Authorization or Outsourcing: Considering the Contrast/Assimilation Effect and Network Externality of Remanufactured Products under Government Subsidy

Abstract

This paper examines the impact of the contrast/assimilation effect and network externality of remanufactured products on remanufacturing mode selection for original equipment manufacturers (OEMs) under government subsidy. We develop a two-period Stackelberg game model in a closed-loop supply chain (CLSC) composed of an OEM and a third-party remanufacturer (TPR) considering two remanufacturing modes: authorization remanufacturing mode and outsourcing remanufacturing mode. The results show the following: (1) The OEM prefers to select authorization when the contrast/assimilation effect and government subsidy level are both relatively low; otherwise, the OEM prefers outsourcing. The TPR always prefers the outsourcing mode. Therefore, a win–win situation between the OEM and the TPR could be achieved through OEM outsourcing remanufacturing when the government raises subsidy levels or the contrast/assimilation effect is relatively obvious. (2) The outsourcing mode is more beneficial in promoting the sales of remanufactured products and is more environmentally friendly, while the authorization mode is better in regards to consumer surplus and social welfare. (3) OEM, TPR and CLSC could benefit from network externality increasing. The stronger contrast effect (assimilation effect) is profitable to the OEM and CLSC (TPR), but hurts the TPR (OEM and CLSC). (4) Government subsidy can significantly reduce consumer spending on remanufactured products. CLSC members encroach government subsidies which are offered to consumers through pricing adjustments. The findings provide managerial implications for OEMs’ remanufacturing mode strategy in the context of the contrast/assimilation effect and network externality of remanufactured products under government subsidy.

1. Introduction

Nowadays, with the rapid development of the economy, environmental and resource issues have become increasingly prominent. Remanufacturing as one of the key approaches to achieve sustainable development, has attracted widespread attention of both business and academia. Besides reducing environmental impact, enterprises can extract residual value in end-of-use products through remanufacturing activities and enhance their profitability [1]. Many enterprises such as HP, Xerox et al. have engaged in remanufacturing operations [2]. However, consumers have low acceptance and willingness to pay for remanufactured products due to their concerns about the quality of remanufactured products [3,4]. To reduce consumers’ concerns and promote the development of the remanufacturing industry, governments have enacted many consumption subsidy polices such as the Trade the Old for Remanufacturing program in 2013 launched by the Chinese government. The government subsidy aims to stimulate uncertain consumers to buy remanufactured products and then increase collection volume for remanufacturing enterprises, which can help them better deal with challenges they face. Many researches have confirmed that the government subsidy could promote the sales of remanufactured products [5,6,7]. In addition, consumers’ concerns for remanufactured products can be eased when more consumers purchase remanufactured products, that is, when the network externality of remanufactured products exists [8]. Therefore, it is necessary for remanufacturers to include consideration of a remanufactured product’s characteristic of network externality into the firm’s strategy.

Although remanufacturing can bring great economic benefits, manufacturers must face an internal competition between the new and remanufactured products [9]. As a lower priced substitution, the sales of remanufactured products cannibalize the market of new ones [10]. And remanufacturing is not always beneficial for original equipment manufacturers (OEMs) [11]. Now, there are more and more professional third-party remanufacturers (TPRs) engaging in remanufacturing processes such as Caterpillar, Foxconn, et al. According to the empirical study of Agrawal et al. [12], the entrance of OEM-remanufactured products could reduce consumers’ perceived value of an OEM’s new products, while the entrance of TPR-remanufactured products can increase consumers’ perceived value of an OEM’s new products. We refer to the former as the assimilation effect and the latter as the contrast effect. For instance, if Samsung provides both new and remanufactured smartphones simultaneously, while its competitor Lenovo only provides new ones, consumers may be concerned that Samsung’s new smartphones may be made of refurbished parts and are not reliable, but would be confident that Lenovo’s new smartphones are made of new materials [13]. Thus, the impact of the presence of remanufactured products on consumers’ perceived value of new products cannot be ignored.

In reality, collecting and remanufacturing are not core businesses for many OEMs [14]. Due to concerns of the cost of investment, brand protection, technology limitation et al., many OEMs lack remanufacturing motivation [15]. Therefore, OEMs prefer to outsource remanufacturing activities to TPRs. The OEM has two remanufacturing strategies: authorization and outsourcing. Under the authorization remanufacturing mode, the OEM licenses both the remanufacturing process and the sales operations to the TPR and the TPR pays authorization fees to the OEM. Under the outsourcing remanufacturing mode, the OEM only outsources remanufacturing process to the TPR with outsourcing fees, and is responsible for the sales of the remanufactured products itself. For example, Foxconn acquired a proprietary license from Apple to remanufacture end-of-life iPhone mobile phones and remarket them in the Chinese market in 2015, and Land Rover outsources their remanufacturing operations to Caterpillar [16].

1.1. Research Questions

In the past, few studies considered the impact of the contrast/assimilation effect and network externality of remanufactured products on the pricing decisions and operations for a closed-loop supply chain (CLSC) simultaneously. To fill the research gaps, the proposed models investigate the optimal pricing decisions and remanufacturing mode selection for a CLSC considering the contrast/assimilation effect, network externality of remanufactured products and government subsidy under two remanufacturing models, i.e., authorization remanufacturing (Model A) and outsourcing remanufacturing (Model O). This paper attempts to answer the following research questions:

(1)

Which remanufacturing mode is optimal for the OEM/TPR/CLSC considering the contrast/assimilation effect and the network externality of remanufactured products under government subsidy?

(2)

Which remanufacturing mode is better from the perspective of the environment and society?

(3)

How do the contrast/assimilation effect, network externality and government subsidy affect OEMs’ remanufacturing mode selection and the operations of the CLSC?

1.2. Flow of Study

To solve these questions, considering the contrast/assimilation effect and network externality under government subsidy, a two-period Stackelberg game model is developed. We first derive the optimal solutions under the two remanufacturing modes, then we compare the CLSC operations in the two models and examine the optimal remanufacturing mode strategy for the OEM. Finally, we validate the theoretical results and compare the environmental impact, consumer surplus and social welfare between the two remanufacturing modes with numerical experiments. The main contributions of this paper are as follows:

(1)

We establish two remanufacturing models which provides managerial guidance for OEMs in regard to their remanufacturing mode-selection strategy.

(2)

We compare the optimal pricing decisions, demands and profits of the CLSC in two remanufacturing models.

(3)

We conduct numerical analysis to explore the impact of the OEM’s remanufacturing mode selection strategy on the environment, consumer surplus and social welfare.

The rest of this paper is organized as follows. In Section 2, we review the relevant studies. Section 3 describes the model. Section 4 deals with the model formulation and solution. The model comparison and analysis are made in Section 5. The numerical analysis is presented in Section 6. Finally, results are summarized in Section 7. All proofs are given in Appendix A.

2. Literature Review

Our research is mainly related to these four streams of literature: (1) government subsidy in CLSCs; (2) the contrast/assimilation effect in CLSCs; (3) the network externality in a supply chain (SC); (4) remanufacturing modes in CLSCs.

2.1. Government Subsidy in CLSCs

The research about government remanufacturing subsidies has achieved various outcomes. Zhao et al. [17] explored the impact of government subsidy or incentive on the remanufacturing supply chain, and they showed that government subsidies to remanufacturers makes the supply chain system more stable. Guo et al. [18] developed a multi-period CLSC model considering government subsidy and supply disruption, and they demonstrated the government subsidy providing strategies to the enterprise. Chen et al. [19] examined government subsidy in a research joint venture with two types of subsidy, i.e., per-unit production subsidy and innovation effort subsidy. They found that the government should never implement these two types of subsidies simultaneously to reduce the cost of research and development efforts. Wang et al. [20] investigated the optimal pricing decisions and the impacts of government subsidy with different subsidized parties in a CLSC composed of one remanufacturer, two retailers and one collector, and they demonstrated that remanufacturing utilization rate affects the allocation strategy of government subsidies significantly. Wang et al. [21] examined the impact of a government subsidy and a remanufacturer’s altruistic preference on the decision making of a low-carbon e-commerce CLSC. Zhang et al. [7] analyzed the effects of government fund policy on the optimal decisions of CLSC members under two remanufacturing modes, and they found the manufacturer remanufacturing mode is more favorable for CLSC members without a government fund policy, while the retailer remanufacturing mode is better with a government fund policy. Zhang and Zhang [22] studied the optimal government subsidies for authorized remanufacturers and analyzed the impact of government subsidies on the stability of the CLSC. Obviously, government subsidy can promote the development of the remanufacturing industry significantly. Differently from the above works, we develop a two-period game model and we assume that the government only subsidizes consumers who purchase remanufactured products in the first period in order to better reflect the non-long-term characteristic of the government policy. Then, we further examine the impact of government subsidy on the decision making of CLSC members and consumers.

2.2. Contrast/assimilation Effect in CLSCs

Most previous studies assumed that the presence of remanufactured products would not change consumers’ value evaluation of new products. In fact, Agrawal et al. [12] confirmed the presence of OEM-remanufactured products can reduce consumers’ perceived value of new products (assimilation effect), while the presence of TPR-remanufactured products can increase consumers’ perceived value for new products (contrast effect). Based on the research results, some scholars have studied the operations of CLSC. Li et al. [23] investigated the effects of consumers’ perceived value on optimal decisions in a CLSC under OEM remanufacturing and TPR remanufacturing. They showed TPR remanufacturing can make OEMs and whole CLSCs obtain more profits, but it is unfavorable to the sales of remanufactured products. Fang et al. [11] studied the competition between the OEM and the TPR under the influence of consumers’ perceived value and they found that it is not always profitable for an OEM to conduct remanufacturing activities and the OEM should leave remanufacturing to the TPR under certain circumstances. Wu et al. [13] examined the impact of contrast and assimilation effects on two competing OEMs’ remanufacturing and pricing strategies in which they assumed that the existence of one OEM’s remanufactured products may reduce consumers’ perceived value of its new products, but enhance that of its competitor’s new products. Dong et al. [24] analyzed the optimal pricing decisions in a CLSC consisting of an OEM and a third-party recycler under different game structures based on consumers’ perceived value. They found that the improvement of consumers’ perceived value for new products can increase the market demand and profit of OEM, but it can damage the market demand and profit of third-party recyclers. Guo et al. [25] studied a monopolist manufacturer’s optimal remanufacturing and pricing strategies under the cap-and-trade regulation with the impact of assimilation effect and they found that the assimilation effect can reduce the manufacturer’s motivation to engage in remanufacturing. Huang et al. [26] assumed that the entry of independent remanufacturers can increase consumers’ perceived value for new products and investigated the optimal pricing decisions of CLSC members. The above works discuss and analyze a CLSC’s optimal decisions considering the changes in consumers’ perceived value of new products in the presence of remanufactured products. In summary, there is little research considering the contrast/assimilation effect and the changes in consumers’ perceived value of new products in CLSC management simultaneously, so the difference between this stream of literature and our work is that we explore the impact of the contrast/assimilation effect on remanufacturing mode selection.

2.3. Network Externality in SCs

When purchasing products, consumers not only consider the product itself; their decisions are also influenced by the number of consumers who have bought the product. Katz and Shapiro [27] initially introduced the concept of network externality, which means customers’ perceived value of a product is increased with the existing customer number. Consequently, some research focused on operation management in a supply chain given the characteristic of product network externality. Liu et al. [28] discussed the sales channel and versioning strategies for a supplier under the impact of network externality. They showed that the products should be offered in a single version with less or no network externality; otherwise, the products should be sold in two versions. In a market with network externality, Yi et al. [29] analyzed how network externality affects the stable evolutionary strategy of retailers’ marketing targets, the wholesale pricing of the manufacturer. Xu et al. [30] analyzed the influence of the consumer-return network externality effect on the buy-back contract in the supply chain. Wang et al. [31] focused on the manufacturer’s carbon emission reduction strategy, and they showed that network externality improves manufacturers’ ability to bear the cost of low-carbon technology and the incentive to reduce carbon emissions. Likewise, the network externality effect also holds in the context of remanufactured products [8]. In other words, the perceived value of remanufactured products is improved with increasing numbers of consumers that have purchased remanufactured products. For example, Zhou and Yuen [8] incorporated the network externality of remanufactured product into the model, and examined the optimal strategies for the OEM and the government. Xie et al. [32] analyzed enterprises’ optimal decisions with different used-product recycling channels based on consumers’ dual preference for product quality and environmental friendliness and network externality for new and remanufactured products. However, except for Zhou et al. [8] and Xie et al. [32], the above research focuses on network externality of the traditional product, and few works focus on the network externality of remanufactured products. Differently from the aforementioned studies, our paper explores CLSC members’ optimal strategies incorporating the network externality of remanufactured products into the research framework.

2.4. Remanufacturing Mode in CLSC

Many scholars have discussed the operations of CLSC under different remanufacturing modes and OEM selection strategies. Under the authorization remanufacturing scenario, Zhao et al. [33] constructed decision models of pricing, service and recycling in a CLSC considering manufacturer remanufacturing and retailer remanufacturing authorized by manufacturer. Zhou et al. [34] explored the OEMs’ and the authorized remanufacturers’ authorization strategies when facing competing unauthorized remanufacturers. Jin et al. [35] analyzed the OEM’s authorization strategies for independent remanufacturers between dealer authorization and remanufacturing authorization, and they found cooperation depends on the effect of authorization on the improvement of consumers’ willingness to pay for a remanufactured product. Under the outsourcing remanufacturing scenario, Zhao et al. [36] developed evolutionary game models and explored the outsourcing collecting and remanufacturing strategy for CLSC members considering information asymmetry of remanufacturing production cost. Xia et al. [37] developed a game model between the OEM and the TPR and analyzed the impact of carbon trade on manufacturing/remanufacturing under outsourcing remanufacturing. Li et al. [38] studied the effects of the tax and tariff regulations on outsourcing decisions in the contemporary international remanufacturing supply chain. Regarding the comparison between remanufacturing modes, Feng et al. [14] examined OEMs’ remanufacturing strategies between authorization and outsourcing remanufacturing considering environmentally responsible behaviors of consumers and firms. They found that, when the green consumers’ preferences for new and remanufactured products differ significantly, both the OEM and the TPR prefer authorization; otherwise, they prefer outsourcing. Zou et al. [16] compared authorization and outsourcing remanufacturing between OEMs and TPRs and they found that OEMs can obtain more profit through outsourcing than through authorization. Zhang et al. [39] explored the remanufacturing selection problem between authorization and outsourcing in a CLSC composed of two leading OEMs and two TPRs based on evolutionary game theory, and they showed that the duopoly OEMs always prefer the outsourcing remanufacturing mode. Xia and Zhu [40] as well as Xia and Ma [41] studied remanufacturing mode selection strategies among authorization, outsourcing and independent remanufacturing modes. Different from this stream of literature, we examine the remanufacturing mode strategy considering the contrast and assimilation effects, and the network externality of remanufactured product under government subsidy.

Table 1. Comparison of our work with related literature.

Research Paper	Government Subsidy	Consumers’ Perceived Value	Network Externality	Remanufacturing Mode	Game Theory
Zhou and Yuen [8]	✓		✓		Stackelberg
Xie et al. [32]			✓		Stackelberg
Agrawal et al. [12]		✓			/
Wu et al. [13]		✓			Stackelberg/Nash
Li et al. [23]		✓		✓	Stackelberg
Zhang et al. [7]	✓			✓	Stackelberg
Zhang and Zhang [22]	✓			✓	Stackelberg
Feng et al. [14]				✓	Stackelberg
Zhang et al. [39]	✓			✓	Evolutionary
This paper	✓	✓	✓	✓	Stackelberg

shows the difference between our study and existing related works.

Differing from the above papers, this paper develops Stackelberg game models in a CLSC composed of one OEM and one TPR under two remanufacturing modes, i.e., authorization remanufacturing and outsourcing remanufacturing. And we discuss the impact of the contrast and assimilation effects, the network externality of remanufactured products and government subsidy on pricing and remanufacturing mode selection decisions. This paper provides some observations on remanufacturing mode selection in CLSCs from a new perspective.

3. Model Overview

3.1. Problem Description

In this paper, a CLSC with an OEM and a TPR is considered. The OEM is the Stackelberg leader, whereas the TPR is the follower. In addition to producing new products with raw materials and selling them to consumers, the OEM owns intellectual property rights of new products and other firms cannot recycle and remanufacture used products without the OEM’s permission. Therefore, there exists two options for the OEM: (1) authorization remanufacturing, which means the OEM charges authorization fees from the TPR for remanufacturing the used products and the TPR sells the remanufactured products by itself; (2) outsourcing remanufacturing, which means the OEM outsources the remanufacturing activity to the TPR by paying the TPR outsourcing fees, then the TPR delivers remanufactured products to the OEM and the OEM resells them to consumers. Figure 1 shows the structure of the CLSC under two remanufacturing modes. Then, we develop two-period game models of the OEM and the TPR under authorization remanufacturing (Model A) and outsourcing remanufacturing (Model O). The government provides a subsidy to consumers who purchase remanufactured products in the first period.

3.2. Notations

Table 2. Notations and definitions.

Notations	Definitions
Indices
$i$	Index of the periods (superscript): $i=1$ (first period) and $i=2$ (second period)
$j$	Index of the remanufacturing modes (superscript): $j=A$ (authorization) and $j=O$ (outsourcing)
$k$	Index of the CLSC members (subscript): $k=M$ (OEM), $k=R$ (TPR), and $k=SC$ (CLSC)
$l$	Index of the product types (subscript): $l=n$ (new) and $l=r$ (remanufactured)
$N$	Index of the scenario with no government subsidy (superscript)
Parameters
$c$	Unit production cost of producing a new product
$\theta$	Consumers’ perceived value of a new product
$\delta$	Discount factor of consumers’ willingness to pay for remanufactured products
$s$	Government subsidy to consumers who purchase remanufactured products
${\beta }_1/{\beta }_2$	The strength coefficient of the contrast/assimilation effect
$\lambda$	The strength coefficient of network externality
$e$	Unit environmental impact of new products
$\eta$	Unit environmental impact discount of remanufactured products relative to the new products
$D_{il}^j$	The demand of product $l$ in the $i$ period under Model $j$ ($i=\mathrm{1,2}$, $j=A,O$, $l=n,r$)
$D_l^j$	The demand of product $l$ in two periods under Model $j$ ($j=A,O$, $l=n,r$)
$D^j$	The total demand of products in two periods under Model $j$ ($j=A,O$)
${\Pi }_{ik}^j$	The profit for $k$ in the $i$ period under Model $j$ ($i=\mathrm{1,2}$, $j=A,O$, $k=M,R,SC$)
${\Pi }_k^j$	The profit for $k$ in two periods under Model $j$ ($j=A,O$, $k=M,R,SC$)
$p_{1c}^j$	Consumers’ actual payment of purchasing a remanufactured product in the first period under Model $j$ ($j=A,O$)
$E^j$	Environmental impact under Model $j$ ($j=A,O$)
${CS}^j$	Consumer surplus under Model $j$ ($j=A,O$)
${SW}^j$	Social welfare under Model $j$ ($j=A,O$)
Decision variables
${\omega }_i$	Unit outsourcing fee in Model O
$p_{il}^j$	Sales price of product $l$ in the $i$ period under Model $j$ ($i=\mathrm{1,2}$, $j=A,O$, $l=n,r$)
$m_{irk}^j$	The marginal profit of $k$ in remanufactured product in the $i$ period under Model $j$ ($i=\mathrm{1,2}$, $j=A,O$, $k=M,R$)

shows the notations used in this paper.

3.3. Assumptions

To better analyze the problem, we make the following assumptions:

(1)

The unit cost of remanufacturing a used product is normalized to 0 [42,43];

(2)

The quantity of used products available for remanufacturing is sufficient; therefore, the decisions of the CLSC members are not restricted by the quantity of used products recycled [44];

(3)

Consumers’ willingness to pay for a new product is $\theta$, which is a uniform distribution with the supporting range $\left[0, 1\right]$;

(4)

Each consumer’s willingness to pay for the remanufactured product is a fraction $\delta$ of their willingness to pay for the new product, where $0\le \delta \le 1$.

(5)

Each consumer maximizes his net utility by purchasing at most one unit of the new or remanufactured product [43];

(6)

Consumers are myopic; they only focus on the utility of the current period and not on the utility of the next period when making a purchase decision [14];

(7)

Based on the work of Agrawal et al. [12], since the remanufactured products in Model O are sold to consumers by the OEM, from the consumers’ view, there is no difference between the remanufactured product in Model O and the remanufactured ones in the OEM self-remanufacturing mode; therefore, it is assumed that it also exists assimilation effect in Model O. For feasibility of the proposed models, we assume the contrast effect coefficient in Model A equals to the assimilation effect coefficient in Model O, i.e., ${{\beta }_1=\beta }_2=\beta$. Then, in the second period, consumers’ willingness to pay for a new product in Model A and Model O can be written as $\left(1+\beta \right)\theta$ and $\left(1-\beta \right)\theta$ separately;

(8)

Compared to new products, consumers are more reluctant to purchase a remanufactured product since they are uncertain about the quality of remanufactured ones. Then, we assume that network externality only occurs among consumers who purchase the remanufactured products. The network externality of remanufactured product is considered in the second period only, where $0\le \lambda \le 1$ [8];

(9)

Both the OEM and the TPR aim to maximize their total profits over the two-period horizon [43];

(10)

The CLSC members’ discount factor in the two periods is 1 [8].

3.4. Demand Functions

Based on the above assumptions, the utilities each consumer obtains from new and remanufactured products in the first period under both two models are provided by ${\mu }_{1n}^j=\theta -p_{1n}^j$ and ${\mu }_{1r}^j=\delta \theta -p_{1r}^j+s$ ($j=A,O$).

In Model A, each consumer obtains the utilities from new and remanufactured products in the second period of ${\mu }_{2n}^A=(1+\beta )\theta -p_{2n}^A$ and ${\mu }_{2r}^A=\delta (1+\beta )\theta -p_{2r}^A+\lambda D_{1r}^A$. In Model O, the utilities each consumer obtains from two products in the second period are given by ${\mu }_{2n}^O=(1-\beta )\theta -p_{2n}^O$ and ${\mu }_{2r}^O=\delta (1-\beta )\theta -p_{2r}^O+\lambda D_{1r}^O$.

For both models in the first period, the consumer will buy a new product when ${\mu }_{1n}^j\ge 0$ and ${\mu }_{1n}^j\ge {\mu }_{1r}^j$, which provides $\theta \ge p_{1n}^j$ and $\theta \ge \frac{p_{1n}^j-p_{1r}^j+s}{1-\delta }$. The consumer will purchase a remanufactured product when ${\mu }_{1r}^j\ge 0$ and ${\mu }_{1r}^j\ge {\mu }_{1n}^j$, which provides $\frac{p_{1r}^j-s}{\delta }\le \theta \le \frac{p_{1n}^j-p_{1r}^j+s}{1-\delta }$. To guarantee the demands of both new and remanufactured products in the first period are non-negative, it is required that $p_{1r}^j\le \delta p_{1n}^j+s$. Thus, the demands of the new and remanufactured products in the first period are

$$D_{1n}^j=1-\frac{p_{1n}^j-p_{1r}^j+s}{1-\delta },$$

(1)

$$D_{1r}^j=\frac{\delta p_{1n}^j-p_{1r}^j+s}{\delta (1-\delta )}.$$

(2)

In the second period in Model A, the consumer will buy a new product when ${\mu }_{2n}^A\ge 0$ and ${\mu }_{2n}^A\ge {\mu }_{2r}^A$, which provides $\theta \ge \frac{p_{2n}^A}{1+\beta }$ and $\theta \ge \frac{p_{2n}^A-p_{2r}^A+\lambda D_{1r}^A}{\left(1+\beta \right)\left(1-\delta \right)}$. The consumer will buy a remanufactured product when ${\mu }_{2r}^A\ge 0$ and ${\mu }_{2r}^A\ge {\mu }_{2n}^A$, which provides $\frac{p_{2r}^A-\lambda D_{1r}^A}{\delta \left(1+\beta \right)}\le \theta \le \frac{p_{2n}^A-p_{2r}^A+\lambda D_{1r}^A}{\left(1+\beta \right)\left(1-\delta \right)}$. When the condition $p_{2r}^A\le \delta p_{2n}^A+\lambda D_{1r}^A$ is satisfied, the demands of both new and remanufactured products in the second period in Model A are non-negative; they are, respectively,

$$D_{2n}^A=1-\frac{p_{2n}^A-p_{2r}^A+\lambda D_{1r}^A}{\left(1+\beta \right)\left(1-\delta \right)},$$

(3)

$$D_{2r}^A=\frac{\delta p_{2n}^A-p_{2r}^A+\lambda D_{1r}^A}{\delta \left(1+\beta \right)\left(1-\delta \right)}.$$

(4)

In the second period in Model O, the consumer will buy a new product when ${\mu }_{2n}^O\ge 0$ and ${\mu }_{2n}^O\ge {\mu }_{2r}^O$, which provides $\theta \ge \frac{p_{2n}^O}{1-\beta }$ and $\theta \ge \frac{p_{2n}^O-p_{2r}^O+\lambda D_{1r}^O}{\left(1-\beta \right)\left(1-\delta \right)}$. The consumer will buy a remanufactured product when ${\mu }_{2r}^O\ge 0$ and ${\mu }_{2r}^O\ge {\mu }_{2n}^O$, which provides $\frac{p_{2r}^O-\lambda D_{1r}^O}{\delta \left(1-\beta \right)}\le \theta \le \frac{p_{2n}^O-p_{2r}^O+\lambda D_{1r}^O}{\left(1-\beta \right)\left(1-\delta \right)}$. Under the condition $p_{2r}^O\le \delta p_{2n}^O+\lambda D_{1r}^O$, the demands of both new and remanufactured products are non-negative; they are, respectively,

$$D_{2n}^O=1-\frac{p_{2n}^O-p_{2r}^O+\lambda D_{1r}^O}{\left(1-\beta \right)\left(1-\delta \right)},$$

(5)

$$D_{2r}^O=\frac{\delta p_{2n}^O-p_{2r}^O+\lambda D_{1r}^O}{\delta \left(1-\beta \right)\left(1-\delta \right)}.$$

(6)

4. Model Formulation and Solution

In this section, we develop two Stackelberg game models under Model A and Model O and derive the optimal pricing decisions for CLSC members in two models.

4.1. Model A (Authorization Remanufacturing)

In Model A, the OEM authorizes the TPR to remanufacture and the TPR pays authorization fees to the OEM. The decision sequence between the OEM and the TPR is as follows: (1) the OEM first determines the sales price of new product $p_{1n}^A$, $p_{2n}^A$ and the authorization fee per unit of remanufactured product $z_1$, $z_2$ in each period separately; (2) then, the TPR determines the sales price of remanufactured product $p_{1r}^A$, $p_{2r}^A$ in each period after obtaining remanufacturing authorization. And the total profit functions of the OEM and the TPR are, respectively,

$${\Pi }_M^A=\left(p_{1n}^A-c\right)D_{1n}^A+z_1{D}_{1r}^A+\left(p_{2n}^A-c\right)D_{2n}^A+z_2{D}_{2r}^A,$$

(7)

$${\Pi }_R^A=\left(p_{1r}^A-z_1\right)D_{1r}^A+\left(p_{2r}^A-z_2\right)D_{2r}^A.$$

(8)

Through reverse induction, the optimal solutions for the model A are presented in Proposition 1.

Proposition 1.

In Model A, under the condition $4{\delta }^2\left(1+\beta \right){\left(1-\delta \right)}^2-{\lambda }^2>0$, the optimal sales prices of both two products and the authorization fee per unit remanufactured product are

$$p_{1n}^{A\ast }=\frac{1+c}{2},$$

(9)

$$p_{2n}^{A\ast }=\frac{1+c+\beta }{2},$$

(10)

$$z_1^{\ast }=\frac{s+\delta }{2},$$

(11)

$$z_2^{\ast }=\frac{\delta \left(1+\beta \right)}{2},$$

(12)

$$p_{1r}^{A\ast }=\frac{2\delta A+s\left(3A-{\lambda }^2\right)+\delta c\left(A-{\lambda }^2\right)-2\lambda {\delta }^{2}c\left(1-\delta \right)}{4A},$$

(13)

$$p_{2r}^{A\ast }=\frac{\delta (1+\beta )}{2}+\frac{\delta (1+\beta )\left(1-\delta \right)\left[2{\delta }^{2}c\left(1-\delta \right)+\lambda \left(\delta c+s\right)\right]}{2A}.$$

(14)

With Equations (9)–(14), the optimal sales volumes of both two products, optimal total sales volume of products and the optimal profits of CLSC members and entire CLSC can be derived as follows:

$${D_n^{A\ast }=D}_{1n}^{A\ast }+D_{2n}^{A\ast }=1-\frac{2{\delta }^2\left(1-\delta \right)\left[c\left(2+\beta \right)-s\left(1+\beta \right)\right]+\lambda \delta \left(s+2\delta c\right)}{2A}-\frac{c\left(2+\beta \right)\left(A-{\lambda }^2\right)}{4A\left(1+\beta \right)},$$

(15)

$${D_r^{A\ast }=D}_{1r}^{A\ast }+D_{2r}^{A\ast }=\frac{2\delta \left(1-\delta \right)\left[s\left(1+\beta \right)+2\delta \left(2+\beta \right)\right]+\lambda \left(s+2\delta c\right)}{2A},$$

(16)

$$D^{A\ast }=1+\frac{s\left(1-\delta \right)\left[2\delta \left(1+\beta \right)\left(1-\delta \right)+\lambda \right]}{2A}-\frac{c\left(2+\beta \right)\left(A-{\lambda }^2\right)}{4\left(1+\beta \right)A}+\frac{\lambda \delta c\left(1-\delta \right)}{A},$$

(17)

$${\Pi }_M^{A\ast }=\frac{{\left(1+\beta -c\right)}^2}{4\left(1+\beta \right)}+\frac{A\left(1-2c\right)+B-2\beta {\delta }^3{c}^2\left(1-\delta \right)+2\lambda \delta c\left(s+\delta c\right)-{\lambda }^2{c}^2}{4A},$$

(18)

$${\Pi }_R^{A\ast }=\frac{\delta \left(1-\delta \right)\left[s\left(1+\beta \right)\left(s+2\delta c\right)+{\delta }^2{c}^2\left(2+\beta \right)\right]+\lambda \delta c\left(\delta c+s\right)}{4A},$$

(19)

$${\Pi }_{SC}^{A\ast }={\Pi }_M^{A\ast }+{\Pi }_R^{A\ast }=\frac{c^2}{4\left(1+\beta \right)}+\frac{c^2+\beta +2}{4}-c+\frac{3\delta \left(1-\delta \right)\left[s\left(1+\beta \right)\left(s+2\delta c\right)+{\delta }^2{c}^2\left(2+\beta \right)\right]+3\lambda \delta c\left(\delta c+s\right)}{4A}.$$

(20)

where $A=4{\delta }^2\left(1+\beta \right){\left(1-\delta \right)}^2-{\lambda }^2>0$ and $B=2\delta \left(1+\beta \right)\left(1-\delta \right)\left[s\left(s+2\delta c\right)+2\delta c^2\right]>0$ are used to simplify the writing of mathematical equations.

In Proposition 1, let $s=0$; we can obtain optimal solutions without government subsidy under authorization remanufacturing, which are not specifically provided here.

4.2. Model O (Outsourcing Remanufacturing)

In Model O, the OEM outsources the remanufacturing activities to the TPR with outsourcing fees, and the TPR delivers remanufactured products to the OEM who resells them to consumers. The decision sequence between the OEM and the TPR is as follows: (1) the OEM first determines the sales prices of new product $p_{1n}^O$, $p_{2n}^O$ and the sales prices of remanufactured product $p_{1r}^O$, $p_{2r}^O$ in each period separately; (2) then, the TPR determines the outsourcing fee ${\omega }_1$, ${\omega }_2$. And the total profit functions of the OEM and the TPR are, respectively,

$${\Pi }_M^O=\left(p_{1n}^O-c\right)D_{1n}^O+\left(p_{1r}^O-{\omega }_1\right)D_{1r}^O+\left(p_{2n}^O-c\right)D_{2n}^O+\left(p_{2r}^O-{\omega }_2\right)D_{2r}^O,$$

(21)

$${\Pi }_R^O={\omega }_1{D}_{1r}^O+{\omega }_2{D}_{2r}^O.$$

(22)

where $p_{1r}^O={\omega }_1+m_{1rM}^O$ and $p_{2r}^O={\omega }_2+m_{2rM}^O$.

Through the reverse induction, the optimal solutions for the model O are presented in Proposition 2.

Proposition 2.

In Model O, under the condition $4{\delta }^2\left(1-\beta \right){\left(1-\delta \right)}^2-{\lambda }^2>0$, the optimal prices and unit outsourcing fees are

$$p_{1n}^{O\ast }=\frac{1+c}{2},$$

(23)

$$p_{2n}^{O\ast }=\frac{1+c-\beta }{2},$$

(24)

$$p_{1r}^{O\ast }=\frac{s+\delta }{2}+\frac{\left(F-{\lambda }^2\right)\left(s+\delta c\right)-2\lambda {\delta }^{2}c\left(1-\delta \right)}{4F},$$

(25)

$$p_{2r}^{O\ast }=\frac{\delta \left(1-\beta \right)}{2}+\frac{\delta \left(1-\beta \right)\left(1-\delta \right)\left[2{\delta }^{2}c\left(1-\delta \right)+\lambda \left(\delta c+s\right)\right]}{2F},$$

(26)

$$m_{1rM}^O=\frac{s+\delta }{2},$$

(27)

$$m_{2rM}^O=\frac{\delta \left(1-\beta \right)}{2},$$

(28)

$${\omega }_1^{\ast }=\frac{\left(F-{\lambda }^2\right)\left(s+\delta c\right)-2\lambda {\delta }^{2}c\left(1-\delta \right)}{4F},$$

(29)

$${\omega }_2^{\ast }=\frac{\delta \left(1-\beta \right)\left(1-\delta \right)\left[2{\delta }^{2}c\left(1-\delta \right)+\lambda \left(s+\delta c\right)\right]}{2F}.$$

(30)

With Equations (23)–(30), the optimal sales volumes of both two products, optimal total sales volume of products and the optimal profits of CLSC members and entire CLSC can be derived as follows:

$$D_n^{O\ast }=D_{1n}^{O\ast }+D_{2n}^{O\ast }=1-\frac{c\left(2-\beta \right)\left(F-{\lambda }^2\right)}{4\left(1-\beta \right)F}-\frac{{2\delta }^2\left[c\left(2-\beta \right)+s\left(1-\beta \right)\right]+\lambda \delta \left(s+2\delta c\right)}{2F},$$

(31)

$$D_r^{O\ast }=D_{1r}^{O\ast }+D_{2r}^{O\ast }=\frac{2\delta \left(1-\delta \right)\left[s\left(1-\beta \right)+\delta c\left(2-\beta \right)\right]+\lambda \left(s+2\delta c\right)}{2F},$$

(32)

$$D^{O\ast }=1-\frac{c\left(2-\beta \right)\left(F-{\lambda }^2\right)}{4\left(1-\beta \right)F}+\frac{2\delta {s\left(1-\beta \right)\left(1-\delta \right)}^2+\lambda \left(1-\delta \right)\left(s+2\delta c\right)}{2F},$$

(33)

$${\Pi }_M^{O\ast }=\frac{2-\beta +c\left(4-c\right)}{4}+\frac{c^2}{4\left(1-\beta \right)}+\frac{I+\lambda \delta c\left(s+\delta c\right)}{2F},$$

(34)

$${\Pi }_R^{O\ast }=\frac{I+\lambda \delta c\left(s+\delta c\right)}{4F},$$

(35)

$${\Pi }_{SC}^{O\ast }={\Pi }_M^{O\ast }+{\Pi }_R^{O\ast }=\frac{2-\beta +c\left(4-c\right)}{4}+\frac{c^2}{4\left(1-\beta \right)}+\frac{3I+3\lambda \delta c\left(s+\delta c\right)}{4F}.$$

(36)

where $F=4{\delta }^2\left(1+\beta \right){\left(1-\delta \right)}^2-{\lambda }^2>0$ and $G=2\delta \left(1+\beta \right)\left(1-\delta \right)\left[s\left(s+2\delta c\right)+2\delta c^2\right]>0$ are used to simplify the writing of mathematical equations.

Similarly, in Proposition 2, let $s=0$; we can obtain optimal solutions without government subsidy under outsourcing remanufacturing, which are not specifically given here.

5. Model Analysis

In this section, we compare and analyze the optimal solutions in Model A and Model O. Then, we obtain the following propositions.

Proposition 3.

(1) $p_{1c}^{A\ast }<p_{1r}^{AN\ast }$, $p_{1c}^{O\ast }<p_{1r}^{ON\ast }$; (2) $p_{1c}^{A\ast }>p_{1c}^{O\ast }$, $p_{1c}^{AN\ast }>p_{1c}^{ON\ast }$.

Proposition 3 states that, regardless of the remanufacturing modes, government subsidy can significantly reduce the consumer spending on remanufactured products, inducing more consumers to purchase remanufactured ones in the first period. In addition, from the perspective of consumers, they prefer to purchase remanufactured products under outsourcing remanufacturing mode no matter whether the government offers a subsidy to consumers or not.

Proposition 4.

In the first period, CLSC members encroach government subsidies which are offered to consumers through adjusting pricing. The OEM always encroach on $s/2$ under two modes. The comparison of allocation proportion of government subsidy among consumers, the OEM and the TPR is as follows:

(1) 

In Model A, if $0<\lambda <\delta \left(1-\delta \right)\sqrt{2\left(1+\beta \right)}$, the sequence is OEM > Consumer > TPR; otherwise, Consumer > OEM > TPR.

(2) 

In Model O, if $0<\lambda <\delta \left(1-\delta \right)\sqrt{2\left(1-\beta \right)}$, the sequence is OEM > Consumer > TPR; otherwise, Consumer > OEM > TPR.

Proposition 4 implies that, although the government provides subsidy directly to consumers who purchase remanufactured products, both the OEM and the TPR could encroach government subsidies that are offered to consumers by adjusting pricing strategies. And the OEM as a leader could obtain more subsidy from consumers. The remanufacturing mode does not affect the proportion of government subsidy obtained by the OEM. Moreover, with the stronger network externality effect of remanufactured products under both modes, the OEM and the TPR obtain less government subsidy and consumers could finally obtain more consumption subsidy. In particular, the OEM (Model A) or the TPR (Model O) will further benefit consumers through markdown pricing as the network externality of remanufactured product becomes stronger.

Proposition 5.

The comparison of optimal sales prices of both new and remanufactured products is as follows:

(1) 

$p_{1n}^{A\ast }=p_{1n}^{O\ast }$, $p_{2n}^{A\ast }>p_{2n}^{O\ast }$.

(2) 

$p_{1r}^{A\ast }>p_{1r}^{O\ast }$; if$J<0$or both$J>0$and$s>s_1$,$p_{2r}^{A\ast }<p_{2r}^{O\ast }$; otherwise,$p_{2r}^{A\ast }>p_{2r}^{O\ast }$, where$J=AF-{\lambda }^2\left(1-\delta \right)\left(2{\delta }^{2}c+\lambda \delta c\right)$,$s_1=\frac{J}{{\lambda }^3\left(1-\delta \right)}$.

Proposition 5 shows that (1) remanufacturing mode does not affect the sales price of a new product in the first period, but it affects such in the second period. The contrast effect in Model A improves consumers’ willingness to pay for new products, while the assimilation effect in Model O decreases consumers’ willingness to pay for new ones. Thus, the sales price of a new product in the second period in Model A is higher than that in Model O. (2) The OEM’s remanufacturing mode selection affects the pricing decision of remanufactured products in both of the two periods. Usually, the sales price of remanufactured products in Model A is higher than that in Model O, which is harmful to the sales of remanufactured products. Only when a certain condition is met will the consumers pay a lower price for a remanufactured product in the second period in Model A, which is beneficial to the sales of remanufactured products.

Proposition 6.

The comparison of optimal sales volumes of both new and remanufactured products is as follows:

(1) 

$D_n^{A\ast }>D_n^{O\ast }$,$D_r^{A\ast }<D_r^{O\ast }$.

(2) 

Only if$K>0$and$0<s<s_2$,$D^{A\ast }>D^{O\ast }$; otherwise,$D^{A\ast }<D^{O\ast }$, where$K=cAF-2{\delta }^{2}c\left(1-{\beta }^2\right){\left(1-\delta \right)}^2\left[4{\delta }^2{\left(1-\delta \right)}^2+4\lambda \delta \left(1-\delta \right)+{\lambda }^2\right]$,$s_2=\frac{K}{2\lambda \delta \left(1-{\beta }^2\right){\left(1-\delta \right)}^2\left[2\delta \left(1-\delta \right)+\lambda \right]}$.

Proposition 6 states that the contrast effect in Model A is more beneficial to the sales of new products, while the assimilation effect in Model O is more favorable to the sales of remanufactured ones. In Model O, the assimilation effect leads some consumers of new products to turn to the purchase of remanufactured products, which ensures the survival space of TPR in terms of quantity. The relationship of total sales volume of products between two remanufacturing modes depends on various parameters such as the network externality of the remanufactured product, contrast/assimilation effects, cost saving, government subsidy level and the discount factor of consumers’ willingness to pay for remanufactured products.

Proposition 7.

The comparison of unit profit per remanufactured product for the OEM and the TPR in each period under two models is as follows:

(1) 

OEM:$m_{1rM}^{A\ast }\left(z_1^{\ast }\right)=m_{1rM}^{O\ast }\left(p_{1r}^{O\ast }-{\omega }_1^{\ast }\right)$,$m_{2rM}^{A\ast }\left(z_2^{\ast }\right)>m_{2rM}^{O\ast }\left(p_{2r}^{O\ast }-{\omega }_2^{\ast }\right)$.

(2) 

TPR:$m_{1rR}^{A\ast }\left(p_{1r}^{A\ast }-z_1^{\ast }\right)>m_{1rR}^{O\ast }\left({\omega }_1^{\ast }\right)$,$m_{2rR}^{A\ast }\left(p_{2r}^{A\ast }-z_2^{\ast }\right)<m_{2rR}^{O\ast }\left({\omega }_2^{\ast }\right)$.

Proposition 7 shows that an OEM could obtain the same unit profit per remanufactured product in the first period under two models. In the second period, higher unit profit per remanufactured product can be achieved by the OEM in Model A compared to Model O. For the TPR, more unit profit per remanufactured product can be obtained in the first period in Model A, but the unit profit per remanufactured product in the second period is higher in Model O.

Proposition 8.

The comparison of optimal profits of CLSC members and entire CLSCs is as follows:

(1) 

Only if$1-c^2-{\beta }^2>0$and$0<s<max\left\{0,s_3\right\}$,${\Pi }_M^{A\ast }>{\Pi }_M^{O\ast }$; otherwise,${\Pi }_M^{A\ast }<{\Pi }_M^{O\ast }$.

(2) 

${\Pi }_R^{A\ast }<{\Pi }_R^{O\ast }$.

(3) 

Only if$1-c^2-{\beta }^2>0$and$0<s<max\left\{0,s_4\right\}$,${\Pi }_{SC}^{A\ast }>{\Pi }_{SC}^{O\ast }$; otherwise,${\Pi }_{SC}^{A\ast }<{\Pi }_{SC}^{O\ast }$.

where$s_3=\frac{\sqrt{{\lambda }^2\delta \left(1-{\beta }^2\right)\left(1-\delta \right)\left(1-c^2-{\beta }^2\right)AF}}{\sqrt{2}{\lambda }^2\delta \left(1-{\beta }^2\right)\left(1-\delta \right)}-\frac{\delta c\left[2\delta \left(1-\delta \right)+\lambda \right]}{\lambda }$,$s_4=\frac{\sqrt{{\lambda }^2\delta \left(1-{\beta }^2\right)\left(1-\delta \right)\left(1-c^2-{\beta }^2\right)AF}}{\sqrt{3}{\lambda }^2\delta \left(1-{\beta }^2\right)\left(1-\delta \right)}-\frac{\delta c\left[2\delta \left(1-\delta \right)+\lambda \right]}{\lambda }$, and$s_3>s_4$.

Proposition 8 states that the TPR can gain more profit in Model O. Usually, Model W is more profitable for the OEM than Model A. Only when the contrast/assimilation effect and government subsidy level are both relatively low does Model A perform better than Model O; thus, the OEM prefers to select the authorization remanufacturing mode. From the perspective of an entire CLSC’s performance, when the certain condition is satisfied, e.g., the contrast/assimilation effect and government subsidy level are both low, the performance of the entire CLSC is better in Model A. In addition, a win–win situation can be achieved between an OEM and TPR under outsourcing remanufacturing through the government increasing subsidy or chain members advertising, hiring green brand spokesmen, etc., to increase the contrast/assimilation effect.

Proposition 9.

Impact of the increase in $\lambda$ on the optimal decisions under Model A and Model O ($j=A,O$).

(1) 

$\frac{\partial p_{1n}^{j\ast }}{\partial \lambda }=0$,$\frac{\partial p_{2n}^{j\ast }}{\partial \lambda }=0$,$\frac{\partial p_{1r}^{j\ast }}{\partial \lambda }<0$,$\frac{\partial p_{2r}^{j\ast }}{\partial \lambda }>0$.

(2) 

$\frac{\partial D_n^{j\ast }}{\partial \lambda }<0$,$\frac{\partial D_r^{j\ast }}{\partial \lambda }>0$,$\frac{\partial D^{j\ast }}{\partial \lambda }>0$.

(3) 

$\frac{\partial {\Pi }_M^{j\ast }}{\partial \lambda }>0$,$\frac{\partial {\Pi }_R^{j\ast }}{\partial \lambda }>0$,$\frac{\partial {\Pi }_{SC}^{j\ast }}{\partial \lambda }>0$.

Proposition 9 states that, in two models, when the network externality strength coefficient ($\lambda$) increases, (1) the sales prices of new products in the two periods are not affected by $\lambda$. The TPR (Model A) or the OEM (Model O) should decrease the sales price of remanufactured products in the first period to motivate consumers to make a purchase. Thus, the sales volume of remanufactured product in the first period increases. Further, in the second period, the enhancement of network externality and the increase in sales volume of a remanufactured product in the first period jointly improve consumers’ value evaluation of remanufactured products, making consumers have a higher willingness to pay for remanufactured ones. Then, the OEM or the TPR can moderately increase the price of remanufactured product in the second period to compensate for the profit loss of the remanufactured product in the first period for CLSC members. (2) The stronger network externality stimulates more consumers to purchase remanufactured products and exacerbates the cannibalization of new product markets by remanufactured ones. Both the sales volume of remanufactured products and the overall supply chain market get improved. (3) The decrease in sales volume of new products caused by the enhancement of network externality of remanufactured products has reduced the OEM’s profit from the new product market. However, the increase in profit from the remanufactured product market has exceeded the decrease in profit from new products. Therefore, the OEM’s profit improved with an increasing $\lambda$. The stronger network externality of remanufactured products is also conducive to the improvement of the TPR’s profit. Thus, the enhancement of $\lambda$ is beneficial to the OEM/TPR/CLSC, and CLSC members are more incentivized to enhance the network externality of remanufactured products.

Comparative remarks: Based on the above analysis, we can obtain the following comparative remarks:

(1)

In the first period, it is more beneficial for consumers to purchase a remanufactured product in Model O, as they can reduce the spending on remanufactured products.

(2)

In two models, there is no difference in the sales price of new products in the first period. Meanwhile, the sales price of new products in the second period in Model A is higher than that in Model O. Usually, the sales price of a remanufactured product in Model A is higher than that in Model O; only when the certain condition is met do the consumers pay a lower price for a remanufactured product in the second period in Model A.

(3)

Model O is more favorable to the sales of remanufactured products, but the cannibalization of the new product market is also more obvious. Model A is beneficial to the sales of new products.

(4)

The TPR can obtain higher profit in Model O. Only when the contrast/assimilation effect and government subsidy level are both relatively low is Model A profitable for the OEM; otherwise, the OEM selects Model O. Similarly, for the entire CLSC, only under the condition that the contrast/assimilation effect and government subsidy level are both relatively low does Model A perform better than Model O; otherwise, Model O is more beneficial for the CLSC.

6. Numerical Analysis

In this section, we conduct numerical experiments to illustrate and complement the aforementioned analysis. The following parameter values are selected: $c=0.1$, $s=0.1$, $\delta =0.7$, $\beta =0.1$, $\lambda =0.1$.

6.1. The Comparison of Product Sales Volumes and Profits in CLSCs under Two Models

Here, we show the changes in the product sales volumes and profits with respect to $\lambda$ and $\beta$ under both of the two models as shown in

Table 3. The product sales volumes and profits with respect to $\lambda$ and $\beta$ under two models.

$$\mathit{\lambda }$$	$$\mathit{\beta }$$	$${\mathit{D}}_{\mathit{n}}^{\mathit{A}\mathit{*}}$$	$${\mathit{D}}_{\mathit{n}}^{\mathit{O}\mathit{*}}$$	$${\mathit{D}}_{\mathit{r}}^{\mathit{A}\mathit{*}}$$	$${\mathit{D}}_{\mathit{r}}^{\mathit{O}\mathit{*}}$$	$${\mathit{\Pi }}_{\mathit{M}}^{\mathit{A}\mathit{*}}$$	$${\mathit{\Pi }}_{\mathit{M}}^{\mathit{O}\mathit{*}}$$	$${\mathit{\Pi }}_{\mathit{R}}^{\mathit{A}\mathit{*}}$$	$${\mathit{\Pi }}_{\mathit{R}}^{\mathit{O}\mathit{*}}$$	$${\mathit{\Pi }}_{\mathit{S}\mathit{C}}^{\mathit{A}\mathit{*}}$$	$${\mathit{\Pi }}_{\mathit{S}\mathit{C}}^{\mathit{O}\mathit{*}}$$
0.05	0.1	0.685	0.658	0.3131	0.338	0.451	0.403	0.0108	0.0113	0.462	0.414
	0.2	0.696	0.639	0.3038	0.355	0.476	0.379	0.0106	0.0117	0.487	0.391
	0.3	0.704	0.614	0.2959	0.378	0.5	0.355	0.0105	0.0121	0.511	0.367
0.1	0.1	0.654	0.618	0.358	0.395	0.454	0.406	0.0121	0.0129	0.466	0.419
	0.2	0.667	0.592	0.345	0.421	0.478	0.383	0.0118	0.0135	0.49	0.396
	0.3	0.678	0.56	0.333	0.456	0.502	0.36	0.0115	0.0142	0.514	0.374
0.15	0.1	0.611	0.561	0.4196	0.476	0.457	0.411	0.0138	0.0152	0.471	0.426
	0.2	0.629	0.526	0.3993	0.516	0.481	0.388	0.0133	0.0162	0.495	0.404
	0.3	0.644	0.479	0.3825	0.571	0.505	0.366	0.0129	0.0175	0.518	0.384
0.2	0.1	0.55	0.477	0.506	0.596	0.463	0.418	0.0164	0.0187	0.479	0.436
	0.2	0.576	0.422	0.475	0.665	0.486	0.396	0.0156	0.0204	0.501	0.417
	0.3	0.597	0.345	0.45	0.763	0.509	0.377	0.0149	0.0229	0.524	0.4

.

From Table 3, we find the following: (1) Considering the contrast/assimilation effect and the network externality of remanufactured products, the sales volume of new products is higher in Model A and the sales volume of remanufactured products is higher in Model O. That is, Model A is beneficial to the sales of new products and Model O is beneficial to the sales of remanufactured products. From Proposition 5 and Proposition 7, it can be seen that an OEM can obtain higher unit profit per new and remanufactured products in Model A. Meanwhile, with the advantages of new product sales, a new product’s total profits and remanufactured product’s unit profit offset the disadvantage of remanufactured product sales; thus, OEMs gain higher profit in Model A. In Model O, combined with Proposition 7, the advantages of a TPR’s unit profit per remanufactured product in the second period and the sales volume of remanufactured products offset the disadvantage of its unit profit per remanufactured product in the first period, and thus TPR can obtain more profit. From the entire CLSC point of view, Model A is more profitable than Model O. (2) In two models, the stronger network externality always improves the sales of remanufactured products, as well as profits of CLSC members and entire CLSC, but accelerates the cannibalization of the new product market by remanufactured products. (3) The stronger contrast effect in Model A can lead to an increase in sales volume of new products and a decrease in sales quantity of remanufactured ones, which is helpful to maintain the new product market. And, the stronger the contrast effect is, the more beneficial it is to the OEM and the CLSC, but it harms the interests of the TPR. In contrast to Model A, the enhanced assimilation effect in Model O leads to a decline in sales of new products and an improvement in sales of remanufactured ones. Meanwhile, the enhancement of the assimilation effect is harmful to the efficiency of the OEM and the CLSC, but beneficial to the long-term development of the TPR.

6.2. The Comparison of Environmental Impact, Consumer Surplus and Social Welfare in CLSCs under Two Models

Under two models, According to Zhang et al. [7] and Liu et al. [45], the environmental impact means the influence of the products’ production process on environmental changes. Then, the environmental impact of CLSC operations is $E^j=e{D}_n^{j\ast }+\eta e{D}_r^{j\ast }$, where $j=A,O$.

According to Ding et al. [46], the consumer surplus refers to the difference between the maximum price consumers are willing to pay for a product and the price they actually pay. The consumer surplus of Model A and Model O are as follows:

$${CS}^A={\int }_{\frac{p_{1r}^{A\mathrm{*}}-s}{\delta }}^{\frac{p_{1n}^{A\mathrm{*}}-p_{1r}^{A\mathrm{*}}+s}{1-\delta }}\left(\delta \theta -p_{1r}^{A\mathrm{*}}+s\right)d\theta +{\int }_{\frac{p_{1n}^{A\mathrm{*}}-p_{1r}^{A\mathrm{*}}+s}{1-\delta }}^1\left(\theta -p_{1n}^{A\mathrm{*}}\right)d\theta +{\int }_{\frac{p_{2r}^{A\mathrm{*}}-\lambda D_{1r}^{A\mathrm{*}}}{\delta (1+\beta )}}^{\frac{p_{2n}^{A\mathrm{*}}-p_{2r}^{A\mathrm{*}}+\lambda D_{1r}^{A\mathrm{*}}}{(1+\beta )(1-\delta )}}\left[\delta (1+\beta )\theta -p_{2r}^{A\mathrm{*}}+\lambda D_{1r}^{A\mathrm{*}}\right]d\theta +{\int }_{\frac{p_{2n}^{A\mathrm{*}}-p_{2r}^{A\mathrm{*}}+\lambda D_{1r}^{A\mathrm{*}}}{(1+\beta )(1-\delta )}}^1\left[(1+\beta )\theta -p_{2n}^{A\mathrm{*}}\right]d\theta ,$$

$${CS}^O={\int }_{\frac{p_{1r}^{O\mathrm{*}}-s}{\delta }}^{\frac{p_{1n}^{O\mathrm{*}}-p_{1r}^{O\mathrm{*}}+s}{1-\delta }}\left(\delta \theta -p_{1r}^{O\mathrm{*}}+s\right)d\theta +{\int }_{\frac{p_{1n}^{O\mathrm{*}}-p_{1r}^{O\mathrm{*}}+s}{1-\delta }}^1\left(\theta -p_{1n}^{O\mathrm{*}}\right)d\theta +{\int }_{\frac{p_{2r}^{O\mathrm{*}}-\lambda D_{1r}^{O\mathrm{*}}}{\delta (1-\beta )}}^{\frac{p_{2n}^{O\mathrm{*}}-p_{2r}^{O\mathrm{*}}+\lambda D_{1r}^{O\mathrm{*}}}{(1-\beta )(1-\delta )}}\left[\delta (1-\beta )\theta -p_{2r}^{O\mathrm{*}}+\lambda D_{1r}^{O\mathrm{*}}\right]d\theta +{\int }_{\frac{p_{2n}^{O\mathrm{*}}-p_{2r}^{O\mathrm{*}}+\lambda D_{1r}^{O\mathrm{*}}}{(1-\beta )(1-\delta )}}^1\left[(1-\beta )\theta -p_{2n}^{O\mathrm{*}}\right]d\theta .$$

The first (second) term represents the consumer surplus of remanufactured (new) products in the first period, and the third (fourth) term represents the consumer surplus of remanufactured (new) products in the second period.

According to Zhang et al. [7] and Cao et al. [47], the social welfare includes CLSC members’ profits, consumer surplus, environmental impact cost and government expenditure. Then, the social welfare of CLSC is ${SW}^j={\Pi }_M^{j\ast }+{\Pi }_R^{j\ast }+{CS}^j-E^j-s{D}_{1r}^{j\ast }$, where $j=A,O$.

In this subsection, we set $e=0.3$, $\eta =0.6$. The results are shown in

Table 4. The environmental impact, consumer surplus and social welfare with respect to $\lambda$ and $\beta$ under two models.

$\mathit{\lambda }$	$\mathit{\beta }$	${\mathit{E}}^{\mathit{A}\mathit{*}}$	${\mathit{E}}^{\mathit{O}\mathit{*}}$	${\mathit{C}\mathit{S}}^{\mathit{A}\mathit{*}}$	${\mathit{C}\mathit{S}}^{\mathit{O}\mathit{*}}$	${\mathit{S}\mathit{W}}^{\mathit{A}\mathit{*}}$	${\mathit{S}\mathit{W}}^{\mathit{O}\mathit{*}}$
0.05	0.1	0.262	0.258	0.221	0.196	0.4	0.331
	0.2	0.263	0.256	0.233	0.184	0.435	0.298
	0.3	0.265	0.252	0.245	0.172	0.47	0.266
0.1	0.1	0.261	0.256	0.222	0.198	0.405	0.337
	0.2	0.262	0.254	0.235	0.187	0.439	0.305
	0.3	0.263	0.25	0.247	0.175	0.474	0.274
0.15	0.1	0.259	0.254	0.225	0.202	0.411	0.346
	0.2	0.261	0.251	0.237	0.191	0.445	0.316
	0.3	0.262	0.246	0.249	0.18	0.48	0.288
0.2	0.1	0.256	0.25	0.229	0.208	0.422	0.361
	0.2	0.258	0.246	0.24	0.199	0.454	0.334
	0.3	0.26	0.241	0.252	0.192	0.488	0.312

.

From Table 4, we can find the following: (1) From the perspective of environmental impact, Model M is better than Model O. Combined with Proposition 6, the sales volume of a new product is less and the sales volume of remanufactured product is higher in Model O, which is more environmentally friendly. Though the environmental impact is higher in Model A, the higher CLSC profit, larger consumer surplus and lower total government subsidies make Model A perform better than Model O from the perspective of social welfare. (2) Under both of the two remanufacturing modes, the enhancement of network externality of remanufactured products is conductive to lowering environmental impact and improving consumer surplus and social welfare. (3) The contrast effect in Model A has a positive impact on environment impact, consumer surplus and social welfare. However, the assimilation effect in Model O has a negative impact on these three aspects.

6.3. The Comparison of Profits for CLSC Members and Entire CLSCs between the First Period and Second Period in Model A

In this subsection, we compare the profits of CLSC members and entire CLSCs between the first period and second period in Model A.

Government subsidies can effectively promote the purchase of remanufactured products for consumers and increase the profits of chain members. Since the network externality of remanufactured products exists, consumers are more willing to purchase remanufactured products in the second period when more consumers buy remanufactured ones in the first period. In Model A, the contrast effect increases consumers’ perceived value for new products. From Figure 2a, we find that, when the contrast effect is not significant, the OEM obtains less profit in the second period than in the first period. And, with the enhancement of $\beta$, the profit of the OEM in the second period increases, which makes the OEM gain more profit than in the first period. From Figure 2b, when the strength of network externality is small, the TPR cannot obtain more profit in the second period compared to the first period. With the increasing of $\lambda$, consumers’ value evaluation of remanufactured products gets improved and more consumers are attracted to the purchase of remanufactured goods; then, the TPR’s profit in the second period grows and exceeds that in the first period. That is, stronger network externality can increase the TPR’s profit in the second period. As in Figure 2c, the stronger contrast effect is beneficial to the profit of the entire CLSC. With the enhancement of the contrast effect, the CLSC’s profit in the second period grows and then exceeds that in the first period. Moreover, the OEM has an incentive to enhance the strength of the contrast effect, and the CLSC members are motivated to enhance the network externality of remanufactured products in Model A.

6.4. The Comparison of Profits for CLSC Members and Entire CLSC between the First Period and Second Period in Model O

In this subsection, we compare the profits of CLSC members and entire CLSCs between the first period and second period in Model O.

In Model O, the assimilation effect reduces consumers’ perceived value of new products, and it is harmful to the OEM. From Figure 3a, we find that, with the increasing of the assimilation effect, the OEM’s profit in the second period decreases and the OEM’s profit in the second period is less than that in the first period. From Figure 3b, when the network externality is stronger, the TPR obtains more profit in the second period and exceeds that in the first period; otherwise, the TPR’s profit is higher in the first period. As in Figure 3c, with the enhancement of the assimilation effect, the CLSC’s profit decreases in the second period and the CLSC can obtain more profit in the first period than in the second period. Therefore, the OEM should strive to reduce the strength of assimilation effects. For example, the OEM can establish an independent remanufactured brand to reduce the impact on the image of OEM’s new products. Also, the CLSC members are motivated to enhance the network externality of remanufactured products in Model O.

7. Discussion

This paper constructs two-period Stackelberg game models in a CLSC consisting of an OEM and a TPR considering the contrast/assimilation effect, network externality of remanufactured products and government subsidy under two remanufacturing modes, i.e., authorization remanufacturing and outsourcing remanufacturing. The government only provides a subsidy to consumers who purchase remanufactured products in the first period. OEMs and TPRs aim to maximize their own profits. We obtain optimal solutions of the OEM and the TPR under two models, then analyze and compare the optimal solutions theoretically. Finally, we further analyze the relevant conclusions through numerical analysis.

In the two remanufacturing models, the TPR always prefers the outsourcing remanufacturing mode. Under the condition $1-c^2-{\beta }^2>0$, since $s_3>s_4$, when the condition $0<s<max\left\{0,s_4\right\}$ is satisfied, it is more profitable for the OEM and CLSC in authorization remanufacturing mode, and it is unfavorable for the TPR; however, when the condition $max\left\{0,s_4\right\}<s<max\left\{0,s_3\right\}$ is satisfied, the TPR/CLSC can obtain more profit in the outsourcing remanufacturing mode, and the OEM still selects authorization remanufacturing; in other cases, a win–win situation in outsourcing remanufacturing can be achieved between the OEM and the TPR.

7.1. Conclusions

The conclusions we obtain are as follows.

(1)

When the conditions $1-c^2-{\beta }^2>0$ and $0<s<max\left\{0,s_3\right\}$ are satisfied, the OEM prefers to select authorization remanufacturing; otherwise, the OEM prefers outsourcing remanufacturing. The outsourcing mode is always more beneficial for the TPR. Therefore, a win–win situation can be achieved between the OEM and the TPR under outsourcing remanufacturing through the government increasing subsidy or chain members advertising, hiring green brand spokesmen, etc., to increase the contrast/assimilation effect.

(2)

Model O only performs better than Model A in terms of sales of remanufactured products and environmental impact, while Model A is better in terms of consumer surplus and social welfare.

(3)

The contrast effect in Model A is beneficial to the OEM and CLSC, but harmful to the TPR. On the contrary, the impacts of the assimilation effect in Model O on OEM, TPR and CLSC are opposite this. Regardless of the remanufacturing mode, the enhancement of network externality could promote the sales of remanufactured products and improve the profits of CLSC members, while exacerbating the cannibalization of the new product market.

(4)

Regardless of the remanufacturing mode, government subsidy can significantly reduce consumer spending on remanufactured products. And, when the government subsidy policy ends, it still has a continuous impact on CLSC members’ decision making. In addition, CLSC members encroach the government subsidies which are offered to consumers through adjusting pricing.

7.2. Managerial Implications

From the above analysis and results, we obtain the following management insights for CLSC members and the government:

(1)

Since the network externality of remanufactured products can improve the profits of the OEM/TPR/CLSC and promote the sales of remanufactured products, the OEM and the TPR are more motivated to enhance the network externality of remanufactured products. For example, the OEM can utilize consumers’ group psychology and design some reward mechanism to encourage more and more consumers to purchase remanufactured products.

(2)

The government should enact a higher government subsidy level, extend the implementation period of the policy and include remanufactured products in the list of the government’s priority procurements to promote the development of the remanufacturing industry. At the same time, the government should actively publicize the high quality and performance of remanufactured products through social media, social networks and other channels to guide the public to form a positive cognition of remanufactured products, thus attracting more and more consumers to purchase remanufactured ones.

7.3. Limitations and Future Research

This paper also has some limitations. Firstly, this study only considers a CLSC consisting of one OEM and one TPR. In reality, there are many competing OEMs or TPRs in the market. Secondly, this paper just considers the scenario that the government provides a subsidy to consumers who purchase remanufactured products. Based on this study, future research could focus on government subsidy to remanufacturing enterprises. Thirdly, this work focuses on myopic consumers, and the existence of strategic consumers should be considered in the future. Moreover, a practical application of the model should be analyzed to verify the validity of the presented theoretical model and the assumptions made.