# How Do Consumer Fairness Concerns Affect an E-Commerce Platform’s Choice of Selling Scheme?

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*J. Theor. Appl. Electron. Commer. Res.*

**2022**,

*17*(3), 1075-1106; https://doi.org/10.3390/jtaer17030055

## Abstract

**:**

## 1. Introduction

- (1)
- In the presence of consumer fairness concerns, what is the strategic selling scheme for an e-commerce platform?
- (2)
- Is the e-commerce platform more inclined to adopt a novel platform pricing scheme rather than a traditional wholesale pricing scheme, and, if so, under what conditions?
- (3)
- Which pricing scheme would be preferred by the upstream manufacturer?
- (4)
- How does the interaction between fairness concerns and an e-commerce platform’s selling scheme choice affect consumer surplus and social welfare?

## 2. Literature Review

#### 2.1. Fairness Concerns in Distribution Channel Management

#### 2.2. Selling Scheme Choice in Platform Retailing

## 3. Model

#### 3.1. Supply Chain Structure

#### 3.2. Consumer Behavior Analysis and Demand Functions

## 4. Analysis

#### 4.1. Wholesale Selling Scheme

**Lemma**

**1.**

#### 4.2. Agency Selling Scheme

**Lemma**

**2.**

**Proposition**

**1.**

- (a)
- The market demand ${D}_{a}^{*}$ decreases and the retail price ${p}_{a}^{*}$ increases with the platform fee $r$.
- (b)
- The profits of the manufacturer and the supply chain system decrease with the platform fee $r$. However, there exists a threshold value for the platform fee $\overline{r}$. If the platform fee is lower than the threshold value (i.e., $r<\overline{r}$), the profit of the platform increases with $r$, whereas, if the platform fee is higher than the threshold value (i.e., $r>\overline{r}$), the profit of the platform decreases with $r$.

## 5. Comparison

#### 5.1. Market Share

**Proposition**

**2.**

#### 5.2. Retail Price

**Proposition**

**3.**

#### 5.3. Profit

**Proposition**

**4.**

- (a)
- For a lower platform fee (i.e.,$\frac{2-\sqrt{2}}{8}<\lambda \le \frac{2-\sqrt{4}}{4}$),
- (1)
- If the fairness concern intensity is relatively low (i.e., $0<\lambda \le {\lambda}_{1}$), then${\pi}_{w}^{{p}^{*}}>{\pi}_{a}^{{p}^{*}}$;
- (2)
- If the fairness concern intensity is relatively high (i.e.,$\lambda >{\lambda}_{1}$), then${\pi}_{w}^{{p}^{*}}<{\pi}_{a}^{{p}^{*}}$.

- (b)
- For a higher platform fee (i.e.,$\frac{2+\sqrt{2}}{8}<\lambda \le \frac{2+\sqrt{4}}{4}$),
- (1)
- If the fairness concern intensity is relatively low (i.e.,$0\lambda \le {\lambda}_{2}$), then${\pi}_{w}^{{p}^{*}}<{\pi}_{a}^{{p}^{*}}$;
- (2)
- If the fairness concern intensity is relatively high (i.e.,$\lambda >{\lambda}_{2}$), then${\pi}_{w}^{{p}^{*}}>{\pi}_{a}^{{p}^{*}}$.

**Proposition**

**5.**

- (a)
- When the platform fee is relatively low (i.e.,$0<r\le \frac{2-\sqrt{2}}{4}$), then${\pi}_{a}^{{m}^{*}}>{\pi}_{w}^{{m}^{*}}$.
- (b)
- When the platform fee is relatively high (i.e.,$\frac{2+\sqrt{2}}{4}<r<$1), then${\pi}_{a}^{{m}^{*}}<{\pi}_{w}^{{m}^{*}}$.
- (c)
- When the platform fee is in the intermediate range (i.e.,$\frac{2-\sqrt{2}}{4}<r<\frac{2+\sqrt{2}}{4}$),
- (1)
- If the fairness concern intensity is sufficiently low (i.e.,$0<\lambda <{\lambda}_{3}$), then${\pi}_{a}^{{m}^{*}}>{\pi}_{w}^{{m}^{*}}$;
- (2)
- If the fairness concern intensity is sufficiently high (i.e.,$\lambda {\lambda}_{3}$), then${\pi}_{a}^{{m}^{*}}<{\pi}_{w}^{{m}^{*}}$.

**Proposition**

**6.**

- (a)
- For a lower platform fee (i.e.,$\frac{2-\sqrt{2}}{8}<r<\frac{2-\sqrt{2}}{4}$),
- (1)
- If the intensity of fairness concern is relatively low (i.e., $0<\lambda <max\left\{{\lambda}_{1},{\lambda}_{3}\right\}$), then the wholesale selling scheme is the dominant strategy for the whole supply chain;
- (2)
- If the intensity of fairness concern is relatively high (i.e., $\lambda >max\left\{{\lambda}_{1},{\lambda}_{3}\right\}$), then both the upstream manufacturer and the downstream platform prefer to choose the agency selling scheme.

- (b)
- For a higher platform fee (i.e.,$\frac{2+\sqrt{2}}{8}<r<\frac{2+\sqrt{2}}{4}$),
- (1)
- If the intensity of fairness concern is relatively low (i.e., $0<\lambda <max\left\{{\lambda}_{2},{\lambda}_{3}\right\}$), then the agency selling scheme is the dominant strategy for the whole supply chain;
- (2)
- If the intensity of fairness concern is relatively high (i.e., $\lambda >max\left\{{\lambda}_{2},{\lambda}_{3}\right\}$), then both the upstream manufacturer and the downstream platform prefer to adopt the wholesale selling scheme.

#### 5.4. Consumer Surplus and Social Welfare

**Proposition**

**7.**

## 6. Extensions

#### 6.1. Consumer Heterogeneity

#### 6.1.1. Wholesale Selling Scheme

**Lemma**

**3.**

**Corollary**

**1.**

#### 6.1.2. Agency Selling Scheme

**Lemma**

**4.**

**Proposition**

**8.**

- (a)
- $\frac{\partial {p}_{a}^{*}}{\partial \beta}<0$, $\frac{\partial {D}_{a}^{*}}{\partial \beta}<0$, and $\frac{\partial {\pi}_{a}^{{p}^{*}}}{\partial \beta}<0$.
- (b)
- If the fraction $\beta $ of the fairness-minded consumer is large (i.e., $\beta >\frac{\left(1-r\right)\left(\lambda +1\right)}{r\lambda}$), then $\frac{\partial {\pi}_{a}^{{m}^{*}}}{\partial \beta}>0$. However, if the fraction $\beta $ of the fairness-minded consumer is small (i.e., $\beta <\frac{\left(1-r\right)\left(\lambda +1\right)}{r\lambda}$), then $\frac{\partial {\pi}_{a}^{{m}^{*}}}{\partial \beta}<0$.

#### 6.1.3. Comparison

**Corollary**

**2.**

**Corollary**

**3.**

#### 6.2. Proportional Platform Fee

**Lemma**

**5.**

**Proposition**

**9.**

#### 6.3. Fairness Concern about the Manufacturer’s Profit

**Lemma**

**6.**

- (a)
- Under the wholesale selling scheme, the manufacturer charges the wholesale price ${w}^{*}=\frac{\lambda +1}{2\left(2\lambda +1\right)}$ and the platform determines the retail price ${p}_{w}^{*}=\frac{4\lambda +3}{4\left(2\lambda +1\right)}$. The market share is ${D}_{w}^{*}=\frac{1}{4}$. The profits of the manufacturer, platform, and supply chain system are ${\pi}_{w}^{{m}^{*}}=\frac{\lambda +1}{8\left(2\lambda +1\right)}$, ${\pi}_{w}^{{p}^{*}}=\frac{1}{16}$, and ${\pi}_{w}^{*}=\frac{4\lambda +3}{16\left(2\lambda +1\right)}$, respectively.
- (b)
- Under the agency selling scheme, the manufacturer charges the retail price ${p}_{a}=\frac{2\lambda r+r+1}{2\left(\lambda +1\right)}$. The market share is ${D}_{a}=\frac{1-r}{2\left(\lambda +1\right)}$. The optimal profits of the manufacturer, the platform, and the supply chain system are ${\pi}_{a}^{m*}=\frac{{\left(1-r\right)}^{2}}{4{\left(\lambda +1\right)}^{2}}$, ${\pi}_{a}^{p*}=\frac{r\left(1-r\right)}{2\left(\lambda +1\right)}$, and ${\pi}_{a}^{*}=\frac{\left(1-r\right)\left(2\lambda r+r+1\right)}{4{\left(\lambda +1\right)}^{2}}$, respectively.

#### 6.4. Endogenous Platform Fee

**Proposition**

**10.**

- (a)
- The optimal platform fee is ${r}_{E}=\frac{\eta \left(\lambda +1\right)}{2\left(2\lambda +1\right)}$.
- (b)
- For $0\le \eta \le 1$, the optimal platform fee ${r}_{E}$ increases with the bargaining power of the platform (i.e., $\frac{\partial {r}_{E}}{\partial \eta}>0$) and decreases with the intensity of consumer fairness concern (i.e., $\frac{\partial {r}_{E}}{\partial \lambda}<0$).

## 7. Discussion

## 8. Conclusions and Management Insights

#### 8.1. Conclusions

#### 8.2. Management Insights

#### 8.3. Future Research Directions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Proof of Lemma**

**1.**

**Proof of Lemma**

**2.**

**Proof of Proposition**

**1.**

- (a)
- For the market demand and the retail price, we have $\begin{array}{c}\frac{\partial {D}_{a}^{*}}{\partial r}=-\frac{2\lambda +1}{2\left(\lambda +1\right)}<0\end{array}$ and $\begin{array}{c}\frac{\partial {p}_{a}^{*}}{\partial r}=\frac{1}{2\left(\lambda +1\right)}>0\end{array}$.
- (b)
- For the profits of the manufacturer and supply chain system, we have $\begin{array}{c}\frac{\partial {\pi}_{a}^{m*}}{\partial r}=-\frac{\left(2\lambda +1\right)\left(1+\lambda -\left(2\lambda +1\right)r\right)}{2{(\lambda +1)}^{2}}\end{array}<0$ and $\begin{array}{c}\frac{\partial {\pi}_{a}^{*}}{\partial r}=-\frac{{\lambda}^{2}+\left(2r+1\right)\lambda +r}{2{(\lambda +1)}^{2}}<0\end{array}$. For the profit of the platform, we obtain that $\begin{array}{c}\frac{\partial {\pi}_{a}^{{p}^{*}}}{\partial r}=\frac{\lambda +1-2\left(2\lambda +1\right)r}{2\left(1+\lambda \right)}\end{array}$. If $\begin{array}{c}r\le \frac{\lambda +1}{2\left(2\lambda +1\right)}\end{array}$, then $\begin{array}{c}\frac{\partial {\pi}_{a}^{p*}}{\partial r}\ge 0\end{array}$. If $\begin{array}{c}\frac{\lambda +1}{2\left(2\lambda +1\right)}<r<\frac{\lambda +1}{2\lambda +1}\end{array}$, then $\begin{array}{c}\frac{\partial {\pi}_{a}^{p*}}{\partial r}<0\end{array}$. □

**Proof of Proposition**

**2.**

**Proof of Proposition**

**3.**

**Proof of Proposition**

**4.**

- (a)
- When $\begin{array}{c}\frac{2-\sqrt{2}}{8}<r\le \frac{2-\sqrt{2}}{4}\end{array}$, if $\begin{array}{c}0\lambda {\lambda}_{1}\end{array}$, then$\begin{array}{c}{\pi}_{w}^{p*}{\pi}_{a}^{p*}\end{array}$. Otherwise, $\begin{array}{c}{\pi}_{w}^{p*}<{\pi}_{a}^{p*}\end{array}$.
- (b)
- When $\begin{array}{c}\frac{2+\sqrt{2}}{8}<r\le \frac{2+\sqrt{2}}{4}\end{array}$, if $\begin{array}{c}0\lambda {\lambda}_{2}\end{array}$, then$\begin{array}{c}{\pi}_{w}^{p*}{\pi}_{a}^{p*}\end{array}$. Otherwise, $\begin{array}{c}{\pi}_{w}^{p*}>{\pi}_{a}^{p*}\end{array}$. □

**Proof of Proposition**

**5.**

- (a)
- When $\begin{array}{c}0<r\le \frac{2-\sqrt{2}}{4}\end{array}$, then $\begin{array}{c}{\pi}_{a}^{m*}>{\pi}_{w}^{m*}\end{array}$.
- (b)
- When $\begin{array}{c}\frac{2-\sqrt{2}}{4}<r\le \frac{2+\sqrt{2}}{4}\end{array}$, if $\begin{array}{c}0<\lambda <{\lambda}_{3}\end{array}$, then $\begin{array}{c}{\pi}_{a}^{m*}>{\pi}_{w}^{m*}\end{array}$. Otherwise, $\begin{array}{c}{\pi}_{a}^{m*}<{\pi}_{w}^{m*}.\end{array}$
- (c)
- When $\begin{array}{c}\frac{2+\sqrt{2}}{4}<r\le 1\end{array}$, then$\begin{array}{c}{\pi}_{a}^{m*}{\pi}_{w}^{m*}\end{array}$. □

**Proof of Proposition**

**6.**

**Proof of Proposition**

**7.**

**Proof of Lemma**

**3.**

**Proof of Corollary**

**1.**

**Proof of Lemma**

**4.**

**Proof of Proposition**

**8.**

- (a)
- $\begin{array}{c}\frac{\partial {p}_{a}^{*}}{\partial \beta}=-\frac{r\lambda}{2\left(\lambda +1\right)}<0\end{array}$, $\begin{array}{c}\frac{\partial {D}_{a}^{*}}{\partial \beta}=-\frac{r\lambda}{2\left(\lambda +1\right)}<0\end{array}$, and $\begin{array}{c}\frac{\partial {\pi}_{a}^{p*}}{\partial \beta}=-\frac{\lambda {r}^{2}}{2\left(\lambda +1\right)}<0\end{array}$.
- (b)
- Notice that $\begin{array}{c}\frac{\partial {\pi}_{a}^{m*}}{\partial \beta}=\frac{\beta r\lambda -\left(1-r\right)\left(1+\lambda \right)}{2{(1+\lambda )}^{2}}\end{array}$. When the fraction$\beta $ of the fairness-minded consumer is large (i.e., $\begin{array}{c}\beta >\frac{\left(1-r\right)\left(\lambda +1\right)}{r\lambda}\end{array}$), then $\begin{array}{c}\frac{\partial {\pi}_{a}^{m*}}{\partial \beta}>0\end{array}$. When the fraction $\beta $ of the fairness-minded consumer is small (i.e., $\begin{array}{c}\beta <\frac{\left(1-r\right)\left(\lambda +1\right)}{r\lambda}\end{array}$), then $\begin{array}{c}\frac{\partial {\pi}_{a}^{m*}}{\partial \beta}<0\end{array}$. □

**Proof of Corollary**

**2.**

**Proof of Corollary**

**3.**

**Proof of Lemma**

**5.**

**Proof of Proposition**

**9.**

**Proof of Lemma**

**6.**

**Proof of Proposition**

**10.**

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Notations | Parameters |
---|---|

$i$ | Index of selling scheme, $i\in \left\{w,a\right\}$ |

$\theta $ | Reservation value, which is uniformly distributed between 0 and 1 |

$\lambda $ | Intensity of fairness concern |

$r$ | Platform fee |

${U}_{i}$ | Consumer utility depending on the platform’s selling scheme |

${D}_{i}$ | Consumer demand depending on the platform’s selling scheme |

${\pi}_{i}^{m}$ | Profit of manufacturer under different selling schemes |

${\pi}_{i}^{p}$ | Profit of platform under different selling schemes |

${\pi}_{i}$ | Profit of the supply chain system under different selling schemes |

$C{S}_{i}$ | Consumer surplus under different selling schemes |

$S{W}_{i}$ | Total social welfare under different selling schemes |

Decision Variables | |

$w$ | Wholesale price of product |

${p}_{i}$ | Retail price of product depending on the platform’s selling scheme |

Articles | Selling Scheme | Fairness Concern Type | Research Method |
---|---|---|---|

Zhang et al. [5] | Wholesale vs. Agency | Fairness-neutral | Nash equilibrium |

Yi et al. [19] | Agent vs. Direct | Consumer fairness concern | Rational expectation equilibrium |

Huang et al. [41] | Self-operated vs. Direct | Consumer fairness concern | Rational expectation equilibrium |

Kwark et al. [49] | Wholesale vs. Agency | Fairness-neutral | Nash equilibrium |

This paper | Wholesale vs. Agency | Consumer fairness concern | Rational expectation equilibrium |

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**MDPI and ACS Style**

Chen, L.; Nan, G.; Liu, Q.; Peng, J.; Ming, J.
How Do Consumer Fairness Concerns Affect an E-Commerce Platform’s Choice of Selling Scheme? *J. Theor. Appl. Electron. Commer. Res.* **2022**, *17*, 1075-1106.
https://doi.org/10.3390/jtaer17030055

**AMA Style**

Chen L, Nan G, Liu Q, Peng J, Ming J.
How Do Consumer Fairness Concerns Affect an E-Commerce Platform’s Choice of Selling Scheme? *Journal of Theoretical and Applied Electronic Commerce Research*. 2022; 17(3):1075-1106.
https://doi.org/10.3390/jtaer17030055

**Chicago/Turabian Style**

Chen, Lin, Guofang Nan, Qiurui Liu, Jin Peng, and Junren Ming.
2022. "How Do Consumer Fairness Concerns Affect an E-Commerce Platform’s Choice of Selling Scheme?" *Journal of Theoretical and Applied Electronic Commerce Research* 17, no. 3: 1075-1106.
https://doi.org/10.3390/jtaer17030055