How Does the Digital Economy Empower Green Development? From the Perspective of the Division of Labor in New Classical Economics

: The rise of the digital economy provides an alternative path for global green development. On the basis of analyzing the connotations of green development, digital economy and division of labor, this paper studies the theoretical mechanisms of the digital economy empowering green development; this is based on the division of labor thought of as the new classical economics. From the research results, it can be seen that the digital economy, through technological change, is conducive to the improvement of transaction efﬁciency and the evolution of the division of labor model. Under the dual role of the government’s green system and the market regulation mechanism, it promotes the transaction from the “black division of labor” mode to the “green division of labor” mode, thereby empowering green development. The impact of the digital economy on the level of green development is not single linear. This paper creatively analyzes the theoretical mechanisms of the digital economy empowering green development, from the perspective of the division of labor. These research results have good theoretical value and practical signiﬁcance for promoting the sustainable development of the global economy.


Introduction
In recent years, energy shortage and environmental pollution have become some of the focuses of the world [1]. Changing the traditional mode of economic growth with high energy consumption and high pollution, to a low-carbon economy marked by low energy consumption and low emissions for achieving sustainable development, is becoming the common choice for economic development for most countries in the world [2]. By the end of last year, more than 130 countries around the world had put forward the "zero carbon" or "carbon neutral" climate goal, and green development under the carbon neutral goal has become the consensus of most countries in the world [3]. At the same time, the digital economy, as one of the most active fields in the world, has developed rapidly and has become a new driving force of economic growth in recent years [4]. According to the data from the 2021 Global Digital Economy Conference, the total scale of the digital economy of 47 countries in the world will reach 32.6 trillion US dollars in 2020, with a nominal year-on-year growth of 3.0%, accounting for 43.7% of GDP [5]. The rapid rise of the digital economy has opened up a new way for global green development. The digital economy has penetrated into all aspects of the economy and society, and is deeply integrated with production and living activities, to promote the formation of green lowcarbon consumption concept, production mode and consumption mode [6,7]. So, from the perspective of economic theory, will the digital economy influence green development? How does the digital economy empower green development?
As a new economic form, the digital economy is becoming the commanding height of a new round of global industrial competition. However, traditional economic theories, such as classical economics and neoclassical economics, lack the power to explain the major social changes caused by the digital economy [8]. Therefore, this paper is different from the previous studies. Based on the division of labor thought of as the new classical economic theory, this paper creatively analyzes the theoretical mechanisms of the digital economy empowering green development, from the perspective of the division of labor; this has good theoretical value and practical significance for promoting the sustainable development of the global economy.
The rest of this study is arranged as follows. In Section 2, a literature review is provided. In Section 3, the connotations of green development, digital economy and division of labor are defined. In Section 4, the theoretical logic of the digital economy empowering green development, from the perspective of the division of labor, is proposed. In Section 5, the research on the mechanism of the digital economy empowering green development from the perspective of division labor, is discussed. In Section 6, the results, discussion and analysis are presented. In Section 7, the conclusions are laid out.

Literature Review
Both green development and the digital economy are related to economic transformation and development. In recent decades, global economic growth is mainly at the cost of a large consumption of natural resources, and carbon emissions, leading to the rise in the price of natural resources and the deterioration of the ecological environment [9]. Restricted by the natural resources and ecological environment, the main economic growth mode of the world is changing, from extensive economy to intensive economy, from unsustainable economy to sustainable economy, and from high carbon economy to low carbon economy [10,11]. Green development can be understood as sustainable development, green transformation, a low-carbon economy, and green growth [12]. The relevant literature on green development mainly concentrates on the influencing factors of green development and the measurement of green development level or efficiency. The influencing factors of green development mainly include financial agglomeration [13,14], industrial structure [15,16], technological innovation [17], opening degree [18,19], environmental regulation [20][21][22], urbanization [23][24][25], etc. The measurement of green development level or efficiency mainly includes the comprehensive index evaluation method [12,26,27] and the efficiency evaluation method [28,29].
From the history of human economic and social evolution, the digital economy is a new economic form following the agricultural economy and the industrial economy. It can be understood as an information economy, intelligent economy and a digital transformation economy, mainly including digital industrialization, industrial digitalization and digital governance [30][31][32][33]. Digital transformation has become the dominant force for major countries and regions to improve global industrial competitiveness and cultivate new economic growth [34]. The research on the digital economy mainly focuses on two aspects: one is the measurement and evaluation of the development level of the digital economy in various regions [35][36][37][38]; the other is the empirical research related to the digital economy [39][40][41][42].
The existing literature rarely studies the relationship between digital economy and green development directly from a theoretical perspective. Relevant research mainly focuses on the relationship between big data and green development, artificial intelligence and green development, digital economy and green economy, and digital economy and urban green transformation. For example, Xu et al. studied big data and green development in China from three perspectives: economy, society, and environment, and they believed that big data had a positive impact on green development [43]. Wang et al. analyzed the opportunities and challenges of AI in promoting green development. They believed that AI could effectively promote green development by establishing some response mechanisms [44]. Qian et al. investigated the digital economy and green economy policies in the post-COVID-19 economic recovery policies of various countries around the world, and concluded that the digital economy and green economy could develop together to help economic recovery as soon as possible [45]. Liu et al. studied the digital economy and urban green transformation by analyzing their impact mechanism from the perspectives of production, life, and ecological space. They conducted an empirical test using cities in the Yangtze River's economic belt as an example, and concluded that the digital economy could promote urban green transformation [46].
Traditional neoclassical economics believes that although green development can improve the overall welfare of the society, it usually has a negative effect on economic growth, and it is difficult to achieve both environmental sustainability and economic growth [47,48]. However, different from the conclusions of neoclassical economics, the analysis of new classical economics from the perspective of the division of labor and specialization, can give novel and meaningful explanations. New classical economics considers that under the core dilemma of "division of labor and transaction costs", if the government takes a role and adopts a strict green system-to promote the evolution of green division of labor through the system-then the government-led evolution of division of labor will reduce the total social transaction cost and expand the market scale of green products; this is conducive to the deepening of the division of labor evolution in the green direction, so as to realize the coordination between green development and economic development [49].
Due to various reasons, few scholars now use the new classical economic theory [50]. The motivation of this study is to fill this research gap. Therefore, this paper uses the division of labor thought of the new classical economics theory to discuss how the digital economy empowers green development.

The Connotation of "Green Development"
Most scholars believe that the main feature of green development is to achieve a winwin situation between environmental protection and economic growth. UNESCAP thinks that green development is based on climate change and resource environmental protection, as its logical end, and that attention should be paid to greenhouse gas emission reduction in the process of economic development, with an emphasis on resources and environmental protection [51]; World Bank defines green growth as an economy that continues to be environmentally friendly and socially inclusive [52]; UNEP believes that a green economy is a low-carbon, resource-saving, and socially inclusive economy [53]. Therefore, this paper holds that "green development" refers to the economic and social development mode aimed to achieve efficiency, harmony and sustainability, and is the organic unity of the green subject, the green economy and the green governance [54,55].
Among them, "Green subject" refers to the subject of microeconomic activities, that is, enterprises and households. Specifically, enterprises promote the low-carbon and efficient operation of the production system and improve the green production level through green technology innovation, while households transform from the traditional household consumption mode to green consumption mode, so as to promote the transformation towards a green lifestyle. "Green economy" refers to the green adjustment of industrial structure. Specifically, it pushes forward the organic integration of various production factors based on new green momentum through the optimization of industrial structure, so as to realize the harmonious development of the economy and environment. "Green governance" is defined as the use of formal or informal institutional systems to regulate the behavior of green subjects, effectively curb the destruction of the ecological environment driven by interests, and create a good ecological environment through formal or informal institutional systems.

The Connotation of "Division of Labor"
The theory of division of labor originated from "An Inquiry into the Nature and Causes of the Wealth of Nations" (generally referred to as "the Wealth of Nations") published by Adam Smith, a classical economist, in 1776, and has been evolving with the evolution of the division of labor in human society [59]. Division of labor refers to the specialization of labor in the production process and is the basis for the continuous development of human society. Adam Smith believed that the division of labor was the leading reason for the growth of per capita output of national wealth, and that the development of the division of labor and specialization was the source of economic growth [60]. On this basis, Marx, Young and Coase further promoted Smith's theory of the division of labor. The new classical economists represented by   [61], creatively integrated the theories of Smith, Young and Coase with new mathematical analysis tools; rewritten modern economics with the basic idea of decision-making on the dilemma between division economy and transaction cost; and revived the long-standing topic of division of labor in the new era. The soul of the new classical economics is the framework of "Smith-Young-Coase", which mainly formalizes Adam Smith's thought of the division of labor, by means of ultra-marginal analysis. Compared with the traditional neoclassical economics, its main characteristics are as follows: firstly, the production conditions are characterized by the specialized economy and division network effect; secondly, there is no absolute separation between pure consumers and enterprises, as everyone is both a consumer and a producer; thirdly, transaction cost has an important influence on the topological nature of an organization; fourthly, the personal optimal decision is always a corner solution (the corner solution means that the optimal decision solution is the maximum or minimum value of the decision variable) [61].  comprehensively studied the role of the division of labor in economic development, which was called "1 + 1 > 2" economic benefits of the division of labor, that was, the output level achieved by two people's division of labor was higher than the output level simply added by two people without the division of labor. The division economy here was different from the scale economy. The former referred to people's operation in different directions and links, which was related to the difference of people's production structure, and the latter referred to the input-output relationship under the given production function [62]. Here is a simple figure to illustrate the basic framework of the division of labor theory. Suppose there are four consumers-producers (A, B, C, D) in an economic system, each of whom consumes 4 products, and can choose to produce 1, 2, 3, 4 products. These three types of labor division are shown in Figure 1. era. The soul of the new classical economics is the framework of "Smith-Young-Coase", which mainly formalizes Adam Smith's thought of the division of labor, by means of ultra-marginal analysis. Compared with the traditional neoclassical economics, its main characteristics are as follows: firstly, the production conditions are characterized by the specialized economy and division network effect; secondly, there is no absolute separation between pure consumers and enterprises, as everyone is both a consumer and a producer; thirdly, transaction cost has an important influence on the topological nature of an organization; fourthly, the personal optimal decision is always a corner solution (the corner solution means that the optimal decision solution is the maximum or minimum value of the decision variable) [61].  comprehensively studied the role of the division of labor in economic development, which was called "1+1 2  " economic benefits of the division of labor, that was, the output level achieved by two people's division of labor was higher than the output level simply added by two people without the division of labor. The division economy here was different from the scale economy. The former referred to people's operation in different directions and links, which was related to the difference of people's production structure, and the latter referred to the input-output relationship under the given production function [62]. Here is a simple figure to illustrate the basic framework of the division of labor theory. Suppose there are four consumers-producers (A, B, C, D) in an economic system, each of whom consumes 4 products, and can choose to produce 1, 2, 3, 4 products. These three types of labor division are shown in Figure 1.  Figure 1a shows a type of self-sufficiency. Each person is self-sufficient in producing four kinds of products. There is no market. The level of production concentration and specialization is low. The productivity of each person is low. There is no transaction or transaction costs generated. The degree of economic structure diversification is also low. Figure 1b shows the type of partial division of labor. The number of varieties produced by each person has decreased from 4 to 3. The level of specialization has increased. The market has appeared, and the number of transactions is 2. Transaction costs have occurred. The concentration of products has increased. Two types of majors with different production and trade structures have emerged, and the degree of economic structure diversification has increased. Figure 1c shows a type of complete division of labor. Each person only produces one product but buys the other three products through the market. Each person's specialization, social structure diversification, commercialization, number of markets, production concentration, transaction times, costs, and productivity are all  Figure 1a shows a type of self-sufficiency. Each person is self-sufficient in producing four kinds of products. There is no market. The level of production concentration and specialization is low. The productivity of each person is low. There is no transaction or transaction costs generated. The degree of economic structure diversification is also low. Figure 1b shows the type of partial division of labor. The number of varieties produced by each person has decreased from 4 to 3. The level of specialization has increased. The market has appeared, and the number of transactions is 2. Transaction costs have occurred. The concentration of products has increased. Two types of majors with different production and trade structures have emerged, and the degree of economic structure diversification has increased. Figure 1c shows a type of complete division of labor. Each person only produces one product but buys the other three products through the market. Each person's specialization, social structure diversification, commercialization, number of markets, production concentration, transaction times, costs, and productivity are all superior to those of the partial division of labor. How can the economic system evolve from a state of self-sufficiency to a state of complete division of labor? Yang and Zhang (2000) believed that there was a dilemma between the benefits of the division of labor and the transaction costs arising from the division of labor. The level of division of labor depended on the level of transaction efficiency (inversely proportional to transaction costs). The higher the transaction efficiency, the greater the space for compromise and conflict, and the higher the level of the division of labor [63].

Theoretical Logic of Digital Economy Empowering Green Development from the Perspective of the Division of Labor
Based on the connotation analysis of green development and digital economy, "green development" focuses on the economic model of sustainable development, while "digital economy" focuses on the technological change. From the perspective of the division of labor, the relationship between the two has a deep theoretical logic correlation, as shown in Figure 2. superior to those of the partial division of labor. How can the economic system evolve from a state of self-sufficiency to a state of complete division of labor? Yang and Zhang (2000) believed that there was a dilemma between the benefits of the division of labor and the transaction costs arising from the division of labor. The level of division of labor depended on the level of transaction efficiency (inversely proportional to transaction costs). The higher the transaction efficiency, the greater the space for compromise and conflict, and the higher the level of the division of labor [63].

Theoretical Logic of Digital Economy Empowering Green Development from the Perspective of the Division of Labor
Based on the connotation analysis of green development and digital economy, "green development" focuses on the economic model of sustainable development, while "digital economy" focuses on the technological change. From the perspective of the division of labor, the relationship between the two has a deep theoretical logic correlation, as shown in Figure 2.

Digital Economy Improves Transaction Efficiency and Promotes the Green Evolution of the Division of Labor
According to Adam Smith, a classical economist, and Yang Xiaokai, a new classical economist, the evolution of the division of labor is the basic driving force for economic development [60,64]. The development of the division of labor usually undergoes the evolution process of "self-sufficiency → partial division of labor → complete division of labor". More specifically, in the self-sufficient structure, different economic entities will independently produce and consume all the products they need, and there is no transaction behavior between different economic entities. In the partial division of labor structure, different economic entities will not produce all products, but choose several of them for production, and transactions begin to occur between economic entities. In the complete division of labor structure, different economic entities produce only one product, and the excess products are sold through transactions between economic entities to buy other required products. From the non-division of labor and non-trading production mode under the self-sufficiency structure, to the complete division of labor and the evolution of market transaction models under the complete division of labor structure, the scope of market transactions, transaction efficiency and the level of division of labor have been continuously improved [65].
According to the theory of new classical economics, the division of labor can be divided into four parts, namely labor specialization, professional diversification, production roundabout and economic organization. Labor specialization, professional diversification and production roundabout can be regarded as aspects of productivity, while economic organization can be seen as an aspect of production relations [66]. The four parts of the division of labor are perfectly integrated. According to Yang Xiaokai's research, transaction efficiency has a decisive impact on the evolution of the division of labor [61]. Relying on digital infrastructure, the digital economy realizes industrial digitization, digital industrialization and digital governance through technological changes; it improves transaction efficiency, promotes the evolution of the division of labor, and improves the efficiency of resource allocation.
Specifically, from the perspective of productivity, industrial digitization and digital industrialization in the digital economy can exert network effects, scale effects, and innovation effects; expand the scale and scope of the market; and enable economic activities to be free from geographical and temporal restrictions, which can bring higher labor productivity, meet the diverse needs of consumers, and promote labor specialization, professional diversification, and production roundabouts. In terms of production relations, digital governance is a comprehensive issue involving system and mechanism, decision-making, supervision and implementation. It is also involved with overall correlation and dynamic balance, realization of data interconnection across levels, regions, systems and businesses of economic organizations, and then the promotion of economic organization. In the era of digital economy, with the rapid development of sharing economy and the emergence of a large number of platform enterprises, buyers and sellers conduct point-to-point accurate transactions, which greatly improve the utilization efficiency of resources. Without the support of platform companies, due to the extremely asymmetric information between the buyer and the seller and high transaction costs, there will be problems in finding trading partners, negotiating prices, and performing transactions smoothly. Once supported by platform enterprises, their big data advantages can successfully solve the problem of extremely asymmetric information between buyers and sellers. Moreover, platform companies have integrated systems such as online evaluation and information feedback, to greatly reduce the cost of consumers looking for satisfactory products, the cost of bargaining and negotiation, and the risk of transactions, thereby greatly reducing transaction costs. Due to the significant reduction in transaction costs, the scale and scope of the market will be further expanded, the division of labor will be further evolved, and the allocation efficiency of resources will be further improved [67].

Green Division of Labor Empowers Green Development
Smith (1776) once pointed out that the division of labor was the source and driving force of economic development, and the level of division of labor was restricted by the scope of the market (i.e., Smith's theorem) [60]. Young (1928) developed Smith's core ideas and believed that the division of labor not only depended on the scope of the market, but that the scope of the market was decided by the population scale and purchasing power. Purchasing power was also related to the level of productivity and income, and the level of productivity depended on the level of division of labor, thus forming a logical chain "the division of labor depends on the market scale, which in turn depends on the division of labor" (i.e., Young's theorem) [68]. The division of labor can be divided into the traditional "black division of labor" mode and the modern "green division of labor" mode. The traditional "black division of labor" mode comes at the cost of sacrificing or destroying the ecological environment. The modern "green division of labor" mode will not cause ecological damage and environmental pollution and will also improve and repair the deteriorating ecological environment. The evolution of the division of labor will promote the development of the organizational structure in a more specialized and diversified direction, but it is uncertain whether it is a "black division of labor" mode or a "green division of labor" mode. As economic entities face long-term high costs and risks in the process of technological change, the direct use of mature traditional technologies results in low cost, low risk, and quick results. In this case, economic entities pursuing profit maximization will naturally choose to use traditional technology for production, and the evolution of the division of labor will eventually inevitably move toward a "black division of labor" structure. Meanwhile, there is a positive externality of knowledge and technology spillover in technological change. Under the unconstrained conditions, not all economic entities will actively turn to the field of green development. Under the automatic configuration of the market, the organizational structure will be locked in the "black division of labor" structure, and the "invisible hand" adjustment of the market mechanism will fail [65].
Therefore, in order to make the division of labor jump out of the "black division of labor" structure, it is necessary to rely on the "visible hand" of the government to formulate a green development system-used to improve the efficiency of market resource allocation-to adjust the evolution of the division of labor towards the "green division of labor" structure. According to the logic of Smith's theorem and Young's theorem, under the intervention of the governmental green system or green policy, the "invisible hand" of the market mechanism affects the level of the division of labor by improving the efficiency of resource allocation, so as to promote the transition of the "black division of labor" mode to the "green division of labor" mode. Simultaneously, the government uses both "black constraints" and "green incentives" to guide green development of digital economy entities. "Black constraint" means to promote the internalization of environmental costs of the "black" digital economic entities and force them to make green transformations by improving emission standards, increasing punishment, and controlling emission quotas. "Green incentive" means to reduce the costs of the digital economy entities through tax incentives and financial subsidies, and encourage them to carry out research and application of green innovative technologies.
Specifically, natural systems provide all the materials needed for social and economic activities. Natural systems provide people with various resources (including energy), and people transform them into products with various functions through production and labor. All kinds of waste (including pollutants) are generated not only during the conversion of raw materials to products, but also in the process of product consumption. These wastes will eventually lose their values and be discarded, and will be returned to the natural system. The traditional economic development model is developed to promote economic growth by expanding the scale of production and consumption, which continues to increase the pressure of economic development on the natural system [69]. As a result, the more the economy develops, the greater the environmental burden. The essence of green production and green consumption is to achieve the ultimate goal of minimizing environmental impact and maximizing resource utilization in the entire economic system process, thereby minimizing social welfare losses. Green production and green consumption are inseparable. Production is for consumption, and consumption, in turn, can force the improvement of production behavior through the market [70]. Therefore, at the level of the green subject, through the transformation of the behaviors of enterprises and households, the green production capacity of enterprises and the green consumption capacity of households will be promoted to drive green development of the digital economy.
In 1989, Pearce, a British environmental economist, first put forward the concept of "green economy" in the blue book of the green economy. Its core idea is to realize the sustainable development of the economy around the coordinated operation of the resource system, environmental system, economic system, and social system [71]. The "green economy" promotes economic growth by investing in natural capital, allowing the economy to grow without causing a natural decline. The research model of the green economy shows that the natural capital in the green economy can achieve the decoupling between the required economic and social development, and the consumption of natural capital. At the level of the green economy, the green adjustment of industrial structure will help build a market mechanism suitable for enterprise environmental information disclosure, expand the market scale of green products, improve the level of green market economy, minimize external diseconomy at the micro level, maximize the efficiency of resource allocation at the macro level, and realize the systematicness, integrity, and coordination of the natural, economic, and social systems [72], thereby driving the green development of digital economy.
As producers and consumers in economics, there is a certain contradiction between the pursuit of maximizing personal interests and minimizing the loss of social welfare. Therefore, as an environmental advocate, the government needs to regulate the external uneconomic boundary between production and consumption, through institutional measures. It also needs to set reasonable prices for environmental factors, to stimulate the behavior improvement of producers and consumers by economic means. Therefore, at the level of green governance, institutional measures and means of incentives are used to enhance green governance capability, to drive green development of the digital economy. As a result, the digital economy will ultimately empower green development.

Research on the Mechanism of Digital Economy Empowering Green Development from the Perspective of Division Labor
According to the ultra-marginal analysis thought of the new classical economics, referring to the new classical economic model of Yang (1988) [73], Kuang and Wen (2019) [74], it is assumed that a society is composed of M consumers producers, and there is a specialized economy. One final product is green development product Z, which can be produced by labor l plus intermediate product X or Y (where the traditional product X is the product produced by traditional production mode, and the digital economy product Y is the product produced by digital technology production mode), that is, the productivity λ 1 of traditional product X is lower than that λ 2 of digital economy product Y (0 < λ 1 < λ 2 ). The green development product Z is produced according to CES production function, and individual decision-making problems can be characterized by the following set of equations: p x x s + p y y s + p z z s = p x x d + p y y d + p z z d (6) Among them: Equations (1) and (2) are, respectively, the utility function and production function of the final green development product. Equations (3) and (4) are, respectively, the production function of the traditional production mode and the digital technology production mode. Equation (5) is the endowment constraint. Equation (6) is the budget constraint. To simplify without losing generality, it is assumed that: Firstly, z p , x p and y p , respectively, represent the output of the green development products Z, traditional products X and digital economy products Y; z, z s and z d , respectively, represent the self-sufficiency, supply and demand of the green development products; x, x s and x d , respectively, represent the self-sufficiency, supply and demand of the traditional products; y, y s and y d , respectively, represent the self-sufficiency, supply and demand of the digital economy products. Secondly, if 1 − k i represents the transaction cost coefficient, k i represents the transaction efficiency coefficient and has the property k i ∈ (0, 1). The higher the transaction efficiency is, the higher the evolution level of labor division is. k 1 and k 2 represent the transaction efficiency of the products X and Y, respectively. Thirdly, ρ is the substitution elasticity coefficient of the two intermediate products X and Y, and 1/ρ is the complementary economic degree of the two intermediate products. Fourthly, β is the output elasticity of green development products, produced by the two intermediate products, and β ∈ (0, 1); α indicates the degree of specialized labor when producing green development products, and α > 1. Fifthly, b represents the degree of specialized labor for the production of the two intermediate products, and b > 1. Sixthly, l x , l y and l z ∈ [0, 1] represent the specialization level of the traditional products, the digital economy products and green development products, respectively. Seventhly µ is the conversion rate of the specialization level of the digital economy products. Because the production of digital economic products has high learning costs, the specialization level of the actual production of the digital economic products is µl y , and µ ∈ (0, 1); The learning cost of the traditional products is low, assuming no learning cost is required, so the specialization level of the actual production of the traditional products is l x . Eighthly, p x , p y and p z , respectively, represent the prices of the traditional product X, the digital economic product Y and the green development product Z. To facilitate research, the price of the green development product Z is used as the pricing standard, i.e., p z = 1.
In real economic activities, each economic subject can choose either self-sufficiency mode or specialization mode. In combination with Wen's Theorem and the above constraints, there are several different decision models as follows, and their general equilibrium analysis is carried out, respectively.

Decision Model A: Self-Sufficiency
Self-sufficiency means that each economic entity independently produces and consumes the green development products, and there is no transaction between different economic entities. Therefore, under the self-sufficient decision-making model, the individual economic behavior usually has two kinds of division structures: A(xz) and A(yz). Among them, the division structure A(xz) means that each economic entity produces the traditional product X by itself and produces the green development product Z based on the traditional products. Therefore, we can get the equation x s = x d = y = y s = y d = z s = z d = 0, l y = 0, x ≥ 0, z ≥ 0. The optimal solution is as follows: Now, l x = bβ α+bβ , l z = α α+bβ . Similarly, the division structure A(yz) means that each economic entity produces the digital economic product Y by itself, and uses the digital economic product Y to further produce the green development product Z. As above, the optimal solution of the division structure A(yz) is obtained as follows: By comparing the optimal solutions of the two division structures under the selfsufficiency decision, it is not difficult to find that U A(xz) > U A(yz) is always true because µ ∈ (0, 1), and the other parameters are greater than 0. The results show that under the condition of self-sufficiency of intermediate technology, the economic benefits of the division of labor structure using the traditional mode of production, are significantly higher than those involving the digital mode of production. Its inherent economic meaning is that under the condition of self-sufficiency of intermediate technology, economic subjects prefer the division structure A(xz) of producing final products in the traditional production mode. The general equilibrium of self-sufficiency decision A and its ultra-marginal comparative static analysis are shown in Table 1. Table 1. General equilibrium of self-sufficiency decision model A and its ultra-marginal comparative static analysis.

Decision Model B: Traditional Complete Division of Labor
The traditional complete division of labor refers to that among M economic entities; some of them choose to produce the traditional product X exclusively and purchase the green development product Z through the market for consumption, which is referred to as division structure B(x/z). Another section of economic entities purchase the traditional product X through the market to produce the green development product Z, consume Z and sell Z, which is referred to as division structure B(z/x) (as shown in Figure 3).
z0  , s z 0  , the optimal solution is obtained as follows: In the division structure B(z/x), according to x = x s = y = y s = y d = z d = 0, l x = l y = 0, l z = 1, x d ≥ 0, z ≥ 0, z s ≥ 0, the optimal solution is obtained as follows: Similarly, it is further calculated that the optimal solution of the division structure B(x/z) is U B(x/z) = k 1 p x . Therefore, in the decision making of the final product in the traditional production mode, combining the optimal solutions of the two division structures, and further calculating according to the principle of equal utility, the corner equilibrium solutions can be obtained:

Decision Model C: Complete Division of Labor of Digital Economy
The complete division of labor of the digital economy refers to that among M economic entities, as some of them choose to produce the digital economic products Y exclusively and purchase the green development products Z through the market for consumption, which is referred to as division structure C(y/z); Another section of economic entities purchase the digital economic products Y through the market to produce the green development products Z, consume Z and sell Z, referred to as division structure C(z/y) (as shown in Figure 4).
Similarly, it is further calculated that the optimal solution of the division structure ( ) Therefore, in the decision making of the final product in the digital economy production mode, combining the optimal solutions of the two division structures, and further calculating according to the principle of equal utility, the cor- In the division structure C(z/y), according to x = x s = x d = y = y s = z d = 0, l x = l y = 0, l z = 1, y d ≥ 0, z ≥ 0, z s ≥ 0, the optimal solution is obtained as follows: Similarly, it is further calculated that the optimal solution of the division structure C(y/z) is U C(y/z) = µ b k 2 p y . Therefore, in the decision making of the final product in the digital economy production mode, combining the optimal solutions of the two division structures, and further calculating according to the principle of equal utility, the corner equilibrium solutions can be obtained:

Result Discussion and Analysis
By synthesizing the equilibrium results of the above decision-making models A, B and C, we can get the results of the ultra-marginal comparative static analysis between productivity, specialization, transaction efficiency and the equilibrium division structure (as shown in Table 2). Table 2. General equilibriums and their ultra-marginal comparative static analysis.
Conversion condition Tables 1 and 2 show that: (1) When the transaction efficiency k 1 and k 2 of the two intermediate products are relatively low (that is, k 1 < µ b θ/λ 1 and k 1 < µ b θ/λ 1 ), the cost of the economic entity's intermediate product transaction is far higher than the benefits brought by the transaction. Its rational choice will be the self-sufficient traditional production model (that is, the decision-making model A(xz)), and the self-sufficiency mode will become an equilibrium structure. In this case, the impact of transaction efficiency on the digital economy shows no effect. With the continuous improvement of k 1 and k 2 , when they reach a certain level, there will be U B > U A(xz) or U C > U A(xz) . Based on the consideration of profit maximization, the economic entity will shift its optimal decision from a self-sufficient structure to a traditional complete division structure or a complete division structure of the digital economy (that is, from the decision-making model A to the decision-making model B or C).
(2) When the transaction efficiency of the traditional products is high ( if a certain condition (k 1 > µ b λ 2 /λ 1 k 2 ) is met at the same time, the decision-making model B using the traditional production mode becomes the general equilibrium, and at this time, the rational economic entities will give priority to the traditional division of labor structure. That is to say, when the ratio between the transaction efficiency of the traditional products and that of the digital economic products is greater than µ b λ 2 /λ 1 , the rational economic entities will give priority to specializing in the traditional products or purchasing the traditional products, to produce the green development products. The traditional complete division of labor structure becomes an equilibrium structure, while the digital economic production mode is difficult to have appear in the market, and the final product production mode will be locked in the "cage" of the traditional production mode.
(3) When the transaction efficiency of the traditional products is low (k 1 < µ b θ/λ 1 ) and the transaction efficiency of the digital economic products is high (k 2 > √ θ/λ 2 ), or when the transaction efficiency of the traditional products is high (k 1 > µ b θ/λ 1 ) and the transaction efficiency of the digital economic products meets certain conditions (k 2 > k 1 / µ b λ 2 /λ 1 ), there will always be U C > U A(xz) > U B or U C > U B > U A(xz) , thus the decision-making model C becomes a general equilibrium. In this case, the impact of transaction efficiency on the digital economy is a positive effect, and the rational economic entities will preferentially engage in the production of the digital economic products or purchase the digital economic products to produce the green development products. Its economic meaning is that with the improvement of transaction efficiency, the division of labor structure of the digital economy has been born, and the production mode of the digital economy has replaced the traditional production mode, which has been applied in the production of final products. This conclusion is more consistent with the economic reality. Compared with the investment risk and immaturity of the production mode of the digital economy, the role of the market mechanism often drives the traditional production mode to dominate in the early stage of the division of labor (manifested in that the transaction efficiency k 1 of the traditional products is far greater than the transaction efficiency k 2 of the digital economy products), so that the economic entities will give priority to the traditional production mode. In this case, the green development level of the digital economy depends more on the government's promotion of green institutional arrangements and supply and demand policies. Under the guidance of the green system and policies of the government, the traditional mode of production should be constrained, and the green mode of production should be encouraged, so as to promote the transition of the traditional complete division structure to the complete division structure of the digital economy.
(4) A further analysis of the above transformation conditions shows that a key and necessary condition for realizing the transaction, from the traditional complete division structure to the complete division structure of the digital economy, is the gradual improvement of the transaction efficiency of digital economy products. According to the theory of the new classical economics, the dilemma between specialized economy and transaction cost determines the evolution direction of the economic organization structure. The transaction cost is measured by the transaction efficiency with the iceberg transaction cost attribute. In the case of low transaction efficiency, the income from the division of labor is lower than the loss in the transaction process. In addition, the technology research and development of the production mode of the digital economy also requires human capital and learning costs. The high transaction costs caused by the low transaction efficiency crowd out the R&D investment of enterprises. Experts specializing in the production mode of the digital economy and the division structure of the digital economy will not appear in the market, and the division structure will certainly not jump; thus, the self-sufficiency decision-making or traditional division structure under the low transaction efficiency level becomes a stable equilibrium. Due to the high cost and risk of digital technology, a large number of digital economy enterprises are barely surviving. This makes the improvement of transaction efficiency, fail to promote the development of the production mode of the digital economy in the early stage of its development, but will make enterprises prefer to use the traditional production mode. In order to break this equilibrium and realize the transition to the complete division structure of the digital economy, we must constantly improve the transaction efficiency of the digital economic products.
Based on the above ultra-marginal decision-making and general equilibrium analysis, the following conclusions can be drawn: The impact of digital economy on the level of green development is not single linear. Further empirical research is needed to determine the impact of nonlinearity.
Compared with the new classical economic models of Yang (1988) [73], Kuang and Wen (2019) [74], this paper expands the relevant theoretical models and preliminarily discusses the theoretical mechanism of the digital economy influencing green development. However, the research scope of the digital economy and green development is too wide, so the theoretical model needs to be further improved.

Conclusions
From the perspective of the division of labor in new classical economics, this paper creatively analyzes the theoretical mechanism of the digital economy empowering green development, which has good theoretical value and practical significance for promoting the sustainable development of the global economy. The main research conclusions are as follows: (1) From the perspective of the division of labor, the digital economy relies on the digital infrastructure to achieve industrial digitalization, digital industrialization and digital governance through technological change, which improves the transaction efficiency, promotes the evolution of the division of labor, and improves the efficiency of resource allocation.
(2) There are the traditional "black division of labor" mode and modern "green division of labor" mode. In order to make the division of labor jump out of the "black division of labor" structure, we must rely on the "visible hand" of the government to formulate a green development system, carry out environmental regulation, and vigorously improve the efficiency of market resource allocation, so as to adjust the transition of the division of labor to the "green division of labor" structure. Driven by the digital economy, green development actors, economic systems and governance mechanisms will gain endogenous capabilities.
(3) According to the ultra-marginal analysis thought of the new classical economics, this paper constructs a theoretical model for the impact of the digital economy on green development. Based on the results of ultra-marginal decision-making and general equilibrium analysis, it can be seen that the impact of the digital economy on the level of green development is not single linear. Further empirical research is needed to determine the impact of nonlinearity. In summary, from the perspective of economic theory, the digital economy can influence and empower green development.
From these conclusions, we can draw policy inspiration that we should vigorously develop the digital economy, promote the evolution of the division of labor, effectively play the role of the market as the "invisible hand", with the government as the "visible hand", guide the economic transformation toward the "green development" direction, to promote sustainable economic development.
In future research, relevant data on the digital economy and green development can be collected, to further conduct empirical tests on the relationship between the digital economy and green development.