Manufacturer’s Green Financing and CER Decisions under the Carbon Tax Policy and Capital Constraints

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Introduction
Dealing with climate change is one of the most urgent issues globally.With the massive emission of greenhouse gases represented by carbon dioxide, global warming, rising sea levels, soil erosion, and other environmental pollution, problems are becoming increasingly severe [1].In response to the climate change disasters and the objective needs of national economic development, many countries actively explore efective strategies to balance environmental preservation and economic development [2,3].For example, in 2019, the European Union released the European Green Deal, proposing that Europe will achieve net-zero greenhouse gas emissions by 2050 and become the world's frst carbon-neutral region.As a major stakeholder, China has always actively responded to and promoted CER.President Xi Jinping announced that China will strive to achieve peak carbon dioxide emissions by 2030 and carbon neutrality by 2060, demonstrating China's frm commitments and important contributions to the global fght against climate change.Simultaneously, governments have introduced carbon subsidies, carbon limits, carbon trading, carbon taxes, carbon labels, and other related institutional policies.Te carbon tax policy is considered a typical global climate governance policy and an efective tool for reducing CO 2 emissions [4].Te carbon tax policy uses taxation to achieve emission reduction in a short period [5], which requires lower management costs and can supplement the control scope that carbon cap-and-trade regulations cannot cover.
Under the infuence of the strong intervention of the carbon tax policy, enterprises need to improve their green production capacity to reduce carbon emissions.Producing low-carbon products can not only reduce the carbon tax cost for manufacturers but also increase market demand for the products and facilitate the development of the company's scale.However, the research and development of green technology and the purchase of green equipment incur additional costs.Te double pressure of production and reducing carbon emissions makes enterprises face the problem of tight funds.To help manufacturers overcome the green production dilemma, supply chain company ofers some solution.Li & Fung (https://www.lifung.com),for instance, ofers credit and other lending services to help fnance the capital needs of upstream enterprises [6].Within the supply chain, in March 2022, Guangdong Midea landed the frst green supply chain fnance business in the home appliance industry, helping their suppliers achieve lower-cost fnancing.When manufacturers face fnancial constraints, they can secure loans from the bank [7], trade credit from the retailer [8,9], or they can apply for advances from a well-funded retailer [10].In the context of "carbon peaking" and "carbon neutrality," we can expect that low-carbon fnance will be applied to more and broader areas for the beneft of society in the future.
Studying frms' green fnancing decision-making and supply chain operation strategies under the carbon tax policy and capital constraints is relevant.However, few studies have considered the impact of the retailer's surplus funds on supply chain fnancing and operation decisions after the capital-strapped manufacturer applies for internal fnancing from the capital-strong retailer.Additionally, the benefts brought by these excess funds to the supply chain have been neglected.Terefore, this study aims to address the green fnancing and CER decisions of the capital-constrained manufacturer under the carbon tax policy.We constructed three fnancing models for the manufacturer.When the manufacturer cannot aford the costs of production and investment in green technology, they can apply for bank loans (the EF mode).Tey can also apply for loans directly from a well-funded retailer, considering the retailer's remaining assets (the IF mode).Te retailer can even prepay any shortfall in advance, provided the manufacturer promises a price discount (the TC mode).In our article, we frst obtain the equilibrium solutions of the three fnancing modes and then analyze how the carbon tax rate changes afect these equilibrium solutions and compare several key parameters that the manufacturer focuses on when making decisions.We try to answer the following questions: (1) From the manufacturer's standpoint, which fnancing mode can maximize the economic benefts to the manufacturer?(2) When the manufacturer chooses the fnancing mode that brings the most economic benefts, can his environmental and social benefts be optimized simultaneously?(3) Are the manufacturer's and supply chain's economic benefts consistent?If not, how do we reconcile the contradictions between them?
Te remainder of this paper is organized as follows.Section 2 presents a related literature review.Section 3 presents the problem description and basic assumptions.Furthermore, we set up three diferent fnancing modes, obtain the equilibrium solutions, and analyze the impact of the carbon tax rate changes on the equilibrium solutions in Section 4. Section 5 compares CER, market demand, and profts of manufacturers, retailers, and supply chains under the three fnancing modes.A numerical simulation is presented in Section 6.Finally, we summarize the conclusions and propose management implications in Section 7.

Literature Review
Tree streams of literature are related to this work: carbon tax policy, supply chain fnance, and low-carbon supply chain with capital constraints.Tis section reviews related literature and highlights how our study difers from theirs.

Carbon Tax Policy.
Scholars have a strong research interest in business operation management under the carbon tax policy.Krass et al. [11] combined the government's carbon tax regulation and the study of frms' technology choices and found that the efect of a carbon tax on frms' technology choices in the context of mono-oligopoly varied nonmonotonically.Giri et al. [12] considered the government's tax advocacy strategy in a two-echelon system consisting of two competing green manufacturers and one distributor and proposed a nonlinear two-level interaction model to evaluate the equilibrium strategy of the government and the supply chain.Ruidas et al. [13] analyzed the impact of diferent carbon tax policies on the carbon emissions of product inventory.In contrast to the above studies, some scholars have explored the efectiveness of carbon taxes for emission reduction strategies.Chen and Hao [14] compared the efects of a carbon tax on two competing frms with diferent operational efciencies, showing that the carbon tax had a more pronounced impact on CER and the profts of inefcient frms.Wang et al. [15] compared the optimal strategies of supply chain members under diferent power structures in decentralized and centralized supply chains under carbon tax policies and gauged the impact of a carbon tax on supply chain decisions.Shu et al. [16] constructed a trade-old-for-remanufactured model in the policy context of a carbon tax and carbon subsidy and analyzed the manufacturer's optimal pricing and production strategies in the model, afrming the carbon tax policy's efectiveness in reducing emissions.With different emission tax policies, Yu et al. [17] compared the efects of varying government environmental policies on pricing and total emissions in the supply chain and proposed that the implementation of environmental taxes can both promote CER and incentivize frms to operate green.
In addition, several studies have analyzed the impact of CER on pollution abatement [18].Cheng et al. [19] believed that when the carbon tax policy and consumer environmental awareness appear simultaneously, it can efectively 2 Complexity stimulate manufacturers to increase the CER investment to improve supply chain operational efciency.Zhang et al. [20] confrmed that when consumers have a level of environmental awareness, the government can achieve the goal of proft maximization in the whole supply chain by setting a reasonable carbon tax rate, which is consistent with the government's low-carbon emission goal.Luo et al. [21] discussed the impact of carbon tax policy formulation on CER decisions in the supply chain.It is believed that carbon tax policy should be tailored to diferent industries and promote supply chain members to reduce carbon emissions by cultivating consumers' environmental awareness.Zhu et al. [22] examined how the carbon tax policy and consumer environmental awareness afect production and CER decisions.

Supply Chain Finance.
Te aforementioned scholars have discussed the operational decisions of low-carbon supply chains, which are primarily based on the premise of sufcient production capital.Many enterprises are inherently prone to fnancial difculties due to inventory redundancy problems.In recent years, supply chain fnancing has gradually solved the problem of fnancial diffculties for some enterprises, and supply chain fnancing has gradually diferentiated into two main ways: internal funding and external fnancing in practical application.Xiao et al. [23] discussed the efectiveness of revenue-sharing, buyback contracts, and all-unit quantity discount contracts for coordinating the supply chain in the presence of default cost and proposed a generalized revenue-sharing agreement for coordinating the corresponding centralized fnancially constrained supply chain.Jing and Seidmann [24] suggested that bank loan fnancing can mitigate double marginalization of the supply chain when production cost is high.
Compared with external funding relying on banks, the external fnancing of supply chain members does not require additional fxed assets as collateral, and supply chain members are more familiar with each other's business situation, so fnancing risks are better controlled.For instance, Bellantuono et al. [25] proposed an early payment discount plan and showed that joint adoption of an early payment discount plan with a revenue-sharing plan has better returns.Chen et al. [26] identifed that trade credit from suppliers can increase the profts of supply chain members and reduce the risk of default.Lee and Rhee [27] demonstrated trade credit as a tool for achieving supply chain coordination from the supplier's perspective and derived optimal price reduction subsidies and risk premiums in trade credit using buyback/markdown allowance contracts.Li et al. [28] derived the optimal selling price and replenishment cycle for retailers under an advance-cash-credit payment scheme and demonstrated a positive correlation between the percentage of payments made in advance and the selling price.Shen et al. [29] compared three fnancing models in the supply chain of capital-constrained manufacturers: bank credit fnancing, dual trade fnancing from competing retailers, and mixed bank fnancing and trade credit fnancing.Te efects of retailer competition and interest rates on the choice of fnancing options are analyzed.Furthermore, some scholars have compared bank/trade fnance to advanced payment fnance strategies [30].Zhou et al. [30] discussed supply chain members and overall supply chain benefts in two fnancing channels: trade credit from the manufacturer to the distributor or advance payment from the platform to the distributor, from the perspective of risk allocation in a threeparty supply chain.Diferent from the above studies, Jiang et al. [31] studied the impact of retailers' credit ratings on supply chain operation management decisions.

Low-Carbon Supply Chain with Capital Constraints.
Te carbon tax policy has increased the incentive of enterprises to reduce carbon emissions, but it has also led manufacturers to bear more carbon reduction costs.Terefore, scholars have conducted in-depth studies on fnancing a low-carbon supply chain under capital constraints.For example, Wua et al. [32], Cao et al. [33], Zhang et al. [34], and Mahato et al. [35] explored the infuence of bank fnancing and trade credit fnancing on the optimal decision-making of low-carbon supply chain members with capital constraints.Qin et al. [36] analyzed both green fnancing and cost-sharing contracts using the Stackelberg game model, considering manufacturers' capital constraints and the carbon cap-and-trade mechanism, and found that green fnance rates do not always adversely afect CER, and retailers' cost-sharing does not always have a positive impact on CER.Jin et al. [37] discussed the infuence of diferent government intervention policies on manufacturing enterprises' green fnancing decisions.Lu et al. [38] analyzed the optimal strategy choice between autonomous fnancing and supply chain cooperative fnancing when the manufacturer cannot aford the cost of CER under carbon quota control.An et al. [39] constructed a two-echelon supply chain consisting of a capital-constrained manufacturer and a supplier, analyzed the supply chain operational decisions under strict carbon emission regulation when the manufacturer adopted green credit fnancing, and compared it with social welfare under the traditional trade fnance mode.Wang et al. [40] combined the order fnancing model in green fnance and found that a carbon tax and green fnance can promote the green transformation of corporate clean technologies.Li et al. [41] constructed a two-echelon lowcarbon supply chain model wherein the manufacturer is capital-constrained to use carbon pledge fnancing and analyze the manufacturer's CER decisions and supply chain members' profts under diferent power structures.Furthermore, some scholars have designed contracts to coordinate cash-constrained supply chain members.Depending on the presence or absence of prepayment fnancing, Qin et al. [42] discussed supply chain models when capital-constrained manufacturers use bank and hybrid fnancing models and extend the models with cap-and-trade regulation.It is also demonstrated that prepayment fnancing with price discounts can improve supply chain members' profts when the manufacturer is capitalconstrained.Wu et al. [43] discussed no-fnancing, trade credit, and bank credit fnancing modes in a manufacturer's capital-constrained low-carbon supply chain and designed a cost-sharing contract, which was later confrmed to improve the proftability of supply chain members.
Tese studies demonstrate the numerous works made by scholars to study carbon tax policy, supply chain fnance, and low-carbon supply chains with capital constraints.However, most of the existing studies on carbon tax policy are based on the case of a well-funded supply chain, and the pricing and CER decisions in a low-carbon supply chain under fnancial constraint deserve equal attention.Although the results of a low-carbon supply chain have been fruitful, some problems still need to be explored, for example, developing and comparing fnancing modes within a supply chain.Additionally, many studies only analyzed the impact of carbon abatement fnancing on production decisionmaking but did not consider the role of the manufacturer's initial capital.In diferent fnancing modes, the equilibrium outputs of the manufacturers are not the same, which means that they incur extra production costs under each fnancing mode.It is inappropriate to consider only the CER cost of the manufacturer without considering the production cost.Terefore, both production and CER costs should be considered when fnancing.In our study, we assume that the initial capital of the manufacturer is zero and that the costs of production and investing in green technology need to be fnanced.Based on this notion, we investigate the EF, IF, and TC modes, compare the equilibrium solutions of the three fnancing modes, and analyze the impact of the carbon tax rate changes on the equilibrium solutions.Table 1 shows how our current model difers from the existing model.

Problem Description and Assumption
3.1.Problem Description.Tis study constructs a twoechelon low-carbon supply chain with the manufacturer as the leader of the Stackelberg game and the retailer as the follower.Te manufacturer uses raw materials to produce low-carbon products and sell them to the retailer at wholesale price.Meanwhile, the retailer faces a singleproduct monopolistic market to sell low-carbon products directly to consumers at the selling price.Te government imposes a carbon tax on the carbon dioxide emitted by the manufacturer during production.We only consider that the manufacturer needs to pay a carbon tax for his carbon emission behavior and ignores the carbon emitted by the retailer in the sales process.To reduce the paid carbon tax while satisfying consumers' preferences for low-carbon products, the manufacturer decides to invest in green technology to reduce emissions, which means that the manufacturer needs to spend a considerable amount of funds.
When the initial capital possessed by the manufacturer is not enough to disburse the costs of production and invest in green technology, the manufacturer can apply for loans from fnancial institutions and pay back the principal and interest of the loan at the end of the production-sale cycle.Te manufacturer can borrow from the retailer when the retailer has sufcient funds.Notably, the manufacturer also has a third option, which is to ask the retailer to pay all the money upfront in exchange for promising the retailer a onetime price discount on all items ordered.
According to Zhao and Ji [44] and Long and Wang [45], a CER decision is usually a long-term decision that needs to be made early and prioritized over the pricing decision.Terefore, the game process was divided into three stages.Te frst stage is the CER decision, wherein the manufacturer decides the level of carbon emissions.Te second stage is the wholesale price decision, wherein the manufacturer determines the price charged when the product is delivered to the retailer.Te third stage is the selling price decision, wherein the retailer sets a selling price for a low-carbon product per unit.Te fowchart of the green fnancing and CER decision-making is shown in Figure 1.

Model Assumptions.
To facilitate modeling and analysis, some assumptions are proposed as follows.
Assumption 1. Market demand faced by the retailer is expressed as a function of selling price and the fnal carbon emissions.Following Lu et al. [38], we have ( Te market demand function implies that market demand is negatively correlated with the selling price and fnal carbon emissions.In the market demand function, a is the potential market scale, b is the sensitivity coefcient of market demand to the selling price and, θ is the level of consumers' environmental awareness.Moreover, e i is the fnal carbon emissions and i � 1, 2, 3 represents the EF, IF, and TC modes, respectively.Assumption 2. To control the amount of carbon dioxide discharged into the atmosphere, the government imposes a carbon tax on the manufacturer.Te carbon tax rate is t, which means that for each unit of carbon dioxide emitted by a manufacturer, t units of carbon tax must be paid to the government at the end of the production-sales cycle.If the fnal carbon emissions per unit product after investing in green technology are e i , then the total carbon tax paid by the manufacturer to the government is te i D i .Assumption 3. Te cost of investing in green technology for the manufacturer is (1/2)k(e 0 − e i ) 2 , where k is the cost coefcient of CER and e 0 is the initial carbon emissions per unit product.Sun and Yang [46] and Song et al. [47] found that when the investment in CER is increased, the cost of investment in green technology and the amount of CER have a quadratic relationship.Tis relationship denotes that as the amount of CER increases, the cost of CER increases, and the marginal cost of CER increases.Assumption 4. To simplify the analysis process, we set the initial capital of the manufacturer to zero without afecting the conclusion.Simultaneously, we assume that the retailer's capital is sufcient and can meet the manufacturer's capital demand for production and investment in green technology.4 Complexity Table 2 summarizes the main notations and defnitions used in this study.

External Financing (Te EF Mode).
In the EF mode, the amount of capital required by the manufacturer is cD 1 + (1/2)k(e 0 − e 1 ) 2 , which includes the cost of producing low-carbon products and investing in green technology.Te manufacturer obtains all funds by applying for bank fnancing.Te action order of supply chain members is as follows: in the CER decision-making phase, the manufacturer determines how much carbon emissions to reduce per unit of low-carbon product based on the carbon tax rate announced by the government.In the pricing decisionmaking phase, the manufacturer and retailer play the Stackelberg game.Te manufacturer is the leader of the game and, therefore, has the priority to make decisions.After the manufacturer determines the wholesale price, the retailer determines the selling price for the low-carbon product.
Te manufacturer's proft function is expressed as follows: ( Te retailer's proft function is expressed as follows: where In formula (2), the frst item is the gross proft from selling low-carbon products to the retailer minus the carbon tax paid to the government, the second item is the cost of investing in green technology, and the third item is the interest paid to the bank on loans.In formula (3), the frst Complexity item is the proft from selling low-carbon products to consumers, and the second item is the interest earned on the funds held in the bank.
Theorem 5.In the EF mode, the optimal CER, wholesale price, selling price, and market demand are given, respectively, by where Proof of Teorem 5. Please refer to Appendix A. Substituting e * 1 , w * 1 , and p * 1 into π M 1 (w 1 , e 1 ) and π R 1 (p 1 ), we obtain the manufacturer, retailer, and supply chain system's profts that are expressed as ( Social responsibility and sustainable development are important issues in the development of modern enterprises.As a member of society, an enterprise needs to undertake social responsibility and promote sustainable development while pursuing economic benefts.John Elkington frst proposed the concept of the triple bottom line in 1997.He believes that no company can only pursue proft; economic, environmental, and social benefts are the triple bottom line that enterprises must adhere to.Tese three indicators are also regarded as the "troika" to evaluate the value of enterprises.In our paper, we mainly discuss the fnancing mode selection from the perspective of the manufacturer.Te manufacturers are frst concerned about the economic benefts of each fnancing mode, followed by environmental and social benefts.In this article, we represent these three indicators in terms of proft, CER, and market demand, respectively.Terefore, analyzing the impact of the carbon tax rate changes on these three indicators is necessary, as they will afect the manufacturer's fnancing decisionmaking.

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Corollary .Regarding CER and the carbon tax rate in the EF mode, we have the following: and Proof of Corollary 6. Please refer to Appendix B.

Internal Financing (the IF Mode).
In the IF mode, the costs of producing low-carbon products and investing in green technology, which should be paid for by the manufacturer, add up cD 2 + (1/2)k(e 0 − e 2 ) 2 .As the initial capital of the manufacturer is zero, all funds needed by the manufacturer are borrowed from the retailer.At the end of the production-sale cycle, the manufacturer pays a certain amount of interest in addition to repaying the principal to the retailer.Te interest rate acceptable to the manufacturer is not higher than that provided by the bank.Otherwise, the manufacturer chooses a loan from the bank.Notably, the interest rate acceptable to the retailer must not be lower than that obtained by depositing funds in the bank.Otherwise, the retailer will choose to deposit funds in the bank.To facilitate the comparison between the EF and IF modes, we assume that the manufacturer borrows from the retailer at the same interest rate as the bank.Te decision-making sequence of the IF mode was consistent with that of the EF mode.First, the manufacturer determines how much carbon is emitted per unit of low-carbon product.Ten, the manufacturer and retailer play a Stackelberg game; that is, the manufacturer frst decides the wholesale price, and the retailer determines the selling price after observing the manufacturer's decision-making.
Te manufacturer's proft function is expressed as follows: Te retailer's proft function is expressed as follows: where In formula (6), the frst item is the gross proft from selling low-carbon products to the retailer minus the carbon tax paid to the government, the second item is the cost of investing in green technology, and the third item is the interest paid to the retailer on loans.In formula (7), the frst item is the proft from selling low-carbon products to consumers, the second item is the interest on the loan from the manufacturer, and the third item is the interest earned on the remaining funds deposited in the bank after deducting the loan given to the manufacturer.Theorem 9.In the IF mode, the optimal CER, wholesale price, selling price, and market demand are presented as follows: where ξ 2 � a − bc(1 + r 2 ) − (θ + bt)e 0 > 0 and c 2 � (θ + bt)t (a − bc(1 + r 2 )).
Proof of Teorem 9. Please refer to Appendix E. Substituting e * 2 , w * 2 , and p * 2 into π M 2 (w 2 , e 2 ) and π R 2 (p 2 ), we obtain the manufacturer, retailer, and supply chain system's profts and are expressed as □ Corollary 10.Regarding CER and the carbon tax rate in the IF mode, we have the following: (i) When e 0 > e I 0 and 0 < t < t I 1 , there is z∆e * 2 /zt > 0 (ii) When e 0 > e I 0 and t I 1 < t < t I 0 , there is z∆e * 2 /zt < 0 (iii) When 0 < e 0 < e I 0 and 0 < t < t I 0 , there is z∆e * 2 /zt > 0 Complexity and Proof of Corollary 12. Please refer to Appendix H. □ 4.3.Trade Credit Financing (the TC Mode).In the TC mode, the amount of capital the manufacturer needs to set aside for production and investing in green technology is cD 3 + (1/2)(e 0 − e 3 ) 2 .Te manufacturer has no initial capital but is fnanced neither by loans from the bank nor by loans from the retailer.Te manufacturer negotiates with the retailer to have the latter prepay the costs of producing lowcarbon products and investing in green technology and gives the retailer a wholesale price discount on all products ordered.In this way, although the retailer loses a small amount of interest income, it also saves part of the procurement cost.Terefore, the retailer can agree to the contract proposed by the manufacturer.Te decision-making sequence of the TC mode is that the manufacturer decides on CER frst and then determines the wholesale price after giving the optimal price discount.Finally, the retailer decides the selling price according to the wholesale price provided by the manufacturer.
Te manufacturer's proft function is expressed as follows: Te retailer's proft function is expressed as follows: where In formula (10), the frst item is the gross proft from selling low-carbon products to the retailer minus the carbon tax paid to the government, and the second item is the cost of investing in green technology.In formula (11), the frst item is the proft from selling low-carbon products to consumers, and the second item is the interest earned by depositing the remaining funds in the bank after paying the manufacturers' production cost and CER investment.In particular, w 3 is the wholesale price after the discount provided by the manufacturer.
Proof of Teorem 13.Please refer to Appendix I. Substituting e * 3 , w * 3 , and p * 3 into π M 3 (w 3 , e 3 ) and π R 3 (p 3 ), we obtain the manufacturer, retailer, and supply chain system's profts and are expressed as

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Corollary 14. Regarding CER and the carbon tax rate in the TC mode, we have the following: (i) When e 0 > e T 0 and 0 < t < t T 1 , there is z∆e * 3 /zt > 0 (ii) When e 0 > e T 0 and t T 1 < t < t T 0 , there is z∆e * 3 /zt < 0 (iii) When 0 < e 0 < e T 0 and 0 < t < t T 0 , there is z∆e Proof of Corollary 14. Please refer to Appendix J.

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Corollary 15.Regarding market demand and the carbon tax rate in the TC mode, we have the following: 8 Complexity (i) When 0 < e 0 < e T 0 and 0 < t < t T 2 , there is zD * 3 /zt < 0 (ii) When 0 < e 0 < e T 0 and t T 2 < t < t T 0 , there is zD * 3 /zt > 0 (iii) When e 0 > e T 0 and 0 < t < t T 0 , there is zD * Proof of Corollary 15.Please refer to Appendix K.

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Corollary 1 .Regarding the manufacturer's proft and the carbon tax rate in the TC mode, we have the following: Proof of Corollary 16.Please refer to Appendix L.
From Corollaries 6, 10, and 14, we know that the impact of the carbon tax rate changes on CER is not only related to the initial carbon emissions but also to the value of the carbon tax rate itself in the three modes.Tere is a threshold value for the initial carbon emissions.When the initial carbon emissions are below the threshold, raising the carbon tax rate will incentivize the manufacturer to increase CER.When the initial carbon emissions are greater than the threshold, in the process of the continuous increase of the carbon tax rate, CER shows a trend of increasing frst and then decreasing.
From Corollaries 7, 11, and 15, we know that the impact of the carbon tax rate changes on the market demand for low-carbon products is related to the initial carbon emissions and the range of the carbon tax rate.For diferent fnancing modes, there is a threshold for the initial carbon emissions.When the initial carbon emissions are greater than the threshold, these equilibrium solutions decrease with an increase in the carbon tax rate.When the initial carbon emissions are less than this threshold, an increase in the carbon tax rate in a lower range will lead to a reduction in these equilibrium solutions, but an increase in the carbon tax rate in a higher degree will promote growth in these equilibrium solutions.
From Corollaries 8, 12, and 16, we know that, regardless of the manufacturer's initial carbon emission level, the manufacturer's proft decreases with an increase in the carbon tax rate.In other words, although increasing the carbon tax rate will stimulate the manufacturer to reduce carbon emissions and thus promote the growth of market demand, the contribution of the evolution of market demand to proft is not sufcient to ofset the side efect of the increase in the carbon tax rate on proft.Consequently, the manufacturer's proft tends to decline with an increase in the carbon tax rate.

Models Comparison
Based on Teorems 5, 9, and 13, we can further compare the EF, IF, and TC modes on CER, market demand, the manufacturer's proft, the retailer's proft, and the supply chain's proft.

Corollary 17. Comparing the EF and IF modes, we obtain the following:
Proof of Corollary 17. Please refer to Appendix M.
As can be seen from Corollary 17, the IF mode is better than the EF mode for the main supply chain equilibrium solutions.From the perspective of the manufacturer, proft is undoubtedly the primary goal for the manufacturer to choose fnance modes.Te most favored fnancing mode will be the one which can bring the greatest economic benefts to the manufacturer.Under the corporate social responsibility requirement, the manufacturer must consider not only economic benefts but also environmental benefts (such as CER) and social benefts (such as the quantity of product supplied, i.e., market demand).If the manufacturer gets the most economic benefts, environmental and social benefts can also be the best; it will be a "multi-win" situation.In terms of the EF and IF modes, the former is inferior to the latter in the aspect of CER, market demand, the manufacturer's proft, the retailer's proft, and the supply chain system's proft.Compared to the IF mode, the EF mode is a strictly inferior strategy for the manufacturer and is excluded in the frst place.

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Corollary 18. Comparing the IF and TC modes, we obtain the following: 2 and π R * 3 , combined with the initial carbon emissions, the discussion is as follows.

Case 1: When
2 , and there is π R * 3 > π R * 2 ; it meets t R 2 < t < t T 0 , and there is π 1 , and there is π 2 , and there is π and π SC * 3 , combined with the initial carbon emissions, the discussion is as follows.

Case 1: When
− θ/b, and there is π SC * 3 > π SC * 2 ; it meets − θ/b, and there is π SC * 3 > π SC * 2 ; it meets , and there is π SC * 3 , and there is Proof of Corollary 18. Please refer to Appendix N. Corollary 18 shows that the economic, environmental, and social benefts of the TC mode are better than those of the IF mode.Combined with the results of Corollary 17, the optimal fnancing mode for the manufacturer, as the fnancing decision maker, is the TC mode.At the same time, we can also see that in the two ways of IF and TC, the retailer and supply chain's profts depend on the initial carbon emissions of the manufacturer and the carbon tax rate imposed by the government.Although the optimal fnancing mode of the manufacturer is the TC mode, if the retailer's proft is smaller than that of the IF mode, then the retailer has every reason to refuse to prepay the production cost and CER investment to the manufacturer.In this case, if the supply chain system's proft in the TC mode is even higher, the manufacturer can design a reasonable coordination contract to give a certain amount of proft compensation to the retailer to ensure that the retailer's fnal proft is not lower than the proft in the IF mode, and then, the TC mode will be adopted by both parties.However, suppose the level of the supply chain system's proft in the IF mode is higher.In that case, the coordination contract cannot efectively coordinate the supply chain, and the manufacturer can only choose the IF mode.□ 6. Numerical Analysis 6.1.Parameter Settings.In this section, we provide a numerical example to illustrate the impact of the carbon tax rate change on CER, market demand, the manufacturer, retailer, and supply chain system's profts.Based on the above analysis, we compare the equilibrium solutions of diferent fnancing modes.Referring to the parameter setting of the demand function by Zhang and Qin [48], we let a � 100, b � 1, c � 20, and θ � 1.Other parameters are assigned as follows: k � 40, r 1 � 10%, r 2 � 5%, and V R � 3000.According to the given parameters, we obtain e E 0 � 5.88, e I 0 � 5.96, and e T 0 � 6.25.For the convenience of the following elaboration, we refer to the manufacturers with the initial carbon emissions per unit product e 0 < min e E 0 , e I 0 , e T 0   as the clean manufacturer and those with the initial carbon emissions per unit product e 0 > min e E 0 , e I 0 , e T 0   as the polluting manufacturer.We used e 0 � 4 as a clean manufacturer and e 0 � 7 as a polluting manufacturer.When examining the infuence of the carbon tax rate change on the equilibrium solutions of the three fnancing modes, it is necessary to ensure that the value range of the carbon tax rate meets the constraints for the three fnancing modes.In our study, when the initial carbon emissions are e 0 � 4, there is 0 < t < 7.10; when the initial carbon emissions are e 0 � 7, there is 0 < t < 10.14.Without loss of generality, the carbon tax rate ranges from 0 to 7 for the clean manufacturer, and for the polluting manufacturer, the carbon tax rate ranges from 0 to 10.

Te Impact of the Carbon Tax Rate Changes on CER.
Figure 2 describes the impact of the carbon tax rate changes on CER for clean and polluting manufacturers.As illustrated in Figure 2(a), for the clean manufacturer, CER increases with an increase in the carbon tax rate.As shown in Figure 2(b), for the polluting manufacturer, CER frst increased and then decreased with an increase in the carbon tax rate, and the number of carbon emissions reduced by the polluting manufacturer was less than that facilitated by the clean manufacturer under the same carbon tax rate.Hence, it can be considered that increasing the carbon tax rate has a relatively efective incentive efect on the clean manufacturer while stimulating the polluting manufacturer to reduce carbon emissions has a limited efect.In terms of the three scenarios, the abatement efect is best in the TC mode, and the IF mode is generally better than the EF mode. 10 Complexity

Te Impact of the Carbon Tax Rate Changes on Market
Demand. Figure 3 describes the impact of the carbon tax rate changes on market demand for clean and polluting manufacturers.As shown in Figure 3(a), for the clean manufacturer, the market demand frst decreases and then increases with an increase in the carbon tax rate.As shown in Figure 3(b), the polluting manufacturer's market demand continues to decrease with an increase in the carbon tax rate.Tis phenomenon shows that a more stringent carbon tax policy is benefcial for increasing the market demand for a clean manufacturer with small initial carbon emissions, but for a polluting manufacturer with large initial carbon emissions, imposing a high carbon tax will only cause a continuous decline in market demand.It is also clear from Figure 3 that when the cleaning manufacturer lacks capital, the IF mode yields a larger market demand than the EF mode, and market demand is always higher in the TC mode.
Tere is little diference in market demand for the polluting manufacturer under diferent fnancing modes.

Te Impact of the Carbon Tax Rate Changes on the
Manufacturer's Profts.As presented in Figure 4, regardless of the manufacturer's initial carbon emissions, the manufacturer's profts continue to decrease with an increase in the carbon tax rate.Increasing the carbon tax rate will stimulate the manufacturer to reduce carbon emissions, thus increasing market demand to a certain extent and contributing to an increase in the manufacturer's profts.On the other hand, increasing the carbon tax rate directly leads to a substantial decline in the marginal profts of the manufacturer selling low-carbon products, and the side efects on the total profts of the manufacturer are so great that they exceed the positive side and lead to a decline in profts.As shown in Figure 4(a), for a clean manufacturer, the proft of the EF mode is signifcantly lower than that of the IF and TC mode, while the proft advantage of the TC mode over the IF mode gradually emerges with an increase in the carbon tax rate.As Figure 4(b) shows, for the polluting manufacturer,  12 Complexity the profts of the three fnancing modes are almost the same, and the proft diference does not change signifcantly with an increase in the carbon tax rate.

Te Impact of the Carbon Tax Rate Changes on the
Retailer's Profts.From Figure 5, it can be seen that when the initial carbon emissions are low, the retailer's profts tend to decrease and then increase with an increase in the carbon tax rate, and when the initial carbon emissions are high, the retailer's profts continue to decrease with an increase in the carbon tax rate.On the other hand, if the initial carbon emissions of the manufacturer are low, the retailer can always make more profts by lending excess funds to the manufacturer or by advancing the costs of production and CER investment required by the manufacturer rather than by depositing extra funds in the bank.Tis result provides a theoretical basis for the retailer to accept the fnancing terms proposed by the manufacturer.However, when the initial carbon emissions are high, the proft advantage in the IF and TC modes is fragile.

Te Impact of the Carbon Tax Rate Changes on the
Supply Chain System's Profts.As shown in Figure 6, for a clean manufacturer, the supply chain system's profts frst decrease and then increase with an increase in the carbon tax rate.By comparing Figures 5(a) and 6(a), it can be seen that although the profts of the supply chain system and the retailer both decline frst and then increase with an increase in the carbon tax rate, the rebound time of the supply chain system's proft lags behind the latter, and the rebound amplitude is smaller because the manufacturer's profts shrink when the carbon tax rate is raised.Te EF mode is clearly inferior, and when the carbon tax rate is high, the advantage of the TC mode is more prominent.For a polluting manufacturer, the supply chain system's profts decline with an increase in the carbon tax rate, and there is no diference in the earnings of the three fnancing modes.

Main Conclusions and Managerial Implications
From the research in this article, we draw the following conclusions.
(1) By comparing the EF, IF, and TC modes, it is found that in the TC mode, CER, market demand, and the manufacturer's proft are the best, and under certain conditions, the retailer and supply chain system also have the highest proft level.In contrast, the EF mode is the worst.Terefore, the EF mode is the frst to be eliminated and will not be one of the options for the manufacturer.Because the manufacturer is the dominant player in the supply chain, that is, the manufacturer has the initiative to choose the fnancing mode.Whether considering economic, environmental, or social benefts, the TC mode is the dominant strategy for the manufacturer.(2) Te impact of carbon tax policy on the supply chain is complicated.Raising the carbon tax rate does not guarantee lower carbon emissions.Our research shows that the efects of the carbon tax rate on key parameters of the supply chain are not only related to the carbon tax rate itself but also to the manufacturer's initial carbon emissions.If the manufacturer's initial carbon emissions are low, then the government increases the carbon tax rate, which can reduce carbon emissions.Otherwise, the conclusion is the Complexity opposite.Moreover, the impact of the carbon tax rate on market demand is not monotonous and related to the manufacturer's initial carbon emissions.However, regardless of the fnancing mode, increasing the carbon tax rate will directly reduce the proft level of the manufacturer.
Tis study can provide the following management inspiration.
(1) For the government, imposing a carbon tax would force the manufacturer to reduce carbon emissions.For reducing emissions, carbon tax policies are efective for clean and polluting manufacturers.Te government could set a higher carbon tax rate for a clean manufacturer, whereas, for a polluting manufacturer, a moderate carbon tax rate might be more efective in reducing carbon emissions.Te marginal cost of CER increases rapidly.Terefore, when the cost of reducing one unit of carbon emissions exceeds the benefts of tax savings and increased demand, the manufacturer is reluctant to continue reducing carbon emissions.Appropriate CER subsidies may help further stimulate the manufacturer to continue cutting emissions.(2) Te manufacturer is the supply chain leader and has the initiative to choose the fnancing mode, but the TC mode is the most appropriate for him.In the TC mode, the main indicators are optimal, such as economic benefts (proft level), social benefts (market demand), and environmental benefts (CER).Although the advantages of market demand and proft for the polluting manufacturer are not obvious, an appropriate carbon tax rate still establishes the advantage of CER, thus providing more low-carbon products and increasing competitiveness.
(3) For the retailer, because the loan interest rate is higher than the deposit interest rate, it is worse for the retailer to earn interest from the bank on excess capital than to lend it to the manufacturer.Tus, the EF mode is an outcome that the retailer is unwilling to accept.Fortunately, the EF mode is not an option for the manufacturer.Although the optimal fnancing mode of the manufacturer is the TC mode, Corollary 18 shows that the retailer's proft may be less than it is in the IF mode.As a result, the retailer will refuse the TC mode.Te manufacturer can induce the retailer to accept "prepayment + discount" by designing properly coordinated contracts.Of course, if the proft of the supply chain system in the TC mode is less than that in the IF mode, then the manufacturer's eforts are in vain.
Tere are some limitations in this research.First, our paper does not consider the retailer's participation in CER action during the selling process.Future research could consider increasing the retailer's green sales eforts on lowcarbon products.In addition, we discussed the comparison of three fnancing modes under the fxed interest rate and did not analyze the impact of the interest rate changes on the supply chain parameters.If fnancial markets are hit hard, and the interest rates are unstable, will the previously dominant fnancing mode still be the frst choice for the manufacturer?Tis issue also deserves our attention.

B. Proof of Corollary 6
Proof of Corollary B.6.Taking the frst-order derivative of ∆e * 1 with respect to t, we obtain 1 (θ + bt) has the same monotonicity as z∆e * 1 /zt.Obviously, f E 1 (θ + bt) is a quadratic function with a parabola going upward, and its discriminant is given by It is not difcult to fnd that when the manufacturer's initial carbon emissions 14 Complexity has two intersections with the horizontal axis, represented by

􏽰
. Considering the second-order condition of the manufacturer's proft maximization, it satisfes 0 Terefore, the intersection θ + b  t E 1 does not meet the condition, and it will not be discussed.Tus, when 0

C. Proof of Corollary 7
Proof of Corollary C.7. Taking the frst-order derivative of D * 1 with respect to t, we obtain 2 (θ + bt) has the same monotonicity as zD * 1 /zt.Obviously, f E 2 (θ + bt) is a quadratic function with a parabola going downward, and its discriminant is given by It is not difcult to fnd that when the manufacturer's initial carbon emissions 0 < e 0 < e E 0 , there is ∆ E 2 > 0. At this point, f E 2 (θ + bt) has two intersections with the horizontal axis, represented by Due to 0 < e 0 < e E 0 , then there is θ

E. Proof of Theorem 9
Proof of Teorem E.9.Taking the second-order derivative of π R 2 with respect to p 2 , we obtain zπ R 2 /zp

G. Proof of Corollary 11
Proof of Corollary G.11. Taking the frst-order derivative of D * 2 with respect to t, we obtain 2 (θ + bt) has the same monotonicity as zD * 2 /zt.Obviously, f I 2 (θ + bt) is a quadratic function with a parabola going downward, and its discriminant is given by It is not difcult to fnd that when the manufacturer's initial carbon emissions 0 < e 0 < e I 0 , there is ∆ I 2 > 0. At this point, f I 2 (θ + bt) has two intersections with the horizontal axis, represented by 16 Complexity

□ J. Proof of Corollary 14
Proof of Corollary J.14.Taking the frst-order derivative of ∆e * 3 with respect to t, we obtain 1 (θ + bt) has the same monotonicity as ze * 3 /zt.Obviously, f T 1 (θ + bt) is a quadratic function with a parabola going upward, and its discriminant is given by It is not difcult to fnd that when the manufacturer's initial carbon emissions e 0 > e T 0 � a − bc(1 + r 2 )/ ��� 4kb √ , there is ∆ T 1 > 0. At this point, f T 1 (θ + bt) has two intersections with the horizontal axis, represented by

Table 1 :
A comparison between this paper and other studies.
Figure 1: Flowchart of the green fnancing and CER decision-making.

Table 2 :
Notations and their defnitions.Regarding market demand and the carbon tax rate in the EF mode, we have the following: r 1 )e 2 0 ). ).