As the landscape of sustainable transportation evolves, new energy electric vehicles (EVs) have emerged as a pivotal solution to mitigate environmental degradation and energy scarcity. Central to this transition is the management of power batteries, whose lifecycle dynamics—from production to recycling—pose significant challenges for supply chain efficiency and environmental sustainability. This research delves into the operational decisions governing EV power batteries under varying government subsidy scenarios, aiming to unravel how production and recycling subsidies influence supply chain strategies, firm profits, and social welfare.
1. Research Context and Objectives
The proliferation of electric vehicles has been accompanied by a surge in end-of-life power batteries. By 2025, an estimated 780,000 tons of power batteries are projected to enter the recycling phase, highlighting the urgency of effective management strategies . Governments worldwide have intervened with subsidy policies to address this challenge, yet the differential impacts of production versus recycling subsidies on supply chain stakeholders remain underexplored.
This study employs a Stackelberg game model to analyze three subsidy scenarios:
- Production subsidy based on demand volume (D)
- Recycling subsidy based on recycled quantity (Q)
- Recycling subsidy based on recycled battery capacity (B)
The core objectives are to:
- Compare how each subsidy type influences battery capacity, recycling efforts, and market demand
- Evaluate the profit implications for suppliers, manufacturers, and third-party recyclers (3PR)
- Assess the social welfare outcomes across scenarios
2. Model Framework and Assumptions
2.1 System Description
The model constructs a supply chain comprising:
- Power battery suppliers
- EV manufacturers
- Third-party power battery recyclers (3PR)
- Consumers
The forward supply chain involves supplier production of batteries, manufacturer integration into EVs, and consumer purchase. The reverse supply chain entails 3PR recycling of used batteries, which are then repurposed by suppliers .
2.2 Key Assumptions
- Demand Function:\(D = \alpha – \beta p + k h\) where \(\alpha\) is market potential, \(\beta\) is price sensitivity, p is retail price, k is consumer preference for battery capacity, and h is battery capacity .
- R&D Cost:\(C_h = \frac{k_h h^2}{2}\) with \(k_h\) as the R&D cost coefficient .
- Recycling Quantity Function:\(Q = Q_0 + \lambda p_r + \gamma e\) where \(Q_0\) is baseline recycling quantity, \(\lambda\) and \(\gamma\) are influence coefficients, \(p_r\) is the recycling price, and e is recycling effort .
- Recycling Effort Cost:\(C_e = \frac{k_e e^2}{2}\) with \(k_e\) as the effort cost coefficient .
3. Subsidy Scenarios and Profit Functions
3.1 Production Subsidy (D)
- Supplier Profit:\(\pi_S^D = (w – c_m – m + s_d) \cdot D – b \cdot Q – C_h\)
- Manufacturer Profit:\(\pi_M^D = (p – w – c_n) \cdot D\)
- 3PR Profit:\(\pi_{3PR}^D = (b – p_r) \cdot Q – C_e\) where \(s_d\) is the per-unit production subsidy, w is the wholesale price, \(c_m\) and \(c_n\) are production costs, m is raw material cost, and b is the supplier’s buyback price .
3.2 Recycling Subsidy by Quantity (Q)
- Supplier Profit:\(\pi_S^Q = (w – c_m – m) \cdot D – b \cdot Q – C_h\)
- Manufacturer Profit:\(\pi_M^Q = (p – w – c_n) \cdot D\)
- 3PR Profit:\(\pi_{3PR}^Q = (b – p_r + s_q) \cdot Q – C_e\) where \(s_q\) is the per-unit recycling quantity subsidy .
3.3 Recycling Subsidy by Capacity (B)
- Supplier Profit:\(\pi_S^B = (w – c_m – m) \cdot D – b \cdot Q – C_h\)
- Manufacturer Profit:\(\pi_M^B = (p – w – c_n) \cdot D\)
- 3PR Profit:\(\pi_{3PR}^B = (b – p_r + s_h h) \cdot Q – C_e\) where \(s_h\) is the per-unit recycling capacity subsidy .
4. Equilibrium Analysis and Key Findings
4.1 Equilibrium Solutions
The equilibrium decisions under each subsidy scenario are derived using backward induction, summarized in Table 1.
| Variable | Production Subsidy (D) | Recycling Subsidy (Q) | Recycling Subsidy (B) |
|---|---|---|---|
| Battery Capacity (\(h^*\)) | \(h_D^* = \frac{k(B + s_d \beta)}{M}\) | \(h_Q^* = \frac{kB}{M}\) | \(h_B^* = \frac{kB}{M}\) |
| Wholesale Price (\(w^*\)) | \(w_D^* = \frac{2(A – s_d \beta)k_h – (c_m + m – s_d)k}{M}\) | \(w_Q^* = \frac{2Ak_h – (c_m + m)k}{M}\) | \(w_B^* = \frac{2Ak_h – (c_m + m)k}{M}\) |
| Retail Price (\(p^*\)) | \(p_D^* = \frac{\alpha + kh_D^* + \beta(c_n + w_D^*)}{2\beta}\) | \(p_Q^* = \frac{\alpha + kh_Q^* + \beta(c_n + w_Q^*)}{2\beta}\) | \(p_B^* = \frac{\alpha + kh_B^* + \beta(c_n + w_B^*)}{2\beta}\) |
| Recycling Effort (\(e^*\)) | \(e_D^* = \frac{\gamma(Q_0 + b\lambda)}{N}\) | \(e_Q^* = \frac{\gamma[Q_0 + (b + s_q)\lambda]}{N}\) | \(e_B^* = \frac{\gamma[Q_0 + (b + s_h h_B^*)\lambda]}{N}\) |
Table 1: Equilibrium Decisions Under Different Subsidy Scenarios Note: \(M = 4\beta k_h – k^2\), \(N = 2\lambda k_e – \gamma^2\), \(A = \alpha – (c_n – c_m – m)\beta\), \(B = \alpha – (c_n + c_m + m)\beta\) .
4.2 Sensitivity Analysis
Corollary 1
- Higher battery R&D cost coefficient (\(k_h\)) decreases manufacturer profits and consumer demand.
- Higher consumer preference for battery capacity (k) increases profits and demand .
Corollary 2
- Recycling quantity and 3PR profits are positively related to baseline recycling quantity (\(Q_0\)) and recycling effort coefficient (\(\gamma\)).
- When recycling cost influence coefficient (\(\lambda\)) exceeds a threshold, it also positively impacts recycling quantity and profits .
4.3 Comparative Analysis of Subsidies
Proposition 1
- Production subsidy enhances battery capacity (\(h_D^* > h_Q^* = h_B^*\)), while recycling subsidies boost recycling effort and prices (\(e_D^* < \min\{e_Q^*, e_B^*\}\), \(p_r^D < \min\{p_r^Q, p_r^B\}\)) .
Proposition 2
- Production subsidy increases demand and profits for suppliers/manufacturers (\(D_D^* > D_Q^* = D_B^*\), \(\pi_M^D > \pi_M^Q = \pi_M^B\)).
- Recycling subsidies benefit 3PR by increasing recycling quantity and profits (\(Q_D^* < \min\{Q_Q^*, Q_B^*\}\), \(\pi_{3PR}^D < \min\{\pi_{3PR}^Q, \pi_{3PR}^B\}\)) .
5. Social Welfare Analysis
Social welfare (SW) is defined as:\(SW = \pi_{total} + CS – GS\) where \(\pi_{total}\) is total supply chain profit, CS is consumer surplus, and GS is government subsidy expenditure .
Consumer surplus:\(CS = \frac{(p_1 – p)D}{2}, \quad p_1 = \frac{\alpha + kh}{\beta}\)
Government subsidy expenditure:
- \(GS_D = s_d \cdot D_D^*\)
- \(GS_Q = s_q \cdot Q_Q^*\)
- \(GS_B = s_h \cdot h_B^* \cdot Q_B^*\)
5.1 Simulation Results
As the price sensitivity coefficient (\(\beta\)) increases, social welfare decreases in all scenarios. Conversely, increasing production subsidy (\(s_d\)) enhances social welfare, which surpasses that of recycling subsidy scenarios when \(s_d = 0.4\) .
| Subsidy Scenario | Social Welfare Trend with \(s_d\) | Comparison at \(s_d = 0.4\) |
|---|---|---|
| Production (D) | Increases monotonically | \(SW_D^* > SW_Q^*, SW_B^*\) |
| Recycling (Q) | Relatively stable | \(SW_Q^* < SW_D^*\) |
| Recycling (B) | Relatively stable | \(SW_B^* < SW_D^*\) |
Table 2: Social Welfare Comparison Under Different Subsidies
6. Extended Models
6.1 Manufacturer as Leader
When the manufacturer leads the supply chain (denoted by subscript m):
- Manufacturer profits increase (\(\pi_{M,m}^N > \pi_M^N\)).
- Supplier profits rise if consumer preference k satisfies \(\sqrt{4k_h\beta/3} < k < \sqrt{2k_h\beta}\).
- Social welfare improves (\(SW_m^N > SW^N\)) .
6.2 Manufacturer-Supplier Merger
For a centralized system formed by manufacturer-supplier merger:
- Merger is beneficial if merger cost \(F < \hat{F} = \frac{2k_h^3\beta^2B^2}{M^2(2\beta k_h – k^2)}\).
- Below this threshold, centralized profits exceed decentralized profits (\(\pi_{MF}^N > \pi_M^N + \pi_S^N\)) .
7. Managerial and Policy Implications
7.1 For Manufacturers
- Balance battery capacity enhancements with R&D costs by leveraging production subsidies to drive innovation and scale .
- Assume leadership in the supply chain when consumer preference for battery capacity is high to maximize profits and social welfare .
7.1 For Recyclers
- Recycling subsidies stimulate effort and scale, but focus on cost efficiency (e.g., process optimization) to leverage high \(\lambda\) scenarios .
7.1 For Governments
- Design subsidy mechanisms that prioritize production subsidies for EV batteries to boost capacity, demand, and social welfare.
- Implement performance-based recycling subsidies to align with environmental goals, monitoring outcomes to adjust policies .
8. Conclusion
This research illuminates the differential impacts of government production and recycling subsidies on new energy electric vehicle power battery supply chains. Key contributions include:
- Demonstrating that production subsidies enhance battery capacity and manufacturer profits, while recycling subsidies benefit recyclers.
- Revealing that production subsidy yields higher social welfare than recycling subsidies as it stimulates demand and innovation.
- Highlighting the strategic value of supply chain leadership and mergers under specific conditions.
Future research could explore dynamic subsidy policies, integrate real-world data, or analyze multi-brand EV supply chains to further refine operational strategies in the sustainable transportation landscape.