The Impact of Government Subsidies and Carbon Taxes on Emission Reductions for Intermodal Transport Operator and Carrier

Abstract

To address carbon emission challenges in the transportation sector, intermodal transport—which enhances both economic and environmental benefits—is becoming ever more crucial. Governments often implement policies like subsidies or carbon taxes to steer intermodal transport towards sustainable development. This paper constructs a Stackelberg game model involving an eco-conscious shipper, an intermodal transport operator, and a carrier to analyze the combined economic and environmental impacts of carbon taxes, subsidies, and their dual-policy implementation on the intermodal transport system. The results of the study were as follows: (1) While either carbon taxes or subsidies alone enhance emission reduction and freight volume, their dual implementation generates synergistic effects, achieving superior emission reduction and freight growth; the study also challenges conventional wisdom by demonstrating that “reducing subsidies for intermodal transport may promote carbon reduction in transportation, while increasing taxes does not necessarily disadvantage logistics companies.” (2) Governments can achieve a win–win outcome for the economy and the environment by first prioritizing the increase of carbon taxes to effective levels, and guiding carriers to bear higher emissions reduction costs, before increasing subsidies. (3) Continuously enhancing shippers’ environmental awareness can effectively reduce total emissions. However, its impact on profits depends on the decision-making mode (decentralized vs. centralized) and the cost sharing among logistics companies. (4) There exists an optimal value for the intermodal operator’s share of emission reduction costs. Values that are too low can weaken the incentives for emission reduction, whereas values that are too high may harm profits. This research quantifies the complex interactions among policy combinations, consumer preferences, and enterprise cooperation modes. It offers valuable guidance for governments to design precise emission-reduction policies and helps upstream–downstream enterprises in intermodal transport systems optimize their operational strategies.

1. Introduction

As the third largest carbon-emitting sector in the world, transport has experienced the most pronounced growth in emissions, surging by nearly 240 Mt globally in 2023 [1] (According to global real-time carbon data, transportation accounts for about 20% of global carbon emissions. It is the third largest carbon-emitting sector in the world. For more details, please refer to https://carbonmonitor.org/ (accessed on 26 June 2025)). In China, over 85% of the total carbon emissions from national transportation come from road transport (Please refer to “China Zero Emission Freight Status Report 2024”, https://www.zefi2050.com/news/publication.jsp (accessed on 26 June 2025).). Excessive carbon emissions intensify the greenhouse effect, causing environmental pollution, climate change, and adverse effects on human life and the economy. Consequently, reducing carbon emissions in the transportation sector has attracted significant attention. Effective reduction in carbon emissions can be achieved through increasing the use and investment in clean energy and emission reduction technologies [2], as well as by adopting environmentally friendly transportation methods like intermodal transport, which combines freight, trains, and ships [3,4] (The two terms of “multimodal” and “intermodal” are well established in the context of freight transportation. Multimodal freight transportation uses at least two transportation modes (e.g., road and rail), while intermodal transportation is regarded as a special form of multimodality whereby the goods do not change the unit of transportation (e.g., a container). SteadieSeifi et al. (2014) [5] showed that the terms “multimodal” and “intermodal” are used interchangeably in the literature. In this study, we use the term “intermodal” for consistency [6].). Governments have introduced policies like carbon taxes and subsidies to promote investment in low-carbon technologies and improve transportation methods for logistics companies. Since 1990, countries such as Finland, Sweden, the United Kingdom, Canada, and the United States have imposed carbon taxes on various industries, including transportation (For more details, please refer to https://www.rff.org/publications/explainers/carbon-pricing-202-pricing-carbon-transportation-sector/ (accessed on 26 June 2025).). These taxes can raise production costs and consumer prices, leading to resistance from both businesses and the public (For more details, please refer to https://thehill.com/policy/energy-environment/415418-washington-state-voters-reject-carbon-tax/ and https://hir.harvard.edu/frances-yellow-vest-movement-and-the-global-debate-on-climate-change/ (accessed on 24 August 2025).). For instance, Washington State’s proposed USD 15 per ton carbon tax was rejected in 2018, and the “Yellow Vest Movement” in France emerged in 2019 due to increased fuel prices from the government’s carbon tax. Governments frequently offer subsidies to promote intermodal transportation. For instance, from 2006 to 2007, the Belgian government provided an annual EUR 30 million subsidy for intermodal transport [7], while in 2023, the Dalian municipal government in China offered CNY 200 per TEU to intermodal companies (For more details, please refer to https://www.dl.gov.cn/art/2023/9/5/art_5476_2297313.html (accessed on 26 June 2025).). However, such policies may be unsustainable in the long term and could foster excessive business dependence on subsidies (To stimulate demand, the Chinese government typically provides large subsidies to encourage the use of rail links. But a high level of subsidy is not sustainable over the long term. For more details, please refer to https://cbk.bschool.cuhk.edu.hk/the-rise-of-rail-along-chinas-belt-and-road/, https://goodhopefreight.com/china-railway-express.html (accessed on 26 June 2025).). Evaluating whether carbon taxes or intermodal subsidies are more effective in reducing emissions and boosting economic benefits within intermodal networks poses a practical challenge due to their differing impacts on market transactions and environmental outcomes.

From a regulatory standpoint, recent studies have separately examined two distinct policies: government subsidies and carbon taxes in intermodal transport networks [8,9] (In intermodal transport, the main participants are intermodal transport operators, carriers, and shippers (or cargo owners). The intermodal transport operator is the entity that organizes and coordinates the entire multimodal transport process and provide one-stop transportation services for shippers; the carrier is the entity that actually undertakes the task of transporting goods; the shipper is the person or entity who has goods that need to be transported from one location to another (in many cases, the cargo owner and the shipper are the same entity).). This paper further examines the differences in economic and environmental benefits between implementing a single policy and a dual policy. From a market perspective, increasing environmental awareness is prompting consumers to pay more attention to the environmental aspects of products and services when making purchases. For example, in 2023, Maersk announced the purchase of six medium-sized container ships that can operate on green methanol fuel. Meanwhile, Cosco Shipping is progressing with its ‘oil-to-electric’ initiative, which involves replacing diesel generators with electric power to lower carbon emissions. Previous studies have identified such consumers as eco-conscious groups [10,11], which are often overlooked in current research on intermodal transport carbon emissions. This study further explores how shippers’ environmental awareness affects the profits of intermodal transport operators and carriers, as well as their emission reduction behaviors. Furthermore, recent research on green supply chains examines how upstream and downstream companies share the costs of environmentally friendly initiatives [12,13]. However, studies on intermodal carbon emissions rarely consider co-opetition and cost-sharing among the involved parties [14]. This paper aims to fill this gap by investigating how the cost-sharing (multiple entities allocate the costs of emissions reduction investments proportionally) ratio between carriers and intermodal operators affects corporate profits and emissions reductions.

Given the practical and theoretical challenges mentioned, we aim to address the following research questions:

(i) How do intermodal subsidies and carbon taxes influence emission reductions and transportation costs for logistics companies?

(ii) Which government policies and decision-making models are more effective in enhancing both environmental and economic benefits?

(iii) How should governments regulate the environmental responsibility of shippers and the cost-sharing ratio for emissions reduction between intermodal operators and carriers to improve environmental and economic benefits?

To address these issues, we developed a game model featuring an intermodal transport operator and a carrier in a market with an eco-conscious shipper. This framework examines the economic and environmental performance of the intermodal transport system across four policy scenarios: (1) no government intervention, (2) subsidy-only, (3) carbon tax-only, and (4) dual subsidy-carbon tax policy. The analysis further investigates outcomes under two distinct decision-making modes: decentralized decision-making—characterized by a non-cooperative Stackelberg hierarchy where the intermodal operator (leader) and carrier (follower) sequentially optimize individual profits, leading to information asymmetry and green double marginalization; and centralized decision-making—a cooperative governance mode where both entities function as a unified entity, jointly optimizing system-wide objectives through complete information sharing. Subsequently, we take Ji’an City in Jiangxi Province, China, as a case study to analyze how different parameters affect equilibrium, and thus put forward policy recommendations. The reasons for choosing Ji’an are as follows: (1) Policy feasibility: Ji’an has implemented an intermodal subsidy scheme since 2023, whose declining subsidy schedule (100%, 90%, 70%) provides real-world data for calibrating the policy parameters. (2) Data availability: Accessible freight-flow statistics and interviews with local operators allow for reliable parameter estimation, ensuring the empirical robustness of the simulation. (3) As a medium-sized inland city where road transport dominates (>85%) the freight structure, Ji’an reflects the economic characteristics and fiscal capacity of many cities in the middle Yangtze River region, enabling cautious extrapolation of the results. Conclusively, actionable pathways for sustainable development are proposed based on systematic findings.

The paper is structured as follows: Section 2 provides a literature review. Section 3 introduces the main model. Section 4 examines the equilibrium under intermodal subsidy, carbon tax, and dual policies. Section 5 discusses the impacts of intermodal subsidy, carbon tax, the carrier’s share of emissions reduction costs, and the shipper’s eco-conscious level on the decisions and profits of intermodal operator and carrier through numerical analysis. Section 6 presents our concluding remarks. Proofs of propositions are provided in Supplementary Materials.

2. Literature Review

Our paper contributes to two streams of literature: (i) carbon emissions abatement and (ii) low-carbon transport.

2.1. Carbon Emissions Abatement

From a regulatory standpoint, the government has implemented low-carbon policies to incentivize enterprises to invest more in emissions reduction and decrease carbon output. Numerous studies have explored corporate decision-making under carbon tax and carbon subsidy, respectively [15,16]. Some scholars argue that carbon taxes can encourage enterprises to invest in emission-reducing technologies, thereby enhancing both economic and environmental benefits [17]. Kök et al. (2020) [18] found that subsidizing inflexible energy sources results in lower investment in renewables, whereas subsidizing flexible sources increases investment in renewable energy. Further studies compared the effects of various low-carbon policies and their combinations on economic and environmental benefits [19,20,21]. Li et al. (2024) [22] examined the joint impact of government subsidies and penalties on the R&D and production of automakers in the field of low-carbon transportation based on quantum game theory. Cai et al. (2024) [23] discovered that government subsidies can incentivize companies to lower carbon emissions and enhance environmental outcomes, but they might diminish economic benefits if the company is highly risk-averse. Bansal and Gangopadhyay (2003) [24] showed that a subsidy improves environmental quality, while a tax worsens it when policies are applied uniformly. Recent methodological advances reveal deeper complexities: Zheng et al. (2023) [25] employed evolutionary game models based on prospect theory, demonstrating that dynamic carbon tax mechanisms incentivize low-carbon production more effectively than static policies. Ali and Kirikkaleli (2024) [26] utilized a Fourier autoregressive distributed lag model to prove that the environmental benefits of carbon taxes in France are moderated by resource efficiency. Li and Li (2022) [27] quantified the spillover effects of green innovation in the transportation sector—showing that every 1% increase in technological innovation level reduces carbon emissions by 0.23%. However, these models still exhibit limitations: while predominantly focusing on single-enterprise decision-making [17,18], they fail to construct a multi-agent collaborative framework for supply chain systems.

From a market perspective, consumers are becoming more concerned about the environmental impact of products and services when making purchases [28]. Wen et al. (2018) [29] proved that improving consumers’ environmental awareness does not always improve environmental and economic benefits. Regulations and market forces provide high-carbon enterprises with greater incentives to reduce their emissions [30]. Several scholars have examined the cost-sharing model for emission reduction between upstream and downstream enterprises, demonstrating that cost-sharing can enhance emission reduction levels [31,32]. Zhao et al. (2014) [12] found that cost-sharing in logistics services boosts profits for both parties, whereas Lin and Liu (2022) [13] reported that cost-sharing might decrease economic benefits when government subsidies are involved. However, few studies have examined the effects of both low-carbon policies and eco-conscious consumers on corporate pricing and emissions reduction choices, as well as on social welfare [11,33].

2.2. Low-Carbon Transport

Given that transportation generates significant carbon emissions, research on low-carbon transport has gained considerable attention. Some scholars propose that subsidies or carbon taxes could incentivize shippers to switch from road transport to road-rail intermodal transport [8,34,35]. These measures could also encourage logistics companies to reduce carbon emissions by adopting clean energy or other methods [36,37]. However, Tamannaei et al. (2021b) [38] discovered that high fuel taxes on road transportation did not necessarily enhance safety or environmental conditions. Using linear demand models to simulate intermodal freight volume, Wang et al. (2015) [39] and Saberi (2018) [40] found that an increase in the carbon tax rate would lead to a decrease in corporate profits and freight volume. Using the linear price-emission demand formula, Wang and Jiao (2022) [37] found that high government subsidies did not reduce the profits of carriers that had not invested in carbon emissions. Several studies have compared the economic and environmental impacts of various policies and their combinations in the transport sector and vehicle market [41]. Santos et al. (2015) [7] examined the impact of policies—such as subsidizing intermodal operations, internalizing external costs, and optimizing intermodal terminal locations—on rail-road intermodal transport. Bouchery and Fransoo (2015) [42] noted that integrating train transportation subsidies with a suitable tax on truck transportation costs can reduce both expenses and carbon emissions. Concerning the negative carbon tax as a fuel subsidy, Tamannaei et al. (2021a) [9] discovered that high taxes or low subsidies contribute to environmental sustainability. A few scholars have examined consumer environmental awareness and co-opetition among enterprises. Rasti-Barzoki and Moon (2020) [43] examined car and fuel taxes in the Korean vehicle market and found that encouraging consumer ecological consciousness enhances environmental benefits while reducing profits. Alsunousi & Göktuğ (2025) [44] employed a nonlinear autoregressive distributed lag model to demonstrate the dynamic interaction between shippers’ environmental willingness-to-pay and policy responsiveness. Their findings reveal that for every 1% increase in renewable energy consumption, the modal choice probability for intermodal transport among high-WTP groups increases by 2.1 times. Jiang et al. (2019) [45] optimized logistics node configurations and uniform carbon taxes for intermodal transport. Their findings indicate that social welfare improves when logistics authorities, shippers, and carriers collaborate on centralized decision-making. Meng et al. (2022) [14] proposed that government subsidies or penalties for port or shipping companies can enhance emissions reductions but might decrease port revenue. Emission reductions are more effective when both parties make decentralized decisions, do not share costs, or when consumers become more environmentally conscious. However, in the context of intermodal transport, the study of carbon taxes, subsidies, shippers’ environmental awareness, and the sharing of carbon reduction costs within a framework model is still quite rare.

In summary, the existing literature has examined carbon taxes and subsidies from multiple disciplinary perspectives, including environmental science, logistics innovation, and behavioral economics (e.g., references [15,16,24]). Research has also focused on green technology innovation in logistics enterprises (e.g., references [27]) and how enterprises’ environmental protection behavior choices (e.g., reference [29]) impact carbon emissions and low-carbon transportation. Both carbon taxes and carbon subsidies serve as crucial government measures to promote carbon emission reduction. After extensive scholarly research, a consensus has emerged that both carbon taxes and subsidies can effectively promote carbon emission reduction. Nevertheless, when it comes to low-carbon intermodal transport, there is a notable research gap: few studies have simultaneously considered carbon taxes and subsidies in their analysis of economic and environmental benefits [9,42]. Secondly, with the growing awareness of ecological protection and the pursuit of sustainable development, an increasing number of enterprises are showing a preference for partners who emphasize low-carbon practices. However, previous studies have generally assumed that freight volume is either predetermined, random, or influenced by transportation costs. Shippers’ eco-consciousness—which refers to their environmental sensitivity toward transportation carbon emissions, as well as their willingness to pay a premium for low-carbon logistics services—is rarely taken into account [14,43]. Moreover, considering the high costs associated with emission reduction, upstream and downstream enterprises in the supply chain usually attain carbon reduction through joint investments and cost sharing. Nevertheless, research on cooperative decision-making for emission reduction among enterprises is still very scarce, whether in general supply chain or in intermodal transport systems [14,45]. To address these quantitative analysis gaps, the paper investigates the environmental and economic performance of intermodal transport under three policy frameworks: carbon tax-only, subsidy-only, and a dual-policy (tax-subsidy combination). The model incorporates shippers’ eco-consciousness as a key variable, comparing decentralized and centralized decision-making processes between intermodal transport operators and carriers. Additionally, through a case study, it analyzes how the carbon tax rate, subsidies, shippers’ eco-consciousness, and companies’ cost-sharing influence pricing strategies and emission reduction outcomes, providing precise guidance for intermodal transport research.

3. The Model

Within a domestic transport network, an intermodal operator and a carrier engage in a game model that includes an eco-conscious shipper and government intervention. In a decentralized system, the intermodal transport operator signs a transportation contract with the shipper. Then, the operator subcontracts the transportation task to the carrier, who transports the goods in accordance with government regulations.

This paper examines two key government policies: carbon tax and intermodal subsidy. It assumes that the carrier encounters these policies consistently across all routes. Taking into account the environmental awareness of shippers, their shipment volume is affected by both transportation costs and environmental factors. Based on prior research [14,28,29,32,39,46], the linear demand function has been widely adopted in studies exploring the interplay between pricing, environmental factors, and consumer behavior. This assumption is consistent with empirical evidence from intermodal transport markets, where marginal changes in price or emissions typically lead to proportional shifts in demand [7,8]. Although nonlinear relationships (e.g., logarithmic or exponential) may exist, linear approximations remain reasonable for policy-focused analyses, where marginal changes are of primary interest. To ensure model solvability and analytical tractability, we adopt a linear demand function in this study (Aguirregabiria and Ho (2012) [47] demonstrated that even if the true demand system is nonlinear (e.g., logit), comparative static results must ultimately be verified through local linear approximations near the equilibrium point. The linear assumption allows us to (i) derive closed-form solutions for equilibrium strategies (emission reduction levels, prices), which are critical for policymakers; (ii) clearly isolate the effects of subsidies, taxes, and shipper awareness without the confounding complexity of nonlinear interactions; and (iii) compare our results directly with prior work (e.g., [12,35,36,37]), ensuring consistency in the literature.).

On a given route, shipper’s intermodal freight volume is formulated as

$$q=a-bp+\lambda x,$$

(1)

where $a$ is freight capacity independent of price and emission reduction level; $p$ is the transaction price per ton of cargo charged by the intermodal operator to the shipper; $x$ is the carbon emissions reduction level transported by the carrier, where $x\in \left[\mathrm{0,1}\right]$; and $b$ and $\lambda$ are shipper’s sensitivities to price and emission reduction level, respectively. A larger $\lambda$ indicates a higher level of eco-consciousness among shippers. For the feasibility of the model, it is assumed that $a>bp$, $a>0$, $b>0$ and $p>w>\mathrm{c}$, where $c$ is the marginal cost per ton of cargo transported by the carrier and $w$ is transport fee per ton of cargo charged by the carrier to the intermodal operator.

The level of emission reduction has a direct impact on freight volume, which in turn motivates intermodal operators and carriers to invest in carbon emission reduction. These may include increasing the utilization of renewable energy sources, purchasing low-carbon equipment, and adopting advanced technologies such as carbon capture and storage. Assuming that investment in emission reduction on a given route is a fixed cost. Based on prior research in green supply chain [10,11,14,28,46], the cost associated with improving emission reduction levels is modeled as a strictly increasing convex function. Importantly, this cost does not influence the carrier’s transportation expenses [48]. This representation aligns well with the economic intuition that marginal costs of emission reduction tend to increase (This combination of a linear demand function and a quadratic cost function has been proven to be the minimal sufficient structure for achieving closed-form equilibrium solutions in quantity/price competition models, offering clear insights for policy analysis through its analytical solution [49].). In the proposed model, the emission reduction cost is expressed as follows:

$$C\left(x\right)=h{x}^2/2.$$

(2)

Here, $h$ represents the coefficient of emissions reduction cost. This cost is shared between the carrier and the intermodal operator. The carrier bears a proportion denoted by $\varphi$ while the intermodal operator bears $1-\varphi$, where $\varphi$ is a constant between 0 and 1. This cost-sharing ratio is determined by prior agreement between the parties [13,14].

Since it is the carrier that transports goods and emits carbon, the government levies the carbon tax only on the carrier. We can assume that the tax rate is $t$ (tax per kilogram of carbon emissions) and the initial carbon intensity of carrier is $e$ (carbon emissions per ton of cargo transport before emission reduction). Therefore, the actual carbon tax levied by the government on the carrier for each ton of cargo transported is $e(1-x)t$. According to policies in Shenzhen and Dalian, the government offers subsidies to carriers that implement intermodal transport (For more details, please refer to https://jtys.sz.gov.cn/jtzx/wycx/slcx/khzc/content/post_10290594.html, https://www.dl.gov.cn/art/2023/9/5/art_5476_2297313.html (accessed on 26 June 2025).). If we assume that the subsidy for each ton of cargo transported via intermodal routes is $\mu \mathrm{s}$, where $s$ represents the unit subsidy provided to the carrier, and $\mu$ is the adjustment coefficient for the subsidy, the carbon tax rate and unit intermodal subsidy are treated as exogenous parameters [14,37,40].

This paper explores emission reductions in intermodal transported along a specific route. Therefore, the transport distance does not influence the equilibrium. Both the intermodal operator and the carrier make fully informed decisions, acting rationally to maximize their profits. The intermodal operator’s profit is

$${\pi }_I=\left(p-w\right)q-\left(1-\varphi \right)h{x}^2/2.$$

(3)

The profit of carrier is

$${\pi }_C=\left(w-c+\mu s-e(1-x)t\right)q-\varphi h{x}^2/2.$$

(4)

In the decentralized mode, the game sequence is as follows: the carrier determines the unit transportation fee and emission reduction level for each route according to different policies. Subsequently, the intermodal operator sets the unit transaction price with the shipper. Ultimately, the eco-conscious shipper decides the freight volume based on the transaction price and the emission reduction levels per shipment.

Furthermore, the intermodal transport operator might also be responsible for the transportation of goods. Alternatively, the carrier could directly sign an intermodal contract with the shipper. In such cases, the intermodal transport operator and the carrier jointly make decisions regarding pricing and emissions reduction. This kind of arrangement is referred to as the centralized mode. Here, the parties make decisions to maximize overall profit, denoted as ${\pi }_{IC}$ equals ${\pi }_I$ plus ${\pi }_C$. Figure 1 illustrates the game sequence under different decision-making modes, and the notations are summarized in

Table 1. Notations of the model.

Parameters	Definitions
$a$	Freight capacity independent of price and emission reduction level.
$b$	Shipper’s sensitivities to price.
$\lambda$	Shipper’s sensitivities to emission reduction level.
$q$	The freight volume of the shipper’s intermodal transportation.
$e$	The initial carbon emission intensity.
$h$	The coefficient of emissions reduction cost.
$\varphi$	The sharing ratio of emission reduction cost born by the carrier.
$c$	Carrier’s transport cost per ton of goods.
$t$	The carbon tax per kilogram of CO2 emissions.
$s$	The intermodal subsidy per ton of goods transported.
$\mu$	The adjustment coefficient for government subsidy.
${\pi }_I$	The intermodal operator’s profit.
${\pi }_C$	The carrier’s profit.
${\pi }_{IC}$	The overall profit of carrier and intermodal operator.
Decision variables	Definitions
$x$	The carbon emission reduction level per ton of goods transported by the carrier.
$w$	The transport fee per ton of goods charged by carrier to the intermodal operator.
$p$	The transaction price per ton of goods charged by intermodal operator to shipper.

.

4. Equilibrium Analysis

The equilibrium strategy for the multi-stage game involving all parties is determined through backward induction; see Supplementary Materials for details. Equilibria are denoted as follows: without government policy (superscript $O$), with carbon tax (superscript $T$), with intermodal subsidy (superscript $S$), and with dual policies (superscript $A$), under decentralized mode (superscript $D$), and under centralized mode (superscript $N$).

4.1. Equilibrium Without Government Policy

When the intermodal operator and the carrier make centralized decisions, they jointly set the transaction price $p$ and emission reduction level $x$ to maximize overall profits, as shown below:

$$\underset{p>c,1\ge x\ge 0}{\mathit{max}}{\pi }_{IC}^O=\left(p-c\right)(a-bp+\lambda x)-h{x}^2/2.$$

(5)

Lemma 1.

When the intermodal operator and the carrier make centralized decisions without government policies, the equilibrium exists when $2bh-{\lambda }^2>0$. The transaction price with the shipper is $p^{ON}={\displaystyle \frac{c\left(bh-{\lambda }^2\right)+ah}{ 2bh-{\lambda }^2}}$, the emissions reduction level is $x^{ON}={\displaystyle \frac{\lambda (a-bc)}{2bh-{\lambda }^2}}$.

In a decentralized decision-making system, the carrier and the intermodal operator independently make sequential decisions aimed at maximizing their own profits. Without government policies, the carrier’s problem can be expressed as

$$\underset{w>c,1\ge x\ge 0}{\mathit{max}}{\pi }_C^O=\left(w-c\right)(a-bp+\lambda x)-\varphi h{x}^2/2.$$

(6)

The intermodal operator’s problem can be expressed as

$$\underset{p>w}{\mathit{max}}{\pi }_I^O=\left(p-w\right)(a-bp+\lambda x)-(1-\varphi )h{x}^2/2.$$

(7)

Lemma 2.

When the intermodal operator and the carrier make decentralized decisions without government policies, the equilibrium exists when $4bh\varphi -{\lambda }^2>0$. The transaction price charged by the intermodal operator is $p^{OD}={\displaystyle \frac{c\left(bh\varphi -{\lambda }^2\right)+3ah\varphi }{ 4bh\varphi -{\lambda }^2}},$ the emissions reduction level is $x^{OD}={\displaystyle \frac{\lambda (a-bc)}{4bh\varphi -{\lambda }^2}},$ the transport fee charged by the carrier is $w^{OD}={\displaystyle \frac{c\left(2bh\varphi -{\lambda }^2\right)+2ah\varphi }{ 4bh\varphi -{\lambda }^2}}$.

4.2. Equilibrium Under Intermodal Subsidy

When the government offers intermodal subsidy to the carrier, the carrier’s profit is

$${\pi }_C^S=\left(w-c+\mu s\right)(a-bp+\lambda x)-\varphi h{x}^2/2.$$

(8)

The intermodal operator’s profit is the same as Equation (3). The overall profit is

$${\pi }_{IC}^S=\left(p-c+\mu s\right)(a-bp+\lambda x)-h{x}^2/2.$$

(9)

Lemma 3.

If the government introduces intermodal subsidy, (i) the equilibrium exists when $2bh-{\lambda }^2>0$ under centralized decisions, the transaction price is $p^{SN}={\displaystyle \frac{(c-\mu s)\left(bh-{\lambda }^2\right)+ah}{ 2bh-{\lambda }^2}},$ the emissions reduction level is $x^{SN}={\displaystyle \frac{\lambda (a-bc+b\mu s)}{2bh-{\lambda }^2}}$0; (ii) the equilibrium exists when $4bh\varphi -{\lambda }^2>0$ under decentralized decisions, the transaction price is $p^{SD}={\displaystyle \frac{\left(c-\mu s\right)\left(bh\varphi -{\lambda }^2\right)+3ah\varphi }{ 4bh\varphi -{\lambda }^2}},$ the emissions reduction level is $x^{SD}={\displaystyle \frac{\lambda \left(a-bc+b\mu s\right)}{4bh\varphi -{\lambda }^2}},$ and the transport fee is $w^{SD}={\displaystyle \frac{(c-\mu s)\left(2bh\varphi -{\lambda }^2\right)+2ah\varphi }{ 4bh\varphi -{\lambda }^2}}.$

Intuitively, the increased intermodal subsidy provides a stronger incentive for the carrier to reduce carbon emissions, i.e., $\mathcal{\partial }{x}^S/\mathcal{\partial }s>0$ and $\mathcal{\partial }{x}^S/\mathcal{\partial }\mu >0$. And higher emission reductions lead to an increase in freight volume, i.e., $\mathcal{\partial }{q}^S/\mathcal{\partial }s>0$ and $\mathcal{\partial }{q}^S/\mathcal{\partial }\mu >0$. These results are consistent with previous research [7,13,14,29]. However, this study reveals a scenario distinct from the findings of Lin and Liu (2022) [13] (Since Lin and Liu (2022) [13] considered government subsidies for consumer spending or enterprise costs, the subsidies have a positive effect on prices. This paper, however, examines the government subsidy for freight volume.), which indicates that government subsidies always result in price hikes. Specifically, as government subsidies go up, transaction prices actually drop when the shipper’s environmental awareness is low. That is, $\mathcal{\partial }{p}^{SN}/\mathcal{\partial }s<0$ and $\mathcal{\partial }{p}^{SN}/\mathcal{\partial }\mu <0$ when ${\lambda }^2\in [0,bh]$, $\mathcal{\partial }{p}^{SD}/\mathcal{\partial }s<0$ and $\mathcal{\partial }{p}^{SD}/\mathcal{\partial }\mu <0$ when ${\lambda }^2\in [0,bh\varphi ]$. Price cuts and emission reductions can drive up freight volume. However, if the shipper has low environmental awareness, the effect of emission reductions will be rather limited. In this case, the intermodal operator will cut transaction prices to increase freight volume and maximize profits. On the other hand, when the shipper is more environmentally conscious, emission reductions can significantly increase freight volume. At this point, moderately raising prices actually benefits the intermodal operator more. By comparing centralized and decentralized decision-making, we obtain the following proposition.

Proposition 1.

Under the intermodal subsidy, centralized decision-making results in higher overall profits than decentralized decision-making. However, when the carrier bears a smaller share of the emission reduction cost, decentralized decision-making brings about greater emission reductions, higher freight volumes, and an increase in transaction prices.

Decentralized decision-making usually leads to lower total profits than centralized decision-making. But the comparison regarding emission reductions and transaction prices differs based on the cost sharing between logistics companies. When the carrier bears a smaller proportion of the emission reduction costs, it gains a stronger motivation to cut emissions, increase freight volume, and obtain higher intermodal subsidies. As emissions are reduced, the intermodal operator will raise the transaction price to increase profits. In specific, when $\varphi \in [1/2,1]$, there is $x^{SD}\le x^{SN}$, otherwise, there is $x^{SD}>x^{SN}$; when $\varphi \in [{\lambda }^2/({3\lambda }^2-2bh),1]$, there is $p^{SD}\le p^{SN}$, otherwise, there is $p^{SD}>p^{SN}$; when $\varphi \in [{\lambda }^2/({\lambda }^2+2bh),1]$, there is $q^{SD}\le q^{SN}$, otherwise, there is $q^{SD}>q^{SN}$.

Proposition 2.

Compared to the no-policy equilibrium, the implementation of an intermodal subsidy leads to greater emissions reductions, increased freight volumes, and higher profits for both the intermodal operator and the carrier. Moreover, when shippers exhibit a high level of eco-consciousness, the transaction price tends to rise.

Although government subsidies are only aimed at carriers, our analysis shows that these subsidies also bring benefits to intermodal operators who invest in emission reductions. This finding is in line with previous research [13,37]. To obtain higher subsidies, the carrier boosts investment in emission reduction and draws in more freight volume. This, in turn, prompts the intermodal operator to raise transaction prices for greater profit, particularly when dealing with shippers who are highly environmentally conscious. That is, $p^{SN}>p^{ON}$ when ${\lambda }^2\in (bh,2bh)$ and $p^{SD}>p^{OD}$ when ${\lambda }^2\in (bh\varphi ,4bh\varphi ).$ Therefore, the implementation of intermodal subsidies can enhance both the environmental and economic benefits of intermodal transport systems.

4.3. Equilibrium Under Carbon Tax

When the government imposes a carbon tax on the carrier, the carrier’s profit is

$${\pi }_C^T=\left(w-c-e(1-x)t\right)(a-bp+\lambda x)-\varphi h{x}^2/2.$$

(10)

The intermodal operator’s profit is represented by Equation (3). The total profit is

$${\pi }_{IC}^T=\left(p-c-e(1-x)t\right)(a-bp+\lambda x)-h{x}^2/2.$$

(11)

Lemma 4.

If the government introduces carbon tax, (i) the equilibrium exists when $2bh-{(\lambda +bet)}^2>0$ under centralization, transaction price is $p^{TN}={\displaystyle \frac{(c+et)\left(bh-{\lambda }^2-\lambda bet\right)+a(h-b{e}^2{t}^2-\lambda et)}{ 2bh-{(\lambda +bet)}^2}}$, emissions reduction level is $x^{TN}={\displaystyle \frac{(\lambda +bet)(a-bc-bet)}{ 2bh-{(\lambda +bet)}^2}}$; (ii) the equilibrium exists when $4bh\varphi -{(\lambda +bet)}^2>0$ under decentralization, the transaction price is $p^{TD}={\displaystyle \frac{(c+et)\left(bh\varphi -{\lambda }^2-\lambda bet\right)+a(3h\varphi -b{e}^2{t}^2-\lambda et)}{ 4bh\varphi -{(\lambda +bet)}^2}},$ the emissions reduction level is $x^{TD}={\displaystyle \frac{(\lambda +bet)(a-bc-bet)}{4bh\varphi -{(\lambda +bet)}^2}},$ and the transport fee is $w^{TD}={\displaystyle \frac{(c+et)\left(2bh\varphi -{\lambda }^2-\lambda bet\right)+a(2h\varphi -b{e}^2{t}^2-\lambda et)}{4bh\varphi -{(\lambda +bet)}^2}}.$

The impact of carbon tax on the intermodal operator and the carrier is akin to that of intermodal subsidies. As governments raise carbon taxes on the carrier, both emission reduction levels and freight volumes increase, i.e., $\mathcal{\partial }{x}^T/\mathcal{\partial }t>0$ and $\mathcal{\partial }{q}^T/\mathcal{\partial }t>0$. Previous studies have indicated that an increase in the carbon tax rate would lead to a decline in freight volume [39,40]. The discrepancy arises because we account for the eco-conscious shipper, whose freight volumes grow as environmental conditions improve. A higher carbon tax would encourage companies to reduce emissions, thereby increasing shipping demand. When the shipper’s eco-conscious level is sufficiently high, the transaction price increases with the carbon tax. Otherwise, the transaction price initially rises and then decreases as the carbon tax increases. Furthermore, the comparison between decentralization and centralization under a carbon tax is consistent with that under an intermodal subsidy, as shown in Proposition 1. That is, $x^{TD}\le x^{TN}$ when $\varphi \in [1/2,1]$; $p^{TD}\le p^{TN}$ when $\varphi \in [{\displaystyle \frac{{b^2{e}^2{t}^2-\lambda }^2}{2bh+b^2{e}^2{t}^2-2\lambda bet-{3\lambda }^2}},1]$; $q^{TD}\le q^{TN}$ when $\varphi \in [{\displaystyle \frac{{\left(\lambda +bet\right)}^2}{2bh+b^2{e}^2{t}^2+2\lambda bet+{\lambda }^2}},1]$.

Proposition 3.

Implementing a carbon tax outperforms the no-policy equilibrium by enhancing emission reductions and increasing freight volumes. However, if shippers’ environmental awareness stays low, it may result in lower transaction prices and reduced profits for both intermodal operators and carriers.

Although the government’s carbon tax is levied exclusively on carriers, it can also lead to a reduction in transaction prices and profits for intermodal operators. When shippers have low environmental awareness, cutting emissions has minimal impact on the increase in freight volume. For intermodal operators, lowering transaction prices to boost freight volume turns out to be more beneficial, especially under a higher carbon tax (When $\lambda$ is low, ${\overline{t}}_p^{TON}$ and ${\overline{t}}_p^{TOD}$ are positive. There are $p^{ON}>p^{TN}$ when $t>{\overline{t}}_p^{TON}$ and $p^{OD}>p^{TD}$ when $t>{\overline{t}}_p^{TOD}$; when $\lambda$ is high, ${\overline{t}}_p^{TON}$ and ${\overline{t}}_p^{TOD}$ are negative. There are always $p^{ON}<p^{TN}$ and $p^{OD}<p^{TD}$, where ${\overline{t}}_p^{TON}={\displaystyle \frac{2b^2{h}^2-3bh{\lambda }^2+a{\lambda }^3-bc{\lambda }^3+{\lambda }^4}{be(abh-b^{2}ch+2bh\lambda -a{\lambda }^2+bc{\lambda }^2-{\lambda }^3)}}$ and ${\overline{t}}_p^{TOD}={\displaystyle \frac{a{\lambda }^3-bc{\lambda }^3+{\lambda }^4+2abh\lambda \varphi -2b^{2}ch\lambda \varphi -5bh{\lambda }^2\varphi +4b^2{h}^2{\varphi }^2}{be(-a{\lambda }^2+bc{\lambda }^2-{\lambda }^3+abh\varphi -b^{2}ch\varphi +4bh\lambda \varphi )}}$.). When intermodal operators face higher costs for emission reductions, their profits will be lower compared to scenarios without such policies. While the carbon tax imposed by the government can enhance environmental benefits, it may also decrease the economic efficiency of intermodal transport systems.

4.4. Equilibrium Under Intermodal Subsidy and Carbon Tax

When the government implements a dual policy of intermodal subsidies and carbon taxes, the carrier’s profit is represented by Equation (4). The intermodal operator’s profit is depicted by Equation (3). The total profit is

$${\pi }_{IC}^A=(p-c+\mu s-e(1-x\left)t\right)(a-bp+\lambda x)-h{x}^2/2.$$

(12)

Lemma 5.

If the government introduces the dual policy,(i) the equilibrium exists when $2bh-{(\lambda +bet)}^2>0$ under centralization, transaction price is $p^{AN}={\displaystyle \frac{(c+et-\mu s)\left(bh-{\lambda }^2-\lambda bet\right)+a(h-b{e}^2{t}^2-\lambda et)}{ 2bh-{(\lambda +bet)}^2}}$, emissions reduction level is $x^{AN}={\displaystyle \frac{(\lambda +bet)(a-bc-bet+b\mu s)}{ 2bh-{(\lambda +bet)}^2}}$; (ii) the equilibrium exists when $4bh\varphi -{(\lambda +bet)}^2>0$ under decentralization, transaction price is $p^{AD}={\displaystyle \frac{(c+et-\mu s)\left(bh\varphi -{\lambda }^2-\lambda bet\right)+a(3h\varphi -b{e}^2{t}^2-\lambda et)}{ 4bh\varphi -{(\lambda +bet)}^2}},$ emissions reduction level $x^{AD}={\displaystyle \frac{(\lambda +bet)(a-bc-bet+b\mu s)}{4bh\varphi -{(\lambda +bet)}^2}},$ transport fee is $w^{AD}={\displaystyle \frac{(c+et-\mu s)\left(2bh\varphi -{\lambda }^2-\lambda bet\right)+a(2h\varphi -b{e}^2{t}^2-\lambda et)}{4bh\varphi -{(\lambda +bet)}^2}}.$

With the increase in intermodal subsidies and carbon taxes, both emission reduction levels and freight volumes have grown. When the shipper exhibits greater environmental awareness, transaction prices tend to rise. The comparison between decentralization and centralization under the dual policy framework is consistent with that observed under the single policy, as illustrated in Proposition 1. That is, $x^{AD}\ge x^{AN}$ when $\varphi \le 1/2$; $p^{AD}\ge p^{AN}$ when $\varphi \le {\displaystyle \frac{{b^2{e}^2{t}^2-\lambda }^2}{2bh+b^2{e}^2{t}^2-2\lambda bet-{3\lambda }^2}}$; $q^{AD}\ge q^{AN}$ when $\varphi \le {\displaystyle \frac{{\left(\lambda +bet\right)}^2}{2bh+b^2{e}^2{t}^2+2\lambda bet+{\lambda }^2}}$.

Proposition 4.

Implementing a carbon tax or an intermodal subsidy can boost emission reductions and freight volume, possibly lowering transaction prices when the shipper’s environmental awareness is low. An intermodal subsidy can increase profits for both the intermodal operator and carrier, while a carbon tax might reduce their profits if the shipper’s environmental awareness remains low.

The simultaneous implementation of intermodal subsidies and carbon taxes further enhances emission reduction effects and freight volume. Our model challenges conventional wisdom by demonstrating that introducing carbon taxes can increase freight volume and lower transaction prices under specific conditions. While carbon taxes may lead to higher per-unit transportation costs, they also incentivize companies to reduce emissions. For the eco-conscious shipper, the increase in freight volume driven by emission reductions may surpass the decline caused by price hikes, resulting in an overall growth in volume. Nevertheless, when the shipper has low environmental awareness, the increase in volume resulting from emission reductions is barely noticeable. In this situation, it is more advantageous for the intermodal operator to reduce prices to further stimulate volume growth. This explains why our findings diverge from those studies which failed to consider shippers’ environmental awareness [9,39,40]. Moreover, as carbon taxes raise costs for carriers and intermodal operators, the improved emission reduction benefits fail to compensate for the higher expenses. This results in a drop in corporate profits, particularly when shippers show low environmental awareness. On the other hand, intermodal subsidies have reduced transportation costs for carriers, thus boosting the economic benefits for all parties involved.

5. Numerical Analysis

Currently, several regions in China, including Huaibei and Huangshi, have implemented intermodal transport subsidy policies. However, the transportation sector has not yet adopted a carbon tax. This section focuses on road–water intermodal transport in Ji’an City, Jiangxi Province, as a case study. It explores whether implementing a carbon tax would be advantageous and investigates how intermodal subsidies, carbon taxes, carriers’ share of emissions reduction costs, and shippers’ environmental awareness influence the carbon emissions and economic benefits of both intermodal operators and carriers. The total carbon emissions from transport are calculated by multiplying the freight volume by the carbon intensity [39], i.e., $(1-x)e\mathrm{q}$. Based on real-world data, the assumptions for the numerical examples are as follows:

According to the “Measures to Further Strengthen Support for High-Quality Development in the Water Transport Industry” (Please refer to http://jtys.jian.gov.cn/news-show-5808.html (accessed on 26 June 2025).), the road transportation of goods from enterprises to Ji’an Port will be subsidized at a standard rate of $0.2$ yuan per ton per kilometer. Starting from 2023, a five-year market cultivation period will be provided, with 100% subsidy of the standard in the first year, 90% subsidy in the second and third years, and 70% subsidy in the fourth and fifth years. Therefore, we set the intermodal subsidy (s) at 0.2 CNY/(t∙km), and the adjustment coefficient $\left(\mu \right)$ between $0$ and $1$.

According to “A Credible Carbon Tax Trajectory for Ireland”, released by the Organization for Economic Co-operation and Development (Please refer to https://www.oecd.org/content/dam/oecd/en/publications/reports/2021/09/ipac-policies-in-practice_1a65968e/a-credible-carbon-tax-trajectory-for-ireland_b07887bd/a39128a3-en.pdf (accessed on 26 June 2025) for more details.) in 2025, Ireland implements a carbon tax on fossil fuels utilized for transportation, charging EUR 56 per ton of $\mathrm{C}{\mathrm{O}}_2$ emissions. The targeted rate is projected to rise to EUR 100 per ton of $\mathrm{C}{\mathrm{O}}_2$ by the year 2030. According to the “Review of Maritime Transport 2024” by the United Nations Conference on Trade and Development (Please refer to https://unctad.org/system/files/official-document/rmt2024overview_en.pdf (accessed on 26 June 2025).), the International Maritime Organization has set a maritime carbon tax of approximately USD 0.1 to USD 0.3 per kilogram of CO₂ emissions for the period between 2027 and 2030. Based on the exchange rates, we set the carbon tax $\left(t\right)$ at CNY $0$ to $2$ per kilogram of $\mathrm{C}{\mathrm{O}}_2$ emissions.

Referring to Tian et al. (2023) [50] (The policies’ documents, such as the ‘Highway Operation Period Mobile Source Carbon Emission Calculation Standard’, released by the Guangdong Provincial Department of Transport, further verify the representativeness and authority of the reference data. Please refer to https://td.gd.gov.cn/zcwj_n/tzgg/content/post_4455759.html (accessed on 26 June 2025).), the carbon emission intensity of road transport is approximately 0.1 kg CO₂/(t∙km). In this study, $e$ represents the initial carbon emission intensity of the transportation enterprise when no emission reduction measures are implemented during transportation, i.e., the highest possible carbon emission intensity. Thus, the parameter $e$ is directly set based on the carbon emission intensity of road transportation, which is 0.1 kg CO₂/(t∙km). Through trial calculations, we found that $e$ synchronously affects various quantitative results under different scenarios but does not affect qualitative conclusions (In fact, initial carbon emission intensity may vary due to factors such as routes, congestion, and weather. However, since the model examines the impact of different policies on logistics companies’ efforts to reduce emissions and pricing decisions within specific routes, this paper does not consider changes in initial carbon emission intensity over time. Additionally, the trial calculations have shown that these variations do not affect the qualitative outcomes.).

According to the “China Road Freight Big Data Carbon Emission Report” (Please refer to https://www.tioe.tsinghua.edu.cn/__local/4/5F/85/1CD5DEFEFD33437221BA37F5149_9198476D_376E68.pdf, http://www.climatechange.cn/article/2023/1673-1719/1673-1719-19-3-347.shtml and https://www.docin.com/p-12751693.html (accessed on 26 June 2025) for more details.), the emissions reduction cost coefficient is assumed to be $h=10$. The sharing ratio of the emission reduction cost borne by the carrier is $\varphi \in \left[\mathrm{0,1}\right]$. Based on the empirical study conducted by Wang (2013) [51] on China’s road transportation cost structure and driving factors using the GTC model, the average cost of long-distance transportation of heavy trucks nationwide is approximately 0.65 yuan per ton-kilometer. Therefore, we set the carrier’s transport cost c = 0.65 CNY/(t∙km). Through numerical simulation, it was found that the value of $c$ does not affect the qualitative results.

According to the Statistical Bulletin on Economic and Social Development of Ji’an City in 2024 (Please refer to http://tj.jian.gov.cn/news-show-1512.html and https://www.hnacargo.com/Portal2/NewsView.aspx?id (accessed on 26 June 2025) for more details.), over eighty companies in Ji’an City have switched to ‘road-to-waterway’ freight, increasing waterway cargo volume by about 800,000 tons. On average, each company increases its freight volume by approximately 27 tons per day. Therefore, we set the market base of an intermodal operator $\left(a\right)$ at 27 (calculated daily). Referring to Tamannaei et al. (2021a) [9] and Ginés and Socorro (2014) [52] (The authors mentioned that there is a degree of product differentiation between unimodal and intermodal transportation modes, denoted by $\delta$. They estimated that $\delta =0.7$. Moreover, in a duopoly market with a unimodal and an intermodal transport mode, their results indicate that the demand is linear in the prices and the following relation holds between the sensitivity and parameter $\delta$: self-price sensitivity equals $1/(1-{\delta }^2)$.), the price sensitivity coefficient $\left(b\right)$ is set to 2. Since $\lambda$ denotes the shipper’s sensitivity to the environment, its range is determined based on the price sensitivity coefficient, varying between 0 and 2.

Figure 2 illustrates the influence of a shipper’s eco-conscious level on both economic and environmental benefits, leading to the following proposition.

Proposition 5.

As shippers become increasingly focused on environmental protection, total carbon emissions will always decrease, and overall profits may decline, especially when the cost of emission reductions borne by the carriers is relatively low.

Figure 2a demonstrates that as the shipper becomes more environmentally conscious, both parties make greater efforts to cut emissions, leading to a reduction in total carbon emissions. This finding is consistent with prior studies [14,43]. Rasti-Barzoki and Moon (2020) [43] noted that heightened environmental awareness could decrease enterprise profits. However, Figure 2b shows that enhancing shippers’ environmental awareness is not always detrimental to enterprises. Specifically, when $\left(3\varphi -1\right)\varphi <{(bet+\lambda )}^2/4bh$, there is $\mathcal{\partial }{\pi }^{AD}/\mathcal{\partial }\lambda <0$, otherwise, $\mathcal{\partial }{\pi }^{AD}/\mathcal{\partial }\lambda \ge 0$. Therefore, when enterprises make centralized decisions or the intermodal operator shares a small portion of the emissions reduction cost, the government can enhance both economic and environmental benefits by raising public environmental awareness (e.g., mandatory carbon disclosure, green training certification for shippers). Moreover, Figure 2 indicates that when the shipper’s environmental awareness and the carrier’s share of emission reduction costs are sufficiently high, centralized decision-making provides greater economic and environmental benefits compared to decentralized decision-making. In such cases, the government should encourage carriers and intermodal operators to make centralized decisions, such as enabling companies to access a unified platform, designing standardized revenue-sharing contracts and reducing the average financing costs of enterprises through centralized decision-making.

The equilibrium of centralization is not influenced by the carrier’s share in reducing emissions costs. Figure 3 and Figure 4 demonstrate how the cost-sharing of emissions reduction affects carbon emissions and profits of the carrier and the intermodal operator in a decentralized mode, leading to the following proposition.

Proposition 6.

In a decentralized model, as the share of carrier’s emission reduction costs increases, total carbon emissions rise, while carrier’s profit decreases. At the same time, overall profit and intermodal operator’s profit first increase and then decrease.

Figure 3 illustrates that emissions reductions are more effective when both parties make decentralized decisions and the carrier bears less emissions reduction cost, or when the shipper becomes more environmentally conscious. This contrasts with the findings of ref. [14], who examined the interplay between cost-sharing and benefit-sharing among the parties involved. Figure 4 shows that it is always beneficial for the carrier to minimize its share of the emissions reduction cost. However, a significant decrease in the intermodal operator’s portion of this cost would lead to a reduction in its profit. This is because a higher $\varphi$ increases the transport fee paid to the carrier, while reducing the carrier’s incentive for emissions reduction. Consequently, this leads to a decrease in freight volume. To maintain a specific freight volume, the intermodal operator would need to lower transaction prices. If the intermodal operator’s share of emission reduction costs falls below a certain threshold, specifically ${(bet+\lambda )}^2/8bh$, the increase in transportation fees combined with the drop in transaction prices will outweigh the savings from emissions reduction. This imbalance ultimately leads to reduced profits. By equilibrium derivation (By solving ${\displaystyle \frac{\mathcal{\partial }{\pi }_{IC}^A}{\mathcal{\partial }\varphi }}=0$, we get $\varphi ={\displaystyle \frac{2}{3}}$.), we find that when the carrier bears two-thirds of the emission reduction costs and the intermodal operator bears one-third, both parties can achieve maximum overall profit.

Based on the intermodal transport subsidy policy in Ji’an City, the subsidy adjustment coefficient is decreasing year by year. This indicates that the actual subsidy amount is reducing annually. Figure 5 and Figure 6 illustrate the impact of the subsidy adjustment coefficient on carbon emissions under different scenarios, leading to the following proposition.

Proposition 7.

When the shipper’s environmental awareness is relatively low or the proportion of emission reduction costs for the carrier is relatively high, the total carbon emissions will increase with the intermodal transport subsidies received by enterprises.

It is widely accepted that boosting intermodal transport subsidies could lead to a reduction in overall carbon emissions [37]. Nevertheless, as Figure 5 illustrates, a high subsidy might actually raise carbon emissions if the shipper has low environmental awareness. When the shipper’s environmental awareness approaches a moderate level, total carbon emissions first rise and then fall as the subsidy goes up. This phenomenon can be attributed to two key factors: the growth in transportation volume and the enhancement of emission reduction levels driven by subsidies. To secure higher subsidies, carriers tend to boost freight volume by lowering prices while simultaneously improving their emission reduction performance. However, when the subsidy amounts are insufficient or the shippers’ environmental awareness is relatively low, the benefits gained from emission reduction become limited. This creates inadequate incentives for enterprises to invest in emission reduction measures. Consequently, the increase in transportation volume outpaces the improvements in unit emission reduction levels, ultimately leading to a rise in overall carbon emissions.

Figure 6 demonstrates that the trend of carbon emissions varying with subsidies is also influenced by cost sharing. Only when the carriers bear lower emission reduction costs or receive higher subsidies will they invest more in emission reduction. In these scenarios, increasing subsidies contribute to a reduction in total carbon emissions. Based on the analysis above, for the government, subsidies should be determined based on shippers’ environmental awareness levels and the cost-sharing ratios between logistics companies. When shippers have low environmental awareness or carriers bear higher costs, introducing subsidies might actually lead to an increase in total carbon emissions. On the other hand, when shippers’ environmental awareness is adequately high or carriers shoulder lower costs, implementing subsidies can effectively encourage companies to cut down on their emissions.

Considering the limited effect of subsidies on emission reduction, the following section further explores the impact of introducing a carbon tax. Figure 7 and Figure 8 illustrate the combined effects of carbon tax and intermodal subsidies on both carbon emissions and corporate profits. Since carbon taxes and subsidies differ across regions and change over time, the values of $\mu$ and $t$ are set within the range of 0 to 5. Trial calculations have shown that values above 5 do not influence the overall trend of the results. To ensure the comparability of the results, we continue to set the subsidy (s) at 0.2 CNY/(t∙km), while using the value of $\left(\mu \right)$ to represent changes in government subsidies.

Proposition 8.

As the intermodal subsidy increases, overall profit consistently rises, and carbon emissions may increase when the carbon tax is high. As the carbon tax increases, carbon emissions always decrease, while total profit first decreases and then increases when the emission reduction costs borne by the carrier are sufficiently high.

Figure 7 demonstrates that raising intermodal subsidies could potentially lead to an increase in total carbon emissions, especially when the carbon tax is at a low level. Conversely, increasing the carbon tax consistently yields more significant environmental benefits. This finding contrasts with earlier research indicating that high subsidies can cut carbon emissions [37] and that a high tax value does not always enhance environmental conditions [38]. The aforementioned study failed to consider the influence of consumers’ environmental awareness on freight volume. In order to more accurately mirror real- world situations, this paper describes the consignment behavior of shippers who are environmentally conscious. It shows that both increasing emission reductions and reducing prices can boost freight volume. Under intermodal subsidy policies, carriers are inclined to maximize freight volume in order to boost subsidy revenue. However, this approach may unintentionally lead to increased carbon emissions. On the other hand, under carbon tax policies, carriers will restrain the growth of freight volume to cut down on both carbon emissions and tax expenses. This suggests that carbon tax policies offer greater emission reduction benefits compared to subsidy policies.

Figure 8 and Figure 9 demonstrate that consistently enhancing intermodal subsidies boosts the overall profits of both the intermodal operator and the carrier. In centralized decision-making scenarios, when the emission reduction cost borne by the carrier is relatively low, the implementation of a carbon tax will lead to a reduction in corporate profits. However, when the emission reduction cost shouldered by the carrier is sufficiently high, an increase in the carbon tax will cause corporate profits to first decrease and then increase. This finding contrasts with earlier research that corporate profits would decrease as carbon tax rates increase [39,40]. However, those studies failed to consider the growing segment of eco-conscious consumers who are willing to pay a premium for low-carbon alternatives. The current research demonstrates that higher tax rates can actually incentivize companies to take more aggressive measures in reducing emissions. This leads to two key outcomes: lower carbon intensity and higher transaction prices. When the tax rate increases substantially, the resulting price hike may surpass the additional tax expenses. This dynamic could potentially boost profits, particularly in scenarios where carriers face significant emission reduction costs. Moreover, numerical simulations reveal that as shippers become more environmentally conscious, the threshold carbon tax rate at which profits start to rise gradually decreases. In this case, a moderate increase in the carbon tax rate can boost both economic and environmental benefits.

Based on the analysis above, in a decentralized model, the government should first increase carbon taxes to an appropriate level while raising the proportion of carriers in emission reduction costs. This approach will effectively reduce carbon emissions and safeguard corporate profits. Subsequently, the government ought to enhance intermodal transport subsidies to further amplify economic and environmental benefits. Furthermore, centralized decision-making consistently generates higher overall profits compared to decentralized approaches. Notably, when carbon taxes are high and carriers bear a significant portion of emission reduction costs, centralized decision-making leads to lower carbon emissions. In such scenarios, government incentives for carriers and intermodal operators to make coordinated decisions—such as integrating companies into a unified platform or providing attractive benefits—can enhance both environmental sustainability and economic efficiency.

6. Conclusions

This study constructs a Stackelberg game model involving an eco-conscious shipper, an intermodal transport operator, and a carrier to analyze the impacts of carbon taxes, subsidies, and their combinations on emission reductions and economic performance. Key findings: (1) Both carbon taxes and subsidies individually enhance emission reduction and freight volume, with their dual implementation generating synergistic effects that outperform single policies. Notably, reducing intermodal subsidies could potentially promote carbon reduction. Interestingly, increasing taxes does not necessarily harm logistics companies, which challenges conventional wisdom. (2) When the carrier bears high emissions reduction costs, prioritizing the increase of carbon taxes to effective levels first and then increasing intermodal subsidies can achieve win-win economic and environmental outcomes. (3) Enhancing shipper eco-consciousness consistently reduces total emissions; however, its impact on profits depends on the decision-making modes (decentralized vs. centralized) and the cost-sharing ratios for emission reduction. (4) Reducing the cost share for emission reduction is always advantageous for the carrier, but it may be detrimental to the intermodal operator. In decentralized settings, the overall profits reach an optimal level when the intermodal operator covers one-third of the cost.

Policy Implications: (1) To enhance the sustainability of intermodal transport, policymakers ought to take a phased approach. Initially, they should raise carbon taxes to a reasonable threshold in order to motivate emission reductions. Subsequently, they can gradually increase intermodal subsidies to maintain economic viability. To guarantee the “tax-first, subsidy-later” sequence, we lock it into law and budget. (i) Two-stage statute: The Carbon Tax Act sets escalating rates for Years 1–3; only after the rate reaches a certain level does the subsidy clause activate. (ii) Revenue-linked fund: All carbon-tax proceeds go into a dedicated green fund; subsidies can be drawn solely from this fund and only after-tax receipts are booked. (iii) Pilot roll-out: Start in provinces that already subsidize intermodal freight; subsidies remain flat until the statutory tax trigger is met, then rise automatically. (2) Additionally, subsidies should be customized to align with shippers’ eco-consciousness and cost-sharing arrangements. Caution is particularly necessary when shippers have low environmental awareness or when carriers bear high reduction costs, as excessive subsidies in these cases may paradoxically lead to an increase in total emissions. (3) Governments should also promote centralized decision-making by establishing unified information platforms, standardizing revenue-sharing contracts, and reducing financing costs for collaborative operations, especially when the proportion of emission reduction costs borne by carriers is too high and the shipper’s environmental awareness or carbon tax rate is relatively high. (4) Moreover, enhancing shippers’ environmental awareness through mandatory carbon disclosure and green certifications can indirectly promote emission reductions. Lastly, regulating cost-sharing ratios (for example, encouraging carriers to bear around two-thirds of the reduction costs in decentralized systems) can improve enterprises’ profitability.

Managerial Recommendations: For the operational entities involved in intermodal transport, this study likewise offers specific managerial recommendations. (1) Intermodal operators are advised to explore revenue-sharing or equity-based partnerships with carriers, particularly when shippers prioritize environmental protection and carbon taxes are on the rise. Additionally, when carriers face capital constraints, operators should consider dynamically increasing the cost-sharing ratio. This strategy can help achieve greater freight volumes and even higher profits, promote long-term contractual relationships, and ensure mutual benefits in a rapidly evolving market. (2) Carriers ought to prioritize upfront investments in low-carbon technologies—such as LNG trucks, electric heavy-duty vehicles, or hydrogen pilot projects—to mitigate the risks posed by potential future tax increases. Additionally, they should open data interfaces and participate in shared TMS platforms to reduce information barriers and promote centralized governance. (3) Shippers should take the initiative to incorporate a “green premium” into their procurement scoring systems, giving priority to certified low-carbon services. Additionally, they ought to engage in industry-level carbon footprint disclosure, thereby encouraging upstream logistics providers to intensify their emission-reduction initiatives.

Limitations and Future Research: (1) Policy Scope: The analysis focuses exclusively on carbon taxes and subsidies, leaving out alternative mechanisms like cap-and-trade systems or carbon offset programs. Additionally, it does not delve into policy variations across different stakeholders, such as operators, carriers, or shippers. (2) Model Simplification: By assuming a single intermodal operator and carrier, the model overlooks the dynamics of competition among multiple entities. This simplification may restrict its applicability to real-world scenarios where market interactions are more complex. (3) Functional Assumptions: The analytical findings are based on two common assumptions: a linear demand function and a quadratic emission-abatement cost function. While these assumptions enable clear marginal interpretations, future studies should explore more flexible setups—such as nonlinear demand (e.g., piecewise linear formulations or dynamic demand learning models) or convex–concave abatement cost curves—to test the robustness of the qualitative insights derived here. (4) Regional Parameterization: The numerical analyses are grounded in parameters from specific regions. To improve generalizability, further validation across diverse contexts and geographies is essential. (5) Carbon-Intensity Dynamics: The model assumes a fixed initial carbon emission intensity per ton-kilometer and does not capture possible time-varying changes arising from technological progress, energy-mix shifts, or vehicle-fleet turnover. While this assumption keeps the model analytically tractable, it may under- or overestimate the abatement potential of a given policy mix. Relaxing this assumption—e.g., by embedding a dynamic carbon-intensity function—constitutes an important avenue for future work.