Enterprise Scenario Analysis: A Systematic Framework for Monetizing CO₂ Compliance

Abstract

The global automotive industry is currently undergoing a period of radical transformation as a result of the ongoing electrification of automobiles. China has established rigorous energy-saving and emission-reduction targets and regulations. Consequently, the automotive industry must take into account the limitations of carbon emission reduction and carbon trading when formulating major business strategies. A related question is how “internal incentives” should be set to maximize the variable profitability of automotive companies while meeting compliance constraints. In response, in this study, a unified and mutually consistent modeling framework for enterprise scenario analysis is proposed to align the product portfolio within an enterprise. Firstly, a game model of the new energy vehicle market is proposed to forecast general trends and provide forward-looking inputs for firms to develop business plans. Next, this paper proposes a framework for monetizing CO₂ compliance using the Pigovian tax/subsidy concept. The equilibrium is achieved through the imposition of a tax or subsidy by the company on each of its internal models. Utilizing historical data from A Motors, we clearly illustrate how our approach works and demonstrate its consistency with observations of the new energy vehicle market.

1. Introduction

In order to mitigate the effects of global warming, reducing industrial carbon emissions has become a significant policy objective for national governments [1]. The automobile industry has become one of the key industries in global carbon emission management due to its large industrial share [2], complex transnational industrial chain [3], large total carbon emissions [4], and the high carbon intensity of individual vehicles [5]. Therefore, in order to promote low-carbon transition, China introduced the dual-credit policy (DCP) in 2017 to promote enterprises’ investment in energy-saving technologies for fuel vehicles and the development of new energy vehicle (NEV) [6]. Against this backdrop, automotive companies are under the dual pressure of supporting environmental protection and maintaining long-term business performance [7]. Increasing corporate demand for ecosystem services and engagement in payment for ecosystem services (PES) requires company-level institutional changes and business strategies to improve supply chain management and mitigate the negative impacts of environmental and climate change [8]. Palea V argues that there is a robust and persistent negative correlation between carbon emissions and financial performance, which is associated with lower returns on sales and capital inefficiencies in high-emission firms [9]. In addition, long-term climate strategy is an essential part of any company’s risk management, and carbon compliance can have a dramatic impact on the competitiveness of products and services, business strategy and investments, and ultimately financial performance [10]. Consequently, the automotive industry must consider carbon reduction and carbon trading constraints when making major business decisions, such as product planning, electrification strategy, production/hybridization, and pricing.

Under the constraints of carbon compliance and carbon trading, there has been some work on DCP, including various aspects such as incentive effects [11,12,13], credit pricing [14,15,16], and corporate strategies [17,18]. From the government’s perspective, Yang D X et al. compared the government pricing model and the market pricing model of the dual-credit policy through the optimization theory to determine the effective pricing in the pre-market and post-market phases [14]. Zheng J. et al. studied supplier output competition, manufacturer output competition, and the R&D investment level of NEV supplier and manufacturer subjects. The DCP has certain disadvantages in stimulating enterprise research and development (R&D) and innovation, and it is necessary to introduce a new subsidy policy to be used in conjunction with the DCP [19]. Wang Xueqin simulated the evolutionary game of decision-making between automobile companies and the government, and proposed that the additional benefits obtained by automobile companies after the government closes the credit channel are the key factor influencing the decision-making of both parties [20]. Optimized for business decision-making, Wang Z et al. explored firms’ choices of green technology innovations (GTIs) under the DCP, including energy-saving technologies for fuel vehicles and production technologies for NEVs [21]. Ma M et al. constructed a Stackelberg game model to obtain the optimal technological innovation strategy for the production system of NEVs under information symmetry and information asymmetry, taking into account the DCP and the private information of the automakers [22]. Considering stochastic credit prices and time-varying NEV investment costs, He H et al. proposed a novel optimal decision model incorporating three metrics: investment timing, R&D intensity, and product line allocation [23]. Li B et al. investigated the impact of the DCP on the quantity and quality of green innovations in automobile companies using a difference-in-differences (DID) model [24]. Yu H et al. constructed an evolutionary game model based on the Hotelling theory to explore the impact of the DCP on the innovation strategies of conventional automobile manufacturers and NEV manufacturers [18].

In the analysis of the assessment of corporate carbon compliance, studies have focused on corporate sustainability [25,26,27], investment strategies [28,29,30], and carbon management [31,32,33]. In order to meet the product requirements of a business cluster while meeting set CO₂ emission limits and maximizing the associated economic returns, Bechara C A et al. introduced a system optimization-based model for developing sustainable utilization strategies [34]. Yao Z et al. studied the R&D investment decisions of two original equipment manufacturers (OEMs) producing electric vehicles (EVs) and fuel-guzzling vehicles (FVs), respectively, in the context of the implementation of environmental protection policies. For each investment strategy profile, a two-stage Stackelberg game was used to optimize the price, market share, and optimal utility of the OEM for each vehicle [35]. Chen K et al. modeled and evaluated technical compliance and policy impacts under multiple regulations in China, and showed that NEV credit limits in the dual-credit regulations may motivate “underperforming” automakers to produce the required number of NEVs and reach the bottom line [36]. Lee K H et al. explored the role and utility of eco-control as a means of identifying and measuring the carbon performance of production plants. The results suggest that eco-controls can facilitate the alignment between corporate carbon management strategies and carbon performance measurement and provide useful quantitative information to corporate decision makers [37]. Considering the improvement of firms’ competitiveness and the legal compliance issues faced by industrial SCs, Cátia da Silva et al. proposed a mixed-integer linear programming model (MILP) and concluded how monetization can support decision makers’ decisions [38].

The results from the research on DCP and the application of carbon compliance assessment methods show that integrating carbon compliance into a company’s long-term operations and strategic processes can effectively improve performance and manage compliance costs. However, current research generally starts from market players and ignores the issue of carbon compliance equilibrium within individual companies. The practical challenge for companies is to develop internal incentives for each model produced to ensure that they maximize their variable profit margins while meeting the carbon compliance constraints of the DCP and other policy uncertainties. At the same time, the actual value to firms of carbon credits for each product is unclear, as are the factors that influence the actual value. To the best of our knowledge, no research has been conducted in this area. In this paper, we aim to establish an analytical framework that integrates the three levels of NEV strategy, business planning, and carbon compliance to establish a market equilibrium with clear compliance constraints, as shown in Figure 1. The key contributions of this paper are as follows:

(1)

A dynamic game model of the NEV market is proposed, consisting of government and business entities, which can be optimized for market decision-making. Through this decision-making framework, the government can optimize its decisions to promote the development of the NEV market, while enterprises can predict the overall trend of the automotive market to provide forward-looking inputs for the development of their business plans.

(2)

A CO₂ compliance monetization framework is proposed, introducing the Pigovian tax/subsidy concept, whereby firms themselves levy a tax or subsidy on each product model, thereby maximizing variable profits within the firm while meeting carbon compliance requirements in a competitive market equilibrium. The competitive market equilibrium is achieved by modelling the carbon compliance of market competitors through the effective cost approach.

(3)

The framework is validated for consistency with market observations using historical data from A Motors. This paper also discusses the factors influencing the shadow price of credits for the DCP, which provides suggestions for car companies to improve the parameters of their models in the context of the policy. It then also discusses how the analytical framework can be extended to address the carbon trading decisions of automotive firms when external credit markets exist.

The remainder of this paper is organized as follows. Section 2 describes the dynamic game model of the NEV market. To compensate for the implicit representation of CO₂ compliance in the game model, Section 3 further proposes a framework for monetizing CO₂ compliance. The simulation is discussed in detail in Section 4, followed by conclusions summarized in Section 5.

2. The Dynamic Game Model of NEV Market

In this section, a dynamic game model of the NEV market is proposed to predict the macro trends of the market. The optimal strategies of the government and automobile companies can be derived from the model to provide forward-looking suggestions for automobile companies to develop business plans.

2.1. Problem Description and Assumptions

The NEV market game model comprises two players: the government and automobile enterprises. The game is regarded as a Stackelberg game, as shown in Figure 2, with the government as the principal and automobile companies as the agent. The decision variable of the government is the dual credit policy $\left(S_{NEV}\right)$, and the decision variable of the automobile companies is the degree of innovation efforts of fuel vehicles and NEVs ($a_1,a_2)$.

In the first stage of the game, the government as a principal makes the first decision, i.e., the DCP. In the second stage of the game, automobile companies rationally adjust their business decisions according to the observable policy decisions. In this paper, the business decisions of automobile companies are simplified to the degree of innovation efforts for fuel models and NEV models. The market automatically returns to the next moment state, i.e., the market penetration rate of NEVs, according to the decisions of both parties. The government then adjusts its own strategy according to the market state and the automobile company’s business decision, and the cycle repeats until it reaches the Nash equilibrium.

The model in this paper makes the following assumptions:

(1)

This paper assumes that the government-automobile manufacturer game is a dynamic Stackelberg game, which is a two-stage, fully-informed dynamic game in which the payoff function of the participants is common knowledge.

(2)

To simplify the model, this subsection assumes that there is only one automaker in the automotive market and that all new energy vehicles and fuel vehicles are of the same type in the market.

(3)

This paper assumes that the government cannot regulate the parameters of the dual-credit policy, but only the price of NEV credits, thus avoiding the problem of dimensional catastrophe caused by too many policy parameters.

2.2. NEV Market Penetration Process

The Diffusion of Innovation (DOI) models can be employed to simulate the process of penetration in the NEV market.

$${\displaystyle \frac{d{X}_{NEV}\left(t\right)}{dt}}=\left(\alpha +b{X}_{NEV}\left(t\right)\right)\left(1-X_{NEV}\left(t\right)\right)+\sigma \left(1-X_{NEV}\right){\displaystyle \frac{dB}{dt}}$$

(1)

where $X_{NEV}\left(t\right)$ is the market penetration rate of NEVs, taking the value range [0, 1], which can be expressed as $X_{NEV}\left(t\right)=N_{NEV}\left(t\right)/M_{NEV}\left(t\right)$; $\sigma$ is the Brownian motion constant perturbation quantity; B is the random perturbation term in the NEV market; and the random perturbation terms are all Brownian motion.

The DOI model augmented by stochastic influences constitutes a first-order differential equation model that can be calibrated to the parameters of the DOI model through the Euler method.

$$\mathrm{d}{X}_t=f\left(X_t,\theta \right)dt+g\left(X_t,\theta \right)d{B}_t$$

(2)

where $\theta$ is the stochastic differential equation fitting parameter; $f\left(X_t,\theta \right)$ is the stochastic differential equation drift term; and $g\left(X_t,\theta \right)$ is the stochastic differential equation diffusion term.

Discretizing the above stochastic differential equation gives:

$$X_{t+\Delta t}-X_t=f\left(X,\theta \right)\Delta t+g\left(X_t,\theta \right)\left(B_{t+\Delta t}-B_t\right)$$

(3)

where the increment $X_{t+\Delta t}-X_t$ is a Gaussian process random variable obeying a mean of $f\left(X,\theta \right)\Delta t$ and a variance of $g^2\left(X_t,\theta \right)\Delta t$.

The parameters of the differential equation are finally fitted using maximum likelihood estimation (MLE). The optimization objective (log-likelihood function) is as follows:

$$h_n=-{\displaystyle \frac{1}{2}}\left({\displaystyle \sum }_{i=1}^n{\displaystyle \frac{(X_i-X_{i-1}-f\left(f\left(X_{i-1},\theta \right)\Delta t{)}^2\right)}{{\sigma }^2\Delta t}}+nlog\left(2\pi {\sigma }^2\Delta t\right)\right)$$

(4)

2.3. Government-Enterprise Dynamic Game Model of NEV Market

The automaker’s utility function $V$ consists of six components: dual-credit gain, made up of CAFC credit tax or subsidy and NEV credit tax or subsidy; sales gain, made up of fuel vehicle sales gain and new energy vehicle sales gain; and innovation cost, made up of fuel vehicle innovation cost and new energy vehicle innovation cost.

$$\begin{gathered} \mathrm{V}=\left\{(P_{ICE}-C_{ICE})\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)\right\}+S_{ICE}\left(\gamma {\phi }_{T_f}-{\phi }_{A_f}-\beta \right)\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)-{({\eta }_1{a}_1)}^2+ \\ \left\{(P_{NEV}-C_{NEV})+S_{NEV}\left[h+(\gamma {\phi }_{T_e}-{\displaystyle \frac{{\phi }_{A_e}}{\omega }})\right]\right\}{M}_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}-{({\eta }_2{a}_2)}^2 \end{gathered}$$

(5)

where $(P_{ICE}-C_{ICE})\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)$ represents proceeds from the sale of fuel vehicles; $S_{ICE}\left(\gamma {\phi }_{T_f}-{\phi }_{A_f}-\beta \right)\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)$ is a CAFC credit tax or subsidy; ${({\eta }_1{a}_1)}^2$ a is the cost of innovation efforts for fuel-vehicle models; $(P_{NEV}-C_{NEV})M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}$ represents proceeds from the sale of NEVs; $S_{NEV}\left[h+(\gamma {\phi }_{T_e}-{\displaystyle \frac{{\phi }_{A_e}}{\omega }})\right]M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}$ is NEV credit tax or subsidy; ${({\eta }_2{a}_2)}^2$ is the cost of innovation efforts for NEVs; $P_{ICE}$ and $P_{NEV}$ represent the sales price of fuel vehicles and NEVs, respectively; $C_{ICE}$ and $C_{NEV}$ represent the total cost of producing a fuel vehicle and the total cost of producing a NEV, respectively; $\beta$ is the NEV credit ratio requirement; ${\phi }_{T_f}\left(\mathrm{L}/100 \mathrm{km}\right)$ and ${\phi }_{A_f}\left(\mathrm{L}/100 \mathrm{km}\right)$ represent the target and the actual CAFC for fuel vehicles, respectively; $h$ is the number of credits per vehicle for NEVs; $\gamma$ is the fuel consumption requirement;$\omega$ is the discount multiplier for new energy models; and $S_{ICE}$ and $S_{NEV}$ are dual-credit priced, with a dual-credit policy of 1-for-1 redemption of CAFC credit and NEV credit, $S_{ICE}=S_{NEV}$.

The government’s objective is to maximize social benefits, so its benefit function includes three components: automobile company benefits, environmental governance, and consumer surplus.

$$\mathrm{U}=\mathrm{V}+\left\{-G_{ICE}\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)-G_{NEV}{M}_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right\}+\left\{P_{ICE}\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)+P_{NEV}{M}_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right\}$$

(6)

where $\mathrm{V}$ is for the automotive company’s earnings; $\left\{-G_{ICE}\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)-G_{NEV}{M}_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right\}$ is the cost of environmental governance; $\left\{P_{ICE}\left(N-M_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right)+P_{NEV}{M}_{NEV}{\displaystyle \frac{d{X}_{NEV}}{dt}}\right\}$ is the consumer surplus; and $G_{ICE}$ and $G_{NEV}$ denote the cost of carbon emission treatment for fuel vehicles and NEVs, respectively. $N$ is the total annual sales of the automobile market.

In the differential game, the government objective is to maximize the sum of discounted returns.

$$\mathrm{E}\left[{{\displaystyle \int }}_0^T{r}_G{e}^{-r_{G}t}U\left(X_{NEV}\left(t\right),S_{NEV}\left(t\right)\right)dt\right]$$

(7)

where $r_G$ is the government’s discount factor.

The automobile company’s objective function is also to maximize the sum of discounted returns.

$$\mathrm{E}\left[{{\displaystyle \int }}_0^T{r}_A{e}^{rt}V\left(X_{NEV}\left(t\right),S_{NEV}\left(t\right),a_1\left(t\right),a_2\left(t\right)\right)dt\right]$$

(8)

$r_A$ is the automobile company’s discount factor.

The automobile market game model can then be summarized as in the following

Table 1. The differential game model of the automobile market.

Player	Government	Automobile Companies
Decision variable	$S_{NEV}\left(t\right)$	$a\left(\mathrm{t}\right)=\left\{a_1\left(t\right),a_2\left(t\right)\right\}$
Benefit function	$\mathrm{U}\left(x_{NEV},S_{NEV}\right)$	$\mathrm{V}\left(S_{NEV},a_1\left(t\right),a_2\left(t\right)\right)$
Objective function	$\underset{S_{NEV}\left(t\right)}{\max }{{\displaystyle \int }}_0^T{r}_G{e}^{-r_{G}t}Udt$	$\underset{a\left(t\right)}{\max }{{\displaystyle \int }}_0^T{r}_A{e}^{-r_{A}t}Vdt$
State variable	$X_{EV}$
State transfer equation	${\displaystyle \frac{d{X}_{NEV}\left(t\right)}{dt}}=\left(a+b{X}_{NEV}\left(t\right)\right)\left(1-X_{NEV}\left(t\right)\right)+\sigma \left(1-X_{NEV}\right){\displaystyle \frac{dB}{dt}}$

.

The Nash equilibrium solution of the game can be expressed by the following equation.

$$\begin{gathered} \underset{S_{NEV}}{\max } E\left[{{\displaystyle \int }}_0^T{r}_G{e}^{-r_{G}t}U\left(X_{NEV}\left(t\right),S_{NEV}\left(t\right)\right)dt\right] \\ \mathrm{s}.\mathrm{t}.a_1^{\ast },a_2^{\ast }=arg \underset{a_1,a_2}{\max } E\left[{{\displaystyle \int }}_0^T{r}_A{e}^{-r_{A}t}V\left(S_{NEV}\left(t\right),a_1\left(t\right),a_2\left(t\right)\right)dt\right] \\ \mathrm{E}\left[{{\displaystyle \int }}_0^T{r}_A{e}^{-r_{A}t}V\left(S_{NEV}^{\ast }\left(t\right),a_1\left(t\right),a_2\left(t\right)\right)dt|{\mathrm{F}}_t\right]\ge \underset{\_}{W} \end{gathered}$$

(9)

Solving the Nash equilibrium directly involves multiple second-order differential equations, which are extremely complex and even impractical. Therefore, this paper employs a simplified method of differential games under principal-agent conditions.

Firstly, the objective function [39] for the automobile company is rewritten as:

$$\mathrm{W}\left(t\right)=\mathrm{E}\left[{{\displaystyle \int }}_t^T{r}_i{e}^{-r\left(s-t\right)}f\left(X\left(s\right),C^{\ast }\left(s\right),a\left(s\right)\right)ds|{\mathrm{F}}_t\right]$$

(10)

where $C^{\ast }\left(t\right)$ is the optimal decision of the principal. ${\mathrm{F}}_t$ is the $\mathrm{\sigma }$-algebraic information flow [40], representing all the information collected by the participant at the moment $t$.

The harness representation theorem [41,42] expresses the above function as:

$$dW\left(t\right)=r\left(W\left(t\right)-f\left(t\right)\right)dt+\sigma r{y}_i\left(t\right)dB\left(t\right)$$

(11)

where $r$ is the sensitivity of $W\left(t\right)$ to $x\left(t\right)$, respectively, and $y_i\left(t\right)$ is the marginal utility of increasing $a_i\left(t\right).$

In Equation (11), using the agent’s value function $W\left(t\right)$ as a state variable, the principal’s decision variable changes from $C\left(t\right)$ to $\left\{C\left(t\right),Y\left(t\right)\right\}$.

The incentive compatibility (IC) constraint can be converted into an equivalent representation as follows.

$$a_i^{\ast }=arg \underset{a_i}{\max } y\left(t\right)g_i\left(\left(a_i\left(t\right),a_{-i}\left(t\right)\right)+f_i\left(a_i\left(t\right),a_{-i}^{\ast }\left(t\right)\right)\right)$$

(12)

Using first-order optimality conditions, $a_i^{\ast }$ can be derived:

$${\displaystyle \frac{\partial f_i}{\partial a_i}}+y_i{\displaystyle \frac{\partial g_i}{\partial a_i}}=0$$

(13)

Through Equations (10)–(13), the differential game in Table 1 can be simplified to

Table 2. The simplified differential game model.

Player	Government
Decision variable	$\left\{S_{NEV}\left(t\right),Y_{NEV}\left(t\right)\right\}$
Objective function	$\underset{S}{\max } E{{\displaystyle \int }}_0^T{r}_G{e}^{-r_{G}t}fdt$
State variable	$\left\{X_{NEV}\left(t\right),W_{NEV}\left(t\right)\right\}$
State transfer equation	$d{X}_{NEV}/dt=\left(a+b{X}_{NEV}\right)\left(1-X_{NEV}\right)+\sigma \left(1-X_{NEV}\right)dB\left(t\right)/dt$
	$\mathrm{d}{W}_{NEV}\left(T\right)=r\left(W_{NEV}\left(t\right)-h\left(S_{NEV}\left(t\right),a^{\ast }\left(t\right)\right)\right)dt+\sigma r{Y}_{NEV}\left(t\right)dB\left(t\right)$

.

The optimal decision of the principal can be derived by solving the following HJB equation

$$-r_G{\displaystyle \frac{\partial V}{\partial t}}=\underset{\left\{S_{NEV},Y_{NEV}\right\}}{\max }\left\{f+L\nabla V+{\displaystyle \frac{1}{2}}{H}^T{\nabla }^{2}VH\right\}$$

(14)

where

$$\begin{gathered} \nabla \mathrm{V}={\left[{\displaystyle \frac{\partial V}{\partial X_{NEV}}},{\displaystyle \frac{\partial V}{\partial W_{NEV}}}\right]}^T \\ {\nabla }^{2}V=\left[\begin{array}{cc}{\displaystyle \frac{{\partial }^{2}V}{{\partial }^2{X}_{NEV}}}& {\displaystyle \frac{{\partial }^{2}V}{\partial X_{NEV}\partial W_{NEV}}}\\ {\displaystyle \frac{{\partial }^{2}V}{\partial X_{NEV}\partial W_{NEV}}}& {\displaystyle \frac{{\partial }^{2}V}{{\partial }^2{W}_{NEV}}}\end{array}\right] \\ \mathrm{L}=\left[\left(a+b{X}_{NEV}\right)\left(1-X_{NEV}\right),W_{EV}-h\left(S_{NEV},a^{\ast }\right)\right] \\ \mathrm{H}={\left[X_{NEV},Y_{NEV}\right]}^T \end{gathered}$$

Carbon compliance is addressed in the dynamic gaming of the NEV market and has been incorporated into the constraints. Compliance, business planning, and NEV strategy are aligned and consistent with each other. However, the NEV market game model proposed only implicitly considers compliance constraints and does not consider explicit monetization of compliance. More importantly, the challenge faced by automobile companies is the variability in carbon compliance of their models. Compliant models have very low or even negative revenues due to cost, selling price, and sales volume. Non-compliant models, on the other hand, are popular with consumers due to their mature technology and lower costs, and are very profitable for automobile companies. Consequently, the issue of how to develop “internal incentives” for automobile company models to maximize variable profitability while meeting compliance constraints has become an important one. Therefore, a framework for monetizing CO₂ compliance is proposed in Section 3. This framework explicitly models a market equilibrium with a compliance constraint and employs a well-known externality-suppressing technique in economics, the Pigovian tax/subsidy concept, to systematically align internal incentives.

3. CO₂ Compliance Monetization Framework

The auto industry is largely a competitive/oligopoly market, with every auto producer arduously vying for every possible customer. Customers have multiple choices from a myriad products that are close substitutes made by various original equipment manufacturers (OEMs). Both sales/volume and transaction prices, as elements of revenue and profit, are determined through competition among firms (i.e., no OEM can act as a monopoly). Firms compete not only in terms of marketing and sales, but also in terms of positioning new technologies/products. At the same time, each OEM has to meet all the compliance mandates. Consequently, any relevant/meaningful modeling framework has to capture/reflect realistically all of the above characteristics of the auto industry. Thus, the modeling described below is performed at the level of a combination of vehicle-line and powertrain types, e.g., sedan ICE, sedan HEV, and sedan PHEV are treated as separate products. Each product is characterized by three major parameters: demand level, variable cost, and fuel economy. These parameters are all understood as mix-weighted averages over the allowed features, such as 4 × 2, 4 × 4, trim, …, within the product. In addition, any production actions or changes can potentially imply changes in their values. The demand system is calibrated using historical transaction data, including historical demand levels and segmentation/substitution patterns. Investments/fixed costs are treated as sunk, and hence only variable profit matters.

3.1. CO₂ Compliance Monetization

The automotive industry is largely a competitive/oligopoly market, with every automaker competing for every possible customer and aiming to maximize profits. The objective function of OEMs is shown below.

$$\underset{\left\{p_i\right\}}{\max }{\displaystyle \sum }_{i\in \mathrm{OEM}}{v}_i\left(p\right)\times \left(p_i-c_i\right)$$

(15)

where $v_i\left(p\right)$ is the volume for product “i” in OEM, a complex function of all trading prices (TPs); $p_i$ is the average transaction price (ATP) for product “i”; and $c_i$ is the variable cost for product “i”.

This paper only considers DCP constraints, which can be described using the following equation. In fact, facing the uncertainty of EU tariffs on Chinese EVs, it is still possible to include their tariffs in their effective costs.

$$\begin{gathered} {\displaystyle \sum }_{i\in OEM}{C}_i\times v_{i\_NEV}-\beta \times v_{i\_CV}+ \\ {\displaystyle \sum }_{i\in OEM}\phi \times T_{i\_CV}\times v_{i\_CV}-{\displaystyle \frac{F_i\times v_{i\_CV}}{W_i\times v_{i\_NEV}+v_{i\_CV}}}\times \left(v_{i\_NEV}+v_{i\_CV}\right)\ge 0 \end{gathered}$$

(16)

where $C_i$ represents the new energy passenger vehicle model credits for product “i”; $v_{i\_NEV}$ is the annual production of new energy passenger car model “i”; $\beta$ represents the NEV points ratio requirements; $v_{i\_cv}$ is the annual production of the conventional energy car model “i”; $\phi$ is the enterprise average annual fuel consumption requirements; $T_{i\_CV}$ represents the target values for fuel consumption corresponding to model “i”; $F_i$ is the fuel economy for product “i”; and $W_i$ is discount multiplier for product “i”.

Thus, the OEM’s decision problem is described as follows.

$$\begin{gathered} \underset{\left\{p_i\right\}}{\max }{\displaystyle \sum }_{i\in \mathrm{OEM}}{v}_i\left(p\right)\times \left(p_i-c_i\right) \\ \mathrm{subject} \mathrm{to} {\displaystyle \sum }_{i\in OEM}{C}_i\times v_{i\_NEV}-\beta \times v_{i\_CV}+ \\ {\displaystyle \sum }_{i\in OEM}\phi \times T_{i\_CV}\times v_{i\_CV}-{\displaystyle \frac{F_i\times v_{i\_CV}}{W_i\times v_{i\_NEV}+v_{i\_CV}}}\times \left(v_{i\_NEV}+v_{i\_CV}\right)\ge 0 \end{gathered}$$

(17)

All OEMs have to satisfy similar equations simultaneously at market equilibrium. Due to the lack of detailed compliance data from other OEMs, this paper implicitly addresses OEM compliance through the effective cost approach. The equilibrium implied effective costs are derived by assuming that the observed average transaction price (ATP)/volume combination for each product from every OEM is optimally set, which should also include effects of compliance, capacity, and so on. The mathematically equivalent OEM decision problem can be described as follows.

$$\begin{gathered} \underset{\left\{p_i\right\}}{\max }{\displaystyle \sum }_{i\in \mathrm{OME}}{v}_i\left(p\right)\times (p_i-{\tilde{c}}_i) \\ {\tilde{c}}_i=c_i+\left\{{\lambda }_{\mathrm{CAFC}}\times \left[{\displaystyle \frac{\left(v_{i\_NEV}+v_{i\_CV}\right)F_i}{W_i\times v_{i\_NEV}+v_{i\_CV}}}-\phi \times T_{i\_CV}+\beta \right]+{\lambda }_{NEV}\times \left[{\displaystyle \frac{F_i\left(1-W_i\right)v_{i\_CV}^2}{{\left(W_i\times v_{i\_NEV}+v_{i\_CV}\right)}^2}}-C_i\right]\right\} \end{gathered}$$

(18)

where $v_i\left(p\right)$ is the volume for product “i” in OEM, a complex function of all TPs; ${\tilde{c}}_i$ is the effective variable cost for product “i”; $\left\{{\lambda }_{\mathrm{CAFC}}\times \left[{\displaystyle \frac{\left(v_{i\_NEV}+v_{i\_CV}\right)F_i}{W_i\times v_{i\_NEV}+v_{i\_CV}}}-\phi \times T_{i\_CV}+\beta \right]+{\lambda }_{NEV}\times \left[{\displaystyle \frac{F_i\left(1-W_i\right)v_{i\_CV}^2}{{\left(W_i\times v_{i\_NEV}+v_{i\_CV}\right)}^2}}-C_i\right]\right\}$ is the Pigovian tax/subsidy (per unit); ${\lambda }_{\mathrm{CAFC}}$ is the shadow price for the CAFC constraint; and ${\lambda }_{NEV}$ is the shadow price for NEV constraint.

In the above model, the Pigovian tax/subsidy (per unit) can be understood as an internal transfer within the OEM’s portfolio. All the shadow prices (aka Lagrange multipliers) are non-negative (zero when the inequality holds for the constraint, positive when the equality holds).

Product i pays unit CAFC tax or receives CAFC subsidy according to ${\lambda }_{\mathrm{CAFC}}\times \left[{\displaystyle \frac{\left(v_{i\_NEV}+v_{i\_CV}\right)F_i}{W_i\times v_{i\_NEV}+v_{i\_CV}}}-\phi \times T_{i-CV}+\beta \right]$.

Product i pays unit NEV tax or receives NEV subsidy according to ${\lambda }_{NEV}\times \left[{\displaystyle \frac{F_i\left(1-W_i\right)v_{i-CV}^2}{{\left(W_i\times v_{i-NEV}+v_{i-CV}\right)}^2}}-C_i\right]$.

$${\displaystyle \sum }_{i\in \mathrm{OEM}}{\lambda }_{\mathrm{CAFC}}\times \left[{\displaystyle \frac{\left(v_{i\_NEV}+v_{i\_CV}\right)F_i}{W_i\times v_{i\_NEV}+v_{i\_CV}}}-\phi \times T_{i\_CV}+\beta \right]\times v_i\left(p\right)+{\displaystyle \sum }_{i\in \mathrm{OEM}}{\lambda }_{NEV}\times \left[{\displaystyle \frac{F_i\left(1-W_i\right)v_{i\_CV}^2}{{\left(W_i\times v_{i\_NEV}+v_{i\_CV}\right)}^2}}-C_i\right]\times v_i\left(p\right)=0$$

One strong property of the Pigovian tax/subsidy defined in our framework is that the total tax/subsidy are balanced, i.e., they all sum to zero automatically from the business perspective (no net tax/subsidy). Consequently, the “internal incentives” of automobile firms are systematically adjusted to maximize profits while meeting the compliance constraints of the DCP. The above budget balance is violated only when credit trading is allowed.

3.2. A Dynamic Game Model of NEV Market After Compliance Monetization

The dynamic game proposed in Section 2 is able to predict the overall development trend of the NEV market. However, only implicitly incorporating carbon compliance into the constraints cannot deal with the problem of product mix within firms due to carbon compliance variability and actual profit contradiction. We build on it by incorporating a carbon compliance monetization framework. The automotive company makes production decisions based on macro-market developments and observed transaction prices of other OEMs, product mix, etc. to achieve market equilibrium. At the same time, due to the variability in the carbon compliance of their own products, companies levy a Pigovian tax or subsidy on each product and bring the sum to zero. This can be interpreted as an internal transfer of the OEM’s product portfolio. To simplify the model, the market includes only A Motors and other firms (B Motors).

The model becomes a multi-layer coupling problem, as shown in Figure 3. The top-level optimization problem is the government-enterprise equilibrium. Then comes the market equilibrium. The last is the internal product carbon compliance portfolio equilibrium. For this multi-layer coupled mathematical model, it is very difficult to solve it using traditional algorithms. In this paper, a reinforcement learning algorithm that combines Analytic Target Cascade (ATC) and self-play is used, as shown in Algorithm 1. In the ATC-self-play algorithm, the target response values and the coupling variables in the top-level system are first input into the subsystem. Then, the subsystems are optimized independently using the self-play method, and finally, the subsystems are coordinated at the system level.

Algorithm 1: ATC-Selfplay

$\mathbf{Input}\mathbf{:} \mathit{Environment}:\left(S, A, O,\mathcal{P}\left(·,·|·,·\right), \mathcal{R}\left(·,·\right), {\rho }_0\right)$   $\mathbf{Input}\mathbf{:} \mathit{Self}-\mathit{play} \mathit{Scheme}: \left(\Omega \left(·|·,·\right), \mathrm{G}\left(·|·,·\right)\right)$   $\mathbf{Input}\mathbf{:} \mathit{Policy} \mathit{to} \mathit{be} \mathit{trained}: \mathrm{\pi }\in {{\displaystyle \prod }}_i$ 1  ${\pi }^0=\left\{\pi \right\};R_{sub,i}^{sub,k};y_{sub,i}^{sub,k};w_{sub,i}^{R,k};w_{sub,i}^{y;k};$ 2  $\mathbf{for} \mathrm{e}=0, 1, 2,\dots \mathbf{d}\mathbf{o}$ 3        ${\pi }^{\prime }~\Omega \left({\pi }^0,\pi \right)$$;R_{sub,i}^{sys,k^{\prime }}~R_{sub,i}^{sys,k};y_{sub,i}^{sys,k^{\prime }}~y_{sub,i}^{sys,k}$; 4        $\pi ={\pi }^{\prime }\cup \left\{\pi \right\}$; 5        $s_0,o_0$$~{\rho }_0$; 6        $\mathbf{for} t=0,\dots ,termination \mathbf{d}\mathbf{o}$ 7              $a_t~\pi \left(o_t\right)$; 8              $s_{t+1},o_{t+1}~P\left(s_t,a_t\right)$; 9              $r_t$$~\mathrm{R}(s_t,a_t$$);w_{sub,i}^{R,k+1}=w_{sub,i}^{R,k}+{\alpha }_{sub,i}^{R,k}\left(R_{sub,i}^k-R_{sub,i}^{sub,k}\right);$                 $w_{sub,i}^{y;k+1}=w_{sub,i}^{y;k}+{\alpha }_{sub,i}^{y,k}\left(y_{sub,i}^k-y_{sub,i}^{sub,k}\right)$; 10            $\mathrm{t}\leftarrow \mathrm{t}+1$; 11      end 12      $\mathrm{\pi }\leftarrow update\left(\mathrm{\pi }\right)$; 13      ${\pi }^o~G\left({\pi }^o,\pi \right)$$; R_{sub,i}^{sys,k^o}~G(R_{sub,i}^{sys,k});$ 14 end $15 \mathrm{return} \pi ; R_{sub,i}^{sys,k}$

4. Simulation and Discussion

The usefulness of assessing the level of corporate carbon management is limited if the data are unreliable, and significant progress can only be expected if standardized and comparable corporate carbon data are used for analysis [43]. In this paper, we use authentic historical data from an automobile company (denoted as Company A for commercial security) for our analysis, including 24 models from Company A’s fleet, each labeled with a suffix. Specifically, we explore: (1) China’s NEV ownership from 2016 to 2023, to calibrate the macro automotive market; (2) Three key parameters (demand level, variable cost, and fuel economy) for each vehicle in the lineup of Company A; (3) Compliance constraints (DCP); (4) Whether segmentation/substitution patterns and price sensitivities are slow to change and thus fixed by historical transaction data; and (5) Effective costs incurred by all other OEMs to circumvent their lack of compliance data.

4.1. Overall Market Analysis

The results of DOI model fitting are shown in

Table 3. The fitting results of Euler method.

Setting Parameters	$\mathbf{\alpha }$	$\mathbf{\sigma }$	Fitting Parameters	${\mathit{a}}_1$	${\mathit{a}}_2$	$\mathit{b}$
value	0.1	0.001		0.0013	0.0017	0.021

.

The coefficient of innovation effort for all automobile companies in fuel vehicles from 2016 to 2024 is $a_1=0.0013$; the coefficient of innovation effort in NEVs us $a_2=0.0017$.

The model-solved predicted dual-credit price and optimal level of innovation effort are shown in Figure 4. The credit price continues to rise until 2029, peaking at about 4.5 K RMB. Then, it keeps dropping and stays at around only a few hundred RMB by 2035. The level of innovation effort invested by automobile companies in fuel vehicles stays almost the same, with only a slight increase, and the level of innovation effort invested in NEVs continues to grow until 2030. Thereafter, a high level of innovation effort is maintained in this area. The results confirm the trends in the automotive market. To accelerate the development of the NEV market, the government will have to introduce measures to protect the value of the credit, or even raise the credit price directly. By 2030, when the NEV market is more mature, it will begin to lower the credit price to eliminate the impact of the dual credit policy. At the same time, the automobile companies predicted the government’s decision, so the automobile companies will not continue to add innovation investment in fuel vehicles, and the geometry of their innovation efforts remains consistent. However, due to the constraints of the dual-credit policy, automotive companies will make additional innovation investments in NEVs to meet carbon compliance requirements. After 2030, when the market for NEVs is more mature and has a larger market share, automotive companies will also maintain a high level of innovation effort. The market trends indicated by the results can provide forward-looking advice to automotive companies in making business decisions, and the model can also be used as a base model for solving market equilibrium.

4.2. Internal Analysis of Company A

4.2.1. Results of Market Calibration

When the market reaches equilibrium, the actual average transaction prices (ATPs) and the model-derived ATPs and the actual and derived equilibrium volumes are as shown in Figure 5. Company A’s actual and derived equilibrium ATPs and the actual and derived equilibrium volumes are basically close to each other, which verifies the consistency of the CO₂ compliance monetization framework with Company A’s market. In addition, the product ATP shows that Company A’s products face the dilemma of overpricing strong products and underpricing weak products. Under compliance constraints, the same problem exists in Company A’s equilibrium volume, i.e., strong products that comply with carbon emission standards tend to be undersold, while weak products tend to be oversold. Therefore, it is necessary to consider monetizing carbon compliance by quantifying the actual value of the credits to Company A’s products by incorporating it into the effective cost of the product and setting internal incentives for each product.

4.2.2. Product Portfolio Change

Company A’s internal estimate of the DCP shadow price (adjusted to vehicle parameter level, not actual accounted individual credit price) is ¥518/(g/km), and the estimated CAFC penalty is approximately ¥511.2 million (or ¥495.36 per unit) without the use of bank credits. Figure 6 shows the products of Company A that are subject to the Pigovian tax or subsidy. All fuel vehicles, except pickup trucks, are subject to the Pigovian tax, while NEVs receive a subsidy. Among them, BEV receives the most subsidies per unit, which is due to the dual credit policy, which enables them to contribute more NEV credits. Although the market margin for selling BEVs is loss-making, as shown in Figure 7, there is a sizable implied profit (effective profit) due to the high marginal gain of NEV credit under the DCP constraint, i.e., credits are used to gain sales volume for other hot-selling fuel models. Pickup truck models are not carbon compliant in the DCP, but the company should still subsidize them a small amount. This is because the NEV credits resulting from these sales and costs under the DCP constraint have a higher marginal benefit to the pickup truck lineup, so the company should still subsidize it to ensure the longevity of the benefits of this product. From the total amount of product subsidies, it can be seen that the pickup truck series is the first one with a very high amount of subsidies due to its sales volume. All other fuel models are effectively constrained by the DCP, and their profits are declining.

The variable, implied, and effective costs of the products solved by the model are shown in Figure 7, where the implied and effective costs of all products are very close to each other. It can be seen that the variable costs of BEVs and PHEVs may be very different from the effective costs due to the DCP. After the Pigovian subsidy within the firm, the true cost of the product is calibrated under the DCP constraint. In addition, the implied and effective unit margins at market equilibrium are very close for all products. The market margins for both A-sedan5BEV and A-sedan4PHEV are loss making, calibrated for compliance monetization, with positive effective margins at market equilibrium. This suggests that the marginal sum of the NEV credit gained from the sale of these two models is greater than their loss. The fact that variable unit margins for electric vehicles can be very different from effective unit margins, and that it is highly unwise to make strategic decisions about models based directly on market margins, also points to the need for a framework for monetizing CO₂ compliance. As shown in Figure 8, using the proposed shadow price by model would result in very different outcomes at equilibrium.

4.2.3. Influencing Factor for Shadow Price

Shadow prices can be influenced by many factors, sometimes drastically. This subsection discusses a number of aspects, as shown in Figure 9, where we use shadow price to illustrate: (A) Demand pattern shift; (B) Variable cost change; (C) Fuel economy improvement; (D) Compliance standard change; (E) Gasoline price shock; and (F) Introducing new products.

In Figure 9A, pickup truck models are rapidly decreasing in shadow price as demand increases. Demand pattern shift has the greatest impact on shadow prices for products with large volumes and a big CO₂ gap. Lower shadow prices imply lower constraints by DCP. Cost reduction has bigger effect than demand increase, as shown in Figure 9B; the trend is similar, however. As shown in Figure 9C, fuel economy improvement lowers the shadow price, and is more pronounced for large volume products. In Figure 9D, shadow price increases when the DCP target (for the whole portfolio) tightens (moving to the left). Even with just a few percentage points of change, the profitability impact can be in the hundreds of millions. This also reflects the fact that the DCP is effectively binding on automobile companies. In Figure 9E, shadow price decreases as gas price increases, as aggregate demand shifts towards positive. Company A introduced a new all-electric vehicle, the A-newBEV, this year. The statistics were as follows: volume: 44,000; price: ¥325,656 (model forecast, including government subsidies); Cost: ¥306,474 (income statement); performance: −21 (sustainability analysis). Using calibrated credits, the shadow price is ¥0, i.e., Company A has met DCP standards, as shown in Figure 9F. The equilibrium volume and price would be ¥17,073 and ¥380,037, respectively.

4.2.4. Existence of Credit Market: OEM’s Decision Problem

The above equilibrium is achieved without taking into account the external credit market, i.e., the internal equilibrium of the firm. When it is possible to purchase points from the credit market, Equation (15) of the automobile company’s objective function becomes:

$$\begin{gathered} \underset{\left\{p_i\right\}}{\max }{\displaystyle \sum }_{i\in \mathrm{OEM}}{v}_i\left(p\right)\times \left(p_i-c_i\right)-\eta \times q \\ \mathrm{subject} \mathrm{to} {\displaystyle \sum }_{i\in OEM}{C}_i\times v_{i\_NEV}-\beta \times v_{i\_CV}+ \\ {\displaystyle \sum }_{i\in OEM}\phi \times T_{i\_CV}\times v_{i\_CV}-{\displaystyle \frac{F_i\times v_{i\_CV}}{W_i\times v_{i\_NEV}+v_{i\_CV}}}\times \left(v_{i\_NEV}+v_{i\_CV}\right)\ge 0 \end{gathered}$$

(19)

where $\eta$ is credit bought externally, and $q$ is the market price of credit (adjusted to vehicle parameter level, not actual accounted individual credit price), treated as a given.

As shown in Figure 10, Company A should buy credit externally when the market price is below A’s original internal shadow price. The potential profitability impact of buying market credit is in the order of RMB 1.4 billion.

5. Conclusions and Policy Implications

This paper proposes a CO₂ compliance monetization framework for ESA. A dynamic model of the new energy vehicle market is used to solve for market equilibrium, and the carbon compliance monetization framework is used to systematically align firms’ “internal incentives” to ensure that they maximize profits while meeting compliance constraints. Using real historical data from Automobile Company A, we explicitly illustrate how our approach works and demonstrate its consistency with market observations. The results of the study explore the macro-market trends of new energy vehicles and the calibration of the carbon compliance variability of Company A’s products.

For the NEV market, the government is inclined to further strengthen the incentives of DCP for market development, and will guarantee the value of points until 2030. After the market is more mature in 2030, the policy influence will be gradually removed and the price of credit will be scaled down. Auto companies are accordingly investing increasing amounts in innovation efforts for NEVs until 2030 to ensure carbon compliance under the DCP constraints. After 2030, when NEVs have a larger market share, automakers will also maintain a higher level of innovation efforts to ensure market share. For fuel vehicles, automakers tend to maintain their current level of innovation effort. Therefore, the government can further optimize the DCP decision through this market trend to promote the growth rate of the NEV market, while ensuring good competition in the market.

For Auto A, the ATP and market equilibrium volume calibrated by the carbon compliance monetization framework are very close to the actual data, which validates the consistency of our framework. Only the pickup truck series among the fuel models is subsidized, which represents a higher marginal gain of NEV credit for the pickup truck series under the DCP constraint. Corporate product carbon compliance is explicitly monetized and quantified. In this study, we treat all products (demand levels, variable costs, fuel economy) as given costs and fixed/investment costs as sunk costs. All three dimensions (demand/cost/fuel economy) are improved by capital investment. We also discussed the factors influencing shadow prices and when to purchase external credit. The potential profitability impact of buying market credit would be in excess of RMB1 billion. The effectiveness of the framework is demonstrated by analyzing historical data from Company A. The product mix adjustments and equilibrium returns analyzed through the framework provide practical guidance for companies to make informed and sustainable business plans.

This paper proposes a CO₂ compliance monetization framework that effectively meets the needs of product adjustment portfolios within enterprises, and provides a certain theoretical framework and decision-making support for enterprises. However, the research in this paper has certain limitations. Carbon compliance strategy for automotive enterprises is a complex systematic project, involving the influence of policies, technologies, market demand, and consumer behavior at multiple levels. This paper simplifies the market model and ignores several important market influences, such as the public opinion effect and the infrastructure of the NEV market. In the future, we will develop and refine the model to incorporate more considerations and seek to incorporate commercial products into the model and complete internal dynamic credit transactions. In addition, further research may focus on how to explicitly consider risk (internal/external), which is also the subject of risk-adjusted capital allocation, refining the risk-adjusted capital allocation model and validating its reasonableness and consistency.