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Viability of a New Road Infrastructure with Heterogeneous Users in Madrid Access by * Pedro Cantos-Sánchez , Rafael Moner-Colonques José J. Sempere-Monerris^* and Óscar Álvarez DOCUMENTO DE TRABAJO 2008-06 Serie Economía de las Infraestructuras CÁTEDRA Fedea – Abertis

January 2008

University of Valencia.

Jorge Juan, 46 28001 Madrid -España Tel.: +34 914 359 020 Fax: +34 915 779 575 infpub@fedea.es

Viability of a New Road Infrastructure with Heterogeneous Users in Madrid Access

Pedro Cantos-S·nchezy, Rafael Moner-Colonquesy, JosÈ J. Sempere-Monerrisy and ”scar £lvarezy

June 14, 2007

Abstract

This paper explores the importance of heterogeneity in value of time when assessing the viability of a new road infrastructure to alleviate congestion problems. The Spanish government has developed a congestion pricing demonstration entering Madrid city centre, where road users have to choose between a free but highly congested road and a priced free-áowing road. We consider a continuum of users who di§er in their value of time. Users dislike congestion and this is more so the more a user values his travel time. A logit estimation is undertaken with information from a questionnaire among road users in the Eastern Madrid area to obtain usersívalue of time.

The impact and viability of artery road R3 under several competitive regimes is examined. The tolls obtained generate a tra¢c reallocation towards the new roadway such that revenues su¢ce to render the infrastructure socio-economically viable. This is so for all the competitive regimes analyzed even for modest tra¢ c growth rates. Regarding economic viability, the artery road infrastructure is always economically viable under the private regime and for the other two regimes, a su¢ciently high tra¢c growth rate is required.

Keywords: Parallel road network, heterogeneus users, viability.

JEL ClassiÖcation numbers: D82, D83, F12, L11.

The authors would like to thank Matilde Fern·ndez for helpful comments and suggestions. We gratefully acknowledge the Önancial support from Ministerio de Fomento under project FOM/2005/03.

yUniversity of Valencia. Facultad de Economia, Campus dels Tarongers, Avda. dels Tarongers s/n. Valencia E-46022. Pedro.Cantos@uv.es

1 Introduction

This paper explores the importance of heterogeneity in value of time when assessing the viability of a new road infrastructure to alleviate congestion problems. Transportation economists acknowledge the importance of congestion in access to large cities and have designed a number of schemes, which include the use of toll pricing by publicly or privately operated Örms, speciÖc tolled express lanes in formerly free highways, no charging of high-occupancy vehicles, and the construction of congestion-priced new highways. In this regard, the Spanish government has developed a congestion pricing demonstration entering Madrid city centre, which consists of a number of arterial tolled roads parallel to existing untolled roads. Road users have to choose between a free but highly congested road and a priced free-áowing road, where users di§er in their value of time and therefore in their willingness to pay for travel-time savings. The government conceded the construction of an artery road to a private company that, in exchange, is given its exploitation for a number of years. Are the prices e§ective in provoking a route split that makes the new infrastructure economically viable? what should be tra¢ c growth to render it profitable? how do the results compare with a setting with private toll roads? are lower tolls desirable in welfare terms? do they favour that new roads be self-Önancing?

We consider a continuum of users that are ordered in terms of their value of time. To do it we propose a Hotelling type model of product di§erentiation, where users dislike congestion and this is more so the more a user values his travel time. Initially, there is a free usage congestible highway. Then, the authorities design a parallel link that connects the same origin and destination points; this is a tolled free-áowing highway (semi-private regime). We characterize the proÖt maximizing toll and the comparison of the initial and the actual settings allows us to evaluate the economic viability as well as the socio-economic gains of the new infrastructure. The case of a low toll regime is also considered. We further formalize the equilibrium prices when both routes are privately operated; the private regime with proÖt maximizing Örms. The model is then applied to examine the impact and viability of artery road R3. We need an estimation of usersívalue of time and of the disutility caused by di§erent amounts of congestion. A logit estimation is undertaken with information from a questionnaire among peak road users in the Eastern Madrid area. Data from the Spanish Tra¢ c O¢ ce are employed to obtain an estimation of peak and o§-peak tra¢c volumes. These computations allow for a comparison of the above mentioned scenarios and give an assessment of the construction of this

new road infrastructure.

Essentially, the tolls obtained generate a tra¢ c reallocation towards the new roadway such that revenues su¢ ce to render the infrastructure socio-economically viable. This is so for all the competitive regimes analyzed even for modest tra¢c growth rates. It is worth mentioning that the low toll regime produces the highest welfare level because it generates the most e¢ cient tra¢ c allocation. Regarding economic viability, it depends on the particular regime. The artery road infrastructure is always economically viable under the private regime and for the other two regimes, a su¢ciently high tra¢c growth rate is required. We conclude that the construction and exploitation of artery roads seems an adequate policy measure as it favours the creation of new infrastructures. The semi-private regime achieves both types of viability with low requirements of tra¢ c growth.

There is recent literature on second-best congestion pricing in parallel networks. This includes Braid (1996), Verhoef, et al. (1996), Liu and McDonald (1998), Small and Yan (2001), and Verhoef and Small (2004). Typically, these papers assume two roadways (a parallel network), one is an express road and another remains unpriced, and study the welfare e§ects of tolling the former. Verhoef et al. (1996) is a single-period model whereas Braid (1996) and Liu and McDonald (1998) distinguish peak and o§-peak time periods. Their theoretical Öndings are mixed and reveal that tolls do not necessarily lead to welfare improvements. These three papers assume a homogeneous population of road users. Arnott et al. (1992) considered two user groups di§ering by value of time. Accounting for such heterogeneity, as done by Small and Yan (2001), and Verhoef and Small (2004), uncovers substantial beneÖts from second best tolls. Our paper is a contribution to the scarce literature that treats heterogenous users and proposes a useful framework to evaluate demonstrations that imply heavy investments, as the current artery roads entering Madrid city centre.

The artery R3 facility.

Madrid R3 is a three-lane expressway (in each direction) that connects residential areas East of Madrid with employment centers in the capital. The highway is 33,9 km in length and has several entry and exit points (four toll points). The artery R3 runs parallel to highway A3, which links the East of Spain and Madrid, it has two lanes in each direction and is heavily congested at peak time. Between October 2003 and April 2004, four artery roads totalling 188 km were open, which represented the most important project to relieve congestion problems in Spain (with an estimated cost of 1135 million e). See Figure 1. Following current practices in many countries, the government decided to permit a private company to build each of the arteries and charge a toll for their use. The Örm Accesos de Madrid constructed highway R3 and was given the exploitation for 50 years. The company behaves as a proÖt maximizer when setting tolls. Artery road R3 opened on February 16, 2004, and the use of this new infrastructure has run below the companyís forecast. The average peak hour toll is km whereas it is 0.061 e for o§-peak in a weekday.

2 The Model

Consider two roadways, A and B; linking the same origin and destination points. All road users value the former as the fast highway, which never gets congested. The latter is the slow highway and is subject to congestion. We suppose that users are heterogeneous as each has a di§erent value of time. We further assume that users dislike congestion and this is more so the higher a userís value of time.

According to their preference for time there is a continuum of users uniformly distributed with density one in an interval of length L; [0; L]. Let denote the distance of user i from zero is the distance to the upper bound of the interval). For user i, such distance is a measure of its value of time. The user at zero does not value trip time at all whereas the user at L holds the highest value of trip time. Every user is characterized by its maximum willingness to pay for the trip v; assumed common to all users and large enough to ensure that all users travel, and by its value of time ; which depends on its location in : The amount of congestion is a function of the number of users travelling by the slow highway.

In terms of the characteristics space, the two roadways are located at the extreme points of the interval [0; L]: Thus, the slow and subject to congestion route is situated at zero whereas the fast uncongested route is at : User i has the following indirect utility function,

\[U _ {i} = \left\{ \begin{array}{l l} v - p _ {r} - \lambda d _ {i} - \mu d _ {r} d _ {i} & \text {if travelling by route r} \\ v - p _ {t} - \lambda | L - d _ {i} | & \text {if travelling by route t} \end{array} \right.\tag{1}\]

where is the price paid for using route ; and is the demand (or number of users) for route r: Finally, is a parameter that measures the unit disutility due to the mismatch between a userís value of time and the route that is used, and captures the unit disutility incurred by the use of the congested route. Thus travelling by the slow congested route implies no utility loss for the user located at zero; on the other hand, the user at L su§ers a loss of because of not taking his preferred route and the additional loss because of travelling by the congested route.

Users take their utility maximizing decisions (about travelling by mode or t) knowing the prices of each mode. Thus, for every pair we can Önd the indi§erent user between travelling by mode r and t: That is, we can Önd deÖned by

\[v - p _ {r} - \lambda \tilde {d} - \mu \tilde {d} ^ {2} = v - p _ {t} - \lambda \left| L - \tilde {d} \right|\tag{2}\]

i.e.

\[\tilde {d} = \frac {- \lambda + \sqrt {\lambda^ {2} + \mu (\lambda L - p _ {r} + p _ {t})}}{\mu}\tag{3}\]

so that if increases then the user indi§erent will approach zero, whereas it approaches when increases. Note that for given prices all consumers to the left of will take route so that represents the demand for that route whereas is demand for route t: SpeciÖcally, for every pair of prices the demand for route r is given by

\[d _ {r} = \left\{ \begin{array}{c c} 0 & \text {if p_{r} >\lambda L+ p_{t}} \\ \frac {- \lambda + \sqrt {\lambda^ {2} + \mu (\lambda L - p _ {r} + p _ {t})}}{\mu} & \text {if p_{t} -L(\mu L + \lambda)\leq p_{r}\leq\lambda L+ p_{t}} \\ L & \text {if 0\leq p_{r} < p_{t} -L(\mu L + \lambda)} \end{array} \right.\tag{4}\]

and the demand for mode t

\[d _ {t} = \left\{ \begin{array}{c c} 0 & \text {if} p _ {t} > p _ {r} + L (\mu L + \lambda) \\ \frac {\mu L + \lambda - \sqrt {\lambda^ {2} + \mu (\lambda L - p _ {r} + p _ {t})}}{\mu} & \text {if} p _ {r} - \lambda L \leq p _ {t} \leq p _ {r} + L (\mu L + \lambda) \\ L & \text {if} 0 \leq p _ {t} < p _ {r} - \lambda L \end{array} \right.\tag{5}\]

The above demand system distinguishes three possible situations. Firstly, the case where all users travel through route t, that is to say, the indi§erent consumer will lie to the left of zero, ; as long as : Secondly, all users travel using route r; i.e. the indi§erent consumer will lie to the right of L; as long as : Finally, the middle branches where both routes have positive demand and all users travel; we concentrate on the latter case.

The above demand functions have the following properties. Maximum aggregate demand is bounded above by so that there is a minimum price below which no further users are gained. Routes are perceived as susbtitutes; demand for route increases with price : Furthermore, demands are symmetric regarding the e§ect of prices, and : Finally, demands are concave in own price.

1. Only one route that is congested.

Consider that users can only travel by route r: Demand is obtained by checking that the (indirect) utility derived from travelling is positive. Solving we get the indi§erent user : Two cases can be distinguished, depending on whether all road users travel or only a fraction of them does . Hence everybody travels at price if and only if ; i.e. : The demand function can then be written as,

\[d _ {r} ^ {0} = \left\{ \begin{array}{c c} 0 & \text {if p_{r} \geq v+ \frac {\lambda^{2}}{4\mu}} \\ \frac {\lambda + \sqrt {\lambda^ {2} + 4 (v - p _ {r}) \mu}}{2 \mu} & \text {if v - L(\muL - \lambda)\leq p_{r} \leq v+ \frac {\lambda^{2}}{4\mu}} \\ L & \text {if 0\leq p_{r}\leq v - L(\muL - \lambda)} \end{array} \right.\tag{6}\]

If the use of route r were free then all users would travel as long as Assume that this is indeed the case, that is, the initial situation is one with one congested route which is free and where all users travel : Consumer surplus (welfare) is the sum of the utility derived by each user that travels. Formally,

\[C S ^ {0} = \int_ {0} ^ {L} (v - \lambda x - \mu x ^ {2}) d x = v L - \frac {\lambda L ^ {2}}{2} - \frac {\mu L ^ {3}}{3}\tag{7}\]

for

2. Di§erent competitive schemes in a parallel network.

2.1 Two routes which are operated by proÖt-maximizing Örms.

We are interested in Önding which are the prices set by Örms given that there is competition between both roadway operators. Firmsí marginal costs are negligible and assumed zero. Firmsí proÖts are given by and . There is strategic behavior and routes compete for users. Each Örm chooses the proÖt maximizing price (given the price of the rival). Solving the pair of Örst order conditions and yields

\[p _ {r} ^ {*} = \frac {2 (- 3 \lambda^ {2} + 8 L \lambda \mu + 2 L ^ {2} \lambda^ {2} + (2 L \mu - \lambda) \sqrt {9 \lambda^ {2} + 9 L \lambda \mu + L ^ {2} \lambda^ {2}})}{2 5 \mu}\tag{8}\]

\[p _ {t} ^ {*} = \frac {2 (3 \lambda^ {2} + 2 L \lambda \mu + 3 L ^ {2} \lambda^ {2} + (3 L \mu + \lambda) \sqrt {9 \lambda^ {2} + 9 L \lambda \mu + L ^ {2} \lambda^ {2}})}{2 5 \mu}\tag{9}\]

And the indi§erent user at equilibrium is

\[\tilde {d} ^ {*} (p _ {r} ^ {*}, p _ {t} ^ {*}) = \frac {- 5 \lambda + \sqrt {1 3 \lambda^ {2} + 1 3 L \lambda \mu + 2 L ^ {2} \lambda^ {2} + 2 (2 \lambda + L \mu) B}}{5 \mu}\]

where . Consumer surplus is now deÖned by the sum of and ; where

\[C S _ {r} = \int_ {0} ^ {d _ {r} (p _ {r}, p _ {t})} (v - p _ {r} - \lambda x - \mu x ^ {2}) d x = (v - p _ {r} - \frac {\lambda}{2} d _ {r} (p _ {r}, p _ {t}) - \frac {\mu}{3} d _ {r} (p _ {r}, p _ {t}) ^ {2}) d _ {r} (p _ {r}, p _ {t})\]

\[C S _ {t} = \int_ {0} ^ {L - d _ {r} (p _ {r}, p _ {t})} (v - p _ {r} - \lambda x) d x = (v - p _ {t} - \frac {\lambda}{2} (L - d _ {r} (p _ {r}, p _ {t}))) (L - d _ {r} (p _ {r}, p _ {t}))\]

2.2.Route r is free whereas route t is operated by a proÖt-maximizing Örm.

We have to solve taking to obtain

\[p _ {r} ^ {*} = 0\]

\[p _ {t} ^ {*} = \frac {2 (L \mu + \lambda) (L \mu - 2 \lambda \sqrt {(L \mu + \lambda) (L \mu + 4 \lambda)})}{9 \mu}\]

3 Empirical Analysis

3.1. An estimation of value of time for highways R3 and A3.

The analysis that will be employed to estimate the theoretical model presented above is based on a questionnaire to road users conducted in May 2005 at access points to Madrid. Users have to make travelling decisions faced with hypothetical situations where trip time, cost and percentage time congestion vary. The information obtained is employed to perform the following estimation in an e§ort to get values for parameters and

In order to perform the estimation we assume that an individual empirical indirect utility function who chooses route is given by

\[V _ {i j} = V _ {i j} ^ {a} (T _ {j}, T _ {c j}, M _ {j}) + \varepsilon_ {i j} = \beta_ {T} T _ {j} + \beta_ {f c} (T _ {c j} / T _ {j}) + \beta_ {M} M _ {j} + \varepsilon_ {i j}\tag{10}\]

and consists of the sum of a deterministic part ; and a random variable the deterministic part is a function of and : Where is total trip time, is trip time under congestion, is the monetary cost of using the chosen route; Önally, captures all unknown factors and follows a logistic distribution. If user i can choose between two routes ; he will take A rather than B as long as ; that is, Note that the value of time in the absence of congestion, , follows easily from the usual expression,

\[V T _ {i} = \frac {\partial V _ {i j} / \partial T _ {j}}{\partial V _ {i j} / \partial M _ {j}} = \frac {\beta_ {T}}{\beta_ {M}}\tag{11}\]

Those individuals with a value of time above the one estimated according to (11) will travel by the faster and yet more expensive alternative. The individuals with a value of time below (11) will take the cheaper though with a longer trip time alternative. This way one or another road is chosen depending on every userís subjective value of time. The value of time therefore determines the e§ect on individual indirect utility of any time saving. In other words, it represents an individualís willingness to pay for a certain travel-time saving.

The speciÖc design of the questionnaire implied the analysis of the most recent tra¢c levels in Madrid roads available from a Department of the Transports Ministry. This allowed us to view average speed at every point in highways R3 and A3 for di§erent times of the day and di§erent days of the week. We may then compute rather accurately the percentage time congestion apart from trip time through every road.² These data were used to design the questionnaire and see how di§erent users responded before changes in trip characteristics. In particular, the questionnaire³ accounts for three basic variables that deÖne every alternative (tolled highway R3 and free highway A3):

V_iA > V_iB

^PiA ^{= P["}iB ^"iA ^{< V}iA ^ViB^]

¹From discrete choice theory models, and since values for the random term are unknown, the probability that is equal to :

- Monetary cost of use, which included tolls, gasoline, vehicle depreciation, etc.

- Trip time, deÖned as the time spent when using highway R3 or by default the corresponding road other than A3.

- Percentage time that a user travelled under congestion with respect to the above referred trip times.

The logit estimation of the probability choice of R-3 using the explanatory variables included in the individualsíutility functions are the following:

Logit estimation

²In particular, we have data about the average speed, kilometre by kilometre, of a control vehicle set by the Ministry of Works for a particular number of days and in particular peak times of the day. Given that, we are able to elicit the kilometre spots where the average speed of the control vehicle signiÖcantly falls. In this way the percentage of total travel time under congestion is computed.

³Surveys were conducted to be answered at home because of their complexity and speciÖc characteristics.

where

- DTIME is the di§erence in trip time between the two roadways.

- DCOST is the di§erence in monetary cost.

- DCONG is the di§erence in percentage time congestion.

- CAUT is a dummy variable that takes on value 1 when the respondent assures to always use R3 in any suggested scenario.

Therefore, : 2 and : In particular, the estimated value of time without congestion is an hour, the one obtained for the average user in the survey, i.e. minute.

To Önd the values for and we divide equation (10) by to get,

\[\frac {V _ {i j}}{\beta_ {M}} = \frac {\beta_ {T} T _ {j}}{\beta_ {M}} + \frac {\beta_ {f c}}{\beta_ {M}} (T _ {c j} / T _ {j}) + M _ {j} + \frac {\varepsilon_ {i j}}{\beta_ {M}}\tag{12}\]

Note Örst that the monetary cost can be interpreted as the price in the theoretical model), the ratio reáects a userís value of time per travelled km so that it can be identiÖed with the term in equation (1), that captures the disutility caused in the absence of congestion. Secondly, since part of the trip is made under congestion, the value of such disutility per travelled km under congestion is gathered in : This term can be thought of as in the model, and reáects the unit monetary value of congestion and is the amount of congestion. Finally, corresponds with the constant v in the model. Therefore, is equal to 0:158e: Parameter depends on total trip duration. The 31 km. trip takes around 15 minutes by R3 and by A3 without congestion, so that the additional unit disutility per minute congestion is 0:221e.

3.2. Obtaining tra¢c volumes.

Finally, a key parameter to be determined in the calibration is market size L as the equilibrium results depend on this value. To do it we take into account only those users who can e§ectively choose between both roadways. The Daily Average Tra¢ c Flow (DATF) weighted by km has been computed for highways R3 and A3, given the available information for di§erent road stretches from tra¢ c maps in 2004 (the opening year of R3). We also separate peak and o§-peak tra¢ c. The following graph displays the evolution of DATF for an average day with information collected at check points in 2004.

In particular, a tra¢c level in excess of 3000 vehicles-hour will be considered as peak time. We then have 6 peak hours in week day (from 7:00 to 10:00 and from

Figure 2: Hourly tra¢ c split

18:00 to 21:00) and 5 peak hours during the weekend (from 17:00 to 22:00). In this way peak time tra¢ c represents 48% of total tra¢ c during week day whereas it amounts to 51% for the weekend tra¢c.

With this information at hand, we proceeded to compute their average day DATF for the year 2004. A distinction between peak and o§-peak DATF was made, and we considered that total DATF was equally assigned to both these time periods. The results appear in Figure 3.

It can be seen that R3 market shares are small. The year 2004 was the Örst year when R3 was working so that a tra¢c increase is expected to occur. Note that it is highway R3 the one that captures tra¢ c from the alternative road.

4 Results

4.1. Calibration and comparison of regimes

Figure 3: Numerical Results

We next determine the prive levels in both routes as well as the tra¢c allocation under three di§erent settings,as speciÖed in section 2 above. Consider the initial situation to be the one without the R3 investment so that only the congested infrastructure exists. The next setting entails two links of a parallel network managed by proÖt maximimizing units, and will be called the private regime. The third setting considers A3 to be free whereas R3 sets a proÖt maximizing toll price; this is the semi-private regime, which is indeed the actual situation. Finally, we deÖne a low toll regime where toll price for R3 is set equal to the disutility value caused by congestion (0.036 e per km). Tra¢c levels are expressed in passenger car units, where we have employed the information about the distribution of heavy and light tra¢c available from Spainís Tra¢c Map 2004; this allows us to transform vehicles in units of homogeneous capacity. The results, that are displayed in Figure 4, make a distinction between peak and o§-peak periods. Note that in the computations, the parameter is assumed zero during o§-peak time.

The following comments are in order:

- The outcome in the semi-private regime resembles most the existing situation. Nevertheless, the estimated results are an indication for the long-term tra¢c adjustment. The (calibrated) toll price for peak hours is very similar to the actual price, although it is slightly below the one in o§-peak hours. See data above. In terms of consumer surplus, there is an important gain as compared with the setting without the R3 infrastructure.

- The private regime supposes, as expected, an increase in both peak and o§- peak prices. Relative to the semi-private regime, there is a notable increase in R3 market share. The reason for this is that now the highway A3 road is also tolled during peak time which provokes a tra¢ c reallocation towards the artery R3. On the other hand, given that o§-peak prices are the same for both roads, tra¢c would be equally shared at this time period. Besides, a signiÖcant loss to consumers produces although Örmsítoll revenues notably increase.

- A low toll only in peak hours for R3 would basically balance the tra¢c allocation during that period. This is the preferred setting for consumers; toll revenue goes down, which might raise economic viability problems for the Örm. We discuss this point later on.

- Concerning market shares, our modelling predicts that R3 will bear 28% of tra¢ c in peak hours and 25% in o§-peak. The available information on market shares reveals that these are actually smaller; yet another three to four years should go by for tra¢ c to stabilize. We must however mention that our predictions are well below the estimates handled by authorities, who were expecting a market share around 30-40%.

4.2. Viability of R3

We next analyze the viability of the artery R3 infrastructure from an economic perspective as well as from a socio-economic viewpoint . Regarding economic viability, note that it obviously depends on the competitive regime under consideration since prices are di§erent. The next Figure o§ers information on costs about several artery road investment projects, which will be useful in the exercise that follows.

Consider then that construction costs of highway R3 are 295 million e, which means 8.91 million e per km. We take 50 years to be the time horizon since this is the duration of the lease contract. It is also necessary to apply some infrastructure maintenance costs. In particular, the Spanish DG for Roads regards the following average costs depending on the road type.

Thus equation (13) incorporates all discounted beneÖts and costs associated with construction of artery R3,

Figure 4: Investment Costs Figure 5: Maintenance costs

\[B f = \sum_ {i = 1} ^ {5 0} \frac {(R - 1 9 , 8 3 0) (1 + n) ^ {t - 1}}{(1 + i) ^ {t}}\tag{13}\]

where R stands for toll revenue, n is annual tra¢ c growth rate, and i is the discount rate. The discounted net proÖt must be set against the (Öxed) construction cost FC. Let us deÖne the ratio so that, if greater than unity, we conclude that the investment is economically viable.

There is the compromise between the government and all the concessionaires that toll revenue from the respective artery road operator will Önance the free ringway M-50. Highways R3 and R5, granted to the same Örm, have to contribute 373 million e. An allocation of costs in terms of distance km. supposes additional 192 million e for R3 infrastructure. Thus, two di§erent analyses will be undertaken. Firstly, only costs associated with the newly built highway will be considered. Secondly, such costs will be augmented by the committed amount to partially Önance the ring M-50. See Ögure 1.

As for the Örst analysis, construction costs are 295 million e. Assuming a 5% discount rate, the ratio BC will depend on the annual tra¢ c growth rate. See Figure 6 .

The setting with a higher ratio is the private regime where tolls are higher and where demand is not much a§ected, given that highway A3 is tolled. Concerning the semi-private regime, it can be seen that the new infrastructure is economically viable for low levels of tra¢ c growth. The low toll regime does not generate the necessary net revenues unless increases in demand above 6% are produced.

Figure 6: Economic viability 1 Figure 7: Economic viability 2

The consideration of the ring M-50 Önancing costs leads to the following table. Viability is notably lower under these circumstances. The semi-private regime is feasible with an annual tra¢ c growth rate of 4%. The private regime is always viable whereas the low cost regime would clearly require subsidization.

We now wish to calculate the socio-economic viability of the investment by comparing with the initial case where there is just the free highway A3. To do it we compute the sum of discounted ÖrmsíproÖts (gross of Öxed costs)⁴ and consumer surplus under every competitive regime and subtract it from that sum in the initial situation . For example,

\[W D = \sum_ {i = 1} ^ {5 0} \frac {\left(S W _ {R 3} - S W _ {0}\right) (1 + n) ^ {t - 1}}{(1 + i) ^ {t}}\tag{14}\]

We say that R3 is socio-economically viable when the ratio WD=FC exceeds one.

In socio-economic terms, the low toll regime is the preferred regime although the operator would need public subsidization to break even. Except for the private regime and the lowest tra¢ c growth considered, all the scenarios the construction of R3 is viable in socio-economic terms. The current semi-private regime appears as the next desirable setting. Modest tra¢c growth levels seem to make the R3 infrastructure viable even if partially Önancing the ring M-50.

⁴For the private regime, the private operator of A3 incurs maintenance costs plus a fee equivalent to the construction costs of artery R3.

Figure 8: Socio-economic viability

5 Conclusions

Toll artery highways, which were constructed parallel to the existing access roads to Madrid, have the main objective of mitigating congestion problems and the continuous tra¢ c jams that occurred at entry to and exit from Madrid. These infrastructures have not yet been at work for too long so that we should still wait for some time to reach some stable tra¢c levels. The lack of information as well as inertia in driversí decisions are reasons to believe that tra¢c on these new highways is expected to grow.

Initially, the predictions were that such artery roads would capture an average of 35% of incoming and outcoming tra¢c in Madrid. The Örst two years of work (2004 and 2005) have generated Ögures well below such predictions.

The present paper has employed survey data from an experiment conducted in the East corridor (including highways A3 and R3) to calibrate a theoretical model where usersídisutility to congestion is taken into account. The semi-private regime entails the new highway to be managed by a proÖt maximizing entity whereas the existing highway is freely used and run by the Spanish Ministry of Works. The e§ect of the infrastructure is evaluated by comparing with the initial setting of one free roadway. We then consider two other regimes: the private regime, where both highways are ruled by proÖt maximizing behaviour, and the low toll regime, where the new infrastructure is granted a concession and the existing highway remains free. The most relevant results are listed below.

- For R3, our modelling predicts a market share of 28% for peak hours and 25% for o§-peak. These Ögures are below those expected by authorities and the actual data of 18% of total tra¢ c during the Örst year of work. This suggests that the

growth expectations are important.

- Market shares would be higher under a private regime, 43% for peak hours and 50% for o§-peak. Although tra¢ c is equally split during the o§-peak period, since there is no congestion, the better infrastructure can di§erentiate and have a higher price than the existing one. Above all, this scenario is not desirable to consumers (they would be better o§ if the investment were not undertaken) but there are signiÖcant gains to Örms. Still, the semi-private regime is preferred to the private regime in total welfare terms.

- In case the new infrastructure were conceded under the terms of a low toll regime (the toll is et equal to user congestion disutility), higher usage rates than in the semiprivate regime are obtained. This situation is preferred by consumers, not so much by Örms but generates the highest total welfare levels. A major disadvantage of this setting is that the Örm will incur losses unless annual tra¢ c growth rate exceeds 9%; this supposes public subsidization of such a service.

- Therefore, with strong budget restrictions, concession to a private Örm of the construction and exploitation of artery roads seems an adequate policy measure as it favours the creation of new infrastructures, which are socially beneÖcial, while avoiding any public funding.

- The commitment to Önance part of the (free) ring M-50 requires some 4% tra¢c growth for the semi-private regime to be economically viable.

- We have applied the analysis to the other three artery roads accessing Madrid. Similar qualitative results are obtained.

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