As the global energy landscape faces uncertainties from geopolitical conflicts and rising demand, the electric vehicle (EV) industry has emerged as a pivotal solution to reduce fossil fuel dependence and mitigate environmental pollution. In China, the rapid adoption of electric vehicles, exemplified by companies like BYD, has positioned the nation as a leader in the “new three” export industries. However, the surge in EV production brings forth the challenge of managing end-of-life power batteries, which pose environmental risks if not properly recycled. With an estimated 200,000 tons of power batteries reaching end-of-life in 2020 and projections of 780,000 tons by 2025, effective recycling mechanisms are critical. Government subsidies, whether for production or recycling, play a crucial role in shaping the operational decisions within the EV supply chain. In this article, I explore how different subsidy scenarios—production subsidies based on demand, recycling subsidies based on quantity, and recycling subsidies based on battery capacity—impact the decisions of stakeholders, including battery suppliers, EV manufacturers, and third-party recyclers (3PRs). Using a Stackelberg game model, I analyze equilibrium decisions, profits, and social welfare, while also examining extensions such as manufacturer leadership and supply chain integration. The findings offer insights for policymakers and enterprises in optimizing subsidy policies to enhance sustainability and economic efficiency in the China EV market.
Introduction to the Electric Vehicle Supply Chain and Subsidy Context
The electric vehicle industry in China has experienced exponential growth, driven by government initiatives and consumer demand for eco-friendly transportation. However, the lifecycle of EV power batteries, typically lasting 5–8 years, necessitates efficient recycling systems to prevent environmental hazards and resource wastage. Current recycling rates for electric vehicle batteries remain low, around 20%, due to high costs associated with testing and disassembly. To address this, governments have implemented various subsidies, such as production subsidies per vehicle or recycling subsidies per unit or per battery capacity. For instance, Shanghai offers a recycling subsidy of 1,000 yuan per battery, while Hefei provides up to 20 yuan per kilowatt-hour based on capacity. These policies aim to incentivize recycling and promote a circular economy in the electric vehicle sector. In this study, I model a supply chain comprising a battery supplier, an EV manufacturer, a 3PR, and consumers, analyzing how subsidies influence key decisions like pricing, battery capacity, and recycling efforts. The goal is to compare the effects of these subsidies on operational outcomes and social welfare, providing actionable recommendations for stakeholders in the China EV ecosystem.
Literature Review on Electric Vehicle Battery Recycling and Subsidies
Previous research on electric vehicle battery recycling has focused on frameworks and channel strategies. For example, studies have examined collaborative recycling models that reduce costs and increase participation among consumers. Others have investigated joint recycling strategies, such as deposit-refund systems, which enhance recovery rates. In terms of subsidies, existing literature often emphasizes recycling subsidies but overlooks production subsidies. For instance, some works analyze how subsidies impact closed-loop supply chains, showing that recycling subsidies can boost recovery rates and recycler profits. However, few studies integrate both production and recycling subsidies while considering battery-specific attributes like capacity. Table 1 summarizes key comparisons with prior research, highlighting the novelty of this article in addressing multiple subsidy types and their effects on social welfare in the context of China’s electric vehicle industry.
| Literature | Subsidy Types | Social Welfare Consideration | Key Findings |
|---|---|---|---|
| Fang et al. (2024) | Fixed recycling cost subsidy | Yes | Optimal reverse channel selection and subsidy impact on welfare |
| Zhang et al. (2023) | Recycling subsidy | No | Carbon emission reduction and recycling mode selection |
| Gu et al. (2021) | Recycling subsidy | Yes | Conditions for government subsidies in battery reuse |
| This article | Production and recycling subsidies | Yes | Comprehensive analysis of operational decisions and welfare under differentiated subsidies |
Model Description and Assumptions
I consider a supply chain for electric vehicles consisting of a power battery supplier, an EV manufacturer, a third-party recycler (3PR), and consumers. The battery supplier produces batteries with capacity \( h \), which are sold to the EV manufacturer at wholesale price \( w \). The manufacturer then produces EVs and sells them to consumers at retail price \( p \). The 3PR collects used batteries through recycling efforts \( e \) and sets a recycling fee \( p_r \). Government subsidies are introduced in three scenarios: production subsidy per demand unit \( s_d \), recycling subsidy per quantity unit \( s_q \), and recycling subsidy per battery capacity unit \( s_h \). The demand function for EVs is given by \( D = \alpha – \beta p + k h \), where \( \alpha \) is the potential market size, \( \beta \) is the price sensitivity, and \( k \) represents consumer preference for battery capacity. The battery研发 cost is \( C_h = \frac{k_h h^2}{2} \), with \( k_h \) as the研发 cost coefficient. The recycling quantity is \( Q = Q_0 + \lambda p_r + \gamma e \), where \( Q_0 \) is the base recycling quantity, and \( \lambda \) and \( \gamma \) are sensitivity coefficients. The recycling effort cost is \( C_e = \frac{k_e e^2}{2} \), with \( k_e \) as the cost coefficient. Key assumptions include \( b > p_r \) to ensure recycling motivation, and constraints like \( Q \leq D \) for feasibility. The profit functions for each stakeholder under the three subsidy scenarios are as follows:
- Production Subsidy (D):
$$ \pi_S^D = (w – c_m – m + s_d) D – b Q – C_h $$
$$ \pi_M^D = (p – w – c_n) D $$
$$ \pi_{3PR}^D = (b – p_r) Q – C_e $$ - Recycling Subsidy per Quantity (Q):
$$ \pi_S^Q = (w – c_m – m) D – b Q – C_h $$
$$ \pi_M^Q = (p – w – c_n) D $$
$$ \pi_{3PR}^Q = (b – p_r + s_q) Q – C_e $$ - Recycling Subsidy per Capacity (B):
$$ \pi_S^B = (w – c_m – m) D – b Q – C_h $$
$$ \pi_M^B = (p – w – c_n) D $$
$$ \pi_{3PR}^B = (b – p_r + s_h h) Q – C_e $$
The game sequence follows a Stackelberg structure: the battery supplier sets \( w \) and \( h \), the EV manufacturer sets \( p \), and the 3PR sets \( e \) and \( p_r \). Social welfare \( SW \) is defined as the sum of total supply chain profit \( \pi \), consumer surplus \( CS \), and minus government subsidy expenditure \( GS \). For example, under production subsidy, \( SW^D = \pi_S^D + \pi_M^D + \pi_{3PR}^D + CS – s_d D \), where \( CS = \frac{(p_1 – p) D}{2} \) and \( p_1 = \frac{\alpha + k h}{\beta} \).
Equilibrium Decisions and Comparative Analysis
Using backward induction, I derive the equilibrium decisions for each subsidy scenario. The results are summarized in Table 2, which includes optimal values for wholesale price, battery capacity, retail price, recycling effort, and recycling fee. For instance, under production subsidy, the optimal battery capacity is \( h^{D*} = \frac{k (B + s_d \beta)}{M} \), where \( M = 4\beta k_h – k^2 \) and \( B = \alpha – (c_n + c_m + m)\beta \). Similarly, demand and recycling quantities are derived, such as \( D^{D*} = \frac{\beta k_h (B + s_d \beta)}{M} \) for production subsidy. The analysis reveals that higher battery研发 cost coefficients \( k_h \) or lower consumer preference \( k \) reduce manufacturer profits and demand across all subsidy scenarios. This underscores the need for China EV manufacturers to balance battery innovation with cost efficiency.
| Variable | Production Subsidy (D) | Recycling Subsidy per Quantity (Q) | Recycling Subsidy per Capacity (B) |
|---|---|---|---|
| Wholesale Price \( w^* \) | \( \frac{2(A – s_d \beta) k_h – (c_m + m – s_d) k^2}{M} \) | \( \frac{2A k_h – (c_m + m) k^2}{M} \) | \( \frac{2A k_h – (c_m + m) k^2}{M} \) |
| Battery Capacity \( h^* \) | \( \frac{k (B + s_d \beta)}{M} \) | \( \frac{k B}{M} \) | \( \frac{k B}{M} \) |
| Retail Price \( p^* \) | \( \frac{\alpha + k h^{D*} + \beta (c_n + w^{D*})}{2\beta} \) | \( \frac{\alpha + k h^{Q*} + \beta (c_n + w^{Q*})}{2\beta} \) | \( \frac{\alpha + k h^{B*} + \beta (c_n + w^{B*})}{2\beta} \) |
| Recycling Effort \( e^* \) | \( \frac{\gamma (Q_0 + b \lambda)}{N} \) | \( \frac{\gamma [Q_0 + (b + s_q) \lambda]}{N} \) | \( \frac{\gamma [Q_0 + (b + s_h h^{B*}) \lambda]}{N} \) |
| Recycling Fee \( p_r^* \) | \( b – \frac{(Q_0 + b \lambda) k_e}{N} \) | \( b + s_q – \frac{[Q_0 + (b + s_q) \lambda] k_e}{N} \) | \( b + s_h h^{B*} – \frac{[Q_0 + (b + s_h h^{B*}) \lambda] k_e}{N} \) |
Where \( A = \alpha – (c_n – c_m – m)\beta \), \( N = 2\lambda k_e – \gamma^2 \), and conditions like \( \gamma < \sqrt{\lambda k_e} \) and \( k < 2\sqrt{\beta k_h} \) ensure unique equilibrium solutions. Propositions derived from sensitivity analysis include:
- Proposition 1: Production subsidies enhance battery capacity (\( h^{D*} > h^{Q*} = h^{B*} \)), while recycling subsidies improve recycling effort and fees (\( e^{D*} < \min\{e^{Q*}, e^{B*}\} \) and \( p_r^{D*} < \min\{p_r^{Q*}, p_r^{B*}\} \)). The comparison between recycling subsidies depends on \( s_q \) and \( s_h \).
- Proposition 2: Production subsidies boost demand and manufacturer-supplier profits (\( D^{D*} > D^{Q*} = D^{B*} \), \( \pi_M^{D*} > \pi_M^{Q*} = \pi_M^{B*} \), and \( \pi_S^{D*} > \max\{\pi_S^{Q*}, \pi_S^{B*}\} \)), whereas recycling subsidies increase recycling quantity and 3PR profits (\( Q^{D*} < \min\{Q^{Q*}, Q^{B*}\} \) and \( \pi_{3PR}^{D*} < \min\{\pi_{3PR}^{Q*}, \pi_{3PR}^{B*}\} \)).
These findings highlight that production subsidies directly benefit upstream stakeholders in the electric vehicle supply chain, while recycling subsidies favor recyclers. For China EV policymakers, this suggests that subsidy design should align with broader goals, such as promoting innovation or enhancing circularity.
Social Welfare Analysis and Numerical Simulations
To evaluate the impact of subsidies on social welfare, I conduct numerical simulations using parameters reflective of the China EV market. Default values include \( m = 0.38 \), \( c_m = 0.43 \), \( c_n = 0.86 \), \( b = 0.45 \), \( \alpha = 2.5 \), \( k = 0.52 \), \( k_e = 1.30 \), \( Q_0 = 0.14 \), \( \lambda = 0.40 \), \( k_h = 0.48 \), \( \gamma = 0.11 \), and \( \beta \in [0.4, 0.8] \). Subsidy values are varied: \( s_d = \{-0.4, 0, 0.4\} \) (representing tax, no intervention, and subsidy), \( s_q = 0.60 \), and \( s_h = 0.45 \). Social welfare is computed as \( SW = \pi + CS – GS \), and results are plotted against price sensitivity \( \beta \).
The simulations show that as \( \beta \) increases, social welfare declines across all subsidy scenarios due to reduced consumer demand and higher price sensitivity. For example, when \( s_d = -0.4 \) (taxation), social welfare is lower than under recycling subsidies, indicating that taxes can deter economic activity. In contrast, as \( s_d \) increases to 0.4 (subsidy), social welfare under production subsidy surpasses that of recycling subsidies, emphasizing the role of production incentives in maximizing overall welfare. This aligns with the growth trajectory of the electric vehicle industry in China, where subsidies have historically driven adoption and innovation.
Extended Models: Manufacturer Leadership and Supply Chain Integration
I extend the analysis to two additional scenarios: (1) the EV manufacturer acts as the Stackelberg leader, and (2) the manufacturer merges with the supplier by paying a fee \( F \). In the first extension, the profit functions are adjusted to reflect the manufacturer’s leadership, and equilibrium decisions are derived. The results show that manufacturer leadership increases its own profit (\( \pi_M^{N*} > \pi_M^{N} \)) and can enhance supplier profit and social welfare when consumer preference for battery capacity is high (\( \frac{4k_h \beta}{3} < k < 2\sqrt{k_h \beta} \)). This suggests that in the China EV market, manufacturers with strong brand influence could lead the supply chain to mutual benefit.
In the second extension, the centralized supply chain profit is \( \pi_{MF}^N = (p – c_n – c_m – m) D – b Q – C_h \). The merger is beneficial only if the integration cost \( F \) is below a threshold \( \hat{F} = \frac{2k_h^3 \beta^2 B^2}{M^2 (2\beta k_h – k^2)} \). Otherwise, the decentralized supply chain remains preferable. This highlights the importance of cost-benefit analysis in supply chain consolidation for electric vehicle companies.
Conclusion and Implications for the Electric Vehicle Industry
In summary, this study demonstrates that government subsidies significantly influence operational decisions in the electric vehicle power battery supply chain. Production subsidies enhance battery capacity, demand, and manufacturer-supplier profits, while recycling subsidies improve recycling efforts and 3PR profitability. Social welfare is maximized under production subsidies, especially as subsidy levels increase. The extended models reveal that manufacturer leadership and strategic mergers can further optimize outcomes under specific conditions. For policymakers in China, these insights advocate for tailored subsidy policies that balance production and recycling incentives to foster a sustainable EV ecosystem. Enterprises should focus on R&D efficiency and consumer preferences to leverage subsidies effectively. Future research could explore dynamic subsidy mechanisms or incorporate consumer behavior models to refine these findings for the evolving electric vehicle market.
References
- Fang, L., Li, Y. L., & Govindan, K. (2024). Entry mode selection for a new entrant of the electric vehicle automaker. European Journal of Operational Research.
- Gu, X. Y., Zhou, L., Huang, H. F., Shi, X. T., & Ieromonachou, P. (2021). Electric vehicle battery secondary use under government subsidy: A closed-loop supply chain perspective. International Journal of Production Economics.
- Zhang, C., Tian, Y. T., & Han, M. H. (2022). Recycling mode selection and carbon emission reduction decisions for a multi-channel closed-loop supply chain of electric vehicle power battery under cap-and-trade policy. Journal of Cleaner Production.