Profit Coordination and Optimization of Agricultural Product Brand Promotion Lead by Farmer Cooperative Organizations

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Introduction
In the past, due to the imbalance in the bargaining power of the supply and demand sides, the supply side only can sell agricultural products to buyers at low prices, which afected the circulation efciency of agricultural products and restricted the healthy development of agricultural products in China [1]. In recent years, the rapid development of ecommerce has provided an opportunity to expand the sales channels of agricultural products in China. According to commerce big data monitoring, China's online retail sales of agricultural products reached RMB 422.1 billion in 2021 [2]. Although the online sales of agricultural products increased, farmers' incomes did not increase much. Terefore, researchers attempt to fnd out a way to increase farmers' incomes.
Practices in India, Myanmar, and Poland have proved that improving the bargaining power of the supply side is the way to increase farmers' income, and establishing agricultural production organizations is an efective way to improve the bargaining power of the supply side [3][4][5]. In China, farmer cooperative organizations help farmers improve the quality of agricultural products to meet the market [6]. For example, the number of specialized farmers' cooperatives in Chongqing has grown from 13400 to 37300, and the participation rate of farmers has reached 44% in 2021. Terefore, farmer cooperative organizations play an essential role in the e-commerce supply chain of agricultural products [7]. Te e-commerce supply chain of agricultural products has three parties: farmer cooperative organizations, e-commerce platforms, and consumers. Ten, the research question of the study is how to coordinate farmer cooperative organizations and e-commerce platforms to maximize the overall profts of the supply chains of agricultural products.
Since the brand efect of an agricultural product is signifcant for the demand for the product, it is necessary to strengthen the brand construction of agricultural products [8]. However, the product brand could be strengthened by brand promotion; therefore, the brand promotion efort of an agricultural product could afect the online sales of the agricultural product [9,10]. Te improvement of the bargaining power of farmers' cooperatives enables farmers' cooperatives to play a leading role in the agricultural product e-commerce supply chain [11]. Te brand promotion eforts of e-commerce platforms can make agricultural products stand out and signifcantly increase sales. Both parties can signifcantly improve their profts and achieve win-win results through cooperation.
In reality, due to farmers' cooperatives' weak brand promotion awareness, the brand efect is yet to be fully utilized [12]. Te failure to reach a consensus on cooperation between farmers' cooperatives and e-commerce platforms resulted in farmers' participation in online platform sales. However, their income still did not increase substantially [13]. Based on this, the main research questions of this study are as follows. (1) What mechanism do the farmer cooperatives and e-commerce platforms use to achieve supply chain coordination? (2) What are the coordination channels and programs between farmers' cooperatives and ecommerce platforms?
For this reason, this study constructs a secondary agricultural product supply chain decision-making model with farmers' cooperatives as the leader and e-commerce platforms as the follower. First, it compares the proft relationship of each decision variable and decision subject under the decentralized decision and centralized decision. Ten, the coordination mechanism of the supply chain is analyzed, and diferent contract coordination schemes are designed. It achieves the efect of centralized decision making and realizes a win-win situation for the supply chain by promoting cooperation between e-commerce platforms and farmers' cooperatives.
Tis study is organized as follows. In Section 2, we present the literature review. In Section 3, we make basic assumptions and notation. Section 4 and Section 5 construct the Stackelberg game model and analyze the coordination mechanism and programs. Section 6 presents the numerical examples. We conclude this study in Section 7.

Agricultural Product Supply Chains.
Previous studies on agricultural product supply chains mainly focused on the supply chain coordination [14][15][16][17][18], risk management [19,20], product brand [21][22][23], bargaining power [3,21,24], etc. Some researchers also consider the impact of government subsidies on the supply chain of agricultural products [10,25]. In the research of agricultural product supply chain coordination, researchers have studied the impact on agricultural product supply chain coordination from consumer preference [15,16,26] and logistics [16,18,27,28]. Among all studies, most researchers believed that the brand of agricultural products is vital to the sales of agricultural products online [8]. On the other hand, most researchers believed that farmer cooperative organizations can improve the bargaining power of agricultural products and increase farmers' income [22]. But no studies have linked agricultural product brand promotion for online sales and contract coordination with farmer cooperative organizations.

E-Commerce Supply Chain for Agricultural Products.
Te research on agricultural e-commerce mainly focuses on the operation and fnancing of agricultural e-commerce, the application of blockchain technology, and supply chain coordination. Scholars generally believe that the operation of agricultural e-commerce is infuenced by blockchain technology, logistics service levels, and agricultural preservation technology [29]. Te application of technologies such as blockchain [30] and the Internet of Tings [31] has afected the level of information technology [32,33], quality traceability [34,35], and electronic marketing [36,37] of agricultural products, thereby improving the circulation efciency of agricultural products and reducing their costs. Logistics services [18,38], especially cold chain logistics [27,39], and the greenness and freshness of agricultural products [40][41][42] have a signifcant impact on the online sales evaluation of agricultural products [43]. Te coordination of the agricultural product e-commerce supply chain mainly focuses on logistics services [27,38], preservation levels [18,44], and online and ofine coordination [45].

Contract Coordination Mechanism.
In terms of the contract coordination mechanism of the agricultural product supply chain, researchers have established Stackelberg game models [14-16, 18, 27, 28, 46, 47] and Nash equilibrium [48] to coordinate supply chain interests. For example, Cao et al. [15] developed a game model based on cost allocation and repurchase contracts, considering sales prices and greenness. Qiu et al. [16], Zhang et al. [27], and Yu and Xiao [28] considered the impact of logistics services on the agricultural product supply chain to establish a Stackelberg game model dominated by logistics service providers. Song and He [18] and Zhong et al. [49] established a logistics service supply chain coordination model based on freshkeeping cost-sharing and revenue-sharing contracts. Yan et al. [46] studied the traditional agricultural product supply chain and established a contract coordination model based on improved revenue sharing. Niu et al. [22] put forward the coordination strategy of the wholesale price and cost sharing with the participation of farmers' cooperative organizations.
Some studies on the e-commerce supply chain and its coordination of agricultural products are shown in Table 1.
From Table 1, it can be seen that scholars' research on the coordination of agricultural e-commerce supply chain mainly focuses on logistics and distribution, with less research on the role of farmers' cooperatives in the supply chain. Game models primarily focus on e-commerce platforms or logistics service providers for research, and few researchers considered the impact of brand promotion on ecommerce sales of agricultural products [50]. Supply chain coordination mainly focuses on revenue sharing and cost sharing, with less consideration for contract coordination. Te contribution of this study lies in the following: (1) constructing an agricultural product e-commerce supply chain led by farmers' cooperatives; (2) introducing agricultural product brand promotion and studying the impact of brand promotion on agricultural product e-commerce supply chain decision making; and (3) proposing coordination mechanism including both "revenue sharing + cost sharing + wholesale price discounts" and the coordination of wholesale prices for agricultural products.
With the vigorous promotion of "one village, one product, one town, one industry" in rural areas, the positioning of agricultural product brands has been dramatically improved. However, the responsibility and efort of product brand promotion are still on the e-commerce platforms. Terefore, it is generally believed that e-commerce platforms dominate the contract coordination mechanism. However, diferent contract coordination mechanisms should be examined to improve farmer cooperative organizations' bargaining power.

Model Description.
Tis study compared two decisionmaking models consisting of a farmer cooperative organization and an e-commerce platform. Suppose that (1) a farmer cooperative organization only sells one kind of agricultural product; (2) the e-commerce platform acts as a middleman, after buying that kind of agricultural product from the farmer cooperative organization, and then sells the products to consumers; and (3) the market demand for that agricultural product depends on the selling price of the agricultural product and the brand promotion efect paid by the e-commerce platform. Te frst decision-making model is a decentralized decision, for which, the farmer cooperative organization plays a leading role in the supply chain. Te second decision-making model is a centralized decision, for which, the farmer cooperative organization and the e-commerce platform form a consortium to lead the supply chain.

Model Symbol Description.
Te descriptions of symbols involved in the model of this research are shown in Table 2.

Research Assumptions.
Te establishment of the model in this study is based on the following assumptions: (1) All members in the agriculture supply chain system are risk-neutral. (2) All the members are rational and make their own decisions to maximize their own proft. (3) Using the function form used by Ghosh and Shah [51] and Zhao and Wei [52], the cost function of the e-commerce platform brand promotion is g(e) � 1/2ke 2 (k > 0). It indicates the cost paid by the e-commerce platform to increase sales by promoting the agricultural product brand, improving popularity and reputation, while k indicates the sensitivity coefcient of the e-commerce platform to the level of brand promotion eforts.
Tis study includes a farmer cooperative organization f and an e-commerce platform l. Based on Liu et al. [53] and Ghosh and Shah's linear demand functions [51], the market demand D is afected by the price p and the brand promotion efort e, which decreases with the price increases and increases with the brand promotion efort. Suppose the relationship among the three (D, p, and e) is Te e-commerce platform determines the selling price (sales price) of the agricultural product p and the brand promotion efort e. Te farmer cooperative organization determines the wholesale price W of the agricultural product, and its unit operating cost is C. According to the market demand, the e-commerce platform decides the order quantity assuming that there is no shortage, that is, q � D. In order to ensure that the decision variables p, W, and e are positive, the relationship between the parameters should be satisfed that 2ak − b 2 > 0 and D 0 − aC > 0. It is assumed that the operation cost of the ecommerce platform is not considered.
Te proft of the e-commerce platform, the proft of the farmer cooperative organization, and the total proft of the supply chain are expressed as follows.
Te market demand of the product is Te proft of the farmer cooperative organization is Te proft of the e-commerce platform is Te supply chain proft is

Decision Models of the Agricultural Products for E-Commerce Supply Chain Based on Revenue-Sharing Contract
Tere are two decision-making models for the supply chain: decentralized decision-making model and centralized decisionmaking model. For the decentralized decision-making model, the e-commerce platform decides the selling price and brand promotion efort, and the farmer cooperative organization decides the wholesale price. For the centralized decisionmaking model, the e-commerce platform and the farmer cooperative organization work together to decide the selling price and brand promotion efort.

Te Proft Model for the Decentralized Decision Making.
Due to the improvement of the bargaining power of farmers' cooperatives, farmers' cooperatives can play a leading role in the agricultural product supply chain, and e-commerce platforms are followers. Te farmer cooperative organization determines the wholesale price W. Te e-commerce platform determines its brand promotion efort e and selling price p of the agricultural product to meet the market demand. Under decentralized decision making, the e-commerce platform and the farmer cooperative organization make decisions based on maximizing their interests. First, the ecommerce platform determines the selling price of agricultural products and brand promotion eforts based on the information it possesses. Ten, farmers' cooperatives determine the wholesale price of agricultural products based on market information.
Tus, the objective functions of the e-commerce platform and the farmer cooperative organization are as follows: Te inverse solution method is used to solve the problem. Te optimal proft for various decision variables, e-commerce platforms, farmer cooperatives, and the overall system is

Te Proft Model for the Centralized Decision Making.
Centralized decision making is to regard the e-commerce platform and the farmer cooperative organization as a consortium, and the proft maximization decision is made from the whole consortium. Ten, Using the optimal decision principle, the supply chain decision variables and profts are

Comparative Analysis of the Two Decision-Making
Models. Te decision variables of the two decision-making models are shown in Table 3.
Comparing the two decision models in Table 3, we can draw the following conclusions:

The Design of Contract Coordination Mechanism
In this research setting, the overall proft of the supply chain under centralized decision making is signifcantly higher than that under decentralized decision making. Terefore, it is necessary to reach a particular contract agreement to ensure both parties have profts under centralized decision making, not less than the individual proft under decentralized decision making. Market base demand for the product a Te elasticity coefcient of market demand to price b Te elasticity coefcient of market demand to brand promotion efort p Selling price of the product α Proportion of the e-commerce platform sharing its own revenue e Brand promotion efort of the e-commerce platform C Unit planting cost of the agricultural product q Order quantity of e-commerce platform k Sensitivity coefcient of the brand promotion efort of the e-commerce platform W Unit wholesale price of the agricultural product β Te proportion of the brand promotion cost borne by the e-commerce platform Proof. Te purpose of contract coordination between the ecommerce platform and the farmer cooperative organization is to make the sum of the individual proft after the coordination achieve the efect of centralized decision making, and the individual proft is not lower than the individual proft in decentralized decision making. So, Ten, □

Supply Chain Coordination Based on Revenue Sharing + Cost Sharing + Wholesale Price Discount
Proposition . Assume that the e-commerce platform transfers part of the profts to farmers' cooperatives, and the proportion is 1 − α. Meanwhile, the farmers' cooperatives bear part of the cost of agricultural product promotion, and the proportion is β. When the relationship between variables meets three conditions, which are α � β, W � αC, and 1/4 ≤ α ≤ 1/2, the coordination of the supply chain can be realized based on revenue sharing + cost sharing + wholesale price discount, and the revenue can be maximized.
Proof. Assume that the e-commerce platform transfers part of the profts to farmers' cooperatives, and the proportion is 1 − α. Meanwhile, the farmers' cooperatives bear part of the cost of agricultural product promotion, and the proportion is β. Ten, the profts of e-commerce platforms and farmers' cooperatives are as follows. Te proft of the e-commerce platform is Te proft of the farmer cooperative organization is Te inverse solution method is used to solve the problem. Bring formula (1) into formula (12), and then

Complexity
Te corresponding Hessian matrix is H � −2aα bα bα −βk , and its frst-order and second-order master subdeterminants are |H 1 | � −2aα < 0 and |H 2 | � α(2akβ − b 2 α). When 2akβ − b 2 α > 0, the Hessian matrix is negative defnite, and there is a unique optimal solution (p, e) making the R l global maximal. Let zR l /zp � 0 and zR l /ze � 0; then, Combining the above two formulas, formula (16) is obtained: Simultaneously, p 3 � p 2 * and e 3 � e 2 * ; then, formula (17) is obtained: When α � β W � αC , the equation set of formula (17) is satisfed. Ten, For farmers' cooperatives, when achieving supply chain coordination through revenue-sharing contracts, the wholesale price of agricultural products is lower than the cost. At the same time, e-commerce platforms need to transfer most of the profts to farmers' cooperatives to achieve centralized pricing and sales efort levels under decision making. Tis requires a considerable understanding between both parties, which is difcult.

Supply Chain Coordination Based on Contracted
Wholesale Price. Te contract coordination principle based on the wholesale price of agricultural products is as follows. On the one hand, the farmer cooperative organization and the e-commerce platform reach a consensus on the selling price of the agricultural product and the brand promotion efort paid by the e-commerce platform through contract, to maximize the overall proft of the supply chain. On the other hand, both parties agree on the wholesale price of the agricultural product to ensure the individual proft is not lower than their respective profts under decentralized decision making. Te core of coordination is the scope of the wholesale price of the farmer cooperative organization. Te specifc coordination mechanism is as follows.

Proposition 3.
Under centralized decision making in setting the selling price and the brand promotion efort, when D 0 + 3aC/4a ≤ W ≤ 3D 0 + 5aC/8a, the supply chain can achieve proft coordination.
Under the contract coordination scheme, it is feasible to negotiate and determine the wholesale price of agricultural products to achieve coordination of the agricultural supply chain in reality [18].

Numerical Analysis
Tis study assumes that the e-commerce platform only sells one agricultural product. Referring to the practice of Yang et al. [54], the allocation of various parameters is as follows: D 0 � 200, a � 6, and b � 5. Te demand function of that agricultural product is D � 200 − 6p + 5e. k � 8, and the brand promotion efort, the cost paid by the e-commerce platform, is g(e) � 4e 2 . Let C � 10 $. Due to the balance of supply and demand, there will be q � D � 200 − 6p + 5e.

AnalysisBasedonRevenueSharing + CostSharing + Wholesale
Price Discount Coordination. When coordinating through revenue sharing + cost sharing + wholesale price, 1/4 ≤ α ≤ 1/2. Te wholesale price depends on the results of the negotiation and game. Te individual proft of each party under diferent wholesale prices is shown in Table 4 and Figure 1. Table 4 and Figure 1 show that the essence of coordination based on revenue sharing + cost sharing + wholesale price discount is the secondary distribution of revenue and cost. Te smaller the α, the greater the proportion of revenue shared by the e-commerce platform, the lower the proft of the e-commerce platform, and the higher the proft of the farmer cooperative organization, and vice versa. When the Complexity 7 proportion of profts transferred by e-commerce platforms decreases by 0.05, the profts of e-commerce platforms increase by 55. 19, and the profts of farmers' cooperatives decrease by 55.19.

Analysis Based on the Contracted Agricultural Wholesale
Price. According to the above example, according to formulas (7) and (8) Table 5 and Figure 2. Table 5 and Figure 2 show that the higher the wholesale price of the agricultural product, the higher the proft of the farmer cooperative organization and the lower the proft of the e-commerce platform. Te specifc pricing of the agricultural product depends on the relative negotiation advantages of the farmer cooperative organization. Te stronger the leading ability of the farmer cooperative organization is and the higher the wholesale price of the agricultural product is, the more proft the farmer cooperative organization will make. When the wholesale price of agricultural products increases by 0.5, the profts of farmers' cooperatives increase by 47.33, and the profts of e-commerce platforms decrease by 47.33.

Conclusions.
Under the background of rural revitalization, in order to reduce the mismatch between the supply and demand of online shopping agricultural products and promote the collaborative cooperation between ecommerce platforms and farmer cooperative organizations, this study shows how to achieve win-win cooperation between e-commerce platforms and farmer cooperative organizations. Taking an agricultural product as an example, this study compares the results of decentralized decisionmaking model and centralized decision-making models, for which the farmer cooperative organization is the prominent leader, and the e-commerce platform is the follower. Trough comparative analysis, it fnds that when the ecommerce platform and the farmer cooperative organization make a centralized decision, the product sales are twice than decentralized decision, and the overall proft of the supply chain is 4/3 times higher than the decentralized decision. Terefore, achieving the efect of centralized decision making through cooperation is the best decision plan for both parties. Tis paper provides two coordination schemes. First, the "revenue sharing + cost sharing + wholesale price discount" coordination plan was adopted. Second, the two sides agreed on the contract coordination plan for the wholesale price of agricultural products.
Tis research has been verifed by case analysis. Te decision of cooperation contract scheme between e-commerce platform and farmers' cooperative depends on the comparative advantages of e-commerce platform and farmers' cooperative in negotiation and game. Tis provides a particular theoretical reference for the selection of cooperation schemes between the two parties in practice and also provides a theoretical basis for the follow-up research on the supply chain contract coordination of fresh agricultural products.

Agricultural Product Supply Chain Coordination.
Previous studies on supply chain coordination of agricultural products mainly focused on consumer demand and agricultural product logistics, and few studies paid attention to agricultural product brand promotion eforts paid by the e-commerce platform. In addition, most research on supply chain coordination is dominated by e-commerce platforms  8 Complexity and rarely from the perspective of farmer cooperative organizations. Tis study stands on the perspective of farmer cooperative organizations and analyzes the impact of the agricultural product brand promotion efort on sales volume and profts among supply chain members. Te results of this study indicate that the sales volume of agricultural products is afected by brand promotion eforts, which is consistent with the reality that consumers' online purchase of agricultural products is often afected by agricultural product brands promoted on online platforms.

Contract Coordination Mechanism.
Previous studies on the contract coordination mechanism of raw agricultural products supply chains mainly focused on consumer demand, the freshness of agricultural products, and the logistics service level. Tis study focuses on the brand promotion efort of agricultural products. Previous contract coordination strategies mainly focused on revenue-sharing and cost-sharing principles or repurchase contracts. Tis study focuses on the contract coordination of agricultural products' online shopping supply chain composed of farmer cooperatives and e-commerce platforms and designs two contract coordination schemes. One is a coordination strategy based on revenue-sharing principle, and the other is a wholesale price coordination strategy for agricultural products. Tis study shows how these two coordination strategies can achieve win-win cooperation in the supply chain.
Tis study contributes to our knowledge in understanding (1) how the development of e-commerce of agricultural products is afected by the marketing strength of agricultural product brands by e-commerce platforms and (2) how wholesale price setting afects the supply chain coordination based on the principle of revenue sharing and cost sharing.

Practical Implications.
From the example analysis, when an e-commerce platform cooperates with a farmer cooperative organization for centralized decision making, a slight reduction in selling price can double the sales volume of the agricultural product. If the level of brand promotion efort is doubled, the overall proft of the supply chain can be increased by 33.33%. Terefore, e-commerce platforms and farmer cooperative organizations should establish alliances to expand sales by reducing the selling price of agricultural products and increasing brand promotion eforts to maximize the supply chains' overall profts. Internally, through coordination methods such as income-sharing contracts and adjusting the wholesale price of agricultural products, a win-win situation can be achieved in which the individual proft of each party can be increased. Some specifc recommendations are provided as follows.

Strengthening the Investment in Brand Promotion.
Te online channel sales of grocery products are not limited by time, place, and region. However, agricultural products are often limited by season or timeliness. Terefore, the promotion of agricultural products is essential to push the sales volume quickly because the online sales of agricultural products are largely afected by brand promotion. Te ecommerce platforms should increase investment in the brand promotion of agricultural products, establish a particular column for sales of agricultural products, and carry out extensive publicity. Te e-commerce platforms can use short videos to promote products and hire celebrities to show how to consume the products.

Strengthening the Contract Management.
Tis study shows that setting the wholesale prices of agricultural products is essential under the centralized decision-making method. Te adjustment of the wholesale prices depends on the specifc cooperation schemes between e-commerce platforms and farmer cooperative organizations. It is necessary to strengthen contract management by constraining the behavior of both parties through contracts, increasing the punishment of breach costs, and achieving the stability and sustainability of contracts. Te farmers can increase their income, get rich, and promote the release of rural domestic demand potential only in this way. Furthermore, it has important strategic signifcance for promoting rural revitalization.

Research Limitations and Future Research Directions.
Tis study has the following limitations. Te demand function for the agricultural product was considered to be a simple linear relationship with price and brand promotion efort. It did not consider other factors into account. Further studies are recommended to add other factors such as logistics services. Te demand function for agricultural products may have very complex nonlinear relationships. In contract coordination, it is not limited to the coordination of the wholesale price. Researchers can consider various contract coordination schemes.

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that there are no conficts of interest regarding the publication of this paper.