Game-Theoretic Analysis of Pricing and Quality Decisions in Remanufacturing Supply Chain: Impacts of Government Subsidies and Emission Reduction Investments under Cap-and-Trade Regulation

Abstract

To analyze the effects of remanufacturing subsidies and emission reduction investments on pricing and quality decisions under cap-and-trade regulation, four profit-maximization Stackelberg game models for a remanufacturing supply chain (RSC), i.e., without remanufacturing subsidies and emission reduction investments, with remanufacturing subsidies only, with emission reduction investments only, and with both remanufacturing subsidies and emission reduction investments, are constructed, derived, compared, and analyzed. Results show that government subsidies and emission reduction investments can improve profits for the RSC members, while possibly leading to more total carbon emissions. Furthermore, it is worth noting that profit growth and emission reduction can be achieved even though reducing remanufacturing subsidies in some scenarios. Moreover, increasing emission reduction targets will reduce profits of the RSC members but does not necessarily contribute to emission reduction. Therefore, to help the RSC improve profits and reduce emission, the policymaker should formulate differentiated policies based on the types of manufacturers. For the non-abating manufacturer, the government should set higher emission reduction targets and cut down subsidies; for the low-efficiency abating manufacturer, higher emission reduction targets and subsidies are more suitable. However, for the high-efficiency abating manufacturer, lower emission reduction targets and subsidies are more effective.

1. Introduction

High quality and sustainability are two key goals for healthy economic development that requires the joint efforts of enterprises and governments [1]. This study is motivated by two key observations. The first is changes in consumption concepts. As living standards rise, consumer willingness to pay for higher quality products increases [2]. Governments and firms have responded accordingly. For instance, the Central Economic Work Conference, held from 8 to 10 December 2021, noted that China should adhere to supply-side structural reform. Similarly, firms such as Apple, Huawei, and Xiaomi continuously upgrade software systems to enhance product performance and strengthen competitive advantage. While quality improvements can expand market share among quality-conscious consumers, they also raise costs. Consequently, how to determine a suitable product price and quality is the key to balance the pros and cons, which triggers an investigation.

The second motivation arises from environmental concerns. Excessive greenhouse gas emissions have accelerated global warming, heightening the risk of extreme weather events and biodiversity loss [3,4]. The 26th United Nations Climate Conference, held from 1 to 13 November 2021, in Glasgow, UK, pointed out that the Earth’s temperature rising should be kept within 1.5 °C, to avoid catastrophic climate change. To curb carbon emissions, the cap-and-trade (CAT for short) regulation is adopted in some regions and countries including Europe, the United States, Canada, Japan, and China [5]. Under the CAT regulation, regulators set an emission cap, allowing firms to trade carbon allowances based on actual emissions [6]. Notably, China, the world’s largest emitter, launched its nationwide carbon market on 16 July 2021.

Under the CAT regulation, many manufacturers adopt remanufacturing to lower carbon emissions and material costs [7]. For example, firms such as Xerox, Caterpillar, and HP, as well as battery manufacturers like CATL, BYD, and LGES, leverage remanufacturing for environmental and economic benefits [8]. However, consumer acceptance and willingness to pay for remanufactured products (RP for short) remain lower than for new products (NP for short), dampening manufacturers’ incentives [9]. Government subsidies, as an effective policy to promote remanufacturing activity [10,11], have been introduced in countries and regions including the European Union, China, and the United States [12]. However, it remains unclear whether remanufacturing subsidies can simultaneously achieve economic and environmental goals.

To further curb emissions, manufacturers increasingly invest in abatement technologies [13,14]. For instance, H&M has introduced cleaner production methods, while Bosch, the world’s largest auto parts supplier, lowers emissions through remanufacturing, abatement equipment, and process optimization. Under the CAT regulation, such investments alongside government remanufacturing subsidies affect manufacturers’ costs and revenues, complicating pricing and quality decisions in the remanufacturing supply chain (RSC for short). Therefore, under the CAT regulation, the impacts of government subsidies and emission reduction investments on the pricing and quality problems of the RSC should be urgently solved.

Motived by those practices, we aim to examine how government subsidies and emission reduction investments affect pricing and quality decisions in the RSC under CAT regulation. The following questions will be addressed:

(1)

Which case is the best to promote profit growth and emission reduction?

(2)

Under what conditions can remanufacturing subsidies and emission reduction investments jointly enhance profitability and environmental performance?

(3)

How should the government tailor emission targets and subsidy policies for different types of manufacturers?

(4)

How will policy, market, and cost factors affect the decisions of the RSC members?

To address the mentioned questions, four models, namely, the case without the remanufacturing subsidy and emission reduction investment (the N case for short), the case with the remanufacturing subsidy only (the S case for short), the case with the emission reduction investment only (the R case for short), and the case with both the remanufacturing subsidy and emission reduction investment (the RS case for short), are developed. Moreover, the impacts of the policy and market, as well as cost factors on the optimal decision, market demand, total carbon emission, and profits of the RSC members and system are analyzed, which has not been performed before as far as we know.

Some key findings were obtained. Firstly, the maximum profits and emission reductions for the RSC can be achieved in the RS case when the emission reduction investment efficiency is high. Investing in emission reduction can also help profit growth and emission reduction, but remanufacturing subsidies contains uncertainty. It indicates that emission reduction investment is not a cost but a lever for reconstructing competitiveness. Secondly, increasing government subsidies or emission reduction targets will not necessarily help increase profits and reduce emissions, which depends on the manufacturer’s emission reduction investment decision and efficiency. Therefore, for different types of manufacturers, the policymaker must be as precise as surgeons: “removing tumors” from the non-abating manufacturer, “transfusing blood and oxygen” to the low-efficiency abating manufacturer, and “cutting off the umbilical cord” for the high-efficiency abating manufacturer. Thirdly, the consumer preference to the product quality is an invisible regulator for carbon emission reduction. The high-efficiency abating manufacturer should seize the opportunity to transform the consumer preference to the product quality into the emission reduction leverage. At last, improving the emission reduction investment efficiency will always help increase profits and reduce carbon emissions, but improving the quality improvement efficiency is uncertain. The two factors have a double helix effect. Product quality improvement is the wings of the market, and emission reduction investment is the anchor of environmental protection. Only when they work together can sustainable development be achieved.

The remaining chapters are arranged as follows. The related literatures are reviewed in Section 2. The problem and model assumption are described in Section 3. Four models are constructed, and their corresponding optimal solutions are given in Section 4. The optimal solutions in the four cases are compared and analyzed in Section 5. A numerical example is given in Section 6. Section 7 discusses the differences of our work and excavates some management insights. In Section 8, the conclusions of this work are drawn. In addition, to help the readers better understand the research ideas, a schematic representation of our work is given, which is presented in Figure 1.

2. Literature Review

The literature review falls into the following four parts: pricing and quality decisions in the RSC, pricing and emission reduction decisions in the RSC under the CAT regulation, pricing decisions in the RSC under the remanufacturing subsidy, and the research gap.

2.1. Pricing and Quality Decisions in the RSC

Product quality improvement is a common way to enhance the quality on the supply side, which has drawn some scholars’ attention. Maiti [15] developed pricing and quality decision models for the RSC under different power structures and discovered that the RSC’s profits can be improved with the adoption of product quality improvement. On this basis, from the perspective of product recycling, Giri et al. [16] and Maiti [17] discussed the impacts of product return. Similarly, Maiti and Giri [18], Mondal and Giri [19], and Gaula and Jha [20] investigated the pricing and quality improvement decisions in dual-recycling channels. From the perspective of product selling, Chen et al. [21] explored the impacts of marketing promotion on product quality improvement. Similarly, Zhang and Dai [22] constructed quality decision models under different selling channels. Furthermore, considering the online-retail channel and marketing promotion, Taleizadeh et al. [23] studied its impacts on product quality decision. In addition, Xie et al. [24] discussed the impacts of online reviews. From the perspective of product competition, Qian et al. [25] and Pal et al. [26] analyzed the relationship between product competition and product quality improvement. From the perspective of industrial policy, Wang et al. [27] explored the relationship between the trade-ins policy and product quality decision. Mao et al. [28] examined the impacts of the CAT policy on product quality decision. The above-mentioned literatures focus only on the manufacturers’ efforts to improve product quality on the supply side, neglecting to consider emission reduction efforts. Although Wang et al. [27] and Mao et al. [28] considered the impacts of macro policies, they only considered a single government subsidy or carbon trading policy and failed to explore the interaction between the two policies.

2.2. Pricing and Emission Reduction Decisions in the RSC Under the CAT Regulation

Once the CAT regulation is implemented, enterprises have to consider the costs or revenues brought by such policy. Therefore, under the CAT regulation, the problems of coordinating the production and pricing strategies for NP and RP have been widely discussed. Chang et al. [29] built two pricing decision models, without and with competition between NP and RP, and claimed that the CAT regulation will affect decisions directly. After that, Chang et al. [30] further analyzed the impact of two carbon quota allocation methods, the industrial benchmark method and historical intensity method, on the production and pricing decisions. Meanwhile, as the emission reduction pressure increases, the problems of the emission reduction investment also draw some attractions. From the perspective of policy itself, Chen et al. [31] investigated the impact of the carbon price on emission reduction decision. Moreover, Cheng et al. [32], Li et al. [33], Panza and Peron [34], and Pal [35] discussed the impacts of the carbon tax and CAT policies on emission reduction decisions. Furthermore, some researchers explored the impacts of other factors on the RSC. For example, the impacts of consumers’ low-carbon preference [36], selling channel [37,38], marketing promotion [39], recycling channel [40], channel power structure [41], blockchain technology [42,43], carbon asset pledge financing [44,45,46], and risk aversion [47] on emission reduction decisions were analyzed. Moreover, Zhang et al. [48], Zhang et al. [49], and Xia et al. [50] studied the emission reduction strategy under the CAT regulation. These literatures mostly explored the impacts of the CAT regulation on the pricing and emission reduction decisions. And except Chang et al. [30], Yuan et al. [38], and Guo et al. [40], they all assumed that the allocation of the free carbon credits had no influence on decisions. Of course, there are a few scholars taking the product quality improvement into consideration. For instance, Taleizadeh et al. [51] proposed an emission reduction and product quality improvement decision model under the CAT regulation and supported that the targets of emission reduction and profit growth of the RSC can be achieved by considering the emission reduction investment and the product quality improvement simultaneously. Furthermore, Taleizadeh et al. [52] designed a cost-sharing contract to coordinate the RSC system. However, both Taleizadeh et al. [51] and Taleizadeh et al. [52] failed to explore the action mechanism of government subsidies on emission reduction.

2.3. Pricing Decision in the RSC Under the Remanufacturing Subsidy

Remanufacturing subsidies, aimed at addressing low consumer acceptance of RP and weak manufacturer incentives, have drawn significant academic attentions. To disclose the impacts of the “trade old for remanufactured” subsidy, Li and Wu [53] set up the pricing decision models without and with subsidy and indicated that it can bring a win-win of economy growth and environment protection when the subsidy is properly provided. On the contrary, considering the “trade old for new” and “trade old for remanufactured” programs simultaneously, Ma et al. [54] maintained that it will reduce the profit of the RSC when there are too many “trade old for remanufactured” consumers. Similarly, Qiao and Su [12] investigated the impacts of the government subsidy on the RSC, and results showed that the emission reduction target and social surplus improvement cannot be realized only by increasing the government subsidy. Hereafter, some scholars explored the impacts of other factors on the RSC. For example, the impacts of differences in consumers’ willingness to pay for product environmental attributes [55], marketing promotion [56], and different selling channels [57] were investigated, and it was found that the government subsidy can help to increase the profit but may do harm to the environment. After that, to alleviate environmental impacts, Zhang and Zhang [58], Tsao and Ai [59], and Qiao et al. [60] further studied the pricing problems in the RSC under the government subsidy and CAT regulation. These above-mentioned literatures mainly concentrated on the impacts of remanufacturing subsidies. However, they did not investigate the action mechanism of product quality improvement and emission reduction investment on the effects of government subsidies.

2.4. Research Gap

Through the review of the previous literatures, this study makes theoretical contributions in the following aspects. (1) Compared with the previous literatures, this study incorporates the CAT regulation and the government subsidy into a unified analytical framework along with emission reduction investments and product quality improvements. It systematically reveals the interaction mechanism between profit growth and emission reduction performance in the RSC under synergistic effects of multiple policy tools and promotes the deepening of related literatures towards multi-dimensional system analysis. (2) This study breaks through the “fixed carbon emission quota” assumption commonly used in the previous literatures and innovatively introduces a dynamic quota allocation model based on the emission reduction target, the historical emission intensity and the actual output, thereby more realistically reflecting the market regulation nature of the CAT regulation and providing a new theoretical perspective for understanding the impact mechanism of the CAT regulation on RSC decision-making. (3) Based on these theoretical breakthroughs, this study obtains several new conclusions of significant theoretical value. Specifically, it reveals the underlying mechanism by which emission reduction investments and remanufacturing subsidies can achieve a win-win situation for both profits and the environment under certain conditions. Moreover, it finds an optimal exit path for government subsidies when emission reduction efficiency is high. Furthermore, it clarifies that emission reduction targets have a double-edged sword effect on environmental benefits, significantly depending on the manufacturer’s emission reduction decision and efficiency. These findings not only enrich the theory of green supply chain management but also provide more refined theoretical support for policymaking. In addition, to highlight these differences,

Table 1. Comparison between this work and the related literatures.

Literatures	CAT	Government Subsidy	Emission Reduction	Product Quality	Pricing
Wang et al. [27]		√		√	√
Mao et al. [28]	√			√	√
Taleizadeh et al. [51]	√		√	√	√
Taleizadeh et al. [52]	√		√	√	√
Zhang and Zhang [58]	√	√			√
Tsao and Ai [59]	√	√			√
Qiao et al. [60]	√	√			√
This work	√	√	√	√	√

“√” indicates that this factor has been taken into consideration.

compares this work with the related literatures.

3. Problem Description and Model Assumption

3.1. Problem Description

The RSC system is shown in Figure 2. First of all, the government implements the CAT regulation and the remanufacturing subsidy by setting emission reduction targets and offering financial incentives. After that, the manufacturer, as the leader of the RSC, is responsible for producing NP and RP and wholesaling them to the retailer. Meanwhile, to satisfy the consumer demand for higher product quality, the manufacturer invests in quality improvement technology. For example, battery manufacturers such as CATL, BYD, and LGES are constantly optimizing and upgrading their battery pack production lines while carrying out battery remanufacturing. Additionally, the electronic product manufacturers such as Apple, Huawei, HP, and Kodak improve their product performance by continuously optimizing its processing system. Obviously, it cannot reduce emissions through such kinds of product quality improvement. Therefore, to release the emission pressure, the manufacturer also invests in emission reduction technology. At the end, the retailer is responsible for selling NP and RP to consumers. In practice, the retailer usually sets different prices for NP and RP and sells them to independent markets since the “remanufacturing” sign on RP can be easily distinguished. To sum up, the decision sequences are as follows: When the emission reduction target and the remanufacturing subsidy are given, the manufacturer first determines the product quality and the emission reduction rate and then determines the wholesale price for NP and RP. The retailer at the end determines the sale price for NP and RP.

3.2. Notation

The notations and definitions are presented in

Table 2. Notations and definitions in this work.

Notation	Definition	Notation	Definition
Decision variables
$\Delta$	the emission reduction rate per product	$w_i$	the wholesale price per $i$ product, $i\in \{\mathrm{n},\mathrm{r}\}$, in which $n$ and $r$ indicate NP and RP, respectively.
$p_i$	the retail price per $i$ product, $i\in \{\mathrm{n},\mathrm{r}\}$	$q$	the quality of NP
Model parameters
$Q_i$	the initial capacity of the $i$ product market, $i\in \{\mathrm{n},\mathrm{r}\}$	$c_i$	the production cost per $i$ product, $i\in \{\mathrm{n},\mathrm{r}\}$
$c_u$	the recycling cost per used product	$e_i$	the carbon emissions per $i$ product, $i\in \{\mathrm{n},\mathrm{r}\}$
$p_c$	the trading price per carbon credit	$\lambda$	the emission reduction target
$m$	the cost coefficient of the product quality improvement	$l$	the quality improvement discount coefficient of RP
$\alpha$	the sensitivity of consumers to the product price	$n$	the cost coefficient of the emission reduction
$D_i$	the demand of the $i$ product, $i\in \{\mathrm{n},\mathrm{r}\}$	$\beta$	the preference of consumers to the product quality
$s$	the remanufacturing subsidy ratio	$E$	the total carbon emission
${\pi }_M$	the manufacturer’s profits	${\pi }_R$	the retailer’s profits
${\pi }_T$	the RSC system’s profits
Scenarios
$N$	the case without government subsidy and emission reduction investment	$S$	the case with government subsidy only
$R$	the case with emission reduction investment only	$RS$	the case with both government subsidy and emission reduction investment
Nomenclatures
$NP$	new products	$RP$	remanufacturing products
CAT	cap-and-trade	RSC	remanufacturing supply chain

.

3.3. Assumption

Assumption 1. 

The free emission credits rely simultaneously on the historical emission intensity, the output, and the emission reduction target [61,62]. Namely, the free credits are $(1-\lambda )e_n{D}_n+(1-\lambda )e_r{D}_r$ , noting that $\lambda \in [0,1]$, $\lambda =0$ means the manufacturer can release emissions totally free, while $\lambda =1$ means the manufacturer will be charged for all emissions. In other words, the larger $\lambda$ is, the smaller the free credits are, and the larger the emission reduction pressure will be. Meanwhile, the subsidies are closely related to the production cost of per RP, the output of RP, and the subsidy ratio [63]. Namely, the subsidies are $s{c}_r{D}_r$, noting that $s\in [0,1)$, $s=0$ implies no subsidy for remanufacturing.

Assumption 2. 

Product quality improvement is a technology-intensive investment, and its marginal investment cost increases with the product quality improvement level, especially, considering that the NP is produced by the whole new hardware and the optimized processing system while the RP is produced by the used hardware and the optimized processing system, making the compatibility of RP worse than that of NP. It is assumed that the quality of RP is lower than NP due to the discrepancy in raw material. Referring to Örsdemir et al. [64] and Niu et al. [65], the costs invested in product quality improvement are determined by the cost coefficient of the product quality improvement and the product quality and are one-time investments, equaling to$m{q}^2$. The smaller $m$ is, the higher the efficiency of the product quality improvement will be. Besides that, to ensure the optimal solutions for all models, it is assumed that $m$ is bigger enough, satisfying $m>{\displaystyle \frac{{\beta }^2(1+l^2)}{8\alpha }}=m_0$, and $m_0$ is the same below.

Assumption 3. 

Emission reduction investment is also a technology-intensive investment, and its marginal investment cost increases with the emission reduction rate. Referring to Yang and Chen [66] and Ma et al. [67], the costs invested in emission reduction depend on the cost coefficient of emission reduction investment and the emission reduction rate and are a one-time investment, equaling to $n{\Delta }^2$. The smaller $n$ is, the higher the efficiency of the emission reduction will be. Similarly, it is assumed that $n$ is bigger enough, satisfying $n>{\displaystyle \frac{\alpha p_c^2[8\alpha m(e_n^2+e_r^2)-{\beta }^2{(l{e}_n-e_r)}^2]}{8\alpha m-{\beta }^2(1+l^2)}}=n_0$, and $n_0$ below remains the same, noting that $\Delta \in [0,1)$, $\Delta =0$ implies no emission reduction investment.

Assumption 4. 

In practice, since the recycling rate of wasted products cannot reach 100% and consumers lack cognitive considerations to the RP, the initial capacity of the product market satisfies $Q_n>Q_r>0$. Besides, to ensure the manufacturer gains profits from the production of NP and RP, the conditions of $w_n-(c_n+\lambda e_n{p}_c)>0$, $w_r-(c_r+c_u+\lambda e_r{p}_c)>0$,  and $c_n>c_u+c_r$should be satisfied. Generally speaking, the improvement in product quality will bring a positive effect to market demand, while the increase in product price will bring a negative effect. The demand functions of NP and RP can be shown as follows [68,69].

$$D_n=Q_n-\alpha p_n+\beta q$$

(1)

$$D_r=Q_r-\alpha p_r+\beta lq$$

(2)

4. Models

4.1. The N Case

The N case means that the government does not provide remanufacturing subsidies, and the manufacturer does not invest in emission reduction, and the profit functions of the RSC members are shown below.

$$\underset{q,w_n,w_r}{\max }{\pi }_M^N=(w_n-c_n)D_n+(w_r-c_r-c_u)D_r-p_c\lambda (e_n{D}_n+e_r{D}_r)-m{q}^2$$

(3)

$$\underset{p_n,p_r}{\max }{\pi }_R^N=(p_n-w_n)D_n+(p_r-w_r)D_r$$

(4)

The equilibrium solutions, market demands, total carbon emissions, and profits of the RSC members in the N case can be obtained by using the inverse inductive method. For ease of presentation, the equilibrium solutions of the N case are shown in Column 2 of

Table 3. The equilibrium solutions in the N and S cases.

Variables	N Case	S Case
$q$	${\displaystyle \frac{\beta [Q_n+l{Q}_r-\alpha (X_2+l{X}_3)]}{X_1}}$	${\displaystyle \frac{\beta [Q_n+l{Q}_r-\alpha (X_2+l{X}_4)]}{X_1}}$
$w_n$	${\displaystyle \frac{Q_n(X_1+{\beta }^2)+l{\beta }^2{Q}_r+\alpha [X_2(X_1-{\beta }^2)-l{\beta }^2{X}_3]}{2\alpha X_1}}$	${\displaystyle \frac{Q_n(X_1+{\beta }^2)+l{\beta }^2{Q}_r+\alpha [X_2(X_1-{\beta }^2)-l{\beta }^2{X}_4]}{2\alpha X_1}}$
$w_r$	${\displaystyle \frac{Q_r(X_1+{\beta }^2{l}^2)+l{\beta }^2{Q}_n+\alpha [C(X_1-{\beta }^2{l}^2)-l{\beta }^2{X}_2]}{2\alpha X_1}}$	${\displaystyle \frac{Q_r(X_1+{\beta }^2{l}^2)+l{\beta }^2{Q}_n+\alpha [X_4(X_1-{\beta }^2{l}^2)-l{\beta }^2{X}_2]}{2\alpha X_1}}$
$p_n$	${\displaystyle \frac{Q_n[3(X_1+{\beta }^2)]+3l{\beta }^2{Q}_r+\alpha [X_2(X_1-3{\beta }^2)-3l{\beta }^2{X}_3]}{4\alpha X_1}}$	${\displaystyle \frac{Q_n[3(X_1+{\beta }^2)]+3l{\beta }^2{Q}_r+\alpha [X_2(X_1-3{\beta }^2)-3l{\beta }^2{X}_4]}{4\alpha X_1}}$
$p_r$	${\displaystyle \frac{Q_r[3(X_1+{\beta }^2{l}^2)]+3l{\beta }^2{Q}_n+\alpha [X_3(X_1-3{\beta }^2{l}^2)-3l{\beta }^2{X}_2]}{4\alpha X_1}}$	${\displaystyle \frac{Q_r[3(X_1+{\beta }^2{l}^2)]+3l{\beta }^2{Q}_n+\alpha [X_4(X_1-3{\beta }^2{l}^2)-3l{\beta }^2{X}_2]}{4\alpha X_1}}$
$D_n$	${\displaystyle \frac{Q_n(X_1+{\beta }^2)+l{\beta }^2{Q}_r-\alpha [X_2(X_1+{\beta }^2)+l{\beta }^2{X}_3]}{4X_1}}$	${\displaystyle \frac{Q_n(X_1+{\beta }^2)+l{\beta }^2{Q}_r-\alpha [X_2(X_1+{\beta }^2)+l{\beta }^2{X}_4]}{4X_1}}$
$D_r$	${\displaystyle \frac{Q_r(X_1+{\beta }^2{l}^2)+l{\beta }^2{Q}_n-\alpha [X_3(X_1+{\beta }^2{l}^2)+l{\beta }^2{X}_2]}{4X_1}}$	${\displaystyle \frac{Q_r(X_1+{\beta }^2{l}^2)+l{\beta }^2{Q}_n-\alpha [X_4(X_1+{\beta }^2{l}^2)+l{\beta }^2{X}_2]}{4X_1}}$

Where $X_1=8\alpha m-{\beta }^2(1+l^2)$, $X_2=c_n+\lambda e_n{p}_c$, $X_3=c_r+c_u+\lambda e_r{p}_c$, and $X_4=(1-s)c_r+c_u+\lambda e_r{p}_c$.

after simplification. See Appendix A for proofs.

4.2. The S Case

The S case means that the government provides remanufacturing subsidies, but the manufacturer does not invest in emission reduction, and the profit functions of the RSC members are presented below.

$$\underset{q,w_n,w_r}{\max }{\pi }_M^S=(w_n-c_n)D_n+[w_r-(1-s)c_r-c_u]D_r-p_c\lambda (e_n{D}_n+e_r{D}_r)-m{q}^2$$

(5)

$$\underset{p_n,p_r}{\max }{\pi }_R^S=(p_n-w_n)D_n+(p_r-w_r)D_r$$

(6)

Similar to Section 4.1, the optimal product quality and wholesale price of NP and RP $(q^S,w_n^S,w_r^S)$ can be obtained easily. Substituting $(q^S,w_n^S,w_r^S)$ into Equations (A1) and (A2), the optimal retail price of NP and RP $(p_n^S,p_r^S)$ can be calculated. Next, substituting $(q^S,p_n^S,p_r^S)$ into Equations (1) and (2), we can obtain the demand of NP and RP $(D_n^S,D_r^S)$ and then the total carbon emissions $E^S=e_n{D}_n^S+e_r{D}_r^S$. Last, substituting $(q^S,p_n^S,p_r^S,D_n^S,D_r^S)$ into Equations (5) and (6), the optimal profits $({\pi }_n^S,{\pi }_r^S)$ can be obtained easily, and the equations are not given due to the complexity of the expression. For ease of presentation, the equilibrium solutions of the S case are shown in Column 3 of Table 3 after simplification.

4.3. The R Case

The R case means that the government does not provide remanufacturing subsidies, but the manufacturer invests in emission reduction, and the profit functions of the RSC members are shown below.

$$\underset{\Delta ,q,w_n,w_r}{\max }{\pi }_M^R=(w_n-c_n)D_n+(w_r-c_r-c_u)D_r-p_c(\lambda -\Delta )(e_n{D}_n+e_r{D}_r)-m{q}^2-n{\Delta }^2$$

(7)

$$\underset{p_n,p_r}{\max }{\pi }_R^R=(p_n-w_n)D_n+(p_r-w_r)D_r$$

(8)

The equilibrium solutions, market demands, total carbon emissions, and profits of the RSC members in the R case can be obtained by using the inverse inductive method. For ease of presentation, the equilibrium solutions in the R case are shown in Column 2 of

Table 4. The equilibrium solutions in the R and RS cases.

Variables	R Case	RS Case
$\Delta$	${\displaystyle \frac{p_c[(6\alpha m{e}_n+X_7)(Q_n-\alpha X_2)+(6\alpha m{e}_r+X_8)(Q_r-\alpha X_3)]}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}$	${\displaystyle \frac{p_c[(6\alpha m{e}_n+X_7)(Q_n-\alpha X_2)+(6\alpha m{e}_r+X_8)(Q_r-\alpha X_4)]}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}$
$q$	$\begin{array}{l}{\displaystyle \frac{\beta (8n+\alpha e_r{p}_c^2{X}_5)(Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\\ +{\displaystyle \frac{\beta (8ln+\alpha e_n{p}_c^2{X}_5)(Q_r-\alpha X_3)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$	$\begin{array}{l}{\displaystyle \frac{\beta (8n+\alpha e_r{p}_c^2{X}_5)(Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\\ +{\displaystyle \frac{\beta (8ln+\alpha e_n{p}_c^2{X}_5)(Q_r-\alpha X_4)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$
$w_n$	$\begin{array}{l}{\displaystyle \frac{[4n({\beta }^2-X_1)+\alpha e_r{p}_c^2(2\alpha m{e}_r+X_8)](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_n}{\alpha }}\\ +{\displaystyle \frac{[4ln{\beta }^2-\alpha e_n{p}_c^2(2\alpha m{e}_r+X_8)](Q_r-\alpha X_3)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$	$\begin{array}{l}{\displaystyle \frac{[4n({\beta }^2-X_1)+\alpha e_r{p}_c^2(2\alpha m{e}_r+X_8)](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_n}{\alpha }}\\ +{\displaystyle \frac{[4ln{\beta }^2-\alpha e_n{p}_c^2(2\alpha m{e}_r+X_8)](Q_r-\alpha X_4)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$
$w_r$	$\begin{array}{l}{\displaystyle \frac{[4ln{\beta }^2-\alpha e_r{p}_c^2(2\alpha m{e}_n+X_7)](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_r}{\alpha }}\\ +{\displaystyle \frac{[4n(l^2{\beta }^2-X_1)+\alpha e_n{p}_c^2(2\alpha m{e}_n+X_7)](Q_r-\alpha X_3)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$	$\begin{array}{l}{\displaystyle \frac{[4ln{\beta }^2-\alpha e_r{p}_c^2(2\alpha m{e}_n+X_7)](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_r}{\alpha }}\\ +{\displaystyle \frac{[4n(l^2{\beta }^2-X_1)+\alpha e_n{p}_c^2(2\alpha m{e}_n+X_7)](Q_r-\alpha X_4)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$
$p_n$	$\begin{array}{l}{\displaystyle \frac{[2n(3{\beta }^2-X_1)+\alpha e_r{p}_c^2{X}_8](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_n}{\alpha }}\\ +{\displaystyle \frac{[6ln{\beta }^2-\alpha e_n{p}_c^2{X}_8](Q_r-\alpha X_3)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$	$\begin{array}{l}{\displaystyle \frac{[2n(3{\beta }^2-X_1)+\alpha e_r{p}_c^2{X}_8](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_n}{\alpha }}\\ +{\displaystyle \frac{[6ln{\beta }^2-\alpha e_n{p}_c^2{X}_8](Q_r-\alpha X_4)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$
$p_r$	$\begin{array}{l}{\displaystyle \frac{(6ln{\beta }^2-\alpha e_r{p}_c^2{X}_7)(Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_r}{\alpha }}\\ +{\displaystyle \frac{[2n(3l^2{\beta }^2-X_1)+\alpha e_n{p}_c^2{X}_7](Q_r-\alpha X_3)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$	$\begin{array}{l}{\displaystyle \frac{(6ln{\beta }^2-\alpha e_r{p}_c^2{X}_7)(Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}+{\displaystyle \frac{Q_r}{\alpha }}\\ +{\displaystyle \frac{[2n(3l^2{\beta }^2-X_1)+\alpha e_n{p}_c^2{X}_7](Q_r-\alpha X_4)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$
$D_n$	$\begin{array}{l}{\displaystyle \frac{2[n({\beta }^2+X_1)-m{\alpha }^2{e}_r^2{p}_c^2](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\\ +{\displaystyle \frac{2[ln{\beta }^2+m{e}_n{e}_r{\alpha }^2{p}_c^2](Q_r-\alpha X_3)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$	$\begin{array}{l}{\displaystyle \frac{2[n({\beta }^2+X_1)-m{\alpha }^2{e}_r^2{p}_c^2](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\\ +{\displaystyle \frac{2[ln{\beta }^2+m{e}_n{e}_r{\alpha }^2{p}_c^2](Q_r-\alpha X_4)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$
$D_r$	$\begin{array}{l}{\displaystyle \frac{2[ln{\beta }^2+m{e}_n{e}_r{\alpha }^2{p}_c^2](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\\ +{\displaystyle \frac{2[n(l^2{\beta }^2+X_1)-m{\alpha }^2{e}_n^2{p}_c^2](Q_r-\alpha X_3)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$	$\begin{array}{l}{\displaystyle \frac{2[ln{\beta }^2+m{e}_n{e}_r{\alpha }^2{p}_c^2](Q_n-\alpha X_2)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\\ +{\displaystyle \frac{2[n(l^2{\beta }^2+X_1)-m{\alpha }^2{e}_n^2{p}_c^2](Q_r-\alpha X_4)}{8n{X}_1-\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}}\end{array}$

Where $X_1=8\alpha m-{\beta }^2(1+l^2)$, $X_2=c_n+\lambda e_n{p}_c$, $X_3=c_r+c_u+\lambda e_r{p}_c$, $X_4=(1-s)c_r+c_u+\lambda e_r{p}_c$, $X_5=l{e}_n-e_r$, $X_6=8\alpha m(e_n^2+e_r^2)$, $X_7=2\alpha m{e}_n-l{\beta }^2{X}_5$, $X_8=2\alpha m{e}_r+{\beta }^2{X}_5$, and $X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8$ are the same below.

after simplification. See Appendix B for proofs.

4.4. The RS Case

The RS case means that the government provides remanufacturing subsidies, and the manufacturer invests in emission reduction, and the profit functions of the RSC members are presented below.

$$\underset{\Delta ,q,w_n,w_r}{\max }{\pi }_M^{RS}=(w_n-c_n)D_n+[w_r-(1-s)c_r-c_u]D_r-p_c(\lambda -\Delta )(e_n{D}_n+e_r{D}_r)-m{q}^2-n{\Delta }^2$$

(9)

$$\underset{p_n,p_r}{\max }{\pi }_R^{RS}=(p_n-w_n)D_n+(p_r-w_r)D_r$$

(10)

Similar to Section 4.3, we can easily obtain the optimal emission reduction rate, product quality, and wholesale price of NP and RP $({\Delta }^{RS},q^{RS},w_n^{RS},w_r^{RS})$. Substituting $({\Delta }^{RS},q^{RS},w_n^{RS},w_r^{RS})$ into Equations (A1) and (A2), the optimal retail price of NP and RP $(p_n^{RS},p_r^{RS})$ can be calculated. Next, substituting $(q^{RS},p_n^{RS},p_r^{RS})$ into Equations (1) and (2), we can obtain the demand of NP and RP $(D_n^{RS},D_r^{RS})$ and then the total carbon emissions $E^{RS}=(1-{\Delta }^{RS})(e_n{D}_n^{RS}+e_r{D}_r^{RS})$. Last, substituting $({\Delta }^{RS},q^{RS},p_n^{RS},p_r^{RS},D_n^{RS},D_r^{RS})$ into Equations (9) and (10), the optimal profits $({\pi }_n^{RS},{\pi }_r^{RS})$ can be obtained easily, and the equations are not given due to the complexity of the expression. For ease of presentation, the equilibrium solutions in the RS case are shown in Column 3 of Table 4 after simplification.

5. Analysis

To identify the most effective case for profit growth and emission reduction, the optimal solutions across the four scenarios are compared, and the impacts of the policy, market, and cost factors on the decision variables are analyzed. Moreover, to ensure the optimal solutions in Table 3 and Table 4 are no-negativity, the condition of $Q_n-\alpha (c_n+\lambda e_n{p}_c)>0$ and $Q_r-\alpha (c_r+c_u+\lambda e_r{p}_c)>0$ should be satisfied. And due to $D_n=Q_n-\alpha p_n+\beta q>0$ and $D_r=Q_r-\alpha p_r+\beta lq>0$, $Q_n>\alpha p_n$ and $Q_r>\alpha p_r$ can be obtained when there is no quality improvement. Then, based on the assumption of $w_n-(c_n+\lambda e_n{p}_c)>0$ and $w_r-(c_r+c_u+\lambda e_r{p}_c)>0$ in the “Section 3.1”, $Q_n-\alpha (c_n+\lambda e_n{p}_c)>0$ and $Q_r-\alpha (c_r+c_u+\lambda e_r{p}_c)>0$ can be obtained. In addition, to make it easier for readers to understand, the contents in this section mainly adhere to the following presentation logic. Firstly, we present the analysis results in mathematical form. Then, we interpret these results in plain language. Finally, we excavate the management implications behind the analysis results.

5.1. Comparisons of the Optimal Solutions in the Four Cases

 Corollary 1.

Table 5. Results of comparisons for optimal solutions in four cases.

Equilibrium Solutions	Results	If $\mathit{m}$, $\mathit{n}$ Meet the Conditions of
$\Delta$	${\Delta }^R<{\Delta }^{RS}$	—
$q$	$q^N<q^S<q^{RS};q^N<q^R<q^{RS}$	—
$w_n$	$w_n^N<w_n^S\le w_n^{RS};w_n^N\le w_n^R<w_n^{RS}$	$m_0<m\le m_1$	$n_1\le n_0$	$n_1\le n_0<n$
	$w_n^N<w_n^S,w_n^{RS}<w_n^S;w_n^{RS}\le w_n^R<w_n^N$	$m>m_1$	$n_0<n_1$	$n_0<n\le n_1$
	$w_n^N<w_n^S,w_n^{RS}<w_n^S;w_n^R<w_n^N,w_n^R<w_n^{RS}$			$n>n_1$
$w_r$	$w_r^N\le w_r^S<w_r^{RS};w_r^N<w_r^R<w_r^{RS}$	$m_0<m\le m_a$	$n_2<n_0$	$n_2<n_0<n$
	$w_r^S<w_r^N,w_r^S\le w_r^{RS};w_r^N\le w_r^R\le w_r^{RS}$	$m_a<m\le m_2$	$n_0\le n_2$	$n_0<n\le n_2$
	$w_r^S<w_r^N,w_r^S\le w_r^{RS};w_r^N\le w_r^R,w_r^{RS}<w_r^R$			$n>n_0=n_2$
	$w_r^{RS}<w_r^S<w_r^N;w_r^{RS}<w_r^R<w_r^N$	$m>m_2$	$n_2<n_0$	$n_2<n_0<n$
$p_n$	$p_n^N<p_n^S\le p_n^{RS};p_n^N\le p_n^R<p_n^{RS}$	$m_0<m\le m_3$	$n_3\le n_0$	$n_3\le n_0<n$
	$p_n^N<w_n^S,p_n^{RS}<p_n^S;p_n^{RS}\le p_n^R<p_n^N$	$m>m_3$	$n_0<n_3$	$n_0<n\le n_3$
	$p_n^N<p_n^S,p_n^{RS}<p_n^S;p_n^R<p_n^N,p_n^R<p_n^{RS}$			$n>n_3$
$p_r$	$p_r^N\le p_r^S<p_r^{RS};p_r^N<p_r^R<p_r^{RS}$	$m_0<m\le m_b$	$n_4<n_0$	$n_4<n_0<n$
	$p_r^S<p_r^N,p_r^S\le p_r^{RS};p_r^N\le p_r^R\le p_r^{RS}$	$m_b<m\le m_4$	$n_0\le n_4$	$n_0<n\le n_4$
	$p_r^S<p_r^N,p_r^S\le p_r^{RS};p_r^N\le p_r^R,p_r^{RS}<p_r^R$			$n>n_0=n_4$
	$p_r^{RS}<p_r^S<p_r^N;p_r^{RS}<p_r^R<p_r^N$	$m>m_4$	$n_4<n_0$	$n_4<n_0<n$
$D_n$	$D_n^N<D_n^S<D_n^{RS};D_n^N<D_n^R<D_n^{RS}$	—
$D_r$	$D_r^N<D_r^S<D_r^{RS};D_r^N<D_r^R<D_r^{RS}$	—
$E$	$E^N<E^S,E^{RS}<E^S;E^{RS}\le E^R<E^N$	—	$n_0<n_a$	$n_0<n\le n_a$
	$E^N<E^S,E^{RS}<E^S;E^R<E^N,E^R<E^{RS}$			$n>n_a$
${\pi }_M$	${\pi }_M^N<{\pi }_M^S<{\pi }_M^{RS};{\pi }_M^N<{\pi }_M^R<{\pi }_M^{RS}$	—
${\pi }_R$	${\pi }_R^N<{\pi }_R^S<{\pi }_R^{RS};{\pi }_R^N<{\pi }_R^R<{\pi }_R^{RS}$	—
${\pi }_T$	${\pi }_T^N<{\pi }_T^S<{\pi }_T^{RS};{\pi }_T^N<{\pi }_T^R<{\pi }_T^{RS}$	—

Notes: “—“ here and hereafter means no condition, where $m_1={\displaystyle \frac{{\beta }^2(l^2{e}_n+2e_n+l{e}_r)}{8\alpha e_n}}$, $m_2={\displaystyle \frac{{\beta }^2(2l^2{e}_r+l{e}_n+e_r)}{8\alpha e_r}}$, $m_3={\displaystyle \frac{{\beta }^2(l^2{e}_n+4e_n+3l{e}_r)}{8\alpha e_n}}$, $m_4={\displaystyle \frac{{\beta }^2(4l^2{e}_r+3l{e}_n+e_r)}{8\alpha e_r}}$, $m_a={\displaystyle \frac{{\beta }^2(2l^2+1)}{8\alpha }}$, $m_b={\displaystyle \frac{{\beta }^2(4l^2+1)}{8\alpha }}$, $n_1={\displaystyle \frac{\alpha e_n{p}_c^2{\beta }^2(2\alpha m{e}_r+X_8)}{4l{\beta }^2}}$, $n_2={\displaystyle \frac{\alpha e_n{p}_c^2(2\alpha m{e}_n+X_7)}{4(X_1-{\beta }^2{l}^2)}}$, $n_3={\displaystyle \frac{\alpha e_n{p}_c^2{\beta }^{2}I}{4l{\beta }^2}}$,$n_4={\displaystyle \frac{\alpha e_n{p}_c^2{X}_7}{2(X_1-3{\beta }^2{l}^2)}}$, and $n_a={\displaystyle \frac{2p_c[(Q_n-\alpha X_2)(8\alpha m{e}_n-l{\beta }^2{X}_5)+(Q_r-\alpha X_2)(8\alpha m{e}_r+{\beta }^2{X}_5)]+\alpha p_c^2(X_6-{\beta }^2{X}_5^2)}{8X_1}}$ and the parameters of $m_1,m_2,m_3,m_4,m_a,m_b,n_1,n_2,n_3,n_4,n_a$ remain the same throughout this paper.

 presents the results of comparisons for the optimal solutions in the four cases. See Appendix C for proofs of Corollary 1.

From Corollary 1, the following conclusions can be summarized:

(1)

Investing in emission reduction can increase profits and reduce total emissions. Compared with the N case, the R case yields a higher carbon emission reduction rate, product quality, market demand, and profits of the RSC members and system, along with lower total emissions. It means that carbon emission costs can be reduced with the adoption of emission reduction technologies. And the cost savings can be utilized to improve the product quality. In turn, enhanced product quality attracts additional consumers, thereby increasing the profits of the RSC members and system.

(2)

Remanufacturing subsidies promote profit growth but do not necessarily reduce emissions. Compared with the cases without subsidies (i.e., the N case and the R case), the cases with subsidies (i.e., the S case and the RS case) results in a higher carbon emission reduction rate, product quality, market demand, and profits of the RSC members and system, no matter whether the manufacturer invests in carbon emission reduction or not. However, from an environmental perspective, the N case is better than the S case. Conversely, total carbon emissions in the RS case are lower than that in the R case, when the efficiency of the emission reduction investment is high (i.e., $n_0<n\le n_a$).

(3)

There are different pricing strategies in different scenarios. Compared with the N case, the S case results in a higher selling price for NP but reverse for RP. In the cases with emission reduction investment (i.e., the R and RS case), the cost coefficients of the product quality improvement and emission reduction investment have significant impacts on the selling prices of NP and RP. Specifically, the selling prices of NP and RP are higher in the RS case, when the cost coefficients of the product quality improvement and emission reduction investment are low (i.e., $m_0<m\le \min \{m_1,m_2,m_3,m_4,m_a,m_b\}$ and $\max \{n_1,n_2,n_3,n_4\}\le n_0<n$). The reason is that subsidies can improve product quality, making consumers willing to buy even at a higher price. In addition, compared with the N case, the R case results in a lower sale price for NP and RP when $m>\max \{m_1,m_2,m_3,m_4,m_a,m_b\}$ and $\max \{n_2,n_4\}<n_0<\min \{n_1,n_3\}<n$; compared with the S case, the RS case results in a lower price for NP and RP when $m>\max \{m_1,m_2,m_3,m_4,m_a,m_b\}$ and $\max \{n_2,n_4\}<n_0<n<\min \{n_1,n_3\}$. It means that it can lower prices for NP and RP in the R and RS case, since the emission reduction investment can bring additional incomes.

To sum up, in the RS case, considering emission reduction investments and remanufacturing subsidies simultaneously, the maximum profits and emission reductions for the RSC can be achieved for $n_0<n\le n_a$. This is because emission reduction investments reduce the carbon emission costs, while subsidies create a synergistic effect by incentivizing the expansion of remanufacturing. Furthermore, the emissions reductions from economies of scale exceed the emission increments from market expansion, and quality improvements and cost savings work together to drive profit growth, when emissions reduction efficiency exceeds a critical threshold. It indicates that emission reduction investment is not a cost but a lever for reconstructing competitiveness. This is because emission reduction investment can reduce emission reduction costs, which can feed back into product quality improvement and increase product market attractiveness. However, for the governments, unconstrained subsidies nourish profits but may increase environmental burdens, which depends on the emission reduction investment efficiency. Therefore, the manufacturer should reduce emission reduction costs through technological innovation and feed efficiency dividends back into product quality premiums, achieving a dual increase in environmental benefits and market attractiveness. The government should implement a “precise subsidy” policy, dynamically adjusting the subsidy intensity based on the emission reduction efficiency of the manufactures.

5.2. Effects of Exogenous Variables on Equilibrium Solutions

Corollary 1 indicates that the RS case is the best one for $n_0<n\le n_a$. Consequently, the analysis about the effects of exogenous variables on the equilibrium solutions mainly focuses on the RS case. The exogenous variables consist of the policy and market, as well as cost factors. Specifically, policy factors include the government subsidy and the emission reduction target (i.e., $s$ and $\lambda$). The market factor is the preference of consumers to the product quality (i.e., $\beta$). Cost factors are an index to weigh the manufacturer’s technology level and made up of the cost coefficients in terms of the quality improvement and the emission reduction investment (i.e., $m$ and $n$). And the cost coefficients will decrease gradually with the manufacturer’s technology maturation.

5.2.1. Analysis of the Policy Factor

 Corollary 2.

The results for the effects of exogenous variables ($s$, $\lambda$) on the emission reduction rate, product quality, and market demand (${\Delta }^{RS}$, $q^{RS}$,$D_n^{RS}$, $D_r^{RS}$) are as follows:

${\displaystyle \frac{\partial {\Delta }^{RS}}{\partial s}}>0,{\displaystyle \frac{\partial q^{RS}}{\partial s}}>0,{\displaystyle \frac{\partial D_n^{RS}}{\partial s}}>0,{\displaystyle \frac{\partial D_r^{RS}}{\partial s}}>0;{\displaystyle \frac{\partial {\Delta }^{RS}}{\partial \lambda }}<0,{\displaystyle \frac{\partial q^{RS}}{\partial \lambda }}<0,{\displaystyle \frac{\partial D_n^{RS}}{\partial \lambda }}<0,\mathrm{and}{\displaystyle \frac{\partial D_r^{RS}}{\partial \lambda }}<0.$ See Appendix D for proofs of Corollary 2.

From Corollary 2, the emission reduction rate (${\Delta }^{RS}$), product quality ($q^{RS}$), and market demand ($D_n^{RS}$ and $D_r^{RS}$) can be improved with the government subsidy increase. But, as the emission reduction target increases, ${\Delta }^{RS}$, $q^{RS}$, $D_n^{RS}$, and $D_r^{RS}$ will go down. It indicates that the manufacturer will increase its investment in emission reduction and product quality improvement when gaining more subsidies, which can improve ${\Delta }^{RS}$, $q^{RS}$, $D_n^{RS}$, and $D_r^{RS}$. However, facing a stricter emission reduction requirement, the manufacturer has to pay more for the emission credits. It makes the manufacturer cut down the investments in emission reduction and product quality improvement, decreasing ${\Delta }^{RS}$, $q^{RS}$, $D_n^{RS}$, and $D_r^{RS}$. It indicates that government subsidies are like “fuel”, which stimulates the manufacturer to invest in emission reduction technologies and quality improvements (such as CATL’s use of subsidies to tackle solid-state batteries). However, strict emission reduction targets are like “brakes”, as emission costs squeeze out R&D funds, leading to technological stagnation and market shrinkage.

 Corollary 3.

Table 6. Effects of $s$ and $\lambda$ on $w_n^{RS}$ and $p_n^{RS}$.

Price of NP	${\mathit{w}}_{\mathit{n}}^{\mathit{R}\mathit{S}}$	${\mathit{p}}_{\mathit{n}}^{\mathit{R}\mathit{S}}$	If $\mathit{m}$, $\mathit{n}$ Meet the Conditions of
Monotonicity on $s$	↑	↑	$m_0<m\le m_1$	$n_3<n_1\le n_0$	$n_3<n_1\le n_0<n$
	↓	↑	$m_1<m\le m_3$	$n_3\le n_0<n_1$	$n_3\le n_0<n\le n_1$
	↑	↑			$n_3\le n_0<n_1<n$
	↓	↓	$m>m_3$	$n_0<n_3<n_1$	$n_0<n\le n_3<n_1$
	↓	↑			$n_0<n_3<n\le n_1$
	↑	↑			$n_0<n_3<n_1<n$
Monotonicity on $\lambda$	↓	↓	$m_0<m\le m_1$	—
	↑	↓	$m_1<m\le m_3$	—
	↑	↑	$m>m_3$	—

Notes: “↑” means increase, and “↓” means decrease here and hereafter.

presents the results for the effects of exogenous variables ($s$ and $\lambda$) on the price of NP ($w_n^{RS}$ and $p_n^{RS}$). See Appendix E for proofs of Corollary 3.

From Corollary 3, the effects of the government subsidy and the emission reduction target on pricing decisions for NP are non-monotonic. Specifically, (1) the sale price of NP will rise with the government subsidy increase, when cost coefficients of the product quality improvement and emission reduction investment are low (i.e., $m_0<m\le m_1$ and $n_3<n_1\le n_0<n$) or are high (i.e., $m>m_3$ and $n_0<n_3<n_1<n$). But the reasons for the rise are varied. It can bring a relatively higher product quality improvement with the government subsidy increase for $m_0<m\le m_1$ and $n_3<n_1\le n_0<n$. At this time, the manufacturer can still slightly raise the price for NP. However, the product quality can just rise a little with the government subsidy increase for $m>m_3$ and $n_0<n_3<n_1<n$. And under high-cost pressure, the manufacturer has to raise the price for NP. (2) Setting a higher emission reduction target will decrease the price of NP for $m_0<m\le m_1$ but increase the price for $m>m_3$. Likewise, the decrease in the price occurs when a higher emission reduction target results in a relatively higher drop in the product quality, making the manufacturer set a lower price for NP. Price increases mainly reflect the high costs from low efficiency in quality improvement, indicating that quality and emission reduction investments strongly influence RSC pricing. Therefore, government policies should align with the capabilities of the manufacturer to prevent high-cost, inefficient manufacturers from falling into a cycle of “raising prices and losing market share, while lowering prices and losing money.”

 Corollary 4.

Table 7. Effects of $s$ and $\lambda$ on $w_r^{RS}$ and $p_r^{RS}$.

Price of RP	Monotonicity on$\mathit{s}$	If $\mathit{m}$, $\mathit{n}$ Meet the Conditions of
$w_r^{RS}$	↑	$m_0<m<m_a$	$n_2<n_0$	$n_2<n_0<n$
	↑	$m_a<m\le m_2$	$n_0\le n_2$	$n_0<n\le n_2$
	↓			$n_0\le n_2<n$
	↓	$m>m_2$	$n_2<n_0$	$n_2<n_0<n$
$p_r^{RS}$	↑	$m_0<m<m_b$	$n_4<n_0$	$n_4<n_0<n$
	↑	$m_b<m\le m_4$	$n_0\le n_4$	$n_0<n\le n_4$
	↓			$n_0\le n_4<n$
	↓	$m>m_4$	$n_4<n_0$	$n_4<n_0<n$
Price of RP	Monotonicity on$\lambda$	If $m$, $n$ meet the conditions of
$w_r^{RS}$	↓	$m_0<m\le m_2$	—
	↑	$m>m_2$	—
$p_r^{RS}$	↓	$m_0<m\le m_4$	—
	↑	$m>m_4$	—

presents the results for the effects of exogenous variables ($s$ and $\lambda$) on the price of $RP$ ($w_r^{RS}$ and $p_r^{RS}$). See Appendix F for proofs of Corollary 4.

Similar to Corollary 3, Corollary 4 shows that the effects of the government subsidy and the target for emission reduction on pricing decisions for RP are also non-monotonic. But, unlike Corollary 3, the sale price of RP will rise with the government subsidy increase, when cost coefficients of the product quality improvement and emission reduction investment are low (i.e., $m_0<m\le \min \{m_a,m_b\}$ and $\max \{n_2,n_4\}<n_0<n$); and the result is opposite for $m>\max \{m_2,m_4\}$ and $\max \{n_2,n_4\}<n_0<n$. It indicates that the product quality improvement is relatively high with the government subsidies increase for $m_0<m\le \min \{m_a,m_b\}$ and $\max \{n_2,n_4\}<n_0<n$. At this time, the manufacturer can still slightly rise the price for RP. However, with the government subsidy increase, it can bring a slight improvement in product quality and a direct cost reduction for RP for $m>\max \{m_2,m_4\}$ and $\max \{n_2,n_4\}<n_0<n$. Under low-cost pressure, the manufacturer can still set a lower price for RP. In addition, the results for the effect of the emission reduction target on the price of RP are consistent with those in Corollary 3 and are omitted here.

 Corollary 5.

The results for the effects of exogenous variables ($s$ and $\lambda$) on total carbon emissions ($E^S$ and $E^{RS}$) are as follows:

(1)

${\displaystyle \frac{\partial E^S}{\partial s}}>0$ and ${\displaystyle \frac{\partial E^S}{\partial \lambda }}<0$;

(2)

when $n_0<n\le n_a$, ${\displaystyle \frac{\partial E^{RS}}{\partial s}}<0$, ${\displaystyle \frac{\partial E^{RS}}{\partial \lambda }}>0$ and when $n>n_a$, ${\displaystyle \frac{\partial E^{RS}}{\partial s}}>0$,${\displaystyle \frac{\partial E^{RS}}{\partial \lambda }}<0$.

See Appendix G for proofs of Corollary 5.

Corollary 5 indicates that there exists a threshold to classify manufacturers based on their environmental character. We define the manufacturer without investing in emission reduction as the non-abating manufacturer (i.e., the manufacturer in the N and S cases) and regard the manufacturer with investing in emission reduction as the abating manufacturer (i.e., the manufacturer in the R and RS cases). Furthermore, the abating manufacturer can be defined as the low-efficiency abating manufacturer when the efficiency of the emission reduction is low (i.e., $n>n_a$) and as the high-efficiency abating manufacturer when the efficiency of the emission reduction is high (i.e., $n_0<n\le n_a$).

Facing the non-abating manufacturer, higher subsidies may increase emissions, while stricter reduction targets help curb emissions. It implies that the product quality and market demand will improve with the government subsidy increase, which brings more emissions. On the contrary, a stricter emission reduction target will shrink the product market, which is conducive to emission reduction. The management lesson is that, for the non-abating manufacturer, subsidies are fire that can ignite the market but may also burn the environment.

Facing the abating manufacturer, the efficiency of the emissions reduction has significant impacts on total carbon emissions. Specifically, when $n_0<n\le n_a$, higher government subsidies reduce total carbon emissions, but stricter emission reduction targets have the opposite effect. It means that an increase in government subsidies can improve both the emission reduction rate and market demand. And for the high-efficiency abating manufacturer, the emission reductions from the improved emission reduction rate outweigh emission increments from market expansion, lowering total emissions. However, for $n>n_a$, higher government subsidies bring more emissions, and stricter emission reduction targets reduce emissions. It reveals that, facing the low-efficiency abating manufacturer, the emission reduction advantage of emission reduction rate improvement no longer exists. The management implication is that, for the abating manufacturer, the critical value of the emission reduction efficiency threshold will determine the direction of the policy effect.

From the perspective of emission reductions, to decrease the output of high-emission products, the government will set a stricter emission reduction target and cut down the remanufacturing subsidy for the non-abating manufacturer. And it is worthwhile to note that the government needs to avoid the “crowding-out effect” produced by the government subsidy overlapping with the high efficiency of the emission reduction when facing the high-efficiency abating manufacturer. Therefore, for the high-efficiency abating manufacturer, to unleash their emission reduction advantage, the government should make full use of the market driving forces of the CAT regulation, reducing both the remanufacturing subsidy and the emission reduction target. Correspondingly, for the low-efficiency abating manufacturer, to spur them to improve the emission reduction efficiency, the government should make good uses of the macro-control means, i.e., improving both the remanufacturing subsidy and the emission reduction target.

The policymaker must be as precise as surgeons: “removing tumors” from the non-abating manufacturer, “transfusing blood and oxygen” to the low-efficiency abating manufacturer, and “cutting off the umbilical cord” for the high-efficiency abating manufacturer. Specifically, facing the non-abating manufacturer, the government should eliminate the high-emission capacities through setting rigorous policies, i.e., a lower remanufacturing subsidy and a stricter emission reduction target. Facing the abating manufacturer, the government should strengthen the market instrument of the CAT regulation and gradually reduce remanufacturing subsidies as the emission reduction technology matures.

5.2.2. Analysis of the Market Factor

 Corollary 6.

The results for the effects of the exogenous variable ($\beta$) on the emission reduction rate, product quality, and market demand ( ${\Delta }^{RS}$, $q^{RS}$, $D_n^{RS}$, and $D_r^{RS}$) are as follows:

${\displaystyle \frac{\partial {\Delta }^{RS}}{\partial \beta }}>0$, ${\displaystyle \frac{\partial q^{RS}}{\partial \beta }}>0$, ${\displaystyle \frac{\partial D_n^{RS}}{\partial \beta }}>0$, and${\displaystyle \frac{\partial D_r^{RS}}{\partial \beta }}>0$.

The proof processes are similar to Corollary 2 and will not be repeated here.

From Corollary 6, an increase in the consumer preference to the product quality will improve the emission reduction rate and the product quality and expand the product market. It implies that the manufacturers will increase their investment in product quality improvement when consumers have a higher preference to the product quality. As a result, the product quality will be enhanced, which attracts more consumers.

 Corollary 7.

Table 8. Effects of $\beta$ on $w_n^{RS}$, $p_n^{RS}$, $w_r^{RS}$, and $p_r^{RS}$.

Price of NP	${\mathit{w}}_{\mathit{n}}^{\mathit{R}\mathit{S}}$	${\mathit{p}}_{\mathit{n}}^{\mathit{R}\mathit{S}}$	If $\mathit{m}$, $\mathit{n}$ Meet the Conditions of
Monotonicity on $\beta$	↑	↑	$m_0<m\le m_1$	$n_{33}<n_{11}\le n_0$	$n_{33}<n_{11}\le n_0<n$
	↓	↑	$m_1<m\le m_3$	$n_{33}\le n_0<n_{11}$	$n_{33}\le n_0<n\le n_{11}$
	↑	↑			$n_{33}\le n_0<n_{11}<n$
	↓	↓	$m>m_3$	$n_0<n_{33}<n_{11}$	$n_0<n\le n_{33}<n_{11}$
	↓	↑			$n_0<n_{33}<n\le n_{11}$
	↑	↑			$n_0<n_{33}<n_{11}<n$
Price of RP	${\mathit{w}}_{\mathit{r}}^{\mathit{R}\mathit{S}}$	${\mathit{p}}_{\mathit{r}}^{\mathit{R}\mathit{S}}$	If $m$, $n$ meet the conditions of
Monotonicity on $\beta$	↑	↑	$m_0<m\le m_2$	$n_{44}<n_{22}\le n_0$	$n_{44}<n_{22}\le n_0<n$
	↓	↑	$m_2<m\le m_4$	$n_{44}\le n_0<n_{22}$	$n_{44}\le n_0<n\le n_{22}$
	↑	↑			$n_{44}\le n_0<n_{22}<n$
	↓	↓	$m>m_4$	$n_0<n_{44}<n_{22}$	$n_0<n\le n_{44}<n_{22}$
	↓	↑			$n_0<n_{44}<n\le n_{22}$
	↑	↑			$n_0<n_{44}<n_{22}<n$

Where $n_{11}=\frac{\alpha p_c^2(2e_n^2+e_r^2+l{e}_n{e}_r)}{8}$, $n_{22}=\frac{\alpha p_c^2(l{e}_n^2+2l{e}_r^2+e_n{e}_r)}{8l}$, $n_{33}=\frac{\alpha p_c^2(4e_n^2+3e_r^2+l{e}_n{e}_r)}{24}$, $n_{44}=\frac{\alpha p_c^2(3l{e}_n^2+4l{e}_r^2+e_n{e}_r)}{24l}$, and the parameters of $n_{11},n_{22},n_{33},n_{44}$.

presents the results for the effects of the exogenous variable ($\beta$) on the prices of NP and RP ($w_n^{RS}$, $p_n^{RS}$, $w_r^{RS}$, and $p_r^{RS}$). The proof processes are similar to Corollary 3 and 4 and will not be repeated here.

Similarly, from Corollary 7, there also exist different pricing strategies for NP for different cost coefficients of the product quality improvement and emission reduction investment. In detail, the price variation trend of NP brought by the change in consumers’ quality preference is consistent with the variation trend brought by the change in the government subsidy. It indicates that an increase in the preference of consumers to the product quality can bring a relatively high improvement in the product quality, when cost coefficients of the product quality improvement and emission reduction investment are low (i.e., $m_0<m\le \min \{m_1,m_3\}$ and $\max \{n_{11},n_{33}\}<n_0<n$). In other words, under low-cost pressure, the manufacturer can improve the product quality significantly and unleash the advantage of the high product quality. On the contrary, the manufacturer will face a higher production apportion cost for $m>\max \{m_1,m_3\}$ and $n_0<\max \{n_{11},n_{33}\}<n$. And under high-cost pressure, the manufacturer has to raise the price for NP.

As for RP, the impacts of the consumer preference to the product quality on pricing decisions for RP is consistent with that for NP. Thus, the results are not repeated. Besides, unlike the impacts of the government subsidy, an increase in the consumer preference do not alleviate cost pressures. Consequently, the manufacturer has no choice but to raise the price for RP for $m>\max \{m_2,m_4\}$ and $n_0<\max \{n_{22},n_{44}\}<n$.

 Corollary 8.

The results for the effects of the exogenous variable (β) on total carbon emissions (E^S, E^RS):

(1) $\frac{\partial E^S}{\partial \beta }>0$; (2) when $n_0<n\le n_a$, $\frac{\partial E^{RS}}{\partial \beta }<0$; and when $n>n_a$, $\frac{\partial E^{RS}}{\partial \beta }>0$.

The proof processes are similar to Corollary 5 and will not be repeated here.

Corollary 8 shows that manufacturers’ emission reduction investment decisions and efficiency critically affect total emissions. Specifically, for the non-abating manufacturer, stronger consumer preference to the product quality leads to more emissions by boosting product quality and demand. However, total carbon emissions are more related to the efficiency of the emission reduction for the abating manufacturer. In detail, a higher consumer preference to the product quality will help to cut down total carbon emissions for $n_0<n\le n_a$ but bring about more emissions for $n>n_a$ It shows that the emission reduction rate and market demand can be improved with the consumer preference to the product quality increase. And facing the high-efficiency abating manufacturer, the emission reductions brought by the emission reduction rate improvement are larger than the emission increments brought by the market expansion, which makes total emissions decrease. The management implication is that the consumer preference to the product quality is an invisible regulator for carbon emission reduction. The high-efficiency abating manufacturer should seize the opportunity to transform the consumer preference to the product quality into the emission reduction leverage.

5.2.3. Analysis of the Cost Factor

 Corollary 9.

The results for the effects of exogenous variables ($m$ and $n$) on the emission reduction rate, product quality, and market demand (${\Delta }^{RS}$, $q^{RS}$, $D_n^{RS}$, and $D_r^{RS}$):

${\displaystyle \frac{\partial {\Delta }^{RS}}{\partial m}}<0$, ${\displaystyle \frac{\partial q^{RS}}{\partial m}}<0$, ${\displaystyle \frac{\partial D_n^{RS}}{\partial m}}<0$, ${\displaystyle \frac{\partial D_r^{RS}}{\partial m}}<0$; ${\displaystyle \frac{\partial {\Delta }^{RS}}{\partial n}}<0$, ${\displaystyle \frac{\partial q^{RS}}{\partial n}}<0$, ${\displaystyle \frac{\partial D_n^{RS}}{\partial n}}<0$, and ${\displaystyle \frac{\partial D_r^{RS}}{\partial n}}<0$.

The proof processes are similar to Corollary 2 and will not be repeated here.

From Corollary 9, the carbon reduction rate, product quality, and market demand can be improved with the efficiency of the product quality improvement and emission reduction increase. That is because advanced technology in the product quality improvement and emission reduction will reduce the apportionment costs. It indicates that the high-efficiency abating manufacturer achieves a higher product quality and emission reduction rate with the same investment, attracting more consumers.

 Corollary 10.

Table 9. Effects of $m$ and $n$ on $w_n^{RS}$, $p_n^{RS}$, $w_r^{RS}$ and $p_r^{RS}$.

Price of NP	${\mathit{w}}_{\mathit{n}}^{\mathit{R}\mathit{S}}$	${\mathit{p}}_{\mathit{n}}^{\mathit{R}\mathit{S}}$	If $\mathit{m}$, $\mathit{n}$ Meet the Conditions of
Monotonicity on $m$	↓	↓	$m_0<m\le m_1$	$n_{33}<n_{11}\le n_0$	$n_{33}<n_{11}\le n_0<n$
	↑	↓	$m_1<m\le m_3$	$n_{33}\le n_0<n_{11}$	$n_{33}\le n_0<n\le n_{11}$
	↓	↓			$n_{33}\le n_0<n_{11}<n$
	↑	↑	$m>m_3$	$n_0<n_{33}<n_{11}$	$n_0<n\le n_{33}<n_{11}$
	↑	↓			$n_0<n_{33}<n\le n_{11}$
	↓	↓			$n_0<n_{33}<n_{11}<n$
Monotonicity on $n$	↓	↓	$m_0<m\le m_1$	—
	↑	↓	$m_1<m\le m_3$	—
	↑	↑	$m>m_3$	—
Price of RP	${\mathit{w}}_{\mathit{r}}^{\mathit{R}\mathit{S}}$	${\mathit{p}}_{\mathit{r}}^{\mathit{R}\mathit{S}}$	If $m$, $n$ meet the conditions of
Monotonicity on $m$	↓	↓	$m_0<m\le m_2$	$n_{44}<n_{22}\le n_0$	$n_{44}<n_{22}\le n_0<n$
	↑	↓	$m_2<m\le m_4$	$n_{44}\le n_0<n_{22}$	$n_{44}\le n_0<n\le n_{22}$
	↑	↓			$n_{44}\le n_0<n_{22}<n$
	↑	↑	$m>m_4$	$n_0<n_{44}<n_{22}$	$n_0<n\le n_{44}<n_{22}$
	↑	↓			$n_0<n_{44}<n\le n_{22}$
	↓	↓			$n_0<n_{44}<n_{22}<n$
Monotonicity on $n$	↓	↓	$m_0<m\le m_2$	—
	↑	↓	$m_2<m\le m_4$	—
	↑	↑	$m>m_4$	—

presents the results for the effects of exogenous variables ($m$, $n$) on the price of NP and RP ($w_n^{RS}$, $p_n^{RS}$, $w_r^{RS}$, and $p_r^{RS}$). The proof processes are similar to Corollary 3 and 4 and will not be repeated here.

Corollaries 3, 7, and 10 show that higher quality improvement costs drive NP pricing in the opposite direction of stronger consumer product quality preferences, while higher emission reduction costs affect NP pricing similarly to stricter targets. It demonstrates that the price decisions for NP are shaped by the consumer preference to the product quality and the cost coefficient of the product quality improvement. Nevertheless, the emission reduction target and cost coefficient of emission reduction mainly influence the production costs directly, which further affects the price decisions for NP.

As for RP, the pricing trend for RP brought by the changes of the cost coefficient of the product quality improvement and emission reduction is consistent with NP. These details are not repeated.

 Corollary 11.

The results for the effects of exogenous variables (m and E^s and E^RS) are as follows:

 (1)

$\frac{\partial E^S}{\partial m}<0$, $\frac{\partial E^S}{\partial n}=0$

 (2)

when $n_0<n\le n_a$, $\frac{\partial E^{RS}}{\partial m}>0$; when $n>n_a$, $\frac{\partial E^{RS}}{\partial m}<0$; and when $Q_n-\alpha [c_n+(\lambda +1)e_n{p}_c]>0$ and $Q_r-\alpha [c_r+c_u+(\lambda +1)e_r{p}_c]>0$, $\frac{\partial E^{RS}}{\partial n}>0$.

The proof processes are similar to Corollary 5 and will not be repeated here.

Likewise, from Corollary 11, total carbon emissions are influenced by the technology level of the product quality improvement and emission reduction significantly. Specifically, facing the non-abating manufacturer, raising the efficiency of the product quality improvement will expand the product market ( $\frac{\partial D_n^N}{\partial m}<0$ and $\frac{\partial D_r^N}{\partial m}<0$) while not changing the unit carbon emission level of the product, which brings more emissions. However, for the abating manufacturer, the impacts of the technology level on total carbon emissions are different. In detail, the rise of the efficiency in the product quality improvement will reduce emissions for the high-efficiency abating manufacturer (i.e., $n_0<n\le n_a$). It implies that the rise of the efficiency in the product quality improvement can improve the product quality, save investment costs, and expand the market demand. And the saving costs can be utilized to invest in emission reduction, which can raise the emission reduction rate. In addition, for the high-efficiency abating manufacturer, emission reductions from higher abatement rates outweigh emission increments from market expansions, lowering total emissions. And the result is opposite for the low-efficiency abating manufacturer (i.e., $n>n_a$). However, under a certain condition, the improvement of the efficiency in the emission reduction will always be conducive to emission reduction. It indicates that the improvement of the emission reduction efficiency can improve the emission reduction rate directly, making the emission reductions brought by the abatement rate improvement exceed emission increments brought by the market expansion.

The key implication is that product quality improvement and emission reduction investment have a double helix effect. Product quality improvement is the wings of the market, and emission reduction investment is the anchor of environmental protection. The manufacturer must remember that a true, sustainable, competitive advantage is born when the dividends of the product quality improvement are converted into emission reduction investment. Therefore, the survival rule for the non-abating manufacturer is to build emission reduction dams before improving product quality. The way out for the low-efficiency abating manufacturer is to carefully improve product quality before emission reduction efficiency reaches a critical point. The golden opportunity for the high-efficiency abating manufacturer is that the dividends from product quality improvement are the best fuel for emission reduction investment.

6. Numerical Results

To validate the applicability of the models and further discuss the effects of the policy and market, as well as cost factors, on the total emissions and profits of the RSC, a numerical example is given. According to the survey, the parameters are arranged as follows:

(1)

The production costs for the NP and RP are set to $c_n=5$ and $c_r=1.5$. Taking the BESTUNE NAT as the example, the initial capacity of the battery is about 53 kWh (https://benteng.faw.cn/. (accessed on 10 April 2021)). And according to a report, issued by the IEA, in 2022, the average battery price stood at about 150 $/kWh (https://www.iea.org/reports/global-ev-outlook-2023/trends-in-batteries. (accessed in 30 April 2023)) Calculating the average exchange rate, $1\$=6.7366 \mathrm{CNY}$, we can obtain $c_n=53\times 150\times 6.7366\approx 50,000 \mathrm{CNY}$ (https://www.exchangerates.org.uk/USD-CNY-spot-exchange-rates-history-2022.html. (accessed in 31 December 2022)). To facilitate the presentation of the results without affecting the conclusions, it is set to $c_n=5$. In addition, considering that the RP can save up to 70% of materials compared to NP, here $c_r=1.5$ is set.

(2)

The recycling cost for per used product is set to $c_u=1$. Considering that the battery energy density of the BESTUNE NAT is 160 Wh/kg (https://equalocean.com/news/2022011816945. (accessed on 18 January 2022)), it can be obtained that the battery weight is 0.33 t. Moreover, according to the survey, the recycle cost of used batteries is about 30,000 CNY/t, and then we can obtain $c_u=0.33\times 30,000\approx 10,000 \mathrm{CNY}$, which is set to $c_u=1$.

(3)

The emissions for the NP and RP are set to $e_n=5$ and $e_r=1$. Data from the Transport & Environment show that the carbon emission is about 0.1t/kWh (https://www.transportenvironment.org/about-us/annual-reports. (accessed in 31 December 2023)). Thus, it can be obtained that the battery carbon emission of the BESTUNE NAT is 5t. In addition, considering that the RP can reduce carbon emission by 80%, $e_n=5$ and $e_r=1$ are set.

(4)

The carbon trading price is set to $p_c=0.07$. Date shows that the carbon trading price in European in 2023 is 70~100€/t (https://www.statista.com/statistics/1322214/carbon-prices-european-union-emission-trading-scheme/. (accessed on 31 December 2023)). Calculating the average exchange rate, $1€=7.6538 \mathrm{CNY}$ (https://www.exchange-rates.org/zh/exchange-rate-history/eur-cny-2023. (accessed on 31 December 2023)), we can obtain the carbon trading price, which is 535~765 CNY/t. And $p_c=0.07$ is set.

(5)

In addition, to ensure that assignments for parameters can satisfy the conditions of $m>m_0$, $n>n_0$, $Q_n-\alpha (c_n+\lambda e_n{p}_c)>0$, and $Q_r-\alpha (c_r+c_u+\lambda e_r{p}_c)>0$, referring to Yuan et al. [70], $Q_n=10$, $Q_r=2.5$, $\alpha =1$, $\beta =0.8$, $l=0.8$, $s=0.2$, $\lambda =0.2$, $m=0.5$, and $n=0.5$ are set.

6.1. Optimal Value of Equilibrium Solutions in Four Cases

Substituting the above parameters into equilibrium solutions, we can obtain the total emissions and profits in

Table 10. The total emissions and profits in four cases.

Variables	N Case	S Case	R Case	RS Case
$E$ (if $n=0.5<n_a$)	7.706	7.867	3.516	3.495
$E$ (if $n=1>n_a$)	7.706	7.857	5.701	5.769
${\pi }_M$	3.694	3.770	3.846	3.928
${\pi }_R$	2.292	2.374	2.489	2.580
${\pi }_T$	5.986	6.144	6.335	6.508

. And under this numerical example, we can easily obtain $n=0.5<n_a\approx 0.57$. In addition, we added a value for $n=1$ when comparing the total carbon emission of the four cases.

From Table 10, we can notice that as follows: (1) Profits of the RSC members and system are the smallest in the N case, in the middle in the S and R cases, and the largest in the RS case. It shows that the emission reduction investment and the remanufacturing subsidy can promote the development of the RSC system. (2) The total carbon emissions are the highest in the S case. And the total carbon emissions in the R and RS cases are lower than those in the N and S cases. Additionally, the smallest total carbon emissions can be obtained in the RS case for $n<n_a$. This indicates that the emission reduction investment is beneficial to reducing total carbon emissions, but the remanufacturing subsidy is uncertain. And only when the manufacturer invests in emission reduction and the emission reduction efficiency reaches a certain threshold can the remanufacturing subsidy help reduce emissions.

According to Corollary 1, next, we only examine the effects of exogenous variables in the RS case, since the RS case can gain the highest profits and the lowest emissions.

6.2. Effects of the Policy Factor

To discuss the effects of the government subsidy ($s$) and the emission reduction target ($\lambda$) on the total emissions and profits of the RS case, we assumed $s\in [0,1)$ and $\lambda \in [0,1]$. Substituting the above parameters into equilibrium solutions of the RS case, we can gain $n=0.5<n_a\in [0.56,0.61)$ when $s\in [0,1)$ and $n=0.5<n_a\in [0.54,0.58]$ when $\lambda \in [0,1]$. Besides, we added a value for $n=1>n_a$ when analyzing the effects of $s$ and $\lambda$ on total carbon emissions. Figure 3 presents the results.

From Figure 3a, as $s$ increases, total carbon emissions gradually increase in the S case. However, in the RS case, an increase in $s$ will be beneficial to emission reduction for $n<n_a$ but lead to more emissions for $n>n_a$. And from Figure 3b, with an $s$ increase, profits of the RSC members and system gradually increase. It implies that the government subsidy will help to achieve the win-win of profit growth and emission reduction for $n<n_a$.

From Figure 3c, as $\lambda$ increases, total carbon emissions gradually decrease in the S case. However, in the RS case, an increase in $\lambda$ will lead to more emissions instead for $n<n_a$ but help reduce emissions for $n>n_a$. And from Figure 3d, as $\lambda$ increases, profits of the RSC members and system gradually decrease. It means that setting a stricter emission reduction target will cause a negative impact on the development and emission reduction for the RSC system for $n<n_a$.

6.3. Effects of the Market Factor

To discuss the effects of the preference of consumers to the product quality ($\beta$) on the total emissions and profits of the RS case, we assume $\beta \in [0.6,1]$. Substituting the above parameters into equilibrium solutions of the RS case, we can gain $n=0.5<n_a\in [0.51,0.68]$ when $\beta \in [0.6,1]$. In addition, we added a value for $n=1>n_a$ when analyzing the effect of $\beta$ on total carbon emissions. Figure 4 presents the results.

From Figure 4a, total carbon emissions gradually increase in the S case with the $\beta$ increase. However, in the RS case, an increase in $\beta$ will be beneficial to emission reduction for $n<n_a$ but bring about more emissions for $n>n_a$. And Figure 4b illustrates that, as $\beta$ increase, profits of the RSC members and system gradually increase. Thus, the preference of consumers to the product quality will help to improve profits of the RSC members and system and reduce total carbon emissions for $n<n_a$.

6.4. Effects of the Cost Factor

To discuss the effects of the cost factor, i.e., the cost coefficient of the product quality improvement ($m$) and the emission reduction investment ($n$), on total emissions and profits of the RS case, we assumed $m\in [0.5,1]$ and $n\in [0.5,1]$. Substituting the above parameters into equilibrium solutions of the RS case, we can gain $n=0.5<n_a\in [0.502,0.570]$ when $m\in [0.5,1]$. Besides that, we added a value for $n=1>n_a$ to analyze the effects of $m$ on total carbon emission. Figure 5 presents the results.

From Figure 5a, as $m$ increases, total carbon emissions gradually decrease in the S case. However, in the RS case, an increase in $m$ will cause more emissions for $n<n_a$ but help reduce emissions for $n>n_a$. And Figure 5b shows that profits of the RSC members and system gradually decrease as $m$ increases. This illustrates that raising the efficiency of the product quality improvement is good to grow profit and reduce emissions for the RSC system in the case of $n<n_a$.

From Figure 5c, in the S case, total carbon emissions do not change with an $n$ increase. However, in the RS case, increasing $n$ will lead to more emissions directly. That is because the manufacturer will directly cut down the emission reduction investment when the efficiency of the emission reduction decreases, which brings about a significant reduction in emission reduction rate. And a significant drop in the emission reduction rate will bring more emissions. And from Figure 5d, profits of the RSC members and system gradually decrease as $n$ increases. Therefore, to gain more profits and reduce the total emissions, the manufacturer should improve the efficiency of the emission reduction.

7. Discussion and Management Insights

This work on the impacts of remanufacturing subsidies and emission reduction investments on the pricing and quality decisions in the RSC under CAT regulation obtains some valuable insight, which makes contributions to the existing theoretical research and provides new policy enlightenments for practical operation.

Compared with the existing literatures, this work integrates core factors such as CAT regulation, government subsidies, emission reduction investment, and quality improvement. It breaks through the limitations of the existing literatures (such as Wang et al. [27], Mao et al. [28], Taleizadeh et al. [51], Taleizadeh et al. [52], Zhang and Zhang [58], Tsao and Ai [59], and Qiao et al. [60]) that analyze single or partial factors and establishes a theoretical framework for multi-factor interaction for remanufacturing supply chain system modeling. Correspondingly, this work obtains some new findings. For example, under certain conditions, a win-win situation of profit growth and emission reduction can be achieved by considering emission reduction investment and remanufacturing subsidy simultaneously, which breaks through the limitations of existing research that explains government subsidies improve profits but harm the environment [12,55,56,57]. It reveals that a positive feedback loop of “cost savings-quality improvement” can be triggered when subsidies match the emission reduction investment efficiency. This mechanism explains why subsidies in high-quality remanufacturing sectors (such as CATL’s battery remanufacturing) can simultaneously achieve profit growth and carbon emission reduction. Furthermore, this work finds some unexpected conclusions that increasing government subsidies is detrimental to profit growth and emission reduction. It indicates that the government subsidy has an exit mechanism under certain conditions, which provides a quantitative basis for dynamic policy adjustments. In addition, this work adopts the historical emission intensity method to set the emission credits, in which the free emission credits are determined by the emission reduction target, the actual output, and the historical emission intensity of NP and RP, and finds that increasing the emission reduction targets will lead to lower profits of the RSC, which resonates with the existing literatures [30,38,40]. However, the further analysis shows that a stricter emission reduction target is not necessary to reduce emissions, which challenges common sense in environmental policy design. It indicates that the emission reduction target has a double-edged sword effect. Based on the key findings, this work can provide new insights for the government to enrich its multi-level collaborative policy toolbox and offer management insights for enterprise practices:

(1)

Formulating differentiated emission reduction targets and subsidy policies for different types of manufacturers is necessary to realize the win-win of profit growth and emission reduction. Specifically, for the non-abating manufacturer, the government should cut down the subsidy and set a stricter emission reduction target to decrease the inefficient capacity, pushing them to transform towards the direction of low carbon. For example, the government can design a tiered emission reduction target and subsidy reduction mechanism, provide financial support for their transformation, and establish low-carbon, production capacity constraint targets. For the low-efficiency abating manufacturer whose technology level of emission reduction is low, the government should make full use of the macro-control means, i.e., improving both the subsidy and the emission reduction target, to spur them to increase investments in emission reduction. For example, the government can set subsidy thresholds linked to emission reduction efficiency, formulate multi-stage progressive emission reduction targets, and establish a regional technology sharing platform. Furtherly, as the manufacturer grows into the high-efficiency abating manufacturer whose technology level of emission reduction is high, the government needs to avoid the “crowding-out effect” produced by the government subsidy overlapping with the high emission reduction efficiency and should make full use of the market driving forces of the CAT regulation, i.e., lowering both the subsidy and the emission reduction target, to unleash their high emission reduction efficiency. For example, the government can implement subsidy exit plans, provide low-carbon incentives linked to emission reduction efficiency, and provide priority development rights for carbon sequestration projects.

(2)

An increase in the consumer preference to the product quality and the product quality improvement efficiency will enhance the profits of the RSC [15]. It demonstrates that, within the RSC, quality improvement efficiency is a profit amplifier, while quality perception and trust are a demand converter. The manufacturers need to transform quality improvement efficiency into a competitive advantage through technological upgrades, while the retailer must address the “quality trust deficit” through experiential and data-driven approaches. Therefore, the manufacturer can achieve collaborative quality innovation with the retailer by designing quality–profit transmission contracts and establishing supply chain quality data platforms. The retailer should strengthen the product quality publicity, by affixing high-quality certification marks, providing experience guarantees, and displaying comparative test reports, and adopt customer segmentation strategies to accurately reach high-value customers.

(3)

Investing in emission reduction and improving the emission reduction efficiency will improve the profits of the RSC and cut down carbon emissions [51,52]. In addition, the increase in the consumer preference to the product quality and the product quality improvement efficiency can also help reduce total emissions when the emission reduction efficiency is relatively high. It means that the manufacturer will enter a golden cycle of “emission reduction drives quality premium, and quality feeds back emission reduction investment” when the emission reduction efficiency exceeds the critical value. On the one hand, the manufacturers can improve their investment efficiency of emission reduction technology by deploying AI-driven decision support systems, implementing modular and hierarchical technology improvement strategies, and building collaborative innovation platforms. On the other hand, the supply chain system can amplify the synergistic effects of the emission reduction investment and quality improvement by building a data-driven, green quality collaboration platform, promoting a full-chain carbon-quality transparency project, and designing a dynamic response mechanism based on consumer classification.

In summary, this study can provide the policymaker with a theoretical basis for classified and precise policy implementation, offer the manufacturer a practical path to cross the emission reduction tipping point through technological investments, offer the retailer an effective idea for transforming quality attributes into market trust, and provide a mechanism design direction for the entire supply chain system to achieve win-win economic and environmental benefits through collaboration. Specifically, the policymaker can implement differentiated policies based on the emission reduction efficiency of the manufacturer—promoting transformation by increasing subsidies and bundling them with higher emission reduction targets for the inefficient manufacturer, while gradually withdrawing subsidies and relying on carbon market incentive mechanisms for the efficient manufacturer—to achieve precise governance and avoid resource mismatch. The manufacturer can cross the efficiency critical point by investing in emission reduction technologies, entering a virtuous cycle of “emission reduction reducing cost and quality premium” and simultaneously improving profits and environmental performance. The retailer can use quality certification labels to enhance consumer trust, match the needs of different customer groups through tiered pricing and precision marketing, and convert emission reduction investments on the manufacturing side into market premiums and repurchase rates. The supply chain system can use data sharing platforms and revenue collaboration contracts to amplify the chain effect of emission reduction investments and quality improvements, achieving a win-win situation of overall carbon emission reduction and profit growth in the system.

8. Conclusions

An RSC comprising the government, a manufacturer, a retailer, and consumers is analyzed. The government sets the emission reduction target and remanufacturing subsidy, after which the manufacturer invests in product quality and emission reduction and wholesales NP and RP to the retailer, who then sells them in separate markets where consumers choose based on price and quality. Four profit-maximization models—N, S, R, and RS cases—are constructed to derive equilibrium solutions. The equilibrium solutions among cases are compared, and the effects of policy, market, and cost factors on the equilibrium solutions are analyzed, obtaining the following conclusions:

(1)

The RS case becomes the optimal case, delivering higher emission reduction, improved quality, more demand, greater profits for RSC members, and lower carbon emissions, when emission reduction investment efficiency exceeds a threshold.

(2)

A remanufacturing subsidy is not essential for achieving both profit growth and emission reduction. It achieves a win-win outcome only when emission reduction investment efficiency exceeds a threshold. However, emission reduction investments increase the RSC profits while lowering carbon emissions.

(3)

Economically, higher subsidies and stronger consumer preferences to the product quality increase the emission reduction rate, product quality, demand, and the RSC profits, whereas stricter emission targets and higher cost coefficients for product quality improvement and emission reduction investment have negative effects. Environmentally, the impacts of subsidies, emission targets, product quality improvement costs, and consumer preferences depend on emission reduction efficiency, with a discernible efficiency threshold. However, higher emission reduction costs consistently worsen outcomes.

(4)

Pricing strategies for NP and RP vary across cases, with the efficiencies of both product quality and emission reduction investment playing a significant role.

Of course, there are some limitations in our work. For example, this work assumes deterministic demand, which may underestimate the risks brought about by market fluctuations and lead to certain deviations in the assessment of policy effects. Therefore, the future research could consider the impact of stochastic demand. In addition, the model assumes that the RSC consists of only one manufacturer and one retailer and does not consider competition between supply chains. Therefore, incorporating multiple manufacturers or competing supply chains can be a focus in the future. Furthermore, this work focuses exclusively on the CAT regulation, and other environmental policies, such as carbon taxes or green certification incentives, could serve as promising directions for future research. Moreover, the results may have certain deviations in their response to the real world as this work uses a mathematical model based on model assumptions. Therefore, empirical analysis methods can be used to further verify the model results.