Abstract
This paper looks at the first and second best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (Netw. Spat. Econ., 4(2): 161–179, 2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network.
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Notes
Whilst Verhoef and Rowendal (2004) have successfully employed the same approach for a simple 3 link network they also encountered problems with the stability of this algorithm. In particular they stated that “a pragmatic trial-and-error approach was employed, where the trade-off concerned speed of convergence on the one hand and instability of the convergence process on the other…. Instability was particularly relevant for sets of policy instruments including both taxes and capacities” (Verhoef and Rowendal 2004, p. 421).
The attractiveness of capacity investment depends on, among other things, the elasticity of demand (d’Ouville and MacDonald 1990). If demand is very elastic (elasticity > 1), then induced traffic undermines the potential benefits from capacity investment if tolls are not present and optimal capacity could then be higher with tolls than without.
While the network we have used comprises only 18 links and 3 OD pairs, the CCA solving the second best toll only pricing problem has already been tested on a much larger network of Hull, Canada with 798 links and 158 OD pairs. For details see Lawphongpanich and Hearn (2004).
We emphasize that the costs of capacity provision in Eq. 1 includes the cost of maintenance discounted over its useful life. It is this cost saving that translates into actual savings.
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Acknowledgements
The research reported here was funded by the UK Engineering and Physical Science Research Council and the Hong Kong Research Grant Council (PolyU 5261/07E). The authors would also like to thank colleagues Tony May, David Watling and Richard Connors for their support during the course of this research. Also, the third author would like to specially thank Prof. Siriphong Lawphongpanich for his support and suggestion on the application of the CCA. We also sincerely thank the constructive comments from the anonymous three referees which helped improving the paper significantly.
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Koh, A., Shepherd, S. & Sumalee, A. Second best toll and capacity optimisation in networks: solution algorithm and policy implications. Transportation 36, 147–165 (2009). https://doi.org/10.1007/s11116-009-9187-y
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DOI: https://doi.org/10.1007/s11116-009-9187-y