# Economic and Environmental Performance of Fashion Supply Chain: The Joint Effect of Power Structure and Sustainable Investment

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Modeling Framework

- The manufacturer makes sustainable investment.$${\Pi}_{r}^{m}\left(p\right)=\left(p-w\right)Q=\left(p-w\right)\left(\alpha -\beta p+\gamma e\right)$$$${\Pi}_{m}^{m}\left(w,e\right)=\left(w-c-T\left(e\right)\right)Q-I\left(e\right)=\left(w-c+te\right)\left(\alpha -\beta \left(w+m\right)+\gamma e\right)-\lambda {e}^{2}$$
- The retailer makes sustainable investment.$${\Pi}_{r}^{r}\left(p,e\right)=\left(p-w\right)Q-I\left(e\right)=\left(p-w\right)\left(\alpha -\beta p+\gamma e\right)-\lambda {e}^{2}$$$${\Pi}_{m}^{r}\left(w\right)=\left(w-c-T\left(e\right)\right)Q=\left(w-c+te\right)\left(\alpha -\beta \left(w+m\right)+\gamma e\right)$$

## 4. The Manufacturer Makes Sustainable Investment

**Lemma**

**1.**

**Proposition**

**1.**

**Corollary**

**1.**

## 5. The Retailer Makes Sustainable Investment

**Lemma**

**2.**

**Proposition**

**2.**

**Corollary**

**2.**

## 6. The Supply Chain Members’ Sustainable Investment Decisions

**Lemma**

**3.**

**Proposition**

**3.**

- 1.
- In the MS power structure, the retailer benefits from her sustainable investment if the investment factor is relatively low (i.e., ${\Pi}_{r}^{r}\left({p}_{m}^{r},{e}_{m}^{r}\right)>{\Pi}_{r}^{m}\left({p}_{m}^{m}\right)$, if $\lambda <\widehat{\lambda}$), where:$$\widehat{\lambda}=\frac{{\left(\gamma +\beta t\right)}^{2}\sqrt{4\beta \widehat{\lambda}-{\gamma}^{2}}}{8{\beta}^{2}t}.$$
- 2.
- In the VN power structure, the retailer benefits from the manufacturer’s sustainable investment (i.e., ${\Pi}_{r}^{r}\left({p}_{n}^{r},{e}_{n}^{r}\right)<{\Pi}_{r}^{m}\left({p}_{n}^{m}\right)$). The manufacturer’s profit is higher when the retailer makes sustainable investment (i.e., ${\Pi}_{m}^{m}\left({w}_{n}^{m},{e}_{n}^{m}\right)<{\Pi}_{m}^{r}\left({w}_{n}^{r}\right)$).
- 3.
- In the RS power structure, the optimal profits of both the retailer and the manufacturer are higher when the manufacturer makes sustainable investment (i.e., ${\Pi}_{m}^{m}\left({w}_{r}^{m},{e}_{r}^{m}\right)>{\Pi}_{m}^{r}\left({w}_{r}^{r}\right)$ and ${\Pi}_{r}^{r}\left({p}_{r}^{r},{e}_{r}^{r}\right)<{\Pi}_{r}^{m}\left({p}_{r}^{m}\right)$).

**Proposition**

**4.**

- 1.
- In the MS power structure, the manufacturer’s sustainable investment is higher than the retailer’s (i.e., ${e}_{m}^{m}>{e}_{m}^{r}$) if $\gamma <\widehat{\gamma}$, while the retailer makes higher investment (i.e., ${e}_{m}^{r}\ge {e}_{m}^{m}$if $\gamma \ge \widehat{\gamma}$. Here, $\widehat{\gamma}$ is obtained by solving the following equation: $8t\lambda {\beta}^{2}-\gamma {\left(\gamma +t\beta \right)}^{2}=0.$
- 2.
- In the VN power structure, the manufacturer’s sustainable investment is higher than the retailer’s (i.e., ${e}_{n}^{m}>{e}_{n}^{r}$);
- 3.
- In the RS power structure, the manufacturer’s sustainable investment is higher than the retailer’s (i.e., ${e}_{r}^{m}>{e}_{r}^{r}$).

## 7. Conclusions and Future Research

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Proof of Lemma**

**1.**

**Proof of Proposition**

**1.**

- From Lemma 1, we have ${w}_{n}^{m}-{w}_{m}^{m}=\frac{2\lambda \left(\alpha -\beta c\right)\left({\gamma}^{2}+\beta \gamma t-4\lambda \beta \right)}{[8\beta \lambda -{\left(\gamma +\beta t\right)}^{2}][6\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}<0,$ that is ${w}_{m}^{m}>{w}_{n}^{m}$. Similarly, from Lemma 1, we have ${w}_{n}^{m}-{w}_{r}^{m}=\frac{\left(\alpha -\beta c\right)\left(2\lambda -\beta {t}^{2}-\gamma t\right)[2\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}{[8\beta \lambda -2{\left(\gamma +\beta t\right)}^{2}][6\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}>0$, that is ${w}_{n}^{m}>{w}_{r}^{m}$. Thus, ${\mathrm{w}}_{m}^{m}>{w}_{n}^{m}>{w}_{r}^{m}$.
- From Lemma 1, we have ${e}_{n}^{m}-{e}_{r}^{m}=\frac{\left(\alpha -\beta c\right)\left(\gamma +\beta t\right)[2\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}{[8\beta \lambda -2{\left(\gamma +\beta t\right)}^{2}][6\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}>0$, that is ${e}_{n}^{m}>{e}_{r}^{m}$. Similarly, we have ${e}_{r}^{m}-{e}_{m}^{m}=\frac{\left(\alpha -\beta c\right)\left(\gamma +\beta t\right){\left(\gamma +\beta t\right)}^{2}}{[8\beta \lambda -{\left(\gamma +\beta t\right)}^{2}][8\beta \lambda -2{\left(\gamma +\beta t\right)}^{2}]}>0$, that is, ${e}_{r}^{m}>{e}_{m}^{m}$. Thus, ${e}_{n}^{m}>{e}_{r}^{m}>{e}_{m}^{m}$.
- From Lemma 1, we have ${p}_{m}^{m}-{p}_{r}^{m}=\frac{\left(\alpha -\beta c\right)\left(2\beta \lambda -{\gamma}^{2}-\beta \gamma t\right){\left(\gamma +\beta t\right)}^{2}}{\beta [8\beta \lambda -2{\left(\gamma +\beta t\right)}^{2}][8\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}>0$, that is ${p}_{m}^{m}>{p}_{r}^{m}$. Similarly, we have ${p}_{r}^{m}-{p}_{n}^{m}=\frac{\left(\alpha -\beta c\right)[2\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]\left(2\beta \lambda -{\gamma}^{2}-\beta \gamma t\right)}{\beta [8\beta \lambda -2{\left(\gamma +\beta t\right)}^{2}][6\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}>0$, that is ${p}_{r}^{m}>{p}_{n}^{m}$, so ${p}_{m}^{m}>{p}_{r}^{m}>{p}_{n}^{m}$. This completes the proof.

**Proof of Corollary**

**1.**

- From Lemma 1 and Equation (4), we obtain the manufacturer’s optimal profit in a MS power structure as ${\pi}_{m}^{m}\left({w}_{m}^{m},{e}_{m}^{m}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$. The manufacturer’s optimal profit in a VN power structure is ${\pi}_{m}^{m}\left({w}_{n}^{m},{e}_{n}^{m}\right)=\frac{[4{\lambda}^{2}\beta -\lambda {\left(\gamma +t\beta \right)}^{2}]{\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$, and his optimal profit in a RS power structure is ${\pi}_{m}^{m}\left({w}_{r}^{m},{e}_{r}^{m}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{4[4\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}$. Then ${\pi}_{m}^{m}\left({w}_{m}^{m},{e}_{m}^{m}\right)-{\pi}_{m}^{m}\left({w}_{n}^{m},{e}_{n}^{m}\right)=\frac{4{\beta}^{2}{\lambda}^{3}{\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}>0$, so that, ${\pi}_{m}^{m}\left({w}_{m}^{m},{e}_{m}^{m}\right)>{\pi}_{m}^{m}\left({w}_{n}^{m},{e}_{n}^{m}\right)$. Similarly, ${\pi}_{m}^{m}\left({w}_{n}^{m},{e}_{n}^{m}\right)-{\pi}_{m}^{m}\left({w}_{r}^{m},{e}_{r}^{m}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}[14\beta \lambda -3{\left(\gamma +t\beta \right)}^{2}][2\beta \lambda -{\left(\gamma +t\beta \right)}^{2}]}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}{[8\lambda \beta -2{\left(\gamma +t\beta \right)}^{2}]}^{2}}>0$, therefore, ${\pi}_{m}^{m}\left({w}_{n}^{m},{e}_{n}^{m}\right)>{\pi}_{m}^{m}\left({w}_{r}^{m},{e}_{r}^{m}\right)$. Then ${\pi}_{m}^{m}\left({w}_{m}^{m},{e}_{m}^{m}\right)>{\pi}_{m}^{m}\left({w}_{n}^{m},{e}_{n}^{m}\right)>{\pi}_{m}^{m}\left({w}_{r}^{m},{e}_{r}^{m}\right)$.
- From Lemma 1 and Equation (3), notice that the retailer’s maximum profit in a MS power structure is ${\pi}_{r}^{m}\left({p}_{m}^{m}\right)=\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$. Her optimal profits in a VN power structure and in a RS power structure are: ${\pi}_{r}^{m}\left({p}_{n}^{m}\right)=\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$ and ${\pi}_{r}^{m}\left({p}_{r}^{m}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{8\lambda \beta -2{\left(\gamma +t\beta \right)}^{2}}$, respectively. We have ${\pi}_{r}^{m}\left({p}_{n}^{m}\right)-{\pi}_{r}^{m}\left({p}_{m}^{m}\right)=\frac{16{\beta}^{2}{\lambda}^{3}{\left(\alpha -\beta c\right)}^{2}[7\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}>0$, so ${\pi}_{r}^{m}\left({p}_{n}^{m}\right)>{\pi}_{r}^{m}\left({p}_{m}^{m}\right)$. Similarly, ${\pi}_{r}^{m}\left({p}_{r}^{m}\right)-{\pi}_{r}^{m}\left({p}_{n}^{m}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}{[2\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}[8\lambda \beta -2{\left(\gamma +t\beta \right)}^{2}]}>0$, hence, ${\pi}_{r}^{m}\left({p}_{r}^{m}\right)>{\pi}_{r}^{m}\left({p}_{n}^{m}\right)$. Then, ${\pi}_{r}^{m}\left({p}_{r}^{m}\right)>{\pi}_{r}^{m}\left({p}_{n}^{m}\right)>{\pi}_{r}^{m}\left({p}_{m}^{m}\right)$.

**Proof of Lemma**

**2.**

**Proof of Proposition**

**2.**

- 1.
- From Lemma 2, we have ${w}_{m}^{r}-{w}_{n}^{r}=\frac{\left(\alpha -\beta c\right)[{\gamma}^{2}\left({\gamma}^{2}-{\beta}^{2}{t}^{2}+6\beta \lambda \right)+2\beta \lambda \left(4\beta \lambda -\beta \gamma t\right)]}{2\beta [4\beta \lambda -\gamma \left(\gamma +\beta t\right)][6\beta \lambda -\gamma \left(\gamma +\beta t\right)]}>0$, then ${w}_{m}^{r}>{w}_{n}^{r}$. Similarly, we have ${w}_{n}^{r}-{w}_{r}^{r}=\frac{4\beta \lambda \left(\alpha -\beta c\right)\left(\lambda +\beta {t}^{2}-\gamma t\right)}{[8\beta \lambda -{\left(\gamma +\beta t\right)}^{2}][6\beta \lambda -\gamma \left(\gamma +\beta t\right)]}>0$, that is ${w}_{n}^{r}>{w}_{r}^{r}$. Thus, ${w}_{m}^{r}>{w}_{n}^{r}>{w}_{r}^{r}$.
- 2.
- From Lemma 2, ${e}_{n}^{r}-{e}_{m}^{r}=\frac{\gamma \left(\alpha -\beta c\right)[2\beta \lambda -\gamma \left(\gamma +\beta t\right)]}{2[4\beta \lambda -\gamma \left(\gamma +\beta t\right)][6\beta \lambda -\gamma \left(\gamma +\beta t\right)]}>0$, then we have: ${e}_{n}^{r}>{e}_{m}^{r}$. Similarly, we have ${e}_{n}^{r}-{e}_{r}^{r}=\frac{2\beta \lambda \left(\alpha -\beta c\right)\left(\gamma -3\beta t\right)}{[6\beta \lambda -\gamma \left(\gamma +\beta t\right)][8\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}$.
- (1)
- If $\gamma <3\beta t$, the above equation is negative, we have ${e}_{r}^{r}>{e}_{n}^{r}>{e}_{m}^{r}$.
- (2)
- If $\gamma >3\beta t$, the above equation is positive, we have ${e}_{n}^{r}>{e}_{r}^{r}$.

From Lemma 2, we have ${e}_{r}^{r}-{e}_{m}^{r}=\frac{\left(\alpha -\beta c\right)[8{\beta}^{2}\lambda t-\gamma {\left(\gamma +\beta t\right)}^{2}]}{2[4\beta \lambda -\gamma \left(\gamma +\beta t\right)][8\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}$.

- 3.
- From Lemma 2, we have ${p}_{m}^{r}-{p}_{n}^{r}=\frac{\left(\alpha -\beta c\right)[2\beta \lambda -\gamma \left(\gamma +\beta t\right)]\left(2\beta \lambda -{\gamma}^{2}\right)}{2\beta [4\beta \lambda -\gamma \left(\gamma +\beta t\right)][6\beta \lambda -\gamma \left(\gamma +\beta t\right)]}>0$, that is ${p}_{m}^{r}>{p}_{n}^{r}$. Similarly, we have: ${p}_{r}^{r}-{p}_{m}^{r}=\frac{\left(\alpha -\beta c\right)\left\{{\gamma}^{2}[2\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]+2{\beta}^{2}\lambda t\left(4\gamma -\beta t\right)\right\}}{2\beta [4\beta \lambda -\gamma \left(\gamma +\beta t\right)][8\beta \lambda -{\left(\gamma +\beta t\right)}^{2}]}>0$, that is ${p}_{r}^{r}>{p}_{m}^{r}$. Then, ${p}_{r}^{r}>{p}_{m}^{r}>{p}_{n}^{r}$ holds. This completes the proof.

**Proof of Corollary**

**2.**

- From Lemma 2 and Equation (6), the manufacturer’s optimal profit in a MS power structure is ${\pi}_{m}^{r}\left({w}_{m}^{r}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{8\lambda \beta -2\gamma \left(\gamma +t\beta \right)}$. His optimal profits in a VN power structure and in a RS power structure are ${\pi}_{m}^{r}\left({w}_{n}^{r}\right)=\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}}$ and ${\pi}_{m}^{r}\left({w}_{r}^{r}\right)=\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$, respectively. We have ${\pi}_{m}^{r}\left({w}_{m}^{r}\right)-{\pi}_{m}^{r}\left({w}_{n}^{r}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}{[2\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}[8\lambda \beta -2\gamma \left(\gamma +t\beta \right)]}>0$, so ${\pi}_{m}^{r}\left({w}_{m}^{r}\right)>{\pi}_{m}^{r}\left({w}_{n}^{r}\right)$. Similarly, ${\pi}_{m}^{r}\left({w}_{n}^{r}\right)-{\pi}_{m}^{r}\left({w}_{r}^{r}\right)=\frac{4\beta \lambda {\left(\alpha -\beta c\right)}^{2}[2\beta \lambda -\beta t\left(\gamma +t\beta \right)][14\beta \lambda -{\left(\gamma +t\beta \right)}^{2}-\gamma \left(\gamma +t\beta \right)]}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}>0$, so ${\pi}_{m}^{r}\left({w}_{n}^{r}\right)>{\pi}_{m}^{r}\left({w}_{r}^{r}\right)$. Then, ${\pi}_{m}^{r}\left({w}_{m}^{r}\right)>{\pi}_{m}^{r}\left({w}_{n}^{r}\right)>{\pi}_{m}^{r}\left({w}_{r}^{r}\right)$.
- From Lemma 2 and Equation (3), we have the retailer’s optimal profit in a MS power structure is ${\pi}_{r}^{r}\left({p}_{m}^{r},{e}_{m}^{r}\right)=\frac{\lambda \left(4\lambda \beta -{\gamma}^{2}\right){\left(\alpha -\beta c\right)}^{2}}{4{[4\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}}$. Her optimal profits in a VN power structure and in a RS structure are ${\pi}_{r}^{r}\left({p}_{n}^{r},{e}_{n}^{r}\right)=\frac{\lambda \left(4\lambda \beta -{\gamma}^{2}\right){\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}}$ and ${\pi}_{r}^{r}\left({p}_{r}^{r},{e}_{r}^{r}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$, respectively. We have ${\pi}_{r}^{r}\left({p}_{n}^{r},{e}_{n}^{r}\right)-{\pi}_{r}^{r}\left({p}_{m}^{r},{e}_{m}^{r}\right)=\frac{\lambda {\left(\alpha -\beta c\right)}^{2}\left(4\lambda \beta -{\gamma}^{2}\right)[14\beta \lambda -3\gamma \left(\gamma +t\beta \right)][2\beta \lambda -\gamma \left(\gamma +t\beta \right)]}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}{[8\lambda \beta -2\gamma \left(\gamma +t\beta \right)]}^{2}}>0$, so ${\pi}_{r}^{r}\left({p}_{n}^{r},{e}_{n}^{r}\right)>{\pi}_{r}^{r}\left({p}_{m}^{r},{e}_{m}^{r}\right)$. Similarly, ${\pi}_{r}^{r}\left({p}_{r}^{r},{e}_{r}^{r}\right)-{\pi}_{r}^{r}\left({p}_{n}^{r},{e}_{n}^{r}\right)=\frac{4\beta {\lambda}^{2}{\left(\alpha -\beta c\right)}^{2}\left(\beta \lambda +6{\gamma}^{2}+{\beta}^{2}{t}^{2}-\beta \gamma t\right)}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}>0$, so ${\pi}_{r}^{r}\left({p}_{r}^{r},{e}_{r}^{r}\right)>{\pi}_{r}^{r}\left({p}_{n}^{r},{e}_{n}^{r}\right)$. Then, ${\pi}_{r}^{r}\left({p}_{r}^{r},{e}_{r}^{r}\right)>{\pi}_{r}^{r}\left({p}_{n}^{r},{e}_{n}^{r}\right)>{\pi}_{r}^{r}\left({p}_{m}^{r},{e}_{m}^{r}\right)$.This completes the proof.

**Proof of Lemma**

**3.**

**Proof of Proposition**

**3.**

**Proof of Proposition**

**4.**

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Papers | Sustainability Issues | Power Structure | |||
---|---|---|---|---|---|

Carbon Emission | Sustainable Investment Decision | Consumer Environment Awareness | |||

Manufacturer Investment Decision | Retailer Investment Decision | ||||

Choi [15], Drake and Spinler [16], Dobos [18], Bouchery et al. [19], Rosič and Jammernegg [23], Chen and Hao [26], Jaber et al. [27] | ✓ | ||||

Benjaafar et al. [14], Letmathe and Balakrishnan [17], Zhang and Xu [20] | ✓ | ✓ | |||

Toptal et al. [22] | ✓ | ✓ | |||

Zhang et al. [28] | ✓ | ✓ | |||

Dong et al. [9], Li and Shen [10], Nouira et al. [21], Yalabik and Fairchild [24], Liu et al. [25], Du et al. [29] | ✓ | ✓ | ✓ | ||

Shi et al. [30], Choi [41], Ertek and Griffin [42], Majumder and Srinivasan [43], Nagarajan and Sošić [44], Xue et al. [45], Chen and Wang [46], Chen et al. [47], Chen et al. [48], Zheng et al. [49] | ✓ | ||||

Chen et al. [13] | ✓ | ✓ | ✓ | ✓ | |

This paper | ✓ | ✓ | ✓ | ✓ | ✓ |

Model | ${\mathit{p}}_{\mathit{i}}^{\mathit{m}}$ | ${\mathit{e}}_{\mathit{i}}^{\mathit{m}}$ | ${\mathit{w}}_{\mathit{i}}^{\mathit{m}}$ |
---|---|---|---|

MS Model ($i=m$) | $c+\frac{\left(6\lambda -\beta {t}^{2}-t\gamma \right)\left(\alpha -\beta c\right)}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ | $\frac{\left(\gamma +t\beta \right)\left(\alpha -\beta c\right)}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ | $c+\frac{\left(4\lambda -\beta {t}^{2}-t\gamma \right)\left(\alpha -\beta c\right)}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ |

VN Model ($i=n$) | $c+\frac{\left(4\lambda -\beta {t}^{2}-t\gamma \right)\left(\alpha -\beta c\right)}{6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ | $\frac{\left(\gamma +t\beta \right)\left(\alpha -\beta c\right)}{6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ | $c+\frac{\left(2\lambda -\beta {t}^{2}-t\gamma \right)\left(\alpha -\beta c\right)}{6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ |

RS Model ($i=r$) | $c+\frac{\left(6\lambda \beta -\left(2\beta t+\gamma \right)\left(\beta t+\gamma \right)\right)\left(\alpha -\beta c\right)}{2\beta \left(4\lambda \beta -{\left(\gamma +t\beta \right)}^{2}\right)}$ | $\frac{\left(\gamma +t\beta \right)\left(\alpha -\beta c\right)}{8\lambda \beta -2{\left(\gamma +t\beta \right)}^{2}}$ | $c+\frac{\left(2\lambda -\beta {t}^{2}-t\gamma \right)\left(\alpha -\beta c\right)}{8\lambda \beta -2{\left(\gamma +t\beta \right)}^{2}}$ |

Model | ${\mathsf{\Pi}}_{\mathbf{r}}^{\mathbf{m}}$ | ${\mathsf{\Pi}}_{\mathbf{m}}^{\mathbf{m}}$ |
---|---|---|

MS Model ($i=m$) | $\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$ | $\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ |

VN Model ($i=n$) | $\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$ | $\frac{[4{\lambda}^{2}\beta -\lambda {\left(\gamma +t\beta \right)}^{2}]{\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$ |

RS Model ($i=r$) | $\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{8\lambda \beta -2{\left(\gamma +t\beta \right)}^{2}}$ | $\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{4[4\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}$ |

Model | ${\mathit{p}}_{\mathit{i}}^{\mathit{r}}$ | ${\mathit{e}}_{\mathit{i}}^{\mathit{r}}$ | ${\mathit{w}}_{\mathit{i}}^{\mathit{r}}$ |
---|---|---|---|

MS Model ($i=m$) | $c+\frac{(6\lambda \beta -\gamma \left(\gamma +2\beta t\right)\left(\alpha -\beta c\right)}{2\beta \left(4\lambda \beta -\gamma \left(\gamma +t\beta \right)\right)}$ | $\frac{\gamma \left(\alpha -\beta c\right)}{2\left(4\lambda \beta -\gamma \left(\gamma +t\beta \right)\right)}$ | $c+\frac{(4\lambda \beta -\gamma \left(\gamma +2\beta t\right)\left(\alpha -\beta c\right)}{2\beta \left(4\lambda \beta -\gamma \left(\gamma +t\beta \right)\right)}$ |

VN Model ($i=n$) | $c+\frac{\left(4\lambda -t\gamma \right)\left(\alpha -\beta c\right)}{6\lambda \beta -\gamma \left(\gamma +t\beta \right)}$ | $\frac{\gamma \left(\alpha -\beta c\right)}{6\lambda \beta -\gamma \left(\gamma +t\beta \right)}$ | $c+\frac{\left(2\lambda -t\gamma \right)\left(\alpha -\beta c\right)}{6\lambda \beta -\gamma \left(\gamma +t\beta \right)}$ |

RS Model ($i=r$) | $c+\frac{\left(6\lambda -\beta {t}^{2}-t\gamma \right)\left(\alpha -\beta c\right)}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ | $\frac{\left(\gamma +t\beta \right)\left(\alpha -\beta c\right)}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ | $c+\frac{\left(2\lambda -\beta {t}^{2}-t\gamma \right)\left(\alpha -\beta c\right)}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ |

Model | ${\mathit{\Pi}}_{\mathit{r}}^{\mathit{r}}$ | ${\mathit{\Pi}}_{\mathit{m}}^{\mathit{r}}$ |
---|---|---|

MS Model ($i=m$) | $\frac{\lambda \left(4\lambda \beta -{\gamma}^{2}\right){\left(\alpha -\beta c\right)}^{2}}{4{[4\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}}$ | $\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{2\left(4\lambda \beta -\gamma \left(\gamma +t\beta \right)\right)}$ |

VN Model ($i=n$) | $\frac{\lambda \left(4\lambda \beta -{\gamma}^{2}\right){\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}}$ | $\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[6\lambda \beta -\gamma \left(\gamma +t\beta \right)]}^{2}}$ |

RS Model ($i=r$) | $\frac{\lambda {\left(\alpha -\beta c\right)}^{2}}{8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}}$ | $\frac{4{\lambda}^{2}\beta {\left(\alpha -\beta c\right)}^{2}}{{[8\lambda \beta -{\left(\gamma +t\beta \right)}^{2}]}^{2}}$ |

Model | ${\mathit{p}}_{\mathit{i}}^{0}$ | ${\mathit{w}}_{\mathit{i}}^{0}$ | ${\mathit{\pi}}_{\mathit{r}}^{0}\left({\mathit{p}}_{\mathit{i}}^{0}\right)$ | ${\mathit{\pi}}_{\mathit{m}}^{0}\left({\mathit{w}}_{\mathit{i}}^{0}\right)$ |
---|---|---|---|---|

MS Model ($i=m$) | $c+\frac{3\left(\alpha -\beta c\right)}{4\beta}$ | $c+\frac{\alpha -\beta c}{2\beta}$ | $\frac{{\left(\alpha -\beta c\right)}^{2}}{16\beta}$ | $\frac{{\left(\alpha -\beta c\right)}^{2}}{8\beta}$ |

VN Model ($i=n$) | $c+\frac{2\left(\alpha -\beta c\right)}{3\beta}$ | $c+\frac{\alpha -\beta c}{3\beta}$ | $\frac{{\left(\alpha -\beta c\right)}^{2}}{9\beta}$ | $\frac{{\left(\alpha -\beta c\right)}^{2}}{9\beta}$ |

RS Model ($i=r$) | $c+\frac{3\left(\alpha -\beta c\right)}{4\beta}$ | $c+\frac{\alpha -\beta c}{4\beta}$ | $\frac{{\left(\alpha -\beta c\right)}^{2}}{8\beta}$ | $\frac{{\left(\alpha -\beta c\right)}^{2}}{16\beta}$ |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shi, X.; Qian, Y.; Dong, C.
Economic and Environmental Performance of Fashion Supply Chain: The Joint Effect of Power Structure and Sustainable Investment. *Sustainability* **2017**, *9*, 961.
https://doi.org/10.3390/su9060961

**AMA Style**

Shi X, Qian Y, Dong C.
Economic and Environmental Performance of Fashion Supply Chain: The Joint Effect of Power Structure and Sustainable Investment. *Sustainability*. 2017; 9(6):961.
https://doi.org/10.3390/su9060961

**Chicago/Turabian Style**

Shi, Xiutian, Yuan Qian, and Ciwei Dong.
2017. "Economic and Environmental Performance of Fashion Supply Chain: The Joint Effect of Power Structure and Sustainable Investment" *Sustainability* 9, no. 6: 961.
https://doi.org/10.3390/su9060961