2. Literature Review
The research presented in this paper primarily addresses three domains: government-intervened agricultural product supply chains, financially constrained supply chains, and the risk preferences of supply chain participants.
The primary means by which the government intervenes in the agricultural product supply chain is through subsidies. Due to the state’s emphasis on agricultural development, an increasing number of scholars recognize the significant impact of government subsidies on the supply chain of agricultural products. Zhang X. M. et al. [
1] analyzed the influence of fresh agricultural product supply chains and designed contractual mechanisms to enhance subsidy effectiveness, demonstrating the validity of subsidy strategies. Peng H. J. et al. [
2] investigated the financing, operational decisions, and profits of key actors in order-based agricultural supply chains when the government provides subsidies based on planting areas. Zhou Y. J. et al. [
3] studied a two-part contractual model combining “farmer’s security deposits” and “e-commerce platform subsidies” to achieve Pareto improvements within the agricultural product supply chain. Agricultural innovation often requires governmental support; Duygu Akkaya et al. [
4] examined how agricultural subsidies influence farmers’ adoption of innovative production methods, producer profits, consumer surplus, and government expenditure returns. Zhu J. H. et al. [
5] analyzed three scenarios under demand uncertainty: no government subsidy, government-implemented procurement subsidies, and sales subsidies. Liu H. Y. et al. [
6] considered mandatory slaughter subsidies and consumer subsidies, studied their effects on various stakeholders and pork supply, and constructed a game-theoretic model to determine optimal government subsidy strategies under different conditions. When examining government subsidies, scholars do not conceptualize the government as an integral part of the supply chain or strategic bargaining process. Instead, they treat subsidies as exogenous factors and analyze their impact on the supply chain accordingly. Yu X. et al. [
7] incorporated government-provided agricultural insurance premium subsidies into a three-stage game model involving agricultural enterprises, retailers, and the government, revealing that insurance subsidies are crucial for enhancing the benefits of all three parties. Zhang W. G. et al. [
8] considered a three-stage Stackelberg game model involving farmers, corporations, and the government, incorporating subsidies for farmers’ production costs and the pricing model for purchase prices fluctuating according to product quality variations, affirming the government subsidies’ positive role. Huang J. H. et al. [
9] constructed a three-stage game model involving the government, retailers, and agricultural enterprises under a natural disaster loss subsidy mechanism, accounting for bankruptcy risks, and proposed subsidy mechanisms to maximize social welfare. These studies include the government in the supply chain and strategic interactions, treating subsidies as endogenous decision variables, but they solely subsidize farmers or retailers. This study compares two subsidy strategies: one where the government gives farmers subsidies based on planting area and another to retailers based on purchase volume, considering past research and national legislation. A comparative analysis of these tactics’ supply chain impacts informs scientific subsidy rate setting and country-specific subsidy policies.
When analyzing agricultural supply chains, many scholars focus on the financial constraints of farmers or other supply chain participants. However, few studies incorporate government subsidy budget limitations into their frameworks. Zhu J. H. et al. [
5] examined procurement and sales subsidies for fresh agricultural products under fiscal constraints, demonstrating that both strategies are viable when budgets are sufficient. Similarly, Ye F. et al. [
10] compared subsidies for energy crop growers versus energy producers, concluding that limited fiscal resources warrant prioritizing direct subsidies to farmers. Lai D. L. et al. [
11] investigated volume-based and price-based e-commerce poverty alleviation subsidies, finding that governments favor price-based policies under budget constraints. While these studies acknowledge fiscal limitations, they largely overlook the role of farm size (defined here as household-owned land area) in shaping subsidy effectiveness. This study argues that optimal subsidy strategies depend on farm size; thus, policymakers must evaluate how farm size influences subsidy policy selection under fiscal constraints.
Agricultural production is highly vulnerable to environmental uncertainties, prompting farmers to adopt risk-averse behaviors. Peng H. J. and Tao Pang [
12] modeled a three-level agricultural supply chain involving risk-averse farmers, suppliers, and distributors with government subsidies allocated to farmers. Their findings demonstrate that subsidy effectiveness is contingent upon farmers’ degree of risk aversion. Lai D.L. et al. [
11] revealed that governments prefer purchase price-based subsidy policies for e-commerce platforms as farmers’ risk aversion intensifies. Shi B. et al. [
13] examined a supply chain with risk-averse farmers and risk-neutral sellers, identifying an inverse relationship between risk aversion and green investment levels in decentralized supply chains. Further supporting this, Fu H.Y. et al. [
14] developed a two-level agricultural product supply chain composed of risk-averse farmers and risk-neutral companies, designing an improved profit-sharing contract related to the degree of risk aversion. Ye F. et al. [
15] examined a “company + farmer” order-based agricultural supply chain model involving risk-neutral companies and risk-averse farmers, demonstrating that the optimal production quantity chosen by risk-averse farmers increases with rising order prices. Lin, Q. et al. [
16] discusses the optimal decision behavior and expected returns of both parties when the company provides targeted financing (financing for agricultural production materials, financing for technical support and training) and non-targeted financing to farmers.
The essence of supply chain finance (SCF) research lies in integrating supply chain operational issues with financing problems. Yan and Sun et al. (2016) [
17] investigated a bank financing model for capital-constrained retailers under partial supplier guarantees, proposing financing decisions to achieve supply chain equilibrium. In practice, trade credit interest rates are often single and fixed, rather than varying with the loan amount. Addressing this context, Ning (2022) [
18] examined the reasons why suppliers use such single-interest contracts and why buyers still choose to finance through suppliers even when the supplier does not bear the buyer’s risk. Lin and Xiao (2018) [
19] studied the credit guarantee schemes used in SCF systems and the operational and financing strategies under different order contracts (push contracts and pull contracts). Kouvelis and Zhao (2008) [
20] considered a newsvendor model where both the retailer and supplier face capital constraints and require short-term financing, while also being exposed to bankruptcy risk. They analyzed the decisions involved in optimizing trade credit contract structures from the supplier’s perspective. Huang et al. (2019) [
21] investigated a multi-player bilateral bargaining model for a retailer obtaining bank financing under supplier credit guarantees, identifying the equilibrium order quantity influenced by initial working capital and interest rates. Hua et al. (2019) [
22] studied the financing and ordering decisions of a capital-constrained retailer under option contracts, where the supplier considers the retailer’s revenue. The research found that retailers always prefer financing from the supplier. Gao et al. (2018) [
23] assumed that either the retailer or the manufacturer faces capital constraints and must obtain funds through online P2P lending platforms, deriving the optimal decisions for both parties under the P2P financing model. Most of the existing literature on SCF compares multiple financing methods, focusing on the supply chain members’ choice of financing options. Xu and Fang (2020) [
24] studied a supply chain comprising one supplier and one manufacturer, where the manufacturer obtains two separate loans for procurement decisions and low-carbon investments. Wu and Chan et al. (2022) [
25] investigated the optimal operational decisions and financing strategies for a supply chain when the supplier adopts repurchase-backed purchase order financing and repurchase-backed advance payment discount schemes to support the buyer. Wang et al. (2022) [
26] proposed three trade credit offering strategies for suppliers: no credit (where the supplier offers no trade credit), exclusive credit (where the supplier offers trade credit only to a subset of retailers), and non-discriminatory credit (where the supplier offers trade credit to all retailers), to examine the preferences of suppliers and retailers for different trade credit provision modes. Wang et al. (2022) [
27] studied the roles of credit guarantee companies and P2P lending platforms in financing operations, categorizing credit guarantee companies into conservative and risk-taking types. The research demonstrated that optimal order quantity settings are more flexible under the risk-taking guarantee type compared to the conservative type and proposed supply chain financing coordination strategies. Shi (2020) [
28] considered the bankruptcy costs faced by capital-constrained retailers, exploring the influence of such costs and the underlying mechanisms on the retailer’s choice between bank credit financing and trade credit financing. Shen (2020) [
29] analyzed three financing schemes: bank credit financing, dual trade credit financing, and a hybrid of bank and trade credit financing, examining the impact of retailer competition and risk aversion among supply chain members on the retailer’s financing mode selection.
This study integrates farmers’ risk aversion characteristics into a Conditional Value-at-Risk (CVaR) decision-making framework designed for risk-averse agricultural producers to make the model more realistic. The CVaR model demonstrates exceptional alignment with the critical risk characteristics of agricultural supply chains, including high uncertainty, frequent extreme events, compounded risks, risk-averse decision-makers, and dynamic decision-making demands. This is due to its core advantages: focusing on extreme tail risks, robustness in distribution assumptions, support for prudent optimization decisions, unified measurement of comprehensive risks, compatibility with risk aversion traits, and adaptability to dynamic environments. Implementing the CVaR model enables supply chain participants to more effectively identify, quantify, and proactively manage the most destructive risks, thereby enhancing overall supply chain resilience and sustainability.
Building upon previous research, this paper establishes a three-level agricultural product supply chain comprising risk-averse farmers, retailers, and government entities. Considering constraints such as farmer scale limitations and restrictions on government subsidy budgets, a Stackelberg game model is developed among the three parties. Two subsidy strategies are analyzed: first, the government provides farmers with subsidies proportional to their planting area; second, it offers retailers subsidies based on their purchase volumes. The study addresses the following research questions: (1) How do these two subsidy strategies influence supply chain members’ optimal decisions and objective functions, and what are the underlying mechanisms? (2) How should the government select the appropriate subsidy strategy? (3) How do farmer scale constraints, risk aversion characteristics, and government fiscal budget limitations affect the choice of subsidy strategies? The originality lies in the simultaneous consideration of two alternative subsidy strategies, structural constraints (land, budget), and risk aversion.
4. SF Strategy Model and Analysis
Under the SF strategy, the government provides a subsidy
based on the farmers’ planting area
q. The farmers’ profit function is:
Considering farmers’ risk aversion characteristics, this paper uses the CVaR method to describe the utility function of risk-averse farmers. Since the farmers’ decision variable, planting area, is constrained by their scale, the farmers’ objective function can be expressed as:
The profit function of retailers mainly includes the income obtained from selling agricultural products to consumers and the cost of purchasing agricultural products. Therefore, the profit function of retailers can be expressed as:
In the above set
and
, from which we can obtain the retailer’s expected profit function:
Therefore, the decision-making objective for retailers is:
The purpose of government subsidies is to maximize social welfare, which consists of four parts: the first part is farmers’ profits, the second part is retailers’ profits, the third part is consumer surplus, and the fourth part is government subsidies. Therefore, the specific form of social welfare is:
The expected social welfare under fiscal budget constraints is:
The government’s decision-making target is:
By using backward induction to figure out the best decisions for farmers, retailers, and the government, we can obtain the balanced results of how the supply chain works under the SF strategy, as shown in Lemma 1:
Lemma 1. Under the SF strategy, the optimal planting area for farmers, the optimal purchase price for retailers, and the optimal subsidy rate for the government are shown in Table 2 below: Table 2 reveals two distinctive cases in the SF strategy. One is when S
and
, the purchase price converges to
. This is because, in this case, the fiscal budget for subsidies is relatively ample. Even if retailers reduce the purchase price to zero to increase their profit margins, farmers are willing to accept this price because they can still obtain income through subsidies. In other words, although farmers directly receive the subsidies, retailers also benefit from them. The other special case occurs when S
, resulting in a subsidy rate (
). This situation arises because farmers with smaller landholdings do not require government subsidies. In other words, to increase social welfare and crop production through subsidies, the government should prioritize subsidies for larger-scale farmers.
Table 2 also shows that
, which aligns with the findings established in the prior literature: when farmers own a small amount of land (S
), both the purchase price offered by retailers and the planting area of farmers decrease as output uncertainty increases. Regarding farmers’ planting area, purchase prices, and government subsidy coefficients under the SF strategy, the number of agricultural products that farmers plant is affected by many factors. The above table mainly considers the equilibrium solution of planting area (q), purchase price (w) and government subsidy rate under different conditions, considering the land area of farmers and the government subsidy budget.
5. SR Strategy Model and Analysis
Under the SR strategy, retailers obtain government subsidies based on the volume of purchases, with a per-unit subsidy rate of
. Under this strategy, farmers’ profit functions mainly include income from selling agricultural products to retailers and the costs of growing crops, specifically as follows:
Similarly, considering farmers’ risk aversion characteristics and scale constraints, their decision-making objectives can be calculated as follows:
Under the SR strategy, retailers receive subsidies based on the quantity purchased per unit, and their profit function is as follows:
The expected profit function for retailers is:
Therefore, the decision objective for retailers is:
Under this strategy, social welfare is:
The expected social welfare is defined as:
The government’s decision-making is formulated as the following optimization problem:
Similarly, using backward induction to find the optimal decisions for farmers, retailers, and the government, we can obtain the equilibrium results of supply chain operations under the SR strategy, as shown in Lemma 2:
Lemma 2. Under the SR strategy, the optimal planting area for farmers, the optimal purchase price for retailers, and the optimal subsidy rate for the government are shown in Table 3 below: Like the SF strategy, there is also a special case in the SR strategy, namely, when S, the government subsidy rate for retailers is , which means that when farmers’ land size is less than a certain level, there is no need to provide subsidies to retailers. In addition, indicate that retailers’ purchase prices and farmers’ planting areas decrease as output uncertainty increases. Regarding farmers’ planting area, purchase price, and government subsidy coefficient under the SR strategy, the number of agricultural products that farmers plant is affected by many factors. The above table mainly considers the equilibrium solution of planting area (q), purchase price (w) and government subsidy rate under different conditions, considering the land area of farmers and the government subsidy budget.
6. Government Subsidy Strategy Selection
Government subsidies usually improve overall social welfare, so this section uses this as a criterion for selecting the optimal strategy.
The calculations conducted above have established the ideal decisions and their corresponding value ranges for each member under the two techniques, with the ranges principally categorized by varying farm sizes (S) and fiscal budgets (B). The comparison of the two procedures must occur within the feasible intervals of each optimal solution. This results in seven separate regions A1–A7 (shown in
Figure 3, where
, when
,
, with the hierarchy
) and the associated best solutions for both methods inside each region (
Table 4). This study evaluates the SF and SR strategies across seven locations and identifies the process that maximizes social welfare as the ideal choice. For clarity, we define
as small farmer scale,
as moderate scale;
as limited budget,
as adequate budget, and
as excessive budget.
Proposition 1. - ①
When, . To maximize social welfare, the government should adopt the farmer subsidy policy (SF strategy). Under this condition: .
- ②
When with , . The government should choose the SF strategy.
Proposition 1 states that when
or
with
, as shown in
Figure 3, the government’s fiscal budget is small (
), and the scale of farmers is not small (
). Choosing the SF strategy to subsidize farmers rather than retailers can achieve higher social welfare. This is because, given the uncertainty of output and the higher the risk aversion of farmers, the lower the purchase price. Direct subsidies to farmers can encourage them to expand their planting area and ensure the yield of crops, thereby achieving higher social welfare. Furthermore, in the regional selection of subsidizing farmers, farmers and retailers expect higher profits than subsidizing retailers.
Proposition 2. - ①
When, , meaning that the SR strategy yields higher social welfare than the SF strategy, and .
- ②
When , similar welfare dominance holds: with:. The government should choose the SR strategy.
- ③
When with , , at which point the government should also choose the SR strategy.
For parameter regions where with or (B,S) ∈ A1∪A6, the SR strategy generates higher social welfare than SF, given sufficient fiscal budgets. This occurs because SF’s direct subsidies to farmers and retailers depress purchase prices ( in extreme cases), reducing planting incentives and output. In contrast, SR retailer subsidies elevate procurement price (), which expands cultivation areas () and enhances welfare. Additionally, in these regions, farmers and retailers under the SR strategy have higher expected profits than those under the SF strategy.
Proposition 3. When, the effects of the SF and SR subsidy strategies are the same, i.e., . When , there is no need for the government to provide subsidies to farmers or retailers.
Proposition 3 states that when , the scale of farming is moderate and there are no fiscal constraints. At this point, the effects of SR and SF subsidies are the same, i.e., social welfare is the same under both strategies, and farmers will fully utilize their land (). When , the scale of farming is small (), and the government does not need to provide subsidies to farmers and retailers because farmers will always choose to utilize their land () fully, and the government does not need to provide subsidies to encourage them to utilize their land to increase output fully.
Furthermore, under conditions of moderate farm scale and constrained fiscal budgets (within region A4), the relative social welfare performance of both strategies exhibits parametric dependence: for small-scale farms, welfare dominance shifts toward the SR strategy as budget B increases; for large-scale farms, the SF strategy becomes superior with expanding B.