Liurui Deng,Chen Cao,Jiawu Dai
How do the carbon emission trading prices affect the financing decision of the supply chain considering carbon neutrality?
Carbon emission cap,Carbon neutrality,Supply chain finance,Carbon emission trading price,Financing decision,Stackelberg game theory
This paper considers a supply chain formed by a manufacturer with constrained capital and a retailer with sufficient capital. By using the Stackelberg game theory, we discuss the manufacturer’s and retailer’s optimization decisions for bank financing, zero-interest early payment financing, and in-house factoring financing under both normal and carbon neutrality scenarios. In the carbon neutrality scenario, numerical analysis shows that improving the efficiency of emission reduction drives manufacturers to switch from external to internal financing methods. The impact degree of green sensitivity on the supply chain’s profit depends on the carbon emission trading prices. In the framework of green sensitivity of products and emission reduction efficiency, manufacturers’ financing decisions are affected by carbon emission trading prices rather than by whether emissions exceed the standards or not. When the price is higher, internal financing is easier to obtain, whereas the space for external financing is constrained.
How do the carbon emission trading prices affect the financing decision of the supply chain considering carbon neutrality?

This paper considers a supply chain formed by a manufacturer with constrained capital and a retailer with sufficient capital. By using the Stackelberg game theory, we discuss the manufacturer’s and retailer’s optimization decisions for bank financing, zero-interest early payment financing, and in-house factoring financing under both normal and carbon neutrality scenarios. In the carbon neutrality scenario, numerical analysis shows that improving the efficiency of emission reduction drives manufacturers to switch from external to internal financing methods. The impact degree of green sensitivity on the supply chain’s profit depends on the carbon emission trading prices. In the framework of green sensitivity of products and emission reduction efficiency, manufacturers’ financing decisions are affected by carbon emission trading prices rather than by whether emissions exceed the standards or not. When the price is higher, internal financing is easier to obtain, whereas the space for external financing is constrained.

Since the industrial revolution, more and more energy has been extracted and consumed, and carbon dioxide emissions have risen sharply. Controlling carbon dioxide emissions is key to achieving sustainable development for countries. As early as 1997, the signing of the Kyoto Protocol established the basic legal framework and action guidelines for countries to reduce carbon emissions. At the Paris Climate Conference, more than 190 countries unanimously agreed and adopted the Paris Agreement, which came into effect in 2016. In 2005, the European Union began operating the EU Emissions Trading System (EU ETS). The California government established the first statewide emission trading market in the USA in 2012. The New South Wales Greenhouse Gas (GHG) Emissions Trading System in Australia was launched in 2003 (Chen 2016). Globally, countries continue to promote the process of carbon emission reduction while gradually establishing their own carbon emission trading systems. China has committed to reaching a peak in carbon dioxide emissions by 2030 and achieving carbon neutrality by 2060. Therefore, the National Development and Reform Commission began implementing China’s National Emissions Trading System (ETS) in December 2017 (Zhang et al. 2021). According to research data reported by the International Energy Agency (IEA), the amount of carbon dioxide emissions from the global energy industry in 2021 surpassed that before the COVID-19 outbreak, reaching 36.3 billion tons and growing 6% per year. BP Statistical Review of World Energy showed that China’s carbon dioxide emissions in 2020 totaled 9.894 billion tons, placing it first in the world. The USA comes in second with 4.432 billion tons, followed by India with 2.298 billion tons, placing it third. To solve this carbon emission reduction challenge, China has set up seven carbon emission trading pilot regions since 2013, including Beijing, Shanghai, Shenzhen, Guangdong, Tianjin, Chongqing, and Hubei (Munnings et al. 2016). The “Overall Plan for the Reform of Ecological Civilization System,” “Outline of the 13th Five-Year Plan,” and “Work Plan for Controlling Greenhouse Gas Emissions During the 13th Five-Year Plan” all recommend implementing total carbon emission control. Beijing, Shanghai, Gansu, Yunnan, and other places have also actively constructed a local decomposition and implementation mechanism as well as a comprehensive carbon emission control system. The industrial sector is the backbone of China’s economy. According to data from the National Bureau of Statistics, in 2022, the value added of the industrial sector accounted for 33.2% of China’s GDP. According to the China Emission Accounts and Datasets (CEADs), China’s cumulative carbon emissions reached 11 billion tons in 2022, with industrial emissions accounting for 4.2 billion tons, or 38.18% of the country’s total emissions. This means that the industrial sector is one of the main contributors to China’s carbon dioxide emissions. The supply chain is also part of the industrial sector and also emits a large amount of carbon dioxide during the production process. Limiting carbon dioxide emissions will undoubtedly affect the normal operation of the supply chain. Therefore, the carbon emission reduction policy will have a significant impact on the supply chain. How to balance supply chain production and emission reduction has become a pressing issue. Therefore, we incorporate carbon emission trading prices into the supply chain perspective. We also study the financing problems of capital-starved manufacturers between the normal situation and the carbon neutrality situation. Our research innovation mainly comes from three aspects. First, most literature on green supply chains assumes that companies operate under carbon emission constraints. This article relaxes this constraint and assumes that companies have incentives to exceed emission limits during the production process. Therefore, we compare the supply chain’s preference for internal and external financing under two scenarios: whether or not companies exceed emission limits. Second, the literature on carbon emission trading prices mainly focuses on the macrolevel (national) and mesolevel (industry), with a lack of research on the microlevel. This article focuses on the microlevel of individual companies and studies the impact of carbon emission trading prices on their profits. Finally, few studies have refined carbon emission reduction policies to carbon neutrality targets. This article compares the impact of carbon emission limits on supply chain financing decisions with and without carbon neutrality targets. The remainder of this paper is organized as follows. The “Literature review” section reviews related literature and sorts out the deficiencies of current literature. “The model” section constructs and compares a basic model with a carbon neutrality model. The “Methodology” section thoroughly describes the solution methods and steps for each model. In the “Numerical analysis” section, sensitivity analysis and equilibrium financing areas are drawn. Finally, we discuss the conclusions, policy suggestions, and further research in the “Conclusions, recommendations, and limitations” section.

After conducting a comprehensive review and analysis of the relevant literature, we discover that the study of both supply chains and carbon neutrality still has a significant knowledge gap. Therefore, we have the urge to analyze financing decisions in the supply chain with or without considering carbon neutrality. Based on this objective, we can separate related literature into three categories: supply chain finance, carbon emission trading, and the impact of carbon emission limits on supply chains.

Because in the supply chain, the service object includes multiple subjects such as suppliers, manufacturers, and retailers, it is also called the “1+N” mode. Timme and Williams-Timme (2000) first put forward the concept of supply chain finance (SCF). It referred to economic activities in that external financial institutions assist supply chain participants to realize capital circulation and effective distribution. Hofmann (2005) believed that supply chain finance is the coordination and transfer of financial resources among participants in the supply chain. Therefore, external financing methods gradually became the main channel for early supply chain finance. Many scholars also thought that small- and medium-sized businesses could use purchase order finance (POF) to manage enormous inventories or supply large businesses during peak seasons (Fullen 2006). Lu et al. (2012) obtained the expected profits of supply chain participants at each stage by choosing accounts receivable financing. As a result of the advancement of inventory management technology, which considerably lowers the amount of money spent on inventory, factoring financing enters the supply chain (Diao and Ren 2010). However, there are problems such as credit risk management and factoring fee ratio setting. Therefore, many scholars have proposed innovative factoring financing models, such as order-to-factoring mode and reverse factoring financing mode (Liu et al. 2014; Chen and Yu 2018; Zhan et al. 2018). According to information display theory, the low transparency of external financing channels creates information asymmetry and principal-agent problems between lenders and borrowers. In contrast, internal financing activities, due to lower industry barriers and information acquisition costs, can to some extent alleviate the problem of information asymmetry. Therefore, there has been increasing research on internal financing. Yang and Birge (2018) studied the impact of the risk-sharing mechanism on production efficiency and production decision-making under the trade credit financing mode. Tang et al. (2018) studied suppliers’ preferences for financing under the purchase order financing method and buyer direct financing (BDF) method. The above literature only focuses on the case where enterprises are financially constrained but fails to consider that enterprises may also be subject to carbon emission constraints under the background of carbon emission limitations. Qin and Li (2021) analyzed the production decisions under the dual constraints of carbon emissions and capital. An (2021) considered both the two constraints and studied how to achieve a win-win situation for social welfare and manufacturer’s profit under different financing models. However, strict carbon emission constraints often do not match the reality. Enterprises operate based on the principle of profit maximization. As long as the extra profits brought by exceeding the carbon emissions standards are greater than the costs, enterprises have the incentive to violate the carbon emission restrictions.

According to the Coase property rights theory, unclear property boundaries are the main cause of externalities. Therefore, the power of the market is needed to eliminate externalities. The carbon emission trading system was created under this theory. As one of the more successful programs for implementing carbon emission cap targets, “Kyoto Protocol” built a carbon emission trading system to reduce emissions. Dales (2002) explained carbon emission rights meant that the obligee had the right to discharge a certain amount of pollutants into the environment within the scope allowed by law and set it in the form of licenses. And a certain amount of carbon emission rights can be bought or sold in the carbon trading market. The allocation methods for carbon credits are primarily separated into two categories: free allocation and auction forms (Cramton and Kerr 2002; Cason et al. 2003). Agarwal and Narain (1992) argued that the allocation methods should be in accordance with the equal per capita rights model. After that, Janssen et al. (1995) proposed an allocation model based on historical responsibility. However, they all examined the allocation of carbon emission rights from a single perspective, without considering the distribution method from the perspective of overall social welfare. Edwards and Hutton (2001) demonstrated that a potential “double dividend” could be realized if the profits from the auction were redistributed in the form of output allowances or tax breaks. With the increasing attention paid to global climate change, more and more carbon emission reduction measures have been proposed and developed. The first to emerge was carbon emission cap-and-trade systems. Chen (2013) used the total carbon emission setting and emission reduction measures of the EU’s carbon emission trading system as the investigation object and provided some reference significance for China. However, market mechanisms may fail to function properly, which is called “market failure.” Coase and Pigou had different views on how to eliminate externalities. Pigou believed that the key to eliminating externalities lies in government intervention and proposed the concept of the Pigouvian tax. The development based on this theory is the carbon tax policy. Wu et al. (2014) contrasted the marginal carbon emission reduction cost curves with the marginal revenue curves and investigated the selection mechanism of carbon emission right trading and carbon tax. Liu et al. (2015) explored the optimal reproduction decisions under the necessary carbon emission reduction, carbon tax, and carbon cap-and-trade system. The carbon emission trading price is determined by the supply and demand of carbon emission rights in the market, reflecting the fundamental information of the carbon emission trading market. Most studies on carbon emission trading prices focus on the macrolevel or mesolevel. Christiansen et al. (2005) thought that the price of EU carbon emission quotas is determined by political and regulatory factors, the ratio of carbon emissions to quotas, the role of fuel conversion, and other market fundamentals. For the first time, Alberola et al. (2009) pointed out that the economic factor is the most obvious factor affecting the quota price. Bunn and Fezzi (2009) further demonstrated how carbon emission trading prices and natural gas prices jointly affected the equilibrium price of electricity. Zhao and Hu (2016) concluded that the market environment is the most important factor influencing carbon emission trading prices, followed by policy factors and climate change. Zhang (2018) analyzed that both market fundamentals and policy information are significant factors influencing carbon emission trading prices on the demand side. Some scholars have innovatively conducted microlevel studies on the impact of carbon emissions. Zhao et al. (2023) took into account the significant differences in endowments among regions in China and chose to study the spatial spillover effects of enterprise financing costs on regional carbon emissions at the enterprise level.

Many scholars have included carbon emissions in their research on the supply chain, because the carbon dioxide emissions generated during the production process of the supply chain account for a significant portion of China’s total carbon emissions. Darvish et al. (2019) also believed that production and inventory-routing issues should take carbon emissions into account, rather than only considering cost factors. Limiting carbon emissions means that production in the supply chain will also be hindered, and how to balance emission reduction and production has become one of the unresolved issues in green supply chains (Zhang et al. 2020; Cheng and Li 2020; Jin et al. 2014). Subsequently, there has been a growing interest in the function of government (Nielsen et al. 2019; Halat and Hafezalkotob 2019; Rout et al. 2020). Some scholars focused on the role of society in the supply chain (Nematollahi et al. 2017; Wang et al. 2020). The characteristics of suppliers and retailers to maximize their interests under the decentralized model led to the problem of “double marginalization,” so many scholars proposed various supply chain contracts (Spengler 1950). Ma et al. (2018) considered the information asymmetry theory in the design of supply chain optimization contracts. Panja and Mondal (2020) found that the revenue-sharing contract could effectively improve the green degree of product and the overall profit of supply chains. Supply chain finance is one of the effective ways to alleviate the problem of information asymmetry, but it may also be affected by carbon emission limitations. Many scholars have conducted in-depth research on this issue (Wang and Wu 2021; Cao et al. 2017). The existence of transaction costs exacerbates market friction and greatly reduces the operational efficiency of the financial market. This problem is particularly evident in collateral financing provided by external financial institutions. Zhou et al. (2020) found that in a Nash game, firms face a free-rider problem when choosing between manufacturer-guaranteed financing (MG) and third-party logistics guaranteed financing (3PLG). However, Reindorp et al. (2018) concluded that POF significantly smoothes the impact of capital market frictions. The above literature focuses on financing activities of companies that passively accept carbon emission limitations and lack the initiative in reducing emissions. Green credit policy (GCP) is a type of green financial service that applies to sustainable development projects and aims to encourage companies to actively invest in green projects (Deng et al. 2021). Kang et al. (2020) argued that the impact of GCP on supply chain emission reduction is achieved through consumer incentives. Tunca and Zhu (2018) analyzed from the perspective of internal financing and found that buyer direct financing led to lower wholesale prices and higher order volumes. To focus the research on the impact of carbon emission limitations, Qin et al. (2020) relaxed the capital constraints and found that early payment financing with low price discounts can increase the profitability of the supply chain. Notably, previous studies overlooked the background of carbon neutrality goals. With the advancement of the “dual-carbon” goal, there are many challenges in measuring carbon neutrality, achieving carbon neutrality goals, and incorporating carbon neutrality goals into various research fields. Wan et al. (2021) used endogenous growth theory to derive the law of carbon neutrality implementation based on the green low-carbon products’ carbon emission growth rate and absorption rate. Zhang (2022) focused on the photovoltaic industry and used a system dynamic model to study the dynamic impact of the life cycle of the photovoltaic industry on carbon emissions under carbon neutrality goals. Although there is much research on green supply chains, few of them take into account both financial constraints and carbon neutrality. In addition to bank financing and zero-interest early payment financing, we propose a new form of factoring financing, positive interest in-house factoring financing, referring to the idea of Chen et al. (2020). In addition, we investigate the impact of carbon emission trading prices on supply chain profit under the scenario of considering carbon neutrality and not considering it. Then, we derive the relationship between carbon emission trading prices and financing methods. Finally, we draw the decision domains of the three financing methods under the two models and the two carbon emission situations. We hope our study can help manufacturers flexibly adjust their financing strategies according to different scenarios.

In this paper, we consider a green supply chain made up of a manufacturer with limited capital and a retailer with sufficient capital. In the supply chain, as a leader, the manufacturer decides the carbon emission reduction cost per unit product, charges the related production cost, and sets the wholesale price. As a follower, the retailer decides the retail price according to the manufacturer’s decision. Based on these premises, we respectively construct a basic model without carbon neutrality and a model considering carbon neutrality. Table 1 displays the remaining variables. We make the following assumptions: Market demand D is proportional to the retail price p and carbon emission reduction cost per unit product y (D(p, y) = a − bp + τy, (a, b, τ > 0)), where a represents the initial market demand. b represents the sensitivity of consumers to the price. τ represents the sensitivity of consumers to carbon emission reduction costs per unit product (i.e., green sensitivity of product). Given the information asymmetry, consumers have difficulty accurately knowing the emission reduction cost compared to the retail price, so we set b ≥ τ. We assume no demand randomness because the manufacturer produces enough products to satisfy consumer demand. The total amount of carbon emission reduction cost C is proportional to carbon emission reduction cost per unit product y and production quantity Q (C(y) = yQ). Carbon emissions are emitted only during the production process. Manufacturers are expected to take the required actions to reduce carbon emissions and shoulder the cost of emission reduction. The total initial amount of carbon emissions E0 is proportional to the initial carbon emission amount per unit product e0 and production quantity Q (E0(Q) = e0Q). The total amount of carbon emission reduction ΔE is proportional to the carbon emission reduction cost per unit product y and production quantity Q (ΔE(Q) = μyQ), where μ is the emission reduction efficiency, which is the actual amount of emission reduction that is proportional to the emission reduction cost. So μy represents the carbon emission reduction amount per unit product. Referring to Rao and Zhao (2011) and Chen (2016), the amount of supply HS and demand HD in the carbon emission trading market is proportional to the carbon emission trading pricepc (, ), where mN and mE, respectively, represent the reciprocal of the carbon emission trading price sensitivity when the carbon emissions do not exceed the standards and exceed the standards. nN and nE separately represent the initial carbon emission trading price in the two emission cases. When carbon emissions do not exceed the standards, the manufacturer saves carbon emission rights that can be traded on the carbon emission trading market. As a supplier of carbon emission rights, the manufacturer is more willing to provide carbon emission rights as the carbon emission trading price raises. When carbon emissions exceed the standards, the required emission reduction per unit product is still μy. The manufacturer must purchase the missing carbon emission rights μy in the market as a demander. Referring to Grainger and Smith (2021), when carbon neutrality is achieved, the total carbon emission amount of society E equals to total carbon absorption amount of society F (E = F). Furthermore, we assume that the amount of carbon dioxide emitted or absorbed along each supply chain is the same. If there are h supply chains in society, the total carbon emission amount of society will be h(e0 − μy)Q/α, and the total carbon absorption amount of society will be hfQ/β. The residual value of products and the impact of manufacturer default risk are not considered. In the following contents, the relevant variables’ superscript i = N, E, respectively, represents that carbon emissions do not exceed and exceed the standard. The subscript N indicates that carbon neutrality is taken into account. The subscript j = B, E, I separately represents bank financing, zero-interest early payment financing, and in-house factoring financing. As the main production body of the supply chain, the manufacturer emits a certain amount of carbon dioxide in the production process, and its production is subject to the carbon emission limits stipulated by the government. Under the carbon cap-and-trade policy, the government limits a cap T on the carbon emission amount. Since this paper assumes that the manufacturer is constrained by capital, the optimal carbon emission reduction cost per unit product y and optimal retail price p can be achieved when the manufacturer seeks bank financing, zero-interest early payment financing, and in-house factoring financing. To simplify the analysis process, the loan period is assumed to be one period.

In this section, we construct a model of bank financing, zero-interest early payment financing, and in-house factoring financing without considering carbon neutrality.

When the banks assess the manufacturer’s creditworthiness and determine that its asset quality complies with bank lending guidelines, they decide to finance the manufacturer. This paper assumes that the manufacturer has no initial capital and must turn to the bank for a loan in order to cover the input costs. According to the Stackelberg game theory, the decision steps for the manufacturer and the retailer under the bank financing approach are as follows: (1) As the leader, the manufacturer decides the optimal carbon emission reduction cost per unit product y. (2) The manufacturer decides to sell (buy) the remaining (insufficient) carbon emission rights in the carbon emission trading market according to its production quantity and carbon emission reduction cost per unit product. (3) The retailer decides the retail price p after observing the manufacturer’s production quantity and carbon emission reduction cost. (4) The bank decides the loan interest rate rB and issues loans cQ to the manufacturer after observing the decisions of the two parties. (5) The retailer pays the manufacturer after receiving the product. (6) The manufacturer uses part of sales revenue to repay the principal and interest of the loancQ(1 + rB). The specific financing process is shown in Fig. 1. In bank financing, the bank’s profit comes from loan interest cQrB. The retailer’s profit mainly consists of retail revenue and wholesale cost of products, so its profit function is When the manufacturer’s carbon emissions do not exceed the cap set by the government (E0 − ΔE ≤ T), the manufacturer can sell the remaining carbon emission rights in the carbon emission trading market for a profit. When the manufacturer’s carbon emissions exceed the cap (E0 − ΔE > T), in order to maintain regular production and sales, the manufacturer has to buy insufficient carbon emission rights in the carbon emission trading market. Therefore, the manufacturer’s profit function is

When banks evaluate the asset quality of the manufacturer, believe that there is a certain risk, and decide not to grant bank financing. The capital-constrained manufacturer turns to internal financing, one of which is to apply for zero-interest early payment financing from the retailer. That is, the retailer advances part of the payment (cQ) to the manufacturer. This paper assumes that the interest rate of early payment financing is zero (rE = 0) and the retailer benefits from the wholesale price wη discount. Zero-interest early payment financing follows the same first three steps as bank financing, the fourth and fifth steps are where they differ: (4) The retailer pays part of the payment cQ(cQ < wQ) to the manufacturer in advance. (5) After the retailer completes the sales of the product, the remaining amount wQ − cQ will be paid to the manufacturer. The specific financing process is shown in Fig. 2. In zero-interest early payment financing, the retailer’s profit consists of retail revenue and wholesale cost of products, so its profit function is Similar to the analysis of the manufacturer’s profit composition under the bank financing, the manufacturer’s profit function under this financing is

When banks do not provide the manufacturer with bank financing, another internal financing method is in-house factoring financing offered by the retailer. Different from traditional factoring financing provided by the third party, the retailer typically has a financing subsidiary in this financing. The manufacturer uses its trade credit as collateral to apply for a loan cQ to the financing subsidiary; then, the retailer issues the loan and charges a positive interest rate rI. In order to investigate the optimal decision under different financing methods, this paper does not consider the establishment cost and financing license cost of the retailer’s financing subsidiary (Chen et al. 2020). In fact, zero-interest early financing is different from in-house factoring financing. The former is not a loan strictly because a portion of the retailer’s payment is provided to the manufacturer in advance without charging interest. However, in-house factoring financing is a loan issued by the retailer’s financing subsidiary that must go through the associated loan process. The first three steps of in-house factoring financing are also the same as those of bank financing, the fourth and fifth steps are where they differ: (4) The financing subsidiary of the retailer decides the interest rate rI and provides loans cQ(cQ < wQ) to the manufacturer. (5) After the retailer completes the sale of the product, the remaining payment wQ − cQ(1 + rI)will be paid to the manufacturer. The specific financing process is shown in Fig. 3. In in-house factoring financing, the income sources of the retailer are not only wholesale income but also loan interest income; its cost is mainly wholesale cost. So its profit function is Similar to the analysis of the manufacturer’s profit composition under the bank financing, the manufacturer’s profit function under this financing is

In this section, we construct a model considering carbon neutrality. In addition to meeting the carbon emission constraint, the total carbon emission amount of society should equal to total carbon absorption amount of society (i.e., E = F) in this situation. When carbon neutrality is achieved, both the manufacturer and the retailer still maximize their profit, and therefore, the supply chain game sequence is the same as in the above section. To simplify content, we only take bank financing as an example: In bank financing, the bank’s profit still consists of loan interest cQrB. The retailer’s profit function is The manufacturer’s profit function is

We consider the financing decisions of the manufacturer and the retailer in the framework of Stackelberg’s game theory. Stackelberg (2011) first proposed the Stackelberg game theory. This theory is a model to solve the optimal decision of each firm when there is asymmetric competition between the leader and the led firm. This paper considers a two-level supply chain consisting of a manufacturer as the leader and a retailer as the follower. There is a difference in the order between them to make decisions, so this paper uses the Stackelberg game to solve the optimization problem.

Based on the characteristics of the Stackelberg game and reverse solving method, the solution sequence should be as follows: Assuming that the carbon emission reduction cost per unit product is known, the retailer makes a decision based on the profit maximization principle to obtain the optimal retail price. The retail price is the reaction function of the carbon emission reduction cost per unit product. Substituting this reaction function into the manufacturer’s profit function, we can obtain the optimal carbon emission reduction cost per unit product y∗ based on the manufacturer’s profit maximization principle. Finally, by substituting the carbon emission reduction cost per unit product into the retail price reaction function, we can get the optimal retail price p∗.

According to the Stackelberg game, first, our objective is to maximize the retailer’s profit: Then, we get a reaction function of the retail price and a reaction function of production quantity . Second, based on the retailer’s decision, the manufacturer’s optimization problem is Finally, the optimal solutions of the whole problem are as follows: Proposition 1. In bank financing, the optimal carbon emission reduction cost per unit product, the optimal retail price, the retailer’s optimal profit, and the manufacturer’s optimal profit are (the proof process can be found in Appendix 1) where L = nN − pc + mNe0, , M = a − wb, and . When T ≥ TB, the carbon emission cap is relaxed, and we denote it as carbon emissions not exceeding the standards (N); when 0 < T < TB, the carbon emission cap is tight, and we denote it as carbon emissions exceeding the standards (E).

According to the Stackelberg game, first, our objective is to maximize the retailer’s profit: Then, we get a reaction function of the retail price and a reaction function of production quantity . Second, based on the retailer’s decision, the manufacturer’s optimization problem is Finally, the optimal solutions of the whole problem are as follows: Proposition 2. In zero-interest early payment financing, the optimal emission reduction cost per unit product, the optimal retail price, the retailer’s optimal profit, and the manufacturer’s optimal profit are whereL = nN − pc + mNe0, , , and . When T ≥ TE, we denote it as carbon emissions not exceeding the standards (N); when 0 < T < TE, we denote it as carbon emissions exceeding the standards (E).

According to the Stackelberg game, first, our objective is to maximize the retailer’s profit: Then, we get a reaction function of the retail price and a reaction function of production quantity . Second, based on the retailer’s decision, the manufacturer’s optimization problem is Finally, the optimal solutions of the whole problem are as follows: Proposition 3. In in-house factoring financing, the optimal emission reduction cost per unit product, the optimal retail price, the retailer’s optimal profit, and the manufacturer’s optimal profit are where L = nN − pc + mNe0, , , and . When T ≥ TI, we denote it as carbon emissions not exceeding the standards (N); when 0 < T < TI, we denote it as carbon emissions exceeding the standards (E).

The method and solution steps of this part are the same as those of the base model. According to the Stackelberg game, first, our objective is to maximize the retailer’s profit: Then, we get a reaction function of retail price and a reaction function of production quantity . Second, based on the retailer’s decision, the manufacturer’s optimization problem is Finally, the optimal solutions of the whole problem are as follows: Proposition 4. In bank financing when considering carbon neutrality, the optimal emission reduction cost per unit product, the optimal retail price, the retailer’s optimal profit, and the manufacturer’s optimal profit are (the proof process can be found in Appendix 2): where , M = a − wb, H = 1 − pcμ, I = e0β − αf, G1 = nN − pc − pc2 − mNw, and G2 = nE − pc − pc2 − mEw. When , we denote it as carbon emissions not exceeding the standards (N); when , we denote it as carbon emissions exceeding the standards (E).

Based on the obtained optimal solutions, this section mainly analyzes the impact of some important factors on the profits of the manufacturer and supply chain under bank financing (BF), zero-interest early financing (EF), and in-house factoring financing (IF). We review related literature and consider the actual situation. The following basic parameters are set in this paper by referring to An et al. (2021), which likewise examines the effect of carbon emission limitations on the supply chain. a = 200, η = 0.02, r = 0.06, rb = 0.08, n1 = 7.13, n2 = 200, m1 = 4.79, w = 4.6, e0 = 91.979, c = 0.9, m2 = 6, f = 50, and β = 30%.

The retailer’s optimal profit function shows that there are no distinctions between the three financing methods when emissions exceed (do not exceed) the standards. In addition, because the manufacturer is responsible for the supply chain’s emission abatement work, the emission reduction efficiency has no impact on the retailer’s profit. Therefore, the following sensitivity analysis concentrates on how the emission reduction efficiency affects the optimal manufacturer’s profit. Figure 4 shows that, when the green sensitivity is constant, the optimal manufacturer’s profit increases with the emission reduction efficiency. The manufacturer’s cost to reduce a given unit of carbon emissions decreases as emission reduction efficiency rises, which helps improve its profit. In addition, Fig. 4 displays that there are three intersection points of the BF, EF, and IF curves. Each point indicates that the manufacturer’s profit is equal under each two financing methods. We compiled a table of sensitivity analysis values for Fig. 4a–c, as shown in Table 2. Sensitivity analysis values in Table 3 correspond to Fig. 4d–f. In Table 2, taking bank financing and early payment financing as examples, when τ = 40, the emission reduction efficiency that makes the manufacturer’s profit between the two financing methods equal is ; when τ = 50, the emission reduction efficiency meeting the same condition is ; when τ = 60, the emission reduction efficiency meeting the same condition is . In Table 3, taking bank financing and early payment financing as examples again, when τ = 40, the emission reduction efficiency that makes the manufacturer’s profit between the two financing methods equal is ; when τ = 50, the emission reduction efficiency meeting the same condition is ; when τ = 60, the emission reduction efficiency meeting the same condition is . Accordingly, we can also analyze the relationship between emission reduction efficiency and green sensitivity when manufacturers’ profits are equal under the other two financing methods. Finally, when the green sensitivity changes continuously, we can draw the relationship between green sensitivity and emission reduction efficiency, as shown in Fig. 6. The sensitivity analysis values show that when the carbon emission trading price is constant, the manufacturer’s profit when emissions exceed the standards is much lower than when emissions do not exceed the standards. However, the relationship between emission reduction efficiency and green sensitivity is the same in the two emission cases. This suggests that even though the manufacturer’s profit is affected by over-emission, the manufacturer’s financing decision will not be changed by whether emissions exceed the standards or not.

The relationship between carbon emission efficiency and the manufacturer’s profit in the carbon neutrality scenario is similar to the above section. In order not to repeat the same work and consider the carbon neutrality macro environment, we investigate the impact of carbon emission trading prices and green sensitivity on the profit of the supply chain. In order to simplify the content, we still use bank financing as an example. When the carbon emissions do not exceed the standards, we can find from Fig. 5a that the supply chain’s profit increases with green sensitivity. There exists an inversion activation mechanism. The increase in green sensitivity means that consumers prefer green products, so the manufacturer must improve the emission reduction efficiency to keep up with consumer demand. This increases the manufacturer’s profit, which further improves the supply chain’s profit. As the carbon emission trading price increases, the increasing trend of the supply chain’s profit first strengthens and then weakens. In other words, green sensitivity has less impact on the supply chain’s profit at both high- and low-carbon emission trading prices. The inversion activation mechanism is ineffective at this moment. This is because high-carbon emission trading prices provide manufacturers with more additional revenue, and there is no need to cater to market demand through emission reduction measures. Low-carbon emission trading prices mean that manufacturers do not have extra funds to upgrade emission reduction technology in the face of market competition; thus, the transmission of this mechanism is blocked. When carbon emissions exceed the standards, Fig. 5b also shows that the supply chain’s profit increases with green sensitivity. In contrast to the situation described above, the increasing trend of the supply chain’s profit becomes more obvious as the carbon emission trading price increases. High-carbon emission trading prices lead to high costs for manufacturers, so they are forced to borrow money to make investments in emission reduction. This action improves their profit in green products, and the mechanism is efficient at this time.

The relationship between emission reduction efficiency and green sensitivity is almost the same whether emissions exceed the standards or not. Therefore, we do not distinguish the emission scenarios in the following decision domains. In Fig. 6, the red line, blue line, and black solid line, respectively, indicate that manufacturer profits are equal under BF and EF, equal under BF and IF, and equal under EF and IF. The three solid lines divide the graph into four regions. Combined with the analysis of Fig. 4, the region above the blue line indicates that the manufacturer favors bank financing. Because the emission reduction efficiency is high and the interest rate determined by the bank is correspondingly lower, choosing bank financing brings higher profit. The region between the blue line and the black solid line shows that the manufacturer favors in-house factoring financing. Because reduced carbon emission efficiency makes bank financing interest rates higher, in-house factoring financing is more profitable. In addition, this preference can also be explained by several interactive effects of in-house factoring financing (Chen et al. 2020). From the perspective of financing risk effects, in-house factoring financing transfers some demand uncertainty risks from manufacturers to retailers. From the perspective of production quantity effects, this risk-sharing mechanism encourages manufacturers to expand production. The area below the black solid line indicates that the manufacturer favors early payment financing. The emission reduction efficiency and green sensitivity are both lower in this area. At this time, the manufacturer has to apply for repayment in advance to reduce carbon emissions and maintain normal production. Similarly, the preference for early payment financing can also be explained by the financing risk effect. In addition, considering the interest effect and the wholesale price discount effect, on the one hand, the manufacturer enjoys interest reduction, while on the other hand, the manufacturer must lower the wholesale price. Overall, the positive impact of the interest effect outweighs the negative impact of the wholesale price discount effect. As can be seen in Fig. 6, when the green sensitivity τ = 0, the three curves converge at a point. We denote this emission reduction efficiency point as μ∗. This indicates that when consumers have no preference difference in low-carbon and polluting products, the manufacturer also equally weighs the three financing methods. The manufacturer’s preference for financing methods can be characterized as follows: When green sensitivity is small and held constant, as emission reduction efficiency increases, the manufacturer’s preferred financing option order is as follows: early payment financing < in-house factoring financing < bank financing. When 0 < μ < μ∗, the green sensitivity of products increases and emission reduction efficiency keeps constant; the manufacturer’s preferred financing option order is as follows: zero-interest early payment financing < in-house factoring financing. When μ ≥ μ∗, the green sensitivity of products increases and emission reduction efficiency keeps constant; the manufacturer’s preferred financing option order is as follows: bank financing < in-house factoring financing. First, when the green sensitivity remains constant, the manufacturer is unable to obtain external financing due to the low emission reduction efficiency. Lacking pre-production funding forces the manufacturer to turn to retailers and apply for payment in advance. As the emission reduction efficiency increases, the manufacturer spends less money on each unit of product to reduce emissions and therefore has additional funds to pay interest on in-house factoring financing. When the emission reduction efficiency reaches a high level, the manufacturer can afford bank financing with higher interest. Second, when the emission reduction efficiency is constant, the lower emission reduction efficiency does not ensure the manufacturer’s ability to withstand market risk, making the manufacturer unable to obtain external financing. When the green sensitivity is low, the retailer can still pay to the manufacturer in advance. When demand declines due to increased green sensitivity, the retailer is no longer willing to make advance payments to the manufacturer. As a result, the manufacturer turns to in-house factoring financing. When the manufacturer has high emission reduction efficiency, it can obtain bank financing. As the green sensitivity increases but the emission reduction efficiency is not improved in time, banks are reluctant to provide the manufacturer loans, so the manufacturer turns to in-house factoring financing. We expand the static analysis of financing equilibrium domains to dynamic analysis. In other words, we compare the changes in the financing equilibrium domain by changing the exogenous variable (carbon emission trading prices). Chen et al. (2020) used manufacturing production costs as an intermediary variable. In contrast, our study uses carbon emission trading prices as an intermediary variable to analyze financing preferences by examining the impact of high- and low-carbon emission trading prices. Comparing with Fig. 6a–c, we can reveal the following: First, the minimum level of emission reduction efficiency (i.e., the key point of emission reduction efficiency) required for external bank financing decreases, indicating that external financing methods become more available. Second, we also found that when the carbon emission trading price is low, the area of bank financing is smaller while the areas of the other two types of financing are larger. This suggests that the conditions for bank financing are more stringent under low-carbon emission trading prices. Conversely, when the carbon emission trading price is high, the area of bank financing expands while the areas of the other two types of financing shrink. This indicates that external financing is more easily obtainable under high-carbon emission trading prices, while internal financing is harder to obtain. This conclusion is consistent with the findings in the literature. For example, An et al. (2021) also found that the area of trade credit financing (TCF) was larger than that of green credit financing (GCF), indicating that the conditions for achieving better social welfare were more relaxed under the TCF model.

When considering the carbon neutrality scenario, we find an interesting phenomenon. In order to compare with the decision domain in the above section, we apply the same approach to obtain the following decision domains. In the carbon neutrality scenario, the economic meaning of all lines and regions in Fig. 7 is the same as above. However, there still exist some different conclusions as follows: First, the financing preferences on each side of the emission reduction efficiency key point change. When 0 < μ < μ∗ and the emission reduction efficiency is held constant, as green sensitivity increases, the order of manufacturers’ financing preferences are as follows: bank financing < in-house factoring financing < early payment financing. When μ ≥ μ∗ and the emission reduction efficiency is held constant, as the green sensitivity increases, manufacturers only prefer early payment financing. In the context of achieving the carbon neutrality target, when manufacturers’ emission reduction efficiency is high, manufacturers are free from carbon emission policy pressure and can flexibly adjust their financial and operational strategies. Based on manufacturers’ excellent emission reduction performance, retailers will actively pay to them part of the payment in advance. That is why in real-life situations, retailers are willing to offer advance payments to manufacturers (Kouvelis and Zhao 2012; Fang and Xu 2020). When emission reduction efficiency is low, early payment financing becomes optimal for manufacturers only when consumers are more sensitive to the green level of products. Although it may seem counterintuitive, the inversion activation mechanism works. A higher level of green sensitivity indicates that consumers have a stronger preference for green products. Manufacturers must proactively reduce emissions in order to maintain their market competitiveness. Once manufacturers take the initiative to reduce emissions, their product sales are guaranteed to some extent, and their market share expands (Wu et al., 2019). Therefore, retailers will place more orders and be willing to make partial prepayments to them. Second, we also found that when the carbon emission trading price is low, the decision domain area of bank financing is larger compared to the other two financing methods. This indicates that it is easier to obtain external financing under lower carbon emission trading prices. This is mainly due to the decreased activity in the carbon emission trading market at lower prices after achieving carbon neutrality goals. As a result, investments in the financial market also become less frequent. The government relaxes its regulations on external financial institutions to adapt to the carbon-neutral environment. When the carbon emission trading price is high, the area of the bank financing domain shrinks, while the areas of the other two financing domains expand. It is indicated that obtaining external financing is harder while obtaining internal financing becomes easier as carbon emission trading prices increase. This is because the carbon emission trading market remains active. The government needs to strengthen regulations to prevent speculation from disturbing the market order. This also indirectly reflects that the achievement of carbon neutrality goals cannot be separated from the effective coordination of the Carbon Emission Trading System (CETS) (Chen and Lin 2021).

Green supply chain management introduces sustainability and environmental considerations into supply chain management. Overall, emission reduction measures to some extent reduce corporate profits. On the one hand, consumer preferences for green products directly affect product demand and thus corporate profits. On the other hand, companies need to incur additional costs to purchase equipment or upgrade technology. Therefore, balancing economic and environmental benefits to achieve win-win situations has become a research focus in green supply chain management. Notably, the reasonable allocation of risks can motivate companies to become more actively involved in reducing emissions. Risk-sharing mechanisms mainly include contractual, financing, and option-based forms. Among them, innovative internal financing methods can not only alleviate the dilemma between economic and sustainable development but also expand financing channels for small- and medium-sized enterprises. However, with the promotion of the “dual-carbon” goal, we are faced with new challenges in choosing the optimal supply chain financing model under carbon neutrality targets. Therefore, this paper focuses on the impact of carbon emission trading prices on supply chain equilibrium financing decisions under carbon neutrality. The main conclusions are as follows: With the development of green supply chains, consumer demand for products has shifted from low price to high quality. The most intuitive expression of this is the level of consumer sensitivity to the green attributes of products. The effect of green sensitivity on the manufacturer’s profit is a result of an inversion activation process. As consumers’ green sensitivity grows, they are more inclined to prefer green products. When carbon neutrality is not considered, manufacturers reduce emissions to match consumer demand, which boosts their profits and ultimately boosts supply chain profits. In the carbon neutrality situation, the conclusions can be divided into two types: When carbon emissions do not exceed the standard, the conclusions are the same as above. However, when carbon emissions exceed the standard, as the carbon emission trading price increases, green sensitivity has a greater effect on manufacturer profits. At this time, this mechanism is more effective. This conclusion reveals the underlying reasons why green supply chains have been vigorously developed in recent years. By strengthening consumers’ environmental awareness, the profit of manufacturers can be increased, thereby achieving a win-win situation of emission reduction and production (Wu et al. 2019). Effectively resolving market risks can promote companies to engage in sound investment and financing. In pledged loans, Cao and Yu (2019) suggest reducing the ratio of carbon emission rights pledged as collateral to ease the risk of carbon asset depreciation for banks. This article believes that manufacturers have a guarantee against market risks due to the improvement in emission reduction efficiency. That is, manufacturers can reduce the same amount of carbon dioxide with less cost. Manufacturers have enough capacity to produce green products when the products change from homogeneous to competitive substitutes. Therefore, as emission reduction efficiency rises, manufacturers gradually migrate from internal to external financing methods when carbon neutrality is not considered, whereas they switch from external to internal financing in the carbon neutrality scenario. The impact of carbon emission trading prices on supply chain financing depends on whether carbon neutrality is considered. Building on the research by An et al. (2021), this study further introduces the carbon neutrality factor. Combining the conclusions drawn above, we have selected two indicators that represent both economic and environmental benefits: emission reduction efficiency and green sensitivity. The impact of carbon emission trading prices on manufacturers’ financing decisions is monotonic in the relationship between the two key variables. When carbon neutrality is not considered, as carbon emission trading prices increase, manufacturers’ optimal financing shifts from internal financing to external financing. However, when considering carbon neutrality, as carbon emission trading prices increase, manufacturers’ optimal financing shifts from external financing to internal financing. This finding provides new guidance for enterprises to timely adapt to changes in the economic environment, opportunities, and challenges in achieving carbon neutrality.

The production, sales, and consumption processes within a supply chain involve a variety of subjects. The development of a low-carbon supply chain can be seen from the following three perspectives in order to better realize financing and increase the output efficiency of the entire supply chain. From the perspective of the green supply chain development, manufacturers can achieve win-win situations through both internal and external approaches. In the internal approach, manufacturers should concentrate on improving industrial technology to reduce carbon emissions during production. Manufacturers should make greater efforts to improve carbon emission reduction efficiency in order to achieve greater carbon emission reductions (Qin et al. 2020). In the external approach, manufacturers can also accurately grasp and quantify the consumers’ information through in-depth market research activities, such as green sensitivity and the distribution of audience characteristics. This can help them utilize the inversion activation mechanism and flexibly respond to different carbon emission scenarios. From the perspective of supply chain financing innovation, the internal financing provided by retailers should be in line with carbon emission reduction policies. Retailers can make funds more accessible to low-carbon emission firms by including quantitative information in their lending rate determination process, such as manufacturers’ performance in reducing emissions. Additionally, considering the win-win nature of low discount prepayment financing, retailers can incentivize manufacturers to actively engage in emission reduction efforts by lowering wholesale price discounts (Qin et al. 2020). Similarly, in zero-interest advance payment financing, retailers can choose to offer longer repayment periods to companies whose carbon emissions are below the standard and shorter repayment periods to those whose emissions exceed the standard. From the perspective of policy regulation, effective external constraints can regulate corporate carbon emissions. When carbon neutrality is not achieved, the government should increase the punishment for enterprises whose carbon emissions exceed the standards, such as setting up a gradient penalty system. That is, the excess carbon emissions should be divided into different tiers, and each tier should have a corresponding fine that increases with the amount of excess emissions. In addition, regulatory agencies should include a company’s carbon emission history in their credit records. Given the significant differences in endowment between regions in China (Zhao et al. 2023), the government can set different carbon emission limits for different companies based on their carbon credit, in order to adapt to the challenges of regional differentiation in emissions reduction. As the interest rate marketization reform is further promoted, the government should make full use of fiscal tools to regulate market interest rates. When carbon neutrality is achieved, in order to reduce the risk caused by the change of green sensitivity, the government should provide preferential treatment to companies that have not exceeded emission standards through targeted reserve requirement ratio reduction measures.

This paper still has some limitations. First, the impact of demand uncertainty on the profit and decision-making of the supply chain is not considered, which is different from the actual situation. The demand in real life is difficult to measure accurately. In the model, by assuming the demand as a function with stochastic variables, the obtained results will have more practical guidance significance. Second, while the carbon cap-and-trade system’s impact on supply chain financing decisions is taken into account only from a quantity perspective in this article, there is another regulatory requirement for a percentage reduction in carbon emissions. Furthermore, considering the actual carbon reduction situations of various countries, most of them have implemented different carbon reduction policies at the same time to enhance the reduction effect. Placing the research background under multiple policies may have some influence on the research results. Finally, in order to evaluate the robustness of the research results, empirical research needs to be supplemented. Although it is difficult to obtain statistical data on the supply chain, empirical analysis still has certain feasibility considering the method of using case data in previous literature (Tunca and Zhu 2018). Therefore, the next research will further consider the impact of carbon neutrality conditions on supply chain financing strategy under several carbon emission reduction policies by using empirical analysis.