The Impact of the Cost-Sharing Contract on Capital-Constrained Agricultural Supply Chains

This study attempts to determine the optimal production and pricing decisions of E-Agri-SCF (agricultural product supply chain financed by e-commerce) and analyzes the influence of financing parameters on the optimal decision. Research indicates that the optimal purchase price decision increases with the expansion of the financing interest rate and declines with the expansion of the capital opportunity cost. The expected output factor of agricultural products has no influence on the optimal purchase price decision. The optimal production decision of the farmer declines with the expansion of the financing interest rate and the opportunity cost of capital and increases with the increase in the expected output factor of agricultural products. In particular, we show that due to the uncertainty in the output of agricultural products, the losses caused by decentralized decision-making in the E-Agri-SCF will increase. Therefore, this article proposes using a cost-sharing contract to promote the coordination of E-Agri-SCF. We prove that when farmers share more costs, they obtain higher benefits, while the e-commerce platform does the opposite. This is because the participation of e-commerce platforms in financing has changed the revenue structure of the supply chain. The findings of this article are very meaningful, as they provide management opinions on the financing terms of E-Agri-SCF.


Background and Motivation
Agricultural production is greatly influenced by climatic disasters and output has greater uncertainty (Dey & Mishra, 2022), which causes farmers to face severe financial exclusion and credit rationing (Antle & Diagana, 2003;Shiferaw et al., 2015), which further limits the production capacity of farmers. Agricultural supply chain finance effectively alleviates the problem of farmers' credit constraints and realizes the commercialization and sustainability of agriculture (X. Li & Sun, 2022). It has two main features. One is the participation of members in the supply chain in financing, that is, the form of commercial credit between entities in the agricultural supply chain. The other is that external financial institutions provide financing services to internal capital-constrained members in the supply chain (Buzacott & Zhang, 2004). With the advancement of internet technology and the popularization of applications, the integrated development of ''Internet + supply chain finance'' has given birth to e-agricultural supply chain finance. E-Agri-SCF refers to the agricultural supply chain in which B2C ecommerce platforms rely on their advantages to replace banks to provide financing services for the farmer. For example, Alibaba Group (Ali), China's influential ecommerce platform, has been developing agricultural supply chain financial services to boost the sustainable development of agricultural supply chains. In 2014, it started to carry out agricultural finance through its subsidiary Ant Financial (AF), hoping to solve the problem of agricultural finance. The latest rural financial data released by AF show that its agricultural financial services cover 231 cities. Another example is Wangnongdai, a financial product launched by JD.com in 2015, which aims to provide farmers with funds to increase their productivity and ensure the stability of agricultural supply 1 Harbin University of Commerce, China chains. E-commerce platform participation in agricultural product supply chain financing can realize online and offline resource synergy and reduce supply chain financing costs (Chen et al., 2019).
When an e-commerce platform provides financing services, its role in the agricultural product supply chain is not only the purchaser of agricultural products but also the provider of farmers' production funds. The optimal decision of the e-commerce platform and farmers will be affected by the financing parameters. Therefore, when considering the participation of e-commerce platforms in financing, exploring the decisions of e-commerce platforms and capital-constrained farmers is of important significance for advancing the sustainable and healthy development of agriculture.

Research Questions and Contributions
E-Agri-SCF in practice has raised several research questions.
RQ1: How does E-Agri-SCF affect the income of farmers and e-commerce platforms? How does a farmer's optimal production input change? RQ2: What role does the cost-sharing contract play in E-Agri-SCF? RQ3: How will cost-sharing contracts affect the profits and optimal decisions of supply chain members? Under what circumstances will cost-sharing contracts be accepted by e-commerce and farmers?
To answer the above questions, we first study the agricultural supply chain consisting of well-funded e-commerce platforms and limited-funded farmers to clarify the optimal decision and optimal profit of each member of the E-Agri-SCF, as well as the influence of parameters such as financing cost on the supply chain decision. Next, we compare and analyze the decentralized model and the centralized model, study the role of cost-sharing contracts in improving the performance of agricultural supply chains, and verify the necessity of supply chain coordination. Finally, we provide some numerical examples to visually test our theoretical conclusions.
Our research results show that the participation of ecommerce platforms in financing will have a significant impact on farmers' production input decisions and ecommerce platform purchase price decisions. The optimal purchase price decision of an e-commerce platform increases with the expansion of the financing interest rate and decreases as the opportunity cost of capital increases. The optimal production decision of farmers decreases with the expansion of the financing interest rate and the opportunity cost of capital and increases with the increase in the expected output factor of agricultural products. The optimal production input volume decision, the optimal agricultural product purchase price and the optimal supply chain overall profit in the decentralized decision-making process are all less than those in the centralized model decision-making process; when an ecommerce platform shares a part of the production financing cost, a win-win situation for e-commerce platforms and farmers in the E-Agri-SCF.

Paper Organization and Structure
The remainder of the article consists of the following. Section 2 brings together the research related to this paper. Section 3 mainly introduces the model description and model assumptions, solves the model solutions in decentralized and centralized systems, and compares the optimal solutions of the two models. Section 4 designs the cost-sharing coordination mechanism and analyzes the threshold of the cost-sharing ratio coefficient. Section 5 gives numerical examples to explain the influence of different financing parameters. In Section 6, we discuss the research results and list future possible research priorities. All proofs are presented in the Appendix.

Literature Review
Supply chain financing has a certain impact on a company's operations and performance (Buzacott & Zhang, 2004;Y. Li & Gu, 2020). Therefore, our work relates to the extensive stream of literature mainly on agricultural product supply chain management, supply chain financing with the participation of e-commerce platforms, and supply chain coordination contracts.

Agricultural Product Supply Chain Management
The first stream is related to the influence of financial constraints on agricultural product supply chain management. Capital constraints will have a certain impact on the decision-making of farmers and inhibit the rapid development of the agricultural economy (Abid et al., 2006). Higher interest rates make it difficult for farmers to obtain financing, which greatly affects the productivity of agricultural products (Osabohien et al., 2020;Oubraham et al., 2021).
To solve the financial constraint problem of farmers to promote the process of agricultural modernization, Soeters et al. (2017) and Larionov (2020) found that injecting large amounts of financial resources into rural areas with weak funds can help increase crop planting areas. Guedes et al. (2021) assessed the impact of rural microfinance on agricultural production value by considering both the amount of the loan issued and the time when the benefit was obtained. Miranda et al. (2019) proposed that agricultural product supply chain members subject to capital constraints can conduct warehouse receipt financing with their partners. Wirakusuma and Irham (2021) believe that agricultural subsidies can effectively alleviate the financial constraints of farmers.
Compared with the industrial supply chain, the uncertainty of output is a risk that is difficult to grasp in agricultural production decision-making. Natural disasters such as climate change will lower output and increase the volatility of market prices (Kazaz & Webster, 2011). Studies that consider the characteristics of output uncertainty to affect the supply chain system mainly include B. Yan et al. (2021), who studied decision-making problems in the case of output uncertainty and farmer default. Nong and Pang (2013), Inderfurth and Clemens (2014), and Liu, Shen, and You (2020), have studied the supply chain coordination problem under output uncertainty.
There are two research gaps in this stream of literature. One is that there are few studies on the ways farmers obtain financing. Most ways of mitigating funds rely on rural credit funds and policy subsidies. Since ecommerce platforms are members of the supply chain, when they participate in financing, the supply chain structure changes, so the production and pricing strategies of the E-Agri-SCF may be different. What is important is that the impact of agricultural output uncertainty under E-Agri-SCF on the optimal decision-making of ecommerce and farmers has not been discussed in the literature.The other is that the existing research does not consider whether the influencing factors of the decisionmaking of supply chain members under the e-commerce participation financing model change. Our research proposes production and pricing strategies for agricultural supply chains based on the participation of e-commerce platforms in financing and analyzes the impact of financing parameters.

Supply Chain Financing With the Participation of e-Commerce Platforms
The second stream is related to supply chain financing with the participation of e-commerce platforms. Scholars start from the following aspects.
One is about the motivation and value of e-commerce platforms participating in financing. First, e-commerce platform participation in financing can help capitalconstrained enterprises solve financing difficulties, reduce financing costs (Lahkani et al., 2020), and help capitalconstrained enterprises improve their production capacity (Ali et al., 2019). Second, as an internal member of the supply chain, the e-commerce platform provides financing services to farmers, which can enhance its premium ability and strive for price concessions. Finally, the e-commerce platform has a huge amount of transaction data, which has advantages in reviewing the credit of capital-constrained enterprises (He & Tang, 2012) and is conducive to reducing financing risks and enhancing stickiness in the supply chain.
The other aspect concerns the interaction between ecommerce platform supply chain finance and operations. For example, J. Liu et al. (2021) found that e-commerce platforms affect financing decisions. H. Yan (2017) studied three modes, supplier-led, dealer-led, and B2B ecommerce platform-led models, and found that supply chain finance with the participation of e-commerce platforms can help solve the common financing difficulties of capital-constrained enterprises. Tunca and Zhu (2018) studied the interest rate and price decision issues of a supply chain with e-commerce platform participation. Bai and Jia (2022) studied the conditions for farmers to choose e-commerce platforms to provide financing for them, considering the risk of output uncertainty.
Similar to Yi et al. (2021), we analyze the decisionmaking problem of agricultural product supply chain under the e-commerce financing model. Moreover, we analyze the influence of the e-commerce interest rate, capital cost, and expected output factor of agricultural products on the optimal decision and optimal profit of each member in the supply chain and coordinating the supply chain, which is different from their work.

Supply Chain Coordination Contracts
The third stream is related to supply chain coordination.
Taking into account the potential impact of the ecommerce platform as an internal member on the Financing decision of the agricultural supply chain. The relationship between farmers and e-commerce platforms will be greatly changed. Therefore, the need to coordinate the agricultural supply chain is urgent. At present, a massive body of literature has conducted relevant research on supply chain coordination. Since Cachon et al. (2005) first proposed the concept of a supply chain coordination contract, it has been widely used in different situations. For example, the repurchasing contract is used to achieve perfect coordination under the uncertainty of demand . Cost-sharing contracts are used for output uncertain supply chain coordination issues (B. Yan et al., 2021). Wholesale prices and revenue-sharing contracts are related to consumer preferences (Liu, Du, & Sun, 2020). According to the application scenarios of different supply chain coordination contracts, the paper uses cost-sharing contracts to coordinate E-Agri-SCF.

Contributions of This Paper
In summary, there are some contributions when compared to the existing research. The above literature shows that the mode of relief of farmers' capital constraints mainly relies on rural credit funds and policy subsidies, and less consideration is given to the direct provision of funds for farmers by e-commerce platforms. Second, our results show the positive role of cost-sharing contracts. The above literature illustrates the usage scenarios of various supply chain coordination contracts. On this basis, we apply cost-sharing contracts to coordinate E-Agri-SCF. Third, this paper enriches the research content on agricultural product supply chain management. Our results provide e-commerce platforms and farmers with practical advice on financing decisions and the impact of cost-sharing contracts on production inputs and wholesale prices.

The Model
We build a model using the stackelberg game method Farmer is limited by funds. E-commerce platform provides financing services for the farmer. First, the ecommerce platform, as the leader, determines the purchase price of agricultural products w. Next, the farmer, as follower, determines the production input of agricultural products s when the farmer already know the purchase price of the e-commerce platform and applies for loans from the e-commerce platform at the same time.
After the agricultural products are harvested, the ecommerce platform purchases all the agricultural products of the farmer according to the agreed-upon purchase price and sells them to the market at the price p. After the sales period ends, the e-commerce platform pays the farmer the remaining purchase amount after deducting the principal and interest of the loan.
The total output of agricultural products is Q, where Q = qs, q is the unit output factor, which is a random variable and q;N 0, m ð Þ, E q ð Þ = m. That is, the expected output factor of agricultural products is m (The smaller the expected output factor of agricultural products, the greater the uncertainty risk of the output of agricultural products).The production input cost of the farmer is C(s). To solve the predicament of capital constraints, the e-commerce platform provides funds to the farmer at an interest rate r. In China, larger e-commerce companies such as Ali provide farmers with Wangnongloans for the production of agricultural products, which are then sold on the platform after they are harvested. At this time, the opportunity cost of e-commerce platform capital is t. In the process of agricultural product sales, the e-commerce platforms' operating costs and transportation costs are c r v, respectively. The profits of e-commerce platforms and farmers are recorded as p e and p f , respectively. The superscripts M, N, and MN are, respectively, the decentralized models, centralized models, and cost-sharing decision-making.
Operation process of the E-Agri-SCF, see Figure 1.
Other assumptions are as follows: Assumption 1. In the financing, production and sales process, the information in the agricultural product supply chain is completely symmetrical Assumption 2. The initial capital of the farmer is 0 (Jing, 2014). Assumption 3. Only one nonperishable agricultural product is sold in this supply chain. Only one nonperishable agricultural product is sold in this supply chain. Assumption 4. The production cost of the farmer is set to C s ð Þ = cs 2 , where c stands for the effort cost parameter of the farmer in production (Niu et al., 2016).

Decentralized E-Agri-SCF
The expected revenue function of farmers is The expected revenue function of the e-commerce platform is Lemma 1Under the decentralized model, the farmer's optimal agricultural product production input is s NÃ = pÀc r Àv ð Þ m 2c 2 + r + t ð Þ , the best purchase price of the ecommerce platform is w NÃ = pÀc r Àv ð Þ1 + r ð Þ 2 + r + t , the expected profit of the farmer is E p NÃ f = pÀc r Àv ð Þ 2 1 + r ð Þ m 2 4c 2 + r + t ð Þ 2 , the expected profit of the e-commerce platform is E p NÃ e = pÀc r Àv ð Þ 2 m 2 4c 2 + r + t ð Þ , and the overall expected profit of the supply chain system is E p NÃ Proposition 1 Under the decentralized model, the optimal production input of farmers will decrease as the financing interest rate of the e-commerce platform and the opportunity cost of capital increase and increase with the increase in the expected output factor of agricultural products. The optimal purchase price increases with the increase in the financing interest rate and reduces with the increase in the opportunity cost of capital.
Proposition 1 illustrates that the increase in the financing interest rate and capital costs of the e-commerce platform has led to an increase in the production costs of the farmer, which has inhibited the farmer's enthusiasm for production. To encourage farmers to expand the proportion of production, e-commerce platforms often increase the purchase price of agricultural products. However, the total cost has increased with the increase in the cost of capital. This greatly reduces the willingness of ecommerce platforms to improve the purchase price. In addition, the uncertainty of the output of agricultural products only affects the production input decision of farmers and does not affect the purchase price decision of the e-commerce platform in the E-Agri-SCF.

Centralized E-Agri-SCF
The expected revenue function of the supply chain is where ms is the expected production of agricultural products and pms is the expected revenue from agricultural product sales. On the cost side,c r ms is the expected operating expense of the e-commerce platform, vms is the expected transportation expense of the e-commerce platform, cs 2 is the production input expense of the farmer, and tcs 2 is the capital expense of the e-commerce platform.
Lemma 2 In the centralized model, the optimal strategy for a farmer under the E-Agri-SCF is s MÃ = pÀc r Àv ð Þ m 2c 1 + t ð Þ , and the optimal expected income of the farmer is E p MÃ l = pÀc r Àv ð Þ 2 m 2 4c 1 + t ð Þ .
Proof All of the proofs are in the ''Appendix.'' Proposition 2 In the centralized mode, farmers' production input decisions are not affected by the interest rate of the e-commerce platform but by the opportunity cost of capital and the expected output factor of agricultural products. The production input decision of farmers decreases with the increase in the capital opportunity cost of the e-commerce platform and increases with the increase in the expected output factor.
Proposition 2 states that e-commerce platforms and farmers are regarded as a whole in a centralized model. The higher the uncertainty of the output of agricultural products and the opportunity cost of capital, the more unfavorable the overall benefit of the supply chain.

Comparative Analysis
Proposition 3 The optimal production input of farmers in the centralized model is greater than that in the decentralized model, and the income of the E-Agri-SCF in the centralized model is higher than that in the decentralized model.
Proposition 3 shows that every participant of the E-Agri-SCF under the centralized model is composed of independent individuals to form the same interest unit, the operation decision is unified, and there is no internal friction under the decentralized model decision-making. The production input of the farmer is optimal, and the profit of the E-Agri-SCF is also at the optimal state.
For the content discussed in Proposition 3, we have also found a good argument in reality. For example, Jingdong Mall is a representative enterprise of the ecommerce platform. To resolve the problem of farmers' financing dilemma, JD.com established Jingnongdai products to provide farmers with financing services. Take the ''running chicken'' fresh produce project launched by JD as an example. It provides each eligible farmer with a loan of 4,500 yuan for the purchase of chickens. These chicks are raised freely by the farmer and will be sold by Jingdong after the chicks are grown.
According to official data from JD.com, during Double 11 in 2018, ''running chickens'' were sold out as soon as they went on the market. Each ''running chicken'' brought nearly 40 yuan in income to farmers, increasing the income by several thousand yuan every year. By granting loans to the farmer and selling them through the JD platform, JD.com has to a certain extent realized the centralized model decision-making of the E-Agri-SCF and obtained more profits than decentralized model decision-making. Therefore, it is necessary to coordinate E-Agri-SCF to enable e-commerce platforms and farmers to obtain more benefits.

Cost-Sharing Contract
Since this article does not consider issues such as the return and repurchase of agricultural products, the E-Agri-SCF cannot be coordinated using options contracts and repurchase contracts. The cost-sharing contract coordination method is that the retailer shares part of the supplier's cost to increase the supplier's output. This mode of operation matches the relationship between the ecommerce platform and farmers under the E-Agri-SCF. Therefore, this paper chooses a ''cost-sharing'' contract that coordinates the E-Agri-SCF. Next, we will analyze and discuss how to design a ''cost-sharing'' contract to realize the coordination of E-Agri-SCF.
Proposition 3 shows that s MÃ .s N Ã . The optimal production input of farmers under the centralized model is higher than that under the decentralized model. To increase the enthusiasm of farmers in production, we consider making the e-commerce platform share some financing costs of the farmer to improve the farmer's production input and reduce the purchase price to improve the income of the e-commerce platform and farmers in the E-Agri-SCF.

The expected revenue function of the farmer is
The expected revenue function of the e-commerce platform is Lemma 3 Under the cost-sharing contract, the optimal production input of the farmer is s MNÃ = wm 2cj 1 + r ð Þ . The optimal purchase price is w MNÃ = pÀc r Àv At this time, the optimal expected revenues of the farmer and e-commerce platform are Lemma 4 To ensure the effective implementation of the contract, we have clarified the value range of the costsharing contract coefficient. Only when the condition of

Numerical Analysis
In Section 5, this paper defined the optimal solution under a centralized model, a decentralized model, and a cost-sharing contract. We used MATLAB software for numerical analysis. We analyzed the influence of the financing parameters and output uncertainty through numerical examples. The initial parameters were set at p = 3500, c r = 1200, v = 500, and c = 1.

The Influence of the e-Commerce Platform Financing Interest Rate
We let m = 0:8, t = 2%, and r 2 0, 0:2 ð Þ. Figures 2 and 3 show the influence of the e-commerce platform financing interest rate on agricultural production input, purchase price, and profit. Figure 2 shows that the optimal decision results of the E-Agri-SCF are consistent with Lemma 2 and Proposition 2, which indicates the robustness of our study. The decline in the production input of agricultural products under the decentralized model and the increase in the purchase price indicate that the interest rate of the e-commerce platform has a significant influence on the e-commerce platform and farmer.
Compared with the decentralized model, the production input of farmer households tends to be stable with the change in interest rate. This is because the unified management under the centralized model reduces internal consumption, and the overall efficiency of the supply chain improves; even if e-commerce increases the financing interest rate, the farmer can still obtain more benefits when they make higher production input decisions. The production input decision of farmers under the centralized model is not only independent of the interest rate of the e-commerce platform but is always higher than in the decentralized model. Figure 3 shows how the farmer's and electronic platform's profit changes with the financing interest rate.
The e-commerce platform's and farmer's profits incur losses at a higher financing interest rate. We found that higher e-commerce platform financing interest rates increase farmers' costs and shorten the gap between farmers' sales revenue and loan costs. This leads to a decline in farmers' profits. Although the loan income of the ecommerce platform increases with the increase in  financing interest rate, the overall profit declines. The platform has to enhance the purchase price of agricultural products to stimulate farmers to expand production. The insight is that both the farmer and electronic business platforms can benefit from the e-commerce financing model under appropriate interest rates.

The Influence of the Opportunity Cost of Capital
We take r = 6% and t 2 0, 0:1 ð Þand analyze the influence of the opportunity cost of capital on agricultural production input, purchase price, and profit (Figures 4 and 5). Figure 4 shows that agricultural production input and purchase price both decrease with sensitivity, and the amount of production input under the centralized model is always greater than that of the decentralized model. This suggests that the opportunity cost of capital inhibits both the e-commerce platform's and the farmer's decision-making. Figure 5 shows that the income of farmers decreases as the opportunity cost of capital for an e-commerce platform increases under the decentralized model. This shows that the opportunity cost of capital affects the profit of the e-commerce platform and at the same time  indirectly affects the profit of the farmer. As the opportunity cost increases, farmers' profits will also decline. When the opportunity cost of capital for an e-commerce platform is high, the farmer can usually accept an appropriate reduction in the purchase price of agricultural products to encourage the e-commerce platform to provide financing services. At this time, the income of farmers will also decline as a result. Figure 5 also analyzes the changes in the profits of ecommerce platforms. As the cost of capital increases, the profits of e-commerce platforms decline. Even if the cost of capital is higher than the interest rate of the ecommerce platform, the e-commerce platform is still willing to provide financing services for farmers. This is because the cost of e-commerce increases when the interest rate of e-commerce is lower than the opportunity cost of capital. At this time, the e-commerce platform will transfer part of the cost to farmers by appropriately reducing the purchase price, and the e-commerce platforms can still get acceptable profits. Therefore, even if the opportunity cost of capital is greater than the interest rate of e-commerce, e-commerce will still be willing to provide financing services for farmers.

The Influence of the Expected Output Factor
We take t = 0:02 and analyze the influence of the expected output factor on agricultural production input, purchase price, and profit (Figures 6 and 7). Figure 6 shows that as the expected output factor increases, the farmer's production input increases. Moreover, in the centralized model, the production input of farmers is always higher than that in the decentralized model. This is consistent with the practical case. Figure 6 also shows that in the agricultural product supply chain in which e-commerce participates, the purchase price decision of the e-commerce platform is not affected by the expected output factor of agricultural products. This is because e-commerce provides farmers with lower interest rates, which reduces the cost of farmers' production inputs. At this time, even if the farmers reduce the production input because the expected output factor is low, they can still accept the original purchase price of agricultural products. Figure 7 shows the influence of the expected output of agricultural products on the profit of the e-commerce platform and farmers when the interest rate of ecommerce is determined. We find that even if the expected output factor of agricultural products is low, ecommerce and farmers can still make profits in the ecommerce participation financing model. As the expected output factor increases, the profits of e-commerce platforms and farmers increase. The participation of ecommerce in agricultural supply chain financing reduces the impact of agricultural output uncertainty on the agricultural supply chain. Table 1 reveals that the cost-sharing contract has indeed increased the income of farmers and e-commerce platforms and achieved Pareto improvements between e-commerce platforms and farmers. While the cost-sharing contract encourages farmers to increase the amount of agricultural production input (the amount of production input under the cost-sharing contract is the same as the amount of production input under centralized decision-making), it also reduces the purchase price of agricultural products. The greater the cost-sharing coefficient is, the higher the optimal purchase price of agricultural products after coordination, and the income of farmers will increase, while the income of e-commerce platforms will decrease. If and only if the cost-sharing coefficient is within a certain threshold will the coordinated e-commerce platform and farmer's income be higher than the decentralized decision-making at the same time, achieving a win-win situation for the e-commerce platform and farmer. At this time, the cost-sharing contract can make the overall benefit of the supply chain reach the benefit of centralized decision-making, improve the overall efficiency of the supply chain, and promote the sustainable development of the supply chain.

Concluding Remarks and Future Research
We investigated how the participation of e-commerce platforms in financing affects the production and pricing strategies of farmers. We consider two situations: centralized model and decentralized model. Through numerical analysis, we further proposed a cost-sharing contract to coordinate the E-Agri-SCF to achieve a win-win situation for the e-commerce platform and farmer. We obtained some meaningful conclusions.
First, we established the income models of e-commerce platforms and farmers under the decentralized and centralized models based on the Stackelberg game method and obtain the influence of financing parameters on the members of the E-Agri-SCF. If an e-commerce platform sets a higher interest rate, he needs to increase the purchase price to stabilize cooperation with the farmer. Therefore, a higher interest rate may reduce e-commerce platform revenue. The optimal decision and optimal profit of the E-Agri-SCF under a centralized model are greater than those under a decentralized model.
Second, our analysis proves the influence of the opportunity cost of capital on the optimal decision-  making and optimal profit of the E-Agri-SCF. The opportunity cost of capital directly affects the purchase price of e-commerce platforms and indirectly causes a reduction in the production input of farmers. In practice, when the opportunity cost of capital is too high, the ecommerce platform will reduce the cost by lowering the purchase price to reduce the loss of funds. The reduction in the purchase price will greatly inhibit farmers' enthusiasm for production and planting. In addition, we also found that the uncertainty of the output of agricultural products only affects the production input decision of farmers and has no impact on the purchase price decision of the e-commerce platform. Third, we have constructed an e-commerce platform and farmer income model under the cost-sharing contract. We determined the parameter range for the Pareto improvement of the e-commerce platform and farmers and proved that the cost-sharing contract may improve the operational performance of the E-Agri-SCF through numerical analysis. However, we found that the larger the parameter setting of the cost-sharing contract is, the higher the income of the farmer and the lower the income of the e-commerce platform. Only when the costsharing parameter is within a certain threshold will the ecommerce platform and farmer benefit from applying the cost-sharing contract and achieve a win-win situation among the participants of the E-Agri-SCF.
The study has important theoretical and practical significance for the management of the e-commerce industry and agricultural supply chain. Theoretically, we expand the literature on the agricultural supply chain by investigating the influencing factors of the e-commerce platform participation financing model on the production and pricing strategy of the agricultural supply chain. Although researchers have studied agricultural supply chain management and e-commerce platforms' participation in supply chain financing, they have not considered the decision-making and profits of supply chain members from the perspective of capital cost and agricultural output uncertainty. Few studies have emphasized the participation of e-commerce platforms in agricultural supply chain coordination under the financing model.
Our study found that the E-Agri-SCF cannot obtain the optimal decision under a decentralized model. The research has proven that the cost-sharing contract can effectively coordinate the E-Agri-SCF. In addition, this research confirms that the participation of e-commerce platforms in financing can effectively solve the problem of farmers' capital constraints, but the financing interest rate, capital opportunity costs, and expected output factor for agricultural products will influence the production and pricing decisions.
These findings reveal the importance of e-commerce platform participation in financing models and the sensitivity of agricultural product supply chains to finance parameters and fill up the gaps in the literature on e-commerce agricultural supply chain management strategies. The research proposes meaningful management advice for e-commerce platforms and agricultural business entities.
First, our findings confirm that the cost-sharing contract is beneficial to the development of E-Agri-SCF. The government should formulate corresponding subsidy policies, increase the enthusiasm of e-commerce platforms to provide financing services to farmers, promote the cost-sharing contract between e-commerce platforms and farmers, and stabilize the development of the E-Agri-SCF.
Second, farmers should increase the trust of ecommerce platforms by repaying on time to increase the possibility of obtaining financing services from an ecommerce platform.
Third, the e-commerce platform can increase the output of agricultural products by providing the farmer with intelligent machinery and equipment, specialized planting knowledge, and enhance the ability to negotiate costsharing factors.
We propose some interesting future research directions to further understand the financing issues of E-Agri-SCF. To simplify the calculation, we only studied the supply chain composed of a single-funded farmer and a single well-funded e-commerce platform. However, in practice, each farmer may face multiple e-commerce platforms, and there is a competitive relationship among the e-commerce platforms. Therefore, the optimal decisionmaking strategy of the one-to-many fund-constrained agricultural supply chain is the focus of future research. We can also explore agricultural insurance. We will further study the incentive effect of agricultural insurance on the provision of financing services by members within the E-Agri-SCF.

Appendix: Proof
Proof of Lemma 1 Using backward induction, according to Formula 1, we have Therefore, based on the equation