# The Impact of Government Dual Policy on the Selection of OEM’s Regulatory Strategy for Third-Party Remanufacturing

Authors: Hongya Cheng; Lijun Meng; Zuqing Huang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Remanufacturing plays an important role in the circular economy and environmental protection. In the development of the remanufacturing closed-loop supply chain (CLSC), the impact of government policy cannot be ignored. However, previous studies have rarely answered the impact of government dual policy (the policy combination of trade-old-for-remanufactured and carbon tax policy) on the optimal decisions of CLSC enterprises. To fill the gap, this work considers the remanufacturing modes and government dual policy simultaneously and investigates a CLSC of waste of electronic and electrical equipment (WEEE) consisting of an original equipment manufacturer (OEM) and a third-party remanufacturer (TPR). Here the OEM has three strategies for regulating third-party remanufacturing activities: outsourcing (Model O), authorization (Model A), and nonregulation (Model D). The results show that: (i) Whether the government implements the dual policy or not, Model O is the best choice for OEM. And compared with nongovernment policy intervention, government dual policy can improve the recovery rate of WEEE products and then effectively promote the recycling of waste resources; (ii) When the government dual policy parameters meet a certain condition, the dual policy could effectively increase supply chain members’ profits and the total profits of CLSC and boost market demand expansion; (iii) Compared with the other two remanufacturing modes, the CLSC under nonregulation strategy is the optimal remanufacturing mode for the whole society; meanwhile, OEM nonregulation strategy is the worst strategy for the environmental protection. In addition, when the government sets appropriate parameters, government dual policy is beneficial to the consumer, supply chain member, and the society simultaneously, but the impact of the dual policy on the environment is also related to the ratio of the two products’ impact on the environment.


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## Body

## 1. Introduction

### 1.1. Background

With the rapid level of technological development and the skyrocketing of consumption levels, the update speeds of electrical and electronic products (such as mobile phone, computers, televisions, and so on) are faster than ever before, which result in a voluminous waste of electronic and electrical equipment (WEEE) [1, 2]. According to the United National report, the generation of WEEE in the world has almost reached 53.6 million tons in 2019 and will grow to 74.7 million tons by 2030 [3]. In addition, the annual average increased rate of WEEE has reached 10.4% in China, and the quantity in 2030 will arrive at 27.22 million tons [4], which not only causes waste of resources but also causes serious pollution to the ecological environment. Therefore, how to carry out effective recycling and remanufacturing has drawn considerable attention. At the same time, more and more consumers put forward higher requirements for enterprise environmental protection. Thus, the closed-loop supply chain (CLSC) focusing on recycling and remanufacturing to develop a sustainable economy has attracted the attention of enterprises, scholars, and the government [5, 6]. Remanufacturing CLSC is one of the important ways to achieve WEEE recycling and remanufacturing, solve resource waste, and reduce environmental pollution [7]. And remanufacturing has potential economic, environmental, and social benefits, which are referred to as “triple-win” effects [8]. However, what kind of remanufacturing mode is more conducive to recycling and remanufacturing of used products has become a global social problem to be solved [9–11].Many practices have proven that remanufacturing is a lucrative business [12, 13]. Driven by economic interests and environmental protection responsibility, many third-party remanufacturers (TPRs) are willing to engage in recycling and remanufacturing activities [14, 15]. In addition, original equipment manufacturers (OEMs) focus on the new production of new products and sales. Due to the limitations of brand reputation and recycling conditions, the OEM does not usually engage in the recycling and remanufacturing business by himself. They often choose to outsource or authorize the TPR to recycle and remanufacture [16]. For instance, Land Rover outsources the remanufacturing operations to Caterpillar [17], and BMW, Xerox, IBM, and Hisense also adopt the outsourcing strategy. The famous cases of authorization remanufacturing are Apple and Foxconn. Foxconn acquires the proprietary rights to remanufacture end-of-life iPhones and sells them in the market [17, 18]. In addition, Canon also assigns remanufacturing operations to TPR [19].Under the dual pressure of resource shortage and aggravated environmental pollution, the government has taken a series of measures to handle the crisis [20–24]. On the one hand, the government implements the carbon tax policy to reduce carbon emission and protect the environment. On the other hand, the government introduced a subsidy policy to encourage consumers to buy remanufactured products [25, 26]. In 2013, for example, the Chinese government initiated a subsidy program called “trade-old-for-remanufactured” (TOR) [27]. The TOR program is that consumers could return used products to the recycling enterprises and receive the corresponding subsidy when purchasing remanufactured products. In 2015, the Chinese government subsidizes consumers for using remanufactured vehicle engines 10% of the trade-in price, with a subsidy as high as ¥2,000 [8, 28, 29]. It can be seen that the development of the manufacturing/remanufacturing industry is under the intervention of the government dual policy.However, different government policies have distinct effects on the operation and management of remanufacturing CLSC systems. For example, the “trade-in” subsidy policy implemented by the government would prompt the OEMs to reduce the price of new products and elevate the remanufacturing power of TPR [30]. On the other hand, the dual regulatory policy (deposit refund and recycling subsidy) is conducive to reducing the recycling cost of waste products and improving the overall efficiency of CLSC [23]. In addition, compared with subsidy policies, carbon tax policies that effectively reduce carbon emissions are conducive to improving the overall efficiency of the supply chain for implementing CSR activities [31]. To sum up, the implementations of different government policies lead to distinct impacts on member companies and the entire supply chain.


### 1.2. Importance of Topics

Under the background of different remanufacturing modes, there is a dilemma: the government uses various policies to promote the development of remanufacturing industry, but under what condition should the government implement the dual policy and what is the best strategy of OEM regulation in third-party remanufacturing activities under government dual policy? These questions must be answered.While many studies have discussed OEM outsourcing or authorization remanufacturing mode separately [8, 32–36], or both modes simultaneously [11, 17], very limited researches focus on the discussion about the comparison of three remanufacturing modes and the impact of government dual policy on the different remanufacturing modes. In reality, the dilemma OEMs face is whether or how they should regulate third-party remanufacturing under the intervention of government dual policy. Therefore, our article studies the impact of government dual policy on the OEM’s decision on how to regulate third-party remanufacturing activities. We analyze the impact of government dual policy on different remanufacturing modes and compare the optimal decision under different modes, which can provide a reference for government decision and OEMs to choose a reasonable means of remanufacturing regulation.


### 1.3. Specific Issues

The aim of this study is to investigate how government dual policy affects the operation and the decisions of CLSC members under different remanufacturing modes, decide which means of regulation is the best choice for OEMs, and further explore the critical conditions for the government to implement different policies. To the best of our knowledge, this article is one of only a few studies that consider both government dual policy and OEM regulation strategy in remanufacturing. To those ends, we comprehensively consider three remanufacturing modes and construct two-period game models to analyze the influence of government dual policy on the decision of different WEEE remanufacturing modes. We aim to solve the following specific problems:(1)
What is the optimal decision of three WEEE remanufacturing CLSC modes under government dual policy? How does the government dual policy effects enterprise decisions? What kind of remanufacturing regulation strategy is the best choice for OEM?(2)
Under what conditions should the government adopt the dual policy to effectively promote the development of the remanufacturing industry? Among three remanufacturing modes, which one is the best from the viewpoint of the OEM, the TPR, the government, and consumers?(3)
Comparing with nongovernment intervention, from the perspective of consumer, social, and environment, is government dual policy more conducive to stimulating the production and sales of remanufactured products?


### 1.4. Paper Structure

The rest of this article is organized as follows: Section2 reviews the literature and positions this work. Section 3 describes the problem and assumptions in this article. Section 4 introduces the models to analyze the impact of government dual policy on the optimal decision. Section 5 shows the numerical analysis. Section 6 sets forth the conclusions and the limitations and future research. And all proofs are presented in Appendices.


## 1.1. Background

With the rapid level of technological development and the skyrocketing of consumption levels, the update speeds of electrical and electronic products (such as mobile phone, computers, televisions, and so on) are faster than ever before, which result in a voluminous waste of electronic and electrical equipment (WEEE) [1, 2]. According to the United National report, the generation of WEEE in the world has almost reached 53.6 million tons in 2019 and will grow to 74.7 million tons by 2030 [3]. In addition, the annual average increased rate of WEEE has reached 10.4% in China, and the quantity in 2030 will arrive at 27.22 million tons [4], which not only causes waste of resources but also causes serious pollution to the ecological environment. Therefore, how to carry out effective recycling and remanufacturing has drawn considerable attention. At the same time, more and more consumers put forward higher requirements for enterprise environmental protection. Thus, the closed-loop supply chain (CLSC) focusing on recycling and remanufacturing to develop a sustainable economy has attracted the attention of enterprises, scholars, and the government [5, 6]. Remanufacturing CLSC is one of the important ways to achieve WEEE recycling and remanufacturing, solve resource waste, and reduce environmental pollution [7]. And remanufacturing has potential economic, environmental, and social benefits, which are referred to as “triple-win” effects [8]. However, what kind of remanufacturing mode is more conducive to recycling and remanufacturing of used products has become a global social problem to be solved [9–11].Many practices have proven that remanufacturing is a lucrative business [12, 13]. Driven by economic interests and environmental protection responsibility, many third-party remanufacturers (TPRs) are willing to engage in recycling and remanufacturing activities [14, 15]. In addition, original equipment manufacturers (OEMs) focus on the new production of new products and sales. Due to the limitations of brand reputation and recycling conditions, the OEM does not usually engage in the recycling and remanufacturing business by himself. They often choose to outsource or authorize the TPR to recycle and remanufacture [16]. For instance, Land Rover outsources the remanufacturing operations to Caterpillar [17], and BMW, Xerox, IBM, and Hisense also adopt the outsourcing strategy. The famous cases of authorization remanufacturing are Apple and Foxconn. Foxconn acquires the proprietary rights to remanufacture end-of-life iPhones and sells them in the market [17, 18]. In addition, Canon also assigns remanufacturing operations to TPR [19].Under the dual pressure of resource shortage and aggravated environmental pollution, the government has taken a series of measures to handle the crisis [20–24]. On the one hand, the government implements the carbon tax policy to reduce carbon emission and protect the environment. On the other hand, the government introduced a subsidy policy to encourage consumers to buy remanufactured products [25, 26]. In 2013, for example, the Chinese government initiated a subsidy program called “trade-old-for-remanufactured” (TOR) [27]. The TOR program is that consumers could return used products to the recycling enterprises and receive the corresponding subsidy when purchasing remanufactured products. In 2015, the Chinese government subsidizes consumers for using remanufactured vehicle engines 10% of the trade-in price, with a subsidy as high as ¥2,000 [8, 28, 29]. It can be seen that the development of the manufacturing/remanufacturing industry is under the intervention of the government dual policy.However, different government policies have distinct effects on the operation and management of remanufacturing CLSC systems. For example, the “trade-in” subsidy policy implemented by the government would prompt the OEMs to reduce the price of new products and elevate the remanufacturing power of TPR [30]. On the other hand, the dual regulatory policy (deposit refund and recycling subsidy) is conducive to reducing the recycling cost of waste products and improving the overall efficiency of CLSC [23]. In addition, compared with subsidy policies, carbon tax policies that effectively reduce carbon emissions are conducive to improving the overall efficiency of the supply chain for implementing CSR activities [31]. To sum up, the implementations of different government policies lead to distinct impacts on member companies and the entire supply chain.


## 1.2. Importance of Topics

Under the background of different remanufacturing modes, there is a dilemma: the government uses various policies to promote the development of remanufacturing industry, but under what condition should the government implement the dual policy and what is the best strategy of OEM regulation in third-party remanufacturing activities under government dual policy? These questions must be answered.While many studies have discussed OEM outsourcing or authorization remanufacturing mode separately [8, 32–36], or both modes simultaneously [11, 17], very limited researches focus on the discussion about the comparison of three remanufacturing modes and the impact of government dual policy on the different remanufacturing modes. In reality, the dilemma OEMs face is whether or how they should regulate third-party remanufacturing under the intervention of government dual policy. Therefore, our article studies the impact of government dual policy on the OEM’s decision on how to regulate third-party remanufacturing activities. We analyze the impact of government dual policy on different remanufacturing modes and compare the optimal decision under different modes, which can provide a reference for government decision and OEMs to choose a reasonable means of remanufacturing regulation.


## 1.3. Specific Issues

The aim of this study is to investigate how government dual policy affects the operation and the decisions of CLSC members under different remanufacturing modes, decide which means of regulation is the best choice for OEMs, and further explore the critical conditions for the government to implement different policies. To the best of our knowledge, this article is one of only a few studies that consider both government dual policy and OEM regulation strategy in remanufacturing. To those ends, we comprehensively consider three remanufacturing modes and construct two-period game models to analyze the influence of government dual policy on the decision of different WEEE remanufacturing modes. We aim to solve the following specific problems:(1)
What is the optimal decision of three WEEE remanufacturing CLSC modes under government dual policy? How does the government dual policy effects enterprise decisions? What kind of remanufacturing regulation strategy is the best choice for OEM?(2)
Under what conditions should the government adopt the dual policy to effectively promote the development of the remanufacturing industry? Among three remanufacturing modes, which one is the best from the viewpoint of the OEM, the TPR, the government, and consumers?(3)
Comparing with nongovernment intervention, from the perspective of consumer, social, and environment, is government dual policy more conducive to stimulating the production and sales of remanufactured products?


## 1.4. Paper Structure

The rest of this article is organized as follows: Section2 reviews the literature and positions this work. Section 3 describes the problem and assumptions in this article. Section 4 introduces the models to analyze the impact of government dual policy on the optimal decision. Section 5 shows the numerical analysis. Section 6 sets forth the conclusions and the limitations and future research. And all proofs are presented in Appendices.


## 2. Literature Review

Three streams of research are directly related to our research: remanufacturing mode of CLSC, managing trade-in policy, and carbon tax policy. Next, we review each stream and position our research work accordingly.


### 2.1. Remanufacturing Model of CLSC

Remanufacturing end-of-life products into new ones has been recognized as an effective way to reduce pollution and be conducive to alleviating resource shortage [37]. According to the practice of enterprise, OEMs have different regulatory attitudes toward TPR’s remanufacturing activities, which mainly include the following: (1) OEM nonregulatory TPR remanufacturing, that is, TPR independent remanufacturing. For example, the U.S. Independent Remanufacturer Gazelle recycles and remanufactures iPhones, and Apple group does not regulate or intervene in the process [3]; (2) OEM regulatory TPR remanufacturing, of which, according to the different behavior of regulation can be further divided into two regulatory modes: OEM outsourcing TPR remanufacturing and OEM authorization TPR remanufacturing. For example, Land Rover outsources the remanufacturing operations to Caterpillar Remanufacturing Services, and a famous example of the authorization remanufacturing case is Apple which authorizes Foxconn to recycle and remanufacture iPhone [17, 19]. Therefore, we have expanded the literature review according to the above three regulatory modes.


#### 2.1.1. OEM Nonregulation TPR Remanufacturing Mode

Some papers that focus on OEM does not supervise product recycling and remanufacturing activities, that is, TPR self-remanufacturing mode. Bulmus et al. [38] and Wu [39] built the game modes between OEM and remanufacturer and indicated that OEM will deliberately reduce the market supply of new products to protect the market share of new products. Subramanian et al. [40] found that OEM’s profit can be significantly higher if remanufacturing is taken into account by OEM. Furthermore, Oersdemir et al. [41] analyzed how OEM uses the quality of new products to reduce the market competitiveness of remanufacturing products. Liu et al. [42] considered the Stackelberg dynamic game model of a two-level remanufacturing closed-loop supply chain and discussed the relationship between the fairness of supply chain member enterprises and the transfer of responsibility based on pricing.


#### 2.1.2. OEM Outsourcing Remanufacturing Mode

Many scholars have cast light on outsourcing remanufacturing mode. Zhang et al. [43] found that the reduction of recovery cost is more conducive to OEMs to deal with the adverse impacts of remanufacturing products. Ferrer and Whybark [44] analyzed and compared the equilibrium strategies of OEM self-remanufacturing and outsourcing remanufacturing modes. Holcomb and Hitt [16] pointed out that, under the new market competition environment, OEM will consider outsourcing remanufacturing operations to TPR to share remanufacturing profit. Karakayali et al. [45] confirmed that the manufacturers should pay more attention to their outsourcing decisions if government regulations set the quality target recovery rate of waste products. Liu et al. [46] indicated that when the consumer’s preference for refurbished products relative to new products is not high enough, the OEM should choose the authorization strategy.


#### 2.1.3. OEM Authorization Remanufacturing Mode

Some scholars considered the case of authorization remanufacturing. Li et al. [7] analyzed the impact of government subsidies and carbon tax policy on authorized remanufacturing respectively and showed that the government subsidy may increase the revenue of the OEM and TPR. Huang and Wang [30] found that OEM will prefer third-party remanufacturing if remanufacturing cost is relatively low and confirmed that remanufacturing business can bring profit growth to OEM and TPR. Li et al. [47] studied a Cournot game model between an OEM and TPR and showed that OEM may not be willing to license TPR’s latest technology to prevent remanufactured products from encroaching on the new product market. Oraiopoulos et al. [48] introduced the secondary market into the authorization remanufacturing model and analyzed the OEM’s strategy in both the monopoly and the duopoly cases.The above literatures discuss and analyze the different remanufacturing modes. Nevertheless, most of the studies focused on a single remanufacturing mode, and there is a lack of comparative analysis among the three remanufacturing modes, so it could not provide sufficient decision support for OEM’s regulation strategy choice for remanufacturing. In addition, the above studies do not consider government policy intervention. Nevertheless, the development of the remanufacturing industry cannot be separated from the guidance of government policy. Therefore, this article introduces government dual policy into the remanufacturing activities and analyzes the influence of government dual policy on CLSC decisions.


### 2.2. TON and TOR Subsidy Policy of CLSC

As the main body of economic regulation, the government policy plays a highly important role in promoting the development of the remanufacturing industry [3, 26, 49]. In order to encourage consumer uptake of remanufactured products, government joins with firm to adopt a trade-in subsidy policy. Trade-in policy generally constitutes either a process of trading old products for new products or remanufactured products, that is, “trade-old-for-new” (TON) and “trade-old-for-remanufactured” (TOR) strategies.Most of the research focus on the TON policy. Li et al. [50] explored a monopoly OEM offers the TON program to improve sales and collect used products and showed that the OEM may not remanufacture or may partially remanufacture. Feng et al. [51] build an OEM self-remanufacturing model in that the manufacturer implements a TON plan through dual channels and showed that the TON policy can effectively intensify or mitigate the double marginalization effect. Miao et al. [52] found that the TON subsidies could increase the system players’ profits and could improve environmental performance under certain conditions. Xiao et al. [53] analyzed the traditional retail channel and the dual channel, which is the best conducive to the implementation of TON policy, and showed that the retailer would accept TON policy only if customers’ market share exceeds a certain value.Under the coexistence of TON and TOR, Ma et al. [54] studied a firm’s optimal decisions, identified the conditions that determine whether the firm should apply TON and TOR policy simultaneously under OEM self-remanufacturing model, and found that adopting two kinds of trade-in strategies simultaneously does not necessarily benefit the firm and should use different trade-in schemes under different conditions. Miao et al. [55] focused on the impact of carbon regulations on the coexistence of TON and TOR policy in the case of OEM self-remanufacturing model and showed that the OEM can make up the negative impact of carbon regulations on their profits through deliberately designed government subsidy schemes.Most studies in this area have focused on TON policy or the coexistence of TON and TOR. In contrast, this study investigates the TOR policy as it can further promote resource conservation in both the collection of WEEE products and the sales of remanufactured products. Although Han et al. [33] discussed the conditions for enterprises to implement TOR strategy from three aspects of product acceptance, durability, and government subsidies, Zhu and Wang [56] investigated the conditions under which TOR strategy for remanufactured products should be adopted and [33, 56] only considered OEM self-remanufacturing situation and seldom involved other remanufacturing mode. In addition, the question of when the TOR and carbon tax are implemented simultaneously, what impact will it have on enterprise decisions will need to be discussed further.


### 2.3. Carbon Tax Policy of CLSC

A carbon tax policy is one of the important means of energy conservation and emission reduction, and some scholars have also discussed it from different angles. Ding et al. [57] found that a carbon tax policy may not motivate firms to direct increased effort toward CER (carbon emission reduction). Yenipazarli [58] analyzed the effects of a carbon tax policy on the decision of a firm that produced both new and remanufactured products and showed that under a higher carbon tax, remanufacturing will have a negative impact on the environment. Zhu et al. [59] compared two measures to promote the remanufacturing industry—cash subsidies and carbon tax—and found that subsidies can improve corporate income, but a carbon tax may damage corporate income. Hu et al. [60], based on the OEM self-remanufacturing model, analyzed the impact between a carbon tax and cap-and-trade on a corporate decision, consumer surplus, and social welfare through a series of numerical studies. Guo and Huang [61] compared the social welfare effect between the policy of carbon tax and subsidy and showed that with the increase of marginal environmental damage caused by high carbon products, the control measures should be changed from subsidy policy to carbon tax policy. Yang et al. [62] analyzed the influence of carbon tax policy on the decision of enterprise members under the authorization and outsourcing remanufacturing mode. Wang et al. [63] confirmed that manufactured can offset the negative economic impact of the carbon emission tax policy by making low carbon emission technology investment. Wang et al. [64] investigated the different government subsidies on production and emission reduction decisions under a carbon tax regulation by formulating three optimization models.The above literatures show that the carbon tax policy and the government subsidy are often considered individually in CLSC. This research differs in that we integrate the carbon tax policy and the government subsidy into a dual policy regime. In addition, the above studies have rarely taken the adverse impact of carbon emissions on society. Given that social welfare, to a great extent, is affected by carbon emission, we would take this critical issue into account in this research.The two closest studies of ours are Li et al. [7] and Cao et al. [8]. Whereas [7] only considered the impact of subsidy and carbon tax policy on authorization remanufacturing mode respectively; meanwhile, it only regards carbon tax levy on the new products and ignores the carbon emission of the remanufactured products. Although [8] considered imposing a carbon tax on new products and the remanufactured ones simultaneously, they only analyzed and compared the optimal decisions of firms in the dual-channel supply chain under the single carbon tax policy. The optimal decisions of enterprises under government dual policy are not considered. Moreover, both [7, 8] considered the subsidy to enterprises, while this article discusses the government policy of TOR, that is, providing purchase subsidy to the consumer of the remanufactured product, which highlights the incentive effect of government policy on consumers in the remanufacturing market.In summary, most of the existing studies focus on the decisions of remanufacturing mode under government.In summary, most of the existing studies focus on the decisions of remanufacturing mode under government single policy, and to the best of our knowledge, no one took into account the combination of government dual policy and OEM's regulation strategy. Our research fills this gap (summarized in Table1). Furthermore, this article makes the following main contributions to the field, which distinguish it from previous studies:(i)
This article explores three strategies of OEM’s regulation in third-party remanufacturing existing in the actual industry;(ii)
We consider the government dual policy for remanufacturing which combines government subsidy with the carbon tax on new and remanufactured products;(iii)
A more comprehensive comparative analysis of the OEM different regulation strategies under government dual policy is carried out from the perspectives of enterprises and social and environmental benefits, respectively, whereby the objective of this article is to help the firms (OEM and TPR) make the optimal production and pricing decision under different remanufacturing modes and help the government find out the more desirable dual policy implementation conditions.Table 1
Comparison of this study and related literature.
StudiesOEM’s regulation strategyTORpolicyCarbontaxConsumerperspectiveEnvironmentalimpactsSavaskan et al. [13]Outsourcing√Oersdemir et al. [41]OEM self-remanufacturing√√Zou et al. [5]Outsourcing and authorization√√Miao et al. [52]OEM self-remanufacturing√Shu et al. [11]OEM self-remanufacturing√√√Han et al. [33]OEM self-remanufacturing√√√Li et al. [7]Authorization√√√Yang et al. [62]Authorization√Wang et al. [49]Nonregulation√Liu et al. [46]Authorization and nonregulation√Feng et al. [17]Outsourcing and authorization√√Cao et al. [8]OEM self-remanufacturing√√√This studyOutsourcing, authorization,and nonregulation√√√√


## 2.1. Remanufacturing Model of CLSC

Remanufacturing end-of-life products into new ones has been recognized as an effective way to reduce pollution and be conducive to alleviating resource shortage [37]. According to the practice of enterprise, OEMs have different regulatory attitudes toward TPR’s remanufacturing activities, which mainly include the following: (1) OEM nonregulatory TPR remanufacturing, that is, TPR independent remanufacturing. For example, the U.S. Independent Remanufacturer Gazelle recycles and remanufactures iPhones, and Apple group does not regulate or intervene in the process [3]; (2) OEM regulatory TPR remanufacturing, of which, according to the different behavior of regulation can be further divided into two regulatory modes: OEM outsourcing TPR remanufacturing and OEM authorization TPR remanufacturing. For example, Land Rover outsources the remanufacturing operations to Caterpillar Remanufacturing Services, and a famous example of the authorization remanufacturing case is Apple which authorizes Foxconn to recycle and remanufacture iPhone [17, 19]. Therefore, we have expanded the literature review according to the above three regulatory modes.


### 2.1.1. OEM Nonregulation TPR Remanufacturing Mode

Some papers that focus on OEM does not supervise product recycling and remanufacturing activities, that is, TPR self-remanufacturing mode. Bulmus et al. [38] and Wu [39] built the game modes between OEM and remanufacturer and indicated that OEM will deliberately reduce the market supply of new products to protect the market share of new products. Subramanian et al. [40] found that OEM’s profit can be significantly higher if remanufacturing is taken into account by OEM. Furthermore, Oersdemir et al. [41] analyzed how OEM uses the quality of new products to reduce the market competitiveness of remanufacturing products. Liu et al. [42] considered the Stackelberg dynamic game model of a two-level remanufacturing closed-loop supply chain and discussed the relationship between the fairness of supply chain member enterprises and the transfer of responsibility based on pricing.


### 2.1.2. OEM Outsourcing Remanufacturing Mode

Many scholars have cast light on outsourcing remanufacturing mode. Zhang et al. [43] found that the reduction of recovery cost is more conducive to OEMs to deal with the adverse impacts of remanufacturing products. Ferrer and Whybark [44] analyzed and compared the equilibrium strategies of OEM self-remanufacturing and outsourcing remanufacturing modes. Holcomb and Hitt [16] pointed out that, under the new market competition environment, OEM will consider outsourcing remanufacturing operations to TPR to share remanufacturing profit. Karakayali et al. [45] confirmed that the manufacturers should pay more attention to their outsourcing decisions if government regulations set the quality target recovery rate of waste products. Liu et al. [46] indicated that when the consumer’s preference for refurbished products relative to new products is not high enough, the OEM should choose the authorization strategy.


### 2.1.3. OEM Authorization Remanufacturing Mode

Some scholars considered the case of authorization remanufacturing. Li et al. [7] analyzed the impact of government subsidies and carbon tax policy on authorized remanufacturing respectively and showed that the government subsidy may increase the revenue of the OEM and TPR. Huang and Wang [30] found that OEM will prefer third-party remanufacturing if remanufacturing cost is relatively low and confirmed that remanufacturing business can bring profit growth to OEM and TPR. Li et al. [47] studied a Cournot game model between an OEM and TPR and showed that OEM may not be willing to license TPR’s latest technology to prevent remanufactured products from encroaching on the new product market. Oraiopoulos et al. [48] introduced the secondary market into the authorization remanufacturing model and analyzed the OEM’s strategy in both the monopoly and the duopoly cases.The above literatures discuss and analyze the different remanufacturing modes. Nevertheless, most of the studies focused on a single remanufacturing mode, and there is a lack of comparative analysis among the three remanufacturing modes, so it could not provide sufficient decision support for OEM’s regulation strategy choice for remanufacturing. In addition, the above studies do not consider government policy intervention. Nevertheless, the development of the remanufacturing industry cannot be separated from the guidance of government policy. Therefore, this article introduces government dual policy into the remanufacturing activities and analyzes the influence of government dual policy on CLSC decisions.


## 2.1.1. OEM Nonregulation TPR Remanufacturing Mode

Some papers that focus on OEM does not supervise product recycling and remanufacturing activities, that is, TPR self-remanufacturing mode. Bulmus et al. [38] and Wu [39] built the game modes between OEM and remanufacturer and indicated that OEM will deliberately reduce the market supply of new products to protect the market share of new products. Subramanian et al. [40] found that OEM’s profit can be significantly higher if remanufacturing is taken into account by OEM. Furthermore, Oersdemir et al. [41] analyzed how OEM uses the quality of new products to reduce the market competitiveness of remanufacturing products. Liu et al. [42] considered the Stackelberg dynamic game model of a two-level remanufacturing closed-loop supply chain and discussed the relationship between the fairness of supply chain member enterprises and the transfer of responsibility based on pricing.


## 2.1.2. OEM Outsourcing Remanufacturing Mode

Many scholars have cast light on outsourcing remanufacturing mode. Zhang et al. [43] found that the reduction of recovery cost is more conducive to OEMs to deal with the adverse impacts of remanufacturing products. Ferrer and Whybark [44] analyzed and compared the equilibrium strategies of OEM self-remanufacturing and outsourcing remanufacturing modes. Holcomb and Hitt [16] pointed out that, under the new market competition environment, OEM will consider outsourcing remanufacturing operations to TPR to share remanufacturing profit. Karakayali et al. [45] confirmed that the manufacturers should pay more attention to their outsourcing decisions if government regulations set the quality target recovery rate of waste products. Liu et al. [46] indicated that when the consumer’s preference for refurbished products relative to new products is not high enough, the OEM should choose the authorization strategy.


## 2.1.3. OEM Authorization Remanufacturing Mode

Some scholars considered the case of authorization remanufacturing. Li et al. [7] analyzed the impact of government subsidies and carbon tax policy on authorized remanufacturing respectively and showed that the government subsidy may increase the revenue of the OEM and TPR. Huang and Wang [30] found that OEM will prefer third-party remanufacturing if remanufacturing cost is relatively low and confirmed that remanufacturing business can bring profit growth to OEM and TPR. Li et al. [47] studied a Cournot game model between an OEM and TPR and showed that OEM may not be willing to license TPR’s latest technology to prevent remanufactured products from encroaching on the new product market. Oraiopoulos et al. [48] introduced the secondary market into the authorization remanufacturing model and analyzed the OEM’s strategy in both the monopoly and the duopoly cases.The above literatures discuss and analyze the different remanufacturing modes. Nevertheless, most of the studies focused on a single remanufacturing mode, and there is a lack of comparative analysis among the three remanufacturing modes, so it could not provide sufficient decision support for OEM’s regulation strategy choice for remanufacturing. In addition, the above studies do not consider government policy intervention. Nevertheless, the development of the remanufacturing industry cannot be separated from the guidance of government policy. Therefore, this article introduces government dual policy into the remanufacturing activities and analyzes the influence of government dual policy on CLSC decisions.


## 2.2. TON and TOR Subsidy Policy of CLSC

As the main body of economic regulation, the government policy plays a highly important role in promoting the development of the remanufacturing industry [3, 26, 49]. In order to encourage consumer uptake of remanufactured products, government joins with firm to adopt a trade-in subsidy policy. Trade-in policy generally constitutes either a process of trading old products for new products or remanufactured products, that is, “trade-old-for-new” (TON) and “trade-old-for-remanufactured” (TOR) strategies.Most of the research focus on the TON policy. Li et al. [50] explored a monopoly OEM offers the TON program to improve sales and collect used products and showed that the OEM may not remanufacture or may partially remanufacture. Feng et al. [51] build an OEM self-remanufacturing model in that the manufacturer implements a TON plan through dual channels and showed that the TON policy can effectively intensify or mitigate the double marginalization effect. Miao et al. [52] found that the TON subsidies could increase the system players’ profits and could improve environmental performance under certain conditions. Xiao et al. [53] analyzed the traditional retail channel and the dual channel, which is the best conducive to the implementation of TON policy, and showed that the retailer would accept TON policy only if customers’ market share exceeds a certain value.Under the coexistence of TON and TOR, Ma et al. [54] studied a firm’s optimal decisions, identified the conditions that determine whether the firm should apply TON and TOR policy simultaneously under OEM self-remanufacturing model, and found that adopting two kinds of trade-in strategies simultaneously does not necessarily benefit the firm and should use different trade-in schemes under different conditions. Miao et al. [55] focused on the impact of carbon regulations on the coexistence of TON and TOR policy in the case of OEM self-remanufacturing model and showed that the OEM can make up the negative impact of carbon regulations on their profits through deliberately designed government subsidy schemes.Most studies in this area have focused on TON policy or the coexistence of TON and TOR. In contrast, this study investigates the TOR policy as it can further promote resource conservation in both the collection of WEEE products and the sales of remanufactured products. Although Han et al. [33] discussed the conditions for enterprises to implement TOR strategy from three aspects of product acceptance, durability, and government subsidies, Zhu and Wang [56] investigated the conditions under which TOR strategy for remanufactured products should be adopted and [33, 56] only considered OEM self-remanufacturing situation and seldom involved other remanufacturing mode. In addition, the question of when the TOR and carbon tax are implemented simultaneously, what impact will it have on enterprise decisions will need to be discussed further.


## 2.3. Carbon Tax Policy of CLSC

A carbon tax policy is one of the important means of energy conservation and emission reduction, and some scholars have also discussed it from different angles. Ding et al. [57] found that a carbon tax policy may not motivate firms to direct increased effort toward CER (carbon emission reduction). Yenipazarli [58] analyzed the effects of a carbon tax policy on the decision of a firm that produced both new and remanufactured products and showed that under a higher carbon tax, remanufacturing will have a negative impact on the environment. Zhu et al. [59] compared two measures to promote the remanufacturing industry—cash subsidies and carbon tax—and found that subsidies can improve corporate income, but a carbon tax may damage corporate income. Hu et al. [60], based on the OEM self-remanufacturing model, analyzed the impact between a carbon tax and cap-and-trade on a corporate decision, consumer surplus, and social welfare through a series of numerical studies. Guo and Huang [61] compared the social welfare effect between the policy of carbon tax and subsidy and showed that with the increase of marginal environmental damage caused by high carbon products, the control measures should be changed from subsidy policy to carbon tax policy. Yang et al. [62] analyzed the influence of carbon tax policy on the decision of enterprise members under the authorization and outsourcing remanufacturing mode. Wang et al. [63] confirmed that manufactured can offset the negative economic impact of the carbon emission tax policy by making low carbon emission technology investment. Wang et al. [64] investigated the different government subsidies on production and emission reduction decisions under a carbon tax regulation by formulating three optimization models.The above literatures show that the carbon tax policy and the government subsidy are often considered individually in CLSC. This research differs in that we integrate the carbon tax policy and the government subsidy into a dual policy regime. In addition, the above studies have rarely taken the adverse impact of carbon emissions on society. Given that social welfare, to a great extent, is affected by carbon emission, we would take this critical issue into account in this research.The two closest studies of ours are Li et al. [7] and Cao et al. [8]. Whereas [7] only considered the impact of subsidy and carbon tax policy on authorization remanufacturing mode respectively; meanwhile, it only regards carbon tax levy on the new products and ignores the carbon emission of the remanufactured products. Although [8] considered imposing a carbon tax on new products and the remanufactured ones simultaneously, they only analyzed and compared the optimal decisions of firms in the dual-channel supply chain under the single carbon tax policy. The optimal decisions of enterprises under government dual policy are not considered. Moreover, both [7, 8] considered the subsidy to enterprises, while this article discusses the government policy of TOR, that is, providing purchase subsidy to the consumer of the remanufactured product, which highlights the incentive effect of government policy on consumers in the remanufacturing market.In summary, most of the existing studies focus on the decisions of remanufacturing mode under government.In summary, most of the existing studies focus on the decisions of remanufacturing mode under government single policy, and to the best of our knowledge, no one took into account the combination of government dual policy and OEM's regulation strategy. Our research fills this gap (summarized in Table1). Furthermore, this article makes the following main contributions to the field, which distinguish it from previous studies:(i)
This article explores three strategies of OEM’s regulation in third-party remanufacturing existing in the actual industry;(ii)
We consider the government dual policy for remanufacturing which combines government subsidy with the carbon tax on new and remanufactured products;(iii)
A more comprehensive comparative analysis of the OEM different regulation strategies under government dual policy is carried out from the perspectives of enterprises and social and environmental benefits, respectively, whereby the objective of this article is to help the firms (OEM and TPR) make the optimal production and pricing decision under different remanufacturing modes and help the government find out the more desirable dual policy implementation conditions.Table 1
Comparison of this study and related literature.
StudiesOEM’s regulation strategyTORpolicyCarbontaxConsumerperspectiveEnvironmentalimpactsSavaskan et al. [13]Outsourcing√Oersdemir et al. [41]OEM self-remanufacturing√√Zou et al. [5]Outsourcing and authorization√√Miao et al. [52]OEM self-remanufacturing√Shu et al. [11]OEM self-remanufacturing√√√Han et al. [33]OEM self-remanufacturing√√√Li et al. [7]Authorization√√√Yang et al. [62]Authorization√Wang et al. [49]Nonregulation√Liu et al. [46]Authorization and nonregulation√Feng et al. [17]Outsourcing and authorization√√Cao et al. [8]OEM self-remanufacturing√√√This studyOutsourcing, authorization,and nonregulation√√√√


## 3. Problem Description

### 3.1. Model Description

We consider a CLSC of WEEE with an OEM and a TPR, where OEM is the market leader and TPR is the follower. Under the government dual policy (the government subsidy for consumers who purchase the remanufactured product and the carbon taxt and ρt against the OEM and TPR respectively for each unit of production products), as shown in Figure 1, we consider three remanufacturing game models: (a) OEM nonregulation remanufacturing (Model D). In Model D, OEM only manufactures the new product and TPR independently completes the process of WEEE recycling, remanufacturing, and sales [44]; (b) OEM outsourcing remanufacturing (Model O). In Model O, OEM outsources recycling and remanufacturing operation to TPR by paying an outsourcing fee, and OEM is responsible for sales of both the new and remanufactured products; (c) OEM authorization remanufacturing (Model A). In Model A, OEM manufactures and sales the new products; TPR recycles, remanufactures, and sells remanufactured products after being authorized by the OEM; and TPR pays unit product authorization fees to OEM [12, 17, 19].Figure 1
Three WEEE remanufacturing game models under government dual policy. (a) Model D, (b) Model O, and (c) Model A.
(a)(b)(c)


### 3.2. Symbolic Notations

In this article, the superscriptj∈D,O,A represents Model D, Model O, and Model A, respectively, while subscript h∈N,ST represents nongovernment intervention and government dual policy, respectively; i∈m,t,z represents OEM, TPR, and CLSC respectively; “∗” represents the optimal solution, for example, ΠmSTO∗ denotes the OEM’s profit in the Model O under government dual policy. Other parameters and variables are shown in Table 2.Table 2
The parameters and variables used in our mode.
SymbolDefinitionθThe consumer willingness to pay for the new productδThe consumer value discount for the remanufactured productvUnit consumption subsidy for consumers who purchase the remanufactured producttUnit carbon tax for new productρCarbon tax discount ratio of remanufactured products compared with new productkRecycling cost coefficientλhjThe recycling rate in modej under government strategy hfUnit authorization feecn/crThe unit production cost of new/remanufactured productptOutsourcing unit price of remanufactured productpn/prThe unit sales price of new/remanufactured productQn/QrThe demand for new/remanufactured productQzTotal market demandCShj/SWhjConsumer surplus/social welfare in modej under government strategy hen/erUnit environmental impact of new/remanufactured productEhjTotal environmental impact in modej under government strategy hΠihjProfit ofi in mode j under government strategy h


### 3.3. Model Assumptions

For the convenience of the study, the following assumptions are put forward:(1)
Consumer’s valuations for remanufactured product are lower than for new product [2]. Then, consumers are with respect to their willingness to pay (WTP) θ and δθ, respectively, for new and remanufactured products, where θ is uniformly distributed on the interval 0,1, and δ∈0,1. Moreover, we assume that each consumer purchases at most one product, and the market size is normalized to 1. Then the utilities for a consumer to purchase a new and remanufactured product are Un=θ−pn and Ur=δθ−pr+v, respectively [3]. Similar to [4, 11], demands for new and remanufactured products are derived as: Qn=1−pn−pr+v/1−δ and Qr=δpn−pr+v/δ1−δ, respectively. Further, based on the demand functions, we can derive the inverse demand functions as: pn=1−Qn−δQr and pr=v+δ1−Qn−Qr.(2)
Producing a remanufactured product’s cost is lower than producing a new product, that is,cr<cn [4, 17]. Moreover, we assume that the demand quantity of remanufactured product is equal to the recycling volume of WEEE (i.e., λQn=Qr) [5]. The cost of recycling products is a convex function of the recycling rate, and it can be formulated as 1/2kλQn2 [22], where 0<λ<1.(3)
Consumer surplus (CS) includes the total consumer surplus of new and remanufactured products. Social welfare (SW) refers to the sum of CS, profits of CLSC members, government income, and outcome. The expressions of CS and SW are obtained as follows [11, 15]:(1)CShj=∫pnhj−prhj+v/1−δ1θ−pnhjdθ+∫prhj−s/δpnhj−prhj+v/1−δδθ−prhj+vdθ=Qnhj2−pnhj+pnhj−prhj+v1−δQnhj+v−prhj+δpnhj+1−2δprhj−v21−δQrhj.SWhj=CShj+Πmhj+Πthj+tQrhj+Qnhj−vQrhj, where j∈D,O,A, h∈N,ST.(4)
The manufacturing/remanufacturing process is regarded as the sole source of carbon emission [8, 58]. It is commonly assumed that the carbon emission generated in producing a unit of new product is higher than that of producing a unit of remanufactured product, that is, en>er [28]; it is further assumed that the total carbon emission is linearly increasing in its products’ output. Thus, the total emission is Ehj=enQnhj+erQrhj; the remanufactured product has less carbon emissions compared with a new product, so the unit carbon tax for the remanufactured product is ρt, ρ∈0,1 [11, 33].(5)
All the members of the CLSC are risk-neutral, profit-maximizing, and have access to the same information. We construct a single-period model, which can be interpreted as the maturity stage of the product’s life cycle [41].


## 3.1. Model Description

We consider a CLSC of WEEE with an OEM and a TPR, where OEM is the market leader and TPR is the follower. Under the government dual policy (the government subsidy for consumers who purchase the remanufactured product and the carbon taxt and ρt against the OEM and TPR respectively for each unit of production products), as shown in Figure 1, we consider three remanufacturing game models: (a) OEM nonregulation remanufacturing (Model D). In Model D, OEM only manufactures the new product and TPR independently completes the process of WEEE recycling, remanufacturing, and sales [44]; (b) OEM outsourcing remanufacturing (Model O). In Model O, OEM outsources recycling and remanufacturing operation to TPR by paying an outsourcing fee, and OEM is responsible for sales of both the new and remanufactured products; (c) OEM authorization remanufacturing (Model A). In Model A, OEM manufactures and sales the new products; TPR recycles, remanufactures, and sells remanufactured products after being authorized by the OEM; and TPR pays unit product authorization fees to OEM [12, 17, 19].Figure 1
Three WEEE remanufacturing game models under government dual policy. (a) Model D, (b) Model O, and (c) Model A.
(a)(b)(c)


## 3.2. Symbolic Notations

In this article, the superscriptj∈D,O,A represents Model D, Model O, and Model A, respectively, while subscript h∈N,ST represents nongovernment intervention and government dual policy, respectively; i∈m,t,z represents OEM, TPR, and CLSC respectively; “∗” represents the optimal solution, for example, ΠmSTO∗ denotes the OEM’s profit in the Model O under government dual policy. Other parameters and variables are shown in Table 2.Table 2
The parameters and variables used in our mode.
SymbolDefinitionθThe consumer willingness to pay for the new productδThe consumer value discount for the remanufactured productvUnit consumption subsidy for consumers who purchase the remanufactured producttUnit carbon tax for new productρCarbon tax discount ratio of remanufactured products compared with new productkRecycling cost coefficientλhjThe recycling rate in modej under government strategy hfUnit authorization feecn/crThe unit production cost of new/remanufactured productptOutsourcing unit price of remanufactured productpn/prThe unit sales price of new/remanufactured productQn/QrThe demand for new/remanufactured productQzTotal market demandCShj/SWhjConsumer surplus/social welfare in modej under government strategy hen/erUnit environmental impact of new/remanufactured productEhjTotal environmental impact in modej under government strategy hΠihjProfit ofi in mode j under government strategy h


## 3.3. Model Assumptions

For the convenience of the study, the following assumptions are put forward:(1)
Consumer’s valuations for remanufactured product are lower than for new product [2]. Then, consumers are with respect to their willingness to pay (WTP) θ and δθ, respectively, for new and remanufactured products, where θ is uniformly distributed on the interval 0,1, and δ∈0,1. Moreover, we assume that each consumer purchases at most one product, and the market size is normalized to 1. Then the utilities for a consumer to purchase a new and remanufactured product are Un=θ−pn and Ur=δθ−pr+v, respectively [3]. Similar to [4, 11], demands for new and remanufactured products are derived as: Qn=1−pn−pr+v/1−δ and Qr=δpn−pr+v/δ1−δ, respectively. Further, based on the demand functions, we can derive the inverse demand functions as: pn=1−Qn−δQr and pr=v+δ1−Qn−Qr.(2)
Producing a remanufactured product’s cost is lower than producing a new product, that is,cr<cn [4, 17]. Moreover, we assume that the demand quantity of remanufactured product is equal to the recycling volume of WEEE (i.e., λQn=Qr) [5]. The cost of recycling products is a convex function of the recycling rate, and it can be formulated as 1/2kλQn2 [22], where 0<λ<1.(3)
Consumer surplus (CS) includes the total consumer surplus of new and remanufactured products. Social welfare (SW) refers to the sum of CS, profits of CLSC members, government income, and outcome. The expressions of CS and SW are obtained as follows [11, 15]:(1)CShj=∫pnhj−prhj+v/1−δ1θ−pnhjdθ+∫prhj−s/δpnhj−prhj+v/1−δδθ−prhj+vdθ=Qnhj2−pnhj+pnhj−prhj+v1−δQnhj+v−prhj+δpnhj+1−2δprhj−v21−δQrhj.SWhj=CShj+Πmhj+Πthj+tQrhj+Qnhj−vQrhj, where j∈D,O,A, h∈N,ST.(4)
The manufacturing/remanufacturing process is regarded as the sole source of carbon emission [8, 58]. It is commonly assumed that the carbon emission generated in producing a unit of new product is higher than that of producing a unit of remanufactured product, that is, en>er [28]; it is further assumed that the total carbon emission is linearly increasing in its products’ output. Thus, the total emission is Ehj=enQnhj+erQrhj; the remanufactured product has less carbon emissions compared with a new product, so the unit carbon tax for the remanufactured product is ρt, ρ∈0,1 [11, 33].(5)
All the members of the CLSC are risk-neutral, profit-maximizing, and have access to the same information. We construct a single-period model, which can be interpreted as the maturity stage of the product’s life cycle [41].


## 4. Model Formulation and Solution

### 4.1. Model Formulation

#### 4.1.1. Model D: OEM Nonregulation Remanufacturing Model

In Model D, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new productsQnSTD; and (2) the TPR determines the recycling rate of WEEE products λSTD based on the reaction of the OEM. And the profit functions of the OEM and TPR can be formulated as follows:(2)maxQnSTDπmSTD=pnSTD−cn−tQnSTD,(3)maxλSTDπtSTD=prSTD−cr−tρQrSTD−k2QrSTD2.Lemma 1.
The function ofπtSTD in equation (3) on the collection rate λSTD of waste products is concave; the optimal solution obtained from equation (3) is substituted into (2), and then the revenue of the OEM πnSTD in equation (2) on QnSTD can be proven to be concave functions.According to Lemma1, the optimal solution can be obtained (see 1). See Appendix A for the Proof of Lemma 1.Conclusion 1.
The optimal equilibrium solution under modeD is as follows:(4)pnSTD∗=k1+cn+t+δ2+2cn+cr+2t+tρ−v−δ2k+2δ,prSTD∗=δF2cr+k+δ+δk+δcnk+2δ−δcr+vδ−tδρkδ−2+δ3δ−4+tδ2k+k2+2kδ+4δ−δ22k+2δF,QnSTD∗=k1−cn−t−δC2F,QrSTD∗=δF+δcn−2crk+2δ+v−tρ2k+4δ−δ2+tkδ+δ2−2k−4δ+crδ22k+2δF,QzSTD∗=QnSTD∗+QrSTD∗=−k2cn+t−1+crk2−δ+δ4−3δ+δv3δ−4+δ2cn+t−3+3δ+tρ4−3δ+kvδ−2+δ3cn+3t+δ−5−tρδ−22Fk+2δ,λSTD∗=cr2k+4δ−δ2−k2v+δ1+t+cn−2tρ+δδ−2−cn−t+tρ−v4−δk+2δkt+cn−1+δC,ΠmSTD∗=kcn+t−1+δC24k+2δF,ΠtSTD∗=crδ2−4δ−2k+vδ−tρδ4−δ+k2v+δ1+cn+t−2tρ+δ221+cn+t−δ28k+2δF2.


#### 4.1.2. Model O: OEM Outsourcing Remanufacturing Model

In ModelO, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new products QnSTO and unit outsourcing fee ptSTO; and (2) the TPR determines the recycling rate of WEEE products λSTO. And the profit functions of the OEM and TPR can be formulated as follows:(5)maxQnSTO,ptSTOπmSTO=pnSTO−cn−tQnSTO+prSTO−ptSTOQrSTO,(6)maxλSTOπtSTO=ptSTO−cr−tρQrSTO−k2λSTOQnSTO2.Lemma 2.
The function ofπtSTO in equation (5) on the collection rate λSTO of waste products is concave; the optimal solution obtained from equation (6) is substituted into (5), and then the revenue of the OEM πmSTO in equation (5) on QnSTO,ptSTO can be proven to be concave functions.According to Lemma2, the optimal solution can be obtained (see Conclusion 2). See Appendix B for the Proof of Lemma 2.(7)pnSTO∗=1+cn+t2,prSTO∗=2kv+kδ1+cn+t+δ1−δcr+v+δ+tρ2M,QnSTD∗=k1−cn−t−δB2M,QrSTO∗=δcn+t+v−tρ−cr2M,QzSTO∗=QnSTO∗+QrSTO∗=1−δv+δ−tρ+crδ−1+k1−cn−t2M,λSTO∗=Ek1−cn−t−δB,ptSTO∗=crk+2δ−2δ2+2tδρ1−δ+v+tρ+δcn+t2M,ΠmSTO∗=1−cn24+v+δcn−cr24M+tk2cn+t−2+δ−12v−t+2δ−2cr4M+t1−ρ2v+2cnδ+2tδ−2cr−tρ−t4M,ΠtSTO∗=kv+δcn+t−cr−tρ28M2.


#### 4.1.3. Model A : OEM Authorization Remanufacturing Model

In Model A, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new productsQnSTA and the unit patent license fee fSTA; and (2) the TPR determines the recycling rate of WEEE products λSTA. And the profit functions of the OEM and TPR can be formulated as follows:(8)maxQnSTA,ftSTAπmSTA=pnSTA−cn−tQnSTA+fSTAQrSTA,(9)maxλSTAπtSTA=prSTA−cr−fSTA−tρQrSTA−k2λSTAQnSTA2.Lemma 3.
The function ofπtSTA in equation (9) on the collection rate λSTA of waste products is concave; the optimal solution obtained from equation (9) is substituted into (8), and then the revenue of the OEM πmSTA in equation (8) on QnSTA,ftSTA can be proven to be concave functions.According to Lemma3, the optimal solution can be obtained (see Conclusion 3). See Appendix C for the Proof of Lemma 3.(10)pnSTA∗=1+cn+t2,prSTA∗=2kv+kδ1+cn+t+δcr+3v+tρ+δ22+cn−cr−v−δ+t−tρ2F,QnSTA∗=k1−cn−t−δC2F,QrSTA∗=δcn+t+v−tρ−cr2F,QzSTA∗=QnSTA∗+QrSTA∗=cr+tρδ−1−kcn+t−1−δcn+v+t+δ+v+2δ2F,λSTA∗=Ek1−cn−t−δC,fSTA∗=δ+v−tρ−cr2,ΠmSTA∗=1−cn24+v+δcn−cr24F+tk2cn+t−2−2v+t4F+t2cr1−δ−4δ+2δcn+v+δ4F+tρ−12cr+tρ+t−2v−2cnδ−2tδ4F,ΠtSTA∗=k+2δδcn+t+v−cr−tρ28F2.We denoteE=v+δt+cn−cr−tρ, B=cn+v+t+δ−cr−1−tρ, C=v+δ+2t+2cn−cr−2−tρ, F=k+2δ−δ2, M=k+δ−δ2. Then, let v=t=0, we have the optimal solution with the nongovernment dual policy under the three remanufacturing modes.


### 4.2. Comparative Analysis of Equilibrium Results

According to the above Conclusions 1, 2, and 3, the following corollaries can be obtained:Corollary 1.
(1)
pnSTO∗=pnSTA∗>pnSTD∗; pnSTO∗>pnNO∗, pnSTA∗>pnNA∗, when t/v>δ/k+3δ, pnSTD∗>pnND∗, otherwise, pnSTD∗<pnND∗;(2)
prSTA∗>prSTO∗, prSTA∗>prSTD∗; prSTD∗>prND∗, prSTO∗>prNO∗, prSTA∗>prNA∗;(3)
Whenδ>cr, pnNO∗=pnNA∗>pnND∗, otherwise, pnND∗>pnNO∗=pnNA∗; when 0<δ<cr, prNA∗<prNO∗, prNA∗<prNW∗, when cr<δ<cr/cn, prND∗<prNA∗<prNO∗, when cr/cn<δ<1, prNA∗>prNO∗, prNA∗>prND∗.Corollary1.
shows that:(1)
Under government dual policy, among the three models, the new products price in Model D is the lowest, which indicates that the Model D is most beneficial to consumers. In Model O and Model A, remanufacturing activities without government dual policy intervention are more beneficial to market consumers; in Model D, when the ratio oft/v is more than a certain value δ/k+3δ, government dual policy can increase the prices of new products, otherwise, it is the contrary.(2)
Under government dual policy, the price of remanufactured products in Model A is highest. Moreover, whether in Model D, Model O, or Model A, compared with no government intervention, government dual policy can increase the price of remanufactured products. Since government dual policy increases the production cost of enterprises and the consumers’ willingness, it caused an increase in the price of remanufactured products.(3)
Without government dual policy, the price of new and remanufactured products is related to theδ, cr, and cn. If δ>cr, the new products price in Model D is lowest, at this time, the Model D is most beneficial to new product consumers. From the perspective of remanufactured products, if 0<δ<cr, the Model A is most beneficial to the consumers; if cr<δ<cr/cn, the Model O is most beneficial to the consumer; if cr/cn<δ<1, the Model A is detrimental to the consumer. See Appendix D for the Proof of Corollary 1.Corollary 2.
(1)
QnSTA∗=QnSTD∗>QnSTO∗; QnSTD∗<QnND∗, QnSTO∗<QnNO∗, QnSTA∗<QnNA∗;(2)
QrSTD∗>QrSTO∗>QrSTA∗; when v/t>δρ4−δ−kδ−2ρ−2δ2/δ4−δ+2k, QrSTD∗>QrND∗, otherwise, QrSTD∗<QrND∗, when v/t>ρ−δ, QrSTO∗>QrNO∗, QrSTA∗>QrNA∗, otherwise, QrSTO∗<QrNO∗, QrSTA∗<QrNA∗;(3)
QzSTD∗>QzSTA∗, QzSTO∗>QzSTA∗; when v/t>k2+3kδ+2δ2−kρδ−2−δρ3δ−4/k2−δ+4δ−3δ2, QzSTD∗>QzND∗, otherwise, QzSTD∗<QzND∗; when v/t>ρ+k−δρ/1−δ, QzSTO∗>QzNO∗, otherwise, QzSTO∗<QzNO∗; when v/t>ρ+k+δ−δρ/1−δ, QzSTA∗>QzNA∗, otherwise, QzSTA∗<QzNA∗;(4)
Whenδ>cr/cn, QnNA∗=QnND∗>QnNO∗, otherwise, QnNO∗>QnNA∗=QnND∗; when 0<δ<cr, QrNO∗<QrNA∗, QrNW∗<QrNA∗, when cr<δ<cr/cn, QrNO∗<QrNA∗<QrND∗, when cr/cn<δ<1, QrNO∗>QrNA∗, QrND∗>QrNA∗.Corollary2.
shows that:(1)
Under government dual policy, the demand for new products in Model O is the lowest; moreover, the implementation of government dual policy will reduce the demand for new products in the three remanufacturing models.(2)
Among the three models, the demand for remanufactured products is the lowest in Model A under the government dual policy. Combined with Corollary1, we can see that government dual policy will lead to the higher price of remanufactured products in Model A than in the other two models, so the demand for remanufactured products in Model A is lowest; if the ratio of v/t is more than a certain value δρ4−δ−kδ−2ρ−2δ2/δ4−δ+2k, government dual policy is conducive to increasing the demand of remanufactured products in Model D; and if the ratio of v/t is more than a certain value ρ−δ, government dual policy is conducive to increasing the demand of remanufactured products. Otherwise, it is the contrary.(3)
Among the three models, the total market demand in the Model A is the smallest under the government dual policy. The government dual policy is not necessarily conducive to expanding market demand; only when the ratio ofv/t meets certain conditions, it is conducive to increasing the total market demand of the three models.(4)
Similar to Corollary1, without government dual policy, when δ>cr/cn, the Model O is most unfavorable to the sales of the new products. If 0<δ<cr, the Model A is most conducive to the sales of remanufactured products; if cr<δ<cr/cn, the Model D is most conducive to the sales of remanufactured products; and if cr/cn<δ<1, the Model A is most unfavorable to the sales of remanufactured products. See Appendix E for the Proof of Corollary 2.Corollary 3.
(1)
λSTD∗>λND∗, λSTA∗>λNA∗, λSTO∗>λNO∗;(2)
λSTO∗>λSTA∗, λSTD∗>λSTA∗.Corollary3.
shows that:(1)
Whether this is Model D, Model O, or Model A, compared the case without government dual policy, the implementation of government dual policy can effectively improve the WEEE recycling rate, which indicates that the government dual policy is conducive to promoting the recycling of waste resources, thus promoting the development of the remanufacturing industry.(2)
Under government dual policy, the WEEE recycling rate is lowest in the Model A. It can be seen from Proposition2 that the demand for remanufactured products in Model O is higher than that in Model A, and the demand for new products in Model O is lower than that in Model A, the sales of new products in Model D and Model A are the same, but the market demand of remanufactured products in Model D is the highest, thus leads to the recycling rate in Model D higher than that in Model A (i.e., QrSTD∗/QnSTD∗>QrSTS∗/QnSTS∗>0, QrSTD∗/QnSTD∗>QrSTS∗/QnSTS∗>0). See Appendix F for the Proof of Corollary 3.Corollary 4.
(1)
ΠmSTO∗>ΠmSTA∗>ΠmSTD∗; ΠtSTD∗>ΠtSTA∗, ΠtSTW∗>ΠtSTO∗, if δ<0.5, ΠtSTA∗>ΠtSTO∗, if δ>0.5 and k>2δ1−δ2/2δ−1, ΠtSTO∗>ΠtSTA∗;(2)
ΠmND∗>ΠmSTD∗; when v>cr−δcn+t1−δ−cr2−kt2cn+t−2−δtt−2+2cncr+t+δ2cr+t2−2t, ΠmSTO∗>ΠmNO∗, if v>cr−δcn+(11)t1−δ−cr2−kt2cn+t−2−2δcncr+t2+2tcn−1+δ2cr+t2−2t,ΠmSTA∗>ΠmNA∗.ΠtSTO∗>ΠtNO∗; ΠtSTA∗>ΠtNA∗; if v/t>k2ρ−δ+δ4ρ−2δ−ρδ/2k+δ4−δ, ΠtSTD∗>ΠtND∗, otherwise, ΠtSTD∗<ΠtND∗;(3)
ΠmNO∗>ΠmNA∗>ΠmND∗; ΠtND∗>ΠtNO∗>ΠtNA∗.Corollary4.
shows the following:(1)
Under government dual policy, OEM’s profit in Model O is the highest and TPR’s profit in Model D is the highest. We can find that the OEM and TPR have different optimal remanufacturing modes selections. Moreover, when the OEM intervention in remanufacturing (i.e., Model A or Model O), ifδ>0.5 and k>2δ1−δ2/2δ−1, Model O may become the common optimal remanufacturing mode choice of OEM and TPR.(2)
In Model D, the implementation of government dual policy can decrease the profit of the OEM, that is to say, under government dual policy, Model D is not the best choice for the OEM; and only when the ratio ofv/t is more than a certain value, the government dual policy is conducive to increasing the TPR’s profits in Model D. In Model O and Model A, the government dual policy can increase the profit of TPR, whereas only when the subsidy satisfies certain conditions, the government dual policy is conducive to improving the OEM’s profits. Since the benefits of the increased price of the new and remanufactured products and subsidy can make up for the loss of decreased demand, the profits of OEM and TPR are all increased in Model O and Model A compared to the case without government dual policy. From the corollaries, we can indicate that when the parameters of policy satisfy certain conditions, the government dual policy can increase the supply chain member’s profits.(3)
When without government dual policy intervention, the OEM and TPR have the highest profit in Model O and Model D, respectively. And combined with (2), we find that the implementation of government dual policy would not change the strategy of OEM regulation in remanufacturing. See Appendix G for the Proof of Corollary 4.Corollary 5.
(1)
Whener/en<δ, ESTD∗>ESTA∗>ESTO∗, otherwise, ESTD∗>ESTO∗>ESTA∗;(2)
ESTD∗<END∗, if t/v>δen−er/erρ−δ+enk+δρ−δ and δ>er/en, ESTO∗>ENO∗, ESTA∗>ENA∗, otherwise, ESTO∗<ENO∗, ESTA∗<ENA∗.Corollary5.
shows that:(1)
Under government dual policy, Model D has the greatest impact on the environment. Moreover, when the ratio ofer/en is less than the δ, the impact of the environment in Model A is greater than that in Model O, otherwise, it is the contrary. It also shows that OEM's nonintervention in remanufacturing is compared, when the OEM's regulation in TPR remanufacturing, which can effectively reduce the impact of manufacturing/remanufacturing on the environment. This result indicates that under the government dual policy and from the viewpoint of environmental protection, if the remanufactured product is not so “clean,” the Model A is the best choice of remanufacturing mode, otherwise, the Model O is the best choice.(2)
Obviously, the government dual policy can effectively reduce the impact of manufacturing/remanufacturing on the environment in Model D. Moreover, when the ratio oft/v is more than a certain value δen−er/erρ−δ+enk+δρ−δ and δ>er/en, the environmental impact of Model O and Model A under the government dual policy is higher than that of no dual policy. From Corollary 5, we can indicate that the purpose of government dual policy is to promote the development of remanufacturing industry and realize the recycling of WEEE. However, since the remanufactured products also have an impact on the environment, and with the number of waste products increases, the impact on the environment will become greater. Therefore, when the government implements the dual policy, one needs to consider the environmental impact ratio of new and remanufactured products, and the ratio of t/v. And when er/en<δ, the government should select Model O for implement dual policy; otherwise, select Model A. In addition, if the ratio of t/v is more than a certain value, the government should non-intervene; otherwise, it is the contrary. See Appendix H for the Proof of Corollary 5.


### 4.3. Comparative Analysis of Equilibrium Results

By analyzing the effects of government dual policy parametersv and t on the optimal prices, demand, profit, and comparing them in the three models, we can obtain the following propositions.Proposition 1.
The influences of subsidy and carbon tax on the optimal retail price in the three models are as follows:(1)
∂pnSTD∗/∂v<∂pnSTA∗/∂v=∂pnSTO∗/∂v=0; ∂prSTA∗/∂v>∂prSTO∗/∂v>∂prSTD∗/∂v>0;(2)
∂pnSTD∗/∂t>∂pnSTO∗/∂t=∂pnSTA∗/∂t>0; ∂prSTD∗/∂t>0, ∂prSTO∗/∂t>0, ∂prSTA∗/∂t>0.Proposition1.
shows that:(1)
The price of remanufactured products in the three models are increasing with the increase of the subsidy; the prices of new products in Model D are decreasing with the increase of the subsidy, while TOR subsidy has no impact on the price of new products in Model O and Model A. The change rate of the price of remanufactured products in Model A is highest.(2)
With the increase of a carbon tax, the prices of new and remanufactured products are all increasing in the three models. Since with the increase in the carbon tax, firms will increase the price of new and remanufactured products and transfer the cost of a carbon tax to consumers. See Appendix I for the Proof of Proposition1.Proposition 2.
The influences of subsidy and carbon tax on the demands in the three models are as follows:(1)
∂QnSTO∗/∂v<∂QnSTD∗/∂v=∂QnSTA∗/∂v<0; ∂QrSTD∗/∂v>∂QrSTO∗/∂v>∂QrSTA∗/∂v>0;(2)
∂QnSTD∗/∂t=∂QnSTA∗/∂t<0, ∂QnSTO∗/∂t<0; ∂QrSTD∗/∂t<0, if ρ<δ, ∂QrSTO∗/∂t>∂QrSTA∗/∂t>0, otherwise, ∂QrSTO∗/∂t<∂QrSTA∗/∂t<0.Proposition2.
shows that:(1)
The demand for new products is decreasing with the increase of the subsidy, while the demand for remanufactured products is increasing with the increase of the subsidy. Since government subsidy reduces the consumer purchase costs of remanufactured products, it increases the demand for remanufactured products and causes the demand for new products to decrease.(2)
Whether this is Model D, Model O, or Model A, the demand for the new products is decreasing with the increase in a carbon tax. Since the prices of new products increase with the increase in the carbon tax, the demand for new products decreases. In Model D, the demand for remanufactured products decreases with the increase in a carbon tax. However, whenρ<δ, the demand for remanufactured products in Model O and Model A are increasing with the increase of the carbon tax, otherwise, it is decreasing. It also shows that government can stimulate the market sales of remanufactured products by setting an appropriate ρ value. See Appendix J for the Proof of Proposition 2.Proposition 3.
The influences of subsidy and carbon tax on the enterprise profit in the three models are as follows:(1)
∂ΠmSTD∗/∂v<0, ∂ΠmSTO∗/∂v>∂ΠmSTA∗/∂v>0; ∂ΠtSTD∗/∂v>0, ∂ΠtSTO∗/∂v>0, ∂ΠtSTA∗/∂v>0;(2)
∂ΠmSTD∗/∂t<0, ∂ΠmSTO∗/∂t<0, ∂ΠmSTA∗/∂t<0; ∂ΠtSTD∗/∂t<0, if ρ<δ, ∂ΠtSTO∗/∂t>0, ∂ΠtSTA∗/∂t>0, otherwise, ∂ΠtSTO∗/∂t<0, ∂ΠtSTA∗/∂t<0.Proposition3.
shows that:(1)
In Model O and Model A, with the increase of the subsidy, the profits of OEM and TPR are all increasing; in Model D, the profit of TPR is increasing and the profit of OEM is decreasing with the increase of the subsidy. In Model D, since the price and demand of new products are all decreasing, it leads to the reduction of OEM’s profit, while the impact of the subsidy on TPR’s profit is the contrary. In Model O, although the decrease in demand for new products caused a decrease in the profitability of new products, The OEM gains through outsourcing remanufacturing are higher than the profit loss caused by the reduction of new product sales, thus the OEM’s profit increases. The outsourcing fee and the demand for remanufactured products are all increasing with the increase of the subsidy, thus the TPR’s profit increases. In Model A, the price of new products is unchangeable, and its market demand is decreasing with the increase of the subsidy, so OEM’s profit will decrease with the increase of the subsidy. However, the authorization fee increases with the increase of the subsidy, which eventually contributes to the increase of OEM’s profit. That is to say, OEM can not only share the remanufacturing profit by authorization but also transfer the adverse effects of government subsidy by authorization. Since the price and demand for remanufactured products are all increasing with the increase of the subsidy, the TPR’s profit is also increasing. This proposition shows that the TOR policy can effectively promote the development of remanufacturing industry.(2)
In the three models, the profits of OEM are decreasing with the increase of the carbon tax; moreover, the change trends in the TPR’s profits with a carbon tax are consistent with that of the demand for remanufactured products. In Model D, with the increase of a carbon tax, the demand for a new and remanufactured product decreases, resulting in the loss of profits of firm higher than the profit increment brought by the increase of price, which eventually decreases the profits of OEM and TPR. In Model O, although the prices of the two products increase, the demand for new products decrease lead to the decrease of the new products’ profit, and the loss of profit is higher than the increase of profits, which ultimately decrease the OEM’s profit. Since the outsourcing fee increases with the increase of the carbon tax, and ifρ<δ, the demand for remanufactured products increases, thus the profit of TPR increases, otherwise, it is the contrary. In Model A, the demand for new products and authorization fees are all decreasing, which caused the OEM’s profit decrease. If ρ<δ, the carbon tax will increase the price and demand for the remanufactured products, that is to say, the consumers have a higher willingness to pay for the remanufactured products, which is conducive to increase the TPR’s profit. If ρ<δ, it is the contrary. See Appendix K for the Proof of Proposition 3.Proposition 4.
The influences of subsidy and carbon tax on the recycling rate in the three models are as follows:(1)
∂λSTD∗/∂v>∂λSTA∗/∂v>0, ∂λSTO∗/∂v>0;(2)
Whenρ<δ+v−cr/1−cn, ∂λSTD∗/∂t>∂λSTA∗/∂t>0, ∂λSTO∗/∂t>0, otherwise, ∂λSTD∗/∂t<∂λSTA∗/∂t<0, ∂λSTO∗/∂t<0.Proposition4.
shows that:(1)
Subsidies not only increase the selling price and sales volume of remanufactured products, but also help to improve the recycling rate. That is to say, the TOR policy can improve the TPR’s enthusiasm for recycling used products.(2)
The carbon tax policy may improve the recycling rate of WEEE, which is also affected by theρ. If ρ is small (i.e., ρ<δ+v−cr/1−cn, the carbon tax levied by the government on the remanufactured products is low), the implementation of carbon tax would be conducive to the recycling rate. If ρ>δ+v−cr/1−cn, it is the contrary. See Appendix L for the Proof of Proposition 4.Proposition 5.
The influences of subsidy and carbon tax on the outsourcing unit price of remanufactured products and the unit authorization fee are as follows:(1)
∂ptSTO∗/∂t>∂ptSTO∗/∂v>0;(2)
∂fSTA∗/∂v>0>∂fSTA∗/∂t.Proposition5.
shows that:(1)
Under the government’s dual policy, for the outsourcing remanufacturing mode (Model O), the unit outsourcing price of OEM remanufactured products is positively correlated with government subsidies and carbon tax, which indicates that the implementation of the government’s dual policy will promote OEM to increase the outsourcing fees. The main reason is that with the increase of subsidy and carbon tax, the price and demand of remanufactured products are increased. Therefore, OEMs are carving up the remanufacturing market profit by raising the outsourcing fees in order to obtain more revenue.(2)
Under the government’s dual policy, for the authorized remanufacturing mode (Model A), the authorization fees paid by TPR to OEM are positively correlated with the government subsidy, but negatively correlated with the carbon tax, that is, the government subsidy increases the unit authorization fee of OEM, and the government carbon tax will reduce the unit authorization fee of OEM. See Appendix M for the Proof of Proposition5.


## 4.1. Model Formulation

### 4.1.1. Model D: OEM Nonregulation Remanufacturing Model

In Model D, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new productsQnSTD; and (2) the TPR determines the recycling rate of WEEE products λSTD based on the reaction of the OEM. And the profit functions of the OEM and TPR can be formulated as follows:(2)maxQnSTDπmSTD=pnSTD−cn−tQnSTD,(3)maxλSTDπtSTD=prSTD−cr−tρQrSTD−k2QrSTD2.Lemma 1.
The function ofπtSTD in equation (3) on the collection rate λSTD of waste products is concave; the optimal solution obtained from equation (3) is substituted into (2), and then the revenue of the OEM πnSTD in equation (2) on QnSTD can be proven to be concave functions.According to Lemma1, the optimal solution can be obtained (see 1). See Appendix A for the Proof of Lemma 1.Conclusion 1.
The optimal equilibrium solution under modeD is as follows:(4)pnSTD∗=k1+cn+t+δ2+2cn+cr+2t+tρ−v−δ2k+2δ,prSTD∗=δF2cr+k+δ+δk+δcnk+2δ−δcr+vδ−tδρkδ−2+δ3δ−4+tδ2k+k2+2kδ+4δ−δ22k+2δF,QnSTD∗=k1−cn−t−δC2F,QrSTD∗=δF+δcn−2crk+2δ+v−tρ2k+4δ−δ2+tkδ+δ2−2k−4δ+crδ22k+2δF,QzSTD∗=QnSTD∗+QrSTD∗=−k2cn+t−1+crk2−δ+δ4−3δ+δv3δ−4+δ2cn+t−3+3δ+tρ4−3δ+kvδ−2+δ3cn+3t+δ−5−tρδ−22Fk+2δ,λSTD∗=cr2k+4δ−δ2−k2v+δ1+t+cn−2tρ+δδ−2−cn−t+tρ−v4−δk+2δkt+cn−1+δC,ΠmSTD∗=kcn+t−1+δC24k+2δF,ΠtSTD∗=crδ2−4δ−2k+vδ−tρδ4−δ+k2v+δ1+cn+t−2tρ+δ221+cn+t−δ28k+2δF2.


### 4.1.2. Model O: OEM Outsourcing Remanufacturing Model

In ModelO, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new products QnSTO and unit outsourcing fee ptSTO; and (2) the TPR determines the recycling rate of WEEE products λSTO. And the profit functions of the OEM and TPR can be formulated as follows:(5)maxQnSTO,ptSTOπmSTO=pnSTO−cn−tQnSTO+prSTO−ptSTOQrSTO,(6)maxλSTOπtSTO=ptSTO−cr−tρQrSTO−k2λSTOQnSTO2.Lemma 2.
The function ofπtSTO in equation (5) on the collection rate λSTO of waste products is concave; the optimal solution obtained from equation (6) is substituted into (5), and then the revenue of the OEM πmSTO in equation (5) on QnSTO,ptSTO can be proven to be concave functions.According to Lemma2, the optimal solution can be obtained (see Conclusion 2). See Appendix B for the Proof of Lemma 2.(7)pnSTO∗=1+cn+t2,prSTO∗=2kv+kδ1+cn+t+δ1−δcr+v+δ+tρ2M,QnSTD∗=k1−cn−t−δB2M,QrSTO∗=δcn+t+v−tρ−cr2M,QzSTO∗=QnSTO∗+QrSTO∗=1−δv+δ−tρ+crδ−1+k1−cn−t2M,λSTO∗=Ek1−cn−t−δB,ptSTO∗=crk+2δ−2δ2+2tδρ1−δ+v+tρ+δcn+t2M,ΠmSTO∗=1−cn24+v+δcn−cr24M+tk2cn+t−2+δ−12v−t+2δ−2cr4M+t1−ρ2v+2cnδ+2tδ−2cr−tρ−t4M,ΠtSTO∗=kv+δcn+t−cr−tρ28M2.


### 4.1.3. Model A : OEM Authorization Remanufacturing Model

In Model A, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new productsQnSTA and the unit patent license fee fSTA; and (2) the TPR determines the recycling rate of WEEE products λSTA. And the profit functions of the OEM and TPR can be formulated as follows:(8)maxQnSTA,ftSTAπmSTA=pnSTA−cn−tQnSTA+fSTAQrSTA,(9)maxλSTAπtSTA=prSTA−cr−fSTA−tρQrSTA−k2λSTAQnSTA2.Lemma 3.
The function ofπtSTA in equation (9) on the collection rate λSTA of waste products is concave; the optimal solution obtained from equation (9) is substituted into (8), and then the revenue of the OEM πmSTA in equation (8) on QnSTA,ftSTA can be proven to be concave functions.According to Lemma3, the optimal solution can be obtained (see Conclusion 3). See Appendix C for the Proof of Lemma 3.(10)pnSTA∗=1+cn+t2,prSTA∗=2kv+kδ1+cn+t+δcr+3v+tρ+δ22+cn−cr−v−δ+t−tρ2F,QnSTA∗=k1−cn−t−δC2F,QrSTA∗=δcn+t+v−tρ−cr2F,QzSTA∗=QnSTA∗+QrSTA∗=cr+tρδ−1−kcn+t−1−δcn+v+t+δ+v+2δ2F,λSTA∗=Ek1−cn−t−δC,fSTA∗=δ+v−tρ−cr2,ΠmSTA∗=1−cn24+v+δcn−cr24F+tk2cn+t−2−2v+t4F+t2cr1−δ−4δ+2δcn+v+δ4F+tρ−12cr+tρ+t−2v−2cnδ−2tδ4F,ΠtSTA∗=k+2δδcn+t+v−cr−tρ28F2.We denoteE=v+δt+cn−cr−tρ, B=cn+v+t+δ−cr−1−tρ, C=v+δ+2t+2cn−cr−2−tρ, F=k+2δ−δ2, M=k+δ−δ2. Then, let v=t=0, we have the optimal solution with the nongovernment dual policy under the three remanufacturing modes.


## 4.1.1. Model D: OEM Nonregulation Remanufacturing Model

In Model D, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new productsQnSTD; and (2) the TPR determines the recycling rate of WEEE products λSTD based on the reaction of the OEM. And the profit functions of the OEM and TPR can be formulated as follows:(2)maxQnSTDπmSTD=pnSTD−cn−tQnSTD,(3)maxλSTDπtSTD=prSTD−cr−tρQrSTD−k2QrSTD2.Lemma 1.
The function ofπtSTD in equation (3) on the collection rate λSTD of waste products is concave; the optimal solution obtained from equation (3) is substituted into (2), and then the revenue of the OEM πnSTD in equation (2) on QnSTD can be proven to be concave functions.According to Lemma1, the optimal solution can be obtained (see 1). See Appendix A for the Proof of Lemma 1.Conclusion 1.
The optimal equilibrium solution under modeD is as follows:(4)pnSTD∗=k1+cn+t+δ2+2cn+cr+2t+tρ−v−δ2k+2δ,prSTD∗=δF2cr+k+δ+δk+δcnk+2δ−δcr+vδ−tδρkδ−2+δ3δ−4+tδ2k+k2+2kδ+4δ−δ22k+2δF,QnSTD∗=k1−cn−t−δC2F,QrSTD∗=δF+δcn−2crk+2δ+v−tρ2k+4δ−δ2+tkδ+δ2−2k−4δ+crδ22k+2δF,QzSTD∗=QnSTD∗+QrSTD∗=−k2cn+t−1+crk2−δ+δ4−3δ+δv3δ−4+δ2cn+t−3+3δ+tρ4−3δ+kvδ−2+δ3cn+3t+δ−5−tρδ−22Fk+2δ,λSTD∗=cr2k+4δ−δ2−k2v+δ1+t+cn−2tρ+δδ−2−cn−t+tρ−v4−δk+2δkt+cn−1+δC,ΠmSTD∗=kcn+t−1+δC24k+2δF,ΠtSTD∗=crδ2−4δ−2k+vδ−tρδ4−δ+k2v+δ1+cn+t−2tρ+δ221+cn+t−δ28k+2δF2.


## 4.1.2. Model O: OEM Outsourcing Remanufacturing Model

In ModelO, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new products QnSTO and unit outsourcing fee ptSTO; and (2) the TPR determines the recycling rate of WEEE products λSTO. And the profit functions of the OEM and TPR can be formulated as follows:(5)maxQnSTO,ptSTOπmSTO=pnSTO−cn−tQnSTO+prSTO−ptSTOQrSTO,(6)maxλSTOπtSTO=ptSTO−cr−tρQrSTO−k2λSTOQnSTO2.Lemma 2.
The function ofπtSTO in equation (5) on the collection rate λSTO of waste products is concave; the optimal solution obtained from equation (6) is substituted into (5), and then the revenue of the OEM πmSTO in equation (5) on QnSTO,ptSTO can be proven to be concave functions.According to Lemma2, the optimal solution can be obtained (see Conclusion 2). See Appendix B for the Proof of Lemma 2.(7)pnSTO∗=1+cn+t2,prSTO∗=2kv+kδ1+cn+t+δ1−δcr+v+δ+tρ2M,QnSTD∗=k1−cn−t−δB2M,QrSTO∗=δcn+t+v−tρ−cr2M,QzSTO∗=QnSTO∗+QrSTO∗=1−δv+δ−tρ+crδ−1+k1−cn−t2M,λSTO∗=Ek1−cn−t−δB,ptSTO∗=crk+2δ−2δ2+2tδρ1−δ+v+tρ+δcn+t2M,ΠmSTO∗=1−cn24+v+δcn−cr24M+tk2cn+t−2+δ−12v−t+2δ−2cr4M+t1−ρ2v+2cnδ+2tδ−2cr−tρ−t4M,ΠtSTO∗=kv+δcn+t−cr−tρ28M2.


## 4.1.3. Model A : OEM Authorization Remanufacturing Model

In Model A, the sequence of the decisions is as follows: (1) the OEM determines the optimal production quantity of the new productsQnSTA and the unit patent license fee fSTA; and (2) the TPR determines the recycling rate of WEEE products λSTA. And the profit functions of the OEM and TPR can be formulated as follows:(8)maxQnSTA,ftSTAπmSTA=pnSTA−cn−tQnSTA+fSTAQrSTA,(9)maxλSTAπtSTA=prSTA−cr−fSTA−tρQrSTA−k2λSTAQnSTA2.Lemma 3.
The function ofπtSTA in equation (9) on the collection rate λSTA of waste products is concave; the optimal solution obtained from equation (9) is substituted into (8), and then the revenue of the OEM πmSTA in equation (8) on QnSTA,ftSTA can be proven to be concave functions.According to Lemma3, the optimal solution can be obtained (see Conclusion 3). See Appendix C for the Proof of Lemma 3.(10)pnSTA∗=1+cn+t2,prSTA∗=2kv+kδ1+cn+t+δcr+3v+tρ+δ22+cn−cr−v−δ+t−tρ2F,QnSTA∗=k1−cn−t−δC2F,QrSTA∗=δcn+t+v−tρ−cr2F,QzSTA∗=QnSTA∗+QrSTA∗=cr+tρδ−1−kcn+t−1−δcn+v+t+δ+v+2δ2F,λSTA∗=Ek1−cn−t−δC,fSTA∗=δ+v−tρ−cr2,ΠmSTA∗=1−cn24+v+δcn−cr24F+tk2cn+t−2−2v+t4F+t2cr1−δ−4δ+2δcn+v+δ4F+tρ−12cr+tρ+t−2v−2cnδ−2tδ4F,ΠtSTA∗=k+2δδcn+t+v−cr−tρ28F2.We denoteE=v+δt+cn−cr−tρ, B=cn+v+t+δ−cr−1−tρ, C=v+δ+2t+2cn−cr−2−tρ, F=k+2δ−δ2, M=k+δ−δ2. Then, let v=t=0, we have the optimal solution with the nongovernment dual policy under the three remanufacturing modes.


## 4.2. Comparative Analysis of Equilibrium Results

According to the above Conclusions 1, 2, and 3, the following corollaries can be obtained:Corollary 1.
(1)
pnSTO∗=pnSTA∗>pnSTD∗; pnSTO∗>pnNO∗, pnSTA∗>pnNA∗, when t/v>δ/k+3δ, pnSTD∗>pnND∗, otherwise, pnSTD∗<pnND∗;(2)
prSTA∗>prSTO∗, prSTA∗>prSTD∗; prSTD∗>prND∗, prSTO∗>prNO∗, prSTA∗>prNA∗;(3)
Whenδ>cr, pnNO∗=pnNA∗>pnND∗, otherwise, pnND∗>pnNO∗=pnNA∗; when 0<δ<cr, prNA∗<prNO∗, prNA∗<prNW∗, when cr<δ<cr/cn, prND∗<prNA∗<prNO∗, when cr/cn<δ<1, prNA∗>prNO∗, prNA∗>prND∗.Corollary1.
shows that:(1)
Under government dual policy, among the three models, the new products price in Model D is the lowest, which indicates that the Model D is most beneficial to consumers. In Model O and Model A, remanufacturing activities without government dual policy intervention are more beneficial to market consumers; in Model D, when the ratio oft/v is more than a certain value δ/k+3δ, government dual policy can increase the prices of new products, otherwise, it is the contrary.(2)
Under government dual policy, the price of remanufactured products in Model A is highest. Moreover, whether in Model D, Model O, or Model A, compared with no government intervention, government dual policy can increase the price of remanufactured products. Since government dual policy increases the production cost of enterprises and the consumers’ willingness, it caused an increase in the price of remanufactured products.(3)
Without government dual policy, the price of new and remanufactured products is related to theδ, cr, and cn. If δ>cr, the new products price in Model D is lowest, at this time, the Model D is most beneficial to new product consumers. From the perspective of remanufactured products, if 0<δ<cr, the Model A is most beneficial to the consumers; if cr<δ<cr/cn, the Model O is most beneficial to the consumer; if cr/cn<δ<1, the Model A is detrimental to the consumer. See Appendix D for the Proof of Corollary 1.Corollary 2.
(1)
QnSTA∗=QnSTD∗>QnSTO∗; QnSTD∗<QnND∗, QnSTO∗<QnNO∗, QnSTA∗<QnNA∗;(2)
QrSTD∗>QrSTO∗>QrSTA∗; when v/t>δρ4−δ−kδ−2ρ−2δ2/δ4−δ+2k, QrSTD∗>QrND∗, otherwise, QrSTD∗<QrND∗, when v/t>ρ−δ, QrSTO∗>QrNO∗, QrSTA∗>QrNA∗, otherwise, QrSTO∗<QrNO∗, QrSTA∗<QrNA∗;(3)
QzSTD∗>QzSTA∗, QzSTO∗>QzSTA∗; when v/t>k2+3kδ+2δ2−kρδ−2−δρ3δ−4/k2−δ+4δ−3δ2, QzSTD∗>QzND∗, otherwise, QzSTD∗<QzND∗; when v/t>ρ+k−δρ/1−δ, QzSTO∗>QzNO∗, otherwise, QzSTO∗<QzNO∗; when v/t>ρ+k+δ−δρ/1−δ, QzSTA∗>QzNA∗, otherwise, QzSTA∗<QzNA∗;(4)
Whenδ>cr/cn, QnNA∗=QnND∗>QnNO∗, otherwise, QnNO∗>QnNA∗=QnND∗; when 0<δ<cr, QrNO∗<QrNA∗, QrNW∗<QrNA∗, when cr<δ<cr/cn, QrNO∗<QrNA∗<QrND∗, when cr/cn<δ<1, QrNO∗>QrNA∗, QrND∗>QrNA∗.Corollary2.
shows that:(1)
Under government dual policy, the demand for new products in Model O is the lowest; moreover, the implementation of government dual policy will reduce the demand for new products in the three remanufacturing models.(2)
Among the three models, the demand for remanufactured products is the lowest in Model A under the government dual policy. Combined with Corollary1, we can see that government dual policy will lead to the higher price of remanufactured products in Model A than in the other two models, so the demand for remanufactured products in Model A is lowest; if the ratio of v/t is more than a certain value δρ4−δ−kδ−2ρ−2δ2/δ4−δ+2k, government dual policy is conducive to increasing the demand of remanufactured products in Model D; and if the ratio of v/t is more than a certain value ρ−δ, government dual policy is conducive to increasing the demand of remanufactured products. Otherwise, it is the contrary.(3)
Among the three models, the total market demand in the Model A is the smallest under the government dual policy. The government dual policy is not necessarily conducive to expanding market demand; only when the ratio ofv/t meets certain conditions, it is conducive to increasing the total market demand of the three models.(4)
Similar to Corollary1, without government dual policy, when δ>cr/cn, the Model O is most unfavorable to the sales of the new products. If 0<δ<cr, the Model A is most conducive to the sales of remanufactured products; if cr<δ<cr/cn, the Model D is most conducive to the sales of remanufactured products; and if cr/cn<δ<1, the Model A is most unfavorable to the sales of remanufactured products. See Appendix E for the Proof of Corollary 2.Corollary 3.
(1)
λSTD∗>λND∗, λSTA∗>λNA∗, λSTO∗>λNO∗;(2)
λSTO∗>λSTA∗, λSTD∗>λSTA∗.Corollary3.
shows that:(1)
Whether this is Model D, Model O, or Model A, compared the case without government dual policy, the implementation of government dual policy can effectively improve the WEEE recycling rate, which indicates that the government dual policy is conducive to promoting the recycling of waste resources, thus promoting the development of the remanufacturing industry.(2)
Under government dual policy, the WEEE recycling rate is lowest in the Model A. It can be seen from Proposition2 that the demand for remanufactured products in Model O is higher than that in Model A, and the demand for new products in Model O is lower than that in Model A, the sales of new products in Model D and Model A are the same, but the market demand of remanufactured products in Model D is the highest, thus leads to the recycling rate in Model D higher than that in Model A (i.e., QrSTD∗/QnSTD∗>QrSTS∗/QnSTS∗>0, QrSTD∗/QnSTD∗>QrSTS∗/QnSTS∗>0). See Appendix F for the Proof of Corollary 3.Corollary 4.
(1)
ΠmSTO∗>ΠmSTA∗>ΠmSTD∗; ΠtSTD∗>ΠtSTA∗, ΠtSTW∗>ΠtSTO∗, if δ<0.5, ΠtSTA∗>ΠtSTO∗, if δ>0.5 and k>2δ1−δ2/2δ−1, ΠtSTO∗>ΠtSTA∗;(2)
ΠmND∗>ΠmSTD∗; when v>cr−δcn+t1−δ−cr2−kt2cn+t−2−δtt−2+2cncr+t+δ2cr+t2−2t, ΠmSTO∗>ΠmNO∗, if v>cr−δcn+(11)t1−δ−cr2−kt2cn+t−2−2δcncr+t2+2tcn−1+δ2cr+t2−2t,ΠmSTA∗>ΠmNA∗.ΠtSTO∗>ΠtNO∗; ΠtSTA∗>ΠtNA∗; if v/t>k2ρ−δ+δ4ρ−2δ−ρδ/2k+δ4−δ, ΠtSTD∗>ΠtND∗, otherwise, ΠtSTD∗<ΠtND∗;(3)
ΠmNO∗>ΠmNA∗>ΠmND∗; ΠtND∗>ΠtNO∗>ΠtNA∗.Corollary4.
shows the following:(1)
Under government dual policy, OEM’s profit in Model O is the highest and TPR’s profit in Model D is the highest. We can find that the OEM and TPR have different optimal remanufacturing modes selections. Moreover, when the OEM intervention in remanufacturing (i.e., Model A or Model O), ifδ>0.5 and k>2δ1−δ2/2δ−1, Model O may become the common optimal remanufacturing mode choice of OEM and TPR.(2)
In Model D, the implementation of government dual policy can decrease the profit of the OEM, that is to say, under government dual policy, Model D is not the best choice for the OEM; and only when the ratio ofv/t is more than a certain value, the government dual policy is conducive to increasing the TPR’s profits in Model D. In Model O and Model A, the government dual policy can increase the profit of TPR, whereas only when the subsidy satisfies certain conditions, the government dual policy is conducive to improving the OEM’s profits. Since the benefits of the increased price of the new and remanufactured products and subsidy can make up for the loss of decreased demand, the profits of OEM and TPR are all increased in Model O and Model A compared to the case without government dual policy. From the corollaries, we can indicate that when the parameters of policy satisfy certain conditions, the government dual policy can increase the supply chain member’s profits.(3)
When without government dual policy intervention, the OEM and TPR have the highest profit in Model O and Model D, respectively. And combined with (2), we find that the implementation of government dual policy would not change the strategy of OEM regulation in remanufacturing. See Appendix G for the Proof of Corollary 4.Corollary 5.
(1)
Whener/en<δ, ESTD∗>ESTA∗>ESTO∗, otherwise, ESTD∗>ESTO∗>ESTA∗;(2)
ESTD∗<END∗, if t/v>δen−er/erρ−δ+enk+δρ−δ and δ>er/en, ESTO∗>ENO∗, ESTA∗>ENA∗, otherwise, ESTO∗<ENO∗, ESTA∗<ENA∗.Corollary5.
shows that:(1)
Under government dual policy, Model D has the greatest impact on the environment. Moreover, when the ratio ofer/en is less than the δ, the impact of the environment in Model A is greater than that in Model O, otherwise, it is the contrary. It also shows that OEM's nonintervention in remanufacturing is compared, when the OEM's regulation in TPR remanufacturing, which can effectively reduce the impact of manufacturing/remanufacturing on the environment. This result indicates that under the government dual policy and from the viewpoint of environmental protection, if the remanufactured product is not so “clean,” the Model A is the best choice of remanufacturing mode, otherwise, the Model O is the best choice.(2)
Obviously, the government dual policy can effectively reduce the impact of manufacturing/remanufacturing on the environment in Model D. Moreover, when the ratio oft/v is more than a certain value δen−er/erρ−δ+enk+δρ−δ and δ>er/en, the environmental impact of Model O and Model A under the government dual policy is higher than that of no dual policy. From Corollary 5, we can indicate that the purpose of government dual policy is to promote the development of remanufacturing industry and realize the recycling of WEEE. However, since the remanufactured products also have an impact on the environment, and with the number of waste products increases, the impact on the environment will become greater. Therefore, when the government implements the dual policy, one needs to consider the environmental impact ratio of new and remanufactured products, and the ratio of t/v. And when er/en<δ, the government should select Model O for implement dual policy; otherwise, select Model A. In addition, if the ratio of t/v is more than a certain value, the government should non-intervene; otherwise, it is the contrary. See Appendix H for the Proof of Corollary 5.


## 4.3. Comparative Analysis of Equilibrium Results

By analyzing the effects of government dual policy parametersv and t on the optimal prices, demand, profit, and comparing them in the three models, we can obtain the following propositions.Proposition 1.
The influences of subsidy and carbon tax on the optimal retail price in the three models are as follows:(1)
∂pnSTD∗/∂v<∂pnSTA∗/∂v=∂pnSTO∗/∂v=0; ∂prSTA∗/∂v>∂prSTO∗/∂v>∂prSTD∗/∂v>0;(2)
∂pnSTD∗/∂t>∂pnSTO∗/∂t=∂pnSTA∗/∂t>0; ∂prSTD∗/∂t>0, ∂prSTO∗/∂t>0, ∂prSTA∗/∂t>0.Proposition1.
shows that:(1)
The price of remanufactured products in the three models are increasing with the increase of the subsidy; the prices of new products in Model D are decreasing with the increase of the subsidy, while TOR subsidy has no impact on the price of new products in Model O and Model A. The change rate of the price of remanufactured products in Model A is highest.(2)
With the increase of a carbon tax, the prices of new and remanufactured products are all increasing in the three models. Since with the increase in the carbon tax, firms will increase the price of new and remanufactured products and transfer the cost of a carbon tax to consumers. See Appendix I for the Proof of Proposition1.Proposition 2.
The influences of subsidy and carbon tax on the demands in the three models are as follows:(1)
∂QnSTO∗/∂v<∂QnSTD∗/∂v=∂QnSTA∗/∂v<0; ∂QrSTD∗/∂v>∂QrSTO∗/∂v>∂QrSTA∗/∂v>0;(2)
∂QnSTD∗/∂t=∂QnSTA∗/∂t<0, ∂QnSTO∗/∂t<0; ∂QrSTD∗/∂t<0, if ρ<δ, ∂QrSTO∗/∂t>∂QrSTA∗/∂t>0, otherwise, ∂QrSTO∗/∂t<∂QrSTA∗/∂t<0.Proposition2.
shows that:(1)
The demand for new products is decreasing with the increase of the subsidy, while the demand for remanufactured products is increasing with the increase of the subsidy. Since government subsidy reduces the consumer purchase costs of remanufactured products, it increases the demand for remanufactured products and causes the demand for new products to decrease.(2)
Whether this is Model D, Model O, or Model A, the demand for the new products is decreasing with the increase in a carbon tax. Since the prices of new products increase with the increase in the carbon tax, the demand for new products decreases. In Model D, the demand for remanufactured products decreases with the increase in a carbon tax. However, whenρ<δ, the demand for remanufactured products in Model O and Model A are increasing with the increase of the carbon tax, otherwise, it is decreasing. It also shows that government can stimulate the market sales of remanufactured products by setting an appropriate ρ value. See Appendix J for the Proof of Proposition 2.Proposition 3.
The influences of subsidy and carbon tax on the enterprise profit in the three models are as follows:(1)
∂ΠmSTD∗/∂v<0, ∂ΠmSTO∗/∂v>∂ΠmSTA∗/∂v>0; ∂ΠtSTD∗/∂v>0, ∂ΠtSTO∗/∂v>0, ∂ΠtSTA∗/∂v>0;(2)
∂ΠmSTD∗/∂t<0, ∂ΠmSTO∗/∂t<0, ∂ΠmSTA∗/∂t<0; ∂ΠtSTD∗/∂t<0, if ρ<δ, ∂ΠtSTO∗/∂t>0, ∂ΠtSTA∗/∂t>0, otherwise, ∂ΠtSTO∗/∂t<0, ∂ΠtSTA∗/∂t<0.Proposition3.
shows that:(1)
In Model O and Model A, with the increase of the subsidy, the profits of OEM and TPR are all increasing; in Model D, the profit of TPR is increasing and the profit of OEM is decreasing with the increase of the subsidy. In Model D, since the price and demand of new products are all decreasing, it leads to the reduction of OEM’s profit, while the impact of the subsidy on TPR’s profit is the contrary. In Model O, although the decrease in demand for new products caused a decrease in the profitability of new products, The OEM gains through outsourcing remanufacturing are higher than the profit loss caused by the reduction of new product sales, thus the OEM’s profit increases. The outsourcing fee and the demand for remanufactured products are all increasing with the increase of the subsidy, thus the TPR’s profit increases. In Model A, the price of new products is unchangeable, and its market demand is decreasing with the increase of the subsidy, so OEM’s profit will decrease with the increase of the subsidy. However, the authorization fee increases with the increase of the subsidy, which eventually contributes to the increase of OEM’s profit. That is to say, OEM can not only share the remanufacturing profit by authorization but also transfer the adverse effects of government subsidy by authorization. Since the price and demand for remanufactured products are all increasing with the increase of the subsidy, the TPR’s profit is also increasing. This proposition shows that the TOR policy can effectively promote the development of remanufacturing industry.(2)
In the three models, the profits of OEM are decreasing with the increase of the carbon tax; moreover, the change trends in the TPR’s profits with a carbon tax are consistent with that of the demand for remanufactured products. In Model D, with the increase of a carbon tax, the demand for a new and remanufactured product decreases, resulting in the loss of profits of firm higher than the profit increment brought by the increase of price, which eventually decreases the profits of OEM and TPR. In Model O, although the prices of the two products increase, the demand for new products decrease lead to the decrease of the new products’ profit, and the loss of profit is higher than the increase of profits, which ultimately decrease the OEM’s profit. Since the outsourcing fee increases with the increase of the carbon tax, and ifρ<δ, the demand for remanufactured products increases, thus the profit of TPR increases, otherwise, it is the contrary. In Model A, the demand for new products and authorization fees are all decreasing, which caused the OEM’s profit decrease. If ρ<δ, the carbon tax will increase the price and demand for the remanufactured products, that is to say, the consumers have a higher willingness to pay for the remanufactured products, which is conducive to increase the TPR’s profit. If ρ<δ, it is the contrary. See Appendix K for the Proof of Proposition 3.Proposition 4.
The influences of subsidy and carbon tax on the recycling rate in the three models are as follows:(1)
∂λSTD∗/∂v>∂λSTA∗/∂v>0, ∂λSTO∗/∂v>0;(2)
Whenρ<δ+v−cr/1−cn, ∂λSTD∗/∂t>∂λSTA∗/∂t>0, ∂λSTO∗/∂t>0, otherwise, ∂λSTD∗/∂t<∂λSTA∗/∂t<0, ∂λSTO∗/∂t<0.Proposition4.
shows that:(1)
Subsidies not only increase the selling price and sales volume of remanufactured products, but also help to improve the recycling rate. That is to say, the TOR policy can improve the TPR’s enthusiasm for recycling used products.(2)
The carbon tax policy may improve the recycling rate of WEEE, which is also affected by theρ. If ρ is small (i.e., ρ<δ+v−cr/1−cn, the carbon tax levied by the government on the remanufactured products is low), the implementation of carbon tax would be conducive to the recycling rate. If ρ>δ+v−cr/1−cn, it is the contrary. See Appendix L for the Proof of Proposition 4.Proposition 5.
The influences of subsidy and carbon tax on the outsourcing unit price of remanufactured products and the unit authorization fee are as follows:(1)
∂ptSTO∗/∂t>∂ptSTO∗/∂v>0;(2)
∂fSTA∗/∂v>0>∂fSTA∗/∂t.Proposition5.
shows that:(1)
Under the government’s dual policy, for the outsourcing remanufacturing mode (Model O), the unit outsourcing price of OEM remanufactured products is positively correlated with government subsidies and carbon tax, which indicates that the implementation of the government’s dual policy will promote OEM to increase the outsourcing fees. The main reason is that with the increase of subsidy and carbon tax, the price and demand of remanufactured products are increased. Therefore, OEMs are carving up the remanufacturing market profit by raising the outsourcing fees in order to obtain more revenue.(2)
Under the government’s dual policy, for the authorized remanufacturing mode (Model A), the authorization fees paid by TPR to OEM are positively correlated with the government subsidy, but negatively correlated with the carbon tax, that is, the government subsidy increases the unit authorization fee of OEM, and the government carbon tax will reduce the unit authorization fee of OEM. See Appendix M for the Proof of Proposition5.


## 5. Numerical Analysis

To verify the above propositions and more clearly illustrate the impacts of government dual policy on different remanufacturing CLSC decisions, we conduct the numerical analysis of the impact of government dual policy on CLSC’s total profit, consumer surplus, social welfare, and environment impact by Mathematica 11.0. Following [21, 32], the parameters are set as: cn=0.4, cr=0.25, δ=0.7, k=0.6, ρ=0.5, en=0.3, and er=0.1.


### 5.1. Impact of Government Dual Policy on Total Profit of CLSC

Figure2 illustrates the impact of government dual policy on the total profit of CLSC in the three remanufacturing modes. From Figure 2, we can find that with the increase of TOR subsidy v and the decrease of carbon tax t, the total profits of CLSC in the three remanufacturing models are increasing. The total profit of CLSC in Model O is higher than that of the other two models. That is to say, the combination of government dual policy and Model O could improve the economic performance of the entire CLSC, compared to the other two modes.Figure 2
The impact of government dual policy on total profit of CLSC.


### 5.2. Impact of Government Dual Policy on Recycling Rate, Consumer Surplus, Social Welfare, and Environment

Figure3 illustrates the impact of government dual policy on the optimal recycling rates of WEEE. Figure 3 indicates that with the increase of TOR subsidy v and carbon tax t, the recycling rates in all the three modes increase. And Model D is most conducive to the recycling of WEEE products. Meanwhile, the decrease rates of recycling rates in Model D are larger than that under Model O and Model A, that is to say, government dual policy has a greater impact on Model D than the other two modes. Moreover, no matter what OEM’s regulation strategy is, government dual policy could always improve the efficiency of recycling WEEE products, compared to the case without government dual policy.Figure 3
The impact of government dual policy on recycling rate.Figure4 illustrates the impact of the government dual policy on the consumer surplus (CS) under the three remanufacturing modes. It indicates that with the increase of carbon tax t and the decrease of subsidies v, the consumer surplus decrease in the three remanufacturing modes. Under government dual policy, consumer surplus in the Model D is highest, that is, from the perspective of consumer surplus, it is more beneficial to the consumer when OEM do not supervise TPR’s remanufacturing activities. Besides, when t/v meets a certain condition, government dual policy can effectively increase the consumer surplus under the three remanufacturing modes. We have learned that no matter what OEM’s regulation strategy is, consumer surplus increases with the increase of the TOR subsidy. Even though the decrease in demand for new products caused the decrease of consumer surplus with new products, the TOR policy increases the consumer surplus of remanufactured products, and the increase of consumer surplus is higher than that its decrease, thus the total consumer surplus is increasing. But when the carbon tax is very high and subsidy is very small, government dual policy will damage consumer surplus.Figure 4
The impact of government dual policy on consumer surplus.Figure5 illustrates the impact of government dual policy on social welfare (SW) under the three remanufacturing modes. Figure 5 shows that with the increase of the subsidy v and carbon tax t, the social welfare decreases in the Model D, and with the increase of the TOR subsidy v and the decrease of carbon tax t, the social welfare increases in the Model O and Model A. In addition, when t/v is small, government dual policy increases the social welfare in the Model O and Model A; on the contrary, when t/v is high, the implementation of government dual policy may decrease the social welfare in the Model O and Model A. Under government dual policy, among the three remanufacturing modes, social welfare can reach the maximum in Model D. Therefore, from the perspective of maximizing social welfare, the government prefers Model D to implement dual policy and also finds that the government should set high subsidy and low carbon tax, which is beneficial to supply members and consumers; in this case, the interests of consumers, enterprises, and government are consistent.Figure 5
The impact of government dual policy on social welfare.Figure6 illustrates the impact of government dual policy on the environment under the three remanufacturing modes. From Figure 6, we can find that with the increase of subsidy v and carbon tax t, the environmental impacts decrease in the three remanufacturing modes. And the environmental impact in Model D is the highest and that in Model O is the lowest, and when er/en<δ, Model O is the best choice for environmental protection. No matter what OEM’s regulation strategy is, government dual policy is conducive to reducing the impact on the environment. Besides, when the carbon tax is high enough, government dual policy can decrease environmental impact; if set a low carbon tax, although this helps to reduce the production cost burden of firms, it will increase the difficulty for the government to control the impact of enterprises on the environment. We can also find that, from the perspective of environmental protection, the government should set a high carbon tax, but which would harm the benefits of supply chain members and increase the purchase cost of consumers. Figure 6 verifies the conclusion of Corollary 5.Figure 6
The impact of government dual policy on environmental impact.Figure7 illustrates the impact of government dual policy on the unit authorization fee and outsourcing price under Model O and Model A. Figure 7 shows that with the increase of subsidy v, the unit authorization fees and outsourcing price of remanufactured products increase; however, with the increase of carbon tax t, the outsourcing price of remanufactured products increases in Model O and the unit authorization fee decreases in Model A. In the Model O, OEMs can share the benefits generated by remanufacturing. With the increase of government subsidy and carbon tax, the OEM’s new product revenue decreases. Therefore, in order to make up for the loss of new product profit, when the government subsidy and carbon tax increase, OEMs will increase the remanufacturing revenue by increasing the outsourcing unit price; in the Model A, with the increase of subsidy, the market income of new products decreases, while the sales volume and price of remanufactured products increase. Therefore, when the government subsidy increases, the OEM will increase the unit authorization fee to obtain more benefits generated by remanufacturing. Due to the increase of carbon tax and the demand of remanufactured products, OEM will promote TPR remanufacturing by reducing unit patent cost, so as to obtain the benefits generated by remanufacturing. Figure 7 verifies the conclusion of Proposition 5.Figure 7
The impact of government dual policy on the unit authorization fee and outsourcing price.


## 5.1. Impact of Government Dual Policy on Total Profit of CLSC

Figure2 illustrates the impact of government dual policy on the total profit of CLSC in the three remanufacturing modes. From Figure 2, we can find that with the increase of TOR subsidy v and the decrease of carbon tax t, the total profits of CLSC in the three remanufacturing models are increasing. The total profit of CLSC in Model O is higher than that of the other two models. That is to say, the combination of government dual policy and Model O could improve the economic performance of the entire CLSC, compared to the other two modes.Figure 2
The impact of government dual policy on total profit of CLSC.


## 5.2. Impact of Government Dual Policy on Recycling Rate, Consumer Surplus, Social Welfare, and Environment

Figure3 illustrates the impact of government dual policy on the optimal recycling rates of WEEE. Figure 3 indicates that with the increase of TOR subsidy v and carbon tax t, the recycling rates in all the three modes increase. And Model D is most conducive to the recycling of WEEE products. Meanwhile, the decrease rates of recycling rates in Model D are larger than that under Model O and Model A, that is to say, government dual policy has a greater impact on Model D than the other two modes. Moreover, no matter what OEM’s regulation strategy is, government dual policy could always improve the efficiency of recycling WEEE products, compared to the case without government dual policy.Figure 3
The impact of government dual policy on recycling rate.Figure4 illustrates the impact of the government dual policy on the consumer surplus (CS) under the three remanufacturing modes. It indicates that with the increase of carbon tax t and the decrease of subsidies v, the consumer surplus decrease in the three remanufacturing modes. Under government dual policy, consumer surplus in the Model D is highest, that is, from the perspective of consumer surplus, it is more beneficial to the consumer when OEM do not supervise TPR’s remanufacturing activities. Besides, when t/v meets a certain condition, government dual policy can effectively increase the consumer surplus under the three remanufacturing modes. We have learned that no matter what OEM’s regulation strategy is, consumer surplus increases with the increase of the TOR subsidy. Even though the decrease in demand for new products caused the decrease of consumer surplus with new products, the TOR policy increases the consumer surplus of remanufactured products, and the increase of consumer surplus is higher than that its decrease, thus the total consumer surplus is increasing. But when the carbon tax is very high and subsidy is very small, government dual policy will damage consumer surplus.Figure 4
The impact of government dual policy on consumer surplus.Figure5 illustrates the impact of government dual policy on social welfare (SW) under the three remanufacturing modes. Figure 5 shows that with the increase of the subsidy v and carbon tax t, the social welfare decreases in the Model D, and with the increase of the TOR subsidy v and the decrease of carbon tax t, the social welfare increases in the Model O and Model A. In addition, when t/v is small, government dual policy increases the social welfare in the Model O and Model A; on the contrary, when t/v is high, the implementation of government dual policy may decrease the social welfare in the Model O and Model A. Under government dual policy, among the three remanufacturing modes, social welfare can reach the maximum in Model D. Therefore, from the perspective of maximizing social welfare, the government prefers Model D to implement dual policy and also finds that the government should set high subsidy and low carbon tax, which is beneficial to supply members and consumers; in this case, the interests of consumers, enterprises, and government are consistent.Figure 5
The impact of government dual policy on social welfare.Figure6 illustrates the impact of government dual policy on the environment under the three remanufacturing modes. From Figure 6, we can find that with the increase of subsidy v and carbon tax t, the environmental impacts decrease in the three remanufacturing modes. And the environmental impact in Model D is the highest and that in Model O is the lowest, and when er/en<δ, Model O is the best choice for environmental protection. No matter what OEM’s regulation strategy is, government dual policy is conducive to reducing the impact on the environment. Besides, when the carbon tax is high enough, government dual policy can decrease environmental impact; if set a low carbon tax, although this helps to reduce the production cost burden of firms, it will increase the difficulty for the government to control the impact of enterprises on the environment. We can also find that, from the perspective of environmental protection, the government should set a high carbon tax, but which would harm the benefits of supply chain members and increase the purchase cost of consumers. Figure 6 verifies the conclusion of Corollary 5.Figure 6
The impact of government dual policy on environmental impact.Figure7 illustrates the impact of government dual policy on the unit authorization fee and outsourcing price under Model O and Model A. Figure 7 shows that with the increase of subsidy v, the unit authorization fees and outsourcing price of remanufactured products increase; however, with the increase of carbon tax t, the outsourcing price of remanufactured products increases in Model O and the unit authorization fee decreases in Model A. In the Model O, OEMs can share the benefits generated by remanufacturing. With the increase of government subsidy and carbon tax, the OEM’s new product revenue decreases. Therefore, in order to make up for the loss of new product profit, when the government subsidy and carbon tax increase, OEMs will increase the remanufacturing revenue by increasing the outsourcing unit price; in the Model A, with the increase of subsidy, the market income of new products decreases, while the sales volume and price of remanufactured products increase. Therefore, when the government subsidy increases, the OEM will increase the unit authorization fee to obtain more benefits generated by remanufacturing. Due to the increase of carbon tax and the demand of remanufactured products, OEM will promote TPR remanufacturing by reducing unit patent cost, so as to obtain the benefits generated by remanufacturing. Figure 7 verifies the conclusion of Proposition 5.Figure 7
The impact of government dual policy on the unit authorization fee and outsourcing price.


## 6. Conclusions

This article investigated the optimal decisions of two firms (OEM and TPR) in the three WEEE remanufacturing modes under the government dual policy (the policy combination of TOR and carbon tax) and further explored the effectiveness of government policy intervention and the optimal choice of OEM’s regulation strategy in third-party remanufacturing. Firstly, the optimal decisions of the two firms under the dual policy are presented. Then, the influence of the policy parameters upon products’ price, quantity, profits, and the comparison with the optimal decision with nongovernment intervention under different models were analyzed. Finally, through numerical analysis, the effect of government dual policy on decisions of CLSC total profits, consumer surplus, social welfare, and the environment benefit were analyzed.


### 6.1. Major Conclusions

(1)
The optimal decision-making and mode choice of supply chain enterprises would affect by the government. Without government dual policy, OEM will prefer Model O and Model A, which harms TPR’s benefit. But when the subsidy and carbon tax meet a certain condition, the government dual policy is conducive to improving the profits of chain members, consumers surplus, and social welfare under each remanufacturing mode.(2)
Whether the government implements the dual policy or not, outsourcing mode is always the best choice for OEM. That is to say, the implementation of government dual policy does not affect the decision of OEM’s regulation strategy to remanufacturing; meanwhile, the dual policy can improve the profit of OEM when the subsidy value is higher than a certain threshold. Moreover, only when the consumer’s value evaluation of remanufactured products is high enough, outsourcing mode may become a common best choice for both OEM and TPR; however, it would have an adverse impact on the consumer and society.(3)
The government dual policy can effectively improve the recycling rates of WEEE. Meanwhile, government dual policy can significantly promote the sale of remanufactured products and drive enterprises to further reduce carbon emission, when the dual policy parameters meet a certain range. And the government dual policy can expand the total demand of market products when the ratio of subsidy and carbon tax meets a certain condition. Whereas, the government dual policy does not always improve the firm’s profits, consumer surplus, and social welfare. Only when the government setting a reasonable subsidy and carbon tax, the government dual policy is beneficial to supply chain members, consumers, and society. In this case, the interests of the government and enterprise are consistent.


### 6.2. Managerial Implications

(1)
OEM should supervise the TPR’s remanufacturing activity, to share the benefits brought by remanufacturing, and outsourcing strategy is the best choice for OEM.(2)
The government should decide whether it should carry out the dual policy intervention according to OEM’s regulation strategy. Moreover, both the TOR policy and carbon tax policy can improve consumer surplus and social welfare under some conditions. The government should carefully set proper the ratio of subsidy and carbon tax to ensure the effectiveness of the dual policy intervention.(3)
Firms should engage in reducing the environmental output of remanufactured products and improving the consumer’s recognition of remanufactured ones. On the one hand, firms should effectively classify the WEEE, improve the remanufacturing technology, ensure the quality of remanufactured products, and finally improve consumer acceptance of remanufactured products; on the other hand, the government should strengthen the publicity of remanufactured products and further promote the implementation of incentive remanufacturing development policy.


### 6.3. Limitations

However, there are still some limitations that are not considered in this study. Firstly, the research constructed a single-period mode. Secondly, this research is based on the assumption of complete information. Research analysis will become more complex if the incompleteness of information is assumed. This will be investigated in further research, and these studies will help enterprises and governments make better decisions.


## 6.1. Major Conclusions

(1)
The optimal decision-making and mode choice of supply chain enterprises would affect by the government. Without government dual policy, OEM will prefer Model O and Model A, which harms TPR’s benefit. But when the subsidy and carbon tax meet a certain condition, the government dual policy is conducive to improving the profits of chain members, consumers surplus, and social welfare under each remanufacturing mode.(2)
Whether the government implements the dual policy or not, outsourcing mode is always the best choice for OEM. That is to say, the implementation of government dual policy does not affect the decision of OEM’s regulation strategy to remanufacturing; meanwhile, the dual policy can improve the profit of OEM when the subsidy value is higher than a certain threshold. Moreover, only when the consumer’s value evaluation of remanufactured products is high enough, outsourcing mode may become a common best choice for both OEM and TPR; however, it would have an adverse impact on the consumer and society.(3)
The government dual policy can effectively improve the recycling rates of WEEE. Meanwhile, government dual policy can significantly promote the sale of remanufactured products and drive enterprises to further reduce carbon emission, when the dual policy parameters meet a certain range. And the government dual policy can expand the total demand of market products when the ratio of subsidy and carbon tax meets a certain condition. Whereas, the government dual policy does not always improve the firm’s profits, consumer surplus, and social welfare. Only when the government setting a reasonable subsidy and carbon tax, the government dual policy is beneficial to supply chain members, consumers, and society. In this case, the interests of the government and enterprise are consistent.


## 6.2. Managerial Implications

(1)
OEM should supervise the TPR’s remanufacturing activity, to share the benefits brought by remanufacturing, and outsourcing strategy is the best choice for OEM.(2)
The government should decide whether it should carry out the dual policy intervention according to OEM’s regulation strategy. Moreover, both the TOR policy and carbon tax policy can improve consumer surplus and social welfare under some conditions. The government should carefully set proper the ratio of subsidy and carbon tax to ensure the effectiveness of the dual policy intervention.(3)
Firms should engage in reducing the environmental output of remanufactured products and improving the consumer’s recognition of remanufactured ones. On the one hand, firms should effectively classify the WEEE, improve the remanufacturing technology, ensure the quality of remanufactured products, and finally improve consumer acceptance of remanufactured products; on the other hand, the government should strengthen the publicity of remanufactured products and further promote the implementation of incentive remanufacturing development policy.


## 6.3. Limitations

However, there are still some limitations that are not considered in this study. Firstly, the research constructed a single-period mode. Secondly, this research is based on the assumption of complete information. Research analysis will become more complex if the incompleteness of information is assumed. This will be investigated in further research, and these studies will help enterprises and governments make better decisions.



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*Source: 1236612-2022-07-12.xml*