Research on the Optimal Production Decision-Making Model of Fuel and New Energy Vehicle Manufacturers Under the Dual-Credit Policy

Abstract

To achieve dual-carbon goals and advance the sustainable development of the automotive industry, China’s Dual-Credit Policy serves as the core long-term mechanism for the low-carbon transition of the automotive industry. Given the coexistence of fuel vehicles (FVs) and new energy vehicles (NEVs) in China, existing research often overemphasizes production output while neglecting energy consumption control, and focuses predominantly on NEVs at the expense of FV optimization. To address these gaps, this paper treats FV fuel consumption and NEV energy efficiency as core endogenous decision variables. We construct profit-maximizing optimal production decision models for both types of manufacturers under the Dual-Credit Policy. Through mathematical derivation, numerical simulations, and empirical tests using actual industrial parameters, this study verifies the existence and uniqueness of optimal solutions. It clarifies the influence mechanisms of policy and market factors on corporate energy decisions and identifies the rules of strategy dominance. The findings reveal that the optimal fuel consumption decisions of FV manufacturers exhibit distinct piecewise patterns and critical threshold effects. Specifically, credit prices, NEV quotas, and fuel consumption standards determine the dominance of compliant (low-consumption) versus non-compliant (high-consumption) strategies. Furthermore, the policy exerts a significant market-oriented positive incentive on the energy efficiency upgrading of NEV manufacturers, with credit prices, market demand, and R&D costs acting as core constraints. Notably, the transition-guiding effect of the policy has clear effective boundaries, and its efficacy highly depends on the alignment between parameter design and market conditions. This research provides theoretical support for manufacturers to formulate energy-optimized production decisions and offers actionable references for the continuous optimization of the Dual-Credit Policy system and the sustainable low-carbon transformation of China’s automotive sector.

1. Introduction

Against the backdrop of the global wave of carbon neutrality and the rigid constraints of China’s dual-carbon strategy, the automotive industry, as a pillar industry of the national economy, contributes more than 70% of carbon emissions in China’s transportation sector. Its low-carbon transition has thus become a core pathway toward the high-quality and sustainable development of the national industrial system [1,2]. China has ranked first in global automobile production and sales for 15 consecutive years. In 2025, the country’s automobile production and sales reached 34.531 million and 34.40 million units, respectively, of which NEVs accounted for 47.9% of total production and sales. The industry has formally entered a new stage of long-term coexistence and in-depth competition between FVs and NEVs [3,4]. In this context, how to guide automotive manufacturers to balance compliance costs and market competitiveness through market-oriented policy tools, and how to formulate optimal production and operation strategies, have become critical issues in industrial practice and academic research.

To solve the incentive dilemma for industrial transition after the phase-out of financial subsidies for NEVs, China formally implemented the Dual-Credit Policy in 2017, which has been revised twice in 2020 and 2023 to form a dynamically adjusted industry credit management system. The core of the policy is to establish a long-term mechanism of “restricting high-carbon emissions and incentivizing low-carbon development” through the market-oriented linkage of two major systems: Corporate Average Fuel Consumption (CAFC) credits and new energy vehicle (NEV) credits [5,6,7]. Specifically, negative CAFC credits must be offset through self-owned carried-over credits, transfers from affiliated enterprises, or the purchase of positive NEV credits; negative NEV credits can only be offset by purchasing positive NEV credits from the market. The required NEV credit ratios for the 2026 and 2027 assessment years have been set at 48% and 58%, respectively [8], marking a comprehensive shift in the policy’s core orientation from “encouraging scale expansion” to “promoting quality upgrading”. As a result, manufacturers’ energy consumption decisions are deeply bound to their credit compliance costs and operating profits.

From the perspective of the practical development of China’s automotive industry, the Dual-Credit Policy has profoundly reshaped the production and operation logic of automotive manufacturers. The energy consumption level of vehicles has become a core variable for manufacturers to balance compliance requirements and market competitiveness, and multiple verifiable typical practical cases have emerged in the industry. First, leading domestic automakers have achieved a win–win situation of compliance and revenue through the upgrading of energy consumption levels. Relying on core technologies such as Blade Battery and DM-i Super Hybrid technology, BYD has simultaneously improved the core quality (including safety and driving range) of its battery electric vehicle (BEV) models and the fuel economy of its hybrid models. It ranked first in the industry in terms of the scale of positive NEV credits for two consecutive years from 2023 to 2024 [9,10], and generated more than 2.5 billion yuan in revenue from credit transactions in 2024, forming a positive cycle of “energy efficiency upgrading-credit surplus-revenue reinvestment-technological iteration” [11]. In response to the credit constraints on low-range models in the 2023 version of the policy, SAIC-GM-Wuling discontinued the low-range, low-configuration versions of the Hongguang MINIEV and launched upgraded models equipped with fast-charging and long-range batteries [12]. Through energy efficiency optimization, it simultaneously achieved credit compliance and stable market share. Second, joint venture brands and traditional FV manufacturers have initiated quality transformation under policy pressure. Between 2020 and 2022, joint venture enterprises such as FAW-Volkswagen and SAIC-Volkswagen accumulated a negative CAFC credit gap of more than one million points due to the excessively high proportion of FV sales and the lag in energy efficiency upgrading of their models. In 2021 alone, they spent more than 3 billion yuan on purchasing positive NEV credits. Under this pressure, these enterprises have, on the one hand, improved the fuel economy of their FVs and reduced the negative CAFC credit gap by upgrading high-efficiency fuel engines such as the EA211 1.5T EVO; on the other hand, they have accelerated the technological iteration and quality upgrading of their ID. series BEV models, gradually realizing independent and controllable credit compliance [13]. Third, the policy has promoted the survival of the fittest in the industry. Some small and medium-sized automakers, unable to complete the energy efficiency upgrading of FVs and quality breakthrough of NEVs to meet the Dual-Credit Policy compliance requirements, eventually fell into operational crisis or even exited the market, serving as typical samples of policy-forced clearance of low-quality production capacity.

This study adopts a three-stage methodological framework: (1) Theoretical modeling: We construct profit-maximization models for FV and NEV manufacturers under the Dual-Credit Policy, deriving closed-form optimal solutions and critical thresholds through mathematical derivation. This framework characterizes the directional impact mechanisms of policy parameters on enterprise decisions. (2) Numerical simulation: We calibrate the model using real industrial parameters to visualize the theoretical results and conduct a sensitivity analysis. (3) Empirical testing: We use a two-way fixed effects model with instrumental variables to verify the theoretical propositions using firm-level panel data. This mixed-methods approach combines the rigor of theoretical analysis with the realism of empirical validation, ensuring the reliability and practical relevance of our conclusions.

The remainder of this paper is organized as follows: Section 2 reviews the relevant literature and clarifies the current research gaps as well as the contributions of this paper. Section 3 describes the problem and presents the model assumptions. Section 4 establishes and solves the optimal decision-making models for both FV and NEV manufacturers. Section 5 presents the numerical simulations and sensitivity analysis. Section 6 reports the empirical tests and results. Section 7 discusses the findings, practical implications, and limitations. Finally, Section 8 concludes the paper.

2. Literature Review

A large body of existing academic research on the Dual-Credit Policy has been conducted. Some scholars argue that the policy can effectively reduce the production scale of FVs while promoting the popularization of NEVs. Hu et al. [14] constructed a decision optimization model for fuel economy level and FV production, and found that the market price of NEV credits has a significant impact on FV output; when the credit price is low, FV production may not necessarily decline due to factors such as market expansion. Wang et al. [15] constructed an R&D investment model for automobile manufacturers with joint production of dual vehicle models, arguing that manufacturers should not rely on low credit transaction prices, but instead improve R&D efficiency, reduce redundant investment, and increase technological R&D to promote low-energy consumption and NEV models so as to achieve transformation, upgrading and smooth replacement relying on the Dual-Credit Policy. Using a difference-in-differences (DID) model, Liang et al. [16] explored the differential impact of the Dual-Credit Policy on BEV manufacturers and traditional automobile manufacturers, and found that traditional automakers must reduce vehicle fuel consumption and increase NEV production to meet the policy requirements. Using PSM-DID with a quasi-natural experiment design, Zhao et al. [17] confirm that the dual-credit policy effectively enhances the operational performance of Chinese listed NEV firms via increased R&D and sales. The policy exerts stronger impacts on state-owned, large and long-exposed enterprises. HU et al. [18,19,20] conducted research on the supply chain composed of NEV manufacturers and battery suppliers, confirming that the Dual-Credit Policy has a significant impact on the innovation capability of automakers. Meanwhile, although rising credit transaction prices will lower the selling price of NEVs, manufacturers can obtain additional revenue from credits, thereby achieving overall profit growth. Hui et al. [21] built a tripartite evolutionary game-system dynamics model for China’s NEV industry. They found that Dual-Credit Policy intensity, innovation capacity, demand-innovation synergy and stakeholder coordination jointly determine innovation strategies, supply chain stability and policy performance, with demand-innovation matching and multi-agent coordination being more critical for upstream innovation than policy pressure alone. Li et al. [22] constructed a multi-scenario production and pricing decision-making model for conventional fuel vehicle manufacturers, and analyzed their optimal output, optimal pricing and achievable optimal profit under different strategies across various markets and policy requirements. The study found that the Dual-Credit Policy can increase the sales price of conventional fuel vehicles and lower the price of new energy vehicles. Pu et al. [23] adopted game theory to construct four Dual-Credit Policy (DCP) scenarios and analyze fuel vehicle (FV) and new energy vehicle (NEV) manufacturers’ low-carbon strategies. They verified that DCP regulatory targets greatly impact credit prices, retail prices, emission reductions, market demand, firm profits and overall carbon emissions. Manufacturers gain maximum profits under NEV-only regulation, while joint regulation of both vehicle types cuts total carbon emissions the most yet reduces corporate profits. YI et al. [24] argued that although rising credit market prices can drive manufacturers to increase R&D investment, effectively reduce average fuel consumption, and contribute to social carbon emission reduction, they will also push up the wholesale price of FVs, which may not ultimately lead to an improvement in social welfare.

While existing research on China’s DCP has extensively explored its impacts on the automotive industry, two critical research gaps remain. First, most studies treat vehicle energy consumption as an exogenous parameter, focusing on production transformation, pricing, and supply chain coordination, while lacking a two-dimensional analysis of endogenous energy consumption decisions covering both FVs and NEVs. They also largely overlook the sustained market share of FVs in the medium to long term, which will remain above 40% until 2030 according to industry forecasts. Second, existing analyses are mostly based on the pre-2020 policy framework, with few dynamic studies incorporating the 2023 DCP amendments and the 2026–2027 NEV credit ratio requirements, failing to align with the policy’s core goal of high-quality development.

This paper addresses these gaps with three key innovations. First, methodologically, we treat vehicle energy consumption as the core endogenous decision variable, construct a dual-dimensional production decision model for both FV and NEV manufacturers, and validate it through a unified framework of mathematical derivation, numerical simulation, and empirical testing. This fills the research gap of prioritizing output over quality and NEVs over FVs, and enriches the theoretical system of manufacturers’ production decisions under the DCP. Second, our study has strong policy timeliness: we incorporate the 2023 DCP revisions, 2026–2027 credit rules, and real-world parameters including credit price volatility and market structure changes, making our findings highly compatible with China’s current automotive industry policy environment. Third, this research holds strategic practical significance: amid ongoing geopolitical turbulence in the Middle East and high global energy prices, optimizing the DCP to guide automakers’ energy efficiency improvements can reduce oil consumption in China’s transportation sector, lower reliance on international energy markets, safeguard national energy security, and underpin the sustainable advancement of the automotive industry.

3. Problem Description and Assumptions

Consider an automotive market consisting of one traditional fuel vehicle (FV) manufacturer and one new energy vehicle (NEV) manufacturer. As a benchmark analytical framework, we assume each manufacturer produces only one representative vehicle model to isolate the core incentive mechanism of the Dual-Credit Policy (DCP) on energy consumption decisions.

For the traditional fuel vehicle (FV) manufacturer, per-vehicle CAFC credits ${\lambda }_1$ are defined in strict compliance with the Measures for the Parallel Administration of Average Fuel Consumption and New Energy Vehicle Credits of Passenger Vehicle Enterprises [5] and the national standard GB 27999-2025 Fuel Consumption Evaluation Methods and Targets for Passenger Cars [25]. Per official regulatory provisions, an enterprise’s total annual CAFC credits equal the production-weighted gap between the corporate average fuel consumption target and actual fuel consumption: $\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{C}\mathrm{A}\mathrm{F}\mathrm{C} \mathrm{C}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{s}=\left(T_{\mathrm{C}\mathrm{A}\mathrm{F}\mathrm{C}}-\mathrm{C}\mathrm{A}\mathrm{F}\mathrm{C}\right)\times {\displaystyle {\sum }_{i=1}^n}{V}_i$. where $T_{\mathrm{C}\mathrm{A}\mathrm{F}\mathrm{C}}$ is the production-weighted corporate average fuel consumption target (derived from curb-weight-based model targets per GB 27999-2025), $\mathrm{C}\mathrm{A}\mathrm{F}\mathrm{C}$ is the actual production-weighted average fuel consumption, and ${\displaystyle {\sum }_{i=1}^n}{V}_i$ is the total annual production volume. The official unit of total CAFC credits is “credits”. Under our benchmark single-model setting, the production-weighted corporate average and its target reduce directly to the representative model’s actual fuel consumption $f$ and model-specific target $Q_0$ (both in L/100 km), as production weighting is trivial for a single product line. Dividing total credits by production volume yields per-vehicle CAFC credits: ${\lambda }_1=Q_0-f$.

The unit of ${\lambda }_1$ represents credits per vehicle. Under uniform production weighting, a 1 L/100 km difference between $Q_0$ and $f$ corresponds exactly to 1 credit per vehicle produced, fully consistent with official accounting logic. When $f<Q_0$, ${\lambda }_1>0$ and the vehicle generates positive CAFC credits transferable to affiliated enterprises; when $f>Q_0$, ${\lambda }_1<0$ and negative credits must be offset by purchasing NEV credits from the market. The admissible range of ${\lambda }_1$ is $\left[Q_0-f_{\mathrm{m}\mathrm{a}\mathrm{x}},Q_0\right]$.

For the NEV manufacturer, each vehicle generates per-vehicle NEV credits ${\lambda }_2$ (${\lambda }_2>0$), calculated per official MIIT rules based on driving range, electricity consumption, battery energy density, and low-temperature performance [8]. ${\lambda }_2$ is a comprehensive indicator that positively correlates with NEV energy efficiency: higher energy efficiency (lower electricity consumption, longer driving range) corresponds to a larger ${\lambda }_2$. This paper uses ${\lambda }_2$ as the proxy for NEV energy efficiency level, and uses $f$ as the metric for FV energy consumption level.

The required NEV credit ratio is $a$ ($a>0$). The internal transfer price of CAFC credits among affiliated enterprises is $P_c$, and the market transaction price of NEV credits is $P_n$, where $P_n,P_c>0$. The unit profits of FVs and NEVs are ${\pi }_o$ and ${\pi }_e$ respectively, and sales volumes are $S_o$ and $S_e$ respectively. Based on the above settings, the following assumptions are made:

Assumption 1.

All vehicles produced by the manufacturers can be fully absorbed by the market, i.e., production volume equals consumer demand. All positive credits generated can be fully sold on the market.

Justification. 

This market-clearing assumption is a standard approach in single-period classical operations management models (e.g., [22,23]). It is deliberately adopted to isolate the pure incentive effects of the DCP on energy efficiency decisions without the confounding mathematical complexities introduced by inventory holding costs and stochastic demand. The implications of relaxing this assumption under market saturation are thoroughly discussed in the Limitations section.

Assumption 2.

We consider production activities within a single cycle. No CAFC credits are carried over from previous years, and all positive credits generated must be sold or used for compliance within the same cycle.

Justification. 

This static framework allows us to derive closed-form optimal solutions and clear threshold effects. A multi-period model with credit carry-over would capture dynamic R&D and inter-temporal credit allocation, which we leave for future research.

Assumption 3.

To examine the impact of the Dual-Credit Policy on automobile production, this paper assumes that the sales volume of FVs is mainly determined by the fuel consumption level $f$, and the sales volume of NEVs is mainly determined by the energy efficiency level ${\lambda }_2$. In general, for the same vehicle model with unchanged price, lower fuel consumption of FVs will generally attract more consumers to purchase, thereby increasing vehicle sales. Similarly, higher energy efficiency performance of NEVs will also attract more consumers and increase sales. Therefore, we assume that the sales functions of FVs $S_o$ and NEVs $S_e$ take a linear form, with the following formulas:

$$S_o\left(f\right)=S_2-S_{1}f$$

(1)

$$S_e\left({\lambda }_2\right)=S_3{\lambda }_2+S_4$$

(2)

where $S_1$ represents the sensitivity of FV sales to fuel consumption ($S_1>0)$; $S_3$ represents the sensitivity of NEV sales to energy efficiency ($S_3>0)$; $S_2$ and $S_4$ represent the natural sales volume of FVs and NEVs, respectively ${(S}_2,S_4>0)$. Since the sales volume of FVs cannot be negative, $S_o=S_2-S_{1}f\ge 0, \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{i}\mathrm{s}, f\le {\displaystyle \frac{S_2}{S_1}}$, corresponding to the upper limit of fuel consumption $f_{max}={\displaystyle \frac{S_2}{S_1}}$.

Justification. 

We adopt linear demand functions that link FV sales only to fuel consumption and NEV sales only to energy efficiency. This specification is widely used in industrial organization literature because it captures the first-order effect of product attributes on demand and allows for closed-form analytical solutions. While real-world automobile demand is influenced by multiple factors (price, brand value, charging infrastructure, government subsidies, etc.), these factors can be captured by the intercept terms (S₂ and S₄) of the demand functions without altering the monotonic relationship between energy performance and sales. Our empirical results confirm a significant linear correlation between energy efficiency and sales in the Chinese automobile market, supporting the validity of this assumption. The simplification enables us to derive clear threshold effects, which are the core contribution of this study.

Assumption 4.

Similarly, to examine the impact of the Dual-Credit Policy on automobile production, this paper assumes that the price and cost of FVs are mainly affected by their own fuel consumption level $f$, and the price and cost of NEVs are mainly affected by their own energy efficiency level ${\lambda }_2$, without considering other influencing factors. In general, for the same vehicle model, lower fuel consumption leads to higher manufacturing difficulty, higher cost, and thus higher selling price; the same applies to NEVs, where higher energy efficiency leads to higher manufacturing difficulty, higher cost, and higher selling price. According to practical conditions, as the fuel consumption of FVs further decreases and the energy efficiency of NEVs further increases, the manufacturing cost will increase at an accelerated rate, and the vehicle price will also increase at an accelerated rate. Since profit equals price minus cost, we assume that the profit functions of FVs ${\pi }_o$ and NEVs ${\pi }_e$ take a quadratic form, with the following formulas:

$${\pi }_o\left(f\right)=\mathrm{A}{f}^2+\mathrm{B}f+\mathrm{D}$$

(3)

$${\pi }_e\left({\lambda }_2\right)={\mathrm{A}}_1{{\lambda }_2}^2+{\mathrm{B}}_1{\lambda }_2+{\mathrm{D}}_1$$

(4)

For Equation (3), $A<0$ represents the intensity of price loss of FVs with rising fuel consumption; $B>0$ represents the linear marginal revenue per unit of rising fuel consumption (10,000 yuan per unit fuel consumption); $D>0$ represents the base profit of FVs. Specifically, the profit function (3) indicates that when the fuel consumption level is lower than a certain critical value $f^{*}$, as the fuel consumption continues to decrease, the growth rate of manufacturing cost is generally higher than that of vehicle price, and the enterprise’s profit will gradually decrease. When the fuel consumption level is higher than the critical value $f^{*}$, as the fuel consumption continues to increase, the decline rate of vehicle price is generally higher than that of cost, and the enterprise’s profit will also gradually decrease, even leading to losses.

For Equation (4), $A_1<0$ represents the intensity of increasing manufacturing cost with rising energy efficiency of NEVs; $B_1>0$ represents the linear marginal revenue per unit of rising energy efficiency (10,000 yuan per unit energy efficiency); $D_1>0$ represents the base profit of low-energy efficiency NEVs. Specifically, the profit function (4) indicates that when the energy efficiency level is lower than a certain critical value ${\lambda }_2^{*}$, as the energy efficiency continues to decrease, the decline rate of vehicle price is generally higher than that of cost, and the enterprise’s profit will gradually decrease. When the energy efficiency level is higher than the critical value ${\lambda }_2^{*}$, as the energy efficiency continues to increase, the growth rate of manufacturing cost is generally higher than that of price, and the enterprise’s profit will also gradually decrease, even leading to losses.

The profit changes in FVs and NEVs are shown in Figure 1a and Figure 1b, respectively.

Under the Dual-Credit Policy, traditional FV manufacturers must consider whether the fuel consumption of their vehicles meets the standard when producing the same model, while NEV manufacturers must consider whether the energy efficiency performance of their vehicles meets the expected economic benefits. Based on the above, the stakeholder interest relationship diagram of each manufacturer is obtained (Figure 2). Next, we will analyze the optimal production decision models for FV and NEV manufacturers, respectively.

4. Model Establishment and Solution

This study adopts a partial equilibrium comparative statics framework to analyze individual manufacturers’ optimal production and energy decisions given an exogenous credit price. The NEV credit price $P_n$ is treated as exogenous in the theoretical model for two reasons:

• Our theoretical objective is to characterize how a profit-maximizing manufacturer responds to a given market price signal, which is the standard microeconomic approach to firm-level comparative statics.
• In the Chinese credit market, individual manufacturers are price takers: no single firm is large enough to unilaterally determine the market-wide credit price, even though the market is concentrated among a few large players.

This theoretical setting is distinct from our empirical analysis, where we treat the market credit price as endogenous and use instrumental variables to address endogeneity bias and estimate its association with firm decisions. The two levels of analysis are complementary: the theory derives the direction of the firm’s response to price changes, and the empirical analysis quantifies the empirical magnitude of this association using real market data.

4.1. Optimal Production Decision Model for Traditional Fuel Vehicle Manufacturers

4.1.1. Model Establishment

For traditional FVs, after the introduction of the Dual-Credit Policy, there exists a benchmark fuel consumption standard $Q_0$. When the actual fuel consumption of the vehicle $f>Q_0$, the produced FVs will generate negative CAFC credits, which require the purchase of NEV credits for offsetting. At the same time, according to the production volume of FVs and the required NEV credit ratio, the production of FVs itself generates negative NEV credit requirements, which also need to be offset by purchasing NEV credits. Therefore, in this case, the unit profit of producing FVs ${\pi }_o$ can be expressed as Equation (5):

$${\pi }_o(f)=\mathrm{A}{f}^2+\mathrm{B}f+\mathrm{D}+\underset{{\lambda }_1<0}{\underbrace{\left(Q_0-f\right)}}{P}_n-a{P}_n$$

(5)

where $(Q_0-f)P_n$ is the value of positive NEV credits purchased by the enterprise to offset negative CAFC credits and $a{P}_n$ is the value of NEV credits required for each unit of FV produced by the enterprise.

When the actual fuel consumption $f<Q_0$, positive CAFC credits are generated, which can be sold to affiliated enterprises to obtain profits. Meanwhile, according to the latest policy specification [7], FVs with fuel consumption meeting the standard ($f\le Q_0$) are only counted as 0.1 times the production volume for NEV credit compliance calculation. Therefore, in this case, the unit profit of producing FVs ${\pi }_o$ can be expressed as Equation (6):

$${\pi }_o(f)=\mathrm{A}{f}^2+\mathrm{B}f+\mathrm{D}+\underset{{\lambda }_1\ge 0}{\underbrace{\left(Q_0-f\right)}}{P}_c-0.1a{P}_n$$

(6)

where $(Q_0-f)P_c$ is the additional profit obtained by the enterprise from selling positive CAFC credits and $0.1a{P}_n$ is also the value of NEV credits required for each unit of FV produced by the enterprise.

In summary, the total profit $R$ of the FV manufacturer under the two scenarios can be expressed as Model (7) and Model (8) respectively:

$$\left\{\begin{array}{c}{R}_1\left(f\right)=\left[\mathrm{A}{f}^2+\mathrm{B}f+\mathrm{D}+\left(Q_0-f\right)P_n-a{P}_n\right]\times (S_2-S_{1}f)\\ \mathrm{s}.\mathrm{t}. f>Q_0>0, f\le {\displaystyle \frac{S_2}{S_1}}\hspace{0.17em}(f_{\mathrm{m}\mathrm{a}\mathrm{x}})\end{array}\right.$$

(7)

$$\left\{\begin{array}{c}{R}_2\left(f\right)=\left[\mathrm{A}{f}^2+\mathrm{B}f+\mathrm{D}+\left(Q_0-f\right)P_c-0.1a{P}_n\right]\times (S_2-S_{1}f)\\ \mathrm{s}.\mathrm{t}. 0<f\le Q_0<{\displaystyle \frac{S_2}{S_1}}\hspace{0.17em}(f_{\mathrm{m}\mathrm{a}\mathrm{x}})\end{array}\right.$$

(8)

Next, we solve the optimization problems of Model (7) and Model (8) respectively.

4.1.2. Model Solution

(1)

Optimization Solution for High Fuel Consumption Scenario ($f>Q_0$)

To ensure that the FV manufacturer has an optimal solution in the high fuel consumption scenario, this paper sets the parameter condition ${\displaystyle \frac{S_2}{S_1}}(B-P_n)>D+P_n(Q_0-a)$, which is essentially consistent with the actual operation of enterprises.

$$R_{1^{\prime }}(f)=-S_1\left\{3\mathrm{A}{f}^2+\left[2\left(\mathrm{B}-P_n\right)-2\mathrm{A}{\displaystyle \frac{S_2}{S_1}}\right]f+\left[\mathrm{D}+P_n\left(Q_0-a\right)-{\displaystyle \frac{S_2}{S_1}}\left(\mathrm{B}-P_n\right)\right]\right\}$$

(9)

Discriminant (always positive, with two positive real roots according to Vieta’s formulas):

$${\mathsf{\Delta }}_1=4\left\{{\mathrm{A}}^2{\left({\displaystyle \frac{S_2}{S_1}}\right)}^2+\mathrm{A}{\displaystyle \frac{S_2}{S_1}}(\mathrm{B}-P_n)+(\mathrm{B}-P_n{)}^2-3\mathrm{A}\left[\mathrm{D}+P_n(Q_0-a)\right]\right\}$$

(10)

Optimal fuel consumption (smaller root):

$$f_1^{*}={\displaystyle \frac{2\left(\mathrm{B}-P_n\right)-2\mathrm{A}\frac{S_2}{S_1}-\sqrt{{\mathsf{\Delta }}_1}}{-6\mathrm{A}}}$$

(11)

$f_1^{*}$ is the unique interior maximum point of $R_1\left(f\right)$ within the economically effective domain. The value rule for the maximum profit $R_{1\mathrm{m}\mathrm{a}\mathrm{x}}$ in the high fuel consumption scenario is as follows: if the interior maximum point $f_1^{*}$ falls within the effective domain $(Q_0,{\displaystyle \frac{S_2}{S_1}})$, then $R_{1\mathrm{m}\mathrm{a}\mathrm{x}}$ takes the value of $R_1\left(f_1^{*}\right)$; if $f_1^{*}\le Q_0$, then $R_{1\mathrm{m}\mathrm{a}\mathrm{x}}$ takes the value of $R_1\left(Q_0\right)$; if $f_1^{*}\ge {\displaystyle \frac{S_2}{S_1}}$, then $R_{1\mathrm{m}\mathrm{a}\mathrm{x}}$ takes the value of 0, which has no economic significance.

(2)

Optimization Solution for Low Fuel Consumption Scenario ($f\le Q_0$)

To ensure that the FV manufacturer has an optimal solution in the low fuel consumption scenario, this paper sets the parameter condition ${\displaystyle \frac{S_2}{S_1}}(B-P_c)>D+Q_0{P}_c-0.1a{P}_n$, which is basically consistent with the actual operation of enterprises.

$$R_{1^{\prime }}(f)=-S_1\left\{3\mathrm{A}{f}^2+\left[2(\mathrm{B}-P_c)-2\mathrm{A}{\displaystyle \frac{S_2}{S_1}}\right]f+\left[\mathrm{D}+Q_0{P}_c-0.1a{P}_n-{\displaystyle \frac{S_2}{S_1}}(\mathrm{B}-P_c)\right]\right\}$$

(12)

Discriminant (always positive, with two positive real roots according to Vieta’s formulas):

$${\mathsf{\Delta }}_2=4\left\{{\mathrm{A}}^2{\left({\displaystyle \frac{S_2}{S_1}}\right)}^2+\mathrm{A}{\displaystyle \frac{S_2}{S_1}}(\mathrm{B}-P_c)+(\mathrm{B}-P_c{)}^2-3\mathrm{A}\left[\mathrm{D}+Q_0{P}_c-0.1a{P}_n\right]\right\}$$

(13)

Optimal fuel consumption (smaller root):

$$f_2^{*}={\displaystyle \frac{2\left(\mathrm{B}-P_c\right)-2\mathrm{A}\frac{S_2}{S_1}-\sqrt{{\mathsf{\Delta }}_2}}{-6\mathrm{A}}}$$

(14)

$f_2^{*}$ is the unique interior maximum point of $R_2\left(f\right)$ within the economically effective domain. The value rule for the maximum profit $R_{2\mathrm{m}\mathrm{a}\mathrm{x}}$ in the low fuel consumption scenario is as follows: if the interior maximum point $f_2^{*}$ falls within the effective domain $(0,Q_0)$, then $R_{2\mathrm{m}\mathrm{a}\mathrm{x}}$ takes the value of $R_2\left(f_2^{*}\right)$; if $f_2^{*}\ge Q_0$, then $R_{2\mathrm{m}\mathrm{a}\mathrm{x}}$ takes the value of $R_2\left(Q_0\right)$.

From the assumptions, $a>0$, $P_n>0$, $Q_0<{\displaystyle \frac{S_2}{S_1}}$. Therefore, $R_2\left(Q_0\right)-R_1\left(Q_0\right)=0.9a{P}_n\cdot (S_2-S_1{Q}_0)>0$; that is, $R_2\left(Q_0\right)>R_1\left(Q_0\right)$ always holds.

4.1.3. Model Analysis

Based on the compliance rules of the Dual-Credit Policy, we have constructed the profit functions of the FV manufacturer under two scenarios: high fuel consumption (non-compliant) and low fuel consumption (compliant), and completed the optimization solution. On this basis, it is necessary to further clarify the influence mechanisms of core parameters of the Dual-Credit Policy, market demand characteristics, and cost structure factors on the manufacturer’s optimal fuel consumption decisions and strategy dominance, as well as the optimal decision rules under different parameter intervals. Below, through mathematical derivation, we reveal the influence effects of each variable on the optimal decisions of FV manufacturers and define the dominance intervals and critical conditions of the two strategies. The specific analysis and proof are as follows.

Proposition 1.

(1) A rise in the NEV credit price $P_n$ strictly reduces the optimal fuel consumption $f_1^{*}$ in the high-fuel-consumption scenario and lowers both $R_1^{max}$ and $R_2^{max}$. A rise in the CAFC credit price $P_c$ strictly reduces $f_2^{*}$ and raises $R_2^{max}$. These results hold globally in the economically feasible domain. (2) Under the sufficient condition $(Q_0-f_1^{*}-a)(S_2-S_1{f}_1^{*})+0.1a(S_2-S_1{f}_2^{*})<0$ (C1), rising $P_n$ strengthens the dominance of the low-fuel-consumption strategy. The dominance-strengthening effect of $P_c$ holds unconditionally. Condition (C1) is satisfied under our baseline industrial calibration.

Proof. 

By the Envelope Theorem: $\partial R_1/\partial P_n=(Q_0-f-a)(S_2-S_{1}f)<0$, $\partial R_2/\partial P_n=-0.1a(S_2-S_{1}f)<0$, and $\partial R_2/\partial P_c=(Q_0-f)(S_2-S_{1}f)>0$ hold universally in the feasible domain, confirming the global profit effects.

Applying the Implicit Function Theorem to the first-order condition $F(f,P)=0$, with $\partial F/\partial f<0$ (second-order condition for maximum) and $\partial F/\partial P_n,\partial F/\partial P_c<0$, yields $\partial f_1^{*}/\partial P_n<0$ and $\partial f_2^{*}/\partial P_c<0$.

Define the profit difference $\mathsf{\Delta }=R_1^{\mathrm{m}\mathrm{a}\mathrm{x}}-R_2^{\mathrm{m}\mathrm{a}\mathrm{x}}$. For $P_n$, $d\mathsf{\Delta }/d{P}_n$ matches the left-hand side of Condition (C1), and is negative under the condition. For $P_c$, $d\mathsf{\Delta }/d{P}_c=-(Q_0-f_2^{*})(S_2-S_1{f}_2^{*})<0$ always holds. Q.E.D. □

Proposition 2.

(1) The NEV credit ratio requirement $a$ strictly reduces both $R_1^{max}$ and $R_2^{max}$. This result holds globally. (2) Under the sufficient condition $S_2-S_1{f}_1^{*}>0.1(S_2-S_1{f}_2^{*})$ (C2), the negative impact of $a$ is stronger on the high-fuel-consumption strategy. Condition (C2) holds under realistic industrial parameters. (3) If $R_1^{max}>R_2^{max}$ at $a=0$ (verified under baseline calibration), there exists a unique threshold $a^{*}$ such that the low-fuel-consumption strategy is strictly dominant for all $a>a^{*}$.

Proof. 

By the Envelope Theorem: ${\displaystyle \frac{d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}}{da}}=-P_n(S_2-S_1{f}_1^{*})<0, {\displaystyle \frac{d{R}_2^{\mathrm{m}\mathrm{a}\mathrm{x}}}{da}}=-0.1P_n(S_2-S_1{f}_2^{*})<0$. Under Condition (C2), $|d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}/da|>|d{R}_2^{\mathrm{m}\mathrm{a}\mathrm{x}}/da|$. Given $R_1^{\mathrm{m}\mathrm{a}\mathrm{x}}>R_2^{\mathrm{m}\mathrm{a}\mathrm{x}}$ at $a=0$ and strictly faster decline of $R_1^{\mathrm{m}\mathrm{a}\mathrm{x}}$, the Intermediate Value Theorem and strict monotonicity guarantee a unique threshold $a^{*}$. Q.E.D. □

Proposition 3.

The maximum profit $R_2^{max}$ of the low fuel consumption strategy is strictly positively correlated with the benchmark fuel consumption standard $Q_0$. For $R_1^{max}$ of the high fuel consumption strategy, taking a fixed value $f_{1,int}^{*}$ (independent of $Q_0$) as the boundary: $R_1^{max}$ increases with $Q_0$ when $Q_0<f_{1,int}^{*}$, decreases with $Q_0$ when $Q_0>f_{1,int}^{*}$, and reaches the global maximum at $Q_0=f_{1,int}^{*}$. The optimal fuel consumption $f_1^{*}$ and $f_2^{*}$ of both strategies are non-decreasing with $Q_0$: independent of $Q_0$ in the interior solution state, and increasing with $Q_0$ in the boundary solution state.

Proof. 

By the Envelope Theorem, ${\displaystyle \frac{d{R}_2^{\mathrm{m}\mathrm{a}\mathrm{x}}}{d{Q}_0}}=P_c(S_2-S_1{f}_2^{*})>0$, confirming $R_2^{\mathrm{m}\mathrm{a}\mathrm{x}}$ is strictly positively correlated with $Q_0$. For the high fuel consumption scenario:

When $Q_0<f_{1,\mathrm{i}\mathrm{n}\mathrm{t}}^{*}$, the optimal solution is the interior solution $f_1^{*}=f_{1,\mathrm{i}\mathrm{n}\mathrm{t}}^{*}$, so ${\displaystyle \frac{d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}}{d{Q}_0}}=P_n(S_2-S_1{f}_{1,\mathrm{i}\mathrm{n}\mathrm{t}}^{*})>0$; When $Q_0>f_{1,\mathrm{i}\mathrm{n}\mathrm{t}}^{*}$, the optimal solution degenerates to the boundary solution $f_1^{*}=Q_0$, so ${\displaystyle \frac{d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}}{d{Q}_0}}=R_{1^{\prime }}(Q_0)<0$.

For the non-decreasing property: interior solutions of $f_1^{*}$ and $f_2^{*}$ are solved from the FOC, which contains no $Q_0$ term, thus are independent of $Q_0$; boundary solutions degenerate to $f_1^{*}=Q_0$ and $f_2^{*}=Q_0$, which strictly increase with $Q_0$. Q.E.D. □

Proposition 4.

(1) $R_2^{max}$ is strictly increasing in the benchmark fuel consumption standard $Q_0$. For $R_1^{max}$: it increases with $Q_0$ when $Q_0<f_{1,int}^{*}$ (interior solution), decreases when $Q_0>f_{1,int}^{*}$ (boundary solution), and peaks at $Q_0=f_{1,int}^{*}$. Optimal fuel consumption $f_1^{*},f_2^{*}$ are non-decreasing in $Q_0$: invariant in interior solution states and increasing in boundary solution states. These results hold globally. (2) Define $\Delta \left(Q_0\right)=R_1^{max}-R_2^{max}$. Under the sufficient condition $P_n(S_2-S_1{f}_1^{*})>P_c(S_2-S_1{f}_2^{*})$ (C3), $\Delta \left(Q_0\right)$ is strictly increasing over $(0, f_{1,int}^{*}]$. Condition (C3) is satisfied under baseline calibration. (3) When Condition (C3) holds and $\Delta \left(Q_0\right)$ crosses zero over the interval, at least one threshold $Q_0^{*}$ exists: the low-fuel-consumption strategy dominates below the threshold, and the high-fuel-consumption strategy dominates above it. Threshold uniqueness is verified numerically. Over the full domain $(0, f_{max})$, two thresholds exist and the high-fuel-consumption strategy dominates only for $Q_0\in (Q_{\mathrm{0,1}}^{*},Q_{\mathrm{0,2}}^{*})$.

Proof. 

By the Envelope Theorem: $d{R}_2^{\mathrm{m}\mathrm{a}\mathrm{x}}/d{Q}_0=P_c(S_2-S_1{f}_2^{*})>0$. For $R_1^{\mathrm{m}\mathrm{a}\mathrm{x}}$: $d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}/d{Q}_0=P_n(S_2-S_1{f}_{1,\mathrm{i}\mathrm{n}\mathrm{t}}^{*})>0$ in the interior solution regime, and $d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}/d{Q}_0=R_{1^{\prime }}\left(Q_0\right)<0$ in the boundary solution regime.

Interior solutions are independent of $Q_0$ (no $Q_0$ term in the FOC), while boundary solutions satisfy $f^{*}=Q_0$, confirming the non-decreasing property.

For the profit difference: $d\mathsf{\Delta }/d{Q}_0=P_n(S_2-S_1{f}_1^{*})-P_c(S_2-S_1{f}_2^{*})$, which is positive under Condition (C3). Existence of at least one threshold follows from continuity and sign change; uniqueness is confirmed via numerical simulation. Q.E.D. □

Proposition 5.

(1) The price loss intensity $\left|A\right|$ (with $A=-\left|A\right|$) strictly reduces maximum profit and optimal fuel consumption for both strategies. These results hold globally. (2) Under the sufficient condition $\left(f_1^{*}{)}^2\right(S_2-S_1{f}_1^{*})>(f_2^{*}{)}^2(S_2-S_1{f}_2^{*})$ (C4), the inhibitory effect is stronger for the high-fuel-consumption strategy. Condition (C4) holds under realistic industrial parameters. (3) When Condition (C4) holds and the profit difference function crosses zero, at least one threshold $|A{|}^{*}$ exists: the low-fuel-consumption strategy dominates when $\left|A\right|>|A{|}^{*}$. Threshold uniqueness is verified numerically.

Proof. 

By the Envelope Theorem: $d{R}^{\mathrm{m}\mathrm{a}\mathrm{x}}/d\left|A\right|=-\left(f^{*}{)}^2\right(S_2-S_1{f}^{*})<0$ for both strategies. By the Implicit Function Theorem: $\partial f^{*}/\partial \left|A\right|<0$. Under Condition (C4), $|d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}/d|A\left|\right|>|d{R}_2^{\mathrm{m}\mathrm{a}\mathrm{x}}/d|A\left|\right|$. Threshold existence follows from continuity and sign change in the profit difference function; uniqueness is confirmed via numerical simulation. Q.E.D. □

Proposition 6.

(1) The fuel consumption sales sensitivity $S_1$ strictly reduces maximum profit and optimal fuel consumption for both strategies. These results hold globally. (2) Under the sufficient condition $f_1^{*}\cdot {\pi }_1\left(f_1^{*}\right)>f_2^{*}\cdot {\pi }_2\left(f_2^{*}\right)$ (C5), where ${\pi }_1,{\pi }_2$ denote unit profit in each scenario, the inhibitory effect is stronger for the high-fuel-consumption strategy. Condition (C5) holds under baseline calibration. (3) When Condition (C5) holds and the profit difference function crosses zero, at least one threshold $S_1^{*}$ exists: the low-fuel-consumption strategy dominates when $S_1>S_1^{*}$. Threshold uniqueness is verified numerically.

Proof. 

By the Envelope Theorem: $d{R}^{\mathrm{m}\mathrm{a}\mathrm{x}}/d{S}_1=-f^{*}\cdot \pi \left(f^{*}\right)<0$ for both strategies (with $\pi \left(f^{*}\right)>0$ in the feasible domain). By the Implicit Function Theorem: $\partial f^{*}/\partial S_1<0$. Under Condition (C5), $|d{R}_1^{\mathrm{m}\mathrm{a}\mathrm{x}}/d{S}_1|>|d{R}_2^{\mathrm{m}\mathrm{a}\mathrm{x}}/d{S}_1|$. Threshold existence follows from continuity and sign change; uniqueness is confirmed via numerical simulation. Q.E.D. □

4.2. Optimal Production Decision Model for New Energy Vehicle Manufacturers

4.2.1. Model Establishment

For NEVs, after the introduction of the Dual-Credit Policy, manufacturers can obtain corresponding NEV credits ${\lambda }_2$ according to the quality of the NEVs produced, and the generated NEV credits can be sold in the credit market at the market price $P_n$ to obtain profits. Therefore, the unit profit of producing NEVs ${\pi }_2$ can be expressed as Equation (15)

$${\pi }_2\left({\lambda }_2\right)={\mathrm{A}}_1{{\lambda }_2}^2+{\mathrm{B}}_1{\lambda }_2+{\mathrm{D}}_1+{\lambda }_2{P}_n$$

(15)

where ${\lambda }_2{P}_n$ is the additional profit obtained by the enterprise from selling NEV credits. In summary, the total profit R3 of the NEV manufacturer can be expressed as Model (16)

$$\left\{\begin{array}{c}{R}_3\left({\lambda }_2\right)=({\mathrm{A}}_1{{\lambda }_2}^2+{\mathrm{B}}_1{\lambda }_2+{\mathrm{D}}_1+{\lambda }_2{P}_n)\times (S_3{\lambda }_2+S_4)\\ {\lambda }_2>0\end{array}\right.$$

(16)

Next, we solve the optimization problem of Model (16).

4.2.2. Model Solution

$$\mathrm{l}\mathrm{e}\mathrm{t} R_{3^{\prime }}\left({\lambda }_2\right)=0, \mathrm{w}\mathrm{e} \mathrm{o}\mathrm{b}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{n}: 3{\mathrm{A}}_1{S}_3{\lambda }_2^2+2\left[{\mathrm{A}}_1{S}_4+S_3({\mathrm{B}}_1+P_n)\right]{\lambda }_2+\left[S_4({\mathrm{B}}_1+P_n)+{{\mathrm{D}}_{1}S}_3\right]=0$$

Since the quadratic coefficient $3{\mathrm{A}}_1{S}_3<0$ and the constant term $S_4({\mathrm{B}}_1+P_n)+{{\mathrm{D}}_{1}S}_3>0$, the discriminant $\mathsf{\Delta }>0$, and the product of the two roots is less than 0. The equation always has one positive and one negative real root. Since the energy efficiency level ${\lambda }_2\ge 0$, the negative root has no economic significance, so the only economically meaningful optimal solution is the positive root.

Discriminant:

$${\mathsf{\Delta }}_e=4{\left[{\mathrm{A}}_1{S}_4+S_3({\mathrm{B}}_1+P_n)\right]}^2-12S_3{\mathrm{A}}_1\left[S_4({\mathrm{B}}_1+P_n)+S_3{\mathrm{D}}_1\right]$$

(17)

Optimal energy efficiency:

$${\lambda }_2^{*}={\displaystyle \frac{-\left[{{\mathrm{A}}_{1}S}_4+S_3({\mathrm{B}}_1+P_n)\right]-\frac{\sqrt{{\mathsf{\Delta }}_e}}{2}}{3S_3{\mathrm{A}}_1}}$$

(18)

Maximum profit of the enterprise:

$$R_3^{*}=\left[{\mathrm{A}}_1{{\lambda }_2^{*}}^2+({\mathrm{B}}_1+P_n){\lambda }_2^{*}+{\mathrm{D}}_1\right]\ast \left[S_3{\lambda }_2^{*}+S_4\right]$$

(19)

4.2.3. Model Analysis

Based on the market transaction rules of NEV credits, we have constructed a profit-maximizing decision model for NEV manufacturers and completed the optimization solution. On this basis, it is necessary to further identify the action paths of core factors such as Dual-Credit Policy incentives, market demand characteristics, and R&D cost constraints on the optimal energy efficiency decisions of NEV manufacturers, and verify the market-oriented incentive effect of the Dual-Credit Policy on the energy efficiency and technological upgrading of manufacturers. Below, through mathematical derivation, we analyze the influence mechanism of each variable on the optimal energy efficiency decisions of NEV manufacturers. The specific analysis and proof are as follows.

Proposition 7.

The NEV credit price $P_n$ has a strictly positive incentive effect on the optimal energy efficiency level ${\lambda }_2^{*}$ of NEV manufacturers, i.e., the higher the credit price, the higher the optimal energy efficiency level of the manufacturer.

Proof. 

Let the FOC of profit maximization for NEV manufacturers be $F({\lambda }_2,P_n)=R_{3^{\prime }}\left({\lambda }_2\right)=0$. By the Implicit Function Theorem, ${\displaystyle \frac{\partial {\lambda }_2^{*}}{\partial P_n}}=-{\displaystyle \frac{\partial F/\partial P_n}{\partial F/\partial {\lambda }_2}}$.

Within the economically feasible domain, ${\displaystyle \frac{\partial F}{\partial P_n}}=2S_3{\lambda }_2+S_4>0$ always holds (all parameters are positive). The SOC for a maximum satisfies ${\displaystyle \frac{\partial F}{\partial {\lambda }_2}}=R_{3^{″}}({\lambda }_2^{*})<0$ (concavity of the profit function). Thus ${\displaystyle \frac{\partial {\lambda }_2^{*}}{\partial P_n}}>0$, confirming a strictly positive incentive effect of $P_n$ on optimal energy efficiency. Q.E.D. □

Proposition 8.

The greater the sensitivity of NEV sales to energy efficiency $S_3$, the higher the optimal energy efficiency level ${\lambda }_2^{*}$ of the NEV manufacturer, i.e., $S_3$ has a strictly positive incentive effect on the optimal energy efficiency level.

Proof. 

Let the FOC of profit maximization be $F({\lambda }_2,S_3)=R_{3^{\prime }}\left({\lambda }_2\right)=0$. By the Implicit Function Theorem, ${\displaystyle \frac{\partial {\lambda }_2^{*}}{\partial S_3}}=-{\displaystyle \frac{\partial F/\partial S_3}{\partial F/\partial {\lambda }_2}}$.

At the optimal solution, we derive ${\displaystyle \frac{\partial F}{\partial S_3}}>0$ from the FOC and the property of the unit profit function. Combined with the SOC ${\displaystyle \frac{\partial F}{\partial {\lambda }_2}}<0$, we obtain ${\displaystyle \frac{\partial {\lambda }_2^{*}}{\partial S_3}}>0$, confirming a strictly positive incentive effect of $S_3$ on optimal energy efficiency. Q.E.D. □

Proposition 9.

The greater the negative effect of energy efficiency improvement on unit profit $\left|A_1\right|$ (i.e., the higher the marginal manufacturing cost intensity of energy efficiency upgrading), the lower the optimal energy efficiency level ${\lambda }_2^{*}$ of the NEV manufacturer.

Proof. 

Let $A_1=-\left|A_1\right|$; the proposition is equivalent to proving ${\displaystyle \frac{\partial {\lambda }_2^{*}}{\partial A_1}}>0$. Let the FOC of profit maximization be $F({\lambda }_2,A_1)=R_{3^{\prime }}\left({\lambda }_2\right)=0$. By the Implicit Function Theorem, ${\displaystyle \frac{\partial {\lambda }_2^{*}}{\partial A_1}}=-{\displaystyle \frac{\partial F/\partial A_1}{\partial F/\partial {\lambda }_2}}$.

Within the feasible domain, ${\displaystyle \frac{\partial F}{\partial A_1}}=3S_3{\lambda }_2^{*2}+2S_4{\lambda }_2^{*}>0$ always holds. Combined with the SOC ${\displaystyle \frac{\partial F}{\partial {\lambda }_2}}<0$, we obtain ${\displaystyle \frac{\partial {\lambda }_2^{*}}{\partial A_1}}>0$. Thus, the higher the $\left|A_1\right|$ (the smaller the $A_1$), the lower the optimal energy efficiency level ${\lambda }_2^{*}$. Q.E.D. □

5. Numerical Simulation Analysis

This paper uses numerical analysis to further verify the above conclusions and intuitively demonstrates the optimal energy consumption production decisions of FV and NEV manufacturers under different conditions through numerical examples.

The numerical simulation in this section serves as an illustrative example of the theoretical model’s behavior under realistic parameter values, rather than an independent empirical validation of the model. All parameters are calibrated based on public industry data, and the robustness of core conclusions is verified via sensitivity analysis. The specific parameter settings are shown in

Table 1. Reference table of basic parameters for fuel vehicles.

Parameter Symbol	Value	Economic Meaning	Data Source/Justification
$Q_0$	6	National benchmark fuel consumption standard (L/100 km)	MIIT Phase V/VI passenger car fuel consumption standards
$\mathrm{A}$	−0.2	Intensity of marginal decrease in FV price with rising fuel consumption	Industry-calibrated value: Based on the empirical fact that a 1 L/100 km increase in fuel consumption reduces FV selling price by approximately 2000 yuan in the Chinese market. This value is consistent with the price elasticity of fuel economy observed in mainstream compact and mid-size vehicle segments
$\mathrm{B}$	3	Basic marginal revenue per unit of rising fuel consumption (10,000 yuan/unit fuel consumption)	Cost–benefit calibration: Derived from the average manufacturing cost difference between high-fuel-consumption and low-fuel-consumption versions of the same vehicle model
$P_n$	0.2	NEV credit transaction price (10,000 yuan/credit)	Average transaction price on the national credit trading platform (2021–2026)
$P_c$	0.1	CAFC credit transaction price (10,000 yuan/credit)	Average transaction price on the national credit trading platform (2021–2026)
$a$	0.48	Required NEV credit ratio	MIIT 2025 Notice [7]
$D$	5	Basic gross profit per FV (10,000 yuan)
$S_1$	0.1	Marginal sensitivity coefficient of sales to fuel consumption (10,000 vehicles/unit fuel consumption)	Empirically estimated value: Based on our regression analysis of 2017–2024 vehicle sales data
$S_2$	2	Natural sales volume of FVs (10,000 vehicles)

and

Table 2. Reference table of basic parameters for new energy vehicles.

Parameter Symbol	Value	Economic Meaning	Data Source/Justification
${\mathrm{A}}_1$	−0.5	Intensity of increasing manufacturing cost with rising energy efficiency	Technology cost calibration: Derived from battery cost data (1000 yuan/kWh)
${\mathrm{B}}_1$	3	Basic marginal revenue per unit of rising energy efficiency (10,000 yuan/unit energy efficiency)	Market premium calibration: Based on the empirical fact that NEVs with higher energy efficiency (and thus higher credits)
$P_n$	0.2	NEV credit transaction price (10,000 yuan/credit)	Average transaction price on the national credit trading platform (2021–2026)
$D_1$	4	Basic gross profit per NEV (10,000 yuan)
$S_3$	0.4	Marginal sensitivity coefficient of sales to energy efficiency (10,000 vehicles/unit energy efficiency)	Empirically estimated value: From our regression analysis of 2017–2024 NEV sales data
$S_4$	0.1	Natural sales volume of NEVs (10,000 vehicles)

.

All parameters in this study are selected based on three criteria:

• Policy authenticity: All policy-related parameters (Q₀, a, Pₙ) are directly taken from official MIIT documents and actual market transaction data.
• Industrial realism: Cost and revenue parameters are calibrated to match the average level of China’s automotive industry in 2024, based on public annual reports and industry white papers.
• Model tractability: Sales volume parameters are normalized to simplify numerical analysis while preserving the relative magnitudes of different effects.

The robustness of our conclusions to parameter variations has been extensively verified through sensitivity analyses presented in Section 5.3. All core findings remain valid across the entire range of parameter values consistent with industrial reality.

5.1. Numerical Simulation Analysis of Optimal Production Decisions for Fuel Vehicle Manufacturers

According to the parameter assignment in Table 1, we use MATLAB R2025a to conduct numerical simulations of the FV manufacturer’s profit function. The results are shown in Figure 3. In the high-fuel-consumption (non-compliant) scenario ($f>Q_0$), $R_1\left(f\right)$ first decreases and then increases over the domain $(Q_0,f_{\mathrm{m}\mathrm{a}\mathrm{x}}]$, with a single interior minimum point, and profit drops to 0 at the right boundary $f=f_{\mathrm{m}\mathrm{a}\mathrm{x}}$. The unconstrained global maximum point of $R_1\left(f\right)$ (the interior optimum $f_{1,\mathrm{i}\mathrm{n}\mathrm{t}}^{*}$) lies to the left of $Q_0$, outside the valid domain of the non-compliant scenario. Therefore, under the constraint $f>Q_0$, the maximum profit is achieved at the left boundary $f_1^{*}=Q_0$, which is a boundary optimum.

In the low-fuel-consumption (compliant) scenario ($f\le Q_0$), $R_2\left(f\right)$ follows an inverted-U shape (first increasing, then decreasing) with a unique interior maximum point $f_2^{*}$. At $f=Q_0=6$, $R_2\left(Q_0\right)-R_1\left(Q_0\right)=1.2$ million yuan $>0$, which verifies that the compliant strategy yields strictly higher profit at the threshold point of the fuel consumption standard.

At the same time, we use numerical simulation to analyze the impact of NEV credit price $P_n$, CAFC credit price $P_c$, and NEV credit ratio requirement $a$ on the manufacturer’s decisions, with the results shown in Figure 4, Figure 5 and Figure 6. It can be seen from these figures that an increase in $P_n$ significantly reduces the maximum profit of the high fuel consumption strategy, but has an extremely weak impact on the profit of the low fuel consumption strategy. An increase in $P_c$ significantly increases the maximum profit of the low fuel consumption strategy, but has no direct impact on the high fuel consumption strategy. An increase in both types of credit prices drives down the optimal fuel consumption level, continuously strengthening the advantage of the low fuel consumption strategy. An increase in $a$ has a negative inhibitory effect on the profits of both strategies, and the intensity of the negative impact on the high fuel consumption strategy is 10 times that on the low fuel consumption strategy. There exists a unique critical value $a^{*}$, and when $a>a^{*}$, the low fuel consumption strategy is always the dominant choice. The above results fully verify Proposition 1 and Proposition 2.

Furthermore, we use numerical simulation to analyze the impact of fuel consumption standards, price loss intensity, and fuel consumption sales sensitivity coefficient. Figure 7 simulates the impact of the fuel consumption standard $Q_0$: the maximum profit of the low fuel consumption strategy increases linearly with the relaxation of $Q_0$; the maximum profit of the high fuel consumption strategy shows a single-peak pattern of first increasing then decreasing, with the peak appearing at $Q_0=5.1$. The optimal fuel consumption of both strategies is non-decreasing with $Q_0$, and there exists a unique critical value $Q_0^{*}=3.97$ within the industrial feasible interval, which divides the dominance intervals of the two strategies. Figure 8 and Figure 9 simulate the impact of the price loss intensity $\left|A\right|$ and the fuel consumption sales sensitivity coefficient $S_1$ respectively; an increase in both has a negative inhibitory effect on the profits of both strategies, with a stronger inhibitory effect on the high fuel consumption strategy, and simultaneously drives the optimal fuel consumption level to strictly decrease. There exists a unique critical value for both, and the low fuel consumption strategy is always dominant after exceeding the critical value. The above results verify Proposition 3–6.

5.2. Numerical Simulation Analysis of Optimal Production Decisions for New Energy Vehicle Manufacturers

For NEV manufacturers, according to the parameter assignment in Table 2, we use MATLAB software to conduct numerical simulation analysis of the impact of NEV energy efficiency level on the manufacturer’s profit, and the results are shown in Figure 10. It can be seen from Figure 10a that the profit curve presents a standard single-peak shape, with a unique global optimal energy efficiency point ${\lambda }_2^{*}$, which verifies the economic feasibility of the optimal solution.

Furthermore, we use numerical simulation to analyze the impact of NEV credit price, energy efficiency sales sensitivity coefficient, and R&D cost intensity on the production decisions of NEV manufacturers. Figure 10b simulates the impact of the NEV credit price $P_n$: the optimal energy efficiency level shows a strictly linear increase with the rise of $P_n$, with no downward interval, which verifies the positive incentive effect of credit price on the energy efficiency upgrading of manufacturers, fully consistent with Proposition 7. Figure 10c simulates the impact of the energy efficiency sales sensitivity coefficient $S_3$: the optimal energy efficiency level continues to increase with the rise of $S_3$, and the energy efficiency preference on the market demand side forms a significant positive pull on the technological upgrading of manufacturers, which verifies Proposition 8. Figure 10d simulates the impact of the R&D cost intensity $\left|A_1\right|$: the optimal energy efficiency level continues to decrease with the rise of $\left|A_1\right|$, and the higher the marginal R&D cost of energy efficiency improvement, the lower the optimal energy efficiency level of manufacturers, which verifies Proposition 9.

5.3. Sensitivity Analysis of Critical Thresholds

To evaluate the robustness of the critical thresholds identified in the theoretical model, we conduct a sensitivity analysis for the most policy-relevant threshold, i.e., the fuel consumption standard threshold $Q_0^{*}$ that determines the dominance of compliant vs. non-compliant strategies. We test how $Q_0^{*}$ changes with variations in three key parameters: NEV credit price ($P_n$), fuel consumption sales sensitivity ($S_1$), and price loss intensity ($\left|A\right|$). The results are presented in Figure 11.

The sensitivity analysis shows that $Q_0^{*}$ decreases monotonically from 4.81 to 3.98 L/100 km as $P_n$ increases from 0.1 to 0.5 ten thousand yuan/credit. This indicates that higher credit prices make the compliant strategy more attractive, lowering the threshold fuel consumption standard; $Q_0^{*}$ decreases from 5.85 to 3.52 L/100 km as $S_1$ increases from 0.05 to 0.15. Higher consumer sensitivity to fuel consumption strengthens the market incentive for low-consumption vehicles. $Q_0^{*}$ decreases from 4.37 to 3.58 L/100 km as $\left|A\right|$ increases from 0.1 to 0.4. Higher price penalties for high-consumption vehicles also favor the compliant strategy.

Importantly, all threshold values remain within the narrow interval of 3.5–6 L/100 km, which is consistent with China’s historical fuel consumption standards (the 2021 target was 5.0 L/100 km, the 2025 target is 4.0 L/100 km). This confirms that the critical thresholds are robust to reasonable parameter perturbations and are not artifacts of specific parameter choices. The results also provide policymakers with a range of feasible values for setting future fuel consumption standards.

6. Empirical Test

In the previous sections, we derived the optimal energy consumption decision model of automotive manufacturers under the Dual-Credit Policy through theoretical modeling and conducted numerical simulation analysis. In this section, using firm-level panel data of Chinese listed passenger vehicle manufacturers, we conduct an empirical test to examine the correlation between policy exposure and firms’ energy decisions and to provide real-world evidence supporting the theoretical mechanism. Given that real enterprises are mostly multi-product mixed firms, the empirical analysis serves as an aggregated-level consistency check rather than a strict structural validation of the single-product theoretical model.

6.1. Research Design

6.1.1. Sample and Data

We take A-share-listed passenger vehicle manufacturers in China from 2017 to 2024 as the research sample. After excluding ST enterprises, enterprises whose main business is not complete vehicle production, and samples with missing data, we finally obtain 22 manufacturers with 176 firm-year observations. Data are sourced from MIIT annual credit announcements, the CSMAR Database, CATARC, and CAAM. All continuous variables are Winsorized at the 1% and 99% levels to mitigate outlier bias. Standard errors are clustered at the firm level to account for serial correlation within firms.

6.1.2. Variable Definition

To avoid perfect collinearity between national-level policy variables and year fixed effects, we construct firm-level policy exposure variables by interacting national policy variables with the firm’s lagged FV sales share. This captures heterogeneous policy impacts on firms with different product structures, and aligns the empirical setting more closely with the multi-product reality of real manufacturers. Detailed definitions and theoretical mappings of all core variables are summarized in

Table 3. Variable definition.

Variable Type	Variable Name	Symbol	Definition	Theoretical Mapping
Explained Variables	Average FV fuel consumption	$f_{it}$	Annual average fuel consumption of the firm’s FV models (L/100 km), larger = higher fuel consumption	Optimal fuel consumption $f^{*}$
	Average per-vehicle NEV credits	${\lambda }_{2it}$	Annual total positive NEV credits / NEV production, larger = higher energy efficiency	Optimal energy efficiency ${\lambda }_2^{*}$
Core Explanatory Variables	NEV credit price exposure	$Pn\_ex{p}_{it}$	Lagged FV sales share × annual average NEV credit market price	NEV credit price $P_n$; higher exposure means the firm is more affected by credit price changes
	CAFC credit price exposure	$Pc\_ex{p}_{it}$	Lagged FV sales share × annual average CAFC credit transfer price	CAFC credit price $P_c$
	NEV quota requirement exposure	$alpha\_ex{p}_{it}$	Lagged FV sales share × national required NEV credit ratio	NEV credit ratio $a$
	Fuel consumption standard exposure	$Q0\_ex{p}_{it}$	Lagged FV sales share × national fuel consumption standard limit	Fuel consumption standard $Q_0$
	R&D intensity	$R{D}_{it}$	Annual R&D expenditure / operating revenue	Control variable capturing firm-level R&D input; higher R&D is generally associated with lower marginal costs of energy efficiency improvement, consistent with the economic interpretation of parameters $A$ and $A_1$
	Fuel consumption sales sensitivity	$S{1}_{it}$	Absolute value of (FV sales growth rate/fuel consumption change rate)	Demand sensitivity parameter $S_1$
	Energy efficiency sales sensitivity	$S{3}_{it}$	Absolute value of (NEV sales growth rate/per-vehicle credit change rate)	Demand sensitivity parameter $S_3$
Control Variables	/	/	Firm size, asset–liability ratio, market share, firm age, industry NEV penetration rate, annual average gasoline price	/

.

6.1.3. Benchmark Model

We construct a two-way fixed effects panel model as the benchmark specification. We control for firm fixed effects (to absorb time-invariant firm heterogeneity) and year fixed effects (to absorb common macro shocks). Firm-level policy exposure variables vary across both firms and years, so they are not collinear with year fixed effects.

FV fuel consumption decision model:

$$\begin{array}{c}{f}_{it}={\beta }_0+{\beta }_{1}Pn\_ex{p}_{it}+{\beta }_{2}Pc\_ex{p}_{it}+{\beta }_{3}alpha\_ex{p}_{it}+{\beta }_{4}Q0\_ex{p}_{it}\\ +{\beta }_{5}R{D}_{it}+{\beta }_{6}S{1}_{it}+{\beta }_{7}Control{s}_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}\end{array}$$

(20)

where ${\mu }_i$ is firm fixed effect, ${\lambda }_t$ is year fixed effect, and ${\epsilon }_{it}$ is the error term.

NEV energy efficiency decision model:

$${\lambda }_{2it}={\gamma }_0+{\gamma }_{1}Pn\_ex{p}_{it}+{\gamma }_{2}R{D}_{it}+{\gamma }_{3}S{3}_{it}+{\gamma }_{4}Control{s}_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(21)

6.1.4. Instrumental Variable Strategy

To address potential endogeneity (reverse causality and omitted variable bias), we adopt IV-2SLS with two Bartik-style shift-share instruments:

IV₁: Initial FV share × international lithium price. We use each firm’s FV sales share in 2017 (the first sample year, pre-determined) multiplied by the annual average spot price of international lithium carbonate. Lithium is the core raw material for power batteries; its price affects NEV production costs and industry-wide credit supply, thus correlating with market credit prices. The initial firm structure is pre-determined, and the global lithium price is exogenous to individual Chinese automakers, satisfying the exclusion restriction.

IV₂: Initial FV share × national NEV promotion policy index. We use the initial FV share multiplied by a national-level NEV promotion policy intensity index. Policy intensity affects overall NEV adoption and credit demand, correlating with credit prices, but is exogenous to individual firm decisions.

We acknowledge that these shift-share instruments may not fully satisfy the strict exclusion restriction. For example, lithium prices may also affect firms’ NEV R&D decisions through battery cost channels, and the NEV promotion policy index may influence market demand directly. We therefore treat the IV-2SLS estimation as a robustness check to mitigate endogeneity bias, rather than a perfect identification of causal effects. The results should be interpreted with appropriate caution.

6.2. Benchmark Regression Results

The baseline regression results for FV manufacturers’ fuel consumption decisions are reported in

Table 4. Benchmark regression results for fuel consumption decisions.

Variable	Coefficient	Robust t-Value	t-Statistic	Significance
$Pn\_ex{p}_{it}$	−0.247	0.069	−3.56	***
$Pc\_ex{p}_{it}$	−0.132	0.067	−1.98	*
$alpha\_ex{p}_{it}$	−0.153	0.058	−2.62	**
$Q0\_ex{p}_{it}$	0.178	0.059	3.04	***
$R{D}_{it}$	−0.062	0.023	−2.75	**
$S{1}_{it}$	−0.118	0.060	−1.96	*
Control Variables	Yes	—	—	—
Firm Fixed Effects	Yes	—	—	—
Year Fixed Effects	Yes	—	—	—
Adjusted $R^2$	0.491	—	—	—
Number of Observations	176	—	—	—
Number of Firms	22	—	—	—

Note: ***, **, * represent significance at the 1%, 5%, and 10% levels, respectively.

.

The baseline regression results for NEV manufacturers’ energy efficiency decisions are shown in

Table 5. Benchmark regression results for NEV energy efficiency decisions.

Variable	Coefficient	Robust t-Value	t-Statistic	Significance
$Pn\_ex{p}_{it}$	0.352	0.077	4.58	***
$R{D}_{it}$	0.228	0.069	3.31	***
$S{3}_{it}$	0.142	0.061	2.32	**
Control Variables	Yes	—	—	—
Firm Fixed Effects	Yes	—	—	—
Year Fixed Effects	Yes	—	—	—
Adjusted $R^2$	0.537	—	—	—
Number of Observations	176	—	—	—
Number of Firms	22	—	—	—

Note: ***, ** represent significance at the 1% and 5% levels, respectively.

.

Consistent with theoretical expectations, higher NEV credit price exposure, CAFC credit price exposure, NEV quota exposure, R&D intensity, and fuel consumption sales sensitivity all significantly reduce average FV fuel consumption. Looser fuel consumption standard exposure significantly increases optimal fuel consumption levels. The coefficient patterns of credit prices, quota requirements, fuel consumption standards and demand sensitivity are consistent with the predictions of Propositions 1–4 and 6.

For NEV manufacturers, NEV credit price exposure, R&D intensity, and energy efficiency sales sensitivity all have significantly positive coefficients. The positive associations of credit price exposure and demand sensitivity with energy efficiency are consistent with the predictions of Propositions 7 and 8. The negative coefficient of R&D intensity in the FV model and the positive coefficient in the NEV model align with the theoretical expectation that higher R&D capacity reduces the cost of energy efficiency upgrading. However, they do not constitute a direct structural test of Propositions 5 and 9.

6.3. Endogeneity Treatment

The IV-2SLS estimation results and corresponding diagnostic statistics are presented in

Table 6. IV-2SLS estimation results.

Panel A: Second-Stage Results	FV Fuel Consumption		NEV Energy Efficiency
Variable	Coefficient	Std. Err.	Coefficient	Std. Err.
$Pn\_ex{p}_{it}$	−0.276 ***	0.082	0.384 ***	0.091
Controls/Fixed Effects	Yes	—	Yes	—
Panel B: First-Stage & Diagnostic Tests
First-stage F-statistic	42.68		45.12
Kleibergen–Paap rk Wald F statistic	39.74		41.29
Stock–Yogo 10% maximal IV size critical value	19.93		19.93
Hansen J overidentification p-value	0.312		0.287
Endogeneity test p-value	0.042		0.037
Number of Observations	176		176

Note: *** represent significance at the 1% levels.

.

The first-stage F-statistic and Kleibergen–Paap F-statistic both exceed the Stock–Yogo 10% critical value of 19.93, rejecting the weak instrument hypothesis. The Hansen J overidentification test p-values are both greater than 0.1, failing to reject the null hypothesis of valid instruments. The endogeneity test rejects the null of exogeneity at the 5% level, confirming that IV estimation is necessary.

After addressing endogeneity, the core coefficients remain significant and have the expected signs, with slightly larger magnitudes than the benchmark results. After mitigating endogeneity bias, the estimated association between credit price exposure and manufacturers’ energy consumption decisions remains statistically significant, consistent with theoretical predictions.

6.4. Robustness Check and Heterogeneity Analysis

6.4.1. Alternative Variable Robustness Test

We conduct a robustness check by replacing core explained variables: we replace the FV fuel consumption indicator with the enterprise’s fuel consumption compliance rate, and replace the NEV energy efficiency indicator with the average driving range of models, then re-run the benchmark regression. The results show that the signs and significance of core explanatory variables are consistent with the benchmark regression, with only small changes in the absolute values of coefficients, indicating that the core conclusions of this paper have high robustness.

6.4.2. Heterogeneity Analysis

We conduct sub-sample regressions from two dimensions to examine heterogeneous policy effects. All sub-samples retain the same sign of core coefficients as the benchmark regression, confirming good external validity of the conclusions.

(1)

Enterprise Scale: Grouped by the median of operating revenue, the inhibitory effect of credit price exposure on fuel consumption is significantly stronger for large enterprises (coefficient −0.312, significant at 1%) than for small and-medium-sized enterprises (coefficient −0.164, significant at 10%). This is consistent with the theoretical model: large firms face lower marginal costs of energy efficiency upgrading and respond more flexibly to policy incentives.

(2)

Ownership Nature: Private and joint venture enterprises show stronger sensitivity to credit prices (coefficient −0.307, significant at 1%) than state-owned enterprises (coefficient −0.198, significant at 5%). Market-oriented firms align their decisions more closely with profit-maximization logic, while state-owned enterprises make more gradual adjustments due to broader policy responsibilities.

6.5. Threshold Effect Test

To empirically verify the piecewise characteristics and critical threshold effects derived from the theoretical model, we adopt the panel threshold model proposed by Hansen (1999) to test the nonlinear relationship between the Dual-Credit Policy and manufacturers’ energy decisions.

6.5.1. Model Specification

Taking firm-level NEV credit price exposure as the core threshold variable, we construct a single-threshold panel model for FV manufacturers’ fuel consumption decisions:

$$\begin{array}{c}{f}_{it}={\beta }_0+{\beta }_{1}Pn\_ex{p}_{it}\cdot I(Pn\_ex{p}_{it}\le \tau )+{\beta }_{2}Pn\_ex{p}_{it}\cdot I(Pn\_ex{p}_{it}>\tau )+{\beta }_{3}Pc\_ex{p}_{it}\\ +{\beta }_{4}alpha\_ex{p}_{it}+{\beta }_{5}Q0\_ex{p}_{it}+{\beta }_{6}R{D}_{it}+{\beta }_{7}S{1}_{it}+{\beta }_{8}Control{s}_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}\end{array}$$

(22)

where $\tau$ is the threshold value to be estimated, $I(\cdot )$ is the indicator function (equals 1 when the condition holds, 0 otherwise), and all other variables are consistent with the benchmark model (20). The model can be extended to a multi-threshold framework if multiple thresholds are detected. We use the bootstrap method (300 replications) to test the significance of threshold effects and determine the number of thresholds.

For NEV manufacturers, we similarly construct a threshold model with per-vehicle NEV credits as the explained variable to verify whether the incentive effect of credit prices has nonlinear characteristics.

6.5.2. Threshold Existence Test

We sequentially test for the existence of zero, one, and two thresholds. The test results for FV manufacturers are reported in

Table 7. Threshold effect existence test results (FV sample).

Test Type	F-Statistic	p-Value	10% Critical Value	5% Critical Value	1% Critical Value
Single threshold	28.34	0.003 ***	18.72	22.15	29.64
Double threshold	12.57	0.214	16.89	20.31	27.58

Note: *** represent significance at the 1% levels.

.

The results show that the single-threshold effect is significant at the 1% level, while the double-threshold effect is not statistically significant. We therefore adopt the single-threshold model for analysis. The estimated threshold value of NEV credit price exposure is 0.087, with a 95% confidence interval of [0.079, 0.095].

For the NEV sample, the single-threshold test yields an F-statistic of 9.26 with a p-value of 0.342, indicating no significant threshold effect. This is consistent with the theoretical prediction that the incentive effect of credit prices on NEV energy efficiency is monotonically positive, supporting the linear specification of the benchmark model.

6.5.3. Threshold Regression Results and Interpretation

The single-threshold regression results for FV manufacturers are presented in

Table 8. Single-threshold regression results (FV fuel consumption).

Variable	Coefficient	Robust Std. Err.	t-Statistic	Significance
$Pn\_ex{p}_{it}\cdot I(Pn\_exp\le 0.087)$	−0.124	0.071	−1.75	*
$Pn\_ex{p}_{it}\cdot I(Pn\_exp>0.087)$	−0.358	0.083	−4.31	***
$Pc\_ex{p}_{it}$	−0.129	0.066	−1.95	*
$alpha\_ex{p}_{it}$	−0.147	0.057	−2.58	**
$Q0\_ex{p}_{it}$	0.181	0.058	3.12	***
$R{D}_{it}$	−0.060	0.022	−2.73	**
$S{1}_{it}$	−0.115	0.059	−1.95	*
Control Variables	Yes	—	—	—
Firm Fixed Effects	Yes	—	—	—
Year Fixed Effects	Yes	—	—	—
Adjusted $R^2$	0.524	—	—	—
Number of Observations	176	—	—	—

Note: ***, **, * represent significance at the 1%, 5%, and 10% levels, respectively.

.

The results confirm a significant piecewise threshold effect:

When NEV credit price exposure is below the threshold (0.087), the inhibitory effect of credit prices on FV fuel consumption is relatively weak, with a coefficient of −0.124, only significant at the 10% level. When credit price exposure exceeds the threshold, the inhibitory effect is substantially strengthened, with a coefficient of −0.358, significant at the 1% level. The magnitude of the effect is nearly three times that of the low-exposure regime.

This empirical finding is highly consistent with the theoretical propositions. When credit prices are low, manufacturers may prefer to maintain high fuel consumption and purchase credits for compliance (non-compliant strategy); when credit prices rise above the critical threshold, the cost of non-compliance becomes too high, and manufacturers switch to the low-fuel-consumption compliant strategy, leading to a significant drop in average fuel consumption. This pattern is consistent with the critical threshold effect and strategy switching mechanism derived from the theoretical model.

7. Discussion

7.1. Comparison with Existing Literature and Theoretical Implications

Our findings extend and refine several key conclusions in the existing DCP literature. Unlike Hu et al. [14] and Wang [15], who primarily focused on how credit prices affect vehicle production quantities, our endogenous energy efficiency framework reveals that credit prices fundamentally drive technological quality decisions. We demonstrate that higher NEV credit prices not only incentivize NEV manufacturers to improve energy efficiency but also force FV manufacturers to lower fuel consumption, a dual-effect mechanism that was previously obscured when energy consumption was treated as exogenous. From a methodological perspective, game theory models excel at capturing strategic interaction between multiple stakeholders such as manufacturers, suppliers, and regulators, but they typically focus on equilibrium properties and comparative statics, and rarely derive closed-form explicit threshold solutions and quantifiable boundary conditions for strategy switching. System dynamics models are suitable for macro-level industry evolution simulation and long-term policy trend forecasting, but they sacrifice the micro-foundation of firms’ profit-maximizing behavior and cannot accurately characterize the internal optimization logic of individual enterprises. In contrast, our profit optimization model is built directly on the micro decision-making logic of manufacturers. Through strict mathematical derivation, we obtain explicit analytical solutions for optimal energy consumption levels and closed-form critical thresholds that determine strategy dominance. This framework retains the rigor of microeconomic decision theory while providing quantifiable policy boundary references, serving as a methodological complement to existing game theory and system dynamics studies. Furthermore, compared to Pu et al. [23], who analyzed competitive strategies under the DCP, our study provides explicit, closed-form mathematical thresholds (e.g., the fuel consumption standard threshold $Q_0^{*}$) that dictate the exact boundary conditions under which specific technological strategies become dominant. Theoretically, this study bridges the gap between macro-level environmental policy design and micro-level operational quality management, providing theoretical and empirical evidence that market-based regulatory instruments can help internalize environmental externalities into corporate R&D optimization.

7.2. Practical Implications

Based on the theoretical model findings and empirical evidence, this paper proposes the following reference implications for DCP optimization:

7.2.1. Policy Implications

• Stabilize credit price expectations: The theoretical model shows that credit prices are a core factor influencing manufacturers’ energy efficiency upgrading incentives. Regulators could consider establishing a price corridor for NEV credits to mitigate excessive market volatility. Our baseline numerical simulation illustrates that under the calibrated parameter set, a credit price range of 0.2–0.4 ten thousand yuan per credit is associated with a balance between compliance pressure and innovation incentives. This result is specific to the benchmark scenario and is provided as an illustrative example.
• Dynamic adjustment of policy parameters: The critical thresholds derived from the model can provide a quantitative reference for the dynamic adjustment of fuel consumption standards and NEV quota requirements.
• Support for small and medium-sized enterprises: Targeted R&D subsidies and credit pooling mechanisms could help reduce compliance costs for smaller manufacturers and prevent excessive market concentration.
• Establish a dynamic adjustment mechanism: Policy parameters may be updated regularly based on market conditions and technological progress to maintain policy effectiveness amid evolving industry conditions.

7.2.2. Enterprise Implications

For automotive manufacturers:

• FV manufacturers: Prioritize fuel consumption optimization over output reduction. Invest in high-efficiency engine technologies and hybrid powertrains to meet compliance requirements while maintaining market competitiveness.
• NEV manufacturers: Integrate credit revenue into R&D accounting systems. Focus on energy efficiency upgrading to maximize both market revenue and credit revenue, forming a positive cycle of “energy efficiency improvement-credit surplus-technological iteration”.
• Mixed-product manufacturers: The threshold mechanism identified in this paper can serve as a reference for product-line-level decision-making. Full portfolio optimization should further incorporate internal credit pooling and cross-product resource constraints, which is an important direction for future research.

7.3. Research Limitations

This study has several limitations that should be addressed in future research:

• Model simplifications: We made several simplifying assumptions (linear demand, market clearing, separate manufacturers, single-period production) to ensure analytical tractability. While these assumptions are justified for our research objectives, they limit the model’s ability to capture all complexities of the real market.
• Limited empirical data: Our empirical analysis uses data only up to 2024. As more data becomes available on the 2023 policy revision and 2026–2027 credit requirements, future studies could further validate our conclusions.
• No macroeconomic modeling: We did not explicitly model macroeconomic risks such as oil price volatility and international supply chain disruptions. Future research could integrate these factors into the model to provide more robust policy recommendations.

8. Conclusions

Taking the Dual-Credit Policy as the background, this paper takes the fuel consumption of FVs and the energy efficiency of NEVs as core endogenous decision variables, constructs profit-maximizing decision models for the two types of manufacturers, and draws the following conclusions through mathematical derivation, numerical simulation and empirical tests:

(1)

The optimal fuel consumption decisions of FV manufacturers present significant piecewise characteristics and critical effects. The profit functions of both the high fuel consumption (non-compliant) and low fuel consumption (compliant) strategies have a unique global maximum point, and the profit of the low fuel consumption strategy is strictly higher at the critical point of the fuel consumption standard. An increase in NEV credit price, NEV ratio requirement, intensity of fuel consumption-related price loss, and consumer sensitivity to fuel consumption will significantly inhibit the revenue of the high fuel consumption strategy and drive down optimal fuel consumption levels, while an increase in CAFC credit price will significantly strengthen the revenue of the low fuel consumption strategy. The impact of fuel consumption standards on the two strategies is heterogeneous: there exists a unique critical value within the industrial feasible interval, and the low fuel consumption strategy is dominant when the standard is stricter than the critical value, while the high fuel consumption strategy is dominant when the standard is looser than the critical value.

(2)

The Dual-Credit Policy exerts a significant market-oriented positive incentive effect on the energy efficiency upgrading of NEV manufacturers. The profit function of NEV manufacturers has a unique economically feasible optimal energy efficiency solution. The higher the NEV credit price and the stronger the market demand sensitivity to energy efficiency, the higher the optimal energy efficiency level of the manufacturer. Conversely, the higher the marginal R&D cost of energy efficiency improvement, the lower the optimal energy efficiency level, and high R&D costs will significantly weaken the incentive effect of the policy.

(3)

The transition-guiding effect of the Dual-Credit Policy on the industrial low-carbon transformation has a clear effective boundary. The policy effectiveness is highly dependent on the matching degree between core parameter design and the market environment. When the parameters are disconnected from industrial reality, it is easy to trigger adverse selection. Only when parameters such as credit price, fuel consumption standard, and NEV ratio requirement fall within the effective interval can the core policy goal of “restricting high-carbon emissions and incentivizing low-carbon development” be achieved.

As the core long-term mechanism for the low-carbon transformation of China’s automotive industry, the full play of the policy effect of the Dual-Credit Policy requires the joint efforts of the precision of policy design, the foresight of enterprise decision-making, and the coordination of market demand. In the future, with the continuous improvement of the policy system and the continuous advancement of industrial technology, the Dual-Credit Policy will continue to drive the deep integration of high-quality industrial development and dual-carbon strategic goals and provide long-term support for the sustainable low-carbon transition of China’s automotive and transportation sectors.