# The effect of complex models of externalities on estimated optimal tolls

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## Abstract

Transport externalities such as costs of emissions and accidents are increasingly being used within appraisal and optimisation frameworks alongside the more traditional congestion analysis to set optimal transport policies. Models of externalities and costs of externalities may be implemented by a simple constant cost per vehicle-km approach or by more complex flow and speed dependent approaches. This paper investigates the impact of using both simple and more complex models of CO_{2} emissions and cost of accidents on the optimal toll for car use and upon resulting welfare levels. The approach adopted is to use a single link model with a technical approach to the representation of the speed-flow relationship as this reflects common modelling practice. It is shown that using a more complex model of CO_{2} emitted increases the optimal toll significantly compared to using a fixed cost approach while reducing CO_{2} emitted only marginally. A number of accident models are used and the impact on tolls is shown to depend upon the assumptions made. Where speed effects are included in the accident model, accident costs can increase compared to the no toll equilibrium and so tolls should in this case be reduced compared to the congestion optimal toll. Finally it is shown that the effect of adding variable CO_{2} emission models along with a fixed cost per vehicle-km for accidents can increase the optimal toll by 44% while increasing the true welfare gained by only 8%. The results clearly demonstrate that model assumptions for externalities can have a significant impact on the resulting policies and in the case of accidents the policies can be reversed.

## Keywords

Congestion Externalities Optimal tolls Accidents Emissions## Notes

### Acknowledgements

The author thanks The Institute for Transport Studies for funding this research under its departmental fellowship. He would also like to thank colleagues Tony May, Chris Nash, Dave Watling and Agachai Sumalee and Erik Verhoef of FUA for useful comments on an early version of this paper. The author is also grateful to Guenter Emberger and Pauli Pfeffenbichler of TUW for their help and contribution to the MARS modelling of Edinburgh. The author also acknowledges the useful comments received from the referees that helped improve the paper. Any errors or shortcomings are, of course, the sole responsibility of the author.

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