Abstract
As the penetration rate of new energy vehicles in China continues to rise, the incentive effect of the CAFC-NEV credits policy has gradually weakened. The Ministry of Industry and Information Technology therefore proposes to transform the CAFC-NEV credits policy into carbon emission management policy. Focusing on the transition plan for CAFC-NEV credits of automotive industry in China, this paper constructs a differential game model of the supply chain that simultaneously manufactures and sells internal combustion engine vehicle (ICEV) and new energy vehicle (NEV), so as to examine the transitional effect of carbon credit on CAFC-NEV credits. The results show that: (1) Implementing carbon credit for NEV on the basis of the current CAFC-NEV credits does not affect capital stock or goodwill. (2) Within a specific range of NEV standard type credit and proportional requirement, the optimal equilibrium solutions for manufacturer and retailer are higher under the carbon credit compared to the CAFC-NEV credits scenario. (3) Neither the single-channel nor the dual-channel sales model affects the basic conclusions of the research. (4) The abolition of CAFC-NEV credits exerts a greater impact on manufacturer’s profit than on retailer’s. Empirical analysis reveals that the profit margins for manufacturer and retailer under the CAFC-NEV credits and carbon credit differ by less than 7% and 1% respectively. This study provides a theoretical basis for promoting the transformation of automotive industry policy from CAFC-NEV credits to carbon emission management in China.
1 Introduction
Achieving carbon peaking and carbon neutrality is a solemn commitment made by the Chinese government to the world, and it is the route one must take for humanity to achieve sustainable development in the future. Developing NEV is a strategic initiative for China to implement carbon peaking and carbon neutrality goals. Chinese government has introduced a series of policies to support the development of NEV industry since 2001, which can be divided into three phases (). NEV is included in the National High-tech R&D Program (863 Program) during the 10th 5-year plan period, marking the commencement of policy support for NEV industry. Since 2009, China has granted subsidy for the promotion of NEV (). However, the unprecedented high subsidies coupled with lax supervision have fueled widespread subsidy fraud (). Subsequently, the subsidy policy for NEV underwent a phased withdrawal. In 2017, the Chinese government has issued the Measures for the Parallel Administration of the Average Fuel Consumption and New Energy Vehicle Points of Passenger Vehicle Enterprises, which placed corporate average fuel consumption (CAFC) credit and new energy vehicle (NEV) credit under unified management and established the CAFC-NEV credits system, which signifies that the NEV market is transitioning from policy-driven to market-driven growth (). Driven by the constraints of credit assessment and revenue incentive, automakers generally increase investment in NEV products, leading to a steady improvement in the performance and quality (; ).
With the implementation of CAFC-NEV credits, a surge of relevant studies has emerged. Earlier qualitative research focuses on the layout strategies of NEV for automotive enterprises (; ). Subsequently, some scholars analyze the implementation effects of CAFC-NEV credits. Among the early quantitative studies, the relevant literature mainly concentrate on policy effect evaluation. Among the early quantitative studies, relevant literature mainly focus on policy effect evaluation, which indicates that CAFC-NEV credits have promoted innovation, enhanced corporate competitiveness, and effectively advanced the adoption of NEV (; ; ). With the adjustment of CAFC-NEV credits, scholars explore the optimization of the automotive supply chain, mainly investigating the optimal decisions for ICEV and NEV through static analysis of game models (; ; ; ). Among the limited dynamic studies, discuss the price change of CAFC-NEV credits and optimal electrification timing of manufacturer. analyze the production strategies for ICEV and NEV. propose a dynamic CAFC-NEV credits policy. As a crucial non-subsidy policy instrument, CAFC-NEV credits play a vital role in promoting the scaled development of NEV industry (; ). However, with the gradual increase in NEV penetration, the incentive effect of CAFC-NEV credits is diminishing, leading to significant fluctuations in credit price and a decline in market regulation efficiency. Against this backdrop, the Ministry of Industry and Information Technology has proposed transforming CAFC-NEV credits into a carbon emission management policy.
Driven by carbon emission reduction targets, the automotive industry continues to witness a constant stream of innovations, with the ongoing competition between ICEV and NEV persisting. At present, academia has proposed three primary approaches to carbon emissions management within the automotive industry, namely carbon tax, carbon quota, and carbon credit (; ; ). Carbon tax is a tax on carbon dioxide emitted during the use of ICEV (), it is widely recognized that carbon tax is an effective measure to reduce carbon emissions (; ). Through computable general equilibrium (CGE) and other professional models, scholars have calculated the optimal tax rate and evaluated the impact of carbon tax. However, existing research remains at the macro level and there is no detailed institutional design around the elements of carbon tax (; ; ). Carbon quota refers to the emission cap for enterprises participating in carbon market (). Based on the practices and simulation analyses of the international transportation sector participating in carbon market, some scholars explore the implementation pathways of carbon trading (; ; ). Game analysis is employed to examine the promotion strategies of NEV that introduce carbon quotas in some studies. However, the CAFC-NEV credits and carbon quota are market instruments, it is almost impossible for them to appear simultaneously in the production process in reality (; ; ). Research on carbon credit remains limited, with the concept first proposed by Academician Fengchun Sun of Beijing Institute of Technology. Carbon credit is a carbon emission reduction incentive designed to encourage the use of NEV, which quantifies the contribution of NEV travel as carbon emission reduction relative to ICEV, NEV owners earn income by trading carbon credit (Zhang, 2021). The findings indicate that carbon credit can promote the adoption of NEV, addressing the limitation that CAFC-NEV credits apply solely to the production phase ().
In conclusion, scholars have long been concerned with the static supply chain decision under the CAFC-NEV credits scenario. However, research regarding the dynamic decision and policy coordination at the usage stage is limited. We therefore explore dynamic optimal decision in automotive supply chain under CAFC-NEV credits and carbon credit scenarios, evaluating the substitution effect of carbon credit on CAFC-NEV credits. The marginal contribution of this paper may lie in the following aspects. First, using differential game, this paper contributes to literature on the dynamic optimal decisions of the automotive supply chain under different policy scenarios. Previous studies focus on the static analyse of CAFC-NEV credits. Second, regarding research design, existing literature focus on a single policy, with few studies examining the effects of policy combinations. By comparing different scenarios involving CAFC-NEV credits, carbon credit, and their combination, we further analyze the potential impacts of abolishing the CAFC-NEV credits. Third, model derivation and data simulation reveal that carbon credit can achieve the same incentive effect on the development of NEV as the CAFC-NEV credits, which provides a theoretical basis for the transition from the CAFC-NEV credits to carbon emission management policy.
2 Problem assumptions and notations
On the basis of the observations from current practice, we consider a single-channel supply chain model. Manufacturer determines the R&D effort for NEV, while retailer determines retail price and marketing efforts. The following conditions are assumed in this paper.
Assumption 1The investment of manufacturer in battery, motor, electronic control system, intelligent connected vehicle, and lightweight material can not only deliver a better user experience to consumers, but also drive the growth of sales and production capacity for NEV. Meanwhile, wear, aging, and technological advancements occurring during the operation of existing production equipment may reduce its value and performance. We refer to to construct the state equation of the capital stock for NEV.where K(t) represents the capital stock at time t, we assume the initial capital stock K (0) = 0. I(t) denotes the NEV R&D effort for manufacturer at time t. δ > 0, indicates the capital depreciation.
Assumption 2The capital accumulation by manufacturer can drive technological innovation, optimize production process and equipment, and improve product quality and performance, thus positively affecting the overall goodwill. Therefore, we assume that goodwill is positively affected by the manufacturer’s capital accumulation. By incorporating the impact of capital stock on goodwill, we modify the famous Nerlove-Arrow model ().where, G(t) represents goodwill, with an initial value of G (0) = 0. A(t) denotes the marketing effort of retailer. φ > 0 and θ > 0, respectively indicate the sensitivity of goodwill to capital stock and marketing efforts. η > 0 reflects the goodwill depreciation.
Assumption 3In a single-channel supply chain, manufacturer sells products exclusively through retail channel. The potential demand for the automotive supply chain is assumed to be M, where ICEV and NEV each account for a certain proportion (). The CAFC-NEV credits policy operates at the production stage and does not directly impact demand. Consequently, NEV demand is negatively correlated with price and positively correlated with the capital stock and goodwill. The market demands for NEV and ICEV are obtained by Equations 3, 4.where k and 1-k represent the proportions of potential demand for NEV and ICEV, respectively, p1 and p2 denote the prices, γ1 and γ1 are the price coefficients for demand. Owing to low-carbon preferences among consumers, the price coefficient of NEV is lower, i.e., γ1 > γ2 (). ϕ represents the marginal effect of capital stock on NEV demand. χ1 and χ2 denote the marginal effects of goodwill on demand. Considering that automakers have accumulated strong goodwill in ICEV market, consumers subsequently recognize their NEV. Therefore, it is assumed that χ1 < χ2.
Assumption 4CAFC-NEV credits simultaneously track both CAFC credit and NEV credit for passenger vehicle enterprises (). Manufacturer must progressively reduce the fuel consumption of ICEV annually to meet standard and earn positive CAFC credit, while also selling sufficient new energy vehicle to earn positive NEV credit. CAFC credit is determined by multiplying the difference between the national average fuel consumption standard (b) and the actual value (a) by the sales volume of ICEV, that is, . If b > a, it means that the automaker effectively achieve energy conservation and emission reduction targets, thereby earning positive CAFC credit. Positive CAFC credit can only be used to offset their own negative credit and cannot be traded. Meanwhile, when the actual value of NEV exceeds the compliance value, positive NEV credit can be obtained, i.e. . α1 represents the NEV standard type credit, while α2 denotes the NEV proportional requirement for NEV.
Assumption 5After the carbon emission reduction of NEV is registered as carbon credit, NEV owners can benefit by trading carbon credit (). The formula for calculating carbon credits is: . BE2 and CE1 represent the carbon emission of ICEV and NEV, respectively. Considering that carbon market operation involves certain transaction costs (), such as transaction fees and taxes, the actual revenue from carbon credit equals the carbon price multiplied by the number of credit minus transaction cost, that is . E denotes the carbon credit revenue, pc represents the price of carbon credit, and τ stands for transaction cost. If we regard BE2 as the emission cap, carbon credit corresponds to surplus allowance in carbon market. Under the carbon credit scenario, the actual purchase price of NEV for consumers decreases, and the demand function is transformed into Equation 5.The Appendix also supplements the optimal equilibrium results when the relevant parameters of carbon credit are treated as an additive term in the demand function. The findings show that these parameters do not enter the expression of the optimal control strategy and thus have no impact on the optimal strategies of manufacturer and retailer, they only affect the expression form of the constant term in the optimal profit function.
Assumption 6Similar to many scholars, we assume that the cost functions for NEV technology investment and marketing activities are quadratic functions of R&D effort and marketing effort, respectively (), Equations 6, 7 are as follow.where μ > 0 and λ > 0, represent the cost rates for NEV R&D effort and marketing effort, respectively.
Assumption 7Manufacturer and retailer maximize their discounted profits over an infinite time horizon, presenting the same discount rate (ρ > 0). NEV R&D effort I(t) and marketing effort A(t) are control variables, while capital stock K(t) and goodwill G(t) are state variables. For ease of notation, we use subscripts D and C to denote the CAFC-NEV credits and carbon credit policies respectively, and subscript CD to denote the combination of CAFC-NEV credits and carbon credit.In a single-channel supply chain, the objective functions for manufacturer and retailer under the CAFC-NEV credits scenario are expressed as Equations 8, 9.where D1 and D2 denote the sales volumes of NEV and ICEV respectively, w1 and w2 represent the wholesale prices, c1 and c2 are production costs, ψ is CAFC-NEV credits price, ρ is discount rate.Under the carbon credit scenario, the objective functions for manufacturer and retailer are expressed as Equations 10, 11.Under the combination scenario of CAFC-NEV credits and carbon credit, the objective functions for manufacturer and retailer are expressed as Equations 12, 13.
3 Model solutions
In the decentralized scenario, the manufacturer and retailer make their own decisions to maximize their profits. Under the CAFC-NEV credits scenario, the optimization problems for manufacturer and retailer are expressed as Equations 14, 15.
By solving the above optimization problem jointly, we obtain the Proposition 1. The proof of Proposition 1 is shown in the Appendix.
Proposition 1Under the CAFC-NEV credit scenario, manufacturer’s NEV R&D effort and retailer’s marketing effort are:By substituting the optimal strategies (16) into the state Equations 1, 2, we obtain Equation 17.The results of the comparative static analysis of parameters under the CAFC-NEV credits scenario are presented in Table 1.It can be observed that when , an increase in credit price incentivizes manufacturer to enhance NEV R&D effort, which implies that when α1 is higher than or α2 is lower than a certain threshold, credit price exerts a positive impact on R&D effort. If α1 is below or α2 exceeds an appropriate range, excessively stringent evaluation criteria will lead to the degradation of R&D effort, thereby weakening the incentive effect. The higher the NEV standard type credit score, the greater the benefit generated by the same production, which motivates the manufacturer to increase the R&D effort. The higher the proportional requirement of NEV, the more positive NEV credit is required, which increases the cost and may inhibit the R&D effort. Therefore, the smooth implementation of the CAFC-NEV credits policy hinges on the government’s regulation of the standard type credit and the proportional requirement of NEV. The CAFC-NEV credits focus on the automobile production process and does not regulate the retail process. Consequently, the capital depreciation coefficient has no impact on marketing effort and only dampens R&D effort. When the goodwill depreciation coefficient increases, it will dampen the enthusiasm of manufacturer and retailer, and reduce their efforts. It is evident that manufacturer’s R&D effort increases with rising wholesale price, and decreases as production cost increases, and are irrelevant to retail price, retailer’s marketing effort decreases with rising wholesale prices, increase as retail prices rise, regardless of rising production price. Increased marginal revenue motivates more efforts by manufacturer and retailer, leading to higher profits. Goodwill diffusion coefficients also motivate manufacturer and retailer to increase R&D and marketing efforts. In practice, manufacturer and retailer can mitigate the negative effect of natural attrition by implementing high-standard operational strategies, they should consider the positive impact of their respective efforts on enhancing capital stock and goodwill, thereby increasing investments.Under the carbon credit scenario, the optimization problems for manufacturer and retailer are expressed as follows.Simultaneous solution Equations 18, 19, we obtain Proposition 2. The proof of proposition 2 is shown in the Appendix.
TABLE 1
| Variables | ψ | α1 | α2 | η | δ | w1 | c1 | p1 | χ1 | χ2 |
|---|---|---|---|---|---|---|---|---|---|---|
| I* D | ↗ | ↗ | ↘ | ↘ | ↘ | ↗ | ↘ | → | ↗ | ↗ |
| A* D | → | → | → | ↘ | → | ↘ | → | ↗ | ↗ | ↗ |
Comparative static analysis of parameters under the CAFC-NEV credits scenario.
↗ indicates a positive impact, ↘ indicates a negative impact, → indicates no impact, the same below.
Proposition 2Under the carbon credit scenario, the optimal equilibrium strategy for manufacturer and retailer are:The optimal trajectories for capital stock and goodwill are expressed as Equation 21.The results of the comparative static analysis of parameters under the carbon credit scenario are shown in Table 2. Comparing Equation 16 and Equation 20 reveals that the equilibrium results under the CAFC-NEV credits and carbon credit scenarios are inconsistent. First, there are conditional differences in the equilibrium R&D effort level, and the following Corollary 2 (2) will clarify the threshold condition for I* C > I* D. Second, the important parameters of carbon credit (pc, CE1, τ) are not included in the optimal strategy expression, so pc, CE1, τ do not directly affect R&D effort I* C, which is a model-driven constraint. The carbon credit-related benefits are treated as an additive term in the demand function during model construction. In the process of deriving the first-order conditions through differentiation, these constant terms that are not directly multiplied with the control variables, disappear and therefore do not appear in the closed-form solution of the optimal control strategy. Such mathematical characteristic reflects the policy logic in reality, namely that carbon credit is a user-side economic incentive that alters the profits rather than directly changing the marginal output structure. The comparative static analysis of other parameters is consistent with the CAFC-NEV credits scenario.Simultaneous solution Equations 22, 23, we obtain Proposition 3. The proof of proposition 3 is shown in the Appendix.
TABLE 2
| Variables | pc | CE1 | τ | η | δ | w1 | c1 | p1 | χ1 | χ2 |
|---|---|---|---|---|---|---|---|---|---|---|
| I* C | → | → | → | ↘ | ↘ | ↗ | ↘ | → | ↗ | ↗ |
| A* C | → | → | → | ↘ | → | ↘ | → | ↗ | ↗ | ↗ |
Comparative static analysis of parameters under the carbon credit scenario.
Under the combination scenario of CAFC-NEV, credits and carbon credit, the optimization problems for manufacturer and retailer are respectively represented as follows.
Proposition 3The optimal equilibrium strategy for manufacturer and retailer are:The optimal trajectories for capital stock and goodwill are expressed as Equation 25.Table 3 reports the comparative static analysis results of parameters under the combination scenario. According to Equation 16 and Equation 24, the R&D and marketing effort of manufacturer and retailer under the combination scenario are the same as those under the CAFC-NEV credits scenario, so the results of the comparative static analysis are consistent and is not repeated here. The relevant parameters of carbon credit do not affect the optimal strategies.
TABLE 3
| Variables | ψ | α1 | α2 | pc | CE1 | τ | η | δ | w1 | c1 | p1 | χ1 | χ2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ↗ | ↗ | ↘ | → | → | → | ↘ | ↘ | ↗ | ↘ | → | ↗ | ↗ | |
| → | → | → | → | → | → | ↘ | → | ↘ | → | ↗ | ↗ | ↗ |
Comparative static analysis of parameters under the combination scenario of CAFC-NEV credits and carbon credit.
4 Comparative analysis
Corollary 1Under three policy scenarios, the optimal marketing efforts for retailer are as follows: .Corollary 1 indicates that neither CAFC-NEV credits nor carbon credit, nor combination scenario, affect retailer’s marketing effort. In this paper, a retailer sells both NEV and ICEV, and thus it can benefit regardless of which type of vehicle consumers purchase.
Corollary 2
Manufacturer’s NEV R&D effort under three policy scenarios are as follows.
.
When , , thereby obtain .
Corollary 3
Capital stock and goodwill under the three policy scenarios are as follows.
, .
When , we obtain , , i.e., , .
Corollary 4
NEV and ICEV sales under three policy scenarios are as follows.
, .
When , we obtain , , ,and thus obtain , .
Corollary 5
Manufacturer’s profit under the three policy scenarios are as follows.
.
When , and conditions 1 and 2 are satisfied, , and thus obtain .
Corollary 6
Retailer’s profit under the three policy scenarios are as follows:
1. .
2. When , , , thus .
5 Numerical experiments
This section analyzes the model results with data examples, aiming to test the above conclusions and further extend the analysis results. We refer to the relevant literature to assign values to parameters with economic significance to ensure the validity of the results in reflecting reality (; ; ; ; ). The conclusions are rigorously demonstrated in Sections 3, 4 as well as in the appendix. Therefore, the values assigned to certain parameters in the numerical simulations do not affect the validity of the conclusions. Parameter assignments and their bases are listed in the Appendix. We substitute the parameter values into the optimal equilibrium results and perform data analysis using Matlab, yielding the simulation analysis in Figures 1–5.
FIGURE 1
5.1 Policy parameters of CAFC-NEV credits and carbon credit
Figures 1a–d shows that within the variation range of parameters set in this paper, NEV demand and the profits of manufacturer and retailer decrease as the price of CAFC-NEV credits declines. In a horizontal comparison, when the price of the CAFC-NEV credits falls below a certain threshold, the NEV demand and the profits of manufacturer and retailer under the carbon credit scenario exceed those under the CAFC-NEV credits scenario. Figures 1e–h shows that if NEV proportional requirement in CAFC-NEV credits policy is higher than a certain level, the demand and profits of manufacturer and retailer may be lower than that in carbon credit scenario.
Figures 2a–d indicates that under the carbon credit scenario, as the price of carbon credit increases, the NEV demand and the profits of manufacturer and retailer rise accordingly. Figures 2e–h shows that as NEV carbon emission increases, NEV demand and the profits of manufacturer and retailer will decline. Based on Figure 2, no significant direct impact of the carbon credit policy on ICEV demand is observed, thus indicating that the introduction of additional carbon credit exerts no significant intervention effect on changes in ICEV demand under the existing CAFC-NEV credit. Corollary 4, Corollary 5, and Corollary 6 are verified. Figures 1, 2 demonstrate that reasonable regulation of carbon credit price in the carbon market and reduction of life cycle carbon emission for NEV can effectively stimulate the NEV demand.
FIGURE 2
Tables 4, 5 present the member strategies, steady-state capital stock, goodwill and demand, profits, and comparisons for CAFC-NEV credits under different credit prices and proportional requirements of NEV. As shown in Table 4, within the parameter test range selected in this paper, R&D effort, together with NEV demand, capital stock, goodwill and profits, increase with the increase in CAFC-NEV credits price. Rising credit prices can increase the marginal revenue of manufacturer and encourage R&D investment, which is conducive to the accumulation of capital and goodwill, improve NEV demand, and expand the profit space of manufacturer and retailer. Table 5 shows that R&D effort and NEV demand, capital stock, goodwill, and profit increase with the proportional requirement of NEV. The higher the proportional requirement of NEV, the more the costs for manufacturer to purchase NEV credit, which may inhibit the manufacturer’s R&D effort. According to Equation 16, the retailer’s equilibrium strategy is independent of ψ and α2, so the marketing effort remains constant as the CAFC-NEV credits price and the proportional requirement of NEV change. The appendix also includes a sensitivity analysis of NEV standard type credit, showing that R&D effort, NEV demand, capital stock, goodwill, and profits increase with NEV standard type credit. Higher NEV standard type credit is more beneficial to manufacturer.
TABLE 4
| Variables | ψ = 0.05 | ψ = 0.2 | ψ = 0.35 | ψ = 0.5 | ψ = 0.65 | ψ = 0.8 | ψ = 0.95 | ψ = 1.1 | ψ = 1.25 | ψ = 1.4 |
|---|---|---|---|---|---|---|---|---|---|---|
| 2.02 | 2.59 | 3.16 | 3.73 | 4.30 | 4.87 | 5.44 | 6.01 | 6.58 | 7.15 | |
| 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | |
| 1757.48 | 1761.26 | 1765.05 | 1768.83 | 1772.61 | 1776.39 | 1780.17 | 1783.96 | 1787.74 | 1791.52 | |
| 8.75 | 11.21 | 13.68 | 16.14 | 18.60 | 21.07 | 23.53 | 26.00 | 28.46 | 30.93 | |
| 14.33 | 17.63 | 20.92 | 24.22 | 27.51 | 30.81 | 34.10 | 37.39 | 40.69 | 43.98 | |
| 342.31 | 397.79 | 453.51 | 509.45 | 565.63 | 622.04 | 678.69 | 735.57 | 792.68 | 850.02 | |
| 324.27 | 324.81 | 325.34 | 325.88 | 326.41 | 326.95 | 327.48 | 328.02 | 328.55 | 329.09 |
Sensitivity analysis of ψ under CAFC-NEV credits policy.
TABLE 5
| Variables | α2 = 0.05 | α2 = 0.1 | α2 = 0.15 | α2 = 0.2 | α2 = 0.25 | α2 = 0.3 | α2 = 0.35 | α2 = 0.4 | α2 = 0.45 | α2 = 0.5 |
|---|---|---|---|---|---|---|---|---|---|---|
| 2.25 | 2.24 | 2.24 | 2.23 | 2.23 | 2.22 | 2.22 | 2.21 | 2.21 | 2.20 | |
| 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | |
| 1758.97 | 1758.94 | 1758.91 | 1758.87 | 1758.84 | 1758.81 | 1758.77 | 1758.74 | 1758.71 | 1758.68 | |
| 9.72 | 9.70 | 9.68 | 9.66 | 9.63 | 9.61 | 9.59 | 9.57 | 9.55 | 9.53 | |
| 15.63 | 15.61 | 15.58 | 15.55 | 15.52 | 15.49 | 15.46 | 15.43 | 15.40 | 15.37 | |
| 373.30 | 371.51 | 369.72 | 367.93 | 366.15 | 364.36 | 362.57 | 360.78 | 358.99 | 357.20 | |
| 324.48 | 324.48 | 324.47 | 324.47 | 324.46 | 324.46 | 324.45 | 324.45 | 324.45 | 324.44 |
Sensitivity analysis of α2 under CAFC-NEV credits policy.
Tables 6, 7 present the member strategies, steady-state capital stock, goodwill and demand, profits, and comparisons for carbon credit under different credit prices and NEV carbon emission. The appendix also includes a sensitivity analysis of transaction cost. According to Equation 20, the optimal equilibrium strategy is independent of pc, CE1, and τ. Numerical analysis consistently shows that the effort level of supply chain members does not change with the change of these parameters within the test range set in this paper. Considering the linear relationship between pc, CE1, τ and NEV demand, NEV demand increases with a rise in the carbon credit price and decreases with an increase in NEV carbon emission and transaction cost. Rising credit price generates additional income for NEV owners, which essentially reduces the actual purchase price for consumers, thereby stimulating the NEV demand and expanding the profit margin within the supply chain. Higher carbon emission of NEV undermines the low-carbon advantages and economics, affecting consumer demand and the profitability of supply chain members. Transaction cost is negatively correlated with NEV demand and profits of manufacturer and retailer. In a mature carbon market, NEV owners can reduce the costs of finding trading partners and negotiating. Conversely, in an underdeveloped carbon market, exorbitant transaction costs may weaken the incentive effect of the carbon credit policy. Other parameters remain consistent with the CAFC-NEV credits scenario. Therefore, policymakers should dynamically regulate the carbon credit price, reduce transaction cost, strengthen carbon emission accounting and other measures to enhance the effect of policy incentives. As the carbon market matures in the future, carbon credit is expected to be an important policy instrument for popularizing NEV and achieving the carbon peaking and carbon neutrality goals.
TABLE 6
| Variables | pc = 0.05 | pc = 0.2 | pc = 0.35 | pc = 0.5 | pc = 0.65 | pc = 0.8 | pc = 0.95 | pc = 1.1 | pc = 1.25 | pc = 1.4 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | |
| 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | |
| 1756.31 | 1757.03 | 1757.75 | 1758.47 | 1759.19 | 1759.91 | 1760.63 | 1761.35 | 1762.07 | 1762.79 | |
| 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | |
| 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | |
| 323.88 | 323.94 | 324.00 | 324.06 | 324.12 | 324.18 | 324.24 | 324.30 | 324.36 | 324.42 | |
| 324.10 | 324.16 | 324.22 | 324.28 | 324.34 | 324.40 | 324.46 | 324.52 | 324.58 | 324.64 |
Sensitivity analysis of pc under CAFC-NEV credits policy.
TABLE 7
| Variables | τ = 0.05 | τ = 0.1 | τ = 0.15 | τ = 0.2 | τ = 0.25 | τ = 0.3 | τ = 0.35 | τ = 0.4 | τ = 0.45 | τ = 0.5 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | 1.83 | |
| 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | |
| 1758.47 | 1758.32 | 1758.17 | 1758.02 | 1757.87 | 1757.72 | 1757.57 | 1757.42 | 1757.27 | 1757.12 | |
| 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | 7.93 | |
| 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | 13.24 | |
| 324.06 | 324.05 | 324.03 | 324.02 | 324.01 | 324.00 | 323.98 | 323.97 | 323.96 | 323.95 | |
| 324.28 | 324.27 | 324.26 | 324.24 | 324.23 | 324.22 | 324.21 | 324.19 | 324.18 | 324.17 |
Sensitivity analysis of τ under CAFC-NEV credits policy.
5.2 The trajectory of capital accumulation
Figure 3 illustrates variation in capital stock with respect to various parameters. First, within the observation timeframe (t∈[0,100]), the capital stock naturally accumulates and converges to a steady state over time across all policy scenarios. This means that once the capital stock reaches a steady state (as shown in Figure 3 after t = 30), eliminating the CAFC-NEV credits policy will not affect the capital stock. Second, at a fixed time point (t = 10), the capital stock under the CAFC-NEV credits or combination scenario generally exceeds that under the carbon credit scenario. However, when NEV proportional requirement is higher than a certain threshold, the capital stock under the carbon credit scenario surpasses that under the CAFC-NEV credits and combination scenario. Finally, in parameter test area, the capital accumulation trajectory shows some effects consistent with expectations as the parameters variation. For example, an increase in goodwill and capital depreciation rates leads to a reduction in capital stock. Carbon credit price does not affect capital stock. The NEV proportional requirement and wholesale prices exhibit decreasing and increasing trends with capital stock, respectively.
FIGURE 3
5.3 The trajectory of goodwill
Figure 4 illustrates the variation in goodwill with respect to various parameters within the parameter range defined in this paper. We observe that the carbon credit price does not affect goodwill. The implementation of carbon credit leads to an increase in goodwill, which shows rapid growth at first and then leveling off. Therefore, whether stimulating production from the production link or boosting consumption from the use link, both approaches exert a long-term positive impact on goodwill. In addition, an increase in goodwill and capital depreciation coefficients will also lead to a reduction in goodwill. The NEV proportional requirement and wholesale price exhibit a decreasing and increasing trend with goodwill respectively, consistent with expectations. Figures 3, 4 validate Corollary 3.
FIGURE 4
5.4 Profit as a function of parameter variation
Figures 5a–d illustrates the variation in profit among manufacturer with respect to various parameters under various policy scenarios. Within the set parameter range, it reveals that, first, manufacturer profit is positively correlated with carbon credit price, CAFC-NEV credit price, and the goodwill marginal coefficient of ICEV and NEV demand, while negatively correlated with NEV retail price and production cost. In particular, the price variation of CAFC-NEV credits and carbon credit affect manufacturer’s profit under different scenarios. Manufacturer should seek the optimal way to maximize their own interests according to specific circumstances. Second, the manufacturer’s profit under the CAFC-NEV credits scenario is higher than that under the carbon credit scenario in most areas. When the CAFC-NEV credits price falls below a certain threshold, manufacturer’s profit under the carbon credit scenario surpass those under the CAFC-NEV credits scenario. On the current parameter configuration plane (excluding the bottom-left subgraph), the average difference in manufacturer profit under the two policy scenarios is 6.523%, 6.512%, and 6.508%. If CAFC-NEV credits is subsequently eliminated based on the combination scenario, manufacturer’s profit will decrease by 6.557%, 6.556%, and 6.542%.
FIGURE 5
Figures 5e–h indicates that retailer profit is positively correlated with carbon credit price, CAFC-NEV credit price, and goodwill diffusion coefficients, while negatively correlated with NEV production cost within the set parameter range. Different from Figures 5a–d, retailer profit is positively correlated with retail price, because rising retail price increases retailer’s marginal revenue, and coupled with the goodwill reference effect, retailer’s profit is elevated. In addition, when the price of CAFC-NEV credits falls below a certain threshold or the price of carbon credit rises above a specific level, the manufacturer’s profit will be higher under carbon credit scenario than under CAFC-NEV credits scenario. On the current parameter configuration plane, the average differences of retailer’s profit across two policy scenarios are 0.053%, 0.034%, 0.020%, and 0.026%, respectively. Eliminating CAFC-NEV credits on the basis of combination scenario reduces retailer’s profit by 0.053%, 0.074%, 0.050%, and 0.057%, respectively. Figure 5 provides strong validation for the conclusions of Corollary 5 and Corollary 6.
6 Discussion
The above analysis examines the optimal strategies for manufacturer and retailer in a single-channel supply chain, neglecting direct sales channel. For instance, manufacturer such as BYD not only operate their own direct sales channel, but also maintain an extensive retail network, and outsource a variety of service cooperation businesses to retailer or third-party provider. Consequently, we further explore optimal strategies within a dual-channel supply chain.
Considering a dual-channel automotive supply chain composed of a manufacturer, a retailer, and a third-party provider, consumers can purchase NEV or ICEV through direct (manufacturer) and indirect sales channel (retailer). During the sales phase, the manufacturer determines the direct sales prices p1d and p2d for NEV and ICEV in the direct sales channel, and sells NEV and ICEV to retailer at wholesale prices w1 and w2. Retailer determines the indirect prices p1i and p2i for NEV and ICEV in the indirect channel. During the usage phase, whether NEV or ICEV, regular maintenance and inspection are required to ensure proper vehicle operation and extend service life. Manufacturer usually outsources warranty services to retailer or third-party provider in a licensing model, charging them fixed licensing fees L1i, L2i, L1p and L2p for NEV and ICEV. Retailer or third-party provider earn a service premium that exceeds operating cost by professional services. When consumers purchase NEV or ICEV through indirect channel, they can only seek after-sales service from the retailer. Third-party provider only offers after-sales service to consumers who purchase NEV or ICEV from direct sales channel.
In a dual-channel supply chain, the manufacturer sells NEV or ICEV through indirect and direct channels. Following , the demand for NEV and ICEV of indirect and direct sales channels are expressed as Equations 26–28.where μ1 and μ2 represent the retail proportions of NEV and ICEV, p1i, p1d, p2i, and p2d denote the indirect and direct sales prices of NEV and ICEV, b1 and b2 indicate the price sensitivity of NEV indirect and direct sales channels, b3 and b4 denote the price sensitivities of ICEV indirect and direct sales channels, ξ1 represents the cross-price sensitivity of NEV, with b1 > ξ1 and b2 > ξ1; ξ2 denotes the cross-price sensitivity of ICEV, with b3 > ξ2 and b4 > ξ2.
Under the carbon credit scenario, NEV demand under indirect and direct sales models are expressed as Equations 30, 31.
In a dual-channel supply chain, the objective functions for manufacturer and retailer under the CAFC-NEV credits scenario are expressed as Equations 32, 33.where subscripts 1 and 2 denote NEV and ICEV, D1i and D2i represent the indirect sales of NEV and ICEV, D1d and D2d denote the direct sales, w1 and w2 are the wholesale prices, c1p and c2p are the production costs, R1i and R2i represent the after-sales service fees charged by retailers to consumers, L1i and L1p denote the NEV after-sales service licensing fees paid by retailer and third-party provider to manufacturer, while L2i and L2p represent the ICEV after-sales service licensing fees.
The objective functions for manufacturer and retailer under the carbon credit scenario are expressed as Equations 34, 35.
The objective functions for manufacturer and retailer under the combination scenario are expressed as Equations 36, 37.
Under the CAFC-NEV credits scenario, the optimization problems for manufacturer and retailer are expressed as follows.
Simultaneous solution Equations 38, 39, we obtain Proposition 4.
Proposition 4The optimal equilibrium strategy for manufacturer and retailer are expressed as Equation 40.The optimal trajectories for capital stock and goodwill are expressed as Equation 41.Under the carbon credit scenario, the optimization problems for manufacturer and retailer are expressed as follows.Simultaneous solution Equations 42, 43, we obtain Proposition 5.
Proposition 5In carbon credit scenario, the optimal equilibrium strategy for manufacturer and retailer are expressed as Equation 44.The optimal trajectories for capital stock and goodwill are expressed as Equation 45.Under the combination scenario, the optimization problems for manufacturer and retailer are expressed as follows.Simultaneous solution Equations 46, 47, we obtain Proposition 6.
Proposition 6In combination scenario, the optimal equilibrium strategy for manufacturer and retailer are expressed as Equation 48.The optimal trajectories for capital stock and goodwill are expressed as Equation 49.Figure 6 illustrates the variation in capital stock and goodwill with respect to various parameters. We observe that capital stock and goodwill all improve over time across different policy scenarios within the set parameter range. Capital stock exhibits a decreasing trend with respect to goodwill and capital depreciation coefficients, as well as the NEV proportional requirement, while showing an increasing trend with NEV wholesale price, and it remains insensitive to carbon credit price. The variation of goodwill with each parameter is consistent with the capital stock. Compared with Figures 3, 4, the variation in capital stock and goodwill with respect to various parameters are similar, but the steady-state values for capital stock and goodwill are higher than those under the single-channel model. Overall, the sales model does not affect the fundamental conclusions of this study.
FIGURE 6
7 Conclusion
Driven by carbon peaking and carbon neutrality goals, as the main source of carbon emission in the transportation sector, it is necessary for the automobile industry to establish a more refined carbon emission management mechanism. The shift from CAFC-NEV credits to carbon emission management in automotive industry of China is not only a requirement for policy upgrading, but also a strategic choice to achieve carbon emission reduction and technological progress. Therefore, this paper constructs a differential game model of a supply chain simultaneously producing and selling NEV and ICEV, examining the linkage effect of carbon credit on CAFC-NEV credits. The main conclusions are summarized as follows.
NEV R&D effort and marketing effort, capital stock and goodwill are the same under CAFC-NEV credits and combination scenarios. Therefore, implementing carbon credit for NEV based on the current CAFC-NEV credit policy does not impact capital stock or goodwill.
Carbon credit policy can promote NEV technology investment and capital accumulation while stimulating NEV demand. Within the specific scope of NEV standard-type credit and proportional requirement, the optimal equilibrium strategies of manufacturer and retailer, and trajectory levels under carbon credit policy are higher compared to CAFC-NEV credits policy.
Capital stock and goodwill improve over time. Both capital stock and goodwill exhibit a decreasing trend with respect to goodwill depreciation rate, capital depreciation rate, and NEV proportional requirement, while showing an increasing trend with respect to NEV wholesale price, they are insensitive to carbon credit price.
Under the combination scenario, the elimination of CAFC-NEV credits leads to a decline in profits for manufacturer and retailer, with a greater impact on manufacturer and a smaller impact on retailer. Data analysis shows that across several parameter configuration planes, the difference of manufacturer’s profit under CAFC-NEV credits and carbon credit does not exceed 7%, while the difference for retailer does not exceed 1%.
Our analysis yields some important managerial insights, as follows:
Policymakers should establish and promote a set of carbon emission accounting standards covering lifecycle, further advancing lifecycle carbon emission oversight, and require enterprises to disclose carbon emission data, gradually establish a carbon management mechanism for the whole industry chain.
CAFC-NEV credits play a positive role in stimulating the early development of NEV, but as regulatory effectiveness diminishes, they struggle to motivate enterprises to take proactive measures in carbon reduction. The competent department should expedite the establishment of a carbon emissions trading system for transportation, incorporate carbon emission targets into the Emission Trading System, and enable NEV to profit from carbon trading through market-based mechanisms.
The key to carbon emission management lies in technological progress, which urges automobile companies to accelerate the R&D and application of new energy technologies. The government should increase financial support for carbon reduction technology of NEV, promote the application of battery technology with higher energy density and low carbon production and lightweight materials, and continuously reduce the lifecycle carbon emission of NEV through technological innovation.
This paper has made some progress on the basis of existing research, but there may still be some imperfections. For instance, this paper only considers single-period decision and ignore the carry-over of credit across years, which thus has certain limitation. In addition, there are some factors affecting demand that are not included in the model. Subsequent research may consider these issues for further expansion.
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Author contributions
NL: Writing – original draft. SC: Writing – original draft. JK: Writing – review and editing. TZ: Writing – original draft.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
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Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fenvs.2026.1737840/full#supplementary-material
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Summary
Keywords
CAFC-NEV credits, carbon credit, differential game, new energy vehicle, Toward 2035
Citation
Liu N, Chen S, Kong J and Zhang T (2026) Toward 2035: exploring a transition plan of the CAFC-NEV credits policy for NEV in China. Front. Environ. Sci. 14:1737840. doi: 10.3389/fenvs.2026.1737840
Received
02 November 2025
Revised
03 February 2026
Accepted
24 February 2026
Published
30 March 2026
Volume
14 - 2026
Edited by
Fengtao Guang, China University of Geosciences Wuhan, China
Reviewed by
Gui Jin, China University of Geosciences Wuhan, China
Lvjiang Yin, Hubei University of Automotive Technology, China
Updates
Copyright
© 2026 Liu, Chen, Kong and Zhang.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Jun Kong, kongjun@nwu.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.