Allocation of the Carbon Emission Abatement Target in Low Carbon Supply Chain Considering Power Structure

Abstract

The proposal of China’s dual carbon strategy is not only a kind of pressure but also an opportunity for enterprises. Both upstream and downstream enterprises in the supply chain pay more attention to carbon emission reduction, and consumers are gradually turning to a low-carbon preference. How carbon reduction targets are allocated among supply chain members with different technical efficiency and market opportunities will directly affect supply chain performance and social welfare. Power structure is an important factor that dominates the decision-making of the supply chain, so we establish the low-carbon supply chain model under three different power structures: manufacturer-led, retailer-led, and power pairs between two parties. We study the government distribution decisions of carbon emissions reduction targets under different supply chain power structures and discuss the influence of supply chain power structures on carbon emissions reduction distribution decisions and social welfare. The study found that if the carbon emissions reduction target increases, the government will adjust the allocation strategy to increase the proportion of enterprises whose emissions cuts have less impact on market demand. The study also found that the government will allocate more emissions reduction to enterprises with higher emissions reduction efficiency, and enterprises whose emissions reductions have a greater impact on market demand. When supply chain enterprises have equal power, the supply chain will have greater social welfare and market demand, but not necessarily greater supply chain profits.

1. Introduction

With the increasingly serious global warming problem, more and more countries are paying attention to environmental problems [1,2,3]. Countries have responded to the UN’s call to reduce emissions, no longer pursuing rapid economic development with excessive resource consumption and carbon emissions. At the United Nations General Assembly in 2020, China proposed the dual carbon target. The aim is for carbon dioxide emissions to peak in 2030 and to achieve carbon neutrality by 2060. The next five years are a key period for China to achieve the dual carbon target [4,5]. As the main source of carbon dioxide emissions, enterprises must achieve energy conservation and emission reduction [6,7]. At the same time, consumers’ environmental awareness and low-carbon preferences have also been further enhanced, expressing their willingness to pay higher prices for lower carbon and environmentally friendly products [7,8,9,10]. This opens up a whole new market opportunity for companies that reduce emissions.

With the deepening of academic research on carbon emission reduction at home and abroad, promoting supply chain collaborative emissions reduction has become the consensus [11,12] in the process of implementing the low-carbon development concept. In the cooperation between supply chain upstream and downstream enterprises in reducing carbon emissions, the allocation of carbon emissions reduction targets among supply chain enterprises is crucial decision-making, not only directly dividing the supply chain of responsibility, but also affecting emissions reduction costs and market benefits [13,14,15], especially when the efficiency of emissions reduction of upstream and downstream enterprises in the supply chain is different, and the pulling effect of carbon emissions reduction of upstream and downstream enterprises on the demand of consumers with low-carbon preference is also different.

Enterprises that pursue profit maximization all hope to obtain the carbon reduction ratio which makes them the most profitable in cooperative emission. Conflicts in carbon cooperation can easily arise from this. When the allocation of the carbon emissions reduction target in the supply chain is completed by the enterprises within the supply chain, different enterprises, as the decision-making body, will make different decisions, and the contradiction between upstream and downstream enterprises is further intensified [16]. When the distribution of the carbon emissions reduction target is completed by the subject outside the supply chain, especially the government, the decision will be based on social welfare rather than the interests of the enterprise itself. The conflict may be alleviated. Therefore, in the coordination of supply chain carbon reduction, it is necessary to explore the distribution decision of carbon emission reduction target made by subjects outside the supply chain from the perspective of social welfare. Upstream and downstream enterprises of the supply chain are also competing with each other while cooperating to reduce emissions. The power structure is an important factor that dominates the competition between upstream and downstream enterprises in the supply chain. The three channel power structures of the supply chain are proposed by Chan [17]. From the current situation, there are supply chains led by manufacturers, such as Gree, Huawei, Galanz, and so on. There are also supply chains led by retailers, such as Wal-Mart, Carrefour, Metro, etc. Furthermore, there are supply chains where manufacturers and retailers have equal power, in which neither manufacturers nor retailers can dominate the supply chain. Therefore, the market may present at least three channel power structures: manufacturer-dominated, retailer-dominated, and equal power between manufacturers and retailers [18,19].

Based on the above analysis, it is of great significance to study the distribution of supply chain emissions reduction target among supply chain upstream and downstream enterprises in different power structures. Therefore, we ask the following questions: (1) Under different power structures, how will the government, as the main body outside the supply chain, allocate the emissions reduction target to the upstream and downstream enterprises in the supply chain? (2) What factors influence the government’s decision to allocate the emissions reduction target? (3) Under the different power structures, what are the differences in the government’s distribution decisions and social welfare?

To answer the above questions, we explore a three-tier low-carbon supply chain composed of governments, manufacturers, and retailers. We assume that the supply chain has a total reduction target, and the government will give companies certain subsidies to reduce emissions per unit. The government has absolute priority by first allocating total supply chain emission reduction target to manufacturers and retailers based on maximizing social welfare. Then, manufacturers and retailers set wholesale and retail prices in different decision orders, based on different power structures (manufacturer-led, retailer-led, both with equal powers). Under these three power structures, we use the game-theory approach to obtain the equilibrium solutions of the emission reduction target ratio of manufacturers and retailers, pricing, market demand, profits, and social welfare. In addition, by comparing the equilibrium solutions under different power structures, the influence of the power structure on the low-carbon supply chain is obtained.

The remainder of the paper is organized as follows. In Section 2, the related literature is reviewed. Section 3 describes the problem and model. Three supply chain models and corresponding equilibrium solutions are given in Section 4. Section 5 presents the model comparison and analysis. Section 6 gives a numerical analysis and discussion is provided in Section 7. Concluding remarks and some directions for future research are provided in Section 8.

2. Literature Review

This study is closely related to two streams of literature: power structures of the supply chain and the allocation of the supply chain emissions reduction target. In this section, we review each stream of literature and highlight the differences between the existing research and our paper.

2.1. Low Carbon Supply Chain

As the problem of greenhouse gas emissions becomes more and more serious, many scholars have conducted studies on the low-carbon supply chain.

With the introduction and implementation of a series of carbon policies in various countries, scholars considered carbon policies in low-carbon supply chains, such as low-carbon subsidies, carbon taxes, carbon cap, and trade. Ma et al. [20] indicated that government subsidies might not increase the emissions reduction and benefits. He et al. [21] found that the government can encourage the manufacturer to adopt desired channel structures by setting appropriate subsidy levels. Zhang et al. [22] found that effective carbon tax regulations are a prerequisite for improving corporate proactive emission reductions. Other scholars enriched the research on the low-carbon supply chain at the level of influencing factors of the low-carbon supply chain, such as low-carbon preferences, fairness preferences, and risk aversion. Arda [23] and Bai et al. [24] found that consumer’s preference motivates companies adopting low carbon technologies to curb the carbon emissions. Wu et al. [25] found a positive correlation between the profits of each member of the low-carbon supply chain and the equity concerns of the manufacturers. Yuan et al. [26] studied the impact of retailers’ risk aversion on the low-carbon supply chain.

Scholars extended the traditional second-level low carbon supply chain [27,28] into the third-level low carbon supply chain. Liu et al. [29] explored the issue of cooperative emissions reduction and sales effort strategies in a three-level supply chain. Xing et al. [30] explored the problem of low carbon supply chain innovation effort decision strategy. Liu et al. [31] studied the investment strategy and coordination problem of the three-level low-carbon supply chain. The above theses discussed the issues related to the three-level low-carbon supply chain consisting of suppliers, manufacturers, and retailers. Further, some theses discussed a three-level low-carbon supply chain consisting of government, manufacturer, and retailer. Jiang et al. [32] studied the influence of government subsidy policy on manufacturers’ low carbon behavior. Liang et al. [33] explored the impact of government subsidies and risk aversion on supply chain members. In recent years, some scholars studied the dual-channel low-carbon supply chain. Li et al. [34] compared the differences in decision outcomes between single-channel and dual-channel low-carbon supply chains. Chen et al. [35] investigated government subsidies and the level of products’ greenness under different sales channel structures. Li et al. [36] studied the pricing of low carbon and common products under a dual-channel supply chain. There are relatively few studies on the influence of power structure on the low-carbon supply chain in the three-level supply chain, especially few with government composition.

2.2. Power Structures of the Supply Chain

Many scholars have done in-depth research on the supply chain power structure. Some scholars studied the power structure of traditional supply chains that do not consider low carbon emissions [37,38,39,40,41]. Li et al. [42] explored the influence of power structures on the pricing and production decisions in a supply chain consisting of two suppliers and one manufacturer. Matsui [43] considered a typical three-echelon supply chain and studied the impact of power structure on the profitability in the supply chain facing stochastic demand. Some scholars focused on closed-loop supply chains. Mondal and Giri [44] explored the optimal decision-making problem of the closed-loop supply chain under four different channel power structures. Zhang et al. [45] studied the influence of the channel power structure on the closed-loop supply chain under different recycling methods. In recent years, the low-carbon supply chain has become a research hotspot. Xia et al. [46] explored the impact of different power structures on the optimal decision of the supply chain for low-carbon supply chain members. Tang et al. [47] studied the low-carbon supply chain composed of limited-funded manufacturers and well-funded retailers, and explored the optimal pricing and emission reduction strategies under different power structures. Both of the above documents studied a two-stage supply chain composed of manufacturers and retailers, wherein the manufacturer decided the level of corporate emissions reduction and did not involve the allocation of the supply chain emissions reduction target.

2.3. The Allocation of the Supply Chain Emissions Reduction Target

As global carbon reduction accelerates, countries are developing carbon reduction plans. Many scholars have studied the allocation of the emissions reduction target. Some scholars focused on the macro field, Xiao et al. [48] studied the allocation of carbon reduction targets among 83 countries signing the Kyoto Protocol; Juan et al. [49] studied the allocation of carbon reduction target among 30 administrative regions in China. Some scholars have studied the allocation of the carbon emissions reduction target between upstream and downstream enterprises in the supply chain. Jie et al. [16] found that, if the supply chain leader allocates the emissions reduction target, the allocation proportion will depend on the marginal emission reduction cost, and the follower allocates all the emissions reduction to the leader. Zhang et al. [45] found that if enterprises whose emissions reductions have a greater impact on demand allocate the emissions reduction target, manufacturers and retailers will share the cuts; if enterprises whose emissions reductions have a lesser impact on demand allocate emission reduction target, the emissions reduction target is all allocated to the other company. The above two articles studied the related issues of the allocation of the carbon emissions reduction target of the supply chain by enterprises within the supply chain. It was found that when the enterprises within the supply chain allocated the carbon emissions reduction target, the allocation strategies are very different and it is difficult to form a consensus.

Most of the studies on the power structure of the supply chain focus on its impact on pricing and emissions reduction level decisions, and few articles consider its impact on the allocation of emissions reduction targets. For articles studying the distribution of the supply chain emissions reduction target, most articles consider giving allocation rights to supply chain companies, but less research considers giving allocation power to the government. When the distribution power of the emissions reduction target belongs to different enterprises within the supply chain, the distribution results are very different, and cooperation cannot be achieved. Therefore, it is necessary to consider the allocation of emission reduction target by subjects outside the supply chain. Therefore, we consider the government allocating the supply chain emissions reduction target to different enterprises within the supply chain, and study the influence of the supply chain power structure on the government’s emissions reduction allocation decision, social welfare, and supply chain profit.

3. Model Descriptions

3.1. Parameter Description

This paper considers that in the context of the government’s low-carbon subsidy policy, a manufacturer and a retailer form a bilateral monopoly supply chain. The manufacturer produces according to the retailer’s order, the unit production cost is $c_0$, the wholesale price is w, and the retailer directly sells the products in the market. Assuming that the supply chain emission reduction target is E, it is assigned to manufacturers and retailers to complete together. The manufacturer’s emissions reduction target ratio is $k_M$, then the retailer’s emission reduction target ratio is $k_R=1-k_M$, where $k_M,k_R\ge 0$. Manufacturers and retailers are committed to maximizing their profits to set optimal wholesale and retail prices. At the same time, to encourage and support enterprises to reduce emissions, the government gives enterprises carbon emission reduction subsidies and is committed to maximizing social welfare to decide the allocation of emissions reduction targets. For the sake of clarity of the model formulation, the notations used in this paper and their meanings are listed in

Table 1. The notations used in this paper.

Notations	Descriptions
E	Supply chain carbon emissions reduction target volume
S	Emissions reduction subsidy per unit of carbon reduction
$c_M,c_R$	Reduction cost factor for manufacturer and retailer
$c_0$	Product production cost
${\lambda }_M,{\lambda }_R$	The sensitivity factor of market demand to manufacturers and retailers
q	Market demand for the supply chain
α	The initial market size of the product
β	Demand sensitivity factor to price
$W{S}^i$	Social welfare in the i power structure
$k_R$	The proportion of emissions reduction target that allocated to retailer
${\mathsf{\Pi }}_j^i$	In the i power structure, the profit of the j
Superscript j	j ∈ {M, R, SC} denote the manufacturer, retailer, supply chain
Subscript {i} (i = MS, RS, NV)	i ∈ {MS, RS, NV} denote manufacturer-led power structure, retailer-led power structure, manufacturer and retailer have equal power
Decision Variables
w	Wholesale price
p	Retail price
$k_M$	The proportion of emissions reduction target that allocated to manufacturer

. Figure 1 illustrates the supply chain structure of our model. Under the three power structures, the government, as a policy maker, firstly allocates a share of emission reduction targets to manufacturers and retailers. Then, the manufacturer and retailer decide the price successively according to the ownership of the dominant power of the supply chain. This paper analyzes the influence of power structure on the emissions reduction cooperation of supply chain members by comparing the decision-making results and respective interests of governments and enterprises under different power structures.

Hypothesis 1.

Refer to the assumptions of Zhang et al. [45]. The market demand q for low-carbon products is linearly affected by the retail price p of products, manufacturer’s emissions reduction  $k_{M}E$, and retailer’s emissions reduction   $\left(1-k_M\right)E$. The more the manufacturer or retailer cuts emissions, the greater the demand for their product. Parameter$\mathrm{r}$  represents the price increment of the retail price relative to the wholesale price, namely the retailer’s marginal profit. Thus, the market demand function and the retail price are:

$$q=\alpha -\beta p+{\lambda }_M{k}_{M}E+{\lambda }_R{k}_{R}E$$

(1)

$$p=w+\mathrm{r}$$

(2)

In Equation (1), $\alpha (\alpha \ge 0)$ represents the initial market size of the product, and $\beta (\beta \ge 0)$ represents the sensitivity coefficient of the demand to the price. ${\lambda }_M\left({\lambda }_M>0\right)$ and ${\lambda }_R\left({\lambda }_R>0\right)$ indicate the sensitivity coefficient of demand on the manufacturer’s emissions reduction and retailer’s emissions reduction, respectively. The greater the sensitivity coefficient, the greater the impact of enterprise emission reduction on market demand. Without loss of generality, to ensure that both manufacturers and retailers are profitable, we assume that $p>w>c_0$.

Hypothesis 2.

To encourage manufacturers to reduce carbon emissions, the government provides a carbon emissions reduction subsidy s per unit of emissions reduction, where  $s\ge 0$. Manufacturers receive emissions reduction subsidies  $s{k}_{M}E$, and retailers receive emissions reduction subsidies  $s{k}_{R}E$.

Hypothesis 3.

The input cost of carbon emissions reduction technology is quadratic. The emissions reduction costs of manufacturers and retailers are  $\frac{1}{2}{c}_M{\left(k_{M}E\right)}^2$,  $\frac{1}{2}{c}_R{\left(k_{R}E\right)}^2$, where  $c_M\left(c_M>0\right)$ and  $c_R\left(c_R>0\right)$ indicate the emissions reduction cost coefficient of manufacturers and retailers, respectively. The higher the cost coefficient, the lower the emissions reduction efficiency, and thus the greater the emissions reduction cost.

Hypothesis 4.

Refer to the assumptions of Han et al. [45]. Manufacturers and retailers make decisions based on their profits, and supply chain profits are the sum of manufacturer profits and retailer profits. Manufacturers, retailers, and supply chain profits are:

$${\mathsf{\Pi }}_M=\left(w-c_0\right)q-\frac{1}{2}{c}_M{\left(k_{M}E\right)}^2+sE{k}_M$$

(3)

$${\mathsf{\Pi }}_R=\left(\mathrm{p}-\mathrm{w}\right)q-\frac{1}{2}{c}_R{\left(\left(1-k_M\right)E\right)}^2+s\left(1-k_M\right)E$$

(4)

$${\mathsf{\Pi }}_{SC}={\mathsf{\Pi }}_M+{\mathsf{\Pi }}_R=\left(\mathrm{p}-c_0\right)q-\frac{1}{2}{c}_M{\left(k_{M}E\right)}^2-\frac{1}{2}{c}_R{\left(\left(1-k_M\right)E\right)}^2+sE$$

(5)

Hypothesis 5.

Refer to the assumptions of Han et al. [50]. Social welfare consists of total supply chain profits (manufacturer and retailer profits sum), consumer surplus  $CS=\frac{q^2}{2\beta }$, total government expenditure  $GS$, where  $GS=sE$, and environmental improvement  $EI=E$ (i.e., environmental emission reduction). Therefore, social welfare is  $SW={\mathsf{\Pi }}_M+{\mathsf{\Pi }}_R+CS+EI-GS$. The specific expression is as follows:

$$SW=\left(w-c_0\right)q-\frac{c_M{E}^2{k}_M^2}{2}+sE{k}_M+\left(\mathrm{p}-\mathrm{w}\right)q-\frac{c_R{\left(1-k_M\right)}^2{E}^2}{2}+s\left(1-k_M\right)E+\frac{q^2}{2\beta }-sE+E$$

(6)

To explore how the different power structures affect government distribution decisions, supply chain profits, and social welfare, we consider three power structures that are described as follows.

3.2. Manufacturer-Led Power Structure (MS)

Under the manufacturer-led power structure (MS), the participants in the low-carbon supply chain include the government, manufacturers, and retailers, who engage in a three-stage Stackelberg game. In the first stage, the government decides the proportion $k_M$ of emission reduction target borne by manufacturers with the goal of maximizing social welfare $SW$. In the second stage, the manufacturer decides the wholesale price w to maximize its profit ${\mathsf{\Pi }}_M$. In the third stage, the retailer decides the retail price p to maximize its profit ${\mathsf{\Pi }}_R$. The decision order under the MS power structure is shown in Figure 1a.

3.3. Retailer-Led Power Structure (RS)

Under the retailer-led power structure (RS), the government, manufacturers, and retailers still play the three-stage Stackelberg game. In the first stage, the government decides the proportion $k_M$ of emission reduction target borne by manufacturers to maximize social welfare $SW$. In the second stage, the retailer decides the retail price p to maximize its profit ${\mathsf{\Pi }}_R$. In the third stage, the manufacturer decides the wholesale price w to maximize its profit ${\mathsf{\Pi }}_M$. The decision order under the RS power structure is shown in Figure 1b.

3.4. Equal Power between Manufacturers and Retailers (NV)

Under the power structure of equal power between manufacturers and retailers (NV), the government decides first, and then the manufacturers and retailers decide simultaneously. The government and businesses play the Stackelberg game, and manufacturers and retailers play the Nash game. In the first stage, the government decides the proportion $k_M$ of emissions reduction target borne by manufacturers to maximize social welfare $SW$. In the second stage, the manufacturers decide the wholesale price w with the goal of profit ${\mathsf{\Pi }}_M$ maximization, the retailers decide the retail price p with the goal of profit ${\mathsf{\Pi }}_R$ maximization. The decision order under the NV power structure is shown in Figure 1c.

4. Equilibrium Solutions

In this part, the game model is established for the three power structures described in the upper part, namely, MS structure, RS structure, and NV structure. Game theory is used to obtain the equilibrium solutions under the three power structures. To ensure that equilibrium solutions exist in all models and that the equilibrium solutions meet the practical significance, we assume: $\left(c_M+c_R\right)\beta >\frac{5}{9}{\left({\lambda }_M-{\lambda }_R\right)}^2$, $0\le \frac{16c_{R}E\beta +7\left(\alpha +E{\lambda }_R-\beta c_0\right)\left({\lambda }_M-{\lambda }_R\right)}{E\left(16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2\right)}\le 1$, and $0\le \frac{9c_{R}E\beta +5\left(\alpha +E{\lambda }_R-\beta c_0\right)\left({\lambda }_M-{\lambda }_R\right)}{E\left(9\left(c_M+c_R\right)\beta -5{\left({\lambda }_M-{\lambda }_R\right)}^2\right)}\le 1$.

We used the superscript “MS”, “RS”, and “NV” to represent the corresponding variables in the three power structures, and used the symbol “*” to represent the optimal value. The optimal solutions of the above three power structures can be obtained by reverse induction.

4.1. Manufacturer-Led Power Structure (MS)

Lemma 1:

Under the MS power structure, the proportion of emissions reduction target allocated to manufacturers, wholesale prices, retail prices, and market demand are

$$k_M^{MS{}^{\ast }}=\frac{16c_{R}E\beta +7\left(\alpha +E{\lambda }_R-\beta c_0\right)\left({\lambda }_M-{\lambda }_R\right)}{E\left(16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2\right)}$$

(7)

$$w^{MS{}^{\ast }}=\frac{8E\left(c_R{\lambda }_M+c_M{\lambda }_R\right)+8\left(c_M+c_R\right)\left(\beta c_0+\alpha \right)-7{\left({\lambda }_M-{\lambda }_R\right)}^2{c}_0}{16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(8)

$$p^{MS{}^{\ast }}=\frac{12E\left(c_R{\lambda }_M+c_M{\lambda }_R\right)+4\left(c_M+c_R\right)\left(\beta c_0+3\alpha \right)-7{\left({\lambda }_M-{\lambda }_R\right)}^2{c}_0}{16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(9)

$$q^{MS{}^{\ast }}=\frac{4\beta \left(E{c}_M{\lambda }_R+E{c}_R{\lambda }_M-\beta c_0{c}_M-\beta c_0{c}_R+\alpha c_M+\alpha c_R\right)}{16\beta \left(c_M+c_R\right)-7{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(10)

Taking the equilibrium solution in Lemma 1 into Equations (3)–(6), we get the optimal manufacturer profit ${\mathsf{\Pi }}_M^{MS{}^{\ast }}$, retailer profit ${\mathsf{\Pi }}_R^{MS{}^{\ast }}$, supply chain profit ${\mathsf{\Pi }}_{SC}^{MS{}^{\ast }}$, and social welfare $W{S}^{MS{}^{\ast }}$.

Under MS power structure, we analyzed the manufacturer’s emissions reduction target ratio and found the correlation with supply chain emission reduction target, manufacturer’s and retailer’s emissions reduction efficiency, the sensitivity of demand to their reducing emissions, and production costs are shown in

Table 2. Under MS power structure, correlation of the manufacturer’s emissions reduction ratio.

Equilibrium Solution	E	cM	cR	λM	c0
$k_M^{MS{}^{\ast }}$	if ${\lambda }_M>{\lambda }_R$, decrease	decrease	increase	if ${\lambda }_M>{\lambda }_R$, increase	if ${\lambda }_M>{\lambda }_R$, decrease
	if ${\lambda }_M<{\lambda }_R$, increase			——	if ${\lambda }_M<{\lambda }_R$, increase

.

Proposition 1.

Under MS power structure, the following relationships hold:  $\frac{\partial k_M^{MS{}^{\ast }}}{\partial c_M}<0,\frac{\partial k_M^{MS{}^{\ast }}}{\partial c_R}>0$; if  ${\lambda }_M>{\lambda }_R$, then  $\frac{\partial k_M^{MS{}^{\ast }}}{\partial E}<0,\frac{\partial k_M^{MS{}^{\ast }}}{\partial {\lambda }_M}>0,\frac{\partial k_M^{MS{}^{\ast }}}{\partial c_0}<0$; if  ${\lambda }_M<{\lambda }_R$, then  $\frac{\partial k_M^{MS{}^{\ast }}}{\partial E}>0,\frac{\partial k_M^{MS{}^{\ast }}}{\partial c_0}>0$.

When the supply chain is dominated by manufacturers, the emissions reduction target ratio allocated to enterprises by the government is positively related to their emissions reduction efficiency, and negatively related to the emissions reduction efficiency of the other party of the supply chain. For enterprises whose emissions reduction have a greater impact on market demand, the proportion of the emissions reduction target allocated by the government is negatively correlated with the supply chain emissions reduction target and product costs. For the enterprises whose emissions reduction has a lesser impact on the market demand, the proportion of the emissions reduction target allocated by the government is positively correlated with the supply chain emissions reduction target.

According to Proposition 1, when the supply chain power structure is dominated by manufacturers, when the supply chain emissions reduction target increases, the net increase of the emissions reduction target is not distributed according to the original emission reduction allocation ratio. The proportion of emission reduction target allocated to enterprises with high emissions reduction sensitivity to market demand will be reduced. The proportion of emissions reduction target allocated to enterprises with low emission reduction sensitivity to market demand will be increased. In contrast, the emissions reduction target ratio allocated to enterprises with low emissions reduction sensitivity to market demand will be reduced. The emissions reduction target ratio allocated to the enterprises with high emissions reduction sensitivity to market demand will be increased. At this time, the emissions reduction subsidy does not have an impact on the distribution mode of the government. That is to say, emissions reduction subsidies have lost the role of encouraging emissions reduction enterprises to increase emissions reduction input.

Analyzing the social welfare under MS power structure, we can find that the correlation between the social welfare and the production cost, the emissions reduction efficiency of both enterprises, and the sensitivity of the market demand to the emissions reduction of both enterprises is shown in

Table 3. Under MS power structure, the correlation of social welfare.

Equilibrium Solution	cM	cR	λM	λR	c0
$W{S}^{MS{}^{\ast }}$	decrease	decrease	increase	increase	decrease

.

Proposition 2.

Under MS power structure, the following relationships hold:  $\frac{\partial W{S}^{MS{}^{\ast }}}{\partial c_M}<0,\frac{\partial W{S}^{MS{}^{\ast }}}{\partial c_R}<0,\frac{\partial W{S}^{MS{}^{\ast }}}{\partial {\lambda }_M}>0,\frac{\partial W{S}^{MS{}^{\ast }}}{\partial {\lambda }_R}>0,\frac{\partial W{S}^{MS{}^{\ast }}}{\partial c_0}<0$.

When the power structure of the supply chain is dominated by the manufacturers, social welfare is positively related to the emissions reduction efficiency of both enterprises and the sensitivity of the market demand to the emissions reduction on both sides. It can be found from Proposition 2 that when the supply chain is dominated by manufacturers, the improvement of the emissions reduction efficiency of any enterprise and the sensitivity of market demand to the emissions reduction of any enterprise can improve social welfare.

4.2. Retailer-Led Power Structure (RS)

Lemma 2.

Under the RS power structure, the proportion of emissions reduction target allocated to manufacturers, wholesale prices, retail prices, and market demand are

$$k_M^{RS{}^{\ast }}=\frac{16c_{R}E\beta +7\left(\alpha +E{\lambda }_R-\beta c_0\right)\left({\lambda }_M-{\lambda }_R\right)}{E(16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2)}$$

(11)

$$w^{RS{}^{\ast }}=\frac{4E\left(c_R{\lambda }_M+c_M{\lambda }_R\right)+\left(c_M+c_R\right)\left(12\beta c_0+4\alpha \right)-7c_0{\left({\lambda }_M-{\lambda }_R\right)}^2}{16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(12)

$$p^{RS{}^{\ast }}=\frac{12E\left(c_R{\lambda }_M+c_M{\lambda }_R\right)+4\left(c_M+c_R\right)\left(\beta c_0+3\alpha \right)-7{\left({\lambda }_M-{\lambda }_R\right)}^2{c}_0}{16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(13)

$$q^{RS{}^{\ast }}=\frac{4\beta \left(E{c}_M{\lambda }_R+E{c}_R{\lambda }_M-\beta c_0{c}_M-\beta c_0{c}_R+\alpha c_M+\alpha c_R\right)}{16\left(c_M+c_R\right)\beta -7{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(14)

Taking the equilibrium solution in Lemma 2 into Equations (3)–(6), we get the optimal manufacturer profit ${\mathsf{\Pi }}_M^{RS{}^{\ast }}$, retailer profit ${\mathsf{\Pi }}_R^{RS{}^{\ast }}$, supply chain profit ${\mathsf{\Pi }}_{SC}^{RS{}^{\ast }}$, and social welfare $W{S}^{RS{}^{\ast }}$.

Under RS power structure, we analyzed the social welfare and the government’s optimal emissions reduction target allocation decision, and found correlation of the manufacturer’s emissions reduction ratio and social welfare, shown in

Table 4. Under RS power structure, correlation of the manufacturer’s emission reduction ratio and social welfare.

Equilibrium Solution	E	cM	cR	λM	λR	c0
$k_M^{RS{}^{\ast }}$	if ${\lambda }_M>{\lambda }_R$, decrease	decrease	increase	if ${\lambda }_M>{\lambda }_R$, increase	——	if ${\lambda }_M>{\lambda }_R$, decrease
	if ${\lambda }_M<{\lambda }_R$, increase			——	——	if ${\lambda }_M<{\lambda }_R$, increase
$W{S}^{RS{}^{\ast }}$	——	decrease	decrease	increase	increase	decrease

.

Proposition 3.

Under RS power structure, the following relationships hold:  $\frac{\partial k_M^{RS{}^{\ast }}}{\partial c_M}<0,\frac{\partial k_M^{RS{}^{\ast }}}{\partial c_R}>0$. If  ${\lambda }_M>{\lambda }_R$, then  $\frac{\partial k_M^{RS{}^{\ast }}}{\partial E}<0,\frac{\partial k_M^{RS{}^{\ast }}}{\partial {\lambda }_M}>0,\frac{\partial k_M^{RS{}^{\ast }}}{\partial c_0}<0$; if  ${\lambda }_M<{\lambda }_R$, then  $\frac{\partial k_M^{RS{}^{\ast }}}{\partial E}>0,\frac{\partial k_M^{RS{}^{\ast }}}{\partial c_0}>0$;  $\frac{\partial W{S}^{RS{}^{\ast }}}{\partial c_M}<0,\frac{\partial W{S}^{RS{}^{\ast }}}{\partial c_R}<0,\frac{\partial W{S}^{RS{}^{\ast }}}{\partial {\lambda }_M}>0,\frac{\partial W{S}^{RS{}^{\ast }}}{\partial {\lambda }_R}>0,\frac{\partial W{S}^{RS{}^{\ast }}}{\partial c_0}<0$.

When the supply chain is dominated by retailers, the correlation between the optimal emissions reduction target ratio allocated to the manufacturer, the social welfare and the supply chain emissions reduction target, and the emission reduction efficiency of both parties are the same as those under the supply chain power structure of MS.

4.3. Manufacturer and Retailer Have Equal Power (NV)

Lemma 3.

Under the NV power structure, the proportion of the emissions reduction target allocated to manufacturers, wholesale prices, retail prices, and market demand are

$$k_M^{NV{}^{\ast }}=\frac{9c_{R}E\beta +5\left(\alpha +E{\lambda }_R-\beta c_0\right)\left({\lambda }_M-{\lambda }_R\right)}{E\left(9\left(c_M+c_R\right)\beta -5{\left({\lambda }_M-{\lambda }_R\right)}^2\right)}$$

(15)

$$w^{NV{}^{\ast }}=\frac{3E\left(c_R{\lambda }_M+c_M{\lambda }_R\right)+\left(6\beta c_0+3\alpha \right)\left(c_M+c_R\right)-5c_0{\left({\lambda }_M-{\lambda }_R\right)}^2}{9\left(c_M+c_R\right)\beta -5{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(16)

$$p^{NV{}^{\ast }}=\frac{6E\left(c_M{\lambda }_R+c_R{\lambda }_M\right)+3\left(c_M+c_R\right)\left(\beta c_0+2\alpha \right)-5{\left({\lambda }_M-{\lambda }_R\right)}^2{c}_0}{9\left(c_M+c_R\right)\beta -5{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(17)

$$q^{NV{}^{\ast }}=\frac{3\beta \left(E{c}_M{\lambda }_R+E{c}_R{\lambda }_M-\beta c_0{c}_M-\beta c_0{c}_R+\alpha c_M+\alpha c_R\right)}{9\beta \left(c_M+c_R\right)-5{\left({\lambda }_M-{\lambda }_R\right)}^2}$$

(18)

Taking the equilibrium solution in Lemma 3 into Equations (3)–(6), we get the optimal manufacturer profit ${\mathsf{\Pi }}_M^{NV{}^{\ast }}$, retailer profit ${\mathsf{\Pi }}_R^{NV{}^{\ast }}$, supply chain profit ${\mathsf{\Pi }}_{SC}^{NV{}^{\ast }}$, and social welfare $W{S}^{NV{}^{\ast }}$.

Under NV power structure, we analyzed the social welfare and the government’s optimal emission reduction target allocation decision, and found correlation of the manufacturer’s emission reduction target ratio and social welfare, shown in

Table 5. Under NV power structure, correlation of the manufacturer’s emissions reduction ratio and social welfare.

Equilibrium Solution	E	cM	cR	λM	λR	c0
$k_M^{NV{}^{\ast }}$	if ${\lambda }_M>{\lambda }_R$, decrease	decrease	increase	if ${\lambda }_M>{\lambda }_R$, increase	——	if ${\lambda }_M>{\lambda }_R$, decrease
	if ${\lambda }_M<{\lambda }_R$, increase			——	——	if ${\lambda }_M<{\lambda }_R$, increase
$W{S}^{NV{}^{\ast }}$	——	decrease	decrease	increase	increase	decrease

.

Proposition 4.

Under NV power structure, the following relationships hold:  $\frac{\partial k_M^{NV{}^{\ast }}}{\partial c_M}<0,\frac{\partial k_M^{NV{}^{\ast }}}{\partial c_R}>0$. If  ${\lambda }_M>{\lambda }_R$, then  $\frac{\partial k_M^{NV{}^{\ast }}}{\partial E}<0,\frac{\partial k_M^{NV{}^{\ast }}}{\partial {\lambda }_M}>0,\frac{\partial k_M^{NV{}^{\ast }}}{\partial c_0}<0$; if  ${\lambda }_M<{\lambda }_R$, then  $\frac{\partial k_M^{NV{}^{\ast }}}{\partial E}>0,\frac{\partial k_M^{NV{}^{\ast }}}{\partial c_0}>0$;  $\frac{\partial W{S}^{NV{}^{\ast }}}{\partial c_M}<0,\frac{\partial W{S}^{NV{}^{\ast }}}{\partial c_R}<0,\frac{\partial W{S}^{NV{}^{\ast }}}{\partial {\lambda }_M}>0,\frac{\partial W{S}^{NV{}^{\ast }}}{\partial {\lambda }_R}>0,\frac{\partial W{S}^{NV{}^{\ast }}}{\partial c_0}<0$.

When the power of supply chain enterprises is equal, the correlation between the optimal emissions reduction target ratio allocated by the government to both parties of the supply chain, the social welfare and the supply chain emissions reduction target, emissions reduction subsidy, and the emissions reduction efficiency of both parties are the same as those when the power of supply chain enterprises is unequal.

Corollary 1.

For the enterprise whose emissions reduction has a greater impact on the market demand, the proportion of emissions reduction target allocated by the government decreases with the increase of emissions reduction target in the supply chain. For the enterprise whose emissions reduction has less impact on the market demand, the proportion of emissions reduction target allocated by the government increases with the increase of the emissions reduction target. The proportion of emissions reduction allocated by the government to supply chain enterprises all increases with the improvement of the emissions reduction efficiency of enterprises themselves, and all decreases with the improvement of emissions reduction efficiency of enterprises on the other side of the supply chain.

Corollary 2.

Supply chain enterprises improve the efficiency of emissions reduction or enhance the influence of enterprise emissions reduction on market demand, which can increase social welfare.

From Corollary 2, we can see that to increase social welfare, the government can consider it from two aspects; first, from the producer level, through some preferential support policies to encourage enterprises to improve emissions reduction technology, and improve emissions reduction efficiency, and the second, from the consumer level, through the publicity of the low-carbon concept to increase consumer environmental awareness, to enhance the sensitivity of consumers to enterprise emissions reduction.

Corollary 3.

The relevance under the three power structures is the same between social welfare and efficiency of enterprise emissions reduction, the sensitivity of market demand to enterprise emissions reduction. The relevance between the proportion of emissions reduction target undertaken by enterprise and those under the three power structures is also same.

Under different power structures, production cost always harms social welfare, and the sensitivity of market demand to enterprise emissions reduction always has a positive impact on social welfare. The higher the efficiency of enterprise emissions reduction, the greater the proportion of emissions reduction target undertaken.

5. Comparisons and Analyses

In this section, we try to compare the optimal decisions, profits, and social welfare under MS, RS, and NV power structures to explore the impacts of power construct.

Proposition 5.

The proportion of the emissions reduction target borne by the manufacturers is met when  ${\lambda }_M\ge {\lambda }_R$,  $k_M^{NV{}^{\ast }}\ge k_M^{MS{}^{\ast }}=k_M^{RS{}^{\ast }}$. When  ${\lambda }_R>{\lambda }_M$,  $k_M^{MS{}^{\ast }}=k_M^{RS{}^{\ast }}>k_M^{NV{}^{\ast }}$.

Proposition 5 shows that when the supply chain has a leader (MS and RS power structure), that is, in two supply chain structures of unequal enterprise power, the government makes the same emissions reduction target allocation decision, which shows that the manufacturer leading or retailer leading does not affect the government’s target allocation decision. In particular, when the manufacturer’s emission reduction and retailer’s emissions reduction have the same impact on market demand, $k_M^{NV{}^{\ast }}=k_M^{MS{}^{\ast }}=k_M^{RS{}^{\ast }}=\frac{c_R}{c_M+c_R}$, which is the same emission reduction target allocation decisions for governments under the three power structures. This shows that the government allocates emission reduction target from the perspective of the overall supply chain and even the social welfare, and does not favor the party with greater or lesser power in the supply chain, which is conducive to alleviating the contradiction caused by the uneven distribution of interests between the two sides, and is conducive to the implementation of China’s emission reduction policy and the realization of the dual carbon target.

From Proposition 5, it can also be found that enterprises whose emissions reduction has a greater impact on market demand will bear a greater emissions reduction proportion in the case of the supply chain members having equal power (NV) than that in the case of a party dominating the supply chain (MS and RS). This shows that enterprises whose emissions reduction has a greater impact on market demand will assume greater responsibility for emissions reduction when neither party dominates the supply chain, and thus will win more carbon-sensitive markets. Upon further analysis, it is not difficult to find that the change in the proportion of emission reduction target allocation affects the market demand from two aspects. First, it can be seen from the demand function $q=\alpha -\beta p+{\lambda }_M{k}_{M}E+{\lambda }_R\left(1-k_M\right)E$ that the increase in the proportion of emissions reduction borne by enterprises whose emission reduction has a big impact on market demand will bring about an increase in market demand, and the increasing degree of market demand is the same under the three power structures. Second, judging from the price reaction function in Section 3.2, Section 3.3 $p^{MS}=p^{RS}=\frac{3\left({\lambda }_M-{\lambda }_R\right)Ek+3{\lambda }_{R}E+\beta c_0+3\alpha }{4\beta }$, and Section 3.4 $p^{NV}=\frac{2\left({\lambda }_M-{\lambda }_R\right)E{k}_M+2E{\lambda }_R+\beta c_0+2\alpha }{3\beta }$, the increase in the proportion of emissions reduction borne by enterprises whose emissions reduction has a greater impact on market demand will lead to an increase in retail prices, but the resulting increasing degree in retail prices and the resulting reduction degree in market demand is different. In the case of supply chain members having equal power, the reduction degree of market demand is greater than that in the case of supply chain members having unequal power. Therefore, for enterprises whose emissions reduction has a great impact on market demand, the increased proportion of emissions reduction has a greater negative effect on market demand when the supply chain members have unequal power than that when the supply chain members have equal power. Therefore, the government will allocate a smaller emissions reduction target proportion to it.

As a result, companies whose emissions reduction has a great impact on market demand always bear a smaller emissions reduction target when the supply chain members have equal power than that when the supply chain members have unequal power.

Under the three power structure, comparing the proportion of emissions reduction target borne by manufacturers and retailers, it is expressed as $\mathrm{\Delta }k=k_M-k_S$. In the case of the supply chain members having unequal power, $\mathrm{\Delta }{k}^{MS{}^{\ast }}=\mathrm{\Delta }{k}^{RS{}^{\ast }}=\frac{16\left(c_R-c_M\right)E\beta +7\left({\lambda }_M-{\lambda }_R\right)\left(2\alpha +\left({\lambda }_M+{\lambda }_R\right)E-2c_0\beta \right)}{E\left(16\beta \left(c_M+c_R\right)-7{\left({\lambda }_M-{\lambda }_R\right)}^2\right)}$. In the case of the supply chain members having equal power, then $\mathrm{\Delta }{k}^{NV{}^{\ast }}=\frac{9\beta E\left(c_R-c_M\right)+5\left({\lambda }_M-{\lambda }_R\right)\left(2\alpha +\left({\lambda }_M+{\lambda }_R\right)E-2\beta c_0\right)}{E\left(9\left(c_M+c_R\right)\beta -5{\left({\lambda }_M-{\lambda }_R\right)}^2\right)}$. According to the expression, the relative size of the proportion of emissions reduction target allocated for manufacturer and retailer is determined by the emissions reduction cost coefficient of both companies and the impact of corporate emissions reduction on the market. When manufacturers and retailers have the same emissions reduction efficiency, companies whose emissions reduction has a great impact on market demand receive a greater emissions reduction target. When the manufacturer’s emissions reduction and the retailer’s emissions reduction have the same impact on market demand, more efficient manufacturers and retailers receive a greater emissions reduction target.

Corollary 4.

Under the three power structures, the emissions reduction target proportion of the manufacturer and the retailer allocated by the government is related to the sensitivity of market demand to both sides’ emissions reduction and the efficiency of both sides. If manufacturers and retailers have the same emissions reduction efficiency, companies whose emissions reduction has a greater impact on market demand will bear a greater proportion of emissions reduction. If both sides’ emissions reductions have the same impact on market demand, companies with high emissions reduction efficiency will bear a greater proportion of emissions reduction.

It can be found from Corollary 3 that the government comprehensively considers the efficiency of emission reduction and the sensitivity of market demand to enterprises’ emissions reduction in allocating emissions reduction. The government tends to allocate greater emissions reduction to enterprises with higher emissions reduction efficiency and enterprises whose emissions reduction has a greater impact on market demand. It can be found that when the government allocates the proportion of emissions reduction, it will adopt the “whip-fast cattle” policy.

Proposition 6.

Under three different supply chain power structures, market demand meets:  $q^{NV{}^{\ast }}>q^{MS{}^{\ast }}=q^{RS{}^{\ast }}$, and social welfare is met:  $W{S}^{NV{}^{\ast }}>W{S}^{MS{}^{\ast }}=W{S}^{RS{}^{\ast }}$.

Proposition 6 shows that in the two supply chain power structures of manufacturer-dominated or retailer-dominated, the market demand is the same, which is less than the market demand in the case of the supply chain members having unequal power. From Equation (1), market demand is affected by three factors: retail price and the proportion of emissions reduction target borne by the manufacturer and by the retailer. These three factors are the same in the two power structures, so market demand is the same in both cases. We also find that the power structures of the supply chain members having equal power is bound to increase market demand, thus increasing consumer surplus and ultimately increasing social welfare. Thus, to improve social welfare, the government should build a fair and open competitive environment to release consumer demand and increase consumer surplus.

Proposition 7.

The total profits of the supply chain meets: if   ${\left({\lambda }_M-{\lambda }_R\right)}^2\le \frac{1855-17\sqrt{865}}{1108}\left(c_M+c_R\right)\beta$, then  ${\mathsf{\Pi }}_{SC}^{NV{}^{\ast }}\ge {\mathsf{\Pi }}_{SC}^{MS{}^{\ast }}={\mathsf{\Pi }}_{SC}^{RS{}^{\ast }}$; if  $\frac{1855-17\sqrt{865}}{1108}\left(c_M+c_R\right)\beta <{\left({\lambda }_M-{\lambda }_R\right)}^2<\frac{9}{5}\left(c_M+c_R\right)\beta$, then  ${\mathsf{\Pi }}_{SC}^{MS{}^{\ast }}={\mathsf{\Pi }}_{SC}^{RS{}^{\ast }}>{\mathsf{\Pi }}_{SC}^{NV{}^{\ast }}$.

Proposition 7 shows that the total profit of the supply chain in two power structures are the same when the supply chain members have unequal power. This shows that in the two power structures, the supply chain profits are only distributed differently between the manufacturers and retailers, and no new profits have been made.

We find that power equivalence in the supply chain members does not necessarily always increase supply chain profits. When the difference in the sensitivity of market demand for manufacturer’s emission reduction and retailer’s emission reduction is slight, the power equivalence of the supply chain members will bring greater total supply chain profit. When the difference is large, the power equivalence of the supply chain members will bring a smaller total supply chain profit.

Corollary 5.

The equal power of all parties in the low-carbon supply chain will certainly bring most social welfare by increasing consumer surplus, but it will not necessarily bring most supply chain profits.

When the power of the low-carbon supply chain members is equal, the market demand is the largest, which better meets the consumers, but it does not necessarily meet the overall interests of the supply chain. When the differences in the sensitivity of market demand for the manufacturer’s and the retailer’s emissions reduction is slight, the power equivalence of the supply chain members will increase the total supply chain profit. When the difference is large, the power equivalence of the supply chain members will decrease the total supply chain profit.

From the perspective of the government, the power structure of the supply chain members having equal power is more compatible with its pursuit of social welfare. Supply chain members’ power equivalence greatly increases the consumer surplus, and even profits are damaged when the supply chain members have unequal power, the gain of social welfare is enough to compensate for the loss of supply chain profits at this time. Therefore, from the perspective of social welfare, the government should encourage enterprises to compete fairly and avoid the situation of one single dominance in the supply chain, to stimulate market vitality and consumer demand, and thus increase social welfare.

6. Numerical Analysis

In this part, we use numerical analysis to further understand the impact of power structure on emissions reduction target allocation decisions, demand, profit, and social welfare in low-carbon supply chains.

Assuming $c_0=5$, $c_M=0.3$, $c_R=0.4$, $\beta =0.2$, $E=500$, $s=1$, $\alpha =100$, then setting ${\lambda }_R=0.2$, ${\lambda }_R=0.5$, ${\lambda }_R=0.7$ in turn, we get the manufacturer emissions reduction ratio under the three power structures, as shown in Figure 2. When the manufacturer’s emissions reduction has a greater impact on the market demand, the manufacturer’s emissions reduction ratio under the NV power structure is greater than that under the MS and RS power structure. Conversely, it is less than that under the MS and RS power structure. Proposition 5 is proven.

To analyze the impact of the sensitivity of market demand to the manufacturer’s emissions reduction on its emissions reduction ratio, when the manufacturer’s emissions reduction efficiency and retailer’s emissions reduction efficiency are the same, we assume that $c_0=5$, $\beta =0.2$, $E=500$, $s=1$, $\alpha =100$, ${\lambda }_R=0.5$, $c_R=c_M=0.3$. As shown in Figure 3, when the manufacturer’s emissions reduction has a greater impact on market demand, the manufacturer bears a greater emissions reduction ratio; when the retailer’s emissions reduction has a greater impact on market demand, the retailer bears a greater emissions reduction ratio.

To analyze the impact of the manufacturer’s emissions reduction efficiency on its emissions reduction ratio, when the sensitivity of market demand to the manufacturer’s and the retailer’s emissions reduction are the same, we assume that $c_0=5$, $\beta =0.2$, $E=500$, $s=1$, $\alpha =100$, $c_R=0.5$, ${\lambda }_M={\lambda }_R=0.5$. As shown in Figure 4, if the sensitivity of market demand to the manufacturer’s and the retailer’s emissions reduction are the same, when manufacturer is more efficient at reducing emissions, manufacturers share more of the emissions; when the retailer is more efficient at reducing emissions, the retailer shares more of emission. Corollary 4 is proven.

Assuming $c_0=5$, $c_M=0.3$, $c_R=0.4$, $\beta =0.2$, $E=500$, $s=1$, $\alpha =100$, ${\lambda }_R=0.5$, graphs are drawn of the variation of the demand, supply chain profit, and social welfare with ${\lambda }_M$ under the MS, RS, NV power structure. From Figure 5, the market demand and social welfare under the NV power structure are always greater than that under MS and RS power structures. When the difference in the sensitivity of market demand to the manufacturer’s and the retailer’s emissions reduction is less, the supply chain profit under NV power structure is greater than that under MS and RS power structures; when the difference is relatively large, the supply chain profit under NV power structure is less than that under MS and RS power structures.

7. Discussion

We studied how the government allocates the emissions reduction target of the supply chain to retailers and manufacturers, built three game models according to different power structures, and compared the distribution schemes, market demand, and social welfare in different models.

Many works have studied the influence of power structure on supply chain. Wang et al. [39] explored the remanufacturing supply chain considering the expectation of consumer regret, Yu et al. [40] studied the live streaming e-commerce supply chain, Yao et al. [41] studied the closed-loop supply chain with social responsibility. Everyone found that the market demand is the largest under the power structure of NV, which is consistent with the conclusion of this paper.

However, the above literature also found that the total profit of the supply chain under the power structure of NV is the largest, which is different from the conclusion of this paper. In this article, it was found that when consumers have a large difference in sensitivity to the emissions reduction of manufacturers and retailers, supply chain profits are smaller under NV power structure.

In the above literature, supply chain profits are always maximized under the NV power structure. This is due to a “double marginal effect”, which is exacerbated when manufacturers or retailers have more power. The reasons why this paper draws different conclusions lie in two aspects: first, the paper considers the government in the supply chain. The government will allocate the overall carbon emission target of the supply chain from the perspective of social welfare, which will partly curb the “double marginal effect”. Second, this paper considers that the emissions reductions of manufacturers and retailers have different impacts on market demand. If the gap between them is too large, the roles of manufacturers and retailers in expanding market demand are different. Therefore, leaders should be allowed to dominate the decision-making of the supply chain, so as to strengthen the cooperation between upstream and downstream enterprises, which is more conducive to improving the overall profit of the supply chain. The above two points are factors that the traditional supply chain does not pay attention to, which is why different conclusions appear.

In the real consumption scenario, for some consumer goods, consumers with low-carbon preference do not care whether the emissions reduction is accomplished by the manufacturer or the retailer. In this case, the pursuit of right equivalence by the supply chain members can bring the maximum total profit of the supply chain. However, in some consumption scenarios, manufacturers and retailers have different market influences on emissions reduction, and consumers pay more attention to the emissions reduction behaviors of manufacturers or retailers. In the existing literature, when studying the low-carbon supply chain with power structure, scholars only consider the different dominant power of manufacturers and retailers, and do not focus on the “identity effect” of manufacturers and retailers; that is, manufacturers or retailers are more concerned by consumers, and their emissions reduction behaviors have a stronger incentive effect. Taking this into account, this paper distinguishes between the driving effect of the emissions reduction behaviors of manufacturers and retailers on market demand, expressed by ${\lambda }_M$ and ${\lambda }_R$ respectively, and draws some new conclusions. When consumers pay different attention to the emissions reduction of upstream and downstream enterprises in the supply chain, and even have large differences in demand-pull effect, the unequal power structure is more conducive to improving the total profits of the supply chain. Therefore, this paper is a useful supplement to the existing research on the power structure of the supply chain, and extends the research on the power structure theory of the supply chain in the field of low carbon, especially in the field of low-carbon supply chains where consumers have different preferences for the emissions reduction behaviors of different emissions reduction subjects.

8. Conclusions

Under the dual carbon strategy, supply chain enterprises cooperating to reduce emissions is a current trend. This paper establishes the corresponding three-stage game model for three different supply chain power structures. Through the analysis and comparison of the equilibrium solutions in the three game models, the influence of the supply chain power structure on the government’s carbon emissions reduction target distribution decision, social welfare, and the supply chain profit are discussed.

The research shows that: (1) Under the three power structures, if the supply chain carbon emissions reduction target increases, the government will adjust the distribution strategy to increase the emissions reduction target ratio allocated to enterprises whose emissions reduction has a lesser impact on market demand. (2) In the three different supply chain power structures, the government tends to allocate a greater emissions reduction target to companies with higher emissions reduction efficiency and the one whose emissions reduction has a greater impact on market demand. (3) When the supply chain members have equal power, the social welfare is the greatest, and the market demand is also the largest. Therefore, the government’s promotion of anti-monopoly and the creation of a fair business environment in the low-carbon supply chain can improve social welfare. (4) Total profits of the supply chain are not necessarily the greatest under the power structure of equal power between manufacturer and retailer.

Inevitably, there are still some limitations to this work. First of all, this paper only considers the cooperative emission reduction between manufacturers and retailers under the government subsidy policy. In fact, the joint action of multiple carbon policies is more in line with the reality faced by enterprises. In the future, we can explore the cooperative emissions reduction of supply chain members under the coexistence of multiple government policies. In addition, with the intensification of economic globalization and market competition, competition between supply chains has become the norm. Therefore, we can study the cooperative emissions reduction among members of the supply chain in the future model considering the competition among multiple supply chains.