Volume 31, Issue 2. Fuel taxes and tolls in cost-benefit analysis

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1 Volume 31, Issue Fuel taxes and tolls n cost-beneft analyss Pedro Godnho Faculty of Economcs of the Unversty of Combra and GEMF Joana Das Faculty of Economcs of the Unversty of Combra and INESC Combra Abstract When a proect ether generates or suppresses traffc, fuel taxes and tolls should be consdered n the cost-beneft analyss. In ths paper we present a smple partal equlbrum model showng that under lnear demand, f factor costs are the unt of account and transfer payments are netted out at the outset, then the usual rule of the half works correctly for the ncorporaton of tolls n the calculus of socal costs and benefts, but the ncorporaton of fuel taxes and other ndrect taxes may requre a correctve term. Ctaton: Pedro Godnho and Joana Das, (011) ''Fuel taxes and tolls n cost-beneft analyss'', Economcs Bulletn, Vol. 31 no. pp Submtted: Mar Publshed: May 1, 011.

2 Economcs Bulletn, 011, Vol. 31 no. pp Introducton When a fxed-trp matrx s used n the traffc forecast of a road nfrastructure proect 1, both tolls and fuel taxes may be treated as socal transfers, and therefore gnored n a cost-beneft analyss presented as a calculus of socal costs and benefts. However, t s now wdely recognzed that the traffc generated or suppressed by an nfrastructure may have a sgnfcant mpact on the results of the nvestment apprasal (Wllams and Moore, 1990; Macke, 1996), and varable trp matrxes are beng more wdely used n the analyses. In such cases, the fuel taxes and tolls pad by the generated traffc do not cancel out as economc transfers, and must therefore be explctly consdered. Recent European Unon (EU) documents and EU sponsored proects emphasze the use of factor costs as the unt of account n cost-beneft analyss (Bckel et al., 006, EC, 008). Several analyses of road nfrastructure proects and hgh speed ral have been produced, based on the factor costs recommended by the Heatco proect, and presented as a calculus of socal costs and benefts, that s, nettng out transfer payments at the outset. That s the case of the recent cost-beneft analyses of Portuguese road nfrastructures (avalable n Portuguese at and hgh-speed ral proect nfrastructures (avalable n Portuguese at We wll present a smple model addressng the ncorporaton of ndrect taxes and tolls n such a framework.. The model Sugden (1998) analyses the treatment of ndrect taxaton n cost-beneft analyss of transport proects, focusng on the COBA method (see, e.g., DfT, 001). Ths method assumes a fxed-trp matrx, and does not ncorporate envronmental mpacts. Snce we are followng the Heatco and EU recommendatons, our analyss s dfferent. We consder a road nfrastructure proect (buldng a new road, or mprovng an exstng one), and we assume there s no savng (as n the model for the ndrect tax correcton factor presented by Sugden, 1998). We use the subscrpt 0 for the Do-mnmum scenaro and 1 for the Do-somethng scenaro and we defne t as the economy-wde rate of ndrect tax on fnal consumpton. We wll consder a non-work trp (the analyss of a work trp would be very smlar). Let us assume for now that the trp wll be made whether or not the proect s undertaken that s, the trp s ncluded n the base traffc. We defne: P : traded resources used n the trp that are pad by the user and perceved as costs of the trp (e.g, fuel) 3, measured at factor prces, = 0,1. U : traded resources used n the trp that are pad by the user but not perceved as costs of the trp (possbly tyres, vehcle deprecaton), measured at factor prces, = 0,1. 1 Ths s the case of the COBA method, used by the Department for Transport of the Unted Kngdom (DfT, 001). For the dfference between a calculus of socal costs and benefts and a calculus of wllngness-to-pay see, e.g., Sugden (1999). 3 Some authors (e.g, Ltman, 009) refer to the costs of traded resources as market costs, and to the costs of non-traded resources as non-market costs. Snce we are usng the concept of market prces to denote the prces ncludng ndrect taxes, the use of such termnology mght be confusng

3 Economcs Bulletn, 011, Vol. 31 no. pp N : non-traded resources used n the trp (e.g, tme), measured at factor prces, =0,1. TP : tolls and ndrect taxes over perceved costs pad by the user, = 0,1. TU : ndrect taxes over unperceved costs pad by the user, = 0,1. E : external cost of the trp (e.g, envronmental cost), measured at factor prces, = 0,1. Snce we explctly consder external costs (ncludng envronmental costs, n lne wth Bckel et al., 006 and EC, 008), we wll not dsregard any specal taxes as beng used to offset such external costs. We are assumng that there s no savng, so we know that n order to make the trp the user wll forfet consumpton of other resources wth a value F calculated as: F P U TP TU 1 t, 0,1 (1) General consumpton s taxed at the ndrect tax rate t, so we must dvde the monetary cost of the trp by a factor that reflects ths tax, n order to measure forfet consumpton at factor prces. Snce the user only perceves part of the costs as effectve costs of the trp, the forfet consumpton that s perceved by the user wll be: FP P TP, 0,1 1 t () We defne V as the gross value of the trp: the value obtaned by the user by makng the trp, gross of all the costs, and measured at factor prces. We assume that V s the same whether the proect s undertaken or not. Snce we are consderng the case n whch the trp s made whether or not the proect s undertaken, the value derved from makng the trp must be larger than the perceved cost. So, the net perceved user beneft from makng the trp, denoted by B and measured at factor prces, wll be non-negatve n both scenaros: 0, 0,1 B V N FP (3) Notce that, snce we consder a non-work trp, the true cost of tangble resources wll be the value of the consumpton forfet by the user n order to obtan them. The net socal mpact of the trp, S, wll be gven by: U TU S B 1 F P U E t, 0,1 (4) The frst term of S s the true net user beneft (perceved net beneft mnus unperceved costs), the second s the effect of the trp on the avalable resources and the thrd s the external cost. Pluggng (1)-(3) nto (4) we get: S V N P U E, 0,1 (5) The changes n the socal mpact of the trp due to the proect wll be: 1374

4 Economcs Bulletn, 011, Vol. 31 no. pp S S N N P P U U E E (6) As expected, ndrect taxes (lke fuel taxes) and tolls do not enter (6), snce they cancel out as transfers. In fact, asde from presentatonal dfferences, ths s a standard result. Now let us assume that the trp s generated by the proect t wll only be made f the proect s undertaken (the analyss of a suppressed trp would be smlar). Snce the trp s made n the Do-somethng but not n the Do-mnmum scenaro, t must be the case that the perceved user beneft s non-negatve n the former scenaro and non-postve n the latter one: B 0 B N FP V N FP (7) If demand s lnear on the perceved cost, V wll be unformly dstrbuted on [ N FP, N FP ]. So, for a generated trp, the expected gross value wll be: N1 FP1 N0 FP0 EV (8) By (3) and (8), the expected value of the net perceved user beneft n the Do-somethng scenaro s: N FP N FP E B 1 (9) Pluggng (9) nto the expected value of (4), we get: N FP N FP U TU E S F P U E 1 t (10) Usng (1)-() n (10), and takng nto account that the trp s made only n scenaro 1 E S ), we get the followng socal mpact of the proect: (meanng that 0 0 TP0 P0 t TP1 P1 t t N0 N1 P0 P1 E S1 E S0 U1 E1 1 (11) The frst two terms of (11) show that the rule of the half should be used for apprasng the mpacts of the proect on the perceved user costs before ndrect taxes and tolls. The thrd and fourth terms show that unperceved and external costs should be subtracted from the socal surplus. We note that the prescrbed treatment of the unperceved costs of generated traffc s not clear n most cost-beneft gudes t s nterestng to fnd out that unperceved costs affect not only the traffc forecast but also the subsequent apprasal, snce they have a dfferent mpact from the perceved costs. So, t s very mportant to know whch user costs should be assumed to be

5 Economcs Bulletn, 011, Vol. 31 no. pp perceved n the traffc forecast, n order to produce an apprasal that s consstent wth the forecast assumptons. What nterests us most s the ffth term of (11). Ths term represents the average excess of tolls and ndrect taxes on perceved costs over the general ndrect tax rate, for the Do-somethng and Do-mnmum scenaros, dscounted by a factor 1+t. Lookng at (6), we notce that there was no correspondng term n the socal surplus of the base traffc. The reason s that taxes and tolls are, n fact, economc transfers that enter expresson (11) only because of what they allow us to nfer about the value of the trp for the new users of the nfrastructure. We wll further examne the meanng of ths term n the next secton. 3. Partcular cases Accordng to (11), the net mpact of ndrect taxes and tolls on generated trps s gven by: TP0 P0 t TP1 P1 t 1t (1) Under multple ndrect taxes and tolls (that s, some perceved costs beng taxed at the general ndrect tax rate, others at specal rates, and possbly addtonal tolls), the value of (1) wll be the sum of the mpacts of the partcular components. If there are n components of the perceved cost and, for component, the resource cost s TP, then P and the ndrect taxes and tolls are TP0 P0 t TP1 P1 t t n TP0 P0 t TP1 P1 t 1 1 t 1 (13) It must be the case that: P TP n 1 n P 1 TP (14) term: We wll now consder, for some dfferent types of resources and tolls, the value of the TP0 P0 t TP1 P1 t 1t (15)

6 Economcs Bulletn, 011, Vol. 31 no. pp Let us consder a resource subect to the general tax rate t. For such a resource, TP P t. Ths means that for such a resource the value of (15) wll be zero, and that the ndrect tax on that resource has no mpact on the apprasal of the socal surplus. Consder now a resource subect to an ndrect tax that s hgher than the general tax rate (ths s usually the case of fuel). Ths means that TP P t, and that (15) wll have a postve value. Let us look at ths specal tax as an addtonal tax v appled after the general tax, so that TP P 1 t 1 v P. Expresson (15) becomes: P v P v 0 1 (16) In lne wth several other authors (e.g, Ltman, 009), we conclude that under specal taxes, only the level of tax above the general tax rate shall be consdered n the analyss. But t s mportant to notce that t s not the value of the taxes above the general rate collected n the Dosomethng scenaro that s added to the socal surplus nstead, as shown by (16), t s the average between the value collected n the Do-somethng and the Do-mnmum scenaros (f the trp was also made n the latter scenaro). When we consder fuel taxes, the relevant mpact s not the value of the fuel taxes of generated traffc collected n the Do-somethng scenaro, but nstead t s the average of ths value and the value of fuel taxes the generated traffc would produce n the Do-mnmum scenaro, f t would be makng the trps. The case n whch the resource s subect to an ndrect tax u that s lower than the general v u t 1t 0, and usng (16). In such case, v 0, the tax can be consdered by defnng mpact of the tax on the socal surplus wll be negatve. In the case of an untaxed resource, we v t 1 t. have Fnally, let us consder tolls. In the case of a toll, there s no physcal resource nvolved, so P 0. So, expresson (15) becomes: TP TP 1t 0 1 (17) The mpact of tolls collected on generated traffc s thus the average between the beforetax value of the tolls collected n the Do-somethng scenaro and the before-tax value of the tolls that would be collected f the generated traffc would be makng the trps n the Do-mnmum scenaro. In the case of a new toll, only appled n the Do-somethng scenaro, we conclude that the socal surplus s equal to half of the before-tax tolls collected on the generated traffc. 4. Conclusons Cost-beneft gudes are often unclear as to the way to ncorporate fuel taxes and tolls n the analyss (e.g, CE, 008). We consdered an analyss based on factor costs and presented as a calculus of socal costs and benefts (as n several recent cost-beneft analyses), and resorted to a

7 Economcs Bulletn, 011, Vol. 31 no. pp smple model to determne the correct way to ncorporate ndrect taxes and tolls n the analyss. From ths model we concluded that: - Unperceved user costs from generated traffc shall be subtracted from the socal surplus. - Only the level of ndrect tax above or below the general rate must be consdered, and only for the generated or suppressed traffc. The net socal mpact s the average between the abnormal amount of ndrect tax that s collected n the Do-somethng scenaro and the one that would be collected f the generated traffc would also be makng the trps n the Do-mnmum scenaro. - Tolls shall only be consdered for the generated traffc, and ther mpact s calculated as the average between the before-tax value of the collected tolls n the Do-somethng scenaro and the before-tax value of the tolls that would be collected f the generated traffc would also be makng the trps n the Do-mnmum scenaro. References Bckel, P., R. Fredrch, A. Burgess, P. Fagan et al. (006) HEATCO Developng Harmonsed European Approaches for Transport Costng and Proect Assessment, Delverable 5: Proposal for Harmonsed Gudelnes, avalable onlne at (accessed 3 May 011). DfT (001) COBA 11 User Manual, Department for Transport: Unted Kngdom, avalable onlne at: (accessed 3 May 011). EC (008) Gude to Cost-Beneft Analyss of Investment Proects, Structural Funds, Coheson Fund and Instrument for Pre-Accesson Fnal Report, Drectorate General Regonal Polcy: European Commsson, avalable onlne at: (accessed 3 May 011). Ltman, T. (009) Transportaton Cost and Beneft Analyss: Technques, Estmates and Implcatons, nd ed., Vctora Transport Polcy Insttute, avalable onlne at: (accessed 3 May 011). Macke, P. (1996) Induced Traffc and Economc Apprasal, Transportaton 3, Sugden, R. (005) The Treatment of Taxaton n the Cost-Beneft Apprasal of Transport Apprasal, report to the Department for Transport, Department for Transport: London. Sugden, R. (1999) Developng a Consstent Cost-Beneft Framework for Mult-modal Transport Apprasal, report to the Department of the Envronment, Transport and Regons, Economcs Research Centre, Unversty of East Angla. Wllams, H., and L. Moore (1990) The Apprasal of Hghway Investments under Fxed and Varable Demand, Journal of Transports Economcs and Polcy 4,