Research on Agricultural Supply Chain Coordination Considering Financial Constraints Under Blockchain Technology

Supply Chain Finance and Capital Constraints

Studies on agricultural supply chain finance and capital constraints have focused on concepts, models, risk management, and financing decisions.

Lam et al. (2019) argued that supply chain finance is about reducing supplier and retailer costs through capital optimization and management, and providing credit and clearing services to supply chain companies. Chakuu et al. (2019) identified fixed assets, inventory, and accounts receivable models as common supply chain finance models. In terms of risk management, Rostamzadeh et al. (2018) used the fuzzy TOPSIS-CRITIC methodology to assess supply chain risks and made recommendations for preventing and monitoring risks. L. Zhang et al. (2015) established a credit risk assessment system based on SVM.

In terms of agricultural supply chain financing decisions, Reindorp et al. (2018) argued that when farmers are constrained by capital and have difficulty in demand forecasting and production, retailers’ commitment to minimum purchasing volume can alleviate farmers’ production difficulties. Zhao and Huchzermeier (2019) compared prepayment discounts and buyer’s purchase order financing models and found that the former financing model is more favorable when the retailer has a certain amount of its funds, and the latter is more favorable to choosing if the value of the marginal cost is higher than the unit discount return. Wang et al. (2016) investigated manufacturers’ optimal production decisions and financing decisions when they are financed through retail advance financing and contractual secured bank loans when manufacturers are financially constrained. In terms of external financing, Reddy and Sasidharan (2021) conducted a study on participation in supply chains under different levels of firms’ financial constraints. Tunca and Zhu (2017) considered the impact of supplier financing models on supply chain performance when large buyers act as intermediaries. Xia et al. (2022) investigated the impact of equity concerns on the optimal production and financing strategies of a closed loop supply chain with financial constraints. An et al. (2023) explore the pricing decisions of financially constrained members of a supply chain under demand uncertainty.

Supply Chain Contractual Coordination

Scholars mostly use contracts to coordinate supply chains. Lee and Rhee (2009) explored a retailer capital constrained supply chain and proposed four supply chain coordination mechanisms, namely price discounts, buybacks, two-step pricing, and revenue sharing, which were calculated and found to be invalidated by the presence of inventory financing costs. Lee and Rhee (2011) further considered inventory financing costs, proposed a supply chain coordination mechanism, and demonstrated the effectiveness of coordination of trade credit in leading to higher overall supply chain revenues and lower inventory financing costs for retailers. Cachon (2004) examined how the allocation of inventory risk under repurchase contracts affects supply chain efficiency. Chen and Chen (2014) analyzed trade credit contracts and repurchased guarantee contracts comparatively and found that repurchased guarantee contracts are more effective for supply chain coordination. B. Li et al. (2016) constructed a value-at-risk model using the Stackelberg game method, explored the impact of retailers’ risk aversion on supply chain revenues, order quantities, etc., and proposed a risk-sharing contract to coordinate the dual-channel supply chain. Freidberg (2017) explored the issue of multi-perspective supply chain coordination from a supply chain perspective. Nie and Du (2017) explored the secondary supply chain equilibrium pricing decision by considering retailers’ fairness preferences and using quantity discount contracts. Huang et al. (2020) investigated the green operation strategies of financially constrained manufacturers under different subsidy models. Tat et al. (2023) analyzed the coordination problem of a green supply chain consisting of a retailer and a manufacturer, and proposed a new combination of consignment and zero-wholesale price contracts, which generates Pareto improvements for both channel members and increases the profitability of the green supply chain.

Blockchain Applications in Supply Chain Finance

For the application of blockchain in agricultural supply chain finance mostly focuses on the empowering effect. Blockchain is a chain structure that utilizes cryptography principles for storage, and is divided into public chain, private chain, and alliance chain. Du et al. (2020) argued that blockchain effectively solves the problem of mistrust between participants in the agricultural supply chain, improves the efficiency of supply chain operations, reduces costs, and provides good financing services for supply chain subjects. Song et al. (2023) suggested that blockchain technology supported the transparency, traceability and verifiability of transmission, which could help to solve the problem of information asymmetry and thus improve financing performance. G. Zhang et al. (2023) suggested that blockchain technology can improve trust among stakeholders because of its secure information-sharing capabilities. Thurner (2018) argued that blockchain can speed up business processes and reduce the cost of financing, bringing significant benefits to the various actors involved. Efanov and Roschin (2018) utilized blockchain technology to innovate the agricultural supply chain financial model so that the information asymmetry can be alleviated. Guo and Liang (2016) pointed out that blockchain can reduce the risk of agricultural supply chain finance. Wu et al. (2023) constructed a green supply chain model consisting of a capital-constrained manufacturer and a retailer, and examined the impact of the application of blockchain technology on the manufacturer’s financing strategy.

One contribution of this paper, this paper examines the integration of blockchain technology in the conventional agricultural supply chain, with a specific focus on addressing the challenges of farmers’ capital constraints. The key parameters considered in this study are the blockchain application cost and value gain. In order to optimize decision-making and maximize benefits, a combination contract involving cost-sharing and benefit-sharing is proposed. The adoption of this approach enables coordination among the members of the agricultural supply chain, facilitating equitable distribution of costs and benefits. This study provides a valuable reference for operational decision-making among supply chain members, enabling them to mitigate the challenges of farmers’ capital constraints and financing.

Decentralization Decision-Making Model Construction

The farmer makes production input quantity decisions based on the seller’s purchase price and the bank loan interest rate, and its expected return is:

π S 1 ( Q 1 ) = E [ w 1 μ Q 1 − ( 1 2 c Q 1 2 ) ( 1 + r ) ]

(1)

The first-order derivative of Equation 1 is ∂ π S 1 ( Q 1 ) / ∂ Q 1 = w 1 μ − c Q 1 ( 1 + r ) , and the second-order derivative is ∂ 2 π S 1 ( Q 1 ) / ∂ Q 1 2 = − c ( 1 + r ) , since ∂ 2 π S 1 ( Q 1 ) / ∂ Q 1 2 < 0 , π S 1 ( Q 1 ) are concave functions about Q 1 , let ∂ π S 1 ( Q 1 ) / ∂ Q 1 = 0 , the optimal amount of production input for the farmer can be calculated as:

Q 1 * = w 1 μ c ( 1 + r )

(2)

The seller’s revenue under blockchain technology is equal to the market sale revenue minus the farm produce acquisition cost paid to the farmer minus the blockchain application cost plus the value gain from the blockchain, so the seller’s expected revenue is:

π R 1 ( w 1 ) = E [ ( p − w 1 − c B + v ) μ Q 1 ]

(3)

w 1 * = ( a − c B + v ) c ( 1 + r ) 2 [ b μ 2 + c ( 1 + r ) ]

(4)

The optimal amount of production input for the farmer at this point is:

Q 1 * = ( a − c B + v ) μ 2 [ b μ 2 + c ( 1 + r ) ]

(5)

The optimal expected returns for farmers and sellers are:

π S 1 ( Q 1 * ) = ( a − c B + v ) 2 μ 2 c ( 1 + r ) 8 [ b μ 2 + c ( 1 + r ) ] 2

(6)

π R 1 ( w 1 * ) = ( a − c B + v ) 2 μ 2 4 [ b μ 2 + c ( 1 + r ) ]

(7)

Proof: Substituting Equation 2 into Equation 3 yields π R 1 ( w 1 ) = ( a − c B + v ) μ 2 w 1 c ( 1 + r ) − b μ 4 w 1 2 c 2 ( 1 + r ) 2 − μ 2 w 1 2 c ( 1 + r ) , the first-order derivative is ∂ π R 1 ( w 1 ) ∂ w 1 = ( a − c B + v ) μ 2 c ( 1 + r ) − 2 b μ 4 w 1 c 2 ( 1 + r ) 2 − 2 μ 2 w 1 c ( 1 + r ) , and the second-order derivative is ∂ 2 π R 1 ( w 1 ) ∂ w 1 2 = − 2 b μ 4 c 2 ( 1 + r ) 2 − 2 μ 2 c ( 1 + r ) . Since ∂ 2 π R 1 ( w 1 ) / ∂ w 1 2 < 0 , π R 1 ( w 1 ) is a concave function of w 1 , ∂ π R 1 ( w 1 ) / ∂ w 1 = 0 , which can be solved by w 1 * = ( a − c B + v ) c ( 1 + r ) 2 [ b μ 2 + c ( 1 + r ) ] . Substituting Equation 4 into Equation 2 yields: Q 1 * = μ ( a − c B + v ) 2 [ b μ 2 + c ( 1 + r ) ] . Substituting Equations 4 and 5 into Equations 1 and 3, the returns of the farmer and the seller can be calculated. Prove the end.

Centralized Decision-Making Model Construction

Only Q 2 is the decision variable in centralized decision making, and the overall benefit of the supply chain is:

π SC 2 ( Q 2 ) = E [ ( p − c B + v ) μ Q 2 − 1 2 c Q 2 2 ( 1 + r ) ]

(8)

Q 2 * = ( a − c B + v ) μ 2 b μ 2 + c ( 1 + r )

(9)

The overall benefit of the supply chain at this point is:

π SC 2 ( Q 2 * ) = ( a − c B + v ) 2 μ 2 2 [ 2 b μ 2 + c ( 1 + r ) ]

(10)

Proof: The first-order derivative of Equation 8 is ∂ π SC 2 ( Q 2 ) / ∂ Q 2 = ( a − c B + v ) μ − 2 b μ 2 Q 2 − c Q 2 ( 1 + r ) , and the second-order derivative is ∂ 2 π SC 2 ( Q 2 ) / ∂ Q 2 2 = − 2 b μ 2 − c ( 1 + r ) .as ∂ 2 π SC 2 ( Q 2 ) / ∂ Q 2 2 < 0 , so π SC 2 ( Q 2 ) is a concave function of Q 2 , so that ∂ π SC 2 ( Q 2 ) / ∂ Q 2 = 0 , solving for Q 2 * = ( a − c B + v ) μ / [ 2 b μ 2 + c ( 1 + r ) ] . The overall return of the supply chain when centralized decision-making can be calculated by substituting Equations 8 and 9. Proof.

Decision-Making Metrics and Benefit Analysis of Agricultural Supply Chain with Blockchain Technology

Combining Propositions 1 and 2 leads to Conclusion 1:

Conclusion 1: The optimal production and returns of the agricultural supply chain at decentralized decision-making do not reach the Pareto optimum at centralized decision-making.

Proof. Q 2 * − Q 1 * = ( a − c B + v ) μ 2 b μ 2 + c ( 1 + r ) − ( a − c B + v ) μ 2 [ b μ 2 + c ( 1 + r ) ] = ( a − c B + v ) μ c ( 1 + r ) 2 [ 2 b μ 2 + c ( 1 + r ) ] [ b μ 2 + c ( 1 + r ) ] > 0 , so, the optimal amount of production inputs is greater in centralized decision making than in decentralized decision making.

The expected total return of the farmer and the seller at decentralized decision making is:

π S 1 ( Q 1 * ) + π R 1 ( w 1 * ) = ( a − c B + v ) 2 μ 2 c ( 1 + r ) 8 [ b μ 2 + c ( 1 + r ) ] 2 + ( a − c B + v ) 2 μ 2 4 [ b μ 2 + c ( 1 + r ) ] = ( a − c B + v ) 2 μ 2 [ 2 b μ 2 + 3 c ( 1 + r ) ] 8 [ b μ 2 + c ( 1 + r ) ] 2 ,

π SC 2 ( Q 2 * ) − [ π S 1 ( Q 1 * ) + π R 1 ( w 1 * ) ] = ( a − c B + v ) 2 μ 2 2 [ 2 b μ 2 + c ( 1 + r ) ] − ( a − c B + v ) 2 μ 2 [ 2 b μ 2 + 3 c ( 1 + r ) ] 8 [ b μ 2 + c ( 1 + r ) ] 2 = ( a − c B + v ) 2 μ 2 c 2 ( 1 + r ) 2 8 [ 2 b μ 2 + c ( 1 + r ) ] [ b μ 2 + c ( 1 + r ) ] 2 > 0

That is, the overall return of the agricultural supply chain in the centralized decision-making is greater than the total return of the decentralized decision-making farmers and sellers. Therefore, the returns and optimal production of the agricultural supply chain in the decentralized decision-making are not Pareto-optimal in the centralized decision-making.

Cost-Sharing Contract Modelling

Let the cost-sharing coefficients for the farmer be λ and λ ∈ [ 0 , 1 ] , and the cost-sharing coefficient for the seller be 1 − λ .

The benefits to the farmer and the seller when coordinated using a cost-sharing contract are respectively:

π S 3 = E [ w 3 μ Q 3 − 1 2 c Q 3 2 ( 1 + r ) − λ c B μ Q 3 ]

(11)

π R 3 = E { [ p − w 3 − ( 1 − λ ) c B + v ] μ Q 3 }

(12)

Q 3 * = ( w 3 − λ c B ) μ c ( 1 + r )

(13)

w 3 * = ( a − c B + λ c B + v ) c ( 1 + r ) + 2 b μ 2 λ c B 2 b μ 2 + c ( 1 + r )

(14)

Therefore, the returns to the farmer and the seller under the cost-sharing contract are, respectively:

π S 3 ( Q 3 * ) = ( a − c B + v ) 2 μ 2 c ( 1 + r ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2

(15)

π R 3 ( w 3 * ) = b μ 4 ( a − c B + v ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2

(16)

Decision-Making Metrics and Benefit Analysis of Agricultural Supply Chain Under Blockchain Technology

Conclusion 2 can be obtained from Proposition 3:

Conclusion 2: Under the cost-sharing contract, supply chain coordination in the agricultural supply chain cannot be achieved due to the unequal distribution of benefits. Although farmers share part of the blockchain application costs, retailers are forced to raise the purchase price of agricultural products to compensate for the farmers’ losses. This, in turn, compresses the retailers’ profit margins, preventing their earnings from reaching Pareto optimality. The cost-sharing contract, in its simplicity, overlooks the dynamic game relationships within the supply chain and fails to balance the coordination of interests among all parties. It neglects the diminishing marginal returns for retailers, making it difficult to stimulate the maximum synergistic effect of cooperation and ultimately failing to achieve supply chain coordination.

Proof: the sum of the benefits of the farmer and the seller under the cost-sharing contract is:

π S 3 ( Q 3 * ) + π R 3 ( w 3 * ) = ( a − c B + v ) 2 μ 2 c ( 1 + r ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2 + b μ 4 ( a − c B + v ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2 = ( a − c B + v ) 2 μ 2 2 [ 2 b μ 2 + c ( 1 + r ) ] = π SC 2 ( Q 2 * )

That is, the total return to decentralized decision-making farmers and sellers is equal to the overall return to the agricultural supply chain when decision-making is centralized.

π S 3 ( Q 3 * ) − π S 1 ( Q 1 * ) = ( a − c B + v ) 2 μ 2 c ( 1 + r ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2 − ( a − c B + v ) 2 μ 2 c ( 1 + r ) 8 [ b μ 2 + c ( 1 + r ) ] 2 . Since the numerators are the same, you only need to compare the size of the denominators. 2 [ 2 b μ 2 + c ( 1 + r ) ] 2 − 8 [ b μ 2 + c ( 1 + r ) ] 2 = − 8 b μ 2 c ( 1 + r ) − 6 c 2 ( 1 + r ) 2 < 0 , so π S 3 ( Q 3 * ) − π S 1 ( Q 1 * ) > 0 .

The difference between the seller’s return under the cost-sharing contract and the seller’s return in the case of decentralized decision-making is: π R 3 ( w 3 * ) − π R 1 ( w 1 * ) = b μ 4 ( a − c B + v ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2 − ( a − c B + v ) 2 μ 2 4 [ b μ 2 + c ( 1 + r ) ] = − ( a − c B + v ) 2 μ 2 c 2 ( 1 + r ) 2 4 [ 2 b μ 2 + c ( 1 + r ) ] 2 [ b μ 2 + c ( 1 + r ) ] < 0 , so π R 3 ( w 3 * ) < π R 1 ( w 1 * ) .

Therefore, supply chain coordination cannot be achieved in agricultural supply chain under cost sharing contract.

It is found through calculations that:

w 3 * − w 1 * = ( a − c B + λ c B + v ) c ( 1 + r ) + 2 b μ 2 λ c B 2 b μ 2 + c ( 1 + r ) − ( a − c B + v ) c ( 1 + r ) 2 [ b μ 2 + c ( 1 + r ) ] = 2 b μ 2 λ c B [ 2 b μ 2 + 3 c ( 1 + r ) ] + c 2 ( 1 + r ) 2 [ ( a − c B + v ) + 2 λ c B ] 2 [ 2 b μ 2 + c ( 1 + r ) ] [ b μ 2 + c ( 1 + r ) ] > 0 , w 3 * > w 1 * , Therefore, it can be concluded that the reason why the supply chain under the cost-sharing contract does not achieve coordination: because farmers help sellers to share the cost of blockchain application, sellers will increase the purchase price of agricultural products, resulting in the seller’s revenue becoming less, so the farmer’s revenue under the cost-sharing contract is smaller than that of the farmer under decentralized decision-making, which results in the failure of supply chain coordination of agricultural products supply chain under the cost-sharing contract.

Cost Sharing-Revenue Sharing Contract Model Construction

As can be seen from the above, the seller will increase the purchase price of agricultural products to a certain extent due to the farmers’ help in sharing the cost of blockchain application, which will motivate the farmers to increase the amount of production inputs, but lead to the reduction of their own profits. In view of the weak position of farmers in the agricultural supply chain, they can no longer share the farmers’ income to compensate for the sellers’ income to achieve supply chain coordination, so we try to share the sellers’ income with farmers to make the purchase price of agricultural products decrease, so that the increased shared income of farmers and the reduced purchase income of agricultural products can reach a balance, and the seller’s income can achieve the Pareto optimal, so as to achieve the coordination of the agricultural products supply chain. After the sale of agricultural products, both parties share the revenue of the seller’s sales p μ Q , and let the revenue sharing coefficients of the farmers be ϕ , ϕ ∈ [ 0 , 1 ] , and the seller be 1 − ϕ .

The expected returns of the farmer and the seller under the cost-sharing-revenue-sharing contract are:

π S 4 = E [ w 4 μ Q 4 − 1 2 c Q 4 2 ( 1 + r ) − λ c B μ Q 4 + ϕ p μ Q 4 ]

(17)

[ ( 1 − ϕ p − w 4 − ( 1 − λ ) c B + v ] μ Q 4 }

(18)

Q 4 ∗ = w 4 − λ c B + ϕ p μ c ( 1 + r )

(19)

w 4 * = ( a − c B + λ c B − ϕ p + v ) c ( 1 + r ) + 2 b μ 2 ( λ c B − ϕ p ) 2 b μ 2 + c ( 1 + r )

(20)

The expected returns to farmers and sellers under the cost-sharing-revenue-sharing contract are:

π S 4 ( Q 4 * ) = ( a − c B + v ) 2 μ 2 c ( 1 + r ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2

(21)

π R 4 ( w 4 * ) = ( 1 + ϕ ) b μ 4 ( a − c B + v ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2

(22)

Proof: the first-order derivative of Equation 17 is ∂ π S 4 ( Q 4 ) / ∂ Q 4 = ( w 4 − λ c B + ϕ p ) μ − c Q 4 ( 1 + r ) , and the second-order derivative is ∂ 2 π S 4 ( Q 4 ) / ∂ Q 4 2 = − c ( 1 + r ) . Since ∂ 2 π S 4 ( Q 4 ) / ∂ Q 4 2 < 0 , π S 4 ( Q 4 ) are concave functions with respect to Q 4 , let ∂ π S 4 ( Q 4 ) / ∂ Q 4 = 0 , and the optimal amount of production inputs for the farmer is Q 4 * = ( w 4 − λ c B + ϕ p ) μ / c ( 1 + r ) .

In order to make the optimal production of the farmer under contractual coordination optimal for centralized decision making, let Q 4 * = Q 2 * ,and solve for w 4 * = ( a − c B + λ c B − ϕ p + v ) c ( 1 + r ) + 2 b μ 2 ( λ c B − ϕ p ) 2 b μ 2 + c ( 1 + r ) .

Decision-Making Metrics and Benefit Analysis of Agricultural Supply Chain Under Blockchain Technology

Conclusions 3 and 4 can be obtained from Proposition 4:

Conclusion 3: Under the cost-sharing-revenue-sharing contract, effective coordination within the agricultural supply chain is achievable. This is due to the optimization of benefit distribution between the parties, built upon the foundation of cost-sharing. Sellers share a portion of the sales revenue, thereby alleviating some of the farmers’ blockchain application costs. By appropriately lowering the purchase price of agricultural products, sellers increase their own profits while compensating for the reduced direct income of farmers caused by the price reduction. The analysis reveals that the designed contract ensures incentive compatibility between the parties. It not only enhances the farmers’ motivation but also optimizes the distribution of profits, thereby strengthening the stability of cooperation between farmers and retailers. This coordination ultimately leads to the achievement of Pareto optimality for the entire supply chain.

π R 4 ( w 4 * ) > π R 1 ( w 1 * ) , π S 4 ( Q 4 * ) = π S 3 ( Q 3 * ) > π S 1 ( Q 1 * ) .

Proof: the optimal production inputs under the cost-sharing-benefit-sharing contract reach the optimum under centralized decision-making. Therefore, it is only necessary to determine whether the returns of the farmer and the seller under the cost-sharing-return-sharing contract are greater than the returns of the farmer and the seller, respectively, under decentralized decision-making.

The difference between the returns of the farmer under the cost-sharing-return-sharing contract and the returns of the farmer under decentralized decision-making is:

π S 4 ( Q 4 * ) − π S 1 ( Q 1 * ) = ( a − c B + v ) 2 μ 2 c ( 1 + r ) 2 [ 2 b μ 2 + c ( 1 + r ) ] 2 − ( a − c B + v ) 2 μ 2 c ( 1 + r ) 8 [ b μ 2 + c ( 1 + r ) ] 2 , Since the numerators are the same, you only need to compare the size of the denominators. 2 [ 2 b μ 2 + c ( 1 + r ) ] 2 − 8 [ b μ 2 + c ( 1 + r ) ] 2 = − 8 b μ 2 c ( 1 + r ) − 6 c 2 ( 1 + r ) 2 < 0 . Therefore, π S 4 ( Q 4 * ) > π S 1 ( Q 1 * ) .

The difference between the seller’s return under the cost-sharing-revenue-sharing contract and the seller’s return in the case of decentralized decision-making is:

π R 4 ( w 4 * ) − π R 1 ( w 1 * ) = ( a − c B + v ) 2 μ 2 4 ϕ b 2 μ 4 + 4 ϕ b μ 2 c ( 1 + r ) − c 2 ( 1 + r ) 2 4 [ 2 b μ 2 + c ( 1 + r ) ] 2 [ b μ 2 + c ( 1 + r ) ]

(23)

To make π R 4 ( w 4 * ) ≥ π R 1 ( w 1 * ) , it is necessary to make Equation 23 ≥ 0, which can be solved for ϕ ≥ c 2 ( 1 + r ) 2 4 b 2 μ 4 + 4 b μ 2 c ( 1 + r ) . Thus when ϕ ≥ c 2 ( 1 + r ) 2 4 b 2 μ 4 + 4 b μ 2 c ( 1 + r ) , supply chain coordination can be achieved under the portfolio contract. because: w 4 * − w 3 * = ( a − c B + λ c B − ϕ p + v ) c ( 1 + r ) + 2 b μ 2 ( λ c B − ϕ p ) 2 b μ 2 + c ( 1 + r ) − ( a − c B + λ c B + v ) c ( 1 + r ) + 2 b μ 2 λ c B 2 b μ 2 + c ( 1 + r ) = − ϕ p < 0 .

It can be summarized that the reason why the cost-sharing-revenue-sharing contract can achieve the coordination of the supply chain is that the seller’s purchase price is reduced under this combination contract, which enables the seller to obtain more profits, and does not harm the interests of the farmers, and achieves a balance between the reduction of the farmers’ revenue from the sale of agricultural products and the increase of the revenue of the shared seller. Under the cost-sharing-return-sharing contract, the returns of both farmers and sellers reach the Pareto optimum, so the agricultural supply chain can reach a coordinated state under this combination contract.

Conclusion 4: Under the cost-sharing-revenue-sharing contract, the optimal purchase price w 4 * of agricultural products exhibits the following characteristics: w 4 * is positively correlated with the cost-sharing coefficient λ . As farmers bear a larger share of the blockchain application costs, their bargaining power increases, resulting in a higher purchase price. Conversely, w 4 * is negatively correlated with the revenue-sharing coefficient ϕ . A higher revenue share for farmers leads retailers to reduce the purchase price to balance the resulting profit loss. The analysis indicates that the interaction between the cost-sharing and revenue-sharing parameters may introduce nonlinear effects. Therefore, contract design must take these parameters into account holistically. While it is important to enhance farmers’ motivation, balancing the incentive structure for retailers is also necessary to achieve overall supply chain coordination.

Proof: w 4 * = ( a − c B + λ c B − ϕ p + v ) c ( 1 + r ) + 2 b μ 2 ( λ c B − ϕ p ) 2 b μ 2 + c ( 1 + r ) , for which the first-order derivative with respect to λ yields ∂ w 4 * ∂ λ = c B > 0 , so w 4 * is an increasing function of λ . The larger the λ , the larger the w 4 * .

The above analysis shows that the supply chain cannot be coordinated when decentralized decision making. Since powerful sellers bear the cost of blockchain application, this paper proposes a cost-sharing contract to coordinate the supply chain. From the analysis, it can be seen that the cost-sharing contract cannot achieve supply chain coordination because the farmers help the sellers to share the cost of blockchain application, and the sellers will give certain benefit compensation to the farmers, which leads to a lower purchase price of the agricultural products, and makes the sellers’ benefits less than those in the case of decentralized decision-making. Therefore, consider introducing a gain-sharing contract, and consider allowing the seller to give a portion of the gain to the supplier, which will result in a lower purchase price and an increase in the shared gain for the farmer that is equal to the reduced gain from the sale of the produce. When the gain-sharing ratio varies within a certain range, the portfolio contract leads to a coordinated state of the agricultural supply chain.

Impact of Agricultural Output Rates on Decision-Making Indicators and Returns

Based on the observations derived from Figure 3a, it is evident that, across the four scenarios, an upward trend followed by a gradual decline can be observed in the optimal production inputs of farmers as the agricultural output rate increases. Specifically, farmers are willing to increase the amount of production inputs when the production rate falls below a certain threshold. However, as the agricultural production rate exceeds a certain threshold, farmers tend to gradually reduce their production inputs due to the higher associated production input costs. Moreover, Figure 3a depicts that the amount of production inputs after both centralized and coordinated decision-making is greater than the amount of production inputs when decision-making is decentralized.

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Figure 3.

(a) Impact of agricultural output rate on optimal production inputs, (b) impact of agricultural output rate on optimal purchase price, (c) impact of agricultural output rate on farmer’s revenue, and (d) impact of agricultural output rate on seller’s revenue.

Observations from Figure 3b reveal a clear trend across the three scenarios: the seller’s optimal purchase price exhibits a declining pattern as the output rate of agricultural products increases. This can be attributed to the fact that as the output rate rises, there is a corresponding increase in the volume of agricultural products entering the market. Consequently, the seller incurs additional acquisition costs to accommodate this surge in supply. As the supply of agricultural products in the market exceeds the demand, the selling price of agricultural products decreases, prompting the seller to lower the purchase price to protect their profit margin.

This observation also provides further insights into Figure 3a, revealing that farmers, in response to the decrease in purchase price, farmers reduce their production levels. In Figure 3b, the optimal purchase price under the coordination of the cost-sharing-revenue-sharing contract is higher than the optimal purchase price at decentralized decision-making, and the optimal purchase price after coordination of the cost-sharing contract is lower than the optimal purchase price at decentralized decision-making. These findings indicate that sellers reduce the purchase price of agricultural products when the cost-sharing-revenue-sharing contract is coordinated in order to balance the loss of self-interest due to the sharing of sales proceeds with farmers.

According to the observations made in Figure 3c, both the decentralized decision-making and contractual coordination of farmers’ revenue exhibit a similar trend with the increase in the output rate of agricultural products. Initially, there is a rapid increase in both the returns and the optimal amount of production inputs. However, beyond a certain point, this trend reverses, and both returns and the optimal production inputs begin to decline. This indicates that farmers must maintain the output rate of agricultural products within a certain range to ensure the appropriate amount of production inputs, thus maximizing their returns.

Figure 3d illustrates the effects of the seller’s revenue as the output rate of agricultural products increases in three scenarios. The results show that, in all three scenarios, the seller’s revenue increases gradually with the agricultural output rate until it reaches a certain threshold, after which the revenue levels off. This phenomenon occurs because when the output rate of agricultural products is too high, the market becomes flooded with products, and the market for agricultural products is in a state of oversaturation leading to a drop in the selling price and a decrease in the seller’s revenue. Therefore, it is crucial to maintain the output rate of agricultural products within an optimal range. The findings emphasize that too much output rate leads to oversaturation of the market which is detrimental to both parties’ returns and the overall returns of the supply chain. Therefore, it is crucial to maintain the output rate of agricultural products within an optimal range.

Impact of Blockchain Value Addition on Decision-Making Indicators and Returns

Figure 4a to d collectively demonstrate a clear relationship between the blockchain value addition per unit of agricultural products and various key indicators. Specifically, the optimal production input volume of farmers, the optimal purchase price of agricultural products, the revenue of farmers, and the revenue of sellers all exhibit a positive correlation with the blockchain value addition per unit of agricultural products. The findings indicate that a higher blockchain value addition increases the income of both farmers and sellers. Furthermore, it serves as a motivator for farmers and sellers to adopt blockchain technology, leading to an increase in the amount of production inputs and the purchase price of agricultural products.

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Figure 4.

(a) Impact of blockchain value addition on optimal production inputs, (b) impact of blockchain value addition on optimal purchase price, (c) impact of blockchain value addition on farmer’s revenue, and (d) impact of blockchain value addition on seller’s revenue.

Impact of Blockchain Application Costs on Decision-Making Indicators and Returns

Figure 5a to d collectively demonstrate that the optimal amount of production inputs for the farmer, the optimal purchase price of agricultural products, the farmer’s revenue, and the seller’s revenue are all inversely proportional to the cost of blockchain adoption per unit of agricultural product. Specifically, as the cost of blockchain applications per unit of agricultural product increases, a decrease in the aforementioned variables is evident.

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Figure 5.

(a) Impact of blockchain application costs on optimal production inputs, (b) impact of blockchain application costs on optimal purchase price, (c) impact of blockchain application costs on farmer’s revenue, and (d) impact of blockchain application costs on seller’s revenue.

Figure 5b illustrates a noticeable trend wherein the purchase price of agricultural products experiences a reduction as the blockchain cost increases within the context of decentralized decision-making. This phenomenon can be attributed to the complete burden of the blockchain application cost on the seller under decentralized decision-making. As the blockchain application cost escalates, sellers, in an endeavor to safeguard their interests, opt to mitigate the impact by lowering the purchase price of agricultural products. However, when examining the coordination facilitated by two contractual agreements, farmers contribute to alleviating a portion of the blockchain application costs borne by the sellers. Therefore, with increasing blockchain application costs, sellers are inclined to adjust the purchase price of agricultural products upwards to offset the expenses shared by the farmers.

According to the observations from Figure 5b, the optimal purchase price under the cost-sharing-revenue-sharing contract is lower than the optimal purchase price under decentralized decision-making. This outcome can be attributed to the dynamic interplay of incentives within the cost-sharing-revenue-sharing contract structure—while farmers assist in defraying the costs associated with blockchain usage, they also partake in the seller’s sales revenue. Consequently, the seller is inclined to reduce the purchase price of agricultural products to safeguard the farmer’s revenue. As depicted in Figure 5d, an intriguing observation emerges when the cost of blockchain application is fixed: despite farmers sharing in the blockchain application costs with the sellers, the seller’s benefits are lower than those under decentralized decision-making within the cost-sharing contract. This outcome signifies that the cost-sharing contract fails to attain the level of supply chain coordination envisioned.

Impact of Cost-Sharing Coefficient on Decision-Making Indicators and Returns

Figure 6a to d collectively demonstrate that the amount of agricultural inputs produced by a farmer, the farmer’s revenue, and the seller’s revenue are independent of the blockchain cost-sharing coefficient. The findings from Figure 6b reveal a notable trend, where the purchase price of agricultural products escalates in conjunction with an increase in the blockchain cost-sharing coefficient. This observation signifies that as the blockchain cost-sharing coefficient grows, reflecting a greater contribution from farmers to defray the blockchain usage costs for sellers, sellers are motivated to raise the purchase price of agricultural products to compensate farmers for their share. Additionally, Figure 6b illustrates that the purchase price of agricultural products under the cost-sharing-revenue-sharing contract is lower than the purchase price under the cost-sharing contract. This discrepancy can be attributed to the sellers allocating a portion of the sales proceeds to the farmers within the cost-sharing-revenue-sharing framework. Consequently, the sellers adjust the purchase price of agricultural products upward to safeguard their own interests, leading to a lower purchase price compared to the cost-sharing contract.

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Figure 6.

(a) Impact of cost-sharing coefficient on optimal production inputs, (b) impact of cost-sharing coefficient on optimal purchase price, (c) impact of cost-sharing coefficient on farmer’s revenue, and (d) impact of cost-sharing coefficient on seller’s revenue.

Impact of Revenue-Sharing Coefficient on Decision-Making Indicators and Returns

Figure 7 collectively demonstrates that the amount of agricultural inputs produced by a farmer, and the farmer’s revenue are independent of the revenue-sharing coefficient, selling price of agricultural products is inversely proportional to the revenue-sharing coefficient. This suggests that as the coefficient of revenue-sharing increases, signifying a greater proportion of sales income shared by the farmers, the sellers are inclined to adjust the purchase price of agricultural products downward in order to protect their own interests. However, the seller’s return exhibits a positive association with the revenue-sharing coefficient. As the revenue-sharing coefficient increases, the seller’s purchase price of agricultural products allocated to the farmer decreases, leading to an enhancement in the seller’s profitability and, consequently, an increase in their return on investment.

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Figure 7.

Impact of revenue-sharing coefficient on decision-making indicators and returns.