (1974, pp. 142-145)). The findingsof the Ministry of Transport, known as the Smeed Report, present a different calculationof the areas of gains and losses indicatedabove, yieldingdifferent insights into the problem (see their Appendix3). The 'British' approachuses the change in total benefits and change in total costs. The change in total benefits accruing to those who are tolled off the road are negativebecause they suffer a loss in valuationequivalentto the vertical area d +g+k. The change in total costs - expressed as the reduction in the total expenditureon travel in the form of savings in time cost - accrues to aU motorists and is given by AVCOQ- AVC"Q' (or PV - P"Q'), that is, the area e+f+g+k. The net gain to societyis the area e+f-d. HeuristicaUy,the remainingusers find that they derive satisfactionfrom the savings in time cost of the area e+f. The losers - those tolled off the road - would clearly experience a welfare loss of the area d. The discussion thus far gives the conclusionand mistaken impression that those who remain behind are in fact better off by the entire savings in time cost of area e+f In fact, 5. drivers who remain on the road have to make toi paymentsof the area b+c+e+f, which in turn become a gain to the governmentin the form of toUrevenues. (This is the notion of a transfer payment excluded in cost-benefit calculations using the British approach, see Gwilliam and Mackde(1975, pp. 105-106).) Yet, paradoxically,it is precisely the impositionof this tax resulting in a transferpayment- whichenables those who remain on the road to benefit the time - 67 savings of an additional area e+f.01 Appendix Page 3 of 6 Without the tax, motorists are not properly induced to save valuabletime resources: the time is completelylost. The ones who remain on the road, however, actually suffer a loss of consumer's surplus of the rectangular area b+c. It is as if a discriminatingmonopolist-- in the guise of the government's tax department -- carves away oart of the users' consumer surplus. Also, to 'benefit' from time savings of the area e+f, drivers are in fact trading a dollar of money for a dollar's worth of time, implying that both a standard and constant value of time and efficiency analysis are assumed. (The rest of the transfer payment of area e+f also accrues to the governmentin the form of tax revenues.) 6. Primafacie, whether or not the net benefitsof introducingroad pricing using this latter approach (i.e., area e+f- and the former approach(i.e., area i) are equal is not at all obvious. The latter procedure gives less indicationof the notion of optimalitywhen compared to the first approach, especiallywith regard to its variant. In the quantityapproach, one could move to the left or right of Q' and observe that the net benefit pie to society would clearly be eroded, suggesting that Q' yields maximal net benefit. Using the latter approach, however, as Q increases past Q', a welfare loss area would increase. This would have to be offset with a new rectangular area of saving in resource cost. The point is that it is unclear whether Q' can be shown to be optimal, at least diagrammically, becausethe new rectangular area may not offset the new (trapezoidal)welfare loss area. Formally, the proof is as follows: the move from Q' to Q0 yields a change in cost to societyof area l+d+g+k because the vertical area below the marginal cost curve is a proper measure of cost. Equivalently,the change in variable cost of 9/ The rectagla areab+c+e+f ahouldbe countedas accruingeitherto the govenmentin termsof toil revenuesor returnedto consumers(viaa hypothetical lumpsum transfermechanism).A lessonto be leamedregardingthe isue of transferpaymentis to avoiddouble-counting.if a doilaris treatd as a is implem , thenthemoveto roadpricing it accruesandthetansfermnchanism dollarto whomsoever resultsin positivenet benefitto societyof areae+f-d Puttng it anotherway, the standardnotionof a transferpaymentof the area b+c+e+f says that moneygoes from the consumer'spocket into the govenmeot's.It is importantto view the timesavingsof area e+f as an additionallayeron top of the transfr paymentitself. Thebottomlayergoesfromthemotorist'spocketto the roadagency's;tho top layeris obtainedbocausethemotoristswhoaretoiledae forcedto trademoneywithtime. Remarkably, it is thiscoercedpaymentof thetaxrevenueaea e+fwhichbringsabouta real savingof timeof an area of equalsize. Appendix Page 4 of 6 - 68 - goingfrom Q' to Q°is the invertedL-shapedarea e+f+g+k. By definition,thesetwo areas it mayappearas if the mustbe equal,implyingthate+f=l+d or l=e+f-d. Diagrammatically, changein totalbenefitsand totalcosts approachyieldslargernet benefitarea-use. However, it needsto be clearlyshownhere.2' C. Consumer'sSurplusand Producer'sSurplusAproach 7. The third approach using the summationof changes in consumer's surplus and producer'ssurplusinvolvesthe term quasi-rent.2/ The travelleris both a consumer(in the sensethat he derivesbenefitsfrompurchasinga transportservice)and a producer(in the sense that he himselfhas to purchasethe inputswith bothhis own timeand operatingcosts). In the absenceof road pricing, becausedrivers travc.lup to the point where averagevariablecost intersectsthe demand(at outputlevel Q°), the entire receipt (from the consumertraveller's expenditure)goes to cover the 'payment'of user-suppliedfactorinputs, so zero quasi-rentis therebygenerated. However,it couldbe equivalentlystatedthat the nil area can be expressed as thedifferenceof twotriangles,i.e., area (e+h) - (c+d+l), by simplyexploitingthe meaning and geometricrelationshipof averageand marginalcost curves. In the adventof road prcing, the quasi-rent - the return to a fixed factor of production - is essentally the amount which the traveller-as-producer 'receives'overand abovehis totalvariablecosts. Thisquasi-rent,instead of accruingto the driversas such,is capturedby the governmentin the form of tollrevenueor a user charge,and henceshouldbe accountedfor properlyin benefit-costcalculus. Note that the quasi-rentof area b+c+e+f can be re-expressedas the area b+e+h. Clearly,the change in the quasi-rentwouldbe equal to the area b+c+d+l. Coupledwiththe loss in consumer's 2QI Lee(1982)claimsthatthetwoares basedonthediffart mdhodologies arethesamebut doesnotprove andNash's(1972)commet on Beesleyand it. Ihe spiritof theanalysisI howhare underlies vAwilliam Walte' (1970)evaluationof uba road investmnts. 1/ Mhenotionof rentis a slpperyone and warrantsclarification REmtis the analogof producer'ssurplus in the iput marlt. Reantis a p*mawetpaymentto a factoroverand abovethatwhichis requiredto drawforthits resourc. Quasi-rentis a tpnporarypaymurtandwouldcontnueonly untilthecapital asset is depreciaedor possiblytansferredto anotheruse (see footnote29 and Mohring (1976, Chapter 2) also). Notethata high priceand willingnesspy yied high quasi-rent,andniotthereverse. -69- Appendix Page 5 of 6 surplusof area b+c+d, the net benefitarea I emerges. Hence, we have shownin different ways that the three approachesare identical.3 / Note, also, however,the secondapproach is usedand extendedbecauseit graphicallyillustratesthe broaddistributionalimplicationsof road pricing. 8. Perhapsone reason why there is confusionregardingthe two approachesabove is becauseof Walters'(1961a, 1961b)treatmentof the MC and AVC curves as marginalsocial cost and margtnalprivatecost curvesrespectively.(My interpretion here is at variancewith the commonuseof the latterterm sinceI regardit as somewhatof a misnomer.)Walters'use of the AVC as MC curveimmediatelybringsto mindstandarddiagramsof an externalitysuch as the classiceconomicstext exampleof a pollutingfactory,with the consequentchangesin consumer'ssurplus,producer'ssurplusand extrnality valuation. As carefullyshownabove, thisexampleis notvalidin our analysisbecausethe marginalprivatecost curveis onlymarginal withrespectto the driverhimself. The individualperceivesand bears the averagevariablecost only: it is merelya decisioncurveand no more. Sincethe area belowthe AVC curve is not integrating the totalprivatecost,onlyan incorrectintepretationcanbe drawnby mathematically the area underthe marginalprivatecost curve, whichturs out to be an averagevariablecost curve. (Further,producer'ssurplusshouldreallybe interpretedas quasi-rentto avoidpossible confusion,especiallyin undstanding the rlationship betweenpricingand investment.)In the absence of he opdmal pnrcingof trips, average (variable)cost pricing prevails with the associated . Tis illusates stronglythe need to reserve the term 'short-run marginalcost pricing' to be consstent with the WorldBank's policyguideline(WorldBank OperationalManualStatement(1977)). I employthe term marginalsocial cost pricingwhen a In fact,if Q'is verycls to Q', do anal os is equivalntto dhohng in tota varae coaLBy evaluangth diffeieo of dl clug in vaiableco withthemail valuaon, to twomet&ods discuad aov (t qu approachnd thedcge in totalbenefits andtol coot poch) ar seam to be equaL Appendix Page 6 of 6 - 70 - accountingfor aU the other externalitiessuch as environmentalpollution and accident costs.L/ A technicalpaperby consultantshiredby the HongKongGovernmentindicatesthatthe 9. net benefitdue to introducingroadpricingcorrespondsto the area e+f+d+g+k (Transpotech, of the extraarea g+k is eitherbasedon a possible (1983,Fig. 4)). Theconsultants'explanation of the first two approaches,or simplya matterof double-ountingareasg +k. misunderstanding The authorsstatethat "this money[referringto the areasg+k] is availableto be spentin other ways,perhapson other modesof travelling". Havingalreadyincludedthe resourcesavingas a reductionin the expenditureon travel, PQ - pftQP,the resourcesavingfrom the tolledoff driversof the verticalarea g+k shouldnot be countedtwice. Thepointhere is that unlesscare is takento ensurerigorouscost-benefitanalysis,the benefit(or cost) figureswouldbe biased, as has been the case with the evaluationof the electronicroad pricingexperimentin Hong Kong.7/ 73/ For examle, Glaister's(1981,Chapter5) use of the term 'marginalsocialcostpicing' is synomymous here. withthemargnalcostprcng conceptemployed 7A1 Basedon the mnuberpresentedfor an illusative cas, thebias is 40% upwards. It shouldbe stressed, however,thatit is unclearfroma readig of th HongKongGoverment'sMainReportote Elecunic outinedin Technical RoadingPricingPilotSchemewhher the finalreportfollowedthe methodology Paper 1 (Traspotech(1983,1985)). FIGURES EconomicFundamentalsof RoadPricing: A Diagammatc Analysis by TimothyD. Hau TransportDivision Infastructureand UrbanDevelopmentDepartment The WorldBank -73 Figure1 Derivatlonof a WavelTime-FlowCurveof an UrbanHighway Figure1 (a) Figure1 (b) Speed, Speed, In km per hour Sm in km per hour s~~ --- ---- 1 \ Sm ----- aa- ------ I\/ 0m Density, Invehicles F IrLax Flow, Engineering Capacity in vehicles per krn per hour . . ~~~per lane Figure 1 (c) Traveli Time Dip or Delay§ e\99egate \Ime t_rr_nL__--.I Fmax FRow, In vehicles-km per hourper larne-km - 74 - Figure2 Derivationof the MarginalCostCurveand CongestionToll AVC (Full) Priceotf MC Marginal CostCurve(MC) I plusvehicleoperatingcost and variableroadmaintenancecost AverageVariableCost Curve(AVC) plus vehicleoperating costand variable roadmaintenance cost a trip, P, I Generalized Cost,GC, of atrip \ I X I <~~~~~~ / \ w \ ~~~~/I ~/ II / < I o /1\Optimal V AVC E o _ . Timel . nme cos t Costsborne 1 …~~~~~~~bymotorist1--i-4privately l lI _ _ -.. _ _…__ _ DemandCurve Qd Vehicle I Copertin I 4.-- __-_L_- VariablARoadI Cost Maintu.nance Q' Q Cf o max Flow,In ~~vehicles perlane-hour Optimal User Charge = Costs Imposed on Other Motorists + Road Author ty = External Congestion Cost + Variable Road Maintenance Cost ~~~~= Optimal Toll + Variable Road Maintenance Cost User Charge Component | - 75 Figure 2(a) 'Dynamic' Phenomenonof Traffic Growth: The RelaxationEffect (Full) Price or a trip, P. Generalized Cost. GC, of a trip \AVC AverageVariableCost Curve (AVC) pius vehidceoperatingcost and cost rc ,d maintenance vadiable \7Ex ~ AVC TimeCs } VehicleOperaUngCost | Varlableroad maintenancecost Q ~ Initial Demand Curve Od Flow,In vehicles per lane4iour - 76 Figure 3 Welfare Impact due to the Introduction of Road Pricing In the Peak Period: Short-RunMarginalCost Pricing \ AVC \ X \ Variable CostCurve(AVC) Average costand onerating plusvehicle cost roadmaintenance vadable \\~~~~~~A Marginal CostCurvehMC) plusvehideoperating costand variableroadmaintenance cost (Full) PriceOf a trip, P Generalized Cost,GC, of a trip Z a *A Efficientp, Price =AVC"+ t' Price0 J =AVC Pu AVC h VCi Td Demand Curve Cost I VehideOperating Cost RoadMaintenance _ Variabe 0 Q0-' C( dQ Effient Observed Output Output Vehicles perlane-hour - 77 Figure3(a) WelfareImpactdueto theintroductionof RoadPricingIn the PeakPeriod: CostPricing Marginal Short-Run Case 'Hypercongestlon' (FUN) a*tap,P cookCC,o iP d b* * AC t CostCurve(MC) Marginal vhide operatincostand pkus coat roadmaintenance vatl AVC CostCurve(AVC) Vauible Average co and operaUng pkJ vehicle coast vartablroad mnteance < -. Primce ! Efficentp'\> *AVC"i.t' \ 0d VeryHigh'I nandCurve nAVC" z AVCE TimeCost Timecost Costsborne ___……__ …___O _-* by motorist privately _ __ _ _ cost operaing Vohicle I Varlable Cost RoadMainterance Q Vehicles perlane-hour - 78 - Figure 4 Effect of the Introduction of Road Pricing In the Peak Period on the Off-Peak Period p(Full Price0 a trip,P rizC Cost, of a trip Original Curve Inthe Demand OPeaik \ d' 0110/, ad>\ Q0 DemandCurveIn the Off-PeakPeriod OPfollowingIntroductionot CongestionToll °P in the PeakPerlod MC MarginalCost Curve(MC) plusvehicleoperatingcostand valiable roadmaintenancecost / AVC AverageVariableCost Curve(AVC) plus vehicleoperatingcostand cost variableroad maintenance I % Timecost Vehideoperatingcost J Variableroadmaintenancecost 0 Vehiclesper lane-hour - 79 - Figure 5 Introducing the (Short-Run Average) Fixed Cost, SRAFC, of a Road, Short-Run Optimal Toll with Economic Profit \ Qd Z SRMC(K') Short-RunMarginalCost plus vehicleoperatingcost and variableroadmaintenancecost (Full) S Price of 1 (K SRAVC(K ) a trip, P. $ Unit Cost,u. Short-RunAverageVariableCost plus vehicleoperatingcostand variableroadmaintenancecost \ SRAFC (K1 SRATC(K fr SRT (K/ / / Efficent P OptimalTollt1 OptimalTollt P:= |: / \ ~~~~~~~~~~Time -v - __ Short-RunAverageTotalCost plus vehicleoperatingcost and cost varable road maintenance Cost\ Od DemandCurve __ - - Vehicleoperatingcost __- - - - - - - -_ Variable Cost Road Maintenance SRAFC(K1) Shdrt-RunAverageFixedCosi Q'. EfficientOutput Vehicles per lane-hour K1 = (Non-optimal)Road capacity t 1= Optimaltoll for a non-optimallybuilt road n'1=Economicprofitfor a non-optimallybullt road - 80 - Figure 6 Long-Run Equilibrlum of an Optimally Designed Road With Both Optimal Pricing and Optimal Investment SRMC *(K) P. Short-RunMarginalCost | plus vehicleoperatingcost and variableroadmaintenancecost \ SRAVC *(K) Short-Run Average Variable Cost $ a, \ / \ plus vehicleoperatingcost and variableroadmaintenancecost OlUmal Price P SRAFC (K) Short-RunAverage \ FixedCost \ SRATC (K*) Short-RunAverageTotalCost plus vehide operatlngcost and variableroadmaintenanoe cost LRATC _4 J = LRMC Long-RunAverageTotalCost = Long-RunMarginalCost / \ / / > Optmal Tollt' SRAFC (K) SRAVCE TimeCost d DemandCurve Vehide operatingcost SRAFC (K) a* OptimalOutput t =OpUmal toll K* Optimalroadcapacity Variableroadmaintenance cost Vehicles per lane-hour - 81 - Figure7(a) Constant Returns to Scale with Road Divisibility: Doubling Optimal Road Capacity (K ) and Traffic (0 ) Result in Doubling FixedCost, Variable Cost and Totai Cost (FC, VC, TC) and Toll Revenues(t. ° L) SRMC 6(K6 ) SRATC6(Ko*) SRAVCO(K6*) SRMr3(K3*) SRATC3 (K3 *) $ *LRMC LRATC - LRRTC SRAFC3* /SRAFCO* s SRAFC3* *03* SRF() 3*) RAFC(K SRAFCS* 06* 0 perlane-hour Vehicles Figure 7(b) The Relationship between Short-Run Average TotalCost and Long-Run Average Total Cost and Marginal Cost with Perfect Road Divisibility and Constant Returns to Scale SRATCm(Km*) * LRMC LRATC L.ATC* LRMC 0 Vehilesperlane-hour thatthatvaiiableLsoptinized () Denotes (L) Denotes anL-laneroad capdityofan K3*denotes theoptimal Forexample, optimally-built 3-laneroad wlh an toNassociated 13*denotestheoptimal 3-laneroad optimally-built - 82 Figure 8(a) Road Indivisibllties under Constant Returns tS. A LRATCo ABCDEFGLine LRMC- HIJKLMLine SRMC2/ - - - -~~~~~~~~~~~ ------- 0LossRegbn Regon024*-Region-4 2 Region 0 446 R°eSgion 06 RteOgion* 68 Figure8(b) Optimal Pricing and Investment with Indivisibilltles: Expansion trom a 2-Lane Road to 4-Lane Road a,~~~~a 5 s Un- lIl Q Q24 Q * Q04.6 Demand Curve I 0 - 83 Figure 9 Economies and Diseconomies of Scale In the Provislon of Road Capacity with the Growth of Travel Demand od od~~ 3 0 Long-Run Marginal Cost LRM\ALAC LR Ca; Unit Loss Lon~~~~~~~~~~~~~~~~~~~~g-Run \ _ I \ Unit Profit ~~~~~I Average Total Cost Inital Demand Curve Q1 3 I t l l j I I l Economies of Scale RegloRegion ---------- e I Constant Sl Retuns ~~~~to Scale Region Vehicles per lane-hour Diseconomies of Scale Region - 84 Figure 10 Doublingthe Numberof Streets-RoadCapacity-ResultsIn Quadruplingthe Numberof IntersectionsandTraffic Lightsand DoublingWaitingTime Figure 10(a) OriginalScenario- Existing Street Configuration D ____________ 0 = Odgin D= B A o Figure10(b) Final Scenario- Numberof Streets are Doubled XI D ~~~~~~~~IF 6 5 0 1 2 3 4 Destination - 85 Figure 11 Diseconomles of Scale: Urban Roads Network with Perfect Divisibility 7r= EconomicProfit P, d S LRMC Q4 ~~~~~~~~~~~~~~SRMC4 0, S4 SRMC2 / LRATC SRAFC2 SRACSRATO SR l r Q2nn IXSRAFC~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Tr 4 4 2 : RAFC2 02 ! 024 | 0 4mIn > 04 4S2RARAFC Vehicles per lane-hour - 86 - Figure 12 Economies of Scale: Rural Roads with Perfect Divisibility L Loss SRMC2 LRATC SRATC2 s SRAFC 2 P4 /SRMCSRATC ^~~~~~~/RA4 2 VC I | I -4.~~~~~~Q2i Q*2 Q2mIna \l nVeiLespRlAne-ou 0 ) .4 Q;1 | ...... 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Carll (1964),"The BasicTheoryof EfficiencyTolls: The Tolled,TheTolled-OffandTheUn-Tolled,"Highs= ResearchReord, No. 47, paper presentedat the 43rdAnnualMeetingof the HighwayResearchBoard,January13-17, 1964,NationalResearchCouncil,Washington,D.C., pp. 46-65. hook_ PA" no& t DaftM7. 1~~Du~ U . UK M -x Policy Research Working Paper Series Title Author Date Contact for paper WPS1047Coted'lvoire:PrivateSector DynamicsandConstraints EnriqueRueda-Sabater November 1992 AndrewStone P. Infante 37642 WPS1048TargetsandIndicators in World BankPopulation Projects GeorgeBaldwin 1992 November 0. Nadora 31091 WPS1049 MoneyDemand andSeignorageMaximizing Inflation 1992 WilliamEasterly November PaoloMauro KlausSchmidt-Hebbel R. Martin 31448 WPS1050MarginalIncomeTaxRatesand Economic Growthin Developing Countries WilliamEasterly SergioRebeto 1992 November R. 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