Understanding Low Carbon Sustainable Development Behaviour and Its Complexity
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Shan Yu, Qiang Hou, "Supply Chain Investment in Carbon EmissionReducing Technology Based on Stochasticity and LowCarbon Preferences", Complexity, vol. 2021, Article ID 8881605, 18 pages, 2021. https://doi.org/10.1155/2021/8881605
Supply Chain Investment in Carbon EmissionReducing Technology Based on Stochasticity and LowCarbon Preferences
Abstract
Due to excessive greenhouse gas emissions, carbon emissionreducing measures are urgently needed. Important emissionreduction measures mainly include carbon trading and lowcarbon cost subsidies. Comprehensive consideration of these two policies is a research hotspot in the field of lowcarbon technology investment. Based on this background, this paper considers the impact of consumer lowcarbon preferences on market demand and the impact of uncertainty in carbon emissionreduction behaviour. We construct a stochastic differential game model with upstream and downstream enterprises based on costsharing coordination under a cost subsidy. From a dynamic perspective, this paper researches the optimal equilibrium strategy and evolution characteristics of the joint emissionreduction mechanism in a supply chain. This paper discusses the sensitivity of the parameters and uses numerical simulation to verify the impact of each parameter on the emissionreduction decisionmaking activities of stakeholders after introducing the cost subsidy. The results show that a cost subsidy policy can promote carbon emissionreduction investment and supply chain profit. Thus, it is important to strengthen technical cooperation and exchange among enterprises.
1. Introduction
Lowcarbon economy is an inevitable choice for the sustainable development of global economy. Developing lowcarbon economy is conducive to breaking through the bottleneck constraints of resources and environment in the process of economic development and taking the new road of industrialization; it is conducive to forming a sound policy mechanism and institutional guarantee system to promote sustainable development; it is conducive to promoting industrial upgrading and technological innovation of enterprises and building the future international core competitiveness of enterprises. It provides a rare opportunity to realize the fundamental transformation of the economic mode. Under the current situation, actively developing circular economy and lowcarbon economy is the best choice to achieve sustainable development. It requires us not only to change the traditional highcarbon economic development mode from the adjustment of industrial structure and energy structure but also to seek energysaving ways and promote energysaving technology from all aspects of the industrial chain. As a major developing country and highcarbonemitting country, China is actively exploring various carbon emissionreduction measures. The government actively adjusts the industrial and energy structures from a macroperspective, implements carbon emissions trading, and encourages technological innovation from a microperspective. With the implementation of China’s carbon trading system, the carbon trading market’s demand for carbondependent enterprises has gradually risen. Designing a carbon trading policy that encourages carbondependent enterprises to invest in production and carbon emissionreduction measures has become a focus of social concern. Due to the dynamic and uncertain nature of innovation, carbon emissionreduction behaviour presents high uncertainty. Therefore, it is important to study the influence of the carbon trading system on corporate emission reduction based on the perspective of stochastic differential games.
Under the background of carbon emission trading and cost subsidies, and considering the lowcarbon preferences of consumers and the randomness of the emissionreduction process, this paper uses a stochastic differential game method to analyse the game relationships between the government, manufacturers, retailers, and consumers under costsharing coordination from a dynamic perspective. The equilibrium strategies of government, supply chains, and consumers are obtained, and the evolutionary paths of emission reduction, manufacturer profit, and retailer profit are obtained.
The object of this paper is to (1) calculate an objective function describing carbon emission reduction, manufacturer profit, retailer profit, and costsharing ratio; (2) consider the lowcarbon preferences of consumers and the randomness of the emissionreduction process and study the optimal equilibrium strategies of the government, supply chains, and consumers under cost subsidies and the evolutionary path of carbon emission reduction and supply chain profit; and (3) explore the sensitivity of cost subsidy rates and other stochastic factors to supply chain emission reductions via a numerical experiment.
The theoretical value of this paper lies in its indepth exploration of supply chain enterprise cooperation mechanisms and the design of carbon emissionreduction investment paths. It provides a theoretical basis for decisionmaking by supply chain enterprises operating under environmental regulation. The practical significance of this paper is to analyse the optimal decisionmaking paths of coordinated costsharing decisionmaking under a carbon trading system and cost subsidy policies from a dynamic perspective. This provides theoretical support for technological investment and output decisionmaking by supply chain enterprises.
The structure of this paper is as follows. Section 2 is a literature review. Section 3 describes the problem in terms of the carbon trading system and emissionreduction technological innovation subsidies under uncertain circumstances of carbon emissionreduction behaviour. A stochastic differential game model is then constructed on this basis. Section 4 uses stochastic differential game theory to solve the Stackelberg equilibrium under a feedback strategy. Section 5 uses the stochastic differential Stackelberg game model to predict emissionreduction inputs and the evolution path of variables. Section 6 provides a parameter sensitivity analysis. Section 7 describes the numerical simulation and the final section makes the conclusions.
2. Literature Review
The essence of sustainable development is that supply chain enterprises start from the energy structure and change the traditional mode of highcarbon economy. Swiader evaluated the natural area surface for carbon fiber assimilation and provided management tools and policy tools for the sustainable development of human settlements [1]. Renwick explored the effect of practice in achieving workplace goals of environmental sustainability [2]. Bashir discussed the relationship between environmental taxes and carbon emissions, as well as the role of environmental technology and financial development [3]. Nong put forward suggestions on energy resources, policies, and scientific research to achieve a cleaner and more sustainable economy in Vietnam [4]. Jackson studied the labor, reciprocity, and care logic needed to reduce or sequester carbon through the case of carbon agriculture to reduce carbon emissions [5]. Douglas made a theoretical and conceptual comparative analysis on the policies and measures of coaldependent employment, determined the measures to successfully improve the social and economic wellbeing of coaldependent communities, and put forward the framework to successfully achieve a just transition [6]. Amundson proposed a quantitative risk analysis method of biomass supply chain based on Bayesian belief network (BBN) [7].
The impact of microeconomic policies on enterprises’ carbon emissionreduction investment behaviour began with the research of Benjaafar, who studied the impact of joint emission reductions by supply chain members on operating costs and carbon emissions [8]. Song et al. proposed a carbon footprint calculation model based on discriminant factors [9]. Elhedhli and Merrick found that the optimal allocation of a supply chain can be achieved by adjusting the cost of carbon emissions [10]. Dai and Hu proposed a doubleobjective network optimization model of a lowcarbon closedloop supply chain [11]. Chen et al. constructed a fuzzy programming optimization model to find the lowest total cost [12]. Lou et al. proposed a Stackelberg game emissionreduction investment model with manufacturers as the leaders and retailers as the followers [13]. Fu et al. obtained the evolutionarily stable strategy for supplier and manufacturer emissionreduction input behaviour [14]. Liu et al. studied the operational decisions of original equipment manufacturers and authorized remanufacturers under the carbon emission quota and trading rules in a twoechelon supply chain [15]. Zhao et al. analysed the joint carbon emissionreduction problem in a secondary supply chain composed of two manufacturers and a dominant retailer [16]. In addition, Yang et al. compared the effects of four lowcarbon policies on supply chain coordination [17]. Xu et al. studied the decisionmaking and coordination of a twolevel supply chain composed of manufacturers and retailers [18]. Yang and Wang compared and analysed carbon emission reduction and supply chain profit under the three situations of decentralization, concentration, and revenuesharing contracts [19]. Xu et al. studied the game coordination of supply chain members under consignment contracts, revenuesharing contracts, and revenuesharing and emissionreduction costsharing contracts [20].
In addition, the impact of government on supply chain emissionreduction decisionmaking is crucial. Zhang et al. studied the optimal investment decisions of a supply chain considering a government carbon tax [21]. Kang et al. studied the behaviour of lowcarbon supply chain enterprises and strategic issues related to government lowcarbon policies and emerging lowcarbon markets [22]. Sun et al. analysed carbon emission transfer and reduction among enterprises in a supply chain [23]. Wang et al. studied the dynamic coordination of longterm cooperative emission reduction in supply chains under government subsidies [24]. Peng analysed the popular quantity discount contract and revenuesharing contract in a supply chain [25]. Li et al. discussed the coordination methods of a lowcarbon supply chain under different channel power structures [26]. Wang compared differences in levels of emissionreduction effort, advertising, and the present value of supply chain total profit under decentralized and cooperative decisionmaking modes [27]. Han et al. established a game model to study the decisionmaking behaviour of manufacturers in a lowcarbon ecommerce supply chain that received government carbon subsidies that considered fairness [28]. Wang et al. studied the longterm dynamic cooperative emission reduction and government subsidy strategies of a twolevel supply chain [29]. Wang et al. established single and joint emissionreduction models in which supply chain members could adopt one or twoway costsharing contracts and analysed the optimal strategy design and appropriate sharing rate contract [30]. Wang studied the decisionmaking problem of a twoechelon supply chain composed of a single manufacturer and a single retailer [31]. Zhang et al. discussed the influences of emissionreduction rate, carbon tax, and unit carbon emissions on order quantity, revenue, and contract parameters [32]. Liu and Li established a differential game model of a twolevel supply chain and introduced a lowcarbon preference into the model. They discussed in detail the impact of lowcarbon reference carbon emission reduction by a supply chain [33]. Zhu et al. compared and analysed two situations of government subsidies to lowcarbon product manufacturers and consumers who purchased lowcarbon products [34]. Li et al. analysed the interactive game between government subsidies and enterprises’ choices of emissionreduction cooperation [35]. Zhao et al. analysed the influence coefficient of different subsidy objects on the pricing decisions and profits of channel members [36]. Wei considered dynamic changes in carbon emissions and constructed a differential game model of emissionreduction investment by a supply chain [37]. Wang et al. studied the joint emissionreduction coordination problem of a threelevel supply chain with centralized and decentralized decisionmaking and costsharing collaborative decisionmaking [38].
The above literature mainly considers the operational cooperation of a lowcarbon supply chain from a static perspective. However, enterprise operations often span multiple cycles. Therefore, it is very important to study coordination and cooperation between the upstream and downstream enterprises in a lowcarbon supply chain from a dynamic perspective. Mohamad et al. analysed the selection of the best cooperation mode for supply chain management when the carbon emission limit is exceeded [39]. Ren et al. researched the influence of government subsidies on enterprise decisionmaking behaviour via a twostage dynamic game [40]. Wang et al. constructed three dynamic game models involving decentralized decisionmaking without costsharing, decentralized decisionmaking, and centralized decisionmaking under costsharing. They analysed the dynamic strategy of regional lowcarbon technology [41]. Huang and Yuan proposed a Stackelberg differential game model of a single government and multiple enterprises in a limited period [42]. Yang et al. constructed a continuoustime dynamic model of differential inequality [43]. Giovanni studied the optimal green advertising investment and pricing strategies of manufacturers and retailers under wholesalepricing and reverserevenuesharing contracts, respectively [44]. Considering a carbon trading market and the lowcarbon preferences of consumers, Liu et al. obtained the lowcarbon technology conditions required to achieve a winwin situation [45]. Zhao et al. studied the vertical cooperative emissionreduction dynamic optimization problem of a lowcarbon supply chain [46]. Ye et al. studied supply chain dynamic optimization and the coordination of joint emission reductions with consideration of consumers’ lowcarbon preferences [47]. You et al. compared the longterm dynamic equilibrium strategies of a twolevel supply chain under decentralized and centralized decisionmaking situations [48]. Xu et al. constructed and analysed three differential game models: decentralized decisionmaking without costsharing, decentralized decisionmaking under a costsharing contract, and centralized decisionmaking under collaborative control [49].
Existing research has mainly focused on manufacturer research and development (R&D) investment. The retailers use lowcarbon publicity or promotion to follow the manufacturers. However, no research has considered that the emission reductions related to product manufacturing decline naturally over time, which affects the incentive for enterprises to reduce emissions. Therefore, this paper uses the stochastic differential game method to expand the research in this field. Considering a scenario of a carbon trading market with a cost subsidy, this paper comprehensively analyses consumers’ lowcarbon preferences and random factors in the process of carbon emission reduction. It obtains the optimal equilibrium strategy and evolution path for joint carbon emission reduction by manufacturers and retailers.
3. Stochastic Differential Game Model
3.1. Problem Description
Actively developing circular economy and lowcarbon economy is the best choice to achieve sustainable development. To develop lowcarbon economy, we should not only change the traditional development mode of highcarbon economy but also seek energysaving ways and promote energysaving technologies from all aspects of the supply chain. Therefore, this paper considers a carbon emissionreduction system of a simple secondary supply chain composed of a manufacturer and a retailer. Widely used lowcarbon supply chain coordination mechanisms include cooperative advertising contracts, revenuesharing contracts, wholesale price contracts, costsharing contracts, and twopart contracts. This paper studies the cooperation between upstream and downstream enterprises in the practice of carbon emissionreduction supply chain management. The upstream manufacturer carries out energy and emission reductions, and the downstream retailer shares certain costs. In general, the manufacturer is the main source of emission reduction and faces more pressure than the retailer. Meanwhile, the manufacturer can transfer the cost of emission reduction downstream through market forces. Therefore, the manufacturer is the decisionmaker in the differential game and the retailer follows the manufacturer to share the R&D cost of emission reduction. In China’s quotabased carbon trading system, the government grants enterprises a certain carbon quota. Emissions that exceed the quota must be purchased from the society. At the same time, carbon trading is carried out in some large markets and the supply chain has no effect on the carbon price. Therefore, it is assumed that the carbon price is exogenous. In addition, this paper assumes that consumers have a lowcarbon preference; i.e., they prefer products associated with lower carbon emissions.
To describe the above problems, this paper defines the parameters shown in Table 1.

This paper simplifies the complex conditions and makes the following hypotheses.
Hypothesis 1 (demand function hypothesis). Referring to the research of Laroche et al. [50] and Ouardighi [51, 52], market demand is mainly affected by price factors and nonprice factors, which affect market demand in the form of separable multiplication. The product demand function is as follows:
Hypothesis 2 (input cost hypothesis of emissionreduction technology). The manufacturer’s emissionreduction cost function is an extension of the hypothesis of the innovation cost function. The function is a convex function describing emissionreduction efforts. Thus, the manufacturer’s emissionreduction cost at time t is given by
Hypothesis 3 (interest intensity hypothesis). Suppose that the upstream manufacturer and downstream retailer have the same interest intensity , and .
3.2. Dynamic Model of Carbon EmissionReduction Investment
The supply chain modelled in this paper is a simple twolevel supply chain with one manufacturer and one retailer. This paper studies a model of investment in carbon emissionreduction technology based on government subsidies and consumer lowcarbon preference. The decisionmaking process of the government, supply chain, and consumers is shown in Figure 1.
The emissionreduction process is affected by investment in emissionreduction subject, facilities maintenance, consumer environmental awareness, and various uncontrollable factors. Thus, the emissionreduction process is random.
Hypothesis 4. The stochastic process of carbon emission reduction is composed of three driving forces. One is a random factor, which can be described as a standard Wiener process , in which is a fluctuation parameter of carbon emission reduction. The second is the carbon emission reduction resulting from R&D investment by the emissionreduction subject , in which is the emissionreduction effort. The third changes in environmental awareness and equipment ageing, , in which is the emissionreduction coefficient. The overall dynamic equation is the sum of the three parts:
3.3. Objective Function of the Manufacturer and Retailer
Carbon trading system based on a carbon quota is essentially the intensity control mode. It is assumed that the carbon quota and carbon emissions per unit product set by the government are fixed in a certain period. Thus, the function of the carbon emissions trading cost is as follows:
In actual operations, for a carbon emissionreduction supply chain that is regulated by the government, the profit function of the manufacturers consists of sales revenue, carbon emissionreduction costs, and carbon trading income. Considering that the retailer will share part of the carbon emissionreduction cost of the manufacturer, the retailer’s profit function is composed of sales revenue and carbon emissionreduction cost. In addition, the goal of the game between the manufacturer and retailer is to maximize profit. For ease of expression, t is not listed below.
Thus, the objective function of the manufacturers is as follows:
The objective function of the retailers is as follows:
3.4. Stochastic Differential Game Model
Assuming that the government, manufacturers, and retailers adopt a progressive Stackelberg game, the stochastic differential game model of the carbon emission system is as follows:
4. Equilibrium Strategy
Based on the stochastic differential game method, this paper discusses the game process between upstream and downstream enterprises of a supply chain and obtains the feedback equilibrium between the manufacturer and the retailer. Firstly, the manufacturer determines the wholesale price and carbon emissionreduction efforts of the products at each moment and carries out a game with the retailer to determine the costsharing proportion. Secondly, the retailer determines the market price of products at each moment and carries out a game with the manufacturer to determine the emissionreduction costsharing ratio.
Theorem 1. The decisionmaking goal of upstream manufacturers and downstream retailers is to maximize their respective profits. The game equilibrium results of the manufacturer and retailer are as follows:
Proof. It is assumed that the wholesale price of manufacturer and the carbon emissionreduction effort are given for any time . This paper uses backward induction and continuoustime dynamic programming theory to obtain the HJB equation. The HJB equation satisfies the retailer’s optimal product pricing and optimal costsharing ratio.where is the retailer’s optimal value function.
Optimizing the righthand side of the retailer’s function, the product priceresponse strategy of the retailer can be obtained as follows:This paper uses continuoustime dynamic programming theory to obtain the HJB equation. In addition, the optimal wholesale price and carbon emissionreduction effort strategy of the manufacturer should satisfy the following HJB equation:The retailer’s product price reflecting strategy is introduced into the above formula, which can be solved aswhere is the optimal value function of the manufacturer.
Solving the optimization problem at the righthand side of the equation, the manufacturer’s optimal wholesale price and optimal carbon emissionreduction effort are as follows:Substituting the emissionreduction effort into the retailer’s HJB equation, and making the firstorder partial derivative equal to zero, we can obtain the following result:To obtain the strategies of the manufacturer and retailer, it is necessary to determine their optimal value functions. These are obtained by introducing the strategies of manufacturer and retailer.Solving the differential equation system separately, the optimal value functions of the manufacturer and retailer are as follows:The first and second derivatives of the optimal value function of the manufacturer and the retailer are given byTo make the optimal value functions of the manufacturer and the retailer assumed in equation (17) is the solution of equations (15) and (16), substituting equations (17)–(19), respectively, into equations (15) and (16), which can be solved asEquations (20) and (21) are valid for all possible values of carbon emission reduction, which indicates that the coefficients and constant terms on both sides of the equation are equivalent. They can be solved asFirstly, we calculate the coefficient according to the given parameters and then calculate the other coefficients. Secondly, we derive the optimal value function according to formula (17). Finally, we use Theorem 1 to obtain the manufacturer’s carbon emissionreduction effort and wholesale price, the retailer’s retail price, and the carbon emissionreduction costsharing ratio.
5. Characteristics of Evolution in the EmissionReduction Rate
Theorem 2. The expectation of random carbon reduction and the expectation limit are, respectively, as follows:
The variance of random carbon reduction and variance limit are, respectively,where and .
Proof. The manufacturer’s carbon emissionreduction efforts in Theorem 1 are brought into the process of carbon emission reduction, which can be solved asIntegrating the two sides by using boundary conditions, it can be solved asTaking the expectations on both sides by using the zeromean property of the Wiener process, it can be solved asIntegrating again, it can be solved asWhen , we can obtain , which can be solved asBased on the ITO theorem, we determine the change process of the square of carbon reduction, which can be solved asIntegrating the two sides by using boundary conditions, we obtainTaking the expectations on both sides by using the zeromean property of the Wiener process, we can obtainBy substituting the result into the above formula, we obtainWe then determine the variance in carbon reduction according to the following equation:Considering , we get . Thus, the variance limit of emission reduction is . It is assumed that the process of carbon emission reduction does not produce random interference (); that is, ; thus, .
6. Parameter Sensitivity Analysis
Assume that the consumer lowcarbon preference coefficient is , the emissionreduction effort influence coefficient of manufacturer is , the emissionreduction cost coefficient is , the carbon trading price is , and the cost subsidy rate is . We then calculate the impact of the above parameters on the optimal emissionreduction effort, wholesale price, retail price, and emission reduction. The results are shown in Table 2.
Inference 1. Under the coordinated decisionmaking of cost subsidy, the increase in the consumer lowcarbon preference coefficient will lead to increased carbon emissions. The manufacturers will increase their emissionreduction efforts, and the wholesale price of the manufacturer and the retail price of the retailer will remain invariant.
Proof.
Inference 2. Under the coordinated decisionmaking of cost subsidy, with increases in the manufacturer’s emissionreduction cost coefficient, the system’s carbon emission reductions will decrease, the manufacturer will reduce emissionreduction efforts, and the manufacturer’s wholesale price and retailer’s retail price will remain invariant.
Proof.
Inference 3. Under the coordinated decisionmaking of cost subsidy, increases in the emissionreduction cost coefficient will lead to increases in carbon emission reductions, the manufacturers will increase carbon emissionreduction efforts, and the manufacturer’s wholesale price and retailer’s retail price will remain invariant.
Proof.
Inference 4. Under the coordinated decisionmaking of cost subsidy, increases in the carbon trading price will lead to increases in carbon emission reduction, the manufacturers will reduce their emissionreduction efforts, and at the same time, the manufacturers will reduce their wholesale price and retailers will reduce their retail price.
Proof.
Inference 5. Under the coordinated decisionmaking of cost subsidy, increases in the cost subsidy rate will lead to increases in carbon emission reduction, the manufacturers will increase their emissionreduction efforts, and the wholesale price of manufacturers and the retail price of retailers will remain invariant.
Proof.
7. Numerical Example
7.1. Evolution Path Analysis
This paper intuitively analyses the supply chain’s optimal strategic trajectory under costsharing and coordinated decisionmaking through parameter assignment. The parameters of this paper are set as follows: ρ = 0.3, σ = 0.2, a = 4.5, b = 1, c = 3, α = 0.8, p_{e} = 0.02, k = 0.6, μ_{M} = 1, e_{M} = 0.5, = 2, E (0) = 0, , and δ = 0.01. The trajectory of the supply chain’s profit and emission reductions under costsharing and coordinated decisionmaking can be obtained, as shown in Figure 2.
(a)
(b)
(c)
In Figure 2, the carbon emission reductions and retailer profit show nonlinear upward trends with time, and the rate of increase becomes slower and slower and finally becomes stable. The change of manufacturer’s profit is opposite to that of the retailer.
7.2. Sensitivity Analysis
7.2.1. Sensitivity Analysis of and
Assuming that other parameters remain unchanged, the simulation of the cost subsidy rate and consumer lowcarbon sensitivity coefficient is as shown in Figure 3.
(a)
(b)
(c)
(d)
As shown in Figure 3, the manufacturer profit, retailer profit, product carbon emissions, and the emissionreduction effort of the manufacturer increase with increases in the cost subsidy rate and consumer lowcarbon sensitivity coefficient. However, the impacts of the cost subsidy rate and consumer lowcarbon sensitivity coefficient on the parameters are different. When the government subsidy rate is fixed, the consumer lowcarbon sensitivity coefficient positively affects product carbon emissions, the emissionreduction effort of the manufacturer, and the profits of upstream and downstream enterprises in the supply chain. At the same time, the cost subsidy rate enhances the impact of the lowcarbon sensitivity coefficient on the parameters, indicating that government subsidies can incentivize enterprises to invest in carbon emission reduction.
7.2.2. Sensitivity Analysis of and
When other parameters remain unchanged, the simulation results of the cost subsidy rate and impact coefficient of manufacturers’ emissionreduction efforts are as shown in Figure 4.
(a)
(b)
(c)
(d)
As shown in Figure 4, the manufacturer profit, retailer profit, product carbon emissions, and manufacturer emissionreduction effort increase with increases in the cost subsidy rate and impact coefficient of manufacturers’ emissionreduction efforts. However, the influences of the cost subsidy rate and manufacturer’s emissionreduction effort influence coefficient on parameters are different. When the government subsidy rate is fixed, manufacturer’s emissionreduction effort influence coefficient positively affects the product carbon emissions, manufacturer emissionreduction effort, and the profits of the upstream and downstream enterprises in the supply chain. Meanwhile, the introduction of government subsidies enhances the influence of the manufacturers’ emissionreduction impact coefficient on the parameters, indicating that government subsidies can incentivize enterprises to invest in carbon emission reductions.
7.2.3. Sensitivity Analysis of and
With other parameters unchanged, the simulation results of the cost subsidy rate and cost coefficient of carbon emission reduction are as shown in Figure 5.
(a)
(b)
(c)
(d)
As shown in Figure 5, the manufacturer profit, the retailer profit, product carbon emissions, and the manufacturer emissionreduction effort increase with increases in the cost subsidy rate and cost coefficient of carbon emission reduction, but the effects of the latter two are different. When the government subsidy rate is fixed, the cost coefficient of carbon emission reduction has a negative influence on product carbon emissions, manufacturer emissionreduction efforts, and supply chain members’ profits. These parameters all decrease with increases in the cost coefficient of carbon emission reduction, but the increase in government subsidy rate leads to an increase in carbon emissions, manufacturer emissionreduction effort, and the profits of the upstream and downstream enterprises in the supply chain. Moreover, the influence of the government subsidy rate on the parameters is greater than that of the emissionreduction effort cost coefficient, so these parameters show an upward trend. Thus, government subsidies can incentivize enterprises to invest in carbon emission reductions.
7.2.4. Sensitivity Analysis of and
With other parameters unchanged, the simulation results of cost subsidy rate and carbon trading price are as shown in Figure 6.
(a)
(b)
(c)
(d)
As shown in Figure 6, manufacturer profit, retailer profit, product carbon emissions, and manufacturer emissionreduction effort increase with increases in the cost subsidy rate and carbon trading price, but the influences of the latter two are different. When the government subsidy rate is fixed, the carbon trading price positively affects the product carbon emissions, manufacturer emissionreduction effort, and the profits of the upstream and downstream enterprises in the supply chain. At the same time, the introduction of a government subsidy enhances the influence coefficient of carbon trading price on the parameters, which shows that government subsidies can incentivize enterprises to invest in carbon emission reduction.
8. Conclusions
Under the background of economic globalization, supply chain enterprises can only improve their competitiveness and achieve the goal of sustainable development by formulating specific strategies and measures based on the perspective of sustainable development. In order to achieve sustainable development, supply chain enterprises need to follow the steps of the world closely and abide by the carbon rules of the international community and international organizations. Supply chain enterprises should give consideration to both economic and ecological benefits and maximize benefits with the minimum cost and carbon emissions. Therefore, this paper comprehensively considered the influences of an efficiencybased carbon quota system and an incentivebased cost subsidy system on supply chain emissionreduction investment decisions. From a dynamic perspective, this paper considered consumer lowcarbon preferences and the randomness of the emissionreduction process. We used a stochastic differential game model to determine the equilibrium strategies of the government, supply chain, and consumers, the evolution path of carbon emission reduction, and manufacturer and retailer profits.
To characterize the impact of carbon trading price, cost subsidy rate, consumer lowcarbon preferences, and various uncontrollable factors on supply chain emissionreduction technology decision process, this paper used the zeromean property of the Wiener process and the Ito theorem to describe the carbon emissionreduction decisionmaking process under stochastic circumstances. According to the profit structure of the manufacturer and retailer, this paper analysed the profit objective function of the manufacturer and retailer. Based on the supply chain emissionreduction technology decision process and the profit objective function of the manufacturer and retailer, this paper established a Stackelberg stochastic differential game model of a dynamic supply chain system. Using a stochastic differential game model and dynamic optimization method, we obtained the manufacturer’s equilibrium wholesale price, manufacturer’s equilibrium emissionreduction effort, retailer’s equilibrium product price, retailer’s equilibrium emission reductions, costsharing rate, and the optimal function of upstream and downstream enterprises’ profits in the supply chain.
This paper analysed the sensitivity of each parameter to the carbon emissionreduction process in supply chain. The results show that the consumer lowcarbon sensitivity coefficient, manufacturer carbon emissionreduction effort coefficient, carbon trading price, and cost subsidy rate have positive effects on carbon system emissions and supply chain profits. The cost coefficient of emission reduction has negative impacts on carbon system emissions and supply chain profits. To grasp the statistical characteristics of stochastic carbon emission reduction in the system, this paper also analysed the statistical properties of expectation and variance. Finally, this paper simulated and assigned the parameters, intuitively analysed the optimal strategy trajectory of the supply chain under costsharing coordination decisions, and verified the influence of different parameter changes on carbon emissionreduction behaviour.
This paper discussed the dynamic investment decisions of carbon emissionreduction technology in an ideal secondary supply chain with one supplier and one retailer under a costsharing coordination decision scenario. However, the simple secondary supply chain is too idealistic and does not meet actual development needs. Future research will focus on investment decisionmaking related to carbon emission reductions in a multilevel supply chain.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare no conflicts of interest.
Authors’ Contributions
Q. H and S. Y conceptualized the study, validated the study, and performed data curation. Q. H was responsible for methodology, software, project administration, and funding acquisition and supervised the study. S. Y performed formal analysis, investigated the data, prepared the original draft, reviewed and edited the manuscript, and visualized the study and was responsible for resources.
Acknowledgments
This research was funded by Liaoning Province Social Science Foundation, grant no. 2019ZD0214.
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