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2023届
2023rd

本科毕业论文
Undergraduate dissertation

论文题目：低碳供应链技术对低碳供应链
Dissertation Title: Low-carbon supply chain technology for low-carbon supply chain

信息共享的影响研究
Research on the impact of information sharing

学生姓名： XXX
Student's Name: XXX

论文类型：学术论文型
Thesis type: academic paper type

所在学院：管理科学与工程学院
Faculty: School of Management Science and Engineering

专业：管理科学
Major: Management Science

学号： 41927011
Student ID: 41927011

指导教师： XXX
Instructor: XXX

成绩：
Achievements:

2023年 03月
2023-03

西南财经大学
Southwestern University of Finance and Economics

本科毕业论文原创性及知识产权声明
Statement of originality and intellectual property rights of undergraduate dissertation

本人郑重声明：所呈交的毕业论文是本人在导师的指导下取得的成果，论文写作严格遵循学术规范。对本论文的研究做出重要贡献的个人和集体，均已在文中以明确方式标明。因本毕业论文引起的法律结果完全由本人承担。
I solemnly declare that the graduation thesis submitted is the result of my work under the guidance of my supervisor, and the writing of the thesis strictly follows the academic norms. Individuals and groups that have made significant contributions to the research of this paper have been clearly identified in the text. The legal consequences arising from this dissertation are entirely the responsibility of the applicant.

本毕业论文成果归西南财经大学所有。
The results of this graduation thesis are owned by Southwestern University of Finance and Economics.

特此声明
It is hereby declared

毕业论文作者签名：（必须手写）
Signature of the author of the dissertation: (must be handwritten).

作者专业：（手写）
Author's Specialty: (Handwritten).

作者学号：（手写）
Author's student number: (handwritten).

2023年月日
2023 March

摘要
Summary

随着人民生活水平和环保意识的提高，人们越来越关注低碳消费。气候变化与碳排放有明确的关联，是人类面临的最紧迫的问题之一，作为最大的能源消费国和二氧化碳排放国中国已承诺其碳排放在2030年左右达到峰值，并在2060年之前实现全国碳中和，这是一个巨大的挑战。针对我国低碳经济发展的现实要求，在碳税收和低碳技术引入的双重背景下，通过选取制造商引入与不引入低碳技术两种方式，分别探讨企业在引入与不引入两种方式下的低碳供应链中的信息共享优化问题。本研究所构建的低碳供应链是一种由生产商和零售商共同构成的、具有 Stacklberg博弈的二级供应链。依据不同的信息共享策略与生产策略，分出四种情形：（1）零售商选择不与制造商共享需求信息，制造商不引进低碳技术进行生产；（2）零售商选择与制造商共享需求信息，制造商不引进低碳技术进行生产；（3）零售商选择不与制造商共享需求信息，制造商引进低碳技术进行生产；（4）零售商选择与制造商共享需求信息，制造商引进低碳技术进行生产。在以上四种不同的情形中公式运算出均衡定价、能源消耗和利润。
With the improvement of people's living standards and environmental awareness, people are paying more and more attention to low-carbon consumption. Climate change is clearly linked to carbon emissions and is one of the most pressing issues facing humanity, and China, as the largest energy consumer and carbon dioxide emitter, has pledged to peak its carbon emissions around 2030 and achieve national carbon neutrality by 2060, which is a huge challenge. In view of the practical requirements of China's low-carbon economic development, under the dual background of carbon taxation and the introduction of low-carbon technology, this paper discusses the information sharing and optimization of enterprises in the low-carbon supply chain with and without the introduction of low-carbon technology by selecting two ways for manufacturers to introduce and not to introduce low-carbon technologies. The low-carbon supply chain constructed in this study is a two-tier supply chain with Stacklberg game composed of producers and retailers. According to different information sharing strategies and production strategies, four scenarios are distinguished: (1) the retailer chooses not to share demand information with the manufacturer, and the manufacturer does not introduce low-carbon technology for production; (2) Retailers choose to share demand information with manufacturers, and manufacturers do not introduce low-carbon technologies for production; (3) Retailers choose not to share demand information with manufacturers, and manufacturers introduce low-carbon technologies for production; (4) Retailers choose to share demand information with manufacturers, and manufacturers introduce low-carbon technologies for production. In these four different scenarios, the formula calculates equilibrium pricing, energy consumption, and profit.

对比分析不同情形的最优结果，得以下结论：（1）信息共享和引进低碳生产技术对市场需求起正向作用，碳税则对市场需求造成负面影响。（2）零售商采取不共享信息策略以及制造商引进低碳生产技术时，销售价格会相应变大。（3）低碳偏好消费者对于低碳产品越喜爱，批发价格就越低，而引进低碳生产技术，制造商可以获得更高的批发价格。（4）当信息差过大时，零售商不会共享需求信息。（5）信息共享策略不影响供应链的总利润，引进低碳生产技术，供应链会获得更多的利润。以上结论是基于消费者对低碳产品的偏好心理的情况下运用Stacklberg理论计算出来的，可为供应链的利润最优提高理论支撑，或零售商做信息共享决策提供参考。
Comparing and analyzing the optimal results of different scenarios, the following conclusions are obtained: (1) Information sharing and the introduction of low-carbon production technologies have a positive effect on market demand, while carbon tax has a negative impact on market demand. (2) When retailers adopt a no-share information strategy and manufacturers introduce low-carbon production technologies, the selling price will increase accordingly. (3) Low-carbon preference consumers prefer low-carbon products the more they like them, the lower the wholesale price, and the introduction of low-carbon production technology allows manufacturers to obtain higher wholesale prices. (4) When the information difference is too large, the retailer will not share the demand information. (5) The information sharing strategy does not affect the total profit of the supply chain, and the supply chain will gain more profits by introducing low-carbon production technology. The above conclusions are calculated based on the psychology of consumers' preference for low-carbon products using Stacklberg's theory, which can provide theoretical support for the optimal profit improvement of the supply chain or the information sharing decision of retailers.

关键词：低碳供应链;信息共享;Stacklberg博弈
Keywords: low-carbon supply chain; information sharing; Stacklberg Game

A区
Zone A

随着人们生活水平的提高，人们越来越重视低碳消费。气候变化与碳排放明显相关，是人类面临的最紧迫问题之一，中国作为最大的能源消费国和二氧化碳排放国，承诺在 2030 年左右实现碳排放达峰，到 2060 年实现全国碳中和，这是一个巨大的挑战。为满足社会向低碳经济转型的需求，本研究设计了碳税政策，在引入低碳技术的情况下，选取了两种制造商的生产策略：引入低碳技术和不引入低碳技术，研究不同生产策略下低碳供应链信息共享的最优决策问题。本文建立了一个由制造商和零售商组成的低碳供应链，供应链的两端都存在 Stacklberg 博弈。根据信息共享策略和生产策略的差异，主要分为以下四种情况：（1）零售商选择不与制造商共享需求信息，制造商不引入低碳技术进行生产;（2）零售商选择与制造商共享需求信息，而制造商不引入低碳技术进行生产;（3）零售商选择不与制造商共享需求信息，制造商引入低碳技术进行生产;（4）零售商选择与制造商共享需求信息，制造商引入低碳技术进行生产。对于四种不同的场景，均衡价格和利润和功耗是分开计算的。
With the improvement of people's living standards, people pay more and more attention to low-carbon consumption. Climate change is clearly related to carbon emissions and is one of the most pressing issues facing humanity, and China, as the largest energy consumer and carbon dioxide emitter, has pledged to peak carbon emissions around 2030 and achieve national carbon neutrality by 2060, which is a huge challenge. In order to meet the needs of the society's transition to a low-carbon economy, this study designs a carbon tax policy, and selects two production strategies of manufacturers in the case of the introduction of low-carbon technologies: the introduction of low-carbon technologies and the non-introduction of low-carbon technologies, and the optimal decision-making problem of information sharing in low-carbon supply chains under different production strategies is studied. This paper establishes a low-carbon supply chain consisting of manufacturers and retailers, with a Stacklberg game at both ends of the supply chain. According to the differences in information sharing strategies and production strategies, they are mainly divided into the following four situations: (1) retailers choose not to share demand information with manufacturers, and manufacturers do not introduce low-carbon technologies for production; (2) retailers choose to share demand information with manufacturers, who do not introduce low-carbon technologies for production; (3) the retailer chooses not to share demand information with the manufacturer, and the manufacturer introduces low-carbon technologies for production; (4) Retailers choose to share demand information with manufacturers, who introduce low-carbon technologies for production. For the four different scenarios, the equilibrium price and profit and power consumption are calculated separately.

本文对 4 种情景的最优结果进行了比较分析，并得出以下结论：（1）信息共享和低碳生产技术的引入对市场需求起着积极作用，而碳税对市场需求起着消极影响。（2）当零售商采用不共享信息策略并且制造商引入低碳生产技术时，销售价格将相应提高。（3）低碳偏好消费者越喜欢低碳产品，批发价格越低，而低碳生产技术的引入，制造商可以获得更高的批发价格。（4）当信息差距过大时，零售商不会分享需求信息。（5）信息共享策略不影响供应链的总利润，引入低碳生产技术，供应链将获得更多的利润。上述结论是基于消费者对低碳产品偏好的心理计算得出的，可以提高零售商信息共享决策的基础，也可以为供应链中利润的最优提升提供理论支持。
This paper compares and analyzes the optimal results of the four scenarios and draws the following conclusions:(1) Information sharing and the introduction of low-carbon production technologies play a positive role in market demand, while carbon tax plays a negative role in market demand. (2) When retailers adopt a no-information sharing strategy and manufacturers introduce low-carbon production technologies, the selling price will increase accordingly. (3) Low-carbon preference The more consumers prefer low-carbon products, the lower the wholesale price, and with the introduction of low-carbon production technology, manufacturers can obtain higher wholesale prices. (4) When the information gap is too large, retailers do not share demand information. (5) The information sharing strategy does not affect the total profit of the supply chain, and the introduction of low-carbon production technology will make the supply chain more profitable. The above conclusions are based on the psychological calculation of consumers' preference for low-carbon products, which can improve the basis of retailers' information sharing decision-making, and can also provide theoretical support for the optimal improvement of profits in the supply chain.

关键词：低碳供应链; 信息共享;Stacklberg 游戏
Keywords: low-carbon supply chain; information sharing; Stacklberg Games

目录
Table of Contents

摘要 3
Abstract 3

摘要 4
Abstract 4

目录 6
Table of Contents 6

1. 绪论 9
1. Introduction9

1.1 研究背景及意义 9
1.1 Background and Significance9

1.2 研究内容及方法 10
1.2 Research content and methodology10

1.3 技术路线与论文结构 11
1.3 Technical route and paper structure11

1.4 创新之处 11
1.4 Innovations11

2.2 考虑政府补贴的低碳供应链 13
2.2 Low-carbon supply chains that consider government subsidies13

2.3 碳交易理论 13
2.3 Carbon Trading Theory13

2.4 信息不对称理论 14
2.4 Theory of information asymmetry14

2.5 文献评述 15
2.5 Literature review15

3. 不引进低碳技术下的低碳供应链信息共享模型 16
3. Low-carbon supply chain information sharing model without introducing low-carbon technologies16

3.1 情景描述 16
3.1 Scenario description16

3.2 模型参数设置和假设 16
3.2 Model Parameter Settings and Assumptions16

3.2.1 参数设置与假设 16
3.2.1 Parameter settings and assumptions16

3.2.2 低碳偏好消费者需求 17
3.2.2 Low-carbon preference consumer demand17

3.3 不引进低碳技术下选择信息不共享策略 18
3.3 Do not introduce low-carbon technologies and choose a non-sharing strategy18

3.4 不引进低碳技术下选择信息共享策略 21
3.4 Choose an information-sharing strategy without introducing low-carbon technologies21

3.5 信息共享策略分析和比较 21
3.5 Analysis and comparison of information-sharing strategies21

3.5.1 影响因子分析 21
3.5.1 Impact factor analysis21

3.5.2 最优解比较和讨论 25
3.5.2 Comparison and discussion of optimal solutions25

4. 引进低碳技术下的低碳供应链信息共享模型 27
4. Introduce a low-carbon supply chain information sharing model based on low-carbon technologies27

4.1 引进低碳生产技术的情形描述 27
4.1 Description of the introduction of low-carbon production technologies27

4.2 低碳生产技术下低碳偏好消费者需求 27
4.2 Low-carbon preference consumer demand under low-carbon production technologies27

4.3 引进低碳技术下选择信息不共享策略 28
4.3 Opt-out of information sharing strategies under the introduction of low-carbon technologies28

4.4 引入低碳生产技术下采用信息共享策略 30
4.4 Adopt information-sharing strategies under the introduction of low-carbon production technologies30

4.5 信息共享决策分析与比较 30
4.5 Information Sharing Decision Analysis and Comparison30

4.5.1 效用影响因子分析 31
4.5.1 Utility Impact Factor Analysis31

4.5.2 引进低碳生产技术下最优解比较和讨论 33
4.5.2 Comparison and discussion of optimal solutions under the introduction of low-carbon production technologies33

4.5.3 信息共享策略下最优解比较和讨论 34
4.5.3 Comparison and discussion of optimal solutions under information sharing strategies34

5. 数值分析 36
5. Numerical analysis36

5.1 未引进低碳生产技术时的信息共享策略数值分析 36
5.1 Numerical analysis of information sharing strategies when low-carbon production technologies are not introduced36

5.2 引进低碳生产技术后的信息共享策略数值分析 41
5.2 Numerical analysis of information sharing strategies after the introduction of low-carbon production technologies41

5.3 引进低碳生产技术后的数值分析 45
5.3 Numerical analysis after the introduction of low-carbon production technologies45

5.4 小结 52
5.4 Summary52

6. 总结与展望 53
6. Summary and outlook 53

6.1 研究结论 53
6.1 Conclusions53

6.2 不足与未来展望 54
6.2 Deficiencies and future prospects54

7. 参考文献 55
7. Ref. 55

8. 致谢 58
8. Acknowledgments58

1. 绪论
1. Introduction

1.1 研究背景及意义
1.1 Background and significance

温室气体排放量日益增多并引发气候问题，全球范围内均需重视碳减排行动。作为碳排放总量约占世界总量的30%的国家，中国的碳减排行动非常重要，事关中华民族永续发展，关乎人类前途命运。中国于2011年开始进行碳排放权交易。经过十余年的摸索，目前已完成了约11亿吨CO2的交易，交易额达到了百余亿元。中国有着全球最大的温室气体排放碳市场，而低碳产业情况介绍大致从以下三个方面展开：
Greenhouse gas emissions are increasing and causing climate problems, and carbon reduction actions need to be taken globally. As a country that accounts for about 30% of the world's total carbon emissions, China's carbon emission reduction actions are very important, which is related to the sustainable development of the Chinese nation and the future and destiny of mankind. China began trading carbon emissions in 2011. After more than 10 years of exploration, about 110 million tons of CO2 transactions have been completed, and the transaction volume has reached more than 10 billion yuan. China has the world's largest carbon market for greenhouse gas emissions, and the introduction of low-carbon industries is broadly carried out from the following three aspects:

（1）碳减碳政策：各国已推行的碳减排政策总共有三大类。直接管制手段，即针对能源消耗和碳排放水平的排放标准、限额等手段。碳排放权交易，一种基于碳排放量的碳排放控制方法，通过直接控制和经济奖励的方法。税收手段，如能源和环境相关的税收及补贴。
(1) Carbon reduction policies: There are three main types of carbon reduction policies that have been implemented by various countries. Direct control means, i.e., emission standards, allowances, etc., for energy consumption and carbon emission levels. Carbon emissions trading, a carbon emission control method based on carbon emissions, through direct control and economic incentives. Tax instruments, such as energy and environment-related taxes and subsidies.

（2）碳税政策：碳税指的是针对温室气体排放而征收的环境税。每年温室气体直接排放量达2万5000公吨或以上的工业设施需要缴纳碳税，我国是最早宣布征收碳税的国家之一。征收碳税的红利主要有：征收碳税能提高传统化石能源的使用成本，促使相关企业通过引进低碳生产技术或利用新能源替代化石能源来进行生产等方式，合理减少碳税支出，从而实现全社会减排。政府开征碳税的同时会相对应的降低其他税种的税率或者相对应的增加转移支付的比例，创造社会福利。碳排放交易和碳税是基于市场机制的两种主要碳减排工具，这是环境经济学争论其优点的经典研究命题。
(2) Carbon tax policy: Carbon tax refers to the environmental tax levied on greenhouse gas emissions. Industrial facilities with direct greenhouse gas emissions of 25,000 metric tons or more per year are required to pay a carbon tax, and China is one of the first countries to announce a carbon tax. The main dividends of the carbon tax are: the levy of carbon tax can increase the cost of traditional fossil energy, and encourage relevant enterprises to reasonably reduce carbon tax expenditure by introducing low-carbon production technologies or using new energy to replace fossil energy for production, so as to achieve emission reduction in the whole society. When the government imposes a carbon tax, it will reduce the tax rate of other taxes or increase the proportion of transfer payments accordingly, creating social welfare. Emissions trading and carbon tax are the two main tools for carbon emission reduction based on market mechanisms, which are classic research propositions in environmental economics to argue for their merits.

（3）减碳减排技术：指所有能降低人类活动碳排放的技术。有无碳或减碳技术、捕存和利用二氧化碳的技术。燃料和碳排放息息相关，企业所用燃料包括煤炭、焦炭、兰炭、燃料油、汽柴油、液化气、煤层气等等。影响燃料消耗及碳排放的主要因素是工艺过程，但在燃料的购入储备、加工转换、终端利用等环节仍有很多减少碳排放的技术，如减少燃料中有机成分无谓的损失，使用的燃料应该符合锅炉等燃烧设备的设计要求，减少燃料燃烧过程的能量浪费等。
(3) Carbon reduction and emission reduction technologies: refers to all technologies that can reduce carbon emissions from human activities. There are carbon-free or decarbonisation technologies, technologies for capturing and utilizing carbon dioxide. Fuel and carbon emissions are closely related, and the fuels used by enterprises include coal, coke, blue charcoal, fuel oil, gasoline and diesel, liquefied gas, coalbed methane, etc. The main factor affecting fuel consumption and carbon emissions is the process, but there are still many technologies to reduce carbon emissions in the purchase and storage, processing and conversion, and terminal utilization of fuel, such as reducing the unnecessary loss of organic components in the fuel, and the fuel used should meet the design requirements of boilers and other combustion equipment, and reducing the energy waste in the fuel combustion process.

本研究集中关注的是在节能减排技术方面，利用减碳技术实现生产消费使用过程的减碳，从而实现高效能和低排放的目标。在减碳的大环境下，政府发布了一系列的相关政策和补贴。随着全球化的进程，企业间的竞争愈演愈烈，若想要实现低碳发展，需要投入巨大的成本，企业的资金问题仍然突出。为帮助解决此问题，本文提出从低碳减碳技术、供应链和信息共享角度展开研究，旨在探索出在不同的政府减碳政策和零售商与制造商之间的信息共享策略下的低碳供应链模型。
This study focuses on energy conservation and emission reduction technologies, and uses carbon reduction technologies to achieve carbon reduction in the process of production, consumption and use, so as to achieve the goals of high efficiency and low emissions. In the context of carbon reduction, the government has issued a series of relevant policies and subsidies. With the process of globalization, the competition between enterprises is becoming more and more fierce, and if you want to achieve low-carbon development, you need to invest huge costs, and the capital problem of enterprises is still prominent. In order to help solve this problem, this paper proposes to conduct research from the perspectives of low-carbon reduction technology, supply chain and information sharing, aiming to explore a low-carbon supply chain model under different government carbon reduction policies and information sharing strategies between retailers and manufacturers.

可以发现，二级供应链上制造商与零售商之间信息共享可以使得供应链达到最优绩效，二者之间存在Stackelberg博弈;在完全信息共享下，零售商的绩效会有一定程度的损失，因而零售商会选择不完全信息共享，零售商的利益也将得到保障。因此本文将利用博弈论计算模型的均衡解。
It can be found that the information sharing between manufacturers and retailers in the secondary supply chain can make the supply chain achieve optimal performance, and there is a Stackelberg game between the two. Under full information sharing, the performance of retailers will be lost to a certain extent, so retailers will choose not to share complete information, and the interests of retailers will also be protected. Therefore, this paper will use the equilibrium solution of the game theory calculation model.

1.2 研究内容及方法
1.2 Research content and methodology

本文研究的二级供应链内，单一零售商需要选择采取两种信息共享策略之一。单一制造商生产产品后，交由零售商销售。在追求低碳消费的背景下，消费者分为低碳产品偏好者和低碳产品不偏好者。零售商可以通过历史信息了解到当期的市场需求，并选择是否和制造商共享需求信息，而制造商无法预知当期的市场需求。制造商可以自由的选择是否引进低碳生产技术，引进低碳生产技术后，制造商可以获得来自政府的补贴以及降低生产的能耗。本文主要采用以下几种方法开展研究：
Within the secondary supply chain studied in this paper, a single retailer needs to choose one of two information sharing strategies. After a single manufacturer produces a product, it is sold by retailers. In the context of the pursuit of low-carbon consumption, consumers are divided into low-carbon product preferences and low-carbon product non-preferences. Retailers can use historical information to understand the current market demand and choose whether to share the demand information with manufacturers, who cannot predict the current market demand. Manufacturers are free to choose whether to introduce low-carbon production technologies, and after the introduction of low-carbon production technologies, manufacturers can obtain subsidies from the government and reduce the energy consumption of production. In this paper, the following methods are used to carry out research:

（1）文献研究法：基于低碳供应链的信息共享这一研究方向，在中国知网、Web of Science、超星等国内外数据库查阅大量文献，较全面地了解掌握供应链管理、信息共享、低碳政策相关研究成果及国内外研究现状，找到研究空白。
(1) Literature research method: Based on the research direction of information sharing of low-carbon supply chain, a large number of literature was consulted in domestic and foreign databases such as CNKI, Web of Science, and Chaoxing, so as to comprehensively understand and grasp the research results related to supply chain management, information sharing, and low-carbon policy, as well as the research status at home and abroad, and find research gaps.

（2）模型方法：根据原型的主要特征创建一个数学模型，再通过模型来间接研究低碳供应链中，制造商同零售商之间的信息共享和制造商所采取的策略同政府减碳政策之间的关系。
(2) Model method: Create a mathematical model according to the main characteristics of the prototype, and then indirectly study the relationship between information sharing between manufacturers and retailers and the strategies adopted by manufacturers and government carbon reduction policies in the low-carbon supply chain.

（3）定性分析：针对低碳供应链方面，制造商和零售商间的关系和政府制定的低碳政策进行分析。
(3) Qualitative analysis: In terms of low-carbon supply chain, the relationship between manufacturers and retailers and the low-carbon policies formulated by the government are analyzed.

（4）运用数据分析法分析低碳偏好因子、碳排放惩罚率因子和单位降低能耗的敏感性。使用Mathematica软件处理预设的数学博弈模型，并调整参数，探讨不同情况下模型的最优结果，得到数值分析的结果并进行研究结论验证。
(4) Data analysis was used to analyze the low-carbon preference factor, carbon emission penalty rate factor and the sensitivity of unit energy consumption. Mathematica software is used to process the preset mathematical game model, adjust the parameters, discuss the optimal results of the model under different circumstances, obtain the results of numerical analysis, and verify the research conclusions.

1.3 技术路线与论文结构
1.3 Technical route and paper structure

图1-1：研究技术路线
Figure 1-1: Research technology route

1.4 创新之处
14 Innovations

（1）在研究市场需求时，引入了价格敏感因子和低碳偏好敏感因子这两个变量，从多角度衡量低碳供应链的最优决策。
(1) In the study of market demand, two variables, price sensitive factor and low-carbon preference sensitive factor, are introduced to measure the optimal decision-making of low-carbon supply chain from multiple perspectives.

（2）以往研究低碳供应链的文献大多是基于理论进行分析，本文在考虑低碳供应链技术的情况下，结合Stackelberg博弈模型分析制造商、零售商和供应链整体的最优决策。
(2) Most of the previous literature on low-carbon supply chain is based on theoretical analysis, and this paper analyzes the optimal decision-making of manufacturers, retailers and supply chains as a whole by combining the Stackelberg game model with the consideration of low-carbon supply chain technology.

2. 相关理论综述
2. A review of relevant theories

2.1 低碳供应链相关研究
2.1 Research on low-carbon supply chains

已有的关于低碳供应链的研究中，以二级供应链为主，但各自从不同的视角展开了研究。Zu等人[1]对以提高可持续收入为目标的单一制造商和单一供应商构成的碳减排供应链进行了研究，通过 Stackelberg博弈分析，得出了制造商和供应商付出最大的努力时，其减排量也是最大的。Wang等学者[2]建立了一个由生产商与零售商构成的两层供应链博弈模型，通过对两个企业的成本分摊与批发价溢价契约的约束，两个企业能够在帕累托改进的条件下合作完成碳排放的目标。
The existing research on low-carbon supply chains focuses on secondary supply chains, but they have been studied from different perspectives. Zu et al. [1] studied the carbon reduction supply chain consisting of a single manufacturer and a single supplier with the goal of increasing sustainable income, and concluded that the manufacturers and suppliers also reduce the largest emissions when they put in the greatest effort. Wang et al. [2] established a two-tier supply chain game model composed of producers and retailers, and through the constraints of the cost-sharing and wholesale price premium contracts of the two firms, the two firms can cooperate to achieve the carbon emission goal under the condition of Pareto improvement.

Peng等学者[3]所研究的供应链，由碳排放配额和交易计划下产量不确定的供应商和制造商构成，采用 Stackelberg模型，对集中和分散的供应链中数量折扣合同和收入共享合同、生产、价格、碳减排决策进行分析。通过引入一种新型的收入共享契约，结合减排补助的协同效应，实现对产量不确定因素的协调；同时，通过引入数量折扣契约，实现对低碳供应链的协调。Yu等学者[4]则指出，零售商只偏好批发价格合约，而生产商甚至供应链更偏好利润分享合约，而非成本分摊合约。较高份额的利益分享能减少成本，减少排放量，造福于消费者。
Peng et al. [3] used the Stackelberg model to analyze quantity discount contracts and revenue sharing contracts, production, price, and carbon emission reduction decisions in centralized and decentralized supply chains, consisting of suppliers and manufacturers with uncertain output under carbon emission allowance and trading schemes. By introducing a new type of revenue sharing contract, combined with the synergistic effect of emission reduction subsidies, the coordination of output uncertainties can be realized; At the same time, through the introduction of quantity discount contracts, the coordination of low-carbon supply chains will be realized. Yu et al. [4] point out that retailers only prefer wholesale-price contracts, while producers and even supply chains prefer profit-sharing contracts rather than cost-sharing contracts. A higher share of benefit-sharing reduces costs, reduces emissions, and benefits consumers.

Hu等学者[5]通过数值分析，将碳税政策和碳总量管制与贸易政策进行了比较，得出结论：只有在碳配额水平太高的时候，碳税政策才会更好。
Hu et al. [5] compared the carbon tax policy with the total carbon cap policy with the trade policy through numerical analysis, and concluded that the carbon tax policy would be better only when the carbon quota level was too high.

谢新鹏等学者[6]针对碳排放配额提供者与两个生产商构成的供应链，构建了纳什均衡问题的博弈模型，对其进行了分析。提出在供应链对碳排放进行严格管控，政府对其设定了一定的碳排放权，可以使得其能够通过契约方式获得更大的收益，从而使得其收益更高。
Xie Xinpeng et al. [6] constructed a game model of the Nash equilibrium problem for the supply chain composed of carbon emission allowance providers and two producers, and analyzed it. It is proposed that carbon emissions should be strictly controlled in the supply chain, and the government has set certain carbon emission rights for it, which can enable it to obtain greater benefits through contracts, so as to make its benefits higher.

Li G[7]研究了国家配额制度和贸易制度对企业节能减排和低碳生产决策的影响，并揭示了消费者的低碳偏好程度对其决策有重要的影响。
Li G. [7] studied the impact of the national quota system and the trade system on the decision-making of enterprises on energy conservation, emission reduction and low-carbon production, and revealed that the degree of consumers' low-carbon preference has an important impact on their decision-making.

2.2 考虑政府补贴的低碳供应链
2.2 Consider government-subsidized low-carbon supply chains

目前，我国已有众多政府针对低碳减排的政策，这些政策对于企业开展生产和减排工作具有比较显著的影响，但是其效果如何以及影响的具体程度还需要通过试验来检验，这也是很多学者所关注的问题。Chen和Hu [8]运用演化博弈的方法，证明，双边动态税负与补贴对企业低碳生产的影响更大。Cao等学者[9]对碳配额交易和补贴政策对制造商生产和减排的影响进行了分析，并探讨了对社会更有利的政策。
At present, there are many government policies for low-carbon emission reduction in China, which have a significant impact on the production and emission reduction work of enterprises, but the effect and the specific degree of impact still need to be tested through experiments, which is also a problem that many scholars are concerned about. Chen and Hu [8] used the evolutionary game method to prove that bilateral dynamic tax burdens and subsidies have a greater impact on firms' low-carbon production. Cao et al. [9] analyzed the impact of carbon allowance trading and subsidy policies on manufacturers' production and emission reduction, and discussed policies that are more beneficial to society.

李友东等学者[10]将最优的碳减排成本与最优补贴纳入到模型中，对补贴政策与合作减排决策的关系进行了较为系统的研究。赵敬华等人[11]研究了不同类型的政府补助对渠道成员的价格和收益的影响，结果表明，当政府补助的目标不同时，会产生不同的补助效应。汪传旭等学者[12]研究了碳排放限制对闭环供应链中政府与供应链决策的影响，并在此基础上探索了政府补贴、碳排放限制、碳排放比率等多个变量对其优化决策执行的作用机制。
Li Youdong et al. [10] incorporated the optimal carbon emission reduction cost and optimal subsidy into the model, and systematically studied the relationship between subsidy policy and cooperative emission reduction decision-making. Zhao et al. [11] studied the impact of different types of government subsidies on the prices and returns of channel members, and the results showed that when the targets of government subsidies are different, different subsidy effects will occur. Wang Chuanxu et al. [12] studied the impact of carbon emission restrictions on government and supply chain decision-making in closed-loop supply chains, and explored the mechanism of multiple variables such as government subsidies, carbon emission restrictions, and carbon emission ratios on the implementation of optimal decision-making.

张正等学者[13]基于技术创新，对政府的研发和消费补贴对供应链决策的影响进行了研究，发现实施研发和消费补贴等激励措施，不但可以提高供应链中企业的技术创新，还能使供应链中的利润得到明显提高。曹裕等学者[14]将无政府补助和单一补助进行比较，并以此为依据，分别考察了在政府和供应链内部两种补助政策下，供应链的最优决策。
Zhang Zheng et al. [13] studied the impact of government R&D and consumption subsidies on supply chain decision-making based on technological innovation, and found that the implementation of incentives such as R&D and consumption subsidies can not only improve the technological innovation of enterprises in the supply chain, but also canSo that the profit in the supply chain has been significantly improved. Cao Yu et al. [14] compared no government subsidies with single subsidies and used this as a basis to examine the benefits of government and supply chains, respectively Under the two subsidy policies of the ministry, the optimal decision-making of the supply chain.

夏西强等学者[15]将政府补贴与碳税政策在低碳经济中的作用纳入考量，在构建两个生产模型的基础上，得出在低碳企业同时生产这两个产品的情况下，政府的补贴同步减低产品的销售价格。而在低碳型企业仅生产低碳型产品的情况下，政府采取碳税政策将导致销售价格提高。
Xia Xiqiang et al. [15] consider the role of government subsidies and carbon tax policies in a low-carbon economy, and on the basis of constructing two production models, they conclude that when low-carbon enterprises produce both products, government subsidies are reduced simultaneouslyThe selling price of the product. In the case of low-carbon enterprises that only produce low-carbon products, the government's adoption of a carbon tax policy will lead to higher selling prices.

2.3 碳交易理论
23 Carbon Trading Theory

碳交易是指将二氧化碳排放权当作一种商品，将碳限额和碳配额交易进行统一，在碳交易合同中，一方通过向另一方支付温室气体减排额，买家可以将购买的减排额用于缓解温室效应，从而实现其减排的目的。排污权交易在20世纪被提出并演化出碳交易，中国的碳交易市场中实施的是免费分配初始碳配额的政策。
Carbon trading refers to the carbon dioxide emission rights as a commodity, the carbon allowance and carbon allowance trading are unified, in the carbon trading contract, one party pays the other party greenhouse gas emission reductions, buyers can use the purchased emission reductions to mitigate the greenhouse effect, so as to achieve their emission reduction purposes. Emissions trading was proposed in the 20th century and evolved into carbon trading, and China's carbon trading market implements a policy of free allocation of initial carbon allowances.
许多学者都在探讨碳交易的监管与发展问题。王科等学者[16]通过整理中国碳市建设的相关政策，对比不同试点区域的运作情况和效果，进行经验分析，归纳不同试点区域所采取的减少和减少措施，并对其效果进行初步评估，最终为中国碳市建设提供相关的政策建议。尹敬东等学者[17]在比较了世界上几种主要的碳排放交易体系后，指出了中国在实施碳排放交易时存在的问题，并提出了解决问题的措施。本课题将在此基础上，对中国的碳排放交易体系进行比较和分析。郭道燕等学者[18]以消费者端的碳交易为切入点，研究博弈行为的演进稳定性，利用政府和家庭组成的博弈模型,进行模拟仿真，指明多个情形下不同主体的关系，为政府制定初始碳配额的政策提供参考。Liu等学者[19]通过建立台湾地区碳市场的供给与需求模型，通过对四种不同的交易方案进行对比，得出最优的交易定价与时机，为政府制定相应的碳交易政策提供参考。
Many scholars have discussed the regulation and development of carbon trading. Wang Ke et al. [16] summarized the reduction and reduction measures taken in different pilot areas by collating the relevant policies of China's carbon city construction, comparing the operation and effects of different pilot areas, conducting empirical analysis, and making a preliminary assessment of their effects. Finally, it provides relevant policy recommendations for the construction of China's carbon city. Yin Jingdong et al. [17] compared several major ETS in the world, pointed out the problems existing in China's implementation of ETS, and proposed measures to solve them. On this basis, this topic will compare and analyze China's ETS. Guo Daoyan et al. [18] took carbon trading on the consumer side as the starting point to study the evolution and stability of game behavior, using government and household compositionThe game model is simulated to indicate the relationship between different subjects in multiple situations, and provide a reference for the government to formulate the policy of initial carbon quotas. Liu et al. [19] established a supply and demand model of Taiwan's carbon market, and compared four different trading schemes to obtain the optimal trading pricing and timing, which provided a reference for the government to formulate corresponding carbon trading policies.
Ivan Kockar[20]分析了碳交易对欧洲国家碳排放的约束，分析了输电容量对发电计划的影响，并对其在碳减排、成本和发电效率等方面的作用进行了评价。Du等学者[21]利用博弈理论，研究了基于碳交易的碳排放相关供应链各成员在碳交易中的行为与决策。在欧盟碳交易体系基础上，Jaber等人[22]利用两级供应链模型对各种碳交易方案及其组合进行了分析，从而为企业在不同的碳交易方式下，最大限度地降低了库存和碳排放成本。
Ivan Kockar [20] analyzed the constraints of carbon trading on carbon emissions in European countries, analyzed the impact of transmission capacity on power generation plans, and evaluated its role in carbon emission reduction, cost, and power generation efficiency. Du et al. [21] used game theory to study the behavior and decision-making of members of the carbon emission related supply chain based on carbon trading. Based on the EU ETS, Jaber et al. [22] used a two-tier supply chain model to evaluate various carbon trading schemes and theirThe combination was analysed to minimize inventory and carbon emission costs for companies under different carbon trading methods.

2.4 信息不对称理论
24 Information Asymmetry Theory

计国君等学者[23] 在信息不对称的情况下利用Satckelberg模型，分析了一个零售商与两个制造商组成的供应链进行决策的问题，解释其中的三方博弈机制，并探讨其对供应链绩效的影响。Wang等学者[24]对在信息不对称的情况下，由风险中立的零售商和具有生产成本的风险中立供应商构成的供应链的契约进行了研究，并对不同契约对供应链绩效的影响进行了分析和对比。
Ji Guojun et al. [23] used the Satckelberg model to analyze the situation of information asymmetryThe problem of a retailer making decisions with a supply chain consisting of two manufacturersExplain the three-way game mechanism and explore its impact on supply chain performance. Wang et al. [24] describe the contract of the supply chain consisting of risk-neutral retailers and risk-neutral suppliers with production costs in the case of information asymmetryA study was conducted and the impact of different contracts on supply chain performance was analyzed and compared.

2.5 文献评述
2.5 Literature Review

通过对上述四个方面和供应链相关的文献整理可得，现有研究已经从不同的视角对低碳供应链各种问题进行了积极探索并取得丰富的研究成果，为制造商进行低碳生产提高了借鉴的思路，但在低碳生产与消费者的效用研究方面还存在一定的研究空间：
Through the literature collation of the above four aspects and supply chain, the existing studies have actively explored various problems of low-carbon supply chain from different perspectives and obtained rich research results, which improves the reference ideas for manufacturers to carry out low-carbon production, but there is still some research space in the research on the utility of low-carbon production and consumers:

（1）目前关于低碳供应链的研究多集中于制造商和零售商方面，以及相关的政策和减排合作，而对于社会中普遍存在的消费者效用的关注较少。然而，随着低碳政策的普及，消费者的低碳商品购买偏好增加，低碳供应链也需要考虑消费者效用对供应链所产生的影响。因此，本文引入消费者效用函数，分析消费者对低碳供应链的影响。
(1) At present, most of the research on low-carbon supply chains focuses on manufacturers and retailers, as well as related policies and emission reduction cooperation, and pays less attention to the consumer utility that is prevalent in society. However, with the popularization of low-carbon policies, consumers' preference for low-carbon goods has increased, and the impact of consumer utility on the supply chain also needs to be considered in the low-carbon supply chain. Therefore, this paper introduces the consumer utility function to analyze the impact of consumers on the low-carbon supply chain.

（2）目前低碳减排方法主要采取的手段是碳减排权交易市场和碳税政策的影响为主，由于低碳政策还属于起步发展的阶段，相关法律法规和优惠政策还不完善，将低碳生产技术和碳补贴结合的研究较少。因此，本文有必要研究低碳生产技术和碳补贴对低碳供应链的促进作用。
(2) At present, the main means of low-carbon emission reduction methods are the impact of carbon emission reduction rights trading market and carbon tax policy, because low-carbon policy is still in the initial stage of development, relevant laws, regulations and preferential policies are not perfect, and there are few studies on the combination of low-carbon production technology and carbon subsidies. Therefore, it is necessary to study the role of low-carbon production technologies and carbon subsidies in promoting low-carbon supply chains.

3. 不引进低碳技术下的低碳供应链信息共享模型
3.Do not introduce a low-carbon supply chain information sharing model under low-carbon technologies

3.1 情景描述
31 Scenario description

在低碳供应链内，零售商可以直接根据消费者的历史需求获取准确的消费者需求，但因为制造商不能获得历史需求，无法直接获得准确的消费者需求。因此当零售商选择不共享需求信息时，制造商需要多生产一定数量的商品防止缺货的情况出现。
Within a low-carbon supply chain, retailers can capture accurate consumer demand directly based on their historical needs, but because: Manufacturers don't have access to historical demand and can't get accurate consumer demand directly. So when a retailer chooses not to share demand information, the manufacturer needs to produce a certain amount of morePrevent stockouts.

零售商选择是否与制造商共享需求信息分为以下两种情况：（1）零售商获得消费者需求，并决定与制造商共享消费者需求，制造商可以准确安排生产计划，避免额外的生产，以达到供应链最优利润。（2）零售商获得需求信息，但是选择不与制造商共享需求信息，制造商需要生产更多的商品来应对消费者需求以下内容分别就上述两种不同的信息共享策略对制造商和零售商的最优利润和决策进行分析。
There are two scenarios in which a retailer chooses whether or not to share demand information with a manufacturer: (1) The retailer obtains consumer demand and decides to share it with the manufacturerManufacturers can accurately schedule production and avoid additional production to achieve optimal profits in the supply chain. (2) The retailer obtains demand information, but chooses not to share the demand information with the manufacturer, and the manufacturer needs to produce more goods to meet consumer demandDifferent information-sharing strategies analyze optimal profits and decisions for manufacturers and retailers.

3.2 模型参数设置和假设
32 Model parameter settings and assumptions

3.2.1 参数设置与假设
3.2.1 Parameter settings and assumptions

在低碳供应链中，消费者对低碳产品的偏爱程度会对市场的总需求产生影响。为方便计算，特作以下假定及解释：
In a low-carbon supply chain, consumers' preference for low-carbon products will have an impact on the total demand in the market. For the sake of calculation, the following assumptions and explanations are made:

假设4-1：消费者根据预期效用判断是否购买商品，当预期效用大于0时，选择购买该商品，每位消费者最多购买一次该商品。
Hypothesis 4-1: Consumers decide whether to buy a product based on the expected utility, and choose to buy the product when the expected utility is greater than 0, each consumer can purchase the product at most once.

假设4-2：市场消费者规模标准化为1，其中低碳商品偏好消费者占比 $β$ ，无偏好消费者占比（1- $β$ ）
Hypothesis 4-2: The size of market consumers is standardized to 1, in which the proportion of consumers who prefer low-carbon goods and the proportion of consumers who have no preference (1- $β$ $β$ ）

假设4-3：制造商所采取的减碳技术为降低能源消耗的技术。
Hypothesis 4-3: The carbon reduction technology adopted by the manufacturer is the technology to reduce energy consumption.

假设4-4：当确定是否引进低碳技术后，市场需求是确定的，且与产量相等，即D= $1-pθ+pβτ$ （选择引进低碳技术时）或 $D=1-pθ-pβτ$ （未引进低碳技术时）。
Hypothesis 4-4: When it is determined whether to introduce low-carbon technologies, the market demand is certain and equal to the output, i.e., D = $1-pθ+pβτ$ (when choosing to introduce low-carbon technologies) or $D=1-pθ-pβτ$ (When low-carbon technologies have not been introduced).

符合说明如下表所示：
The compliance instructions are shown in the following table:

符号 symbol	符号说明 Description of the symbol
L、F	低碳偏好消费者、无低碳偏好消费者 Low-carbon preference consumers, non-low-carbon preference consumers
y、z	低碳偏好消费者人数、无低碳偏好消费者人数 The number of consumers with a low-carbon preference and the number of consumers without a low-carbon preference
U	消费者的效用 Consumer utility
V	消费者估值 Consumer valuation
	消费者对低碳商品的敏感程度 Consumers' sensitivity to low-carbon goods
	消费者对价格的敏感程度 The degree of price sensitivity of consumers
	低碳偏好消费者所占比重 The proportion of low-carbon preference consumers
m、r	制造商、零售商 Manufacturers, retailers
	制造成本 Manufacturing costs
e	单位耗能 Unit energy consumption
	单位耗能成本 Cost per unit of energy consumption
p	零售价格 Retail price
w	批发价格 wholesale prices
D	消费者总数 Total number of consumers
σ	无信息共享时多生产的商品数量 The number of goods produced when there is no information sharing
t	t碳排放惩罚率 Carbon emission penalty rate
x	改进技术后单位降低能耗 After improving the technology, the unit energy consumption is reduced
T	引进改进技术资金 Introduce funds for improvement technology

3.2.2 低碳偏好消费者需求
32.2 Low-carbon preference consumer demand

在这种情况下，销售商采取的是无差异的价格，消费者则以期望的效用作为决策依据。通过对消费者的效用函数分析，可得到消费者对商品的需求与价格的关系。
In this case, the seller adopts an undifferentiated price, and the consumer bases the decision on the desired utility. Through the analysis of the utility function of consumers, the relationship between consumers' demand for goods and prices can be obtained.

因为消费者是理性人，因此当价格越高时，消费者购买商品的倾向就越小，反之，当价格越低时，消费者购买该商品的可能也就越大。因而引入价格敏感因子 $θ$ ，又因为低碳消费者喜欢低碳商品，因而当销售商品为低碳商品时，消费者的预期效用是： $U_{L1} = V_{L}$ - $θ$ *p+ $τ*p$ ；而当销售商品不是低碳商品时，消费者的预期效用是： $U_{L2} = V_{L}$ - $θ$ *p- $τ*p$
Because consumers are rational people, when the price is higher, the consumer is less inclined to buy the goods, and conversely, when the price is lower, the consumers are more likely to buy the goods. Therefore, the price sensitivity factor $θ$ is introduced, and because low-carbon consumers like low-carbon goods, when the goods sold are low-carbon goods, the expected utility of the consumer is: $U_{} = V_{}$ - $θ$ *p+ $τ*p$ ; And when the goods sold are not low-carbon goods, the expected utility of consumers is: $U_{} = V_{}$ - $θ$ *p- $τ*p$

而消费者选择是否购买该商品是基于该商品的预期效用是否大于0，当商品预期效用大于0时，消费者会选择购买该商品，而当商品的预期效用小于0时，消费者不会购买该商品。因而当预期效用等于0时，可以获到商品的临界估值： ${V_{L1}}^{*} = θ$ *p- $τ*p$ 和 ${V_{L2}}^{*} = θ$ *p+ $τ*p$
The consumer's choice to buy the product is based on whether the expected utility of the product is greater than 0, and when the expected utility of the product is greater than 0, the consumer willChoose to buy the product, and when the expected utility of the product is less than 0, the consumer will not buy the product. Therefore, when the expected utility is equal to 0, the critical valuation of the commodity: ${V_{}}^{} = θ$ *p- $τ*p$ and ${V_{}}^{} = θ$ *p+ $τ*p$

因为无低碳商品偏好消费者对低碳商品不敏感，因此无低碳商品偏好消费者的预期效用为： $U_{F} = V_{F}$ - $θ$ *p，同理可以得到无低碳商品偏好消费者的临界估值： ${V_{F}}^{*} = θ$ *p
Because consumers without a preference for low-carbon goods are not sensitive to low-carbon goods, the expected utility of consumers without a preference for low-carbon goods is: $U_{} = V_{}$ - $θ$ *p, the same can be done to obtain a critical valuation for consumers with no preference for low-carbon goods: ${V_{}}^{} = θ$ * p

根据假设4-2，可以得出低碳商品偏好消费者和无低碳商品偏好消费者的总人数y1（未引进低碳生产技术时）、y2（引进低碳生产技术后）和z：
According to hypothesis 4-2, the total number of consumers with a preference for low-carbon goods and consumers without a preference for low-carbon goods can be obtained, y1(when low-carbon production technologies are not introduced), y2 (after the introduction of low-carbon production technologies) and z:

y1= $β$ (1- ${V_{L}}^{*}$ )= $β$ (1- $θ$ *p- $τ*p$ )

y2= $β$ (1- ${V_{L}}^{*}$ )= $β$ (1- $θ$ *p+ $τ*p$ )

z=(1- $β)$ (1- ${V_{F}}^{*}$ )= (1- $β)$ (1- $θ$ *p)

加后可以得到购买该商品的消费者总人数，即总需求为：D1= $β$ (1- ${V_{L1}}^{*}$ )+(1- $β)$ (1- ${V_{F}}^{*}$ ) = $1-pθ-pβτ$ （未引进低碳生产技术时）和D2= $β$ (1- ${V_{L2}}^{*}$ )+(1- $β)$ (1- ${V_{F}}^{*}$ ) = $1-pθ+pβτ$ （引进低碳生产技术后）
After adding, the total number of consumers who buy the product can be obtained, that is, the total demand is: D1= $β$ (1- ${V_{}}^{}$ ) + (1- $β)$ (1- ${V_{}}^{}$ ) = $1-pθ-pβτ$ (when low-carbon production technologies are not introduced) and D2= $β$ (1- ${V_{}}^{}$ )+(1- $β)$ (1- ${V_{}}^{}$ ) = $1-pθ+pβτ$ (after the introduction of low-carbon production technologies).

对D1和D2分别对p求导后可得 $-θ-βτ$ 和 $-θ+βτ$ 。因为市场需求与价格p相关，当价格升高时，需求减小因而 $-θ-βτ<-θ+βτ<0$ ，即 $βτ<θ$
For D1 and D2, we can obtain $-θ-βτ$ and after finding the derivatives for p, respectively $-θ+βτ$ . Because market demand is related to price p, when the price increases, the demand decreases, i.e $βτ<θ$ $-θ-βτ<-θ+βτ<0$ .

3.3 不引进低碳技术下选择信息不共享策略
3.3 Choose a non-sharing strategy for information without introducing low-carbon technologies

当零售商选择不与制造商共享消费者需求时，制造商需要多生产σ数量的商品。而生产时所需成本和所缴纳的税收由制造商来承担。生产该商品所需要的成本原材料为 $c_{0}$ ，同时生产一个单位的商品需要消耗 $e$ 的能量，并且每单位的能耗需要缴纳 $c_{e}$ 单位的费用。因此生产成本为：
e , and the energy required to produce one unit of the commodity is e. And each unit of energy consumption needs to pay $c_{}$ the unit fee. Therefore, the production cost is:

c= $c_{0} +e* c_{e}$

而制造商除了需要承担生产成本外，还需缴纳碳税，每单位能耗的碳税惩罚率为：t。由此可以得到零售商和制造商的利润分别为：
In addition to the production costs, manufacturers also need to pay a carbon tax, and the carbon tax penalty rate per unit of energy consumption is: t. From this, the profits for retailers and manufacturers are as follows:

$\prod_{}^{} r 1$ =（p-w）（D1）

$\prod_{}^{} m$ 1=（w- $c_{0} +e* c_{e} -e*t$ ）（D1+σ）

在不引进低碳技术下零售商选择信息不共享策略，得到的最优定价和利润为：
Retailers who choose the information non-sharing strategy without introducing low-carbon technologies will get the following optimal pricing and profits

w1= $\frac{1+etθ+2σ+etβτ+θ c_{0} +βτ c_{0} -eθ c_{e} -eβτ c_{e}}{2 (θ+βτ)}$

$p = (3+et θ +2 σ +et βτ + θ c_{0} + βτ c_{0} -e θ c_{e} -e βτ c_{e}) / 4 (θ + βτ)$

D= $\frac{1}{4} (1-etθ-2σ-etβτ-θ c_{0} -βτ c_{0} +eθ c_{e} +eβτ c_{e})$

$\prod_{}^{} r 1$ = $\frac{{(-1+etθ+2σ+etβτ+ (θ+βτ) c_{0} -e (θ+βτ) c_{e})}^{2}}{16 (θ+βτ)}$

$\prod_{}^{} m$ 1= $\frac{{(-1+etθ-2σ+etβτ+ (θ+βτ) c_{0} -e (θ+βτ) c_{e})}^{2}}{8 (θ+βτ)}$

证明：
Prove:

利用逆向归纳求导法，求解供应链中的博弈问题。
The reverse induction derivation method is used to solve the game problem in the supply chain.

首先，算零售商的最优利润函数：
First, calculate the optimal profit function for retailers:

将D1= $1-pθ-pβτ$ 代入 $\prod_{}^{} r 1$ =（p-w）（D1）得： $\prod_{}^{} r 1 = (-p+w+ p^{2} θ-pwθ+ p^{2} βτ-pwβτ)$ ，对 $\prod_{}^{} r 1$ 求p的一阶导数有： $-1-2pθ-wθ-2pβτ-wβτ$ ，二阶导有： $-2θ-2βτ$ <0，所以零售商的利润函数为凹函数，令一阶偏导的结果为0，得到p1和D1：
Substitute D1= $1-pθ-pβτ$ into $\prod_{}^{} r 1$ =(p-w)(D1Gotta : $\prod_{}^{} r 1 = (-p+w+ p^{} θ-pwθ+ p^{} βτ-pwβτ)$ , the first derivative of $\prod_{}^{} r 1$ p is: $-1-2pθ-wθ-2pβτ-wβτ$ , and the second derivative is: $-2θ-2βτ$ <0, so the profit function of the retailer is a concave function, so that the result of the first partial derivative is 0, and p is obtained1 and D1:

p1 = $\frac{1+wθ+wβτ}{2 (θ+βτ)}$ D1= $\frac{1}{2} (1-wθ-wβτ)$

将上述得到的p1和D1代入 $\prod_{}^{} m 1$ ，计算制造商利润：
Substituting the above obtained p1 and d1 into $\prod_{}^{} m 1$ , the manufacturer's profit is calculated:

将p1和D1代入 $\prod_{}^{} m 1 \prod_{}^{} m 1$ =（w- $c_{0} +e* c_{e} -e*t$ ）（D1+σ）
Substitute p1 and d1 into $\prod_{}^{} m 1 \prod_{}^{} m 1$ =(w- $c_{} +e* c_{} -e*t$ ）（D1+σ）

代入得：
Substitution:

$\prod_{}^{} m 1$ = $\frac{1}{2} (et+w+etwθ- w^{2} θ-2etσ+2wσ+etwβτ- w^{2} βτ- c_{0} +wθ c_{0} -2σ c_{0} +wβτ c_{0} +e c_{e} -ewθ c_{e} +2eσ c_{e} -ewβτ c_{e})$

对 $\prod_{}^{} m 1$ 求w的一阶偏导得： $\frac{1}{2} (1+etθ-2wθ+2σ+etβτ-2wβτ+θ c_{0} +βτ c_{0} -eθ c_{e} -eβτ c_{e})$ ，二阶偏导为： $\frac{1}{2} (-2θ-2βτ)$ <0，令一阶偏导的结果为0，可以得到批发价格的最优解w1。
$\prod_{}^{} m 1$ The first-order partial derivative of w is obtained: $\frac{1}{2} (1+etθ-2wθ+2σ+etβτ-2wβτ+θ c_{} +βτ c_{} -eθ c_{} -eβτ c_{})$ , and the second-order partial derivative is: $\frac{1}{2} (-2θ-2βτ)$ %3C0, so that the result of the first-order partial derivative is 0, and the optimal solution of the wholesale price w 1 can be obtained.

w1= $\frac{1+etθ+2σ+etβτ+θ c_{0} +βτ c_{0} -eθ c_{e} -eβτ c_{e}}{2 (θ+βτ)}$

最后再将得到的w1代入p1和D1中可以得到最优价格和相对应的消费者人数为：
Finally, substituting the obtained w1 into p1 and D1 can obtain the best price and the corresponding number of consumers as:

$p 1 = (3+et θ +2 σ +et βτ + θ c_{0} + βτ c_{0} -e θ c_{e} -e βτ c_{e}) / 4 (θ + βτ)$

D1= $\frac{1}{4} (1-etθ-2σ-etβτ-θ c_{0} -βτ c_{0} +eθ c_{e} +eβτ c_{e})$

最后再将上述得到的结果分别代入 $\prod_{}^{} r 1$ 和 $\prod_{}^{} m 1$ 中可以得到：
Finally, the above results can be substituted into $\prod_{}^{} r 1$ and respectively, and $\prod_{}^{} m 1$ we can get the following

$\prod_{}^{} r 1$ = $\frac{1}{16} (-2et+ e^{2} t^{2} θ+4etσ+ e^{2} t^{2} βτ+ \frac{1}{θ+βτ} - \frac{4σ}{θ+βτ} + \frac{4 σ^{2}}{θ+βτ} -2 c_{0} +2etθ c_{0} +4σ c_{0} +2etβτ c_{0} +θ +βτ +2e c_{e} -2 e^{2} tθ c_{e} -4eσ c_{e} -2 e^{2} tβτ c_{e} -2eθ c_{0} c_{e} -2eβτ c_{0} c_{e} + e^{2} θ + e^{2} βτ)$

化简后可得：
Simplified, you get:

$\prod_{}^{} r 1 = \frac{{(-1+etθ+2σ+etβτ+ (θ+βτ) c_{0} -e (θ+βτ) c_{e})}^{2}}{16 (θ+βτ)}$

$\prod_{}^{} m 1$ = $\frac{1}{8} (-2et+ e^{2} t^{2} θ-4etσ+ e^{2} t^{2} βτ+ \frac{1}{θ+βτ} + \frac{4σ}{θ+βτ} + \frac{4 σ^{2}}{θ+βτ} -2 c_{0} +2etθ c_{0} -4σ c_{0} +2etβτ c_{0} +θ +βτ +2e c_{e} -2 e^{2} tθ c_{e} +4eσ c_{e} -2 e^{2} tβτ c_{e} -2eθ c_{0} c_{e} -2eβτ c_{0} c_{e} + e^{2} θ + e^{2} βτ)$

= $\frac{{(-1+etθ-2σ+etβτ+ (θ+βτ) c_{0} -e (θ+βτ) c_{e})}^{2}}{8 (θ+βτ)}$

最后将得到的 $\prod_{}^{} r 1$ 和 $\prod_{}^{} m 1$ 相加可以得到不引进低碳技术下选择信息不共享策略的供应链总利润为：
Finally, the sum $\prod_{}^{} m 1$ of the $\prod_{}^{} r 1$ obtained can be added to obtain the total profit of the supply chain that chooses the information non-sharing strategy without introducing low-carbon technologies as:

$\prod_{}^{} sc 1$ = $\frac{1}{16 (θ+βτ)} (3+4σ (1+3σ) -2et (3+2σ) (θ+βτ) +3 e^{2} t^{2} {(θ+βτ)}^{2} + (θ+βτ) (c_{0} -e c_{e}) (-6-4σ+6et (θ+βτ) +3 (θ+βτ) (c_{0} -e c_{e})))$

3.4 不引进低碳技术下选择信息共享策略
3.4 Choose an information-sharing strategy without introducing low-carbon technologies

零售商获得准确的消费者需求，并选择与制造商共享需求信息。在信息共享的情况下， $σ=0$ 。所以制造商利润为： $\prod_{}^{} m 2$ =（w- $c_{0} +e* c_{e} -e*t$ ）（D1）
Retailers get accurate consumer demand and choose to share demand information with manufacturers. In the case of information sharing. $σ=0$ So the manufacturer's profit is: $\prod_{}^{} m 2$ =(w- $c_{} +e* c_{} -e*t$ )(D1).

同样采用逆向归纳法对供应链的博弈进行计算，结果如下所示：
The reverse induction method is also used to calculate the game of the supply chain, and the results are as follows:

w2= $\frac{1+etθ+etβτ+θ c_{0} +βτ c_{0} -eθ c_{e} -eβτ c_{e}}{2 (θ+βτ)}$

$p 2= \frac{1}{4} (et+ \frac{3}{θ+βτ} + c_{0} -e c_{e})$

D $2= \frac{1}{4} (1-etθ-etβτ-θ c_{0} -βτ c_{0} +eθ c_{e} +eβτ c_{e})$

$\prod_{}^{} r 2$ = $\frac{{(-1+etθ+etβτ+θ c_{0} +βτ c_{0} -eθ c_{e} -eβτ c_{e})}^{2}}{16 (θ+βτ)}$

$\prod_{}^{} m 2$ = $\frac{{(-1+etθ+etβτ+ (θ+βτ) c_{0} -e (θ+βτ) c_{e})}^{2}}{8 (θ+βτ)}$

$\prod_{}^{} sc 2$ == $\frac{3 {(-1+etθ+etβτ+ (θ+βτ) c_{0} -e (θ+βτ) c_{e})}^{2}}{16 (θ+βτ)}$

3.5 信息共享策略分析和比较
3.5 Analysis and comparison of information sharing strategies

本节主要分析消费者对低碳商品敏感程度τ、对价格敏感因子θ和碳排放惩罚率t对均衡解的影响，并分析了在不同的信息分享策略下的均衡解，为零售商对生产商的需求信息分享问题给出了相应的依据。
This section mainly analyzes consumers' sensitivity τ to low-carbon commodities, price sensitivity factor θ, and carbon emission penalty rateThe influence of t on the equilibrium solution, and the equilibrium solution under different information sharing strategies are analyzed, which gives a corresponding basis for the demand information sharing problem of retailers and manufacturers.

3.5.1 影响因子分析
3.5.1 Impact factor analysis

本研究的低碳供应链中，低碳偏好消费者的商品效用不单取决于商品价值，还取决于是否为低碳商品。下面对对低碳商品敏感程度 $τ$ 、价格敏感因子 $θ$ 和碳排放惩罚率t对不同信息共享策略得到的最优销售价格的影响。因此，假设制造商生产的商品多于实际的消费者需求，即 $σ$ >0。
In the low-carbon supply chain of this study, the utility of goods of low-carbon preference consumers depends not only on the value of the goods, but also on whether they are low-carboncommodity. The following is the sensitivity $τ$ to low-carbon commodities and price sensitivity factors $θ$ and the impact of carbon emission penalty rate t on the optimal selling price obtained by different information sharing strategies. Therefore, the hypothetical manufacturer produces more goods than the actual consumer demand, i.e $σ$ ., >0.

通过计算一阶偏导可以得出以下结果：
By calculating the first-order partial derivative, the following results can be obtained:

$\frac{∂D1}{∂ t} = \frac{∂D2}{∂ t} = \frac{1}{4} (-eθ-eβτ)≤0$

$\frac{∂D1}{∂τ} = \frac{∂D2}{∂τ} =- \frac{1}{4} β(c_{0} +e(t- c_{e})) ≤0$

$\frac{∂D1}{∂θ} = \frac{∂D2}{∂θ} =- \frac{1}{4} (c_{0} +e(t- c_{e})) ≤0$

对价格敏感因子越大，就意味着消费者对商品的价格越敏感。消费者由于是理性的决策人，因此当商品的价格越高时，消费者就会越不想购买该商品，因此购买的总人数也会相对应的减少。
The greater the price sensitivity factor, the more sensitive consumers are to the price of goods. Since consumers are rational decision-makers, when the price of a product is higher, the less consumers will want to buy the product, so the total number of people who buy it will decrease correspondingly.

因为，低碳偏好消费者喜好低碳商品，因此当商品不是低碳商品时，当对低碳商品敏感程度 $τ$ 越高，消费者购买该商品的可能也就越小，因此市场需求也就随着对低碳商品敏感程度 $τ$ 的增大而减小。而当碳排放惩罚率t增大时，制造商为了维持一定水平的利润，选择提高批发价w，而面对批发价格w的上涨，零售商也会相对应的提高零售价格，而当零售价格升高时，根据需求函数的模型，消费者购买商品的意愿会降低，而商品的销量也会减少，所以市场需求随着碳排放惩罚率t的增大，而减少。
Because, low-carbon preference consumers prefer low-carbon goods, so when the goods are not low-carbon goods, when the low-carbon goodsSensitivity $τ$ The higher it is, the less likely consumers are to buy the product, so the market demand decreases as the sensitivity $τ$ to low-carbon goods increases. When the carbon emission penalty rate t increases, manufacturers choose to increase the wholesale price w in order to maintain a certain level of profit, and face the rise of the wholesale price wWhen the retail price increases, according to the model of the demand function, consumers' willingness to buy goods will decrease, and the sales of goods will also decrease. Therefore, the market demand decreases with the increase of the carbon emission penalty rate.

在制造商选择不引进低碳生产技术的情况下，零售商选择不与制造商共享需求信息时一阶偏导的计算结果如下所示：
In the case where the manufacturer chooses not to introduce low-carbon production technologies, the calculation results for the first-order bias derivation when the retailer chooses not to share demand information with the manufacturer are as follows:

$\frac{∂ p 1}{∂ t} = \frac{1}{4} (βτ+θ)(eθ+eβτ)$ >0

$\frac{∂ w 1}{∂ t} = \frac{e}{2} >0$

$\frac{∂ p 1}{∂τ} = \frac{1}{4} β(βτ+θ)(c_{0} +e(t- c_{e}))>0$

$\frac{∂ w 1}{∂τ} =- \frac{β(1+2σ)}{2 {(θ+βτ)}^{2}}$ <0

$\frac{∂ p 1}{∂θ} = \frac{1}{4} (3+etβτ+2etθ+2σ+etβτ+(βτ+2θ+βτ) c_{0} -e(βτ+2θ+βτ) c_{e})$ >0

$\frac{∂ w 1}{∂θ} =- \frac{1+2σ}{2 {(θ+βτ)}^{2}}$ <0

从上述结果可得：在零售商不共享需求信息时，在零售商选择不共享需求信息时，价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 和碳排放惩罚率t，三者的系数变大，销售价格也增大。而当低碳商品敏感程度因子变大时，消费者更倾向购买低碳商品，对低碳商品的承受能力增大，因而提高售价，获得更多利润。而对价格敏感因子 $θ$ 因子求导结果小于0，说明消费者对价格越敏感，价格也会越低。这也与我们市场生活相符合，若消费者对价格变动敏感，当商品出现折扣，消费者基于占便宜的心理，会优先选择效用高的商品。
From the above results, it can be concluded that when retailers do not share demand information, when retailers choose not to share demand information, the price sensitivity factor $θ$ and the sensitivity to low-carbon commodities $τ$ and carbon emission penalty rate t, the coefficient of the three becomes larger, and the sales price also increases. When the sensitivity factor of low-carbon commodities increases, consumers are more inclined to buy low-carbon commodities and have an increased tolerance for low-carbon commodities, thus increasing the selling price and obtaining more profits. The derivative result of the price sensitivity factor $θ$ is less than 0, indicating that consumers are more sensitive to the price, the lower the price. This is also in line with our market life, if consumers are sensitive to price changes, when there is a discount on goods, consumers will give priority to products with high utility based on the psychology of taking advantage of the bargain.

而最优批发价格随着对低碳商品敏感程度 $τ$ 和碳排放惩罚率t因子的增大而减少，且低碳商品敏感程度 $τ$ 因子与低碳商品偏好消费者 $β$ 有关。当碳排放惩罚率增大时，生产成本增多，为了保持销量，维持利润，制造商选择降低批发价格。
The optimal wholesale price decreases with the increase of the sensitivity $τ$ to low-carbon commodities and the t-factor of carbon emission penalty rate, and the sensitivity of low-carbon commodities $τ$ The factor is related to the preference of consumers $β$ for low-carbon goods. When the carbon emission penalty rate increases, the cost of production increases, and in order to maintain sales and maintain profits, manufacturers choose to reduce wholesale prices.

在制造商选择不引进低碳生产技术的情况下，零售商选择共享需求信息时，一阶偏导的计算结果如下所示：
When a retailer chooses to share demand information in a scenario where the manufacturer chooses not to introduce low-carbon production technologies, the calculation results for the first-order bias are as follows:

$\frac{∂ p 2}{∂ t} = \frac{e}{4}$ >0

$\frac{∂ w 2}{∂ t} = \frac{e}{2} >0$

$\frac{∂ p 2}{∂τ} = \frac{3β}{4 {(θ+βτ)}^{2}} >0$

$\frac{∂ w 2}{∂τ} = - \frac{β}{2 {(θ+βτ)}^{2}}$ <0

$\frac{∂ p 2}{∂θ} = - \frac{3}{4 {(θ+βτ)}^{2}}$ <0

$\frac{∂ w 2}{∂θ} = - \frac{1}{2 {(θ+βτ)}^{2}}$ <0

将该结果与上述求导结果对比可知：碳排放惩罚率影响因子对批发价格的影响与信息共享与否无关，而消费者对价格敏感因子在无信息共享时对价格求导结果大于0，而在信息共享下，结果小于0，说明当信息共享时，零售商利润受损，当消费者对价格更敏感时，零售商选择降低销售价格，提高销量，增加利润。而对比批发价格对低碳商品敏感程度和碳排放惩罚率因子的求导，批发价格在信息共享的情况下，批发价格的变低趋势更小。证明在信息共享的情况下，增大碳排放惩罚率和消费者对低碳商品的敏感程度对制造商的利润影响更小，制造商可以以更高的价格销售商品。
Comparing this result with the above derivative results, it can be seen that the impact of the influencing factor of carbon emission penalty rate on wholesale price has nothing to do with information sharing, but consumers have toThe derivative result of the price sensitivity factor is greater than 0 when there is no information sharing, while the result is less than 0 under information sharing, indicating that when the information is shared, the retailer's profit is damaged, and when consumers are more sensitive to price, the retailer chooses to reduce the sales price, increase sales and increase profits. Compared with the derivative of wholesale price sensitivity to low-carbon commodities and carbon emission penalty rate factor, the downward trend of wholesale price is smaller in the case of information sharing. It is proved that in the case of information sharing, increasing the carbon emission penalty rate and consumer sensitivity to low-carbon goods have less impact on manufacturers' profits, and manufacturers can sell goods at higher prices.

在不引进低碳生产技术下对制造商利润和零售商利润和供应链利润进行求导，并为了方便计算，令 $β=0.4 、 c_{0} =0.2 、 c_{e} =0.2 、 e=0.3 、 θ=0.5 、 σ=0.2 、 τ=0.6 、 t =0.2$ ，结果如下所示：
Without the introduction of low-carbon production technologies, the derivatives of manufacturers and retailers and supply chain profits are derived, and for the convenience of calculation, the $β=0.4 、 c_{} =0.2 、 c_{} =0.2 、 e=0.3 、 θ=0.5 、 σ=0.2 、 τ=0.6 、 t =0.2$ result is as follows:

$\frac{∂ \prod_{}^{} r 1}{∂ θ} = \frac{(et+ c_{0} -e c_{e})(-1+etθ+2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{8(θ+βτ)} - \frac{{(-1+etθ+2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}^{2}}{16 {(θ+βτ)}^{2}} =-0.0386$

$\frac{∂ \prod_{}^{} r 1}{∂ t} = \frac{1}{8} e(-1+etθ+2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e}) = -0.01695$

$\frac{∂ \prod_{}^{} r 1}{∂τ} = \frac{1}{16 {(θ+βτ)}^{2}} β(-1+etθ+2σ+etβτ+(θ+βτ) c_{0} -e[θ+βτ] c_{e})(1+etθ-2σ+etβτ+(θ+βτ) c_{0} +e[θ+βτ] c_{e} -2θ c_{e} e^{'} [θ+βτ]-2βτ c_{e} e^{'} [θ+βτ])$ = $-0.015435$

$\frac{∂ \prod_{}^{} m1}{∂ θ}$ = $\frac{1}{8 {(θ+βτ)}^{2}} (-1+etθ-2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})(1+etθ+2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})$ = $-0.4424$

$\frac{∂ \prod_{}^{} m1}{∂ t}$ = $\frac{1}{4} e(-1+etθ-2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})$ = $-0.0939$

$\frac{∂ \prod_{}^{} m1}{∂τ}$ = $\frac{1}{8 {(θ+βτ)}^{2}} β(-1+etθ-2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})(1+etθ+2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})$ = $-0.17696$

$\frac{∂ \prod_{}^{} r 2}{∂ θ}$ = $\frac{(-1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})(1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{16 {(θ+βτ)}^{2}}$ = $-0.1116$

$\frac{∂ \prod_{}^{} r 2}{∂ t}$ = $\frac{(eθ+eβτ)(-1+etθ+etβτ+θ c_{0} +βτ c_{0} -eθ c_{e} -eβτ c_{e})}{8(θ+βτ)} = - 0.03195$

$\frac{∂ \prod_{}^{} r 2}{∂τ}$ = $\frac{β(-1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})(1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{16 {(θ+βτ)}^{2}} = - 0.04465$

$\frac{∂ \prod_{}^{} m 2}{∂τ} = \frac{β(-1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})(1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{8 {(θ+βτ)}^{2}}$ = $-0.089$

$\frac{∂ \prod_{}^{} m 2}{∂ t}$ = $\frac{(eθ+eβτ)(-1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{4(θ+βτ)}$ = $-0.0639$

$\frac{∂ \prod_{}^{} m 2}{∂ θ}$ = $\frac{(-1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})(1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{8 {(θ+βτ)}^{2}}$ = $-0.223$

制造商选择不引进低碳生产技术时，无论零售商是否选择共享需求信息，；零售商最优利润和供应商最优利润都随着价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 和碳排放惩罚率t，三者的系数变大而减少。
When a manufacturer chooses not to introduce low-carbon production technologies, whether or not the retailer chooses to share demand information; The optimal profit of retailers and suppliers are all different from the price sensitivity factor $θ$ , the sensitivity $τ$ to low-carbon commodities and the carbon emission penalty rate. The coefficient of the three becomes larger and decreases.

当价格敏感因子越高时，市场需求和价格呈现下降的趋势，进而减少零售商和制造商的利润。
When the price sensitivity factor is higher, the market demand and price show a downward trend, which in turn reduces the profits of retailers and manufacturers.

此外，通过对比信息共享和无信息共享情况下的求导结果，可以发现，在无信息共享的情况下，制造商对价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 和碳排放惩罚率t，三者的波动较大，而在信息共享的情况下，零售商对价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 和碳排放惩罚率t，三者的波动较大。这也进一步证明了在信息共享下，零售商的利润相较于无信息共享时有所降低。
In addition, by comparing the derivative results of information sharing and non-information sharing, it can be found that in the absence of information sharing, manufacturers are sensitive to price factors $θ$ and low-carbon commodities $τ$ and carbon emission penalty rate t, the three fluctuate greatly, and in the case of information sharing, retailers are sensitive to price factors $θ$ and low-carbon goodsSensitivity $τ$ and carbon emission penalty rate t, which fluctuates greatly. This is further evidence that retailers' profits are lower when information is shared than when information is not shared.

3.5.2 最优解比较和讨论
3.5.2 Comparison and discussion of optimal solutions

我们利用制造商与零售商之间的博弈，探讨零售商在不同信息分享策略下的最佳决策。当制造商没有采用低碳技术时，两个不同的信息分享策略之间的差异可以通过下面的分析得到：
We use the game between manufacturers and retailers to explore the best decisions for retailers under different information-sharing strategies. When manufacturers do not adopt low-carbon technologies, the difference between two different information-sharing strategies can be seen through the following analysis:

$\prod_{}^{} r 1 - \prod_{}^{} r 2 = \frac{σ(-1+etθ+σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{4(θ+βτ)}$

$\prod_{}^{} m1 - \prod_{}^{} m2 = \frac{σ(1-etθ+σ-etβτ-(θ+βτ) c_{0} +e(θ+βτ) c_{e})}{2(θ+βτ)}$

$p1-p2= \frac{1}{4} (-et- \frac{3}{θ+βτ} - c_{0} +e c_{e} +(θ+βτ)(3+etθ+2σ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e}))$

$w1-w2=$ 0

$D1-D2= \frac{1}{4} (-1+etθ+etβτ+θ c_{0} +βτ c_{0} -eθ c_{e} -eβτ c_{e})+ \frac{1}{4} (1-etθ-2σ-etβτ-θ c_{0} -βτ c_{0} +eθ c_{e} +eβτ c_{e})= - \frac{σ}{2}$

$\prod_{}^{} sc1 - \prod_{}^{} sc2 =$ 0

上述结果表明零售商和制造商的最优利润和销售价格与信息差 $σ$ 、价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 、碳排放惩罚率t、原材料成本 $c_{0}$ 、单位商品耗能 $e$ 和能源价格有关。而在制造商选择不引进低碳生产技术的情况下，零售商无论选择何种方式，对批发价格和供应链总利润都没有影响。此外，市场需求，在制造商选择不引进低碳生产技术的情况下，仅与信息差 $σ$ 有关。
e , price sensitivity factor $θ$ , and low-carbon commoditiesSensitivity $τ$ , carbon emission penalty rate t, raw material cost $c_{}$ , energy consumption per unit of commodity eIt's about energy prices. In the case of manufacturers choosing not to introduce low-carbon production technologies, retailers will have no impact on wholesale prices and total supply chain margins, regardless of the method they choose. In addition, market demand, in cases where manufacturers choose not to introduce low-carbon production technologies, is only related to poor $σ$ information.

当 $σ> 1-etθ-etβτ-θ c_{0} -βτ c_{0} +eθ c_{e} +eβτ c_{e} =4D2$ 时, $\prod_{}^{} r1 > \prod_{}^{} r2$ ，且 $\prod_{}^{} m1 < \prod_{}^{} m2$ ；
$σ> 1-etθ-etβτ-θ c_{} -βτ c_{} +eθ c_{} +eβτ c_{} =4D2$ When , $\prod_{}^{} r1 > \prod_{}^{} r2$ and $\prod_{}^{} m1 < \prod_{}^{} m2$ ;

当 $0<σ<4D2$ 时， $\prod_{}^{} m1 > \prod_{}^{} m2$ ，且 $\prod_{}^{} r 1 < \prod_{}^{} r 2$ 。
$0<σ<4D2$ When , $\prod_{}^{} m1 > \prod_{}^{} m2$ , and $\prod_{}^{} r 1 < \prod_{}^{} r 2$ .

因此当制造商与零售商之间的需求信息差大于四倍D2时，零售商不会将需求信息共享给制造商；当制造商与零售商之间的需求信息差小于四倍D2时零售商会将不会将需求信息共享给制造商。当需求信息差过大时，零售商不将需求信息共享给制造商，制造商会选择多进行生产，来应对缺货，而零售商则拥有充足的货物。
Therefore, when the difference in demand information between the manufacturer and the retailer is greater than four times D2, the retailer will not share the demand information with the manufacturer; When the difference in demand information between the manufacturer and the retailer is less than four times D2, the retailer will not share the demand information with the manufacturer. When the demand information is too large, the retailer does not share the demand information with the manufacturer, and the manufacturer chooses to produce more to cope with the shortage, while the retailer has sufficient goods.

而最优批发价格和供应链最优利润的差值为0，说明了供应链内的利润是固定的，改变信息共享的模式，发生变化的只有零售商和制造商之间利润的转移。而批发价格为0，说明了制造商在生产商品时，生产数量的多少与生产总成本没有关系。
The difference between the optimal wholesale price and the optimal profit of the supply chain is 0, indicating that the profit in the supply chain is fixed, and the only thing that changes is the transfer of profits between retailers and manufacturers is the mode of information sharing. The wholesale price is 0, which indicates that when the manufacturer produces the goods, the amount of production has no relationship with the total cost of production.

当 $σ> - \frac{(-1+ θ^{2} +2βθτ+ β^{2} τ^{2})(3+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{2 {(θ+βτ)}^{2}}$ >0且0< $τ$ < $\frac{1-θ}{β}$ 时，p1>p2
$σ> - \frac{(-1+ θ^{} +2βθτ+ β^{} τ^{})(3+etθ+etβτ+(θ+βτ) c_{} -e(θ+βτ) c_{})}{2 {(θ+βτ)}^{}}$ When >0 and 0< $τ$ < $\frac{1-θ}{β}$ , p1>p2

当0< $σ< - \frac{(-1+ θ^{2} +2βθτ+ β^{2} τ^{2})(3+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}{2 {(θ+βτ)}^{2}}$ 且0< $τ$ < $\frac{1-θ}{β}$ ，时p2>p1。
When 0< $σ< - \frac{(-1+ θ^{} +2βθτ+ β^{} τ^{})(3+etθ+etβτ+(θ+βτ) c_{} -e(θ+βτ) c_{})}{2 {(θ+βτ)}^{}}$ and 0< $τ$ < $\frac{1-θ}{β}$ , p2>p1。

说明当不信息共享时，制造商生产的商品越多，销售价格可以定的更高；而当 $σ>0$ 时，D2>D1，这说明了当信息共享时价格降低，购买商品的消费者人数增多。
It shows that when information is not shared, the more goods the manufacturer produces, the higher the selling price can be set; And at that time $σ>0$ , D2% 3ED1, which indicates that when information is shared, prices are lower and the number of consumers who buy goods increases.

4. 引进低碳技术下的低碳供应链信息共享模型
4.Introduce a low-carbon supply chain information sharing model under low-carbon technology

4.1 引进低碳生产技术的情形描述
4.1 Description of the introduction of low-carbon production technologies

基于企业生产时，缴纳的碳税会给企业的生产带来巨大的压力，此外，政府出台了一系列的碳补贴政策，企业引进低碳生产技术进行生产后，可以获得一定的政府补贴，而企业在使用低碳生产技术后，生产商品所需要的消耗能量也会相对应的减少，而分摊到每件商品的碳税也会降低，进而整体的碳税也会降低。而新引进的低碳生产技术，生产出的低碳商品，对低碳商品偏好的消费者是有利于提高其整体效用的，进一步扩大市场需求，获得更多的利润。
In addition, the government has introduced a series of carbon subsidy policies, after enterprises introduce low-carbon production technology for production, they can obtain certain government subsidies, and enterprises use low-carbon production technology, the energy consumption required to produce goods will also be reduced correspondingly, and apportioned to each pieceThe carbon tax on goods will also be lowered, and the overall carbon tax will also be reduced. The newly introduced low-carbon production technology and the low-carbon goods produced are conducive to improving the overall utility of consumers who prefer low-carbon goods, further expanding market demand and obtaining more profits.

4.2 低碳生产技术下低碳偏好消费者需求
4.2 Low-carbon preference consumer demand under low-carbon production technology

在供应链中，零售商选择无差别定价，预期效用决定消费者的购买行为。因此可以利用消费者效用函数分析价格和需求的关系。
In the supply chain, retailers choose to price indiscriminately, and the expected utility determines the purchasing behavior of consumers. Therefore, the relationship between price and demand can be analyzed using the consumer utility function.

因为消费者是理性人，其效用函数受商品价格p的影响，此外，由于零售商售卖的商品是低碳商品因此，对应低碳消费者的消费者预期效用是： $U_{L2} = V_{L}$ - $θ$ *p+ $τ*p$
Because consumers are rational people, their utility function is affected by the price of goods p, and since the goods sold by retailers are low-carbon goods, they correspond to low-carbon consumersConsumers expect utility to: $U_{} = V_{}$ - $θ$ *p+ $τ*p$

而消费者选择是否购买该商品是基于该商品的预期效用是否大于0，当商品的预期效用大于0时，消费者会选择购买该商品，而当商品的预期效用小于0时，消费者不会购买。因而当预期效用等于0时，可以得到临界的商品估值： ${V_{L3}}^{*} = θ$ *p- $τ*p$ 。
The consumer's choice to buy the product is based on whether the expected utility of the commodity is greater than 0, and when the expected utility of the commodity is greater than 0, the consumer willChoose to buy the product, and the consumer won't buy it when the expected utility of the product is less than 0. Thus, when the expected utility is equal to 0, the critical commodity valuation can be obtained: ${V_{}}^{} = θ$ *p- $τ*p$ .

根据假设4-2，可以得出低碳商品偏好消费者和无低碳商品偏好消费者的总人数：y2（引进低碳生产技术后）和z：
Based on hypothesis 4-2, the total number of consumers with a preference for low-carbon goods and consumers without a preference for low-carbon goods can be obtained: y 2(after the introduction of low-carbon production technologies) and z:

y2= $β$ (1- ${V_{L}}^{*}$ )= $β$ (1- $θ$ *p+ $τ*p$ )

z=(1- $β)$ (1- ${V_{F}}^{*}$ )= (1- $β)$ (1- $θ$ *p)

相加后可以得到购买该商品的消费者总人数，即总需求为： D2= $β$ (1- ${V_{L2}}^{*}$ )+(1- $β)$ (1- ${V_{F}}^{*}$ ) = $1-pθ+pβτ$ （引进低碳生产技术后）
After summing up, we can get the total number of consumers who buy the product, that is, the total demand is: D2= $β$ (1- ${V_{}}^{}$ )+(1- $β)$ (1-) = $1-pθ+pβτ$ (after the introduction of low-carbon ${V_{}}^{}$ production technologies).

D2对p求导后可得 $-θ+βτ$ 。因为市场需求与价格p相关，当价格升高时，需求减小因而 $-θ+βτ<0$ ，即 $βτ<θ$
D2 is derived from $-θ+βτ$ p. Because market demand is related to price p, when the price increases, the demand decreases, i.e $βτ<θ$ $-θ+βτ<0$ .

4.3 引进低碳技术下选择信息不共享策略
4.3 Choose a non-sharing strategy under the introduction of low-carbon technologies

当零售商选择不共享需求信息时，制造商需要多生产σ数量的商品。而生产时所需成本和所缴纳的税收由制造商来承担。生产该商品所需要的成本原材料为c_0，同时生产一个单位的商品需要消耗（e-x）的能量，其中x为采用新技术减少的耗能，并且每单位的能耗需要缴纳c_e单位的费用，而引进新技术的费用扣除补贴后还需要T那么多的支出。因此生产成本为：
When a retailer chooses not to share demand information, manufacturers need to produce σ more quantities of goods. The cost of production and the taxes paid are borne by the manufacturer. The cost of raw materials required to produce the commodity is c_0, and the production of one unit of the commodity requires the consumption of (e-x), where x is the energy consumption reduced by the use of new technology, and each unit of energy consumption needs to pay c_e unit fee, The cost of introducing new technologies after deducting subsidies will require as much expenditure as T. Therefore, the production cost is:

c= $c_{0} + （ e-x ） * c_{e}$

$\prod_{}^{} r3$ =（p-w）（D3）

$\prod_{}^{} m$ 3=（w- $c_{0} + (e-x) * c_{e} - (e-x) *t$ ）（D3+σ）-T

在引进低碳技术下零售商选择信息不共享策略，得到的最优定价和利润为：
Under the introduction of low-carbon technology, retailers choose the information non-sharing strategy, and the optimal pricing and profit obtained are:

W3= $\frac{-1-etθ+txθ-2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e}}{-2θ+2βτ}$

$p3 = \frac{3+etθ-txθ+2σ-etβτ+txβτ+θ c_{0} -βτ c_{0} -eθ c_{e} +xθ c_{e} +eβτ c_{e} -xβτ c_{e}}{4 (θ-βτ)}$

D3= $\frac{1}{4} (1-etθ+txθ-2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})$

$\prod_{}^{} r3$ = $\frac{{(1-etθ+txθ-2σ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}^{2}}{16(θ-βτ)}$

$\prod_{}^{} m$ 3 $= \frac{{(1-etθ+txθ+2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})}^{2}}{8 (θ-βτ)}$

$\prod_{}^{} sc3$ = $\frac{{(1-etθ+txθ+2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})}^{2}}{8 (θ-βτ)}$

证明：
Prove:

本文采用逆向归纳求导法对供应链内部的博弈进行求解。
In this paper, the reverse inductive derivation method is used to solve the game within the supply chain.

首先，将零售商的最优利润函数对价格p求二阶偏导 $-2θ+2βτ$ <0，又一阶偏导 $1-2pθ+wθ+2pβτ-wβτ>0$ ，所以零售商的利润函数是销售价格p的严格凹函数。
Firstly, the retailer's optimal profit function is given the second-order partial derivative $-2θ+2βτ$ <0 for the price p, and the second-order partial derivative is obtained $1-2pθ+wθ+2pβτ-wβτ>0$ , so the retailer's profit function is a strictly concave function of the selling price p.

令一阶偏导的结果为0，得到p3和D3：
Let the result of the first-order partial derivative be 0, and we get p3 and D3:

P3= $\frac{1+wθ-wβτ}{2 (θ-βτ)}$ D3= $\frac{1}{2} (1-wθ+wβτ)$

将上述得到的p3和D3代入 $\prod_{}^{} m 3$ ，计算制造商利润：
Substituting the p3 and D3 obtained above into $\prod_{}^{} m 3$ , the manufacturer's profit is calculated

将p3和D3代入 $\prod_{}^{} m 3$ ,得：
Substituting p3 and D3 into $\prod_{}^{} m 3$ , we get:

$\prod_{}^{} m 3$ = $\frac{1}{2} (\frac{1}{2} (-et+w+tx+etwθ- w^{2} θ-twxθ-2etσ+2wσ+2txσ-etwβτ+ w^{2} βτ+twxβτ- c_{0} +wθ c_{0} -2σ c_{0} -wβτ c_{0} +e c_{e} -x c_{e} -ewθ c_{e} +wxθ c_{e} +2eσ c_{e} -2xσ c_{e} +ewβτ c_{e} -wxβτ c_{e})$

对 $\prod_{}^{} m 3$ 求w的一阶偏导得： $\frac{1}{2} (1+etθ-2wθ-txθ+2σ-etβτ+2wβτ+txβτ+θ c_{0} -βτ c_{0} -eθ c_{e} +xθ c_{e} +eβτ c_{e} -xβτ c_{e})$ ，二阶偏导为： $\frac{1}{2} (-2θ+2βτ)$ <0，令一阶偏导的结果为0，可以得到批发价格的最优解w3。
$\prod_{}^{} m 3$ For finding the first-order partial derivative of w, we get: $\frac{1}{2} (1+etθ-2wθ-txθ+2σ-etβτ+2wβτ+txβτ+θ c_{} -βτ c_{} -eθ c_{} +xθ c_{} +eβτ c_{} -xβτ c_{})$ , the second-order partial derivative is: $\frac{1}{2} (-2θ+2βτ)$ <0, so that the result of the first-order partial derivative is 0, The optimal solution for the wholesale price w3 can be obtained.

w3= $\frac{-1-etθ+txθ-2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e}}{-2θ+2βτ}$

最后再将得到的w3代入p3和D3中可以得到最优价格和相对应的消费者人数为：
Finally, substituting the obtained w3 into p3 and d3 can obtain the best price and the corresponding number of consumers:

$p3 = \frac{-3-etθ+txθ-2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e}}{-4θ+4βτ}$

D3= $\frac{1}{4} (1-etθ+txθ-2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})$

最后再将上述得到的结果分别代入 $\prod_{}^{} r3$ 和 $\prod_{}^{} m3$ 中可以得到：
Finally, the above results can be substituted into $\prod_{}^{} r3$ and respectively, and $\prod_{}^{} m3$ we can get the following

$\prod_{}^{} r3 = \frac{{(1-etθ+txθ-2σ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}^{2}}{16(θ-βτ)}$

$\prod_{}^{} m3 = \frac{{(1-etθ+txθ+2σ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})}^{2}}{8 (θ-βτ)}$ -T

将 $\prod_{}^{} r3$ 和 $\prod_{}^{} m3$ 相加可以得到供应链的最优利润 $\prod_{}^{} sc3$ ：
$\prod_{}^{} r3$ $\prod_{}^{} m3$ Add up and get the optimal profit $\prod_{}^{} sc3$ for the supply chain

$\prod_{}^{} sc3$ = $\frac{1}{16(θ-βτ)} ({(1-etθ+txθ-2σ+etβτ-txβτ+(-θ+βτ) c_{0} +(e- x)(θ-βτ) c_{e})}^{2} +2 {(1-etθ+txθ+2σ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}^{2})$ -T

4.4 引入低碳生产技术下采用信息共享策略
4.4 Adopt information sharing strategies under the introduction of low-carbon production technologies

在信息共享策略时，零售商和制造商的利润函数如下：
When it comes to information sharing strategies, the profit functions for retailers and manufacturers are as follows:

$\prod_{}^{} r4$ =（p-w）（D2）

$\prod_{}^{} m$ 4=（w- $c_{0} + (e-x) * c_{e} - (e-x) *t$ ）（D2）-T

采用逆向归纳求导法求解得结果。
The results are obtained by using the reverse inductive derivation method.

观察最优解，不难发现销售价格p与制造商和零售商的利润同低碳商品偏好消费者占比 $β$ 关系紧密。
Observing the optimal solution, it is not difficult to find that the selling price p is the proportion of the profit of the manufacturer and retailer to the preference of consumers for low-carbon goods $β$ The relationship is close.

引进低碳生产技术下采用信息共享策略，得到的最优定价和最优利润为：
Under the introduction of low-carbon production technology, the information sharing strategy is adopted, and the optimal pricing and profit are as follows:

w4= $\frac{-1-etθ+txθ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e}}{-2θ+2βτ}$

$P4= \frac{1}{4} (et-tx+ \frac{3}{θ-βτ} + c_{0} -e c_{e} +x c_{e})$

D $4= \frac{1}{4} (1-etθ+txθ+etβτ-txβτ-θ c_{0} +βτ c_{0} +eθ c_{e} -xθ c_{e} -eβτ c_{e} +xβτ c_{e})$

$\prod_{}^{} r4 = \frac{{(1-etθ+txθ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})}^{2}}{16 (θ-βτ)}$

$\prod_{}^{} m4 = \frac{{(1-etθ+txθ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})}^{2}}{8 (θ-βτ)}$ -T

$\prod_{}^{} sc4$ = $\frac{3 {(1-etθ+txθ+etβτ-txβτ+ (-θ+βτ) c_{0} + (e-x) (θ-βτ) c_{e})}^{2}}{16 (θ-βτ)}$ -T

4.5 信息共享决策分析与比较
4.5 Information sharing decision-making analysis and comparison

本节主要分析制造商在引进低碳生产技术后，零售商采取不同的信息共享策略时，价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 、碳排放惩罚率t以及改进后节省的能耗x的影响；对比在零售商选择共享策略的情况下，制造商引进低碳生产技术的影响，并比较均衡解，帮助零售商和制造商进行最优决策。
This section mainly analyzes the price sensitivity factors and sensitivity to low-carbon products when retailers adopt different information sharing strategies after manufacturers introduce low-carbon production technologies $θ$ $τ$ , carbon emission penalty rate t and the impact of energy savings x after improvement; Compare the impact of manufacturers introducing low-carbon production technologies when retailers choose a sharing strategy, and compare the equilibrium solution to help retailers and manufacturers make optimal decisions.

4.5.1 效用影响因子分析
4 5.1 Utility Impact Factor Analysis

主要分析不同价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 、碳排放惩罚率t以及改进后节省的能耗x对供应商和制造商的影响，还分析了不同信息共享策略的情况。
Mainly analyze different price sensitivity factors $θ$ , sensitivity to $τ$ low-carbon commodities, The impact of the carbon penalty rate t and the improved energy savings x on suppliers and manufacturers is also analyzed.

市场需求与影响因子间关系的计算结果如下所示：
The results of the calculation of the relationship between market demand and impact factors are as follows:

$\frac{∂D3}{∂t} =- \frac{1}{4} (e -x) (θ-βτ) <0$

$\frac{∂D3}{∂τ} = \frac{1}{4} (c_{0} -(c_{e} -t) (e-x)) β>0$

$\frac{∂D3}{∂θ} = \frac{1}{4} ({-c}_{0} +(c_{e} -t) (e-x)) <0$

$\frac{∂D3}{∂x} =- \frac{1}{4} (c_{e} -t) (θ-βτ) <0$

$\frac{∂D4}{∂t} = \frac{1}{4} (- e θ+xθ+ e βτ-xβτ) <0$

$\frac{∂D4}{∂τ} = \frac{1}{4} (c_{0} -(c_{e} -t) (e-x)) β>0$

$\frac{∂D4}{∂θ} = \frac{1}{4} ({-c}_{0} +(c_{e} -t) (e-x)) <0$

$\frac{∂D4}{∂x} =- \frac{1}{4} (c_{e} -t) (θ-βτ) <0$

在制造商选择引进低碳生产技术，零售商选择何种信息共享策略，消费者总人数都随着价格敏感因子 $θ$ 、碳排放惩罚率t以及改进后节省的能耗x的增长而降低；而市场需求随着对低碳商品敏感程度 $τ$ 因子的增大而升高。这是因为，低碳商品偏好型消费者追求低碳商品，当对低碳商品敏感程度 $τ$ 越大，消费者购买该商品的可能也就越大，购买该商品的总人数也会随之增加。
When manufacturers choose to introduce low-carbon production technologies, and retailers choose information sharing strategies, the total number of consumers decreases with the increase of price sensitivity factors $θ$ , carbon emission penalty rates, and energy savings after improvement. The market demand increases with the increase of sensitivity $τ$ to low-carbon commodities. This is because consumers who prefer low-carbon commodities pursue low-carbon commodities, and the more sensitive they are to $τ$ low-carbon commodities. The more likely consumers are to buy the product, the more likely they are to buy the product, and the more people will buy the product.

制造商引进低碳生产策略时，无论零售商选择何种共享策略，最优销售价格都随着对低碳商品敏感程度 $τ$ 、碳排放惩罚率t以及改进后节省的能耗x因子的增加而增加；最优价格p随着价格敏感因子 $θ$ 因子的增加而减少。
When manufacturers introduce low-carbon production strategies, the optimal selling price increases with the increase $τ$ of sensitivity to low-carbon goods, carbon emission penalty rate t, and energy savings after improvement, regardless of the sharing strategy chosen by retailers. The optimal price p decreases with the increase of the price sensitivity factor $θ$ .

当低碳敏感程度增加时，低碳倾向消费者更愿意去购买低碳商品，而零售商选择适当提高销售价格以获得更好利润。制造商选用低碳生产技术可以降低生产成本，制造商会选择适当的提高一部分的批发价格，而零售商为了应对，也会选择提高销售价格。
When the sensitivity to low carbon increases, consumers with low carbon tendencies are more willing to buy low-carbon goods, while retailers choose to raise the selling price appropriately to obtain better profits. Manufacturers can reduce production costs by choosing low-carbon production technologies, manufacturers will choose to increase some wholesale prices appropriately, and retailers will also choose to increase sales prices in response.

计算结果如下：
The result of the calculation is as follows:

$\frac{∂p3}{∂t}$ = $\frac{e-x}{4}$ >0

$\frac{∂p3}{∂t}$ = $\frac{β(3+2σ)}{4 {(θ-βτ)}^{2}}$ >0

$\frac{∂p3}{∂ θ}$ = $- \frac{3+2σ}{4 {(θ-βτ)}^{2}}$ <0

$\frac{∂p3}{∂x}$ = $\frac{1}{4} (-t+ c_{e})$ >0

$\frac{∂p4}{∂t} = \frac{e-x}{4}$ >0

$\frac{∂p4}{∂τ} = \frac{3β}{4 {(θ-βτ)}^{2}}$ >0

$\frac{∂p4}{∂ θ} =- \frac{3}{4 {(θ-βτ)}^{2}}$ <0

$\frac{∂p4}{∂x} = \frac{1}{4} (-t+ c_{e})$ >0

制造商采取引进低碳生产策略的政策时，批发价格并不受信息差 $σ$ 的影响。批发价格随着对低碳商品敏感程度 $τ$ 、碳排放惩罚率t以及改进后节省的能耗x因子的增加而增加；最优批发价格w3、w4随着价格敏感因子 $θ$ 因子的增加而减少。当改进后减少的能耗越多时，碳税对批发价格的影响也就越小。此外，在该情况下，消费者对价格敏感过是否为低碳商品。
When manufacturers adopt policies to introduce low-carbon production strategies, wholesale prices are not affected by poor $σ$ information. The wholesale price increases with the increase of the sensitivity $τ$ to low-carbon commodities, the carbon emission penalty rate t, and the energy consumption saved by the improved energy consumption x-factor. The optimal wholesale prices w3 and w4 decrease with the increase of the price sensitivity factor $θ$ . The more energy consumption is reduced after the improvement, the less the carbon tax will have an impact on wholesale prices. In addition, in this case, consumers are price-sensitive to whether it is a low-carbon commodity.

计算结果如下所示：
The result is as follows:

$\frac{∂w3}{∂t} = \frac{∂w4}{∂t}$ = $\frac{e-x}{2}$ >0

$\frac{∂w3}{∂τ}$ = $\frac{β+2βσ}{2 {(θ-βτ)}^{2}} > \frac{∂w4}{∂τ}$ >0

$\frac{∂w3}{∂θ}$ = $- \frac{1+2σ}{2 {(θ-βτ)}^{2}} < \frac{∂w4}{∂θ}$ <0

$\frac{∂w3}{∂x} = \frac{∂w4}{∂x}$ = $\frac{1}{2} (-t+ c_{e})$ >0

4.5.2 引进低碳生产技术下最优解比较和讨论
4 5.2 Comparison and discussion of optimal solutions under the introduction of low-carbon production technologies

本文通过计算制造商和零售商之间的博弈情况，获得零售商选择不同信息共享策略下的最优解，并比较和分析最优结果。制造商引进低碳生产技术时，计算两种情形下的差值得如下结果：
In this paper, the retailer choice is obtained by calculating the game between the manufacturer and the retailerThe optimal solution under different information sharing strategies, and the optimal results are compared and analyzed. When a manufacturer introduces a low-carbon production technology, the difference between the two scenarios is calculated as follows：

$\prod_{}^{} r3 - \prod_{}^{} r4 = \frac{σ(-1+etθ-txθ+σ-etβτ+txβτ+(θ-βτ) c_{0} -(e-x)(θ-βτ) c_{e})}{4(θ-βτ)}$

$\prod_{}^{} m3 - \prod_{}^{} m4 = \frac{σ(1-etθ+txθ+σ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}{2(θ-βτ)}$

$p3-p4= \frac{σ}{2θ-2βτ}$

$w3-w4=$ 0

$D3-D4= \frac{1}{4} (-1+etθ-txθ-etβτ+txβτ+θ c_{0} -βτ c_{0} -eθ c_{e} +xθ c_{e} +eβτ c_{e} -xβτ c_{e})+ \frac{1}{4} (1-etθ+txθ-2σ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})= - \frac{σ}{2}$

$\prod_{}^{} sc3 - \prod_{}^{} sc4 = \frac{σ(1-etθ+txθ+3σ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}{4(θ-βτ)}$

根据以上结果，得知制造商引进低碳生产技术时，零售商和制造商最优利润还有最优销售价格与信息差 $σ$ 、价格敏感因子 $θ$ 、对低碳商品敏感程度 $τ$ 、碳排放惩罚率t、改进节约耗能x有关。而在制造商选择引进低碳生产技术的情况下，零售商无论选择何种方式，对批发价格w都没有影响。此外，市场需求，在制造商选择引进低碳生产技术且 $θ>βτ$ 时，仅与信息差 $σ$ 有关。
According to the above results, it is known that when manufacturers introduce low-carbon production technologies, the optimal profit of retailers and manufacturers also includes the optimal selling price and information gap $σ$ , and price sensitivity factors $θ$ , sensitivity to low-carbon commodities $τ$ , carbon emission penalty rate t, and improvement of energy conservation x. In the case where manufacturers choose to introduce low-carbon production technologies, no matter which method retailers choose, there is no impact on wholesale prices. In addition, market demand, when manufacturers choose to introduce low-carbon production technologies $θ>βτ$ , is only related to poor $σ$ information.

当 $σ> 4(θ-βτ)(\frac{1}{4(θ-βτ)} - \frac{etθ}{4(θ-βτ)} + \frac{txθ}{4(θ-βτ)} + \frac{etβτ}{4(θ-βτ)} - \frac{txβτ}{4(θ-βτ)} - \frac{c_{0}}{4} + \frac{1}{4} (e-x) c_{e})$ =4D4时, $\prod_{}^{} r3 > \prod_{}^{} r4$ ，且 $\prod_{}^{} m3 < \prod_{}^{} m4$ ；
$σ> 4(θ-βτ)(\frac{1}{4(θ-βτ)} - \frac{etθ}{4(θ-βτ)} + \frac{txθ}{4(θ-βτ)} + \frac{etβτ}{4(θ-βτ)} - \frac{txβτ}{4(θ-βτ)} - \frac{c_{}}{4} + \frac{1}{4} (e-x) c_{})$ WHEN =4D4, $\prod_{}^{} r3 > \prod_{}^{} r4$ , AND $\prod_{}^{} m3 < \prod_{}^{} m4$ ;

当 $0<σ<4D4$ 时， $\prod_{}^{} m3 > \prod_{}^{} m4$ ，且 $\prod_{}^{} r3 < \prod_{}^{} r4$ 。
$0<σ<4D4$ When , $\prod_{}^{} m3 > \prod_{}^{} m4$ , and $\prod_{}^{} r3 < \prod_{}^{} r4$ .

因此当制造商与零售商之间的需求信息差大于四倍D4时，零售商不会将需求信息共享给制造商；当零售商与制造商之间的需求信息差小于四倍D4时零售商会将需求信息共享给制造商。
Therefore, when the difference in demand information between the manufacturer and the retailer is greater than four times D4, the retailer will not share the demand information with the manufacturer; When the difference in demand information between the retailer and the manufacturer is less than four times D4, the retailer shares the demand information with the manufacturer.

而最优批发价格的差值为0，说明了制造商在生产商品时，生产数量的多少与生产总成本没有关系。
The difference between the optimal wholesale price is 0, which indicates that the quantity produced by the manufacturer has no relationship with the total cost of production when producing goods.

当 $σ>0$ 时，D4>D3，这说明了当信息共享时购买商品的消费者人数增多。
$σ>0$ D4>D3, which indicates that the number of consumers who purchase goods increases when information is shared.

当0> $σ> \frac{1}{3} (-1+etθ-txθ-etβτ+txβτ+(θ-βτ) c_{0} -(e-x)(θ-βτ) c_{e})$ 时， $\prod_{}^{} sc3 > \prod_{}^{} sc4$ ，但显然信息差 $σ$ 大于0，因此 $\prod_{}^{} sc3 > \prod_{}^{} sc4$ 。因为无信息共享时，可以获得更高的消费者需求，又因为批发价格不变，制造商利润增加，供应链内的利润也随之增加。
When 0> $σ> \frac{1}{3} (-1+etθ-txθ-etβτ+txβτ+(θ-βτ) c_{} -(e-x)(θ-βτ) c_{})$ , $\prod_{}^{} sc3 > \prod_{}^{} sc4$ but apparently the information difference $σ$ is greater than 0, therefore $\prod_{}^{} sc3 > \prod_{}^{} sc4$ 。 This is because there is no information to share, there is higher consumer demand, and because the wholesale price remains the same, the manufacturer's profit increases, and the profit within the supply chain also increases.

4.5.3 信息共享策略下最优解比较和讨论
4.5.3 Comparison and discussion of optimal solutions under information sharing strategies

本文计算了制造商和零售商之间的博弈并得出在零售商采取不同信息共享行策略时的最优解，通过对比分析最优结果可知当零售商选择信息共享策略之后，两种情形之间，差值计算结果如下：
This paper calculates the game between manufacturers and retailersThe optimal solution when retailers adopt different information sharing strategies, through comparative analysis of the optimal results, we can see two scenarios when retailers choose information sharing strategies, the difference is calculated as follows:

$\prod_{}^{} r2 - \prod_{}^{} r4 = \frac{1}{16} (- \frac{{(1-etθ+txθ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}^{2}}{θ-βτ} + \frac{{(-1+etθ+etβτ+(θ+βτ) c_{0} -e(θ+βτ) c_{e})}^{2}}{θ+βτ})$

$\prod_{}^{} m2 - \prod_{}^{} m4 = \frac{1}{8} (- \frac{{(1-etθ+txθ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}^{2}}{θ-βτ} + \frac{{(-1+etθ+etβτ+(θ+βτ) c_{0} -e[θ+βτ] c_{e})}^{2}}{θ+βτ})+T$

$p2-p4= \frac{-tx θ^{2} +6βτ+tx β^{2} τ^{2} +x(θ^{2} - β^{2} τ^{2}) c_{e}}{-4 θ^{2} +4 β^{2} τ^{2}}$

$w2-w4= \frac{-tx θ^{2} +2βτ+tx β^{2} τ^{2} +x(θ^{2} - β^{2} τ^{2}) c_{e}}{-2 θ^{2} +2 β^{2} τ^{2}}$

$D2-D4= \frac{1}{4} (-2βτ c_{0} -(2eβτ+x(θ-βτ))(t- c_{e}))$

$\prod_{}^{} sc2 - \prod_{}^{} sc4 = \frac{3}{16} (- \frac{{(1-etθ+txθ+etβτ-txβτ+(-θ+βτ) c_{0} +(e-x)(θ-βτ) c_{e})}^{2}}{θ-βτ} + \frac{{(-1+etθ+etβτ+(θ+βτ) c_{0} -e[θ+βτ] c_{e})}^{2}}{θ+βτ})+T$

5. 数值分析
5.Numerical analysis

5.1 未引进低碳生产技术时的信息共享策略数值分析
5.1 Numerical analysis of information sharing strategies when low-carbon production technologies are not introduced

在考虑制造商不引进低碳生产技术时，零售商选择两种不同的信息共享策略，根据上述的计算结果，运用数值计算探究碳排放惩罚率对最优解的影响。
When considering that manufacturers do not introduce low-carbon production technologies, retailers choose two different information sharing strategies, depending on the aboveNumerical calculations are used to explore the influence of carbon emission penalty rate on the optimal solution.

考虑低碳商品偏好消费者占比 $β=0.4 、原材料成本 c_{0} =0.25 、单位耗能成本 c_{e} =0.1 、单位耗能 e=0.4 、$ 消费者对价格敏感程度 $θ=2 、$ 制造商和零售间的信息差 $σ=0.2$ 、 $消费者对低碳商品敏感程度 τ=0.6$ ，在t∈ [0,1]的范围内，有无信息共享下最优均衡解与t之间的关系。
Consider the proportion of $β=0.4 、原材料成本 c_{} =0.25 、单位耗能成本 c_{} =0.1 、单位耗能 e=0.4 、$ consumers who prefer low-carbon goods and the degree of price sensitivity of consumers $θ=2 、$ The information gap $σ=0.2$ $消费者对低碳商品敏感程度 τ=0.6$ between the manufacturer and the retailer is within the range of t∈ [0,1], The relationship between the optimal equilibrium solution and t with or without information sharing.

图5-1：在不引进低碳生产技术时，制造商和零售商的利润差、 $制造商和零售间的信息差 σ$ 、碳惩罚率t之间的关系
Figure 5-1: Relationship between profit margins, carbon penalty rates, and carbon penalty rates between manufacturers and retailers when low-carbon production technologies are not introduced $制造商和零售间的信息差 σ$

图5-2：不引进低碳生产技术时，制造商和零售商的利润差、 $制造商和零售间的信息差 σ$ 、 $消费者对价格敏感程度 θ$ 之间的关系
Figure 5-2: The relationship between the profit margin, and the retailer when low-carbon production technologies are not introduced $消费者对价格敏感程度 θ$ $制造商和零售间的信息差 σ$

图5-3：不引进低碳生产技术时，制造商和零售商的利润差、 $制造商和零售间的信息差 σ$ 、 $消费者对低碳商品敏感程度 τ$ 之间的关系
Figure 5-3: The relationship between the profit margin $制造商和零售间的信息差 σ$ $消费者对低碳商品敏感程度 τ$ , and retailer of manufacturers and retailers without the introduction of low-carbon production technologies

从上述三张图中可以得到，不引进低碳生产技术时，制造商与零售商在两种情况下的利润之差，与 $消费者对低碳商品敏感程度 τ$ 和 $消费者对价格敏感程度 θ$ $因子的大小无关$ ；且当碳惩罚率t<0.6时，零售商选择不共享需求信息，那么制造商所获得的利润总是比共享需求信息时多，并且信息差 $σ$ 越大，制造商在不进行信息共享时所获得的利润也就越大。
From the above three graphs, it can be seen that when low-carbon production technologies are not introduced, the difference between the profits of manufacturers and retailers in the two cases is the same as $消费者对低碳商品敏感程度 τ$ $消费者对价格敏感程度 θ$ $因子的大小无关$ and； And when the carbon penalty rate t<0.6, the retailer chooses not to share the demand information, then the manufacturer always gets more profit than when the demand information is shared, and the information difference $σ$ is greater. The more profit manufacturers make when they don't share information.

图5-4：不引进低碳生产技术时，零售价格的之差、 $制造商和零售间的信息差 σ$ 、 $碳惩罚率 t$ 之间的关系
Figure 5-4: Relationship between retail price differentials, $制造商和零售间的信息差 σ$ , , and $碳惩罚率 t$ when low-carbon production technologies are not introduced

图5-5：不引进低碳生产技术时，零售价格的之差、 $制造商和零售间的信息差 σ$ 、 $消费者对价格敏感程度 θ$ 之间的关系
Figure 5-5: The relationship between retail price differentials, $制造商和零售间的信息差 σ$ , , and $消费者对价格敏感程度 θ$ when low-carbon production technologies are not introduced

图5-6：不引进低碳生产技术时，零售价格的之差、 $制造商和零售间的信息差 σ$ 、 $消费者对低碳商品敏感程度 τ$ 之间的关系
Figure 5-6: The relationship between retail price differentials, $制造商和零售间的信息差 σ$ , , and $消费者对低碳商品敏感程度 τ$ when low-carbon production technologies are not introduced

图5-7：不引进低碳生产技术时，零售价格的之差、 $制造商和零售间的信息差 σ$ 、低碳商品偏好消费者占比 $β$ 之间的关系
Figure 5-7: When low-carbon production technologies are not introduced, the difference in retail prices, and $制造商和零售间的信息差 σ$ the proportion of consumers who prefer low-carbon goods $β$ relationship

从上述四张图中可以得到，不引进低碳生产技术时，零售价格的之差、 $制造商和零售间的信息差 σ$ 与 $碳惩罚率 t$ 、 $消费者对价格敏感程度 θ$ 、低碳商品偏好消费者占比 $β$ 、 $消费者对低碳商品敏感程度 τ$ 之间呈正相关关系，其中当改变 $消费者对价格敏感程度 θ$ 时，零售价格的之差、 $制造商和零售间的信息差 σ$ 二者间的变化开始时并不显著，随着 $θ$ 的增大，价格之间的差异也在变大。
From the above four figures, it can be seen that when low-carbon production technologies are not introduced, the difference between retail prices, $制造商和零售间的信息差 σ$ , $碳惩罚率 t$ $消费者对价格敏感程度 θ$ There is a positive correlation between the proportion of $β$ consumers who prefer low-carbon goods, $消费者对低碳商品敏感程度 τ$ and when it changes $消费者对价格敏感程度 θ$ The difference $制造商和零售间的信息差 σ$ between retail prices was not significant at first, but as $θ$ it increased, the difference between prices increased.

5.2 引进低碳生产技术后的信息共享策略数值分析
5.2 Numerical analysis of information sharing strategies after the introduction of low-carbon production technologies

在考虑制造商引进低碳生产技术时，零售商选择两种不同的信息共享策略，根据上述的计算结果，运用数值计算探究碳排放惩罚率对最优解的影响。
When considering manufacturers to introduce low-carbon production technologies, retailers choose two different information sharing strategies, depending on the aboveNumerical calculations are used to explore the influence of carbon emission penalty rate on the optimal solution.

考虑低碳商品偏好消费者占比 $β=0.4 、原材料成本 c_{0} =0.25 、单位耗能成本 c_{e} =0.1 、单位耗能 e=0.4 、$ 消费者对价格敏感程度 $θ=2 、$ 制造商和零售间的信息差 $σ=0.2$ 、 $消费者对低碳商品敏感程度 τ=0.6$ 、降低耗能x=0.2，在t∈ [0,1]的范围内，有无信息共享下最优均衡解与t之间的关系。
Consider the proportion of consumers who prefer low-carbon goods, the degree of $θ=2 、$ consumer price sensitivity, the information gap $σ=0.2$ between manufacturers and retailers, and $消费者对低碳商品敏感程度 τ=0.6$ the reduction of energy consumption $β=0.4 、原材料成本 c_{} =0.25 、单位耗能成本 c_{} =0.1 、单位耗能 e=0.4 、$ =0.2, in the range of t∈ [0,1], the relationship between the optimal equilibrium solution and t with or without information sharing.

图5-8：在引进低碳生产技术时，零售商利润和 $信息差 σ$ 、碳惩罚率t之间的关系
Figure 5-8: Retailer margins and $信息差 σ$ carbon penalty rates t when low-carbon production technologies are introducedrelationship

图5-9：在引进低碳生产技术时，制造商利润和 $信息差 σ$ 、碳惩罚率t之间的关系
Figure 5-9: When low-carbon production technologies are introduced, manufacturers' profits and $信息差 σ$ , carbon penalty rate t

图5-10：在引进低碳生产技术时，供应链的利润差和 $信息差 σ$ 、
Figure 5-10: When low-carbon production technologies are introduced, the profit margins of the supply chain are $信息差 σ$

碳惩罚率t之间的关系
carbon penalty rate t

图5-11：在引进低碳生产技术时，制造商和零售商的利润差和
Figure 5-11: Profit margins between manufacturers and retailers when low-carbon production technologies are introduced

$信息差 σ$ 、碳惩罚率t之间的关系
$信息差 σ$ , carbon penalty rate t

由上述四幅图可得，在制造商引进低碳生产技术时，当信息差较小时，零售商选择信息共享，会获得更多的利润；零售商选择信息共享策略，制造商会获得更多利润；当信息差越大时，供应链整体利润越多。
As can be seen from the above four figures, when manufacturers introduce low-carbon production technologies, when the information gap is small, retailers will get more profits by choosing to share information. Retailers choose an information-sharing strategy, and manufacturers get more profits; When the information gap is larger, the overall supply chain is more profitable.

图5-12：引进低碳生产技术时，零售商的利润和碳惩罚率t以及 $消费者对低碳商品敏感程度 τ$ 的关系
Figure 5-1-2: When low-carbon production technologies are introduced, retailers' profits and carbon penalty rates are as well as $消费者对低碳商品敏感程度 τ$ relationship

图5-13：引进低碳生产技术时，制造商的利润和碳惩罚率t以及 $消费者对低碳商品敏感程度 τ$ 的关系
Figure 5-13: Manufacturers' margins and carbon penalty rates when low-carbon production technologies are introduced $消费者对低碳商品敏感程度 τ$ and the relationship

图5-14：引进低碳生产技术时，供应链的差值和碳惩罚率t以及 $消费者对低碳商品敏感程度 τ$ 的关系
Figure 5-14: When low-carbon production technologies are introduced, the difference in the supply chain and the carbon penalty rate t and $消费者对低碳商品敏感程度 τ$ relationship

从上述三张图可知，在制造商引进低碳生产技术时，当消费者对低碳商品敏感程度τ增加时，供应链内的利润增加，此外，在信息共享时，制造商会比无信息共享时获得更多的利润，而零售商会比无信息共享时获得更少的利润。与制造商未引进低碳生产技术的情况对比，引进低碳生产技术后，在信息共享情况下，供应链会获得更多的利润。
From the above three figures, it can be seen that when manufacturers introduce low-carbon production technologies, consumers are sensitive to low-carbon goodsWhen it increases, profits within the supply chain increase, and in addition, when information is shared, manufacturers get more profit than when information is not shared, and retailers get less profit than when information is not shared. In contrast to manufacturers who do not introduce low-carbon production technologies, the supply chain gains more profits when information is shared when low-carbon production technologies are introduced.

5.3 引进低碳生产技术后的数值分析
5.3 Numerical analysis after the introduction of low-carbon production technologies

当零售商选择信息共享策略时，根据上述的计算结果，使用数值计算探究碳税对最优解的影响。
When retailers choose an information sharing strategy, based on the above calculation results, numerical calculations are used to explore the impact of carbon tax on the optimal solution.

考虑低碳商品偏好消费者占比 $β=0.4 、原材料成本 c_{0} =0.25 、单位耗能成本 c_{e} =0.1 、单位耗能 e=0.4 、$ 消费者对价格敏感程度 $θ=2 、$ 制造商和零售间的信息差 $σ=0.2 、$ 消费者对低碳商品敏感程度 $τ=0.6 、$ 单位节约能耗 $x=0.15$ 、补贴 $T =0$ 时，在t∈ [0,0.6]的范围内，两者情形的最优均衡结果与t的关系。
Consider the proportion of $β=0.4 、原材料成本 c_{} =0.25 、单位耗能成本 c_{} =0.1 、单位耗能 e=0.4 、$ consumers who prefer low-carbon goods, the degree of price sensitivity of $θ=2 、$ consumers, and the information gap between manufacturers and retailers $σ=0.2 、$ Consumers' sensitivity $τ=0.6 、$ to low-carbon commodities Unit energy $x=0.15$ saving, subsidies $T =0$ , in the range of t∈ [0,0.6], the relationship between the optimal equilibrium results of the two cases and t.

图5-15：最优利润差与碳惩罚系数t的关系
Figure 5-15: Relationship between optimal profit spread and carbon penalty coefficient t

图5-16：最优利润差与减少耗能x的关系
Figure 5-16: Relationship between optimal profit margin and reduced energy consumption x

从上述图中可以看出，在信息共享的情况下，引入低碳生产技术后，制造商的利润无论碳惩罚系数t和减少耗能x如何变化， $\prod_{}^{} m4 - \prod_{}^{} m2$ 都是大于0的，且最优利润差随着减少耗能x的增大而增大，也就是说当技术越先进，企业获得的利润更高；最优利润差与碳惩罚系数t之间的函数呈现为凹函数，当t=0.35左右，得到最小值，此外当t>0.2时，选择引进低碳生产技术会给零售商利润带来缩减。
As can be seen from the above figure, in the case of information sharing, after the introduction of low-carbon production technology, the manufacturer's profit is greater than 0 regardless of the change in the carbon penalty coefficient t and the reduction of energy consumption x, $\prod_{}^{} m4 - \prod_{}^{} m2$ andThe optimal profit margin increases with the increase of reduced energy consumption x, that is, when the technology is more advanced, the higher the profit obtained by the enterprise; The function between the optimal profit spread and the carbon penalty coefficient t is presented as a concave function, when t=about 0.35, the minimum value is obtained, and when t>0.2, the choice to introduce low-carbon production technology will bring a reduction to the retailer's profit.

图5-17：最优利润差与碳惩罚系数t还有减少耗能x之间的关系
Figure 5-17: The relationship between the optimal profit margin and the carbon penalty coefficient t and the reduction of energy consumption x

图5-18：最优利润差与碳惩罚系数t还有 $消费者对低碳商品敏感程度 τ$ 之间的关系
Figure 5-18: There is a $消费者对低碳商品敏感程度 τ$ relationship between the optimal profit spread and the carbon penalty coefficient t

当碳惩罚率t=0.2时，
When the carbon penalty rate is t=0.2,

图5-19：最优制造商利润差与减少耗能x还有 $消费者对低碳商品敏感程度 τ$ 之间的关系
Figure 5-19: There is also a relationship between the profit margin of the optimal manufacturer and the reduction of energy consumption x $消费者对低碳商品敏感程度 τ$

图5-20：最优制造商利润差与减少耗能x还有 $消费者对价格敏感程度 θ$ 之间的关系
Figure 5-2 0: There is also $消费者对价格敏感程度 θ$ a relationship between the profit margin of the optimal manufacturer and the reduction of energy consumption x

从上述五幅图中，可以得到当其他条件恒定时，消费者对低碳商品敏感程度 $τ 、$ 低碳商品偏好消费者占比 $β 因子$ ，对最优利润差几乎没有影响；
From the above five figures, it can be obtained that when other conditions are constant, the sensitivity of $τ 、$ consumers to low-carbon goods Low-carbon goods prefer consumersPercentage $β 因子$ , which has little effect on the optimal profit margin;

当碳惩罚系数t=0.2时，最优利润差与减少耗能x成正相关关系，且逐步递减；
When the carbon penalty coefficient t=0.2, the optimal profit difference is positively correlated with the reduction of energy consumption x, and decreases gradually.

当碳惩罚率t=0.1时，引进低碳生产技术所制造的效益更高，因此当碳税增高时，为鼓励制造商进行低碳生产，政府应该加大补贴额度。且消费者对价格敏感程度 $θ 、消费者对低碳商品敏感程度 τ$ 越小时，制造商的利润更大。
When the carbon penalty rate is t=0.1, the benefits of introducing low-carbon production technologies are higher, so when the carbon tax increases, the government should increase the subsidy amount to encourage manufacturers to carry out low-carbon production. And the less price-sensitive $θ 、消费者对低碳商品敏感程度 τ$ consumers are, the more profitable the manufacturer is.

图5-21：最优供应链利润差与碳惩罚系数t还有减少耗能x之间的关系
Figure 5-2 1: The relationship between the optimal supply chain profit margin and the carbon penalty coefficient t and the reduction of energy consumption x

如上图可得，当制造商引用低碳生产技术后，无论政府采用何种碳税比率和减碳技术水平的高低，供应链的总利润都是增加的。
As can be seen in the figure above, when manufacturers adopt low-carbon production technologies, the total profit of the supply chain increases regardless of the carbon tax rate adopted by the government and the level of carbon reduction technology.

图5-22：最优销售价格差与碳惩罚系数t还有减少耗能x之间的关系
Figure 5-2-2: The relationship between the optimal sales price spread and the carbon penalty coefficient t and the reduction of energy consumption x

图5-23：最优批发价格差与碳惩罚系数t还有减少耗能x之间的关系
Figure 5-2-3: The relationship between the optimal wholesale price spread and the carbon penalty coefficient t and the reduction of energy consumption x

图5-24：最优市场需求差与碳惩罚系数t还有减少耗能x之间的关系
Figure 5-2-4: The relationship between the optimal market demand difference and the carbon penalty coefficient t and the reduction of energy consumption x

从上述三张图中可以得到，减少耗能x越大，最优市场需求差、最优销售价格差、最优批发价格差随着碳惩罚率的增大，增大的幅度更明显。当采取低碳生产技术时，销售价格无论采取多大的碳惩罚率都是比引进低碳生产技术前更高的，制造商在引进低碳生产技术后，在合理的碳惩罚率时，会提高批发价格。而市场需求也随着碳惩罚率的增大而增大，因为随着碳惩罚率增大，企业为了保证利润，会选择降低批发价格和销售价格，来促进销量增长。
From the above three figures, it can be concluded that the greater the reduction of energy consumption x, the more obvious the increase in the optimal market demand, the optimal sales price and the optimal wholesale price is with the increase of the carbon penalty rate. When low-carbon production technologies are adopted, the sales price is higher than before the introduction of low-carbon production technologies, regardless of how much carbon penalty rate is adopted, and manufacturers will increase wholesale prices when the carbon penalty rate is reasonable after the introduction of low-carbon production technologies. The market demand also increases with the increase of the carbon penalty rate, because with the increase of the carbon penalty rate, enterprises will choose to reduce the wholesale price and sales price in order to ensure profits to promote sales growth.

5.4 小结
54 Summary

本章第一节对第三章中零售商采取不同模式下的利润以及销售价格进行了分析，得出了 $消费者对低碳商品敏感程度 τ 、$ 低碳商品偏好消费者占比 $β 因子$ 、制造商和零售间的信息差σ、消费者对价格敏感程度θ这些因素如何影响选择不同信息共享模式的零售商。
The first section of this chapter analyzes the profits and selling prices of retailers under different models in Chapter 3 to determine the $消费者对低碳商品敏感程度 τ 、$ proportion of consumers who prefer low-carbon goods $β 因子$ , information disparity between manufacturers and retailers σ and how consumers' price sensitivity θ affect the choice of different information sharing modelsretailers.

在第二、三节中，对前文的模型求解结果及第三章、第四章得出的模型结果进行了数值分析。从结果数据来看，本文得到的模型结论与预期结果基本一致。
In sections 2 and 3, the results of the model solution in the previous article and the model results obtained in Chapters 3 and 4 are numerically analyzed. From the results data, the conclusions of the model obtained in this paper are basically consistent with the expected results.

本章通过对零售商采取不同信息共享策略和制造商是否引进低碳生产技术下的不同决策模型结果进行了数值验证分析，得出了消费者对价格敏感程度θ、制造商和零售间的信息差σ以及降低耗能x因子可直接影响模型结果；同时在在政府加大碳惩罚率t时，应该同时增大补贴资金，降低引进低碳生产技术的成本，促进低碳生产的良性循环；在考虑是否采取信息共享策略时，制造商和零售间的信息差σ增大，制造商在无需求信息时要获得更多的利润，零售商便获得更少的利润。而且随着碳惩罚率t的增大，制造商的利润会减少，零售商的利润则相反。此外，引进低碳生产技术后，供应链也会获得更多的利润，销售价格也随着减少耗能x的增大而增大，随着碳惩罚率的增大而减少。
This chapter analyzes the results of different decision-making models under different information sharing strategies adopted by retailers and whether manufacturers introduce low-carbon production technologies, and concludes that consumers' price sensitivity θ, information differences between manufacturers and retailers σ and the reduction of energy consumption x factor can directly affect the model results. At the same time, when the government increases the carbon penalty rate, it should also increase the subsidy funds to reduce the cost of introducing low-carbon production technologies and promote the virtuous cycle of low-carbon production. When considering whether to adopt an information-sharing strategy, the information gap between manufacturers and retailers σ widen, with manufacturers getting more profit when they don't need information, and retailers getting less profit. And as the carbon penalty rate increases, the manufacturer's profit decreases, and the retailer's profit does the opposite. In addition, the introduction of low-carbon production technologies will lead to more profits in the supply chain, and the selling price will increase as the reduction of energy consumption x increases, and the carbon penalty rate decreases.

6. 总结与展望
6.Summary and outlook

6.1 研究结论
6.1 Conclusions

低碳偏好消费者对于商品的估值不仅取决于商品的基本价值，还与低碳敏感程度等因素有关。本研究从消费者的角度出发，构建了消费者效用函数，分析了消费者对产品的需求，并得出了消费者对产品的需求与价格的关系。
Low-carbon preference consumers' valuation of goods depends not only on the basic value of the goods, but also on factors such as low-carbon sensitivity. From the perspective of consumers, this study constructs a consumer utility function and analyzes consumersdemand for the product, and derives the relationship between consumer demand for the product and price.

本研究以单一零售商和单一制造商为研究对象，结合是否引进低碳生产技术及信息共享，建构了基础博弈模型。分为以下四种情况：（1）制造商选择不引进低碳生产技术，零售商不与制造商共享需求信息；（2）制造商选择不引进低碳生产技术，零售商与制造商共享需求信息；（3）制造商选择引进低碳生产技术，零售商不与制造商共享需求信息；（4）制造商选择引进低碳生产技术，零售商与制造商共享需求信息。基于上述四种情形，计算分析得到的结论如下：
This study takes a single retailer and a single manufacturer as the research object, and constructs a foundation based on whether to introduce low-carbon production technologies and information sharingGame model. There are four scenarios: (1) the manufacturer chooses not to introduce low-carbon production technologies, and the retailer does not share demand information with the manufacturer; (2) manufacturers choose not to introduce low-carbon production technologies, and retailers share demand information with manufacturers; (3) manufacturers choose to introduce low-carbon production technologies, and retailers do not share demand information with manufacturers; (4) Manufacturers choose to introduce low-carbon production technologies, and retailers share demand information with manufacturers. Based on the above four scenarios, the conclusions obtained from the calculation and analysis are as follows:

效用影响因子与市场总需求的关系：无论制造商选择何种生产技术，当零售商选择信息共享策略时，市场总需求总是比未信息共享时高。由于消费者是理性的博弈人，无论制造商生产的是什么商品，当价格和碳惩罚率越高，总需求也就越小，而当商品不是低碳商品时，低碳偏好消费者会导致总需求下降，当是低碳商品时，因为低碳偏好消费者的存在，总需求会上升。当引进低碳生产技术后，市场需求增多，并且市场需求会随着碳惩罚率的变大而变大。
Relationship between Utility Influencing Factor and Total Market Demand: Regardless of the production technology chosen by the manufacturer, when retailers choose an information-sharing strategy, the total market demand is always higher than when information is not shared. Since consumers are rational gamblers, no matter what goods manufacturers produce, when the price and carbon penalty rate are higher, the aggregate demand will be smaller, and when the commodity is not a low-carbon commodity, low-carbon preference consumers will lead to a decline in aggregate demand. When it is a low-carbon commodity, aggregate demand rises because of the presence of low-carbon preference consumers. When low-carbon production technologies are introduced, the market demand increases, and the market demand will increase as the carbon penalty rate increases.

效用影响因子与销售价格的关系：无论制造商和零售商选择何种共享策略，销售价格都随着，碳惩罚率，消费者对价格敏感程度、低碳偏好因子的增大而增大。此外，无论什么情况下，当消费者对价格越敏感时，销售价格会随之下降。当零售商选择不共享信息时，销售价格会升高，当引进低碳生产技术后，零售商会随着碳惩罚率的增大而降低销售价格，但始终比未引进低碳生产技术时的销售价格大。
Relationship between utility influencing factor and selling price: Regardless of the sharing strategy chosen by manufacturers and retailers, the selling price increases with the increase of carbon penalty rate, consumer price sensitivity, and low-carbon preference factor. In addition, in any case, the more price-sensitive consumers are, the lower the selling price. When retailers choose not to share information, the selling price increases, and when low-carbon production technologies are introduced, retailers lower their selling prices as the carbon penalty rate increases, but always higher than when low-carbon production technologies are not introduced.

效用影响因子与批发价格的关系：无论零售商选择何种共享策略，批发价格都不会改变。当制造商选择不引进低碳生产技术时，批发价格随着低碳消费者对低碳商品越偏好以及价格影响因子的升高而降低，而当引入低碳生产技术时，情况则相反。并且批发价格也与零售商是否共享需求信息无关。在合理的碳惩罚率时，引进低碳生产技术，制造商可以获得更高的批发价格，并获得更多的利润。
Relationship between Utility Influencing Factor and Wholesale Price: Wholesale prices do not change regardless of the sharing strategy chosen by retailers. When manufacturers choose not to introduce low-carbon production technologies, wholesale prices decrease with the increasing preference of low-carbon consumers for low-carbon goods and the price influencing factors, while the opposite is true when low-carbon production technologies are introduced. And the wholesale price is also independent of whether the retailer shares demand information or not. By introducing low-carbon production technologies at a reasonable carbon penalty rate, manufacturers can obtain higher wholesale prices and make more profits.

不论制造商采用的是否低碳生产技术，当制造商与零售商间存在较大的需求信息差，则零售商不会与制造商共享信息；在制造商和零售商的需求信息差比较小的情况下，零售商会与制造商共享需求信息。当制造商不引进低碳生产技术时，供应链的总利润并不会受到信息共享与否的影响。
Regardless of whether the manufacturer adopts low-carbon production technology, when there is a large demand information gap between the manufacturer and the retailer, the retailer will not share the information with the manufacturer; In cases where the gap between the manufacturer and the retailer's demand information is small, the retailer shares the demand information with the manufacturer. When manufacturers do not introduce low-carbon production technologies, the total profit of the supply chain is not affected by the sharing of information.

6.2 不足与未来展望
6.2 Deficiencies and Future Prospects

本文在参考了现有文献的基础上，构建了一个零售商和一个制造商的基础供应链，横向对比分析考虑有无信息共享策略供应链模型的求解结果，纵向对比分析制造商在采取不引进和引进低碳生产策略时的不同利润。此外，本文就低碳供应链中消费者的低碳偏好为起点，考虑了是否引进低碳生产技术、碳税政策、是否进行信息共享、消费者心理因素，研究结果可以为该行业的实际发展提供一些参考依据。
Based on the existing literature, this paper constructs the basic supply chain of a retailer and a manufacturer, analyzes the solution results of the supply chain model with or without information sharing strategy, and compares the different profits of manufacturers when they adopt low-carbon production strategies without introducing or introducing low-carbon production strategies. In addition, this paper takes the low-carbon preference of consumers in the low-carbon supply chain as a starting point, and considers whether to introduce low-carbon production technology, carbon tax policy, information sharing, and consumer psychological factorsThe actual development of the industry provides some references.

值得重点注意的是，政府在实际中所采取的碳税政策是实行阶梯制的，并不是一成不变的。本文考虑的仅仅是单一零和售商单一制造商所组成的基础供应链，但通常有多个零售商和制造商以及多级供应链存在于市场上。本文假设的消费者心理因素是不全面的，在现实中，影响消费者购买商品的因素有很多，消费者可以选择的商品也有很多，未来可考虑更加复杂的情况进行探究分析。
It is important to note that the carbon tax policy adopted by the government in practice is a tiered system, not static. This article only considers the basic supply chain of a single zero-sum seller and a single manufacturer, but there are often multiple retailers and manufacturers and multiple levels of supply chain in the market. In reality, there are many factors that affect consumers' purchase of goods, and there are many products that consumers can choose from.

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7.References

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8. 致谢
8.Acknowledgments

时光飞逝，四年大学时光转眼即逝，四年来我从一个懵懂的少年到现在完成毕业论文准备毕业的大学生，内心在激动之余，更多的是感谢。
Time flies, four years of college time in a blink of an eye, in the past four years, I have gone from an ignorant teenager to a college student who has completed his graduation thesis and is ready to graduate.

感谢每一位在我的论文撰写工程中给予我帮助的人，感谢指导老师，感谢女朋友，感谢室友，感谢其他的好朋友，是他们的陪伴和鼓励让我在漫漫长夜中，能够坚持完成我的论文，并在我遇到困难的时候伸出援手，感谢你们的支出和付出。
Thank you to everyone who helped me in my dissertation writing project, thank you to my advisor, thank you to my girlfriend, thank you to my roommates, thank you to other good friends, it was their company and encouragement that allowed me to persevere in completing my thesis during the long night, and lend a helping hand when I encountered difficulties, thank you for your expenditure and dedication.

除此之外，我还想感谢我的父母，你们生我养我，在过去的22年里，如同辛勤的园丁，但时光流逝，与我的印象中相比，现如今的你们，新添了许多白发，脸上多出了几道皱纹。正是你们的支持让我完成了大学四年的学业。此外，我还感谢我的女朋友，是你在我论文选题毫无思路时，帮我分析，确定选题。而大学遇到的老师，所上过的课至今任然记在心中，还有我们社团以及学生会的朋友，与你们相处的四年，虽然因为疫情而短暂，却也显得更加珍贵，印象深刻，相信日后会成为我人生路上的宝贵财富。
In addition to this, I would like to thank my parents, you gave birth to me and raised me, and in the past 22 years, you have been like a diligent gardener, but as time passes, compared to my impression, you now have a lot of gray hair and a few more wrinkles on your face. It was your support that allowed me to complete my four years of university. In addition, I would like to thank my girlfriend for helping me analyze and determine the topic when I had no idea about the topic of my thesis. The teachers I met in college, the classes I took are still in my heart, and the friends of our club and the student union, although the four years I spent with you were short because of the epidemic, they also seemed more precious and impressive, and I believe that they will become a valuable asset on my life road in the future.

经世济民，孜孜以求，山水相逢，终有一别，西南财经大学和亲爱的朋友们，愿我们都未来可期，不负韶华。
Southwestern University of Finance and Economics and dear friends, I hope we all have a promising future and live up to our time.

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2023．03