Navigating the Carbon Challenge: Strategic Integration of Hybrid Policies in Green Supply Chains

Abstract

In the context of climate change, the increasing urgency to mitigate environmental impacts has driven firms to adopt green supply chain strategies. Existing research primarily focuses on either carbon tax or emission trading schemes, leaving a gap in understanding the combined impact of hybrid carbon policies. This study addresses this gap by developing a dual-tier supply chain model with a manufacturer and retailer, exploring the effects of a carbon tax, emission trading, and a hybrid policy on emission reduction strategies and pricing decisions. Using a reverse inductive method within a Stackelberg game framework, we identify optimal strategies for emission reduction and profit maximization under each policy scenario. Results indicate that the hybrid policy achieves the lowest unit carbon emissions when the manufacturer’s initial pollution level is below a critical threshold. This research contributes to the literature by providing actionable insights into the strategic advantages of hybrid carbon policies for firms seeking both profitability and sustainability in green supply chains.

1. Introduction

The contemporary global business landscape is undergoing a seismic transformation, driven by the dual imperatives of fostering robust economic growth and embracing unwavering ecological responsibility. This paradigm shift is particularly poignant due to the escalating challenges of depleting natural resources, intensifying pollution levels, and a burgeoning array of societal concerns. In this context, the United Nations unveiled the Sustainable Development Goals (SDGs) in 2015, a visionary framework comprising 17 objectives meticulously designed to guide global efforts toward a more sustainable and equitable future. These goals are explicitly connected to climate action, economic growth, and social equity, which resonate directly with the operational shifts that businesses must undergo to align with ecological responsibility [1]. As businesses grapple with the urgency of aligning their operations with these ambitious goals, the role of environmental policies has assumed unprecedented significance.

Traditional strategies, exemplified by carbon taxes and carbon trading, have played pivotal roles in incentivizing sustainable practices within industries. The carbon tax system, as a key policy instrument, aligns closely with SDG 13 (Climate Action) by providing a financial disincentive for carbon emissions, encouraging businesses to reduce their environmental footprint. A carbon tax, a direct levy on the carbon content of fuels, offers a clear-cut economic incentive for reducing emissions. However, as industries navigate its implementation, it becomes increasingly apparent that this approach is not without its challenges. Issues such as potential economic inefficiencies and resistance from sectors disproportionately impacted by the tax have become central considerations [2].

Similarly, carbon trading introduces a market-based mechanism that allocates emission allowances for trading, providing flexibility and cost-effectiveness in devising emission reduction strategies. This mechanism directly supports SDG 12 (Responsible Consumption and Production) by creating an efficient market for emissions, encouraging industries to adopt cleaner technologies and optimize resource use. However, challenges such as market volatility and the potential for manipulation have surfaced, prompting a reevaluation of its long-term effectiveness. The evolving landscape of environmental governance necessitates a nuanced understanding of the strengths and limitations inherent in these policies, particularly as industries strive for sustainability on multiple fronts [3].

In response to recognized deficiencies in singular policies, a noticeable global trend has emerged towards the adoption of dual policies, specifically integrating carbon tax and carbon trading mechanisms. This dual approach addresses multiple SDGs, particularly SDG 7 (Affordable and Clean Energy) and SDG 9 (Industry, Innovation, and Infrastructure), by promoting the transition to cleaner energy sources and encouraging sustainable industrial practices. Several countries and regions, including Denmark, Finland, and the Netherlands, have implemented such composite policies [4]. These nations, after imposing carbon taxes, have integrated their systems with carbon trading mechanisms, such as the European Union Emissions Trading Scheme (EU ETS). For instance, Sweden extends its carbon tax to sectors not covered by the EU ETS [5]. Additionally, studies have shown that the combination of these policies can lead to a “double dividend” effect, where both carbon emission reduction and economic efficiency improvements are achieved due to the carbon tax, and carbon trading is gaining momentum globally, with several countries exploring their synergistic potential for enhancing climate mitigation efforts [6,7]. This underscores the necessity for a multifaceted toolkit in environmental governance to address the diverse challenges of sustainability.

The introduction of a dual-policy framework aims to leverage the inherent strengths of both carbon tax and carbon trading while mitigating their respective weaknesses. By integrating these policies, this research aligns with SDG 17 (Partnerships for the Goals) by fostering collaborative efforts between government bodies, industries, and other stakeholders to create synergies in sustainability efforts. However, as the business community adopts this dual-policy approach, outcomes remain uncertain, and the intricate interplay between carbon tax and carbon trading introduces complexities beyond the scope of traditional analyses. In particular, for manufacturers with lower initial pollution levels, the combined effect of carbon tax and emission trading mechanisms creates a more powerful incentive for emission reduction than either policy alone. The carbon tax increases the cost of emissions, providing direct economic pressure for manufacturers to reduce emissions. Meanwhile, the carbon trading mechanism offers flexibility, allowing firms to reduce emissions in a more cost-effective manner through the trade of allowances, thus providing a synergistic effect. When the initial pollution level is low, these mechanisms are more easily implemented and result in more efficient emission reductions. The ongoing narrative of environmental responsibility in the global business arena necessitates an in-depth exploration, revealing the dynamic interplay between economic imperatives and ecological stewardship.

In light of these profound challenges and uncertainties, this research embarks on a meticulous exploration of the dynamics of supply chain management within a two-tier structure—comprising a single manufacturer and a single retailer—under the influence of carbon tax, carbon trading, and a hybrid of both policies. By considering the integration of these policies, the research aims to directly contribute to the achievement of SDG 12, 13, and 9, focusing on responsible industrial practices, climate action, and the development of clean technologies. By scrutinizing the implications of dual policies, we aim to contribute insights that transcend current understanding, paving the way for more informed decision-making in the pursuit of sustainable supply chain management. The effectiveness of the hybrid policy in this context is particularly evident for low-emission manufacturers, as the synergy between both policies helps them reduce carbon emissions more effectively, leading to a more sustainable supply chain.

This study meticulously recognizes the limitations of singular policies and endeavors to provide a comprehensive analysis of the dual-policy landscape. By delving into the intricate nuances of navigating both carbon tax and carbon trading within a supply chain context, this research aims to offer invaluable perspectives for industries and policymakers alike. Ultimately, the research aims to empower decision-makers to contribute more effectively to SDG 8 (Decent Work and Economic Growth) by fostering sustainable and resilient business models, ensuring that economic growth is coupled with ecological responsibility in the face of global challenges. The ultimate goal is to empower decision-makers with the knowledge needed to navigate the complex terrain of achieving both economic and environmental sustainability in a rapidly changing global landscape.

2. Literature Review

2.1. Research on Carbon Emission Trading Scheme

In the aftermath of the Kyoto Protocol, the carbon emission trading scheme (ETS), commonly referred to as carbon trading, has become a pivotal and highly sought-after instrument for reducing carbon emissions. Currently, researchers are intensely focused on several critical issues surrounding carbon trading. These key topics include the scope of carbon markets, covering considerations such as covered industries and inclusion standards [8], as well as concerns about carbon leakage between regions [9,10]. Additionally, discussions revolve around the potential linkage of carbon markets between countries, exploring the concept of a global carbon market [11,12,13]. Financial aspects, known as carbon finance [14], and the implications of carbon tariffs [15] are also topics that have garnered significant attention.

Furthermore, researchers delve into the multifaceted impacts of ETS, ranging from its structural components to the influence of carbon pricing. Mechanism design, supplementary mechanisms, and the broader implications of ETS on climate change policies and global trading systems are areas of critical exploration. This paper provides a comprehensive review and discussion of the impact and mechanism design of ETS, offering insights into the prospects for the development of carbon emission trading initiatives.

• (1). Efficiency and implications of Carbon Emission Trading Scheme

Efficiency and implications of carbon markets have been a focal point in numerous scholarly investigations. Scholars have extensively assessed carbon trading systems globally. Sousa et al. [16] analyzed the economic impact of introducing an emission trading system in Colombia, suggesting that implementing a comprehensive industry-wide Emission Trading Scheme (ETS) would lead to an average annual GDP growth rate reduction of 0.8 percentage points. Nong et al. [17] employed the GTAP-E model to study the economic and environmental impacts of carbon trading on Vietnam, concluding that restricting emissions from industrial sectors in the trading market significantly affected Vietnam’s economy, resulting in a 4.57% decline in actual GDP. However, when the entire industry participated in ETS, the adverse impact on the country reduced to 1.78%.

Diverse studies in different regions, and even within the same region, present varying perspectives on the negative economic impacts of ETS. The variations arise from differences in fundamental assumptions, such as methodologies like Difference-in-Differences (DID), which assesses actual potential GDP reductions, being influenced by factors like indicator selection, model design, timeframes, and geographical scopes. Scenario analysis models, such as Computable General Equilibrium (CGE) models, yield vastly different results due to variations in simulated carbon trading mechanisms influenced by factors such as carbon quotas, allocation methods, and covered industries.

In 2013, China officially launched pilot projects for the carbon trading market, prompting numerous scholars to conduct research on the effectiveness and impact of the domestic carbon trading market. Therefore, in this section, we will focus on summarizing the studies conducted in China. Wen et al. [18], using the Logarithmic Mean Divisia Index (LMDI) model and DID model, analyzed the effectiveness of the carbon trading pilot in Hubei Province. They argued that after the implementation of ETS, the impact of energy structure effects on emissions was limited, and the contribution of economic structure effects to emissions was negligible. Additionally, the implementation of ETS had almost no noticeable impact on industrial CO2 emissions, Gross Domestic Product (GDP), energy consumption intensity, and CO2 emission intensity. The reasons for these impacts were attributed to insufficient greenhouse gas monitoring capabilities and irrational quota distribution by the local development and reform commission. However, Xuan et al. [19], using the DID model, arrived at a completely opposite conclusion, asserting that the carbon trading market pilot promoted a reduction in carbon emissions and carbon intensity. Gao et al. [20], applying the same model, argued that the carbon trading market contributed to emission reduction in pilot regions and industries in China.

Carbon trading appears to have a positive impact on technological innovation. Hu et al. [21], using the Difference-in-Differences-in-Differences (DDD) model, analyzed China’s carbon trading pilot and found a significant positive influence of carbon trading on both the quantity and quality of innovation. However, the impact diminished successively concerning the quantity of innovation, low-quality innovation, and high-quality innovation. Ren et al. [22], based on panel data of Chinese-listed companies from 2004 to 2015 and utilizing the DID model, examined the innovation effects of the SO₂ emission trading pilot policy. The study suggested that market-based emission trading policies indeed stimulated corporate innovation and environmental innovation, contributing to a win–win scenario for environmental protection and economic growth.

Additionally, carbon emission trading may lead to other forms of dividends. Yang et al. [23] indicated that, after controlling for critical variables such as environmental regulations, population size, and economic levels, the pilot carbon emission trading policy drove an expansion in employment and a reduction in carbon emissions. This implies that China’s carbon trading holds a dual dividend of employment growth and emission reduction.

Furthermore, some alternative studies on the impact of carbon markets, such as Jarke–Neuert and Perino [24], argue that under a carbon cap-and-trade system (an alternative term for carbon trading), improving energy efficiency could backfire. Due to rebound effects, the emission savings from enhanced energy efficiency often fall below technically feasible levels or even lead to a reversal in carbon reduction, becoming a means of increasing carbon emissions.

• (2). Mechanism Design of Carbon Markets

The exploration of carbon trading mechanisms has been most extensively studied in relation to the European Union (EU), primarily due to the strategy of “learning by doing” in mechanism design. Guo et al. [25] conducted a study on the complete enterprise-level trading records of the EU Emission Trading System (ETS) in its first and second phases. They found a positive correlation between trading profits and emission reductions by participating enterprises, with a stronger correlation observed in the second phase compared to the first. The study suggests that the EU’s emission trading mechanism operates in line with its intended design, establishing a positive linear relationship between enterprise profits and efforts in emission reduction. In 2018, the EU initiated a reform regarding the total carbon quota of the ETS, introducing a dynamic mechanism that adjusts the quota based on demand rather than being controlled by EU policymakers [26]. This mechanism is considered a significant outcome for the fourth phase of the EU ETS agreement. Although the effectiveness of emission reduction in the EU ETS has faced scrutiny, it remains an affirmative emission reduction system employing a “learning by doing” approach. To provide a robust price signal for greenhouse gas emission reduction, Europe decided to strengthen the EU ETS by implementing the Market Stability Reserve (MSR), increasing the linear reduction factor from 1.74% to 2.2% after 2020 [27].

Similar to carbon taxes, carbon trading has encountered resistance from different governments and the public, primarily due to issues of fairness. The carbon trading mechanism has substantial negative impacts on sectors such as petrochemicals and agriculture. Different countries possess diverse conditions, and varying levels of economic development can result in fairness concerns with the indiscriminate application of carbon trading systems [28].

2.2. Impact of Carbon Tax Policies

Carbon taxes are generally considered an effective pricing incentive for reducing carbon emissions and promoting the transition to cleaner energy sources [29]. In 1990, Finland officially implemented carbon taxes, becoming the first country to levy carbon emission taxes on households and businesses. The Nordic countries have developed a relatively mature carbon tax system over the years, with Finland serving as an example [30]. In this system, in addition to taxation, considerations are provided to tax rebates: a portion of carbon tax revenue is allocated to subsidize energy-saving projects for industrial enterprises, which, in turn, benefit from tax rebates and concessions. For instance, in Denmark, the effective carbon tax rate for the industrial sector is equivalent to 35% of the household tax rate. While Denmark, Sweden, Norway, and Finland share similar entities responsible for carbon tax collection, each has its unique mechanism for tax rebates.

This section primarily conducts a literature review on the impact of carbon taxes and issues related to policy coordination.

• (1). Carbon Tax Emission Reduction Capacity and Impact

In general consensus, scholars and the public perceive carbon taxes as an effective policy for carbon reduction. Carbon taxes have a significant impact on reducing carbon emissions and carbon intensity while having a relatively low impact on GDP [31]. The efficiency of carbon taxes is a focal point in related research. Runst and Thonipara [32] suggest that the carbon tax rate directly influences its emission reduction capacity. Using European panel data, this study examines the impact of Sweden’s carbon tax on residential carbon emissions. Runst and Thonipara employ Synthetic Control Methods (SCMs) and Difference-in-Difference (DID) regression to assess the causal effects of the carbon tax on residential area carbon emissions. Adetutu et al. [33] conduct a mechanism analysis of carbon taxes reducing energy intensity, emphasizing the challenges posed by an overreliance on narrow energy policy goals (such as improving energy efficiency) and indicating that broader policy approaches aimed at improving overall resource allocation in enterprises may be more appropriate.

However, behind the emission reduction capacity of carbon taxes, there are implicit economic costs. Marz and Pfeiffer et al. [34] argue that imposing a USD 100-per-ton carbon tax (levied on an ad valorem basis) would lead to a 1.28% reduction in petroleum extraction, and for each ton of carbon, the quantity extracted from ad valorem taxation would increase by 0.52%. This suggests that carbon taxes may also have far-reaching effects on capital markets.

• (2). Political, Legal, and Policy Coordination Issues of Carbon Tax

While the use of carbon taxes to reduce greenhouse gas emissions is deemed effective, recent developments portray carbon taxes as unpopular emission reduction policies, facing substantial implementation challenges in many countries [35]. Umit and Schaffer [36], based on the European Social Survey (44,387 questionnaires), provide insights into public attitudes toward increasing mineral fuel taxes to mitigate climate change across 23 countries. The results indicate a general aversion to carbon taxes due to concerns about potential negative economic impacts and additional burdens on the public. Simultaneously, carbon taxes may result in issues like carbon leakage [37].

The potential adverse impact of carbon taxes on employment is a contributing factor to their unpopularity. However, some studies suggest that carbon taxes could enhance employment opportunities. Brown et al. [38] argue that carbon taxes could increase job opportunities in the United States, projecting an increase of 511,000 jobs by 2030.

The design of carbon taxes should be approached with caution, considering various aspects of rights and responsibilities. For instance, Reanos [39] argues that the design of carbon taxes should be linked to environmental responsibility. The author explores the impact of imposing additional carbon taxes on German car owners, suggesting that if carbon taxes are imposed only on the transportation sector (generally referring to public transportation), without considering redistribution, the tax becomes regressive. However, if additional carbon taxes are imposed on fuel used for private transportation (referring to gasoline and diesel used for household vehicles), carbon taxes can become progressive. Since carbon taxes may not influence high-frequency vehicle owners to reduce energy consumption, they need to be designed in coordination with other tax policies to reduce emissions from heavy polluters.

The design of carbon tax systems is highly sensitive and must focus on environmental responsibility to be effective. This challenge, involving both environmental and economic considerations, could be a subject of an entirely new research paper. However, within the scope of this paper, we focus on how carbon tax design interacts with the dual-policy framework we study. The integration of carbon tax with carbon trading systems highlights the necessity of a carefully structured design that ensures both economic and environmental sustainability. Our research investigates how a hybrid policy can minimize the inefficiencies of individual policies, such as economic distortion from carbon tax or potential market manipulation in carbon trading. Furthermore, a well-structured carbon tax incentivizes businesses to innovate and adopt cleaner technologies, which supports the broader goals of the dual-policy framework by promoting both emission reductions and technological advancements in sustainability.

In addition, the design of carbon taxes can be coordinated with various related policies, potentially yielding synergistic effects. For example, Zhao et al. [40] propose the synergy of Renewable Portfolio Standards (RPS) and carbon tax policies as effective regulatory tools for achieving low-carbon energy transformation. This coordination can leverage both visible and invisible hands in determining resource utilization and allocation, providing incentive-based regulation for power generation enterprises. Li and Yao [41] argue that, from the perspectives of energy conservation, emission reduction, and economic growth, coal capacity reduction and carbon taxes exhibit significant synergistic effects. Therefore, it is advisable to advance mixed policies suitable for carbon taxes and adopt policy combinations with appropriate degrees of stringency.

2.3. Hybrid Policies in Emission Reduction Strategies

The exploration of hybrid emission reduction policies represents a relatively understudied yet crucial aspect in the landscape of environmental governance. This section delves into the realm of hybrid policies, focusing on two key dimensions: the exemplary practices of typical nations and a comprehensive examination of the implementation effects of such policies. While the literature on hybrid strategies may be limited, the significance of understanding the interplay between different policy instruments and their collective impact on emission reduction cannot be overstated. By delving into the practices of leading nations and scrutinizing the outcomes of their hybrid approaches, this section aims to contribute valuable insights to the evolving discourse on effective emission reduction strategies.

• (1). Typical National Practices

Sweden, Norway, Denmark, and other Nordic countries were among the first to implement carbon tax policies in the early 1990s, marking the initial wave of countries worldwide to impose carbon taxes [42]. In contrast to countries that implement either a standalone carbon tax or carbon emissions trading, the United Kingdom simultaneously implemented both carbon tax and carbon emissions trading. In 2001, the UK introduced a Climate Change Levy, a comprehensive form of carbon tax, and the following year implemented a carbon emissions trading system, providing valuable experience for the European Union’s implementation of the carbon emissions trading plan [43]. In 2005, Nordic countries joined the EU’s carbon emissions trading plan, initiating the simultaneous implementation of both carbon reduction systems.

Based on the different scopes of implementation for carbon tax and carbon emissions trading systems, Nordic countries provide tax exemptions or reductions for businesses included in the EU’s carbon emissions trading system. Denmark and Norway exempt these businesses from carbon taxes, while Sweden imposes a 15% carbon tax rate on them. Additionally, carbon taxes can play a role in stabilizing carbon trading prices and preventing policy failures caused by excessively low carbon trading prices. For instance, in 2014, when the EU carbon trading prices fell, Norway increased the carbon tax rate from NOK 100 per ton of carbon dioxide to NOK 330 [44].

In the UK, the climate change tax serves as a supplement to the carbon emissions trading system. Taxation targets include coal, natural gas, liquefied petroleum gas, and others. The initial purpose of taxation was to achieve the UK government’s goal of reducing greenhouse gas emissions by 20% compared to 1990 levels by 2010 [45]. The UK provides incentives to companies voluntarily implementing carbon reductions through the climate change agreement. It uses a support mechanism to stabilize carbon trading prices.

• (2). Policy Implementation Effects

TAMURA et al. [46], using a prospective approach under uncertainty conditions, compared the cost savings of a standalone carbon tax/carbon emissions trading system and its hybrid system. They concluded that a standalone carbon emissions trading system cannot achieve the carbon reduction goals set out in the Kyoto Protocol, while both a standalone carbon tax and a hybrid system can achieve the goals, with the hybrid system having the lowest carbon reduction cost. Thus, they suggest that the synergistic application of carbon taxes and carbon emissions trading systems is more effective in achieving carbon reduction goals compared to a single system. JEFFREY et al. [47], based on over 30 years of data from EU countries, indicated that carbon emissions intensity decreases as energy tax rates increase. After the introduction of the EU carbon emissions trading system, overall carbon emissions intensity significantly weakened, mitigating the political negative impacts of implementing energy taxes. Kiss et al. [48] analyzed the carbon reduction policies of EU countries and concluded that a hybrid system of carbon taxes and carbon emissions trading can achieve the expected carbon reduction goals with minimal Gross Domestic Product (GDP) loss, demonstrating superior effectiveness.

While the existing literature has significantly contributed to understanding the dynamics of carbon emissions management, there is a noticeable gap in the quantitative modeling and analysis of supply chain dynamics within these frameworks. Previous studies have laid a robust foundation by examining the broader aspects of carbon policies, but a more focused exploration into the supply chain’s quantitative modeling is essential. This gap in research motivates the need for a more in-depth investigation into the specific dynamics of supply chains within the context of carbon emission management. This study aims to bridge this gap by addressing the aforementioned limitation and providing a quantitative analysis of supply chain models under different carbon management policies.

3. Problem Formulation and Assumptions

3.1. Basic Assumptions

Prior to establishing the fundamental mathematical model, the following assumptions are made:

• (1). In this paper, the carbon trading price “k” is treated as an exogenous variable, jointly determined by the carbon trading market and governmental decisions [49].

• (2). Research and development (R&D) investment for carbon emission reduction is considered a one-time investment, and the emission reduction investment has no impact on the production cost of the product. A higher emission reduction investment coefficient indicates greater difficulty in achieving emission reduction [50].

• (3). The supply chain is assumed to exclusively provide customers with a singular low-carbon product, with product carbon emissions primarily generated in the manufacturing process of the producer [51,52].

• (4). The carbon emissions per unit product are assumed to be constant, and the total carbon emissions of the enterprise form a linear function of production volume [52].

• (5). Market product demand is assumed to be a linear function of price [53].

3.2. Model Assumptions

This paper primarily focuses on the context of the government implementing a coordinated policy of carbon tax and carbon trading. The research is conducted within the framework of a two-tier supply chain consisting of a green manufacturer and a retailer, examining pricing strategies from various stakeholders and the impact of government policies.

The market demand for the green product is assumed to be influenced linearly by the product’s selling price “p” and the carbon emission-reduction-per-unit product “t” [54]. In this paper, we assume the market demand to be expressed as follows:

(1)$\mathrm{D}=\mathrm{Q}-\mathrm{\beta }\mathrm{p}+\mathrm{\gamma }\mathrm{t}$

Here, Q represents the potential market demand for green products, β denotes the consumer price sensitivity coefficient, and γ represents the consumer sensitivity coefficient to the product’s greenness. Both β and γ are greater than 0.

As the emission reduction increases, the reduction becomes more challenging, requiring a substantial increase in research and development (R&D) investment. The marginal cost of emission reduction experiences an increase with the rise in the emission reduction rate, indicating the presence of diminishing marginal returns. Therefore, the R&D investment for the enterprise can be expressed as:

(2)$\mathrm{C}\left(\mathrm{t}\right)={\displaystyle \frac{{\mathrm{mt}}^2}{2}}$

It represents the relationship between environmental improvement and investment [55]. Here, m is the carbon emission reduction cost coefficient, typically assumed to be a relatively large value.

In this model, the unit carbon emission tax is represented by “r”. The taxation mechanism for carbon emissions involves levying a fixed tax amount “r” for each unit of carbon emissions. Under the carbon trading mechanism, the green manufacturer is initially allocated free-unit carbon quotas, represented by “g”, and the unit carbon trading price is denoted by “k”. Additionally, to ensure that the parameters have practical significance, the following conditions must be satisfied:

$\mathrm{w}>\mathrm{c}, \mathrm{e}>\mathrm{g}, \mathrm{Q}>\mathrm{\beta }\mathrm{c},\mathrm{p}>\mathrm{w},\mathrm{k}>\mathrm{r},\mathrm{Q},\mathrm{\beta }, \mathrm{\gamma }, \mathrm{r},\mathrm{k},\mathrm{c},\mathrm{m},\mathrm{g},\mathrm{e}>0$

where w > c and p > w ensure positive profits for the manufacturer and retailer, respectively. Q > βc ensures meaningful market demand and k > r ensures that the unit carbon trading price is greater than the unit carbon tax, making it more aligned with practical significance. These relationships are summarized in Table 1, which outlines the relevant symbols and their corresponding meanings.

4. Model Construction and Solution

4.1. Carbon Tax Policy Model (Model A)

When the government only adopts a carbon tax policy, with the government setting the unit carbon tax as “r”, the profit functions for the manufacturer and retailer are as follows:

(3)${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}=\left[\mathrm{w}-\mathrm{c}-\left(\mathrm{e}-\mathrm{t}\right)\mathrm{r}\right]\mathrm{D}-{\displaystyle \frac{{\mathrm{mt}}^2}{2}}$

(4)${\mathrm{\pi }}_{\mathrm{r}}^{\mathrm{A}}=\left(\mathrm{p}-\mathrm{w}\right)\mathrm{D}$

assuming a Stackelberg game with the manufacturer as the leader and employing backward induction for the solution. Due to the manufacturer’s specified values for “w” and “t”, the derivative of the retailer’s profit function is calculated:

(5)${\displaystyle \frac{{\mathrm{\sigma }\mathrm{\pi }}_{\mathrm{r}}^{\mathrm{A}}}{\mathrm{\sigma }\mathrm{p}}}=\mathrm{Q}-\mathrm{\beta }\mathrm{p}-\left(\mathrm{p}-\mathrm{w}\right)\mathrm{\beta }+\mathrm{\gamma }\mathrm{t}$

(6)${\displaystyle \frac{{\mathrm{\sigma }}^2{\mathrm{\pi }}_{\mathrm{r}}^{\mathrm{A}}}{{\mathrm{\sigma }\mathrm{p}}^2}}=-2\mathrm{\beta }$

As evident, “${\mathrm{\pi }}_{\mathrm{r}}^{\mathrm{A}}$” is a concave function with respect to “p”. Setting its first derivative to zero, let us find the value of “${\mathrm{p}}_{\mathrm{A}}^{*}$” at this point:

(7)${\mathrm{p}}_{\mathrm{A}}^{*}={\displaystyle \frac{\mathrm{Q}+\mathrm{w}\mathrm{\beta }+\mathrm{\gamma }\mathrm{t}}{2\mathrm{\beta }}}$

Substituting Equation (7) into Equation (3) and differentiating with respect to “w” and “t”, respectively:

(8)${\displaystyle \frac{{\mathrm{\sigma }\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}}{\mathrm{\sigma }\mathrm{w}}}={\displaystyle \frac{\mathrm{Q}+\mathrm{c}\mathrm{\beta }+\mathrm{er}\mathrm{\beta }-\mathrm{rt}\mathrm{\beta }-2\mathrm{w}\mathrm{\beta }+\mathrm{t}\mathrm{\gamma }}{2}}$

(9)${\displaystyle \frac{{\mathrm{\sigma }\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}}{\mathrm{\sigma }\mathrm{t}}}={\displaystyle \frac{\mathrm{Qr}-2\mathrm{mt}-\mathrm{rw}\mathrm{\beta }-\mathrm{c}\mathrm{\gamma }-\mathrm{er}\mathrm{\gamma }+2\mathrm{rt}\mathrm{\gamma }+\mathrm{w}\mathrm{\gamma }}{2}}$

Also, the Hessian matrix “H” for “${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}$” is as follows:

(10)$\mathrm{H}=\left[\begin{array}{cc}-\mathrm{\beta }& {\displaystyle \frac{\mathrm{\gamma }-\mathrm{r}\mathrm{\beta }}{2}}\\ {\displaystyle \frac{\mathrm{\gamma }-\mathrm{r}\mathrm{\beta }}{2}}& \mathrm{r}\mathrm{\gamma }-\mathrm{m}\end{array}\right]$

It is evident that −β < 0. When the carbon emission reduction cost coefficient “m” satisfies $\mathrm{m}>{\displaystyle \frac{{\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)}^2}{4\mathrm{\beta }}}$, the Hessian matrix “H” is negative definite. This implies that the profit function “${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}$” for the supply chain is concave with respect to “w” and “t”. Setting “${\displaystyle \frac{{\mathrm{\sigma }\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}}{\mathrm{\sigma }\mathrm{w}}}$” and “${\displaystyle \frac{{\mathrm{\sigma }\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}}{\mathrm{\sigma }\mathrm{t}}}$” to 0, the solution yields “w^*_A” and “t^*_A”. Substituting “w^*_A” and “t^*_A” into Equations (1)–(3) results in “${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{A}}$”, “${\mathrm{p}}_{\mathrm{A}}^{*}$”, and “${\mathrm{\pi }}_{\mathrm{r}}^{\mathrm{A}}$”. Thus, the maximum profits for each party can be determined. The results are as follows:

(11)${\mathrm{w}}_{\mathrm{A}}^{*}={\displaystyle \frac{2\mathrm{m}\left[\mathrm{Q}+\left(\mathrm{c}+\mathrm{er}\right)\mathrm{\beta }\right]-\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)\left[\mathrm{Qr}+\left(\mathrm{c}+\mathrm{er}\right)\mathrm{\gamma }\right]}{4\mathrm{m}\mathrm{\beta }-{(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma })}^2}}$

(12)${\mathrm{t}}_{\mathrm{A}}^{*}={\displaystyle \frac{\left[\mathrm{Q}-\left(\mathrm{c}+\mathrm{er}\right)\mathrm{\beta }\right]\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)}{4\mathrm{m}\mathrm{\beta }-{\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)}^2}}$

(13)${\mathrm{p}}_{\mathrm{A}}^{*}={\displaystyle \frac{\mathrm{m}\left[3\mathrm{Q}+\left(\mathrm{c}+\mathrm{er}\right)\mathrm{\beta }\right]-\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)\left[\mathrm{Qr}+\left(\mathrm{c}+\mathrm{er}\right)\mathrm{\gamma }\right]}{4\mathrm{m}\mathrm{\beta }-{\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)}^2}}$

(14)${\mathrm{\pi }}_{\mathrm{mA}}^{*}={\displaystyle \frac{\mathrm{m}{\left[\mathrm{Q}-\left(\mathrm{c}+\mathrm{er}\right)\mathrm{\beta }\right]}^2}{8\mathrm{m}\mathrm{\beta }-2{\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)}^2}}$

(15)${\mathrm{\pi }}_{\mathrm{rA}}^{*}={\displaystyle \frac{{\mathrm{m}}^2\mathrm{\beta }{\left[\mathrm{Q}-\left(\mathrm{c}+\mathrm{er}\right)\right]}^2}{{\left[-4\mathrm{m}\mathrm{\beta }+{\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)}^2\right]}^2}}$

4.2. Carbon Emission Trading Scheme Model (Model B)

When the government only adopts a carbon emission trading scheme, the government determines the initial free carbon quota allocated to the manufacturing enterprise, denoted as “g” (assuming, in line with reality, that g < e). The unit carbon trading price “k” is treated as an exogenous variable. In this scenario, the profit functions for each party in the supply chain are as follows:

(16)${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{B}}=\left(\mathrm{w}-\mathrm{c}\right)\mathrm{D}-\left(\mathrm{e}-\mathrm{t}-\mathrm{g}\right)\mathrm{kD}-{\displaystyle \frac{{\mathrm{mt}}^2}{2}}$

(17)${\mathrm{\pi }}_{\mathrm{r}}^{\mathrm{B}}=\left(\mathrm{p}-\mathrm{w}\right)\mathrm{D}$

Assuming a Stackelberg game between the manufacturer and the retailer, with the manufacturer as the leader, the solution process using backward induction is similar to Model A. The results are as follows:

(18)$\mathrm{H}=\left[\begin{array}{cc}-\mathrm{\beta }& {\displaystyle \frac{\mathrm{\gamma }-\mathrm{k}\mathrm{\beta }}{2}}\\ {\displaystyle \frac{\mathrm{\gamma }-\mathrm{k}\mathrm{\beta }}{2}}& \mathrm{k}\mathrm{\gamma }-\mathrm{m}\end{array}\right]$

From the Hessian matrix of ${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{B}}$, it can be determined that when the emission reduction coefficient “m” satisfies m > ${\displaystyle \frac{{\left(\mathrm{\gamma }+\mathrm{k}\mathrm{\beta }\right)}^2}{4\mathrm{\beta }}}$, the optimal solution for the supply chain is as follows:

(19)${\mathrm{w}}_{\mathrm{B}}^{*}={\displaystyle \frac{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)\left[\mathrm{c}\mathrm{\gamma }+\mathrm{k}\left(\mathrm{Q}+\mathrm{e}\mathrm{\gamma }-\mathrm{g}\mathrm{\gamma }\right)\right]-2\mathrm{m}\left[\mathrm{Q}+\mathrm{\beta }\left(\mathrm{c}+\mathrm{ek}-\mathrm{gk}\right)\right]}{{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)}^2-4\mathrm{m}\mathrm{\beta }}}$

(20)${\mathrm{t}}_{\mathrm{B}}^{*}={\displaystyle \frac{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)\left[\mathrm{\beta }\mathrm{c}-\mathrm{Q}+\mathrm{\beta }\mathrm{k}\left(\mathrm{e}-\mathrm{g}\right)\right]}{{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)}^2-4\mathrm{m}\mathrm{\beta }}}$

(21)${\mathrm{p}}_{\mathrm{B}}^{*}={\displaystyle \frac{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)\left[\mathrm{c}\mathrm{\gamma }+\mathrm{k}\left(\mathrm{Q}+\mathrm{e}\mathrm{\gamma }-\mathrm{g}\mathrm{\gamma }\right)\right]-\mathrm{m}\left[3\mathrm{Q}+\mathrm{\beta }\left(\mathrm{c}+\mathrm{ek}-\mathrm{gk}\right)\right]}{{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)}^2-4\mathrm{m}\mathrm{\beta }}}$

(22)${\mathrm{\pi }}_{\mathrm{mB}}^{*}={\displaystyle \frac{\mathrm{m}{\left[\mathrm{Q}-\mathrm{c}\mathrm{\beta }+\mathrm{k}\mathrm{\beta }\left(\mathrm{e}-\mathrm{g}\right)\right]}^2}{8\mathrm{m}\mathrm{\beta }-2{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)}^2}}$

(23)${\mathrm{\pi }}_{\mathrm{rB}}^{*}={\displaystyle \frac{{\mathrm{m}}^2\mathrm{\beta }{\left[\mathrm{Q}-\mathrm{c}\mathrm{\beta }+\mathrm{k}\mathrm{\beta }\left(\mathrm{e}-\mathrm{g}\right)\right]}^2}{{\left[-4\mathrm{m}\mathrm{\beta }+{\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)}^2\right]}^2}}$

4.3. Hybrid Carbon Tax and Carbon Emission Trading Scheme (Model C)

In this scenario, the government simultaneously implements carbon tax and carbon trading policies, and the profits for each party are as follows:

(24)${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{C}}=\left[\mathrm{w}-\mathrm{c}-\left(\mathrm{e}-\mathrm{t}\right)\mathrm{r}\right]\mathrm{D}-\left(\mathrm{e}-\mathrm{t}-\mathrm{g}\right)\mathrm{kD}-{\displaystyle \frac{{\mathrm{mt}}^2}{2}}$

(25)${\mathrm{\pi }}_{\mathrm{r}}^{\mathrm{C}}=\left(\mathrm{p}-\mathrm{w}\right)\mathrm{D}$

Assuming a Stackelberg game between the manufacturer and the retailer, with the manufacturer as the leader, the solution process using backward induction is similar to Model A. The results are as follows:

(26)$\mathrm{H}=\left[\begin{array}{cc}-\mathrm{\beta }& {\displaystyle \frac{\mathrm{\gamma }-\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)}{2}}\\ {\displaystyle \frac{\mathrm{\gamma }-\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)}{2}}& \mathrm{\gamma }\left(\mathrm{k}+\mathrm{r}\right)-\mathrm{m}\end{array}\right]$

From the Hessian matrix of ${\mathrm{\pi }}_{\mathrm{m}}^{\mathrm{C}}$, it is evident that when the emission reduction coefficient “m” satisfies m > ${\displaystyle \frac{{\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]}^2}{4\mathrm{\beta }}}$. The supply chain has an optimal solution as follows:

(27)${\mathrm{w}}_{\mathrm{C}}^{*}={\displaystyle \frac{\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]\left\{\mathrm{Qr}+\mathrm{\gamma }\left(\mathrm{c}+\mathrm{er}\right)+\mathrm{k}\left[\mathrm{Q}+\left(\mathrm{e}-\mathrm{g}\right)\mathrm{\gamma }\right]\right\}-2\mathrm{m}\left\{\mathrm{Q}+\mathrm{\beta }\left[\mathrm{c}-\mathrm{gk}+\mathrm{e}\left(\mathrm{k}+\mathrm{r}\right)\right]\right\}}{{\left[\mathrm{\gamma }+\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)\right]}^2-4\mathrm{m}\mathrm{\beta }}}$

(28)${\mathrm{t}}_{\mathrm{C}}^{*}={\displaystyle \frac{\left\{\mathrm{\beta }\left[\mathrm{c}-\mathrm{gk}+\mathrm{e}\left(\mathrm{k}+\mathrm{r}\right)\right]-\mathrm{Q}\right\}\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]}{{\left[\mathrm{\gamma }+\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)\right]}^2-4\mathrm{m}\mathrm{\beta }}}$

(29)${\mathrm{p}}_{\mathrm{C}}^{*}={\displaystyle \frac{\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]\left\{\mathrm{Qr}+\left(\mathrm{c}+\mathrm{er}\right)\mathrm{\gamma }+\mathrm{k}\left[\mathrm{Q}+\left(\mathrm{e}-\mathrm{g}\right)\mathrm{\gamma }\right]\right\}-\mathrm{m}\left\{3\mathrm{Q}+\mathrm{\beta }\left[\mathrm{c}-\mathrm{gk}+\mathrm{e}\left(\mathrm{k}+\mathrm{r}\right)\right]\right\}}{{\left[\mathrm{\gamma }+\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)\right]}^2-4\mathrm{m}\mathrm{\beta }}}$

(30)${\mathrm{\pi }}_{\mathrm{mC}}^{*}={\displaystyle \frac{\mathrm{m}{\left\{\mathrm{Q}-\mathrm{\beta }\left[\mathrm{c}-\mathrm{gk}+\mathrm{e}\left(\mathrm{k}+\mathrm{r}\right)\right]\right\}}^2}{8\mathrm{m}\mathrm{\beta }-2{\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]}^2}}$

(31)${\mathrm{\pi }}_{\mathrm{rC}}^{*}={\displaystyle \frac{{\mathrm{m}}^2\mathrm{\beta }{\left\{\mathrm{Q}-\mathrm{\beta }\left[\mathrm{c}-\mathrm{gk}+\mathrm{e}\left(\mathrm{k}+\mathrm{r}\right)\right]\right\}}^2}{{\left\{{\left[\mathrm{\gamma }+\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)\right]}^2-4\mathrm{m}\mathrm{\beta }\right\}}^2}}$

Accordingly, this paper proposes the following theorem and corollary:

Theorem 1.

Assuming the default carbon emission reduction coefficient “m” satisfies the requirements for each model (m > ${\displaystyle \frac{{\left[\beta \left(k+r\right)+\gamma \right]}^2}{4\beta }}$), the condition $t_C^{*}$ > $t_A^{*}$ holds if and only if the initial unit carbon emissions of the manufacturing enterprise “e” satisfy g < e < A.

Proof. 

Proving the inequality ${\mathrm{t}}_{\mathrm{C}}^{*}-{\mathrm{t}}_{\mathrm{A}}^{*}$ > 0 is sufficient, where

(32)$\mathrm{A}={\displaystyle \frac{4\mathrm{m}\mathrm{\beta }\left\{\mathrm{Q}-\mathrm{c}\mathrm{\beta }+\mathrm{g}\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]\right\}-\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]\left[\mathrm{g}\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)-\mathrm{Q}+\mathrm{c}\mathrm{\beta }\right]}{4\mathrm{m}\mathrm{\beta }\left(2\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)-\mathrm{\gamma }{\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)}^2+\mathrm{k}\mathrm{\beta }\left[4\mathrm{m}\mathrm{\beta }-\mathrm{\gamma }\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)\right]}}$

Theorem 2.

The condition $t_C^{*}$ > $t_B^{*}$ holds if, and only if, the initial unit carbon emissions of the manufacturing enterprise “e” satisfy g < e < B, and it is independent of the carbon tax rate “r”.

The proof is omitted, where

(33)$\mathrm{B}={\displaystyle \frac{-\left(\mathrm{Q}-\mathrm{c}\mathrm{\beta }+\mathrm{gk}\mathrm{\beta }\right)\left\{4\mathrm{m}\mathrm{\beta }+\left(\mathrm{k}\mathrm{\beta }+\mathrm{\gamma }\right)\left[\mathrm{\beta }\left(\mathrm{k}+\mathrm{r}\right)+\mathrm{\gamma }\right]\right\}}{{\mathrm{k}}^2{\mathrm{\beta }}^2\mathrm{\gamma }-\left(\mathrm{r}\mathrm{\beta }+\mathrm{\gamma }\right)\left(4\mathrm{m}\mathrm{\beta }-{\mathrm{\gamma }}^2\right)+\mathrm{k}\mathrm{\beta }\left[\mathrm{\gamma }\left(\mathrm{r}\mathrm{\beta }+2\mathrm{\gamma }\right)-8\mathrm{m}\mathrm{\beta }\right]}}$

By comparison, A > B.

Corollary 1.

Solely considering the government’s perspective and aiming to maximize emission reduction, with a fixed carbon tax rate “r”, when the initial carbon emissions of the enterprise are below a certain threshold (B), the government can achieve a greater emission reduction by implementing a hybrid policy of carbon tax and carbon quotas than with any single policy.

Theorem 3.

Comparing the profits of the manufacturer and the retailer under two policies for low-emission enterprises—adopting a single carbon quota policy (Model B) and adopting a hybrid policy (Model C):

${\mathrm{\pi }}_{\mathrm{m}\mathrm{C}}^{*}-{\mathrm{\pi }}_{\mathrm{m}\mathrm{B}}^{*}>0$

Solving the inequality reveals that when satisfying:

(34) $\mathrm{m}<{\displaystyle \frac{\left(\mathrm{Q}-\mathrm{c}\mathrm{\beta }+\mathrm{g}\mathrm{k}\mathrm{\beta }+\mathrm{e}\gamma \right)\left[2\left(\mathrm{e}-\mathrm{g}\right){\mathrm{k}}^2{\mathrm{\beta }}^2-\mathrm{Q}\left(\mathrm{r}\mathrm{\beta }+2\mathrm{\gamma }\right)+\mathrm{k}\mathrm{\beta }\left(-2\mathrm{Q}+2\mathrm{c}\mathrm{\beta }+2\mathrm{e}\mathrm{r}\mathrm{\beta }-\mathrm{g}\mathrm{r}\mathrm{\beta }+2\mathrm{e}\mathrm{\gamma }-2\mathrm{g}\mathrm{\gamma }\right)+\mathrm{\beta }\left(\mathrm{c}\mathrm{r}\mathrm{\beta }+2\mathrm{c}\mathrm{\gamma }+\mathrm{e}\mathrm{r}\mathrm{\gamma }\right)\right]}{4\mathrm{e}\mathrm{\beta }\left[-2\mathrm{Q}+\mathrm{\beta }\left(2\mathrm{c}+2\mathrm{e}\mathrm{k}-2\mathrm{g}\mathrm{k}+\mathrm{e}\mathrm{r}\right)\right]}}$

the inequality holds true.

${\mathrm{\pi }}_{\mathrm{r}\mathrm{C}}^{*}-{\mathrm{\pi }}_{\mathrm{r}\mathrm{B}}^{*}>0$

Solving the inequality reveals that when satisfying:

(35)$\mathrm{Q}+\mathrm{g}\mathrm{k}\mathrm{\beta }\le {\displaystyle \frac{\mathrm{e}\mathrm{\beta }\left\{-4\mathrm{m}\mathrm{\beta }\left(1+2\mathrm{k}+\mathrm{r}\right)+2{\mathrm{k}}^3{\mathrm{\beta }}^2+\left(1+\mathrm{r}\right){\mathrm{\gamma }}^2+{\mathrm{k}}^2\mathrm{\beta }\left[3\left(1+\mathrm{r}\right)\mathrm{\beta }+4\mathrm{\gamma }\right]+\mathrm{k}\left[{\left(1+\mathrm{r}\right)}^2{\mathrm{\beta }}^2+4\left(1+\mathrm{r}\right)\mathrm{\beta }\mathrm{\gamma }+2{\mathrm{\gamma }}^2\right]\right\}}{\left[2{\mathrm{k}}^2+2\mathrm{k}\left(1+\mathrm{r}\right)+{\left(1+\mathrm{r}\right)}^2\right]{\mathrm{\beta }}^2-8\mathrm{m}\mathrm{\beta }+2\left(1+2\mathrm{k}+\mathrm{r}\right)\mathrm{\beta }\mathrm{\gamma }+2{\mathrm{\gamma }}^2}}$

the inequality holds true and Corollary 2 is derived.

Corollary 2.

For low-emission enterprises, when the government adopts a hybrid policy, the manufacturer on the supply chain can achieve greater profits than under a single carbon emission trading scheme, provided the manufacturer satisfies certain conditions. To maximize profits, the manufacturer has a reason to take measures to reduce the emission reduction cost coefficient. For the retailer, under certain conditions, the retailer’s profit is greater than that under a single policy. Due to the complexity of these conditions, illustration through numerical analysis is warranted.

In the in-depth analysis of the model solutions, we have unveiled the behaviors and decisions within the supply chain under carbon tax policy, carbon emission trading scheme, and the combined policy of carbon tax and carbon trading. These findings offer profound insights into understanding the optimal strategies of businesses under different policy frameworks. However, for a more comprehensive assessment of the practical effects of these policies, we will conduct a case study in the next chapter. Through specific numerical experiments, we aim to validate the effectiveness of the models and delve into the challenges faced in policy formulation and implementation within real-world scenarios. This endeavor will contribute to bridging theoretical research with practical applications, providing substantive guidance and recommendations for constructing a more viable and sustainable green supply chain.

5. Case Study Analysis

This paper employs Mathematica 12 for the case study analysis, aiming to visually illustrate the changes in emission reduction under three policies with the increase of the initial unit carbon emissions of enterprises. Additionally, the impact of the emission reduction cost coefficient m on the optimal decisions of both parties is examined, and sensitivity analysis is conducted on the parameters. The objective is to provide insights for government and enterprise decision-making at supply chain nodes. For the case study analysis, to simplify the cases and conform to the feasible region, fixed parameter values are set as follows: Q = 500, c = 25, $\mathrm{\beta }$ = 1, and $\mathrm{\gamma }$ = 0.5. The carbon trading price refers to historical data of international carbon emission trading prices, set as k = 15. Since the emission reduction investment coefficient is generally a large value, m is set as 1000 in this paper. For calculating optimal decision values, g = 5, r = 5 are set. Additionally, to ensure that the retail price p in all three models is greater than the wholesale price w, it is calculated that $0<\mathrm{e}<{\displaystyle \frac{\mathrm{Q}-\mathrm{c}\mathrm{\beta }+\mathrm{gk}\mathrm{\beta }}{\mathrm{k}\mathrm{\beta }}}={\displaystyle \frac{110}{3}}$, $\mathrm{m}>{\displaystyle \frac{{\mathrm{k}}^2{\mathrm{\beta }}^2+2{\mathrm{kr}\mathrm{\beta }}^2+{\mathrm{r}}^2{\mathrm{\beta }}^2+2\mathrm{k}\mathrm{\beta }\mathrm{\gamma }+2\mathrm{r}\mathrm{\beta }\mathrm{\gamma }+{\mathrm{\gamma }}^2}{4\mathrm{\beta }}}=$ 105.063.

5.1. Impact of Initial Unit Carbon Emissions on Government Policy Selection

From Figure 1, it can be observed that as the unit initial carbon emissions (e) increase, the unit optimal emission reductions under the three policies all decrease, when e < 16.74, ${\mathrm{t}}_{\mathrm{C}}^{*}$ > ${\mathrm{t}}_{\mathrm{B}}^{*}$, and when e < 23.15, ${\mathrm{t}}_{\mathrm{C}}^{*}$ > ${\mathrm{t}}_{\mathrm{A}}^{*}$. By observing the slopes, it is evident that the sensitivity of the three policies to changes in e follows the order: hybrid policy > carbon trading > carbon tax.

In a more in-depth analysis, we observe that the initial unit carbon emissions have a profound impact on the effectiveness of different policies in reducing emissions along the supply chain. Under the carbon tax policy, since the additional tax imposed by the government on businesses is relatively low, manufacturers are less stimulated, making it challenging to achieve significant emission reductions when the initial unit carbon emissions are high. Conversely, under the carbon emission trading scheme, manufacturers show a relatively higher enthusiasm for emission reductions as they can adjust their emission reduction costs by buying and selling carbon emission rights. However, with the increase in initial unit carbon emissions, it becomes progressively difficult for manufacturers to achieve substantial economic benefits through emission reductions, resulting in a gradual reduction in the effectiveness of emission reductions.

Remarkably, the hybrid policy demonstrates significant advantages when the initial unit carbon emissions are relatively small. In the hybrid policy, manufacturers not only gain profits from emission reductions but also alleviate the burden of carbon taxes, making manufacturers with lower initial unit carbon emissions more inclined to take proactive emission reduction measures. However, as the initial unit carbon emissions increase, the emission reduction effectiveness of the hybrid policy also experiences a diminishing trend. This phenomenon arises from the fact that the hybrid policy comprehensively considers the pros and cons of both approaches, achieving optimal emission reduction effects in specific operational contexts.

Overall, when formulating emission reduction policies, the government needs to consider the early emission reduction potential of businesses and the difficulty of implementing subsequent emission reduction measures. Flexibly choosing between carbon taxes, carbon trading, or hybrid policies at different stages will help maximize emission reduction benefits. This analysis not only provides crucial insights for policymakers in developing sound environmental policies but also serves as a valuable reference for businesses to choose the most suitable strategies when facing environmental pressures. In real-world business environments, policymakers and business decision-makers can better plan sustainable development strategies by understanding the impact of different policies on initial carbon emissions.

5.2. Comparative Analysis of Supply Chain Policies for Low-Pollution Enterprises

For ease of discussion, enterprises with initial carbon emissions greater than B are referred to as high-pollution enterprises, while those with e < B are considered low-pollution enterprises. Considering the international predominance of using ETS as the primary choice for carbon reduction policies, this study contrasts ETS with hybrid policies. We specify the initial carbon emissions for low-emission enterprises as ${\mathrm{e}}_1$ (${\mathrm{e}}_1$ < B) and analyze the supply chain nodes under both single-carbon emission trading scheme and hybrid policy. In both scenarios, the free allocation of carbon quotas (g) and carbon trading price (k) remain unchanged despite the policy differences.

We select a low-pollution manufacturer with ${\mathrm{e}}_1$ = 10 (meeting the requirements for adopting a hybrid approach in Figure 1) for a comparative analysis under the carbon emission trading scheme and hybrid policy.

From Figure 2, it can be observed that for low-pollution manufacturers, as the emission reduction cost coefficient (m) increases, the profits of manufacturers under both policies decrease, with the rate of decline gradually slowing down; when m < 251.15, ${\mathrm{\pi }}_{\mathrm{mC}}^{*}>{\mathrm{\pi }}_{\mathrm{mB}}^{*}$.

In the realm of hybrid policies, the escalating cost coefficient of emission reduction (denoted as m) introduces heightened decision complexity for manufacturers operating within the dual-policy framework of carbon tax and carbon quota trading. Examining Figure 2 reveals a discernible trend: manufacturers exhibit a proactive stance toward emission reduction activities when the cost coefficient is relatively low, striving for elevated emission reduction levels. However, as the emission reduction cost mounts, economic incentives for manufacturers gradually diminish, as the additional profit derived from emission reduction proves inadequate to offset the escalating cost.

Transitioning into the context of hybrid policies, a pivotal threshold emerges. When the emission reduction cost coefficient (m) is below a certain inflection point, low-pollution manufacturers manifest a heightened commitment to emission reduction within hybrid policies in contrast to scenarios governed solely by carbon quota trading. The additional carbon tax expenditure serves as a catalyst, propelling manufacturers toward more assertive emission reduction measures and, consequently, higher profits than those achieved under the carbon quota trading policy. In response, manufacturers strategically lower wholesale prices under hybrid policies, positioning them below the wholesale prices observed under carbon quota trading policies. This reduction in wholesale prices, intricately depicted in Figure 3, serves a dual purpose: augmenting manufacturers’ profitability through heightened market demand and fostering a more competitive market environment.

The nuanced dynamics highlighted by the reduction in wholesale prices under hybrid policies, as illustrated in Figure 3, reveal a two-fold impact. On the one hand, enhanced profitability for manufacturers results from increased market demand. On the other hand, the reduced wholesale prices contribute to a heightened competitive landscape. Therefore, the conclusion derived from the analysis of Figure 3 reinforces the premise that, under specific conditions, hybrid policies yield superior profits for manufacturers compared to carbon quota trading policies. This comprehensive understanding underscores the intricate interplay between emission reduction efforts, pricing strategies, and market dynamics within the hybrid policy framework.

Simultaneously, the overarching narrative emphasizes the intricate balancing act required of manufacturers within the mixed policy framework. As the cost coefficient of emission reduction (m) fluctuates, manufacturers must judiciously weigh the economic gains from emission reduction against the associated carbon tax expenditure. The observation that low-pollution manufacturers sustain their commitment to emission reduction within the mixed policy underscores the motivation driven by the additional profit gained through the carbon tax policy. This proactive behavior reflects not only economic interests but also a sense of responsibility toward environmental sustainability.

In summary, manufacturers under the mixed policy need to comprehensively consider the impact of emission reduction costs, carbon tax, and carbon quota trading when formulating emission reduction strategies to achieve a balance between economic efficiency and environmental sustainability. This also provides some reference for the government in policy formulation, emphasizing the need to refine incentive mechanisms for enterprises in different cost scenarios to promote more targeted emission reduction behavior.

From Figure 4, it is evident that as the emission reduction cost coefficient increases, the change in retailer profit follows a pattern similar to that of manufacturer profit; specifically, when the emission reduction cost coefficient is less than 405.96, ${\mathrm{\pi }}_{\mathrm{rC}}^{*}>{\mathrm{\pi }}_{\mathrm{rB}}^{*}$.

As the parameter (m) gradually increases, manufacturers observe an upward trend in wholesale prices, accompanied by a corresponding continuous decline in emission reduction levels. Throughout this process, retailers, aiming to ensure continuous profit growth, strategically raise retail prices. This dual effect of increasing retail prices and decreasing emission reduction levels adversely impacts market demand, ultimately leading to a diminishing profit margin for retailers.

When (m) is below a certain threshold, Figure 5 illustrates that retail prices under hybrid policies are comparatively lower than those under carbon quota trading policies. This phenomenon stems from the fact that wholesale prices set by manufacturers under hybrid policies are lower than those under carbon quota trading policies. The combination of lower retail prices and higher emission reduction levels collectively stimulates market demand, resulting in higher profits for retailers under hybrid policies compared to those under carbon quota trading policies.

The ability of retailers to achieve higher profits under hybrid policies is contingent upon the emission reduction cost coefficient of manufacturers. Importantly, the level of emission reduction cost coefficient is independent of retailers. Manufacturers, in pursuit of enhanced profits, actively engage in emission reduction technology development to lower the emission reduction cost coefficient. As a consequence of this proactive stance, retailers can also benefit from higher profits, highlighting the phenomenon of retailers “free riding” under hybrid policies.

Through a comprehensive observation of Figure 1, Figure 2, Figure 4 and Figure 5, when the emission reduction cost coefficient (m) is relatively low, the unit carbon reduction amount (t), manufacturer profit (${\mathrm{\pi }}_{\mathrm{m}}$), retailer profit (${\mathrm{\pi }}_{\mathrm{r}}$), and retail price (p) under the mixed policy are significantly superior to those under the carbon quota policy. Additionally, the retail price under the mixed policy is relatively lower. In this situation, implementing the mixed policy for a low-pollution supply chain not only achieves a Pareto improvement for the government, manufacturers, retailers, and consumers but also demonstrates the synergistic effects of policies, providing a viable path for the sustainable development of the entire industry.

6. Conclusions and Discussion

Through an in-depth investigation into the emission reduction strategies of the second-tier supply chain under carbon quota trading and carbon tax policies, we compared the optimal decisions under three modes: the government implementing a carbon tax policy, a carbon quota trading policy, and a hybrid policy. We analyzed the impacts of various variables on decisions related to emission reduction, pricing, and profits for the government and supply chain node enterprises in different scenarios. The results suggest that when the initial unit carbon emissions of the manufacturer are below a critical threshold, the government’s adoption of a hybrid policy involving both carbon tax and carbon trading can induce manufacturers to achieve higher levels of emission reduction, thus enhancing the overall effectiveness of the emission reduction strategies. For low-pollution manufacturers already implementing the hybrid policy, their profits exceed those under a single carbon quota trading policy when their emission reduction cost coefficient falls below a certain threshold. This incentivizes manufacturers to actively cooperate with the government, ensuring the smooth implementation of the policies.

In the case of retailers under the hybrid policy, their profits also exceed those under a single carbon quota trading policy when the emission reduction cost coefficient of their upstream manufacturers falls below a specific threshold, suggesting the presence of “free riding” behavior by retailers. However, while the hybrid policy is particularly advantageous for low-pollution manufacturers, high-pollution industries may face higher initial emission reduction costs due to their higher emissions. Despite this, the flexibility provided by carbon trading, along with the incentives from the carbon tax, can help mitigate these costs over time. High-pollution industries can take advantage of trading allowances or adopt cleaner technologies as part of a longer-term strategy, potentially lowering their overall reduction costs in the future.

The hybrid policy results in a Pareto improvement when the emission reduction cost coefficient is below a certain threshold, leading to higher unit carbon reduction, manufacturer profits, and retailer profits compared to the carbon quota policy. Additionally, the retail price under the hybrid policy is lower than under the carbon quota policy. This suggests that implementing a hybrid policy in a low-pollution supply chain can achieve a Pareto improvement for the government, manufacturers, retailers, and consumers. These findings provide valuable insights into optimal emission reduction strategies and policy implications for the government and supply chain entities, highlighting the importance of considering manufacturer profit incentives, evaluating retailer behavior, and realizing Pareto improvements in promoting sustainable development.

6.1. Theoretical Contributions

This research holds theoretical significance in several aspects:

Firstly, the study delves deeply into the carbon emission reduction strategies of the second-tier supply chain under carbon quota trading and carbon tax policies, addressing a gap in related research areas. Through the comparative analysis of three modes—carbon tax policy, carbon quota trading policy, and hybrid policy—our research provides a more comprehensive theoretical framework, offering scholars a new perspective for further exploration in the field of carbon emission reduction.

Secondly, this research, from the perspectives of the government, manufacturers, and retailers, thoroughly analyzes the interrelationships between emission reduction, pricing, and profit decision factors. It provides important insights into the decision-making behaviors of various nodes in the supply chain when dealing with carbon emission regulations. This is crucial for understanding the decision-making behaviors within the supply chain in response to carbon emission control policies, offering a reference basis for the formulation of more scientific and precise policies in the future.

Furthermore, the study emphasizes the optimization of manufacturers’ emission reduction levels and profits and extensively explores the profit advantages of low-pollution manufacturers under hybrid policies. This substantive contribution provides practical guidance for enterprises to better coordinate economic and environmental benefits in their actual operations. This theoretical contribution offers a clearer path for enterprises to choose emission reduction strategies, aiding in achieving sustainable economic and environmental development.

6.2. Managerial Implications

Governments should design personalized emission policies based on the specific pollution levels of each enterprise, avoiding a one-size-fits-all approach. Businesses vary significantly in size, sector, existing technology, and financial capacity. A uniform policy could impose unequal burdens, particularly on small- and medium-sized enterprises (SMEs), which may struggle with high compliance costs. Larger enterprises with more resources may have a comparative advantage in meeting stringent emissions targets, potentially widening the gap between different-sized firms. Moreover, businesses in energy-intensive sectors or those with limited green alternatives may find it more difficult to transition quickly. This emphasizes the need for policies that account for the sectoral characteristics of each industry. Tailored policies can thus create a more equitable distribution of responsibility, ensuring that each enterprise has the opportunity to meet emission reduction targets in a cost-effective manner.

For manufacturers already implementing a mixed policy, investing in research and development (R&D) to enhance emission reduction technologies is advisable. Such investments can reduce associated costs and improve the economic benefits of emission reductions. Technological readiness and innovation potential should be key factors in determining which businesses are best suited for the early adoption of stringent emission reduction policies. Manufacturers that invest in green technologies may gain long-term economic advantages, including lower operating costs and enhanced market competitiveness.

Additionally, manufacturers and retailers can establish cost-sharing agreements, particularly under mixed policies, to prevent “free-riding” behavior by retailers and promote joint efforts in achieving emission reduction goals. The success of these agreements depends on the bargaining power of each party, the nature of their supply chain relationships, and the trust between manufacturers and retailers. Ensuring an equitable sharing of both costs and benefits is essential for sustainable collaboration.

Lastly, governments should consider not only the initial pollution levels but also the overall profitability of businesses in the supply chain when selecting enterprises for the implementation of mixed policies. Choosing manufacturers with lower emission reduction costs ensures the simultaneous achievement of both economic and environmental benefits. Strategic alignment among supply chain actors, including their willingness to collaborate on environmental goals, is also crucial. Governments must account for the interdependencies within the supply chain to avoid merely shifting emissions between companies instead of reducing them.

These recommendations aim to guide governments and businesses in making informed decisions to more effectively pursue emission reduction goals while maximizing economic benefits throughout the environmental conservation process.

7. Limitations and Future Research

In undertaking this study, it is essential to acknowledge certain limitations inherent in our research methodology. These constraints, while not diminishing the significance of our findings, merit careful consideration for a nuanced interpretation of the results. Our research relies on specific assumptions to model the complex dynamics of carbon emission policies and their impact on supply chain decisions. While these assumptions simplify the modeling process, they may not fully capture the complexity of real-world scenarios, which could limit the generalizability of our findings. Additionally, the outcomes of our study are contingent on the values assigned to various parameters. Small changes in these values might lead to different results, highlighting the need for caution when applying our findings universally. The business landscape is also dynamic, subject to changes in regulations, market conditions, and technological advancements. As such, while our study captures a snapshot of these dynamics, the long-term effectiveness of the proposed policies may be influenced by unforeseen changes in the future business environment.

Looking ahead, future research should focus on how emission reduction strategies can be adapted and optimized for practical application in business management and on-the-ground practices. Specifically, future studies can incorporate a broader range of external factors, such as market competition and fluctuations in the international carbon market, to provide a more comprehensive assessment of the impact of these policies. Additionally, while our study primarily focused on a second-tier supply chain, further research could explore multilevel supply chain structures, considering the interactive relationships among more nodes to offer more detailed strategic recommendations. Finally, the development of dynamic models that better align with real-world situations is essential, as these models would allow for a more effective response to the uncertainties surrounding adjustments in carbon tax rates and emission trading changes. By addressing these areas, future research can provide valuable insights into how emission reduction strategies can be more effectively applied in both managerial contexts and practical implementations, thereby offering more effective decision support for achieving sustainable development goals.

Author Contributions

Conceptualization, R.T., D.Y. and Y.T.; Software, R.T., D.Y. and Y.T.; Formal analysis, R.T.; Writing—original draft, R.T. and Y.T.; Visualization, D.Y. and Y.T.; Writing—review & editing, R.T. and Y.T. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. Influence of unit initial carbon emission on unit optimal carbon reduction under three models.

Figure 2. Impact of emission reduction cost coefficient on profits of low-pollution manufacturers.

Figure 3. Impact of emission reduction cost coefficient on wholesale price of low-pollution manufacturers.

Figure 4. Impact of emission reduction cost coefficient on retailer profit.

Figure 5. Impact of emission reduction cost coefficient on retailer retail price.

Table 1

Relevant symbols and their meanings.

Non-Decision Variables	Meanings
D	Market demand
Q	Potential market demand for green products
β	Consumer price sensitivity coefficient
$\mathrm{\gamma }$	Consumer sensitivity coefficient to the carbon emission reduction rate
r	Tax on unit carbon emissions
k	Unit carbon trading price
c	Unit production cost of a green product
m	Emission reduction cost coefficient
g	Initial free carbon quota for the green manufacturer
e	Unit carbon emissions when the manufacturer does not take emission reduction measures
Decision Variables	Meanings
P	Retailer’s selling price, as determined by the retailer
w	Manufacturer’s wholesale price, as determined by the manufacturer
t	Manufacturer’s carbon emission reduction rate, as determined by the manufacturer

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