Manufacturer Encroachment in the Presence of Production Economies of Scale

Abstract

It is well established that a manufacturer generally benefits from encroachment with a profitable direct channel and may also benefit from using encroachment as a threat (i.e., without sales in the direct channel); the retailer may also benefit from both encroachment strategies. Our study provides new insights into the manufacturer encroachment literature by considering the upstream manufacturer's production economies of scale. Contrary to conventional wisdom, we show that an increasing level of economies of scale may reduce the manufacturer's profit if the manufacturer encroaches. Furthermore, we find that under strong economies of scale, refraining from encroachment may be the optimal strategy, even if encroachment could increase the manufacturer's wholesale profit. This finding suggests that a manufacturer may choose not to encroach solely due to profit losses in direct selling. Interestingly, we also find that the manufacturer can benefit from encroachment by maintaining an unprofitable direct channel with sales, provided that the level of economies of scale is below a threshold. Moreover, our findings reveal that the retailer can benefit from manufacturer encroachment only when the level of economies of scale remains below this threshold, and that an increasing level of economies of scale reduces the likelihood that the retailer can benefit.

1. Introduction

Manufacturer encroachment occurs when a manufacturer sells directly to consumers through its own channel, such as an online outlet or a flagship store, in addition to selling indirectly through a retailer. The rapid growth of e-commerce and the shift in consumer preferences toward online shopping have greatly facilitated this practice across various industries. For instance, leading electronics manufacturers (e.g., Apple, Huawei, and Samsung) and major apparel brands (e.g., Adidas, Nike, and Uniqlo) employ dual-channel distribution, combining their own direct online channels with brick-and-mortar retailers. According to eMarketer, online direct sales by manufacturers in the United States are projected to reach $159.76 billion in 2024, marking an 18.7% increase from the previous year (Feger, 2024).

While encroachment offers manufacturers the potential for sales growth, it also risks channel conflict with incumbent retailers, who may perceive it as a competitive threat (Guan et al., 2020; Ha et al., 2016). This potential conflict can discourage manufacturers from pursuing encroachment due to concerns about straining relationships with their retail partners. However, some studies suggest that encroachment can benefit a manufacturer without necessarily posing a significant threat to the retailer or undermining its ordering incentives (e.g., Arya et al., 2007; Chiang et al., 2003; Yoon, 2016). In some cases, encroachment can even alleviate double marginalization within the retailer channel. In the context of quantity competition, and assuming that the manufacturer's unit selling cost is higher than that of the retailer, Arya et al. (2007) demonstrate that encroachment with direct sales occurs when the manufacturer's unit selling cost is not too high. They identify a wholesale price effect: Encroachment induces the manufacturer to set a lower wholesale price than under no encroachment to stimulate demand in the retailer channel. As the unit cost of direct selling increases, this effect becomes stronger (i.e., the wholesale price reduction becomes more pronounced), thereby motivating the retailer to order more and enhancing the efficiency of indirect selling. Consequently, through encroachment, the manufacturer not only earns additional revenue from direct selling but may also achieve higher wholesale revenue. The retailer can also benefit from manufacturer encroachment when direct selling is relatively costly, as the benefit from the wholesale price reduction can outweigh the loss from downstream market competition due to encroachment.

This research examines the impact of economies of scale in upstream production on a manufacturer's encroachment decision, motivated by two key observations. First, leveraging economies of scale to reduce average production cost is a common practice in manufacturing (The Economist, 2008). In industries such as consumer packaged goods (CPGs), manufacturers typically produce in large quantities to benefit from economies of scale, which allows them to keep average unit production costs low (Appinio Research, 2023; Smith, 2016). Therefore, understanding economies of scale is crucial because cost savings provide manufacturers with a competitive edge (Corporate Finance Institute Team, 2022). Second, prior studies suggest that encroachment enables a manufacturer to increase total output by adding a direct sales channel (Arya et al., 2007; Chiang et al., 2003; Yoon, 2016). In the presence of economies of scale, a lower average unit production cost driven by increased output through encroachment could potentially enhance a manufacturer's profitability and mitigate channel conflict with the retailer through a lower wholesale price. Consequently, one might expect that economies of scale would strengthen a manufacturer's incentive to pursue encroachment and increase the likelihood that the retailer benefits as well. However, in practice, manufacturers exhibit diverse attitudes toward encroachment under economies of scale.

In the CPG industry, several large firms with strong economies of scale continue to rely exclusively on the traditional wholesale business model, despite having the capacity to encroach into the retail market. For instance, Procter & Gamble (P&G), one of the largest firms in the CPG market, while leveraging economies of scale for high process efficiency and cost-effectiveness, primarily distributes through indirect channels (Liu et al., 2021; Thompson, 2017). Similarly, Kao Corporation, a leading chemical and cosmetics manufacturer in Japan, maintains its use of the indirect distribution channel despite its significant economies of scale (Essay Sauce, 2021). General Mills, a major food company, also benefits from cost efficiencies associated with large-scale operations but continues to depend on resellers for product distribution (Barnes, 2018). In contrast, in response to increasing demand, many other CPG manufacturers have actively developed online direct-selling businesses since early 2020, even though profit margins from e-commerce can be slim. For some manufacturers, online direct selling was not initially profitable. A McKinsey & Company poll of U.S. CPG executives revealed that more than 25% of respondents cited low profitability as their primary concern regarding e-commerce, partly because online selling costs, including logistics and advertising, are typically higher than those for offline sales. For CPG companies, shipping and warehousing costs account for about 9.3% of gross sales in online channels, compared to only 7.3% for brick-and-mortar stores. However, McKinsey also found that higher online sales volumes appeared to enhance profitability; CPG firms with larger online sales volumes in a category were more likely to achieve profitability due to economies of scale (Chapple and Sivaeva, 2021; Chapple et al., 2021).

These observations suggest that while some manufacturers with strong economies of scale refrain from encroachment, others increasingly adopt e-commerce to sell directly, even when direct selling is not always profitable. This discrepancy raises intriguing questions that have not been well-explored in the existing literature on manufacturer encroachment:

(1)

How do economies of scale influence a manufacturer's encroachment decision? In particular, why would a manufacturer choose to encroach even when profitability from direct selling is challenging?

(2)

In the presence of economies of scale, how does a manufacturer's encroachment decision affect the retailer's profitability?

Our paper seeks to investigate the underlying rationale behind manufacturers’ differing attitudes toward the encroachment strategy and how a manufacturer's decision to encroach affects the retailer's profitability. We consider a supply chain where a manufacturer sells the product indirectly through a retailer. The manufacturer can decide whether to encroach into the retail market by establishing a direct channel. If the manufacturer chooses to encroach, it has a higher unit selling cost than that of the retailer, and the two firms engage in Cournot competition. Our model extends Arya et al. (2007) by examining the impact of economies of scale, which can lead to a reduction in the manufacturer's average unit production cost as total output increases. The key findings of our research are summarized as follows.

First, conventional wisdom suggests that stronger economies of scale generally benefit a manufacturing firm. We confirm that this intuition holds true in the absence of manufacturer encroachment. In this setting, as the level of economies of scale increases, the manufacturer lowers the wholesale price to stimulate the retailer's order quantity, thereby mitigating double marginalization and benefiting both the manufacturer and the retailer. Conversely, if the manufacturer encroaches and sells directly, an increasing level of economies of scale may hurt both members’ profits. Specifically, an increasing level of economies of scale introduces two opposing effects on the encroaching manufacturer's profitability. On the one hand, it enables the manufacturer to increase total output and lower the average unit production cost. On the other hand, it incentivizes the manufacturer to increase the direct selling quantity while reducing the retailer's order quantity, shifting sales from the more efficient retailer channel to the less efficient direct channel, which has a selling cost disadvantage. This shift adversely affects the manufacturer's profitability. Moreover, a higher unit cost of direct selling reduces the manufacturer's total output, weakening the benefit from stronger economies of scale. Consequently, when direct selling is relatively costly, the loss from reduced sales through the more efficient retailer channel dominates, reducing the manufacturer's profit as the level of economies of scale increases. Clearly, the retailer's profit also declines due to a lower order quantity.

Second, we find that a high level of economies of scale can deter the manufacturer from pursuing encroachment with direct sales. By extending Arya et al. (2007), prior studies (e.g., Liu et al., 2021; Wang and Li, 2021) demonstrate that without economies of scale, the manufacturer may be worse off from having the encroachment option, as the loss in wholesale revenue cannot be offset by the additional gain from direct selling. Our research provides a complementary perspective: With economies of scale, the manufacturer may refrain from encroachment because it may reduce profits in one or both channels. Specifically, an increasing level of economies of scale lowers the average unit production cost, thereby increasing the manufacturer's incentive to engage in direct sales if it encroaches. That is, the threshold of the unit direct-selling cost, below which the encroaching manufacturer sells directly, increases with the level of economies of scale. However, the manufacturer may incur profit losses from direct selling because its profit margin in the direct channel decreases and eventually becomes negative as the unit direct-selling cost increases. Regarding the manufacturer's wholesale profitability, in addition to the wholesale price effect, there is a quantity distortion effect induced by encroachment under stronger economies of scale: The encroaching manufacturer is incentivized to shift sales from the retailer channel to the direct channel as economies of scale strengthen (i.e., the percentage of products sold through the direct channel increases with the level of economies of scale). A lower unit cost of direct selling amplifies this quantity distortion effect by encouraging further direct sales. Thus, although encroachment can lead to wholesale price reduction, this wholesale price effect may be insufficient to counterbalance the quantity distortion effect. When the quantity distortion effect dominates, the retailer's order quantity declines, hurting the manufacturer's profit from indirect selling. As a result, it is optimal for the manufacturer not to encroach when economies of scale are strong and the unit cost of direct selling is intermediate. In particular, under moderately strong economies of scale and moderately high unit costs of direct selling, the manufacturer's no-encroachment decision can be solely attributed to its profit loss from direct selling.

Third, our study uncovers an intriguing and novel finding. Beyond the well-established strategies of encroachment with a profitable direct channel (e.g., Arya et al., 2007) and encroachment as a threat (e.g., Guan et al., 2019), we show that the manufacturer may optimally sustain an unprofitable direct channel with sales when the level of economies of scale is below a threshold. To the best of our knowledge, this encroachment strategy has not been documented in the existing literature on manufacturer encroachment. The key mechanism is that direct sales can expand total output, thereby reducing the average unit production cost through economies of scale. Moreover, the quantity distortion effect is weakened when either the level of economies of scale is lower or the unit direct-selling cost is higher. Hence, when the level of economies of scale remains below the threshold and the unit cost of direct selling is relatively high, the wholesale price effect, strengthened by a lower average unit production cost, can effectively boost the retailer's order quantity and mitigate double marginalization. As a result, even if the direct channel is unprofitable, the benefit from indirect selling can outweigh the loss from direct selling, thereby making encroachment optimal for the manufacturer. This result is robust regardless of whether the manufacturer sells through one or multiple retailers, whether the products in the two channels are perfect or imperfect substitutes, and whether the channels compete in quantity or price.

Finally, our study complements Arya et al. (2007) by demonstrating that the “bright side” of manufacturer encroachment that can benefit the retailer exists only when the level of economies of scale is below a threshold. An increasing level of economies of scale intensifies the market competition caused by encroachment. Consequently, under sufficiently strong economies of scale, the benefit from wholesale price reduction cannot surpass the loss from intensified market competition, making the retailer strictly worse off from encroachment. Market competition intensity stays low only when the level of economies of scale remains below the threshold and the manufacturer's unit selling cost is relatively high. Under such conditions, the benefit from wholesale price reduction dominates and enables the retailer to benefit from encroachment, regardless of whether the manufacturer's direct channel is profitable or unprofitable. However, as the level of economies of scale increases, the likelihood that the retailer benefits from encroachment declines.

2. Literature Review

Manufacturer encroachment has been extensively studied in the literature. Encroachment creates potential conflict between a manufacturer's direct channel and the retailer (Tsay and Agrawal, 2004). Several papers emphasize that while encroachment generally benefits the manufacturer, it often hurts the retailer, especially when the retailer employs a personalized pricing strategy (Liu and Zhang, 2006) or when the manufacturer's product quality decision is endogenized (Ha et al., 2016). However, other studies suggest that encroachment can be mutually beneficial for both the manufacturer and the retailer by mitigating double marginalization within the retailer channel (Arya et al., 2007; Cattani et al., 2006; Chiang et al., 2003; Guan et al., 2019; Tsay and Agrawal, 2004; Yoon, 2016). For instance, in the context of price competition, Chiang et al. (2003) demonstrate that even when no sales occur through the direct channel, introducing it as a threat can benefit the manufacturer by influencing the retailer's pricing decision. The wholesale price reduction induced by encroachment can also benefit the retailer, when consumers do not strongly prefer the direct channel over the retailer channel. In a quantity competition context, Arya et al. (2007) find that the manufacturer benefits from encroachment, and the retailer can also benefit due to the wholesale price effect when direct selling is relatively costly. Yoon (2016) extends Arya et al. (2007) by allowing the manufacturer to endogenously decide the investment level in production cost reduction, showing that encroachment leads to higher profits for both the manufacturer and the retailer, even when they are equally efficient in sales. This is because expanded sales potential motivates the encroaching manufacturer to increase cost-reducing investments and lower the wholesale price, ultimately generating Pareto gains in the supply chain. Unlike Yoon (2016), our study extends Arya et al. (2007) by considering economies of scale, which reduce the manufacturer's average unit production cost as total output increases. In other words, the manufacturer with economies of scale cannot directly control the level of production cost reductions but can achieve it indirectly through increasing output. Moreover, we show that the presence of economies of scale leads to qualitatively different results.

Several studies have highlighted the negative implications of having the encroachment option for the manufacturer's profitability. These studies extend Arya et al. (2007) by considering asymmetric market demand information (Li et al., 2014, 2015) and product quality information (Guan et al., 2020). Under information symmetry, only a few studies have shown that the manufacturer may be worse off when given the option to encroach. For example, Liu et al. (2021) demonstrate that when the number of downstream competing retailers is sufficiently large, the wholesale price reduction from encroachment is significantly weakened, diminishing the retailer's incentive to order. Therefore, the loss from indirect selling may outweigh the benefit from direct selling, making the manufacturer worse off when given the option to encroach. Wang and Li (2021) consider the retailer's interest in consumer surplus, while Shi et al. (2023) examine manufacturer encroachment implemented through a decentralized e-commerce division, where online business decisions are delegated. Both studies show that the presence of the encroachment option may hurt the manufacturer, as intensified market competition undermines its wholesale revenue.

In the context of symmetric information, our study differs from previous studies (e.g., Liu et al., 2021; Wang and Li, 2021) in two key respects. First, while previous studies primarily explore the impact of manufacturer encroachment by focusing on downstream (sales-side) factors, our study investigates how upstream production-side economies of scale shape the manufacturer's encroachment decision. Second, and more importantly, in prior studies, the erosion of wholesale revenue drives the manufacturer's profit loss when exercising the encroachment option, as wholesale price reductions fail to effectively stimulate the retailer's order quantity. However, our study identifies a new driving mechanism by demonstrating that the manufacturer may choose not to encroach because doing so could result in profit losses in direct selling, wholesaling, or both. This newly identified mechanism expands the existing literature.

Our paper also relates to the literature on economies of scale. Existing research in operations management and marketing has primarily focused on how cost reductions in production or services through economies of scale influence manufacturers’ outsourcing decisions (Akan et al., 2011; Cachon and Harker, 2002; Gray et al., 2009; Heese et al., 2021; Xiao and Gaimon, 2013). For example, Cachon and Harker (2002) demonstrate that economies of scale strongly motivate competing manufacturers to outsource production to a common supplier, even without a cost advantage. Gray et al. (2009) develop a two-period game between an original equipment manufacturer (OEM) and a contract manufacturer to investigate the OEM's make-or-buy decision, showing that partial outsourcing can be an optimal strategy in the presence of economies of scale. Heese et al. (2021) examine how an OEM's choice between a third-party supplier and a rival that also sells a self-branded product is influenced by economies of scale. In contrast to these studies, which primarily focus on the manufacturer's upstream production outsourcing strategy, our study examines the manufacturer's downstream distribution channel strategy. Sun et al. (2021) extend the work of Li et al. (2014) by investigating the joint impact of demand information asymmetry and production cost decline on the manufacturer's encroachment incentive. They demonstrate that, compared to Li et al. (2014), cost decline increases the likelihood that the retailer distorts its order quantity downward to credibly signal a smaller market size, making the manufacturer more likely to be worse off when given the option to encroach. Differing from Sun et al. (2021), which shows that the manufacturer may suffer from the presence of the encroachment option due to information asymmetry, our study eliminates this asymmetry and instead focuses on the impact of economies of scale, exploring the underlying rationale behind manufacturers’ differing attitudes toward encroachment.

Recently, Gupta et al. (2024) develop a two-period model to examine the impact of manufacturer encroachment on firms’ profits. Our study differs from theirs in several key respects. First, they focus on the manufacturer's production cost learning in the second period, assuming that the manufacturer sells exclusively through the retailer in the first period and decides whether to encroach in the second period. In their model, the first-period manufacturing cost remains constant, while the second-period cost decreases based on the first-period production volume. In contrast, motivated by observations from the CPG industry, we consider the impact of economies of scale, where the manufacturer's average unit production cost decreases with total output rather than through intertemporal learning. Second, they show that the manufacturer may be worse off when given the option to encroach, as it can reduce the retailer's first-period order quantity and increase the second-period manufacturing cost. The losses from increased production cost in the second period and reduced wholesale revenue across both periods may surpass the gains from direct selling in the second period. This intuition aligns with previous studies (e.g., Liu et al., 2021; Wang and Li, 2021), given that direct sales are always profitable. In contrast, our findings indicate that while encroachment can lower the average unit production cost and increase wholesale revenue in the presence of economies of scale, the manufacturer may still prefer not to encroach due to the profit loss in direct selling. This highlights a key distinction between economies of scale and manufacturing cost learning: Economies of scale make direct selling more likely if the manufacturer encroaches, but due to high unit selling costs, such direct selling may generate a negative profit margin. Third, similar to Arya et al. (2007), they suggest that encroachment benefits the retailer as long as the manufacturer's unit selling cost remains moderate, independent of the degree of cost learning. However, we show that the retailer can benefit from manufacturer encroachment only when economies of scale are relatively limited. Lastly, we find that even when the direct channel is unprofitable, encroachment can still benefit the manufacturer by effectively coordinating with the retailer channel. To the best of our knowledge, these insights into manufacturer encroachment have not been previously discussed in the existing literature.

3. Model Setting

Consider a supply chain where a manufacturer (she) produces a product and sells it to the consumer market through an independent retailer (he) at a unit wholesale price ( $w$ ). In addition to this indirect distribution channel, the manufacturer needs to decide whether to encroach into the retail market by establishing a direct channel. The direct channel can take the form of an online store or a flagship shop, offering consumers an alternative purchasing avenue.

Consumer demand in the retail market is represented by a linear inverse demand function: $p=a-bQ$ , where p signifies the market-clearing price, a represents the market potential, Q denotes the total quantity of the product produced and sold in the market, and b reflects the price sensitivity to the total quantity. If the manufacturer does not encroach, then $Q=q_R$ , where $q_R$ is the retailer's selling quantity. If the manufacturer encroaches by operating a direct channel with a selling quantity of $q_M$ , then the total quantity sold becomes $Q=q_R+q_M$ . We adopt this demand function for the following reasons. First, perfect substitution between the two channels suggests that introducing a direct channel does not expand the total market potential, thereby eliminating the possibility that a direct channel would broaden the consumer base, a factor often cited as a motivation for manufacturer encroachment (Li et al., 2015). Second, uniform retail pricing allows the manufacturer to maintain a consistent brand image, prevent consumer confusion, and preserve brand value. It can also avoid severe channel cannibalization caused by price differentiation, where consumers would naturally prefer the cheaper option, ultimately undermining the profitability and effectiveness of the other channel.

In practice, a manufacturer can commonly gain a competitive advantage by increasing production quantity to reduce the unit production cost, leveraging economies of scale in upstream production. Following Raman and Chatterjee (1995), Gray et al. (2009), Shang et al. (2016), Shum et al. (2017), and Heese et al. (2021), we model the impact of economies of scale by representing the manufacturer's total production cost as $cQ-k{Q}^2$ . This cost function is concave in total production quantity Q, and the manufacturer's average unit production cost for any given Q is $c-kQ$ , where c denotes the initial unit production cost without economies of scale (i.e., $k=0$ ). Producing each additional unit enables the manufacturer to reduce the average unit production cost at a rate of k, which reflects the level of economies of scale. A larger k signifies a higher level of economies of scale, leading to more significant production cost reductions.

If the manufacturer encroaches, she incurs a unit selling cost ( $s$ ) for each product sold through the direct channel, while the retailer's unit selling cost is normalized to zero. The manufacturer's selling cost disadvantage implies that the direct channel is less efficient than the retailer channel, reflecting the manufacturer's lack of retail experience or the additional costs associated with e-commerce (Arya et al., 2007; Ha et al., 2016). This assumption aligns with industry practice. In the CPG industry, for example, manufacturers’ online channels typically incur higher shipping and warehousing costs than brick-and-mortar retailers do (Chapple and Sivaeva, 2021; Chapple et al., 2021).

The game sequence is as follows: First, the manufacturer decides whether to encroach into the retail market. Second, she sets the wholesale price ( $w$ ) charged to the retailer. Third, the retailer decides the order quantity ( $q_R$ ). Fourth, the manufacturer decides the direct selling quantity ( $q_M$ ) if a direct channel exists. Finally, products are sold to consumers at the market-clearing price for both channels. Here, we assume that quantity decisions are made sequentially, because the manufacturer can observe the retailer's order decision, whereas the retailer typically cannot observe the manufacturer's direct selling quantity decision. This reflects the manufacturer's inability to credibly commit not to revise her direct selling quantity after receiving the retailer's order (Arya et al., 2007; Ha et al., 2016).

Our assumptions, including Cournot competition, uniform retail pricing, asymmetric selling costs between channels, and sequential quantity decisions, are consistent with the existing literature on manufacturer encroachment (e.g., Arya et al., 2007; Guan et al., 2019; Li et al., 2014, 2015; Liu et al., 2021; Wang and Li, 2021). These assumptions allow us to explore new insights and implications resulting from the impact of economies of scale compared to prior studies. The notation used in this paper is summarized in Table 1.

Table 1.

Notation.

Indexes
$M,R$	Subscript, indexes of the manufacturer and the retailer, respectively
$N,E$	Superscript, indexes of the no-encroachment and encroachment settings, respectively
Parameters
$a$	Market potential
$b$	Price sensitivity to the total quantity of the product sold in the market
$s$	Manufacturer's unit direct-selling cost
$c$	Manufacturer's initial unit production cost without economies of scale
$k$	Level of economies of scale
Decision variables
$w$	Wholesale price offered by the manufacturer to the retailer
$q_R$	Retailer's order/selling quantity
$q_M$	Manufacturer's direct selling quantity
Other notations
$p$	Market-clearing price
$Q$	Total quantity of the product produced and sold in the market
$m_M,m_R$	Manufacturer's profit margins from direct and indirect selling, respectively
${\pi }_M$ , ${\pi }_R$	Profits of the manufacturer and the retailer, respectively

4. Equilibrium Outcomes

In this section, we first derive the equilibrium wholesale price, selling quantities, and profits of the manufacturer and the retailer under two settings using backward induction: The no-encroachment setting where the manufacturer sells the product exclusively through the retailer (denoted by the superscript $N$ ), and the encroachment setting where she establishes a direct channel and can sell the product directly to consumers (denoted by the superscript $E$ ). We then examine how the level of economies of scale affects these equilibrium outcomes. All thresholds for the unit direct selling cost ( $s$ ) are provided in Table A1 in the online Appendix A.

4.1. The No-Encroachment Setting

In the no-encroachment setting, the manufacturer's production quantity is $Q=q_R$ . The profit functions of the manufacturer ( ${\pi }_M$ ) and the retailer ( ${\pi }_R$ ) are

$$\begin{array}{r}{\pi }_M=(w-(c-k{q}_R))q_R\text{and}{\pi }_R=(a-b{q}_R-w)q_R.\end{array}$$

(1)

Then, the equilibrium outcomes are

$$\begin{array}{rl}{w}^N& =\frac{a(b-k)+bc}{2b-k},q_R^N=\frac{a-c}{2(2b-k)},\\ {\pi }_R^N& =\frac{b{(a-c)}^2}{4{(2b-k)}^2},\text{and}{\pi }_M^N=\frac{{(a-c)}^2}{4(2b-k)}.\end{array}$$

(2)

Note that the positivity of the average unit production cost in Equation (2) requires $k<{\overline{k}}^N=\frac{4bc}{a+c}$ .

4.2. The Encroachment Setting

In the encroachment setting, the manufacturer can sell the product through both the retailer and her direct channel. Her total production quantity is $Q=q_R+q_M$ . The profit functions of the manufacturer ( ${\pi }_M$ ) and the retailer ( ${\pi }_R$ ) are

$$\begin{array}{rl}{\pi }_M& =(a-bQ-s-(c-kQ))q_M+(w-(c-kQ))q_R,\end{array}$$

(3)

$$\begin{array}{rl}{\pi }_R& =(a-bQ-w)q_R.\end{array}$$

(4)

The two terms in Equation (3) represent the manufacturer's profits from direct and indirect selling, respectively. The total production cost is $(c-kQ)Q$ .

In the absence of economies of scale (i.e., $k=0$ ) and with the manufacturer's initial unit production cost normalized to zero (i.e., $c=0$ ), our model becomes identical to that of Arya et al. (2007). However, their study focuses on the case where the encroaching manufacturer sells a positive quantity through the direct channel. We also consider the case where the manufacturer does not sell directly but instead uses the direct channel as a threat to the retailer, as discussed in Guan et al. (2019) and Wang and Li (2021).

For the remainder of this study, we consider $k<\overline{k}$ (where $\overline{k}=\frac{2bc}{a+c}<{\overline{k}}^N$ ) to ensure a positive average unit production cost for any s, and $\frac{a}{3}<c<a-s$ to ensure positive equilibrium outcomes. The following lemma presents the equilibrium outcomes under the encroachment setting (All proofs are provided in the online Appendix A).

Lemma 1.

The equilibrium outcomes under the encroachment setting are summarized in Table 2 . The following characterizes the equilibrium regions:

1. (i)

the manufacturer sells directly (i.e., $q_M^E>0$ ) if $k\ge \frac{b}{2}$ , or if $k<\frac{b}{2}$ and $s<\overline{s}$ ;

(ii)

the direct channel serves as a threat (i.e., $q_M^E=0$ ) otherwise.

Note that when $k=0$ and $c=0$ , the equilibrium outcomes and the threshold ( $\overline{s}$ ) that separates the two equilibrium regions in Table 2 (under Lemma 1) are identical to those in Section 3.2.3 of Wang and Li (2021).

Table 2.

Equilibrium outcomes under the encroachment setting.

	When $k\ge {\displaystyle \frac{b}{2}}$ or $k<{\displaystyle \frac{b}{2}}$ and $s<\overline{s}$	When $k<{\displaystyle \frac{b}{2}}$ and $s\ge \overline{s}$
$w^E$	$a-{\displaystyle \frac{b(a-c-s)}{2(b-k)}}-{\displaystyle \frac{2s}{3}}$	$a-{\displaystyle \frac{b(3b-2k)(a-c-s)}{2(b-2k)(b-k)}}$
$q_R^E$	${\displaystyle \frac{2s(b-k)}{3b^2}}$	${\displaystyle \frac{a-c-s}{b-2k}}$
$q_M^E$	${\displaystyle \frac{a-c-s}{2(b-k)}}-{\displaystyle \frac{(b-2k)s}{3b^2}}$	0
${\pi }_R^E$	${\displaystyle \frac{2s^2(b-k)}{9b^2}}$	${\displaystyle \frac{b^2{(a-c-s)}^2}{2(b-k){(b-2k)}^2}}$
${\pi }_M^E$	${\displaystyle \frac{{(a-c-s)}^2}{4(b-k)}}+{\displaystyle \frac{(b-k)s^2}{3b^2}}$	${\displaystyle \frac{(2k^2-b^2-2bk){(a-c-s)}^2}{2{(b-2k)}^2(b-k)}}+{\displaystyle \frac{(a-c-s)s}{b-2k}}$

In the presence of economies of scale, Lemma 1 (illustrated in Figure 1) shows that under the encroachment setting, when the level of economies of scale exceeds a threshold ( $k\ge b/2$ ), the manufacturer always prefers to sell the product through the direct channel, regardless of her unit selling cost ( $s$ ). The reason is that a higher k leads to a more pronounced reduction in the average unit production cost, thereby strengthening the manufacturer's incentive to sell directly. By doing so, she can potentially increase total output and leverage economies of scale.

Figure 1.

Equilibrium regions under the encroachment setting.

When k remains below its threshold ( $k<b/2$ ), a threshold direct-selling cost $\overline{s}$ exists, delimiting whether the manufacturer sells directly or uses the direct channel as a threat. Since a higher s decreases the efficiency of direct selling, the manufacturer sells directly only when $s<\overline{s}$ . When $s\ge \overline{s}$ , the direct channel becomes significantly less efficient than the retailer channel. In this case, the retailer is incentivized to order a large enough quantity to drive the market-clearing price down to a sufficiently low level, leaving the manufacturer with no incentive to sell directly due to the significant selling cost disadvantage. Anticipating the retailer's ordering incentive, the manufacturer therefore sets a wholesale price to avoid direct sales, while using the direct channel as a threat to the retailer.

Additionally, when $k<b/2$ , $\overline{s}$ increases with k (i.e., $\mathrm{\partial }\overline{s}/\mathrm{\partial }k>0$ ), and $\overline{s}=a-c$ when $k=b/2$ . This indicates that as k increases, the manufacturer engages in direct sales for a larger range of s values while using the direct channel as a threat for a smaller range of s values. This is because a higher k makes direct selling more attractive to the manufacturer despite a selling cost disadvantage.

4.3. Impact of the Level of Economies of Scale

With Equation (2) and Table 2, we now investigate the impact of the level of economies of scale ( $k$ ) on the equilibrium wholesale price and selling quantities under the two settings. The results are summarized in Lemma 2.

Lemma 2.

As k increases, in equilibrium,

1. (i)

under the no-encroachment setting, $w^N$ decreases while $q_R^N$ increases;

(ii)

under the encroachment setting, if the manufacturer sells directly, $w^E$ and $q_R^E$ decrease, while $q_M^E$ and $Q^E$ increase, where $Q^E=q_R^E+q_M^E$ ; otherwise, $w^E$ decreases while $q_R^E$ increases.

Lemma 2 shows that as the level of economies of scale increases, the average unit production cost declines more substantially, incentivizing the manufacturer to lower her wholesale price to encourage orders from the retailer. Under the no-encroachment setting, this reduction in wholesale price allows the retailer to increase his order quantity, thereby alleviating double marginalization in the supply chain. Similarly, if the manufacturer uses the direct channel solely as a threat, an increase in k leads to a lower wholesale price and a higher retailer order quantity. However, if the manufacturer encroaches by selling directly, she decreases the wholesale price but simultaneously increases her direct selling quantity as k increases. Anticipating intensified market competition, the retailer reduces his order quantity despite the lower wholesale price. Notably, the increase in the direct selling quantity outweighs the decrease in the retailer's order quantity, leading to a larger total output for the manufacturer as k increases.

Proposition 1 further provides how the equilibrium profits of the manufacturer and the retailer under the two settings are affected by an increase in k.

Proposition 1.

As k increases, in equilibrium,

1. (i)

under the no-encroachment setting, the profits of both the manufacturer and the retailer increase;

(ii)

under the encroachment setting, the manufacturer's profit decreases if $s_1\le s<s_2$ , and the retailer's profit decreases if $k\ge \frac{b}{2}$ , or if $k<\frac{b}{2}$ and $s<\overline{s}$ .

Conventional wisdom suggests that manufacturing firms can benefit from an increasing level of economies of scale (a higher $k$ ) due to a more substantial reduction in production costs. Proposition 1 shows that this intuition holds true if the manufacturer does not encroach, and the benefit also extends to the retailer, as an increase in k mitigates double marginalization in the supply chain (see the discussion following Lemma 2).

Interestingly, Proposition 1 also indicates that an increase in k may hurt the manufacturer's profit if she encroaches, as illustrated in the shaded region of Figure 2. Moreover, the retailer's profit decreases with k as long as the manufacturer sells directly.

Figure 2.

Impact of the level of economies of scale ( $k$ ) on the encroaching manufacturer's profit.

To facilitate the discussion, we define the encroaching manufacturer's profit margins from direct and indirect selling, respectively, as follows:

$$\begin{array}{r}{m}_M^E=a-b{Q}^E-s-(c-k{Q}^E)\text{and}{m}_R^E=w^E-(c-k{Q}^E),\end{array}$$

(5)

where $Q^E=q_M^E+q_R^E$ , and $c-k{Q}^E$ is the encroaching manufacturer's average unit production cost. With equilibrium outcomes in Table 2, we can show that $m_M^E-m_R^E=-2s/3<0$ when $q_M^E>0$ . This confirms that the manufacturer's direct channel is less efficient than the retailer channel in terms of unit profitability due to the cost disadvantage of direct selling.

When the manufacturer sells directly, an increase in k has two opposing effects on her profitability. On the one hand, it enables the manufacturer to increase total quantity and lower the average unit production cost. On the other hand, it increases the manufacturer's direct selling quantity while reducing the retailer's order quantity (see Lemma 2), shifting sales from the more efficient retailer channel to the less efficient direct channel. This shift negatively affects her profitability. Additionally, a higher unit cost of direct selling ( $s$ ) impairs the manufacturer's ability to benefit from stronger economies of scale $(\text{i.e.},\frac{{\mathrm{\partial }}^2{Q}^E}{\mathrm{\partial }k\mathrm{\partial }s}<0$ and $\frac{{\mathrm{\partial }}^2(c-k{Q}^E)}{\mathrm{\partial }k\mathrm{\partial }s}>0)$ . Consequently, as shown in Figure 2, when s is within an intermediate range ( $s_1\le s<\overline{s}$ ), the manufacturer's profit decreases with k because the combined gains from market expansion and reductions in the average unit production cost fail to compensate for the loss from reduced sales through the more efficient retailer channel. Clearly, the retailer's profit always decreases with k due to the reduction in his order quantity.

When the direct channel serves as a threat, as k increases, the decrease in the wholesale price encourages the retailer to increase his order quantity (see Lemma 2), thereby benefiting him. For the manufacturer, however, the wholesale price reduction diminishes her profit margin from indirect selling. Meanwhile, a larger s weakens the threat of encroachment, making the retailer less sensitive to wholesale price changes. This allows the manufacturer to raise the wholesale price and earn a higher indirect profit margin. As a result, when s is not too high ( $\overline{s}\le s<s_2$ ), the loss due to a lower indirect profit margin outweighs the benefit from a larger indirect selling quantity, reducing the manufacturer's profit as k increases. The reverse is true when $s$ becomes sufficiently high.

5. Manufacturer's Optimal Encroachment Strategy

In this section, we first compare the manufacturer's profit under the encroachment setting to that under the no-encroachment setting, and then investigate her optimal encroachment strategy in the first stage of the game. In the absence of economies of scale, prior studies (e.g., Arya et al., 2007; Yoon, 2016) have shown that the manufacturer is always better off if she encroaches and sells directly than if she sells exclusively through the retailer. However, the following proposition (illustrated in Figure 3(a)) demonstrates that this result may no longer hold when economies of scale are present.

Figure 3.

Impact of encroachment on the profits of the manufacturer and her two channels: (a) Manufacturer's profit; (b) Profits of the manufacturer's two channels.

Proposition 2.

${\pi }_M^E<{\pi }_M^N$ if $k\ge \frac{b}{4}$ and $s_{M1}\le s<s_{M2}$ , or if $k<\frac{b}{2}$ and $s\ge \hat{s}$ ; otherwise, ${\pi }_M^E>{\pi }_M^N$ .

Proposition 2 indicates that, compared to no encroachment, the manufacturer may become worse off if she encroaches. To understand the underlying mechanism, we analyze the impact of encroachment on the manufacturer's profit from each channel, as shown in Figure 3(b). In particular, due to encroachment, the manufacturer's profit change in the direct channel is $\mathrm{\Delta }{\pi }_{MM}^E=m_M^E{q}_M^E$ since no direct channel exists without encroachment; her profit change in the retailer channel is $\mathrm{\Delta }{\pi }_{MR}^E=m_R^E{q}_R^E-{\pi }_M^N$ , where $m_M^E$ and $m_R^E$ are the encroaching manufacturer's profit margins from the two channels, respectively (see Equation 5). In Figure 3(b), $s_{M3}$ is the critical value of s that solves $\mathrm{\Delta }{\pi }_{MM}^E=0$ when $q_M^E>0$ . $s_{M4}$ and $\hat{s}$ are two critical values of s that solve $\mathrm{\Delta }{\pi }_{MR}^E=0$ when $q_M^E>0$ and $q_M^E=0$ , respectively. Additionally, the symbols “ $+$ ”, “ $-$ _,” and “0” in brackets denote an increase, decrease, or no change, respectively, in the manufacturer's profit from each channel due to encroachment. Specifically, the first symbol refers to the direct channel, and the second refers to the retailer channel.

We first focus on the first condition ( $k\ge b/4$ and $s_{M1}\le s<s_{M2}$ ), under which the manufacturer would be hurt if she sells directly. Intuitively, without economies of scale, encroachment with direct sales benefits the manufacturer in two primary ways, as shown in Figure 3(b) when $k=0$ and $s<\overline{s}$ . First, it allows the manufacturer to generate a positive profit from direct selling. Second, as identified by Arya et al. (2007), encroachment introduces a wholesale price effect: It induces the manufacturer to set a lower wholesale price than she would without encroachment, to stimulate demand in the retailer channel (i.e., $w^N-w^E=s/6>0$ with $k=0$ and $c=0$ in this study). The wholesale price effect becomes more pronounced as the unit cost of direct selling ( $s$ ) increases, incentivizing the retailer to order more than under no encroachment. This mitigates double marginalization and turns the manufacturer's indirect profitability from negative to positive.

The presence of economies of scale would significantly alter these supply chain dynamics. Specifically, an increasing level of economies of scale lowers the manufacturer's average unit production cost, strengthening her incentive to sell directly if she encroaches. That is, the unit direct-selling cost threshold $\overline{s}$ , below which the encroaching manufacturer chooses to sell directly, increases with k (see Figure 1 under Lemma 1). However, as shown in Figure 3(b), the manufacturer incurs a profit loss from direct selling when s is relatively high ( $s\ge s_{M3}$ ), because her direct profit margin decreases and eventually becomes negative as s increases, despite the presence of direct sales. Regarding the manufacturer's profitability from indirect selling, in addition to the wholesale price effect, there is a quantity distortion effect induced by encroachment under stronger economies of scale: When the manufacturer encroaches and sells directly, a higher k shifts product sales from the retailer channel to the direct channel (i.e., $\mathrm{\partial }{q}_M^E/\mathrm{\partial }k>0$ and $\mathrm{\partial }{q}_R^E/\mathrm{\partial }k<0$ ; see Lemma 2). This quantity distortion effect also intensifies as s decreases because a lower s increases the direct selling quantity (i.e., $\mathrm{\partial }{q}_M^E/\mathrm{\partial }s<0$ ) while suppressing the retailer's order quantity (i.e., $\mathrm{\partial }{q}_R^E/\mathrm{\partial }s>0$ ). Thus, while encroachment can lead to a reduction in the wholesale price, ¹ this wholesale price effect fails to offset the quantity distortion effect when $k<b/2$ and $s<s_{M4}$ , or when $k\ge b/2$ . The dominant quantity distortion effect consequently reduces the retailer's order quantity and hurts the manufacturer's profit from indirect selling, as illustrated in Figure 3(b). As a result, when k exceeds a certain threshold ( $k\ge b/4$ ) and s is in an intermediate range ( $s_{M1}\le s<s_{M2}$ ), the manufacturer becomes worse off if she encroaches because of profit losses either in both channels (region ( $-$ , $-$ )), or in one channel (regions ( $+$ , $-$ ) or ( $-$ , $+$ )), where the loss in one channel outweighs the gain in the other.

We now focus on the second condition ( $k<b/2$ and $s\ge \hat{s}$ ), under which the manufacturer would be worse off if the direct channel serves as a threat. Recall that in this case, the retailer has an incentive to deter the manufacturer's direct sales by ordering a sufficiently large quantity. This, in turn, allows the manufacturer to increase her wholesale price as s increases, potentially leading to a higher wholesale price than under no encroachment. ² When s is sufficiently high ( $s\ge \hat{s}$ ), the increase in the wholesale price due to the threat of encroachment reaches a level that significantly reduces the retailer's order quantity compared to the case of no encroachment. The decreased indirect selling quantity and the increased average unit production cost consequently make the manufacturer worse off when using the direct channel merely as a threat (region ( $-$ , $0$ ) in Figure 3(b)).

Proposition 2 provides new insights into the literature on manufacturer encroachment. Prior studies without considering economies of scale, such as Liu et al. (2021) and Wang and Li (2021), demonstrate that the manufacturer may be worse off when given the option to encroach because the loss in wholesale revenue cannot be fully offset by the additional gain from direct selling. In contrast, we find that this intuition holds true in the presence of economies of scale only under certain conditions (in the region $s_{M1}\le s<min\{s_{M2},s_{M3}\}$ ), as illustrated in Figure 3(b). The negative impact of encroachment on the manufacturer's profitability can also be driven by profit losses in both channels (in the region where $s_{M3}\le s<s_{M4}$ ), or even solely by the profit loss in the direct channel (in the region where $s_{M4}\le s<s_{M2}$ ). This is because a higher level of economies of scale increases the manufacturer's incentive to sell directly, but she may end up with a negative profit margin from direct selling as her unit selling cost continues to increase.

Proposition 2 also identifies the conditions under which the manufacturer can be better off if she encroaches (see the region where ${\pi }_M^E>{\pi }_M^N$ in Figure 3(a)). Based on the results in Proposition 2 and the preceding analysis of the manufacturer's profitability from the two channels, the following proposition characterizes her optimal encroachment strategy. Without economies of scale, existing literature has shown that either encroachment with profitable direct sales or encroachment as a threat can be the manufacturer's optimal strategy. However, Proposition 3 (illustrated in Figure 4) shows that, in addition to these two encroachment outcomes, encroachment with unprofitable direct sales can also emerge as an optimal strategy due to the unique impact of economies of scale.

Figure 4.

The manufacturer's optimal encroachment strategy.

Proposition 3.

The manufacturer's optimal encroachment strategy is:

1. (i)

no encroachment ( $N$ ) if $k\ge \frac{b}{4}$ and $s_{M1}\le s<s_{M2}$ , or if $k<\frac{b}{2}$ and $s\ge \hat{s}$ ;

(ii)

encroachment with an unprofitable direct channel ( $EUD$ ) if $k<\frac{b}{2}$ and $max\{s_{M2},s_{M3}\}\le s<\overline{s}$ ;

(iii)

encroachment as a threat with no direct sales ( $END$ ) if $k<\frac{b}{2}$ and $\overline{s}\le s<\hat{s}$ ;

(iv)

encorachment with a profitable direct channel ( $EPD$ ) otherwise.

Intuitively, if a manufacturer chooses to encroach and sell directly, she would gain additional revenue from direct sales. Interestingly, Proposition 3 indicates that she may strategically maintain an unprofitable direct channel with sales. This strategy is preferred when the level of economies of scale is below a threshold ( $k<b/2$ ) and the unit cost of direct selling is relatively high ( $max\{s_{M2},s_{M3}\}\le s<\overline{s}$ ); see the pink region in Figure 4. To the best of our knowledge, this insight has not been discussed in prior studies. The underlying reason is that by selling directly, the manufacturer can expand total output and thus reduce her average unit production cost due to economies of scale. Moreover, the quantity distortion effect is weakened either by a lower level of economies of scale or by a higher unit cost of direct selling. When $k<b/2$ and s is relatively high, the quantity distortion effect is subdued, allowing the wholesale price effect, driven by the lower average unit production cost, to effectively boost the retailer's order quantity. This strengthens the benefit of encroachment in mitigating double marginalization, making the manufacturer's gain from indirect selling sufficient to offset the loss from direct selling. Consequently, the manufacturer becomes better off through encroachment despite having unprofitable direct sales.

Proposition 3 and Figure 4 also demonstrate that when s is relatively low, the manufacturer prefers encroachment with a profitable direct channel (see the yellow region in Figure 4). This is intuitive because the profitability of the direct channel increases as s decreases. Thus, under relatively low values of s, the benefit gained from direct selling surpasses the potential profit loss incurred in the retailer channel. Furthermore, when $k<b/4$ , such a strategy is preferred over a larger range of s values compared to when $k\ge b/4$ (as $s_{M3}>s_{M1}$ ), because a lower k weakens the quantity distortion effect and reduces the manufacturer's wholesale profit loss. When $k<b/2$ and s is not too high, it is optimal for the manufacturer to use the direct channel to as a threat (see the green region in Figure 4). Under this strategy, a higher s allows the manufacturer to raise the wholesale price. Therefore, as s increases, the primary benefit of the threat of encroachment shifts from stimulating the retailer's order quantity (via wholesale price reduction) to leveraging a higher wholesale price itself, compared to no encroachment. However, as aforementioned, the manufacturer becomes worse off if she encroaches by selling directly when $k\ge b/4$ and s is intermediate, or if she uses the direct channel as a threat when $k<b/2$ and s is sufficiently high (refer to Proposition 2). Consequently, no encroachment is strictly optimal in both cases.

In addition, as shown in Figure 4, the region where the manufacturer prefers encroachment with unprofitable direct sales first expands (i.e., $\mathrm{\partial }\overline{s}/\mathrm{\partial }k>\mathrm{\partial }{s}_{M3}/\mathrm{\partial }k>0$ ) and then shrinks (i.e., $\mathrm{\partial }{s}_{M2}/\mathrm{\partial }k>\mathrm{\partial }\overline{s}/\mathrm{\partial }k>0$ ) as k increases. This occurs because an increase in k amplifies the cost-saving benefit enabled by encroachment, while the quantity distortion effect erodes the manufacturer's profitability from wholesaling. At low k, the cost-saving benefit dominates, but the quantity distortion effect takes over at intermediate k. This dominance shift thus also expands the region where no encroachment is optimal (i.e., $\mathrm{\partial }{s}_{M2}/\mathrm{\partial }k>0$ ) when k is intermediate. However, when $k\ge b/2$ , such a region slightly shrinks as k increases (i.e., $\mathrm{\partial }{s}_{M1}/\mathrm{\partial }k>0$ ) because the manufacturer can earn higher direct-selling profits despite the loss from wholesaling, provided that s is not too high. Furthermore, a higher k reduces the manufacturer's incentive to use the direct channel merely as a threat (i.e., $\mathrm{\partial }\overline{s}/\mathrm{\partial }k>\mathrm{\partial }\hat{s}/\mathrm{\partial }k>0$ ).

Proposition 3 provides valuable insights into manufacturer encroachment practices. First, our findings may help explain why CPG manufacturers have varying attitudes toward encroachment strategies. Some large companies with strong economies of scale, such as P&G, Kao Corporation, and General Mills, often avoid encroachment, relying solely on retailer channels. Conversely, many other CPG manufacturers actively develop their e-commerce businesses to increase sales, even though e-commerce may not always be profitable. This divergence highlights the influence of economies of scale in shaping encroachment decisions. Second, our research suggests that manufacturers should adopt a coordinated omnichannel strategy rather than evaluating the direct channel in isolation. Even if direct sales appear unprofitable initially, increasing total output can lower average unit production costs through economies of scale. Maintaining a lower average unit production cost than competitors enable more competitive wholesale pricing and better coordination with retailers, ultimately improving overall omnichannel performance. Third, as manufacturers increasingly engage in e-commerce, they must enhance their management of online selling costs and improve the efficiency of direct selling to increase profitability. One effective strategy is product packaging redesign tailored for e-commerce, such as lighter, more compact formats to reduce shipping costs. For instance, a laundry product manufacturer not only redesigned packaging but also removed water from the detergent, substantially reducing shipping costs and improving compatibility for direct online sales (Chapple and Sivaeva, 2021). While such redesigns could benefit both channels, they align better with the direct channel's operational flexibility, where the manufacturer controls packaging, logistics, and fulfillment. Traditional retailers, constrained by shelf space and standard display requirements, may find such adaptations challenging. This supports our model's assumption that the direct channel's initial selling cost disadvantage can be mitigated through targeted innovations. Additionally, re-evaluating the end-to-end supply chain infrastructure can lead to improvements. Strategies such as segmenting warehouses based on distribution channels and collaborating with retailers or third-party platforms for last-mile delivery can optimize deliveries and reduce associated costs (Chapple et al., 2021).

6. Impact of the Manufacturer's Optimal Encroachment Strategy

This section first examines the impact of the manufacturer's optimal encroachment strategy on the retailer's profit. The result is presented in Proposition 4 and illustrated in Figure 5.

Figure 5.

Impact of the manufacturer's optimal encroachment strategy on the retailer's profit.

Proposition 4.

The retailer benefits from manufacturer encroachment if $k<\frac{b}{2}$ and $max\{s_{R1},s_{M2}\}\le s<s_{R2}$ ; otherwise, the retailer is worse off.

Without economies of scale, Arya et al. (2007) introduced the “bright side” of manufacturer encroachment: The retailer can benefit from encroachment because the benefit from wholesale price reduction outweighs the loss from downstream market competition, provided that the unit direct-selling cost ( $s$ ) falls within an intermediate range.

However, Proposition 4 shows that this bright side persists only when the level of economies of scale is below a threshold ( $k<b/2$ ). Recall that with economies of scale, an increase in k stimulates the retailer's order quantity if the manufacturer remains solely a wholesaler. In contrast, it intensifies market competition and reduces the retailer's order quantity if the manufacturer encroaches by selling directly (see Lemma 2). Consequently, when $k\ge b/2$ , manufacturer encroachment never benefits the retailer, even with wholesale price reductions. Conversely, when $k<b/2$ and s is relatively high ( $max\{s_{R1},s_{M2}\}\le s<\overline{s}$ ), market competition intensity remains low because of the manufacturer's significant selling cost disadvantage. In this case, the benefit from wholesale price reduction dominates, making the retailer better off, regardless of whether the encroaching manufacturer's direct channel is profitable. Furthermore, when $k<b/2$ and $\overline{s}\le s<s_{R2}$ , the threat of encroachment can also benefit the retailer due to the wholesale price reduction.

Proposition 4 complements Arya et al. (2007) by demonstrating that the bright side of manufacturer encroachment exists only when economies of scale are relatively limited. Moreover, an increasing level of economies of scale makes the retailer less likely to benefit from manufacturer encroachment. As shown in Figure 5, when $k<b/2$ , the region where the retailer benefits from encroachment shrinks as k increases (i.e., $\mathrm{\partial }max\{s_{R1},s_{M2}\}/\mathrm{\partial }k>\mathrm{\partial }{s}_{R2}/\mathrm{\partial }k>0$ ).

Next, we discuss how the manufacturer's optimal encroachment strategy influences total supply chain profit ( ${\pi }_{SC}={\pi }_M+{\pi }_R$ ) and consumer surplus ( $CS=b{Q}^2/2$ ). As shown in Figure 6(a), when the unit cost of direct selling is sufficiently low, it is intuitive that the supply chain can benefit from manufacturerencroachment with a profitable direct channel. Interestingly, when $k<b/2$ and s is relatively high, the supply chain can also benefit from all three encroachment strategies: encroachment with a profitable direct channel, encroachment with an unprofitable direct channel, or encroachment as a threat. This improvement in supply chain performance primarily stems from encroachment's role in mitigating double marginalization within the retailer channel. Figure 6(b) further reveals that regardless of the direct channel's profitability, consumer surplus always increases under encroachment, as encroachment leads to a higher total production quantity, which lowers the market-clearing price. However, when the unit direct-selling cost is not too high, although the threat of encroachment benefits the manufacturer through a higher wholesale price, it reduces the retailer's order quantity and creates supply chain inefficiency, thereby hurting consumer surplus.

Figure 6.

Impact of the manufacturer's optimal encroachment strategy on total supply chain profit and consumer surplus: (a) Total supply chain profit; (b) Consumer surplus.

7. Extensions

We now explore several extensions of the main model to assess the robustness of our main findings. The models in this section are solved using backward induction.

7.1. Multiple Retailers

We first extend the main model by considering a downstream market with multiple competing retailers. All thresholds and proofs for this section are provided in the online Appendix B.

In the no-encroachment setting, the manufacturer sells the product through multiple retailers at a wholesale price w. The total quantity sold through retailers is ${\sum }_1^n{q}_{Rj}$ , where $q_{Rj}$ represents the quantity sold by retailer j ( $j=1,2,\dots ,n)$ . If the manufacturer introduces a direct channel with selling quantity $q_M$ , total quantity sold becomes $Q={\sum }_1^n{q}_{Rj}+q_M$ . The profit functions of the manufacturer and retailer j under the encroachment setting are given by

$$\begin{array}{rl}{\pi }_M& =(a-bQ-s-(c-kQ))q_M+(w-(c-kQ)){\sum }_1^n{q}_{Rj},\end{array}$$

(6)

$$\begin{array}{rl}{\pi }_{Rj}& =(a-bQ-w)q_{Rj}.\end{array}$$

(7)

Equilibrium outcomes under the settings without and with encroachment in this extension (denoted by an additional superscript $n$ ) are summarized in Table B2 in the online Appendix B. For $k=0$ , $c=0$ , and $b=1$ , the equilibrium outcomes in this extension are identical to those in Section 4 of Liu et al. (2021). As in the main model, ensuring a positive average unit production cost for any value of s and positive equilibrium outcomes requires $k<\overline{k}=\frac{2bc}{a+c}$ and $\frac{a}{3}<c<a-s$ . Table B2 in the online Appendix B shows that the encroaching manufacturer sells directly (i.e., $q_M^{En}>0$ ) if $k\ge \frac{b}{2}$ or if $k<\frac{b}{2}$ and $s<{\overline{s}}^n$ ; otherwise, the direct channel serves only as a threat (i.e., $q_M^{En}=0$ ). A higher k increases the manufacturer's incentive to sell directly (i.e., $\mathrm{\partial }{\overline{s}}^n/\mathrm{\partial }k>0$ ), which is consistent with the main model.

Proposition 5 presents the manufacturer's optimal encroachment strategy and its impact on a retailer's profit.

Proposition 5.

In the presence of multiple retailers,

1. (i)

the manufacturer's optimal encroachment strategy is:

1. (a)

no encroachment ( $N$ ) if $k\ge \frac{b(2-n)}{4}$ and $s_{M1}^n\le s<min\{s_{M2}^n,{\overline{s}}^n\}$ , or if $k<\frac{b}{2}$ and $s\ge {\hat{s}}^n$ , or if $k<\frac{b}{2}$ , ${\overline{s}}^n\le s<{\overline{s}}^n$ , and $n\ge \overline{n}$ ;

(b)

encroachment with an unprofitable direct channel ( $EUD$ ) if $k<\frac{b}{2}$ , $max\{s_{M2}^n,s_{M3}^n\}\le s<{\overline{s}}^n$ , and $n<\overline{n}$ ;

(c)

encroachment as a threat with no direct sales ( $END$ ) if $k<\frac{b}{2}$ and $max\{{\overline{s}}^n,{\overline{s}}^n\}\le s<{\hat{s}}^n$ ;

(d)

encroachment with a profitable direct channel ( $EPD$ ) otherwise.

(ii)

a retailer benefits from manufacturer encroachment if $k<\frac{b}{2}$ , $max\{s_{R1}^n,s_{M2}^n\}\le s<{\overline{s}}^n$ , and $n<\overline{n}$ , or if $k<\frac{b}{2}$ , $max\left\{{\overline{s}}^n,{\stackrel{=}{s}}^n\right\}\le s<s_{R2}^n$ , and $n<\hat{n}$ .

Similar to Proposition 3, Proposition 5 shows that with multiple retailers, encroachment with unprofitable direct sales can emerge as an optimal strategy when $k<b/2$ (see Figure 7(a) for the case $k=b/4$ ). However, unlike in Proposition 3, when the number of downstream retailers ( $n$ ) is sufficiently large (e.g., $\overline{n}$ can be as large as 7 when $k=b/4$ ), the manufacturer has no incentive to maintain an unprofitable direct channel. The underlying reason is that an increasing number of retailers intensifies market competition and squeezes the manufacturer's profit margin from direct selling, thereby making her profit loss from direct selling more significant. It also diminishes the positive effect of wholesale price reduction (i.e., the manufacturer needs to lower the wholesale price more substantially to stimulate the retailer's order quantity as n increases), thereby reducing her profit gain from indirect selling. As a result, a sufficiently large n discourages the manufacturer from encroaching with unprofitable direct sales, leading her to switch to a no-encroachment strategy.

Figure 7.

Manufacturer's encroachment decision and its impact on a retailer ( $k=b/4$ ): (a) Manufacturer's encroachment strategy; (b) Impact on a retailer.

Proposition 5 also confirms that a retailer can benefit from manufacturer encroachment when $k<b/2$ . Without economies of scale, Liu et al. (2021) consider encroachment as an exogenous decision made by the manufacturer and find that when the number of retailers exceeds four, intensified internal competition always makes the retailer worse off under manufacturer encroachment. Here, we demonstrate that with economies of scale, the bright side of manufacturer encroachment for the retailer also disappears when n is sufficiently large ( $n\ge \overline{n}$ for $q_M^{En}>0$ and $n\ge \hat{n}$ for $q_M^{En}=0$ ), as illustrated in Figure 7(b). However, the primary reason behind our result is that the manufacturer prefers not to encroach when n is sufficiently large. Additionally, both $\overline{n}$ and $\hat{n}$ increase with k, suggesting that an increase in k can mitigate the negative impact of intensified internal competition induced by a larger n on a retailer.

7.2. Imperfect Product Substitutes

We consider an extension where the products sold through the two channels are imperfect substitutes for consumers. All thresholds and proofs for this section are given in the online Appendix C.

In the encroachment setting, the inverse demand functions for the two channels are

$$\begin{array}{r}{p}_R=a-b{q}_R-\theta b{q}_M\text{and}{p}_M=a-b{q}_M-\theta b{q}_R,\end{array}$$

(8)

where $\theta \in (0,1)$ represents the degree of substitution between the products across the two channels. A higher $\theta$ indicates greater similarity between the products, thereby intensifying market competition. To maintain analytical tractability, we normalize $b=1$ in Equation (8) without loss of generality. The profit functions for the manufacturer and the retailer are then given by

$$\begin{array}{rl}{\pi }_M& =(a-q_M-\theta q_R-s-(c-kQ))q_M+(w-(c-kQ))q_R,\end{array}$$

(9)

$$\begin{array}{rl}{\pi }_R& =(a-q_R-\theta q_M-w)q_R.\end{array}$$

(10)

With imperfect substitutes (denoted by an additional superscript $I$ ), the equilibrium outcomes under the no-encroachment setting are given in Equation (2) with $b=1$ , while the outcomes under the encroachment setting are summarized in Table C2 in the online Appendix C. We consider

$$\begin{array}{r}k<{\overline{k}}^I=min\left\{\theta ,\frac{(3a+7c)(4-2\theta -{\theta }^2)-4c\theta -\sqrt{{((3a+7c)(4-2\theta -{\theta }^2)-4c\theta )}^2-96c(a+c)(1-\theta )(8-5{\theta }^2)}}{24(a+c)(1-\theta )}\right\}\end{array}$$

and $\frac{3a\theta }{8+\theta }<c<a-s$ to ensure a positive average unit production cost for any value of s and positive equilibrium outcomes.

In Proposition 6, we present the manufacturer's optimal encroachment strategy and its impact on the retailer (illustrated in Figure 8).

Figure 8.

Manufacturer's encroachment decision and its impact on the retailer with imperfect substitutes: (a) Manufacturer's encroachment strategy; (b) Impact on the retailer.

Proposition 6.

With imperfect substitutes,

1. (i)

the manufacturer's optimal encroachment strategy is:

1. (a)

no encroachment ( $N$ ) if $k\ge \frac{\theta }{4}$ and $s_{M1}^I\le s<s_{M2}^I$ , or if $k<\frac{\theta }{2}$ and $s\ge {\hat{s}}^I$ ;

(b)

encroachment with an unprofitable direct channel ( $EUD$ ) if $k<\frac{\theta }{2}$ and $max\{s_{M2}^I,s_{M3}^I\}\le s<{\overline{s}}^I$ ;

(c)

encroachment as a threat with no direct sales ( $END$ ) if $k<\frac{\theta }{2}$ and ${\overline{s}}^I\le s<{\hat{s}}^I$ ;

(d)

encroachment with a profitable direct channel ( $EPD$ ) otherwise.

(ii)

the retailer benefits from manufacturer encroachment if $k<\frac{\theta }{2}$ and $max\{s_{R1}^I,s_{M2}^I\}\le s<s_{R2}^I$ .

Comparing the results in Proposition 6 with those in Propositions 3 and 4 suggests that regardless of whether the products sold through the two channels are perfect or imperfect substitutes, the manufacturer's optimal encroachment strategy and its impact on the retailer's profit remain qualitatively the same. In particular, when the level of economies of scale is below a threshold ( $k<\theta /2$ ), the manufacturer can benefit from encroachment with unprofitable direct sales, as highlighted in the pink region of Figure 8(a).

Additionally, if the manufacturer encroaches by selling directly, $s_{M1}^I$ decreases with $\theta$ for $k\ge \theta /2$ , $s_{M2}^I$ decreases with $\theta$ for $\theta /4\le k<\theta /2$ , and $s_{R1}^I$ decreases with $\theta$ for $k<\theta /2$ , as illustrated in Figure 8. This suggests that as $\theta$ increases, the likelihood that the manufacturer prefers no encroachment decreases, while the likelihood that the retailer can benefit from manufacturer encroachment increases. The intuition behind this result is that when the manufacturer's unit selling cost is not too low, an increase in $\theta$ reduces her direct selling quantity, potentially making her more reliant on the more efficient retailer channel. Consequently, the quantity distortion effect arising from the interplay between manufacturer encroachment and stronger economies of scale may weaken as $\theta$ increases. Moreover, when $\theta$ is below a certain threshold, this weaker quantity distortion effect expands the region where encroachment with unprofitable direct sales is preferred as $\theta$ increases.

7.3. Price Competition

In this section, we examine an extension where the manufacturer and the retailer engage in price competition rather than quantity competition. If the manufacturer encroaches, with Equation (8) (where b is normalized to 1), the demand functions for the two channels are given by

$$\begin{array}{rl}{q}_R& =\frac{a(1-\theta )-p_R+\theta p_M}{1-{\theta }^2}\text{and}\\ q_M& =\frac{a(1-\theta )-p_M+\theta p_R}{1-{\theta }^2}.\end{array}$$

(11)

Under price competition, the equilibrium outcomes under the no-encroachment setting remain the same as in Equation (2) with $b=1$ . However, the full characterization of equilibrium outcomes under the encroachment setting and the comparison of firms’ profits are analytically intractable. Thus, we analyze the manufacturer's optimal encroachment strategy and its impact on the retailer through numerical studies.

Our numerical analysis (refer to Figure D1 in the online Appendix D) shows that under price competition, the manufacturer may prefer encroachment with an unprofitable direct channel when the degree of channel substitution ( $\theta$ ) is sufficiently low and the level of economies of scale ( $k$ ) is relatively high. Moreover, when k is not too low and the unit direct-selling cost ( $s$ ) is relatively high, no encroachment can be optimal for the manufacturer. This confirms the robustness of Proposition 3 in our main model. Unlike in the main model, where encroachment with unprofitable direct sales may occur when k is below a certain threshold, under price competition, this encroachment strategy may emerge when k is relatively high. The intuition is as follows. When the manufacturer and the retailer engage in price competition, an increase in k induces both firms to lower their selling prices, leading to increased sales in both channels. This implies that the quantity distortion effect may no longer exist under price competition. Consequently, when k is relatively high, although the manufacturer may incur a profit loss from direct selling as s increases, her profit gain from indirect selling can offset this loss, motivating her to pursue encroachment despite unprofitable direct sales. However, an increase in $\theta$ reduces the manufacturer's incentive to pursue such an encroachment strategy. As discussed in Section 7.2 on imperfect substitutes, an increase in $\theta$ may induce the manufacturer to reduce her direct selling quantity. Under price competition, this reduction in direct selling quantity is achieved by raising her selling price, thereby lowering the likelihood that she sells directly with a negative direct profit margin.

The retailer can benefit from manufacturer encroachment when direct selling is relatively costly. This result supports the robustness of Proposition 4 in the main model. Unlike in quantity competition, where an increase in k makes the retailer less likely to benefit from manufacturer encroachment, under price competition, the retailer becomes more likely to benefit as k increases. This is because, compared to quantity competition, price competition amplifies the retailer's selling advantage (Arya et al., 2007). Therefore, as k increases, the manufacturer decreases the wholesale price more substantially under encroachment compared to the case of no encroachment. This more significant wholesale price reduction can effectively boost the retailer's demand, thereby increasing the likelihood that the retailer benefits from manufacturer encroachment.

7.4. Simultaneous Quantity Decisions

Here, we explore an extension where the manufacturer and the retailer choose quantities simultaneously when the manufacturer introduces a direct channel for encroachment. The equilibrium outcomes under the encroachment setting are summarized in Table E2 in the online Appendix E.

By examining the impact of encroachment on the profits of both the manufacturer and the retailer, we find that under simultaneous quantity decisions, encroachment with an unprofitable direct channel is never optimal, and manufacturer encroachment always hurts the retailer's profit. These results differ from Propositions 3 and 4 in the main model, although the result that no encroachment can be optimal remains valid under simultaneous quantity decisions. The intuition is that, compared to a sequential game, a simultaneous game intensifies market competition resulting from manufacturer encroachment (Ha et al., 2016). This intensification amplifies the quantity distortion effect. Anticipating the retailer's reduced ordering incentive and her potential profit loss from wholesaling, the manufacturer avoids maintaining a direct channel with a negative profit margin. Consequently, encroachment with unprofitable direct sales never occurs in a simultaneous game. Moreover, as the manufacturer's unit selling cost increases, her profit gain from direct selling decreases, giving her an incentive to shift from encroachment with profitable direct sales to no encroachment. Additionally, since the retailer loses the first-mover advantage in quantity competition, he is consistently worse off under manufacturer encroachment due to the intensified market competition.

8. Conclusion

This study explores the crucial role of production economies of scale in shaping an upstream manufacturer's encroachment decision and its impact on the retailer. Our analysis suggests that an increasing level of economies of scale not only increases the likelihood that the encroaching manufacturer sells a positive quantity directly, but also makes her more dependent on the direct channel despite a selling cost disadvantage. This increased likelihood and dependence yield several interesting findings. First, we show that as the level of economies of scale increases, the profits of both the manufacturer and the retailer may decline if the manufacturer encroaches and sells directly. Second, we show that it is optimal for the manufacturer not to encroach when economies of scale are strong and the unit direct-selling cost is intermediate. This result is interesting, as it can be driven solely by the manufacturer's profit loss from direct selling. Third, we identify the conditions under which the manufacturer opts for encroachment with a profitable direct channel or encroachment as a threat. Interestingly, beyond these two well-documented encroachment outcomes, we identify a new encroachment outcome that contributes to the existing literature: When the level of economies of scale is below a threshold and the unit direct-selling cost is relatively high, encroachment with an unprofitable direct channel can be optimal for the manufacturer. Lastly, we show that an increasing level of economies of scale reduces the likelihood that the retailer can benefit from manufacturer encroachment. Thus, the bright side of manufacturer encroachment for the retailer exists only when the level of economies of scale remains below a threshold.

This study has several limitations. First, while we focus on economies of scale, diseconomies of scale may arise in certain industrial settings. In our model, diseconomies of scale correspond to the case where $k<0$ , under which encroachment with unprofitable direct sales no longer arises. Moreover, as the level of diseconomies of scale increases, the manufacturer becomes less likely to encroach and sell directly, while relying more on the use of the direct channel as a threat. Since analyzing the impact of diseconomies of scale is beyond the scope of this paper, we suggest this as an avenue for future research. Second, consumer preferences across distribution channels are not considered in our analysis. In practice, some consumers may strongly prefer the direct channel, while others favor the retailer channel. Examining how these distinct preferences interact with economies of scale could offer deeper insights into the manufacturer's encroachment strategy. Third, following the existing literature, we assume a direct-selling cost disadvantage for the manufacturer relative to the retailer. Future research could explore how relaxing this assumption might influence the manufacturer's encroachment strategy, particularly in the context of economies of scale. Finally, validating our theoretical findings with empirical data from real-world supply chains would enhance the robustness of our conclusions and provide a richer understanding of manufacturer encroachment dynamics in practice.

Supplemental Material

sj-docx-1-pao-10.1177_10591478251378836 - Supplemental material for Manufacturer Encroachment in the Presence of Production Economies of Scale

Supplemental material, sj-docx-1-pao-10.1177_10591478251378836 for Manufacturer Encroachment in the Presence of Production Economies of Scale by Wei Li, Jing Chen and Hubert Pun in Production and Operations Management