Green and Efficient Technology Investment Strategies for a Contract Farming Supply Chain Under the CVaR Criterion

Abstract

Synergizing soil quality improvement and greening for increased yields are essential to ensuring grain security and developing sustainable agriculture, which has become a key issue in agricultural cultivation. This study considers a contract farming supply chain composed of a risk-averse farmer and a risk-neutral firm making green and efficient technology (GET) investments, which refers to the use of technology monitoring to achieve fertilizer reduction and yield increases with yield uncertainty. Based on the CvaR (Conditional value at Risk) criterion, the Stackelberg game method is applied to construct a two-level supply chain model and analyze different cooperation mechanisms. The results show that when the wholesale price is moderate, both sides will choose the cooperative mechanism of cost sharing to invest in technology; the uncertainty of yield and the degree of risk aversion have a negative impact on the agricultural inputs and GET investment, and when yield fluctuates greatly, the farmer invests in GET to make higher utility but lowers profits for the firm and supply chain. This study provides a theoretical basis for GET investment decisions in agricultural supply chains under yield uncertainty and has important practical value for promoting sustainable agricultural development and optimizing supply chain cooperation mechanisms.

1. Introduction

Amid the dual challenges of global population growth and intensifying resource and environmental constraints [1], sustainable agricultural development has emerged as a critical priority for policymakers and researchers. In conventional farming systems, the absence of scientific guidance and limited access to agricultural knowledge often lead to the excessive and indiscriminate use of fertilizers to boost yields [2]. This practice severely degrades soil health and contributes to environmental pollution [3]. Consequently, transitioning to sustainable agricultural practices that enhance soil quality has become an urgent imperative.

Despite being a major agricultural producer, China continues to face a pronounced imbalance between food supply and population demands. Empirical studies indicate that the nation’s crop yields still possess a 50–60% untapped potential. In terms of fertilizer use efficiency, there is still a gap of 10–20% compared with developed agricultural countries. This shows that China’s agricultural production in resource utilization efficiency and yield enhancement still has a large space for improvement [4]. Consequently, the development of innovative green technologies for high-yield and high-efficiency farming has become imperative for achieving sustainable agricultural growth.

In recent years, China has set out the strategic goal of “accelerating the overall green transformation of agricultural development” and issued the Action Plan for Fertilizer Reduction by 2025, which emphasizes the realization of sustainable agricultural development through measures such as fertilizer reduction, efficiency enhancement, and soil protection [5]. Practices like straw returning [6] and organic fertilizer application [7] can enrich soil nutrients, thereby improving soil quality and stabilizing crop yields. Precise fertilizer application and efficiency improvement can be achieved by real-time monitoring of soil dynamic parameters through big data technology [8]. The green and efficient technologies (GET) application in this paper is specifically represented by monitoring the quality of arable land, crop growth, and water and fertilizer environment through digitalization and IoT devices, and then formulating fertilizer formulation information precisely. Through scientific and precise fertilizer application, chemical fertilizer reduction and yield increase can be achieved. However, despite the potential of GET to enhance productivity, their widespread adoption remains challenging for resource-constrained smallholder farmers due to financial and technical barriers.

Empirical evidence in agricultural production demonstrates that environmental conditions outside the control of the farmer significantly influence crop growth, resulting in substantial yield uncertainty [9]. Prolonged reliance on unsustainable fertilization practices exacerbates soil degradation, leading to declining fertility and yields [10], which in turn heightens farmers’ risk aversion toward new technologies. Uncertainty in yield outcomes tends to promote risk-averse behaviors, especially for farmers with insufficient capital and weak risk tolerance [11]. Wong and Kahsay confirmed through random field trials that risk aversion exists among farmer groups [12]. Due to the characteristics of green production technologies, such as high inputs, long payback periods, and complex operations, their promotion and adoption rates are low [13]. Szvetlana et al. studied the transition from traditional agriculture to organic agriculture and found that many farmers are unwilling to take risks and need policy incentives to achieve a complete transition [14]. Compared to farmers, enterprises have more capital and professional personnel, are generally risk-neutral, and may even subsidize farmers [15]. Improvement in crop yields can increase firms’ profits [16]. To encourage farmers to increase output and technological innovation, some firms will choose to participate in new technology investments together, such as designing price agreements and incentive contracts [17]. Previous studies have focused on the improvement of product greenness, with less research on green and efficient production methods. As for fertilizer application, it is mostly based on quantitative analysis. Given that supply chain decisions are influenced by risk preferences [18], a critical research gap persists: how to effectively incentivize agricultural stakeholders to invest in GET to ensure sustainable growth.

Yield uncertainty and farmers’ risk preferences significantly influence GET adoption. In previous literature, there have been three widely used risk measurement criteria: mean variance [19], value-at-risk (VaR) [20], and conditional value-at-risk (CVaR) [21]. The mean-variance method is widely used as a risk measurement criterion in finance [22], but it is insufficient. The VaR allows decision-makers to specify the confidence level for achieving a certain level of wealth, but it still has limitations. The CVaR criterion measures the average value of profits below the $\eta$ percentile and is easy to calculate. CVaR ignores the portion of profits exceeding the percentile level and primarily considers the average profits below the percentile, which is precisely what decision-makers are most concerned about. Therefore, this study uses the CVaR criterion to characterize risk.

Based on game theory, this study discusses the investment decision problem of GET in the agricultural supply chain in “firm + farmer” contract farming. The GET investment decisions and cooperation mechanism between farmers and firms in production are analyzed under the CvaR criterion, taking into account the risk aversion attitude of the farmer under an uncertain yield. The study aims to answer the following questions:

• When will the risk-averse farmer adopt GET for agricultural production?
• Which investment strategies will the firm and farmer choose for the adoption of GET, and what cooperative mechanisms can facilitate implementation?
• How do the wholesale prices of contract farming, the degree of farmers’ risk aversion, and the uncertainty of yield affect the decisions and profits of supply chain members?

The remainder of this study is organized as follows: Section 2 reviews the relevant literature and identifies key research gaps. Section 3 formalizes the problem statement and specifies modeling assumptions. Section 4 analyzes and solves the models. Section 5 comparatively analyzes the results of the different models. Section 6 performs numerical simulations to validate the model’s robustness. Finally, Section 7 summarizes key findings, discusses managerial implications, and suggests directions for future research.

2. Literature Review

This study is closely related to three aspects of literature: technology applications for sustainable agricultural development, contract farming, and risk preference.

2.1. Technology Applications for Sustainable Agricultural Development

In recent years, with the intensive application of digital technology in agriculture, more and more research has focused on how to improve the efficiency and yield of agricultural production by methods of informationization and intelligence. Tang et al. [23] emphasized that agricultural information could make production decisions more scientific and precise, thus increasing farmers’ profits. Dusadeerungsikul et al. [24] investigated the monitoring of crop diseases and pests by an agricultural robotic system. Gentilhomme et al. [25] found that image processing tools can improve precision in areas such as crop maintenance and pruning. The use of digital technology and equipment to obtain more information about agriculture is also important for yield improvement. Patil et al. [26] analyzed digital tools to monitor crop health for predictive yield analysis. Cisdeli et al. [27] developed a yield database to provide farmers with important information for production decision-making. Niu et al. [28] explored how different contracts can affect decision making and profitability in cases where the application of new planting techniques has improved yields. Masunga et al. [29] focused on the relationship between soil fertility and fertilizer use efficiency and used numerical tools to develop rational fertilization recommendations to improve crop yields.

In agricultural production, crop yield is a key indicator of economic and sustainable development, while proper fertilization practices are an important factor in yield and soil health. The quality of crops has been affected by crude traditional fertilization practices, which have led to soil degradation and decreased soil fertility [30]. Therefore, scholars have paid attention to the improvement of fertilizer application to repair soil fertility and increase crop yields. Zambrano et al. [31] showed that scientific and accurate fertilization can reduce the yield instability caused by traditional fertilization through the analysis of soil nutrients. Liu et al. [24] experimentally verified that organic fertilizers reduce pollution, improve soil quality, and increase yields relative to chemical fertilizers. It can be seen that crop yield is not only affected by the weather but also by the use of fertilizers [15], and the full use of production data information can help growers to decide on the use of fertilizer strategies. Guo et al. [32] demonstrated that the use of agricultural production information for soil tailored to the appropriate fertilizers can achieve yield increases and reduce soil damage [33].

2.2. Contract Farming

Contract farming tends to make the revenue and risk of farmers and firms more closely linked through the establishment of a reasonable cooperation mechanism between them. Cai et al. [34] analyzed the impacts of contracts between raw material producers and farmers on supply chain decision-making and profits by exploring the effects of cooperation mechanisms such as full purchase and sales revenue sharing. Tang et al. [35] proposed a partial guaranteed price contract to analyze how to better achieve mutual benefits between farmers and firms. Nematollahi et al. [36] compared three contract farming mechanisms, namely no contract, penalty-based, and incentive-based, and found that incentive-based cooperative contracts are more likely to improve supply chain profits. Li et al. [37] considered price protection mechanisms and revenue sharing mechanisms for agricultural contracts based on weather risk, and explored different cooperative mechanisms for agricultural investment, farmers’ resilience to risk, and profit sharing among members within the supply chain.

Contract farming has emerged as a promising approach to promote green and sustainable agricultural development. Liu et al. [32] examined how dynamic adjustments to revenue-cost-sharing ratios influence product environmental performance. Complementing this, Cui et al. [33] developed a theoretical model for green agricultural supply chains involving farmers and retailers, demonstrating that revenue-sharing contracts can effectively coordinate supply chain activities. Wang et al. [34] further extended this research by incorporating farmers’ risk aversion into green investment decisions, showing that revenue-sharing contracts not only improve supply chain coordination but also enhance overall profitability for all participants. Cao et al. [38] argued that the level of green investment should be decided by both parties of the decision-making process and coordinated the policy of the level of green investment by designing a cost-sharing contract and a repurchase contract. Liu et al. [36] developed a dual-contract mechanism comprising cost-sharing and revenue-sharing agreements to coordinate green investment levels in agricultural supply chains, leveraging blockchain and big data technologies to enhance transparency and data-driven decision-making.

2.3. Risk Preference

Studies addressing supply chain risk preference often use mean-variance [39], value-at-risk (VaR) [20], mental accounts [40], and conditional value-at-risk (CVaR) [21] to portray risk. In this study, the CVaR criterion is used to portray a farmer’s risk preference. Nan et al. [41] used CVaR to assess the retailer’s risk aversion and applied option contracts to facilitate supply chain coordination. Huang et al. [42] developed a theoretical framework to analyze supply chain coordination and risk-sharing between retailers and risk-averse manufacturers, demonstrating that CVaR-based contracts improve supply chain efficiency. Liu et al. [43] studied the supply chain composed of suppliers and risk-averse retailers and considered the dominant position of suppliers and retailers in the supply chain. Deng and Liu [44] investigated the effects of risk-averse decision-making on low-carbon supply chain operations, revealing that a strong aversion to risk can negatively impact supply chain profitability and carbon reduction outcomes. The majority of existing literature predominantly focuses on decision-makers’ risk aversion behaviors arising from demand uncertainty.

In our model, the farmer exhibits risk-averse behavior due to yield uncertainty. Peng and Pang [45] used CvaR to portray a risk-averse farmer who faced stochastic output and analyzed the impact of risk aversion on subsidy decisions. Liao et al. [46] considered uncertain yield and demand, and considered both the farmer’s and retailer’s risk aversion under the CvaR criterion. Focusing on agricultural supply chains with uncertain yield, Golmohammadi and Hassin [47] examined the mechanism by which the degree of risk aversion affects the dynamics of agricultural yield and price. Ye et al. [9] used the CvaR criterion to quantitatively model suppliers’ risk preference and explored the mechanism for supply chain risk sharing. Xing et al. [48] found that higher levels of risk aversion lead to lower profits and reduced production. Therefore, we construct a secondary supply chain comprising a risk-averse farmer and a risk-neutral firm under the CvaR criterion. This framework examines how risk preferences and yield uncertainty jointly influence the achievement of sustainable agricultural operations in GET investments.

In summary, while previous studies have focused on digitalization investments or investments in the greenness of agricultural products, limited attention has been paid to the impact of GET investment in cropping methods on yield increases. Under the requirements of green transformation and sustainable development of agriculture, the impact of GET investment on environmental protection and sustainable yield increase is particularly important. Therefore, unlike traditional agricultural supply chains that focus on pricing decisions, this study focuses on the farmer’s and firm’s decisions on the level of GET investment in agricultural production and production inputs in the context of the farmer’s risk aversion and uncertain yield, and explores the different mechanisms for bearing the costs of GET investment, and analyzes the impacts of the degree of risk aversion, uncertain yield, and the wholesale price on the level of GET and the profits of the supply chain.

3. Problem Description and Notations

This study examines an agricultural supply chain comprising a risk-averse farmer and a risk-neutral firm. In this framework, the farmer undertakes agricultural production and cultivation, while the firm procures the produce for subsequent commercialization. The agricultural production is faced with the problem of choosing an investment strategy of whether or not to make improvements in fertilization methods and applications. In the face of yield risk and soil quality decline pressure, the farmer needs to consider whether to make a GET investment. In order to safeguard yield and meet market demand, the firm expects the farmer to adopt green and efficient fertilizer application methods for planting and also to participate in the GET investment.

Therefore, both the farmer and the firm are faced with two investment strategies: not participating in GET investment (N) or participating in GET investment (Y). Let $S_{ij}\left\{S_{NN},S_{YN},S_{NY},S_{YY}\right\}(i,j=N,Y)$ denote the strategy choice. Where the $S_{NN}$ model indicates that both the farmer and the firm do not engage in GET investment, and the farmer only decides the planned production quantity $I$. In the $S_{YN}$ model, to grow agricultural crops, only the farmer will participate in the GET investment, and they are solely responsible for paying the investment costs. The farmer determines the level of GET investment. In the $S_{NY}$ model, only the firm will engage in GET investment, and the level of GET investment is decided by the firm. The firm will decide on the level of GET investment by providing the farmer with equipment and technology that adopts organic fertilizers and efficient fertilizer application equipment and technology in the planting process and later purchasing the agricultural products at a lower wholesale price. In the $S_{YY}$ model, both the farmer and the firm make GET investments, and the investment cost is shared by them. The level of GET investment is determined by the firm with strong capital.

The farmer and the firm sign a purchase contract before the growing season: before planting, the firm decides on the wholesale price $w$ of agricultural products; in the production stage, the farmer considers maximizing their income and decides on the planned production quantity $I$ in that season; and in the sales stage, considering the risk-averse feature of the farmer, the firm with strong risk-resistant ability will purchase all the actual yield of the farmer in that season with the wholesale price $w$ of the contract and sell it at retail price $p$, with $p>w>0$ [49]. Referring to Niu’s study [28], this paper assumes that the retail price is exogenous. The firm has rich experience and enough market potential to be able to clear all the products without taking into account the shortage cost and the residual value of farm products.

There will be some gap between the planned quantity and the actual yield of the farmer, and the yield is uncertain. With reference to the relevant research literature [50], the output random factor $\mu$ is a random variable with a distribution function $G\left(\cdot \right)$, a probability density function $g\left(\cdot \right)$, mean value $\overline{\mu }$, and standard deviation $\sigma$. Assuming that the farmer’s planned production quantity is $I$, the farmer’s actual yield is $\mathsf{ɤ}=\mu I$.

There are diseconomies of scale in agricultural production due to the constraints on the capacity of the farmer [28]. When the quantity of production exceeds a certain level, there will be an increasing marginal cost. Our analysis is based on the assumption that the production cost function of the farmer is $C(I)=c_{1}I+c_2{I}^2$, $c_1$ is the production cost per unit of agricultural products such as seeds and feeds, and $c_2$ denotes the cost coefficient of the farmer’s effort in production [9,51].

In this study, it is assumed that $g$ is the level of GET investment, which refers to the level of application of new products, technologies, and equipment in fertilizers, integrated innovation, and promotion in the cultivation process of the farmer. Referring to Shi’s [52] study on green chemical reduction technology inputs, the cost of GET investment is assumed to be ${\displaystyle \frac{1}{2}}k{g}^2$, where $k$ is the cost coefficient of GET investment. Based on practical production experience and actual data, the promotion of green and efficient wheat production technologies in Jiangsu, Henan provinces have resulted in annual yield increases of 15% and 3%, respectively, through the use of formula fertilization and precision pesticide application [53]. In a certain area of Hebei Province, the adoption of green and efficient water and fertilizer management technologies for pear cultivation has increased yields from 5.3% to 13.8% and reduced fertilizer use by 37.9% [54]. This demonstrates that efforts to reduce fertilizer use while increasing efficiency can enhance crop yields. Therefore, we assume that $\alpha$ ($\alpha >0$) is expressed as the sensitivity coefficient of GET investment to yield, the actual yield of agricultural products is $\left(\mu +\alpha g\right)I$ [55].

Building upon the previous assumption that farmers are risk-averse, this study uses conditional value-at-risk (CVaR) to measure the degree of risk aversion of farmers. CvaR measures the average value of profits below the interquartile level [56]. According to the generalized definition of CvaR, the objective function of a farmer with the risk-averse characteristic can be expressed as follows: $CVa{R}_{\eta }\left({\pi }_F(I)\right)={\max }_{v\in R}\left\{v+{\displaystyle \frac{1}{\eta }}E[min({\pi }_F(I)-v,0)]\right\}$ where ${\pi }_F$ is the farmer’s profit function, and $\eta$ is the risk-measure factor with $\eta \subset \left(0,1\right]$. The smaller the $\eta$ is, the more risk-averse the farmer is, and when $\eta =1$ indicates that the farmer is risk-neutral.

In this study, the farmer and the firm play a Stackelberg game in which the risk-neutral firm is the leader, and the farmer is the follower. The supply chain members make decisions after the firm gives the contracted purchase price $w$. The farmer’s goal is to maximize $E{U}_F$, and the firm’s goal is to maximize $E{\pi }_R$. The key parameters and variables are described in

Table 1. Notations and meaning.

Notations	Meaning
$I$	The planned production quantity of the farmer
$g$	The green and efficient technology (GET) investment level
$w$	Wholesale price
$p$	The unit retail price
$r$	The marginal profit of the firm, $r=p-w$
$\mu$	A random output factor with support on $[A,B]$, mean value $\overline{\mu }$, probability density function (PDF) $g\left(\cdot \right)$ and cumulative distribution function (CDF) $G\left(\cdot \right)$
$\alpha$	The sensitivity coefficient of the GET investment to yield, $\alpha >0$
$c_1$	The production cost per unit of agricultural products, $c_1>0$
$c_2$	The cost coefficient of the farmer’s effort, $c_2>0$
$k$	The cost coefficient of digital investment, $k>0$
$\lambda$	Proportion of the GET investment cost shared by the firm, $0<\lambda \le 1$
$\eta$	The degree of the farmer’s risk aversion, $0<\eta \le 1$
$v$	The possible upper limit of the farmer’s profit under a certain η
${\pi }_F^{ij}$, ${\pi }_R^{ij}$	The profit of the farmer and the firm
$E{U}_F^{ij}$, $E{U}_R^{ij}$	The farmer’s and the firm’s expected utility, $E{U}_R^{ij}=E{\pi }_R^{ij}$ [57]
$E{U}_{SC}^{ij}$	The supply chain’s expected utility in different models, $E{U}_{SC}^{ij}$= $E{U}_F^{ij}+E{U}_R^{ij}$ [58]

. The game sequence is shown in Figure 1.

4. Model and Results

4.1. Case $S_{NN}$: Neither Invests

In this model, neither the farmer nor the firm makes GET investments. The objective functions of the farmer and the firm are, respectively:

$${\pi }_F^{NN}=w\mu I_1-c_1{I}_1-c_2{I}_1^2$$

(1)

The first item is the income of the farmer from the agricultural products being purchased. The second and third items are the cost of production for the farmer, including the basic cost of cultivation and the cost of effort inputs.

$${\pi }_R^{NN}=\left(p-w\right)\mu I_1$$

(2)

Equation (2) represents the profit made from the sale of agricultural products.

According to the generalized definition of $CVaR$, the decision objective function of the farmer with the risk-averse characteristic can be described as follows:

$$CVa{R}_{\eta }\left({\pi }_F^{NN}(I_1)\right)={\max }_{v\in R}\left\{v_1+{\displaystyle \frac{1}{\eta }}E[min({\pi }_F^{NN}(I_1)-v_1,0)]\right\}=v_1-{\displaystyle \frac{1}{\eta }}E{[v_2-{\pi }_F^{NN}(I_1)]}^{+}$$

(3)

$$E{U}_F^{NN}=v_1-{\displaystyle \frac{1}{\eta }}{\displaystyle {\int }_A^B{\left(v_1-w{I}_1\mu +c_1{I}_1+c_2{I}_1^2\right)}^{+}}dG(\mu )$$

(4)

where ${[z]}^{+}=$ max $[z,0]$.

From Equation (4), we obtain the optimal $v_1^{\ast }=w{I}_1{G}^{-1}(\eta )-c_1{I}_1-c_2{I}_1^2$ under the $S_{NN}$, which is substituted into the farmer’s objective function to obtain the following equation:

$$E{U}_F^{NN}={\displaystyle \frac{w{I}_1}{\eta }}{\displaystyle {\int }_A^{G^{-1}(\eta )}\mu }dG(\mu )-c_1{I}_1-c_2{c}_2{I}_1^2$$

(5)

The optimal production quantity that maximizes the risk-averse farmer’s utility above is given in Theorem 1.

Theorem 1. 

The risk-averse farmer’s optimal planned production quantity under the CvaR criterion is

$$I_1^{\ast }={\displaystyle \frac{w\tau -c_1}{2c_2}}$$

(6)

where $\tau ={\displaystyle \frac{1}{\eta }}{\displaystyle {\int }_A^{G^{-1}\left(\eta \right)}\mu dG(\mu )}$.

All proofs are provided in Appendix A.

By substituting Equation (6) into Equations (2) and (5), we get the optimal expected utility of the farmer and the optimal expected profit of the firm as follows:

$$E{U_F^{NN}}^{\ast }={\displaystyle \frac{{\left(w\tau -c_1\right)}^2}{4c_2}}$$

(7)

$$E{{\pi }_R^{NN}}^{\ast }={\displaystyle \frac{\mu r\left(w\tau -c_1\right)}{2c_2}}$$

(8)

Proposition 1. 

• (1) ${\displaystyle \frac{\partial I_1^{\ast }}{\partial w}}>0,{\displaystyle \frac{\partial E{U_F^{NN}}^{\ast }}{\partial w}}>0$; if $w<{\displaystyle \frac{p\tau +c_1}{2\tau }}$, ${\displaystyle \frac{\partial E{{\pi }_R^{NN}}^{\ast }}{\partial w}}>0$, otherwise, ${\displaystyle \frac{\partial E{{\pi }_R^{NN}}^{\ast }}{\partial w}}<0$; if $w<{\displaystyle \frac{p-c_1}{2-\tau }}$, ${\displaystyle \frac{\partial E{U_{SC}^{NN}}^{\ast }}{\partial w}}>0$, otherwise, ${\displaystyle \frac{\partial E{U_{SC}^{NN}}^{\ast }}{\partial w}}<0$;
• (2) ${\displaystyle \frac{\partial I_1^{\ast }}{\partial c_1}}<0,{\displaystyle \frac{\partial E{U_F^{NN}}^{\ast }}{\partial c_1}}<0$, ${\displaystyle \frac{\partial E{{\pi }_R^{NN}}^{\ast }}{\partial c_1}}<0$, ${\displaystyle \frac{\partial I_1^{\ast }}{\partial c_2}}<0,{\displaystyle \frac{\partial E{U_F^{NN}}^{\ast }}{\partial c_2}}<0$, ${\displaystyle \frac{\partial E{{\pi }_R^{NN}}^{\ast }}{\partial c_2}}<0$;

Proposition 1(1) shows that under the neither invests case, as the firm’s wholesale price increases, the farmer’s incentive to produce improves. Both the farmer’s optimal planned production quantity and utility will increase. However, for the firm, the firm’s optimal expected profit will increase with the increase in wholesale price only if the wholesale price satisfies the condition $w<{\displaystyle \frac{p\tau +c_1}{2\tau }}$. Beyond this threshold, the firm’s profit will decline. This is caused by the fact that the revenue from production is smaller than the increased acquisition cost. Proposition 1(2) demonstrates that farmers’ optimal output, utility, and the firm’s expected profit are decreasing in the unit cost of production $c_1$ and the coefficient of the cost of production effort $c_2$. As the cost of production increases, it reduces farmers’ production inputs and yields decline, which in turn leads to a decline in returns for each principal. GET investment plays an important role in reducing the cost of fertilizers and medicines, as well as increasing yield and reducing fluctuations.

4.2. Case $S_{YN}$: The Farmer Invests in GET

Under the $S_{YN}$, only farmers will invest in GET to produce agricultural products. The farmer alone bears the expense of the GET investment, and the farmer determines the level of GET. The objective functions of the farmer and the firm are, respectively:

$${\pi }_F^{YN}=w(\mu +\alpha g_2)I_2-c_1{I}_2-c_2{I}_2^2-{\displaystyle \frac{1}{2}}k{g}_2^2=w{I}_2\mu +w\alpha g_2{I}_2-c_1{I}_2-c_2{I}_2^2-{\displaystyle \frac{1}{2}}k{g}_2^2$$

(9)

The first term is the farmer’s income from increased yields. The second and third terms are the farmer’s cost of production. The fourth term indicates the cost of investment in GET.

$${\pi }_R^{YN}=(p-w)(\mu +\alpha g_2)I_2$$

(10)

Equation (10) represents the firm’s sales profit after the yield increase.

The utility function of the risk-averse farmer is

$$E{U}_F^{YN}=v_2-{\displaystyle \frac{1}{\eta }}{\displaystyle {\int }_A^B{\left(v_2-w\alpha g_2{I}_2-w{I}_2\mu +c_1{I}_2+c_2{I}_2^2+\frac{1}{2}k{g}_2^2\right)}^{+}}dG(\mu )$$

(11)

From Equation (11), we obtain the optimal $v_2^{\ast }=w{I}_2{G}^{-1}(\eta )+w\alpha g_2{I}_2-c_1{I}_2-c{I}_2^2-{\displaystyle \frac{1}{2}}k{g}_2^2$ under the $S_{YN}$, which is substituted into the farmer’s objective function to obtain the following equation:

$$E{U_F^{YN}}^{\ast }={\displaystyle \frac{w{I}_2}{\eta }}{\displaystyle {\int }_A^{G^{-1}(\eta )}\mu }dG(\mu )+w\alpha g_2{I}_2-c_1{I}_2-c_2{I}_2^2-{\displaystyle \frac{1}{2}}k{g}_2^2$$

(12)

Theorem 2. 

If $k>{\displaystyle \frac{w^2{\alpha }^2}{2c_2}}$, the optimal planned production quantity and GET investment level are

$$I_2^{\ast }={\displaystyle \frac{k\left(w\tau -c_1\right)}{2c_{2}k-{\alpha }^2{w}^2}}$$

(13)

$$g_2^{\ast }={\displaystyle \frac{w\alpha (w\tau -c_1)}{2c_{2}k-{\alpha }^2{w}^2}}$$

(14)

By substituting Equations (13) and (14) into Equations (10) and (12), we get the optimal expected utility of the farmer, and the optimal expected profit of the firm as follows:

$$E{U_F^{YN}}^{\ast }=CVa{R}_{\eta }\left({\pi }_F^{YN}(I_2^{\ast },g_2^{\ast })\right)={\displaystyle \frac{k{\left(-w\tau +c_1\right)}^2}{2\left(2c_{2}k-w^2{\alpha }^2\right)}}$$

(15)

$$E{{\pi }_R^{YN}}^{\ast }={\displaystyle \frac{rk\left({\alpha }^2{w}^2(\mu -\tau )+{\alpha }^2{c}_{1}w-2c_{2}k\mu \right)(-w\tau +c_1)}{{\left(2c_{2}k-w^2{\alpha }^2\right)}^2}}$$

(16)

Proposition 2. 

• (1) ${\displaystyle \frac{\partial I_2^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial g_2^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial E{U_F^{YN}}^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial E{{\pi }_R^{YN}}^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial E{U_{SC}^{YN}}^{\ast }}{\partial \alpha }}>0;$
• (2) ${\displaystyle \frac{\partial I_2^{\ast }}{\partial w}}>0,{\displaystyle \frac{\partial g_2^{\ast }}{\partial w}}>0,{\displaystyle \frac{\partial E{U_F^{YN}}^{\ast }}{\partial w}}>0;$
• (3) ${\displaystyle \frac{\partial I_2^{\ast }}{\partial c_1}}<0,{\displaystyle \frac{\partial g_2^{\ast }}{\partial c_1}}<0,{\displaystyle \frac{\partial E{U_F^{YN}}^{\ast }}{\partial c_1}}<0$, ${\displaystyle \frac{\partial E{{\pi }_R^{YN}}^{\ast }}{\partial c_1}}<0$, ${\displaystyle \frac{\partial I_2^{\ast }}{\partial c_2}}<0,{\displaystyle \frac{\partial g_2^{\ast }}{\partial c_2}}<0{\displaystyle \frac{\partial E{U_F^{YN}}^{\ast }}{\partial c_2}}<0$, ${\displaystyle \frac{\partial E{{\pi }_R^{YN}}^{\ast }}{\partial c_2}}<0$;

Proposition 2(1) shows that when the farmer invests in GET, as the sensitivity coefficient to yield increases, the farmer’s optimal planned production yield, the level of GET investment, the farmer’s optimal expected utility, and the firm’s expected profit all increase. This suggests that the greater the positive impact of yield from the GET application, the more the farmer is incentivized to produce. Proposition 2(2) shows that in contract farming, the increase in the wholesale price of agricultural products can effectively promote the adoption of GET by the farmer, which in turn expands the production scale and increases the level of their expected profit. Proposition 2(3) shows that farmers’ planned production yield, the farmer’s utility, and the firm’s profit are similar to the neither invests case, and the level of GET investment also decreases with the increase in $c_1$ and $c_2$. This implies that higher daily production costs negatively impact the farmer’s investment in GET. The main reason may be the lack of capital of the farmer.

4.3. Case $S_{NY}$: The Firm Invests in GET

Under the $S_{NY}$, only the firm makes the GET adoption investment, and the level of GET adoption is decided by the firm. The firm provides the farmer with some of the financial and technical support needed to adopt GET cultivation and later purchase at a lower wholesale price. The objective functions of the farmer and the firm are, respectively:

$${\pi }_F^{NY}=w(\mu +\alpha g_3)I_3-c_1{I}_3-c_2{I}_3^2=w{I}_3\mu +w\alpha g_3{I}_3-c_1{I}_3-c_2{I}_3^2$$

(17)

The first term represents the income of the farmer after the increase in yield, while the second and third terms represent the cost of production for the farmer.

$${\pi }_R^{NY}=(p-w)(\mu +\alpha g_3)I_3-{\displaystyle \frac{1}{2}}k{g}_3^2$$

(18)

The first term represents the firm’s profit from sales, and the second term is the cost of the firm’s GET investment.

The utility function of the risk-averse farmer is

$$E{U}_F^{NY}=v_3-{\displaystyle \frac{1}{\eta }}{\displaystyle {\int }_A^B{\left(v_3-w\alpha g_3{I}_3-w{I}_3\mu +c_1{I}_3+c_2{I}_3^2\right)}^{+}}dG(\mu )$$

(19)

From Equation (19), we obtain the optimal $v_3^{\ast }=w{I}_3{G}^{-1}(\eta )+w\alpha g_3{I}_3-c_1{I}_3-c{I}_3^2$ under the $S_{NY}$, which is substituted into the farmer’s objective function to obtain the following equation:

$$E{U_F^{NY}}^{\ast }={\displaystyle \frac{w{I}_3}{\eta }}{\displaystyle {\int }_A^{G^{-1}(\eta )}\mu }dG(\mu )+w\alpha g_3{I}_3-c_1{I}_3-c_2{I}_3^2$$

(20)

Theorem 3. 

If $k>{\displaystyle \frac{{\alpha }^{2}rw}{c_2}}$, the optimal planned production quantity and GET investment level are

$$I_3^{\ast }={\displaystyle \frac{r{\alpha }^2{w}^2(\mu -\tau )+{\alpha }^2{c}_{1}rw+2c_{2}k(w\tau -c_1)}{4c_2\left(c_{2}k-{\alpha }^{2}rw\right)}}$$

(21)

$$g_3^{\ast }={\displaystyle \frac{\alpha r(w(\mu +\tau )-c_1)}{2(c_{2}k-{\alpha }^{2}rw)}}$$

(22)

By substituting Equations (21) and (22) into Equations (18) and (20), we get the optimal expected utility of the farmer, and the optimal expected profit of the firm as follows:

$$E{U_F^{NY}}^{\ast }={\displaystyle \frac{{[r{\alpha }^2{w}^2(\mu -\tau )+{\alpha }^2{c}_{1}rw+2c_{2}k(w\tau -c_1)]}^2}{16c_2{\left(c_{2}k-{\alpha }^{2}rw\right)}^2}}$$

(23)

$$E{\pi }_R^{NY}={\displaystyle \frac{r\left({\left((\mu -\tau )-w+c_1\right)}^2{\alpha }^{2}r+4k\mu c_2\left(w\tau -c_1\right)\right)}{8c_2\left(c_{2}k-{\alpha }^{2}rw\right)}}$$

(24)

Proposition 3. 

• (1)${\displaystyle \frac{\partial I_3^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial g_3^{\ast }}{\partial \alpha }}>0$;
• (2) When  $\eta =1$, if  $\mu >{\displaystyle \frac{c_1}{w}},{\displaystyle \frac{\partial E{U_F^{NY}}^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial E{{\pi }_R^{NY}}^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial E{U_{SC}^{NY}}^{\ast }}{\partial \alpha }}>0$, otherwise,
• ${\displaystyle \frac{\partial E{U_F^{NY}}^{\ast }}{\partial \alpha }}<0,{\displaystyle \frac{\partial E{{\pi }_R^{NY}}^{\ast }}{\partial \alpha }}<0,{\displaystyle \frac{\partial E{U_{SC}^{NY}}^{\ast }}{\partial \alpha }}<0$;
• (3) When  $w<{\displaystyle \frac{p}{2}}$,${\displaystyle \frac{\partial g_3^{\ast }}{\partial w}}>0$, otherwise,${\displaystyle \frac{\partial g_3^{\ast }}{\partial w}}<0$;

Proposition 3(1) is similar to Proposition 2. When only the firm bears the cost of the GET investment, if its sensitivity coefficient to yield increases, both the level of investment and the planned production quantity increase. This suggests that the application of GET has a positive impact on yield, whether the farmer or the firm alone bears the cost of GET investment. When $\eta =1$, if $\mu >c_1/w$, the farmer’s expected utility, the firm’s expected profit, and the supply chain’s expected utility increase with the GET sensitivity coefficient and decrease otherwise. This suggests that a stochastic output rate that is too small affects the positive effect of GET on the participants’ profit. Thus, increasing the yield is more necessary. Under the neither invests case, the level of GET investment increases with an increase in wholesale price only if the wholesale price $w<{\displaystyle \frac{p}{2}}$ and decreases otherwise. Since a high wholesale price greatly harms the firm’s earnings, they choose to reduce GET investment to alleviate cost pressure. Therefore, if the firm invests in GET, the wholesale price in the order contract will not be very high.

4.4. Case $S_{YY}$: Cost-Sharing Between the Parties

In this model, both the farmer and the firm make GET investments. The farmer applies GET to the cultivation of agricultural products. The investment cost is shared by the farmer and the firm, and the level of investment is decided by the well-funded firm. The objective functions of the farmer and the firm are, respectively:

$$\begin{array}{cc}{\pi }_F^{YY}& =w(\mu +\alpha g_4)I_4-c_1{I}_4-c_2{I}_4^2-{\displaystyle \frac{1}{2}}(1-\lambda )k{g}_4^2\hfill \\ & =w{I}_4\mu +w\alpha g_4{I}_4-c_1{I}_4-c_2{I}_4^2-{\displaystyle \frac{1}{2}}(1-\lambda )k{g}_4^2\hfill \end{array}$$

(25)

The first term is the farmer’s income from increased yields. The second and third terms are the farmer’s production costs. The fourth term is the farmer’s share of the GET investment costs.

$${\pi }_R^{YY}=(p-w)(\mu +\alpha g_4)I_4-{\displaystyle \frac{1}{2}}\lambda k{g}_4^2$$

(26)

The first item is the firm’s profit on sales, the second is the firm’s share of the cost of the GET investment.

The utility function of the risk-averse farmer is

$$E{U}_F^{YY}=v_4-{\displaystyle \frac{1}{\eta }}{\displaystyle {\int }_A^B{\left(v_4-w\alpha g_4{I}_4-w{I}_4\mu +c_1{I}_4+c_2{I}_4^2+\frac{1}{2}(1-\lambda )k{g}_4^2\right)}^{+}}dG(\mu )$$

(27)

From Equation (27), under the $S_{YY}$, we can obtain the optimal threshold of loss as $v_4^{\ast }=w{I}_4{G}^{-1}(\eta )+w\alpha g_4{I}_4-c_1{I}_4-c{I}_4^2-{\displaystyle \frac{1}{2}}(1-\lambda )k{g}_4^2$, which is substituted into the farmer’s objective function to obtain the following equation:

$$E{U_F^{YY}}^{\ast }={\displaystyle \frac{w{I}_4}{\eta }}{\displaystyle {\int }_A^{G^{-1}(\eta )}\mu }dG(\mu )+w\alpha g_4{I}_4-c_1{I}_4-c_2{I}_4^2-{\displaystyle \frac{1}{2}}(1-\lambda )k{g}_4^2$$

(28)

Theorem 4. 

If $k>{\displaystyle \frac{{\alpha }^{2}rw}{c_2}}$, the optimal planned production quantity and GET investment level are

$$I_4^{\ast }={\displaystyle \frac{r{\alpha }^2(\mu -\tau )w^2+\left({\alpha }^2{c}_{1}r+2c_{2}k\lambda \tau \right)w-2c_1{c}_{2}k\lambda }{4\left(c_{2}k\lambda -{\alpha }^{2}rw\right)c_2}}$$

(29)

$$g_4^{\ast }={\displaystyle \frac{\alpha r(w(\mu +\tau )-c_1)}{2(\lambda c_{2}k-{\alpha }^{2}rw)}}$$

(30)

By substituting Equations (29) and (30) into Equations (26) and (28), we get the optimal expected utility of the farmer, and the optimal expected profit of the firm as follows:

$$\begin{array}{cc}E{U_F^{YY}}^{\ast }& ={\displaystyle \frac{w^2{\left(\left(\mu -\tau \right)w+c_1\right)}^2{r}^2{\alpha }^4+4k^2{c}_2^2{\lambda }^2{\left(w\tau -c_1\right)}^2}{16{\left(-{\alpha }^{2}rw+c_{2}k\lambda \right)}^2{c}_2}}\hfill \\ & {\displaystyle \frac{+2k{c}_2\left({\left(\left(\mu +\tau \right)w-c_1\right)}^2\left(-1+\lambda \right)r+2\lambda \left(w\tau -c_1\right)w\left(\left(\mu -\tau \right)w+c_1\right)\right)r{\alpha }^2}{16{\left(-{\alpha }^{2}rw+c_{2}k\lambda \right)}^2{c}_2}}\hfill \end{array}$$

(31)

$$E{{\pi }_R^{YY}}^{\ast }={\displaystyle \frac{{\alpha }^2{r}^2{\left(\left(\mu -\tau \right)w+c_1\right)}^2+4k\mu c_2\lambda r\left(w\tau -c_1\right)}{8c_2\left(\lambda c_{2}k-{\alpha }^{2}rw\right)}}$$

(32)

Proposition 4. 

• (1) ${\displaystyle \frac{\partial I_4^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial g_4^{\ast }}{\partial \alpha }}>0,{\displaystyle \frac{\partial E{{\pi }_R^{YY}}^{\ast }}{\partial \alpha }}>0$;
• (2) When $\eta =1$, if $\mu >{\displaystyle \frac{c_1}{w}}$ and $\alpha >\sqrt{{\displaystyle \frac{2k{c}_{2}r({(2w\tau -c_1)}^2(1-\lambda )+2\lambda wc(w\tau -c_1)}{w^2{c}_1^{2}r}}}$, ${\displaystyle \frac{\partial E{U_F^{YY}}^{\ast }}{\partial \alpha }}>0$, otherwise, ${\displaystyle \frac{\partial E{U_F^{YY}}^{\ast }}{\partial \alpha }}<0$;
• (3) When  $w<{\displaystyle \frac{p}{2}}$,${\displaystyle \frac{\partial g_4^{\ast }}{\partial w}}>0$, otherwise,${\displaystyle \frac{\partial g_4^{\ast }}{\partial w}}<0$;

Proposition 4(1) demonstrates that under the cost-sharing model, both the firm and farmer jointly invest in GET, and the optimal planned output and GET investment level exhibit positive sensitivity to yield enhancement. Specifically, as the yield sensitivity coefficient increases, both decision variables increase monotonically. This directional consistency holds across with the case where the farmer or firm invests alone. The increase in the sensitivity coefficient of the GET level to yield still leads to an increase in the firm’s optimal expected profit even though the farmer is risk-averse, as compared to the case where the firm invests alone. This suggests that cost sharing reduces the negative impact of the farmer’s risk-averse characteristics on the firm. Proposition 4(2) shows that when $\eta =1$, the utility of the farmer increases with an increase in the sensitivity coefficient of GET only if the impact of yield increases from GET application exceeds a certain level. This is because the benefit from yield increases exceeds the farmer’s shared cost of GET. Proposition 4(3) is similar to Proposition 3. The wholesale price needs to be kept within a reasonable range to incentivize the firm to invest in GET.

Proposition 5. 

• (1)${\displaystyle \frac{\partial I_4^{\ast }}{\partial \lambda }}>0,{\displaystyle \frac{\partial g_4^{\ast }}{\partial \lambda }}>0,{\displaystyle \frac{\partial E{{\pi }_R^{YY}}^{\ast }}{\partial \lambda }}>0$;
• (2) When $\eta =1$, if $\mu >{\displaystyle \frac{c_1}{2}}$ and ${\displaystyle \frac{{\alpha }^{2}rw}{k{c}_2}}<\lambda <{\displaystyle \frac{2k{c}_2(2\mu -c_1)-w^2{\alpha }^2{c}_1}{k{c}_2(2\mu -c_1)}}$, ${\displaystyle \frac{\partial E{U_F^{YY}}^{\ast }}{\partial \lambda }}>0$, otherwise,${\displaystyle \frac{\partial E{U_F^{YY}}^{\ast }}{\partial \lambda }}<0$;

Proposition 5(1) shows that the optimal planned output, the level of GET investment, and the firm’s expected profit decrease as $\lambda$ increases. The more that costs are shared by the firm, the more the firm is likely to reduce costs by reducing GET investment. This tends to lead to a reduction in yield, which ultimately reduces the firm’s expected profits because of the decline in production and the increase in cost. It follows that overloading firms with the cost of investment in the GET application may be detrimental to agricultural production. Proposition 5(2) shows that when $\eta =1$, i.e., when farmers are risk neutral, the expected utility of farmers increases only if $\lambda$ remains within a certain range and $\lambda$ increases. Otherwise, an increase in $\lambda$ decreases the farmer’s expected utility. This may be because the firm sharing the cost will mostly choose to reduce the wholesale price to alleviate the cost pressure, which ultimately leads to a decrease in the farmer’s utility.

5. Models’ Comparison

Building on the preceding analytical framework, this part analyzes the optimal decision variables and expected profits of two members under different models.

Proposition 6. 

• (1) $I_4^{\ast }>I_3^{\ast }>I_1^{\ast },I_2^{\ast }>I_1^{\ast }$;
• (2) When ${\displaystyle \frac{(w\tau -c_1)\left(2c_{2}kw-r\left(w^2{\alpha }^2+2c_{2}k\right)\right)}{rw\left(2c_{2}k-w^2{\alpha }^2\right)}}<\mu <B$, $I_4^{\ast }>I_3^{\ast }>I_2^{\ast }>I_1^{\ast }$;
• When $A<\mu <{\displaystyle \frac{(w\tau -c_1)\left(2c_{2}kw-r\left(w^2{\alpha }^2+2c_{2}k\right)\right)}{rw\left(2c_{2}k-w^2{\alpha }^2\right)}}$ and
• ${\displaystyle \frac{{\alpha }^{2}r{w}^2}{k{c}_2}}<\lambda <{\displaystyle \frac{urw(2c_{2}k-{\alpha }^2{w}^2)+(\tau rw-c_{1}r)({\alpha }^2{w}^2+2c_{2}k)}{2c_{2}kw(w\tau -c_1)}}$, then $I_4^{\ast }>I_2^{\ast }>I_3^{\ast }>I_1^{\ast }$;
• When ${\displaystyle \frac{urw(2c_{2}k-{\alpha }^2{w}^2)+(\tau rw-c_{1}r)({\alpha }^2{w}^2+2c_{2}k)}{2c_{2}kw(w\tau -c_1)}}<\lambda <1$, then $I_2^{\ast }>I_4^{\ast }>I_3^{\ast }>I_1^{\ast }$;

The proof of Proposition 6 is provided in Appendix A.

Proposition 6(1) indicates that when no investment is made, the optimal planting quantity is minimal, and when investment costs are shared, the farmer’s production quantity is maximized. This means that regardless of the method of agricultural investment chosen, it can incentivize the farmer to increase production. Furthermore, when the firm and the farmer share costs, the farmer is more willing to increase planting quantities. This suggests that cost-sharing mechanisms can indeed alleviate the farmer’s concerns about production risks to some extent, making them more willing to increase input.

Proposition 6(2) states that the farmer’s decisions on how many agricultural products to grow are influenced by two factors: the productivity $\mu$ and the proportion of costs $\lambda$ borne by the firm. If productivity $\mu$ is low, the farmer is more likely to adopt GET to increase yields, and they are more willing to increase planting quantities under the cost-sharing model. When ${\displaystyle \frac{(w\tau -c_1)\left(2c_{2}kw-r\left(w^2{\alpha }^2+2c_{2}k\right)\right)}{rw\left(2c_{2}k-w^2{\alpha }^2\right)}}<\mu <B$ and ${\displaystyle \frac{{\alpha }^{2}r{w}^2}{k{c}_2}}<\lambda <{\displaystyle \frac{urw(2c_{2}k-{\alpha }^2{w}^2)+(\tau rw-c_{1}r)({\alpha }^2{w}^2+2c_{2}k)}{2c_{2}kw(w\tau -c_1)}}$, the farmer expects higher yield and has low adoption of GET. But the farmer remains the most motivated to production under the cost-sharing model. When ${\displaystyle \frac{urw(2c_{2}k-{\alpha }^2{w}^2)+(\tau rw-c_{1}r)({\alpha }^2{w}^2+2c_{2}k)}{2c_{2}kw(w\tau -c_1)}}<\lambda <1$, planned production is instead higher when only the farmer invests in GET. This is because when $\lambda$ is high, the firm will depress the wholesale price, which affects the farmer’s incentives to produce.

Proposition 7. 

• (1) $g_4^{\ast }>g_3^{\ast }$;
• (2) When ${\displaystyle \frac{(w\tau -c_1)\left(2c_{2}kw-r\left(w^2{\alpha }^2+2c_{2}k\right)\right)}{rw\left(2c_{2}k-w^2{\alpha }^2\right)}}<\mu <B$, $g_4^{\ast }>g_3^{\ast }>g_2^{\ast }$;
• When $A<\mu <{\displaystyle \frac{(w\tau -c_1)\left(2c_{2}kw-r\left(w^2{\alpha }^2+2c_{2}k\right)\right)}{rw\left(2c_{2}k-w^2{\alpha }^2\right)}}$ and
• ${\displaystyle \frac{{\alpha }^{2}r{w}^2}{k{c}_2}}<\lambda <{\displaystyle \frac{urw(2c_{2}k-{\alpha }^2{w}^2)+(\tau rw-c_{1}r)({\alpha }^2{w}^2+2c_{2}k)}{2c_{2}kw(w\tau -c_1)}}$, $g_4^{\ast }>g_2^{\ast }>g_3^{\ast }$;
• When ${\displaystyle \frac{urw(2c_{2}k-{\alpha }^2{w}^2)+(\tau rw-c_{1}r)({\alpha }^2{w}^2+2c_{2}k)}{2c_{2}kw(w\tau -c_1)}}<\lambda <1$, $g_2^{\ast }>g_4^{\ast }>g_3^{\ast }$;

Proposition 7(1) indicates that under the cost-sharing model, the level of GET investment is higher than when the firm invests independently. Because this reduces the cost pressure on the firm compared to the firm investing alone and can incentivize the firm to invest more. Proposition 7(2) suggests that if $\mu$ is low, output pressure drives the farmer to make GET investment on their own. The farmer wants to work on increasing the level of the GET application to boost yield. Meanwhile, when ${\displaystyle \frac{{\alpha }^{2}r{w}^2}{k{c}_2}}<\lambda <{\displaystyle \frac{urw(2c_{2}k-{\alpha }^2{w}^2)+(\tau rw-c_{1}r)({\alpha }^2{w}^2+2c_{2}k)}{2c_{2}kw(w\tau -c_1)}}$, the cost-sharing mechanism leads to the highest level of GET investment. When $\lambda$ is too high, the firm reduces investment due to high input costs, at which point the $S_{YN}$ has the highest level of GET investment.

Proposition 8. 

$E{U_F^{YN}}^{\ast }>E{U_F^{NN}}^{\ast },E{U_F^{NY}}^{\ast }>E{U_F^{NN}}^{\ast }$;

Proposition 8 shows that the optimal expected utility of the farmer is always higher under the case where the farmer or firm invests alone than under the neither invests case. This indicates that the application of GET during cultivation can bring higher utility. Since the increase in yield due to GET can increase the utility of the farmer, GET should be actively used to grow agricultural products.

Proposition 9. 

$E{{\pi }_R^{YN}}^{\ast }>E{{\pi }_R^{NN}}^{\ast }$, $E{{\pi }_R^{YY}}^{\ast }>E{{\pi }_R^{NY}}^{\ast }>E{{\pi }_R^{NN}}^{\ast }$;

Proposition 9 shows that when the farmer adopts GET for planting and bears the cost alone, the firm’s profit will be higher than under the neither invests case. Combined with Proposition 8, the farmer’s adoption of GET can improve their own and the firm’s benefit and realize a win-win situation. When the firm decides the level of GET investment, selecting a cost-sharing mechanism can maximize the firm’s optimal expected profit.

6. Numerical Analysis

We conduct numerical simulations to analyze the impact of wholesale price, the degree of the farmer’s risk aversion, and yield uncertainty on supply chain decisions and profits. Based on the relevant price indicators and cost-benefit indicators from the wheat statistics of the Ministry of Agriculture and Rural Affairs of the People’s Republic of China over the past two years, and with reference to Niu et al. [28] and Jiang et al. [33], we assume $c_1=0.03,c_2=0.005,\alpha =0.05,k=1,p=1.34$, $\mu$ adheres to a normally distributed pattern with $\mu ~N[0,{0.2}^2]$ and $\mu \in [0,2]$. For example, according to statistical data, the recent price of wheat is 3198 CNY/ton, so we can get an approximate price of 1.34 CNY per 500 g [59]. In the process of agricultural technology promotion, when promoting technology application through specialized enterprises, we combine data from the ‘Three Subsidies’ policy [60] for promoting agricultural production socialized services and the smart agriculture construction project at Youyi Farm of the Beidahuang Group [61]. We assume that under the firm-led cost-sharing mechanism, the firm’s cost-sharing ratio $\lambda$ is set at 0.7/0.8.

6.1. Effect of Wholesale Price

Figure 2a shows that an increase in wholesale prices leads to an increase in the farmer’s planned production quantity. Only when the wholesale price is very high, the planned production quantity exceeds the cost-sharing mechanism under the farmer-only investment model. As shown in Figure 2b, when the farmer bears the GET investment costs alone, higher wholesale prices lead to a significant increase in GET adoption rates. When only the firm invests in GET, this depresses agricultural product wholesale prices, causing GET investment levels to rise initially but then decline as wholesale prices fall, and investment levels remain the lowest compared to other models. Combining Figure 2a,b, when $w$ is low, the GET investment level and planned production quantity are highest under the cost-sharing mechanism. As wholesale prices rise, the farmer is incentivized to increase planned production and GET investment. However, when the wholesale price exceeds a critical threshold, the loss of corporate profits leads to excessive cost pressure and reduces GET investment. Therefore, in real life, the wholesale prices agreed upon in contracts between the firm and farmer are unlikely to be very high. As shown in Figure 2c,d, the utility of the risk-averse farmer also tends to increase, while the firm’s profits first increase and then decrease. When the wholesale price is low, the firm invests alone model maximizes the farmer’s utility. When the wholesale price is high, the farmer invests alone model maximizes both the farmer’s utility and the firm’s profits. When the wholesale price is moderate, the farmer’s utility is highest under the cost-sharing model. Based on the above and Figure 2d, when the wholesale price is moderate, both parties will choose the cost-sharing model; when the wholesale price is high, the farmer is more proactive and chooses to bear the GET investment costs independently.

6.2. Effect of the Degree of Risk Aversion

As can be seen from Figure 3a,b, the smaller $\eta$, i.e., the higher the degree of risk aversion of the farmer, the smaller the GET investment and the planned production quantity will be, especially under the farmer invests alone case, which is significantly lower than other cases. From the Figure 3c–e, the Figure 3a,b results in a downward trend in both parties’ returns, leading to a loss for the whole supply chain. In addition, under the cost-sharing case, the larger the proportion of cost sharing $\lambda$ borne by the firm, the smaller the expected profit of the firm and the larger the utility of the farmers. It is worth noting that higher cost-sharing ratios reduce the firm’s profitability. But it is higher than in other cases. Although the utility is highest for the farmer under the firm invests alone case, the choice of the cost-sharing mechanism still leads to the highest optimal expected profit for the entire supply chain.

6.3. Effect of Yield Uncertainty

As can be seen in Figure 4a,b, as the standard deviation of yield increases, i.e., as the volatility of agricultural yield increases, there is a significant decrease in the planned production quantity and a decrease in the level of GET investment. But the decrease is more moderate compared to the decrease in yield. However, under the cost-sharing model, the planned production yield and GET investment are consistently higher than in other models. The level of investment by the firm alone is higher than that by the farmer alone. This may be since the firm is more capitalized and risk-resistant relative to the farmer. From the Figure 4c,d, for the farmer, as yield fluctuates more, the firm invests alone case is more favorable to the farmer and has the greatest utility. However, for the firm, the excessive cost pressure on the farmer will lead to $I$ and $g$ extremely low prices, as the farmer invests alone. As a result, the expected profit of the firm is lower than under the neither invests case. Therefore, from the above figures and Figure 4e, the choice of cost-sharing mechanism should be made to maximize yield, GET investment level, and supply chain utility.

6.4. Analysis of the Conditions for Cooperation Mechanisms

As can be seen from Figure 5, when the wholesale price is low, the farmer chooses the $S_{NY}$ (the firm invests in GET case), while the firm chooses the $S_{YY}$ (the cost-sharing case), and the two sides cannot reach an agreement. Since the low wholesale price makes the farmer less utility, the benefits from GET cannot offset the shared costs. When $w$ is moderate, both the farmer and the firm choose the $S_{YY}$ (the cost-sharing case) and can reach an agreement. The lower the GET investment cost coefficient, the greater the possibility of cooperation. When $w$ is high, to encourage the firm to increase GET investment, the farmer is willing to bear part of the GET investment cost, but there will be a higher acquisition cost for the firm. To alleviate the cost pressure, firms will not carry out GET investment. At this time, the two sides cannot reach an agreement. When $w$ is very high, the farmer is highly motivated to produce and will independently carry out the GET investment. While the firm’s cost pressure is greater, it will not invest. At this stage, the $S_{YN}$ (the farmer invests in GET case) will bring the maximum benefit to both sides, to reach an agreement.

7. Discussion and Conclusions

Promoting the adoption of GET in agricultural production is important for production and ecological sustainability. In our study, we construct a secondary contract agricultural supply chain featuring a risk-averse farmer and a risk-neutral firm. We consider whether to adopt GET to realize green cultivation and increased yield in the face of a context where yield has uncertainty. We construct four models based on game theory, focusing on the GET investment problem with different cooperation mechanisms. Finally, we also analyze the impacts of contractual wholesale price, yield volatility, risk aversion, and the cost coefficient of GET investment on related decisions and profits. The following conclusions and insights are obtained from this study.

7.1. Key Findings

We conducted a systematic analysis of GET investment strategies by constructing a ‘firm+ farmer’ contract farming model, which yielded both consensus and new findings compared to existing research. We found that GET investments by the farmer or firm can significantly enhance the farmer’s utility and overall supply chain profits. However, under the cost-sharing cooperation mechanisms, if wholesale prices are too low or the firm’s cost-sharing ratio is too low, cost-sharing contracts may actually reduce farmers’ benefits from adopting new fertilization methods. This is consistent with the findings of Niu et al. [28], who noted that the acquisition price set by the firm and its efforts in cost-sharing can influence the success of contract farming coordination.

The research findings indicate that if GET is adopted for agricultural production, both the farmer and the firm tend to choose a cost-sharing mechanism when the wholesale price is moderate. This model maximizes yield and GET investment levels, but this effect weakens as the proportion of cost-sharing increases. If wholesale prices are high, the farmer and the firm choose to allow the farmer to independently invest in GET, but both parties’ returns are lower than under the cost-sharing mechanism. This validates findings similar to those of Nematollahi et al. [36], indicating that cost-sharing mechanisms can effectively incentivize farmers to invest and increase profits for all parties. However, we further define the impact of the wholesale price on cooperative mechanisms and clarify the applicable range of wholesale prices, thereby supplementing existing research.

We also note that when the farmer’s risk aversion increases, they reduce production inputs and GET investment, thereby lowering yield and profits for both parties. Our findings align with Shi et al. [52], indicating that farmers’ risk aversion has a negative impact on the adoption of agricultural chemical reduction technologies. Therefore, when dealing with risk-averse farmers, promoting new technologies must take into account their attitude toward risk. This further validates the research by Peng and Pang [45], who showed that government subsidies can mitigate the negative effects of risk aversion for farmers with higher levels of risk aversion. As incentives and support increase, farmers’ total target output also increases.

Interestingly, although greater yield uncertainty leads to a decrease in the farmer’s investment and utility, this is the optimal case for the farmer to independently adopt the GET investment model. However, for the firm and supply chain, this causes the lowest profits. Utility is highest only under a cost-sharing mechanism between both parties. This finding is consistent with Ye et al. [9], but also differs in some aspects. They found that when yield uncertainty is high, cooperative mechanisms should be used to encourage farmers to increase yield and improve their own profits. However, their research also suggests that when yield uncertainty reaches a certain level, wholesale prices should be reduced to avoid a decline in their own utility. This differs from the finding in this paper that the higher the yield uncertainty, the more farmers should be incentivized. The primary reason may be that this paper considers the role of new technologies in increasing yield. Therefore, in agricultural production facing yield uncertainty, relying solely on farmers’ efforts is insufficient. Policies should prioritize incentivizing firms to participate in GET investments rather than solely relying on farmers’ autonomous adoption. This provides a theoretical basis for the ‘firm + farmer’ cooperation model in the current agricultural green transition.

In summary, the GET investment by either party increases their gains compared to non-investment. When the wholesale price is moderate, both sides will choose the cooperative mechanism of cost sharing to invest in technology. When the wholesale price is high, the farmer also chooses to invest. The uncertainty of yield and the degree of risk aversion have a negative impact on the agricultural inputs, GET investment, and benefit.

7.2. Theoretical and Managerial Implications

The innovation of this study lies in the inclusion of yield uncertainty, GET, risk aversion, and cooperative mechanisms in the research under CvaR guidelines, which is of great significance in sustainable agricultural development. The theoretical implications of this paper include the following aspects: First, unlike previous studies that analyzed the improvement of green technology on the greenness of products, it focuses on the improvement of GET on agricultural production methods and proposes a model of agricultural yield increase by combining big data with green and precise fertilization. Second, game theory and CvaR criterion are used to explore the optimal production decisions and investment strategies of the supply chain under different modes, providing new management insights for contract agricultural supply chains. Third, we build various cooperation methods for the GET application from the standpoint of supply chain cooperation optimization, which enriches the realization path of sustainable agricultural development.

Practice has shown that the application of GET not only brings economic benefits but also highlights its multidimensional social value. On the one hand, reducing fertilizer use through precision fertilization can improve soil pollution and meet the needs of sustainable development. On the other hand, promoting green and efficient technology models suitable for local production conditions can achieve a double increase in agricultural production efficiency and environmental benefits. This enhances its ability to cope with market risks and provides an effective path for small farmers to integrate into the modern agricultural system.

Based on these findings and the social value of GET, we provide important management insights for the practice of sustainable agricultural supply chains. First, whether farmers themselves or firms alone bear the cost of GET investment, farmers should adopt new fertilizer equipment and technology for green cultivation. Second, scientifically designed cost-sharing mechanisms are key to promoting green transformation. While the adoption of new fertilizer application methods by farmers can improve yields and efficiency, firms need to avoid setting a wholesale price too low or bearing too low a proportion of the costs. This may weaken farmers’ willingness to participate and even harm the profit of the supply chain. A reasonable combination of cost-sharing and moderate wholesale prices can maximize incentives for both parties to work together, balancing risks and benefits. Third, supply chain collaboration is crucial. Firms should take the initiative to participate in green and high-efficiency investments or lower the threshold of farmers’ transformation through price subsidies, rather than relying on farmers’ solo efforts to avoid a lack of investment due to farmers’ risk aversion. The establishment of a synergistic mechanism of “firm-farmer” risk-sharing and revenue-sharing is a win-win path to realize sustainable efficiency gains in the supply chain. Finally, this study found that the cost of technology investment and farmers’ risk aversion affect their adoption of technology. Therefore, in actual promotion, it is necessary to distinguish between different types of technology. For high-cost, highly specialized technologies, joint support from firms and the government is needed, while low-cost and easy-to-operate technologies can be rapidly popularized through direct subsidies.

7.3. Limitations and Future Studies

Although this study has revealed the cooperative mechanisms of GET in the ‘firm+ farmer’ model, there are still certain limitations and areas worthy of further exploration. The current model focuses on yield uncertainty, but in reality, fluctuations in market demand also impact supply chain stability. Future research could combine agricultural product price elasticity with green consumption preferences to analyze the robustness of GET investments under dual uncertainty. On the other hand, the soil improvement effects of GET exhibit significant time lags; for example, organic fertilizers may require 3–5 years to fully realize their yield-enhancing potential. It is recommended to construct a dynamic model to examine the evolutionary pathways of intertemporal technology benefits and cost-sharing. Additionally, field control experiments can serve as an important validation tool. For example, a GET group and a traditional farming control group could be established to compare changes in farmers’ risk preference parameters (η) under GET and traditional technology cooperation contracts. Such empirical data would significantly enhance the applicability of theoretical models. Furthermore, the economic decision-making framework of this study can be extended to social welfare assessment, including quantifying the environmental benefits of reducing fertilizer use, incorporating social utility as an objective function, and exploring coordination to maximize benefits for farmers, businesses, and society. These extensions not only deepen the theoretical findings of this paper but also address the multidimensional synergistic requirements of economic, ecological, and social benefits in sustainable agricultural development.