Optimal welfare price for a road corridor with heterogeneous users
Abstract
In some countries it is fairly common to see two roads with the same origin and destination competing in the same corridor. One of them is usually a toll highway that offers a better quality to the users compared to its alternative: a free parallel single road, which might be tolled as well. This kind of transport network has been largely studied in the academic literature and particularly the optimal combination of tolls that maximizes economic efficiency. If both roads are tolled the problem is known as the first best, otherwise it is called the “untolled alternative”. There is a gap regarding how income distribution affects the optimal toll. The main objective of this paper is to add knowledge in the area by analysing the influence of the distribution of the Values of Travel Time (VTT) of the users of this corridor on the optimal combination of tolls. To solve this problem, the authors define a mathematical model aimed at obtaining the optimal welfare price for this kind of corridor under the hypothesis that drivers decide over the expectation of free flow conditions. The results show that the higher the average VTT the higher the optimal price, and the higher the dispersion (variance) of this VTT the lower the optimal price. It was also found that low income users who are not able to internalize externalities should not travel. Finally, first best pricing and untolled alternative schemes match for high income users.
Keyword : transportation pricing, optimal price, competing roads, social welfare, value of travel time distribution
How to Cite
Ortega Hortelano, A., Vassallo, J. M., & Pérez, J. I. (2019). Optimal welfare price for a road corridor with heterogeneous users. Transport, 34(3), 318-329. https://doi.org/10.3846/transport.2019.9685
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Dieplinger, M.; Fürst, E. 2014. The acceptability of road pricing: evidence from two studies in Vienna and four other European cities, Transport Policy 36: 10–18. https://doi.org/10.1016/j.tranpol.2014.06.012
Du, B.; Wang, D. Z. W. 2014. Continuum modeling of park-and-ride services considering travel time reliability and heterogeneous commuters – a linear complementarity system approach, Transportation Research Part E: Logistics and Transportation Review 71: 58–81. https://doi.org/10.1016/j.tre.2014.08.008
Fosgerau, M. 2006. Investigating the distribution of the value of travel time savings, Transportation Research Part B: Methodological 40(8): 688–707. https://doi.org/10.1016/j.trb.2005.09.007
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Shires, J. D.; De Jong, G. C. 2009. An international meta-analysis of values of travel time savings, Evaluation and Program Planning 32(4): 315–325. https://doi.org/10.1016/j.evalprogplan.2009.06.010
Small, K. A.; Winston, C.; Yan, J. 2005. Uncovering the distribution of motorists’ preferences for travel time and reliability, Econometrica 73(4): 1367–1382. https://doi.org/10.1111/j.1468-0262.2005.00619.x
Van den Berg, V. A. C. 2014. Coarse tolling with heterogeneous preference, Transportation Research Part B: Methodological 64: 1–23. https://doi.org/10.1016/j.trb.2014.03.001
Verhoef, E. T. 2002. Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points, Transportation Research Part B: Methodological 36(8): 707–729. https://doi.org/10.1016/S0191-2615(01)00025-X
Verhoef, E. T.; Koh, A.; Shepherd, S. 2010. Pricing, capacity and long-run cost functions for first-best and second-best network problems, Transportation Research Part B: Methodological 44(7): 870–885. https://doi.org/10.1016/j.trb.2009.12.002
Verhoef, E. T.; Small, K. A. 2004. Product differentiation on roads: constrained congestion pricing with heterogeneous users, Journal of Transport Economics and Policy 38(1): 127–156.
Wardman, M.; Ibáñez, J. N. 2012. The congestion multiplier: variations in motorists’ valuations of travel time with traffic conditions, Transportation Research Part A: Policy and Practice 46(1): 213–225. https://doi.org/10.1016/j.tra.2011.06.011
Xu, S.-X.; Liu, T.-L.; Huang, H.-J. 2014. Efficiency and equity of redistribution of toll revenue with user heterogeneity, in 11th International Conference on Service Systems and Service Management (ICSSSM), 25–27 June 2014, Beijing, China, 1–6. https://doi.org/10.1109/ICSSSM.2014.6874097
Yang, H.; Huang, H.-J. 2005. Mathematical and Economic Theory of Road Pricing. Elsevier. 486 p.
Yang, H.; Huang, H.-J. 2004. The multi-class, multi-criteria traffic network equilibrium and systems optimum problem, Transportation Research Part B: Methodological 38(1): 1–15. https://doi.org/10.1016/S0191-2615(02)00074-7
Yang, H.; Tang, W. H.; Cheung, W. M.; Meng, Q. 2002. Profitability and welfare gain of private toll roads in a network with heterogeneous users, Transportation Research Part A: Policy and Practice 36(6): 537–554. https://doi.org/10.1016/S0965-8564(01)00021-0
Yang, H.; Zhang, X. 2003. Optimal toll design in second-best link-based congestion pricing, Transportation Research Record: Journal of the Transportation Research Board 1857: 85–92. https://doi.org/10.3141/1857-10
Yin, Y.; Yang, H. 2004. Optimal tolls with a multiclass, bicriterion traffic network equilibrium, Transportation Research Record: Journal of the Transportation Research Board 1882: 45–52. https://doi.org/10.3141/1882-06
Zhang, K.; Mahmassani, H. S.; Lu, C.-C. 2013. Dynamic pricing, heterogeneous users and perception error: Probit-based bi-criterion dynamic stochastic user equilibrium assignment, Transportation Research Part C: Emerging Technologies 27: 189–204. https://doi.org/10.1016/j.trc.2012.05.001
Braid, R. M. 1996. Peak-load pricing of a transportation route with an unpriced substitute, Journal of Urban Economics 40(2): 179–197. https://doi.org/10.1006/juec.1996.0028
Brownstone, D.; Small, K. A. 2005. Valuing time and reliability: assessing the evidence from road pricing demonstrations, Transportation Research Part A: Policy and Practice 39(4): 279–293. https://doi.org/10.1016/j.tra.2004.11.001
Calvo Gonzalez, J. L.; Cortiñas Vázquez, P.; Sánchez Figueroa, C. 2012. A study in Spanish regions’ poverty: a new methodological perspective, Advances in Management and Applied Economics 2(1): 163–183.
Chung, C.-L.; Recker, W. W. 2012. Evaluation of operational effects of joint managed lane policies, Journal of Transportation Engineering 138(7): 882–892. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000385
Cruz, C. O.; Marques, R. C. 2013. Risk-sharing in highway concessions: contractual diversity in Portugal, Journal of Professional Issues in Engineering Education and Practice 139(2): 99–108. https://doi.org/10.1061/(ASCE)EI.1943-5541.0000131
De Palma, A.; Lindsey, R. 2004. Congestion pricing with heterogeneous travelers: a general-equilibrium welfare analysis, Networks and Spatial Economics 4(2): 135–160. https://doi.org/10.1023/B:NETS.0000027770.27906.82
De Rus, G.; Betancor, O; Campos, J.; et al. 2010. Evaluación Económica de Proyectos de Transporte [Socio-Economic and Financial Evaluation of Transport Projects] Research Project. University of Las Palmas de Gran Canaria, Spain. Available from Internet: http://www.evaluaciondeproyectos.es
Diaz, A.; Proost, S. 2014. Second-best urban tolling with distributive concerns, Economics of Transportation 3(4): 257–269. https://doi.org/10.1016/j.ecotra.2015.02.003
Dieplinger, M.; Fürst, E. 2014. The acceptability of road pricing: evidence from two studies in Vienna and four other European cities, Transport Policy 36: 10–18. https://doi.org/10.1016/j.tranpol.2014.06.012
Du, B.; Wang, D. Z. W. 2014. Continuum modeling of park-and-ride services considering travel time reliability and heterogeneous commuters – a linear complementarity system approach, Transportation Research Part E: Logistics and Transportation Review 71: 58–81. https://doi.org/10.1016/j.tre.2014.08.008
Fosgerau, M. 2006. Investigating the distribution of the value of travel time savings, Transportation Research Part B: Methodological 40(8): 688–707. https://doi.org/10.1016/j.trb.2005.09.007
Guo, X.; Yang, H. 2010. Pareto-improving congestion pricing and revenue refunding with multiple user classes, Transportation Research Part B: Methodological 44(8–9): 972–982. https://doi.org/10.1016/j.trb.2009.12.009
Huang, C.; Burris, M. W. 2015. The short-run impact of gas prices fluctuations on toll road use, Case Studies on Transport Policy 3(2): 137–150. https://doi.org/10.1016/j.cstp.2014.12.005
Kenyon, S.; Rafferty, J.; Lyons, G. 2003. Social exclusion and transport in the UK: a role for virtual accessibility in the alleviation of mobility-related social exclusion?, Journal of Social Policy 32(3): 317–338. https://doi.org/10.1017/S0047279403007037
Kraemer, C.; Pardillo, J. M.; Rocci, S.; Romana, M. G.; Sánchez Blanco, V.; Del Val, M. A. 2004. Ingeniería de Carreteras. Volumen I. McGraw-Hill. 516 p. (in Spanish).
Litman, T. A. 2007. Economic development impacts of transportation demand management, in TRB 86th Annual Meeting Compendium of Papers CD-ROM, 21–25 January 2007, Washington, DC, US, 1–15.
Liu, L. N.; McDonald, J. F. 1999. Economic efficiency of secondbest congestion pricing schemes in urban highway systems, Transportation Research Part B: Methodological 33(3): 157–188. https://doi.org/10.1016/S0191-2615(98)00025-3
Liu, L. N.; McDonald, J. F. 1998. Efficient congestion tolls in the presence of unpriced congestion: a peak and off-peak simulation model, Journal of Urban Economics 44(3): 352–366. https://doi.org/10.1006/juec.1997.2073
Mayet, J.; Hansen, M. 2000. Congestion pricing with continuously distributed values of time, Journal of Transport Economics and Policy 34(3): 359–369.
Nie, Y.; Liu, Y. 2010. Existence of self-financing and Pareto-improving congestion pricing: Impact of value of time distribution, Transportation Research Part A: Policy and Practice 44(1): 39–51. https://doi.org/10.1016/j.tra.2009.09.004
Ortega Hortelano, A. 2014. Optimización del peaje en autopistas interurbanas que compiten con carreteras convencionales libres de pago: una perspectiva de eficiencia y equidad: Tesis Doctoral. Universidad Politecnica de Madrid, España. 199 p. Available from Internet: http://oa.upm.es/32634 (in Spanish).
Ortega, A.; Vassallo, J. M.; Pérez-Díaz, J. I. 2018. Optimal welfare price for a highway competing with an untolled alternative: influence of income distribution, Journal of Infrastructure Systems 24(1). https://doi.org/10.1061/(ASCE)IS.1943-555X.0000412
Ortiz, I.; Cummins, M. 2011. Global Inequality: Beyond the Bottom Billion. A Rapid Review of Income Distribution in 141 Countries. UNICEF. 65 p. Available from Internet: https://www.unicef.org/socialpolicy/files/Global_Inequality_REVISED_-_5_July.pdf
Schmitt, L.; Currie, G.; Delbosc, A. 2015. Lost in transit? Unfamiliar public transport travel explored using a journey planner web survey, Transportation 42(1): 101–122. https://doi.org/10.1007/s11116-014-9529-2
Shires, J. D.; De Jong, G. C. 2009. An international meta-analysis of values of travel time savings, Evaluation and Program Planning 32(4): 315–325. https://doi.org/10.1016/j.evalprogplan.2009.06.010
Small, K. A.; Winston, C.; Yan, J. 2005. Uncovering the distribution of motorists’ preferences for travel time and reliability, Econometrica 73(4): 1367–1382. https://doi.org/10.1111/j.1468-0262.2005.00619.x
Van den Berg, V. A. C. 2014. Coarse tolling with heterogeneous preference, Transportation Research Part B: Methodological 64: 1–23. https://doi.org/10.1016/j.trb.2014.03.001
Verhoef, E. T. 2002. Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points, Transportation Research Part B: Methodological 36(8): 707–729. https://doi.org/10.1016/S0191-2615(01)00025-X
Verhoef, E. T.; Koh, A.; Shepherd, S. 2010. Pricing, capacity and long-run cost functions for first-best and second-best network problems, Transportation Research Part B: Methodological 44(7): 870–885. https://doi.org/10.1016/j.trb.2009.12.002
Verhoef, E. T.; Small, K. A. 2004. Product differentiation on roads: constrained congestion pricing with heterogeneous users, Journal of Transport Economics and Policy 38(1): 127–156.
Wardman, M.; Ibáñez, J. N. 2012. The congestion multiplier: variations in motorists’ valuations of travel time with traffic conditions, Transportation Research Part A: Policy and Practice 46(1): 213–225. https://doi.org/10.1016/j.tra.2011.06.011
Xu, S.-X.; Liu, T.-L.; Huang, H.-J. 2014. Efficiency and equity of redistribution of toll revenue with user heterogeneity, in 11th International Conference on Service Systems and Service Management (ICSSSM), 25–27 June 2014, Beijing, China, 1–6. https://doi.org/10.1109/ICSSSM.2014.6874097
Yang, H.; Huang, H.-J. 2005. Mathematical and Economic Theory of Road Pricing. Elsevier. 486 p.
Yang, H.; Huang, H.-J. 2004. The multi-class, multi-criteria traffic network equilibrium and systems optimum problem, Transportation Research Part B: Methodological 38(1): 1–15. https://doi.org/10.1016/S0191-2615(02)00074-7
Yang, H.; Tang, W. H.; Cheung, W. M.; Meng, Q. 2002. Profitability and welfare gain of private toll roads in a network with heterogeneous users, Transportation Research Part A: Policy and Practice 36(6): 537–554. https://doi.org/10.1016/S0965-8564(01)00021-0
Yang, H.; Zhang, X. 2003. Optimal toll design in second-best link-based congestion pricing, Transportation Research Record: Journal of the Transportation Research Board 1857: 85–92. https://doi.org/10.3141/1857-10
Yin, Y.; Yang, H. 2004. Optimal tolls with a multiclass, bicriterion traffic network equilibrium, Transportation Research Record: Journal of the Transportation Research Board 1882: 45–52. https://doi.org/10.3141/1882-06
Zhang, K.; Mahmassani, H. S.; Lu, C.-C. 2013. Dynamic pricing, heterogeneous users and perception error: Probit-based bi-criterion dynamic stochastic user equilibrium assignment, Transportation Research Part C: Emerging Technologies 27: 189–204. https://doi.org/10.1016/j.trc.2012.05.001