Dynamic decision and its complex dynamics analysis of low-carbon supply chain considering risk-aversion under carbon tax policy

Jin-Chai Lin(林金釵), Ru-Guo Fan(范如國), Yuan-Yuan Wang(王圓緣), and Kang Du(杜康)

1Management School,Chongqing University of Technology,Chongqing 400054,China

2Economics and Management School,Wuhan University,Wuhan 430072,China

Keywords: carbon tax,risk-avers,low-carbon supply chain,complex dynamics

1.Introduction

In recent years, a series of natural disasters caused by global warming has become increasingly prominent,seriously restricting the high-quality development of the global economy.To cope with the global climate change and improve the living environment of mankind,developing low-carbon economy has become the universal consensus of the international community.The carbon emissions of global brands and multinational companies are mainly concentrated in their supply chains, generally accounting for more than 70% of the total carbon emissions of brands, and some even reach 80% or 90%.[1]This poses a great challenge to the living environment,competition rules,cost composition and operation mode of the global supply chain.

Many countries have introduced policies such as carbon tax, carbon quota and carbon trading to regulate the carbon emissions of enterprises.Among them, carbon tax can not only increase government revenue for investment and development of new emission reduction technologies,but also have lower management and operation costs than carbon trading.Scholars have introduced carbon tax into the study of supply chain operation to explore its influence on decision and performance of supply chain.

It is worth noting that the carbon emission reduction decision and pricing decision are management activities mainly conducted by person.In an uncertain environment,the degree of cooperation and related decisions are affected by subjective factors such as people’s psychology, emotions, and their cognitive capabilities.[2-4]With the increase of complexity and uncertainty of the market environment, enterprises often show risk aversion when making decisions.For example, after McKinsey surveyed 1500 executives in 90 countries, it is found that managers show a high level of risk aversion regardless of the size of the investment.[5]Therefore,it is necessary to consider the influence of enterprises’ risk aversion on carbon emission reduction decision-making,pricing,and profit of the supply chain.

It is not difficult to find that in the current study, scholars have abstracted and simplified the social and economic systems such as the supply chain into deterministic and linear systems.In reality, the evolution process of supply chain system often has complex characteristics such as nonlinearity and uncertainty, owing to heterogeneity and autonomy attributes of social subjects, randomness of social environment and other factors.[6,7]Therefore, using static linear model to analyze supply chain system has certain limitations.

Above all, this study introduces the risk aversion behavior of the manufacturer and constructs the game models of low-carbon supply chain.We explore the influence of the manufacturer’s risk aversion on the optimal decision, profit and coordination of the supply chain from the static perspective and dynamic evolution perspective, respectively.Then,the operation of the supply chain system under the decentralized decision-making situation and the centralized decisionmaking situation are compared and analyzed,with the centralized decision-making situation taken as a benchmark.Finally,a carbon emission reduction cost-sharing contract is proposed to improve the carbon emission reduction level and supply chain efficiency,which realizes Pareto improvement.

The rest of this study is organized as follows.In Section 2, the existing reseraches are reviewed.In Section 3, model assumptions and notation are described.In Sections 4 and 5,model construction and analysis are shown in the frame of decentralized decision-making model and centralized decisionmaking,respectively.In Section 6,cost-sharing contract game model is designed.Conclusions and suggestions are presented in Section 7.

（六）實現心理健康教育個性化。針對個別寄宿生出現的厭學、逃學、打架、抽煙等不良現象，我們注重及時發現疏導，由生活指導教師和班主任分別進行個別談話，細致入微地了解學生的所思所想，找準問題的思想根源，耐心地對學生進行教育引導，避免學生因心理健康問題發現不及時、疏導不到位引發不良后果。

因此一方面對新建、改建110kV及以上的線路參數，要求按照有關基建工程驗收規程的規定，在設備投入運行前進行實際參數測試；二方面進一步加強全網主變中性點接地方式的管理；三方面根據雙側電源復雜電網的線路零序電流保護中，零序電流I段作為速動段保護，對于超短線路（2km以下）及短線路（10km以下）宜退出運行的規定，建議將110千伏乃嘎I線、奪城線、柳西雙線等長度15km以內共計12條線路的零序電流I段保護功能退出運行。

2.Review on existing researches

Equation (14) is the manufacturer’s decision variable,wheredi,i=1,2 represent the adjustment parameter of wholesale price and carbon emission reduction level, respectively.According to Eq.(6),the dynamic retail price can be expressed as

耕地質量級別監測重點是基于年度內土地資源增多、縮減與建設現狀進行。實現地區耕地質量級別與整體生產水平提高的重要技術路線是管理縮減的土地資源，要削減低質土地；要多擴大耕地，擴大的耕地主要保證高；通過耕地修建不斷提高耕地質量級別，基本技術路線見圖1。

2.1.Carbon emission reduction decision and pricing in supply chain

Considering the influence of consumers’low-carbon preferences on enterprise decision-making is a current research hotspot.[8,9]In addition,the influence of the government’s carbon tax on the decision-making of carbon emission reduction in the supply chain is also the focus of attention of academia and enterprises.Wanget al.[10]found that the carbon tax policy affects the product pricing and emission reduction strategy of enterprises.Huang and Zhang[11]found that the increase of carbon tax rate can increase the emission reduction level of products in low emission industries, but it reduces the emission reduction level of products in high emission industries.Lu and Yi[12]found that with the increase of carbon tax rate,the phenomenon of “less new products and more remanufactured products”appears.

The above studies on carbon emission reduction in supply chain are all based on the risk neutral assumption,ignoring the risk aversion characteristics of decision makers, and the obtained research results can not accurately provide theoretical reference for real supply chain decision makers.

2.2.Risk avoidance in supply chain

Proposition 3 When the cost-sharing contract is implemented,the carbon emission reduction level will beimproved,and it increases with the cost-sharing proportion increasing.

The above-mentioned researches show that risk aversion behavior of enterprises will change the optimal decisions and corporate profits.However, there have been many studies on the influence of the risk aversion behavior of decisionmakers on supply chain financing,[21,22]but few researches involve with the influence of low-carbon supply chain decisionmaking and coordination,which mainly focus on the study of static models.

2.3.Applications of nonlinear dynamical system theory to supply chain

On the construction of low-carbon supply chain game model, the existing literature mainly focuses on static models.However,supply chain management system is a nonlinear system with uncertainty, variability, openness, and dynamics.Xi and Zhang[23]found that the dynamic subsidy of the government to the nitrogen emission reduction behavior of agricultural enterprises will affect the stability of the supply chain system and thus the performance of the supply chain.Tianet al.[24]showed that when consumers’channel preference is too strong,it will damage the profits of supply chain members,no matter how hard enterprises try to improve sales efforts.Maet al.[25]studied dynamic complexity of a multi-channel supply chain considering cap-and-trade regulation.Liet al.[26]incorporated fairness concern into a dynamic model of the closedloop supply chain.This literature only studied the pricing decision and took the carbon emission reduction strategy as an exogenous variable.Unlike this literature, the present study takes carbon emission reduction strategy as a decision variable of the manufacturer.

工程上，風機荷載疲勞一般通過雨流計數法將風機時程疲勞載荷轉化為等效疲勞載荷，再利用等效疲勞載荷進行疲勞損傷計算。

3.Model assumptions and notation

Under the carbon tax policy, this study takes a two-level supply chain consisting of a single manufacturer and a single retailer as the research object.We only consider the carbon emission of product production,i.e.,only the manufacturer is affected by the carbon tax.To improve competitiveness and meet consumers’demand for low-carbon products,the manufacturer needs to invest in carbon emission reduction and sells the products to consumers through the retailers.The manufacturer is the leader of the game and first determines optimal carbon emission reduction effort leveleand wholesale pricew.The retailer is the follower and makes optimal retail pricepmaximize its own profit according to the manufacturer’s decision.

Assuming that there are uncertain factors in the market demand.According to Ref.[27], the market demand can be expressed by the following function:

（6）增加與約旦能源合作。約旦頁巖油富足，中國資金技術雄厚，且中國已投資阿塔拉特油頁巖電站項目。在能源合作方面，中國可以加大投資力度。加快中國“走出去”戰略，讓約旦對中國友好合作的決心更堅定，從而最大限度地對中國開放。

where ˉa=a+ε,ais the factor determined by the potential demand of the market,εis the random item,which obeys the normal distributionε～N(0,σ2),and the distribution information is common knowledge of both sides;tis the low-carbon preference of consumers.Equation (1)indicates that the increasing of the carbon emission reduction level of the low-carbon product can increase the market demand.

Assume that the initial carbon emission of unit product ise0, and unit carbon tax is set tof, so the manufacturer needs to pay carbon emission tax of unit productf(e0-e).Assume thatcis unit cost when carbon emission reduction investment is not considered, thenw-c-f(e0-e)＞0 will need satisfying in order to ensure that the manufacturer is profitabl.The cost function of carbon emission reduction isC=(1/2)ke2,which has been widely used,[11,28]whereC＇＞0,C＇＇＞0,and the parameterkis the cost coefficient related to emission reduction investment, parametersaandkare much larger than other parameters.

According to the above assumptions, the profit function of the retailer, the manufacturer and the supply chain are as follows:

When the manufacturer shows risk aversion characteristics, owing to market uncertainty, emission reduction investment, and carbon tax, not only should attention be paid to its own profit, but also to how to avoid risks.As for the utility function of risk aversion, this study uses the mean variance method which is widely used in theory and practice to measure the utility function of decision-makers’ risk aversion behavior.[29,30]The manufacturer’s expected utility is expressed asE(Um)=E(πm)-Var(πm)/2Rm, whereRmis the manufacturer’s risk tolerance.According to the mean variance method,the variance of the manufacturer’s expected return is Var(π) = (w-c-f(e0-e))2σ2.Therefore, the manufacturer’s utility function can be expressed as

4.Decentralized decision game model of lowcarbon supply chain

4.1.Static model

The superscript “R?m” represents the optimal solution of the manufacturer in the case of risk aversion.Reverse induction method is used to solve the Stackelberg game between the manufacturer and the retailer.Solving the second partial derivative of Eq.(5) with respect top, we obtain?E2(πr)/?p2=-2＜0.Therefore,πrhas a unique optimal solution with respect top.Letting?πr/?p=0, the response function of the retailer is calculated from

Substituting Eq.(6)into Eq.(5)and calculating the firstpartial derivatives of the decision variableswande, from the resulting equation,we obtain

When 4k(Rm+σ2)＞Rm(f+t)2,the Hessian matrix of Eq.(7)is negative-definite,and the utility function of the manufacturer has a unique maximum solution with respect towande.Under this constraint,the optimal decision of the manufacturer can be obtained by solving Eq.(7):

Substituting the above two optimal solutions into Eq.(5),the optimal retail price is as follows:

Substituting the optimal decisions obtained from Eqs.(8)-(10)into Eqs.(2)-(4),respectively,we obtain