# Implications of CSR Practices for a Development Supply Chain in Alleviating Farmers’ Poverty

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Development Supply Chain

#### 2.2. CSR Practices in Supply Chains

## 3. Model Assumptions

## 4. Model Analysis

#### 4.1. Model N: The Base Model

**Lemma**

**1.**

**Proposition**

**1.**

#### 4.2. Model S: Model with a Cost-Sharing Retailer

**Lemma**

**2.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proposition**

**4.**

#### 4.3. Model A: Model with an Altruistic Preference Retailer

**Lemma**

**3.**

**Proposition**

**5.**

**Proposition**

**6.**

**Proposition**

**7.**

#### 4.4. Model F: Model with a Fair-Minded Retailer

**Lemma**

**4.**

**Proposition**

**8.**

**Proposition**

**9.**

**Proposition**

**10.**

## 5. Comparison of Four Models

**Proposition**

**11.**

**Proposition**

**12.**

**Proposition**

**13.**

**Proposition**

**14.**

**Proposition**

**15.**

## 6. Numerical Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Proof**

**of**

**Lemma**

**1.**

**Proof**

**of**

**Proposition**

**1.**

**Proof**

**of**

**Lemma**

**2.**

**Proof**

**of**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**3.**

**Proof**

**of**

**Proposition**

**4.**

**Proof**

**of**

**Lemma**

**3.**

**Proof**

**of**

**Proposition**

**5.**

**Proof**

**of**

**Proposition**

**6.**

**Proof**

**of**

**Proposition**

**7.**

**Proof**

**of**

**Lemma**

**4.**

**Proof**

**of**

**Proposition**

**8.**

**Proof**

**of**

**Proposition**

**9.**

**Proof**

**of**

**Proposition**

**10.**

**Proof**

**of**

**Proposition**

**11.**

**Proof**

**of**

**Proposition**

**12.**

**Proof**

**of**

**Proposition**

**13.**

**Proof**

**of**

**Proposition**

**14.**

**Proof**

**of**

**Proposition**

**15.**

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**Figure 2.**(

**a**) Effects of the retailer’s CSR practices on ${w}_{1}$ and ${w}_{2}$. (

**b**) Effects of the retailer’s CSR practices on ${q}_{1}$ and ${q}_{2}$. (

**c**) Effects of the retailer’s CSR practices on ${p}_{1}$ and ${p}_{2}$.

**Figure 3.**(

**a**) Effect of retailer’s CSR practice on ${\pi}_{1}$ and ${\pi}_{2}$. (

**b**) Effect of retailer’s CSR practice on ${\pi}_{R}$. (

**c**) Effect of retailer’s CSR practice on ${\pi}_{SC}$.

**Figure 4.**(

**a**) Effect of $\tau $ and $\Delta $ on supply chain profit under retailer’s cost-sharing practice. (

**b**) Effect of $\theta $ and $\Delta $ on supply chain profit under retailer’s altruistic preference practice. (

**c**) Effect of $\varphi $ and $\Delta $ on supply chain profit under retailer’s fairness concern practice.

Poor Farmer | Supply Chain | Cost-Sharing Practice | Altruistic Preference Practice | Fairness Concern Practice | Competition | Game Theory | |
---|---|---|---|---|---|---|---|

Sodhi & Tang [9] | √ | √ | |||||

Sodhi & Tang [39] | √ | √ | |||||

Zhou et al. [15] | √ | √ | √ | ||||

Chen et al. [16] | √ | √ | √ | ||||

Zhou et al. [20] | √ | √ | √ | √ | |||

Xie et al. [21] | √ | √ | √ | ||||

Wu [40] | √ | √ | √ | ||||

Yu et al. [17] | √ | √ | √ | ||||

Wang et al. [24] | √ | √ | √ | ||||

Wan et al. [25] | √ | √ | √ | √ | |||

Xu & Wang [26] | √ | √ | √ | ||||

Guan et al. [29] | √ | √ | √ | ||||

Zheng et al. [33] | √ | √ | √ | √ | |||

Zhou et al. [34] | √ | √ | √ | ||||

This paper | √ | √ | √ | √ | √ | √ | √ |

CSR Practices | Explanation |
---|---|

Cost-sharing practice | Due to technical and infrastructure disadvantages, the rural farmer pays more than the suburban farmer to grow the same agricultural products. As a CSR practice, the CSR-conscious retailer shares the rural farmer’s cost, but not the suburban farmer’s. |

Altruistic preference practice | The CSR-conscious retailer has altruistic behavior toward the rural farmer but not the suburban farmer. |

Fairness concern practice | Typically, the retailer will order more products from the suburban farmer due to the cost advantage. As a fairness concerns practice, the CSR-conscious retailer tries to order a similar amount from both farmers. |

Notation | Definition |
---|---|

${a}_{i}$ | Market potential of farmers’ products |

$b$ | The quantities sensitivity parameter of two products |

$\gamma $ | The competition intensity of two farmers’ products |

$\kappa $ | The elasticity of market price with regard to CSR performance |

$\mu $ | The cost difference between two farmers’ products |

$\tau $ | The degree of retailer’s cost-sharing practice |

$\theta $ | The degree of retailer’s altruistic preference practice |

$\varphi $ | The degree of retailer’s fairness concern practice |

${p}_{i}^{j}$ | Market prices of the two products |

${w}_{i}^{j}$ | The wholesale price of two products (farmers’ decision variable) |

${q}_{i}^{j}$ | The order quantities of two products (retailer’s decision variable) |

${\pi}_{i}^{j}$ | Profit of two farmers |

${\pi}_{R}^{j}$ | Profit of the retailer |

${\pi}_{SC}^{j}$ | Profit of the supply chain |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Q.; Luo, T.
Implications of CSR Practices for a Development Supply Chain in Alleviating Farmers’ Poverty. *Mathematics* **2022**, *10*, 3762.
https://doi.org/10.3390/math10203762

**AMA Style**

Zhang Q, Luo T.
Implications of CSR Practices for a Development Supply Chain in Alleviating Farmers’ Poverty. *Mathematics*. 2022; 10(20):3762.
https://doi.org/10.3390/math10203762

**Chicago/Turabian Style**

Zhang, Qingyu, and Tianlong Luo.
2022. "Implications of CSR Practices for a Development Supply Chain in Alleviating Farmers’ Poverty" *Mathematics* 10, no. 20: 3762.
https://doi.org/10.3390/math10203762