Blockchain-Enabled Supply Chain Internal and External Finance Model

Abstract

This study applies Stackelberg game theory to analyze and compare optimal operational strategies in four supply chain finance scenarios: traditional trade financing (TI), trade financing through the blockchain platform (BI), traditional external financing (TE), and external financing through the blockchain platform (BE). The main findings are as follows: First, the adoption of the blockchain platform reduces the interest rate threshold, making external financing more advantageous for retailers with higher capital constraint. Further, financing through the blockchain platform leads to higher wholesale prices, retail prices, and order quantities compared to traditional financing scenarios. Second, internal trade financing and the use of blockchain technology are preferred over external bank financing. However, conducting external bank financing through the blockchain platform yields greater profit growth for manufacturers and retailers. Accessing the blockchain platform is the optimal strategy for retailers and banks, leading to a favorable “multi-win” situation when the manufacturer’s platform fees are reasonable. Third, the manufacturer’s risk guarantee ratio plays a crucial role in determining the choice of financing mode, particularly when the retailer faces the risk of debt default. This study contributes to the literature by quantifying the impacts of blockchain technology deployment for three aspects that have been overlooked in previous studies: the set-up cost and access fee of the blockchain platform, the service level provided by the platform, and the demand increase resulting from blockchain technology adoption.

1. Introduction

Small and medium-sized enterprises (SMEs) play an important role in driving economic growth, job creation, and innovation in a country. For example, in China, small and medium-sized enterprises (SMEs) represent the largest and most dynamic group of enterprises. They make up over 90% of all businesses and contribute more than 50% of the tax revenue, over 60% of the GDP, more than 70% of the technological innovation, and more than 80% of the urban labor employment. However, SMEs often encounter various challenges, including high demand/supply uncertainty, frequent cash flow disruptions, and difficulties in recruitment and employment [1]. Of these challenges, cash flow disruptions caused by insufficient internal funds and external financing constraints pose particular problems for SMEs [2]. These constraints can limit their ability to manage day-to-day operations, invest in growth opportunities, and navigate through economic fluctuations. As a result, finding effective solutions for improving cash flow management and accessing adequate financing is crucial for the success and sustainability of SMEs.

Supply chain finance (SCF) has been widely recognized as one such solution [3]. SCF is an innovative financing method that integrates operational management and finance [4]. It differs from traditional credit models by being based on the entire supply chain system and the cooperative relationships between upstream and downstream partners, utilizing real transaction information [3,4,5]. However, despite the potential benefits of SCF, its implementation in business practice still faces several pain points [6]. One of the key issues is the lack of quality and transparent transactional information provided by SMEs [7,8,9]. This poses difficulties for lending institutions in conducting proper information screening and risk assessment [10,11], leading to limited interest in providing financing to SMEs. Therefore, finding ways to strengthen the credit rating of SMEs and reduce financing risks for lending institutions is of great practical significance. It can help address the financing difficulties and high costs associated with SMEs and improve the overall operational efficiency of the supply chain.

Blockchain technology has gained significant attention and interest across various industries, including healthcare [12], agri-food [13], energy [14], and supply chain management [15]. It leverages asymmetric encryption, has functions, consensus mechanisms, and smart contracts to create a decentralized, transparent, and non-tamperable database system [16,17]. These features make blockchain particularly suitable for SCF scenarios that require multi-party cooperation but lack trust among the participants. The combination of blockchain and SCF can enable the transformation and upgrade of traditional SCF into digital and intelligent SCF [18]. While qualitative analyses have been conducted on the impacts of blockchain on SCF operations, quantitative analyses (e.g., [19,20,21]) are scarce and such research is still in its early stages. This study, thus, aims to examine the impacts of blockchain technology on optimal operations strategies in internal and external SCF scenarios, which have not been thoroughly investigated so far. Specifically, our goal in this paper is to address four sets of research questions:

• What is the optimal pricing of the traditional supply chain internal trade financing and external bank financing mode? What is the optimal pricing of the blockchain-enabled internal trade financing and external bank financing mode? What are the differences between the two modes in terms of optimal pricing?
• Is the internal trade financing mode always a better choice relative to the external bank financing mode? How does blockchain technology influence interest rates, consumer demand, and the expected profits of all the participating businesses in the two financing modes? Is the blockchain-enabled financing mode always better than the traditional financing mode?
• How do the blockchain-related costs influence supply chain operations? What are the incentives for SCF participants to access the blockchain platform? What are the conditions under which the blockchain-enabled financing mode creates a win-win situation?
• How does blockchain technology impact the strategies of each SCF participant when the financing enterprise has default risk?

Our contribution to the SCF literature are that we quantify the impacts of three aspects associated with blockchain technology deployment, which have been largely ignored in the extant literature. First, we examine the impacts of the set-up cost and the access fee of the blockchain platform. Second, we examine the impacts of the service level afforded by the blockchain platform. Lastly, we examine the impacts of the demand increase caused by blockchain technology deployment.

The remainder of this paper is structured as follows: Section 2 offers a comprehensive review of the relevant literature. Section 3 describes and explains the specific SCF modes in detail. Section 4 focuses on developing and analyzing mathematical models for the SCF modes. Section 5 employs numerical examples and simulations to illustrate the effects of the models’ parameters. Furthermore, Section 6 presents an extended model that considers the financing risk scenario. Finally, Section 7 discusses the management implications and points out future research directions.

2. Literature Review

2.1. SCF

SCF, as the preferred solution for small and medium-sized enterprises (SMEs), can effectively reduce financing costs, improve financing efficiency, and optimize cash flow [22]. As a result, it has garnered significant attention from both the academic and business communities [23,24]. SCF is an innovative financial service that takes a holistic approach from the perspective of the entire supply chain system. It evaluates the credit and risk levels of financing based on real transactions and data established through long-term collaboration between core enterprises and their upstream and downstream partners. This type of financing service provides a combination of production and finance to help financially constrained enterprises [25].

Based on the different sources of funding, SCF can be categorized into two modes: internal financing and external financing. Internal financing involves a financially strong member within the supply chain providing financial resources to other members. This financing process occurs within the supply chain system through trade credit, establishing a creditor–debtor relationship between supply chain members [26,27]. A typical example of internal financing is deferred payment, also known as trade credit [28]. In external financing, supply chain members obtain financial support from financial institutions, such as banks [29].

Qin et al. [30] compared three financing modes in a supply chain network composed of a well-funded supplier, a financially constrained manufacturer, and an e-commerce platform: e-commerce platform financing, internal trade financing, and hybrid financing. The analysis shows that the manufacturer is more inclined to choose e-commerce platform financing when the manufacturer’s funding is slightly constrained, and the e-commerce platform offers a lower financing interest rate than the internal trade financing. However, when the funding constraints on the manufacturer are moderate and the e-commerce platform charges relatively high usage fees, the manufacturer tends to prefer internal trade financing. Lai et al. [31] examined a green supply chain financing system, comprising a fully capitalized supplier and a manufacturer facing constraints to both its operating capital and green innovation capital. In this system, the manufacturer has two options to seek financial support: internal collaboration financing and external investment. The research findings reveal the most advantageous roles for the supplier within internal collaborative financing schemes, as well as the manufacturer’s preferences concerning internal and external financing approaches. Lai et al. [32] conducted a study on a green supply chain composed of a supplier and a manufacturer. The study focused on two financing schemes, with constraints on the manufacturer’s operating capital and green innovation capital, namely: bank credit financing (BCF) and supplier green investment (SGI). The results indicate that the manufacturer’s financing decision preference and the bank loan interest rate play significant roles in selecting the appropriate financing scheme. In addition, the study showed that both cost-sharing and quantity discount contracts demonstrate the ability to achieve supply chain coordination when the cost-sharing ratio and quantity discount rate are set at appropriate levels.

2.2. Blockchain and Sustainable Supply Chain Management

Blockchain technology achieves a decentralized database by combining knowledge and techniques from cryptography, economics, and computer science [33,34]. It utilizes an encrypted chain of blocks to validate and store data, uses distributed consensus algorithms to generate and update the data, and uses automated script code (smart contracts) for programming and operating the data [33]. Each block, the basic unit of storage [35], consists of a block header and block body [36]. The block header contains metadata, such as the protocol version number, parent block hash, and timestamp, while the block body stores transaction data [37]. Blocks are connected in chronological order through hash functions to form a blockchain, which operates on a peer-to-peer network. Multiple nodes on the network participate in data generation and verification through distributed consensus algorithms, with each node holding a complete copy of the data [38]. The data recorded on the blockchain possesses excellent characteristics, such as being traceable, transparent, anonymous, and immutable [39].

Blockchain technology has the potential to significantly enhance supply chain sustainability [40] in three key aspects: Firstly, blockchain provides a decentralized, immutable, and transparent ledger that traces the entire product journey. This visibility enables organizations to identify inefficiencies and optimize processes, reducing waste and improving overall efficiency [41]. Secondly, blockchain creates an auditable trail, allowing verification of product authenticity, quality, and ethical standards at each stage. It promotes traceability, accountability, and responsible behavior among supply chain participants, discouraging fraudulent activities and reducing risks [42,43]. Thirdly, blockchain facilitates the establishment of a decentralized and immutable record of product quality and certifications. Stakeholders can access reliable information about product origin, composition, and compliance, ensuring the distribution of safe and high-quality products throughout the supply chain [44].

2.3. Impacts of Blockchain on SCF Decision-Making

The primary challenge in SCF practices lies in the significant information asymmetry between financing institutions and financing enterprises [45]. In most cases, the ERP systems of core enterprises, upstream and downstream enterprises, financial institutions, and other major members within the SCF system are not interconnected, leading to serious data barriers. Consequently, it becomes challenging to integrate information across the entire supply chain. Additionally, this information asymmetry among member enterprises poses difficulties for banks and other financial institutions in terms of risk control, leading to issues such as adverse selection [46] and moral hazard [47]. Blockchain technology provides a new way to solve these problems. The application of blockchain technology cannot only simplify the communication process and trace the source of products, but also nurture mutual trust among member enterprises in the SCF system [48], so as to effectively avoid the risks of SCF and improve the availability of financing.

As shown in

Table 1. Literature summary.

Author	Year	Financing Mode	Decision-Making Model	Market Demand	Blockchain Technology
					Access Fee and Set-Up Cost	Application Level
Jiang et al. [49]	2022	External Financing	Trust Transitivity Model	Fixed	Not considering	Not Considering
Dong et al. [50]	2021	External Financing	Game Theory (Decentralized Decision-making)	Fixed	Considering Access Fee but not Set-up Cost	Not Considering
Wang et al. [51]	2023	Internal Financing	Game Theory (Decentralized Decision-making)	Fixed	Considering Access Fee but not Set-up Cost	Not Considering
Wang and Zhou [52]	2021	External Financing	Game Theory (Decentralized Decision-making)	Fixed	Considering Access Fee but not Set-up Cost	Not Considering
Shibuya and Babich [53]	2021	Internal Financing	Game Theory (Decentralized Decision-making)	Fixed	Not Considering	Not Considering
Dong et al. [20]	2022	Internal Financing	Game Theory (Decentralized Decision-making)	Fixed	Not Considering	Not Considering

, scholars have conducted research on the impacts of blockchain on SCF decision-making. Jiang et al. [49] proposed an electronic payment voucher based on blockchain technology to address the lack of trust in financing for SMEs. By using fuzzy set theory, they analyzed the trust transfer model and found that blockchain technology allows deep-tie SMEs to obtain indirect credit endorsement from core enterprises through trust transfer. Dong et al. [50] investigated an SCF system with a capital-constrained manufacturer and a retailer. They used game theory to examine whether the retailer should establish their own originated channel with or without blockchain technology. The results showed that when the production cost or the marginal cost of using blockchain technology was high, the retailer should not establish their own originated channel. However, the introduction of blockchain technology increased the credibility of the supply chain member enterprises, leading to a dual effect of reducing service and financing interest rates. Wang et al. [51] examined upstream sellers providing internal trade financing to downstream buyers. The study compared and analyzed traditional financing with blockchain-enabled financing. The analysis revealed that under the drive of blockchain technology, the reduction in financing costs and risk-sharing effects increased the order quantity from the downstream buyers and the profit of the participants. However, it was also noted that blockchain-based solutions had some limitations and could not completely coordinate the profit distribution within the supply chain. Wang and Zhou [52] reported, in collateralized financing using warehouse receipts, the bank was more inclined to choose blockchain for financing and supervision as information sharing on the blockchain increased and the bank’s ability to absorb and utilize information improved. Moreover, setting higher penalties for on-chain defaults promoted a stable equilibrium in the game. Shibuya and Babich [53] compared blockchain-based SCF with traditional SCF in a three-tier supply chain. They identified conditions under which blockchain-based SCF was preferred over traditional SCF. Dong et al. [20] compared traditional advance payment financing with blockchain-enabled advance payment financing in a multi-tier supply chain. The results indicated that the blockchain-enabled mode was always favorable to the manufacturer, but potentially unfavorable to the first-tier and second-tier suppliers. A three-way win-win outcome could only be achieved when the first-tier supplier’s working capital was severely constrained and the second-tier supplier’s working capital was moderately constrained.

To sum up, it can be seen that existing studies only consider the single-scenario SCF model (i.e., internal or external financing), but our study makes a cross-scenario comparison (i.e., internal versus external financing). Further, existing studies virtually ignore the impact of economic factors of blockchain technology (i.e., the platform building cost, service level cost, and usage cost) on supply chain operations. Our study, on the other hand, considers these factors in the analytic framework.

3. Model Description and Parameter Description

3.1. Model Description

This paper explores a two-tier pull supply chain system, comprising a manufacturer (the core enterprise with sufficient capital) and a retailer (the capital-constrained SME). The retailer has two financing options: internal trade financing, such as deferred payment, from the manufacturer or external financing from a bank, with the condition that the manufacturer acts as the credit guarantor. Additionally, the manufacturer has established a supply chain finance (SCF) platform powered by blockchain technology. The retailer may choose to utilize this platform when seeking internal or external financing. Consequently, there are four SCF scenarios: the traditional internal trade financing model (TI), the traditional external bank financing model (TE), the blockchain-enabled internal trade financing model (BI), and the blockchain-enabled external bank financing model (BE), as illustrated in Figure 1a–d.

The supply chain distribution process: First, the retailer orders products from the manufacturer according to consumer demand $D=a-bp$, where $a$ represents the potential market size and $b$ represents the consumer price sensitivity coefficient. The manufacturer then produces products at the cost of $c$ and sets the wholesale price at $\epsilon$. Finally, the retailer sells the products to consumers at a retail price $p$.

The SCF process: The retailer has funds $n$($n\prec \epsilon D$). It, thus, needs to obtain financial support from other sources. The first option is to request trade financing, such as deferred payment, from the manufacturer. The amount requested is denoted as $\epsilon D-n$. The manufacturer charges an interest rate of $r_M$. It repays the principal and interest after the sales are realized. This option is illustrated in Figure 1a,c. The second option is to request prepayment financing from the bank on the condition that the manufacturer provides a credit guarantee. This option is illustrated in Figure 1b,d. The bank also charges an interest rate of $r_B$. The retailer pays the principal and interest to the bank after the sales are realized. The bank incurs an offline credit check cost of $C_B$. Assume that the highest probability in which the retailer obtains financial support either from the manufacturer or the bank is the same as $q$. If the retailer’s financing request is rejected, the supply chain system will be disrupted, and no participants will have profits.

The blockchain management business platform: If the manufacturer builds a management business platform based on blockchain technology, by virtue of the resource advantages of the core enterprises, in order to help the retailers realize their financing needs and create supply chain information traceability, the retailer can choose to conduct business operations on the chain, as shown in Figure 1c,d. At this time, the manufacturer shall bear the corresponding cost of the blockchain platform $C_M=F+\frac{1}{2}k{\gamma }^2$, where $F$ represents the fixed cost of building the blockchain platform, $k$ represents the difficulty in operating the blockchain platform (e.g., the technical difficulty or cost factor of providing services), $\gamma$ represents the application degree of the blockchain technology, and $\frac{1}{2}k{\gamma }^2$ [30] represents the relevant cost of maintaining the operation of the blockchain platform. The more difficult it is to operate the blockchain platform and the more widely it is used, the more expensive it will be for manufacturers to maintain the platform. At the same time, if the retailer chooses to access the blockchain platform, it needs to pay a certain platform use fee to the manufacturer $C_R=\theta D$, where $\theta$ represents the marginal cost associated with using the blockchain platform. A manufacturer can build a business platform (Foxconn’s Chained Finance is an example) that can use blockchain technology to record its business dealings and transactions with retailers, including production, sales, logistics, and finance information. For retailers, with the help of information vouchers on the chain, the credit qualification of the enterprises can be significantly improved and the possibility of obtaining financing from capital lenders can be increased. For banks, the use of on-chain data can effectively reduce credit investigation costs and eliminate the risk of false financing. For manufacturers, building this platform not only helps to match the financing business between retailers and capital lenders, so as to strengthen the robustness of the downstream supply chain, but also charges retailers and banks for the use of the platform. So, retailers and banks have an incentive to access the blockchain platform, as long as the manufacturers’ fee ranges are reasonable. In addition, due to the information sharing and traceability, and the anti-counterfeiting function of blockchain technology [54,55], it can stimulate demand growth in the product market, expressed as $D=a-bp+\beta \gamma$. In terms of consumer demand, the degree of application of blockchain technology can be understood as the level of traceability and the anti-counterfeiting service of the product, and $\beta$ represents the degree of consumer preference for traceability and anti-counterfeiting products.

3.2. Model Assumptions and Parameter Descriptions

• Assumption 1: The decision-making cycle is a complete supply chain process, and the member enterprises in the supply chain are risk neutral and completely rational.
• Assumption 2: Retailers order on demand, regardless of overstock and shortages.
• Assumption 3: In decentralized decision-making, both parties follow the Stackelberg game model with the manufacturer as the leader and the retailer as the follower.
• Assumption 4: The blockchain platform shall be built by the manufacturer.
• Assumption 5: If the retailer and the bank choose to access the blockchain platform, they need to pay the manufacturer for the use of the blockchain platform. Considering that banks have no direct incentive to access the platform, it is assumed that the use of the platform will be borne by the retailer.
• Assumption 6: When the retailer cannot obtain supply chain financing, the retailer goes bankrupt, the whole supply chain channel breaks, and the profit is 0.
• Assumption 7: In the traditional financing mode, there is certain information noise (information asymmetry) between the two financing parties, which can be effectively eliminated by the application of blockchain technology. Therefore, it is assumed that the probability of the retailer obtaining financing is lower when the traditional financing mode is adopted.
• Assumption 8: The risk-free interest rate of the capital lender is 0.
• M, R, and B in the subscripts of the model represent the manufacturer, retailer, and bank, respectively. The S, TI, BI, TE, and BE in the superscript represent sufficient capital, the traditional internal trade financing mode, the blockchain-enabled internal trade financing mode, the traditional external bank financing mode, and the blockchain-enabled external bank financing mode, respectively.
• Market demand under the traditional financing mode is expressed as $D^{TI/TE}=a-bp$; market demand under the blockchain enabling financing model is expressed as $D^{BI/BE}=a-bp+\beta \gamma$. Where $a$ represents the market size, b represents the consumer price sensitivity coefficient, $p$ represents the retailers’ sales price, $\gamma$ represents the degree of blockchain technology application, $\beta$ represents the degree of consumer preference for traceability anti-counterfeiting products, and $\beta \prec b$ is satisfied.
• $\epsilon$ stands for the unit wholesale price set by the manufacturer.
• $c$ represents the manufacturer’s unit cost of production.
• $C_M$ is the total single-cycle cost of the blockchain platform $C_M=F+\frac{1}{2}k{\gamma }^2$, where $F$ represents the fixed cost of building the blockchain platform, $k$ represents the difficulty in operating the blockchain platform, and $\frac{1}{2}k{\gamma }^2$ represents the related cost of maintaining the operation of the blockchain platform.
• $C_B$ is the early-stage credit investigation cost under the external bank financing mode, $C_B^{TE}\gg C_B^{BE}\to 0$.
• $C_R=\theta D$ stands for the blockchain platform usage fee, where $\theta$ represents the marginal cost associated with using the blockchain platform, which shall be borne by the retailer.
• $n$ is the retailer’s own funds. If it is satisfied $n\prec \epsilon D$, the purchase price cannot be paid in full.
• $q$ is the highest probability that retailers obtain supply chain financing under ideal conditions.
• $\varphi$ is the information noise between the financing parties, which is a random variable evenly distributed as $[0, 1]$.
• $r$ stands for interest rate and the exogenous variable. $\hat{r}$ represents the threshold of the interest rate.
• $I$ is the financing line.
• $E(\pi )$ is the expected profit function for all the parties in the supply chain system.

4. Model

4.1. Well-Funded Model

Under the condition of sufficient funds, the retailer can realize the full payment of the purchase price without financial constraint. The Stackelberg game unfolds in the following sequence: the manufacturer first sets the wholesale price, then the retailer determines the retail price according to the principle of expected profit maximization, and then the manufacturer adjusts the initial price according to the retailer’s behavior to achieve the overall optimal.

The retailer’s expected profit function:

$$E({\pi }_R^S)=(p-\epsilon )D=(p-\epsilon )(a-bp)$$

(1)

The manufacturer’s expected profit function:

$$E({\pi }_M^S)=(\epsilon -c)D=(\epsilon -c)(a-bp)$$

(2)

Proposition 1.

Under the scenario of sufficient funds of retailers, the optimal pricing, optimal ordering, and optimal expected profit for the member enterprises in the supply chain are:

$${\epsilon }^S=\frac{a+bc}{2b}, p^S=\frac{3a+bc}{4b}, D^S=\frac{a-bc}{4}, E({\pi }_R^S)=\frac{{(a-bc)}^2}{16b}, E({\pi }_M^S)=\frac{{(a-bc)}^2}{8b}.$$

Proof. 

The reverse calculation method is adopted to solve the problem. Firstly, the optimal pricing conditions for the retailer’s expected profit are calculated $\frac{\partial E({\pi }_R^S)}{\partial p}=0$, $p=\frac{a+b\epsilon }{2b}$, and then, the conditions are put into the manufacturer’s expected profit function $E({\pi }_M^S)$, Let $\frac{\partial E({\pi }_M^S)}{\partial \epsilon }=0$, the optimal wholesale price for the manufacturer is solved ${\epsilon }^S=\frac{a+bc}{2b}$, and then, the optimal retail price is put into the retail pricing formula for the retailer inversely $p^S=\frac{3a+bc}{4b}$. Furthermore, according to the consumer demand function and the expected profit formula, the optimal order quantity, and the optimal expected profit for the member enterprises in the supply chain can be obtained. In addition, by calculating the second derivative of the wholesale price $\frac{{\partial }^{2}E({\pi }_M^S)}{\partial {\epsilon }^2}=-b\prec 0$, it shows that the manufacturer’s expected profit function has a maximum value. □

4.2. Traditional Supply Chain Financing Model

4.2.1. Traditional Trade Finance Model within the Supply Chain

Cash-constrained retailers apply to manufacturers for internal trade financing, financing lines $I^{TI}={\epsilon }^{TI}{D}^{TI}-n$, through traditional means. Because of the information asymmetry between the two parties, there is supply chain information noise, so the probability that the manufacturer agrees to the intra-retailer trade financing is $(1-\varphi )q$. The Stackelberg game order is similar to Section 4.1.

The retailer’s expected profit function:

$$E({\pi }_R^{TI})=(1-\varphi )q[(p-\epsilon )D-(\epsilon D-n)r_M]$$

(3)

The manufacturer’s expected profit function:

$$E({\pi }_M^{TI})=(1-\varphi )q[(\epsilon -c)D+(\epsilon D-n)r_M]$$

(4)

Proposition 2.

In the traditional internal trade financing model, the optimal pricing, optimal ordering, and optimal expected profit for the member enterprises in the supply chain are, respectively:

$$\begin{gathered} {\epsilon }^{TI}=\frac{a+bc}{2b(1+r_M^{TI})}, p^{TI}=\frac{3a+bc}{4b}, D^{TI}=\frac{a-bc}{4}, \\ E({\pi }_R^{TI})=(1-\varphi )q[\frac{{(a-bc)}^2}{16b}+n{r}_M^{TI}], E({\pi }_M^{TI})=(1-\varphi )q[\frac{{(a-bc)}^2}{8b}-n{r}_M^{TI}]. \end{gathered}$$

Proof. 

The reverse calculation method is adopted to solve the problem. Firstly, the optimal pricing conditions for the retailer’s expected profit are calculated $\frac{\partial E({\pi }_R^{TI})}{\partial p}=0$, $p=\frac{a+b\epsilon (1+r_M)}{2b}$, and then, the conditions are put into the manufacturer’s expected profit function $E({\pi }_M^{TI})$, Let $\frac{\partial E({\pi }_M^{TI})}{\partial \epsilon }=0$. Then, the optimal wholesale price for the manufacturer is solved ${\epsilon }^{TI}=\frac{a+bc}{2b(1+r_M^{TI})}$, and then, the optimal retail price is put into the retail pricing formula for the retailer inversely $p^{TI}=\frac{3a+bc}{4b}$. Furthermore, according to the consumer demand function and the expected profit formula, the optimal order quantity, and the optimal expected profit for the member enterprises in the supply chain can be obtained. In addition, by calculating the second derivative of the wholesale price $\frac{{\partial }^{2}E({\pi }_M^{TI})}{\partial {\epsilon }^2}=-(1-\varphi )qb{(1+r_M^{TI})}^2\prec 0$, it shows that the manufacturer’s expected profit function has a maximum value. □

4.2.2. Traditional External Bank Financing Model of the Supply Chain

With the credit guarantee from the core enterprise of the manufacturer, the retailer can also apply for prepayment financing from an external bank. The financing process is similar to the situation for internal trade financing, which is not described here.

The retailer’s expected profit function:

$$E({\pi }_R^{TE})=(1-\varphi )q[(p-\epsilon )D-(\epsilon D-n)r_B]$$

(5)

The manufacturer’s expected profit function:

$$E({\pi }_M^{TE})=(1-\varphi )q(\epsilon -c)D$$

(6)

The bank’s expected profit function:

$$E({\pi }_B^{TE})=(1-\varphi )q(\epsilon D-n)r_B-C_B^{TE}$$

(7)

Proposition 3.

In the traditional external bank financing model, the optimal pricing, optimal ordering, and optimal expected profit for the supply chain member enterprises are, respectively:

$$\begin{gathered} {\epsilon }^{TE}=\frac{a+bc(1+r_B^{TE})}{2b(1+r_B^{TE})}, p^{TE}=\frac{3a+bc(1+r_B^{TE})}{4b}, D^{TE}=\frac{a-bc(1+r_B^{TE})}{4}, \\ E({\pi }_R^{TE})=(1-\varphi )q\{\frac{{[a-bc(1+r_B^{TE})]}^2}{16b}+n{r}_B^{TE}\} \\ E({\pi }_M^{TE})=\frac{(1-\varphi )q{[a-bc(1+r_B^{TE})]}^2}{8b(1+r_B^{TE})} \end{gathered}$$

Proof. 

The reverse calculation method is adopted to solve the problem. Firstly, the optimal pricing condition for the retailer’s expected profit is calculated $\frac{\partial E({\pi }_R^{TE})}{\partial p}=0$, and then, the conditions are solved $p=\frac{a+b\epsilon (1+r_B)}{2b}$ and then, put it into the manufacturer’s expected profit function $E({\pi }_M^{BE})$. Let $\frac{\partial E({\pi }_M^{TE})}{\partial \epsilon }=0$. Then, the manufacturer’s optimal wholesale price can be solved ${\epsilon }^{TE}=\frac{a+bc(1+r_B^{TE})}{2b(1+r_B^{TE})}$, and inversely put it into the retailer’s retail pricing formula to get the optimal retail price $p^{TE}=\frac{3a+bc(1+r_B^{TE})}{4b}$. Furthermore, according to the consumer demand function and the expected profit formula, the optimal order quantity, and the optimal profit for the member enterprises in the supply chain can be obtained. In addition, by calculating the second derivative of the wholesale price $\frac{{\partial }^{2}E({\pi }_M^{TE})}{\partial {\epsilon }^2}=-(1-\varphi )qb(1+r_B^{TE})\prec 0$, it shows that the manufacturer’s expected profit function has a maximum value. □

4.3. Blockchain-Enabled Supply Chain Financing Model

4.3.1. Blockchain-Enabled Intra-Supply Chain Trade Finance Model

The manufacturer is responsible for building a blockchain business platform. After accessing the blockchain platform, the retailer applies for internal trade financing on the chain, but it needs to pay certain additional fees for the use of the platform. In addition, the application of blockchain technology can not only effectively eliminate the supply chain information noise between the manufacturer and the retailer, but can also provide the consumer with highly credible products with traceability and anti-counterfeiting functions. Therefore, after accessing the blockchain platform, the probability of retailers obtaining financing increases to $q$, and consumer demand increases to $D=a-bp+\beta \gamma$.

The retailer’s expected profit function:

$$E({\pi }_R^{BI})=q[(p-\epsilon )D-(\epsilon D-n)r_M-\theta D]$$

(8)

The manufacturer’s expected profit function:

$$E({\pi }_M^{BI})=q[(\epsilon -c)D+(\epsilon D-n)r_M+\theta D-\frac{k{\gamma }^2}{2}]-F$$

(9)

Proposition 4.

When a retailer with limited funds conducts internal trade financing through the blockchain platform, the optimal degree of application of the blockchain technology, the optimal pricing, the optimal ordering, and the optimal expected profit for the supply chain member enterprises are:

$${\gamma }^{BI}=\frac{\beta (a-bc)}{4kb-{\beta }^2}, {\epsilon }^{BI}=\frac{2k(a-2b\theta +bc)-{\beta }^2(c-\theta )}{(4kb-{\beta }^2)(1+r_M^{BI})},$$

$$p^{BI}=\frac{3ka+kbc-{\beta }^{2}c}{4kb-{\beta }^2}, D^{BI}=\frac{kb(a-bc)}{4kb-{\beta }^2},$$

$$E({\pi }_R^{BI})=\frac{q[k^{2}b{(a-bc)}^2+n{r}_M^{BI}{(4kb-{\beta }^2)}^2]}{{(4kb-{\beta }^2)}^2},$$

$$E({\pi }_M^{BI})=\frac{qk{(a-bc)}^2-2(4kb-{\beta }^2)(qn{r}_M^{BI}+F)}{2(4kb-{\beta }^2)}.$$

Proof. 

The reverse calculation method is adopted to solve the problem. Firstly, the optimal pricing conditions for the retailer’s expected profit are calculated $\frac{\partial E({\pi }_R^{BI})}{\partial p}=0$, and then, the conditions are solved $p=\frac{a+\beta \gamma +b\epsilon (1+r_M)+b\theta }{2b}$, and then put into the manufacturer’s expected profit function $E({\pi }_M^{BI})$, Let $\frac{\partial E({\pi }_M^{BI})}{\partial \epsilon }=0$, $\frac{\partial E({\pi }_M^{BI})}{\partial \gamma }=0$, as such the simultaneous equations are solved, and the manufacturer’s optimal degree of application of the blockchain technology and the optimal wholesale price are obtained as follows ${\gamma }^{BI}=\frac{\beta (a-bc)}{4kb-{\beta }^2}$, ${\epsilon }^{BI}=\frac{2k(a-2b\theta +bc)-{\beta }^2(c-\theta )}{(4kb-{\beta }^2)(1+r_M^{BI})}$, and then it is reversed into the retail pricing formula for the retailer to obtain the optimal retail price $p^{BI}=\frac{3ka+kbc-{\beta }^{2}c}{4kb-{\beta }^2}$. Further, according to the consumer demand function and the expected profit formula, the optimal order quantity and the optimal expected profit for the member enterprises in the supply chain can be obtained. In addition, the manufacturer’s Hessian matrix for the expected profit function is $H^{BI}=\left[\begin{array}{cc}-bq{(1+r_M^{BI})}^2& \frac{\beta q(1+r_M^{BI})}{2}\\ \frac{\beta q(1+r_M^{BI})}{2}& -kq\end{array}\right]$, where the first-order principal subexpression is less than 0 and the second-order principal subexpression is greater than 0 to satisfy the condition of the existence of a maximum. □

4.3.2. Blockchain-Enabled External Bank Financing Model of the Supply Chain

The manufacturer builds a blockchain platform, and the retailer with financial constraint can apply for prepayment financing from an external bank on the chain by virtue of the credit guarantee from the core enterprise.

The retailer’s expected profit function:

$$E({\pi }_R^{BE})=q[(p-\epsilon )D-(\epsilon D-n)r_B-\theta D]$$

(10)

The manufacturer’s expected profit function:

$$E({\pi }_M^{BE})=q[(\epsilon -c)D+\theta D-\frac{k{\gamma }^2}{2}]-F$$

(11)

The bank’s expected profit function:

$$E({\pi }_B^{BE})=q(\epsilon D-n)r_B-C_B^{BE}$$

(12)

Proposition 5.

When the retailer with limited funds proceeds with external bank financing through the blockchain platform, the optimal degree of application of the blockchain technology, the optimal pricing, the optimal ordering, and the optimal expected profit for the supply chain member enterprises are:

$${\gamma }^{BE}=\frac{\beta [a+b\theta r_B^{BE}-bc(1+r_B^{BE})]}{4kb(1+r_B^{BE})-{\beta }^2}, {\epsilon }^{BE}=\frac{2k[a-b\theta +b(1+r_B^{BE})(c-\theta )]-{\beta }^2(c-\theta )}{4kb(1+r_B^{BE})-{\beta }^2},$$

$$p^{BE}=\frac{{\beta }^2\theta r_B^{BE}+(1+r_B^{BE})[3ka-{\beta }^{2}c+kb\theta +kb(1+r_B^{BE})(c-\theta )]}{4kb(1+r_B^{BE})-{\beta }^2},$$

$$D^{BE}=\frac{kb(1+r_B^{BE})[a-bc(1+r_B^{BE})+b\theta r_B^{BE}]}{4kb(1+r_B^{BE})-{\beta }^2},$$

$$E({\pi }_R^{BE})=q[\frac{k^{2}b{(1+r_B^{BE})}^2{[a-bc(1+r_B^{BE})+b\theta r_B^{BE}]}^2}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}+n{r}_B^{BE}],$$

$$E({\pi }_M^{BE})=\frac{qK{[a+b\theta r_B^{BE}-bc(1+r_B^{BE})]}^2}{2[4kb(1+r_B^{BE})-{\beta }^2]}-F.$$

Proof. 

The reverse calculation method is adopted to solve the problem. Firstly, the optimal pricing condition for the retailer’s expected profit is calculated $\frac{\partial E({\pi }_R^{BE})}{\partial p}=0$, $p=\frac{a+\beta \gamma +b\epsilon (1+r_B)+b\theta }{2b}$, and then put it into the manufacturer’s expected profit function $E({\pi }_M^{BE})$. Let $\frac{\partial E({\pi }_M^{BE})}{\partial \gamma }=0$, $\frac{\partial E({\pi }_M^{BE})}{\partial \epsilon }=0$, and solve the equations simultaneously to obtain the manufacturer’s optimal degree of application of blockchain technology and the optimal wholesale price, respectively, as ${\gamma }^{BE}=\frac{\beta [a+b\theta r_B^{BE}-bc(1+r_B^{BE})]}{4kb(1+r_B^{BE})-{\beta }^2}$ ${\epsilon }^{BE}=\frac{2k[a-b\theta +b(1+r_B^{BE})(c-\theta )]-{\beta }^2(c-\theta )}{4kb(1+r_B^{BE})-{\beta }^2}$. Then, inversely put them into the retailer’s retail pricing formula to obtain the optimal retail price $p^{BE}=\frac{{\beta }^2\theta r_B^{BE}+(1+r_B^{BE})[3ka-{\beta }^{2}c+kb\theta +kb(1+r_B^{BE})(c-\theta )]}{4kb(1+r_B^{BE})-{\beta }^2}$.

Furthermore, according to the consumer demand function and the expected profit formula, the optimal order quantity, and the optimal expected profit for the member enterprises in the supply chain can be obtained. In addition, the manufacturer’s Hessian matrix for the expected profit function is $H^{BE}=\left[\begin{array}{cc}-qb(1+r_B^{BE})& \frac{q\beta }{2}\\ \frac{q\beta }{2}& -qk\end{array}\right]$, where the first-order principal subexpression is less than 0 and the second-order principal subexpression is greater than 0, to satisfy the condition of the existence of a maximum. □

Corollary 1.

In the intra-supply chain trade financing model, the threshold for the interest rate decreases with the increase in the retailer’s own funds, and has nothing to do with the information noise between the two financing parties. However, in the bank financing mode outside the supply chain, the threshold for the interest rate increases with the increase in the self-owned funds and information noise, which are completely opposite.

Proof. 

According to Assumption 6, if the internal trade financing is not obtained by the manufacturer, the retailer will go bankrupt, the supply chain will be broken, and the manufacturer’s expected profit will be 0. Therefore, the condition that the manufacturer is willing to provide the retailer with internal trade financing only needs to be met $E({\pi }_M^{TI/BI})\succ 0$. It can be solved as follows $r_M^{TI}\prec \frac{{(a-bc)}^2}{8bn}=\widehat{r_M^{TI}}$, $r_M^{BI}\prec \frac{qk{(a-bc)}^2-2F(4kb-{\beta }^2)}{2qn(4kb-{\beta }^2)}=\widehat{r_M^{BI}}$. Similarly, for the external bank financing mode, the condition that bank is willing to provide prepayment financing for the cash-constrained retailer should be met $r_B^{TE}\succ \frac{C_B^{TE}}{(1-\varphi )q[{\epsilon }^{TE}(a-bp)-n]}=\widehat{r_B^{TE}}$, $r_B^{BE}\succ \frac{C_B^{BE}}{q[{\epsilon }^{BE}(a-bp+\beta \gamma )-n]}=\widehat{r_B^{BE}}$. According to the above threshold formula for the interest rate, the threshold for the trade interest rate within the supply chain has nothing to do with the information noise $\varphi$. But in the external bank financing mode, the bank needs to bear the fixed credit investigation costs in the early stage, so it is necessary to consider the degree of information symmetry between the two financing parties, hoping to increase the lending probability as much as possible to make up for the expenditure on the credit investigation costs. In addition, by calculating the monotonicity of each interest rate threshold relating to its own funds, it can be shown that:

$$\frac{\partial \widehat{r_M^{TI}}}{\partial n}=-\frac{{(a-bc)}^2}{8b{n}^2}\prec 0, \frac{\partial \widehat{r_M^{BI}}}{\partial n}=-\frac{[qk{(a-bc)}^2-2F(4kb-{\beta }^2)](4kb-{\beta }^2)}{2q{n}^2{(4kb-{\beta }^2)}^2}\prec 0,$$

$$\frac{\partial \widehat{r_B^{TE}}}{\partial n}=\frac{C_B^{TE}}{(1-\varphi )q{({\epsilon }^{TE}{D}^{TE}-n)}^2}\succ 0, \frac{\partial \widehat{r_B^{BE}}}{\partial n}=\frac{C_B^{BE}}{q{({\epsilon }^{BE}{D}^{BE}-n)}^2}\succ 0$$

It shows that in the intra-supply chain trade financing model, the larger the amount of self-owned funds owned by the retailers, the lower the internal trade interest rate set by the manufacturer. On the contrary, in the external bank financing model of the supply chain, the larger the amount of self-owned funds owned by the retailer, the higher the external financing interest rate set by the bank. The influence mechanism from the retailer’s own capital on the two financing modes is completely opposite. □

Corollary 2.

(1) In the intra-supply chain trade financing model, the retail price and order quantity have nothing to do with the interest rate, and only the wholesale price decreases with the increase in the interest rate. In the bank financing mode outside the supply chain, the wholesale price and order quantity both decrease with the increase in the interest rate, while the retail price increases with the increase in the interest rate under certain conditions. (2) In the traditional intra-supply chain trade financing model, the retailer can achieve the same strategy as in the case with sufficient funds. (3) Regardless of whether the blockchain platform is built or not, the manufacturer can set a slightly higher wholesale price to replace the internal trade interest rate, that is, the interest rate can be internalized into the wholesale price.

Proof. 

(1) In the trade financing mode within the supply chain, the retail price $p^{TI}$, $P^{BI}$, and the order quantity $D^{TI}$, $D^{BI}$, do not contain the parameter $r_M$. But $\frac{\partial {\epsilon }^{TI}}{\partial r_M^{TI}}=-\frac{a+bc}{2b{(1+r_M^{TI})}^2}\prec 0$, $\frac{\partial {\epsilon }^{BI}}{\partial r_M^{BI}}=-\frac{2k(a-2b\theta +bc)-{\beta }^2(c-\theta )}{(4kb-{\beta }^2){(1+r_M^{BI})}^2}\prec 0$, indicates that whether it is the traditional financing mode or the financing mode based on the blockchain platform, if the manufacturer wants to raise the interest rate for internal trade financing, it must reduce the wholesale price to achieve the equilibrium for the supply chain game. In the bank financing model outside the supply chain, through the calculation for the monotone of the interest rate, we can see that:

$$\begin{gathered} \frac{\partial {\epsilon }^{TE}}{\partial r_B^{TE}}=-\frac{a}{2b{(1+r_B^{TE})}^2}\prec 0, \frac{\partial {\epsilon }^{BE}}{\partial r_B^{BE}}=-\frac{2kb[4k(a-b\theta )-{\beta }^2(c-\theta )]}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}\prec 0, \\ \frac{\partial D^{TE}}{\partial r_B^{TE}}=-bc\prec 0, \\ \frac{\partial D^{BE}}{\partial r_B^{BE}}=-\frac{4k^2{b}^3{(1+r_B^{BE})}^2(c-\theta )+{\beta }^{2}kb[a-2bc(1+r_B^{BE})+b\theta (2r_B^{BE}+1)]}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}\prec 0, \end{gathered}$$

$$\begin{gathered} \frac{\partial p^{TE}}{\partial r_B^{TE}}=bc\succ 0, \\ \frac{\partial p^{BE}}{\partial r_B^{BE}}=\frac{2kb(1+r_B^{BE})(c-\theta )[2kb(1+r_B^{BE})-{\beta }^2]+{\beta }^4(c-\theta )-3k{\beta }^2(a-b\theta )}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}. \end{gathered}$$

The value condition for the external bank interest rate based on the blockchain platform is

$$(1+r_B^{BE})[2kb(1+r_B^{BE})-{\beta }^2]\succ \frac{{\beta }^2[3k(a-b\theta )-{\beta }^2(c-\theta )]}{2kb(c-\theta )}, \mathrm{then} \frac{\partial p^{BE}}{\partial r_B^{BE}}\succ 0.$$

(2) According to Propositions 1 and 2, $p^{TI}=p^S$, $D^{TI}=D^S$, indicates that in the traditional internal trade financing model, the retailer’s pricing and order quantity are the same as the decision under the situation with sufficient funds, and the delay in payment for goods will not affect the retailer.

(3) It can also be seen from Proposition 1 and Proposition 2, $(1+r_M^{TI}){\epsilon }^{TI}={\epsilon }^S$, that the traditional internal trade interest rate can be internalized into the wholesale price, and the same law is also shown in the internal trade financing model based on the blockchain platform. Therefore, if the retailer adopts the internal trade financing model, the manufacturer can simplify the supply chain management process by setting a slightly higher wholesale price instead of the interest rate. □

Corollary 3.

(1) When the blockchain platform is used for internal trade financing, the usage rate of the platform can also be internalized into the wholesale price for the manufacturer, the retail price, the order quantity, and the degree of application of the blockchain technology have nothing to do with it, and the wholesale price decreases monotonically with the increase in the usage rate of the platform. When the blockchain platform is used for external bank financing, the wholesale price and retail price decrease monotonically with the increase in the platform usage rate, while the order quantity and the degree of application of the blockchain technology increase monotonically. (2) After accessing the blockchain platform, whether it is for trade financing within the supply chain or external bank financing, the supply chain pricing, order quantity, and degree of application of the blockchain technology are positively correlated with consumer preferences on traceability and anti-counterfeiting products.

Proof. 

(1) When conducting internal trade financing based on the blockchain platform, the formula applies for $p^{BI}$, $D^{BI}$, ${\gamma }^{BI}$, and it does not contain the rate parameter $\theta$. And it is found through calculation $\frac{\partial {\epsilon }^{BI}}{\partial \theta }=\frac{{\beta }^2-4kb}{(4kb-{\beta }^2)(1+r_M^{BI})}\prec 0$, that the wholesale price decreases monotonously with the platform usage rate. This change is similar to the mechanism of the interest rate on the wholesale price, and the manufacturer can replace the platform charges and interest rate income with a slightly higher wholesale price. When external bank financing is conducted based on the blockchain platform,

$$\frac{\partial {\epsilon }^{BE}}{\partial \theta }=\frac{-2kb(2+r_B^{BE})+{\beta }^2}{4kb(1+r_B^{BE})-{\beta }^2}\prec 0,\frac{\partial p^{BE}}{\partial \theta }=-\frac{kb(1+r_B^{BE})-{\beta }^2}{4kb(1+r_B^{BE})-{\beta }^2}\prec 0,$$

$$\frac{\partial D^{BE}}{\partial \theta }=\frac{k{b}^2(1+r_B^{BE})r_B^{BE}}{4kb(1+r_B^{BE})-{\beta }^2}\succ 0, \frac{\partial {\gamma }^{BE}}{\partial \theta }=\frac{\beta b{r}_B^{BE}}{4kb(1+r_B^{BE})-{\beta }^2}\succ 0$$

It indicates that the wholesale price and retail price decrease with the increase in the platform usage rate, while the order quantity and the degree of application of the blockchain technology increase with the increase in the platform usage rate.

(2) In the internal trade financing mode based on the blockchain platform:

$$\frac{\partial {\epsilon }^{BI}}{\partial \beta }=\frac{4\beta (1+r_M^{BI})(a-bc)}{{[(4kb-{\beta }^2)(1+r_M^{BI})]}^2}\succ 0, \frac{\partial p^{BI}}{\partial \beta }=\frac{6k\beta (a-bc)}{{(4kb-{\beta }^2)}^2}\succ 0.$$

$$\frac{\partial D^{BI}}{\partial \beta }=\frac{2kb\beta (a-bc)}{{(4kb-{\beta }^2)}^2}\succ 0, \frac{\partial {\gamma }^{BI}}{\partial \beta }=\frac{(4kb+{\beta }^2)(a-bc)}{{(4kb-{\beta }^2)}^2}\succ 0.$$

In the external bank financing mode based on the blockchain platform:

$$\frac{\partial {\epsilon }^{BE}}{\partial \beta }=\frac{4k\beta [a-bc(1+r_B^{BE})+b\theta r_B^{BE}]}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}\succ 0,$$

$$\frac{\partial p^{BE}}{\partial \beta }=\frac{6k\beta (1+r_B^{BE})[a-bc(1+r_B^{BE})+b\theta r_B^{BE}]}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}\succ 0,$$

$$\frac{\partial D^{BE}}{\partial \beta }=\frac{2kb\beta (1+r_B^{BE})[a-bc(1+r_B^{BE})+b\theta r_B^{BE}]}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}\succ 0,$$

$$\frac{\partial {\gamma }^{BE}}{\partial \beta }=\frac{[4kb(1+r_B^{BE})+{\beta }^2][a-bc(1+r_B^{BE})+b\theta r_B^{BE}]}{{[4kb(1+r_B^{BE})-{\beta }^2]}^2}\succ 0.$$

This indicates that whether the retailer chooses internal trade financing or external bank financing, the traceability and anti-counterfeiting functions of the blockchain technology can help promote sales and improve the service level of the blockchain platform. □

Corollary 4.

(1) Compared with the traditional financing mode, the wholesale price, retail price, and order quantity with blockchain platform financing can be increased under certain conditions. (2) The retail price in the intra-trade financing mode of the blockchain platform is the highest, while the retail price in the traditional intra-trade financing mode is the lowest, under certain conditions $p^{BI}\succ p^{BE}\succ p^{TE}\succ p^{TI}$. (3) Compared with external bank financing, internal trade financing has greater market demand and a higher degree of application of the blockchain technology.

Proof. 

(1) The quantitative relationship between the traditional financing model and the blockchain platform financing model in relation to the wholesale price, the retail price, and the order quantity is calculated as follows:

$${\epsilon }^{BI}-{\epsilon }^{TI}=\frac{2b[2k(a-2b\theta +bc)-{\beta }^2(c-\theta )](1+r_M^{TI})-(4kb-{\beta }^2)(1+r_M^{BI})(a+bc)}{2b(4kb-{\beta }^2)(1+r_M^{BI})(1+r_M^{TI})}$$

When the ratio between the principal and the interest rate for intra-blockchain trade financing and traditional intra-blockchain trade financing meets $\frac{1+r_M^{BI}}{1+r_M^{TI}}\prec \frac{2b[2k(a-2b\theta +bc)-{\beta }^2(c-\theta )]}{(4kb-{\beta }^2)(a+bc)}$, it figures that ${\epsilon }^{BI}\succ {\epsilon }^{TI}$.

The equivalent calculation is:

$${\epsilon }^{BE}-{\epsilon }^{TE}=\frac{\begin{array}{l}2b(1+r_B^{TE})[2k[a-b\theta +b(1+r_B^{BE})(c-\theta )]-{\beta }^2(c-\theta )]-\\ [4kb(1+r_B^{BE})-{\beta }^2][a+bc(1+r_B^{TE})]\end{array}}{2b(1+r_B^{TE})[4kb(1+r_B^{BE})-{\beta }^2]},$$

when $\beta \succ \sqrt{\frac{4kb[b\theta (2+r_B^{BE})(1+r_B^{TE})-a(r_B^{TE}-r_B^{BE})]}{a-bc(1+r_B^{TE})(c-2\theta )}}$, it figures that ${\epsilon }^{BE}\succ {\epsilon }^{TE}$.

$$p^{BI}-p^{TI}=\frac{3{\beta }^2(a-bc)}{4b(4kb-{\beta }^2)}\succ 0,$$

$$p^{BE}-p^{TE}=\frac{\begin{array}{l}{\beta }^2[3a+bc(1+r_B^{TE})-4bc(1+r_B^{BE})+4b\theta r_B^{BE}]-\\ 4k{b}^2(1+r_B^{BE})[c(r_B^{TE}-r_B^{BE})+\theta r_B^{BE}]\end{array}}{4n[4kb(1+r_B^{BE})-{\beta }^2]},$$

when $\beta \succ \sqrt{\frac{4k{b}^2(1+r_B^{BE})[\theta r_B^{BE}+c(r_B^{TE}-r_B^{BE})]}{3a+bc(1+r_B^{TE})-4bc(1+r_B^{BE})+4b\theta r_B^{BE}}}$, it figures that $p^{BE}\succ p^{TE}$.

$$D^{BI}-D^{TI}=\frac{{\beta }^2(a-bc)}{4(4kb-{\beta }^2)}\succ 0,$$

$$D^{BE}-D^{TE}=\frac{4k{b}^2(1+r_B^{BE})[c(r_B^{TE}-r_B^{BE})+\theta r_B^{BE}]+{\beta }^2[a-bc(1+r_B^{TE})]}{4[4kb(1+r_B^{BE})-{\beta }^2]}\succ 0.$$

The above analyses show that the adoption of blockchain technology not only helps increase the wholesale and retail prices, but also helps increase the market demand. Such results are hardly achievable in the supply chain system without blockchain technology.

(2) By calculating $p^{TE}-p^{TI}=\frac{c{r}_B^{TE}}{4}\succ 0$,

$$p^{BE}-p^{BI}=\frac{\begin{array}{l}{r}_B^{BE}[4k^2{b}^{2}c(1+r_B^{BE})-3ka{\beta }^2+{\beta }^{4}c-kbc{\beta }^2(2+r_B^{BE})+\\ (4kb-{\beta }^2)\theta [{\beta }^2-kb(1+r_B^{BE})]]\end{array}}{[4kb(1+r_B^{BE})-{\beta }^2][4kb-{\beta }^2]},$$

when $\theta \succ \frac{4k^2{b}^{2}c(1+r_B^{BE})-3ka{\beta }^2+{\beta }^{4}c-kbc{\beta }^2(2+r_B^{BE})}{(4kb-{\beta }^2)[kb(1+r_B^{BE})-{\beta }^2]}$, it figures that $p^{BE}\prec p^{BI}$. Then, when combined with the conclusion in Corollary 4 (1), it can be concluded that retail prices under certain conditions exist and the following quantitative relation is achieved $p^{BI}\succ p^{BE}\succ p^{TE}\succ p^{TI}$.

(3) By calculating the quantitative relationship between the order quantity and the degree of application of the blockchain technology in the internal trade financing mode and the external bank financing mode:

$$D^{TE}-D^{TI}=-\frac{bc{r}_B^{TE}}{4}\prec 0,$$

$$D^{BE}-D^{BI}=-\frac{kb{r}_B^{BE}(1+r_B^{BE})[4k{b}^2(c-\theta )+{\beta }^{2}b\theta ]+kb{\beta }^2{r}_B^{BE}[a-bc(2+r_B^{BE})]}{[4kb(1+r_B^{BE})-{\beta }^2][4kb-{\beta }^2]}\prec 0$$

$${\gamma }^{BE}-{\gamma }^{BI}=-\frac{\beta b{r}_B^{BE}[4k(a-b\theta )-{\beta }^2(c-\theta )]}{[4kb(1+r_B^{BE})-{\beta }^2][4kb-{\beta }^2]}\prec 0.$$

These indicate that the retailer can obtain greater market demand and a higher service level for the blockchain platform through internal trade financing. □

Corollary 5.

In the intra-supply chain trade financing model, compared to the traditional method, when the operating difficulty of the blockchain platform is higher than a certain critical value, the adoption of the blockchain platform makes the interest rate threshold set by the manufacturer lower, and vice versa. In the external bank financing mode of the supply chain, the adoption of the blockchain platform always makes the interest rate threshold set by the bank lower, $\widehat{r_B^{BE}}\prec \widehat{r_B^{TE}}$, making the financing of the retailer more attractive.

Proof. 

In the intra-supply chain trade financing model, let $\widehat{r_M^{TI}}-\widehat{r_M^{BI}}\succ 0$, it can be calculated that $k\succ \frac{{\beta }^2[8bF+q{(a-bc)}^2]}{32b^{2}F}$, when the operating difficulty of the blockchain platform is higher than a certain critical value, the manufacturer will usually set a lower internal trade interest rate, because the greater the operating difficulty of the blockchain platform, the higher the wholesale price set by the manufacturer. However, the wholesale price is negatively correlated with the internal trade interest rate. Therefore, compared with traditional internal trade financing, when the blockchain platform is more difficult to operate, the rational decision for manufacturer is to lower the internal trade interest rate. In the external bank financing mode of the supply chain, compared with the traditional way, after accessing the blockchain platform there are: $C_B^{TE}\gg C_B^{BE}\to 0$, $\varphi \succ 0$, ${\epsilon }^{TE}\prec {\epsilon }^{BE}$, $D^{TE}\prec D^{BE}$. Thus, it is determined that $\widehat{r_B^{TE}}\gg \widehat{r_B^{BE}}\to 0$. This result suggests that the bank will lower its interest rate threshold to a large extent when the blockchain platform is employed. As such, a low interest rate is one of the major benefits of adopting blockchain technology in SCF. For the convenience of the quantitative analysis, we regard $r_B^{BE}\prec r_B^{TE}$ without a loss of generality. □

Corollary 6.

(1) In the internal trade financing mode of the blockchain platform, increasing the promotion of the application of the traceability and anti-counterfeiting functions in products is a marketing strategy to achieve win-win results for both sides. (2) In the external bank financing mode of the blockchain platform, the strategy involving a traceability incentive, a low interest rate, and unnecessary charges is an effective means of achieving a three-way win-win.

Proof. 

(1) Combined with Proposition 4, Corollary 2 and 3, it can be seen that in the internal trade financing model, both the interest rate and the blockchain platform usage rate can be internalized into the wholesale price, so the expected profits for both the manufacturer and retailer in this model are irrelevant. However, the application of the traceability and anti-counterfeiting functions of blockchain technology are conducive to improving the profits of both parties,

$$\frac{\partial {\pi }_M^{BI}}{\partial \beta }=\frac{q\beta k{(a-bc)}^2}{{(4kb-{\beta }^2)}^2}\succ 0 \mathrm{and} \frac{\partial {\pi }_R^{BI}}{\partial \beta }=\frac{4\beta q{k}^{2}b{(a-bc)}^2}{{(4kb-{\beta }^2)}^4}\succ 0.$$

These results suggest that the application of the traceability and anti-counterfeiting functions in supply chain products is a dominant strategy for both the manufacturer and the retailer. This helps improve supply chain sustainability.

(2) (1) The traceability incentive and low interest rate: For the retailer, $E({\pi }_R^{BE})-E({\pi }_R^{TE})=\Delta {\pi }_R(\beta ,r)-\Delta {\pi }_R(\theta )$, compared with the traditional external bank financing of the supply chain, when blockchain technology brings a decrease in the interest rate and incentivizes the sales growth of the retailer, it is profitable when the overall income is greater than the required payment for the use of the blockchain platform. According to Corollary 3 (2), $\frac{\partial p^{BE}}{\partial \beta }\succ \frac{\partial {\epsilon }^{BE}}{\partial \beta }\succ 0$, $\frac{\partial D^{BE}}{\partial \beta }\succ 0$, $\frac{\partial D^{BE}}{\partial \beta }\succ 0$, it can be seen that $\Delta {\pi }_R(\beta ,r)\succ 0$, if and only if $\Delta {\pi }_R(\beta ,r)\succ \Delta {\pi }_R(\theta )$, as a rational decision-maker, the retailer chooses to access the blockchain platform, otherwise it is more advantageous to use the traditional external bank financing model. (2) The traceability incentive, low interest rate, and non-essential charge: For the manufacturer, $E({\pi }_M^{BE})-E({\pi }_M^{TE})=\Delta {\pi }_M(\beta ,r,\theta )-C_M$, as it can be seen from Proposition 5, the manufacturer’s expected profit function is $\Delta {\pi }_M(\beta ,r,\theta )\succ 0$, as such the manufacturer can also benefit from blockchain technology, as long as the total cost of the blockchain platform is not particularly high, the manufacturer has the possibility to provide the retailer with access services free of charge, if and only if $\Delta {\pi }_M(\beta ,r,\theta )\prec C_M$, in order to cover the high cost of the blockchain platform, the manufacturer has an incentive to charge higher fees for platform use. (3) Similarly, for the bank, accessing the blockchain platform can save on the traditional credit investigation fees and increase the amount of financing for the retailer, when these benefits cover the interest loss caused by the interest rate reduction, the optimal decision is still to access the blockchain platform. □

5. Numerical Analysis and Discussion

In the previous part, the TI, BI, TE, and BE modes were compared and analyzed by the analytical method in game theory. In this part, we will study the coordination mechanism between the corresponding parameters, the financing methods, and the supply chain decision-making by using simulation examples. Assume that the related parameters are as follows:

$$\begin{array}{l}a=200, c=20, b=3, \beta =2, q=0.9, \varphi =0.3, r_M^{TI}=r_B^{TE}=0.2, r_M^{BI}=r_B^{BE}=0.05, \\ C_B^{TE}=10, C_B^{BE}=0, k=2, \theta =10, n=10, F=300\end{array}$$

As can be seen from Figure 2, the interest rate, and the application of blockchain technology play an important regulatory role in the pricing by the supply chain member enterprises. The specific performance is as follows: (1) No matter what kind of financing mode is adopted, the wholesale price by the manufacturer is always negatively correlated with the interest rate. This is because in the internal trade financing model, since the interest rate can be internalized into the pricing of the wholesale price, if the manufacturer sets a higher interest rate, it is bound to reduce the wholesale price to achieve the game equilibrium. In the external bank financing model, the interest income is generated by the bank, and the higher the interest rate, the higher the financing cost to the retailer. In order to realize stability in the supply chain system, the retailer expects to “purchase at a low price” to make up for the heavy financing cost. (2) When the retailer chooses the external bank financing mode, the wholesale price for external bank financing is slightly higher than that with internal trade financing because the manufacturer has no interest rate income. (3) Compared with the traditional financing mode, the wholesale price in financing based on the blockchain platform is higher. The application of blockchain technology can not only eliminate the information asymmetry between the two financing parties, improve the probability of financing availability, and reduce the interest rate, but can also stimulate a growth in market demand by using the traceability and anti-counterfeiting functions. So, the manufacturer has a motivation to increase the wholesale price. (4) Whether it is internal trade financing or external bank financing, the retail price can be increased after accessing the blockchain platform. (5) In addition, we also find that when the retailer adopts the internal trade financing model, the retail price has nothing to do with the interest rate, as shown in the horizontal line in Figure 2, and the retail price is the highest when the retailer conducts internal trade financing based on the blockchain platform. In the traditional external bank financing model, the retail price rises with the increase in the interest rate. But, after the access to the blockchain platform, the retail price shows a trend of “decreasing first and then rising”, because if $r_B^{BE}\to 0$, it reaches the highest retail price $p^{BE}\to p^{BI}$. When the interest rate increases within a low range, the financing cost will not increase too much. In this case, the retailer’s optimal decision is to stimulate the increase in demand by reducing the retail price. However, when the interest rate increases in a large range, the burden of the financing cost will be too heavy. Subsequently, the retailer can only increase the income by raising the price and selling, which corresponds to the conclusion in Inference 2 (1). However, compared with the traditional external bank financing mode, the retail price essentially becomes stable after accessing the blockchain platform, and is close to the highest price level $p^{BI}$ in internal trade financing. Therefore, blockchain technology can also help the retailer nullify the retail price increase introduced by the interest rate. This is a benefit of blockchain technology deployment that has not been discussed in the extant research.

As it can be seen from Figure 3, when a retailer accesses the blockchain platform, both the wholesale price and retail price are positively correlated with the traceability incentive effect of blockchain technology. And the pricing of intra-supply chain trade financing is very close to that of the external bank financing mode. In combination with Figure 2, it is further illustrated that with the support of blockchain technology, external bank financing can achieve a pricing strategy similar to that of internal trade financing, which avoids the influence from the introduction of an external bank on supply chain decision-making to some extent.

Combining Proposition 4 and Corollary 2 (3), we can see that in the internal trade financing mode, the interest rate can be internalized into the wholesale price. So, the degree of application of blockchain technology in the internal trade financing mode only increases monotonically with the traceability incentive effect, and has nothing to do with the interest rate, as shown in the edge curve pointed out by the arrow in Figure 4. However, in the external bank financing mode, the level of the interest rate set by the bank will directly affect the optimal level in the operation of the blockchain platform by the manufacturer. As shown in the curved surface in Figure 4, the degree of application of the blockchain technology decreases with the increase in the bank interest rate and increases with the increase in the traceability incentive. When blockchain technology can significantly reduce the interest rate and stimulate consumer demand, it is the ideal application environment for blockchain technology. Therefore, commodities with serious information asymmetry or those very sensitive to product quality are some of the main application scenarios for blockchain technology, such as cross-border e-commerce, maternal and child products, electronic products, medical products, jewelry, and other high-value products.

As it can be seen from Figure 5, firstly, from the perspective of the financing limit, the amount of financing based on the blockchain platform is higher than that in the traditional financing mode. And the amount of internal trade financing through the blockchain platform is the highest, while the amount of financing through a traditional external bank is the lowest. Secondly, when the interest rate set by the capital lender is within a low range, the difference between the traditional financing line and the financing line based on the blockchain platform is larger. It reflects the fact that the reduction in the interest rate after access to the blockchain platform can bring more working capital to the whole supply chain system, and is more conducive to revitalizing the transaction business between the supply chain member enterprises. Finally, for the bank, although the access to the blockchain platform causes “interest rate loss”, it can effectively reduce the bank’s early credit investigation costs and increase the amount of financing. Therefore, the bank needs to achieve a reasonable balance between the “interest rate loss” and the “blockchain platform benefit”. As shown in Figure 5, the bank’s expected profit at point a is higher than that at point b.

Proposition 4 and Corollary 3 (1) show that in the intra-supply chain trade financing model, the blockchain platform usage rate can also be internalized into the wholesale price, and the expected profit for both the manufacturer and retailer is irrelevant. However, in the external bank financing mode of the supply chain, the platform usage rate directly affects the charging and decision-making mechanism in the supply chain.

Considering that the bank has no direct incentive to access the blockchain platform, for the sake of simplifying the model, we assume that the platform use cost for a single financing transaction within the single-cycle supply chain system is borne by the retailer. As shown in Figure 6, for example $\beta =1$, in the traditional external bank financing mode of the supply chain, $E({\pi }_M^{TE})=409.6$, $E({\pi }_R^{TE})=247.2$, and in the blockchain-enabled external bank financing mode, in order to make the manufacturer willing to provide the blockchain platform for the retailer and the retailer willing to access the blockchain platform, it must simultaneously meet $E({\pi }_M^{BE})\succ E({\pi }_M^{TE})$, $E({\pi }_R^{BE})\succ E({\pi }_R^{TE})$, which can calculate when the operating difficulty of the blockchain platform is $k\prec 1.43$, thus the expected profit for the manufacturer is always better than the profit in the traditional financing mode. At this time, the charging mechanism for the blockchain platform is relatively flexible. The “cde” area in Figure 6 is called the “not necessary to charge area” or “may be free area”. The manufacturer can charge a platform usage fee of no more than $E({\pi }_R^{BE})-E({\pi }_R^{TE})$, or offer free services. This is because the application of blockchain technology can promote the expected profit growth for both the manufacturer and the retailer, when the operating difficulty of the blockchain platform is not high, the manufacturer can completely provide the corresponding platform services to the retailer free of charge. On the contrary, when the operating cost for the blockchain platform is high, $k\ge 1.43$, the manufacturer will certainly charge the retailer no higher fees than $E({\pi }_R^{BE})-E({\pi }_R^{TE})$ for the use of the blockchain platform in order to make up for the high cost of the blockchain platform, so as to achieve a win-win situation. This is shown in the “efg” area in Figure 6. Similarly, it can be calculated that $\beta =1.2$, when $k\prec 2.06$, the “dhi” area in the figure is the “not necessary to charge area”, and the “dhi” area is obviously larger than the “cde” area. When $k\ge 2.06$, the “ifg” area in the figure is the “necessary to charge area”, and the “ifg” area is obviously smaller than the “efg” area. As a result, the manufacturer can reasonably charge fees based on the extent to which the blockchain platform helps both parties. When blockchain technology can significantly reduce the financing costs or stimulate sales growth, the range of platform fees available to the manufacturer becomes broader and more flexible, at the same time, the bank will also benefit from financing business. This also corroborates with the conclusion in Corollary 6, the strategy for blockchain technology (the traceability incentive, low interest rate, and unnecessary charges) is an effective means to achieve win-win results among all three parties.

As it can be seen from Figure 7 and Figure 8, the expected profit for the manufacturer and the retailer decrease with the increase in the operating difficulty of the blockchain platform, and it increases with the increase in the traceability incentive effect. When the operating difficulty is low and the traceability incentive effect is strong, there will be a sharp steepening trend. Moreover, when the blockchain platform is difficult to operate, the manufacturer’s strategy may change from “not to build blockchain platform” to “build blockchain platform” with the enhancement of the traceability incentive. For the manufacturer and the retailer, if and only if simultaneously satisfying the “positive effect” of the traceability and anti-counterfeiting functions of the blockchain technology is greater than the “negative effect” of the difficulty of platform operation, “the manufacturer chooses to build the blockchain platform and the retailer chooses to access the blockchain platform” is the optimal decision for the supply chain system. Otherwise, internal trade financing can only be conducted through traditional means.

As it can be seen from Figure 9 and Figure 10, the expected profit for the manufacturer and the retailer decrease with the increase in the bank interest rate and increase with the enhancement of the traceability incentive. In the external bank financing mode, the manufacturer has no financing interest income, and combined with Corollary 2 (1) $\frac{\partial {\epsilon }^{BE}}{\partial r_B}\prec 0$, $\frac{\partial D^{BE}}{\partial r_B}\prec 0$, it can be seen that the increase in the bank interest rate will have a large negative impact on the manufacturer. It can be seen from Figure 9 that only when the interest rate set by the bank is relatively small, will the manufacturer have the motivation to build the blockchain platform. Similarly, for the retailer, a low interest rate and significant market demand growth are necessary conditions for accessing the blockchain platform. In addition, interestingly, if the manufacturer builds a blockchain platform, the optimal decision by the retailer must be to access the blockchain platform. Because it can be seen from Figure 9 that the interest rate threshold for the manufacturer building a blockchain platform is significantly lower than that of the retailer accessing the blockchain platform. Thus, it can be seen that the “interest rate effect” and “demand effect” of blockchain technology have basically the same influence on the decision-making of the manufacturer and the retailer.

In the blockchain-enabled external bank financing model, different from the blockchain-enabled internal trade financing model, the manufacturer and the retailer are more tolerant to the difficulty of the platform operation and less sensitive to the incentive effect of traceability. As it can be seen from Figure 11 and Figure 12, compared with the traditional external bank financing mode, both the manufacturer and the retailer achieve better expected profits in the blockchain-enabled financing mode. It indicates that as long as the charges for the blockchain platform are within a reasonable range, even if the platform is more difficult to operate or the traceability incentive is less, the optimal decision by the manufacturer may still be to build the blockchain platform, and the optimal decision for retailer may still be to access the blockchain platform. There are two reasons for this. On the one hand, the introduction of an external bank for financing makes the profit from the supply chain system “segmented”. On the other hand, in the traditional external bank financing mode, the interest rate set by the bank is usually high, but the interest rate can be greatly reduced after access to the blockchain platform, which is very attractive for the manufacturer and the retailer, Figure 9 and Figure 10 also illustrate this point. It can be seen that in the external bank financing mode, blockchain technology brings more gains for the manufacturer and the retailer than internal trade financing. The enabling role of blockchain technology is more prominent. Besides, in the supply chain scenario where platform operation is difficult and the incentive effect of product traceability is not obvious, priority can be given to the construction of the external bank financing mode based on the blockchain platform.

6. Extended Model

Risk control is indeed a crucial aspect of finance, and it holds true in the context of SCF as well. One of the significant challenges faced by lenders in SCF is the risk of repayment defaults by financing entities. This risk poses a major obstacle to the sustainable development of SCF. However, the above analysis does not incorporate the retailer’s default risk into the analytic framework. Therefore, the extended model will analyze how the retailer’s default risk impacts the financing decisions of the supply chain participants.

It is assumed that the retailer has a default risk and may not repay or be unable to repay the principal and interest on the financing. The default risk is jointly borne by the lender and the guarantor. $\eta$ represents the probability of normal repayment by the retailer (the probability of keeping faith). $(1-\eta )$ represents the probability of default by the retailer. $\mu$ represents the proportion of risk shared by the manufacturer when retailer default occurs. $(1-\mu )$ represents the proportion of risk shared by the bank, where it is $\eta ,\mu \in [0,1]$. In particular, in the intra-supply chain trade financing model, the default risk of retailer repayment is fully borne by the manufacturer, $\mu =1$. At this time, the internal and external financing modes of the supply chain are denoted as TIE and TEE, respectively.

In the financing model based on the blockchain platform, if the retailer violates the contract and tries to conceal the breach, by tampering with the information on the chain, it will pay a high cost. Also, the whole network broadcast will cause serious damage to the reputation and credit of the enterprise. The penalty for breach at this time will be much larger than that of the traditional financing model. In addition, the blockchain platform provides permanent proof for all transaction records. If the retailer wants to apply for supply chain financing after a default, it will be difficult to gain trust from the relevant enterprises. Therefore, as a rational decision-maker, the probability of a retailer defaulting after accessing the blockchain platform is extremely low. Without a loss of generality, this paper assumes that in the financing mode based on the blockchain platform, the retailer will choose normal repayment, and the default probability is 0. At this time, the financing model is the same as Section 4.3, and this section is not repeated.

6.1. Traditional Internal Trade Financing Model Considering the Financing Risk

The retailer’s expected profit function:

$$E({\pi }_R^{TIE})=(\eta -\varphi )q[(pD-\eta (\epsilon D-n)(1+r_M)-n]$$

(13)

The first item in square brackets is the sales proceeds, and the second is the possible repayment of the financing principal and interest. The third is the disbursement of its own funds.

The manufacturer’s expected profit function:

$$E({\pi }_M^{TIE})=(\eta -\varphi )q[n+\eta (\epsilon D-n)(1+r_M)-cD]$$

(14)

The first item in square brackets is the retailer’s own funds received, and the second item is the retailer’s possible repayment of the financing principal and interest. The third item is the production cost for the product.

Proposition 6.

Considering the financing default risk of the retailer, when the cash-constrained retailer finances through traditional internal trade, the optimal pricing, optimal ordering, and optimal expected profit of the supply chain member enterprises are, respectively:

$${\epsilon }^{TIE}=\frac{a+bc}{2\eta b(1+r_M^{TIE})}, p^{TIE}=\frac{3a+bc}{4b}, D^{TIE}=\frac{a-bc}{4},$$

$$E({\pi }_R^{TIE})=(\eta -\varphi )q\frac{{(a-bc)}^2-16bn[1-\eta (1+r_M^{TIE})]}{16b},$$

$$E({\pi }_M^{TIE})=(\eta -\varphi )q\frac{{(a-bc)}^2+8bn[1-\eta (1+r_M^{TIE})]}{8b}.$$

Proof. 

The reverse calculation method is adopted to solve the problem. Firstly, the optimal pricing condition for the retailer’s expected profit function is calculated. Let $\frac{\partial E({\pi }_R^{TIE})}{\partial p}=0$, then it is obtained $p=\frac{a+\eta b\epsilon (1+r_M)}{2b}$. Then, it is put into the manufacturer’s expected profit function $E({\pi }_M^{TIE})$, $\frac{\partial E({\pi }_M^{TIE})}{\partial \epsilon }=0$. The manufacturer’s optimal wholesale price is solved ${\epsilon }^{TIE}=\frac{a+bc}{2\eta b(1+r_M^{TIE})}$. Then, it is reversed into the retailer’s retail pricing formula to obtain the optimal retail price $p^{TIE}=\frac{3a+bc}{4b}$. Furthermore, according to the consumer demand function and the expected profit formula, the optimal order quantity, and the optimal expected profit for the member enterprises in the supply chain can be obtained. In addition, by calculating the second derivative of the wholesale price $\frac{{\partial }^{2}E({\pi }_M^{TIE})}{\partial {\epsilon }^2}=-(\eta -\varphi )q{\eta }^2{(1+r_M^{TIE})}^2\prec 0$, it shows that the manufacturer’s expected profit function has a maximum value. □

6.2. Traditional External Bank Financing Model Considering the Financing Risk

In the external bank financing model of the supply chain, if the retailer defaults after financing, the manufacturer needs to bear the guarantee cost in proportion $\mu$ to the financing line. The bank bears the financing risk in proportion $(1-\mu )$.

The retailer’s expected profit function:

$$E({\pi }_R^{TEE})=(\eta -\varphi )q[(pD-n-\eta (\epsilon D-n)(1+r_B)]$$

(15)

The first item in square brackets is the sales revenue. The second item is the advance payment of its own funds, and the third item is the sum of the financing principal and interest that the retailer may repay.

The manufacturer’s expected profit function:

$$E({\pi }_M^{TEE})=(\eta -\varphi )q[(\epsilon -c)D-\mu (1-\eta )(\epsilon D-n)(1+r_B)]$$

(16)

The first item in square brackets is the profit from wholesale sales. The second item is the guarantee cost borne by the manufacturer if the retailer defaults.

The bank’s expected profit function:

$$E({\pi }_B^{TEE})=(\eta -\varphi )q[\eta (\epsilon D-n)(1+r_B)-(\epsilon D-n)+\mu (1-\eta )(\epsilon D-n)(1+r_B)]-C_B^{TE}$$

(17)

The first item in square brackets is the sum of the financing principal and interest that may be received. The second item is the prepayment financing line paid by the bank to the manufacturer, and the third item is the guarantee indemnity paid by the manufacturer to the bank.

Proposition 7.

Considering the financing default risk of the retailer, when it is satisfied $\mu (1-\eta )(1+r_B^{TEE})\prec 1$, the optimal pricing, optimal ordering, and optimal expected profit for the member enterprises in the supply chain are: 

$${\epsilon }^{TEE}=\frac{a[1-\mu (1-\eta )(1+r_B^{TEE})]+\eta bc(1+r_B^{TEE})}{2\eta b(1+r_B^{TEE})[1-\mu (1-\eta )(1+r_B^{TEE})]},$$

$$p^{TEE}=\frac{3a[1-\mu (1-\eta )(1+r_B^{TEE})]+\eta bc(1+r_B^{TEE})}{4b[1-\mu (1-\eta )(1+r_B^{TEE})]},$$

$$D^{TEE}=\frac{a[1-\mu (1-\eta )(1+r_B^{TEE})]-\eta bc(1+r_B^{TEE})}{4[1-\mu (1-\eta )(1+r_B^{TEE})]},$$

$$E({\pi }_R^{TEE})=(\eta -\varphi )q\left\{\frac{{[a[1-\mu (1-\eta )(1+r_B^{TEE})]-\eta bc(1+r_B^{TEE})]}^2}{16b{[1-\mu (1-\eta )(1+r_B^{TEE})]}^2}-n[1-\eta (1+r_B^{TEE})]\right\},$$

$$E({\pi }_M^{TEE})=(\eta -\varphi )q\left\{\frac{{[a[1-\mu (1-\eta )(1+r_B^{TEE})]-\eta bc(1+r_B^{TEE})]}^2}{8\eta b(1+r_B^{TEE})[1-\mu (1-\eta )(1+r_B^{TEE})]}+\mu n(1-\eta )(1+r_B^{TEE})\right\}.$$

Proof. 

The reverse calculation method is adopted to solve the problem. Firstly, the optimal pricing condition for the retailer’s expected profit function is calculated $\frac{\partial E({\pi }_R^{TEE})}{\partial p}=0$, $p=\frac{a+\eta b\epsilon (1+r_B)}{2b}$. It is put into the manufacturer’s expected profit function $E({\pi }_M^{TEE})$, Let $\frac{\partial E({\pi }_M^{TEE})}{\partial \epsilon }=0$. The optimal wholesale price of the manufacturer is solved ${\epsilon }^{TEE}=\frac{a[1-\mu (1-\eta )(1+r_B^{TEE})]+\eta bc(1+r_B^{TEE})}{2\eta b(1+r_B^{TEE})[1-\mu (1-\eta )(1+r_B^{TEE})]}$. Then, it is reversed into the retail pricing formula for the retailer to obtain the optimal retail price $p^{TEE}=\frac{3a[1-\mu (1-\eta )(1+r_B^{TEE})]+\eta bc(1+r_B^{TEE})}{4b[1-\mu (1-\eta )(1+r_B^{TEE})]}$. Furthermore, according to the consumer demand function and the expected profit formula, the optimal order quantity, and the optimal expected profit for the member enterprises in the supply chain can be obtained. In addition, by calculating the second derivative of the wholesale price $\frac{{\partial }^{2}E({\pi }_M^{TEE})}{\partial {\epsilon }^2}=-(\eta -\varphi )q\eta b(1+r_B^{TEE})[1-\mu (1-\eta )(1+r_B^{TEE})]$, when there is $\mu (1-\eta )(1+r_B^{TEE})\prec 1$, $\frac{{\partial }^{2}E({\pi }_M^{TEE})}{\partial {\epsilon }^2}\prec 0$, it indicates that the manufacturer’s expected profit function has a maximum value. □

Corollary 7.

Compared with the risk-free financing scenario, when considering the default risk of the retailer, whether choosing internal trade financing or external bank financing, adopting blockchain technology can lower the threshold for the interest rate to a greater extent.

Proof. 

If supply chain financing is not obtained, the retailer will go bankrupt, the supply chain will be broken, and the profit for the manufacturer will become zero. Therefore, when considering the default risk, the interest rate threshold for the manufacturer to provide the retailer with internal trade financing is:

$$0\prec r_M^{TIE}\prec \frac{8(1-\eta )bn+{(a-bc)}^2}{8\eta bn}=\widehat{r_M^{TIE}}, \frac{\partial \widehat{r_M^{TIE}}}{\partial \eta }=-\frac{8bn+{(a-bc)}^2}{8bn{\eta }^2}\prec 0.$$

And when there is $\eta \to 1$, $\widehat{r_M^{TIE}}\to \widehat{r_M^{TI}}$, combined with Corollary 5, it can be concluded that $\widehat{r_M^{TIE}}\succ \widehat{r_M^{TI}}\succ \widehat{r_M^{BI}}$. Similarly, it can be calculated in the external bank financing model, $r_B{}^{TEE}\succ \frac{C_B^{TE}+(\eta -\varphi )q({\epsilon }^{TEE}{D}^{TEE}-n)(1-\mu )(1-\eta )}{(\eta -\varphi )q({\epsilon }^{TEE}{D}^{TEE}-n)[\eta +\mu (1-\eta )]}=\widehat{r_B^{TEE}}$, $\frac{\partial \widehat{r_B^{TEE}}}{\partial \eta }\prec 0$. Compared to when the retailer is completely trustworthy, it can be concluded that $\widehat{r_B^{TEE}}\succ \widehat{r_B^{TE}}\succ \widehat{r_B^{BE}}$.

The above quantitative relationships indicate that the application of blockchain technology in the risk environment can reduce the threshold for the interest rate to a greater extent and bring into play greater technical efficiency. □

Corollary 8.

(1) In the internal trade finance model, the retailer’s own default risk does not interfere with its supply chain decisions. (2) In the external bank financing model, where the retailer has financing default risk, the wholesale price for the manufacturer decreases with the increase in the retailer’s trustworthiness degree and increases with the increase in the risk-sharing ratio. When the proportion of the manufacturer’s risk sharing is less than a certain critical value, the retail price increases with the increase in the degree of trustworthiness and the proportion of risk sharing, the market demand decreases with the increase in trustworthiness and the risk-sharing ratio. (3) In the external bank financing mode, the application of blockchain technology can not only help the retailer to increase its sales prices, but can also effectively mitigate the impact of the financing risks on the wholesale prices and market demand.

Proof. 

(1) Comparing Proposition 6 and Proposition 2, $\eta (1+r_M^{TIE}){\epsilon }^{TIE}={\epsilon }^S$, $p^{TIE}=p^{TI}=p^S$, $D^{TIE}=D^{TI}=D^S$, it indicates that in the intra-supply chain trade financing model, the retailer’s debt default risk is completely transferred to the manufacturer together with the interest rate, and will not have any impact on the retailer’s pricing and market demand. Combined with Corollaries 2 (3) and 3 (1), it can be concluded that in the internal trade financing model, all the factor variables except supply and demand can be absorbed by the manufacturer. So, the retailer can achieve the same decision-making strategy as when the funds are sufficient.

(2)

$$\frac{\partial {\epsilon }^{TEE}}{\partial \eta }=-\frac{a{[1-\mu (1-\eta )(1+r^{TEE})]}^2+bc\mu {\eta }^2{(1+r^{TEE})}^2}{2b{\eta }^2(1+r^{TEE}){[1-\mu (1-\eta )(1+r^{TEE})]}^2}\prec 0,$$

$$\frac{\partial p^{TEE}}{\partial \eta }=\frac{c(1+r^{TEE})[1-\mu (1+r^{TEE})]}{4{[1-\mu (1-\eta )(1+r^{TEE})]}^2},$$

When there is $\mu \prec \frac{1}{1+r_B^{TEE}}$, $\frac{\partial p^{TEE}}{\partial \eta }\succ 0$,

$$\frac{\partial D^{TEE}}{\partial \eta }=-\frac{bc(1+r^{TEE})[1-\mu (1+r^{TEE})]}{4{[1-\mu (1-\eta )(1+r^{TEE})]}^2},$$

When there is $\mu \prec \frac{1}{1+r_B^{TEE}}$, $\frac{\partial D^{TEE}}{\partial \eta }\prec 0$,

$$\frac{\partial {\epsilon }^{TEE}}{\partial \mu }=\frac{c(1-\eta )(1+r^{TEE})}{2{[1-\mu (1-\eta )(1+r^{TEE})]}^2}\succ 0,$$

$$\frac{\partial p^{TEE}}{\partial \mu }=\frac{\eta c(1-\eta ){(1+r^{TEE})}^2}{4{[1-\mu (1-\eta )(1+r^{TEE})]}^2}\succ 0,$$

$$\frac{\partial D^{TEE}}{\partial \mu }=-\frac{\eta bc(1-\eta ){(1+r^{TEE})}^2}{4{[1-\mu (1-\eta )(1+r^{TEE})]}^2}\prec 0.$$

These indicate that in a risk environment, the trustworthiness of the retailer and the risk-sharing ratio of the manufacturer are important conditions for financing decisions.

(3) Following the monotone conclusion in the previous step, we can see that ${\epsilon }^{TEE}\succ {\epsilon }^{TE}$, $p^{TEE}\prec p^{TE}$, $D^{TEE}\succ D^{TE}$. Combined with Corollary 4 (1), we can compare the external bank financing mode: ${\epsilon }^{TEE/BE}\succ {\epsilon }^{TE}$, $p^{BE}\succ p^{TE}\succ p^{TEE}$ and $D^{TEE/BE}\succ D^{TE}$. This indicates that compared with the traditional financing model it is completely trustworthy, wholesale prices and market demand before and after the application of blockchain technology in a risk environment show little change and it can effectively maintain the stability of the manufacturer and market demand. At the same time, the retailer also has a high willingness to access the blockchain platform, which can further increase the sales price to achieve Pareto improvement. □

Corollary 9.

In the traditional financing mode where the retailer has default risk, when the risk-sharing ratio of the manufacturer is not high, the manufacturer should give priority to providing the retailer with a credit guarantee for external bank financing. But, after building a blockchain platform, the manufacturer is more likely to want the retailer to finance internal trade.

Proof. 

In the traditional financing model where the retailer is at risk of default,

$$\begin{array}{l}E({\pi }_M^{TEE})-E({\pi }_M^{TIE})=\\ \frac{\begin{array}{l}[a^2[1-\mu (1-\eta )(1+r^{TEE})]-b^2{c}^2\eta (1+r^{TEE})-8bn\eta (1+r^{TEE})[1-\mu (1-\eta )(1+r^{TEE})]]\times \\ [1-u(1-\eta )(1+r^{TEE})-\eta (1+r^{TEE})]\end{array}}{8\eta b(1+r^{TEE})[1-u(1-\eta )(1+r^{TEE})]}\end{array}$$

When there is $\mu \prec \frac{a^2-b\eta (1+r^{TEE})(b{c}^2+8n)}{[a^2-8bn\eta (1+r^{TEE})](1-\eta )(1+r^{TEE})}$, $E({\pi }_M^{TEE})\succ E({\pi }_M^{TIE})$.

However, after building the blockchain platform, the expected profit for the manufacturer changes to:

$$\begin{array}{l}E({\pi }_M^{BI})-E({\pi }_M^{BE})=\\ q\frac{\begin{array}{l}[k{(a-bc)}^2-2n{r}_M^{BI}(4kb-{\beta }^2)][4kb(1+r_B^{BE})-{\beta }^2]-\\ k(4kb-{\beta }^2){[a-bc(1+r_B^{BE})+b\theta r_B^{BE}]}^2\end{array}}{2(4kb-{\beta }^2)[4kb(1+r_B^{BE})-{\beta }^2]}\succ 0,\end{array}$$

In the traditional financing model, if the manufacturer’s risk sharing responsibility is less than a certain critical value, $\mu \prec {\mu }_0$, as shown in Figure 13, its optimal decision is to close the internal trade financing channel and urge the retailer to choose external bank financing. But, once a blockchain platform is built, the result is reversed. At this time, the manufacturer prefers to provide internal trade financing based on the blockchain platform for the retailer. □

7. Management Significance and Conclusions

7.1. Management Implications

Our research results have management implications: First, for the supply chain leader (i.e., the manufacturer), building a blockchain platform helps sustain supply chain operations and, thus, maintains and even increases the revenue generated from it. However, whether this can be achieved depends on the costs of setting up and operating the blockchain platform. Therefore, the manufacturer should evaluate the difficulty and cost of implementing the blockchain platform, maintain the platform access fee within a reasonable range, and attract more SMEs to access the platform to jointly build a “blockchain ecosystem”. Secondly, for the supply chain follower (i.e., the retailer), if the manufacturer offers the blockchain platform for free, it should definitely use the platform. Because doing so can not only improve the probability of obtaining funds from the lender, but can also greatly reduce the interest rate. For the bank, it needs to evaluate the “interest rate loss” against the increased total financing amount and the reduced risk control costs. It should only access the blockchain platform when the former is less than the latter. In addition, in the consumer market, products that require a high level of quality control should be primarily targeted for blockchain technology application. Examples of such products include maternal and child products, medical products, and jewelry.

7.2. Conclusions

Although previous research has examined the differences between intra-supply chain trade finance and external bank finance in traditional financing settings, we compare the two SCF models in traditional and blockchain-enabled financing settings. Furthermore, we extend this comparison to the scenario where the financing entity is at risk of default. In addition, we incorporate the building of a blockchain platform, the charging mechanism, and the traceability and anti-counterfeiting functions into the analytical framework of the model, which can further enrich the research on the integration of blockchain technology and SCF in decision-making. Our answers to the research questions introduced at the beginning are as follows: (1) In the traditional SCF setting, the manufacturer and retailer should set higher wholesale and retail prices, respectively, when opting for external bank financing than when opting for internal trade financing. However, in the blockchain-enabled SCF setting, the retailer should set a lower retail price when opting for external bank financing than when opting for internal trade financing. Moreover, both the wholesale and retail prices are higher in the blockchain-enabled SCF than in the traditional SCF. (2) The adoption of a blockchain platform has a dual effect on financing: On the one hand, it reduces the interest rate threshold, making external bank financing more advantageous, especially when the retailer has a significant capital gap. On the other hand, blockchain-enabled SCF can lead to higher wholesale and retail prices and increased order quantities compared to traditional SCF. Additionally, in internal trade financing, both the order quantity and the degree of application of the blockchain technology improve compared to external bank financing. However, the manufacturer and the retailer experience greater growth in the expected profit when external bank financing is conducted through the blockchain platform. (3) When using the blockchain platform for internal trade financing, the platform’s usage fee can be internalized into the manufacturer’s wholesale price. In this case, the retail price, order quantity, and the extent of blockchain technology application are unrelated to the platform’s usage fee. On the other hand, when using the blockchain platform for external bank financing, the wholesale and retail prices are negatively correlated with the platform’s usage fee. Additionally, the order quantity and the extent of blockchain technology application are positively correlated with the platform’s usage fee. Moreover, when the manufacturer’s fees for using the blockchain platform are reasonable, both the retailer and the bank prefer to access the blockchain platform as the optimal strategy. This scenario creates a favorable “win-win” situation for all the parties involved. (4) In internal trade financing, the retailer’s default risk does not impact its operational decision-making. In external bank financing, the utilization of blockchain technology can effectively mitigate the impacts of financing risk on the wholesale prices and order quantities. In the traditional SCF setting, when the manufacturer’s risk-sharing ratio is not high, the manufacturer should prioritize providing credit guarantees to help the retailer obtain financial support from the bank. However, in the blockchain-enabled SCF setting, the manufacturer prefers the retailer to employ internal trade financing.

The study represents an initial exploration into the differential impacts of blockchain technology on internal trade and external bank financing, but further research is needed to fully understand this emerging field. For example, the study investigated the supply chain’s internal and external financing modes using both traditional methods and a blockchain-based platform. Future research can delve into the application of blockchain technology in mixed internal and external financing scenarios and explore its potential in multi-tier supply chain financing. It also would be beneficial for future studies to examine the situation where enterprises, such as banks and e-commerce platforms, actively develop and apply blockchain platforms. This could provide valuable information on how established entities are incorporating blockchain technology into their operations.