# Pricing and Subsidy Models for Transshipment Sustainability in the Three Gorges Dam Region of China

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## Abstract

**:**

## 1. Introduction

- What is the economic benefit from carriers’ choice of a lockage or transshipment mode when the ship lock approaching channel is congested?
- Given the 3-year subsidies on the transshipment cost provided by the local government, what is the impact on the environmental emissions measured by CO
_{2}? - What are the carriers’ pricing strategies based on profit under different modes with or without the government subsidies and lockage congestion?

## 2. Literature Review

## 3. Model Construction

#### 3.1. Notations

#### 3.2. Formulation of the Basic Model

#### 3.3. Formulation of Mathematical Components

**Corollary**

**1.**

**Proof.**

#### 3.4. Optimization Model Under the Transshipment Mode

**Corollary**

**2.**

**Proof.**

## 4. Results and Analyses

_{,}$\alpha =1$, $\rho =0.035$, ${x}_{1}=0.1$, ${x}_{2}=0.1$, Figure 4 shows that the ${p}_{t}^{*}$ of the transshipment mode goes down sharply when $\beta $ is smaller than 0.2, and descends gradually at a certain level when $\beta $ increases from 0.2 to 1. The curve of ${p}_{l}^{*}$ shows a different trend with minor changes when $\beta $ increases. In Figure 4b,c, two curves are near the coincidence state when $\beta =1$. For the scenario under subsidies and congestion, the freight price ${p}_{t}^{*}$ of the transshipment mode intersects with the freight price ${p}_{l}^{*}$ of the lockage mode when $\beta =0.4$ because the subsidies from the government play an important role in reducing the transshipment cost.

## 5. Conclusions

## 6. Policy Implications

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

## References

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**Figure 9.**Changes in optimal prices (${p}_{{}_{t}}^{*}$) and optimal profits (${\pi}_{{}_{t}}^{*}$) with respect to subsidy ${\eta}_{i}$.

Parameters | Descriptions |
---|---|

$\alpha $ | Market potential, $\alpha >0$ |

$\beta $ | Customer’s price sensitivity $\beta \in [0,1]$ |

$\rho $ | The degree of carriers’ loyalty to the lockage mode, $\rho \in [0,1]$ |

${\eta}_{i}$ | Unit subsidy offered by the government |

${e}_{i}$ | Unit environmental cost (CO2) |

${p}_{i}$ | Freight rate |

${q}_{i}$ | Demand functions |

${c}_{i}^{l}$ | Unit cost of lockage mode |

${c}_{i}^{t}$ | Unit cost of transshipment mode |

${\pi}_{i}^{l}$ | Profit function of lockage mode |

${\pi}_{i}^{t}$ | Profit function of transshipment mode |

$CS$ | Consumer’ surplus |

$S{W}_{i}^{l}$ | Social welfare function of lockage mode |

$S{W}_{i}^{t}$ | Social welfare function of transshipment mode |

${E}_{i}^{l}$ | Unit environment cost of lockage mode |

${E}_{i}^{t}$ | Unit environment cost of transshipment mode |

Unit Freight Volume (100 cars/unit) | 1 | 5 | 8 | |||||||||

Unit Subsidy (100 RMB/car) | 0 | 1 | 1.5 | 2 | 0 | 1 | 1.5 | 2 | 0 | 1 | 1.5 | 2 |

Unit Pricing (100 RMB/car) | 1.019 | 0.545 | 0.308 | 0.071 | 2.254 | 1.780 | 1.543 | 1.307 | 3.180 | 2.707 | 2.470 | 2.233 |

Unit Profit (10 RMB/car) | −0.287 | −0.373 | −0.273 | −0.078 | 1.738 | 0.654 | 0.256 | −0.047 | 4.963 | 3.132 | 2.359 | 1.682 |

Unit Social Welfare (10 RMB/car) * | 0.098 | 0.581 | 0.974 | 1.468 | 0.737 | 0.167 | 0.034 | 0.016 | 3.017 | 1.658 | 1.130 | 0.703 |

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**MDPI and ACS Style**

Yang, L.; Li, E.Y.; Zhang, Y.
Pricing and Subsidy Models for Transshipment Sustainability in the Three Gorges Dam Region of China. *Sustainability* **2020**, *12*, 7026.
https://doi.org/10.3390/su12177026

**AMA Style**

Yang L, Li EY, Zhang Y.
Pricing and Subsidy Models for Transshipment Sustainability in the Three Gorges Dam Region of China. *Sustainability*. 2020; 12(17):7026.
https://doi.org/10.3390/su12177026

**Chicago/Turabian Style**

Yang, Lijuan, Eldon Y. Li, and Yu Zhang.
2020. "Pricing and Subsidy Models for Transshipment Sustainability in the Three Gorges Dam Region of China" *Sustainability* 12, no. 17: 7026.
https://doi.org/10.3390/su12177026