metadata: authors: 0: author: Heggie, Ian G.
1: author: Fon, Vincy
count: Tunisia
docna: 0: docna: Optimal user charges and cost recovery for
            roads in developing countries
docty: Policy Research Working Paper
subtopic: Macro-Fiscal Policy,Taxation & Subsidies,Economic Adjustment and Lending,Public Sector Economics,Roads & Highways,Flood Control,Public Finance Decentralization and
            Poverty Reduction,Transport Services,Intelligent Transport Systems
teratopic: Transport
abstracts: cdata!: The optimal charge for road use is equal
            to variable costs for road maintenance, together with the
            costs road users impose on other road users and on the rest
            of society.  One persistent question raised about such
            charges is what impact they have on cost recovery.  The
            theoretical literature argues that if there are constant
            returns to scale in road construction and in road use, the
            optimal user charge will recover the capital costs of the
            road network and the total expenditures on road maintenance.
            Empirical estimates for such a system of road user charges
            in Tunisia similarly suggest that they would generate twice
            the revenues currently spent on roads.  The authors examine
            these issues from both theoretical and practical
            perspectives.  They conclude that there are substantial
            economies of scale in both road construction and road use.
            Also, road maintenance costs include a number of fixed costs
            that do not vary with traffic.  Moreover, since roads cannot
            be smoothly adjusted to traffic, marginal costs for the
            entire road network are significantly lower than average
            costs in most developing countries, unless capacity is
            artificially constrained by environmental or other
            constraints. Under these conditions, optimal user charges
            result in a substantial financial deficit.  The authors also
            address the question of how this deficit should be financed.
geo_reg_key: 517202,517191,119229
repnme: repnme: Optimal user charges and cost recovery for
            roads in developing countries
display_title: Optimal user charges and cost
            recovery for roads in developing countries
listing_relative_url: /research/1991/10/699848/optimal-user-charges-cost-recovery-roads-developing-countries
topicv3: Transport m1326661 135,Taxation m1327615 1121,Road Construction m1505347 4030,Road Maintenance m1505354 4031,Traffic Management m1583399 4231
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Transport
origu: Transportation, Water and Urban Development Department
no_of_pages: 60
model_extractions: **Policy, Research, and External Affairs**

**Transport** WPS **(8U**

This paper -- a product of the 1'ransport Division, Infrastructure and Urban Development Department - is part ol' a larger effort in PRE to understand pricing, cost recovery, and efficient use of resources in transport. Copies are available free from the World Bank, 1818 H Street NW, Washington DC 20433. Pleazsc conitact Pant Cook, room S10-055, extension 33462 (50 pages). October 1991.

The optimal charge for road use is equal to variable costs for road maintenance, together with the cosLs road users impose on other road users and on the rest of society (usually confined to the costs of road congestion).

One persistent question raised about such charges is what impact they have on cost recovery. And when they fail to cover total costs, how the resulting deficit should be financed?

The theoretical literature argues that if there are constant returns to scale in road construction aand in road use. the optimal user charge will recover the capital costs of the road network and the total expenditures on .ouad maintenance. Empirical estimates for such a system of road user charges in Tunisia similarly suggest that they would generate twice the revenues currently spent on roads. It seems therefore that optimal road user charges would not only recover all costs but would constribute substantially to general fiscal revenues.

Heggie and Fon examine these issues from both theoretical and practical perspectives. They conclude that there arm substantial economies of scale in both road construction and road use. Also, road maintrnance costs include a number of fixed costs that do not vary with traffic (up to lhalf of annual expenditures on road maintenance are usually fixed). Moreover, since roads cannot be smoothly adjusted to traffic, maiginal costs for the entire road network are significantly lower than avc,rage costs in most developing countries, unless capacity is artificiall) constrained by environnmental or other constraints. Ulnder these (realistic) conditions, optimal user charges result in a substantial financial deficit.

'rhe question is, how should this dericit be financed'?

On roads carrying heavy volumes of traffic, it is Tiot economically efficient to bridge the financing gap by cutting back on maintenance. The gap has to be bridged by collecting the required revenues through user charges, or b) mobilizing additional general tax revenues. But the costs of mobilizing additional general tax revenues are high and, given the generally low price elasticity of demand for roads, it is nearlv always more economically efficient to collect the required revenues from road users.

It is generally agreed that marginal costscorresponding to variable road maintenance costs - should be the floor below which user charges should never fall. But there is no reason to stop at marginal costs. An important group of costs are avoidable, attributable to individual groups of users (although not to the individual users tiiciitscives), Cuid ii **si1** 3ti.a - grounds of simplicity, equity, and political - expediency to charge these costs against the appropriate user group.

The remaining costs, although also avoidable, are common to all users and, to minimize loss of consumer surplus, should be charged to them using the inverse elasticity rule (Ramsey pricing).

Heggie and Fon point out that there are significant dif'ferences between current user charges in Tunisia and the user charges calculated using the avoidable cost methodology described in this paper.

The PRE Working Paper Series disseminates the findings of work under vav in thc Banks Policy, RKscatch, and Extemal AffairsComplex. An objective of thescrics is to gettihese findings out quickly, even if presentations are lcss than fully-polished. The findings, interpretations, and conclusions in the'e papers do not necessarily reprcsent official Bank polhcy Produced by the PRE Dissemination Center
i

# OPTIMAL USER CHARGES AND COST RECOVERY FOR ROADS IN DEVELOPING COUNTRIES

## TABLE OF CONTENTS

||||PA"|
|---|---|---|---|
|Execu|tiveS|wnmary..................|iv|
|I.|INT|RODUCTION.............................|1<br>I|
|II.|OPT|IMAL PRICING MODEL..|3|
|III.|ASS|UMPTONS UNDERLYITNG<br>OPTIMAL PRICING<br>|.<br>.<br>9<br>|
||3.1|Acceptable Simplifying Assumptions ..|_9_<br>|
||3.2|Unacceptable Simplifying Assumptions ..|11|
|IV.|REL|AX1NG UNACCEPTABLE<br>ASSUMPTIONS<br>AND||
||THE|CASE OF TUNISiA.....**.......**..............|....<br>15<br>|
||4.1|Relaxing Unacceptable Assumptions .<br>.........................|15<br>|
||4.2|The Case of Tunisia .........................|17|
|V.|FIN|ANCING REMAINING EXPENDITURES..............|...........<br>19|
|**vTr**||_C_<br>**_Ir_**<br>**_rt_**flEVCOWERY<br>........................|.<br>_2A_|
||6.1|Variable and Common Costs<br>............<br>...........|..<br>24|
||6.2|Recovering Collective Common Costs .........................|26<br>|
||6.3|Is it Feasible to Charge for Congestion? .........................|30|
|_VII._|APP|LYING THE PRICIYiGMODEL|**-22**|
|VIII.|**OTH**|**ER ISSES**AND CONCLUSIONS .37||
|Annex|1|Calculation of Congestion Costs for Tunisia .39||
|Annex|2|Recent Estimates of the Price Elasticity<br>||
|||ofD=m=_dfor Transpol-A<br>.........<br>.................|<br>. . . ....<br>43|
|Refere|nces|.......|47|
|Fig.|1.|Relationship Between Vehicle Operating Costs in||
|||Tunisia and the Roughness of the Road Pavement .|11|
||ii||
|---|---|---|
|Fig.<br>2.|Eonomies of Scale in Constructing Inter-Urban Roads .....<br>....|........<br>12|
|Fig.<br>3.|Rdationship Between Road Capacity and Number of Lanes ....|..........<br>14|
|Fig.<br>4.|Effect of Marginal and Average Cost Pricing<br>on Total Surplus .20||
|Fig.<br>_5._|Threshold Value of the Marginal Cost of Public Funds as<br>a Function of the Proportional Fall Price, Given<br>Different Price Elasticities of Demand .21||
|Fig.<br>6.|Loss of Consumer Surplus Associated with Covering<br>Collective Common Costs .<br>.<br>...........|27|
|Fig.<br>7.|Using the Inverse Elasticity Rule to Compute the<br>Mark-ups Needed to Cover Collective Common Costs ....|29|
|Table 1.|Changing Condition of Brazil's Road Network ........|10|
|Table 2.|Actual Costs and Those Covered by Optimal Pricing<br>Model: Tunisia, 1982 ..........|18|
|Table 3.|Optimal User Charges and Ad Valorem Mark-up Needed<br>to Cover Unfunded Road Expenditures: Tunisia, 1982 .22||
|Table 4.|Analysis of Costs in Terms of their Avoidability:<br>Tunisia, 1982 .25||
|Table 5.|Calculation of User Charges Using Avoidable Cost<br>Principles and the Inverse Elasticity Rule:<br>Tunilsia, 1982 .34||
|Table 6.|User Charges Calculated Using Avoidable Costs<br>Compared with those Used in Tunisia .35||
# **Acknowledgements**

The report was prepared as part of a project on Pricing, Cost Recovery and Efficient Resource Use in Transport. It was prepared by Ian Heggie and Vincy Fon (Consultant). An early draft of the report was reviewed by an external panel consisting of Professors William J. Baumol, Princeton University, M. Schankerman, London School of Economics, and Kenneth Small, University of California, Irvine. The report was also reviewed by a group of Bank staff including Philip Blackshaw, EMTIN, Jose Carbajo, INUTD, Ciell Harral, ASTIN, and Vinaya Swaroop, CECPE.

The author would also like to thank the many other World Bank staff and consultants who commented on specific sections of the text, or supplied some of the empirical data presented in the report. They included Jeffrey Gutman, Asif Faiz, Tim Hau, Roy Knighton, Charles J. Lane, Bill Paterson, Sigfus Sigfusson, Rachel Kranton (Consultant), Graham Smith, Rodrigo Archondo-Callao, Pradeep Mitra, Slobodan Mitric, Richard Barrett, Peter Midgley, John Flora, Dick Podolske, and Margaret Callan (Consultant) The artwork in the report was prepared by Cathy Kocak, GSDAD, and the text was finalized and formatted by Rita Vartanian and Barbara Gregory.

Ian G. Heggie is a Principal Economist in the Transport Division of the Worid Bank's Infrastructure and Urban Development Department. Vincy Fon is an Associate Program Director at National Science Foundation and an Assistant Professor of Economics at George Washington University.
iv

# Executive Swaumary

## i.

i. Current theories of road pricing argue that net economic benefits will be maximized when prices are set equal to short-run marginal costs (variable road maintenance costs and the costs of externalities, usually confined to road congestion). Several empirical studies have rlaimed to show that such a system of user charges would cover the entire costs of the road network and make a reasonable contribution to overall fiscal revenues. (Paras 1-3).

ii. The above conclusions have been formalized into two theorems: (i) if there are constant returns to scale in road construction and in road use, the optimal user charge will recover the capital costs of the road network and total expenditures on road maintenance; and «ii) if, in addition, heavy vehicles are confined to the outer lanes of roads with four or more lanes and all road damage is attributable to traffic, the optimal user charge will recover the capital costs of the road network and twice total expenditures on road maintenance. (Para 5).

## iii.

iii. Since roads with four or more lanes comprise less than 10 percent of the road network in most countries, the second proposition has limited application. rne paper therefore focusses on the first theorem, applies it to roads in Tunisia and shows that the optimal user charges (as defined by the model) do _not_ cover total expenditures on road maintenance and make no contribution to capital costs. The paper then examines how to finance the balance of the unfunded expenditures in the most economically efficient way. The paper does not examine distributional issues, how much road users should contribute to overall fiscal revenues, the choice of pricing instrument, or how pricing strategies affect the costs of supplying roads. (Para 5).

## iv.

iv. Optimal theories of road pricing are based on a series of explicit and implicit assumptions. They assume: (I) the road network has a fixed length and is subjected to a constant flow of traffic; (II) the road network has a uniform age distribution and the road agency adopts a condition-responsive maintenance strategy; (III) road capacity can be smoothly adjusted to traffic so that the entire road network is in equilibrium; (IV) vehicle operating costs are linearly related to the average roughness of the road pavement; (V) routine maintenance costs are zero; (VI) there are constant returns to scale in road construction; and (VII) there are constant returns to scale in road use (i.e. the time related cost function is homogenous of degree 0). The effect of these assumptions is to ensure that the optimal user charge (levied to cover road damage and congestion costs) exactly covers the annualized costs of the road network and variable expenditures on periodic road maintenance. (Pams 6-21).

v. Assumptions I, II and IV are either reasonable simplifying assumptions, or are unavoidable in the interests of simplifying the analysis, (Paras 23-25). The remaining assumptions are too strong. Periodic maintenance costs do not **all** vary with traffic; between 20 percent and 65 percent of these costs **are** fixed (assumption V). Routine maintenance costs likewise are not zero; they account for nearly half total road maintenance costs and an estimated 30 percent are variable. On inter-urban roads there are likewise strongly increasing returns to scale in road
v construction (aamption VI) and in road use (assumption VIID; on urban roads this is partly offset by -Ising land valucs. Finally, roads cannot be smoothly adjusted to traffic (assumption III); they are not infinitely divisible and always operating at their optimal capacity. (Paras 26-29).

vi. When the above assumptions are relaxed, the optimal pricing model breaks down. Relaxation of assumptions V, VI and VII all lead to the same result: when they are relaxed, the optimal user charges fall short of the annualized costs of the road network and total expenditures on road maintenance. In each case, relaxation of the assumption brings in scale economies which leads to attendant deficits when prices are set equal to marginal costs. Finally, assumption III cannot really be relaxed; it follows as a consequence of using differential calculus. It requires that the costs of congestion on each km of road be just equal to the costs of adding a margina increment in road capacity. This takes no account of the substantial spatial and tempora variations in road traffic and, since indivisibilities are generally recognized to be a source of scale economies, autou-iicoly causes deficits when prices are set equal to marginal costs. (Paras 3036).

vii. When the optimal pricing model is applied to Tunisia, and the costs of urban roac congestion are estimated using a traffic simulation model (Annex 2), the resulting user charges only cover just over half the total costs incurred. User charges set on the basis of the above optimal pricing model will therefore leave a large block q'f expenditures unifunded. (Paras 37-38).

viii. The remainder of the paper considers how to finance these unfunded expenditures in the most economically efficient way. It focusses on roads carrying significant volumes of traffic and considers the options of raising user charges or using general tax revenues (it does not consider taxes on beneficiaries which are normally only relevant on roads carrying low volumes of traffic and primarily providing access to property). The options are examined in terms of their **-. 4..4.** WU &&%, F&*^ ***SI&. Wv.th.** 1.% #,a"t 0111 associated with marginal cost pricing have to be financed. This introduces the costs of general taxation (deadweight and administrative costs) associated with financing these deficits. Th conclusion from this analysis is that, provided the administrative costs of road user taxes are similar to general revenue taxes, the welfare costs of marginal cost pricing _plus_ general taxation lfr14YLU **U%.£ASIAI%14** _ _ _~~..16 **USWAS** !1__1_ 4. AL%, t_L:_ V*t.__*._ -14J;A **UWA 4G , W4AN.4** **_V1_** _- Q **_I&A wl3*k&%.A_ kJAAs.AAA6** **_£_** _c* A_ **_)4 %A%'_** --ws It follows that a pricing system which raises the extra revenues from users using optimal departures from marginal cost pricing will be more attractive in welfare terms. (Paras 39-44).

ix. The paper introduces the concept of avoidability to classify the costs of operating, maintaining and improving the road network. Three levels of avoidability are identified: (i) costs which are variable and incurred on behalf of identifiable users; (ii) costs which can be avoided over a short period of time and are incurred on behalf of an identifiable group of users (but not the individual member of the group); and (iii) costs which are common to all users and can onl! be avoided by closing the road network. In Tunisia, these categories account for 29, 26 and 4' percent respectively of total road expenditures. It is suggested that the first group, being marginal, should be recovered from users in terms of veh-km (for variable routine maintenance
vi costs) and **ESA-hm** (for variable periodic maintenance costs). Since the second category are avoidable, it is suggested they should be recovered uniformly from the groups olt whose behalf they are incurred: in terms of ESA-km (for heavy vehicles) and in terms of PCE-km (to expand road capacity for rural and urban road users). (Paras 45-48).

x. The paper shows that the most economically efficient way of financing the remaining collective common costs, is by using thc inverse elasticity rule. This minimizes the relative loss of consumer surplus per dollar of collective common costs covered by each user group. It is done by equalizing the ratios of the mark-up over base-costs (variable and grouped common costs), divided by the sum of the respective supply and demand elasticities, for each user group. The procedure is illustrated in graphical form and is solved using trial-and-error. (Paras 49-52).

xi. The paper also looks at the scope for financing common costs by way of congestion charges. It concludes, based on a review recently completed by the World Bank, that most road congestion in developing countries is attributable to the poor performance of the road agency; it is self-inflicted. The overall conclusions are that: (i) serious road congestion is limited to about twenty large cities in the Bank's developing member countries; (ii) inethods of charging for congestion are limited and difficult to administer; and (iii) the charging method selected will be determined by the nature of the city, the administrative complexity of the charging instrument, and its affordability. Since serious (non-self inflicted) congestion is limited in developing countries, it will make little contribution to cost recovery for the road network as a whole. (Paras 53-60).

xii. Finally, the paper applies the above pricing model to Tunisia and concludes that, when the mark-ups are applied to all vehicles, it results in lower charges for cars and much higher charges for all other vehicles. Without pure taxation of freight vehicles (i.e. the mark-ups are applied to passenger vehicles only), the charges for most vehicles e lQ _ivurly_ ithl b±iiie. Tlhey are, nevertheless, much higher for buses, lower for gasoline cars and higher for heavy trucks. (Paras 61-64).

xiii. The overall conclusions of the paper are: (i) it is unrealistic to assume there are r-crurns **tow** scale in road construction **and** in road use and to ignore routine road maintenance costs; **(ii)** roads canrot be smoothly adjusted to traffic, so that the marginal costs of the entire road network **will** usually be lower than average costs; (iii) congestion charges may be justifiable in the limited number of cities experiencing serious road congestion, but the revenues from these charges are unlikely to cover the common costs for the road network as a whole; (iv) it is nearly always more economical to collect the revenues required to cover unfunded road expenditures by raising user charges using to the inverse elasticity rule (rather than by using general tax revenues); and (v) there are significant differences between current road user charges in Tunisia and those calculated using the above avoidable cost methodology. (Paras 65-66).
# **I.** INTROL'UCTION

1. Economists have repeatedly urged governments to "get prices right" or, more strongly, have argued that "getting prices right [might not be] the end of economic development, but getting prices wrong frequently is" (Meier, 1983, pp. 1 and 231; Timmer, 1987, p. 39). Prices influence resource allocation, revenue mobilization and the distribution of income; they provide the indispensable information needed to reach rational economic decisions on what and how much to produce. To maximize net economic benefits, prices should be set equal to the social external costs directly attributable to a small increase or decrease in output, i.e., equal to short-run marginal costs. In the case of roads, these prices (or optimal user charges) are equal to the value of the resources consumed when using the road. They consist of the damage done to the road surface (variable road maintenance costs) and the additional costs (usually confined to congestion costs) which each user imposes on other road users and on the rest of society (Walters, 1968; Churchill, 1972).

2. One of the persistent queries raised by the above pricing rule is what impact it has on cost recovery and, when it results in deficits, how these should be finianced. One of the seminal works on road user charging reached the following conclusion, "on the rural and interurban highways, the revenue collected from user charges at marginal costs is likely to be insufficient to cover the (annualized) investment cost of the roads; whereas in the case of congested city streets it is likely that the revenue from marginal cost pricing will be more than sufficient to meet the total costs". It also argued, however, that "we find that there are no grounds for requiring a particular road, a class of roads, or the highway system as a whole to cover its costs by user charges" (Walters, 1968, p. 114). On the other hand, the author also claimed there was no overwhelming presumption that such user charges would necessarily result in large deficits. This was an empirical question and the only way to test the consequences of usine ontimal user charges was to calculate them to sq( whe-ther they racidtZ ;ind1eficeits.

3. Initial results from calculating such charges were encouraging. A rough calculation for Thailand during the 1960s suggested that optimal user charges would have raised existing road user revenues from between $40 and $50 million p.a. to over $60 million (Walters, 196R. nn. 226-227' and **a** more detailed htlldV nf five **rn,mtripe** 1n **i'antr.31** AnMV _e^nc A_ that "the net impact of these changes [in road user charges] would be to raise public revenues from user taxes by 32 percent to _50_ percent, depending on the country" (Churchill, 1972, p. 3). Recent estimates for Tunisia likewise suggest that optimal user charges would generate twice the revenues currently spent on roads (Newbery et al, 1988). These results are nevertheless critically dependent on the estimated costs of congestion and there are reasons to believe that some of the estimates were too high. A more cautious approach results in estimates of optimal user charges which are significantly lower.j/

> I/ **WWaters,** 1968, **bases his estinate** on **the cosa** of congestion on urban highways in the UK (pp. 178 and 226) **where** avemgc per capita GNP was nearly **thitte¢n times that** in **Ihailand.** Estimated **tavel** time costs, and **hence the** yield of a congeston tax, **may** therefore be too high. Newbery, **et aI,** 1988, **liks** assume AU urban traffic in Tunisia is congested **and** assume **very** high m **argua time cots.** Annex 1 of this paper suggests **the** estimates for Tunisia may also be too high.
2 4. 11wd ulwreeai **hiU;&idrX.** *! -. ~.'- _obsuf_ na_ginal cost pricing on cost recovery. An early analytical model showed that an optimal pricing<sup>and</sup> investment strategy would be exactly self-financing if there were constant returns to scale<sup>in road</sup> construction. When there were decreasing returns it would earn a surplus,<sup>while if there were</sup> increasing returns it would incur a deficit (Mohring and Harwitz, 1962). The model nevertheless ignored road maintenance costs and was recognized as being too simplistic.<sup>A more</sup> recent model has overcome some of these objections and has arrived at the folI. wing<sup>two</sup> propositions: (i) if there are constant returns to scale in road construction and in road use,<sup>then</sup> the optimal road user charge will recover the capital costs of the road network and the<sup>total</sup> expenditures on road maintenance; and (ii) if, in addition, heavy vehicles are confined<sup>to the</sup> slow lanes (i.e., the outer lanes on roads with four or more lanes) and all road<sup>damage is</sup> attributable to traffic, the optimal user charge will recover the capital costs of the road<sup>neLwork</sup> and twic the total expenditures on road maintenance.

_5._ The second proposition has limited application, since few countries have many four-lane roads. In the U.S.A., only 8.4 percent of the paved road network (excluding<sup>local</sup> roads) have four or more lanes and the proportion in Japan is 3.5 percent, Mexico 3.5 percent and Tunisia 1.0 percent. These roads usually carry between 5 to 10 percent of<sup>total traffic.</sup> Engineers furthermore take account of differential use when designing road pavements.<sup>The</sup> following paper therefore concentrates on the first proposition, applies it to the road network<sup>in</sup> Tunisia (as described in Newbery et al, 1988) and shows that the optimal user charges do not cover the total expenditures on road maintenance and make no contribution to capital<sup>costs. The</sup> paper then examines ways of recovering these costs in the most economically efficient manner. It is also important to say what the paper does not do. It does not deal with the<sup>impact of</sup> pricing policies on income distribution, does not examine what contribution the road sector might be expected **o** make **iu** overall fiscal reveiues, ii noi dalca wiul Ulf choicc _of_ charging instrument (i.e., whether, and how, to use licence fees, fuel taxes, sales and excise taxes, import duties, etc. to collect road user revenues) and does not deal with noise, air pollution and other externalities. It likewise does not deal with the important relationship between the choice<sup>of</sup> pricing strategy and the impact this has on management incentives and hence on the costs of suppiying road services.
3

# II. OPTEMAL PRICING MODEL

6. In their attempt to derive optimal road user charges, Mohring<sup>and Harwitz (1962)</sup> considered the problem of maximizing long-run net<sup>benefits. Net benefits, NB, equal consumer</sup> private benefits minus total costs. Consumer private benefits,<sup>PB(N), are a function of the</sup> number of trips, or le-!el of traffic, N, and can be represented<sup>as the area underneath the demand</sup> curve.2/ Total costs, TC(N,w), are assumed to depend<sup>on the level of traffic N and highway</sup> capacity w, a function of the width of the road measured in number<sup>of lanes of standard width.</sup> The TC function has t--o components, The first is users' total<sup>costs, N VV(N,w). The term</sup> VV, the time-cost function per trip, or the vehicle operating<sup>cost (VOC), increases with</sup> increases in N and with decreases in w. The second component<sup>of TC is the capital expenditure</sup> for roads and is written r-KK(w) where r is the interest rate<sup>for public investments and KKw(w)</sup> > zero.j/ Note that this formulation of costs omits all road<sup>maintenance costs. The problem</sup> here is to choose the optimal level of traffic N and capacity w to<sup>maximize net benefits:</sup>

## Mdx NB = PB(N) - TC(N,w) = PB(N) - [NVW(N,w) + r'KK(w)l

7. In this formulation, the marginal private benefits of the trip, MPBN<sup>are given by</sup> the derivative of PB(N). The marginal social costs of the<sup>trip, MSCN, or the additional social</sup> costs due to an additional trip, are given by the partal derivative<sup>of TC(N,w) with respect to</sup> N, which is equal to the partial derivative of N*W(N,w)<sup>with respect to N, or, [VV(N,w) +</sup> N'WN(N,w)J. Since W is the VOC borne by users,<sup>it is the marginal private cost of the trip,</sup> **MPCN.** Since N-VVN(N,w) denotes the additional congestion costs<sup>imposed on other users from</sup> one more trip, we call this the marginal external costs<sup>of the trip. MEC.. Therefore, we see</sup> that MSCN equals MPCN + MECN. The net marginal<sup>costs of highway capacity are given by</sup> the partial derivative of TC(N,w) with respect to w, which<sup>is equal to NWVV,(N,w) +</sup> r KK(w). The term N*WwV(N,w) is negative and denotes the decrease in time-costs when highway capacity is expanded; it therefore represents benefits<sup>to users. We will refer to</sup> -N*WV(N,w) as the marginal private benefits of expanding<sup>capacity, MPBW,,. The term</sup> rKK(w) represents additional road costs and will be called marginal<sup>road costs of expanding</sup> capacity, MRCW. To conclude, the net marginal costs of highway<sup>capacity are equal to marginal</sup> - road costs of capacity minus marginal private benefits of capacity, or,<sup>**[MRCW**</sup> MPBW].

8. 'he optimal levels of traffic and highway capacity must satisfy<sup>the first-order</sup> conditions for maximizing net benefits. These conditions<sup>are found by equating the partial</sup> V **The** notatiots used in **this** paper **is** clour to **that** of **Neaery (1987).** _I/_ We **shall abus the standard mamaial notation** for **partil derivatives** by **also ui ing** it to denote derivatives.
4 derivatives of **ND** with respect to N and w to zero. With the help of the notation introduced above, we can easily **see** that the conditions are as follows:

**MPBN** = MSCN **=** MPCN + MECN (1) MPB. **= MRCW.** (2)

In words, equation (1) says that the marginal private benefits from an additional trip should be equated to the sum of private VOCs (VV) and the marginal external costs of this trip (due to congestion). Equation (2) rays that the marginal private benefits of additional capacity (due to reduction in time costs) should be equated to the marginal costs of additional highway capacity.A/ 9. From the maximization condition (1), we see that in order to have an efficient -ghway svstem, the external costs from congestion must be internalized. That is, an appropriate congestion charge equal to MECN should be levied. The remaining question is to find out when revenue from congestion charges will cover the road costs. Assume that **V** V is homogeneous of degree 0 in N and w, meaning that doubling both traffic and highway capacity leaves VOCs unchanged, and that **KK** is homogeneous of degree 1 in **w,** meaning that there are neither economies nor diseconomies of scale in highway construction. Under these assumptions, the optimal user taxes would be just sufficient to cover all road costs. Since this model will be generalized and discussed carefully later, we defer the explanation of cost recovery until then.

# 10.

10. Because road width, w, does not enter the demand function dirxtly and only influences total costs, the problem of maximizing net benefits decomposes into two stages. For any given N, minimize total costs of supplying that N. This yields the optimal highway capacity w as a function of N, w = g(N).5/ Then in the sLcond stage, solve: Max PB(N) - TC(N,g(N)) to find the optimal amount of traffic

# 11.

11. Specifically, an efficient highway system can therefore be found by first solving the total cost minimization problem:

# **Min TC** = NVV(N,w) + r KK(w) (3)

to **find the optimal highway capacity,** assuming that the level of traffic N is constant. **This** means that **the partial derivative of TC** with respect **to w** must be set to zero, giving **MPB,** = **MRC,,** as in equation (2). Since **MPB** depends on w as well as N, **otie** must make sure that the level of traffic **N** is also optimal. This means that N must satisfy equation (1). Or,

> d/ **lt** should **be noted that the Lrst-order conditions (1) and (2) are only necessay but** not sufficient. Mohring **and Harwitz** implicitly **asumed** the existence of the second-order sufficient conditions.

> **I/1** In pratice, the first-order condition, (2), for total cost minimization may not present w **as an** explicit function of **N. W/ith fth** help of Implicit Function ITeorem, **w'** can **indood** be thought of **a a function of N.**
**_S_**

**MPBN** must be made equal to MSCN by imposing a congestion charge of MECN. In general, to describe the efficient highway system, it is sufficient to investigate the problem of minimizing total costs and apAlying MECN as the optimal tax. In fact, this approach was adopted by Newbery (1987), who extends the model of Mohring and Harwitz (1962) by incorporating maintenance costs.

12. The following presents the essence of Newbery's model mathematically. It contains three important implicit assumptions: (i) the road network has a fixed length and is subjected to a constant flow of traffic per lane (assumption I); (ii) the road network has a uniform age distribution anal the highway agency adopts a condition-responsive maintenance regime (assumption ID); and (iii) road capacity can be smoothly adjusted to traffic, so that the entire road network is in equilibrium (assumption III). These assumptions, together with the explicit mathematical assumptions made in this section, are discussed in section 3.

13. Newbery considers the problem of minimizing total costs when choosing an optimal highway capacity w with pavement strength S. There are three parts to the total cost function. First are the VOCs, which consist of overhead costs v0, time related costs per km V, and wear and tear to the vehicle. Item V is an increasing function of traffic flow N and a decreasing function of highway capacity w. That is, we have V(N,w) with VN > 0 and V, < 0. The wear and tear on the vehicle is assumed to be linearly dependent on average roughness, written as bR, where b is positive and R represents average roughness (assumption IV). Therefore, the total vehicle operating costs to al users are N (v,+V(N,w)+bR).

14. The second component of total costs are the annualized costs per kilometer of road construction. It is specified as a function of highway capacity w and strength S and is written as r.[KO+wK(S)], where r is the cost of funds, Ko is a non-negative constant and Ks > 0. When Ko is zero, the construction costs corresponds to the case of constant returns to expanding road cpacity, holding road strength constant.fi/ The case of increasing returns to scale is reflected in Ks being positive.

**_15._** The last component in the total costs are the annual maintenance costs per kilometer, w.M(D/w,S), where D/w represents the number of equivalent standard axles (ESAs) per unit of capacity and the maintenance cost function per lane M is an increasing function of Diw, and a decreasing function of S. That is, MD},. > 0 and M8 < 0. The term D, the number of heavy axles, is assumed to be N-E, the total traffic flow N times the vehicles' avexage damaging power E.Z/ Road maintenance costs, M, are assumed to consist of periodic

> / **When Ks** is zero, ruwK(S) in **this** model extendS **the capital** investment **function** r.KK(w) **in** the previous **model** when **KK is homognous** of degree **1** by incorporting **an** additional **vaiable** S.

> **1/ We simplify Ntwbery's** model by **usumdng** that **there** is **only** one type of **vehicle.** If many types of vehicles **are considerd,** then D **is** the sum of **the** product of **traffic low** of ewh **type** of vehicle and the **repetive an Sge damaging power** of **this** type **over all** typer.
6 (resurfacing) cost only. Routine maintenance is ignored (assumption V). Note that in this formulation, road maintenance costs omit fixed maintenance custs and any maintenance costs which may depend on the volume of traffic, rather than on the passage of heavy vehicles.

16. The road system is optimally designed by first choosing values of capacity w and strength S to minimize total costs:

# Min TC = N [v*+V(N,w)+bRJ + r [K+wK(S)] + w M(D/w,S). (4)

By taking the partial derivatives of TC with respect to w and S and equating them to zero, we have the minimization conditions:J/ N V, + rK + M + wMD,,(-D/w-) = **0** _(5)_ r'wK 8 + wMs = **0.** (6) Rewriting equations (5) and (6), we have

-N-V,, = rK + M - (D/w)MD,W (7) w*Ms = r*w'Ks. (8)

17. The left-hand side of (7), representing the reduction in user time-costs due to an additional lane, is the marginal private benefit of capacity MPB,. The first two terms on the right-hand side of (7) represent the increased costs of adding capacity, since K is the road construction costs per unit of capacity and M are the variable periodic maintenance costs of that unit of capacity. The last term in (7) represents the reduction in periodic maintenance costs per unit of capacity since an additional unit of capacity reduces the number of heavy axles per unit of capacity and hence decreases the total periodic maintenance costs of the road. The three right-hand terns sum to become the marginal costs of adding an additional unit of capacity; they can also be written as r*K + M(1 - O), where t is the elasticity of M with respect to D/w. Equation (7) therefore prescibes that for an optimally designed roadway, the marginal benefit of adding capacity should equal the marginal costs of capacity. For this conclusion to be meaningfui, it must be assumed that road capacity can be smoothily aujusted to traffic (as per assumption p).

18. Likewise, the left-han( 'de of (8) represents the marginal benefits of additional strength through a reduction in periodic maintenance costs (M8 is negative), and the right-hand side of (8) represents the marginal increase in road construction costs due to additional strength. Equation (8) then prescribes that an optimally designed roadway should choose the strength of roads appropriately so as to eq marginal benefits of strength with marginal costs of strength.

U In the following, we suppru **the arguma** of **al fwcions** to **faciltte the** undenanding of vanous conditions. **Like** Mohring and **Harwitz, Newbery** implicitly auumed **the exisence** of **the** econd-order sufficient conditions.
7 With these interpretations, one can easily see why equations (7) and (8) extend equation (2) in the prcvious simpler model.

19. To ensure that the right level of traffic N is induced, the marginal external costs must be internalized through taxes, as was mentioned earlier. To determine the road tax, we need to know the marginal social costs of traffic MSCN, which is the partial derivative of TC with respect to N. In this case, we have:

# MSCN = [vO+V(N,w)+bRJ + N-VN + E'MDI,. (9)

The first three terms consist of the VOCs and represent the user's marginal private costs MPCN. The term **N-VN** represents the external costs imposed on other road users through congestion. The last term EMDW, which is the simplification of the partial derivative of w*M with respect to N, or, w*MDj,.(E/w), represents the additional periodic maintenance costs caused by the additional traffic. Hence the last two terms together become the marginal external costs of traffic, MECN, or, MECN = **NVN +** EMD,w. (10) As noted before, MECN, is the efficient road tax for each user. In fact, it is readily seen that the unit congestion charge should be N-VN and the unit road damage tax should be EMD,I. Note how equation (9) extends the right-hand equality in equation (1).

20. To extend his analysis, Newbery assumes constant returns to scale in road construction with respect to capacity, holding road strength constant, so that Ko = 0 (assumption VI). He also assumes that the time related cost function V is homogeneous of degree 0 (tuIIIpdoII VMI).2i By definition, V homogeneous of degree U means that:

# V(&N,arw) = a°eV(N,w) = V(N,w).

The above equation says that doubling traffic and highway capacity (oa = 2) leaves the time related costs V the same. That is, as far as the users' time-costs are concerned, **it** is the average traffic per unit of capacity not the absolute amounts of traffic and capacity, that counts. In other words, measured in terms of user time-costs, additional capacity is the same as the average capacity. By Euler's equation, V homogeneous of degree 0 implies that: N*VN + W'V, = 0. (11) 2/ Thecse two **homogneity assumption wee also** adopted by Mohring and Harwitz.
8 It is easier to understand equation (11) if it is rewritten as: (N/w)VN = **-V,.** (12) The right-hand side of (12), -V4, gives the time-cost saving<sup>due to additional capacity, since V.</sup> < 0. This saving in time-costs from additional capacity can<sup>be translated to saving in time-costs</sup> due to a decrease in traffic. When V is homogeneous of degree<sup>0, having one more unit of</sup> capacity is equivalent to having N/w less traffic. We therefore<sup>conclude that</sup><sup>**(N/w)*VN**gives</sup> the capacity-equivalent savings in time-costs due to a decrease in traffic.

21. The total revenues raised from the congestion charges, G', and the total<sup>revenue</sup> raised from the road damage charge, **Gd,** are as follows:

**G;** = N*(N*VN), **Gd** = **N-(E*MDJ).**

Meanwhile, the average road costs per trip borne by<sup>the highway authority will be referred to</sup> as the average road costs per trip **ARCN-** Since the first<sup>term in (4) is borne privately, the last</sup> two terms represent the road costs borne by the highway agency.<sup>Hence we have:</sup> ARCN = (r-w-K + wM)/N since Ko is assumed to be zero = **(r-K** + M)lW/N)

**-= (D/w).MD,. -** N V,,J'(w/N) by (7) = **E*MD/,** - **w*V,,** since D = N*E = **E-MDIW +** N*VN by (11) = **MECN** by (10).

From the above calculation, we also readily see that: G' + Gd **= N(NVN** + E'MDIW) =N(rwK + w M)/N = rw-K + w-M.

Hence we see that, if there are constant returns to scale in<sup>road construction and in road use,</sup> then the optimal road **user** charge, **GI** + **Gd,** will cover the<sup>annualized capital costs of the road</sup> network and the total (variable] expenditures on periodic<sup>road maintenance. In spite of its</sup> familiar tone, this result is a little surprising: while all of the<sup>(total as well as average) road</sup> costs are **borne by** the **highway** agency, only **part** of the marginal<sup>external cost (E'MD/) is borne</sup> by it. However, given that all of MECN is taxed as the unit<sup>tax, which becomes the average tax</sup> revenues, and that appropriate assumptions guarantee the equality<sup>of ARCN and MECN, it then</sup> becomes clear that total tax revenues will exactly balance total<sup>road costs.</sup>
9

# **m. ASSUMIONS UNDERLYING OPTIMAL** PRICING

22. The above pricing model is based on two important sets of assumptions. The first set deal with the nature of the road network and its usage (assumption I), the condition of the road pavement and the type of road maintenance regime adopted by the highway agency (assumption II), and the effect of pavement conditions on vehicle operating costs (VOCs) (assumption IV). These assumptions appear reasonable and are merely introduced to simplify the analysis. The second set relate to the way road maintenance costs are specified (assumption V), the construction cost function (assumption VI), the nature of the congestion cost function (assumption VI), and the relationship between congestion costs and adjustments to road capacity (assumption 1II). These assumptions are also introduced to simplify the analysis, but do so at the expense of making the model unrealistic. Furthermore, they cannot easily be avoided and have an important effect on cost recovery.

## 3.1 Accentable Simnlifving Assurngtlons

23. Assumption I is that the road network has a fixed length and there is a constant flow of traffic per km. Extending the road network therefore reduces the traffic flow per kin, while growth in traffic increases it (hence partly offsetting the effect of extending the network). The optimum pricing model is therefore formulated in static, rather than dynamic terms. The prices calculated from the model only apply at a particular point in time and need to be recalculated each time the network is extended and/or there are changes in the volume of traffic. Although the model could be reformulated in a dynamic setting, this would complicate the model and hinder interpretation of the results (Newbery, 1987, p. 3). Provided the model is only used to estimate user charges for a particular point in time, anld is ri4x!i! re eztimat^! tz account of changes in road lengths and traffic volumes, the first assumption is reasonable in the interests of simplification.

24. Assumption II deals with the strength and condition of the road pavement. It 'iuntes th.o !m.iiante. (i) the road network is taken to be made up of individual road sections with uniformly distributed ages; and (ii) the highway agency is assumed to operate a conditionresponsive maintenance regime (i.e., road maintenance is carried out when each section of road reaches a pre-specified terminal degree of roughness). This means that the average roughness of the road pavement remains constant across the entire road network. This is a fairly strong assumption, since there are historical rhythms in the building of roads and significant parts of the road network usually become due for rehabilitation at the same time (Gakenheimer, 1989). Highway agencies are, furthermore, generally prevented from adopting a condition-responsive maintenance regime by **external** budgetary constraints. The average roughness of the road network can therefore vary quite widely. For exam,ple, between 1979 and 1984, average road roughness in Brazil increased by nearly one percent each year (see Table 1), while the average
10 roughness of paved roads in Ethiopia and Ghana decreased by 15 percent and 8 percent respectively between 1984 and 1988, and in Sudan and Nigeria increased by 3 percent and 2 percent respectively over the same time period (Harral and Faiz, 1988, Table A-2; Mason and Thriscutt, 1989, Table 3). At times the actual roughness of the road pavement will thus be higher than the long-term average, while at others it will be lower. This creates an awkward inconsistency. A sub-optimal road maintenance regime delivers perverse signals to users. When road maintenance is reduced, roughness increases and this increases VOCs: lower road quality thus costs road users more, while higher quality costs less. The assumption of constant average roughness is nevertheless unavoidable in the interests of simplifying the analysis.

Table 1. Changing Condition of Brazil's Road Network (percent and weighted average)

||**-1979-**||**-1984--**||**Cbange**<br>**1979-1984**|
|---|---|---|---|---|---|
|Road**Condition**|**km**|et|Ian|perce|percent|
|**Good**|10,000|24|14,000|30||
|Fair|23,000|**58**|19,000|42||
|Poor|7,000|**18**|13,000|28||
|**Weightod Averae**<br>**weghs**(a)||_1S6_||163|**4.5**|
|**weigbts**(b)||**135**||141|3.8|
|**(a)**Good - **1.0,**Fair =<br>|1.5, Poor - 2.5.<br>|||||
|(bh**(iood**- 1.U,**tatr**=|**1U,**roor - X.u.|||||

Note: **lbe increm in the** -ber of **roads in** good **condition was** caused by **new constuion.** About 6,000m **of newpaed roadswes** added to thedetwork, **while2,000km** formerly i good **codon decined** to fair. **Soums (Hd and Fa4z, 1988, Boz 1-3)** 25. Assumption IV assumes that vehicle operating costs are a linear function of the average roughness of the road pavement. This is a reasonable assumption. Although they are not strictly a linear function of the average roughness, they are nearly so and the discrepancy is of little practical importance. This is illustrated in Figure 1 for Tunisia. Since the figures are based on generic VOC figures, the relationship will hold in other countries as well.
11 <!-- Start of picture text --> 700<br>GM M<br>Bus<br>540 -<br>1300-<br>3200 Ug rk<br>100<br>0<br>0 4 a 1 0 12 I6 20<br>Road Roughness (tffVm IRI)<br>Source: Paterson, 198S, Table 2.13.<br><!-- End of picture text -->

**F%Mw 1:0** Relationship Between Vehicle Opermting Costs _in_ Tunisia and the Roughness of the Road Pavement

# 3.2 lSnaicwptable^mD1itfing Assumptiion

# 26.

26. Assumption V assumes that road maintenance costs consist exclusively of the variable costs of the periodic overlays (resurfacing) which are applied to the road pavement every 10 to 20 years. _The_ fixed costs of this periodic maintenance, which account for between 20 percent and 65 prcent of these costs, have been omitted..lQ/ These periodic expenditures are incurred at intervals greater **an** one year and consist of surface dressing and overlays for paved roads and re-graveling for un-paved roads. Note that, on an individual road, such expenditur would normally be treated as fixed costs. However, since between one-tenth and one-twendeth of the road network is resurfaced each year, these expenditures can be treated like <!-- Start of picture text --> 1Q/<br><!-- End of picture text -->

**Thc** propodaau of the overlay cow **which** am **xd are** specifid **in** tems of **climatic** conditions **a** follow: dry non-froze - 20%, dry frez - 45X, _wet_ non-fiez - 30%, and wet freeze **_-_ 65%** (Newbery, **at** &I, **18.** p. 84).
12 marginal costs. The model also ignores all routine maintenance costs, which generally account for at least half total road maintenance expenditures.il/ Routine maintenance amounts to between $1,000 and $3,000 per km for paved roads and between $500 and $1,500 per km for unpaved roads, depending on the country and volume of traffic. Up to 70 percent of these costs are typically fixed, the remainder being attributable to the passage of vehicles (patching) and the incidence of heavy vehicles (e.g., shoulder maintenance).

<!-- Start of picture text --> __Vefta Profil D _ _<br>Tuvfajn Roswa<br>4 2 a ,1.<br>300 000<br>122 ~~/Q / 3.<br>/ 2 4<br>I ,~~~~~~I Number of Lanes<br>N1i Shoulderan arnll 1.5 m wide, pavemcents ae3.5, 7.0 and 2 x ?.0 m wide and the<br>2-lane road has a S m central reservation.<br>sow= Amedo-C:n 1990. r<br>liS= 2: &,onornis<br><!-- End of picture text --> <!-- Start of picture text --> &,onornis of Scalc in Constructing Inter-Urban Roads<br><!-- End of picture text --> D1 In Arizona, U.S.A., with over 100,000 Ian of road and sw, fixed costs accounted for about 65 per cent of annual rod ma_nac expendkuu in 1989 (Arizona De-partment of Transportation, 1989).
13

# 27.

27. Assumption VI deals with the costs of road construction. These are specified as, K. + wK(S), where K, is a constant term reflecting the incidence of economies of scale in road construction. To simplify the analysis, it is assumed there are constant returns to scale in road construction so that Ko is equal to zero. The author recognizes this assumption is unrealistic, since there are substantial economies of scale in constructing non-urban roads up to four lanes. This is illustrated in figure 2; it is based on empirical data trom several countries and is equally applicable to Tunisia. In urban areas, on the other hand, rising land values increases the average cost function and this decreases the effect of increasing returns to scale. The two effects may therefore cancel out in urban areas and the assumption of constant returns to scale may be reasonable (Newbery, 1987, p. 9; Small et al, 1989, pp. 101-102). However, urban roads in developing countries generally account for less than 20 percent of the paved road network and perhaps 10 percent of the classified network (the figures for Tunisia are 19.1 percent and 10.5 percent respectively) (Paterson, 1985) and even in developed countries they still only account for between 18 percent (USA) and 47 percent (W. Germany) of the total road network (Annual Bulletin, 1986, Table 11). When applied to an entire road network, the assumption of constant returns to scale in road construction is therefore too strong.

# 28.

28. Assumption VII assumes that the time costs associated with traffic congestion are homogeneous of degree zero in N and w. In other words, if the volume of traffic doubles and the number of lanes is doubled, vehicle speeds will remain the same. This is unfortunately untrue. Regardless of whether road capacity is compared on the basis of constant speeds, or constant levels of service (LOS), which describe how the interactions between vehicles affect road speeds and capacity, it is clearly not directly related to the number of lanes. The relationship between these two quantities is illustrated in Figure 3. It is based on generic data and therefore applies to all countries, including Tunisia. The continuous lines refer to constant speeds and the broken lines to constant levels of service. On an uncongested inter-urban road **(Raverage sneed** _'SR_ mph, or LOS = A), the capacity of a four-lane road is 4.6 to 5.0 times that of a two-lane road and over 30 times that of a single-lane road. With moderate congestion (average speed 52 mph, or LOS = C), the ratio falls to 2.7 to 3.5 and 18 to 23 respectively, and only approaches 2.0 on roads with two or mcre lanes experiencing serious congestion (average speed 45 mph, or LOS = E), or on roads with more than four lanes. Since a relatively small proportion of the road network in most countries will be seriously congested, or exceed four-lanes (in Tunisia there are no roads over four lanes) (Paterson, 1985), the assumption that time costs are homogeneous of degree zero is too strong.

29. Finally, assumption mII assumes that road capacity can be smoothly adjusted to traffic. In other words, roads are assumed to be infinitely divisible and are always operating at their optimal capacity. This is an important weakness. Roae investments are inherently lumpy, at least at the network level, and although there is scope fo increasing road capacity at the margin, particularly in urban areas (Starkie, 1982), the main increments in capacity - from one lane to two and from two to four - can only be added in indivisible lumps. This means that much of the road network will be operating well below **:Is** optimal capacity and congestion
14 <!-- Start of picture text --> Consta Lv of Sevo (LOS) LOS E<br>8.000 - Constan Sped/ capacty)<br>7.000-<br>6,000 - 45 mph<br>£ / / ~~~~~~~~~~~~~~~~~~LOS C<br>5.000 - ~~~~~~~~~~~~~~~~~~~~~~Of Other vehcles<br>45,000-<br>i 4 °°Z \ ~~~~~~~~~~~~~~~~~52 mp<br>14000 - LS<br>3.000 - / / / - - ~~~~~~~~~~~~~~~(Ffee llow)<br>2.000- 8fp<br>1.000 Zo<br>0 2 3 4 5 6<br>Number of Lanes<br><!-- End of picture text --> <!-- Start of picture text --> Two and 4-lane road, Trnsportaton Reseach Board, 1985; single lane roads, Hoban, 1987, Table 11, figu<br>for India.<br>F;e 3: Rclaionship Between Road Capacity and Number of Lanes<br><!-- End of picture text --> costs will be **less than** the marginal costs of adding additional road capacity. This creates special pr6uiers in countries with low traffic densities. The lumpiness of investments means therc .s - - little traffic congesion a common feature of the road systems in most developing countries and congestion costs are close to zero. There are only limited sections of road where the network is operatng at capacity, unless investment is sub-optimal (or there are physical and/or environmental constraints restricting capacity) which allows congestion to build up beyond the point where further investment would be economically justified.
**1S**

# **IV. RELAXING UNACCEPIABLE ASSUMMONS AND** '1 **I;fL** tl **UIt I UNIBI**

## 30.

30. The following section examines what happens to cost recovery when the unacceptable limiting assumptions discussed in section 3 are relaxed. In each case relaxation of the assumption seems to bring in scale economies which leads to the attendant deficits when prices are set equal to marginal costs. The section then applies the optimal pricing model to a case study in Tunisia to show, in quantitative terms, the importance of these assumptions for cost recovery. It is important to point out, however, that the case study only considers the classified road network in Tunisia (17,000 km) and roads in urban agglomerations (1,800 kmn). The remaining 14,000 km of unclassified roads have been omitted (Paterson, 1985).

## 4.1 Relaxing Unacceptable Assumptions

## 31.

31. Let us see how the balanced budget conclusion in the optimal pricing model is affected if the unacceptable assumptions are relaxed. Specifically, we investigate the following cases: (A) the constant Ko in the road construction function is not zero; (B) there is a positive constant M0, denoting fixed maintenance cost, in the total cost function;12/ (C) the time cost function **V** is not homogeneous of degree zero (in particular, we consider the case where an additional lane can handle more traffic than the previous lane); and (D) the road capacity cannot be smoothiy adjusted to traffic, so that the network is not in an optimal equilibrium condition.

## 32.

32. Consider case (A) and assume that the constant Ko in the road construction function is not zero. If optimal pricing is still adopted, the minimization conditions (7) and (8) still **hnled since** an additional constant in the **TC** function does not affect any derivative at 11, and a tax of MECN is imposed. Hence **ARCN** is still equal to MECN,. Let us refer to the average road costs of the trip in the previous model and in this relaxed case as **ARCN** and ARC'N respectively. Then we have ARC'N = **ARCN +** r'KJN. But this implies that:

### **ARC'.** = **MEC. + r*KJN >** MNr..

and the total revenue raised by **G'** and **Gd** will then be **_1** than the road costs borne by the highway agency.11/

**_12_ It would be fairly simple in the Newbery model to include the routine maintenance costs which vary with the volume** of traffic, **N, as well as D,** the number of heavy axles.

**12/**

**Since** cases A and B involve adding a constant to the objective function **in** Newbery's model, **the** same second-order sufficient conditions **are** required to hold. **In case C.** we assume the existence of second-order sufficient conditions **as wel.**
**16**

1 33. It is clear that the inclusion of a constant, Mo, to denote the fixed maintenance cost in the **TC** function has the same effect as the inclusion of a non-zero constant Ko in the TC function. Therefore, the average external cost of a trip will exceed the marginal external cost of the trip in case (B) as well.

34. Next, we consider the case where V is no longer homogeneous of degree 0, and additional capacity is better than average capacity.14/ As mentioned earlier, capacity in this model is indirectly presented: it is not given by the volume of traffic, but is given by the saving in time-cost when capacity is increased. Hence, the additional capacity is represented by

-VN units of cost saved (recall that as w increases, users time-cost decreases and V, is negative). Given that there are w units of capacity and the total volume of traffic is N, the average volume of traffic per unit of capacity is N/w. The marginal impact on time-cost of an additional trip is **VN,** or, to put it differently, one less trip saves **VN** units of time-cost. Hence N/w less trips saves a total of **(N/w) VN** units of cost. Since adding an existing unit of capacity is equivalent to having N/w less traffic, the average capacity is given by the total cost saved: **(N/w) VN.**

35. In case (C), since additional capacity is better than existing capacity, we have: N. > **(N/w)'VN.** As before, relaxing the homogeneity assumption of V does not affect the minimization conditions (7) and (8) and the marginal external cost of the traffic, **MECN,** is still given by (10). However, in this case, as in the above two cases, the average road cost per trip exceeds the marginal external cost of a trip:

**ARC, = (r-'wK +** w M)/N **= E-MD/,*** - **w*V.r** by (7) **> E.MD/,** + N*VN **=** MECN. by (10).

Again, the cost recovery proposition is lost and the total revenue raised by **GI** and **Gd** will be IX than the road costs borne by the highway agency.

36. Case D is not really an assumption, but follows as a consequence of using - differential calculus. The analysis is all done in terms of a single km of road carrying a constant flow of traffic **-** which can be smoothly adjusted to traffic, i.e. the number of lanes can be smoothly **adjusted to** ensure that **the costs of congestion are** just **equal** to the costs of adding a marginal increment in road capacity. The one km section of road is then generalized IN **Mathematically, weassume that V is homogeneous of a negative degree. The current paragraph prsents the intuition to explaLn why this should be the case. By Euler's equation, if V(w,N)** is **homogeneous of 0 degree k < O, w-. + N-VN** = **k < O. Thisisthe first inequality in the next pargraph.**
17 and applied to the road network as a whole. This formulation cannot handle spatial and temporal variations in traffic, changes in travel demand and the obvious indivisibilities associated with expanding capacity. Since these factors are not assumptions, but follow from the nature of the mathematics, they cannot be relaxed. Furthermore, since indivisibilities are generally recognized to be a source of scale economies, they automatically cause deficits when prices are set equal to marginal costs.

# 4.2 The Case of Tunisia

37. The impact of the above assumptions are illustrated in Table 2. The table shows that actual expenditures on highways in Tunisia amounted to $91.62 million in 1982, including the shortfall of regular routine maintenance and financing charges. This does not, however, necessarily represent the economically efficient costs of delivering road services (i.e. these costs may be inflated by allocative inefficiencies on the input side). This will not be dealt with in the present paper, even though it is known that production inefficiencies can be important for pricing and cost recovery policies (Kranton, 1990). Instead, the paper will focus on the pricing of road services to optimize allocative efficiency on the demand side.

38. Table 2 shows several discrepancies between the costs incurred and the revenues generated by optimal pricing. The variable costs of resurfacing (item (iv), column 2), are less than half the costs actually incurred on road maintenance (item (v), column 1), even when the shortfall of routine maintenance (item (iii), column 1) is excluded. When capital and financing costs are included, the optimum pricing model only covers just over half the total costs. User charges set on the basis of the above optimal pricing model will therefore leave a large block of expenditures unfunded.
18 Table 2. Actual Costs and Those Covered<sup>by Optimal Pricing Model: Tunisia 1982</sup> (Dollar Million at 1982 Prices)

||_tens_|_AcAl_<br>_Costs_<br>_Incurred_<br>_(I)_|_RevsGenerated_<br>_by Opdmal_<br>_PricingModel_<br>/2)|
|---|---|---|---|
|Recur|rent Expenditures:|||
|(i)<br>|Administration<br>|2.44<br>||
|(ii)<br>|Routine Maintenance<br>|22.48||
|(iii)<br>|Shortfall of Routine<br>Maintenance (a)<br>|'.62||
|(iv)|Resurfacing:|||
||<br>fixed (b)<br>|5.17<br>||
||variable|20.68|20.68|
|(v)|Sub-Total|56.39|20.68|
|CaDit|al Exoenditures: (c)|||
|(vi)<br>|Extension/Improvement<br>|9.80<br>||
|(vii)<br>|Expansion of Capacity<br>|19.60||
|(viii)|Annualized Construction Cost (d)<br>|||
||non-urban roads<br>||13.68<br>|
||urban roads<br>||20.00|
|(ix)|Fixed Resurfacing Cost (e)|||
||non-urban roads<br>||0.20<br>|
||urban roads||0.30|
|Finan|cin2 Char2es:**(f)**|||
|(x)|Debt Service/Repayment|5.83|_|
||Sub-Total|35.23|34.18|
||Grand Total|91.62|54.86|
||Unfunded Road Expenditure|-|36.76|

Notes:

- (a) Since road conditions were generally deteriorating,<sup>it is estimated that allocations for</sup> routine maintenance were about 20 percent lower than needed<sup>to maintain the road network</sup> in a svaia iong-tenn condiiion.

- (b) The. reesent weather related resurfacing costs which<sup>are unrelated to traffic. They</sup> comprise about 20 percent of total resurfacing costs in<sup>"dry non-freeze" countries like</sup> Tunisia.

- (c) Assuming onethird of capital expenditures are new construction<sup>and the remainder are to</sup> expand capacity. Real capital expenditure between 1976<sup>and 1982 was fairly stable and</sup> fluctuated within about 20 percent of the mean expenditure<sup>for the period.</sup>

- (d) See Annex 1 for derivation of these figures.

- (e) The additional fixed resurfacing costs associated with<sup>expanding capacity. They are</sup> calculated as 1.5 percent of initial costs.

- (f) This it refers to World Bank loans only. It appears elsewhero in<sup>the government's</sup> accoun. i and is usually omitted from financial statements<sup>of road revenues and</sup> expendiLures.

Source. World Bank, 1987 (b); Newbery et al, Table<sup>21, 1988.</sup>
**19**

# **V. FINANCING REMAING EXPENDITURES**

39. Figures 2 and 3 showed that there are substantial economies of scale in road construction and in road use. Road maintenance costs also contain a number of important fixed costs. Furthermore, since roads cannot be smoothly adjusted to traffic, marginal costs for the entire road network will be significantly lower than average costs, unless capacity is artificially constrained by environmental or other constraints. User charges based on the above optimal pricing model will therefore result in substantial financial deficits. This was shown in the Tunisian example presented in Table 2. The question which then arises is, how should this deficit be financed? The only feasible options on a network basis are by raising revenues from users, raising additional general tax revenues, or by taxing beneficiaries. Taxing beneficiaries, i.e. imposing taxes on the property which benefits from provision of roads, are only suitable for roads which primarily provide access to property like residential streets and rural access roads. For other roads - those which primarily provide services to traffic - the alternatives are user charges or general tax revenues. This paper concentrates on these roads and does not examine - the option of taxing beneficiaries.lJ/ The other option cutting back expenditures on maintenance and investment to reduce the deficit - is not economically efficient, since it increases user costs more than it reduces road expenditures (Harral and Faiz, 1988).

40. The economic consequences of the above choices can be examined in termns of - Figure 4. In this figure, demand for travel is shown by D, while costs including VOCs and marginal external road costs - are shown by **ASC** and MSC. Under average cost pricing, the volume of travel is N at price P. Likewise, under marginal cost pricing, the volume of travel would be N' at price **P'.** The move from point A, where roads are priced at average costs, to point B, where they are priced at marginal costs, leads to a net increase in total surplus equal to the area of triangle **ABC.** However, the move from A to B also results in a deficit equal to the area of **EBP'F. The** welfare comparison is thus between the welfare gain, **ABC,** attributable to the move from average to marginal cost pricing, less the welfare costs of the taxation required to finance the **deficit.** Let m denote the costs of taxation (deadweight and administrative costs) expressed as a **constant percentage** of the tax revenues. Then it immediately follows that the **welfare costs of financing the required** deficit is just **mnEBP'F.** Provided the administrative **costs of mobilizing these tax revenues** are similar to those associated with road taxationj!, the benefits **of marginal cost** pricing will exceed **the** costs only if mnEBP'F **< ABC,** or m **< ABC/EBP'F.**

**II/ The alernave** of **fnancing** the deficits through domestic and/or intnational borrowing, merely defers payment, since the **loas still** need to be serviced and **repaid.**

- If/ **The administraive costa** should be similar, **since** many of the tax instruments - import duties, sales **and** excise taxes - **are** used to collect both road user taxes and **general** revenues.
20 41. Since the non-marginal costs (the difference between MSC and ASC) are fixed, the rectangle **EBP'F, EB.N',** is also equal to AC.N. The above inequality can thus be written as

**m < (1/2) AC*(N'-N)/(AC*N)**

or **m** < ( O2)(N'-N)/N or **m <** (1/2)AN/N where A denotes a finite charge: **AN** = (N'-N), **AP = (P-P').** Since the point elasticity e evaluated at point A is defined to be (AN/N)/(AP/P), it follows that: m < - (1/2)e AP/P The right-hand side of this inequality has been plotted in Figure 5 as a function of the proportional fall in price, **AP/P,** given the all-day price elasticities of demand for automobiles and buses, and the aggregate price elasticity of demand for trucks (from Annex 2).

<!-- Start of picture text --> D<br>4.)<br>A<br>o ~~~~~~~~~~~~~E<br>F ...-<br>tv B~1<br>83 I I MSC<br>l I<br>° N N'<br>Amount of travel<br><!-- End of picture text -->

**Figure 4:**

Effect of **Marginal** and **Averagc** Cost Pricing on **Total** Surplus
21 42. Figure _5_ can now be used to examine whether in Tunisia it is more economically efficient to mobilize the required revenues from road users, or by raising additional general tax <!-- Start of picture text --> 0.10<br>a .<br>iD 0 -1.3<br>03 0D<br>E<br>O 0.05 0<br>e = 0.9<br>e -0.7<br>to<br>e-0.1<br>0-<br>0 0.029 0.05 0.10<br>Proportional fail In price, A P/P = (P-P/PTP<br><!-- End of picture text --> Figure 5: Threshold Value of the Marginal Cost of Public Funds as a Function of the Proportional Fall in Price, Given Different Elasticities of Demand.

revenues. Recall that the unfunded road expenditures shown in Table 2 amount to about $37 million (costs of about $92 million, less revenues from optimal user charges of about _$55_ million). The marginal external costs of road use per veh km (for each class of vehicle) are set out in Table 3, column 15. If user charges are set equal to these marginal external costs, they will generate total revenues of about $55 million. Column 17 shows the size of the ad valorem mark-up over the marginal external costs of car use (optimal user charges, plus VOCs) needed to generate the required additional $37 million to cover the unfunded road expenditures shown in Table 2. It does so by charging average costs, i.e., by raising the marginal costs of car use (shown in column 16) by the amounts shown in column 17. The average mark-up comes to
t4 t4 T $. °eY_Id **Unr** Charges ad Ad Valoem _Mak-UP_ Nedd **t.** Cover Unfwided Road Expeadiluu: TmWa, I* (cIweb k- sd $ maUllk)

||Vehclie|_aa|eSsgh||||Us4cof|Road N|dtwok|||Optim|a Uscr asaig<br>_______<br>______|<br>(a veh km<br>______|)<br>______|Oplimd<br>Usci|Ad_Vs hM_<br>MaD ksp|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
||VOCs|IE|||Vh|I||||||||||||
|<br>|<br>cc_Nic<br>|cs<br>|||to|(am)<br>'km||PCE|m (mill)||ESA|Road<br>Damagc|Coegion|Coo||aCaug-<br>*VOCr|Ocr<br>C*a|
|Veb<br>Type|_(IAM)_<br>|I-U<br>|UAaa<br>|a"<br>|I-U<br>|Ua6m<br>|Tod<br>|l-U<br>|Usban<br>|TOal<br>|(mill)|Cao|I-U|Uslm|TOlW|_(cethkm)_|(evM b bo|
||(I)|(2)|(3)|(4)|(5)|(6)|(7)|**(8)**|(9)|(10)|(I1)|(12)|(13)|(14)|(ls)|(16)|**(**7)|
|Car aso)la<br>|8.79<br>|2.00<br>|R.0<br>|0.0001<br>|1404<br>|330<br>|2284<br>|1,404<br>|880<br>|2.264<br>|0.2|0.00|0.16|0.23|0.39|9.18|0.26|
|CarDbeci<br>|6.44<br>|1.00<br>|1.00<br>|0.0002<br>|464<br>|292<br>|755<br>|464<br>|291<br>|755<br>|0.2<br>|0.00|0.16|0.23|0.39|6.83|0.20|
|UWily Vedicl<br>|12.44<br>|1.00<br>|2.00<br>|o.o0<br>|1721<br>|851<br>|2572<br>|1.721<br>|851<br>|2.572|20.6<br>|0 o1|0.6|0.23|0.40|12.84|0.37|
|Li& TMs<br>|30.37<br>|1.50<br>|1.50<br>|0.092D<br>|442<br>|218<br>|659<br>|662<br>|32|989|60.6|0.09|0.25|0.34|0.63|31.05|o.89|
|Med_um Truck<br>|32.3<br>|1.70<br>|2.00<br>|0.5800<br>|161<br>|16<br>|177<br>|274<br>|32<br>|306|102.7|0.59|0.29|0.45|1.32|33.69|0.97|
|Hwy Sigb Truck<br>|39.23<br>|2.00<br>|2.50<br>|2.6M0<br>|204<br>|20<br>|224<br>|408<br>|50<br>|458<br>|582.4|2.65|0.33|0.56|3.55|42.68|1.23|
|Hvy Taad.Truck<br> <br>|39.13<br>|2.00<br>|3.00<br>|S.80o0<br>|12<br>|1<br>|13<br>|24<br>|3<br>|27<br>|69.9<br>|5.49|0.33|063|6.50|45.63|1.31|
|Alcule<br>Tmwk<br>|**7S.78**<br>|2.00<br>|3.00<br>|6.8000<br>|233<br>|7<br>|240<br>|266<br>|21|287|952.0|6.94|0.33|0.68|7.94|83.72|2.41|
|Ba<br>|62.38<br>|2.00<br>|3.00<br>|0.4900<br>|125<br>|63<br>|I8n<br>|250<br>|189<br>|439<br>|92.1<br>|0.50|0.33|068|2 5.|63.89|1.84|
|Special Vehiclk|62.38|1.50|1.50|0.4900|220|78|298|330|117|447|146.0|0.50|0.25|0.34|1.08|63.46|1.U3|
|_ToWed_|||||4885|2425|7310|5.802|2761|8,563|2026.6|||||||
|||||||||Total U|ser CostltR|evcnuea||2068|13.88|20.30|54.66||36.76|

Notes: Heavy sk-axe-xe the have v me VOC as bcavy adm-aie It:t a-s special vcices have he same VOCcsa buses. Source: (Ncwbesy. ct a*, 19U)
23 about 2.9 percent and the final user charge would then consist of column 15 plus column 17. When the percentage mark-up, 2.9 percent, is applied to Figure 5, it intersects the highest relevant elasticity curves at points A (truck), B (car) and **C** (bus) resulting in threshold values of m, representing the costs of mobilizing additional general tax revenues, of 1.3, 1.6, and 1.9 percent respectively. In other words, if the value of m is less than 1.9 percent it will be more economically efficient to raise the required revenues through general taxation; while if it is greater than 1.9 percent, it is better to do so by collecting the required revenues from road users. Even if the percentage mark-up increases to 10 percent, the value of m still has to be less than 6.5 percent before it is more economically efficient to raise the required revenues through general taxation.

# 43.

43. Recent work has shown, however, that the deadweight losses caused by general taxatic.n are high. Using a general equilibrium model, it has been shown that the welfare loss from a one percent increase in all existing (distortionary) tax rates in the USA is between 17 and 56 cents per dollar of extra revenues raised (Ballard et al, 1985). Other estimates for the USA (Browning, 1986), Canada and Sweden are similar, while in the UK a more limited partial equilibrium approach suggests that the economic costs of raising public revenues lie in the range 11 percent to 21 percent for local property and income taxes respectively (Dodgson and Topham, 1987). In developing countries like Tunisia, with narrow tax bases and weak tax administration, the costs of mobilizing additional tax revenues are likely to be even higher. This means that m is likely to be well above 2.9 percent in Tunisia and is also likely to be above this figure in other developing countries.

44. The above analysis has shown that, provided the administrative costs of road user taxes are similar to general revenue taxes, the welfare costs of marginal cost pricing plus general taxation are likely to be higher than the welfare costs of average cost pricing in most developing countries. It follows that a pricing system which uses optimal departures from marginal cost pricing to finance the deficit **EBP'F** (where some services may be priced below average costs and others above it) will be even more attractive in welfare terms. This leads to the overall conclusion that, **given** the generally high costs of general taxation, welfare will nearly always be greater if **the** financial deficits associated with marginal cost pricing are financed using optimal **mark-ups over** marginal costs.
24

# VI. **EFFICIENT COST** RECOVERY

45. The above analysis has established two important conclusions. First, if the user charges for an entire road network are based on short-run marginal costs (variable road maintenance costs, plus the costs of traffic congestion), they will nearly always generate insufficient revenues to cover total costs. This has been demonstrated for Tunisia - and will - generally hold for all road networks with low traffic densities unless road capacity is artificially constrained and congestion is allowed to increase well beyond the point where benefit/cost criteria would recommend expanding capacity to reduce congestion. Second, the high costs of mobilizing public revenues, suggests that the additional revenues needed to balance the road budget should be collected from road users, preferably by using an optimal mark-up over marginal costs. These conclusions also raise three further questions: (i) while it is generally accepted that marginal costs should be regarded as the floor below which user charges should never fall, is it necessary to stop at short-run marginal costs when a significant number of the remaining costs are avoidable, but not necessarily marginal? (ii) how does one calculate the optimal departures from marginal costs needed to finance the unfunded road expenditures? and (iii) is road congestion pervasive and is it feasible to charge for it.

## **6.1** Variable **and** Common **Costs**

46. All the costs in Table 2, column 1, other than the financing costs, are - at least - in principle avoidable. 17/ They are not all marginal, but can be avoided over a reasonable period of time. Indeed, there are three broad levels of avoidability, costs which: (i) are variable and are incurred on behalf of identifiable users (these are the variable costs of the road agency and include the luad damage costs from the optimum pricing model): (ii) can be avoided over a short period of time and are incurred as common costs on behalf of an identifiable group of users, but not of individual members of the group (e.g. heavy vehicles); and (iii) are avoidable, but are common to all users (they can only be avoided by closing the entire road network). In practice, road users cannot be excluded from using the road network. TIh.e concept of avoidability nevertheless provides a pragmatic way of attributing ex post expenditures to specific user groups. In the rest of this paper these three groups of costs will be referred to as variable costs, grouped common costs and collective common costs.

47. Table 4 has divided the costs set out in Table 2, column 1, into these three categories and shows that they comprise 29, 26 and _45_ percent respectively of total road expenditures in Tunisia. The first category, column 1, are caused by the passage of vehicles

**17!** The financing **costs** can only be avoided by defaulting, or rescheduling the loans.
25 over the road pavement (variable administrative and routine maintenance costs) and by the passage of heavy axles (variable resurfacing costs). Being marginal, such costs should clearly be recovered from users: uie former in terms of veh km (since there is no other straight-forward way of attributing them to users), the latter according to ESA km (to reflect the damage done to the road pavement by the passage of heavy axles).

**Table** 4. **Analysis** of **Costs in Tarn** of Thdr **Avoidability:** Tunisia, 1982 (a) **(Dollar,** milGlon)

|Item|Immediately<br>Avoidable<br>Costs<br>(Marginal)<br>(1)|Comm<br>_Grou_<br>Heavy<br>Vehicles<br>(2)|on_to Spec_<br>_ps of User_<br>Urban<br>Roads<br>(3)|_ufc_<br>_s_<br>Rural<br>Roads<br>(4)|Common<br>to all<br>Users<br>(Fixed)<br>_(5)_|Total<br>User<br>Costs<br>_(6)_|
|---|---|---|---|---|---|---|
|Administration (b)|0.49|-|-|-|1.95|2.44|
|Routine Maintenance (c)|5.62|2.81||-|19.68|28.11|
|Resurfacing (d)|20.68|-|-|-|5.17|_2S.85_|
|Extensions/lmprovements|(e)<br>-|4.42|_5.55_|11.10|8.33|29.40|
|Financing Charges (f|-|-|-|-|_5.83_|5.83|
|Total|26.79|7.23|_5.55_|11.10|40.96|91.63|
|Percent of Grand Total|29.20||26.10|-|44.70|100.0|

Notes: (a) lduding shortfal of regular road maintenance.

- (b) Fixed cost include ai expenditures on buDdings and 70 percent of salaries.

- (c) 70 percet of these costs are fimed and 10 percent are attributable to heavy vehicles.

- (d) In dry non-freeme conditions, 20 percent of resurfacing costs are attributable to **esfronmental** factors.

(e) Assuming one-third is new construction and the remainder is to expand capacity (of tbis, **one4lUr@** i in urban areas and two-thirds in rural areas) and that 15 percent of these **cost** are incurred to ensure **roads** are strong enougb to carry heavy vehicles. **(fM These** costs **can only** be avoided by defaulting, or cancelling the loans.
26 48. There are two possible ways of dealing with the second category of costs. The first is to simply treat them in the same way as collective common costs and charge them against all users. This has some attractions on grounds of simplicity and economic efficiency. The second way is to charge them against each group of common users. This is more equitable and may hence be more politically acceptable. Each of the grouped common costs can, at least in principle, be avoided by withdrawing service from that specific user group: either heavy vehicles, urban road users, or rural road users. To justify scoving them, each group should be willing to pay for the costs they incur: heavy vehicle; again in terms of ESA km and urban and rural road users in terms of passenger car equivalent (PCE) kilometers (which measures the road space they occupy).l8/ Finally, the collective common costs should be recovered from all users in a way which minimizes loss of consumer surplus.

# 6.2 Recovering Collective Coumnon Costs

49. The collective common costs shown in Table 4, column 5, are incurred on behalf of several groups of common users and the aim is to define a mark-up over base costs (VOCs and variable and grouped common costs) which: (i) generates sufficient revenues to cover all collective common costs; while (ii) minimizing the consequent loss of consumer surplus. This is similar to the classical tax problem in which the overall excess burden of the tax is minimized by equalizing the marginal excess burden of the last dollar of tax revenues raised from each commodity (Ramsey, 1927; Rosen, 1988). In the case of roads, this translates into minimizing the relative loss of consumer surplus per dollar of collective common costs covered by each user group. This is illustrated in Figure 6. In this figure D represents the compensated demand curve for one particular type of traffic. The curve **BC** refers to base costs and represents VOCs and the variable and grouped common costs set out in Table 4, columns (1) to (4). Without any mark-up, demand would be in equilibrium at point B, with output N at price P. The amount **T*P1,** the ad valorem mark-up over the base costs, represents the contribution (per veh km) which this type of traffic makes towards covering collective common costs. The deadweight loss per dollar of revenue raised through the increased user charge, S, is equal to the triangular deadweight loss area **ABC** divided by the contribution to collective common costs, **P"CAP'.** In other words: S **= 1/2*AC*(N-N')/AC'N' = 1/2-AN/N'** where **AN = (N-N').** 18/ PCEs **measure** the impact which vehicles have on **the** speed, **and** hen:e the cost, of other vehicles. They vary by type of road. **terrain and** condition of traffic.
27 <!-- Start of picture text --> P--Markup to cover coilectrve<br>Base costs. BC<br>0 N' N<br>Amount of Uravel by one class of traffic<br>FE 6: Loss of Consumer Surplus Associated with Covering Collective Conmmon Costs<br><!-- End of picture text --> _50._ The own-price elasticity of demand at point A, e, is equal to (AN/N')-(P'/hP) and the elasticity of supply at point A is equal to **(AN/N') (P'/AP'),** where **AN** = (N-N'), **AP** = **(P'-P)** and **AP'** = **(P"-P).** Provided the cross-pnicp elasticities of demarnd eee n the different user groups are relatively small, they can be ignored.19/ Likewise, since the proportion of the budget allocated for spending on roads is small, the uncompensated demand elasticitites (Annex 2) can be taken as a reasonable approximation of the compensated demand elasticities. The price elasticities of demand and supply, and the ad valorem mark-up, can then be used **to** calculate **the deadweight** loss, **S,** as follows:

# **_li/e_ =** N'AP/ANP', ; 1/s = N'AP'/ANP" **1/g =** **_li/e_ - l/s** = N'/AN **(APP -AP' P')/(P'P")**

19/ They are effectively zero for passenger versu freight trnsipost, au low for public transport versus car (Baum and Kcntner, p. 19, 1980) and even lower for car versus public transport. They are more significant when there are competing public transport modes (e.g., mini-bus versus bus). In such **cases** the price elasticity needs to be adjusted by subtracting the relevant cross-price elasticity (Taplin and Waters, 1985).
**28**

Substituting for **AP** and AP' and simplifying:

**1/g** = **(N'/AP)-P(P'-P")/(P'P")** or **1/g** = **(N'/AN) P'TP'/P' P"** = **(N'/AN)'TP/P`** or AN/N' = **g-TP/P"** where T, the ad valorem mark-up = **(P'-P")/P'.**

Substituting this in the expression for the area S gives:

> S = **-1/2 g TP/P"**

51. Since there are several types of traffic, the overall loss of welfare is minimized by equalizing S across all user groups: S = **g,T1 P1 /P 2"** = **g2 T2P2/P 2"** .*X = **g.T,P./Pn"** This is the so-called inverse elasticity rule (the term g being the inverse elasticity). The process of equalizing S across the different user groups is illustrated in Figure 7. With a constant elasticity demand curve, the lines representing car, bus and truck are straight lines; otherwise they are curves.

_52._ The revenue generated by the above mark-ups is calculated by multiplying each mark-up by the appropriate values of P' and N', corresponding to that particular type of traffic. In other words:

# Revenue = **T,P',N', + T2P'2N'2** + ... + **TnP'3N'.n**

The appropriate value of S needed to generate the revenues required to cover common costs, can either be solved by trial-and-error, or by plotting a graph of total revenue as a function of S and taking the point where it intersects the horizontal total cost line.
29 <!-- Start of picture text --> Bus<br>Car<br>Trtik<br>A 3 C<br>0)<br>_° IV I I<br>Tul (P)/P<br><!-- End of picture text --> Figwre 7: Using the lnverse Elasticity Rule to Compute the Mark-ups Needed to Cover Collective Common Costs
30

# 6.3 Is it Feasible to Charee for Congestion?

# 53.

53. The optimum pricing model charges road users for the external congestion costs they impose on other road users. It is worth noting that the avoidable cost methodology outlined in previous sections also charges road users for some of the congestion they incur. Expenditures on expanding capacity (Table 2, column 1, item (vii)), which amounted to an estimated $19.60 million in 1982, are charged to road users as an avoidable cost on the basis of the road space they occupy (measured in terms of PCE km). These congestion charges are nevertheless too low (i.e., the costs currently charged to them, $19.60 million, are less than the $34.18 million [the sum of items (viii) and (ix) in Table 2, column 2] implied by the optimum pricing model). Furthermore, since motorists are only aware of the private costs they incur when making a journey, it would be more economically efficient to levy an explicit congestion charge to ensure they consciously paid for the entire social costs their journey imposed on others. It is also essential, on both distributional and economic efficiency grounds, to charge congestion against the specific road users who cause it, rather than to average it over the entire road network and over all users. This is particularly relevant with regard to the distinction between urban and rural road users. Most road congestion occurs in urban areas and averaged congestion charges will generally charge urban road users far too little and rural road users far too much.20/ Finally, when there are physical and/or environmental constraints which prevent road capacity being expanded -- even though such expansion may be economically - justified it will usually be desirable to use an explicit charging mechanism to help ration scarce road space.

# 54.

54. However, although there is a strong case for introducing explicit congestion charges, the literature makes little attempt to identify: (i) the causes of road congestion (and hence tne efficacy of road pricing); (ii) the extent of congestion (i.e., is it pervasive, or only confined to selected cities in some countries); and (iii) whether it is feasible and cost-effective to charge for congestion (see for example, Churchill, 1972; Newbery, et al, 1985; Walters, 1968). Low speeds in urban areas are only partly attributable to the presence of other vehicles. In most cities in developing countries, vehicle speeds are significantly influenced by the wlsfl;guraduon1 and state of the road network, the preseice f olii u-afi&ic **.i** wdestriials, liandcarts, head-loading, cycles, three-wheelers, etc.), parked vehicles and encroaching road-side activities. Under these circumstances, road pricing wili have less effect on vehicle speeds than,

**_2QI_** In **Tunisia,** congeaion costs **were aveaged** over **the enie road network** and **then added** to **the d** user **charge. Thi resulted** in **urban peak-period** car **uwe** paying **l1s** than one-eighth of **tde congcsion cost** they imposed on other motorists, while **rural car** users (cecounting for over 60 **percent** of **car ve kmn),** paid neely ten times thewe **cost (Newbery,** et **aI,** 1988, Tables 3 **nd 7). It** is not **inmWively** obvious **that such gross** avenging, even wben appropritely weighted (Heady, 1989, Appendix **Model** 4), **improves economic** efficiency.
31 say, implementing a broad package of measures including traffic management, minor road improvements and traffic restraint.

_55._ _55._ It is likewise doubtful whether road congestion - in the sense of vehicles - interfering with other vehicles -s a universal phenomenon. Work currently underway at the World Bank has identified two main types of city. The first are those where road congestion could be virtually eliminated by introducing simple traffic management measures (improved maintenance, road-signing and enforced traffic regulations) and minor road improvements (junction improvements, stopping and parking bays and relief roads). In other words, the congestion in these cities is mainly self-inflicted and attributable to the poor performance of the road agency. Most cities in developing countries fall into this category. In these cities, combined traffic management and minor road improvements are the most cost-effective ways of dealing with road congestion. Second, there are a limited number of cities in the Bank's main borrowing countries where road congestion is so serious that traffic management and minor road improvements need to be supplemented by explicit measures of traffic restraint. In general terms, there are only two cities in Africa which currently fall into this category (Lagos and, to a more limited extent, Nairobi), five in Asia (Bangkok, Bombay, Jakarta, Manila and Seoul), six in Latin America (Buenos Aires, Bogota, Mexico City, Rio de Janeiro, Sao Paulo, and Santiago) and five in the World Bank's Europe, Middle East and North African region (Algiers, Budapest, Cairo, Istambul, and Tunis). Serious congestion, requiring explicit traffic restraint measures, is therefore limited to a relatively small number of developing countries.

_56._ Charging for road congestion in developing countries is also quite difficult. There are clearly socio-political difficulties. This explains why Singapore (World Bank, 1986, Box 1) is the only city with a scheme in operation, although Hong Kong has experimented with one and Stockholm in Sweden is in the final stages of planning to introduce one in 1991 (designed to reduce both congestion and pollution). There are also implementation difficulties related to the characteristics of the road network. It is fairly easy to devise ways of charging vehicles travelling to and from the city centers in Bombay and Lagos (in both cases, vehicles must use one of three arterial corridors for part of their journey). On the other hand, it is considerably more difficult to devise ways of doing so in cities like Jakarta, Manila and Bangkok which are more spread out and experience local congestion in several locations.

# 57.

57. Finally, congestion charging is relatively expensive and can be difficult to administer. The simplest method is to establish a cordon and to charge vehicles as they cross it. T'his could be done in cities like Bombay and Lagos where the layout of the city lends itself to such treatment. A cordon, or toll ring, is nevertheless relatively expensive. The cost of implementing the proposed toll ring in Oslo is estimated at $40 million, with annual operating and maintenance costs of $17 million. The area licencing scheme in Singapore is much simpler and less expensive. Vehicles must display a license in the restricted zone (there is no need for toll booths), but this makes it more difficult to administer. Even in a well-disciplined society **liMe** Singapore the cost of administering and enforcing the Singapore scheme are nearly $1.6
32

**million** per year. This represents a substantial investment at the city level in a developing country.

# 58.

58. The other alternative, electronic road pricing (ERP), is relatively easy to administer, but is also expensive to install and difficult to maintain. Initial installation costs for an electronic number plate system in Hong Kong were estimated as $31 million for 210,000 vehicles with an annual operating cost of $2.6 million. In Cambridge, U.K., where a smart-card system has been proposed, the estimated costs of installation are roughly $50 million for 250,000 vehicles with an annual operating cost of $10 million to cover enforcement, servicing of equipment and installation of metering devices on annual additions to the vehicle fleet. Maintenance in developing countries is also a problem and, since the electronic number plate system debits the car owner's bank account, the rudimentary nature of personal banking in developing countries poses further difficulties.

59. An added complication is that congestion charges can also weaken financial discipline. The amount of congestion is a function of both road traffic and the physical configuration of the road network and the way it is managed. It follows that there are a variety - of potential interventions the improved traffic management and minor road improvemesits - referred to in para. 55 which can go some distance towards lowering congestion costs. Conversely, there are a number of current interventions which, if not actively administered (e.g., repair of traffic lights, enforcing traffic regulations, controlling road-side land use, etc.), will result in more congestion than necessary. The amount of congestion is not determined exogenously; it is partly determined by the performance of the road agency. It follows that, if - the revenue from congestion charges accrues to the road agency, it will have little incentive - other than possible public indignation to actively intervene to reduce congestion. Congestion charges should therefore be administered as a pure tax and collected by the government (which also has little incentive to intervene, since intervention would reduce government tax revenues).

60. The overall conclusions are therefore that: (i) serious road congestion, warranting explicit interventions to restrain traffic in the interests of economic efficiency, is fairly limited in developing countries; (ii) where there is serious congestion, it makes sense to introduce congestion charges to ration scarce road space; (iii) methods of charging for congestion are limited; and (iv) **tde** charging instrument selected will depend on the nature of the city and its road network, the administrative complexity of the charging method, its maintenance requirements and its affordability. Simple cordon pricing schemes are likely to be the preferred solution in cities like Bombay 4nd Lagos, while electronic methods would be relatively more appropriate in cities like Bangkok, Mexico City and Seoul. Furthermore, to the extent that congestion caused by motor vehicles is limited in developing countries vis-'a-vis the developed world, congestion charges will make little contribution to the fixed costs of the road network in most countries and only a **small** contribution in those countries expcriencing serious road congestion.
33

# **VII.** APPLYING THE PRICING MODEL

61. The above avoidable cost methodology, together with the inverse elasticity rule, can now be used to calculate a set of road user charges for Tunisia. The price elasticities have been taken from Annex 2 and are equal to -0.6, -0.7 and _-0._ for car, bus and truck respectively (the figure for truck being the mid-point between -0.9, representing strong integ-modal competition, and -0.1, representing no inter-modal competition). The supply elasticities have been estimated from the slope of BC in Figure 6; the values for car, bus and truck are 46.61, 34.82 and 13.21 respectively. In other words, BC is fairly elastic. The calculations are set out in Table _5_ which shows, in column 21, the resulting user charges and, in column 22, the revenues which would result from levying such charges.2I/ The total revenues generated by the user charges, $91 million (which appear in Table _5_ as $91.8 million due to rounding), correspond to the total expenditures set out in Table 2. The user charges vary from 0.52 cents per veh km for cars (gasoline) to 2.71 cents per veh km for buses and 12.70 cents per veh km for articulated trucks.

62. Table 6 compares the results frcm the avoidable cost methodology with the existing user charges in Tunisia (shown in column 7). It does not include the user charges recommended by Newbery, et al (1988), since the over-estimation of congestion costs would have caused these charges to generate $285.0 million, tather than the more modest figure of $54.86 given in Table 2, column (2). Table 6 includes three comparisons. The first set of user charges (column 1) correspond to the ones derived in Table _5_ and are designed to cover all avoidable costs by generating total revenues of $91.6 million. The next two sets were designed to generate $385.7 million, these being the revenues generated by current user charges.22/ The first of these sets, column 3, has been calculated or, the same basis as those set out in column 1. In other words, the difference between the $91.6 million generated by the user charges set out in column (1) and the $385.7 million generated by those set out in column (7), has been treated as a collective common cost and recovered from all users using the inverse elasticity rule. The second set, column (5), has treated the difference between the $91.6 million and the $386.7 million as a pure tax and, following the procedure adopted by Newbery, et al (1988), has recovered these additional collective common costs from passenger vehicles only (the user charges for vehicle types 3 to 6 and 8 have been kept the same as in column (1)).

- 2j/ Table S **ha been laid** out **as** X Lotus spread-sheet. **The inverse** elasticity rule is applied by choosing a _coll_ well away from the table, say AS35, to represent S. This cell is then set equal to the initial guessed value of S. The ceUs in column 19 are sat equal to (AS3S/g), with 8 representing the appropriate price and supply elasticities for that type of traffic. Column 20 is then **set** equal to (col. 19 col. 18). The value of AS3S is then altered iteratively until the total of column 22 equals the total revenues required.

- _fI_ The govemrnment in Tunisia collected about S200 million in road **user** charges during 1982 (World Ba.k and Intenational Road Federation statistics). **The** higher **figures** of $285 miUion and $386 milion given in **Newbery** et al (1988), **sugget** (i) **the** VOC **model** used in Tunisia **contains** some **bias;** end/or (ii) there were **imporant** exemptions (e.g. of diplomatic **and** government **vehicles);** and/or (iii) the collection of road user charges was subject to significant levels of avoidance, evasion and **lealage.**
TaM. S. Calcm,atim or ltr Cdxe c Us-, Avoidable Cod Priatipk ma t lvcrsc Elicity Rauk: Taia. 192 _(ctvh im ad_ S Mibi)

||VdMe|is charal|gka|||Uqe of|Road Mc|twark||||||Avokiab|le ad Ci|mm<br>Co|de (ct*rA|km)||||TOWl|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|||FIM|||Vb_k_|mii|P|CE|ill|||||||||||||us"t<br>|
||VOCa||||e|()||m|u(m)|||Vadabkl|Cod|omqc|Cmo.||S-Tow||camisa_Co_|_dn_|GRAND|_Omc_|
||.||||||||||BSA<br>||||||||||TOTAL|Ruc|
|Vhice T|k|U|Uh||||||||km<br>|Al<br>|Hq<br>|Hvy<br>|||U<br>|c<br>*<br>|_u_<br>8||||
|ype|(cm)<br>|-<br>|a<br>|MSA<br>|1-U<br>|Utts<br>|Tdal<br>|I-U<br>|Uiba<br>|T4a<br>|(mill)<br>|vbts<br>|vebs<br>|vdaa<br>|I-U<br>|U|Cage|VOCa|(S)<br>(|Ct||_S_<br>)|
||(I)|(|(3)|(4)|(s)|(6)|_(7)_|(8)|(9)|(10)|(t1)|(12)|(13)|(14)|(15)|(16)|(17)|(18)|(19)|(|(21)|(2|
|Cu choIic<br>CDid|8.79<br>|1.0O<br>|1.00<br>|0.0001<br>|1404<br>|_8o_<br>|2284<br>|1404<br>|880<br>|2284<br>|0.2<br>|0.08<br>|0.00<br>|0.00<br>|0(17|0.13|0.28|9.07|0.03|0 24|0.52|<br>11.8|
|arce<br>Ulilit|6.44<br>12 44|1.00<br>|1.00<br>|0.0001<br>|464<br>|291<br>|75s<br>|464<br>|291<br>|755<br>|0.1<br>|0.08<br>|O.O<br>|0.00<br>|0.07<br>|0.13|0.28|6.72|0.03|0.18|046|3.4|
|y<br>LI1Tk|<br>|1.00<br>|1.00<br>|0.000D<br>|1721<br>|851<br>|2572<br>|1721<br>|851<br>|2572<br>|20.6<br>|0.08<br>|0.01<br>|0.00<br>|0.07|0.13|0.29|12.73|0.03|0.39|0.68|17.5|
|ane<br>MYdmTnack|30.37<br> <br>3237|L.so<br>27|1.50<br>|0.09m0<br>|441<br>|218<br>|659<br>|662<br>|327<br>|989<br>|60.6<br>|0.08<br>|0.09<br>|0.03<br>|0.10<br>|0.19<br>|0.53|30.85|003|0.95|1.45|9.6|
|<br>HB SY k Tk|<br>.<br>|.0<br>|2.00<br>|0 50o<br>|161<br>|16<br>|177<br>|274<br>|32<br>|306<br>|102.7<br>|0.08<br>|0.59|0 21|0.11|0.26|1.26|33.63|0.03|1.03|<br>2.30|4.1|
|y nx<br>H T<br>|39.13<br>|2.00<br>|2.50<br>|2.6000<br>|204<br>|20<br>|224<br>|408<br>|50<br>|4sS<br>|582.4<br>|0.08<br>|2.66|0.96|0.13|0.32|4.16|43.29|0.03|1.33|<br>5.49|12.3|
|vy ant<br>Tck<br>AtlTk|39.13<br>5|2.00<br>|3.00<br>|5.380<br>|12<br>|1<br>|13<br>|24<br>|3<br>|27<br>|69.9<br>|0.08<br>|s.so<br>|1.99|0.13|0.39|8.09|47.22|0.03|1.45|9.54|1.2|
|zcnae<br>|7.78<br>6238|2.00<br>|3.00<br>|6.eoo<br>|133<br>|7<br>|140<br>|266<br>|21<br>|287<br>|952.0<br>|0.08<br>|6.95<br>|2.52<br>|0.13<br>|0.39|10.07|S5.85|0.03|2.64|12.70|17.8|
|as<br>SlW<br>Vlk|.<br>|2.00<br>|3.00<br>|0.49ML<br>|125<br>|63<br>|188<br>|250<br>|189<br>|439<br>|92.1<br>|0.08<br>|0.50<br>|0.18|0.33|0.39|1.29|63.67|0.02|1.42|<br>271|5.1|
|peca<br>ce|62.38|1.50|1.50|0.490D|220|7S|29|330|117|447|146.0|0.08|0.50|0.38|0.30|0.19|1.06|63.44|0.03|1.95|<br>3.01|90|
|_Thata_|||||4US|242s|7310|s8D2|2761|8563|3026.6|||||||TOWl te<br>U|r|40.2||91.8|

Nol= Hay doc'axle SwA km 11 sa w_ VOCt - beavy AM-alde _tIucka,_ an l VAts have s m VOC " htes. Soww Qc ,ty. cda 1988)
35 3Then Jstiflcation for the latter procedure is that freight transport, being an intermediate good, should not be subjected to any form of pure taxation (Newbery, et al, 1988, pp. 37-38).23/ It is not clear these principles are applicable in a developing country like Tunisia. Quite apart from the theoretical conditions which underlie the proposition - there are - constant retums to scale and perfect competition the principle is only applicable in countries with well-developed tax systems (ideally those operating a value added tax system) with broad tax bases and where most final sales bear tax (Myles, 1989). In countries like Tunisia, with narrow tax bases and weak tax administration, it is often not possible to tax all final goods and services. There is then a strong argument for levying positive taxes on intermediate goods and services as a means of taxing final sales indirectly.

Table **6.** User Charges Calculated Using Avoidable Costs Compared with Those Used in Tunisia (Cents/veh Ion and **_$,_** million)

|||||Higher R|evenLies||||
|---|---|---|---|---|---|---|---|---|
||From Table S||Mark-up A<br>All Veh|pplied to<br>icles|No Pure Ta<br>Freight V|xation of<br>ehicles|Current C|harges|
|Vehicle Type|User<br>Chargc<br>(c/veh km)<br>(1)|TotAl<br>Revenue<br>(S,mill)<br>(2)|User<br>Charge<br>(c/veh km)<br>(3)|Total<br>Revenue<br>($,mnill)<br>(4)|User<br>Charge<br>(c'veh_km)_<br>_(5)_|Total<br>Revenue<br>(S,mill)<br>_(6)_|Uier<br>Charge<br>(c/veh km)<br>7)|Total<br>Revenue<br>(S,mill)<br>(8)|
|I Gasoline|0.52|11.8|2.25|51.4|7.91|180.8|10.59|241.9|
|1 Diesel|0.46|3.4|1.74|13.1|5.94|44.8|5.26|39.7|
|2 Utility|0.68|17.5|3.54|91.0|0.68|17.5|0.59|15.2|
|3LightT|1.45|9.5|8.38|55.2|145|Q c|!.77|!!.7|
|4 Medium T|2.30|4.1|9.84|17.4|2.30|4.1|2.28|4.0|
|5a Hvy Sgle T|5.49|12.3|15.20|34.0|5.49|12.3|2.91|6.5|
|5b Hvy Tandem|9.54|1.2|20.13|2.6|9.54|1.2|3.02|0.4|
|6 Antic|12.70|17.8|31.96|44.7|12 10|17 8|7.50|10.5|
|7**Bus**|**2.71**|5.1|13.18|24R|**47**T)|**RR**|**I**<br>**_JG_**||
|8 Special|3.01|8.9|17.24|51.4|3.01|8.9|1148|34.2|
|**Total Revenue (a)**||**91.6**||385.7||385.7||385.7|

64. The relevant comparisons in Table 6 are therefore between columns 3 (all vehicles charged according to the same avoidable cost methodology) and 5 (no pure taxation of freight

> _oT%_ **Newbery, eta** , **sa the chargcs** on trucks equal to marginal costs. In **other words,** trucks made no contribution either to **fixed** costs, or to pure taxaion. **This** may be valid in an economy where all sectors charge marginal costs, but is not valid in Tunisia where the railways (which mainly carry freight) have to recover all their costs from users.
36 vehicles) on the one hand and column 7 on the other (the current user charges used in Tunisia). There are significant differences between columns 3 and 7, but less difference between columns _5_ and 1. When the mark-ups are applied to all vehicles they result in lower charges for cars, higher charges for trucks and roughly the same charge for buses. Without pure taxation of freight vehicles, the charges for most vehicles are roughly the same. They are, nevertheless, much higher for buses, lower for gasoline cards and higher for heavy trucks.
37

# **VIM. OTHR ISSUES** AND CONCLUSIONS

## 65.

65. There are, as mentioned in the introduction, several other issues relevant to charging for roads which have not been dealt with in the present paper. It has not dealt with distributional issues (i.e. the way user charges affect income distribution and what to do about it), fiscal considerations (i.e., what contribution the road sector should make to the govemment's overall fiscal revenues), or with the question of which charging instruments to use and how to charge for accidents, noise, air pollution and other externalities. It has also ignored, other than in relation to congestion charges, the important relationship between the choice of pricing strategy and the impact this has on management incentives and hence on the costs of supplying road services. These are all important issues which, though not covered in the present paper, need to be addressed when designing road user charges.

## 66.

66. The above analysis has, however, pointed to several important conclusions for policies on charging for roads.

- (i) It is unrealistic to assume, for the road network as a whole, that there are constant returns to scale in road construction and in road use. Road maintenance costs also contain a number of fixed costs which do not vary with traffic (up to half the annual expenditures and road maintenance are usually fixed).

- (ii) Roads cannot be smoothly adjusted to traffic, so that marginal costs for the entire road network are significantly lower than average costs in most developing countries. Congestion charges will therefore generate insufficient revenues to cover all fixed costs. Congestion in a few large cities is nevertheless sufficiently serious to warrant congestion charges. While this ma) help to recover the fixed costs of congested urban roads, the revenues are unlikely to cover the fixed costs of the road netwo.k as a whole.

- (iii) Under the above conditions, optimal road user charges will generate insufficient revenues to cover the capital costs of the road network and total expenditures on road maintenance.

- (iv) Since it is not economically efficient to bridge the financing gap by cutting back on maintenance, it has to be bridged by collecting the required revenues by taxing beneficiaries, raising user charges, or by mobilizing additional general tax revenues. Taxes on beneficiaries were not examined in the present paper, but are usually the preferred method of charging for residential streets and rural access roads. For roads carrying significant volumes of traffic, the choice is generally between user charges and general tax revenues. The costs of mobilizing additional general tax revenues are, however, high and, given the generally low
38 price elasticity of demand for roads, it is nearly always more economically efficient to collect the required revenues from road users.

- (v) While it is generally agreed that marginal costs, corresponding to variable costs, should be the floor below which user charges should never fall, there is no reason to stop at marginal costs. An important group of costs are avoidable, attributable to individual groups of users (though not to the individual users themselves) and it seems reasonable - on grounds of simplicity, equity and political -

- expediency to charge these costs against each individual user group. The remaining costs, although also avoidable, are common to all users and, to minimize loss of consumer surplus, should be charged to them using the inverse elasticity rule.

- (vi) There are significant differences between the user charges calculated using the avoidable cost methodology and current user charges in Tunisia.