# Optimal Transport Pricing in an Age of Fully Autonomous Vehicles: Is It Getting More Complicated?

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## Abstract

**:**

## 1. Introduction

## 2. Optimal Transport Tax: Basic Model

#### 2.1. The General Model Setup

#### 2.2. Optimization

#### 2.2.1. Private Optimum

#### 2.2.2. Social Optimum

#### 2.2.3. Optimal Energy Tax

## 3. Optimal Transport Tax: Extended Model

## 4. Optimal Transport Tax: Extended Model with Driverless Vehicle Relocation

## 5. Final Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Derivation of the Marginal Welfare Change

## Appendix B. Derivation of the Optimal Energy Tax

## References

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**Figure 1.**Example of the marginal welfare effect of the gasoline tax and optimal gasoline tax (reproduced from [41]).

Study | Instrument | Region |
---|---|---|

Parry and Small (2005) [8] | Gasoline tax, Miles tax | US, UK |

Santos (2017) [9] | Gasoline tax, Diesel tax | Various European countries |

Parry and Timilsina (2010) [40] | Gasoline tax, Miles tax | Mexico City |

Parry (2011) [41] | Gasoline tax, Diesel tax (heavy-duty trucks) | US |

Tscharaktschiew (2014) [42] | Gasoline tax | Germany |

Tscharaktschiew (2015) [43] | Gasoline tax (with EV substitution) | Germany |

Lin and Prince (2009) [44] | Gasoline tax | California |

Wangsness (2018) [45] | Kilometer tax (peak, off-peak) | Norway (urban, rural) |

West and Williams (2007) [46] | Gasoline tax ${}^{1}$ | US |

Hirte and Tscharaktschiew (2020) [47] | Gasoline tax, Miles tax ${}^{1}$ | US, UK |

Parry (2008) [48] | Diesel tax (heavy-duty trucks) | US |

Parry and Strand (2012) [49] | Gasoline tax, Diesel tax (commercial trucks) | Chile |

Antón-Sarabia and Hernández-Trillo (2014) [50] | Gasoline tax | Mexico |

^{1}Focus on the role of labor supply.

Notation | Description |
---|---|

U | Utility |

X | General consumption |

L | Leisure |

v | Vehicle stock of the household |

m | Vehicle mileage per traveler (occupied trips) |

M | Vehicle mileage per household (occupied trips) |

t | Travel time per mile |

T | Aggregate travel time of the household |

f | Fuel/energy consumption per mile |

F | Aggregate fuel/energy consumption of the household |

E | Externality index |

${p}_{F}$ | Fuel/energy price |

${p}_{X}$ | Price of the composite commodity |

${\tau}_{F}$ | Fuel/energy tax |

$c\left(f\right)$ | Costs of car ownership not related to energy consumption |

I | Household labor income |

$GOV$ | Revenue recycling instrument of the government (tax or transfer) |

$\mathrm{\Gamma}$ | Total time endowment of the household |

$\lambda $ | Marginal utility of monetary household income |

$\theta $ | Value of travel time |

${e}_{F}$ | Marginal external cost of fuel/energy consumption |

${e}_{M}$ | Marginal external cost of vehicle mileage |

W | Welfare |

$\mathrm{\Omega}$ | Set of parameters exogenous to the household |

$\varphi $ | Parking requirement per vehicle |

P | Parking requirement per household |

n | Driverless vehicle mileage per traveler (unoccupied trips) |

N | Driverless vehicle mileage per household (unoccupied trips) |

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**MDPI and ACS Style**

Tscharaktschiew, S.; Evangelinos, C.
Optimal Transport Pricing in an Age of Fully Autonomous Vehicles: Is It Getting More Complicated? *Future Transp.* **2022**, *2*, 347-364.
https://doi.org/10.3390/futuretransp2020019

**AMA Style**

Tscharaktschiew S, Evangelinos C.
Optimal Transport Pricing in an Age of Fully Autonomous Vehicles: Is It Getting More Complicated? *Future Transportation*. 2022; 2(2):347-364.
https://doi.org/10.3390/futuretransp2020019

**Chicago/Turabian Style**

Tscharaktschiew, Stefan, and Christos Evangelinos.
2022. "Optimal Transport Pricing in an Age of Fully Autonomous Vehicles: Is It Getting More Complicated?" *Future Transportation* 2, no. 2: 347-364.
https://doi.org/10.3390/futuretransp2020019