Should Multinational Suppliers Relocate Their Production Capacity to Preferential Tariff Regions with Unreliable Supply under the Impact of Tariffs?

Abstract

This paper investigates the impact of tariff escalation on multinational suppliers relocating their production capacity to tariff-preferential regions with unreliable supply caused by low-production technology. We build a game theory model to analyze this issue based on three decisions for supplier-capacity relocation: no relocation, partial relocation, and full relocation. Our analysis finds that when tariffs are low or the production technology of the base in a preferential tariff region is not advanced, the supplier tends to adopt a partial-relocation strategy, but this strategy may be hindered by a manufacturer’s order-allocation decision, leading to a no-relocation strategy as the supply chain’s equilibrium. This may result in greater losses for the supplier. When tariffs are high or the production technology of the base in the preferential tariff region is advanced, the equilibrium strategy for the supply chain shifts to a full-relocation strategy. Interestingly, in the partial-relocation strategy, the higher production technology in the preferential tariff region negatively impacts the manufacturer’s expected profits but benefits the supplier’s expected profits due to the increased double marginalization. Finally, we find that the supplier can reduce the impact of tariffs by relocating their production capacity, especially with the partial-relocation strategy, as the supplier is always motivated to improve the production technology of the base in the preferential tariff region, with a potential purpose of transferring tariff costs to the manufacturer and consumers.

1. Introduction

Recently, the U.S. government has actively sought to narrow the trade deficit with China and promote the reshoring of manufacturing to the U.S. Tariff policies have been the main tool for both reducing the trade deficit with China and advancing the ‘Made in USA’ movement [1]. In the digital product industry, the U.S. government has implemented a series of tariff measures. For example, Apple’s products produced in China, including headphones, watches, and other products, are subject to a 15 percent tariff [2]. This tariff policy has resulted in a USD 500 million increase in sourcing costs for Apple [3]. Many other industries have also experienced tariff increases, such as the 25% and 10% tariffs imposed under Section 232 on imported steel and aluminum, respectively [4], and the 25% import tariffs on bicycle industry components under Section 301. Tariff policies play a crucial role in the operation of multinational firms, and some firms even consider relocating their production capacity out from China [5].

Among the firms relocating their production capacity, many Chinese suppliers serving U.S. manufacturers have moved to emerging economies like Southeast Asia [6] instead of the U.S. [7]. For example, Luxshare Precision, an Apple wearable device supplier in China, relocated a portion of its capacity to Vietnam. It now has production bases in both Vietnam and China to serve Apple [8]. Similarly, Samsung has relocated all its production factories from China to Southeast Asia [7]. These firms are attracted by two main factors. First, Southeast Asian countries’ favorable trade relations with the U.S. allow them to enjoy low or zero tariffs in the region [9]. Second, Southeast Asia offers a demographic dividend [10], which effectively reduces their production cost [11,12,13]. At the same time, some Chinese suppliers are hesitant to relocate to Southeast Asia [14], such as Honeywell and Volkswagen [15]. One of the concerns of these suppliers is that relocating their production capability to Southeast Asia may lead to unreliable supply due to electricity shortages [16], traffic congestion, and most importantly, the lower level of the production technology in Southeast Asia [17]. Unreliable supply always results in product shortages in the market, which may be beyond considerations of cost [18].

The different behaviors of suppliers pose interesting questions. How do tariffs and unreliable supply affect suppliers’ strategy of relocating their production capacity and the manufacturers’ sourcing strategy? How do different strategies of relocating production capacity affect the performance of the supply chain and consumers? To answer these questions, we analyze three production-relocation strategies already implemented in practice: the no-relocation strategy, also known as the basic strategy (B); the partial-relocation strategy (P); and the full-relocation strategy (F).

Under strategy B, the supplier does not relocate its production capacity and focuses on producing key components at its home production base (HPB). Due to the superior production technology of the HPB, there is no unreliable supply. Thus, the manufacturer’s order quantity matches the supplier’s actual delivery quantity. However, while allocating orders to the HPB ensures a stable and reliable supply, it also incurs additional tariff costs. In the context of trade escalation, these costs can be quite high. This situation is common [7], as observed with firms such as Honeywell and Volkswagen [15], which supply products to U.S. firms exclusively from a Chinese production base.

Under strategy F, the supplier relocates all its production capacity to a preferential tariff region and establishes a new production base there. Since the region where the new production base is located enjoys preferential tariffs in the manufacturer’s country, the manufacturer does not need to pay additional tariffs when sourcing key components from the new base. Therefore, we refer to the new base as a duty-free production base (DFPB). It is important to note that the production technology of a DFPB is generally lower, which can impact the yield of key components and result in unreliable supply. Consequently, the manufacturer must consider the issue of unreliable supply. We can observe that Samsung employs this strategy [7].

Under strategy P, the supplier chooses to relocate part of its production capacity to a preferential tariff region while maintaining a production base at home. The manufacturer can choose to source key components solely from one base or allocate orders to both bases. When the manufacturer sources from the HPB, it ensures a stable and reliable supply but incurs an additional tariff cost. Conversely, sourcing from a DFPB is duty-free but may lead to unreliable supply. Consequently, the manufacturer must weigh these sourcing options to optimize the overall sourcing cost. Luxshare Precision is a typical example of a firm employing this strategy [8].

Our study indicates that tariffs and unreliable supply are key factors in determining a supplier’s decision to relocate its production capacity. When tariffs are low or the production technology of DFPB is less advanced, the supplier tends to adopt strategy P. In this strategy, the supplier adjusts the manufacturers’ order allocation through flexible pricing to balance the cost of tariffs with the losses due to unreliable supply. However, manufacturers prefer strategy B, where they can obtain a stable and reliable supply at a lower sourcing cost. Thus, the equilibrium strategy of the supply chain, depending on the manufacturer, is strategy B. Interestingly, manufacturers’ order-allocation decisions may result in significant losses for the supplier. However, when the production cost of HPB is sufficiently high and the production cost of DFPB is relatively low, the manufacturer will favor strategy P, suggesting that strategy P could become the new equilibrium strategy of the supply chain. When tariffs are high or the production technology of DFPB is advanced, if the supplier continues with strategy P, the manufacturer will fully allocate orders to DFPB. Consequently, strategy P becomes infeasible. Due to high tariffs or the advanced production technology of DFPB, the advantages of a stable and reliable HPB become less significant, leading the supplier to relocate all its production capacity to a preferential tariff region. The supply chain equilibrium strategy shifts to strategy F. Interestingly, the impact of the advanced production technology of DFPB on the manufacturers’ expected profits varies depending on the supplier’s relocation strategy. In strategy F, the manufacturer benefits from the high-production technology of DFPB. However, in strategy P, this high technology may decrease the manufacturers’ profits. Another noteworthy result is that the supplier is always willing to improve the production technology of DFPB to enhance supply reliability, with a potential aim of transferring the tariff cost to the manufacturer and consumers, which could change the supplier’s role as the primary bearer of the tariff cost.

The rest of this paper is organized as follows. In Section 2, we review the relevant literature. In Section 3, we describe our model. In Section 4, we analyze the effects of tariffs and production technology on the supplier and manufacturer under different strategies. We extend the model in Section 5 and conclude our paper in Section 6.

2. Literature Review

Our work is related to the effect of tariffs on global supply chain management. Research on this topic is rich and continually evolving and can be categorized into several areas. Firstly, there is a focus on the impact of tariffs on supply chain performance. This includes studies on how tariffs and negotiated prices affect procurement strategies [1], pricing strategies [19], the impact of different export tariffs on supply chain strategies [20], and the influence of export tax rebates on procurement contract choices [21]. Secondly, some research examines the effects of tax differences between economies. Shunko et al. [22] studied the impact of production cost and tax differences on transfer pricing and the sourcing strategies of multinational firms. Xiao et al. [23] analyzed the effect of tax cross-credits on the manufacturing-capacity decisions of multinational firms’ overseas subsidiaries in low-tax countries under demand uncertainty. Hsu et al. [24] considered the decision faced by global firms on whether to sell products (and at what price) to external competitors in the retail market. The research most relevant to our study concerns the impact of tariffs on the supply chain structure. Kopel and Löffler [25] investigated the impact of tax rate differences and international transfer pricing rules on the profit-maximizing location strategies of multinational corporations. They pointed out that the optimal location strategy and transfer pricing methods balance the benefits of shifting profits to low-tax countries against the losses caused by the distortions in choice. Shunko et al. [26] compared two strategies: keeping production in high-tax regions versus relocating to low-tax areas. Their results indicate that strategically placing part of the supply chain in low-tax locations enables multinational firms to allocate profits across divisions to enhance post-tax profits. Niu et al. [27] focused on the impact of national culture on multinational corporations’ production-strategy decisions. They specifically compared whether manufacturers should relocate production departments domestically or abroad. They found that when the variable costs of factory construction are low and fixed costs are moderate, multinational corporations’ preference for production strategies shifts twice—from local production to overseas production, and then back to local production as channel substitutability increases. Unlike these studies, we shift focus from intracompany transactions between suppliers and manufacturers to the strategic interactions between independent suppliers and manufacturers. We also analyze the coordination motives of the supplier between two production bases. Additionally, we incorporate the element of production unreliability at the supplier’s DFPB into our model. As more Chinese suppliers relocate production to emerging economies, the reliability of supply has become a primary concern for firms. Beyond the theoretical insights mentioned above, our work also addresses a highly debated issue: whether tariffs have a greater impact on suppliers [1] or on manufacturers [28,29,30].

Research on unreliable supply is also closely related to this paper. Early studies on unreliable supply focused on its impact on optimal production, sourcing, and inventory replenishment. A seminal work by Yano and Lee [31] provided a comprehensive review of the early literature on unreliable supply. Other studies primarily addressed whether introducing unreliable suppliers is a viable option. Tomlin [32] investigated risk management strategies for supply disruptions when there are two suppliers: one reliable but expensive, and the other cheap but with unreliable supply. Tang and Kouvelis [33] assumed suppliers with proportionally random supply and demonstrated that dual sourcing strategies by competing buyers could alleviate the inefficiencies caused by unreliable supply. Li et al. [34] considered a setting with two heterogeneous suppliers and a common retailer with information asymmetry. Niu et al. [35] developed an analytical model to study dual sourcing decisions by original equipment manufacturers (OEMs) facing competitive and non-competitive suppliers with unreliable outputs. Other research includes topics such as inventory [36], supplier selection [37], procurement from multiple unreliable suppliers [38], and blockchain for unreliable supplier selection [39]. The research most relevant to this paper is Niu et al. [35]. However, unlike their study, we focus on the strategic interactions between supplier and manufacturer under tariff shocks. In our decision-making framework, the wholesale prices for both production bases are determined by the supplier. Our study emphasizes the impact of tariffs on suppliers’ capacity-relocation decision and the effect of capacity relocation on supply chain members and consumer surplus.

3. Model Setting and Assumptions

We consider a supply chain model consisting of a supplier (she) located in a developing country and a global manufacturer (he) located in a developed country. The supplier has the capability to produce key components, which are then used to produce final products for consumers. We assume that the manufacturer needs to source key components from the supplier and assemble them into new products under its brand name. Without losing generality, we assume that the manufacturer uses one unit of the key component to assemble one unit of the final product. Depending on the motivation, if the trade relations between the country where the supplier is located and the country where the manufacturer is located deteriorate, leading to increased tariffs, the supplier can choose from three strategies to address this situation. The first is the no-relocation strategy, also known as the basic strategy (B). Under this strategy, the supplier provides key components exclusively from the HPB. The second is the partial-relocation strategy (P). Under this strategy, the supplier maintains its HPB and builds a new production base in a preferential tariff region, named the DFPB, supplying key components from both bases. The third is the full-relocation strategy (F). Under this strategy, the supplier supplies key components exclusively from the DFPB.

When the manufacturer sources key components from the DFPB, he must contend with potential issues related to unreliable supply. Like the previous literature [31,33,35], we capture the concept of unreliable supply from a technical industry perspective by considering the lower level of production technology. For an order size of q, the actual delivered quantity by the supplier will be $\xi q$, where $\xi$ is a random variable with mean $\mu$ and variance $\sigma$. And we have $Var\left(\xi \right)=E\left({\xi }^2\right)-{\left(E\xi \right)}^2$, thus $E\left({\xi }^2\right)={\mu }^2+{\sigma }^2$.To capture the characteristic that the supplier’s actual delivered quantity is a fraction of the order quantity, we constrain $\xi \in [0,1]$. The increase in $\mu$ or the decrease in $\sigma$ can be interpreted as an improvement in the production technology. Furthermore, we define $x={\left({\displaystyle \frac{\mu }{\sigma }}\right)}^2$ as the production technology of the DFPB (for further discussion, see Niu et al. [35]). Additionally, to avoid some trivial cases, we assume the production technology satisfies $0<x<{\displaystyle \frac{4\gamma +4}{{\gamma }^2}}$. This assumption ensures a sufficiently significant difference in the production technology between the supplier’s two production bases. We also summarize the notations in

Table 1. Main notations used.

Notations	Description
s	Supplier
m	Manufacturer
h	Home production base
$df$	Duty-free production base
a	The market size
$\xi$	Random variable represents unreliable supply
$\mu$	The mean of random variable $\xi$
${\sigma }^2$	The variance of random variable $\xi$
$\gamma$	Tariff rate
$q_i$	The orders of i production base $(i\in \{h,df\left\}\right)$
$w_i$	The wholesale price of i production base $(i\in \{h,df\left\}\right)$
${\pi }_j$	The profit of j $(j\in \{s,m,h,df\left\}\right)$

.

We use a game theory model to describe the decision of supply chain players because the mathematical formulation of a game theory model allows us to precisely define real-life concepts and better understand the motivations behind the actions and decisions of supply chain players [40]. By using a game theory model, we can model important features of real situations and derive optimal decisions for players, leading to a deeper understanding of these situations [41]. Specifically, due to the geographical distance from the market, sourcing key components from abroad often results in longer delivery lead times [42]. In industries with long production lead times, firms cannot promptly adjust their production quantities [43]. As we focus on unreliable supply, we consider the Cournot model to be appropriate for our issue.

We model the above issues using a three-stage setting to capture the impact of tariffs’ escalation on the supplier’s relocating-production-capacity decision and the manufacturer’s order-allocation decision. The event sequence is shown in Figure 1.

In stage 1, the supplier remains keenly aware of international trade market regulations and decides whether to invest in building a new production base in preferential tariff regions based on this awareness. Clearly, such a decision is strategic planning, which may have long-term implications for future operations. We focus on the impact of tariffs on the supplier’s strategic decision to relocate its production capacity. The expenditure on building a new production base is considered a sunk cost, which restricts the flexibility of the player’s decisions. Therefore, we normalize the sunk cost of investing in a new production base to zero.

In stage 2, the supplier sets different wholesale prices based on the characteristics of different production bases.

In stage 3, referencing assumptions from the literature [32,44,45], we consider the manufacturer as a price-taker of a key component’s wholesale price. Based on the supplier’s component quotes, the manufacturer decides on the sourcing quantity and allocates orders.

This setting allows us to capture the changes in the supplier’s strategic decisions under external tariff escalation and the impact of these changes on the supply chain system’s decisions. Moreover, this setting also represents the manufacturer’s consideration of the unreliable supply at the DFPB. We focus on the supplier’s incentives for relocating its production capacity and how the manufacturer balances upstream orders considering tariff escalation, as well as how these factors influence the performance of supply chain members.

We follow the assumptions from the previous literature [1,46], where consumers purchase at most one unit of product. The population in the market either buys one unit of the product from the manufacturer or does not buy at all. Consumers are heterogeneous in their willingness to pay for a product, which is denoted by v. We assume that consumer types are uniformly distributed with a unit density over the interval $[0,a]$. The unit-density assumption captures the population of consumers in the market, where a can be interpreted as the market size [47,48]. Without a loss of generality, we assume that the market potential is large enough so that the market demand is always positive. Thus, the consumer surplus obtained by consumers in the terminal market is given by

$$U\left(v\right)=max\{v-p,0\},$$

(1)

where p represents the market price of the product. Following the methods from the literature [1,46], we can derive the market-clearing price for the product:

$$p=a-Q.$$

(2)

The parameter Q represents the total quantity of products in the market. To focus on the impact of tariff escalation on the supplier relocating its production capacity and the manufacturer’s order allocation, we assume, without a loss of generality, that the production cost for both the supplier and the manufacturer is zero. This technical treatment also implies an important underlying assumption: the production costs at the supplier’s two bases are similar. In Section 5, we will relax this assumption, whereby the production cost is positive and differentiated. We assume that the manufacturer pays only for the order quantities they receive, which will not change our main conclusion [33].

4. Model Analysis

In this section, we investigate the impact of tariffs on the supplier’s capacity-relocation strategy and the effects of unreliable supply on the decisions of both parties. We begin by modeling the three strategies to be discussed and obtain the subgame perfect equilibrium by solving the models in reverse order. Then, we examine the decisions of the supply chain players under each strategy. To understand tariffs and the unreliable supply of the DFPB on the supplier-capacity-relocation strategy, we also compare equilibrium results across different strategies. Finally, to comprehend the impact of the supplier-capacity-relocation strategy on consumers, we compare consumer surplus under different strategies. All proofs for this paper are put in Appendix A.

4.1. No-Relocation Strategy

We use the superscript “B” to denote this case. The supplier provides key components exclusively from the HPB. Since the supplier’s HPB has excellent production technology and there is reliable supply, the manufacturer’s product quantity Q in the market exactly equals the order quantities $q_h$ allocated with the supplier’s HPB. However, it is important to note that all the key components sourced by the manufacturer will incur additional tariffs. In this case, the supplier’s profit solely comes from sales at its HPB, ${\pi }_s^B={\pi }_h^B$. The event sequence is as follows: First, the supplier determines the HPB’s wholesale prices $w_h^B$. Next, the manufacturer determines orders $q_h^B$. Finally, the manufacturer completes production and sells the final product. We use the backward induction method to solve the problem.

For a given $w_h^B$, the manufacturer’s profit function is as follows:

$${\pi }_m^B=\underset{q_h^B}{max}\left[\left(a-q_h^B-\gamma w_h^B-w_h^B\right)q_h^B\right].$$

(3)

Due to the second-order sufficient condition, i.e., ${\displaystyle \frac{{\partial }^2{\pi }_m^B}{\partial {\left(q_h^B\right)}^2}}<0$, the profit function is concave with respect to $q_h^B$. Therefore, we have a response function of $q_h^B$ with respect to $w_h^B$ through ${\displaystyle \frac{\partial {\pi }_m^B}{\partial q_h^B}}=0$ as follows:

$$q_h^B\left(w_h^B\right)={\displaystyle \frac{1}{2}}\left(\alpha -(\gamma +1)w_h^B\right).$$

(4)

The supplier anticipates the manufacturer’s reaction and determines the optimal wholesale price through the profit function:

$${\pi }_h^B=\underset{w_h^B}{max}\left(q_h^B{w}_h^B\right).$$

(5)

Similarly, we have ${\displaystyle \frac{{\partial }^2{\pi }_h^B}{\partial {\left(w_h^B\right)}^2}}<0$, so by setting ${\displaystyle \frac{{\partial }^B{\pi }_h^B}{\partial {\left(w_h\right)}^B}}=0$, we obtain the optimal $w_h^B$. Consequently, we can derive the equilibrium decisions for all members. We derive the subgame perfect equilibrium in Theorem 1.

Theorem 1. 

Under strategy B, the supplier’s wholesale price is $w_h^B={\displaystyle \frac{a}{2\gamma +2}}$, and the manufacturer’s order quantity is $q_h^B={\displaystyle \frac{a}{4}}$. Correspondingly, the expected profits of the supply chain members are ${\pi }_h^B={\displaystyle \frac{a^2}{8(\gamma +1)}}$ and ${\pi }_m^B={\displaystyle \frac{a^2}{16}}$.

In addition, the following results hold in equilibrium:

(i) 

$w_h^B$ is decreasing in γ;

(ii) 

$q_h^B$ is a constant and not affected by γ;

(iii) 

${\pi }_h^B$ is decreasing in γ; ${\pi }_m^B$ is a constant and not affected by γ.

Theorem 1(i) demonstrates that the HPB’s whole price is monotonically decreasing with respect to tariffs. As tariffs escalate, the manufacturer experiences higher sourcing costs, resulting in a reduction in the product’s marginal profit. The supplier is not exempt from this, as her marginal profits also decline, resulting in a lower wholesale price as tariffs increase. Interestingly, in Equation (4), $q_h^B$ to $w_h^B$ is monotonically increasing in both $\gamma$ and $w_h^B$, but the optimal equilibrium solution of $q_h^B$ remains constant and is unaffected by $\gamma$. This is because the increase in $\gamma$ causes $w_h^B$ to decrease, and the interaction between the two keeps the manufacturer’s sourcing price unchanged, and thus $q_h^B$ remains unaffected by tariffs. This indicates that the supplier absorbs the tariff cost through the wholesale price, thereby preventing tariffs from impacting the manufacturer’s ordering quantity. Furthermore, Theorem 1(iii) shows the effect of tariffs on ${\pi }_h^B$ and ${\pi }_m^B$. As the ordering quantity remains unchanged and the wholesale price decreases with tariffs, the supplier’s profit ${\pi }_h^B$ decreases with tariffs. However, since both the manufacturer’s sourcing cost and ordering quantity remain constant with tariffs, the manufacturer’s profit ${\pi }_m^B$ remains constant and is unaffected by tariffs.

4.2. Partial-Relocation Strategy

We use the superscript “P” to denote this case. The supplier maintains her HPB and builds a new production base in preferential tariff regions, providing key components from both production bases. When the manufacturer sources from the HPB, it ensures a stable and reliable supply but incurs additional tariff costs. Conversely, sourcing from a preferential tariff region’s production base, referred to as the duty-free production base (DFPB), is duty-free but may lead to unreliable supply. The event sequence is as follows: First, the supplier simultaneously determines wholesale prices for different production bases, $w_{df}^P$ and $w_h^P$. Next, the manufacturer allocates $q_{df}^P$ and $q_h^P$ based on wholesale prices and the production technology of each production base. Finally, the manufacturer completes production and sells the final product.

For a given $w_{df}^P$ and $w_h^P$, the manufacturer’s profit function is as follows:

$$\begin{array}{cc}E\left[{\pi }_m^P\right]\hfill & =\underset{q_h^P,q_{df}^P}{max}E[q_h^P\left(a-\left(\xi q_{df}^P+q_h^P\right)-\gamma w_h^P-w_h^P\right)\hfill \\ \hfill & +\xi q_{df}^P\left(a-\left(\xi q_{df}^P+q_h^P\right)-w_{df}^P\right)].\hfill \end{array}$$

(6)

The manufacturer makes a sourcing decision before the realization of production uncertainty, and Equation (6) can be rewritten as

$$\begin{array}{cc}E\left[{\pi }_m^P\right]\hfill & =\underset{q_h^P,q_{df}^P}{max}[q_h^P\left(a-\mu q_{df}^P-q_h^P-\gamma w_h^P-w_h^P\right)\hfill \\ \hfill & +\mu q_{df}^P\left(a-w_{df}^P-q_h^P\right)-\left({\mu }^2+{\sigma }^2\right){\left(q_{df}^P\right)}^2].\hfill \end{array}$$

(7)

Since Equation (7) requires simultaneous optimization with respect to $q_{df}^P$ and $q_h^P$, we need to judge whether $E\left[{\pi }_m^P\right]$ is concave in $q_{df}^P$ and $q_h^P$.

Because ${\displaystyle \frac{{\partial }^{2}E\left[{\pi }_m^P\right]}{\partial {\left(q_h^P\right)}^2}}=-2<0,{\displaystyle \frac{{\partial }^{2}E\left[{\pi }_m^P\right]}{\partial {\left(q_{df}^P\right)}^2}}=-2\left({\mu }^2+{\sigma }^2\right)<0$, we can determine that $E\left[{\pi }_m^P\right]$ is concave in $q_{df}^P$ and $q_h^P$.

Next, we derive the second-order Hessian matrix for $q_{df}^P$ and $q_h^P$. Given that ${\displaystyle \frac{{\partial }^{2}E\left[{\pi }_m^P\right]}{\partial q_{df}^P\partial q_h^P}}={\displaystyle \frac{{\partial }^{2}E\left[{\pi }_m^P\right]}{\partial q_h^P\partial q_{df}^P}}=-2\mu$, the Hessian matrix is $H_1$ as follows:

$$H_1=\left[\begin{array}{cc}-2& -2\mu \\ -2\mu & -2({\mu }^2+{\sigma }^2)\end{array}\right].$$

And $\left|H_1\right|=4{\sigma }^2>0$. Thus, we have the best response functions by setting ${\displaystyle \frac{\partial E\left({\pi }_m^P\right)}{\partial q_h^P}}=0$ and ${\displaystyle \frac{\partial E\left[{\pi }_m^P\right]}{\partial q_{\mathrm{df}}^P}}=0$ as follows:

$$\left\{\begin{array}{c}{q}_h^P(w_h^P,w_{df}^P)={\displaystyle \frac{\alpha -(1+\gamma )w_h^P}{2}}-{\displaystyle \frac{(w_h^P+\gamma w_h^P-w_{df}^P){\mu }^2}{2{\sigma }^2}}\hfill \\ q_{df}^P(w_h^P,w_{df}^P)={\displaystyle \frac{(w_h^P+\gamma w_h^P-w_{df}^P)\mu }{2{\sigma }^2}}\hfill \end{array}\right..$$

(8)

The supplier anticipates the manufacturer’s reaction and determines the optimal wholesale price through her profit function:

$$E\left[{\pi }_s^p\right]=\underset{w_h^P,w_{df}^P}{max}E\left[\xi q_{df}^P{w}_{df}^P+q_h^P{w}_h^P\right].$$

(9)

Substitute Equation (8) into Equation (9). Equation (9) is also optimized with respect to $w_{df}^P$ and $w_h^P$, following the same procedure as the previous solution. Firstly, ${\displaystyle \frac{{\partial }^{2}E\left[{\pi }_s^P\right]}{{\left.\partial {(}_h^p\right)}^2}}=-{\displaystyle \frac{(\gamma +1)\left({\mu }^2+{\sigma }^2\right)}{{\sigma }^2}}<0$, ${\displaystyle \frac{{\partial }^{2}E\left[{\pi }_s^P\right]}{\partial {\left(w_{df}^P\right)}^2}}=-{\displaystyle \frac{{\mu }^2}{{\sigma }^2}}<0$, so we can judge that $E\left[{\pi }_s^P\right]$ is concave in $w_{df}^P$ and $w_h^P$.

Next, we derive the second-order Hessian matrix for $w_{df}^P$ and $w_h^P$. Due to ${\displaystyle \frac{{\partial }^{2}E\left[{\pi }_s^P\right]}{\partial w_{df}^P\partial w_h^P}}={\displaystyle \frac{{\partial }^{2}E\left[{\pi }_s^P\right]}{\partial w_h^P\partial w_{df}^P}}={\displaystyle \frac{(\gamma +2){\mu }^2}{2{\sigma }^2}}$, the Hessian matrix is $H_2$, as follows:

$$H_2=\left[\begin{array}{cc}-{\displaystyle \frac{(1+\gamma )({\mu }^2+{\sigma }^2)}{{\sigma }^2}}\hfill & {\displaystyle \frac{(2+\gamma ){\mu }^2}{2{\sigma }^2}}\hfill \\ {\displaystyle \frac{(2+\gamma ){\mu }^2}{2{\sigma }^2}}\hfill & -{\displaystyle \frac{{\mu }^2}{{\sigma }^2}}\hfill \end{array}\right].$$

And we find that $\left|H_2\right|>0$, if ${\displaystyle \frac{{\mu }^2}{{\sigma }^2}}<{\displaystyle \frac{4\gamma +4}{{\gamma }^2}}$. Thus, we can determine the equilibrium decisions for $w_{df}^P$ and $w_h^P$ by setting ${\displaystyle \frac{\partial E\left[{\pi }_s^P\right]}{\partial w_h^P}}=0$ and ${\displaystyle \frac{\partial E\left[{\pi }_s^P\right]}{\partial w_{df}^P}}=0$. Substituting equilibrium decisions of $w_{df}^P$ and $w_h^P$ into Equations (6), (8), and (9) will yield the equilibrium decisions for the supply chain members. We summarize the equilibrium decisions of the players in Theorem 2. Next, we reorganize and analyze the results using $x={\left({\displaystyle \frac{\mu }{\sigma }}\right)}^2$.

Theorem 2. 

Under strategy P, if $\gamma \ge {\displaystyle \frac{2}{x}}$, the manufacturer will allocate all orders to the DFPB, and strategy P is no longer an executable strategy. If $\gamma <{\displaystyle \frac{2}{x}}$, the equilibrium outcomes are as follows: wholesale prices are $w_h^P={\displaystyle \frac{2a{\sigma }^2}{4(\gamma +1){\sigma }^2-{\gamma }^2{\mu }^2}}$ and $w_{df}^P={\displaystyle \frac{{\sigma }^2\left(a(\gamma +2)\right)}{4(\gamma +1){\sigma }^2-{\gamma }^2{\mu }^2}}$; order quantities are $q_h^P={\displaystyle \frac{\left(a(\gamma +1)\right)\left(2{\sigma }^2-\gamma {\mu }^2\right)}{8(\gamma +1){\sigma }^2-2{\gamma }^2{\mu }^2}}$ and $q_{df}^P={\displaystyle \frac{a\gamma \mu }{8(\gamma +1){\sigma }^2-2{\gamma }^2{\mu }^2}}$; and correspondingly, the expected profits of the supply chain members are $E\left[{\pi }_s^P\right]={\displaystyle \frac{a^2{\sigma }^2}{8(\gamma +1){\sigma }^2-2{\gamma }^2{\mu }^2}}$ and $E\left[{\pi }_m^P\right]={\displaystyle \frac{a^2\left({\gamma }^4{\mu }^4-\left({\gamma }^2(4\gamma +3)\right){\mu }^2{\sigma }^2+4{(\gamma +1)}^2{\sigma }^4\right)}{4{\left(4(\gamma +1){\sigma }^2-{\gamma }^2{\mu }^2\right)}^2}}$, respectively.

In addition, the following results hold in equilibrium:

(i) 

$w_h^P$ is decreasing in γ and increasing in x; $w_{df}^P$ is first decreasing and then increasing in γ, and increasing in x;

(ii) 

$q_h^P$ is decreasing in γ and decreasing in x; for any σ, $q_{df}^P$ is increasing in γ and increasing in x.

Theorem 2(i) illustrates that the wholesale price of the HPB decreases with tariffs. As shown in Equation (8), $q_h^P$ is monotonically decreasing in $w_h^P$, while $q_{df}^P$ is monotonically increasing in $w_h^P$. In other words, given the wholesale price of the DFPB, the higher wholesale price of the HPB will encourage the manufacturer to allocate more orders to the DFPB, reducing both the supplier’s and manufacturer’s tariff costs and thereby benefiting both parties. However, it is important to note that a higher wholesale price of the HPB will decrease the actual demand quantity of the HPB. The gains from order relocation by the supplier cannot compensate for the losses caused by the reduced demand of the HPB. Therefore, as tariffs increase, the supplier will set a lower wholesale price of the HPB to mitigate the loss resulting from the decrease in the actual demand of the HPB.

Unlike the wholesale price of the HPB, the wholesale price of the DFPB exhibits non-monotonic behavior with respect to tariffs. By further examining Equation (8), we observe that the actual delivery quantity ($E\left[\xi \left(q_{df}^P\left(w_h^P,w_{df}^P\right)\right)+q_h^P\left(w_h^P,w_{df}^P\right)\right]$) obtained by the manufacturer is ${\displaystyle \frac{1}{2}}\left(\alpha (\gamma +1)w_h^P\right)$, independent of $w_{df}^P$. Instead, the wholesale price of the HPB is the key factor that truly influences the manufacturer’s actual delivery quantity. Here, the wholesale price of the DFPB acts as a tool for the supplier to adjust the manufacturer’s order allocation to maximize profits. When $\gamma$ is relatively low, the impact of tariffs on the manufacturer’s sourcing cost of the HPB is not significant, and the manufacturer lacks strong motivation to relocate orders to the DFPB. In this case, the supplier may lower the wholesale price of the DFPB to attract more orders and reduce the additional tariff burden from the HPB. However, when $\gamma$ is high, tariffs substantially increase the manufacturer’s sourcing cost of the HPB, prompting the manufacturer to allocate a significant portion of orders to the DFPB to avoid tariff expenses. In this case, the supplier will raise the wholesale price of the DFPB to maximize profit extraction from the manufacturer.

Theorem 2(i) also illustrates that, for any given $\gamma$, the wholesale prices at both the HPB and the DFPB increase with the production technology of the DFPB. The higher production technology of the DFPB encourages the manufacturer to allocate more orders to this base, reducing tariff costs from the HPB. For the supplier, the wholesale price of the DFPB is a key tool for extracting profit from the manufacturer. As the manufacturer allocates more orders to the DFPB, the supplier raises the wholesale price of the DFPB to further increase its profit. However, as the wholesale price of the DFPB rises, the manufacturer’s order-allocation strategy may change, leading to a reallocation of more orders back to the HPB. This order reallocation will increase tariff costs, prompting the supplier to raise the wholesale price of the HPB to discourage the manufacturer from shifting more orders back to the HPB.

Theorem 2(ii) is directly derived from the manufacturer’s sourcing cost. For any given $\gamma$ and x, the sourcing cost of the HPB for the manufacturer increases, causing $q_h^P$ to decrease with both $\gamma$ and x. On the other hand, the relative sourcing cost advantage of the DFPB increases with $\gamma$ and x, leading $q_{df}^P$ to increase with both $\gamma$ and x. It is important to note that the scale of the manufacturer’s order transfer is not solely dependent on the sourcing cost difference between the two bases but is also significantly influenced by the production technology level of the DFPB. The higher the production technology of the DFPB, the more inclined the manufacturer is to transfer additional orders there, aiming to reduce the overall sourcing cost.

Next, we analyze the impact of tariffs and the production technology of the DFPB on the profits of both the supplier and manufacturer. To distinguish the profits obtained by the supplier and manufacturer through different channels, we define $E\left[{\pi }_{s-h}^P\right]$ ($E\left[{\pi }_{s-df}^P\right]$) and $E\left[{\pi }_{m-h}^P\right]$ ($E\left[{\pi }_{m-df}^P\right]$) in the following analysis as the profits earned by the supplier from selling the key components produced at the HPB (DFPB) and the profits earned by the manufacturer from selling products assembled using the key components procured from the HPB (DFPB), respectively.

Theorem 3. 

Under strategy P,

(i) 

For a given x, $E\left[{\pi }_s^P\right]$ and $E\left[{\pi }_m^P\right]$ are both decreasing in γ; $E\left[{\pi }_{s-h}^P\right]$ and $E\left[{\pi }_{m-h}^P\right]$ are decreasing in γ and $E\left[{\pi }_{s-df}^P\right]$ and $E\left[{\pi }_{m-df}^P\right]$ are increasing in γ.

(ii) 

For a given γ, $E\left[{\pi }_s^P\right]$ is increasing in x while $E\left[{\pi }_m^P\right]$ is decreasing in x; $E\left[{\pi }_{s-h}^P\right]$ and $E\left[{\pi }_{m-h}^P\right]$ are increasing in x and $E\left[{\pi }_{s-df}^P\right]$ and $E\left[{\pi }_{m-df}^P\right]$ are increasing in x.

Theorem 3(i) shows that both the supplier’s and manufacturer’s expected profits decrease with tariffs, which is intuitive. For any x, tariffs will raise sourcing costs for the manufacturer at the HPB, leading to a reduction in actual demand for key components deliveries and a contraction of the market size. For the supplier, in the HPB channel, the impact of tariffs forces the supplier to lower the wholesale price to mitigate the demand reduction caused by the rising sourcing cost. However, despite these efforts, the order quantity of the HPB decreases, resulting in a decline in the supplier’s profits from the HPB sales under the influence of tariffs. In the DFPB channel, the supplier sets a wholesale price higher than that in the HPB but still lower than the manufacturer’s sourcing cost of the HPB. This pricing decision allows the supplier to extract more profit from the DFPB as tariffs increase, along with an increase in the actual delivery quantity of the DFPB. However, although the supplier can partially offset the losses by increasing the profits of the DFPB, this is insufficient to compensate for the overall losses caused by the shrinking whole market size and the reduced profits of the HPB. Therefore, the supplier’s total profit decreases as tariffs increase. Similarly, the manufacturer’s profits are negatively impacted by higher tariffs, as the increased profits of the DFPB are not enough to counterbalance the adverse effects of a shrinking market and the reduced profits of the HPB.

We investigated the preferences of the supplier and the manufacturer regarding x. An intuitive expectation about the attitudes of supply chain members toward x is that both of them would prefer a higher x, as a higher x implies lower unreliable supply, allowing them to better manage the impact of tariffs. However, our study reveals a surprising result: while the supplier prefers higher, the manufacturer exhibits an aversion to a higher x. For the supplier, a higher x results in a contraction of the whole market size, as it raises the manufacturer’s sourcing cost of the HPB. However, the wholesale prices of both production bases also increase in x. The gains from the rise in the wholesale prices outweigh the losses due to the shrinking market size, allowing the supplier to benefit from the improved production technology of the DFPB.

For the manufacturer, in the HPB channel, the supplier sets higher wholesale prices, which reduces the total product quantity and raises the product’s sale price. However, this also increases the manufacturer’s sourcing cost, leading to a decrease in the sourcing quantity. In fact, as x increases, the increase in the sourcing cost outpaces the rise in product prices, causing the marginal profit of the products procured at the HPB to decrease. Consequently, the manufacturer’s profit in the HPB channel decreases as x increases. In the DFPB channel, although the marginal profit of products also decreases with x, the supplier encourages the manufacturer to increase the sourcing quantity of the DFPB by offering more favorable wholesale prices. As a result, the manufacturer’s profit in the DFPB channel rises in x. However, since the decrease in profit from the HPB channel outweighs the increase in the DFPB channel, the manufacturer’s whole profit decreases monotonically with x. In other words, the higher production technology of the DFPB exacerbates the double marginalization effect within the supply chain, benefiting the supplier while harming the manufacturer as the DFPB’s production technology improves.

Theorem 3 reveals that tariffs always have a negative impact on supply chain members, but the supplier consistently benefits from a high x. This implies that the supplier has a strong incentive to improve the production technology of the DFPB to avoid the burden of high tariff costs. However, the manufacturer’s profit will decrease as the production technology of the DFPB improves. Recalling Theorem 1, the supplier absorbed all the tariff costs by lowering the wholesale price of the HPB. So, in strategy P, as x increases, is the supplier still the primary bearer of tariff costs? This is a central topic in recent research on trade conflicts, specifically addressing the question of who pays for tariffs [28,29,30]. Next, we will compare the sensitivity of the players’ expected profits to tariffs to investigate this issue, and we summarize the analysis results in the following Proposition 1:

Proposition 1. 

Under strategy P, there exists a threshold, $x_o$, such that when $0<x<x_o$, $0>{\displaystyle \frac{\partial E\left[{\pi }_m^P\right]}{\partial \gamma }}>{\displaystyle \frac{\partial E\left[{\pi }_s^P\right]}{\partial \gamma }}$; when $x\ge x_o$, $0>{\displaystyle \frac{\partial E\left[{\pi }_s^P\right]}{\partial \gamma }}>{\displaystyle \frac{\partial E\left[{\pi }_m^P\right]}{\partial \gamma }}$, where $x_o={\displaystyle \frac{2\left({\gamma }^2+6\gamma +3\right)}{{\gamma }^2(2\gamma +7)}}-2\sqrt{{\displaystyle \frac{{\gamma }^4+4{\gamma }^3+6{\gamma }^2+8\gamma +9}{{\gamma }^4{(2\gamma +7)}^2}}}$.

Proposition 1 indicates that the impact of tariffs on the expected profits of the supplier and the manufacturer is not always the same; in some cases, the effect of tariffs on the supplier may even surpass that on the manufacturer. The tariff cost primarily arises when the manufacturer procures key components from the HPB. Therefore, the manufacturer’s order-allocation decision directly determines the tariff cost within the supply chain. When the manufacturer allocates more orders to the HPB, the supply chain faces higher tariff costs; conversely, when more orders are allocated to the DFPB, tariff costs are lower. In addition, the wholesale price can regulate the allocation of the tariff cost in the supply chain. Recalling Theorem 1, when the HPB’s wholesale price is low, the supplier bears the majority or even all the tariff costs. Consequently, tariffs have a significant impact on the supplier’s profit. On the other hand, when the HPB’s wholesale price is high, the manufacturer bears a larger share of the tariff cost, meaning that the tariff’s impact is more substantial on the manufacturer’s profit. The DFPB’s wholesale price acts as a tool for the supplier to adjust the manufacturer’s order allocation to maximize profits (Theorem 2). The higher DFPB’s wholesale price allows the supplier to extract more profit from the manufacturer (Theorem 3(ii)), effectively transferring the burden of the tariff cost onto the manufacturer.

When x is relatively low, meaning that the production technology of the DFPB is not advanced, the cost difference for the manufacturer between sourcing from different bases is small. This situation makes the manufacturer more inclined to allocate a significant portion of orders to the HPB, resulting in higher tariff costs. In this case, the supplier tends to set a lower wholesale price of the DFPB, but this lower HPB whole price leads to the supplier bearing a large share of tariff costs in the HPB channel. Additionally, the lower wholesale price of the DFPB fails to extract significant profits from the manufacturer, making it difficult to effectively transfer the tariff cost to the manufacturer. Consequently, the impact of tariffs on the supplier’s profit is substantial. Therefore, under any given tariffs, when the production technology of the DFPB is not advanced, the supplier bears most tariff costs, meaning that the tariff’s impact on the supplier’s expected profit is greater than its impact on the manufacturer’s expected profit.

When x is high, meaning that the supplier’s production technology at the DFPB is advanced, the cost difference for the manufacturer between sourcing key components from different bases is large. At that time, the manufacturer will allocate more orders to the DFPB. Moreover, a higher x further enhances the manufacturer’s incentive to allocate orders to the DFPB due to cost differences. In this case, the supplier tends to set higher wholesale prices at both production bases. The higher HPB’s wholesale price allows the supplier to avoid bearing more of the tariff cost. At the same time, the higher wholesale price of the DFPB allows the supplier to extract more profit from the manufacturer, further transferring the burden of the tariff cost onto the manufacturer. Thus, under any given tariffs, when the production technology at the DFPB is advanced, the manufacturer bears most tariff costs, meaning that the tariff’s impact on the manufacturer’s expected profit is greater than its impact on the supplier’s expected profit. We summarize the above discussion in Figure 2.

4.3. Full-Relocation Strategy

We use the superscript “F” to denote this case. The supplier completely abandons her HPB and builds a fully substitutable production base in a preferential tariff region, relocating all production activities to the DFPB. It is worth noting that the manufacturer needs to consider unreliable supply in the DFPB. The supplier’s expected profit only comes from the DFPB, $E\left[{\pi }_s^F\right]=E\left[{\pi }_{df}^F\right]$. The event sequence is as follows: First, the supplier determines the DFPB’s wholesale prices $w_{df}^F$. Next, the manufacturer determines orders $q_{df}^F$. Finally, the manufacturer completes production and sells the final product.

For a given $w_{df}^F$, the manufacturer’s profit function is as follows:

$$E\left[{\pi }_m^F\right]=\underset{q_{df}^F}{max}E[\left(\xi q_{df}^F\left(a-\xi q_{df}^F-w_{df}^F\right)\right].$$

(10)

The function can be written as

$$E\left[{\pi }_m^F\right]=\underset{q_{df}^F}{max}\left(\mu q_{df}^F\left(a-w_{df}^F\right)-\left({\mu }^2+{\sigma }^2\right){\left(q_{df}^F\right)}^2\right).$$

(11)

Due to ${\displaystyle \frac{{\partial }^{2}E\left[{\pi }_m^F\right]}{\partial {\left(q_{df}^F\right)}^2}}=-\left({\mu }^2+{\sigma }^2\right)<0$. Therefore, we can determine the optimal response function of $q_{df}^F$ with respect to $w_{df}^F$ by solving by ${\displaystyle \frac{\partial E\left[{\pi }_m^F\right]}{\partial q_{df}^F}}=0$. Thus, we have

$$q_{df}^F\left(w_{df}^F\right)={\displaystyle \frac{\mu \left(a-w_{df}^F\right)}{2\left({\mu }^2+{\sigma }^2\right)}}.$$

(12)

The supplier anticipates the manufacturer’s reaction and determines the optimal wholesale price through the following profit function:

$$E\left[{\pi }_{df}^F\right]=\underset{w_{df}^F}{max}E\left(\xi q_{df}^F{w}_{df}^F\right),$$

(13)

Due to ${\displaystyle \frac{{\partial }^{2}E\left[{\pi }_s^F\right]}{\partial {\left(w_{df}^F\right)}^2}}=-{\displaystyle \frac{{\mu }^2}{{\mu }^2+{\sigma }^2}}<0$, we can obtain $w_{df}^F$ by setting ${\displaystyle \frac{\partial E\left[{\pi }_s^F\right]}{\partial w_{df}^F}}=0$. Substituting $w_{df}^F$ into Equations (11)–(13) will yield all equilibrium decisions. We summarize the equilibrium decisions of the players in Theorem 4.

Theorem 4. 

Under strategy F, the supplier’s wholesale price is $w_{df}^F={\displaystyle \frac{a}{2}}$, and the manufacturer’s order quantity is $q_{df}^F={\displaystyle \frac{a\mu }{4\left({\mu }^2+{\sigma }^2\right)}}$. Correspondingly, the expected profits of the supply chain members are $E\left[{\pi }_s^F\right]={\displaystyle \frac{a^2{\mu }^2}{8\left({\mu }^2+{\sigma }^2\right)}}$ and $E\left[{\pi }_m^F\right]={\displaystyle \frac{a^2{\mu }^2}{16\left({\mu }^2+{\sigma }^2\right)}}$, respectively.

In addition, the following results hold in equilibrium:

(i) 

$w_{df}^F$ is a constant;

(ii) 

For any given σ, $q_{df}^F$ is unimodal in x;

(iii) 

$E\left[{\pi }_s^F\right]$ and $E\left[{\pi }_m^F\right]$ are monotonically increasing in x.

Theorem 4(i) states that in strategy F, the supplier’s wholesale price remains unchanged with respect to the production technology of the DFPB. Here, the production technology does not directly impact the manufacturer’s sourcing cost. Therefore, the manufacturer adjusts the sourcing quantity to maintain the supplier’s actual delivery quantity at a stable level. Since production orders do not fluctuate significantly due to changes in the production technology, the wholesale price remains stable with respect to the production technology of the DFPB.

Theorem 4(ii) shows that the ordering quantity first increases and then decreases with respect to the production technology of the DFPB. Given that the supplier provides a stable wholesale price, the manufacturer only needs to focus on maintaining a stable actual delivery quantity. When the production technology of the DFPB is not advanced, the manufacturer increases order quantities to keep actual deliveries stable. As the production technology of the DFPB improves, the manufacturer reduces order quantities to avoid excessive actual deliveries, which could lead to a decrease in product marginal profit and potential losses.

Theorem 4(iii) indicates that the higher production technology of the DFPB benefits both the supplier and manufacturer. For the supplier, even though the manufacturer dynamically adjusts the sourcing quantities, the actual delivery quantity increases in the production technology of the DFPB, directly enhancing the supplier’s profits. Although the marginal profit of the product decreases with increased actual deliveries, the manufacturer can benefit through a strategy of “small profits but quick turnover”. This result also suggests that the supplier has a strong incentive to enhance the production technology of the DFPB to create a win–win situation.

4.4. Strategies Comparison

Next, we are interested in comparing the expected profits of supply chain members under different strategies. This will help us understand the impact of the interaction between tariffs and the production technology of the DFPB on the players.

Proposition 2. 

Comparing strategy B and strategy F holds that

(i) 

For any γ and x, $w_h^B<w_{df}^F=(\gamma +1)w_h^B$ and $\mu q_{df}^F<q_h^B<q_{df}^F$;

(ii) 

If $\gamma \le {\displaystyle \frac{1}{x}}$, $E\left[{\pi }_s^F\right]\le E\left[{\pi }_s^B\right]$; if $\gamma >{\displaystyle \frac{1}{x}}$, $E\left[{\pi }_s^B\right]<E\left[{\pi }_s^F\right]$; for any γ and x, $E\left[{\pi }_m^F\right]<E\left[{\pi }_m^B\right]$.

Proposition 2(i) indicates that, compared to strategy F, the supplier offers a lower wholesale price under strategy B. This is because, under strategy B, the manufacturer encounters tariff costs when sourcing key components from the HPB, leading to increased sourcing costs. To mitigate the impact of the tariff cost on sourcing orders, the supplier proactively reduces the wholesale price to maintain order stability ($w_{df}^F>w_h^B$). Under both strategy B and strategy F, the manufacturer’s sourcing costs are the same ($w_{df}^F>w_h^B$). However, under strategy B, since the HPB has advanced production technology, the manufacturer’s order quantity matches the supplier’s actual delivery quantity. Therefore, the manufacturer only needs to make sourcing decisions based on the sourcing cost. In contrast, under strategy F, the manufacturer must consider not only the sourcing cost but also the production technology of the DFPB to determine a larger order quantity to manage the unreliable supply due to the not-advanced production technology of the DFPB ($q_{df}^F>q_h^B$). However, even if the manufacturer increases the order quantity, the not-advanced production technology of the DFPB still leads to a smaller actual delivery quantity ($q_h^B>\mu q_{df}^F$).

Proposition 2(ii) demonstrates the relationship between the expected profits of the supplier and manufacturer under the two strategies. For the supplier, switching from strategy B to strategy F may be either advantageous or disadvantageous. Under strategy F, the supplier can provide key components at a higher wholesale price, but the lower production technology results in reliable supply, which might lead to fewer actual deliveries. When tariffs are low, the supplier has insufficient incentive to shift all capacity to a preferential tariff region, because even though the wholesale price of the DFPB is higher, it cannot compensate for the reduction in actual deliveries due to the lower production technology. When tariffs are high, the wholesale price of the HPB under strategy B will be significantly lower, which harms the supplier’s profits. For the manufacturer, switching from strategy B to strategy F is always disadvantageous. Although the sourcing costs are the same under both strategies, the reduction in the actual delivery quantity under strategy F leads to a decrease in the sales quantity in the end-user market. Even if the marginal profit of the product increases, it cannot offset the losses caused by the reduction in the product quantity. Therefore, under any tariff, the decision for the supplier to relocate all capacity to the preferential tariff region is always detrimental to the manufacturer’s profit.

Proposition 3. 

Comparing strategy P and strategy F, if $\gamma \ge {\displaystyle \frac{2}{x}}$, the manufacturer will allocate all orders to the DFPB, and strategy P is no longer an executable strategy. If $\gamma <{\displaystyle \frac{2}{x}}$, there holds

(i) 

For any γ and x, $w_h^P<w_{df}^P<w_{df}^F<(\gamma +1)w_h^P$;

(ii) 

For any γ and x, $q_{df}^P+q_h^P<q_{df}^F$ and $\mu q_{df}^F<\mu q_{df}^P+q_h^P$;

(iii) 

For any γ and x, $E\left[{\pi }_s^F\right]\le E\left[{\pi }_s^P\right]$ and $E\left[{\pi }_m^F\right]<E\left[{\pi }_m^P\right]$.

Proposition 3(i) indicates that, compared to strategy F, the supplier will offer a lower wholesale price under strategy P. It is straightforward that the supplier generally responds to the order fluctuations caused by tariffs by lowering the wholesale price in the HPB. However, when setting the wholesale price of the DFPB, the supplier encounters an opposite motivation. From a channel coordination perspective, the supplier aims to avoid tariffs by supplying key components through the DFPB, so she balances the manufacturer’s sourcing cost across different bases by setting the wholesale price of the DFPB lower than the HPB to achieve channel coordination ($w_{df}^F<(\gamma +1)w_h^P$). From a profit-maximization standpoint, since the manufacturer’s sourcing cost at the DFPB is lower, the supplier seeks to increase the wholesale price of the DFPB to extract more profit. Therefore, the supplier sets a higher wholesale price of the DFPB ($w_h^P<w_{df}^P$), but it cannot exceed the wholesale price under strategy F, or else strategy P would fail to be effective ($w_{df}^P<w_{df}^F$).

Proposition 3(ii) shows that order quantity is significantly higher under strategy F than under strategy P, but the actual delivery quantity is greater under strategy P. The order quantity is influenced not only by the sourcing cost of the manufacturer but also by the production technology of the DFPB. When the manufacturer acquires more key components through the DFPB, he must place larger orders to cope with unreliable supply ($q_{df}^P+q_h^P<q_{df}^F$). Under strategy F, the supplier’s actual delivery quantity decreases due to production uncertainty ($\mu q_{df}^F<\mu q_{df}^P+q_h^P$).

Proposition 3(iii) illustrates that the incentives of the supplier and manufacturer are aligned—they both prefer strategy P over strategy F. For the manufacturer, it can be concluded that strategy F is the worst strategy because it results in the lowest profit. Under strategy F, the manufacturer does not need to pay additional tariffs, but the supplier tends to charge a higher wholesale price, keeping the manufacturer’s sourcing cost at a high level. Moreover, the insufficient actual delivery quantity from the supplier significantly harms the manufacturer’s profits. For the supplier, the profit under strategy P is higher than under strategy F, mainly because the manufacturer allocates many orders to the DFPB, allowing the supplier to extract profit through the higher wholesale price of the DFPB.

Based on Propositions 2 and 3, we can determine the manufacturer’s profit preferences across the three strategies: the manufacturer achieves the highest profit under strategy B, followed by strategy P, and finally, strategy F. This indicates that the supplier’s capacity-relocation decisions have a negative impact on the manufacturer’s profits, with full relocation (strategy F) resulting in the lowest profits for the manufacturer. However, the underlying driving factors behind this preference are still unclear. Additionally, the supplier’s preferences for capacity-relocation decisions are also uncertain. Next, by comparing the equilibrium decisions and profit relationships of supply chain members under strategies P and B, we will further analyze why the manufacturer prefers strategy B and identify the supplier’s capacity-decision preferences.

Proposition 4. 

Comparing strategy B and strategy P, if $\gamma \ge {\displaystyle \frac{2}{x}}$, the manufacturer will allocate all orders to the DFPB, and strategy P is no longer an executable strategy. If $\gamma <{\displaystyle \frac{2}{x}}$, there holds

(i) 

For any γ and x, $w_h^B<w_h^P<w_{df}^P<(\gamma +1)w_h^B<(\gamma +1)w_h^P$;

(ii) 

For any γ and x, $q_h^B<q_{df}^P+q_h^P$ and $\mu q_{df}^P+q_h^P<q_h^B$;

(iii) 

For any γ and x, $E\left[{\pi }_s^B\right]<E\left[{\pi }_s^P\right]$ and $E\left[{\pi }_m^P\right]<E\left[{\pi }_m^B\right]$.

Proposition 4(i) indicates that under strategy P, compared to strategy B, the supplier will charge a higher wholesale price of the HPB to encourage the manufacturer to source more key components from the DFPB. The supplier’s motive for doing this is to set a higher wholesale price of the DFPB ($w_h^B<w_h^P<w_{df}^P$), thereby extracting more profit from the manufacturer. This strategy leads to higher sourcing costs for the manufacturer in the HPB ($(\gamma +1)w_h^B<(\gamma +1)w_h^P$), which negatively impacts the manufacturer. Proposition 4(ii) is directly derived from Proposition 4(i).

According to the above analysis, we find that when the supplier can effectively implement strategy P, they prefer strategy P over strategy B. The reason is that, under strategy B, the supplier needs to lower the wholesale price to mitigate the negative impact of tariffs on the manufacturer’s order quantity, which reduces the supplier’s profit. However, in strategy P, the supplier can obtain more profit from the manufacturer by raising the wholesale price of the DFPB, resulting in higher expected profits for the supplier in strategy P. Despite the higher profits that strategy P brings to the supplier, we find that the manufacturer’s expected profit is lower under strategy P. This result is surprising. The reason behind it is that the supplier’s more aggressive whole pricing of the HPB under strategy P leads to a decrease in the actual quantity of key components that the manufacturer can obtain, which in turn reduces the number of products available for sale in the market. The profit loss from the reduced sales quantity exceeds the gains from the lower sourcing cost, resulting in higher expected profits for the manufacturer under strategy B.

According to Propositions 2–4, we can derive the following Propositions 5 and 6:

Proposition 5. 

If $\gamma <{\displaystyle \frac{2}{x}}$, the supplier prefers to adopt strategy P. If $\gamma \ge {\displaystyle \frac{2}{x}}$, the supplier prefers to adopt strategy F; the manufacturer always prefers strategy B.

Proposition 5 illustrates that when tariffs are relatively low, the supplier choosing either the full-relocation strategy or no-relocation strategy instead of the partial-relocation strategy will lead to a lose situation. This means that the supplier always benefits from a strategy of production base diversification. It suggests that if tariff levels have not reached a certain threshold, hastily relocating all production capacity to a preferential tariff region is not a wise decision for the supplier. Specifically, in strategy F, the supplier sets a higher wholesale price, resulting in fewer actual delivered orders, which leads to greater losses. In strategy B, although the supplier delivers more orders, she must bear all tariff costs alone, and the increased number of orders cannot offset the losses caused by the tariff cost. Therefore, the supplier’s best choice is strategy P. Through strategy P, the supplier can balance the tariff cost and reliable supply between two bases, thereby profiting from the production-base-diversification strategy. When tariffs are high, due to the manufacturer’s order-allocation incentives, strategy P is no longer a viable strategy. At that time, the supplier can only choose between strategy B and strategy F. The key lies in comparing the impact of tariffs with the impact of reduced actual delivered orders. When the tariff cost exceeds the losses caused by order reduction, strategy F becomes the supplier’s best choice.

For the manufacturer, the optimal strategy is strategy B. In this case, the supplier adjusts the wholesale price to absorb the impact of tariff fluctuations on the manufacturer’s orders, shielding the manufacturer from direct tariff volatility. In contrast, under strategy F, the manufacturer faces higher sourcing costs and greater shortage risks. Although product prices may be higher, the increased revenue is insufficient to compensate for the loss in profit. In strategy P, the rise in sourcing cost also negatively affects the manufacturer’s profits. Therefore, the manufacturer performs best under strategy B.

Proposition 6. 

If $\gamma <{\displaystyle \frac{2}{x}}$, the supply chain equilibrium strategy is strategy B. If $\gamma \ge {\displaystyle \frac{2}{x}}$, the supply chain equilibrium strategy is strategy F.

The equilibrium strategy of the supply chain is jointly determined by members of the supply chain. When the supplier adopts either strategy B or strategy F, the manufacturer can choose to adhere to the supplier’s decision or exit the supply chain. However, exiting would result in zero profit for the manufacturer, which is clearly not in his best interest. In the case where the supplier adopts strategy P, the manufacturer determines the final equilibrium strategy of the supply chain by deciding how to allocate orders. If the manufacturer allocates all orders to the supplier’s HPB, it effectively forces the supply chain back to strategy B; if all orders are allocated to the DFPB, the supply chain is effectively using strategy F.

When $\gamma$ is low ($\gamma <{\displaystyle \frac{2}{x}}$), the supplier can effectively execute all three strategies. According to the previous analysis, the supplier’s preferred strategy is strategy P. However, since the manufacturer would face higher sourcing costs under strategy P, his expected profit would decrease. As analyzed in Proposition 5, the manufacturer’s expected profit is highest under strategy B. Therefore, the manufacturer is more likely to distort the supplier’s strategy F by allocating all orders to the supplier’s HPB, causing the supply chain’s equilibrium strategy to revert to strategy B. Interestingly, according to the conclusions from Propositions 2 and 5, when ${\displaystyle \frac{1}{x}}<\gamma <{\displaystyle \frac{2}{x}}$, the supplier’s expected profit under strategy B is the lowest. This indicates that, under moderate tariff levels, implementing strategy P can significantly harm the supplier.

When $\gamma$ is high ($\gamma \ge {\displaystyle \frac{2}{x}}$), if the supplier adopts strategy P, the manufacturer may reject this strategy due to higher sourcing costs. In this case, the supplier is left to choose between strategy B and strategy F. As previously analyzed, under such a high-tariffs environment, the supplier is more likely to adopt strategy F. Strategy F allows the supplier to completely avoid the cost pressure brought by high tariffs. Therefore, the supply chain equilibrium strategy is strategy F. This result is illustrated in Figure 3.

4.5. Consumer Surplus Analysis

In this section, we represent consumer surplus and explore consumer surplus with different strategies. The consumer surplus in the end-user market can be expressed as

$$CS={\int }_p^a(v-p)dv.$$

(14)

Proposition 7. 

For any given γ, the inequality $C{S}^B>C{S}^P>C{S}^F$ always holds.

When the manufacturer sources key components exclusively from the supplier’s HPB, consumers experience the highest utility. In strategy B, the supplier plays a crucial role in maintaining supply chain stability in the face of tariffs by lowering the wholesale prices to bear the full tariff impact. This mechanism prevents the tariff cost from being passed on to consumers, ensuring consumers do not pay extra for products. In strategy P, consumer interests may suffer due to higher product prices. As discussed in Theorem 2, with rising tariffs, the wholesale price increases, and the quantity of products decreases, leading to higher prices. Consumer surplus may suffer due to higher product prices. In strategy F, consumer surplus deteriorates even more due to the unreliable supply of the DFPB. This result is illustrated in Figure 4.

Interestingly, we observe varying consumer attitudes toward x under different scenarios. In strategy P, a higher x alleviates shortage losses, increases market supply, and lowers product prices, benefiting consumers. However, in strategy P, consumers dislike a higher x. As stated in Theorem 3, a higher x exacerbates double marginalization, hurting the manufacturer’s profits. Then, the manufacturer passes on some of its losses to consumers through higher wholesale prices, causing consumers to also dislike the higher production technology of the DFPB.

5. Extensions

The Positive Production Costs

In this section, we relax the zero-production-cost assumption by assuming that the unit production costs of two production bases are positive. Beyond mitigating tariff impacts, the lower production costs in preferential tariff regions are also a significant consideration for firms when deciding on production-capacity-relocation strategies. According to Lee and Wong [10], we assume that the production cost of the HPB $c_1$ is higher than the production cost of the DFPB $c_2$. Although the equilibrium decisions of all players can be obtained in closed form, an additional analysis becomes complicated. Therefore, we use a numerical analysis to derive the results of this study. Referencing Niu et al. [35] and to better fit our real-world scenario, we chose $\sigma =0.2$ and $x=2$.

We first clarify the incentive mechanism for the supplier to relocate its production capacity. When the production cost of the DFPB is positive, if the production technology of the DFPB is too low, the supplier is not motivated to build a new base there. In this case, providing key components directly from the HPB is the only option. The reason is that a lower x may lead to more production-cost wastage, and the payment that the supplier receives might not cover the production cost. This means that the primary factor for a supplier in choosing to build a new base in preferential tariff regions is assessing whether the local production technology is reliable enough, ensuring that the relocating-production-capacity strategy can be smoothly implemented.

Due to considering new factors, our conclusions have become more comprehensive. We summarize these new findings as follows:

(1)

In Theorem 1, when production costs are positive, the supplier will choose to transfer a portion of the costs to the manufacturer.

(2)

The production-cost waste caused by the low-production technology of the DFPB will also be transferred to the manufacturers. When it is sufficiently high and tariffs reach a certain threshold $\underline{\gamma }$, the manufacturer only considers allocating orders to the supplier’s DFPB. There exists a tariff interval $\gamma \in \left(\underline{\gamma },\overline{\gamma }\right)$ that renders the supplier’s relocating-production strategy feasible. However, when $c_2$ is sufficiently low, $\underline{\gamma }$ will be less than zero and $\overline{\gamma }$ will be smaller. This implies that when the production cost of the DFPB is sufficiently high, the supplier’s choice of strategy F will only incentivize the manufacturer to allocate a portion of orders to the DFPB if tariffs reach a critical threshold. The unreliable supply of the DFPB leads to reduced production efficiency and drives up the wholesale prices of the DFPB, resulting in excessively high sourcing costs for the manufacturer. Consequently, the manufacturer has no incentive to allocate orders to the DFPB unless the sourcing costs at the HPB rise to a certain level due to increased tariffs, forcing the manufacturer to consider relocating a portion of the orders. Figure 5 summarizes this supplementary explanation.

We discovered that Proposition 6 may no longer hold true when there is a significant difference in production cost between the two production bases. As the cost difference between the two production bases becomes sufficiently large, the partial-relocation strategy can become an equilibrium strategy. Figure 6a illustrates the profitability of players under different scenarios where all three strategies are feasible. The supplier’s profit is maximized under strategy P, and hence the supplier is always willing to operate two production bases. However, when strategy P cannot be effectively executed (which depends on the manufacturer), the supplier will adopt strategy F. For the manufacturer, when $\gamma$ is low ($0<\gamma <{\gamma }_1$), he tends to support strategy P. However, as tariffs gradually increase (${\gamma }_1\le \gamma <{\gamma }_2$), the manufacturer allocates all orders to the HPB. When $\gamma$ reaches a certain threshold ($\gamma \ge {\gamma }_2$), the manufacturer instead allocates all orders to the DFPB. Figure 6b summarizes these results, illustrating how the supply chain strategy shifts from strategy B to strategy P when $\gamma$ is low, driven by the manufacturer’s strategic adjustments.

Recalling Proposition 4, whether the manufacturer shifts from strategy B to strategy P depends on the trade-off between the benefits of the flexible order allocation and the losses from the decreased actual delivery quantities. First, if the production cost of the HPB is high, the supplier’s wholesale price will be correspondingly high, causing the manufacturer’s sourcing cost to increase significantly due to the tariffs’ impact. Correspondingly, if the production cost of the DFPB is low, the wholesale price of the DFPB will be lower, reducing the manufacturer’s sourcing cost since purchasing from the DFPB is not affected by tariffs. Clearly, the benefit gained by the manufacturer from the reduced sourcing cost through order allocation depends on the difference in the production cost between the two bases. When $\gamma$ is low, the cost of procuring key components from the HPB under strategy P is like that under strategy B. The actual quantity of the key components received is also similar. However, if the HPB’s production cost is high and the DFPB’s cost is low, the benefits of flexible order allocation can outweigh the losses from reduced product sales. We show the supplier’s wholesale price and the manufacturer’s sourcing cost in Figure 7.

This means that when the supplier adopts the relocation strategy, she needs to pay attention to the cost differences between the preferential tariff region and home. If the production cost of the HPB is sufficiently high and the cost of the DFPB is sufficiently low, the adoption of the partial-relocation strategy by the supplier may actually lead to a win–win situation for both parties in the supply chain.

We find that when both production bases have a positive differentiated production cost, the surplus results are consistent with those of the model:

• $E\left[{\pi }_s^P\right]$ is increasing monotonically in x, while $E\left[{\pi }_m^P\right]$ is decreasing monotonically in x;
• When x is low, the supplier bears most of the tariff burden, whereas when x is high, the manufacturer bears most of the tariff burden;
• For any tariff, $C{S}^B>C{S}^P>C{S}^F$ holds. Consumer attitudes toward technology levels do not vary significantly across different strategies.

6. Conclusions

Recently, the turbulent trade situation has accelerated the restructuring of global supply chains, with tariffs being a major force. From 2018 to 2019, the U.S. government implemented a series of protective tariffs, which triggered retaliatory tariffs from China and other trading partners. As tensions between nations escalate, multinational firms, especially those partial/all end-user markets in the U.S., have been intensifying efforts to relocate their production capacity from China to preferential tariff regions with unreliable supply, such as Vietnam and Malaysia. Understanding how tariffs and unreliable supply affect the supplier’s strategy of relocating its production capacity is particularly important, as this can provide policy guidance and crucial management insights for practitioners in multinational supply chains.

We developed a game theory model to analyze how tariffs and unreliable supply affect the supplier’s strategy of relocating its production capacity and the manufacturer’s sourcing strategy. After that, by conducting a comparison of the results, several findings can be summarized as follows:

(1)

Tariffs and the production technology of a base in a preferential tariff region play a critical role in the supplier’s relocation decision. When tariffs are high or the production technology of the base in a preferential tariff region is advanced, the manufacturer’s order-allocation decision may render the partial-relocation strategy infeasible. In this case, due to the impact of tariffs or the advanced technology of bases in preferential tariff regions, the supplier is likely to opt for a full-relocation strategy, potentially prompting the manufacturer to follow, thus shifting the supply chain’s equilibrium strategy toward full relocation. Notably, when tariffs are low or the production technology of bases in preferential tariff regions is not advanced, the supplier may benefit from flexible pricing decisions under the partial-relocation strategy rather than opting for a no-relocation strategy. However, the manufacturer might distort the supplier’s relocation strategy by adjusting order allocation, leading the supply chain’s equilibrium strategy back to the no-relocation strategy. In some cases, if the supplier blindly pursues expected profits by adopting the partial-relocation strategy without considering the manufacturer’s decision, it could lead to a situation where the supplier’s profits are harmed while the manufacturer benefits, creating a lose–win scenario. Only when the supplier’s production cost of the home production base is sufficiently high and the cost of the production base in a preferential tariff region is sufficiently low will the partial-relocation strategy become the equilibrium strategy for the supply chain.

(2)

Interestingly, the manufacturer and consumers do not always prefer the supplier to build a new production base with higher production technology in preferential tariff regions. In the full-relocation scenario, the manufacturer and consumers benefit from the higher production technology of a duty-free production base. However, in the partial-relocation strategy, higher production technology will serve as leverage to increase wholesale prices from the supplier. This will exacerbate the double marginalization in the supply chain, leading to losses for the manufacturer and consumers in higher production technology of DFPB

(3)

In addition, another interesting result is that the suppliers relocating their production capacity can enable them to bear less tariff responsibilities. In the no-relocation strategy, the supplier bears most of the tariff cost. In the partial-relocation strategy, especially when there is high-production technology in a duty-free production base, the manufacturer will bear most of the tariffs. This is because higher production technology has led to an increase in wholesale prices, and the process of increasing the wholesale prices of the supplier also transfers the tariff cost to the manufacturer. In the full-relocation scenario, the supplier does not bear the tariff cost.

Our findings provide valuable managerial insights. When analyzing the supplier’s capacity-relocation issues, close attention should be paid by both businesses and governments to the capacity-relocation strategies of the supplier. When tariffs escalate, the supplier needs to recognize that the partial-relocation strategy is advantageous, as having two supply channels can enhance their pricing flexibility. However, careful attention must be paid to the manufacturer’s order-allocation decisions, as failing to do so may result in a situation where the supplier’s interests are harmed. For the manufacturer, it is crucial to understand that unless tariffs are sufficiently high, the supplier will retain its home production base, giving the manufacturer significant leeway in allocating orders. However, in this balancing act, it is essential to continually monitor the production technology in the supplier duty-free regions, as high-production technology may lead to profit losses for the manufacturer. In terms of tariff policy formulation, governments are advised to exercise caution in raising tariffs as high tariffs can squeeze the manufacturer’s profits, and higher tariffs may instead lead the manufacturer to focus on the supplier’s home production base. Consumers may also suffer from higher product prices due to the transmission of tariff increases.

We acknowledge some limitations in our study and offer hopeful avenues for future research. In our analysis, we focused on the impact of tariffs on production capacity relocation for industries requiring certain technological specifications, such as electronic products. Through these industries, we gain a clearer understanding of the effects of tariffs and production technology levels on industrial transfer. Future research could expand to industries with lower technological requirements, such as the apparel industry. Additionally, while we discussed improvements in production technology during our analysis, in practice, improving technology may incur high costs, and considering the cost of technological improvements may lead to interesting outcomes. Furthermore, we focused on the supplier building a mature production base in duty-free zones. However, during the process of production capacity relocation, the supplier’s duty-free locations may face production capacity constraints. Although we indicated in the incentives that the supplier may be reluctant to relocate capacity back to developed countries, exploring the issue of supplier reflows could yield intriguing insights. Despite certain flaws in our study, we firmly believe that this research represents the first step toward understanding the issue of relocating capacity by suppliers.