Low-Carbon Strategies Considering Corporate Environmental Responsibility: Based on Carbon Trading and Carbon Reduction Technology Investment

Abstract

This paper focuses on the optimal strategic choice of carbon trading and carbon reduction technology investment under the cap-and-trade system. We consider a carbon-dependent production enterprise that trades carbon emission rights or invests in carbon reduction technologies under the regulation of the cap-and-trade system. The enterprise undertakes corporate environmental responsibility (CER) and aims to maximize the comprehensive benefits of both the economy and the environment. Using numerical simulation, we analyze the impacts of the CER coefficient and initial carbon quotas on the comprehensive benefits, optimal emission reduction rate, and production quantity of the enterprise. Our main contribution is studying the low-carbon strategic option for CER production enterprises to maximize the comprehensive benefits by trading carbon emission permits or investing in carbon emission reduction technologies. We found that the carbon emission trading mechanism plays an important role in promoting enterprises to reduce carbon emissions and is a beneficial supplement to the carbon cap policy. Under different initial carbon quotas allocated by the government, the manufacturer strategically chooses to trade carbon emission rights or invest in carbon reduction technologies. CER is a significant factor in encouraging companies to reduce carbon emissions proactively.

1. Introduction

With the increase in greenhouse gas emissions, the danger of global warming is becoming more and more jeopardizing. The 2016 Paris Agreement set the goal of global “carbon neutrality”, and many countries have actively responded to make carbon reduction commitments. In 2020, China proposed in its 14th Five-Year Plan that it would accelerate green development and formulate an action plan to reach a peak in carbon emissions by 2030. In 2021, the European Commission unveiled a climate package called Fit for 55, which promised to reduce greenhouse gas emissions by 55% by the end of 2030 compared with 1990 levels. This means that various industries, especially the fossil fuel industry, transportation industry, and other energy-intensive industries, are facing a tougher test of carbon emission reduction. To achieve the carbon reduction commitments, countries have adopted relevant systems to reduce the carbon emissions of such enterprises [1,2]. The cap-and-trade system introduced by the EU in 2005 is regarded as an effective way to promote carbon emission reduction among enterprises [3]. Under a cap-and-trade scheme, companies are subject to a cap on their carbon emissions; if they can meet their targets and have a surplus of emissions quotas, they can sell the remaining carbon emission rights to companies that fail to meet their carbon emission targets.

The last decade has witnessed significant progress in the domain of the cap-and-trade system; many researchers focused on the influence of the cap-and-trade system on enterprises’ production and pricing decisions [4,5,6,7] and the impact of the cap-and-trade system on corporate carbon reduction decisions [8,9,10]. However, few researchers took corporate environmental responsibility into account when conducting cap-and-trade studies. As an important part of corporate social responsibility (CSR), CER conforms to the trend of pursuing sustainable development and plays an important role in solving environmental problems [11,12]. While facing increasingly severe environmental pressure worldwide, pursuing profit simply is not conducive to the sustainable development of enterprises; enterprises should take the initiative to undertake corporate environmental responsibilities [13]. Therefore, it is of practical significance to consider CER when performing decision analysis.

Producing enterprises that undertake CER aim to maximize the comprehensive benefits of both the economy and the environment. Under a cap-and-trade system, manufacturing enterprises can choose to adopt some emission reduction strategies to save energy consumption in the production process [14,15], or choose to trade carbon emission rights, or adopt a combination of the two. Therefore, it is worth discussing which strategy can bring the maximum comprehensive benefit to the producing enterprise.

Based on the above framework, this paper discusses the choice of carbon reduction strategies for enterprises considering CER under the cap-and-trade system.

(1)

What is the optimal strategy for the producing enterprise when the initial carbon quotas change?

(2)

What are the impacts of initial carbon quotas on the strategy choice, optimal carbon reduction rate, and production quantity of the producing enterprise?

(3)

What is the impact of undertaking CER on the optimal decision-making of the producing enterprise?

This paper proposes a comprehensive benefit model for the production enterprise considering CER to answer these questions. Based on this model, different optimal emission reduction strategies according to different initial carbon quotas are determined, the carbon emission reduction rate and production capacity under different strategies are compared, and the impacts of CER on these decisions are explored. The results have guiding significance for enterprises’ strategy selection under different initial carbon quota levels.

The structure of the paper is as follows. Section 2 introduces the literature review, Section 3 describes the problem and basic assumptions, Section 4 establishes and solves the comprehensive benefit model of the producing enterprise under different scenarios, Section 5 analyzes the emission reduction strategy through numerical experiments, and Section 6 draws the conclusions and proposes the future development direction.

2. Literature Review

This section reviews the literature that is closely related to our research. The studies can be classified into three categories: (1) research on production and pricing decisions of enterprises under the cap-and-trade system; (2) research on low-carbon strategy choices under the cap-and-trade system; (3) research on corporate environmental responsibility (CER).

2.1. Optimal Decisions of Enterprises under the Cap-and-Trade System

In recent years, many researchers have discussed the influence of the cap-and-trade system on the decision-making of enterprises. Zhang et al. [16] studied the influence of the corporate social responsibility (CSR) concern level and cap-and-trade system on the pricing decisions of the social responsibility supply chain. It is found that CSR can promote the channel profitability of the centralized model but damage the channel profitability of the decentralized model. Kushwaha et al. [17] analyzed the influence of the quantity and quality of recycled products, carbon emission caps, trade constraints, and other factors on the recycling channel selection strategy of manufacturers. Yang et al. [18] discussed the influence of “grandfathering” and “benchmarking” carbon quota allocation rules on green technology investment and product pricing decisions. Taleizadeh et al. [19] studied the optimal decision in the green production of dual-channel supply chain members under the regulation of the cap-and-trade policy and analyzed the impact of the decision on carbon emissions. Li et al. [20] studied the optimal emission reduction decision and product strategy of enterprises under the cap-and-trade system considering low-carbon consumers. Mondal et al. [21] considered a supply chain consisting of two competitive retailers and a manufacturer, and studied the optimal pricing decision of the supply chain under the cap-and-trade policy. Zou et al. [22] studied the impact of the emission reduction cost coefficient and green cost coefficient on the profits of manufacturers and retailers when the government implements carbon tax and carbon trading policies. These studies have laid the foundation for the analysis of the optimal decision in this paper. Through reviewing the above literature, we found that when analyzing the optimal decision under the cap-and-trade policy, the researchers tended to take the maximization of profit of all parties or the total profit of the supply chain as the criterion for decision-making, but this did not involve the maximization of the comprehensive benefits. Different from previous studies, we considered that production enterprises aim to maximize the comprehensive benefits of the environment and economy when exploring a low-carbon strategy.

2.2. Carbon Reduction Strategy under the Cap-and-Trade System

With the deepening of the research on the cap-and-trade policy, researchers found that the dynamic carbon quota policy can effectively promote carbon emission reduction, and the investment strategy of carbon reduction technology under the cap-and-trade policy has gradually become a research hotspot. Liu et al. [23] studied the influence of consumers’ low-carbon preference and manufacturers’ emission reduction levels on decision-making and profits under cap-and-trade regulations. Lu et al. [24] discussed the potential competition and cooperation in the sustainable product inventory model co-invested by carbon emission reduction technologies under cap-and-trade and carbon offset policies. Vakili et al. [25] developed an energy management framework to improve energy efficiency and reduce energy consumption in the shipbuilding industry. Yang et al. [26] studied the joint emission reduction strategy choice of manufacturers and retailers under the cap-and-trade policy considering consumer environmental preferences. Cong et al. [27] considered uncertain returns and studied the optimal strategy of carbon emission reduction investment in a low-carbon supply chain under capital constraints. Chen et al. [28] developed a model to analyze the impact of cap-and-trade schemes on companies’ decisions to invest in renewable energy based on three cap-and-trade schemes. Da et al. [29] studied the strategy of investing in clean coal technology and carbon emission reduction technology under the leadership of coal companies and manufacturers, respectively. Through reviewing the above literature, we found that research on enterprises’ low-carbon strategies under the cap-and-trade policy studied enterprises’ investment behavior and strategy of emission reduction technology, but most of the literature only considered selling carbon emission rights, while few studies considered the case of purchasing when the carbon quota is insufficient. Different from previous studies, we took into account the strategy wherein enterprises can buy or sell carbon emission rights and considered the shortage of purchasable carbon emission permits when analyzing the investment strategy of enterprise emission reduction.

2.3. Corporate Environmental Responsibility (CER)

Producing enterprises are the main users of ecological resources and the main producers of environmental pollution [30]. With the gradual exposure of environmental problems, the public’s awareness of environmental protection is continually awakening, and many enterprises are beginning to pursue sustainable development and shift the focus of corporate social responsibility to environmental protection, namely corporate environmental responsibility (CER) [11]. Some researchers have studied the relevant factors affecting CER and the impact of CER on corporate performance. Tsendsuren et al. [31] investigated the impact of product market competition on CER and corporate performance. Chen et al. [32] investigated the influence of ownership concentration on CER participation from two dimensions, which are time and space. Zeng et al. [33] discussed the impact of CER on green investment efficiency and found that the level of concern about CER has a positive impact on investment efficiency, and CER is conducive to the sustainable development of enterprises. Peng et al. [34] suggested that enterprises should consider introducing advanced environmental protection technologies to save resources, diminish energy, and reduce pollution. Xia et al. [35] studied the influence of the menu of contracts on the profits of manufacturers and the performance of retailers’ environmental responsibility under the condition of information asymmetry. Through the above literature, we found that the current research on CER consists of mainly empirical analyses, and only literature [35] used the mathematical model method to study the CER fulfillment of the retailer under the cap-and-trade policy. However, the literature did not study the influence of CER on the strategic choice of carbon emission reduction investment and carbon trading by manufacturers. Different from previous studies, we used the mathematical model method to study the impact of CER on enterprise low-carbon strategy selection based on carbon trading and carbon emission reduction technology investment.

This paper makes the following contributions.

First, this study takes the maximization of the comprehensive benefits of the economy and environment as the decision-making criterion when analyzing the optimal low-carbon strategy of enterprises. Taking into account both economic and environmental benefits is more conducive to the sustainable development of an economic society.

Second, this work comprehensively considers the two strategies of carbon trading and carbon emission reduction technology investment, as well as the shortage of purchasable carbon emission permits, to study the low-carbon strategic choice of enterprises under the regulation of the cap-and-trade policy. It provides a theoretical reference for the low-carbon transformation of manufacturing enterprises.

Third, the current research method of CER effects is mainly empirical analysis, and the influence of CER on the strategic choice of carbon trading and carbon reduction technology investment has not been studied. Therefore, using the mathematical model method to study the impact of CER on enterprises’ low-carbon strategy can enrich the relevant research.

3. Problem Description and Basic Assumptions

3.1. Problem Description

This paper considers a carbon-dependent production enterprise. The carbon emissions in the production process of enterprises are restricted by initial carbon quotas; the production enterprise can invest in carbon reduction technology or trade carbon emission rights, and the enterprise could discontinue the production if necessary. Under the regulations of the cap-and-trade policy, the producing enterprise will face two situations: the initial carbon quotas are sufficient or the initial carbon quotas are insufficient.

When the manufacturer does not adopt any strategy, the initial carbon quota can meet the optimal production quantity of the manufacturer, and we assume that the initial carbon quotas are sufficient in this case, so that the manufacturing enterprise does not need to buy additional carbon emissions rights. Since the remaining carbon emissions rights can be sold, the producing enterprise will consider adopting carbon emission reduction technologies to improve economic returns. At this point, the producing enterprise has two choices: choice 1 (take no action) and choice 2 (invest in carbon reduction technology, hereinafter called “Invest”).

When the manufacturer does not adopt any strategy, the initial carbon quota cannot meet the expected production of the manufacturer, and we assume that the initial carbon quotas are insufficient in this case. The producing enterprise has five choices: choice 1 (take no action), choice 2 (Invest), choice 3 (trade carbon emission rights, hereinafter called “Trade”), choice 4 (invest in carbon reduction technology and trade carbon emission rights, hereinafter called “Invest and Trade”), choice 5 (discontinue the production, hereinafter called “Discontinue”). Among these, choice 2, choice 3, and choice 4 will face two scenarios, respectively. The specific situation is described in Figure 1 and Figure 2.

In addition, the manufacturing enterprise also has to undertake CER. In this paper, CER is described as the concern of the manufacturing enterprise for the total carbon emission reduction after investing in carbon reduction technology.

The relevant parameters and symbolic variables are illustrated in

Table 1. Symbolic explanation.

Symbol	Description
$a$	$\mathrm{Market} \mathrm{size}, a>0$
$p$	$\mathrm{Product} \mathrm{price}, p>0$
$c$	$\mathrm{The} \mathrm{marginal} \mathrm{cost} \mathrm{of} \mathrm{production}, c>0$
$q$	$\mathrm{Production} \mathrm{quantity}, q=a-bp$
$e$	$\mathrm{Marginal} \mathrm{carbon} \mathrm{emissions} \mathrm{of} \mathrm{products}, e>0$
$\lambda$	$\mathrm{Carbon} \mathrm{emission} \mathrm{reduction} \mathrm{rate} \mathrm{per} \mathrm{unit} \mathrm{product}, 0\le \lambda <1$
$E$	The free initial carbon quotas
$p_e$	$\mathrm{Price} \mathrm{per} \mathrm{unit} \mathrm{of} \mathrm{carbon} \mathrm{emission} \mathrm{permit}, p_e>0$
$k$	$\mathrm{Carbon} \mathrm{reduction} \cos \mathrm{t} \mathrm{coefficient}, k>0$
$\beta$	$\mathrm{CER} \mathrm{coefficient}, 0\le \beta \le 1$
$u_M$	The comprehensive benefit of the producing enterprise
${\pi }_M$	Economic benefits of the producing enterprise

.

3.2. Basic Assumptions

Considering the practical significance of the model, this paper makes the following assumptions:

(1)

The producing enterprise considers both economic and environmental benefits in the production process, to achieve the maximum comprehensive benefit. The enterprise’s comprehensive benefit function is $u_M=\left(1-\beta \right){\pi }_M+\beta \lambda eq$.

(2)

The cost of carbon emission reduction is a one-time input, in line with the law of the diminishing marginal effect: with the gradual increase in carbon emission reduction investment, carbon emission reduction per unit investment decreases. The investment cost of carbon reduction technology is $C\left(\lambda \right)=\frac{1}{2}k{\lambda }^2$ [32].

(3)

Considering that it is very difficult to achieve almost zero carbon emissions in real life, and it also requires huge carbon reduction costs, we assume that when the producing enterprise adopts carbon reduction technology, $\underset{\lambda \to 1}{\lim }{u}_M\left(\lambda \right)\to -\infty$.

(4)

The manufacturer produces the products according to the order quantity, which means that the manufacturer can exactly produce the products to meet the market demand, and there is no inventory.

(5)

Under the cap-and-trade policy, the government’s quota allocation method is free allocation, which means that the total amount of carbon emissions is determined based on the carbon reduction target, and then the carbon quota is allocated to enterprises for free.

4. Optimal Strategy of the Producing Enterprise under Different Scenarios

4.1. The Initial Carbon Quotas Are Sufficient

Choice 1:

When adopting this strategy, the total carbon emissions of the enterprise are lower than the initial carbon quotas, and the enterprise can sell the remaining carbon emission rights. The production quantity of the enterprise is $q^N$ and the product price is $p^N$, so the expected comprehensive benefit of the producing enterprise is

$$\underset{q^N}{\max }{u}_M^N=(1-\beta ){\pi }_M^N=(1-\beta )((p^N-c)q^N+(E-e{q}^N)p_e)$$

(1)

Theorem 1.

When the initial carbon quotas are sufficient, if the enterprise does not invest in carbon reduction technology, there is a unique optimal production quantity $q^{N*}$, which maximizes the comprehensive benefit of the enterprise.

Proof of Theorem 1.

Due to $\frac{{\partial }^2{u}_M^N}{\partial q^N{}^{{}^2}}=-\frac{2(1-\beta )}{b}<0$, there is a maximum value of the comprehensive benefit of the producing enterprise. By solving the first-order condition $\frac{\partial u_M^N}{\partial q^N}=0$, the optimal production quantity $q^{N*}$

$$q^{N*}=\frac{a-b(c+e{p}_e)}{2}$$

(2)

The comprehensive benefit of the producing enterprise is

$$u_M^{N*}=(1-\beta )\left(\frac{{(a-bc-be{p}_e)}^2}{4b}+E{p}_e\right)$$

(3)

□

Choice 2:

After investing in carbon reduction technology, the carbon quotas are still sufficient. The manufacturing enterprise can sell the remaining carbon emission rights, and it also needs to pay low-carbon investment costs. The carbon reduction rate is ${\lambda }^Y$, the production quantity of the enterprise is $q^Y$, and the product price is $p^Y$. Since the carbon quotas of the producing enterprise are still sufficient after adopting the carbon emission reduction technology, ${\lambda }^Y\in \left[1-\frac{E}{e{q}^Y},1\right)$. The expected comprehensive benefit of the producing enterprise is

$$\begin{array}{l}\underset{q^Y,{\lambda }^Y}{\max }{u}_M^Y=(1-\beta )((p^Y-c)q^Y-\frac{1}{2}k{\lambda }^Y{}^{{}^2}+(E-e(1-{\lambda }^Y)q^Y)p_e)+\beta {\lambda }^{Y}e{q}^Y\\ \mathrm{s}.\mathrm{t}. e(1-{\lambda }^Y)q^Y\le E\end{array}$$

(4)

Theorem 2.

When the initial carbon quotas are sufficient and meet $e(1-{\lambda }^Y)q^Y\le E$, if the enterprise invests in carbon reduction technology, there exists the optimal production quantity $q^{Y*}$ and the optimal carbon reduction rate ${\lambda }^{Y*}$, which maximizes the comprehensive benefit of the enterprise.

Proof of Theorem 2.

The Lagrange function is

$$\mathrm{L}(q^Y,{\lambda }^Y,\mu )=-u_M^Y(q^Y,{\lambda }^Y)+\mu (e(1-{\lambda }^Y)q^Y-E)$$

(5)

The optimal solution of the above problems should meet the following KKT conditions:

$$\left\{\begin{array}{l}\frac{\partial \mathrm{L}(q^Y,{\lambda }^Y,\mu )}{\partial q^Y}=-(1-\beta )\left(\frac{a-2q^Y}{b}-c-e{p}_e(1-{\lambda }^Y)\right)-\beta e{\lambda }^Y+\mu e(1-{\lambda }^Y)=0\\ \frac{\partial \mathrm{L}(q^Y,{\lambda }^Y,\mu )}{\partial {\lambda }^Y}=-(1-\beta )(e{q}^Y{p}_e-k{\lambda }^Y)-\beta e{q}^Y-\mu e{q}^Y=0\\ \mu (e(1-{\lambda }^Y)q^Y-E)=0\\ \mu \ge 0\end{array}\right.$$

(6)

(a). When $\mu =0$, the optimal production quantity and optimal carbon emission reduction rate are

$$q^{Y*}=\frac{k{\left(1-\beta \right)}^2\left(a-bc-be{p}_e\right)}{{\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)}$$

(7)

$${\lambda }^{Y*}=\frac{\left(1-\beta \right)\left(\beta e+e{p}_e-\beta e{p}_e\right)\left(a-c-e{p}_e\right)}{{\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)}$$

(8)

According to Equations (7) and (8), it can be concluded that the comprehensive benefit of the producing enterprise is

$$u_M^{Y*}=(\beta -1)\left(\begin{array}{l}\frac{J_2{J}_3(J_1(bc-a)+J_2{J}_3)}{b{J}_1^2}-p_{e}E+\frac{k{(\beta -1)}^2{J}_4^2{J}_2^2}{2J_1^2}\\ -\frac{p_{e}e{J}_2{J}_3(J_1+J_2{J}_4(\beta -1))-\beta e(\beta -1)J_2{}^2{J}_3{J}_4}{J_1^2}\end{array}\right)$$

(9)

where

$$\begin{array}{l}{J}_1={\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)\\ J_2=bc-a+be{p}_e\\ J_3=k{\left(1-\beta \right)}^2\\ J_4=\beta e+e{p}_e-\beta e{p}_e\end{array}$$

(b). When $\mu >0$, $e\left(1-{\lambda }^Y\right)q^Y-E=0$, the carbon quotas can precisely meet the carbon emission demand of the producing enterprise. Because the comprehensive benefit function of the producing enterprise can be derived in the range of real numbers, i.e., it is a continuous function in the range of real numbers, this unit point does not need to be computed separately. □

4.2. The Initial Carbon Quotas Are Insufficient

Choice 1:

When the initial carbon quotas are insufficient, the production enterprise neither invests in carbon emission reduction technology nor purchases carbon emission rights. The production quantity of the enterprise is $q^{NN}$ and the product price is $p^{NN}$, and the expected comprehensive benefit of the producing enterprise is

$$\underset{q^{NN}}{\max }{u}_M^{NN}=\left(1-\beta \right)\left(p^{NN}-c\right)q^{NN}$$

(10)

The optimal production quantity is

$$q^{NN*}=\frac{E}{e}$$

(11)

The comprehensive benefit of the producing enterprise is

$$u_M^{NN}=\frac{\left(1-\beta \right)\left(Ee\left(a-bc\right)-E^2\right)}{b{e}^2}$$

(12)

Choice 2 Scenario 1:

When the initial carbon quotas are insufficient, the production enterprise purchases the carbon emission rights, and the purchasable carbon emission rights in the carbon market are sufficient. The production quantity of the enterprise is $q^{YN1}$ and the product price is $p^{YN1}$, and the expected comprehensive benefit of the manufacturing enterprise is

$$\underset{q^{YN1}}{\max }{\pi }_M^{YN1}=\left(1-\beta \right)\left(\left(p^{YN1}-c\right)q^{YN1}-\left(e{q}^{YN1}-E\right)p_e\right)$$

(13)

Theorem 3.

When the initial carbon quotas are insufficient and the carbon emission right in the carbon trading market can meet the purchase demand of the enterprise, the enterprise has the optimal production quantity $q^{YN1*}$, which maximizes the comprehensive benefit of the enterprise.

Proof of Theorem 3.

Due to $\frac{{\partial }^2{u}_M^{YN1}}{\partial q^{YN1}{}^{{}^2}}=-2\left(1-\beta \right)<0$, the expected comprehensive benefit of the producing enterprise has a maximum value. By solving the first-order condition $\frac{\partial u_M^{YN1}}{\partial q^{YN1}}=0$, the optimal production quantity $q^{YN1*}$ is

$$q^{YN1*}=\frac{a-b\left(c+e{p}_e\right)}{2}$$

(14)

The comprehensive benefit of the producing enterprise is

$$u_M^{YN1*}=\left(1-\beta \right)\left(\frac{{\left(a-bc-be{p}_e\right)}^2}{4b}+E{p}_e\right)$$

(15)

□

Choice 2 Scenario 2:

When the initial carbon quotas are insufficient, the production enterprise purchases the carbon emission rights, and the purchasable carbon emission rights in the carbon market are not sufficient. The producing enterprise can only purchase the carbon emission rights of quantity $E_0$, the production quantity is $q^{YN2}$, and the product price is $p^{YN2}$, so the expected comprehensive benefit of the producing enterprise is

$$\underset{q^{YN2}}{\max }{u}_M^{YN2}=\left(1-\beta \right)\left(\left(p^{YN2}-c\right)q^{YN2}-E_0{p}_e\right)$$

(16)

The optimal production quantity of the producing enterprise is

$$q^{YN2*}=\frac{E+E_0}{e}$$

(17)

The comprehensive benefit of the producing enterprise is

$$u_M^{YN2*}=\left(1-\beta \right)\left(\frac{\left(E+E_0\right)e\left(a-bc\right)-{\left(E+E_0\right)}^2}{b{e}^2}-E_0{p}_e\right)$$

(18)

Choice 3 Scenario 1:

When the initial carbon quotas are insufficient, the production enterprise invests in carbon reduction technology; after investing in carbon emission reduction technology, the carbon quotas become sufficient. The producing enterprise can sell the remaining carbon emission rights and should pay the carbon emission reduction investment cost. The carbon emission reduction rate is ${\lambda }^{NY1}$, the production quantity of the enterprise is $q^{NY1}$, and the product price is $p^{NY1}$. Since the carbon quotas become sufficient after the producing enterprise adopts the carbon emission reduction technology, ${\lambda }^{NY1}\in \left[1-\frac{E}{e{q}^{NY1}},1\right)$. The expected comprehensive benefit of the producing enterprise is

$$\begin{array}{l}\underset{q^{NY1},{\lambda }^{NY1}}{\max }{u}_M^{NY1}=(1-\beta )((p^{NY1}-c)q^{NY1}-\frac{1}{2}k{\lambda }^{NY1}{}^{{}^2}+(E-e(1-{\lambda }^{NY1})q^{NY1})p_e)\\ \hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}+\beta {\lambda }^{NY1}e{q}^{NY1}\\ \mathrm{s}.\mathrm{t}. e(1-{\lambda }^{NY1})q^{NY1}\le E\end{array}$$

(19)

Theorem 4.

When the initial carbon quotas are insufficient and meet $e(1-{\lambda }^{NY1})q^{NY1}\le E$, if the enterprise invests in carbon reduction technology, there exist the optimal production quantity $q^{NY1}$ and the optimal carbon emission reduction rate ${\lambda }^{NY1}$, which maximizes the comprehensive benefit of the enterprise.

Proof of Theorem 4.

The Lagrange function is

$$\mathrm{L}(q^{NY1},{\lambda }^{NY1},\mu )=-u_M^{NY1}(q^{NY1},{\lambda }^{NY1})+\mu (e(1-{\lambda }^{NY1})q^{NY1}-E)$$

(20)

The optimal solution of the above problems should meet the following KKT conditions:

$$\left\{\begin{array}{l}\frac{\partial \mathrm{L}(q^{NY1},{\lambda }^{NY1},\mu )}{\partial q^{NY1}}=-(1-\beta )(\frac{a-2q^{NY1}}{b}-c-e{p}_e(1-{\lambda }^{NY1}))-\beta e{\lambda }^{NY1}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +\mu e(1-{\lambda }^{NY1})=0\\ \frac{\partial \mathrm{L}(q^{NY1},{\lambda }^{NY1},\mu )}{\partial {\lambda }^{NY1}}=-(1-\beta )(e{q}^{NY1}{p}_e-k{\lambda }^{NY1})-\beta e{q}^{NY1}-\mu e{q}^{NY1}=0\\ \mu (e(1-{\lambda }^{NY1})q^{NY1}-E)=0\\ \mu \ge 0\end{array}\right.$$

(21)

It can be obtained from the above formula.

(a). When $\mu =0$, the optimal production quantity and optimal carbon emission reduction rate are

$$q^{NY1*}=\frac{k{\left(1-\beta \right)}^2\left(a-bc-be{p}_e\right)}{{\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)}$$

(22)

$${\lambda }^{NY1*}=\frac{\left(1-\beta \right)\left(\beta e+e{p}_e-\beta e{p}_e\right)\left(a-c-e{p}_e\right)}{{\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)}$$

(23)

According to Equations (22) and (23), it can be concluded that the comprehensive benefit of the manufacturing enterprise is

$$u_M^{NY1*}=(\beta -1)\left(\begin{array}{l}\frac{J_2{J}_3(J_1(bc-a)+J_2{J}_3)}{b{J}_1^2}-p_{e}E+\frac{k{(\beta -1)}^2{J}_4^2{J}_2^2}{2J_1^2}\\ -\frac{p_{e}e{J}_2{J}_3(J_1+J_2{J}_4(\beta -1))-\beta e(\beta -1)J_2{}^2{J}_3{J}_4}{J_1^2}\end{array}\right)$$

(24)

where

$$\begin{array}{l}{J}_1={\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)\\ J_2=bc-a+be{p}_e\\ J_3=k{\left(1-\beta \right)}^2\\ J_4=\beta e+e{p}_e-\beta e{p}_e\end{array}$$

(b). When $\mu >0$, $e\left(1-{\lambda }^{NY1}\right)q^{NY1}-E=0$, the carbon quotas can precisely meet the carbon emission demand of the producing enterprise. Because the comprehensive benefit function of the producing enterprise can be derived in the range of real numbers, i.e., it is a continuous function in the range of real numbers, this unit point does not need to be computed separately. □

Choice 3 Scenario 2:

When the initial carbon quotas are insufficient, the production enterprise invests in carbon reduction technology; after investing in carbon emission reduction technology, the carbon quotas are still insufficient. The carbon emission reduction rate is ${\lambda }^{NY2}$, the production quantity is $q^{NY2}$, and the product price is $p^{NY2}$. The optimal production quantity of the producing enterprise is

$$q^{NY2*}=\frac{E}{e\left(1-{\lambda }^{NY2}\right)}$$

(25)

The expected comprehensive benefit of the producing enterprise is

$$\underset{{\lambda }^{NY2}}{\max }{u}_M^{NY2}=\left(1-\beta \right)\left(\left(p^{NY2*}-c\right)q^{NY2*}-\frac{1}{2}k{\lambda }^{NY2}{}^{{}^2}\right)+\beta {\lambda }^{NY2}e{q}^{NY2*}$$

(26)

Substituting Equation (25) into Equation (26), the expected comprehensive benefit of the producing enterprise is

$$\begin{array}{l}\underset{{\lambda }^{NY2}}{\max }{u}_M^{NY2}=\left(1-\beta \right)\left(\left(\frac{ae\left(1-{\lambda }^{NY2}\right)-E}{be\left(1-{\lambda }^{NY2}\right)}-c\right)\frac{E}{e\left(1-{\lambda }^{NY2}\right)}-\frac{1}{2}k{\lambda }^{NY2}{}^{{}^2}\right)\\ +\frac{E\beta {\lambda }^{NY2}}{1-{\lambda }^{NY2}}\end{array}$$

(27)

Since $\underset{{\lambda }^{NY2}\to 1}{\lim }{u}_M^{NY2}\left({\lambda }^{NY2}\right)<0$, and $u_M^{NY2}\left(0\right)>0$, there exists ${\lambda }_i^{NY2}\in \left[0,1\right)\left(i\in N^{+}\right)$, which makes $u_M^{NY2}\left({\lambda }^{NY2}\right)=0$. When the comprehensive benefit of the producing enterprise is negative, the producing enterprise will no longer invest in carbon reduction technology. Let $M=\underset{i\in N^{+}}{\max }{\lambda }_i^{NY2}$, according to the extremum theorem, the optimal carbon emission reduction rate ${\lambda }^{NY2*}=\arg \underset{{\lambda }^{NY2}}{\max }{u}_M^{NY2}\left({\lambda }^{NY2}\right)$, where ${\lambda }^{NY2*}\in \left[0,M\right]$.

Choice 4 Scenario 1:

When the initial carbon quotas are insufficient, the production enterprise invests in carbon reduction technology and purchases carbon emission rights; after adopting this strategy, the carbon quotas become sufficient. The carbon emission reduction rate is ${\lambda }^{YY1}$, the production quantity is $q^{YY1}$, and the product price is $p^{YY1}$. Since the carbon quotas are still insufficient after the producing enterprise adopts the carbon emission reduction technology, it needs to purchase additional carbon quotas, so ${\lambda }^{YY1}\in \left[0,1-\frac{E}{e{q}^{YY1}}\right)$. The expected comprehensive benefit of the producing enterprise is

$$\begin{array}{l}\underset{q^{YY1},{\lambda }^{YY1}}{\max }{u}_M^{YY1}=(1-\beta )((p^{YY1}-c)q^{YY1}-\frac{1}{2}k{\lambda }^{YY1}{}^{{}^2}-(e(1-{\lambda }^{YY1})q^{YY1}-E)p_e)\\ +\beta {\lambda }^{YY1}e{q}^{YY1}\\ \mathrm{s}.\mathrm{t}. e(1-{\lambda }^{YY1})q^{YY1}>E\end{array}$$

(28)

Theorem 5.

When the initial carbon quotas are insufficient and meet $e(1-{\lambda }^{YY1})q^{YY1}>E$, if the enterprise both purchases the carbon emission right and invests in carbon reduction technology, there exists the optimal production quantity $q^{YY1}$ and the optimal carbon emission reduction rate ${\lambda }^{YY1}$, which maximizes the comprehensive benefit of the enterprise.

Proof of Theorem 5.

The Lagrange function is

$$\mathrm{L}(q^{YY1},{\lambda }^{YY1},\mu )=-u_M^{YY1}(q^{YY1},{\lambda }^{YY1})+\mu (e(1-{\lambda }^{YY1})q^{YY1}-E)$$

(29)

The optimal solution of the above problems should meet the following KKT conditions:

$$\left\{\begin{array}{l}\frac{\partial \mathrm{L}(q^{YY1},{\lambda }^{YY1},\mu )}{\partial q^{YY1}}=-(1-\beta )\left(\frac{a-2q^{YY1}}{b}-c-e{p}_e(1-{\lambda }^{YY1})\right)-\beta e{\lambda }^{YY1}\\ +\mu e(1-{\lambda }^{YY1})=0\\ \frac{\partial \mathrm{L}(q^{YY1},{\lambda }^{YY1},\mu )}{\partial {\lambda }^{YY1}}=-(1-\beta )(e{q}^{YY1}{p}_e-k{\lambda }^{YY1})-\beta e{q}^{YY1}-\mu e{q}^{YY1}=0\\ \mu (e(1-{\lambda }^{YY1})q^{YY1}-E)=0\\ \mu \ge 0\end{array}\right.$$

(30)

From the above equation, there must be $\mu =0$, and the solution is

$$q^{YY1*}=\frac{k{\left(1-\beta \right)}^2\left(a-bc-be{p}_e\right)}{{\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)}$$

(31)

$${\lambda }^{YY1*}=\frac{\left(1-\beta \right)\left(\beta e+e{p}_e-\beta e{p}_e\right)\left(a-c-e{p}_e\right)}{{\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)}$$

(32)

Substitute Equations (31) and (32) into the comprehensive benefit function of the producing enterprise in Equation (28), and we can obtain

$$u_M^{YY1*}=(\beta -1)\left(\begin{array}{l}\frac{J_2{J}_3(J_1(bc-a)+J_2{J}_3)}{b{J}_1^2}-p_{e}E+\frac{k{(\beta -1)}^2{J}_4^2{J}_2^2}{2J_1^2}\\ -\frac{p_{e}e{J}_2{J}_3(J_1+J_2{J}_4(\beta -1))-\beta e(\beta -1)J_2{}^2{J}_3{J}_4}{J_1^2}\end{array}\right)$$

(33)

where

$$\begin{array}{l}{J}_1={\left(1-\beta \right)}^2\left(2k-b{e}^2{p}_e^2\right)+b\beta e^2\left(2\beta p_e-\beta -2p_e\right)\\ J_2=bc-a+be{p}_e\\ J_3=k{\left(1-\beta \right)}^2\\ J_4=\beta e+e{p}_e-\beta e{p}_e\end{array}$$

□

Choice 4 Scenario 2:

When the initial carbon quotas are insufficient, the production enterprise invests in carbon reduction technology and purchases carbon emission rights. Due to a shortage of tradeable carbon permits in the carbon market, after adopting this strategy, the carbon quotas are still insufficient. The producer can only buy a quantity $E_0$ of carbon emission rights, the carbon emission reduction rate is ${\lambda }^{YY2}$, the production quantity of the enterprise is $q^{YY2}$, and the product price is $p^{YY2}$. We can easily find that the optimal production quantity of the manufacturing enterprise is

$$q^{YY2*}=\frac{E+E_0}{e\left(1-{\lambda }^{YY2*}\right)}$$

(34)

The expected comprehensive benefit of the manufacturing enterprise is

$$\underset{q^{YY2},{\lambda }^{YY2}}{\max }{u}_M^{YY2}=\left(1-\beta \right)\left(\left(p^{YY2}-c\right)q^{YY2}-\frac{1}{2}k{\lambda }^{YY{2}^2}-E_0{p}_e\right)+\beta {\lambda }^{YY2}e{q}^{YY2*}$$

(35)

In the same way as Choice 4 Scenario 1, it can be concluded from the extremum theorem that there must be an optimal carbon emission reduction rate ${\lambda }^{YY2*}$, which maximizes the comprehensive benefit of the manufacturing enterprise.

Choice 5:

When the carbon quota is insufficient, the company stops the production of the product. The production quantity of the product is 0. Companies can sell all the carbon quotas allocated by the government, and the profit is $E{p}_e$. If the enterprise does not stop production, the production quantity is

$$q^D=\frac{E}{e}$$

(36)

Therefore, the total carbon emission reduction of the enterprise is $e{q}^D$. We can directly conclude that the comprehensive benefit of the manufacturing enterprise is

$$u_M^D=(1-\beta )E{p}_e+\beta e{q}^D$$

(37)

Because the calculation of the influences of the initial carbon quotas and CER coefficient on the comprehensive benefits, emission reduction rate, and production quantity is complicated, the explicit solution cannot be obtained directly, so we analyze it through numerical simulation.

5. Analysis of Carbon Reduction Strategy of Producing Enterprise

In this section, we perform a numerical simulation for the model, in which the problem parameters are obtained from a petrochemical company in China that trades carbon emission rights and invests in carbon reduction technology under the regulation of the cap-and-trade policy. China’s current quota allocation method for this enterprise is to use the industry benchmark method for free quota allocation.

The “carbon peaking and carbon neutrality” goals pose significant challenges to the development of the global energy and petrochemical companies, and the COVID-19 pandemic has adversely affected the progress of clean energy transformation. Traditional petrochemical industries are facing unprecedented pressure for transformation and upgrading [36,37]. The green transformation of economic development requires the petrochemical industries to eliminate the dependence on high consumption, high emissions, and environmental damage; the petrochemical industries are actively promoting the development of safety, environmental protection, and green and low-carbon production. Therefore, we analyze our model using the case of a petrochemical enterprise. The company has joined China’s carbon trading market, where it can sell or buy carbon emission rights. Moreover, the enterprise actively invests in carbon emission reduction technologies, such as photovoltaic power generation and green hydrogen manufacturing technology to coordinate structural optimization and carbon emission control. The following results are based on an analysis using one of the petroleum products produced by this enterprise.

Here, we explore the optimal strategy of the producing enterprise under different carbon quotas and study the influence of carbon quotas and the CER coefficient on the producing enterprise’s comprehensive benefit, optimal emission reduction rate, and production capacity. We assume that $e=2$, $p_e=5$, $b=1$, $c=40$, $a=100$, $k=1500$, $E_0=20$. These parameter values all meet the research hypothesis mentioned above.

5.1. The Influence of CER Coefficient

We try to analyze the influence of the CER coefficient on the comprehensive benefit and optimal carbon emission reduction rate in this subsection. According to the previous analysis, when the initial carbon quota is $e{q}^{N*}$, it is exactly sufficient for the enterprise. Therefore, we value $E=(10,60)$ to represent the two cases of an insufficient carbon quota and a sufficient carbon quota, respectively.

Figure 3 demonstrates the impacts of the CER coefficient on comprehensive benefits under different strategies in the cases of an insufficient carbon quota and a sufficient carbon quota. As shown in Figure 3a, with the gradual increase in the CER coefficient, the comprehensive benefits of the five strategies all decline, among which the comprehensive benefits of the “Trade and Invest” strategy decline the most, and those of the “Discontinue” strategy decline the least. This shows that CER has the greatest negative impact on the comprehensive benefits under the “Trade and Invest” strategy, but this strategy is always the optimal strategy for manufacturers. This is because relying on investment in carbon emission reduction technologies to reduce carbon emissions requires high emission reduction costs, while purchasing carbon emission rights at the same time as emission reduction can relieve the pressure of emission reduction and improve the comprehensive benefit of the enterprise. The comprehensive benefits under the “Discontinue” strategy are always the lowest, indicating that it is not an effective strategy for enterprises to give up the economic benefits of the product and stop production. It is worth noting that when the CER is 0.8, the comprehensive benefits of the enterprise under the strategies of “Trade” and “Invest” are equal, and the two strategies have the same effect. As shown in Figure 3b, when the initial carbon quotas are sufficient, with the gradual increase in the CER coefficient, the decrease in comprehensive benefits under the two strategies is the same, but the strategy of “Invest” is always the optimal strategy for the enterprise, indicating that the cap-and-trade policy can indeed encourage the enterprise to reduce its carbon emissions.

Figure 4 demonstrates the impacts of the CER coefficient on the optimal carbon reduction rates under different strategies in the cases of an insufficient carbon quota and a sufficient carbon quota. We can see that the optimal carbon emission reduction rates under different strategies are positively correlated with the CER coefficient; this shows that the enterprise bearing CER can improve the carbon emission reduction rate, so as to reduce the carbon emissions in production, which is of great significance to the sustainable and low-carbon development of the industry.

As shown in Figure 4a, the optimal carbon emission reduction rate is always the highest when the enterprise only invests in carbon emission reduction technology. Combining this with Figure 4b, we find that with the increase in the CER coefficient, the carbon emission reduction rate increases the most in the case of a sufficient carbon quota, because, in this case, selling carbon emission rights can obtain additional economic benefits, and enterprises will actively reduce their carbon emissions under the joint promotion of CER and carbon trading policies.

5.2. The Influence of the Initial Carbon Quotas

Based on the above research, we try to further explore the influence of the initial carbon quotas on the optimal decisions of enterprises. We value $\beta =(0.1,0.9)$ to represent the two cases of low CER enterprise and high CER enterprise.

Figure 5 demonstrates the impacts of the initial carbon quotas on the strategies of the production enterprise under different CER coefficients. As shown in Figure 5a, the comprehensive benefits of the five strategies are positively correlated with the initial carbon quota, and the initial carbon quota has the most significant impact on the comprehensive benefits under the “Take no action” strategy. In this case, companies do not need to consider additional expenditures such as purchasing carbon emission rights or investing in carbon reduction technologies; the increase in carbon quotas has only positive effects, so the impact is most significant. If $E_1^L<E\le E_2^L$, the strategy of “Trade and Invest” does not exist; if $E>E_2^L$, the production enterprise only needs to consider whether to invest in carbon reduction technology, where $E_1^L=e\left(1-{\lambda }^{NY1*}\right)q^{NY1*}$, $E_2^L=e{q}^{N*}$. Similar conclusions can be drawn from Figure 5b.

With Figure 5a,b, we can conclude that when the initial carbon quotas are insufficient, the optimal strategy is “Trade and Invest”, and when the initial carbon quotas are sufficient, the optimal strategy is “Invest”. This occurs because the purchase of carbon emission permits can alleviate the production pressure brought by the quota policy. When the carbon quota can meet the production demand, enterprises can obtain additional economic benefits by selling carbon emission rights. At this time, CER and carbon trading policies will motivate enterprises to continue to reduce their emissions. The manufacturing enterprise with low CER is more dependent on purchasing carbon emission rights, while the manufacturing enterprise with high CER is more inclined to invest in carbon reduction technology. The producing enterprise with low CER pays more attention to the improvement of economic benefits; only when the initial carbon quotas are high ($E>E^{L*}$) and the cost of carbon reduction is very low, the producing enterprise will consider investing in carbon reduction technology. The producing enterprise with high CER pays more attention to the improvement of environmental benefits, because the higher emission reduction cost can be offset by the environmental benefits brought by carbon emission reduction and the economic benefits brought by expanding production. In this case, using carbon reduction technology will achieve a higher comprehensive benefit.

Figure 6 compares and analyzes the impact of the initial carbon quotas on the optimal carbon reduction rates under the strategies of “Trade and Invest” and “Invest”. It shows that the optimal carbon reduction rates firstly decrease and then remain constant as the initial carbon quotas increase under the strategy of “Trade and Invest”; the optimal carbon reduction rates firstly increase rapidly, then decrease, and finally remain constant as the initial carbon quotas increase under the strategy of “Invest”. In addition, the CER coefficient is positively correlated with the optimal carbon reduction rate, and with the increase in the initial carbon quotas, the optimal carbon emission reduction rate of the production enterprise with high CER remains unchanged earlier; this means that a high CER manufacturer will be the first to reach the optimal production quantity.

When the initial carbon quotas are seriously insufficient and the production enterprise only invests in carbon reduction technology, the negative effects of the increased cost of carbon reduction investment can be offset by the positive effects (economic and environmental gains) of carbon reduction; the production enterprise has a strong desire to reduce their carbon emissions. As the carbon quota gradually increases, the investment cost of carbon emission reduction technology becomes expensive, the negative effects outweigh the positive effects, and the production enterprise will gradually reduce the input of carbon emission reduction technology to reduce the investment cost until the optimal production quantity is achieved. If the production enterprise not only invests in carbon reduction technology but also buys additional carbon permits, there is both the investment cost of carbon reduction technology and the cost of purchasing carbon emission rights; the negative effects always outweigh the positive effects, and with the increase in the initial carbon quotas, the production enterprise will gradually reduce the input of carbon emission reduction technology until the optimal production quantity is achieved.

5.3. Changes in Production Quantity

This subsection illustrates how the initial carbon quotas and CER coefficient influence the production quantity of the enterprise.

Figure 7a depicts that under the strategy of “Trade and Invest”, the production quantity is positively related to the initial carbon quotas and CER coefficient. Figure 7b depicts that under the strategy of “Invest”, when the initial carbon quotas remain unchanged, the production quantity is positively related to the CER coefficient. When the coefficient of CER remains unchanged, the production quantity of the manufacturing enterprise with low CER does not always increase with the increase in the initial carbon quotas. When the initial carbon quotas are high, the production will first decrease and then continue to increase. Figure 7c depicts that under the strategy of “Trade”, the production quantity of the enterprise has no relation with the CER coefficient; the decision of the enterprise is only related to the initial carbon quotas, and its production quantity will increase with the increase in the initial carbon quotas.

It can be concluded that the higher the CER of the producing enterprise, the smaller the production restriction caused by the initial carbon quotas’ constraints. Because the higher CER can motivate the producing enterprise to reduce their carbon emissions, the high carbon emission reduction rate leads to lower carbon emissions per unit product, so that the production enterprise can produce more products. The strategy of “Trade and Invest” can cause the enterprise to achieve the maximum comprehensive benefit and produced quantity; the strategy of “Invest” can enable the enterprise to achieve a higher produced quantity, but damages the comprehensive benefit of the enterprise.

6. Conclusions

Under the condition of equal supply and demand, we consider a carbon-dependent production enterprise that takes on corporate environmental responsibility (CER). The enterprise trades carbon emission rights or invests in carbon reduction technologies under the regulation of the cap-and-trade system, aiming to maximize the comprehensive benefits of both the economy and the environment. On this basis, we study the strategic choice of the production enterprise to invest in carbon reduction technologies or trade carbon emission rights under the cap-and-trade system.

After analyzing the impacts of the CER coefficient and initial carbon quotas on the comprehensive benefit, optimal carbon emission reduction rate, and production quantity, we obtain novel insights into the low-carbon strategy choices for carbon-dependent producers. Firstly, the optimal carbon emission reduction rate is positively correlated with the CER coefficient, indicating that undertaking CER can promote enterprises to reduce their carbon emissions. However, with the increase in the CER coefficient, the comprehensive benefit of the enterprise gradually decreases, indicating that enterprises undertake CER to reduce carbon emissions at the cost of sacrificing more economic benefits. The government should take appropriate incentive measures to encourage enterprises to assume environmental responsibility. Secondly, when the initial carbon quotas are insufficient, “trade carbon emission rights and invest in carbon reduction technology” is always the optimal strategy for the enterprise; when the initial carbon quotas are sufficient, “invest in carbon reduction technology” is always the optimal strategy for the enterprise. The government’s implementation of a carbon quota policy can motivate the producing enterprise to invest in carbon reduction technology and reduce its carbon emissions, and the carbon emission trading policy can alleviate the production pressure brought by the carbon quota policy on enterprises. The comprehensive benefits of “discontinue the production” and “trade carbon emission rights” are always at a low level, indicating that sustainable development should take into account both the environment and the economy, and should not completely favor either side. Finally, undertaking CER can alleviate the production pressure brought by the carbon quota policy. The production enterprise with high CER achieves their production targets more easily due to their carbon emission reduction efforts and low carbon emissions. The enterprises with low CER rely more on purchasing carbon emission rights, make fewer investments in carbon reduction, and their product production is often limited due to an insufficient carbon quota, which cannot reach the optimal level.

This paper studies the strategy selection of a single manufacturing enterprise under the ideal condition of equal supply and demand, but the actual operation of carbon trading between enterprises will be more complicated. Moreover, we only take the maximization of the comprehensive benefit as the decision-making criterion in the strategic analysis, which may not be applicable to a wider range of enterprises. On this basis, it would be meaningful to further study the multi-criteria low-carbon decision-making problem considering multi-manufacturing enterprises under uncertain environments.