How carbon trading policy should be integrated with carbon tax policy—laboratory evidence from a model of the current state of carbon pricing policy in China

China is planning to introduce carbon tax policy to control the carbon emissions of the country better and achieve the “3060 goals”, but there is still widespread discussion about how to introduce it and how to combine it with cap and trade. China has already established a national carbon emission trading market; however, there is also disagreement on whether to impose the carbon tax on companies and projects that have been included in scope of cap and trade. This paper adopts the research method of experimental economics to study the effect on social economy and social emission reduction under cap and trade, carbon tax, and carbon tax-carbon trading policies, and analyzes average prices of carbon market under cap and trade and carbon tax-carbon trading policies. The study finds that under the carbon tax-carbon trading policy, carbon emissions cannot be reduced significantly; but the profits of manufacturers will be reduced significantly; meanwhile, this reduction effect is even more severe for high consumption manufacturers; and it will be resulting in a lower average carbon market price under the carbon tax-carbon trading policies than under the cap and trade policy. This paper will provide theoretical suggestions for introducing carbon tax policy into China in the future and make policy recommendations for the better development of China’s carbon market.


Introduction
In recent years, the issues of climate change have attracted more and more attention in the field of public policy. Meanwhile, the international community is taking various measures to combat the climate change. The United Nations Framework Convention on Climate Change (UNFCCC) holds the United Nations Climate Change Conference every year, and a series of conventions such as Kyoto Protocol and Paris Agreement have been signed. Reduction of carbon dioxide emissions has also become the focus of the world's response to climate change at this stage. EU took the lead in issuing the European Green Deal in 2019, proposing to achieve carbon neutrality in the entire European by 2050; the USA has pledged to reduce its greenhouse gas emissions by 50 to 52% by 2030 compared to 2005, and to achieve carbon neutrality by 2050; in addition, Japan, South Korea, and Canada have announced that they will achieve carbon neutrality by 2050, and the Swedish government has even set 2045 as the target date for achieving carbon neutrality in the country. As to China, the world's largest emitter at the Responsible Editor: Roula Inglesi-Lotz The 3060 goals refer to the Chinese government's proposal that China will strive to achieve its carbon peak by 2030 and its carbon neutrality by 2060.
In this paper, cap-and-trade and carbon trading are the same policy, and they both represent the policy of trading carbon allowances in the carbon market for emission-controlled enterprises under government carbon quota control. Two representations are used in this paper to avoid ambiguity in expressing compound policies. current stage, its president Xi Jinping promised the world that China will strive to reach its carbon peak by 2030 and strive to realize carbon neutrality by 2060 at the general debate of the 75th UN General Assembly on September 22, 2020. China, as a responsible major country, its commitment concerning carbon neutrality also greatly encouraged countries around the world to continue to increase their ambitions to tackle climate change. China has established a national carbon emission trading market on July 16, 2021. The carbon emissions of the first batch of companies covered by the carbon market exceeded 4 billion tons carbon dioxide, resulting in it the carbon market with the largest coverage of greenhouse gas emissions in the world. However, some experts pointed out that due to the access standards of China's carbon market, a full-scale carbon market can only cover 50% of China's carbon emissions (Zhu 2022), while many small-and medium-sized enterprises cannot be included. In 2021, the Central Committee of the Communist Party of China and the State Council issued the Opinions on Completely Accurately Implementing the New Development Concept and Doing a Good Job in Carbon Neutralization, which has clearly proposed to study tax policies related to carbon emission reduction. Therefore, the introduction of carbon tax has also been widely discussed. Whether to introduce carbon tax and how to integrate the carbon tax system with the existing cap and trade system have also become problems.
Regarding the two carbon pricing policies of cap and trade and carbon tax, there has been a great deal of literatures in the academic world to study these two policies separately and compare them; however, few scholars have studied the composite policy of cap and trade and carbon tax. Furthermore, from the composite perspective of research policy, most scholars still separated the departments that implement carbon tax and cap and trade while setting a research compound system, and few studies truly combine carbon tax and cap and trade. In terms of research methodology, most scholars have established mathematical models for research; therefore, it was impossible to study the possible impact of the "bounded rationality" of traders in the carbon market on the results of policy implementation.
Based on the requirement of the society and the existing problems of academic world, this paper attempts to explore the combination of cap and trade and carbon tax; investigates the impact of compound policy on the economy, society, and emission reduction; and suggests a combination of carbon pricing policies which will be suitable for China. This paper uses experimental economics as the research method to study the impact of cap and trade, carbon tax, and carbon tax-carbon trading policies on Enterprises Output Value, Corporate Profits, and Corporate Carbon Emission; analyzes the price of carbon market under carbon trading and carbon tax-carbon trading policies; and finally gives suggestions on the composite carbon pricing policy.
The first part of this paper is the introduction, the second part is the literature review, the third part is the experimental design and experimental process, the fourth part is the statistical indicators and experimental data analysis, and the fifth part is the conclusion and policy recommendations.

Literature review
The use of experimental methods to study environmental economics has become increasingly popular among academics in recent years (Greenstone and Gayer 2009;Jones and Vossler 2014;Li et al. 2022;Stranlund et al. 2014), allowing for both the simulation of arbitrary policies and the full consideration of market and human-related responses.
The carbon tax and cap-and-trade policies are important tools in promoting national energy conservation and emission reduction. For many years, scholars have used various research methods to study these two policies. From the studies of scholars in the existing literature, the theoretical development of cap and trade and carbon tax was roughly as follows: from the initial researches concerning a single policy on cap-and-trade or carbon tax, then developed into comparative studies of the two policies, and recently some scholars also tried to combine the two policies and studied the compound carbon pricing policy. Here we only review the studies that were highly relevant to the theme of this paper, which can be roughly divided into three categories: the first category: separate studies on Cap and Trade and Carbon Tax policies; the second category: comparative studies on Cap and Trade and Carbon Tax policies; the third category: studies on the composite system of Cap and Trade and Carbon Tax.

Separate studies on Cap and Trade and Carbon Tax
Cap and Trade, as a policy aiming at energy conservation and emission reduction, most scholars took its impact on the emission choices of enterprises as one of the indicators of their researches. Murphy and Stranlund used the method of experimental economics to explore the influence of enforcement strategies on the emission behavior of firms in trading plan under quota trading (Murphy and Stranlund 2006), and the results of experiments found that enforcement strategies indirectly affect emissions through their effect on prices, so that stronger enforcement leads to lower carbon emissions. From the perspective of the cap study, Benjaafar et al. (2013) studied the variation of emissions versus total costs under cap-and-trade by developing a specific operations management model, concluding that lowering the emissions cap increases total costs and reduces total emissions and does not significantly increase total costs with a significantly lower emissions cap. Feng et al. (2018) established a CGE model to connect the carbon markets in Guangdong with Hubei and gave corresponding policy recommendation; relatively poor and backward countries or regions should adjust their emission caps upward in order to achieve fair. Cao et al. (2019) studied the optimal policy under the carbon reduction target by establishing the Stackelberg game and analyzed that the government should issue a cap-and-trade policy when the environmental damage factor was greater than a certain threshold and suggested that the government should appropriately increase the optimal cap quota amount when the market trading price of carbon allowances was low. Economic efficiency as a measure of traded market performance has also received extensive scholarly attention: Jiang et al. (2021) introduce the banking and borrowing system (BB) into the tradable license market to study the role played by intertemporal trading in the market between the effects of market power on economic efficiency. Accordingly, in addition to studying the impact of cap and trade on firms' emission choices, the level of low-carbon technology innovation, an important indicator of energy saving and emission reduction, has also been studied by scholars through cap-and-trade. Taking Germany as the research background, Rogge and Hoffmann (2010) conducted interviews with 42 experts in the EU ETS, the power industry, and technology innovation, and empirical analysis concluded that the emission trading system can promote low carbon technology innovation; Yang et al. (2016) concluded from an empirical analysis of interviews with selected Chinese firms that the level of low-carbon technology of Chinese firms was in an inverted U-shape with the firm's activity towards ETS. There was also a wealth of empirical research on the impact of carbon emission reductions on micro firms: H. Zhang et al. (2019) explore the impact of China's carbon emissions trading system on firms' low-carbon technology innovation through an empirical approach, using pilot firms as research subjects. Similarly, Li et al. (2020) studied green innovation and corporate sustainability with energy-intensive industries. The role of emissions reduction policies was explored by examining the impact of leadership and environmental regulation of green transition on employee turnover intentions in energy-intensive firms . Sun et al. (2019) then studied the effect of institutional quality on energy efficiency using a sample of 71 developed and developing countries, and this effect was positive. Edziah et al. (2022) examine the role of exogenous technological factors and renewable energy in CO2 reduction in developing economies in sub-Saharan Africa. In addition to studying the impact of cap and trade policy on the goal of carbon reduction, some scholars have studied the price of allowances in cap-and-trade. Li et al. (2015) innovatively replaced the subject of cap and trade with individuals and studied the downstream cap and trade situation by building a PCT equilibrium model. The equilibrium model results showed that PCT plan could play a buffer role between energy and quota price. There were also studies focusing on the market performance of market traders in different scenarios. Huang et al. (2015) innovatively proposed a hybrid interactive simulation method, which combined experimental economics and agent-based computational economics to explore subjects' trading frequency and volume in different market environments. Some scholars even analyzed the operation of the carbon market by establishing a comprehensive evaluation model. Hu et al. (2017) established a TOPSIS model and used the coefficient of variation method for assigning weights to evaluate the two main indicators of operational performance and maturity of the Beijing carbon market.
Also as a policy aimed at energy conservation and emission reduction, carbon tax has been widely studied by scholars. The level of carbon tax rate has been the research point of most scholars. Zhang et al. (2017) simulated the implementation of carbon tax in China by building a CGE model and found that: high tax rates have a greater negative impact on the economy, and it is recommended to start with low tax rates. From the perspective of the impact of carbon tax policy on the industry, Yenipazarli (2016) developed a Stackelberg game model to study the impact of carbon tax policy on manufacturers and found that the implementation of a carbon tax system could stimulate the potential of the remanufacturing industry. Cao et al. (2020) established a Stackelberg game model to study the optimal production and pricing decisions of two firms in a dual-channel supply chain that simultaneously sells remanufactured products and new products. The results show that the production quantity of new products will decrease under the carbon tax policy, while the increase or decrease of the production quantity of remanufactured products depends on the carbon intensity of the remanufactured products; Mishra et al. (2021) developed a sustainable EOQ model to study the impact of carbon taxes on greenhouse farms and showed that carbon taxes can lead to an increase in total profits. Regarding firms' preferences for carbon tax policies, Liu et al. (2015) interviewed energy or environmental managers of several companies through an experimental questionnaire and showed that tax rates were negatively related to firms' policy choice preferences and tax breaks were positively related to firms' choice preferences.

Comparative studies of Cap-and-Trade and Carbon Tax policies
The main indicator of emission reductions was often used by scholars as a criterion to compare Carbon Tax policy with Cap-and-Trade, and there were differences in scholars' views on this in existing studies. Some scholars believed that the emission reduction from carbon trading policy was more deterministic; Zakeri et al. (2015) established an analytical supply chain planning model to study the carbon emissions of supply chain manufacturers and found that the overall carbon emission reduction of the society was linearly decreasing under the carbon trading system. In contrast, under the carbon tax policy, the overall carbon emission reduction of society was non-linearly decreasing, and it means that the carbon emission reduction of society was more deterministic under the cap-and-trade system; some scholars also argued that the emission reductions from cap-and-trade and carbon tax depended on external environmental factors. Xu et al. (2016) built a Stackelberg game to study the joint production and pricing problem, and found that the environmental damage factor changed while the carbon tax and carbon trading regimed. There was no condition that one regulatory regime was better than the other in terms of emission reductions. He et al. (2015) developed an EOQ model to study the optimal production and corresponding carbon emissions of firms under the regulation of cap-and-trade and carbon tax, and the results showed that the carbon emissions of firms depended not only on the parameters of the regulation (license price, tax rate) but also on the internal production capacity of firms. In addition to the comparison from the perspective of emission reduction, some scholars have gone deeper into it and studied the efficiency of emission reduction. Jia and Lin (2020), by building the China Environmental-Energy-Economy Analysis (CEEEA) model, studied the impact of carbon trading and carbon tax on social economics and emission reduction, and concluded that under the same GDP impact, carbon tax has higher emission reduction efficiency, which meant lower emission reduction cost. Similarly, low-carbon technology innovation, as another important indicator to measure the effectiveness of low-carbon policies, has also been widely studied by scholars. Chen et al. (2020) established a static optimal model to study the comparison of Cap-and-Trade and Carbon Tax. Compared with carbon tax, carbon trading could promote enterprises to reduce carbon emissions and innovate low-carbon technologies; regarding social welfares, Xu et al. (2016) argued from the results of the stackelberg game established that the social welfare of carbon tax was higher than that of the carbon trading system in most cases. Some scholars even studied the policy effects of Cap-and-trade and Carbon Tax by examining the indicators of cost and efficiency. Mohammed et al. (2017) established a closed-loop supply chain to study the total cost and carbon emissions within the supply chain, and found that under the implementation of carbon tax, the total cost was insensitive to the emission reduction target, and Capand-Trade policy was the most flexible and efficient. Some existing studies have argued that carbon trading can generate higher profits for manufacturers compared to carbon taxes. Drake et al. (2016) studied the impact of cap-and-trade and carbon tax on firms' capacity mix and production decisions, and concluded that under cap-and-trade, due to the uncertainty of emission rights price, it can lead to greater expected profits for the firm. Cao et al. (2019) established ETS and hybrid systems (ETS-CT), and compared the social welfare, industry price level, and other indicators under the two policies, and concluded that under hybrid systems, carbon prices would be lower. Mandell (2008) developed a hybrid system model of a carbon tax-carbon trading system that taxed carbon emissions of the fully mixed pollutant and imposed cap-and-trade for the remaining emitters, and showed that the size of the sector subject to the carbon tax increased with the relative steepness of the total marginal abatement cost function.

Studies on the composite policy of Carbon Trading and Carbon Tax
From the existing literature, we can see that scholars have done detailed research on the single and comparative study of Carbon Tax and Cap-and-Trade, but few scholars have studied the combination policy of Cap-and-Trade and Carbon Tax. We believe that the following research points and issues still exist in the field of Cap-and-Trade and Carbon Tax system: (1) The composite policy of Cap-and-Trade and Carbon Tax should be studied in depth, including considering the way of combining the two policies and the impact of different combinations on social economic, carbon emission reduction, manufacturers' profit and other indicators.
(2) In the existing literature on the hybrid system of Capand-Trade and Carbon Tax, few scholars have studied whether enterprises that have participated in Cap-and-Trade should be included in the scope of Carbon Tax, so this issue is also a point worth studying. (3) Since there are few examples of countries implementing policies that combine the carbon tax with cap-andtrade, so that concerning data are difficult to obtain. There is an existing problem that empirical methods are more difficult to conduct in-depth studies. (4) In order to explore the market effects, that is the performance behavior of market subjects, of the new composite carbon trading and carbon tax regime, traditional modeling approaches are difficult to achieve because humans have limited rationality and it is difficult to truly measure market participants' attitudes toward the new regime and their own behavioral performance through mathematical models (Huang et al. 2015).
Compared with existing articles, the academic contributions and innovations of this paper are as follows: (1) This paper innovatively combines Carbon Tax and Capand-Trade, and investigates the situation of manufacturers' output value, carbon emission and manufacturers' profit under Cap-and-Trade, Carbon Tax and Carbon Tax-Carbon Trading to enrich the existing research situation.
(2) This paper takes high-emission enterprises included in the scope of Cap-and-Trade as the research objects, and explores whether enterprises in the scope of Cap-and-Trade need to levy carbon tax, solving the problem of whether carbon tax needs to be levied on enterprises already included in Cap-and-Trade under the simultaneous implementation of Carbon Tax and Cap-and-Trade policy, making the relevant researches more rigorous. (3) This paper adopts an experimental economics approach to study the performance of market subjects under different policies, since experiment data have limited human rationality, so that it solves the difficulty of measuring human behavior that exists in traditional mathematical models. Meanwhile, this paper solves the problem of missing data volume that exists if the empirical research method is used, enriching the research in this field.

Overview of experiment
Through the method of experimental economics, this paper simulates the production decision-making and carbon market environment of manufacturers, and studies the market situation under the carbon trading, carbon tax, and carbon tax-carbon trading composite policies. Since the carbon market trading system and environment settings are completely in line with the characteristics of the real market, so that the behavioral psychology of traders is also similar to reality, which is convenient for researchers to simulate different carbon reduction policies by controlling variables, and analyze their impact on the real society. The experiment this paper designed has 4 rounds, each round has 10 times, and lasts about 1.5 h. The participants participate in the experiment through the experimental economics software Zleaf (Fischbacher 2007). The experimental design and experimental process will be introduced in detail below.

Design of experiment
This experiment mainly draws on the experimental design ideas of Murphy and Stranlund (2006) and Holt and Shobe (2016). The purpose of the experiment is to explore the performance of manufacturers under different carbon reduction policies in the market. The experiment is divided into 4 rounds, including a control group and three experimental groups. The control group is not set any carbon reduction policies. Other three experimental groups correspond to different carbon reduction policies, including carbon trading, carbon tax, and carbon tax-carbon trading composite policies. Except for the different carbon reduction policies (see Table 1), the other settings of each experimental group are exactly the same. In this experiment, 18 students were recruited to participate in the economics laboratory of the Zhuhai campus of Jinan University (Table 2) . Before the formal experiment, a preparatory experiment has been organized with the aim of exploring the rationality of some of the experimental parameters through the behavior of the subjects in the preexperiment. The 18 subjects in each round of the experiment each represents a manufacturer that participating in Cap-and-Trade and production decisions in a simulated market. Each round of the experiment includes low consumption manufacturers and high consumption manufacturers, with the former consuming 1 unit of carbon quota for each product produced and the latter consuming 2 units of carbon quota for each unit of product produced. Under the carbon trading, carbon tax-carbon trading, only with a sufficient amount of carbon quota can manufacturers produce the corresponding number of products.
Referring to the setup of the product cost in Wei et al. (2018), the marginal cost of manufacturers in each round Table 1 Differences between the control group and the experimental groups

Group
Carbon reduction policy Experimental design

Control Group
There is no carbon reduction policy, and manufacturers are free to produce within the allowed range Experimental Group I Cap-and-trade Manufacturers must have carbon allowances to produce, and they can trade carbon allowances in the carbon market Experimental Group II Carbon tax Manufacturers are free to produce within their means, but pay carbon tax on the carbon generated by the products they produce Experimental Group III Carbon trading and carbon tax Manufacturers must have carbon allowances to produce, and they can trade carbon allowances in the carbon market and pay carbon tax on the carbon generated by producing their products is randomly generated by the computer, and the marginal cost of high-consumption manufacturers is [0,30] and the marginal cost of low-consumption manufacturers is [10,30], and the manufacturers can produce up to 12 products in each round, and the production cost of manufacturers in this experiment is marginal increasing. The manufacturers in the experiment should consider the production cost, quota purchase cost, and carbon tax for decision making.
The market price of the product in the experiment is 30 units of experimental currency, and it is assumed that all products produced by the manufacturers are sold.
For the setting of the carbon tax rate, we searched for the carbon tax rate of several major countries that have implemented carbon taxes when we studied. The carbon tax rate in Sweden is US$137/tCO 2 , in Spain US$16/tCO 2 , in Portugal US$26/tCO 2 , and in Chile US$5/tCO 2 . (Data from World Bank) 1 Since carbon tax is a quantitative tax, the rate is calculated per unit of carbon dioxide. Therefore, the carbon tax rate varies from country to country and is not applicable to the setting of carbon tax rate in this paper. Regarding the setting of carbon tax rate in China, Ni (2016) proposed that the carbon tax rate should start from low. We prepared through the test of the pre-experiment and determined that 5 experimental currency/unit of carbon quota is the carbon tax rate in this experiment, which is consistent with the condition of starting a low carbon tax rate.
In this experiment, the interface is compiled with Ztree (Fischbacher 2007) software, and the experimental page is designed with reference to the interface design of the national carbon emission trading market. The subjects made simulated business activities such as carbon quota purchase and sale, production decisions, etc. in response to external shocks such as carbon quota price changes and carbon reduction policy changes, and earned experimental coins. Eventually, they obtained experimental incentive rewards according to the exchange of 30 experimental currency for 1 RMB. The total time spent for all the experiments was about 1.5 h, and the student subjects got an average of 50 RMB in reward income.

Research hypothesis
Hypothesis 1 Imposing carbon tax on manufacturers already included in cap-and-trade may have a relatively small impact on the reduction of carbon emissions, or the impact on carbon emissions is not statistically significant. Meanwhile, the impact on corporate output value should be the same.
The implementation of the cap-and-trade policy has made clear limits on the carbon emissions of manufacturers, and the imposition of a carbon tax on top of this. From the perspective of manufacturers, the production costs of products increase, and manufacturers may be interested in reducing the production of products from the consideration of profits. The carbon tax policy may also have an impact on the production of enterprises, that is, their carbon emissions.
Hypothesis 2 Imposing carbon tax on manufacturers already included in cap-and-trade may have a relatively large impact on their profits. Meanwhile, the carbon tax may have different effects on the profits of different types of manufacturers.

Hypothesis 3
The imposition of a carbon tax on manufacturers already included in cap-and-trade may have an impact on the carbon trading market, which may be negative.
The imposition of a carbon tax policy on manufacturers already included in the cap-and-trade may make the expected price of carbon allowances lower for manufacturers; and also may reduce the demand for production of their products, which in turn may affect the activity of the trade and the amount of expected transactions.

Procedure of experiment
Before the experiment begins, the trading system will match each subject with a manufacturer role, including high and low consumption manufacturers. Then, subjects enter the formal experimental session, and there are slightly different experimental processes in the four experiments.
(1) Control group: This experiment simulates a free market with no policy constraint. Since there is no policy constraint, the manufacturers can make production decisions based on the marginal cost of production to maximize the profit of the firm as long as the conditions allow. Subjects enter the output of the decision in the experimental interface by observing the marginal cost of production in each round of the experiment. Each round lasts 30 s for a total of 10 rounds.   Treatment 1  Treatment 2   E1  CAT-NCT-H  CAT-NCT-L  E2  NCAT-CT-H  NCAT-CT-L  E3 CAT-CT-H CAT-CT-L market. Experimental group I contains two processes: subjects first conduct carbon trading to obtain the required carbon quota, and then make production decisions. Due to the existence of Cap-and-Trade policy, companies can act as traders in the market for quota trading activities, and traders can act as both sellers and buyers for quotations. In this experiment, the subjects are able to enter quotations via the keyboard and have access to real-time dynamic quotation and trading information on the trading market in the trading interface for 180 s. After the carbon trading process, the subjects make a production decision by entering the output of the decision in the experiment interface, and this process lasts for 30 s. Each round of the experiment lasts 210 s, and a total of 10 rounds are conducted.
(3) Experimental group II: This experiment simulates the implementation of Carbon Tax policy. Due to the Carbon Tax policy, manufacturers should consider not only the marginal cost of production but also the carbon tax cost incurred by production when making decisions. Subjects input the production volume for decision in the experiment interface, and each round of experiment lasts 30 s, and a total of 10 times are conducted. (4) Experimental group III: This experiment simulates imposing carbon tax on manufacturers included in the scope of Cap-and-Trade. Experimental Group III contains two processes, similar to Experimental Group I. Subjects first conduct carbon trading to obtain the required carbon quotas, and this process lasts 180 s; then the production decision stage is conducted, and due to the existence of carbon tax policy, in the production decision process, subjects not only have to consider the marginal cost of production, but also the carbon tax cost to be paid, and this process lasts 30 s. The carbon trading phase in this experiment is consistent with Experimental Group I. Each round of experiment lasts 210 s, and a total of 10 times are conducted (Figs. 1 and 2).

Initial endowment
(1) Control group: At the beginning of each round of experiment, subjects will be given a manufacturer role and will be informed of the marginal cost of each product produce in the experimental software interface, with the marginal cost of [0, 30] for high consumption manufacturers and the marginal cost of [10,30] for low consumption manufacturers, with the increasing marginal cost of production.
(2) Experimental group I: At the beginning of each round of experiment, subjects will be given a manufacturer role and will be informed of the marginal cost of each product in the experimental software interface, the initial carbon quotas owned by the manufacturers. High consumption manufacturers own 12 carbon quotas initially, and the low consumption manufacturers own 6 carbon quotas initially. The system will also give the subjects initial assets that can be used to make a trading bid in the carbon market. Since the manufacturers' initial assets are not the research point of this paper and after pre-experiments, the starting assets range is set to [350,370], which is enough for the subjects to make a trading bid in the market, making this variable not affect the findings of this experiment.
(3) Experimental group II: At the beginning of each round of experiment, the subjects will be given a manufacturer role and will be informed of the marginal cost of each product and the carbon tax required for each product in the interface of the experiment software. (4) Experimental group III: At the beginning of each round of experiment, the subject will be given a manufacturer role and will be informed of the marginal cost of each product, the initial carbon allowance owned by the manufacturers, and the carbon tax required to be paid for each product in the experiment software interface.

Statistical indicators and analysis of experimental data
During the experiments, the Ztree trading system will automatically record and save the data. For further analysis, this paper chose enterprises output value, enterprises carbon emissions, enterprises profit, and market transaction price to compare different carbon reduction policies.

Enterprises output value
The sum of the output value of all enterprises in the market can measure GDP, so this paper study the impact of different carbon reduction policies on GDP by studying the changes in enterprises output value. The calculation method of enterprises output value is: where PV it refers to the output value of the i-th manufacturers in the t-th round of experiments, n it refers to the i-th manufacturers' output in the t-th round of experiments, and P in this experiment is 30 experimental currency/unit of product.

Carbon emission
Carbon emission is the carbon dioxide produced by the enterprises in the production. In this paper, the high consumption manufacturer produces 2 units of carbon doxide per unit of product, and the low consumption manufacturer produces 1 unit of carbon dioxide per unit of product. The calculation method of enterprises carbon emissions is as follows: (1) PV it = p * n it where CE it refers to the carbon emissions of the i-th firm in the t-th round of the experiments, and PCE it refers to the carbon emissions per unit product produced by the i-th enterprise in the t-th round of the experiments.

Enterprises profit
In this paper, in addition to the manufacturers' output value and production cost, the calculation of enterprises profit should also consider the income and expenditure of enterprises in carbon market in the experimental group I, the cost of carbon tax in the experimental group II, the transaction income and expenditure of enterprises in carbon market and carbon tax in the experimental group III.
where C it refers to the production cost of the product of the i-th manufacturers in the t-th round of the experiment, E it refers to the expenditure cost of the i-th enterprise in purchasing carbon allowances in the carbon market in the t-th round of the experiment, and I it refers to the income of the ith enterprise in selling carbon allowances in the carbon market in the tth round of the experiment. CT it represents the amount of carbon tax for the i-th firm in the t-th round of the experiment. Table 3 summarizes all the parameters and variables that appear in this paper and their assignments and meanings.

Experimental data analysis and conclusion
Tables 4, 5, 6, and 7 summarize all relevant statistical data of the experiments. We collected the data of high-consumption manufacturers and low-consumption manufacturers of the The i-th enterprises product output in the t-th round of experiments N/A

CE it
The carbon emissions of the i-th firm in the t-th round of the experiments N/A profit it The profit of the i-th firm in the t-th round of the experiment N/A C it Production cost of the product of the i-th enterprise in the t-th round of the experiment N/A

E it
The expenditure cost of the i-th enterprise in purchasing carbon allowances in the carbon market in the t-th round of the experiment N/A

I it
The income of the ith enterprise in selling carbon allowances in the carbon market in the tth round of the experiment N/A

CT it
The amount of carbon tax for the i-th firm in the t-th round of the experiment N/A three experimental groups and the trading data of the carbon market. The following four tables show the average, quantity, median, maximum, minimum, and variance of carbon emissions, output value, profits, and market transaction prices. We conducted Wilcoxon signed-rank test on three indicators: manufactures' output value, carbon emission, and profit, and the results are shown in Table 8.

Conclusion 1
Since the fact that the carbon emissions of manufacturers in Experimental Group I and Experimental Group III in Table 8 are significantly smaller than those in Experimental Group II, it is clear that the state's carbon emission control on manufactures under Cap-and-Trade has more certainty compared to the Carbon Tax policy. This is because under the carbon tax policy, once manufactures determine the boundary of marginal profit equal to zero, they can produce products within this boundary to maximize their own profit, and this feature is more obvious when the carbon tax rate is lower. But it is undeniable that Carbon Tax policy does have a role in regulating carbon emissions, see Table 8 A > C (0.0000 *** ), and carbon tax raises the cost of production by raising the cost of carbon emissions for manufacturers.
In addition to conducting non-parametric tests, this paper refers to Li et al. (2022)'s regression analysis of laboratory data for the main study site of this paper, data from Experimental Group I and Experimental Group III, using the following ordinary least squares regression and random effects to provide regression evidence.
Equation (4) is the baseline regression model that investigates whether the introduction of carbon tax will have an (4)  impact on the relevant activities of firms already covered by carbon trading. For further study, this paper makes heterogeneity analysis on the experimental data and investigates whether the introduction of carbon tax will have different effects on different types of manufacturers (high consumption/low consumption manufacturers) already included in the scope of cap-and-trade by constructing the cross term Type it * CT , see Eq. (5) The variable Type it is a dummy variable represents the type of manufacturers, with 1 representing the high-consumption manufacturers and 0 representing the low-consumption manufacturers. Similarly, the variable CT is also a dummy variable represents the implementation of the carbon tax policy, with a value of 1 representing the implementation of the carbon tax and a value of 0 representing the non-implementation of the carbon tax. That is, when the carbon tax is implemented on a cap-andtrade basis for high-consumption manufacturers, all variables take the value of 1. The variable Type it * CT is an interaction term that captures the difference in the impact of the carbon tax policy between high and low consumption manufacturers.
The dependent variable y it can represent both the carbon emissions of a manufacturer and the output value of a manufacturer as well as the profit of a manufacturer. When y it represents carbon emissions over time, the subscript i indexes the subject, and t indexes the period. There are a total of 360 observations when we group the carbon emissions by period and manufacturer type. This is also the case when y it represents other variables.

Conclusion 2
Implementing carbon tax on manufacturers that are already covered by Cap-and-Trade will not significantly reduce their carbon emissions and output value, whether they are high-consumption manufacturers or low-consumption manufacturers.
From Table 8, we can see that the differences in carbon emissions (p = 0.3457) and enterprise output value (p = 0.7356) of Experimental Group I and Experimental Group III are not significant, and this result is consistent with Hypothesis 1. From the regression results  (1) and (3) in Table 10 report a statistically significant coefficient of 4.36 before the variable Type it , which indicates an increase in carbon emissions of 4.36 units for high consumption manufacturers. Meanwhile, the coefficient of the variable CT is not statistically significant, which indicates that the introduction of a carbon tax or not has no significant effect on the carbon emissions of manufacturers already included in cap-and-trade.
Similarly, in Table 9, the impact of the introduction of the carbon tax on the output value of manufacturers already included in the cap-and-trade is reported in columns (1) and (3) for the OLS and random effects models respectively. In both regression models, the variable Type it is − 34 and significant, which indicates that high consumption manufacturers will reduce their output by 34 units.The variable CT is insignificant in both the OLS and random effects models, indicating that the introduction of the carbon tax has no significant effect on the manufacturers already included in the cap-and-trade.
Columns (2) and (4) of Tables 9 and 10 are the further study done in this paper, by adding the cross term Type it * CT , it is found that the variable Type it remains significant, while the variable CT is insignificant both before and after adding the cross term. It shows that in the CT treatment, the difference between high consumption manufacturers and low consumption manufacturers is not significant. In this paper, we refer to the interpretation method in Zhi Li et al.'s (2022) paper in the interpretation of the heterogeneity results.
The carbon tax on manufacturers that have been included in the cap-and-trade does not play a significant role in the impact of manufacturers' carbon emissions and output value; and according to the box line diagram on carbon emissions and output value (see Fig. 4), we can see that there is no significant change in the overall output value and carbon emission data for Experimental Group I and Experimental Group III, and the median is basically the same, which is also consistent from the case of the distribution of the mean value of carbon emission and enterprise output value as reflected in the image Fig. 3 that has been drawn. The comparison of carbon emissions and enterprise output value between Experiment Group I and Experiment Group III by the above four qualitative and quantitative methods proves that it is not a right choice to impose carbon tax on manufactures that have been included in the cap-and-trade, and this method cannot significantly affect the carbon emissions of manufactures.

Conclusion 3
Implementing carbon tax on manufactures already covered by cap-and-trade would significantly reduce their profits, and this impact is more severe for high consumption manufacturers. From Table 8, we can see that the profits of enterprises in Experimental Group I are significantly larger than those in Experimental Group III (p = 0.0000), which is basically consistent with Hypothesis 2. From the columns (1) and (3) of Table 11, the coefficients of variable CT in Table 11 are significantly negative (p < 0.01) in OLS and random effect model, this shows that when the carbon tax is introduced it reduces the profit of the manufacturer included in the scope of cap-and-trade by 46.19 units. The coefficient of the variable Type it is 27.74 and statistically significant, which suggests that the high consumption manufacturers have 27.74 units more profit relative to the low consumption manufacturers (Table 11).
Columns (2) and (4) of Table 11 are further analyses of the experimental data in this paper, and the interaction term Type it * CT is − 40.23 and statistically significant (p < 0.01), which indicates that the reduction is significantly greater for high consumption manufacturers than for low consumption manufacturers under the carbon tax treatment.
As we can see in Fig. 4, the experimental data on profits for Experimental Group I are overall significantly larger than those for Experimental Group III, as also shown by the position of the median. Similarly, for Fig. 3, we can see that after the implementation of the carbon tax, the average profit of Experimental Group III is reduced compared to Experimental Group I, by approximately 49.17% for high consumption manufacturers and 29.98% for low consumption manufacturers. From the analysis Table 8 Wilcoxon signed-rank test under different policies * , **, *** indicate significant at the 10%, 5%, and 1% levels respectively. The greater than or less than signs in the table indicate the alternative hypothesis (H1) tested between different experimental groups, and the values in parentheses are the p-values of Wilcoxon signed-rank test   (1) and (2) are based on OLS regressions and (3) and (4) are based on random effects models. *p < 0.10, **p < 0.05, ***p < 0.01 (1)   (3) and (4) are based on random effects models. *p < 0.10, **p < 0.05, ***p < 0.01 (1)  . 3 Bar graph of the average values of carbon emissions, output value, and profits grouped by manufacturer type and experimental groups. The number above the bar in the bar graph represents the mean of the experimental data for that variable  (1) and (2) are based on OLS regressions and (3) and (4) are based on random effects models. *p < 0.10, **p < 0.05, ***p < 0.01 (1)  of the profit data of Experiment Group I and Experiment III by the above four methods that include qualitative and quantitative approaches, it is clear that the implementation of carbon tax on enterprises that have been included in carbon trading will significantly reduce the profits of enterprises.
In the case that cap-and-trade and carbon tax are implemented at the same time, manufacturers can only produce at most the quantity of products corresponding to the carbon quota they have, and beyond that, the imposition of carbon tax will have little impact on enterprises carbon emission, especially if the carbon tax rate is low. Compared to the cap-and-trade policy, the implementation of the composite policy of carbon tax and carbon trading does not play a significant role in reducing the carbon emissions of manufacturers, but creates a higher cost pressure on manufacturers, leading to a significant reduction in their profits, which may affect their ability to produce and innovate lowcarbon technologies.

Conclusion 4
While making manufacturers emit less carbon, it must be at the cost of losing enterprises output value.
From Table 8, the enterprises output value of Control Group is significantly larger than that of Experimental Group I, Experimental Group II and Experimental Group III, and the manufacturers' output value of Experimental Group II is significantly larger than that of Experimental Group I and Experimental Group III. The results show that when a manufacturer's carbon emissions decrease, the manufacturer's output also decreases.
This paper conducts the Mann-Whitney test on the transaction price of carbon quotas in the carbon market in Experimental Group I and Experimental Group III, and plots the average price of market transactions in each round of Experimental Group I and Experimental Group III (see Fig. 5).

Conclusion 5
The price of carbon quota in the market under the cap-andtrade policy is significantly higher than the price in the market under the composite policy of carbon tax and carbon trading policy.
From both Fig. 5 and Table 12, we can clearly see that the price of carbon quotas in Experimental Group I is significantly larger than the price of carbon quotas in Experimental Group III. From Fig. 6, a box plot is drawn for the trading price data of Experiment Group I and Experiment Group III, and we can clearly see that the data distribution of Experiment Group III is significantly lower than that of Experiment Group I, and the same is true for the position of the median. From Fig. 7, we can see that after the implementation of the carbon tax policy, the trading price in the market is reduced by about 49.98% on average. This result indicates that the implementation of the carbon tax policy leads to a significant reduction in the price of allowances in the carbon trading market. From the analysis of the market trading data in Fig. 8, the overall trading volume of Experimental Group I and Experimental Group III is roughly the same, and there will be a slight difference between them. In order to further investigate the impact of the introduction of carbon tax policy on the carbon market trading volume and traders' enthusiasm for trading, this paper does a Wilcoxon signed-rank test on the market trading volume data of Experiment Group I and Experiment Group III. See Table 13, we can also conclude that the introduction of carbon tax has no significant (p = 0.6831) impact on the activity of the carbon trading market. Under the composite policy of carbon trading and carbon tax policy, the price of carbon quota is lower compared to the price under the cap-and-trade policy. The result may be caused by the increased pressure of production costs on manufacturers, their lack of confidence in entering carbon trading market, and their lower expected price of carbon quotas. Regarding price of carbon quotas, Lili Wei and Ren (2021) concluded through empirical analysis that carbon price has a significant promotion effect on enterprises' green innovation technology. It is said that the higher the carbon price, the more it can promote enterprises' green technology innovation. Therefore, under the composite policy of carbon trading and carbon tax, it is difficult for a low carbon price to effectively promote enterprises' green technology innovation.

Summary and policy recommendations
Through the method of experimental economics, this paper explores the impact of different carbon reduction policies on the production of manufacturers and the carbon market, and analyzes the impact of indicators consisting of enterprises carbon emissions, enterprises output value, enterprises profits, and quota trading price in carbon market under different carbon reduction policies. The conclusion is that the cap-andtrade policy is more predictable and certain for the realization of carbon reduction goals, and requires the enterprises to bear the lower additional production cost, and the carbon taxcarbon trading policy imposes the carbon tax on the enterprises which has been already included in the scope of capand-trade, the impact on manufacturers' carbon emissions is very limited, meanwhile, it significantly reduce enterprises profits and lower the price of carbon quotas, thus potentially reducing the ability of firms to innovate in green technology.    On March 15, 2022, the Carbon Border Adjustment Mechanism (CBAM), also known as the EU carbon tariff, was preliminarily adopted by the Council of the European Union and was scheduled to come into force on January 1, 2023, with a three-year transition period. At the same time, experts and government officials from all walks of life have strongly debated the introduction of a carbon tax policy in order to control small and medium-sized carbon emissions enterprise in China. Once again, the hot spot topic of carbon tax has been widely discussed, and it is worthwhile for experts and scholars from social circles to study how to introduce carbon tax, how to regulate the relationship with cap-and-trade and carbon tax, and whether carbon tax should be levied on enterprises that have already implemented cap-and-trade. In this paper, we study the comparison between cap-and-trade and carbon tax, the combination of cap-and-trade and carbon tax, and put forward the following policy recommendations: (1) Actively promote the cap-and-trade policy and integrate more enterprises in high-emission industries into the cap and trade. So far, China's national carbon emissions trading market has only included the power generation industry. In the future, more high carbon emission industries should be included, such as petrochemical, chemical, building materials, iron and steel, non-ferrous, paper making, and aviation industries, so that the lager scope of emission control will be more conducive to the realization of China's "3060 targets." The government should actively promote the layout of enterprise carbon asset management, do a good job of training on enterprise carbon asset management, and encourage enterprises to join carbon trading.
(2) Reasonably set the lower limit of the carbon price and appropriately raise the market carbon price. The carbon price means the cost of emission reduction, and the increase of carbon price also means the increase in social carbon emission reduction cost, which can promote enterprises to carry out low-carbon technology innovation to a certain extent and solve China's carbon emission problems from the root, instead of just limiting production and losing GDP as the price to reach China's carbon peaking and carbon-neutral goals. According to the ClientEarth's China Carbon Price Survey Report 2021 on China's national carbon emission trading system, the carbon price in 2021 was close to 50 yuan per ton, which was far from the carbon price in Canada and the EU, so China should set a reasonable lower limit for the carbon price to make the carbon quotas price steadily increase. (3) The implementation departments of carbon tax and carbon trading should not be highly overlapped, and carbon tax should not be levied or given preferential carbon tax reduction or exemption for enterprises that have implemented carbon trading or carbon emissions that have been included in cap-and-trade. As indicated in the results of this paper: it is difficult to influence the carbon emissions of enterprises that have already been included in capand-trade, but it will significantly reduce the profits of enterprises and carbon prices in the market, which may further affect their ability to innovate in low-carbon technologies. Therefore, when considering the introduction of carbon tax and its combination with cap-and-trade, China should be careful to avoid overlapping with the emission control objectives of those already included in cap-andtrade, which is also consistent with Smith (2008). (4) For enterprises or projects with low emissions and difficult to enter the scope of cap-and-trade, the carbon tax can be considered. And because of the uncertainty of the effect of carbon tax policies on corporate carbon emission limits, the government may also consider combining carbon emission limits with carbon taxes. Levying carbon tax on small-and medium-sized enterprises is a measure for government to supervise enterprises' energy saving and emission reduction and to urge enterprises to carry out green technology innovation. The results of this paper show that with a low carbon tax rate, carbon tax on enterprises can reduce their carbon emissions, but it will lead to a loss of production value and profits. For the carbon tax, it is suggested that China should set up a carbon fund to help enterprises to carry out low-carbon technology innovation or return it to the enterprises with good emission reduction effect in the form of energy subsidies. Zhang et al. (2017) et al. believe that the joint implementation of energy subsidies and carbon tax can improve performance, so we suggest that the carbon tax should be used to promote enterprises to carry out green technology innovation. (5) Under the carbon tax policy, the carbon tax rate should be changed in time based on the marginal abatement cost to society. Haites (2018)studied the policy of cap-and-trade and carbon tax in jurisdictions and found that most of the tax rates are low and few jurisdictions adjust the tax rates regularly. In this paper, we use most scholars' suggestion of a low start in setting the carbon tax rate, so the emission control effect on enterprises carbon emissions is weaker than that of cap-and-trade. We suggest that the government can adjust the carbon tax rate based on the change in social carbon emission reduction cost and the change of carbon quotas' price in the carbon market, to achieve the expected emission reduction target. (6) Improve the preferential tax policies related to green investment, and encourage the society to make the green investment. Shen et al. (2021) believed that green investment can suppress carbon emissions. This paper studies the policy to restrict enterprises to reduce production and emission reduction. However, to truly achieve the "3060 goals," China should start by upgrading green and low-carbon technologies, to achieve the goal of carbon reduction while driving sustainable and stable economic growth.
Author contribution The author, Hanting Wang, was responsible for Ztree experimental programming, experimental data analysis, and paper writing. And the author Yuxuan Li was responsible for organizing the experiments, graphing, writing the introduction of the paper, and searching for relevant data. Author Bu Guoqin was responsible for the formulation of the thesis topic, the revision of this paper, and the guidance of the thesis writing.
Funding This work was supported by "2022 Guangdong University Student Innovation and Entrepreneurship Training Program" (S202210559156) and "Special Funds for the Cultivation of Guangdong College Students' Scientific and Technological Innovation. ("Climbing Program" Special Funds.)"(pdjh2023b0069).

Data availability
The authors declare that the data related to the experiments in this paper are available to the journal or to the readers upon request.

Declarations
Ethical approval The authors declare that all subjects who participated in the experiment were informed and volunteered to participate in the experiment and were eventually paid for the experiment, which was approved by the Dean of International Business School of Jinan University. The ethical and moral issues related to this experiment are not related to the journal, and the authors and their organization assume the ethical and moral responsibility.
Consent to participate Not applicable.

Consent for publication
The authors declare that all authors of this article have given their knowledge and consent to the publication of the paper.

Competing interests
The authors declare no competing interests.