Abstract
This paper presents a game-theoretic model of a liberalized railway market, in which train operation and ownership of infrastructure are vertically separated. We analyze how the regulatory agency will optimally set the charges that operators have to pay to the infrastructure manager for access to the tracks and how these charges change with increased competition in the railway market. Our analysis shows that an increased number of competitors in the freight and/or passenger segment reduces prices per kilometer and increases total output in train kilometers. The regulatory agency reacts to more competition with a reduction in access charges in the corresponding segment. Consumers benefit through lower prices, while individual profits of each operator decrease through a higher number of competitors. We further show that the welfare effect of increased competition in the freight and/or passenger segment is ambiguous and depends on the level of competition. Finally, social welfare is higher under two-part tariffs than under one-part tariffs if raising public funds is costly to society.
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Notes
Freight was fully opened to competition as of January 1st, 2007. International passenger services are open since January 1st, 2010.
Directive 2001/14/EC of the European Parliament and of the Council of 26 February 2001 on the allocation of railway infrastructure capacity and the levying of charges for the use of railway infrastructure and safety certification.
The First Package comprised Directives 2001/12, 2001/13 and 2001/14.
The decision to invest in new high-speed lines rests in part on their potential profitability.
Note that the number of operators is exogenously given. Moreover, if not otherwise stated, the parameter k denotes the segment with k ∈ {f, p}. The subscript f stands for the freight segment, while p denotes the passenger segment.
In Section 5.1, we extend our framework and analyze two-part tariffs which are composed of a variable and fixed part.
As shown in Section 5.3, where we relax the assumption regarding symmetric variable costs, the analysis would become very cumbersome without adding any new insights. To streamline the exposition and to highlight the competition effects, we have therefore decided to focus our analysis on a setting in which operators differ with respect to their fixed costs only.
The costs of the infrastructure manager can be referring to maintenance and operation costs but they can also encompass renewals or part of the investment needs (CER and EIM 2008).
Our results do not change qualitatively if we utilize a strictly convex cost function for the infrastructure manager. However, as correctly pointed out by an anonymous referee, our assumptions regarding the cost structure of the infrastructure manager are simplistic. Symmetric variable network costs do not reflect reality due to different firm sizes, economies or diseconomies of scale or different financing conditions. Moreover, asymmetric fixed network costs might be present in reality as it is the case, for example, in Germany where one big public infrastructure manager and many smaller infrastructure managers of different sizes are active.
Note that our results hold for a larger set of cost function. For example, the results do not change qualitatively if we assume that marginal variable costs are constant.
It can easily be verified that the second-order conditions for a maximum are satisfied.
Formally, the cross derivatives are given by \(\partial (\partial \pi _{k}^{\ast }/\partial a_{k}+\partial CS_{k}^{\ast }/\partial a_{k})/\partial n_{k}<0\) and \(\partial (\partial T^{\ast }/\partial a_{k})/ \partial n_{k}<0\) . Recall that lower transfers have a positive effect on social welfare.
To guarantee that access charges \(a_{k}^{\ast }\) do not fall below marginal costs v, we assume that \(n_{k}< n_{k}^{v}\equiv 1/2\left( 1+\lambda +(\lambda (\lambda +6+4c_{k})-3)^{1/2}\right) \).
It should be noted that the results in part (i) rest on the assumption that no congestion exists on the railroad network.
The derivation of the optimal access charges is analogous to Lemma 2. A formal proof is available from the corresponding author upon request.
We are grateful to an anonymous referee, who suggested promising avenues for future research.
See Pedersen (1994) for an analysis with private information about costs.
The market volume θ k in segment k must be larger than marginal infrastructure costs v because otherwise the demand function would not be defined.
Remember that operator i in segment k realizes zero profits because T ik = (p k − a k )q ik − 1/ \(2c_{k}q_{ik}^{2}-f_{ik}\).
References
Armstrong M (2008) Access pricing, bypass and universal service in post. Rev Network Econ 7(2):1
Armstrong M, Doyle C, Vickers J (1996) The access pricing problem: a synthesis. J Ind Econ 44(2):131–150
Armstrong M, Vickers J (1998) The access pricing problem with deregulation: a note. J Ind Econ 46(1):115–121
Bassanini A, Poulet J (2000) Access pricing for interconnected vertically separated industries. In: Nash C, Niskanen E (eds) Helsinki workshop on infrastructure charging on railways. VATT, Helsinki
Baumol W (1983) Some subtle pricing issues in railroad deregulation. Int J Transport Econ 10:341–355
Beckers T, von Hirschhausen C, Haunerland F, Walter M (2010) Long-distance passenger rail services in Europe: market access models and implications for Germany. In: The future for interurban passenger transport: bringing citizens closer together. OECD Publishing, pp. 287–310
Bozicnik S (2009) Opening of the market in the rail freight sector. Built Environ 35(1):87–106
Cave M, Vogelsang I (2003) How access pricing and entry interact. Telecommun Policy 27(10–11):17–727
CER, EIM (2008) Rail charging and accounting schemes in Europe—case studies from six countries. Technical report, Community of European Railways and European Rail Infrastructure Managers
Crozet Y (2004) European railway infrastructure: towards a convergence of infrastructure charging? Int J Transp Manag (1):5–15
Dodgson J (1994) Access pricing in the railway system. Util Policy 4(3):205–213
ECMT (2005) Railway reform and charges for the use of infrastructure. OECD Transport 200:1–134
Erhan K, Robert B (2005) A railway capacity determination model and rail access charging methodologies. Transp Plan Technol 28:27–45
Freebairn J (1998) Access prices for rail infrastructure. Econ Rec 74(226):286–296
Friebel G, Gonzalez A (2005) Vertical integration, competition and efficiency. Technical report, IDEI Report Nr. 10 - Rail Transport
Gibson S, Cooper G, Ball B (2002) The evolution of capacity charges on the UK rail network. J Transp Econ Policy 2:341–354
ITS (2009) European transport policy—progress and prospects. Technical report, Institute of Transport Studies
Kennedy D (1997) Regulating access to the railway network. Util Policy 6(1):57–65
Laffont J, Tirole J (1994) Access pricing and competition. Eur Econ Rev 38:1673–1710
Link H (2004) Rail infrastructure charging and on-track competition in germany. Int J Transp Manag 2(1):17–27
Nash C (2005) Rail infrastructure charges in Europe. J Transp Econ Policy 39(3):259–278
Nash C (2008) Passenger railway reform in the last 20 years-European experience reconsidered. Res Transp Econ 22(1):61–70
Nash C, and Sansom T (2001) Pricing European transport systems: recent developments and evidence from case studies. J Transp Econ Policy 35(3):363–380
OECD (2005) Railway reform and charges for the use of infrastructure. Technical report, OECD
Pedersen P (1994) Regulating a transport company with private information about costs. J Transp Econ Policy 28(3):307–318
Pittman R (2003) Vertical restructuring (or not) of the infrastructure sectors of transition economies. J Ind Compet Trade 3(1):5–26
Pittman R, Diaconu O, Sip E, Tomova A, Wronka J (2007) Competition in freight railways: ’above-the-rail’ operators in Central Europe and Russia. J Compet L & Econ 3(4):673
Quinet E (2003) Short term adjustments in rail activity: the limited role of infrastructure charges. Transp Policy 10:3–79
Quinet E, Vickerman R (2004) Principles of transport economics. Edward Elgar, Cheltenham; Northampton, MA
Sanchez-Borras M, Nash C, Abrantes P, Lopez-Pita A (2010) Rail access charges and the competitiveness of high speed trains. Transp Policy 17(2):102–109
Savignat M, Nash C (1999) The case for rail reform in Europe: evidence from studies of production characteristics of the rail industry. Int J Transport Econ 26(2):201–217
SBB (2010) Annual report 2009. Technical report, SBB Bern, Switzerland
SteerDaviesGleave (2005) Implementation of EU Directives 2001/12/EC, 2001/13/EC and 2001/14/EC. Technical report, Report for the European Commission
Thompson L, Perkins S (2006) Mixed signals on access charges. Railw Gaz Int 62(1):27–29
Vickers J (1995) Competition and regulation in vertically related markets. Rev Econ Stud 2(1):1
Wills-Johnson N (2006) Competition in rail: a likely proposition? Planning and Transport PATREC Working Paper, p 5
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Previous versions of this article were presented at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland and at the European Transport Conference 2010 in Glasgow, UK. We wish to acknowledge useful comments and suggestions by an anonymous referee and the co-editor Michael Peneder. We further would like to thank Helmut Dietl, Martin Grossmann, Matthieu Lapparent, Emile Quinet, Urs Trinkner, seminar participants at EPFL and conference participants at ETC. Financial assistance was provided by a grant of the Swiss National Science Foundation (Grant No. 100014-120503) and the Foundation for the Advancement of Young Scientists (FAN) of the Zürcher Universitätsverein (ZUNIV). The authors are solely responsible for the views expressed here and for any remaining errors.
A Appendix
A Appendix
1.1 A.1 Proof of Lemma 2
The break-even condition for the infrastructure manager will be satisfied with equality in equilibrium because increasing governmental transfers above the break-even level is costly to society. The maximization problem of the regulatory agency can thus be rewritten as:
with \(Q_{k}=\sum_{i=1}^{n_{k}}q_{ik}\). The first-order conditions of the maximization problem (17) are derived as:
with k ∈ {p, f}. Note that the second-order conditions for a maximum are satisfied if the number of competitors is sufficiently small with
Solving the system of first-order conditions yields:
with φ ≡ n k (2 − n k ) + 2λ(n k + 1 + c k ) + c k . To guarantee that access charges are not below marginal infrastructure costs v, we assume that the number of competitors is sufficiently small with
Thus, in the subsequent analysis, we assume that \(n_{k}<n_{k,\max }\equiv \min \{n_{k}^{SOC},n_{k}^{v}\}\).
Finally, to show that access charges increase with higher costs c k , we compute
By noting that n k ≥ 1 and θ k > v, we derive that \(\frac{ \partial a_{k}^{\ast }}{\partial c_{k}}>0\).Footnote 19
1.2 A.2 Proof of Proposition 1
The partial derivatives of \(a_{k}^{\ast }\) with respect to n k is given by:
By noting that n k ≥ 1 and θ k > v, we derive that \(\frac{ \partial a_{k}^{\ast }}{\partial n_{k}}<0\).
1.3 A.3 Proof of Proposition 2
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Part (i)
Let φ ≡ n k (2 − n k ) + 2λ(n k + 1 + c k ) + c k . To prove that more competition in segment k reduces the price \(p_{k}^{\ast }\) per kilometer and increases total output \(Q_{k}^{\ast }\) in train kilometers, we derive the partial derivatives with respect to n k as:
$$ \begin{array}{rll} \frac{\partial p_{k}^{\ast }}{\partial n_{k}} &=&-\frac{1}{\varphi ^{2}} (\theta _{k}-v)(1+\lambda )\left(c_{k}+n_{k}^{2}+2\lambda (1+c_{k})\right)<0, \\ \frac{\partial Q_{k}^{\ast }}{\partial n_{k}} &=&\frac{1}{\varphi ^{2}} (\theta _{k}-v)(1+\lambda )\left(c_{k}+n_{k}^{2}+2\lambda (1+c_{k})\right)>0. \end{array} $$Furthermore, we compute:
$$ \frac{\partial q_{ik}^{\ast }}{\partial n_{k}}=\frac{2}{\varphi ^{2}}(\theta _{k}-v)(1+\lambda )(n_{k}-(1+\lambda ))<0\Leftrightarrow n_{k}<n_{k}^{\prime } $$Thus, the effect of increased competition on individual output \(q_{ik}^{\ast }\) of operator i is negative if \(n_{k}<n_{k}^{\prime }\).
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Part (ii)
To prove the claim, we substitute equilibrium access charges \( a_{k}^{\ast }\) in the operator’s profit function (10) and derive that \(\pi _{ik}^{\ast }=\left( 1+c_{k}/2\right) \left( q_{ik}^{\ast }\right) ^{2}-f_{ik}\), where \(q_{ik}^{\ast }\) are the Stage 1 equilibrium outputs (Eq. 13) of operator i in segment k. From Proposition 2, we know that \(\frac{\partial q_{ik}^{\ast }}{\partial n_{k}}<0\) if \( n_{k}<n_{k}^{\prime }\equiv 1+\lambda \). Thus, \(\frac{\partial \pi _{ik}^{\ast }}{\partial n_{k}}<0\) if \(n_{k}<n_{k}^{\prime }\). We deduce that individual profits \(\pi _{ik}^{\ast }\ \)of operator i in segment k decrease with a higher number of competitors, until the minimum is reached for \(n_{k}=n_{k}^{\prime }\).
1.4 A.4 Proof of Proposition 3
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Part (i)
To prove the claim, we have to show that \(\frac{\partial T^{\ast }}{\partial n_{k}} <0\Leftrightarrow n_{k}<n_{k}^{T}\) and \(\frac{\partial T^{\ast }}{\partial n_{k}}>0\Leftrightarrow n_{k}>n_{k}^{T}\). Remember that \(T^{\ast }=F+(v-a_{f}^{\ast })Q_{f}^{\ast }+(v-a_{p}^{\ast })Q_{p}^{\ast }\). We derive:
$$ \frac{\partial T^{\ast }}{\partial n_{k}}=\underset{<0}{\underbrace{ (v-a_{k}^{\ast })}}\underset{>0}{\underbrace{\frac{\partial Q_{k}^{\ast }}{ \partial n_{k}}}}-\underset{<0}{\underbrace{\frac{\partial a_{k}^{\ast }}{ \partial n_{k}}}}\underset{>0}{\underbrace{Q_{k}^{\ast }}} $$We define \(z(n_{k}):=\frac{\partial T}{\partial n_{k}}\) and note that z(n k ) is a continuous function in the range of feasible n k . From the discussion of Proposition 2, we know that \(a_{k}^{\ast }\geq v\Leftrightarrow n_{k}\leq n_{k}^{v}\). Thus, \( z(n_{k}^{v})>0\). It follows that \(n_{k}<n_{k}^{v}\) is a necessary condition for z(n k ) = 0. We compute:
$$ z(0)=\frac{(\theta _{k}-v)^{2}(1+\lambda )(1-\lambda (1+c_{k}))}{\left[ c_{k}+2\lambda (1+c_{k})\right] ^{2}}<0\Leftrightarrow \lambda >\lambda ^{\prime }\equiv \frac{1}{1+c_{k}}. $$-
(a)
Suppose that λ > λ′. According to the intermediate value theorem, there exists a number of competitors \( n_{k}^{T}<n_{k}^{v}\), such that \(z(n_{k}^{T})=0\). This proves the claim because T is a convex function in n k .
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(b)
Suppose that λ < λ′. In this case, it holds that z(0) > 0. It follows that there does not exist a number of competitors \( n_{k}^{T}\in (0,n_{k}^{v})\), such that \(z(n_{k}^{T})=0\). Thus, z(n k ) > 0 for all feasible n k . This completes the proof of part (i).
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(a)
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Part (ii)
To prove the claim, we substitute equilibrium access charges \( a_{k}^{\ast }\) in consumer surplus (Eq. 11) and derive that \( CS_{k}^{\ast }=n_{k}^{3}/2\left( q_{ik}^{\ast }\right) ^{2}\). We compute the partial derivative of \(CS_{k}^{\ast }\) with respect to n k as:
$$ \frac{\partial CS_{k}^{\ast }}{\partial n_{k}}=\frac{2n_{k}^{2}}{\varphi ^{3} }(\theta _{k}-v)^{2}(1+\lambda )^{2}\left[ n_{k}(2+n_{k})+2\lambda (3+n_{k})+3c_{k}(1+2\lambda )\right] $$with φ ≡ n k (2 − n k ) + 2λ(n k + 1 + c k ) + c k . Thus, \( \frac{\partial CS_{k}^{\ast }}{\partial n_{k}}>0\) because φ is always positive for all \(n_{k}<\min \{n_{k,\max }^{\prime },n_{k,\max }^{\prime \prime }\}\). This proves the claim that consumer surplus always increases with a higher number of competitors.
1.5 A.5 Proof of Proposition 4
Let φ ≡ n k (2 − n k ) + 2λ(n k + 1 + c k ) + c k . To prove the claim, we substitute equilibrium access charges \(a_{k}^{\ast }\) in the welfare function (6) and derive the partial derivative of social welfare with respect to n k as:
From Eq. 19, we derive that in a scenario without fixed costs, i.e., f ik = 0, social welfare would always increase with a higher number of competitors. However, in a scenario with fixed costs, i.e., f ik > 0, the effect on social welfare is ambiguous.
To prove this claim, we define \(\mu (n_{k}):=\frac{\partial W}{\partial n_{k} }\) and note that μ(n k ) is a continuous function in the range of feasible n k . We compute \(\mu (0)=\frac{(\theta _{k}-v)^{2}(1+\lambda )^{2}}{2c_{k}+4(1+c_{k})\lambda }-f_{ik}<0\Leftrightarrow f_{ik}>f_{ik}^{\ast }\equiv \frac{(\theta _{k}-v)^{2}(1+\lambda )^{2}}{ 2c_{k}+4(1+c_{k})\lambda }\). Moreover, we derive that \(\lim_{n\rightarrow n_{k}^{SOC}}\mu (n_{k})=\infty \). According to the intermediate value theorem, there exists a number of competitors \(n_{k}^{W}<n_{k}^{SOC}\), such that \(w(n_{k}^{W})=0\). However, it is not guaranteed that \( n_{k}^{W}<n_{k,\max }\).
We conclude that social welfare always decreases through more competition in segment k if \(n_{k}^{W}>n_{k,\max }\). This is the case if the fixed costs f ik of the train operators are sufficiently high because \(n_{k}^{W}\) is an increasing function in f ik . On the other hand, if the fixed costs of the train operators are sufficiently low then \(n_{k}^{W}<n_{k,\max }\). In this case, social welfare initially decreases through more competition in segment k and reaches its minimum for \(n_{k}=n_{k}^{W}\). For \( n_{k}>n_{k}^{W}\), welfare increases through more competition in segment k.
1.6 A.6 Proof of Proposition 5
To prove that access charges under two-part tariffs \(a_{k}^{\ast \ast }\) are lower than access charges \(a_{k}^{\ast }\) under single tariffs if λ > 0, we compute:
with φ = n k (2 − n k ) + 2λ(n k + 1 + c k ) + c k and τ = n k (2 − n k ) + λ(2n k + c k ) + c k . It follows that \(a_{k}^{\ast }>a_{k}^{\ast \ast }\) if λ > 0, while \(a_{k}^{\ast }=a_{k}^{\ast \ast }\) if λ = 0.
In the next step, we compare social welfare under single tariffs with social welfare under two-part tariffs. From the maximization problems (17) and (15), we know that social welfare under single tariffs is given by:
while social welfare under two-part tariffs yields:Footnote 20
with \(T_{k}^{\ast \ast }=\sum_{i=1}^{n_{k}}T_{ik}^{\ast \ast }\).
Suppose that λ > 0: because \(a_{k}^{\ast }>a_{k}^{\ast \ast }\), we derive that \(CS_{k}^{\ast \ast }>CS_{k}^{\ast }\), \(Q_{k}^{\ast \ast }>Q_{k}^{\ast }\) and \(T_{k}^{\ast \ast }>\Pi _{k}^{\ast }\). One can show that the higher consumer surplus and operators’ lump sum fees under two-part tariffs compensate for the (eventually) higher value of \(F+(v-a_{f}^{\ast \ast })Q_{f}^{\ast \ast }+(v-a_{p}^{\ast \ast })Q_{p}^{\ast \ast }\), such that W ∗ ∗ > W ∗ always holds.
Suppose that λ = 0: because \(a_{k}^{\ast }=a_{k}^{\ast \ast }\), we derive that \(CS_{k}^{\ast \ast }=CS_{k}^{\ast }\), \(Q_{k}^{\ast \ast }=Q_{k}^{\ast }\) and \(T_{k}^{\ast \ast }=\Pi _{k}^{\ast }\). It follows that W ∗ = W ∗ ∗ .
1.7 A.7 Proof of Proposition 6
By computing the first-order conditions of the maximization problem (16) and solving the resulting equations systems, we derive the access charges in the passenger segment as:
The access charges in the freight segment are given in both regimes by:
Let φ = (c p (1 + 2λ) + 4λ + 1)(c p (1 + λ) + 4λ + 3).
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ad (i)
We compute \(a_{p}^{A}-a_{p}^{B}=-\frac{1}{\varphi } (2+c_{p})^{2}(1+\lambda )(\theta _{p}-v)<0.\) Thus, access charges are higher in Regime B than in A.
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ad (ii)
Note that governmental transfers are given by \(T^{s}=F+(v-a_{p}) \widehat{q}_{p}+2(v-a_{f})\widehat{q}_{f}\) in Regime s ∈ {A, B}. Substituting equilibrium access charges from Regimes A and B in T s, we compute \(T^{A}-T^{B}=\frac{1}{\varphi ^{2}}(2+c_{p})(1+\lambda )(\theta _{p}-v)^{2}\left[ 5+8\lambda +c_{p}(5+c_{p}+\lambda (6+c_{p}))\right] >0\). Thus, governmental transfers are higher in Regime A than in Regime B.
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ad (iii)
Substituting equilibrium access charges from Regimes A and B in the welfare function, we compute \(W^{A}-W^{B}=\frac{1}{2\varphi ^{2}} (2+c_{p})^{2}(1+\lambda )^{2}(\theta _{p}-v)^{2}>0\). Thus, social welfare is higher in Regime A than in B.
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Lang, M., Laperrouza, M. & Finger, M. Competition Effects in a Liberalized Railway Market. J Ind Compet Trade 13, 375–398 (2013). https://doi.org/10.1007/s10842-011-0117-2
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DOI: https://doi.org/10.1007/s10842-011-0117-2