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Economic Fundamentals of Road Pricing: a Diagrammatic Analysis ___ IS (070 Pollcy Research WORKING PAPERS L Transport Public Disclosure Authorized Infrastructureand Urban Development Department TheWorld Bank December1992 WPS1070 EconomicFundamentals of RoadPricing Public Disclosure Authorized A DiagrammaticAnalysis Public Disclosure Authorized TimothyD. Hau Most economists agree that road pricing benefits society by curtailingcongestion. Efficiency analysis demonstrates why the Public Disclosure Authorized public rejects congestionpricing. A dedicatedroad or transport fund is more viable whenthe road users are chargednot only for the damagecaused by heavyvehicles but also for congestion. PolicyRearchWoding PapsdismLataeth rmdingsofwoiprogrcsatncountgethccxchangeofideaunangB nkstaffand til othas iMacenedin de-volopnelttssues. Them papcgs cary thenanm of die autho, reflactealy theirviews, znd shel be usedand citedaccordingly. hefindn.inu cprcsttion, andconduws aretheauthoz' own Tley shouldnoto atttbutedtotheWeWd Bank, its Boardof Directos,its managment,or any of itsmember counties. PolicyResearchl Transport| WPS1070 This paper - a product of the TransportDivision, Infrastructure and Urban DevelopmentDepartment'- is part of a larger effort in the departmentto evaluateoptions for chargingfor roaduse. Copiesof the paper are availablefree from the WorldBank, 1818H StreetNW,Washington, DC 20433.Please contact Jennifer Francis,room S 10-063,extension 31005 or 35205 (December1992, 96 pages). Hau presentsa conceptualframework for road On urban roads with indivisibilitiesand pricing based on a rigorousdiagrammatic - but diseconomiesof scale, efficient pricing may nonmathematical- frameworkderived from curtail the extent of profitableundertakings. On first (economic)principles. His analysisof rural roads with indivisibilitiesand economiesof traditionalarguments about road pricing shows scale, marginalcost pricing can produce short- why implementingcongestion pricing as prac- run profits.Economic efficiency is enhancedby ticed in the past has encounteredobstacles. pursuingoptimal pricing in the short run and Partly, it is because both types of road users- optimal investmentin capacity in the long run. the tolled and the tolled off (thosewho avoid the The rule is to implementshort-run marginalcost road to shun a toll) - are shown to be worse off pricing while varying road capacity over the long under a constantvalue of time, exceptfor the run. government.And when differencesin time valuationare taken into account,primarily those Insightsby Newbery, Small,and Winston- with very high time values are better off. Unless about the economicimplications of the extensive congestiontoll revenues are earmarkedand damage that heavy vehiclescause to roads - travelersperceive that the money is channeled enrich the basic Mohring model. Chargingfor back in reduced taxes, lower user charges,or both the external and variablecost of road improvedtransport services, neither the tolled damage,by assigninga fee basedon vehicle nor the tolled off will support road pricing. Only weight per axle, can help cover deficits arising where thcre is hypercongestionis everyone from road congestion. better ofi with congestionpricing. Even if a road networkis broadly character- In the absenceof scale economiesor ized by increasingreturns to scale in building diseconomies,the level of economicprofits- and strengtheningroads, the deficit could be toll revenuecollections less a road's fixed and closedby diseconomiesof scope.A road net- non-use-relatedcosts - serves as a surrogate work that accommodatesboth cars and trucks market mechanismindicating that a road should costs more than the sum of an autos-onlyand a be expandedor downsized.The decision to let (smaller)trucks-only road system.So the surplus roads deteriorateover time is iiself an act of associatedwith diseconomiesof scope offsets d;sinvestment. the potential loss associatedwith scale-specific economies.A dedicated road or transportfund is Hau shows that if a road authoritylevies all the more viable because road users are economicallyefficient chargesfor congestion,it chargednot only for the damagecaused by is possibleto make money on a road. Roads can trucks and heavy vehiclesbut also for conges- be profitablein urban areas in the long run tion. becauseland rents are high; congestiontolls reflect the associatedhigh opportunitycosts. 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 conclusionls in 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 Urban DevelopmentDepartment The WorldBank Economic Fundamentals of Road Pricing: A Diagrammatic Analysis by Timothy D. Hau CONTENTS ACKNO.lEDGvMENn .............. iv ABSTRACT ........................................ , v I. CoNCEnUAL GiDELES .................................. 3 H. CAusE OF CONGeBsTION:PuBLIC/PiVATE OWNERSP OF RoAS ... .......4 HI. FOuNDATIONSOF RoAD CONGESTION- THE CLASSICALCASE (IN TH SHORT R.UN) ............................................... 8 IV. DEI@DAND AM SUPPLY..................................... 10 V. VERYCONoEsTED RoA AMD BorLNEcKS ...................... 12 VI. THL WELFAE PACTOF RoAD PRicIN ......................... 13 VI. THE EFFEC ON TH TOLLD, TH ToED OFF AND THEUNTOLLD ...... 13 Policy nIplications . ...... 17 V L. SHORTRUN EQULMRIUM................................... 18 IX. CONVERGENCE TOWARDS LONG-RUN EQUILBRUM UNDER CONSTANT RiIU.Ns ............................................. 20 X. Op*M>L NvsT .. .. ...............................* *.. 22 Xl. LoNo-RUN VS. SHORT-RUN MARGNAL COSTPRICING.................. 24 XI. TRADE-OFFBETWEEN INDiDUAlS' Tm AND EASURY AccouNTs ... ....25 xm. FnsT-BEsT OPTMAL PRICING AND INvSTmEN RULES................ 28 Empnjri1Considerations. .................................. 28 The First Rule -- The Optimal Pricing Rule ........................ 28 The Second Rule -- The Optimal Capacity Rule ..................... 29 Perspective on the Result ......... 29 XlV. RELAXATIONOFASSUMPTIONS ................................ 31 1) Differences in Time Valuation .. 31 2) Demand Variability and Peak-Load Pricing ...................... 32 3) Indivisibilities .................. 4....................... 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 D. Economies of Scale and Indivisibilities .......... .......... 42 E. The Extent of Indivisibilities vs. Divisibility and Their Effects on Scale (Dis)economies ............................ 44 F. Empirical Evidence on the Scale Economy Issue ........ ...... 45 G. Recent Results on Cost Recovery ....................... 47 5) Vanability of Road Thickness .. 51 The first rde -- the optimal pricirg rule ..................... 52 The second rule -- the optimal capacity;,xle................... 52 The third rle -- the optimal durability rue ................... 52 Economies of Scope vs. Diseconomies of Scope. ............... 53 XVh. SUMMAY AMDCONCLUSIONS................................ 56 A. The Role of a Road Fund ................................ 61 B. The Role of a Transport Fund .. 62 APPElDMI: ................... .................... 65 Measurement of the Welfare Impactof Road Pricing .................. 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 .... 74 Figure 2(a) 'Dynamic' Phenomenon of Traffic Growth: The Relaxation Effect ... 75 Figure 3 Welfare Impact due to the Itroduction of Road Pricing in the Peak Period: Short-Run Marginal Cost Pricing .76 Figure 3(a) Welfare Impact due to the Introductionof Road Pricing in the Peak Period: Short-RunMarginal Cost Pricing 'Hypercongestion' Case ......... ................... 77 Figure 4 Effect of the Introductionof Road Pricing in the Peak Period on the Off-Peak Period . .................. 78 Figure 5 Introducing the (Short-RunAverage) Fixed Cost, SRAFC, of a Road, Short-RunOptimal Toll with Economic Profit .... .... 79 Figure 6 Long-RunEquilibrium of an Optimally DesignedRoad with Both Optimal Pricing and Optimal Investment ............. .. 80 Figure 7(a) ConstantReturns to Scale with Road Divisibility: Doubling Optimal Road Capacity, K, and Traffic, Q, Result in Doubling Fixed Cost, Variable Cost and Total Cost (FC, VC, TC) and Toll Revenues (t*- Q*) .... ...... 81 Figure 7(b) 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 .................. 82 Figure 8(b) Optimal Pricing and Investmentwith Indivisibilities: Expansion from a 2-Lane Road to 4-Lane Road .... .......... 82 Figure 9 Economies and Diseconomiesof Scale in the Provision of Road Capacity with the Growth of Travel Demand .... ........ 83 Figure 10 Doubling the Number of Streets - Road Capacity -- Results
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