___ IS (070 Pollcy Research WORKING PAPERS L Transport Infrastructure and Urban Development Department The World Bank December 1992 WPS 1070 Economic Fundamentals of Road Pricing A Diagrammatic Analysis Timothy D. Hau Most economists agree that road pricing benefits society by curtailing congestion. Efficiency analysis demonstrates why the public rejects congestion pricing. A dedicated road or transport fund is more viable when the road users are charged not only for the damage caused by heavy vehicles but also for congestion. PolicyRearchWoding PapsdismLataeth rmdings ofwoiprogrcsatncountgethccxchangeofideaunangB nkstaffand til othas iMacened in de-volopnelt tssues. Them papcgs cary the nanm of die autho, reflact ealy their views, znd shel be used and cited accordingly. hefindn.inu cprcsttion, andconduws aretheauthoz' own Tley should noto atttbutedtotheWeW d Bank, its Board of Directos, its managment, or any of its member counties. Policy Researchl Transport| WPS 1070 This paper - a product of the Transport Division, Infrastructure and Urban Development Department'- is part of a larger effort in the department to evaluate options for charging for road use. Copies of the paper are available free from the World Bank, 1818 H StreetNW, Washington, DC 20433. Please contact Jennifer Francis, room S 10-063, extension 31005 or 35205 (December 1992, 96 pages). Hau presents a conceptual framework for road On urban roads with indivisibilities and pricing based on a rigorous diagrammatic - but diseconomies of scale, efficient pricing may nonmathematical - framework derived from curtail the extent of profitable undertakings. On first (economic) principles. His analysis of rural roads with indivisibilities and economies of traditional arguments about road pricing shows scale, marginal cost pricing can produce short- why implementing congestion pricing as prac- run profits. Economic efficiency is enhanced by ticed in the past has encountered obstacles. pursuing optimal pricing in the short run and Partly, it is because both types of road users- optimal investment in capacity in the long run. the tolled and the tolled off (those who avoid the The rule is to implement short-run marginal cost road to shun a toll) - are shown to be worse off pricing while varying road capacity over the long under a constant value of time, except for the run. government. And when differences in time valuation are taken into account, primarily those Insights by Newbery, Small, and Winston- with very high time values are better off. Unless about the economic implications of the extensive congestion toll revenues are earmarked and damage that heavy vehicles cause to roads - travelers perceive that the money is channeled enrich the basic Mohring model. Charging for back in reduced taxes, lower user charges, or both the external and variable cost of road improved transport services, neither the tolled damage, by assigning a fee based on vehicle nor the tolled off will support road pricing. Only weight per axle, can help cover deficits arising where thcre is hypercongestion is everyone from road congestion. better ofi with congestion pricing. Even if a road network is broadly character- In the absence of scale economies or ized by increasing returns to scale in building diseconomies, the level of economic profits- and strengthening roads, the deficit could be toll revenue collections less a road's fixed and closed by diseconomies of scope. A road net- non-use-related costs - serves as a surrogate work that accommodates both cars and trucks market mechanism indicating that a road should costs more than the sum of an autos-only and a be expanded or downsized. The decision to let (smaller) trucks-only road system. So the surplus roads deteriorate over time is iiself an act of associated with diseconomies of scope offsets d;sinvestment. the potential loss associated with scale-specific economies. A dedicated road or transport fund is Hau shows that if a road authority levies all the more viable because road users are economically efficient charges for congestion, it charged not only for the damage caused by is possible to make money on a road. Roads can trucks and heavy vehicles but also for conges- be profitable in urban areas in the long run tion. because land rents are high; congestion tolls reflect the associated high opportunity costs. 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 Dissemiination Center Economic Fundamentals of Road Pricing: A Diagrammatic Analysis by Timothy D. Hau Tansport Division Infiratructure and Urban Development Department The World Bank 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. FOuNDATIONS OF RoAD CONGESTION - THE CLASSICAL CASE (IN TH SHORT R.UN) ............................................... 8 IV. DEI@D AND AM SUPPLY ..................................... 10 V. VERY CONoEsTED RoA AMD BorLNEcKS ...................... 12 VI. THL WELFAE PACT OF RoAD PRicIN ......................... 13 VI. THE EFFEC ON TH TOLLD, TH ToED OFF AND THE UNTOLLD ...... . 13 Policy nIplications . ...... 17 V L. SHORT RUN 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-OFF BETWEEN 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. RELAXATION OF ASSUMPTIONS ................................ 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 Introduction of Road Pricing in the Peak Period: Short-Run Marginal Cost Pricing 'Hypercongestion' Case ......... ................... 77 Figure 4 Effect of the Introduction of Road Pricing in the Peak Period on the Off-Peak Period . .................. 78 Figure 5 Introducing the (Short-Run Average) Fixed Cost, SRAFC, of a Road, Short-Run Optimal Toll with Economic Profit .... .... 79 Figure 6 Long-Run Equilibrium of an Optimally Designed Road with Both Optimal Pricing and Optimal Investment ............. .. 80 Figure 7(a) Constant Returns 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 Relationship between Short-Run Average 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 lndivisibilities under Constant Retums .................. 82 Figure 8(b) Optimal Pricing and Investment with Indivisibilities: Expansion from a 2-Lane Road to 4-Lane Road .... .......... 82 Figure 9 Economies and Diseconomies of Scale in the Provision of Road Capacity with the Growth of Travel Demand .... ........ 83 Figure 10 Doubling the Number of Streets - Road Capacity -- Results in Quadrupling the Number of Intersections and Traffic Lights and Doubling Waiting Time .84 Figure 10(a) Original Scenario-Existing Street Configuration .84 Figure 10(b) Final Scenario - Number of Streets are Doubled .84 Figure 11 Diseconomies of Scale: Urban Road Network with Perfect Divisibility .... ..85 Figure 12 Economies of 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 rudimentary version of this resech paper was pented at the 2nd International Conference on Privatization and Deegulaton, Tampere, Finland, June 16-20, 1991. Part of the findings of this researck was presented at the 6th World Conference on Transport Research, Lyon, France, June 29 July 3, 1992; Seminaiio de Tarificacion Vial 1992 (Road Pricing Seminar), sponsored by the Ministr* of Trnsport, Santiago, Chile, July 20-21, 1992; the Symposium on Road Pricing, sponsored by the Swedish National Road Adminisation and the Department of Regional Planning, Royal Institute of Technology, Sigtuna, Sweden, November 9-10, 1992; and the Southwest Congestion Pricing Conference, sponsored by the University of Houston's Center for Publih Policy and Citzens Advocating Reponsibl Tansportation, Houston, Te.as, January 4-5, 1993. Comments by participants at these places are gratefully acknowledged. I have benefitted from the discussions and comments of many people on the controversal subject of road pricing and I take this opportunity to thank William. Vickrey, Michael Beedey, Kiran Bhatt, Richard Bird, Andrew Evans, Stephen Glaister, Phil Goodwin, Jose G6mez-Bdflz, Chris Hendrckson, Peter J. Hills, Jake Jacoby, Jan Jansson, Peter Jones, Theodore Keeler, Damien Kulash, Odd Larsen, Henning Iauridsen, Douglass B. Lee, Peter Mackie, Anthony May, Robert McGillivray, Herbert Mohring, Richw-d Musgave, Yew Kwang Ng, Esko Niskanen, Tae Oum, Farideh Ramjerdi, Gabniel Roth, Kenneth Small, Antti Talvitie, Tom Tietenberg, Burkhard von Rabeaau and Sir Alan Walters. I am also grateful to World Bank staff, including Esra Bennathan, Philip Blackshaw, Jose Carbajo, Anthony Churchill, Shanta Devarajan, Asif Faiz, Jeffrey Gutman, Clell Harral, Ian Heggie, Chris Hoban, Gregory Ingram, Frida Johansen, Kyu Sik Lee, William McCleary, William Paterson, Richard Scurfield, Zmarak Shalii and Larry Summers. Support sevices from Marat Callan, Pam Cook, Barbar Gregory, Beatrice Sito and Gabriella St_imetz are gratefully ackmowledged. These acknowledgements do not mean that they share in the views expressed in this paper. I alone etain full responsibility for its contents. Timothy D. Hau v - ABSTRACT Economic Fundamentals of Road Pricing: A Diagrammatic Analysis 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-load problem 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 Newbery into a single analytical framework. Analysis of the traditional road pricing arguments demonstrates why congestion pricing as practiced in the past has understandably encountered obstacles to implementation. This is partly because both types of road users, the tolled and the tolled off (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 constant value of time. Even if differences in 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 channeled back in the form of reduced taxes, lower user charges or improved transport services, neither the priced nor the pnced off would support road pricing. It is only in the case of hypercongestion can congestion pricing be shown to make everyone better off. In the absence of scale economies or diseconomies, the level of economic profits, i.e., toll revenue collections less the fixed and non-use related costs of a road, serves as a surrogate market mechanism indicating that a road ought to be expanded or 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 opportunity costs. Yet, efficient pricing in the presence of both indivisibilities and diseconomies of scale in urban roads may curtail the xent of profitable undertakings, whereas pursuing marginal cost pricing under the restrictive - vi - conditions of both indivisibilities and scale economies in rural roads cou d result in profits in the short run. Economic efficiency would be enhanced if optimal pricing were pursued in the short run and optin'l investment in capacity were pursued in the long run. The rule is therefore to implement short-run marginal cost pricing while varying road capacity over the long run. Recent extensions by Newbery, Small and Wimston have enriched the basic Mohrng model that this paper develops diagrammatically by incorpomting the fact that heavy vehicles are responsible for extensive road damages. Charging for both the extemal and variable cost of road damages on a vehicle weight per axle basis can help cover the deficit that may arise from congestion tolling. Even if a road network is broadly characterized by increasing returns to scale in road construction's use and strengthening, the deficit could be closed by diseconomies of scope. The existence of scope diseconomies in highways means that a road network that accommodates both loading and traffic volume, as found universally, costs more than the sum of an autos-only and a (smaller) trucks-oniy road system. Hence, the surplus associated with diseconomies of scope offsets the potential loss associated with scale-specific economies. The viability of a dedicated road or transport fund is enhanced by the fact that the road pavement is charged in two dimensions: once when traffic flow creates congestion and another when traffic loadings cause road damages. Economic Fundamentals of Road Pricing: A Diagrammati Analysis 1. is major conurbations of both developed and developing countries, congestion is inctssant during the peak periods and oftentimes the interpeak.Y/ Yet the traditional methods of effectively curtailing congestion are few, and their usefulness limited. On the supply side, the expansion and improvement of roads is restricted by increasingly tight fiscal and physical onstraints. On the demand side, however, the problem can be addressed by pricing or regulation. This paper uses the pricing (or market-based) approach to grapple with congesrion because of its inherent flexibility and power of discrimination31 The aim of road pricing is to internalize the externalities generated by road use. My focus here is on removing the external effects caused by motorists by charging for congestion and road damage externalities. Congestion is recognized as an important type of externality from vehicle usage in both developed and developing countries in that it represents a large share of total esumated road use costs (Newbery (1988bc, 1990) and Newbery, Hughes, Paterson and Bennathan (1988).I 2. This research begins with a series of two papers on road pricing in theory and practice. The first paper presents a conceptual framework for road pricing. It gives an interpretative abridgment of the literature on the theory of optimal pricing, investment and durability of roads By the tum of the centuy, mory o tan four-fifths of the world's most heavily-ppulted agglomeratons are proect to be in tho developing wodd (World Bank (1991), p. 3 and p. 22). ZI Tho regulaoy approach on quanity - the so-called command and control measures - suffers from its inability to provide correct market sipals to induce the most efficient trips to be undertaken. In contrast to priing incentives, it gfferates virbtally no revenues for the public sector (see Pozdena, Schmidt, and Martin (1990)). 3/ The total cost of undetkWng a trip - both 'private' and 'social' - involves: 1) congestion (which is bome by road users); 2) pavement wear (which is covered by the road authority); 3) air and noise pollution; and 4) costs of accidents (both of which are bome by society at large); in addition to 5) vebiele operating costs. 'Social cost' (i.e., both inta and extenal costs) here are distinguished from 'pivate costs' (i.e., intanal costs), the ltter of which are self-financd. Those taveller-borne interal costs include: 1) vehicle opeating costs as weol as 2) tim co sts and delay in conested traffic (Newbery's definition of road use costs refers only to the extel cost.) This paper deals mainly with the marginal cost pricig of congestion and pavement wear charges as opposed to margial social cost picig, which is defined to include - in addition to private costs - all th arnal costs of coagwestion, air polluton, noise pollution, accidents, rod damages and externalities. Hence, stictly speing, 'congestion pricing' refers solely to the pricing of congestion extenality whereas 'road pricing' refers more genally to the priing of al externalities from mobile sources. - 2 - based on the works of Herbert Mohring, Robert Strotz, William Vickrey, Alan Walters, Theodore Keeler, Kenneth Small, Clifford Winston and David Nowbery.4/ It aims to integrate their ideas and principles into a single analytical framework. I am convinced that the presentation of a rigorous and unified diagrammatic -- but non-mathematical -- framework derived from first economic principles casts important light en congestion pricing systems and on issues surrounding short-run and long-run marginal cost pricing, scale economies and diseconomies, indivisibilities, the poak-load problem in urban transport, optimal road durability, financial viability and cost recovery in the public provision of road services. While there are several automatic road user charging and electronic toll collection systems in use in parts of Norway, Italy, France, and the United States, as well as bills in parliament to implement various forms of road pricing in Santiago and Stockholm, one congestion pricing system is currently operating (Hau (1992)). That is Singapore's Area Licensing Scheme, which is now in the process of being converted into the Electronic Road Pricing System, to be operational in 1995 (see Watson and Holland (1976, 1978), Behbehani, Pendakur and Armstrong-Wright (1984)). Even so, the charging of vehicles by daylight hours in Trondheim, Norway (with further differential pricing for electronic tag users) since 1991 could be regarded as a rudimentary form of congestion pricing. 3. Recent technological breakthroughs in automatic road user charging have brought electronic road pricing nmuch closer to reality. Thus, the second paper (Hau (1992)) in this research presents a taxonomy of alternative technologies of congestion pricing. It drops the crucial assumption that the implementation of short-run marginal cost pricing is costless (Hau (1990)). In particular, it compares and contrasts the methods of manual versus electronic charging schemes. Electronic approaches are analyzed progressively by discussing first, the increasingly popular electronic toll collection mechanisms which incorporate recent technological advances *n automatic vehicle identification - commonly known as AVI - as well as smart cards. The ariateness and applicability of electronic toll collection mechanisms to I owe much intellcul debt to these authors and I am very gratefil for the opportunity of discussing my work with several of them -3- electronic road pricing are then dealt with. The companion paper also analyze% the relative cost° effectiveness of each technology and performs benefit-cost analysis where data permits. The implications of using each of theme technologies for relieving congestion are discussed and policy recommendations are drawn. I. CoNcEPTuAL GuIDELNS 4. Rising real incomes result in increased aspirations for the ownership of private automobiles. Barring major restraint measures, an increasing number of motor vehicles means that travel demand swells concomitantly. Because municipalities are finding it increasingly difficult to finance new road construction and improvements, the rate of growth of trvel demand outstrips the growth of road capacity (Hau (1988)). Transport planners, with limited options available, find it very difficult to combat effectively mounting traffic problems in the face of increasing urbanization. The resulting traffic explosion is an illustration of Parkinson's Law or Downs' law of peak-hour expressway congestion, in which commuter traffic ascends rapidly to the level of new capaity in urban areas (Downs (1962), Mohring (1965)). Traffic engineers have long been familiar with this "fundamental law of highway congestion" in which latent demand expands to fill the gap created whenever highway capacity is improved (Small, Winston and Evans (1989), p. 85). In this section, I set up the conceptual guidelines that allow authorities to curtail traffic congestion in an efficacious manner at the same time as satisfying the World Bank's general guidelines for public sector projects and urban transport policy (World Bank's Operational Manual Statement No. 2.25 (1977), World Bank's Urban Transport Policy Paper (1986), and Julius and Alicbusan (1989)). 5. In a nutshell, the essential principles include: 1) implementing short-run marginal cost pricing (short-run efficiency) to generate maximum net benefits for society: efficiency pricirg; 2) undeaking investment in infrastructure whenever the additional benefits exceed the costs (long-ran efficiency) to society of doing so: econonuc iabilty; - 4 - 3) investing in transport services when benefits exceed costs; promoting public transport services especially when revenues exceed costs: financial viability; 4) maintaining 'fairness' among beneficiaries, for example, via benefit taxation - equity -- where possible; and 5) using pricing and cost recovery policies to improve the efficiency of managing the public sector - cost-effectveness and managerial efficiency - if possible. H. CAuSE OF CONGESTION: PUBLIC/PRIVATE OWNERSHP OF RoADs 6. Roads which are infrequently utilized possess the characteristic of nonrival consumption among users and are traditional examples of public goods. Joint consumption means that roads yield services that are simultaneously enjoyed by more than one user, without substantial detriment to the satisfaction of others. If roads are totally nonrivalrous, then neoclassical economic principles dictate that roads ought to be provided for by the public sector and financed from general revenue taxation (and perhaps land value taxation), fully taking into account the socia opportunity cost of public funds. On the other hand, roads which are heavily utilized have the nature of rival consumption among users and are called congested public goods. These varisble-use congested public facilities then approximate to varying degrees the rival nature of private goods. Private goods are of course provided contingent upon payment, excluding those who are not willing to pay for them. Alas, with free access to roads, people are not banred from the use of scarce services, resulting in overuse. Hence market failure due to nonexcludabiliy cals for governmental intervention in the form of better designed road user charges and motivating charges which correct for externalities. (the failure of the voluntary pricing mechanism due to nonexcludability is referred to as the 'free-rider problem' in the public finance literature (Boadway and Wlldasin (1984), Chapter 3)). Note that it is the traditional inability to exclude motorsts from the use of crowded streets that is die cause of market failure. However, when refinements in automatic vehicle identfication technology become even more cost-effective, automatic road user charging means that market failure is somewhat overcome. This is because priccs are then able to reflect both the intensity of demand and the true economic cost of road use. The problems of nonexcludability and preference revelation would then be - 5 - virtualy eliminated and the advantages of price incentives reaped. Thus the standard public finance text (see, for example, Musgrave and Musgrave (1989, Chapter 4)) argues that both the nonrval consumption characteristic of public goods and the nonexcludability - or rather, costly excludability -- of congested public goods are causes of market failure, calling for government intervention. Hence, roads which possess the attribute of congested public goods, and thus have a partally rival consumption characteristic, ought to be treated by the relevant governmental authorities as mixed or impure public goods, if not private or club goods (Buchanan (1965)). 7. The foregoing discussion leads naturally to the transport economist's definition of congestion. That is, as more and more vehicles join a traffic stream, the travel times of all motorists making trips are raised, resulting in delay to all. In essence, the congestion phenomenon is one of excess demand, given a fixed road network. 8. Yet the fundamental reason why congestion occurs so ubiquitously is because property nghts are not clearly delineated, yielding market failure. If roads are both privately owned and competition prevails in the provision of roads, usage would be (Pareto) optimal in the absence of scale economies (Knight's conjecture (1924))Y If roads are not privately owned, access to and usage of roads are effectively free to the traveller, resulting in excessive use of those roads where taffic is heavy enough to produce significant adverse interaction among vehicles. 5/ We know that comption rsuls in conomc efficiency. in the context of roads, owners maxim the return to thir land by setting do pic equa to the short-nm marinal cost of production, where the difference between the short-n maginad cost adthe averg vaiable cost represa the quasi-ent to the fixed factor of produon. CM notio of qi-ent is discussed in footnote 29.) This is the analog to society mimicking the decetalized competitive ladowner' no maximizg behavior by chari the optimal (Pigouvian) toil - the divergence beween maI cost d averg variable cost (see dio n in Section Vm and the proof of this conecture in Vwkrey (1968)). Kniht furter argues that the case of increasing returs is dealt with by the maket alowing any one gent to rmin boind to exhaust scale economies (see Waltors' (1954) interpretation of Knight's cojectu (1924), which does not accord with my intpretaion here). I argue that the government is left wi the rol of being the aget tt char the congetion toll, in order to .Jfevent monopoly pricing. After all, it is uncla a pori that the biformational reqirments and transaction costs of public ownership would exceed the socil cost (sch as rn-sekig) of reguatig prvate ownersip. In other word, it is debatale whethr gove _ment failure is neemily gter than market failure, especially in developing countios. For instae tho govenmet's power of eminent domain over public projects may reduce its land acquisition and road cadmact cost whers the common property natur of roads would encourage rent dissiain - 6 - (rhe overcrowding occurs despite the fact that motorists already have to pay fuel taxes and registration/license fees and purchase taxes for owning a vehicle, which can be regarded as entry fees only.) V On the other hand, it is unlikely that private ownership of roads would yield a perfectly competitive market structure because alternative routes are in general not perfect substitutes. Hence, those road owners might exploit their locational attributes and monopolistic prerogatives by raising charges above marginal cost. In addition, incentives would arise for collusion. Thus competition would at best be imperfect in the case of road provision where lumpiness is found. The relevant comparison, based on efficiency consideration, is the welfare cost associated with government intervention vis-a-vis the dead-weight loss associated with the monopolistic or oligopolistic pricing practices of private ownership. In addition, it seems reasonable to argue that there are other grounds - such as equity - for regarding landowners' super-normal profits, or collusive tendencies, as undesirable. 9. In practice, virtually all roads belong to the government and not to private owners. Because of free-access roads, one should not be surprised to be confronted with the pervasiveness of congestion. This is the common property resource problem, which yields an externality.2/ One might ask whether or not some congestion-prone roads ought to be privatized to internalize the externality. The key factor is whether (sufficient) competition could be made to prevail to ensure, in the absence of regulatory restraints, that these roads are not overpriced. A testable hypothesis in contestable markets theory is to check whether the fi/ The fuel taxes which motorists pay are generally used to contibute to: 1) the maitenance and operating (and in part the investment) costs of roads, 2) debt service on highway bonds, and/or 3) general tax revenues. (Independent of how fuel tax revenues are disposed of, the main problem of the uniform fuel tax is its inability to vary by time and place of use (see Hau (1992)).) The combination of a fuel tax, first registation taxes and annual license fees can be regarded as, to a rough order of approximation, a two-part or multi-part taiff. 2/ As long as property rights are well-defined, exchangeable and enforceable, private bargaining would internalize all 'extenalities' and yield an efficient allocation of resources independent of who is held liable for creatn external effects in the first place (Cosae (1960, 1988)). Since Coae's so-called theorem holds only if the costS of transactions are nil and income effects are negligible, it applies mainly to the case of small numbers. With congestion and mobile-source externalities, I argue that the large numbers of people affected cleady result in large trnsactions costs, and hence market failure, beckoning govenment itervention. Further, Cooter (1982) argues that Coae does not distnguish between zero tansactions costs and zero bargaining costs, and that the generait of the Coase Theoom is oveted. - 7 - condition of potential competition and not actual competition is satisfied (Baumol, Panzar and Willig (1982, Chapter 1)). One surmises that it may be difficult to assume that it would be effective in practice, especially in the case of roads where irreversibility and lumpiness exists (Baumol and Lee (1991)). Also, noncomparability may occur because a competitor would find it difficult to duplicate a road on the same alignment and would likely settle for inferior alignment. Economic efficiency could be enhanced in some cases if there were a mixture of both private and public roads, since the existence of publicly-providedfireeways might limit the degree to which those who use private expressways would be charged monopoly prices. Similarly, private toll roads could serve to over-zealous govemments from overcharging on public toll roads.A/ 10. In short, the congested public good nature of roads suggests that these facilities should be treated more like club goods or private goods, yet the status quo appears to suggest that public ownership of roads is insdtutionally preferable. If so, municipalities ought to simulate the worldngs of a competitive, private firm and industry by setting congestion tolls on public roads to internalize the congestion externality. This thereby deals with the problems of nonexcludability and preference revelation explored earlier. If a private ownership arrangement is deemed beneficial at times, the government could exercise its power of eminent domain in reverse by altering the structure of property nghts of the relevant facilities from public to private ones. This could be done, for example, by auctioning off govenmment land to the highest bidder (and simultaneously reducing general taxes and/or providing more public goods), or, alternatively, by designating the competitive provision of highway services to corporations or private contractors via 'franchise bidding" (Mills (1981)). I have argued, on both efficiency and equity grounds - following our conceptual guidelines - that the facility's ownership arrangement 8/ Note tbat a relatively uncongeated toil road would yield inefficint tc allocatiao if its effect is to plice traffic off to alternative public roads which ar eady congted. Soo Johan (1989) and Catling and Roth (1987) for a discussion of toll rads and road privadition. -8- ought to reside with the government, with the proviso of setting cost-effective congestion tolls.2/ I next show how a congestion toll can be derived from a transportation engineering speed-flow curve. In the proces, the equivalence of efficient congestion tolling and the short- run marginal cost pricing of vehicle flow is established. IIm. FOUNDATIONS OF ROAD CONGESTION - THE CLASSICAL CASE (IN TME SHORT RUN) 11. Road congestion is well founded in the economics and transportation engineering literature (Dupuit (1844, 1849), Pigou (1920) and Waltes (1961a, 1961b)).p It begins by considering a rpresentative driver cruising under low traffic conditions along a given stretch of urban road with fixed beginning and end points. The representative driver would be able to achieve a mean free speed that balances the benefits to him of a faster trip against the costs to him of higher energy requirements and a greater risk of an accident. CeterLs paribus, as other vehicles enter the road thereafter, density increases, speed drops and travel time (or delay) lengthens (and accident probability rises). The causality is as follows: traffic density determines speed and not vice versa. Paalleling the theory of fluid dynamics, tffic flow is the product of density, in vehicles per kllometer, and speed, in kilometers per hour. Note that the rectangular area in Fig. l(a) - the speed-concentration reationship - is equivalent to traffic flow, expressed in vehicles per hour (see Gerlough and Huber (1975, Fig. 4.12) and May (1990, Chapters 7, 10), for example). Hence, taffic flow is the product of traffic density and speed, with traffic flow attaining a maximum at F" with speed at S' in Fig. l(b) - the speed-flow relationship (see Haight's (1963) 'fundamental diagram of road traffic' - a flow-density curve - 2/ Whilo I am convncd of to advuto s of _arkt hoes, I bhwe sornis reevatons about tdir extnt. For eample, sono have arued dot may 1sowlem shul be prvided for by the mt, and aso that tansport infrastructur soud ao be pivavtd (Raoth (1987, aptr 6) nd Cating and Roth (1987)). It is difficult to sme, in to abso of raod divisibility and competitive foae, how mainal cost pricing would be pursued and _maaed by pnvat toad owws Frm a public choico perpctvo, the uno argumnt could be reversod and applihd withp repc to govemmta authores. This explain why I arue hat perps a mixed system of public/pivate o would be able to nap the dteh of both. IQ/ While Wale (1968, pp. 31-34, aC._ 3 Annex) diaees aptma investnt, his work emphasie the short run cdaacter of road ping. 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 similar figures in Monison (1986)). (Touted maximum flow figures of the 'capacity' for a typical expressway are about 1800-2000 vehicles per lane-hour at 50-55 kilometers per hour (30-35 mph) (see Gerlough and Huber (1975, Chapter 4) and any Highway Capacity Manual, for example, Transportation Research Board (1985, Chapters 2-3));w 12. Given a fixed distance of say a kilometer of road, the traffic engineer's speed-flow curve can be straightforwardly converted to a travel time-flow curve as travel time is the reciprocal of speed, with vehicles-kilometer per lane-kilometer-hour on the horizontal axis (see Fig. l(c)). Using a constant value of time as a shadow price for the representative driver, tr,--el time is then converted to a money basis which yields time cost, called the average variable cost, AVC (see Fig. 2). Low traffic volume corresponds with relatively high speed, so fuel cost would be high. With high traffic flow and low speed, however, fuel cost would also be kept high because of fuel inefficiencies caused by the alternate acceleration and deceleration associated with dense traffic. These two factors roughly cancel one another out, leading to the plausible assumption that the costs of opeating an automobile (which include fuel, oil, maintenance and depreciation costs) are approximately independent of the level of taffic flow (Mohring (1976, Chapter 3), AASHO's (1960) 'Red Book'). A fixed money cost for the vehicle operating cost can therefore be added to the time cost portion to form the generalized cost - an accpted construct of transport economists (Nash (1976) and Button (1982)). Similarly, the road's variable maintenance cost, which is assumed to be proportional to the traffic level, following Walters (1968, p. 24), can be added up also (see Fig. 2).1/ So it is the time cost element that is mainly responsible for the upward-sloping portion of the AVC curve. The AVC curve climbs upwards because significant negative interactions occur before traffic reaches maximum basic capacity, Q; it is variable in the sense that as trffic flow, Q, is inased, congestion delay JJ Economists' notion of 'cpcity' is whever congeio dday bogins, which is considerably less t traffic engineer' concepL Furte, vehicula flow is sometimes normaized by the capacity of a crtain road to yield a 'volun_eocapacityq ratio. 12/ Hence the margi co curve, MC, when summed up verticaly with the vehicle openg cost and vaiable road maintenance cot, yields a anlad mginal os curve, MC. The sm notaions pply to the average variable co curve. - 10- actually sets in rapidly at substantially below the traffic level Q01r (contrary to the engineering notion of a constant average variable cost curve extending up 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 supply curve is nonexistent in the context of roads.ia/ IV. DEMAND AND SUPPLY 13. The 'supply' side can be made to be congruent with the demand side when a conventional demand curve is specified to depend on the travel cost (price) facing a traveller for a single trip. When an initial demand function, Q", intersects the 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-pay curve, 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 equilibrium point, unfettered use results in a return to the observed traffic level, Q°, hence the equilibrium is 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 difference between the two cost curves is 13/ The solid portion of the speed-flow curve and travel time-flow curves in Figs. 1 and 2 denote the 'normal' part of the curves. The non-soLid backward-bending portion of the cost curve (Fig. 2) means tat time cost increases because traffic flow is reduced after the gineering capacity is reached. The backward-bending curve, far from being fictitious, has been substantiated in the litrature (Gerlough and Huber (1975, Chapter 4), Keeler, Smal and Associates (1975, Fig. 1)). Schiff (1991) explores this backward-bending case. 14/ The demand fimction, Qd, is an observed, constant-money-income Marshallian dmand curve, with the usual regularity conditions. It approximates the exact Hicksian demand curve, which yields the true reflection of willingness-to-pay and marginal benefit. Formally, at equilibrium GC(Q) = Q'P), and Q"(GC(QO)) = Q°, where GC is the generalized cost. Since GC is simply a tra tion of AVC, the interpretation of one is synonymous with the other. 15/ Marginal cost is obtained as 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 elasticity of the AVC curve, i.e., the rate at which time cost rises with respect to a one percent rise in traffic flow (Walters (1961)). The first term composes of only time cost and the second term is the marginal (external) congestion cost, set equal to the congestion toll. Marginal cost pricing of a trip, P, is achieved by setdng P = MC. This is known as the first-best optimal pricing rule: our first optimality rule. (Note that AVC depends parametrically on the capacity level K, and can be expressed - 11 - the marginal (external) congestion cost - the additional delay that one driver imposes on 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 associated optimal output in the sense that the generalized cost which includes extemal congestion cost and other variable costs (i.e., constant (unit) operating cost of a vehicle and variable maintenance cost of a road), is equated to the price. The congestion cost is the additional time cost that a motorist imposes on others, calculated by taking the increment in 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 between the marginal cost and average variable cost curves by emitting the correct signal wrd creating appropriate (dis)incentives. 15. This Pigouvian toll-tax is equal to the marginal external congestion cost. It is also known as the net-benefit maximizing, economicaUy efficient, (Pareto) optimal and marginal cost 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 environmental and 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 allocation of resources. The optimal road user charge is then comprised of a congestion toll and another component which covers the variable road maintenance cost (see Fig. 2's legend). as AVC (Q, K). Without loSS of generality, the inclusion of the averge vehicle operating cost and variable road maintenanccost-both being constant with respect to taffic -simply alters both the left-hand side and the right-hand side by the same amount). Implementing marginal cost pricing in this case means pricing the difference between marginal cost and the average variable cost of a trip, plus a component which covers the cost which the motorist imposes on the community (see Fig. 2's legend). We shall return to an intuitive discussion of this subtle but important distinction. Note further that marginal cost rises asymptotically to the engineering capacity level of Q and is undefined for the AVC curve at points beyond V. - 12 - V. VERY CONGESTED RoAS AND BoTrLENEcKs 16. Observe that at the equilibrium point U in Fig. 2, the resultant throughput is 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 equilibrium point can be seen intuitively by perturbing the price level while point w is unstable in that any disturbance will result in a movement to 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 dynamic phenomenon of traffic growth as shown in Fig. 2 (a). Suppose the initial demand curve intersects the 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 identical to point U of Fig. 2). A further increase in demand beyond point 4 would result in a discontinuous jump to the backward-bending part of the unit variable cost curve at point 5. Intuitively, traffic congestion worsens 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 moving at a snail's pace as queuing develops. This corresponds diagrammatically to the positive sloping part - as opposed to the relatively smooth trffic of the 'normal' downward sloping portion - of the speed-flow curve, Fig. l(b). As travel demand continues to 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 slackening of demand results in traffic retumning to 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 equilibrium point W, are never reached in realityl1 We conclude that it is precisely the daily recufrent peaking characteristic of travel 16/ In other contexts such as Waltms (1987), point W is desuibed u an unstable equiIibriumL - 13 - demand that calls for innovative solutions. That the trffic level at those nsh hour periods seems to be near gridlock -- an illustration of 'hypercongtion' - is too important a case to be ignored (Walters (1987)). VI. TBE WELFARE IMPACT OF ROAD PRICING 18. The purpose of this section is to highlight one of the main points of this paper, the proof of which is relegated to the appendix. Economists know that road pricing results in improvement in welfare to society, yet politicians and the public almost unanimously regard it with skepdcism. Why? To economists, the increase in welfare comes about because of the imposition of an externality-corrective (toll-)tax. Yet, for those motorists remaining on the road, the congestion toll is similar to a tax increase. Under conditions of 'normal' traffic (or non-hypercongested situations), note that the toll-tax paid by the motorist exceeds the valuation of time savings resulting from road pricing on average, so that the 'tolled' is worse off.1 Those who are priced off the road to an inferior mode or time of travel in order to avoid paying the toll are also worse off, while those who remain on other indirecdy impacted roads are either worse off, if congestion arises there, or just as well off, if there is no resulting congestion. It tums out that the government, in collecting toll revenues, becomes the main party that is better off. VII. THB EFF S ON THE TOLLED, TH TOLLED OFF AD TH UNTOLLED 19. In the appendix, I establish the proposition that marginal cost pricing of trips maximizes the net benefit to society in the sense that a Pareto-efficient situation is attained, that is, no one can be made better off without making someone else worse off. The quantity approach (the 'American' approach) yields the welfare gain 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 coined by Zeds ad Call (1964). My approach difl_tiatee f*om both Zettol and Carl and Wold ad Hamidckacs (1984, pp. 114-116) in that I apply the standard noesoai method of wdfre onalym ys the appdix to detive my reaut and policy implications. - 14 - e+f+g+k less the loss of the use value of area g+k+d. We note that there are two groups of travellers that are clearly adversely affected by road priing: the tolled and the tolled off. Briefly, the British approach to the calculation of welfare gain says that those who remain on the road after road pricing is introduced incur a cost by making a toll payment of the rectangular area b+c+e+f. On the other hand, the traveller benefits in the form of reduced travel time -- 'forcibly' induced -- and the resultant time savings is the smaller rectangular area e+f. Hence the consumer-traveller would regard this exchange as not getting good value for money because the traveller is still faced with a net payment of area b+c relative to the no toll situation: this area is his loss of consumer's surplus. Despite such a trade, the traveller would undertake the trip because his willingness-to-pay still exceeds the price. 20. The other identifiable group includes all those marginal users whose willingness to pay is not high enough and hence are tolled off the road. As a group, their loss in valuation, the vertical trapezoidal area d+g+k, exceeds their saving in time cost of the area g+k by the (welfare) loss in consumer's surplus of area d. So both groups are necessarily worse off vis-a- vis the original situation. This is shown to be true despite an argument that those who remain benefit from reduced time cost! They do benefit from reduced travel time, but they have to exchange money for time. In addition, the "tolled on" is either just as well off, or worse off, depending on whether or not congestion arises. So it appears that, a move from a Pareto inferior position to a Pareto optimal state leaves everyone worse off! How could this happen? It comes about because we have not yet accounted for one agent: the government. The toll revenue collected by the government is considered an actual gain to society in that it is counted once only. Indeed, it may have a greater value than the dollar amount itself if it replaces other (income) revenue sources with an excess burden. 21. Suppose the toll revenue is collected and then put aside. An 'efficient' amount of traffic and congestion would still exist on the road in question, yet society - an aggregation of both gainers and losers - would be definitely worse off. Unless the public in general, or road users II/ It is as if a blakmie - the governmt - ca ou pat of t motoris's consumers suplus. - 15 - in particular, can partake in the tax proceeds either in the provision of public goods and/or reduction in tax revenues, they will definitely be worse off from this imposition of an 'optimal' congestion toll. If funds are not channeled back to road users, the government, or the rest of society, gains, but only at the expense of those faced with road pricing. However, because of the nature of the Pigouvian tax, which possesses an asymmetric price signal, generators of externalities are taxed but those affected by the externality are not supposed to be. compensated. This is a requirement of optimality in the case of both public and private good- type externality-corrective taxes (Baumol and Oates (1988, Chapter 4))?Ql 22. Two choices to those who are tolled off the road are to use the road during the off-peak period or switch over to public transport during the peak. The analysis is similar in spirit for both classes, so I will illustrate it for the off-peak period, for simplicity, following the same notation used thus far. Substitution of travel demand from peak to off-peak has the effect of shifting the off-peak demand curve to the right, from Q0,, to Qdqt (Fig. 4). It is easy, as is sometimes done, to regard the area m as an additional 'benefit'. This procedure is incorrect because the area bounded by the demand curves in the substituted off-peak period is in fact a pseudo-benefit and is already accounted for by the welfare gain to road pricing in the peak period, i.e., the triangular area 1, in Fig. 3 (Mishan (1988, Chapter 8)). Intuitively, since there are no changes in consumer's or producer's surpluses, there are no net changes in benefits or costs: the additional trips made during the off-peak period are entirely self-financing in the short run. If congestion were to set in during an off-peak period with relatively medium levels of congestion, say, during the inter-peak, efficiency suggests that another congestion toll level be set to internalize the congestion externality. In this way, traffic will settle to another equilibrium 1/ The Smeed Report of 1964 and others effectively asswne away the problem by stating tbat the congestion toll revenues will be retuned to the popuaion in a lump sum nondistorionary manner. 2QI Note tat Baumol & Oates (1988, 2nd edition, Chapter 4) correcs the mistake made in the earlier edition (1975, 1st ed., Chapter 3), which says that only the victims of private good-ype externalities ought to be compensated for after the imposition of a Pigouvian tax. This result is contray to accepted notions of justice. However, Baumol and Oates (1988, pp. 236-240) point out that if the tax revenues were funelled bacwk eabwrcy, then ther would perhaps be only insignificant divergences fiom Paeto optimality. The idea is that wedth effects an consmption ought to be minimized. - 16 - level with a smaller congestion toll in the inter-peak peiod. 'Ais is the idea behind peak-load or differential pdcing. A dynamic process takes place among the peak and inter-peak periods until an equilibrium is settled upon. Proper cost-benefit analysis requires at the changes in net benefits be calculated only in the periods which encounter changes in travel time due to congestion or decongestion. Wit}. a two market model, the welfare effects of road pricing in the peak period are simply repeated in the inter-peak period whenever congestion is encountered. 23. It turns out that there is a case often overlooked in which everyone, including the government, can be shown to be better off. This is the case of 'hypercongestion', where density is beyond the point of maximum flow. Here the traffic density is so high that both traffic flow and speed diminish, with the generalized cost PO and traffic Q0 occurring at point A (Fig. 3(a)). (Even though it violates economic rationality to end up at such a point A, this type of traffic jam does in fact transpire fairly regularly, though limited to peak periods such as peak-of-the-peak.) The implementaton of a marginal cost toll would result in travellers reverting to the normal non- hypercongested portion of the speed-flow curve (such as may be observed downstream of a bottleneck), which corresponds to the lower branch of the AVC curve at point C in Fig. 3 (a). In addition, the travellers have to pay a unit toll payment of distance BC, resulting in a genemlized cost to the motorist of P', which is still lower than P0. Because of the price decrease from PI to P', traffic therefore increases from Q to Q' correspondingly. In this case, literally everyone is made better off: the tolled, what I call the "tolled on," and the government.31 If the speed-flow curve is as depicted in Fig. 1 (b), then hypercongestion appears more often than is commonly realized: it occurs whenever speed drops to half (approximately 60%) of the maximum speed limit. 2/ It can also be shown, using te technique of wdlfr, anDaysis elaborated in the appendix, tbat ai net fit to society from 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 since the French engineer, Jules Dupuit (1844), introduced the powerfiul concept of consumer's surplus to analyze issues of the efficient pricing of (toll) roads, economists have embraced that notion, extending and deepening knowledge in that area. Efficiency analysis carefully shown here indicates that society would unequivocally gain from road pncing. The question that arises naturally is why road pricing, with one single exception worldwide, has failed in the sixties, seventies and eighties to get off the ground. I show, using the analytical framework developed above, that road pricing as sold in the past is most likely doomed to political failure. This is because almost all motorists, including both the ones who are tolled and tolled off, find that they are invariably worse off as a result, except in the case of hypercongestion (see footnote for qualification). The sole unmistakable gainer is the government. If road users do not perceive or are not persuaded that they benefit from the government's newly collected revenues in the form of provision of transport services and worthwhile public expenditures or receive transfers in the form of reduced general tax payments, albeit indirectly, it is highly unlikely that these groups would acquiesce to the pricing of existing roads. Cooperation would be more likely if they are guaranteed a reduction in motor vehicle- related taxes such as import duties, first registration taxes, annual license fees and/or fuel taxes. In particular, the replacement of - rather than an addition to - existing vehicle-related taxes by cost-effective congestion tolls would especially be welcome by road users. 25. A natural question then is as follows: is there a theoretical argument for dedicated funds or earmarking so that society as a whole would benefit from the implementation of road pricing? Restated another way, is there a way in which road users can act as beneficiaries and be 22/ The policy implications discud bero a based on the assumption of costat vduo of tme - the as_mpm used by Walteos and othr n deriving the avegp variable coat curvo (see section XIV, subsaecon , below). My reuk that road pcing makes eveayone wor off except the govenmnt is meant in an averg sune. People's tim valuations differ in reaity, so that this result is modified to say that oly those with fairly hg valuation of time would be better off, and eveyone elso still worse off. Te condition is that the weighted valuation assciated witht time savimgs rectagle of area e+f must exceed their total mony 'ayment of ae b+c+e+f based on a weighted congestion toll. Otrwis, even thos who remain on the toiled road wold continue to pay but would actually be worse off relativo to their status quo. - 18 - indirectly 'compensated for' the payment of tolls by satisfying a commonly accepted notion of fairness, while carefully skirting the first-best pricing rule? I think that the answer is 'yes', although not entirely without qualifications. VI. SHORT RuN EQUILIRIUM 26. The proposition that optimal pricing of and investment in a highway system parallels the short and long run equilibrium conditions of a competitive industry of a textbook commodity was first shown by Herbert Mohring (Mohring and Harwitz (1962), (Mohring (1965, 1976)).3/ Economic analysis of transport problems is simplified considerably by explicitly recognizing the traveller as both consumer and producer, and as producer-traveller he purchases factor inputs such as travel time from himself. This short-run/long-run approach is advanced both cogently and lucidly by Mohring and used by established transportation economists such as Keeler, Small, Kraus, Glaister, Morrison, Winston and Oum. 27. In the short run, some inputs for producing a textbook commodity are regarded as fixed. Under competition, an economically efficient output level is achieved when the market-determined price equals the short-run marginal cost of producing that good. A competitive producer purchases variable inputs by hiring labor and procuring raw materials, in addition to investing in a fixed input, capital. Thereafter, the firm combines the inputs via the production process and creates commodities to be sold to a consumer. In other words, the producer uses the revenue which he obtains from selling the good at the given price to pay for the variable inputs of labor and raw materials, plus the fixed input in the form of quasi-rent on the capital equipment, normally regarded as the accounting profit. The graphs for the textbook commodity are similar to (but not exactly the same as) the case of roads considered in Figures ZV See survey by Winston (1985). 4/ Mhm standard definition of short run is a situaion in which some productive inputs are regarded as fixed, and hence cetain costs would be fixed. However, the definiton of long run refers to a sitation in which all npUtS vary. In the road context, the duration of the long run depends on the rate at which, say, the size of a road and hence the basic or enginering capacity, can be varied. - 19 - 2 and 3.2/ In transport, the short-run marginal cost of a trip, which we derived rigorously from an engineering speed-flow curve, 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. Analogous to 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 competitive level of trips exceeds the efficient quantity in the presence of congestion. Hence, because the quasi-rent of a highway facility would be dissipated due to free competition, an optimal toll should be 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) mathematical statement of 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 maintenance cost of a road discussed in Walters' (1968, p.24) and Newbery's (1989) Proposition 2 (see Fig. 2's legend).X/ As discussed before, to focus our efforts here, the optimal user charge should ultimately include air, noise pollution, accident cost and road damage externalities. 29. Walters (1968, Chapter 2) defines the term 'user charge' as the money charge that governmental authorities levy on travellers for the congestion cost they impose on others and for the variable maintenance cost of the road incurred due to their use of that road. In the absence of congestion, the user charge covers the unit road maintenance cost component only and would be independent of the traffic level. Walters (1968, Chapter 4) then coins the term -economic 251 With sandard goods, both dh short run nmrginal and average variable cost curves canl decline and swing upwards, whers I have shown that both the short run marginal and average variable cost curves i transpt newc decline but only rs upwards. 2I More precisely, Newbery's (1989) Propositions 1 and 2 include the invariate maintenace cost due to weathr. - 20- user charge (EUC)" to be equivalent to the generalized cost concept or user price employed here. This latter usage might lead to a possible misunderstanding about the demand and supply side or even double- counting and is the-efore avoided here. 30. To recapitulate, short run equilibrium in transport occurs when the government, in the form of a highway agency, behaves in an optimizing fashion just as a private competitive firm would were it possible to organize the industry in a competitive fashion. The optimal user charge should not be set equal to the price but wo the difference between the marginal cost and the average variable cost of a trip. IX. CONVRGENCE TOWARDS LONG-RUN EQunITMBR UNDER CONSTANT RETURS 31. So far we have confined ourselves to short-run equilibrium. The fixed cost component has been deliberately left out of the analysis of the marginal cost of a trip.= The motorist is oblivious to the capital cost of a road, and his behavior is independent of it. However, from the highway agency's planning point of view, the capital cost of a road is very much taken into account. Once a highway is built, however, it is regarded as sunk. The sunk cost of a road, once incurred, is irrelevant to a planner: only current and future costs, not historical cost, serve as a correct guide to planning future investment. Since the variable road maintenance cost is assumed to be constant, the marginal cost of a trip thus remains the same. 32. In the long run, however, a highway agency can vary the fixed capital input by expressway expansion, if the investment is deemed justifiable. On the other hand, if a rural road has been built as a result of past planning errors, it can be allowed to deteriorate or be downgraded (or be even auctioned oft. Expanding a road until the additional benefit equals the additional cost of building it would yield maximal net benefit to the community. How might this be done without resortg to a full-scale cost-benefit study? Z1/ Ih fid cost of a firm is defined to be Xt minum amount of outay necessary to str production. - 21 - 33. To see how this might be done, we introduce the fixed cost, i.e., the cost of construction, together with the 'invariate' maintenance, depreciation and operating costs of a road that are incunred by a governmental authority in Figure 5.W1 We then convert the entire fixed cost into the cost per time period of a unit of capital for utilizing the flow of highway services. This is done in order to make it commensurate with the average variable cost of a trip discussed thus far. The summation of the short-run average fixed cost and the average variable cost curve yields the average total cost curve. Charging the optimal toll of the distance t' in Figure 5 seems to be more than sufficient to cover the short-run average fixed cost of the facility. In this case, the optimal toil, t', exceeds the short-run average fixed cost of the facility, SRAFC', by the unit profit difference of u'. In general, there is no a priori reason why toll revenue collections based on short-run margnal cost pricing cannot cover the non-use-related costs of a given highway facility. 34. In the case of a textbook commodity, whenever the quasi-rent being earned by a firm's existing capital equipment exceeds its cost, there is an incentive to expand production. Ultimately, the quasi-rent earned by the existing capital equipment would then be equal to its (fixed) cost.2 Putting it another way, upon seeing the existence of economic profits, other firms enter the industry also, shifting the industry supply outward, increasing output and lowering price as a result. The unrestricted mobility of resources and the entry and exit of firms serve as the instument by which profits would be competed away in due course. When capital is freely varying, long-run equilibrium is reached when zero economic profit occurs. Equivalently sated, the quasi-rent earned on the firm's capital equipment equals its cost, i.e., 71/ hm twm lnvarlaw, ie., non-taffiC rlated nit c cot is found in Walftr (1968, p. 23). aI / e quasim-reit to a firm is the acounti profits p1w interest expens on borrowed fiuds, if any. The acomting profit is the finr's total revu lesa its contwua costs, including interest expse on borrowed fiuds, wags to labor, cost of vw maters, and rental coat of leased buildings. Accounting profit less the madmt run of the owner-mupli.d ma_s i t oconomic profit Altenaively, th qua-rent on imvest capit is te total evau lm the variabb costs, La., including wages, cost of raw mateials and rental cost, but ewludig interet expens an borrowed funds. Total reve leso total vaiable and fixed cost yields economic profits. Tbe fixed cost of invested capital includes tih entire opportunity cost of capital, regardless of wheter funds bonowed or not. (See te thiW footnote of Appendix (footnote 71) and Moaring (1976, pp. 8-11)). I am gratful to HEbrt Mahring for clarifying these points. - 22 - the market return of the cost of reproducing the invested capital. This condition holds under constant returns to scale, where a proportionate increase in all inputs is compatible with the same proportionate increase in outputs. Given fixed factor prices, total cost also doubles, so marginal cost remains constant in the long run. With a slight but crucial modification, this analysis carries over to the case of roads. When the quasi-rent of the existing capital stock exceeds the normal market return on the cost of reproducing the invested capital plus the highway facility's invariate maintenance and depreciation costs, new investment is expected to find its way in that road segment of the highway industry if the appropriate price signals are given. Equivalently, in the long run, if toll revenues - which recover quasi-rents throughout time periods - exceed the entire fixed cost of the existing facility, the highway authority woull have the appropriate incentive to expand a stretch of that road until aU economic profits are eroded away. As we have seen in the case of roads, the variable cost is composed of the user- supplied time and operating costs and are fuUly self-financing. The non-use related costs are then financed separately by the road agency via toll revenue collections. In this way, full costs are covered and there is no need to raise charges when there are constant retums to scale. X. OPrwAL INVSTMNT 35. In the long run, toll revenues would then exactly cover the amorized cost of construction, invaniate maintenance and depreciation costs of roads - a powerful result first shown by Mohring and Harwitz (1962, Chapter 2) and Mohring (1965) - under the technical conditions of constant returns to scale in road construction, maintenance and road use. Constant returns to scale intuitively means that the cost of building and maintaining an expressway is proportional to the capacity. Constant returns to road use yields an intuitive interpretation: travel time depends solely on the volume-cacity ratio. If the engineenng capacity and the QI The (opportunity) cost of a resource used here is the highest reatun of it elsewhere, hence the cost is the maket return on reproduction cost and not historical cost. - 23 - traffic flow were doubled, unit travel times would remain the same.#'1 The final long-run equilibrium is shown in Fig. 6. By faithfully pursuing the policy of marginal cost pricing of a trip by charging a congestion tol - the difference between the marginal cost and the unit variable (time) cost -- and by expanding or appropriately reducing the capacity of the road until there is zero economic profit, the output (of vehicle-kilometers per lane-km per hour) is considered optimal. At a moment in time for an existing road, output is optimal in the sense that, given the marginal-cost price, the efficient level of trips is achieved. Undertaking either more or less trips would involve lowering the net benefit to the community. In the long run, output would be 'doubly' optimal if it is the efficient level of trips for that link of road which has been optimally built. Diagrammatically, not only does the implementation of a congestion toll internalize the external congestion cost, it can be seen that the toll covers the short-run average fixed cost of the road in a stationary state. Recall that for homogeneous traffic the average fixed cost of a road is simply defined to be the difference between the average total cost and the average variable cost. Clearly, collecting a unit toll would cover the entire average fixed cost of the road and yield zero profit only because the existence of economic profit or loss serves as a quasi-market mechanism in the investment decision of whether to expand or contract the highway capacity. With zero profit, the minimum point of a short-run average total cost curve is obtained. For any given level of output, the minimum total cost of yielding this output would be obtained only if the optimal investment level in capacity had been chosen. Looldng at it the other way, the optimum size of a road is obtained by drawing a locus of all the minima of the varous short-run average total cost curves of different sizes (and capital costs) of 3I/ i 1) the capital and invariate maintenance cost of highway capacity, KC, is directly preportional to tbe engineering capacity, K, i.e., KC (K) = aK, wher a is a constant, dhen there exists constat trns to scale in highway construction (and invarate road _mnce). (In mtematical jargon, KC is homogeneous of degroe one in capacity.) The engiering capacity is measired by lane-width and is treated as a continuous variable. Further, tf2)(a) traffic can be expressed in terms of a homogeneous unit, Q, in vehicle per lne-hour, and the time cost function AVC(Q,K) depends direcdy on e traffic flow but is invetsely related to the capacity and (b) {(doubling both highway capacity and traffic flow resut in the travel time of a tt4p remain the same, then there exists constant returns to road use. (Ma cally, the AVC functicn is homogeneous of degree zero in traffic volume and capacity.) With constant retrns to road uw, AVC(Q,K) can be formally rewritten as AVC(QIK), where Q/K is the volume-capacity ratio. Since unit vehicle opeating and variable road maintenace costs are both indepdent of the level of output, and capital cost, KC, is proportional to lane expansion, ATC(Q,K) = ATC(Q/K) holds also. These two technical conditions are crucial to Morng and HaMritz's (1962, pp. 85-90) so-called theorem and to Keele and Small's (1977) extsion of Mohring's theorem. - 24 - highways and choosing that particular size of the road associated with the point where the demand curve intersects its marginal cost curve. We do this because the demand reflects motorists' maximum willingness-to-pay and hence the incremental benefit of the last trip. Since the minimum points of the short-run average total costs under constant returns are of the same height, the long-run average total cost is a horizontal line tangent to all the minima. With the long-run average total cost being constant, so also is the long-run marginal cost. Hence, it is only at the minimum SRATC point that long-rn margin cost pricing holds. X. LoNG-RuN VS. SHORT-RUN MARGINAL COST PICINGRI 36. Intuitively, the long-run marginal cost of producing a trip yields the total cost of undertaking a trp to the community when all fixed and variable inputs can be varied continuously in the long run. Proponents of long-mn marginal cost pricing argue that the market return to capital investment would presumably be fully covered. Yet the equivalence of short- un and long-run marginal cost pricing holds only in certain cases, including the static demand and single period case considered here. As shown in Fig. 6, long-run marginal cost pricing would cover aU the variable costs, including time cost, vehicle operatig cost and variable road maintenance cost, phw the fixed construction, invariate maintenance, depreciation and opeating costs of the road. In fact, short-run marinal cost pricing covers the entire capital cost of the facility just as much as long-run marginal cost pricing does, as can be seen diagrammaticaly in Fig. 6. After all, both the short-run and long-run marginal and average costs are equal in the long mn, with both sets of cost curves intersecting the demand curve at the same point. However, if a road is not optimally constucted but underbuilt, then long-run marginal cost pricing would bend out too low a price signal, thereby exacerbatdng congestion. Short-run marginal cost pricing, on the other hand, would give the corect signal of higher wllingness-to- 321 Pro (1969, p.8), Water (1968, p.33), BDunahn sad Waltn (1979, p.33) and Bird (1976, pp.33-39) argue for ihort-run rq maurl coat pricng whbwru othes argue f1r loun murgnasl comt pncins. Since the msue of long-rm vs. shost-mu maqprnl cot pncnig has bean with u for SmO tinum, a claification in order (swe tfe ntw debate beiwehm Jordan (1983a, 1983b, 1985) ad Vwikoy (198S)). Vikry poinls out tht th concept of log-nm maurginl coat beoome. obfuscated wbh swveal demand priods, e.g., peak, mitepeak and off-peak, occur diunmaUy, givan dlo came of a an sportaion bifrstrucur dot hs aleudy bean constructed - 25 - pay and also yield positive toll revenues and economic profits as a by-product. Short-run marginal cost pricing is the rule to use whenever long-run equilibrium is not reached (and of course when it is). Looking at it another way, if short-run marginal cost is below long-run marginal cost at the current output, it means that the road has been overbuilt. But, of course, this does not mean that the size of the expressway should be or indeed can be varied instantaneously whenever demand fluctuates daily. Rather, it means that the price ought to be varied according to demand patterns using short-run marginal cost pricing. 37. Indeed, Professor WfIliam Vickrey has emphatically argued that there can be no solution to the urban transportation problem without peak-load pricing. Proper time-of-day pricing can be implemented only using short-run marginal cost. (We shall explore this point further in the section on demand variability.) Pursuing short-run marginal cost pricing period by period by varying road capacity incrementally over time would not only guarantee the best use of society's resources but would also enable road agencies to recover all costs - as an incidental by-product - in the long run. It is therefore recommended that short-run marginal cost pricing be used since the concept of long-run margnal cost cannot be unambiguously defined whenever cyclical vaiatons in demand are involved. XII. TRADE-OFF BETWEEN INDBVDUALS' TIM AND TREASURY AccouNTs 38. Another way of obtaining the optimal investment level for roads is to answer the following question: what is the minimum cost to the community of road building, taking into account both the highway agency's desire to minimize the fixed cost of capital facilities and the travelling public's desire to save time' By minimizing the 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 found between individuals' time and the teasury's accounts. Given a non-optimal capital stock (K') assodated with a particular highway, as in the previous graph, 3/ Solving tho problem of codt mininiutios quivalet to solviug tbe problem of maximiton of net benefit to the community. - 26 - Fig. 5, it can be seen that the least cost for the community involves having a road that is too small, for the level of demand depicted. Expanding the capacity of the road may reduce the user's trip cost evaluated at a given traffic level. Long-run equilibrium is reached when the minimum point of the short-run average total cost curve (equals the short-run marginal cost curve) intersects the demand curve. For the governmental authority, road capacity is a choice variable. By increasing its size, the volume-capacity ratio drops in the short run, and so does time cost. However, the cost of road capacity increases. Intuitively, the highway agency continues to expand the road until the marginal benefit from saving users' time costs is just offset by the marginal cost of one unit of capacity. It is at the output, Q* with an optimally built road K*, in Fig. 6 that the valuation of the last trip taken just equals its marginal cost, that is, the incremental cost of the trip to others, the motorist's own time cost in congested traffic, plus the vehicle operating cost and the road maintenance cost.3' The highway agency, by setting an optimal road user charge which is equal to the congestion toll and the variable road maintenance cost component, would be able to induce the motorist to travel up to the point where the price of a trip equals its short-run marginal cost. By pursuing this pricing policy for each stretch of road, the use of a non-optimal, existing highway network would be optimized. Further, by expanding highway capacity up to the point where the quasi-rent of each capital facility just covers the cost of reproducing it, with zero (economic) profit remaining, the net benefit to the community would be maximized. By symmety, abandoning or downgrading roads is necessary when economic losses occur. The decision of not maintaining roads is tantamount to the act of disinvesting roads. AII Formally, given a particular level of output, the cost-iniming autority would expand the road up to the poiat where the marginal valuation in time savings due to a unit increase in capacity, - Q * AAVC(Q,K)/IK, equals to the marginal cost of a unit of capacity, R. R is the rental cost per time period of capacity, which includes the invariate maintenance and other opeting costs of a road, depreciation and imputed interest on invested capital. The negative sign would offset the inverse relationahip of AVC and K, yielding a positive magnitude for the entire term. Alternatively, the road is to be expanded up to the point where the marginal extenal congestion cost just offsets the marginal cost of investment in capacity. This is the second optimality le: the optimal investmt in capacity nle. D1/ The superscript * symbol indicates that that variable is optimized. - 27 - 39. Henceforth, to simplify both our discussion and the diagrams, we ignore the individual's vehicle operating cost and the variable road maintenance cost since they are self-financing.2/ Note that our conclusions thus far hold under the assumption of constant returns to scale and perfect divisibility of 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 congestion toll t3* and optimaly built the road by investing at 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 conveniently left 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 component costs under constant returns are doubled, then i) the fixed costs of construction, maintenance and depreciation, ii) the variable time costs, and fii) the total costs are all doubled.38/ Intuitively, the geometric doubling of the rectangular areas of road construction and maintenance costs is synonymous with 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 supplied by individual users is akin to the technical condition of zero economies of scale in road use. 36/ I have tberefore grouped the non-traffic related ma_itc and operting costs as part of dte short-run average fixed coat curve. Bear il mind that the variable road maitenance cost (not drawn in Fig. 7(a)) is being recovered by a separate road user charge component as shown in Fig. 2. With the condition of zero economies of scale in total road mainltnce, the total mintenance cost is thus exactly doubled. Also, economic profits from now on will be refenred to as 'profits'. n/ Three lane roads are found in Australia where they are referred to as, 'two-and-a-half lane roads' by Hoban (1987). Lg/ The stringent assumption of a road being finely divisible will be relaxed and indivisibilities introduced later on. - 28 - XH. FIRST-BBST OPTIMAL PRICING AM INVESIMNT RuLE Empda Considerations: 40. By estimatng behavioral travel demand functions using state-of-the-art logit mode choice models, one could obtain empirical esdmates of marginal valuation of time (as a function of income levels) (Hau (1986)). When combined with a fine-grained, parametric transportation corridor supply model of the San Francisco Bay Area (Talvitie and Associates (1978)), multi- market demand and supply could be equilibrated and cost-benefit analysis of alternative policies performed (Hau (1987)). Heuristically, the adjustment process towards the final equilibium parallels that of the cobweb equilibrium model of adjustment. Optimal tolls and welfare gains and losses could thus be simulated with apprpriat specification of the marginal travel time function. The results obtained are for a short-run equilibrum model of demand and supply. 41. Even with poor data, one could make some progress in empirical work. Given an estimate of a speed-flow curve and the corresponding travel-time flow curve, we know how these engineering curves can be converted to a short-run average variable cost curve of a trip, using an estimate of the value of time. A 'supply' elasticity estimate together with a value for unit variable cost would yield a one-to-one coaepondence between the short-run average variable cost and the marginal cost (see footnote 15 for formula). A rmugh estimate of the demand elasticity and the traffic level of a particular road would yield a first order approximation of the proper congestion toll. Now, in order to maximize aggregate net benefit, two operating rules should be followed by the road authority. The First Rule - The Optimal Pridng Rule: For each stretch of road, short-run marginal cost pricing is fulfilled by setting a toll at the excess of short-run marginal cost over short-nm average variable cost. The intuition is that this congestion toll would serve to internalize the congestion cost that a driver imposes on others. In addition, the motorist is charged another component which covers the variable maintenance and opeating costs of a road which he imposes on the road authority. Thus the public authority's imposition of an optimal road user -29 - charge would cover both the extrnal cost of congestion as well as the variable road maintenance and operating costs. The Second Rule - The Optimal Capacit Rule: Under constant returns to scale and optimal pricing, whenever economic profit is found in the operton of one road link, the procedure would be to expand the capacity of that stretch of road. The existence of a loss under short-run marginal cost pricing suggests that the road has been overbuilt. By altering the capacity of each road in the long run according to the quasi-market signal of profits and losses, the entire highway network's investment level in capacity would be aptimized, with the fixed cost of each road covered. Alternatively, the road authority, by trading its direct resource costs against individuals' travel time, follows the rule of setting the marginal travel time savings equal to the matginal cost of investment for an additional unit of capacity. The capacity of a road is expanded until the marginal capital cost equals the marginal (external) congesdon cost. erWpective on the Result: 42. What we have descibed is the long-run equilibrium of an optimally designed capacity of a road network under constant ren. If the road authority were: 1) to pursue the efficiency-enhancing policy of pricing according to the margnal cost of a trip, and 2) to minimize the sum of the direct resource costs of providing a road and the value of user-supplied travel time inputs, then the road would be both efficiently utlized and optimally expanded. Notice that the optimally designed road has a positive amount of external congestion cost. This results from the road agency's desire to minimize both the sum of the direct cost of the investment in capacity and individual drivers' travel time cost. In our simple framework, congestion delay would never be entirely absent, contrary to what environmentalists and road users would prefer, because achieving zero congeson is very costy to the community. in other words, an optimal amount of congestion extenality is a valid concept, just as an optimal amount of pollution has long been recognized in the envinmental economics literature. What if there is no congestion on a particular road? Zero congestion means that that stretch of road has been overbuilt (or priced non-optimally) and should perhaps be downgraded or even abandoned. If - 30 - excess capacity occurs all the time, the road possesses the non-rival consumption characteristic of a pure public good. Then we are faced squarely with the standard task of provision of public goods. If resources are plentiful, financing the shortfall via general revenue taxation has been the conventional dictum. Similarly, if public resources are scarce, the opportunity cost of public funds must be accounted for.& If lump sum taxation is infeasible and resources are severely inadequate because of political constraints, then it is possible for one to consider the feasibility of financing via Ramsey pricing.0 If it is uncertain whether the (marginal) deadweight losses from general revenue financing exceed those obtained from Ramsey taxation, financial and other considerations such as equity may then have to be appealed to in order to justify the potential use of Ramsey pricing in the road sector. 43. By contrast, a road would possess the .ival consumption characteristic of a private good when excess demand occurs. Hence a congested road is also regarded as a congested variable- use public facility. Because of this mixed good nature, and based on the theory derived here from first principles, the provision of road services ought to reside with the public sector. Under tL ;ondition of constant returns, the optimal toll revenue, which captures the quasi-rent earned from the invested capital, would cover the entire fixed cost of the road in the long run. No residual or overhead cost need be allocated. If profit exists, then it is because there is insufficient road capacity (or pricing at a level above marginal cost). The road is therefore not 9/ In the comion paper (Hau (1991)), I present calclatios of the opporunity cost of finacing alternative chang mechianms. 40I Frank Ramsey's (1927) inverse elasticity formula under the case of independent demands was discovered in rens to Pigou's question of how to set tax rates in order to minimize the welfare losses associated with meefting a tax revenue requirem The problem of the choice of optimal tax rates which are subject to a revenue conshaint is formally equivalent to that of the setting of optimal prices which are budget-constrained. Ramsey prcing in the presence of axtalities reqires that it be computed on the basis of maginal cost and a facdon of the marginal extemd cost (Oum and Trethaway (1988)). Clearly, in the presence of leakages, non- excludability and partid rivalry in consumption, the uirements for the implemtaton of Ramsey pricing are considerably mmre stingent than those of pursuing marginal cost pricing. On conceptual, empirical and implementation grounds, marginal cost pricing is superior to even the simplest form of Ramsey pricing: the invene elasticity nrle. The computaton of Ramsey prices, for instance, requires the estimation of margial cost as a prerequisite and the determination of revenue targets. Despite all the problems with which Ramsey pricing is fraught, research into this itring issuo is potentially useful. After all, increasingly tight fiscal constains, countries will demand alteative funding machaims. - 31 - in long-run equilibrium. The existence of profit serves as a surrogate market signal to expand capacity. The motto is as follows: "If a road makes money (i.e., economic profit), expand it, else not." Similarly, if a road loses money, it suggests that planners made the wrong decision or were given over-opdimistic forecasts of travel demand. In that case, marginal cost pricing is still to be adhered to, with the congestion toll set close to nil. A user charge component is still needed to cover the variable road maintenance cost. Thus it may even be worthwhile to abandon a money-losing road and save on any annual invariate maintenance costs that might arise. Efficient pricing, financial viability and cost recovery are therefore entirely consistent with one another under constant returns to scale in long-run equilibrium. XNV. RELAXAnON OF AssuMPTIONs 44. The above discussion assumes that the government aims to maximize welfare of the community by simulating the workings of a competitive industry and pricing highway services at marginal cost. There are a few major assumptions that need to be relaxed: 1) constant value of time, 2) static demand, 3) perfext divisibility, 4) constant returns to scale and 5) variability of road thickness. We consider the relaxation of each assumption in turn. 1) Differences in Time Valtion 45. The traditional presentation of road pricing and my ensuing critique assume a constant value of time (Walters (1961a))A'1 The diagrammatic analysis in Figs. 2 and 3 implicitly assumes that every driver is identical and maintains the same time valuation. What happens when there are heterogeneous motorists, with different time valuation and tastes? A mathematical proof that generalizes the above result for homogeneous drivers to heterogeneous ones with different values of time is shown by Mohring ((1975), (1976, Chapter 4 Appendix) and Strotz (1964a, 1964b), but the intuition behind it is not difficult. Instead of the optimal toll 41/ In his pionering work on road pricing, Walters (1961) (and authors thereafter) assues that traffic is homogeneous, with all vehicles and drivers being the same, with the resultant identical valuation of time for all. - 32 - being based on a representative driver's value of ime, the time value is now a weighted average of the different motorists' valuation of time, weighted by the number of trips taken by those motorists who actually use the facility. If a traveller's time value and the number of trips are close to the average, he will pay the average toll payment. If another motorist's time value is higher [lower] than average, he would be willing to pay more (lessi than the average toll payment for taking a trip. He thus would be willing to, though begrudgingly, pay the difference. The congestion toll, P' - P", in Fig. 3 then can be labeled the wighted congestion toll, and the constant value of time is re-interpreted as the weighted average valuation of time. For a trip with a sufficiently higher than average time value, the time saving of a trip, (P - PI% can be even higher than the weighted congestion toll, P' - P", thus making the motorist better off. On the other hand, for a (shopping) trip having a lower time valuation, the user still has to make the average payment and therefore would be made worse off. Nevertheless, they both remain on the tolled road, as opposed to being tolled off, because their individual trips' marginal valuation or maximum willingness-to-pay still exceeds the generalized cost of their respective journeys. The use of alternative values of time would relax the point I made earlier that road pricing would make aUl groups except the government worse eff. By relaxing the assumption of a constant value of time for everyone, those people with high values of time would be made better off at the expense of those with low values of time. This intuitive analysis assumes that everyone is faced with the same toll, as in the workings of a competitive economy, and that a perfectly discriminating monopolistic authority is non-existent. 46. We conclude that a single transportation facility with differences in values of time would not alter fundamentally our derived result, uing the standard assumpton of constant returns. Again, with efficient pnrcng, financial viability and full cost recovery are achievable. 2) Demand Variabilit and Peak-Load Pricing 47. We have in fact considered the case of variable demands, Iwr ala, when we discussed the welfare impact of road pricing on the peak and the off-peak periods. There it was shown that a congestion toll is needed during the peak when there is excess demand but not during the - 33 - off-peak when there is excess capacity. Notice that because there is free-flowing traffic in the off-peak, no tolling is required because no external cost of congestion is generated. Therefore no quasi-rent is being earned on the invested capital and only the variable costs are paid for by the traveller. On the other hand, during the peak period, a positive quasi-rent is earned. (Suppose further that there is an inter-peak period, some quasi-rents are also generated.) With highway capital stock remaining unchanged, the systematic, diurnal nature of travel demand (as opposed to the static, invariant demand case) means that the sum of quasi-rents (rather than just the quasi-rent from the singular peak period itself) of the invested capital should be compared with the cost of the highway facility. In other words, when all the quasi-rents over the entire demand cycle are summed up and compared with the capital cost, expansion of the highway is either warranted or not, under constant returns. The same conclusions obtained thus far again hold.F 48. P intereting implication is that the entire capital cost of the highway is 'allocated to' and bome by peak travelers, mainly nsh-hour commuters. This surprising result may seem 'inequitable', yet it is perfectly consistent with efficiency analysis. After all, it is peak users themselves that create congestion and they that demand the use of heavily congested expressways which require massive infrastructure developments. Without them, the optimal size of the road would be considerably smaller. The result of allocating all capital costs to users of the peak period has long been recognized in the literature on the pricing of public utilities a la Boiteux (1960). Following our earlier example, the extent to which there is another period - the interpeak or shoulder period - with even a modest amount of congestion, would allow for differential pricing and thus the allocation of some capital costs to these interpeak travellers. The optimal investment rule is then to expand a road until the sum of the quasi-rents over the demand cycle equals the entire capital cost of the facility under constant returns. By inplementing peak-load pricing and altering the investment level of the highway facility, depending on whether profits are positive or negative, the highway network is again optimized. 4/ The ouput vuiable needs to be rodefined as vehicles pe lane per cycle, with the cycle being the durton of a particular chugin period. - 34 - Hence, the consideration of demand variability and peak-load pricing would not change the status of our conclusions, in the presence of differences in valuation of time. The fact that the fluctuating demands over the various peak, off-peak and inter-peak periods of a demand cycle are linked by a fixed capital facility and the observation that the consumption of trips must be satisfied by the production of trips during that particular time period combine to yield a simple modification of our result. Pricing, financial viability and cost recovery are again consistent with one another. 49. Keeler and Small (1977) show rigorously how the Mohring-Harwitz framework developed here is extended to the case of variable demands using peak-load pricing in the presence of independent demands and no indivisibilities.43 By assuming the demand in each period in fact depends on other periods, i.e., the case of dependent demands, the derived results still go through (Mohring (1970))AY' 3)ndisiaik 50. While still retaining the assumption of constant returns, but accounting for differences in values of time and demand variability, we proceed to drop the assumption of a road being finely divisible. Road construction, in fact, involves significant indivisibilities that cannot be ignored. For example, a road must possess the minimum width for accommodating a standard- sized automobile and should also, ideally, be bi-directional. In the perfectly divisible case, the long-run average total cost carve which envelopes a continuwm of closely-packed short-run average total cos; cur. es at their minimum points is made horizontal. A flat LRMC curve also coincides with the corresponding LRATC curve (see Fig. 7(b)). Due to the presence of 431 It is due to the asumption of independet dems Ihat long-rn marginal cost pricing (equals to short-nm margnal cost pricing) stil holds at each time period. The concept of long-nm marginal cost pricing is blurrd in the case of jointness of demand 44/ Using the distibution of current demand distribution as given, which is synonymous with asumig independent demands, would result in upward bias in peak periods and downward bias in off-peak penods because of the possibility of substitution (Keeler and Small (1977)). - 35 - indivisibilities, however, the formerly neat and continuous pattern of the LRMC curve is broken (Neutze (1966), Kraus (1981b)). The new long-run average total cost curve is now composed of a series of short-run average total cost curves, where SRATC2, SRATC4 and SRATC6 denote a two-lane, four-lane and six-lane road respectively. The long-nm average total cost curve is a series of short-run average total cost curves connected together in a scalloped-like pattem (see the solid LRATC curve labelled ABCDEFG in Fig. 8).AV The long-run marginal cost curve takes on the various short-run marginal cost curves in the respective regions, resulting in a discontinuous shark's tooth-shaped LRMC curve (see the thick LRMC curve in Fig. 8(a)). Hence one is always working with the short-run curves themselves since one could only operate with a capital facility which is given. By now, it should be clear that whenever a short-run marginal cost curve rises above a short-run average total cost curve, profits can be obtained under short-run marginal cost pricing. Thus, if demand happens to intersect the short-run marginal cost curves in the region of Q2Q24, Q4Q4 and Q6Q&, and multiples thereof, then the road makes money in the long run under constant returns. 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-lane road, as traffic increases, the road's large fixed cost is spread over the additional traffic, and as congestion sets in, the road begins to make money. In other words, as travel demand continues to grow along the trend, adherence to short-run marginal cost pricing suggests that the road would go through an unavoidable cyclical pattern of deficit, surplus, deficit, surplus, etc. Whether or not one undertaks a road expansion project from two to four lanes depends on the magnitude of the net benefit pie, taking into account the welfare gain and loss triangles. Optimal Pricing and Investment with Indivisibilities: An Example 51. Consider the demand as depicted in Fig. 8(b), with the actual consideration of indivisibilities. First, we follow the first-best pricing rule of tolling the difference between 4S/ A similr set of discontinuous curves is found in, for example, Bennathan and Walters (1979, Fig. 2.2). Note that the scalloped-like pattern is asymmetric because the unit cost curves for four and six lane roads are horizontal multiples of those of the two-lane road. In other words, under constant retns to scale, the AVC and AFC curves, and hence ATC curves fan out horizontally - a mistake that is quite frequently made in the literature (see, for example, Hayutin (1984, Fig. 2.8 and 2.16)). - 36 - short-run marginal cost and short-run average variable cost, t*. This yields the optimal traffic level of Q* and a positive profit. Without the indivisibility constraint, the existence of profit would indicate that the road is underbuilt. With indivisibilities, the direct one-to-one correspondence between economic profit and road expansion is lost. One is therefore left with the binary choice of, say, expanding the road from a 2-lane road to a 4-lane road. Using the welfare apparatus that we have developed in the Appendix and Figs. 3 and 4, however, the net benefit of such a move is shown to be the sum of the welfare gain of going from Qz to Q**, as indicated by the triangular areas b+c, and the welfare loss of moving from Q* to Qz4, as shown by the triangular area a. Such a move would clearly be desirable. With a 4-lane road, however, the optimal toll of t** would be insufficient to cover the fixed cost of this new road, resulting in a shortfall. Thus, even though the move from Q* to Q** is a beneficial one, it would mean that the road authonty would switch from a profitable regime to a loss regime after incurring the investment cost. 52. Thus the optimal sequence of decision-making is first to establish the policy of implementing marginal cost pricing and then to plan future adjustments of the road network according to exeed future demand and established pricing policies. When demand fluctuates, pursuing short-run marginal cost pricing at present would mean setting different prices, or tolls, in response to expected current conditions. 53. Suppose the govermment were faced with a tight budget constraint. It would understandably then be unable to undetak all public projects with positive net benefits. If this road authority were mainly concened about cash flow and financial viability, it could opt not to expand a road, i.e., under-invest, but stll charge a congestion toll on the built-up traffic and satisfy economic efficiency in the short run. This option however would not lead to the maximization of society's welfare in the long run. - 37 - * Returms to Scale 54. The issue of whether constant returns to scale exists or not in road transport is a controversial and imporant one. Uldmately, it can be answered only via careful statistical analysis. The available evidence in road transportation indicates that aU three cases exist: decreasing, constant and increasing returns to scale (see Fig. 9) - paraleling the case of a competitive private firm and industry - with profit, zero profit and loss, respectively. (This is but a well-known result of economic theory applied with slight modification to the highway.) It is important to realize at the outset that the case of scale economies, or increasing returns to scale with fixed factor pnces under least cost combinations, is merely a case of insufficient demand with respect to the market size in the long run - a point that is sometimes neglected. The implication is that if traffic were to grow to a point where the capacity of a road is reached, congestion delay would set in, and congestion toll revenues could be collected. After all, the short-run marginal cost curve is always non-decreasing, as shown in Fig. 8. Profits may occur despiue the fact that the long-run average and cost curve may be declining and the conesponding long-mn marginal cost curve lies below the average cost curve.46 Then if traffic were to continue to grow as real incomes and auto ownership rise, concomitant with expressway expansion, the decreasing retun region would then be encountered (see Fig. 9). In the case of incresn returns with perfect divisibility (where natural monopoly arguments lie), the long- run marginal cost curve below the long-run average total cost curve pulls it downwards, resulting in losses, beckoning government subsidization. On the other hand, if travel demand is sufficiently high relative to the engineering capacities of roads, the money-maldng road enteprises would provide much sought-after funds which could be used to finance efficiently priced but money-losing roads - only if these roads yield positive net benefits to society. We turn next to a disussion of the theory underlying the economies vs. diseconomies issue, together with perfect divisibility vs. indivisibilities, and end with a review of the empirical evidence and recent work. di/ This poiut wM be e_bid laer in Fig. 12 and 13(a). Basically, with paefct or lmost perfect divisibility and scaleo e_ondes, only lossks will occur, wh with indiviibilies, eithe profits or losses will mlt depadu athM level of travel demand - 38 - A. Economies of Scale and Rural Roads 55. There is a preponderance of evidence -- geometric, engineering and otherwise - supporting the case that there are significant economies 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 minimum of a twelve-feet width for each lane and a few feet for shoulders and drainage ditches. What this means is that a non-trivial proportion of the provision of a road's right-of-way involves dead space. These indivisibilities - required to contribute to the building of a minimum acceptable standard such as a given pavement thickness and road size - help contribute to economies of scale as the large fixed cost of construction and invariate maintenance costs are shared over greater amounts of traffic. Thus doubling the 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 engineering or basic capacity of a two-lane road is about 2000 vehicles per hour. Since the standard four-lane road has an average engineering capacity of 1800 - 2000 vehicles per lane-hour, doubling the width of a two- lane 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 associated with road use. However, capacity per lane remains constant beyond four-lane roads, resulting in zero economies of road use thereafter. Further, in order to level hilly terrain and/or fill valley for transportation purposes, the earth moving costs rise less than proportionately. In fairly flat or rolling country selected as sites for road building, doubling the width of a two-lane road generally involves less than doubling the earth moving costs. (On steep hillsides, however, the reverse may be true.) Hence, for these three reasons of: 1) the existence of large fixed costs due to indivisibilities, 2) the technology of road capacity, and 3) the possible reduction in earth moving costs, we can claim that there are economies of scale associated with the construction of a two-lane to a four-lane road. Nevertheless, despite the fact that typical four-lane highways 471 Meyer, lain and Wohl (1965, pp. 200-204) also found some evidence of scale economies of ur*a roads. However, Keeler and Smal (1977, p. 5) query Meyer, Kain and Wohl's findings, stadng that their results are in fact based on their inital assumptions. - 39 - possess two-thirds dead space and eight-lane highways have only half the dead space, it is not clear from the geometry of highway rights-of-way that economies of scale in urban highway construction exist. This is because it is rather difficult to control econometrically for the effects of urbanization and separate it from the effects of size. For example, four-lane roads tend to be built in rural areas, where interchanges and overpasses are widely dispersed, and right-of-way costs are low. On the other hand, six-lane or eight-lane roads are built mainly near metropolitan conurbations, where expressway interchanges and overpasses are closely spaced together, and land acquisition costs are high. In practice, the road authority tends to trade off (and avoid) high right-of-way costs with increased tunnelling and flyover construction costs. Lane expansion from a six-lane to an eight-lane expressway at the margin, for example, would increasingly encounter alignment constraints associated with the terrain. (rhese constraints might explain why capacity per lane is reduced with six- to eight-lane expansion (Mohring and Harwitz (1962, p. 97)).) This argument is quite independent of whether the expressway is located near urban areas. Hence all three cases of returns to scale occur, resulting in the classic, U-shaped long-run average cost curve, paralleling that of a firm within a competitive industry as we have seen in Fig. 9. B. Diseconomies of Scale and Urban Roads 56. The discussion thus far has centered on economies of scale to road width for single roads, as opposed to a system of roads. Strotz (1964a) conjectures, and Vickrey argues convincingly, that there are considerable disecononr -- of scale associated with an urban road networks.48/ The reasoning is based on the geometry of rc I network. Given a rectangular grid for an urban road network spaced 2 kilometers apart, as in Fig. 10(a), there are 9 sets of (space-intensive) intersections and traffic lights in a 6 kilometer-wide area. Suppose the number of streets is doubled in order to double road capacity, yielding a grid of a one kilometer-wide spacing (Fig. 10(b)). Quite apart from the possible increase of construction or land acquisitions Al/ I am extremely gratefil to William Vickrey for pointing out the subtleties of these argumets. See Vickrey (1965, pp. 287-288) and Mohring (1976, pp. 144-145) also for the basic line of reasoning. - 40 - costs, the number of intersections - and the required land area and tffic light installations - is quadrupled to 36. (If no taffic lights are installed, each intersection requires an even costlier overpass or perhaps even a full interchange, a case considered by Mohring (1976, pp. 144-145).) Moreover, despite the fact that trip length remains unchanged between the origin, 0, and the destination, D, the number of traffic lights encountered, and hence waiting costs, would then double from 4 to 8 (unless overpasses or interchanges are constructed). Either the installation of traffic lights or the building of overpasses and interchanges would serve to bid up the opportunity cost of land (because less non-highway space would be left for business or other activity) as well as to increase substantially the sum total of the costs of undertaking a trip to the community, resulting in a rising long-run average cost and also a long-run marginal cost curve. The resultant long-run equilibrium for an urban road network in the presence of diseconomies of scale is depicted in Fig. 11. The analysis of the rlationship between long- and short-run cost curves is similar to the case of constant reurns to scale and is not repeated here. However, because the long-run average cost curve is rising, the short-run average total cost curve for a two-lane road, SRATC2, is tangent to the long-run average cost curve to the right of the minimum SRATC2 point. Because the SRMC2 lies above the SRATC2, SRMC2 intersects the LRMC from below. Short-run marginal cost pricing is equivalent to long-run marginal cost pricing at the efficient output level Q2*. Notice that the optimal toll, tV*, follows from pricing at short-run marginal cost and tolling the difference between short-run marginal cost and short- run average variable cost. The difference between SRATC2 and SRAVC2 is, by definition, SRAFC2. The optimal toll, t2*, cLearly exceeds the SRAF4 by the unit profit of 12*, with the corresponding rectangular area of profit wa* Q2*. As the urban road network expands from an existing single two-lane road to a double two-lane road, say, substantially costlier construction, tunnelling and land acquisition costs are encountered.10 We have also established that time costs rise because of additional interons and wait time required. Either of the above two factors would serve to push the SRAFC and SRAVC curves up, together with the SRATC curve. Just as the congestion toll filled in the wedge caused by the divergence of short-run marginal and 49/ raing finai cost of otuctin via tu ig aNd/or flyover., together with high land r_smption cod, ae comdmt with the findiyp of Hau (1989) for Hong Kog. - 41 - average variable cost curves, the divergence between long-run marginal and average total cost curves serves as an indicator of the unit profit (or loss). In competitive equilibrium, all economic profits are competed away in the long run, so the questions that follow are: in what sense is the case of diseconomies of scale a 'long-run' concept, and what is the interpretation of the profit areas of r2* Q2* and v4* Q4* (for demand curves Q24 and Q, respectively)? The existence of economic profits in the long run is attributable to the rents earned by an invaluable fixed factor of production - land.5Q/ Even though both the SRAFC and the SRAVC curves reflect the increase in costs mentioned above, the existence of the rising opportuniy cost of the fixed factor of the remaining parcels of land is still left unaccounted for. Intuitively, just as the driver, in the short run, by imposing external congestion cost on others due to his presence on the road, is charged for it, so also should the urban community, in the long run, charge for the use of scarce urban land in a market economy. Putting it another way, if all factors of production -- including land - were doubled, so that a scarcity value could be imputed to land, all economic profits would be competed away and vanish in the long run. Clearly, the supply of land cannot be doubled, so it is the existence of land rents which yields (the areas of) economic profits in Fig. 11. Notice that we could no longer use of the existence of profits as a surrogate market signal because of decreasing returns to scale. Since the urban road network is supposed to generate substantial sums of money because of high land values, relying solely on the profit mechanism and incautiously investing on urban roads until aU economic profits are competed away would result in over-investment in road capacity. With diseconomies of scale and divisibility, roads geneate positive profits. Performing proper project appraisal of roads cannot therefore be circumvented. C. Diseconomies of Scale and Indivisibilities 57. The case of disoconomies of scale combined with indivisibilities is similar in spirit to the analysis of the constant returns case with indivisibilities in Fig. 8. For instance, at any IQ/ A puristMh agu ttthes rs actully acorns to lanonesmd thusual udoly of longnm super- profits beg zeo sotill holds i pn tb po of risng log-nm aveag costs. - 42 - moment in time, the regions to the right of Qz,, and Qg in Fig. 11 would yield profits. In the rise of decreasing returns to scale, with or without indivisibilities, the correct recourse is to invest only if the road project in question passes a stringent cost-benefit test and only if rising costs of roads are compared to the quasi-rents generated L the variable demand periods diurnally. In other words short-run marginal cost pricing, or congestion tolling, as opposed to long-run marginal cost pricing, should be implemented for each period over the demand cycle and the quasi-rents summed up, regardless of whether the facility is optimally built. When demand is not known with certainty, probabilistic or expected demand could be used instead and all real benefits and costs over the economic life and time periods of a project should be properly measured, discounted and compared with the capital cost of implementing the change. If finely divisible projects are available, we have seen that the procedure is to invest until the marginal benefit of a project -- in the form of time savings -- equals the marginal cost of constructing the capital facility. If indivisibilities abound, then traditional public investment criteria using the net present value criterion or Mishan's (1988, Chapters 35-38) normalized intemal rate of return procedure could then be complemented with the diagrammatic welfare analysis presented in this paper. In such a case, unfortunately, the neat linkage between profits and losses as a 'market' mechanism and guide to investment is severed. Thus it is possible for a project with high net benefit to yiew a financial deficit. As mentioned before, if a road authority were faced with a severe fiscal constraint, then the road agency could choose to under- invest, rather than over-invest, when faced with an all-or-nothing situation of indivisibilites. Still, it should pursue marginal cost pricing in the short run, while fully takdng into account the opportunity cost of congestion toll financing (see Hau (1992)). In this way, short-run marginal cost pricing would yield both economic efficiency and profit, even though an optimal investment strategy would generate an even higher level of net benefit for the community in the long run. D. Economies of Scale and Indivisibilites 58. Per contra, the above analysis for the case of decreasing retums to scale of an urban road network carries over in reverse to the case of increasing returns to scale for rural roads. There the sum total of the quasi-rents captured via short-run marginal cost pricing is insufficient - 43 - to cover the entire fixed cost of a particular rurl road. Scale economies abound in the construction of rural roads, so that unit losses, 12* and L4*, result in the case of an optimized two-lane and four-lane rural road, respectively (see Fig. 12). Standard neoclassical arguments then call for subsidization out of the public treasury for the case of scale economies. The presence of both indivisibilities and scale economies :iuld alter the calculation of optimal tolls and subsidies substantially (Kraus (1981b)). It turns out, perhaps surprisingly, that the existence of indivisibilities serves to improve the state of affairs vis-a-vis the government because, as was shown in the constant and decreasing returns to scale cases with indivisibilities, both surpluses and deficits would occur alternately, depending on the level of travel demand. Similarly, in the case of rural roads with both scale economies and indivisibilities, there are regions (such as those to the right of QO,, and Q4.1. in Fig. 12) where short-run marginal cost pricing yields profits rather than losses. This is because, with indivisibilities, the long-run marginal cost curve - composed of joined segments of the short-run marginal cost curves -- is no longer declining all the way but possesses a sawtoothed pattern, alternately exceeding its corresponding long-run (and short-run) average total cost curves and rising at an even faster rate. Thus, just as in the case of constant returns with indivisibilities, whenever a SRMC curve exceeds a SRATC curve, profit exists and vice versa. It is therefore quite conceivable to have a congested two-lane road which generates profits even when subject to increasing returns to scale for sufficiently large changes in capacity. The existence of losses does not mean that the road agency should cut back on the provision of highway services. On the contrary, it merely means that other sources of funds ought to be sought in order to finance a worthy project. The government authority's decision to cut back services just because of losses in such a situation would yield under- investment and possibly stifle economic development and growth in the longer run. The neat linkage between road expenditures and toll revenues has disappeared. Again, the passage of a tough cost-benefit criterion is then a prerequisite for a project to result in maximizing society's welfare. To repeat, only (fcongestion toll financing is all that is sought by the road agency, and not optimnl investment, is it possble to let a two-lane road become congested in the face of rising urbanization and motorization, while differentially pricing it via congestion tolls. In this way, efficient use of a given road is enhanced via short-run marginal cost pricing, but the efficient level of road capacity is not being achieved in the long run. - 44 - E. The Extent of Indivisibilities vs. Divsibilty and Their Effects on Scak Qs)=coomies 59. How often do we encounter surpluses in the presence of scale economies and deficits in the presence of diseconomies? The answer depends on the extent of the presence or absence of indivisibilities. There are two views on this issue. The fist perspective a la Keeler, SmaU and Starkie argues that the aggregate road network could be regarded as divisible. The other view, presented by Walters (1968, Chapter 3) and Kraus (1981b), contends that roads are indivisible because the main measure of highway capacity involves the discreetness of the number of lanes. 60. The construction of a road or an additional lane may not be finely divisible in and of itself, but taking the road network as a whok, a single newly constructed facility can be regarded as an icremental addition to the network, resulting in the applicability of the foregoig marginal analysis (Keeler, SmaU and Associates (1975, Chapter 2)). Also, often times, varying some dimensions of road features, other than the number of lanes, increases the capacity of the road network. For example, the lane width, the provision of auxiliary lanes, horizontal and vertical alignments, and the surfacing of road shoulders can all be varied incrementally (Starkie (1982)). One could characterize this view by treating the lane capacity as a continuous variable rther than a discrete one (Small, Winston and Evans (1989, p. 103)). If the road authority pursues the twin optimizing rules of pricing and investment in capacity, then the road network would be in long-run equilibrium. So with constant returns and a divisible road network, roads would break even. However, some individual roads would make money and some would lose money. On the whole, if the economies and diseconomias of scale are "probably roughly offsetting" as Meyer and G6mez-Ibgflez (1981, pp. 191-192) concluded, then the highway budget would be balanced. Whether or not scale economies and diseconomies are counter-balancing would depend on the degree of urbaniation. With increasng urbanizaton, profits would tend to predominate even after charging land rents as a cost. With indivisibilities, the profit (or loss) A/ Consnt or even decreang raturns would be satified if two bi-directional roadwys ae built in proximity to on another. -45 - regime occurs about half the time but it is unclear what the relative weights would be when travel demand is reasonably assumed to grow over time. 61. Under decreasing returns and perfect divisibility, we have shown in Fig. 11 that profits always occur. The essence of that figure is combined with Figs. 13(a) through 13(c). Perfect (Fig. 11) and almost perfect divisibility (Fig. 13(a)) and an urban road network would mean that the marginal cost priing of trips would always be profitable. Note that the continuous regime of profit will not be uniform once a threshold level of indivisibilities is reached, resulting in regions where losses also occur. If the extent of indivisibilities progresses from small but significant (Fig. 13(b)) to severe (Fig. 13(c)), the regions which yield potential losses become even larger. The symmetry caries over to the increasing returns to scale case. Again, the substance of Fig. 12 is culled and combined with Figs. 14(a) through 14(c). With perfect (Fig. 12) and almost perfect divisibility (Fig. 14(a)) in the presence of scale economies, losses would always occur. With scale economies and a 'significant' level of indivisibilities (Fig. 14(b)), smaller regions of profit would become available but would disappear when approaching the neighborhood of the limit (Fig. 14(a)). Nevertheless, even if one were to accept Walters' (1968, Chapter 6) argument that there are sgnificant indivisibilities and scale economies in rural roads, we have demonstrated that profits (and losses, of course) would nevertheless arse under congestion tolling. Scale economies in the presence of indivisibilities and financial viability are not necessarily incompatible. F. Empirica Evidence on the Scale Economy Issue 62. Fitch and Associates (1964, p. 131) give some numerical support for the case of scale diseconomies in the United States. Walters (1968, pp. 184-185), using Meyer, Kain and Wohl's (1965, p. 205) data, shows that there are diseconomies of scale in the construction of four-lane, six-lane and eight-lane urba road segments. (By employing Walters' straightforward approach, Hau (1989) demonstrates that there are increasing costs assocated with a sample of four-lane, five-lane and six-lane roads in Hong Kong.) Without imposing any prior specifications about the extent of return to scale - Keeler and Small (1977) find evidence of constant returns to - 46 - scale for a sample of San Francisco Bay Area roads. Their often cited econometric study is important because of the balance budget implication for congestion pricing, a result which was also quoted by Newbery (1990).F' By contrast, using engineering specifications to estimate each of the cost components of an urban highway network model, Kraus (1981a) finds that there are increasing returns to scale in road construction in terms of length of freeway and interchanges but not for overpasses and length of arterials. He makes the crucial observation that factor prices (such as right-of-way prices) are to be held constant for making relevant comparisons of scale - specific (dis)economies. The reciprocal of his best "pseudo-empirical" estimate of returns to scale in urban highway network capital costs is 0.84, which translates to the economies of scale degree of 1.19. Meyer and Gomez-lbgilez (1981, pp. 191-192), in assessing the available estimates in the conflicting literature, conclude that economies and diseconomies of scale are "probably roughly offsetting." Hayutin (1984), in an unpublished dissertation, refined the Keeler-Small model and applied it to a sample of U.S. Interstate Highways. By including both intercity (or rural) and urban routes in her data set, she estimates that there are clearly increasing returs with respect to the number of lanes. Her x,aults bear out Mohring's scale economy implications of highway geometry with respect to the "shoulder 5I Keeler and Small's (1977) result is one of the more rigorous econometric analyses bearing on the scale economy issue, iD that they are able to separate the confounding effects of size and urbanization. In particular, they regressed constuction cost per lane-mile on the number of lanes and various discrete variables which capture the dfes between urban, suburban and rural-suburban areas. It is the inclusion of the latter variables which enable them to ecomometrically control for the effects of expressway capacity on construction cost. The selected sample of 57 roads was based on all state-miainned roads for nine San Francisco Bay Area counbes, including arterials, expressways and rural roads. They estimated both a non-linear and log-linear specification, with both yielding statistically insigificant stastics for the esfimaed degree of homogeneity. Based on the slightly better fit for the log-linear specification, the rturms to scale parmeter of (-)0.0305 translates itself into the cae of ^mildly- increasing rtuns to scale of 1 - 0.0305 = 0.9695. By taing the reciprocal of the estimaed retwns to scale puamete, the economies of scde degree of 1.0315 is obtained. Since 1.03 is staiscally indiinpuisable^ fiom 1, they conclude that there is no firm evidence for scale economies in road conruction masured in terms of lanes. The fr-reaching policy ramifications of this result could perbaps be buttesd if there were calculations or discussion of the power of their hypothesis tests. This is because not being able to trect a null hypothesis is not necessarily equivalent to accepting the null hypothesis. One hopes that the typo II error is relatively small. However, to be fair to their important contribution, the power function for publishd papers are seldom to be found in the literaue. -47 - effect" More recently, in reassessing the earlier work of Keeler and Small (1977), Small, Wimston and Evans (1989, Chapter 6) use the result of zero economies (corresponding to the scale economy parameter of 1.00) as well as the mildly increasing returns case of 0.97 (corresponding to the scale economy parameter of 1.03) (see Small (1992, Chapter 3) for a review also). Fully cognizant of the possibility of the existence of increasing returns to scale in urban highway travel a la Kraus, they presented their simulation results on highway finance based on three encompassing parameters 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 highway finance by relaxing the assumption of an infinitely durable highway whose capacity can be continuously adjusted. It is common knowledge that pavements wear out after extended use, but it is less well known that the damage of a vehicle on the road pavement is related to the weight per axle, as opposed to the gross vehicle weight per se. Common Practice (Highway Research Board (1962)) is to measure this damaging power by the number of equivalent standard axle loads (ESAL), where one ESAL is equivalent to the load of 18,300 lbs. (8.2 tons or 80 kilo newtons) single axle. The American Association of State %ighway and Transportation Officials' milestone road test indicates that the damaging power ot a vehicle on pavement is proportional 53/ Hayutin (1984, Chapter 4) regressed constuction investment per mile ol the number of lanes and other variables simila to those used by Keer and Small (1977) (see previous footnote). Further, by including the paved width per lane variable aeoconomies to width measured in feet. rather than in lanes, result. Hayutin (1984, Chapter S) conludes that the stronger effect of scaPl economies with respect to the number of lanes dominates the effect of dmiecomies associated with building wider footage. In an excellent review of the litentue surrounding the scale economy iasue, Hayutin (1984, pp. 158-159) observes that 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 comment regarding the power of the hypotbesis tests applies to her study also. - 48 - to the fourth power of individual axle loads, acquiring the title of the "fourth-power law. For instance, the rear axle of a 13-ton light 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 operating costs to subsequent motorsts for the rest of the periodic life cycle of a road. (Thus, the various costs of undertaking a trip mentioned in the introduction of this paper (footnote 3) should now be more narrowly defined as eermal costs, namely: 1) marginal exteral congestion cost; 2) road wear cost and damage exteralities (grouped under the rubric of road damage cost); 3) environmental costs; and 4) costs due to increased risk of accidents not borne by private parties.),W /AI Formally, the damagig power (in EASLe) of an axle load, 1, in tons, is approximately equal to: (U8.2y), hece we say tht the damaging power is proportional to the fourth power of the axle load. As a hypotheical eample, a 24 ton truck whose weight is distributed evenly among 2 axles would cause more than 3 times as much damage as the s truck whose weight is distributed evenly among 3 axles: (2/3) - (12V8)' = 3.37S. S/ Mhe example assumes that more of tho weight -8 tns - is distributed on the rear axle of the light tbuck whers a fily loaded automobile has its weight uniformly distrbuted among the two axles. Small and yag (1988) and Small, Winston and Evans (1989, Chapter 2 Appendix) have recently dsput the fourth-pwe law and perfimd a statistica analysis of AASHO's road test data to show that the equivalence factor for an axle load rises steeply to dte third power, thereby proposiAg a Zthird-power law instead. Whether the power term is actually 3, 3.5 or 4 (as respectively claimed by Small, Pateron, or engineers conventionally) is not as crucial as the significant mantenanc cost savings to be made if vehicle damage is efficiently charged for. Conceivably, an increase in the power term would enlarge the small deficit tht Small, Winston and Evans obtained by charging for congesion and road damage costs. I argue tht the chargi of aU extraities including envirmentl and acciet costs would very likely close any rmining ap. 6/ Based aon empirical ovidenc for the whole oad network of Tuna, Nwboery, Hughes, Paterson and Beanathan (1988, Table 7, 23 and pp. 58-59) and Newbery (198&, Table 1) deamnstrut that the extenal urban cogesion costs alon account for tho 'ovewhelmng fiaciaon (about nin4enths or more) of total extenal coss of road use (excludig environmea and accdet cost) for autmobiles and ulities. For heavy vehicles, the reverse appear to apply in both Tuniia and Ghana, with road damage costs doin_ating instead (8e Gronau (1991) also). (Heggie and Fan (1991, Annex 1) argue that some of Newbory's calcuaos of congestion costs for Tunisia arM overtdmates.) Cog restion costs constitut a argo shae of total road costs for both the United Kingdom (nine-tens) and the United States (one-filfh) in the klon run, whlera road damage costs a about 3 to 3.5% in the United Kingdom and only 2% in the United States (Neowbory (1988a), Small, Winston and Evans (1989), Chapter 6). Pollution costs - 49 - 64. Newbery's (1988a) "Fundamental Theorem of Road User Charges' says that if. 1) the maintenance policy pursued by a highway authority is condition-responsive, i.e., road maintenance is carried out whenever a road's pre-determined roughness level is reached, without being optimaUy set (Paterson (1987)); 2) the age distribution of roads over the life cycle is uniformly distributed; 3) there is no traffic growth, i.e., traffic flow is constant over time; and 4) all road damage is caused solely by vehicles, dten the external road damage cost is nil on average (Newbery (1988a), Proposition 1). The variable road maintenance user charge component, applied on a per ESAL basis, wiU fully cover the average cost of repair (Newbery (1988a), Proposition 2). When viewed diagrammatically, this result is analogous to charging for maintenance cost in another dimension, as opposed to charging solely for the congestive effect of automobiles on a per passenger car equivalent (PCE) basis in Fig. 3. Intuitively, the damaging force of an additional ESAL has the external effect of raising the vehicle operatng costs of subsequent vehicles over time, just as the external congestive effect of an additional car has on other vehicles behind it within a traffic stream. in addition, the indirect impact of accumulating more ESALs is to reach the preset, maximum allowable roughness level of the road earlier than expected, thereby precipitatng an overlay and a corresponding lowering of vehicle operating costs. It is unclear a priorl which of these two magnitudes dominate. Hence Newbery's (1988a, 1989) breakthrough was to prove, in a variety of ways, that the additional vehicle oeaing costs attibuted to road damage exnalities just cancel out with the vehicle operating cost savings when averaging over roads of different vintages. 65. In the general case, the fundamental theorem relaxes Assumption 4) above by allowing for road damages that are independent of use, such as weather-related deterioration. In this case of a condition-responsive maintenance policy, the road damage externality is no longer zero but is quantitatively negligible. While the use-related part of maintenance costs is chargeable because of the road damage cost, the fracdon due to weather is not allocable. Hence the presence of weather-related road damage results in only partal recovery of all maintenance costs appear to account for less tdan o _enh of 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 constant returns to scale and road use, the efficient congestion toll 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). (Following Mohring (1965), we have seen how this is done in our simple investment rule of comparing optimal toll revenues with fixed costs, be they construction or maintenance costs, see Fig. 5 and the surrounding text.) It then naturally follows that the optimal road user charge, i.e., the optimal congestion toll-cum-road damage charge, will then yield revenues that cover the capital cost of the road and the total road maintenance cost 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-allocable fraction of road maintenance, whereas the allocable fraction of road maintenance is still chargeable to traffic loadings via the average variable road maintenance cost component per ESAL. This explains why the total expenditure on road maintenance is fully recoverable. Ifthe same constant returns 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 highway and twice the total maintenance costs of the road (Newbery (1989), Proposition 3). If all heavy vehicles are confined to the slow lane, then the damage costs are accumulated in a shorter time span than if they were to be spread out evenly over all lanes. This has the effect of raising the maintenance cost 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 expansion to reap time savings suggests that the marginal cost of investment in capacity would now have to account for both the increased road maintenance cost for road strengthening and the annuitized capital cost on a PCE basis. Tis is a slightly modified version of our earlier optimal investment rule.) Moreover, heavy vehicles are charged for the traffic loadinigs they create. While stronger roads are cheaper to maintain, investment in road strengthening is costly, resulting in costlier upkeep and higher capital cost. The larger fixed - 51 - costs translate themselves, in the long run, into a requirement for higher congestion charges, which heal contribute to an overall budget surplus for the road authority, despite "massive" increasing returns to road strengthening (Newbery (1989)). Another way of looking at this result is that the congestion toll effectively covers the road's entire capital cost as before, whereas the maintenance cost is recovered twice -- once via the variable road maintenance user charge component applied on a PCE basis and the second time around via heavy vehicles per ESAL. 66. The most serious drawback in the propositions above is the condition of constant returns to scale.S7/ We have reviewed the empirical evidence and find that there are increasing as well as decreasing returns to scale operating on different parts of the road network, meaning that deficits as well as surpluses would most likely co-exist. 5O Mariabili of Road Thickness 67. We are now in a position to formally relax the implicitly used assumption of a given road thickness and to incorporate the latest work into our model. In Road Work: A New Highway Pricing and Investment Policy, Small, Winston and Evans recently provided a comprehensive exposition of their technical extension of Mohring and Harwitz's long-run result on highway economics with optimal durability, within a standard neoclassical welfare maximization framework.a/ Instead of taking current highway design standards as given, 57/ Newbey (1988a) regards the lack of the pursuit of a condition-responsive mainnteace strategy as the most serious limitadon. Further, Neowbey (1989) cites Keeler and Small's (1977) result of constnt reuns to scale, which is based on a sample of San Francisco Bay Area roads. Newbery (1990) also cites Kraus (1981a) as evidence suwporting constant reatuns when Kraus demonstates lightly cicsing retuss (see previous section). Based on an earlier version of Newbery (1989), Heggie and Fon (1991) take issue with many of Newbery's assumptions. 58 Newbery (1989), for example, derives opimal durability (or strenglh, rather) and confines the extent of his analysis pricipally to the contant reus to scale world. By coDtra, Small, Winston and Evans (1989, Chapter 6) explicitly explore the case of incrasing retuns to scale of road consruction, as well as durability, and preet simulation reslts of an urban expressway and arteial - with sensitivity analysis - witdin a long-rn equilibum famewor Ihe first order conditions of their optimization problem yield the optimal pricing, investment and durability rles. - 52 - another characteristic of a road -- its thickness - can be varied. A thicker pavement would serve to withstand the damaging power of trucks more and thereby prolong the life of a road. Despite the fact that there are tremendous economies assocated with road durability, the additional strengthening of the road would still substantially increase the total investment cost of an overlay. Using the standard optimization technique of consumer's surplus and producer's surplus maximization, the intuition of the three allocation rules derived are again based on the simple notion of setting marginal benefit equals to marginal cost. That is: 1) The first rde - the optimal pricing rie - says that the traveller should undertake a trip only up to the point where the incremental benefit just offsets the incremental cost to the community. A vehicle's entry into a transport corridor results in two effects: the congestive effect which depends on the number of PCEs, and the damaging effect based on the number of ESALs. Thus our optimal pricing rule derived earlier is adjusted to include an extra component - a road damage charge - which balances out any short-fall. 2) The second rude - the optimal capacity rde - says that, with a condition-responsive maintenance strategy built in, optimal investment for highway capacity is then to expand the width of the road up to the point where the marginal cost of capacity plus maintenance cost is equivalent to the resultant time savings. 3) The third rile - die optmal durability rie - says that the road is optimally strengthened by investing up to the point where the marginal cost of durability just equals the savings in vehicle operating costs to other motorists plw the associated savings in maintenance costs due to a thicker pavement. The two latter rules could be regarded as an investment rule extended into two different dimensions. Thus the three rules of optimal pricing, opimal capacity and optimal durability yield efficient prices and trips, as well as the optimal number of lanes and inches of pavement thickness. 68. There is evidence that there exist economies assodated with road strengthening (Small, Winston and Evans (1989, Chapters 2-3), Winston (1991)). By reanalyzing AASHO's road test data within an economic optimization frmwork, Small and Winston report that the opimal thickness for a rigid pavement is an inch and a half higher than the current ten inch standard, -53 - which follows AASHO's guidelines. The remarkable finding is that a mere increase in thickness of 15% would lead to a doubling of pavement life from 13 to 26 years (Small and Winston (1986, 1988), SmaU and Zhang (1988). The logical implication of massive economies to increasing road thickness - a fact long known to highway engineers - is losses for the road authority. We therefore ask: is there a theoretical reason that would allow us to still adhere to the impeccable marginal cost pricing principle and yet achieve the goal of cost recovery? To answer this question we turn to the notion of diseconomies of scope. Economies of Scope vs. Diseconomies of SMcpe 69. The condition of constant, increasing or decreasing returns to scale yields the respective result of break even, loss or profit, respectively (see section XIV - 4 and Fig. 9). Tbe empirical findings of returns to scale evaluated earlier suggest that decreasing returns to scale in road construction in urban areas may perhaps offset the increasing returns to scale in rual areas, but that the highway budget may stiU be in deficit due to economies of road strengthening. The answer can only be established using econometric analysis. Even if we were to accept Keeler and Small's (1977) carel finding of constant returns, would it not seem plausible to argue that the pavement deficit due to significant economies to road durbility necessarily yield an overall deficit for the road authority? The answer is no. 70. Up til now, we have confined ourselves to the single product world of traffic volume. But road transport involves two products: namely traffic volume and loadings, which carries us into the literature of multiproduct industries and returns (Bailey and Friedlaender (1982)). The issue is whether a multproduct firm can joindy manufacture the various products cheaper than if each firm were to produce an output separately. If it is cheaper to combine operaions and share in the joint costs, there are economies of scope. The notion of diseconomies of scope can best be grsped by ilusating the design of a railway track (Kim (1987)). A railroad track that is built to withstand the axle loadings of freight would need greater strength and thickness, which conflict with the requirement of securing a smooth ride for train passengers. Ensuring both thickness and smoothness of tracks is more costly, resulting in diseconomies of scope. The - 54 - analogy canries over to roads, where it would cost more to produce a highway that is thick enough to handle heavy vehicles and yet wide enough to accommodate the considerably larger number of automobiles. Thus there are no economies of scope even though one product -- the number of loadings -- is clearly subject to increasing returns to durability, whereas the other product - the traffic volume -- is potentially subject to increasing returns to scale due to road construction. In other words, it is the other characteristic of production -- the scope -- that would tip the budget balance away from a deficit (Small, Winston and Evans (1989), Chapter 6). 71. Automobiles cause virtually no road damages compared with heavy vehicles but trucks are fewer in number and therefore cause lesser amount of congestion. Hence one could separate, roughly speaking, traffic flow from loadings by identifying automobiles with the former and trucks with the latter. Traffic flow, in tum, requires road capacity whereas loadings require road strengthening. The empirical finding of "modest but significant" diseconomies of scope by Small, Winston and Evans (1989, Chapter 6) of about 6 to 10% tips the product- specific economies of scale closer to one - the constant returns case. (The multi-product economies of scale range from 1.00 to 1.06.) Their bottom line simulation results of an urban expressway and arterial and sensitivity analysis demonstrates that a budget balance and hence cost recovery are achievable. The shortfall of a few percent of total road costs can still be recovered by maintaining some level of first registration fees, annual licenses and/or fuel taxes. Finally, since all externalities ought to be internalized in principle, air, noise pollution and accident costs should also be appropriately charged for (Carbajo (1990) and Cameron (1991)). In this way, the highway budget would most likely make a profit (see footnote 56). 72. The basic intuition behind this remarkable result is as follows: because most roads are currently built to accommodate both automobiles and heavy vehicles, a neat dichotomy of allocating pavement wear costs between automobiles and trucks cannot be achieved. Thus 1) the marginal cost pricing of traffic flow requires a congestion charge - which effectively covers the capital cost of investment in the long run - and 2) the marginal cost pricing of pavement wear - associated with the investment cost of strengthening the road -- results in a relatively -S5 - steep road damage charge. The marginal cost-based road user charges combine to yield the double-charging of roads, depicting diseconomies of scope.nj One logical implication of the diseconomies of scope argument is that savings could be reaped from building a thinner autos-only road system (the savings of which are estimated to be on the order of 23% by Keeler and Small (1977)). With a universal road system, roads should then be built or resurfaced durably on the slow lane only and heavy vehicles should be confined to that lane. (This experiment is being carried out in California and Florida (Small, Winston and Evans (1989, p. 15)). S9/ Ibe theorecal finding of tho double- ng of roads is dso deived by Nevwery (1989) for the cae of consant returns to scale and road use. However, he neither cites nor employs spexficaily the concept of multiproduct rtums in his wor - 56 - XV. SUMRY AND CONCLUSIONS 73. One of the earliest contributions to the economic analysis of road pricing was from a French engineer, Jules Dupuit (1844). He was the one (and not Alfred Marshall) who introduced the concept of consumer's surplus -- the comerstone of the welfare analysis of any public project - and brought it to bear on the subject of toll roads. It is a similar tack that this paper has taken, in the belief that a picture would perhaps speak a thousand words. I have synthesized the dominant thinking to date on the topic of road pricing by the main protagonists and integrated them into a consolidated, analytical framework. 74. According to my analysis of the traditional road pricing arguments, it is hardly surprising that road pricing as advanced in the past encountered its share of difficulties. This is because the congestion toll has the effect of a tax (increa) on trip-makers, despite the fact that it is an externality-corrective tax. The gist of the argument is as follows: people are against congestion pricing because: 1) those who are tolled would face a higher price relative to a no tax situation on average;§/ 2) those who are priced off the road in order to circumvent paying the toll are clearly worse off as a result of the 'forced' switch onto a different mode or time of day; and 3) the other road users who are not tolled-the tolled on - are no better off and, indeed, may even be worse off if congestion is encountered. My applied welfre analysis actually takes into account the increase in revenue to the government and the issue of transfer payment. If each of the partes is separated out as: 1) the tolled, 2) the tolled off, 3) the tolled on, and 4) the government, the group that stands to gain the most is the govemment (and the untolled - the rest of society), unless the toll revenues are earmarked. The other party that is primarily better off are those with very high values of time. Only in the hypercongestion case could aU groups be made better off on average. 6Q0 Considor a mro alisic siuatiaon whr the exitence of a uifom fiel tax offtively tdsates ibslf ino a tip pricetat is higher (buotno a high a th peak-perod pnice), and exactly tho sam analysis follows. -57 - 75. It has been argued that the disposition of the revenues of externality corrective (toll-) taxes should accrue to the public treasury (Baumol and Oates (1988), p. 29)AY' Conventional cost-benefit analysis treats a dollar as a dollar to whomsoever it accrues, and also implicitly assumes that only consumers derive satisfaction from revenues. Hence, unless toll re;'enues are channeled back through reduced transportation related taxes, user charges or improved public services, neither the tolled nor the tolled off would endorse road pricing. 76. In this paper, I have also shown step-by-step how to implement short-run marginal cost pricing in transport following Walters and others. In particular, I have established that implementing the optJmal pricing rule -- the first rule - is equivalent to setting an optimal road user charge, where: 1) a congestion toll on the difference between the marginal cost and the average variable cost of a trip is imposed, and 2) the maintenance cost of road use is also charged. Further, I have shown that the process of determining an optimally priced and invested road system is similar, albeit with a couple of important differences, to the process of achieving long-run equilibrium of a typical product within a competitive environment, inspired by the basic Mohring-Harwitz model. The issue of short-run vis-a-vis long-run marginal cost pricing is clarified inter alia. For instance, implementing short-run marginal cost pricing is equivalent to pursuing long-nm marginal cost pricing in a steady-state world in the long run. However, only short-run marginal cost pricing would be able to capture the peak/off-peak nature of travel demand. In the absence of scale economies, the optimal capacity rude - the second rule - says that the existence of economic profit, i.e., toll revenue collection less the fixed and non-use- related costs of a road, would serve as a surrogate market mechanism indicating that the road ought to be expanded. Putting it another way, the investment rule says that a road ought to be expanded to the point where the additional cost of investment in capacity equals the additional savings in travel time. In the long run, toil revenues would cover the interest on the capital investment, invariate maintenance, depeciation and operating costs of the road. Maximizing society's welfare dictates that one should implement short-run margnal cost pricing over the .J/ This is beas a Pigouvin tax is one which impose a positive price on a producer of an externality and a zro pice on a consum_r of X exterality. - 58 - long run by varying the size of the highway capital stock. In this way, the pursuit of efficient pricing and a self-financing road system would be compatible with one another and no residual cost need be covered. In one stroke, the same congestion tolling mechanism solves the pricing- cum-investment problem, satisfying the conceptual guidelines of efficiency pricing, economic and financial viability as set out in the introductory section of this paper. 77. Relaxing and flushing out major assumptions indicate that the result derived here is robust and applicable to: 1) a multiplicity of roads, 2) a road which is subject to diurnal variation of demand and the peak-load problem, and 3) differences in values of time. If constant returns to scale can be shown to hold on average for a particular city with severe congestion, it could potentially aid in greatly simplifying the planning of highway investment. It could also be used as a yardstick, against which scale economies or diseconomies could be measured. 78. Economic efficiency would be enhanced if marginal cost pricing of a trip were done in the short run and optimal investment in capacity were pursued over the long run. I have established that, if governmental authorities were to charge correctly for congestion, it is possible for them to make money on a road while satisfying economic efficiency. Profitable roads arise in heavily utilized or urban areas because land rents of real estate are high and congestion tolls reflect the rising opportunity costs. Yet, it is possible that congestion pricing in the presence of both indivisibilities and diseconomies of scale in urban roads may curtail the extent of profitable undertakings. Similarly, pursuing marginal cost pricing under the restrictive conditions of both indivisibilities and scale economies of rural roads could also result in profits in the short run. Thus far the points I have made are based on first principles. 79. In the long run, the simple pricing and investment model implies that the marginal cost pricing of trips covers all the fixed costs of the road and the congestion toll (which captures the quasi-rent) behaves as if it is a capital charge. This analysis also mea that an optimally invested road system is in fact one where a road should not always be uncongested during the peak period. An optimally congested road is akin to the commonly accepted notion of an optimal pollution level in the field of environmental externalities. An uncongested road 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 downsizing it in the long run may be unavoidable on narrow cost-benefit criteria. The act of downgrading lightly used roads in order to save on the costs of maintaining higher standards of road pavement is a form of disinvested.u/ Alas, given that almost all existing road systems are non-optimally designed 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-economic grounds. 80. One may ask: starting off with an overbuilt road system, say, is there a way in which road pricing based on the marginal cost concept can be implemented within an institutional context where severe fiscal constraints on public expenditures prevail? To answer this question requires that we go beyond first principles. 81. Recent extensions a la Newbery-Small-Winston have enriched the basic model developed diagrammatically here 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 strengthened to the point where the additional cost of investing in durability just balances out the incremental savings from maintenance and 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 accident costs 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 common practce of downgradng roads is constent with the findngs of road detenoration in developing countries (Hal and Faiz (1988, p.32)). -60- 82. Given point estimates (or preferably, functional specifications) of speed-flows, demands and the value of time, one can estimate and simulate some of the analytical results developed here. When combined with the associated optimal pricing and investment rules, the efficient l-vel of prices, user charges, speed, volume-pacity ratios, and trips, as well as the optimal number of lanes and inches of pavement thicknesses can be obtained. 83. The fact that in the transport context, the consumer-producer is both a willing 'victim' as well as a 'beneficiary' has policy implications. As 'victims' of congestion externalities, perhaps travellers ought to be compensated. Note, however, that Pigouvian toll-tax revenues are not supposed to be used to compensate 'victims' of extmalities (Baumol and Oates (1988), p. 23). Also, intuitively, motorists would be induced to drive more because the level of compensatory payments would depend on their car usage, so economic efficiency would be violated. In this context, a road fund would be consistent with first-best pricing only if the funds were used in an indirect manner. Travellers are also 'beneficiaries' of road transport by virtue of their being present on congested roads, and their contributions to the toll revenue component of 'user charges' reveal their willingness to pay. In the absence of lump sum transfers, earmarking of toll revenues could serve as a useful device in principle to approximating benefit axation as a way of satisfying a commonly accepted notion of 'fairness.' Similarly, heavy vehicles ought to incur their 'fair' share of hety pavement wear fees. Combining these plausible arguments and our earlier results of optimal pricing and investment principles, suggests that some form of dedicated funds is perhaps necessary - either in the form of a road fund or a transport fund - if road pricing is to gain political acceptance.w/ 63/ Recet developments in electonic toil collection and electrnic road picing in Norway, Sweden and Cabridge, (England) point to the fct that traveller do not object to road pricing when the toil revemu ar earmaked tor both road construction and i1provement andor the provision of better public tnort (With optimal tolling, however, high purchase taxe and rgsation/licens fees of vehicles ought to be reduced to a level sufficient to cover the administrave and enforcmet coats of colection. If the road maintenancct is constmt with reapec to the trffic level, a sppopriat fue tx could perhaps be usd to aoximate uwe.) Inded, a recent natonal m8uvey conducted in England idicates thit when people were asked whether they an for or against road pricing, about 57% sr aainst iL However, when the question was posed in a different way: would they be supportive of apac*age approach to road pricing, with the revenues from road pricing used only to fimmce public tranpoit, 57% of the same surveyed population were in favor - 61 - A. The Role of a Road Fund 84. If a road fund were to be set up, compensaion would need to be made sufficiently indirect to satisfy Pareto efficiency. Thus the funds for road construction should be used both to maintain existing roads and to finance new roads, and the profits generated from urban roads could be used to finance the fixed capital cost of worthwhile rural roads in a nondistortionary manner.o To what extent can the profits collected from heavily used roads offset the losses arising from the construction of lightly used roads? The answer depends on the extent of the interacdon of both scale economies and indivisibilities and should be examined on a country by country and case by case basis using econometric analysis. 85. A road fund is attive because of the high marginal cost of raising a tax dollar. Moreover, a road fund run by an autonomous authonty would increase the linkage between revenues and expenditures, currently lacldng in a politically-based budgeting process, thereby improving managerial efificiency. Without the setting up of such a fund, however, deficits from lightly used rural roads (with increasing reuns to scale) would demand subsidization from 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 alytical resut preseted he.) Using an eqiirum trvel demand model of modal choice applied to tie San Fancisco Bay Aea, Smal (1983) concludes tt congestion pricing combined with the redistnrbutio of toll revenues would rudt in benefits to aU incom groups. As an ilustrion, the Oslo Toil Ring, cumently i operatio, charges privat cars (light vehicles) going into the city center a toll of 10 kronos (approximately US$1.50). Roughly 60% of motorists apt for the subscriber lanes in 1991, which are opeated via electric toll collection, rather than manually-opeated toil blaes. About 80% of the eamarke fiunds r used to fimmce road consuction and 20% for busways, buses imd tms. The optio nature of tho sucesfl Oslo Toll Ring raises the inguing idea that congestion tolling dsould pedrps be implemeated an a voluntary basis: with the choice of a combination registiton fee/fuel tax based an 'averao' usge, or a subscription to the use of electronic devices j4/ The common sense notion of uing the profits from eavily ued roads to fiance lighly used roads has its intelleal rots in Alfred Masal's 'tax and bounty' syaem of pticing: 0no simple pln would be th levying of a ta by the community on their own incomes, or on tho production of Soods which obey the law of diminsing retun, and devoting tho tax to a bounty on the production of those goods with road to which the law of incrai retum acS sharply. Alfred MasrlA, c o 1920, p. 392 Mua also obsvwes dat it is noeoo_y to conider to caot of adminisering suh a tax-subsidy systeLm - 62 - public treasury, and would thus compete for tax money valued at a high opportunity cost. By symmetry, surpluses that acue in heavily utiliwd urban areas (with decreasing returns to scale) should then be priced at a pre,mwn. These welfare losses and premiums would presumably offset one another if viewed within the same (transport) sector - with a nominal value of a dollar being treated at its face value - so that we are back to the case of pure efficiency concerns. 86. Even if a certain city in a developing country, say, is found to be faced with mainly increasing returns to scale, the deficit could be closed, in principle, by appealing to the notion of diseconomies of scope. Meeting the requirement that a road network be both large enough, in terms of capacity, and strong enough in terms of pavement thickness, can be quite costly. Scope diseconomies in highways mean that a road network that accommodates both loading and traffic volume found universally is more costly than the sum of an autos-only and a tailored trucks-only road system. Hence, the surplus associated with diseconomies of scope offsets the potential deficits associated with scle-specific economies of road construction or use. The viability of the fund is enhanced by the fact that the maintenance cost of the road pavement is recovered twice: once when traffic flow creates congestion, and the second time when traffic loadings cause road damage. Thus, the idea of a trust fund administered by an independent agency according to strict cost-benefit prnciples is likey to be feasible. B. The Role of a Transort Fund 87. Alternatively, taking the transport sector as a whole, a transportation find ought to be set up.i/ If dedicated funds are set up in this way, indirect 'compensatory' payments can be achieved and would not depart far from optimalty. I recommend this both because the 65/ I am indebted to Sir Alan Walus for this inight. f&I Usig an entirely diffrent o th the on used here, Vickrey (1977) establises tho result that cities should use land rent tax reveues aiing fwom agglomeration economies to finance mass transit and public trnportaion vwhich ae subject to increasing remus. Indeed, he argues forcefilly and proves the case that no subsidizing tes fixed coats woud be inefficient - 63 - problem of highway congestion is tied intrinsically to the provision of poor transit alternatives and because public transport encompasses a substantial if not the lion's share of trips undertaken in both newly industrializing and developing countries (Deaton (1987)).R Typically, the production of bus services is subject to consumer-side bus route and frequency economies of scale. Hence additional funds in the form of user-side subsidies are required to meet the financial shortfall arising from the capital equipment, if bus usage is priced at marginal cost. Road pricing would result in more crowded and inferior public transport services unless bus companies were to offer more bus services (and hence lower generalized prices) as a supply response. Then 'untolled' public transport users or captive riders would be made better offWM Here the double charging of automobiles via traffic volume and heavy vehicles via loadings would help to close the deficit gap. Increasing by popular rapid mass transit and light rail systems - both of which are subject to significant scale economies - also require capital funds, the construction of which should be based on economic viability. Unless a global view is taken of the congestion problem and more rational time-of-day pricing practiced in all modes (in contrast to tacing individual, non-optimally priced modes), the urban tWansportation problem will continue to be pervasive. 88. Even without dedicated funds, it is essential to pursue efficient pricing and stringent benefit-cost analysis link by link and mode by mode on both a volume and loading dimension. Thereafter, the results can be presented for public scrutiny, thereby improving manageral efficiency and public accountability. The competitive tendering and private provision of certain transport services could also serve to enhance manageral efficiency in the public sector. Issues warranting further investigation include the corporatization of certain transport agencies. 89. Subject to further research, the idea of setting up a transportation or road fund and the pursuit of marginal cost pricing in aU its dimensions would enable us to satisfy the quinpartite Z/ The provision of public traort mentioned in Section ViI, umed to operate under constant retms was ued merely a an iliustrative convenience but this assumption does not result in loss of generality. 68/ Notably, captive bw pasage would benefit ftom road pncing if equilibrum tramnsit travel times m lowerd. - 64 - principles of the World Bank's general guideines, as stated at the outset of this paper, namely to: 1) implement efficiency pricing, 2) meet economic viability, 3) meet (to a considerable extent) financial viability, 4) achieve (some degree of) 'fairness' among beneficiaries, and 5) attain (somewhat) managerial efficiency of the public authority. The conception of a fund passes many of the criteria for a 'good' earmarldng arrangement as presented in McCleary (1991). The implementation of marginal cost pricing in both the traffic and loading dimension could be done with the advent of recent technological breakthroughs in automatic road user charging ulizing automatic vehicle identification and classification, all of which are subject to remarkable scale economies (Elau (1992)). Alternatively, less powerfil road pricing instuments such as area licensing, simple cordon pricing schemes and the monitoring of vehicle and axle loading via weigh-in motion scales can be used. Timothy D. Hau -65- Appendix Page 1 of 6 APPENDix: Measurement of the Welfare Imyact of Road Pricing 1. A brief analysis of the measurement of the welfare impact of road pricing would help explain why road pricing is unpopular. We will consider several acceptable approaches to measuring the net benefits offered by the introduction of road pricing on a non-perturbed equilibrium. Each casts different light and insights on the controversy surrounding road pricing. A. Ouantity Approach 2. The first approach, which is more popular in the U.S. literature, is to measure the so-called welfare gain or loss areas (see Kraus, Mohring and Pinfold (1976), for example). This standard method is labelled the quantity approach or the 'Amencan' approach (see Fig. 3). The loss in valuation to the consumer-traveller from a reduction in trips from Ql to Q' as a result of increasing the generalized travel cost to him from P to P' is the verdcal, tWapezoidal area d+g+k. The saving in resource cost to travellers from the reduction in traffic, together with the saving of congestion in the form of externality reduced, is the vertical area l+d+g+k. The net benefit to society of the introduction of road pricing is given by the trangular area 1. Net Benefit Aroach 3. A variant of this approach is the net benefit approach (see Fig. 3). The net benefit in the case of the optimal traffic level of Q' is typically a large trangle (the pie area a+b+e+h between the demand function and the marginal cost curve), with the pie tiangle emanating from the point of optimum. Similarly, the net benefit in the case of the non-optimal level of Q° is given by the difference of the pie area a+b+e+h and the small triangular area 1. The latter area is of course the welare cost saved when the traffic level is induced to be lowered from Q' to Q'. This variant is intuitively appealing as it graphically illustrates that net benefit is Appendix -66 - Page 2 of 6 maximized with marginal cost 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 4. 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 approach is widely used in the British literature (Ministry of Transport (1964), Tanner (1963, p. 318); Gwilliam and Mackie (1975, pp. 105-106), Thomson (1970) and Thomson (1974, pp. 142-145)). The findings of the Ministry of Transport, known as the Smeed Report, present a different calculation of the areas of gains and losses indicated above, yielding different insights into the problem (see their Appendix 3). The 'British' approach uses 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 negative because they suffer a loss in valuation equivalent to the vertical area d +g+k. The change in total costs - expressed as the reduction in the total expenditure on 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 society is the area e+f-d. HeuristicaUy, the remaining users find that they derive satisfaction from 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. 5. The discussion thus far gives the conclusion and 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, drivers who remain on the road have to make toi payments of the area b+c+e+f, which in turn become a gain to the government in the form of toU revenues. (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 imposition of this tax - resulting in a transfer payment - which enables those who remain on the road to benefit the time - 67 - Appendix Page 3 of 6 savings of an additional area e+f.01 Without the tax, motorists are not properly induced to save valuable time resources: the time is completely lost. 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 discriminating monopolist -- 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 government in the form of tax revenues.) 6. Prima facie, whether or not the net benefits of introducing road 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 indication of the notion of optimality when compared to the first approach, especially with regard to its variant. In the quantity approach, 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, because the 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 society of 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 area b+c+e+f ahould be counted as accruing either to the govenment in terms of toil revenues or returned to consumers (via a hypothetical lump sum transfer mechanism). A lesson to be leamed regarding the isue of transfer payment is to avoid double-counting. if a doilar is treatd as a dollar to whomsoever it accrues and the tansfer mnchanism is implem , then the move to road pricing results in positive net benefit to society of area e+f-d Puttng it another way, the standard notion of a transfer payment of the area b+c+e+f says that money goes from the consumer's pocket into the govenmeot's. It is important to view the time savings of area e+f as an additional layer on top of the transfr payment itself. The bottom layer goes from the motorist's pocket to the road agency's; tho top layer is obtained bocause the motorists who are toiled ae forced to trade money with time. Remarkably, it is this coerced payment of the tax revenue aea e+fwhich brings about a real saving of time of an area of equal size. Appendix - 68 - Page 4 of 6 going from Q' to Q° is the inverted L-shaped area e+f+g+k. By definition, these two areas must be equal, implying that e+f=l+d or l=e+f-d. Diagrammatically, it may appear as if the change in total benefits and total costs approach yields larger net benefit area-use. However, it needs to be clearly shown here.2' C. Consumer's Surplus and Producer's Surplus Aproach 7. The third approach using the summation of changes in consumer's surplus and producer's surplus involves the term quasi-rent.2/ The traveller is both a consumer (in the sense that he derives benefits from purchasing a transport service) and a producer (in the sense that he himself has to purchase the inputs with both his own time and operating costs). In the absence of road pricing, because drivers travc.l up to the point where average variable cost intersects the demand (at output level Q°), the entire receipt (from the consumer traveller's expenditure) goes to cover the 'payment' of user-supplied factor inputs, so zero quasi-rent is thereby generated. However, it could be equivalently stated that the nil area can be expressed as the difference of two triangles, i.e., area (e+h) - (c+d+l), by simply exploiting the meaning and geometric relationship of average and marginal cost curves. In the advent of road prcing, the quasi-rent - the return to a fixed factor of production - is essentally the amount which the traveller-as-producer 'receives' over and above his total variable costs. This quasi-rent, instead of accruing to the drivers as such, is captured by the government in the form of toll revenue or a user charge, and hence should be accounted for properly in benefit-cost calculus. Note that the quasi-rent of area b+c+e+f can be re-expressed as the area b+e+h. Clearly, the change in the quasi-rent would be equal to the area b+c+d+l. Coupled with the loss in consumer's 2QI Lee (1982) claims that the two ares based on the diffart mdhodologies are the same but does not prove it. Ihe spirit of the analysis I how hare underlies vAwilliam and Nash's (1972) commet on Beesley and Walte' (1970) evaluation of uba road investmnts. 1/ Mhe notion of rent is a slppery one and warrants clarification REmt is the analog of producer's surplus in the iput marlt. Reant is a p*mawet payment to a factor over and above that which is required to draw forth its resourc. Quasi-rent is a tpnporary paymurt and would contnue only until the capital asset is depreciaed or possibly tansferred to another use (see footnote 29 and Mohring (1976, Chapter 2) also). Note that a high price and willingnesspy yied high quasi-rent, and niot the reverse. -69- Appendix Page 5 of 6 surplus of area b+c+d, the net benefit area I emerges. Hence, we have shown in different ways that the three approaches are identical.3/ Note, also, however, the second approach is used and extended because it graphically illustrates the broad distributional implications of road pricing. 8. Perhaps one reason why there is confusion regarding the two approaches above is because of Walters' (1961a, 1961b) treatment of the MC and AVC curves as marginal social cost and margtnal private cost curves respectively. (My interpretion here is at variance with the common use of the latter term since I regard it as somewhat of a misnomer.) Walters' use of the AVC as MC curve immediately brings to mind standard diagrams of an externality such as the classic economics text example of a polluting factory, with the consequent changes in consumer's surplus, producer's surplus and extrnality valuation. As carefully shown above, this example is not valid in our analysis because the marginal private cost curve is only marginal with respect to the driver himself. The individual perceives and bears the average variable cost only: it is merely a decision curve and no more. Since the area below the AVC curve is not the total private cost, only an incorrect intepretation can be drawn by mathematically integrating the area under the marginal private cost curve, which turs out to be an average variable cost curve. (Further, producer's surplus should really be interpreted as quasi-rent to avoid possible confusion, especially in undstanding the rlationship between pricing and investment.) In the absence of he opdmal pnrcing of trips, average (variable) cost pricing prevails with the associated . Tis illusates strongly the need to reserve the term 'short-run marginal cost pricing' to be consstent with the World Bank's policy guideline (World Bank Operational Manual Statement (1977)). I employ the term marginal social cost pricing when a In fact, if Q' is very cls to Q', do anal os is equivalnt to dho hng in tota varae coaL By evaluang th diffeieo of dl clug in vaiable co with the mail valuaon, to two met&ods discuad aov (t qu approach nd the dcge in total benefits and tol coot poch) ar seam to be equaL Appendix - 70 - Page 6 of 6 accounting for aU the other externalities such as environmental pollution and accident costs.L/ 9. A technical paper by consultants hired by the Hong Kong Government indicates that the net benefit due to introducing road pricing corresponds to the area e+f+d+g+k (Transpotech, (1983, Fig. 4)). The consultants' explanation of the extra area g+k is either based on a possible misunderstanding of the first two approaches, or simply a matter of double-ounting areas g +k. The authors state that "this money [referring to the areas g+k] is available to be spent in other ways, perhaps on other modes of travelling". Having already included the resource saving as a reduction in the expenditure on travel, PQ - pftQP, the resource saving from the tolled off drivers of the vertical area g+k should not be counted twice. The point here is that unless care is taken to ensure rigorous cost-benefit analysis, the benefit (or cost) figures would be biased, as has been the case with the evaluation of the electronic road pricing experiment in Hong Kong.7/ 73/ For examle, Glaister's (1981, Chapter 5) use of the term 'marginal social cost picing' is synomymous with the margnal cost prcng concept employed here. 7A1 Based on the mnuber presented for an illusative cas, the bias is 40 % upwards. It should be stressed, however, that it is unclear from a readig of th Hong Kong Goverment's Main Report ote Elecunic Roading Pricing Pilot Scheme whher the final report followed the methodology outined in Technical Paper 1 (Traspotech (1983, 1985)). FIGURES Economic Fundamentals of Road Pricing: A Diagammatc Analysis by Timothy D. Hau Transport Division Infastructure and Urban Development Department The World Bank -73 - Figure 1 Derivatlon of a Wavel Time-Flow Curve of an Urban Highway Figure 1 (a) Figure 1 (b) Speed, Speed, In km in km per hour per hour Sm --- ----1 Sm ----- aa- ------ I\/ s~~ \ 0 m Density, F IrLax Flow, In vehicles Engineering Capacity in vehicles per krn per hour . . ~~~per lane Figure 1 (c) Traveli Time Dip or Delay§ e\99egate \Ime t_rr_n L__--.I Fmax FRow, In vehicles-km per hour per larne-km - 74 - Figure 2 Derivation of the Marginal Cost Curve and Congestion Toll MC A VC Marginal Cost Curve (MC) Average Variable Cost Curve (AVC) I plus vehicle operating cost and plus vehicle operating cost and variable road maintenance cost (Full) variable road maintenance cost Price otf a trip, P, I Generalized \ Cost, GC, I of atrip X I <~~~~~~ / \ ~~~~/I \ ~/ I w I /1\Optimal V / II < o AVC E o _ . Timel . Demand Curve nme cos t Costs borne 1 Qd …~~~~~~~bymotorist1--i-4- privately l Vehicle I lI Copertin I …__ _ _ _ _ _ __-_L_- -..4.-- - VariablA Road I Maintu.nance Cost Q' Cf Q Flow, In o max ~~vehicles per lane-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' Phenomenon of Traffic Growth: The Relaxation Effect (Full) Price or a trip, P. Generalized Cost. GC, of a trip \ AVC Average Variable Cost Curve (AVC) pius vehidce operating cost and vadiable rc ,d maintenance cost \7Ex AVC ~ ~ Initial Demand Curve Od Time Cs } Vehicle OperaUng Cost | Varlable road maintenance cost Q Flow, In vehicles per lane4iour - 76 - Figure 3 Welfare Impact due to the Introduction of Road Pricing In the Peak Period: Short-Run Marginal Cost Pricing \ AVC \ Average Variable Cost Curve (AVC) plus vehicle onerating cost and X \ vadable road maintenance cost \\~~~~~~A Marginal Cost Curve hMC) plus vehide operating cost and variable road maintenance cost (Full) Price Of a trip, P Generalized Cost, GC, Z of a trip a *A Efficient p, Price =AVC"+ t' Price =AVC0 J Pu AVC h VCi Td Demand Curve I Vehide Operating Cost _ Variabe Road Maintenance Cost 0 Q0-' C( dQ Effient Observed Vehicles Output Output per lane-hour - 77 - Figure 3(a) Welfare Impact due to the introduction of Road Pricing In the Peak Period: Short-Run Marginal Cost Pricing 'Hypercongestlon' Case (FUN) a* tap, P Marginal Cost Curve (MC) AVC pkus vhide operatin cost and cook CC,o Average Vauible Cost Curve (AVC) vatl road maintenance coat d b* iP t pkJ vehicle operaUng co and vartabl road mnteance coast * AC -.< Efficent p'\> ! Primce *AVC"i.t' \ 0d Very High' I nand Curve nAVC" z AVC E Time Cost Time cost Costs borne …___O ___……__ _-* by motorist __ _ _ _ privately Vohicle operaing cost Varlable I Road Mainterance Cost Q Vehicles per lane-hour - 78 - Figure 4 Effect of the Introduction of Road Pricing In the Peak Period on the Off-Peak Period p(Full Original Price 0 Demand a trip, P Curve In the Cost, rizC OPeaik MC Marginal Cost Curve (MC) of a trip \ plus vehicle operating cost and 0110/, d' / valiable road maintenance cost ad>\ Q0 Demand Curve In the Off-Peak Period °P OP following Introduction ot Congestion Toll in the Peak Perlod AVC Average Variable Cost Curve (AVC) plus vehicle operating cost and variable road maintenance cost I % Time cost Vehide operating cost J Variable road maintenance cost 0 Vehicles per lane-hour - 79 - Figure 5 Introducing the (Short-Run Average) Fixed Cost, SRAFC, of a Road, Short-Run Optimal Toll with Economic Profit SRMC (K') Short-Run Marginal Cost \ Qd Z plus vehicle operating cost and variable road maintenance cost (Full) Price of S (K1 a trip, P. SRAVC (K ) $ Short-Run Average Variable Cost Unit Cost, u. plus vehicle operating cost and variable road maintenance cost SRAFC (K1 \ fr SRATC (K SRT (K/ Efficent P Short-Run Average Total Cost P:= Optimal Toll t1 / \ / / plus vehicle operating cost and Optimal Toll t varable road maintenance cost |: ~~~~~~~~~~Time Cost\ -v - __ __ - - - Od Demand Curve Vehicle operating cost __ - - - - - - - -_ Variable Road Maintenance Cost SRAFC (K1) Shdrt-Run Average Fixed Cosi Q'. Vehicles Efficient Output per lane-hour K 1 = (Non-optimal) Road capacity t 1= Optimal toll for a non-optimally built road n'1= Economic profit for a non-optimally bullt road - 80 - Figure 6 Long-Run Equilibrlum of an Optimally Designed Road With Both Optimal Pricing and Optimal Investment SRMC *(K) Short-Run Marginal Cost P. \ | plus vehicle operating cost and variable road maintenance cost $ SRAVC *(K) a, \ / \ Short-Run Average Variable Cost plus vehicle operating cost and variable road maintenance cost SRAFC (K) SRATC (K*) Short-Run Average \ / Short-Run Average Total Cost OlUmal \ Fixed Cost \ / / plus vehide operatlng cost and Price variable road maintenanoe cost P > _4 J LRATC = LRMC Optmal Toll t' Long-Run Average Total Cost = Long-Run Marginal Cost SRAFC (K) SRAVC E Time Cost d Demand Curve Vehide operating cost SRAFC (K) Variable road maintenance cost a* Vehicles Optimal Output per lane-hour t =OpUmal toll K* Optimal road capacity - 81 - Figure 7(a) Constant Returns to Scale with Road Divisibility: Doubling Optimal Road Capacity (K ) and Traffic (0 ) Result in Doubling Fixed Cost, Variable Cost and Totai Cost (FC, VC, TC) and Toll Revenues (t. ° L) $ SRMr3(K3*) SRMC6(K 6 ) SRATC3 (K 3*) SRATC6(Ko*) SRAVCO(K6*) LRATC - LRRTC *LRMC SRAFC3* /SRAFCO* s RAFC(K 3*) SRF() SRAFC 3* SRAFCS* * 03 * 06* 0 Vehicles per lane-hour Figure 7(b) The Relationship between Short-Run Average Total Cost and Long-Run Average Total Cost and Marginal Cost with Perfect Road Divisibility and Constant Returns to Scale SRATCm(Km*) L.ATC * LRMC LRATC * LRMC 0 Vehiles per lane-hour () Denotes that that vaiiable Ls optinized (L) Denotes an L-lane road For example, K3*denotes the optimal capdity of an optimally-built 3-lane road 13*denotes the optimal toN associated wlh an optimally-built 3-lane road - 82 - Figure 8(a) Road Indivisibllties under Constant Returns LRATC o ABCDEFG Line LRMC- HIJKLM Line tS. A SRMC2/ - - - -~~~~~~~~~~~ ------- 0LossRegbn 2 Regon024*-Region-4 Region0 446 R°eSgion 06 RteOgion* 68 Figure 8(b) Optimal Pricing and Investment with Indivisibilltles: Expansion trom a 2-Lane Road to 4-Lane Road a,~~~~a 5 s Un- lIl Demand Curve I Q Q24 Q * Q04.6 0 - 83 - Figure 9 Economies and Diseconomies of Scale In the Provislon of Road Capacity with the Growth of Travel Demand od 3 od~~0 Long-Run Marginal Cost LR LRM\ALAC Ca; \ Lon~~~~~~~~~~~~~~~~~~~~g-Run Unit Loss _ Average Total Cost I \ ~~~~~I Unit Profit Inital Demand Curve Q1 3 I t l l I e l I j I Vehicles per lane-hour Economies of Scale Constant Diseconomies of Reglo ---------- Sl Retuns Scale Region Region ~~~~to Scale Region - 84 - Figure 10 Doubling the Number of Streets-Road Capacity-Results In Quadrupling the Number of Intersections and Traffic Lights and Doubling Waiting Time Figure 10(a) Original Scenario - Existing Street Configuration ____________ D 0 = Odgin D = Destination o A B Figure 10(b) Final Scenario - Number of Streets are Doubled X I ~~~~~~~~IF D 6 5 0 1 2 3 4 - 85 - Figure 11 Diseconomles of Scale: Urban Roads Network with Perfect Divisibility 7r = Economic Profit P, d S Q4 LRMC 0, ~~~~~~~~~~~~~~SRMC4 S4 / SRMC2 LRATC ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Tr 4 SRAFC2 SRACSRATO SR 2 IXSRAFC4 l r : RAFC2 ! | > 4S2RARAFC Q2nn 02 024 04mIn 04 Vehicles per lane-hour - 86 - Figure 12 Economies of Scale: Rural Roads with Perfect Divisibility L Loss LRATC SRMC2 SRATC 2 s VC 2 /SRMCSRATC ^~~~~~~/RA4C SRAFC2 | I \l I ) | RFcSr ......SAFC 41 Q*2 Q2mIn a1.4 Q; aSmR Vehicies per lan4huRA P4 -4.~~~~~~Q2i 0 nVeiLespRlAne-ou - 87 - Figure 13(a) Figure 14(a) Decreasing Returns to Scale and Extent of Increasing Returns to Scale and Extent of Indivisibilitles Indivisibilitles $S Q LRMC , LATC LRATC LRMC Profit Region -0 0 Vehicles - Loss Region - 0 Vehicles per lane-hour per lane-hour Figure 13(b) Figure 14(b) $ LRATC $ 0,0 LRATC *4w-.- /p. 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