# Recycling Model Selection for Electronic Products Considering Platform Power and Blockchain Empowerment

^{*}

## Abstract

**:**

## 1. Introduction

- RQ1:
- Under what conditions does the recycler choose to implement blockchain technology to increase the amount of real recycling of waste products?
- RQ2:
- What are the impacts of the implementation of blockchain technology on pricing and marketing strategies as well as the recycling model selection?
- RQ3:
- How to take advantage of the combination of blockchain and recycling model to enhance the triple benefits of economy, environment, and society in the CLSC?

## 2. Literature Review

#### 2.1. Electronic Products Supply Chain

#### 2.2. Selection of Recycling Model for Waste Products

#### 2.3. Application of Blockchain Technology in Supply Chain

## 3. Model Description and Assumptions

## 4. Model Analysis

#### 4.1. Manufacturer Recycling Model without Blockchain Technology ($NM$)

**Proposition**

**1.**

**Proof.**

#### 4.2. Platform Recycling Model without Blockchain Technology ($NP$)

**Proposition**

**2.**

**Proof.**

#### 4.3. Manufacturer Recycling Model Empowered by Blockchain ($BM$)

**Proposition**

**3.**

**Proof.**

#### 4.4. Platform Recycling Model Empowered by Blockchain ($BP$)

**Proposition**

**4.**

**Proof.**

## 5. Implementation Conditions and Value of Blockchain Technology

#### 5.1. Implementation Conditions of Blockchain

**Proposition**

**5.**

**Proposition**

**6.**

**Proposition**

**7.**

#### 5.2. Implementation Value of Blockchain

**Proposition**

**8.**

**Proposition**

**9.**

**Proposition**

**10.**

**Proposition**

**11.**

**Proposition**

**12.**

**,**and the influence coefficient $\rho $ of marketing effort input on brand goodwill. All decrease with the increase in the coefficient of platform marketing cost $ks$, price sensitivity $\beta $ of consumers, the discount rate $r$, and the coefficient of the decay of brand goodwill $\delta $. In the absence of blockchain technology, if the real recycling $\xi $ is increased, the impact of the false recycling rate on the brand goodwill of the product will be reduced, thus improving the brand goodwill of the product. Based on the expressions for each control variable that we derived in Section 4 and Section 5, we can find that the wholesale price of the product, the retail price, the marketing effort, and the recycling effort of the platform in both recycling model strategies increase as the real recycling rate increases.

## 6. Numerical Analysis

- (1)
- The effect of the change in the share ratio $\alpha $ on the growth rate of recycling rate, the growth rate of supply chain profit, and the growth rate of social welfare;
- (2)
- The impact of the ratio of real to theoretical recycling volume on profit of manufacturer, platform and supply chain, and social welfare under two recycling models;
- (3)
- The impact of platform power on profit of manufacturer, platform and supply chain, and social welfare under two recycling models;
- (4)
- Proposition 7 shows that, when $F<B$, both the manufacturer and the platform prefer to use blockchain technology in both recycling models. Proposition 9 shows that, when the self-built cost of the blockchain is $\alpha \Delta \left(a+\frac{\alpha {\epsilon}^{2}\Delta}{2{k}_{u}}\right)<F<\alpha \Delta a+\frac{{\left(\Delta \epsilon \right)}^{2}}{{k}_{u}}\left[\frac{1}{2}-\left(1-\alpha \right)\alpha \right]$, the manufacturer chooses the manufacturer recycling model and the platform can also gain more revenue from it. Then, whether there is an intersection between the two, both the manufacturer and the platform will choose the manufacturer recycling model empowered by blockchain from their own interests. If so, what is the range of $F$ as well as $\alpha $, and are the economic, environmental, and social aspects of choosing the manufacturer recycling model enabled by blockchain better than other modes?

#### 6.1. Brand Goodwill Time Trajectory Chart

#### 6.2. Influence of the Ratio of Real to Theoretical Recycling (Real Recycling Rate) on Profits of Supply Chain Participants and Supply Chain, and Social Welfare

#### 6.3. Impact of Platform Power on Profits of Supply Chain Participants and Supply Chain and Social Welfare

#### 6.4. Impact of Residual Value Share Ratio and Blockchain Fixed Cost of Waste Electronics on Recycling Model Selection

#### 6.5. Influence of the Change of Revenue Sharing Coefficient on Economy, Society, and Environment

## 7. Extension with Unit Cost of Blockchain

**Proposition**

**13.**

**Proposition**

**14.**

**Proof.**

## 8. Discussion and Conclusions

#### 8.1. Discussion

#### 8.2. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Proof**

**of**

**Proposition**

**1.**

**Proof**

**of**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**3.**

**Proof**

**of**

**Proposition**

**4.**

**Proof**

**of**

**Proposition**

**12.**

- Effect of the correlation parameter on the steady-state value of brand goodwill. (If the partial derivative is greater than 0, the two are positively correlated; the partial derivative is less than 0, indicating negative correlation).$$\frac{\partial}{\partial \rho}{G}_{\infty}^{N}=\frac{\rho {\left(\theta +\lambda \right)}^{2}}{8\beta {k}_{s}\left(r+\delta +1-\xi \right)\left(\delta +1-\xi \right)}>0\frac{\partial}{\partial \rho}{G}_{\infty}^{B}=\frac{\rho {\left(\theta +\lambda \right)}^{2}}{8{k}_{s}\beta \delta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial \theta}{G}_{\infty}^{N}=\frac{{\rho}^{2}\left(\theta +\lambda \right)}{8\beta {k}_{s}\left(r+\delta +1-\xi \right)\left(\delta +1-\xi \right)}>0\frac{\partial}{\partial \theta}{G}_{\infty}^{B}=\frac{{\rho}^{2}\left(\theta +\lambda \right)}{8{k}_{s}\beta \delta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial \lambda}{G}_{\infty}^{N}=\frac{{\rho}^{2}\left(\theta +\lambda \right)}{8\beta {k}_{s}\left(r+\delta +1-\xi \right)\left(\delta +1-\xi \right)}>0\frac{\partial}{\partial \lambda}{G}_{\infty}^{B}=\frac{{\rho}^{2}\left(\theta +\lambda \right)}{8{k}_{s}\beta \delta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial \beta}{G}_{\infty}^{N}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16{\beta}^{2}{k}_{s}\left(r+\delta +1-\xi \right)\left(\delta +1-\xi \right)}<0\frac{\partial}{\partial \beta}{G}_{\infty}^{B}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta {\delta}^{2}\left(r+\delta \right)}0$$$$\frac{\partial}{\partial r}{G}_{\infty}^{N}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16\beta {k}_{s}{\left(r+\delta +1-\xi \right)}^{2}\left(\delta +1-\xi \right)}<0\frac{\partial}{\partial r}{G}_{\infty}^{B}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta \delta {\left(r+\delta \right)}^{2}}0$$$$\frac{\partial}{\partial {k}_{s}}{G}_{\infty}^{N}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16\beta {k}_{s}{}^{2}\left(r+\delta +1-\xi \right)\left(\delta +1-\xi \right)}<0\frac{\partial}{\partial {k}_{s}}{G}_{\infty}^{B}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16{k}_{s}{}^{2}\beta \delta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial \xi}{G}_{\infty}^{N}=\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16\beta {k}_{s}{\left[\left(r+\delta +1-\xi \right)\left(\delta +1-\xi \right)\right]}^{2}}\left[r+2\left(\delta +1-\xi \right)\right]>0$$$$\frac{\partial}{\partial \delta}{G}_{\infty}^{N}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16\beta {k}_{s}{\left[\left(r+\delta +1-\xi \right)\left(\delta +1-\xi \right)\right]}^{2}}\left[\left(\delta +1-\xi \right)+\left(r+\delta +1-\xi \right)\right]<0$$$$\frac{\partial}{\partial \delta}{G}_{\infty}^{B}=-\frac{{\rho}^{2}{\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta {\left[\delta \left(r+\delta \right)\right]}^{2}}\left(r+2\delta \right)<0$$
- Influence of related parameters on the steady-state value of electronic product retail price. (If the partial derivative is greater than 0, the two are positively correlated; the partial derivative is less than 0, indicating negative correlation.)$$\frac{\partial}{\partial \theta}{p}_{\infty}^{N}=\frac{3}{4\beta}\sqrt{{G}_{\infty}^{N}}+\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \theta}\sqrt{{G}_{\infty}^{N}}>0\frac{\partial}{\partial \theta}{p}_{\infty}^{B}=\frac{3}{4\beta}\sqrt{{G}_{\infty}^{B}}+\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \theta}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \lambda}{p}_{\infty}^{N}=\frac{3}{4\beta}\sqrt{{G}_{\infty}^{N}}+\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \lambda}\sqrt{{G}_{\infty}^{N}}>0\frac{\partial}{\partial \lambda}{p}_{\infty}^{B}=\frac{3}{4\beta}\sqrt{{G}_{\infty}^{B}}+\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \lambda}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \rho}{p}_{\infty}^{N}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \rho}\sqrt{{G}_{\infty}^{N}}>0\frac{\partial}{\partial \rho}{p}_{\infty}^{B}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \rho}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial r}{p}_{\infty}^{N}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial r}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial r}{p}_{\infty}^{B}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial r}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial {k}_{s}}{p}_{\infty}^{N}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial {k}_{s}}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial {k}_{s}}{p}_{\infty}^{B}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial {k}_{s}}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \delta}{p}_{\infty}^{N}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \delta}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial \delta}{p}_{\infty}^{B}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \delta}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \beta}{p}_{\infty}^{N}=-\frac{3\left(\theta +\lambda \right)}{4{\beta}^{2}}\sqrt{{G}_{\infty}^{N}}+\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \beta}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial \beta}{p}_{\infty}^{B}=-\frac{3\left(\theta +\lambda \right)}{4{\beta}^{2}}\sqrt{{G}_{\infty}^{B}}+\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \beta}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \xi}{p}_{\infty}^{N}=\frac{3\left(\theta +\lambda \right)}{4\beta}\frac{\partial}{\partial \xi}\sqrt{{G}_{\infty}^{N}}>0$$
- Influence of related parameters on steady-state value of wholesale price of electronic products. (If the partial derivative is greater than 0, the two are positively correlated; the partial derivative is less than 0, indicating negative correlation).$$\frac{\partial}{\partial \theta}{w}_{\infty}^{N}=\frac{\sqrt{{G}_{\infty}^{N}}}{2\beta}+\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \theta}\sqrt{{G}_{\infty}^{N}}>0\frac{\partial}{\partial \theta}{w}_{\infty}^{B}=\frac{\sqrt{{G}_{\infty}^{B}}}{2\beta}+\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \theta}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \lambda}{w}_{\infty}^{N}=\frac{\sqrt{{G}_{\infty}^{N}}}{2\beta}+\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \lambda}\sqrt{{G}_{\infty}^{N}}>0\frac{\partial}{\partial \lambda}{w}_{\infty}^{B}=\frac{\sqrt{{G}_{\infty}^{B}}}{2\beta}+\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \lambda}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \rho}{w}_{\infty}^{N}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \rho}\sqrt{{G}_{\infty}^{N}}>0\frac{\partial}{\partial \rho}{w}_{\infty}^{B}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \rho}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \beta}{w}_{\infty}^{N}=-\frac{\left(\theta +\lambda \right)}{2{\beta}^{2}}+\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \beta}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial \beta}{w}_{\infty}^{B}=-\frac{\left(\theta +\lambda \right)}{2{\beta}^{2}}+\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \beta}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial {k}_{s}}{w}_{\infty}^{N}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial {k}_{s}}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial {k}_{s}}{w}_{\infty}^{B}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial {k}_{s}}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial r}{w}_{\infty}^{N}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial r}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial r}{w}_{\infty}^{B}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial r}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \delta}{w}_{\infty}^{N}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \delta}\sqrt{{G}_{\infty}^{N}}<0\frac{\partial}{\partial \delta}{w}_{\infty}^{B}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \delta}\sqrt{{G}_{\infty}^{B}}0$$$$\frac{\partial}{\partial \xi}{w}_{\infty}^{N}=\frac{\left(\theta +\lambda \right)}{2\beta}\frac{\partial}{\partial \xi}\sqrt{{G}_{\infty}^{N}}>0$$
- Influence of relevant parameters on steady-state value of marketing effort. (If the partial derivative is greater than 0, the two are positively correlated; the partial derivative is less than 0, indicating negative correlation.)$$\frac{\partial}{\partial \rho}{s}_{\infty}^{N}=\frac{{\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta \left(r+\delta +1-\xi \right)}>0\frac{\partial}{\partial \rho}{s}_{\infty}^{B}=\frac{{\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial \theta}{s}_{\infty}^{N}=\frac{\rho \left(\theta +\lambda \right)}{8{k}_{s}\beta \left(r+\delta +1-\xi \right)}>0\frac{\partial}{\partial \theta}{s}_{\infty}^{B}=\frac{\rho \left(\theta +\lambda \right)}{8{k}_{s}\beta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial \lambda}{s}_{\infty}^{N}=\frac{\rho \left(\theta +\lambda \right)}{8{k}_{s}\beta \left(r+\delta +1-\xi \right)}>0\frac{\partial}{\partial \lambda}{s}_{\infty}^{B}=\frac{\rho \left(\theta +\lambda \right)}{8{k}_{s}\beta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial {k}_{s}}{s}_{\infty}^{N}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}{}^{2}\beta \left(r+\delta +1-\xi \right)}<0\frac{\partial}{\partial {k}_{s}}{s}_{\infty}^{B}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}{}^{2}\beta \left(r+\delta \right)}0$$$$\frac{\partial}{\partial \beta}{s}_{\infty}^{N}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}{\beta}^{2}\left(r+\delta +1-\xi \right)}<0\frac{\partial}{\partial \beta}{s}_{\infty}^{B}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}{\beta}^{2}\left(r+\delta \right)}0$$$$\frac{\partial}{\partial r}{s}_{\infty}^{N}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta {\left(r+\delta +1-\xi \right)}^{2}}<0\frac{\partial}{\partial r}{s}_{\infty}^{B}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta {\left(r+\delta \right)}^{2}}0$$$$\frac{\partial}{\partial \delta}{s}_{\infty}^{N}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta {\left(r+\delta +1-\xi \right)}^{2}}<0\frac{\partial}{\partial \delta}{s}_{\infty}^{B}=-\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta {\left(r+\delta \right)}^{2}}0$$$$\frac{\partial}{\partial \xi}{s}_{\infty}^{N}=\frac{\rho {\left(\theta +\lambda \right)}^{2}}{16{k}_{s}\beta {\left(r+\delta +1-\xi \right)}^{2}}>0$$
- Influence of related parameters on steady-state value of recycling effort. ${u}_{\infty}^{NM},{u}_{\infty}^{NP},{u}_{\infty}^{BM},{u}_{\infty}^{BP}$ represents the recycling effort when the manufacturer recycling model and platform recycling model without blockchain technology and the recycling effort when the manufacturer recycling model and platform recycling model with blockchain technology, respectively. (If the partial derivative is greater than 0, the two are positively correlated; the partial derivative is less than 0, indicating negative correlation.)Manufacturer recycling model:$$\frac{\partial}{\partial \Delta}{u}_{\infty}^{NM}=\frac{\xi \epsilon}{{k}_{u}}>0\frac{\partial}{\partial \Delta}{u}_{\infty}^{BM}=\frac{\epsilon}{{k}_{u}}0$$$$\frac{\partial}{\partial \epsilon}{u}_{\infty}^{NM}=\frac{\Delta \xi}{{k}_{u}}>0\frac{\partial}{\partial \epsilon}{u}_{\infty}^{BM}=\frac{\Delta}{{k}_{u}}0$$$$\frac{\partial}{\partial {k}_{u}}{u}_{\infty}^{NM}=-\frac{\Delta \xi \epsilon}{{k}_{u}{}^{2}}<0\frac{\partial}{\partial {k}_{u}}{u}_{\infty}^{BM}=-\frac{\Delta \epsilon}{{k}_{u}{}^{2}}0$$$$\frac{\partial}{\partial \xi}{u}_{\infty}^{NM}=\frac{\Delta \epsilon}{{k}_{u}}>0$$Platform recycling model:$$\frac{\partial}{\partial \alpha}{u}_{\infty}^{NP}=\frac{\epsilon \Delta \xi}{{k}_{u}}>0\frac{\partial}{\partial \alpha}{u}_{\infty}^{BP}=\frac{\epsilon \Delta}{{k}_{u}}0$$$$\frac{\partial}{\partial \Delta}{u}_{\infty}^{NP}=\frac{\alpha \xi \epsilon}{{k}_{u}}>0\frac{\partial}{\partial \Delta}{u}_{\infty}^{BP}=\frac{\alpha \epsilon}{{k}_{u}}0$$$$\frac{\partial}{\partial \epsilon}{u}_{\infty}^{NP}=\frac{\alpha \Delta \xi}{{k}_{u}}>0\frac{\partial}{\partial \epsilon}{u}_{\infty}^{BP}=\frac{\alpha \Delta}{{k}_{u}}0$$$$\frac{\partial}{\partial {k}_{u}}{u}_{\infty}^{NP}=-\frac{\alpha \Delta \xi \epsilon}{{k}_{u}{}^{2}}<0\frac{\partial}{\partial {k}_{u}}{u}_{\infty}^{BP}=-\frac{\alpha \epsilon \Delta}{{k}_{u}{}^{2}}0$$$$\frac{\partial}{\partial \xi}{u}_{\infty}^{NP}=\frac{\alpha \Delta \epsilon}{{k}_{u}}>0$$

**Proof**

**of**

**Proposition**

**13.**