A decision-making model for echelon utilization of retired batteries in competitive duopoly: the role of government subsidy

Research related to competition in or between closed-loop supply chain

Over the past decade, numerous scholars have delved into research concerning competition within and between closed-loop supply chains. Additionally, studies have examined competition among manufacturers and retailers. For instance, Jena and Sarmah (2014) investigated the effects of various cooperation models with retailers in the context of manufacturer competition^[16]. Likewise, Liu et al. (2017) explored the interplay between channel structure and price- and quality-based competition among two manufacturers characterized by customer loyalty asymmetry^[17]. In the realm of retailer competition research, Savaskan et al. (2006) pioneered the examination of competition intensity’s influence on decision-making within the context of retailer competition in closed-loop supply chains^[18]. Similarly, Guo et al. (2020) investigated the impact of retail competition on developing green products, revealing that heightened market competition intensity leads to a lower optimal level of greenness^[19]. Zhang et al. (2023) constructed a two-period pricing game that involves two competing platforms to investigate the influence of network effects on optimal pricing strategies and profits^[20].

Numerous scholars have researched competition within the recycling sector. Liu et al. (2017) explored reverse channel choice decisions involving collection competition under three recycling options. Their findings suggest that manufacturers consistently benefit from the joint recycling mode with recyclers^[17]. In the context of echelon utilization, Tang et al. (2018) investigated mechanisms and policies under various recycling modes, including both single and competitive dual recycling channel modes^[21]. Wang et al. (2019) focused on remanufacturing space, exploring recycling competition between remanufacturers and recyclers and between recyclers and retailers^[22]. Giri and Dey (2019) addressed decision-making issues involving manufacturer-built recycling channels and traditional competition among recyclers^[23], while Wei et al. (2019) analyzed the remanufacturer's decision-making in the context of dual recycling channels^[24]. Zhou et al. (2023) investigated channel leadership and performance in a closed-loop supply chain that involves the competition among an electric vehicle manufacturer, an electric vehicle recycler, and a third-party recycler^[25]. Suvadarshini et al. (2023) studied a closed-loop supply chain consisting of an original equipment manufacturer (OEM), a retailer and a third-party vendor where the OEM designs an efficient multi-channel recollection structure when recollection agents competitively recollect used products^[26].

While competition has been explored extensively from various angles, such as customer service perspective by Boyaci and Gallego (2004)^[27], Cournot competition among supply chains considering leader position and cost structure as investigated by Majumder and Srinivasan (2008)^[28], and the influence of competition on product pricing strategy by Wang et al. (2017)^[29], relatively limited attention has been given to competition among echelon utilization enterprises. Our research breaks new ground by introducing competitive conditions into the echelon utilization domain, shedding light on its impact on decision-making within the supply chain.

While existing research has explored competition in various aspects of supply chains, including manufacturer, retailer, recycler, and supply chain competition, there has been limited investigation into the introduction of competition in echelon utilization. Furthermore, research on competition among echelon utilization enterprises is scarce. Our paper innovatively introduces the concept of competition into echelon utilization and uniquely centers on echelon utilization enterprises as the primary agents of competition.

Research related to government subsidizing the sustainable supply chain

Considerable research has examined the effects of various government subsidies on supply chains. Mitra and Webster (2008) examined the impact of government subsidies on promoting remanufacturing activities, suggesting that partial subsidies to manufacturers could be effective^[30]. Mo et al. (2009) proposed the use of recycling tax incentives as a means for government intervention, based on their field investigations^[31]. Aksen et al. (2009), meanwhile, established supportive and legislative models, discovering that the supportive model necessitates more subsidies when recycling rates and profitability are the same^[32]. In a recent study, Zhang et al. (2020) suggested strategic options that account for the effects of tax policy, subsidy policy, and tax-subsidy policy on the supply chain^[33].

In green products and innovation, Li et al. (2018) find that consumption subsidies can improve social welfare and replacement subsidies can promote environmental protection^[34]. Yi et al. (2021) also introduced a novel extended producer responsibility (EPR) system emphasizing resource conservation^[35]. They argue that a combined tax subsidy approach can optimize social welfare and foster ecological innovation. Bai et al. (2021) introduce a three-stage Stackelberg game model to find the optimal allocation of the subsidy budget among multiple products covered by the trade-in program^[12].

Bai et al. (2019) asserted that government R&D subsidies play a significant role in promoting green innovation among energy-intensive enterprises^[13], although Yu et al. (2016) reached the opposite conclusion^[36]. Chang et al. (2019) highlighted the role of the joint tax-subsidy mechanism in incentivizing ecological innovation by manufacturers^[37]. Wang et al. (2020) investigated the impact of government subsidies and altruistic preferences on decision-making in a low-carbon e-commerce closed-loop supply chain^[38]. Zhang and Yu (2022) considered mode selection and coordination in a low-carbon closed-loop supply chain under compound government subsidies from a long-term dynamic perspective^[39].

Despite the abundance of research into the mechanism of government subsidies in various industries, there has been little exploration of the role of these subsidies in battery echelon utilization and into how the government should best disburse the subsidies. A major innovation of our research is in its study of how government subsidies in echelon utilization affect the decision-making of echelon utilization enterprises.

Research related to the management of echelon utilization

The last decade has seen the emergence of a robust literature related to used battery recycling and echelon utilization.

Most recently, Lai et al. (2021) researched echelon utilization in the context of battery recycling; they systematically reviewed the echelon utilization and recycling of the retired lithium-ion batteries (LIBs) and proposed two valuable sorting methods to improve the rapidity and accuracy of the LIB sorting^[40]. While Turner and Nugent (2016) analyzed how EPR policies address problems of the environmental cost and benefits of end-of-life management in the European Union, Canada, and the United States, they argued that for such policies to be effective, they need to be extended to address waste collection practices, the life cycle consequences of EOL management, and the quality of recovered materials^[41]. Gu et al. (2017) studied the vehicle manufacturer’s decision-making problem regarding the battery recycling rate under conditions of government subsidies; they found that either subsidy or battery recycling can offset the negative effects of loss aversion on the optimal production quantity and expected utility^[42]. Gu et al. (2018) subsequently found that compared to new battery manufacturing, battery recycling and reusing would contribute to lowering raw material consumption and, hence, reducing environmental impact, but may not gain financial benefits^[43]. Zhang et al. (2020) considered the Chinese echelon utilization policy from the two perspectives of basic policy tools and the industrial chain process. They suggested that the government should increase the use of interactive impact instruments, optimize their classification, and emphasize the matching between basic policy instruments and the recycling industry chain^[6].

The above summary highlights that the present literature lacks a focus on the companies involved in echelon utilization practices. As a response, our paper focuses on the decision-making process of echelon utilization and how it can be influenced by the business environments and government subsidies. Our article is most similar to (Zhang et al. 2022). They also explored the impact of government policies and third-party recycling on echelon utilization enterprises and new energy vehicle manufacturers, but they did not examine the impact of competition among echelon utilization enterprises on the recycling of used batteries^[14]. Secondly, regarding government policies, they overlooked the impact of government subsidies on the competition between enterprises and environmental factors. Overall, our article investigates the combined effects of competition among echelon utilization enterprises and government subsidies to maximize environmental benefits on supply chain members.

Model description

This research focuses on evaluating the influence of the internal and external business environment and government subsidies on echelon utilization enterprises in a competitive setting. To achieve this, a competitive duopoly supply chain for echelon utilization is established, which comprises a new energy vehicle manufacturer, a third-party recycler, and two competing echelon utilization enterprises. The manufacturer sells new energy vehicles to consumers, and the echelon utilization enterprises entrust the third-party recycler to handle used battery recycling. The third-party recycler collects the used power batteries from customers, resells the echelon-utilizable batteries to the echelon utilization enterprise, and disposes of those excess used batteries. The echelon utilization enterprises 1 and 2 process the echelon-utilizable batteries into echelon utilization products for sale and transfer the non-echelon-utilizable power batteries and the post-echelon-utilized residues to the manufacturer for extracting raw materials.

In view of the nascent stage of echelon utilization for used new energy batteries in China, it is assumed that the number of used batteries reclaimed by recyclers exceeds the demand from the two echelon utilization enterprises. Consequently, the excess used batteries must be managed by the third-party recycler to avert potential ecological pollution. The used batteries are sold by the two echelon utilization enterprises to specialized consumers (e.g., power plants) for the initial stage of the echelon utilization process, encompassing dismantling, testing, and sorting. Subsequently, the processed used batteries are recycled and supplied to the new energy vehicle manufacturer for remanufacturing.

In this process, the new energy vehicle manufacturer holds a dominant position due to its influence on the entire process. The manufacturer determines the retail price, denoted as P for new energy vehicles. For model simplification, we assume that the actual recycling ratio and the unit recycling price of recyclers are exogenous. Consequently, the third-party recycler solely determines the wholesale price of used batteries (w), while the two echelon utilization enterprises independently establish retail prices for their respective used batteries (p₁, p₂). The specific flow chart of the model is shown in Figure 1.

Figure 1. Flow chart of new energy battery echelon utilization.

In Figure 1, the solid line illustrates the journey of new energy vehicles; a new energy vehicle manufacturer provides products to consumers at the retail price P, and the third-party recycler collects used batteries from consumers at the recycling price h. In contrast, the dotted line delineates the recycling of used batteries after the initial echelon utilization stage; the manufacturer then decides the transfer payment price F for the remanufactured materials. To simplify the model, C₁ and C₂ in Figure 1 denote the unit costs associated with echelon utilization. These costs encompass activities such as dismantling, detection, classification, and recovery, and they are contingent solely upon the echelon utilization level of each enterprise.

Model construction

Based on the descriptions in Section “Model description”, we establish the decision-making sequence for all parties within the supply chain. Initially, the new energy vehicle manufacturer determines the sales price for its vehicles. Subsequently, the third-party recycler sets the wholesale price for used batteries. Finally, the two echelon utilization firms independently establish the retail prices for their respective used batteries.

The model’s relevant symbols and the decision variables for each party are detailed in Table 1.

To align the model with real-world dynamics and facilitate the generation of meaningful results, this paper incorporates the following assumptions in the model construction, drawing inspiration from the work of Tang et al. (2018)^[21].

Assumption 1. In the model constructed in this paper, the new energy vehicle manufacturer is in the leading position, with the third-party recycler and echelon utilization enterprises being the followers. The third-party recycler makes decisions before the echelon utilization enterprises^[6,11]. This is because, based on the research of Liu et al. (2022), compared to the collector-dominated supply chain, the manufacturer can improve the product collection rate and increase the total profit in the manufacturer-dominated model. Therefore, it is reasonable to assume that manufacturers occupy a dominant position in the model^[44].

Assumption 2. All parties in the dynamic game are profit-maximizing and exhibit complete rationality while possessing full information^[6,45].

Assumption 3. Since echelon utilization is still in its initial phase in China, we assume that the demand for it is less than the actual number of batteries in need of recycling, with third-party recyclers needing to handle the resulting excess^[6]. Therefore, the relationship between the actual amount of recycling and the demand for echelon utilization services is as follows.

Assumption 4. To make the model’s conclusions more reasonable and in line with reality, there is a range of competition intensity between two echelon utilization enterprises. This constraint mainly means that the demand for a product is more sensitive to the changes in its own sale price than to the changes in the sale price of the other competitive product, which is reasonable in reality^[46].

Assumption 5. For simplicity of representation, our model uses a linear function to express market demand for new energy vehicles and echelon utilization^[5,6,45].

Assumption 6. To facilitate calculation and highlight the focus of our research, we assume that the third-party recycler chooses the reasonable recycling ratio and the unit recycling price according to their actual situation and experience. In other words, θ and h are exogenous. The third-party recycler also provides one uniformly wholesale price of used batteries for two echelon utilization enterprises. Simultaneously, both echelon utilization enterprises are privy to this pricing information. Consequently, the actual amount of recycling can thus be expressed as^[6,8]

This study follows the aforementioned assumptions and employs a literature review approach, drawing insights from previous research and model construction. We utilize the backward induction method within a dynamic game with complete information to derive the decision-making process and relevant parameters at equilibrium. Subsequently, we apply sensitivity analysis and numerical experiments to explore the influence of the supply chain's internal dynamics. Lastly, we analyze the effects of government subsidies and offer managerial recommendations.

The equilibrium situation without government subsidies

The equilibrium situation without government subsidies is provided in Proposition 1.

Proposition 1. The equilibrium situations of the game without government subsidies are:

Proof. See the Supplementary Materials.

By substituting the optimal decision variables P^*, F^*, w^*, p₁^*, and p₂^* into the defined functions of each variable, we get the actual market demand for new energy vehicles Q^* = 1/2(a − bC_m) and the actual recycling amount of used batteries G^* = 1/2θ(a − bC_m). Based on these variables, we can get the demand of the two echelons of utilization and the profit of each member of the supply chain at this time. Because the formula is too complicated, we will not show it here, and readers can see it in Supplementary Table 1.

From Proposition 1, two corollaries can be derived. Corollary 1 evaluates how unit echelon utilization costs affect the optimal decision variables related to echelon utilization products. This analysis offers insights into whether echelon utilization enterprises should adjust their retail prices, whether the third-party recycler should modify wholesale prices for used batteries, and whether the new energy vehicle manufacturer should change transfer payments in response to fluctuations in unit echelon utilization costs.

Corollary 1. The influence of the total unit cost of echelon utilization on the optimal decision variables related to echelon utilization products is given in Table 2.

Proof. See the Supplementary Materials.

Table 2 reveals several significant findings. First, it demonstrates that when the costs of one echelon utilization enterprises increase, the competitor tends to lower their retail prices to capture a larger market share. Conversely, when the costs of one echelon utilization enterprises decrease, the competitor tends to raise retail prices to safeguard their profits. This result can be explained as follows: Increased costs signifies a weaker competitive position, allowing competitors to raise their retail prices of echelon utilization products while maintaining a competitive edge.

Second, as the unit cost of echelon utilization increases, the wholesale price of used batteries for the third-party recycler will decrease. This shows that as its unit cost rises, the third-party recycler tends to reduce the price, benefitting the echelon utilization industry by ensuring market demand. When the unit cost of echelon utilization services declines, the third-party recycler tends to protect their interests by raising their retail prices.

Third, the effect of echelon utilization costs on transfer payments for remanufactured materials can be derived and represented in Figure 2, where we let a = 3,000, b = 1.6, C_m = 800, C_r = 600, C₀ = 3, θ = 0.8, e = 100,β = 2, h = 100, and γ = 0.8. According to Figure 2, as the cost of echelon utilization escalates, the new energy vehicle manufacturer will elevate the transfer payments to ease the pressure on echelon utilization enterprises. The new energy vehicle manufacturer hopes to maintain demand in the echelon utilization market, thereby stabilizing the resource of remanufactured materials. It should be noted here that the setting of this and subsequent parameters are obtained by partly referring to the research of Tang et al. (2019) and satisfying the basic constraints of the model^[15].

Figure 2. Impact of costs on transfer payments.

Corollary 2 evaluates the impact of unit echelon utilization costs on the optimal profits of two echelon utilization enterprises.

Corollary 2. The profits earned by echelon utilization firms vary according to their operating costs, expressed as follows.

(1) When C₁ < C₁^*, π₁^* decreases with the increase of C₁; When C₁ > C₁^*, π₁^* increases with C₁.
(2) When C₂ < C₂^*, π₁^* decreases with the increase of C₂; When C₂ > C₂^*, π₁^* increases with C₂.
(3) When C₁ < C₃^*, π₂^* decreases with the increase of C₁; When C₁ > C₃^*, π₂^* increases with C₁.
(4) When C₂ < C₄^*, π₂^* decreases with the increase of C₂; When C₂ > C₄^*, π₂^* increases with C₂.

In which C_i^*, i = 1, 2, 3, and 4 are defined below.

Proof. See the Supplementary Materials.

Corollary 2 explores how changes in the unit cost of echelon utilization impact the profits of echelon utilization enterprises. It shows that as echelon utilization costs increase, profits earned by the echelon utilization firms always decrease first and then increase later. This is because the change in cost affects both the retail price and the number of echelon utilization products. In the actual situation, considering the non-negativity of demand, price, and cost, these profits tend to change monotonically with the changes of C₁ and C₂, that is, monotonically increasing or decreasing.

The equilibrium situation with government subsidies

According to the relevant proof method in Proposition 1, we can obtain the equilibrium situations with government subsidies as given in Proposition 2.

Proposition 2. The equilibrium situations of the game with government subsidies are:

Proof. Similar to the proof of Proposition 1.

By substituting the optimal decision variables P^S*, F^S*, w^s*, p₁^S*, and p₂^S* into the defined functions of each variable, we get the actual market demand for new energy vehicles Q^S* = 1/2(a − bC_m) and the actual recycling amount of used batteries G^S* = 1/2θ(a − bC_m). As before, we again do not show the demand of the echelon utilization firm and the profit of each member of the supply chain, and readers can see it in Supplementary Table 2.

From Proposition 2, some corollaries can be derived. Corollary 3 assesses the impact of government subsidy on the optimal decision variables related to echelon utilization products. This analysis offers insights into whether echelon utilization enterprises should adjust their retail prices, whether the third-party recycler should modify wholesale prices for used batteries, and whether the new energy vehicle manufacturer should change transfer payments in response to government subsidy changes.

Corollary 3. The influence of the government subsidy (S) on the optimal decision variables related to echelon utilization products is presented in Table 3.

Proof. See the Supplementary Materials.

Table 3 indicates several important findings. First, as government subsidies increase, the subsidized echelon utilization firm 1 will reduce its retail price, while unsubsidized firm 2 will raise it. This indicates that the more government subsidies, the more the subsidized enterprises will lower their retail prices to stimulate demand in the echelon utilization market. Conversely, unsubsidized firms raise their prices to protect their profits.

Second, the wholesale price of used batteries from third-party recyclers increases with government subsidies. This suggests that these third-party recyclers will raise their price in the hopes of earning some dividends from the increased subsidies.

Third, the new energy vehicle manufacturer similarly seeks to benefit from the subsidies. The impact of government subsidies on transfer payments is illustrated in Figure 3. We set a = 3,000, b = 1.6, C_m = 800, C_r = 600,C₀ = 3, θ = 0.8, e = 100, β = 2, h = 100, and γ = 0.8, C₁ = 9, C₂ = 5 in Figure 3. With the gradual increase in government subsidies, the new energy vehicle manufacturer will pay lower transfer payments.

Figure 3. Impact of government subsidies on transfer payments.

The following Corollary 4 can be obtained by a sensitivity analysis of the equilibrium situation obtained in Proposition 2.

Corollary 4. The profits earned by the echelon utilization enterprises change with government subsidies as follows.

(1) When S < S₁^*, π₁^S* decreases with the increase of government subsidies S; When S > S₁^*, π₁^S* increases with the government subsidies S.
(2) When S < S₂^*, π₂^S* decreases with the increase of government subsidies S; When S > S₂^*, π₂^S* increases with the government subsidies S.

In which S_i^*, i = 1, 2, are defined below.

Proof. See the Supplementary Materials.

Corollary 4 evaluates the impact of government subsidy on the optimal profits of two echelon utilization enterprises. It shows that as government subsidies rise, industry profits always decrease first and then increase later because the subsidies affect not only the price of echelon utilization products but also the demand for them. In the actual situation, considering the non-negativity of demand, price, cost, and government subsidies, echelon utilization company profits tend to change monotonically with the S variations, that is, monotonically increasing or decreasing.

Influence of competition intensity on echelon utilization

This section considers the effect of competition intensity on echelon utilization enterprises and third-party recyclers in the absence of subsidies. By referring to relevant literature and meeting the constraints of the model, we set a = 3,000, b = 1.6, C_m = 800, C_r = 600, C₀ = 3, C₁ = 9, C₂ = 5, θ = 0.8, e = 100, β = 2, h = 100 and substitute them in Proposition 1 to get Figures 4-6. Observation 1 can be drawn from the three Figures.

Figure 4. Influence of competitive intensity on profits.

Figure 5. Influence of competitive intensity on demand.

Figure 6. Influence of competitive intensity on retail price.

Observation 1. With the increase in competition intensity (γ), echelon utilization firms will raise retail prices (p₁, p₂), leading to a decline in demand for their products and then in company profits. At the same time, third-party recycler profits will rise in proportion to the competition intensity- the higher it is, the faster profits will rise.

Figures 4-6 and Observation 1 show that: (1) According to Figure 4, since we assume that the cost of enterprise 1 is higher than that of enterprise 2, it is reasonable for enterprise 2 to have higher profits under the same competition intensity; (2) According to Figure 5, we find that with the increase of competition intensity, the demand of both firm 1 and Firm 2 continues to decline. This is because the increasing intensity of competition makes enterprises increase the retail price of products excessively, which leads to consumers becoming less and less willing to buy their products and ultimately results in a lose-lose situation; (3) Finally, based on Figure 4, we can find that the profits of third-party recycling enterprises are on the rise with the competition intensity. On the one hand, due to the fierce competition, the retail price of products keeps rising, enabling the third-party recycling enterprises to charge higher wholesale prices to obtain higher profits. On the other hand, the fierce competition makes both enterprises want to obtain more products from third-party enterprises to increase their competitive advantage, which invisibly gives third-party recycling enterprises greater bargaining power.

Influence of echelon utilization costs on the supply chain

This section investigates the influence of echelon utilization costs on the entire supply chain in the absence of government subsidies. We set π^* = π_m^* + π_r^* + π₁^* + π₂^* to represent the total profit of the supply chain, with the numerical settings in this section consistent with those in Section “Influence of competition intensity on echelon utilization”. It should be noted that we set that γ = 0.8, with the result of the numerical experiment shown in Figure 7, from which Observation 2 can be drawn.

Figure 7. Influence of costs on profits in the supply chain.

Observation 2. The total profit of the supply chain (π^*) will diminish as the echelon utilization costs (C₁, C₂) of both echelon utilization firms increase. In general, excessive echelon utilization costs will hurt the overall supply chain.

Figure 7 and Observation 2 demonstrate that, from the standpoint of the overall supply chain, it is logical that an increase in the echelon utilization cost of any echelon utilization enterprise under competition will decrease the total profit of the supply chain. Hence, even within a competitive environment, echelon utilization enterprises with superior echelon utilization capabilities, meaning lower echelon utilization costs, should be preferred for cooperation.

Influence of government subsidies on echelon utilization enterprises

This section discusses the influence of government subsidies on market demand, retail price, and echelon utilization enterprise profits, with numerical settings consistent with those in Section “Influence of competition intensity on echelon utilization”. For the convenience of expression, we set the additional demand after government subsidies as ΔT₁ = T₁^S* − T₁^*, ΔT₂ = T₂^S* − T₂^*, set the changes in the retail prices of echelon utilization products as Δp₁ = p₁^S* − p₁^*, Δp₂ = p₂^S* − p₂^*, and set the competing firms’ additional profits as Δπ₁ = π₁^S* − π₁^*, Δπ₂ = π₂^S* − π₂^*. The results of the numerical experiments are presented in Figures 8-10. According to these figures, we can get the corresponding Observations 3-5.

Figure 8. Impact of government subsidies on additional demand.

Figure 9. Impact of government subsidies on changes in retail price.

Figure 10. Impact of government subsidies on additional profits.

Observation 3. Government subsidies will increase demand for the subsidized echelon utilization firm and reduce demand for the unsubsidized firm, but the overall demand will increase. In other words, ΔT₁ increases with the government subsidies, and ΔT₂ decreases as subsidies increase.

Observation 3 shows that government subsidies do affect competition such that the subsidized firm will increase market demand and gain market share while the unsubsidized firm will lose it. Yet, from the perspective of the entire market, government subsidies are beneficial overall because they can increase total demand and promote the development of the echelon utilization industry. Even subsidizing the firm with the higher costs will also increase total demand. When taken together with Observation 2, it becomes clear that the government should prioritize offering subsidies to the firm with the lower echelon utilization costs, so that the echelon utilization market can be further regulated and accelerated.

Observation 4. Government subsidies will cause the recipient enterprise to lower its retail price, but will also lead its unsubsidized competitor to raise its retail price, with the resulting price decrease greater than the increase. Or, written another way, Δp₁ decreases as government subsidies increase, and Δp₂ increases with the subsidies.

Observation 4 shows that government subsidies can significantly affect the retail prices of echelon utilization competitors, with the subsidized echelon enterprise reducing its price to benefit consumers, while the unsubsidized one increases its own in order to maintain its profits. For the unsubsidized firm, government subsidies relax its willingness to compete and put it at a competitive disadvantage. From the perspective of the subsidized firm, government subsidies increase its willingness to compete but can also ultimately benefit consumers. This once again shows that when the government selects subjects for its subsidy policies, it should select the enterprises with the strongest capabilities, as determined by a thorough investigation. Doing so can optimize consumer benefit, thereby promoting the development of the industry efficiently.

Observation 5. Government subsidies will lead to higher profits for the recipient echelon utilization firm but reduced profits for the unsubsidized one, causing total market revenue to rise. Or, Δπ₁ increases with the government subsidies, and Δπ₂ decreases as subsidies increase.

Observation 5 shows that government subsidies can significantly affect the potential of echelon utilization competitors to earn additional profits. The subsidy recipient will obtain obvious additional profits, and the greater the subsidies, the faster the growth rate. At the same time, the unsubsidized firm will suffer additional losses, but the growth rate will gradually slow down as subsidies increase. When looking at the whole market, it becomes clear that subsidies can increase the total profit and play an important role in promoting development. Similar to the suggestions mentioned in Observations 4 and 5, Figure 10 further illustrates that the government should be cautious from the perspective of industry profits when selecting subject firms to receive subsidies.