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Journal of Geographical Sciences >

2024 , Vol. 34 >Issue 1: 3 - 24

DOI: https://doi.org/10.1007/s11442-024-2192-4

Research Articles

Can the integration between urban and rural areas be realized? A new theoretical analytical framework

  • WANG Yi , 1 ,
  • LU Yuqi 2 ,
  • ZHU Yingming 1
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  • 1. Research Base of Jiangsu Industrial Cluster, School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China
  • 2. School of Geography, Nanjing Normal University, Nanjing 210023, China

Wang Yi (1989-), PhD and Associate Professor, specialized in human settlements and regional development. E-mail:

Received date: 2022-08-11

  Accepted date: 2023-05-09

  Online published: 2024-01-08

Supported by

The Philosophy and Social Science Research Major Project of Jiangsu University(2023SJZD056)

National Natural Science Foundation of China(41901205)

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Abstract

Urban-rural integration is an advanced form resulting from the future evolution of urban-rural relationships. Nevertheless, little research has explored whether urban and rural areas can move from dual segmentation to integrated development from a theoretical or empirical perspective. Based on the research framework of welfare economics, which offers an appealing paradigm to frame the underlying game between cities and villages, this study clarifies the ideal state of urban-rural integration. It then proposes a series of basic assumptions, and constructs a corresponding objective function and its constraints. Moreover, it assesses the possibility of seeing the transmutation from division to integration between urban and rural areas with continuous socio-economic development. The authors argue that the ideal state of urban-rural integration should be a Pareto-driven optimal allocation of urban-rural resources and outputs, and the maximization of social welfare in the entire region. Based on a systematic demonstration using mathematical models, the study proposes that urban and rural areas can enter this ideal integrated development pattern when certain parameter conditions are met. In general, this study demonstrates the theoretical logic and scientific foundations of urban-rural integration, enriches theoretical studies about urban-rural relationships, and provides basic theoretical support for large developing countries to build a coordinated and orderly urban-rural community with a shared future.

Key words： urban-rural integration development; ideal state; parameter conditions; welfare economics; theoretical framework

Cite this article

WANG Yi , LU Yuqi , ZHU Yingming . Can the integration between urban and rural areas be realized? A new theoretical analytical framework[J]. Journal of Geographical Sciences, 2024 , 34(1) : 3 -24 . DOI: 10.1007/s11442-024-2192-4

1 Introduction

The urban-rural relationship is the most basic economic and social relationship in the development of human society (Liu, 2018). Urban-rural integrated development is essentially a stage in the evolution of urban-rural relationships (Yang et al., 2021), and an ideal vision for countries and regions worldwide (Fang, 2022). However, in the process of urbanization and modernization, the contrast between rural recession and urban prosperity has become a global phenomenon (Ann et al., 2014; Liu and Li, 2017). Facing the problem of urban-rural binary opposition, many developed countries, including the United Kingdom, Germany, the United States, and Japan, have adopted and implemented targeted projects that align with national conditions to promote rural revitalization and balanced urban-rural development (Martin and Jennife, 2014; Conley and Whitacre, 2016; Long et al., 2019; Nizam and Tatari, 2022). Unfortunately, there are also many developing countries that have fallen into the “middle-income trap” due to their failure to effectively handle the urban-rural relationship (Kapotwe, 2021).
China, the largest developing country in the world, also faces these challenges (Yang and Zhou, 1999). Long-standing city-centrism and city-biased development has caused a significant lack of equilibrium in the urban-rural balance, with inadequate rural development. This has resulted in the emergence of an endogenous demand for symbiotic development (integration) in the traditional urban-rural dual order (Liu et al., 2021). To this end, China has successively implemented policies and strategies such as new countryside construction, the beautiful villages initiative, and a rural revitalization strategy; the goal is to mitigate the shortcomings of rural development and realize a more integrated approach to urban-rural development (Oliver-Márquez et al., 2020; Wang et al., 2021; Yang et al., 2021; Ge and Lu, 2022).
Urban-rural integration is essentially a stage in urban-rural transformation. The idea of urban-rural integration first emerged from the thought of urban-rural relations in Utopia. In 1847, Engels first proposed the concept of urban-rural integration, providing a theoretical explanation in the Principles of Communism. Since then, urban-rural integrated development has received extensive attention from diverse perspectives. It generally refers to the multi-dimensional integration between urban and rural areas with respect to the economy, population, space, society, and ecology, based on the free flow and optimal allocation of resource elements within urban and rural areal system. The goal is to form a compound system of organic coordination, complementary functions, and shared benefits (He, 2018; Liu, 2018; Yang et al., 2021; Gao et al., 2023). In recent years, many scholars have devoted works to promote urban-rural integrated development. In particular, some scholars have analyzed and explored this development from the perspectives of interpretation of meaning (Ma et al., 2019a; Baffoe et al., 2021), cognition of basic theory (Friedman, 1966; Sokol, 2017; Fan et al., 2022), measurement of integration level, analysis of the spatio-temporal pattern (Azam, 2019; Zhu et al., 2019; Yang et al., 2021), and the evolutionary mechanism (Chen et al., 2020; Vigdor, 2010; Ruixin and Sami, 2019).
In summary, the academic community has conducted extensive research on urban-rural integration. These achievements have provided significant theoretical and practical references for countries around the world to promote high-quality urban-rural integration. However, these studies also have limitations. Although the logic and paradigm of the “meaning explanation - theoretical cognition - pattern evolution - mechanism identification - countermeasure regulation” pattern for urban-rural integration research has been very comprehensive, a key question deserves further exploration: Can urban and rural areas move from dual segmentation to integrated development? Existing studies have not yet addressed this question, or simply assumed such a move is possible. However, this remains a fundamental question worth considering. In addition, to determine whether a region can achieve urban-rural integration, it is also important to ask: What are the basic standards or signs for urban-rural integrated development?
Admittedly, some scholars have noted that the ultimate goal of urban-rural integration is to form a new-style urban-rural relationship, in which urban and rural areas complement each other, develop symbiotically, and prosper together (Liu et al., 2013; Liu, 2017; Zhou et al., 2020). Scholars have also argued that globalization and urbanization continue to enhance the transformation and reshaping of urban-rural relations, and the changes in global urban-rural relations should experience an orderly evolution from urban-rural division and confrontation, to urban-rural coordination and integration (Tacoli, 1998; Liu et al., 2021; Fang, 2022). However, these discourses merely reflect qualitative analyses and historical summaries, based on development patterns in different countries; they lack sufficient explanations about the mechanism involved and lack mathematical descriptions.
While a few scholars have initially explored these questions from the perspective of political economy, and based on China’s unique institutional background (Chen and Lu, 2008), the universality of their conclusions needs to be improved from a global perspective. Based on the urban-rural equivalence theory, some scholars have also established a general urban-rural spatial equilibrium model to determine the process and mechanism of urban-rural integrated development (He, 2018). However, this model reflects a theoretical and qualitative analysis. The equilibrium model’s construction, and equilibrium condition solutions, remain a conceptual framework, without rigorous assumptions and mathematical demonstrations. As such, they are currently scientific propositions needing further investigation.
Specifically, we need to further answer and clarify the following questions: What is the ideal state of urban-rural integration? Will city and country areas realize the transmutation from dual segmentation to integrated development? What conditions are needed to achieve the integration? Undoubtedly, exploring these issues is of important theoretical value and policy guiding significance. Based on this, this paper constructs a normative economic model, applying the basic concepts of Pareto efficiency and optimal social welfare in economics, and consequential phase diagram analysis, to explain the ideal state, possibility, and essential conditions of urban-rural integration. In this way, the research offers a new perspective for understanding the formation mechanism involved in urban-rural symbiosis during urbanization. It also provides an important scientific basis for systematically understanding the urban-rural relationship and its interaction process. Moreover, it provides basic theoretical support for vast developing countries to further promote urbanization and rural revitalization, and build a coordinated and orderly urban-rural community with a shared future.

2 Literature review

This study sits at the intersection of several branches of literature. However, three specific branches are most critical: the first relates to meanings and basic theories; the second relates to measurement and spatio-temporal evolution; and the third relates to influencing mechanisms and practical approaches.

2.1 The meaning and basic theories of urban-rural integration

Urban-rural integration is a complex system with multiple levels, elements, and functions, and it has profound meaning and implications. Scholars have developed diverse interpretations with respect to the meaning of urban-rural integration from different perspectives. For example, Lynch (2004) and other sociological researchers have noted that urban-rural integration is the inevitable result of the development of urban-rural relations. From an economics perspective, scholars have argued that urban-rural integration should be reflected in the coordinating division of labor with respect to productive forces and optimal benefits in urban and rural areas (Vandercasteelen et al, 2018; Jin, 2019). From a factor flow perspective, some scholars have held that urban-rural integration is the reasonable free flow and optimal allocation of substantive and non-substantive factors in the urban-rural regional system (Zhou et al., 2020). Moreover, some researchers have interpreted the meaning of urban-rural integration from the perspectives of spatial coordination (Baffoe et al., 2021), system theory (Ma et al., 2019a), and other constructs. Despite the different points of view, researchers generally want to enhance equal status between cities and villages, and realize common prosperity for all people (Zhou et al., 2021).
With the deepening of the meaning of urban-rural integration, corresponding basic theories have also been developed. These theories include the urban-rural dual structure theory (Lewis, 1954) and the core-periphery theory (Friedman, 1966). These are grounded in economic development as a guiding ideology. Other approaches include the human-land relationship areal system theory, utilizing big-picture thinking (Lu and Guo, 1998); the spatial equilibrium theory, based on spatial justice and equity (Fan et al., 2022); the urban-rural equivalence theory, aiming to achieve equal quality of life for residents (Liu et al., 2013; Sokol, 2017); and the flow space theory, focusing on dynamic factor flow (Lynch, 2004); Zhou et al., 2020). The theories above have provided significant theoretical support for the scientific research and practice of urban-rural integrated development. In general, the construction of the theory of urban-rural integration remains at a stage of deepening and differentiation.

2.2 The measurement and spatio-temporal evolution of urban-rural integration

Measuring the urban-rural integration level is a foundational need for conducting quantitative research in this field, and constructing a multi-index evaluation system has become a mainstream paradigm. Scholars have tended to construct an index system using the dimensions of economy, society, life, space, and ecology (Afrakhteh et al., 2016; Azam, 2019; Ma et al., 2019b; Yang et al., 2021). Popular empirical evaluation methods include the comprehensive index method, coupling coordination degree model, social network analysis, and similar approaches (Liu et al., 2015; Molano et al., 2015; Zhu et al., 2020; Tian et al., 2021). For example, Yang et al. (2021) selected 39 indices from the three dimensions (i.e., the basis, driver and goal) to construct an index system to measure the urban-rural integration level from 2000 to 2018 in China. The data used in these measurements remain dominated by statistical data; however, multi-source data have begun to be applied, such as social survey data and nighttime lighting data (Baier et al., 2020; Wang et al., 2021; Zhou et al., 2021).
After measuring the level of urban-rural integration, scholars have explored its spatio-temporal evolution characteristics. Tools used to explore the temporal evolution and regional differences of urban-rural integration include the kernel density estimation, Theil index, Dagum Gini coefficient, and other methods (Zhou et al., 2020). Exploratory spatial data analysis (ESDA), Markov chain model, cluster analysis, landscape analysis, and other similar approaches are usually applied to reveal spatio-temporal dynamic characteristics in different regions (Liu et al., 2013; Wu and Cui, 2016; Zarifa et al., 2019; Zhu et al., 2019). From the perspective of spatial scale, most studies have focused on large-scale areas in research hotspots such as regions around the capital (Beijing), the Pearl River Delta, the Yangtze River Delta, the Huaihai Economic Zone, and economically developed provinces such as Jiangsu and Zhejiang (Zhang et al., 2020; Yang et al., 2021; Zhou et al., 2021; Luo et al., 2023).

2.3 The influencing mechanism and practical approach of urban-rural integration

Clarifying the mechanism influencing urban and rural integration is the logical starting place to seek a practical path forward. Qualitative judgment and quantitative identification are two main ways to determine the associated influencing factors. For example, with respect to qualitative judgment, Tacoli (2003), for example, discussed the influence of macroeconomic policies, geographical location, population characteristics, transportation, and other multi-dimensional factors on the evolution of urban-rural relations. With respect to quantitative identification, commonly used methods include spatial econometric models, geographic detectors, multiple linear regression models, and panel regression models (Zhang et al., 2020; Zhou et al., 2020; Luo et al., 2023). With respect to specific influencing factors, scholars have initially identified the impact of factors such as land market and land use transition, urban renewal, and financial development on urban-rural integration (Vigdor, 2010; Ruixin and Sami, 2019; Chen et al., 2020; Fu et al., 2022).
Seeking the path to realizing urban and rural integrated development provides a foothold in associated scientific research. For example, Douglass (1998) proposed a “Regional Network Strategy” from the perspective of urban-rural interdependence. Ye and Liu (2020) proposed a new theoretical framework of urban-rural co-governance, emphasizing that urban-rural co-governance and integration require combining multidisciplinary knowledge and multi-scale practice. Long and Chen (2021) discussed the theoretical framework, influential approaches, and land use transition paths in promoting urban-rural integrated development from the perspective of land system scientific research. Fang (2022) conducted a theoretical analysis on the mechanism and evolutionary rules governing urban-rural integrated development, and proposed a triangular model for urban-rural multi-integrated development.

3 Theoretical background analysis

Cities and villages are the two basic regional types, and urban-rural integrated development is an advanced form of urban-rural relationship evolution. The operating mechanism of the urban-rural integration system is more complicated compared to a single rural regional system or urban regional system. Despite this, there are commonalities in goals, whether it is an urban regional system, a rural regional system, or an urban-rural integrated system. They all strive to promote the efficient allocation and full utilization of urban-rural factors and outputs; facilitate urban and rural regional systems to achieve balanced development at a higher level; and realize harmonious coexistence through benign interaction (He et al., 2018; Ye and Liu, 2020; Liu et al., 2021). In other words, by advancing national strategies such as new-style urbanization and rural revitalization, we can ultimately build a community that has a shared future in urban and rural areas, realizing “inhomogeneity, but equivalence” between urban and rural systems, and transforming the urban-rural confrontation and separation pattern into a balanced urban-rural integration pattern (Figure 1). This requires finding the optimal equilibrium point between efficiency and equity in urban-rural development (Liu et al., 2015).
Figure 1 The main logical threads associated with the transformation of the urban-rural relationship

Note: This figure refers to the results of Professor Fang (2022) in the external form.

Optimally allocating and effectively utilizing resources and outputs in an urban-rural integration system is similar to efficiently allocating factors and products among different manufacturers in an economic system. When economists evaluate economic systems, they often apply the criterion of Pareto optimality or efficiency (Molina-Abralde and Pintos-Clapés, 2008; Eveson and Thijssen, 2016). This is because Pareto optimality avoids comparing the utility of two consumers; instead, it is a fundamental criterion, and any socially optimal result should conform to the underlying principle (Tian and Yang, 2006). Given this, we argue that Pareto optimality should also be an ideal state for the balanced development of urban and rural systems. Pareto optimality, also known as Pareto efficiency, is an ideal state of resource allocation. Assuming that the resources available to a group of people are inherently limited, it is a Pareto improvement if a change from one state of allocation to another makes at least one person better off without making anyone worse off (Eveson and Thijssen, 2016). Pareto improvement can also be used to define an optimal level of resource allocation: it is optimal when, for a given resource allocation state, no arbitrary change in that state can make at least one person better without making anyone worse. In short, a Pareto optimal state is a state in which no more Pareto improvements are possible.
Pareto optimality is not a complete description of the optimal allocation of urban-rural resources, as it does not consider the issue of income distribution or fairness across an entire society. The ultimate goal of urban-rural integration is to maximize the comprehensive benefits of urban and rural areas, and to realize the common prosperity and all-round development of all people (Azam, 2019; Zhou et al., 2020; Liu et al., 2021). Therefore, determining the level of equilibrium and integration of urban-rural systems from the perspective of maximizing social welfare is closer to targets associated with national or regional managers (Das et al., 2021).
Therefore, it is important to consider other theories that can inform the study problem. The concept of social welfare was first proposed by Burk (1938), who posited that social welfare is based on individual welfare, but differs from individual utility. Maximizing welfare is not necessarily about achieving a Pareto optimal state, but rather, a balance that considers fairness and efficiency. This point is consistent with the appeal of urban and rural integrated development, where the ideal state is that welfare can be reasonably distributed among regions; economic efficiency is a necessary condition; and reasonable distribution is a sufficient condition. By further theorizing the concept of social welfare, social welfare function can be constructed and used for empirical analysis (Camagni et al., 2013).
From the perspective of social welfare, regional development costs, such as resource consumption and environmental pollution, can be internalized, breaking through the cost-benefit research dimension of economics. Additionally, setting the maximization of the utility of the entire region as the criterion for examining urban-rural integration is likely to generate results that are closer to the vision of modern regional management and the requirements of high-quality development. Therefore, we argue that the ideal state of urban-rural integrated development is a Pareto optimal allocation of urban-rural resources and outputs, and the maximization of overall social welfare. Accordingly, we establish corresponding mathematical models to further explore whether this perfect state can be realized, and what kind of parameter conditions are required to do so.

4 Construction of the theoretical model for urban-rural integration

This section constructs a series of theoretical models of urban-rural integration, supported by the basic framework of welfare economics (Gao, 2021). This illustrates whether we can detect the evolution from division to integration between urban and rural areas given the continuous advancement of urbanization.

4.1 The basic assumptions

Urban-rural integration theory is grounded in the theory of the human-land relationship areal system. Cities and villages are complex regional systems with spatial mosaics, complementary structures, and coupling functions (Liu, 2018). Therefore, we assume that a regional system is a dual system consisting of two subsystems: the urban system and rural system, denoted as C and V, respectively. In a regional system, there are many resources and production factors, such as labor, land, capital, ecological resources, and technology. To simplify the analysis, we select land and labor as the representatives of production factors, and do not consider their urban-rural heterogeneity. Similar assumptions were made by Chen and Lu (2008). The letters L and G represent labor and land, respectively. Various products are created in the process of regional development. Considering the respective endowment advantages of urban and rural areas, combined with existing research assumptions (Chen, 2008; Yang et al., 2012), we define regional output as economic goods and ecological goods, denoted by E and B, respectively. Based on the above assumptions, we further divide regional production into the urban production sector and rural production sector, and divide regional consumption into the urban consumption sector and rural consumption sector. To focus the supply side analysis, we assume that economic populations have the same preferences.
The next question is: In a regional system with only two subsystems (i.e. urban system and rural system), only two types of production factors (i.e. labor and land), and only two kinds of products (i.e. economic goods and ecological goods), how can we promote the optimal allocation and full utilization of urban-rural resource factors and outputs to maximize the comprehensive benefits of urban and rural areas? This is a question of how to achieve optimal social welfare. To address this problem, we propose the following assumptions:
Assumption 1: Le and Lb denote the labor resources allocated to the production of economic goods and ecological goods, respectively. Then, the total labor resources (Lt) in the region is expressed as:
${{L}_{t}}={{L}_{e}}+{{L}_{b}}$
Similarly, Ge and Gb represent the land resources allocated to producing economic goods and ecological goods, respectively. Then, the total land resources (Gt) in the region is expressed as:
${{G}_{t}}={{G}_{e}}+{{G}_{b}}$
Assumption 2: Ec and Bc denote the output of economic and ecological goods in the urban system, respectively. Ev and Bv signify the output of economic and ecological goods in the rural system, respectively. Hence, the total output values for economic goods and ecological goods in the region are expressed as:
$E={{E}_{c}}+{{E}_{v}}$
$B={{B}_{c}}+{{B}_{v}}$
Assumption 3: In terms of the production side, the total product yield is a function of the input of production factors. Therefore, the following two equations represent the production functions of economic goods and ecological goods respectively:
$E=E\left( {{L}_{e}},{{G}_{e}} \right)$
$B=B\left( {{L}_{b}},{{G}_{b}} \right)$
where E(••) and B(••) are the production function forms of economic goods and ecological goods, respectively. It is assumed that both rural and urban production use a Cobb-Douglas production function.
Equations (5) and (6) are established because, in terms of production, there are differences in endowments between urban and rural areas. As such, they have diverse forms of production models. The resource allocation pattern and production efficiency of the two regional subsystems are not the same. Equations (5) and (6) indicate that the functions E(••) and B(••) comprehensively describe the production functions of the economic and ecological goods independently produced by cities and villages. In fact, such a functional form implicitly assumes that resource factors flow freely between urban and rural areas. This is an important prerequisite for realizing urban-rural integration and rural revitalization (He, 2018).
In general, cities have a strong comparative advantage and supply capacity in producing economic goods, while villages have a strong comparative advantage and supply capacity in producing ecological goods (Chen, 2008). In addition, without considering the influence of other factors, production efficiency and resource input change in opposite directions (Gao, 2021). Restricted by this law, the production efficiency of both the urban production department and the rural production department eventually tend to be equal. When producing the same product (E or B), their production function is also the same. This makes it tenable to establish the above functional forms (5) and (6). These assumptions are made for ease of analysis; Jorgenson (1967) and Mas-Colell (1973) made similar assumptions.
Assumption 4: With regard to the consumption side, the use and consumption of different products generate a certain level of utility or satisfaction. Uc and Uv denote the utilities obtained by cities and villages, respectively, when consuming products; Uc and Uv are determined using the following equations:
${{U}_{c}}={{U}_{c}}\left( E,B \right)$
${{U}_{v}}={{U}_{v}}\left( E,B \right)$
where Uc (••) and Uv (••) are the urban and rural utility function form, respectively.
These two equations are mainly demonstrated from a consumption perspective. The urban consumption sector and rural consumption sector adopt different consumption models, and their product structure and the way of obtaining utility are not the same. Therefore, there are two different forms of utility functions, expressed in equations (7) and (8). The consumption of products (i.e. ec or bc) absorbed by the urban consumption sector is not the same in quantity as the products (i.e. Ec or Bc) produced by the urban production sector. The same is true for the rural regional system. To determine the consumption function, it is assumed that products flow freely in both urban and rural systems. An analysis similar to the production function indicates that regardless of how many economic or ecological goods the urban consumption sector or rural consumption sector absorbs, the utility function form follows the functional form described by equations (7) and (8).
Assumption 5: W is utilized to denote the social welfare of the regional system, which is a quantity related to the utility of the urban system (Uc) and the utility of the rural system (Uv):
$W=W\left( {{U}_{c}},{{U}_{v}} \right)$
where W(••) is the social welfare function form of the regional system.

4.2 The establishment of objective function

Given the assumptions above, the question about the ideal state of urban-rural integrated development is transformed into the following problem. Given the constraints of equations (1) to (8), how is the optimal solution of Equation (9) calculated to ensure the social welfare of the entire regional system? If an optimal solution is obtained, the urban-rural integration system may realize the maximization of comprehensive benefits, and the goal of urban-rural integration may be achieved. Accordingly, we construct the basic objective function (Eq. 10) and its constraint conditions (Eq. 11):
$MaxW=MaxW\left( {{U}_{c}},{{U}_{v}} \right)$
$~s.t.:\left\{ \begin{array}{*{35}{l}} {{L}_{t}}={{L}_{e}}+{{L}_{b}},\quad {{G}_{t}}={{G}_{e}}+{{G}_{b}} \\ E={{E}_{c}}+{{E}_{v}},\quad B={{B}_{c}}+{{B}_{v}} \\ E=E\left( {{L}_{e}},{{G}_{e}} \right),\quad B=B\left( {{L}_{b}},{{G}_{b}} \right) \\ {{U}_{c}}={{U}_{c}}(E,B),\quad {{U}_{v}}={{U}_{v}}(E,B) \\ \end{array} \right.$
The equation set indicates this is a problem with 13 variables but only 9 equations. To address this problem, some additional conditions are required, in the form of at least four additional equations. These conditions are considered to be necessary parameters for the integrated development of urban and rural systems. Therefore, we further demonstrate the necessary conditions and feasibility of urban-rural integrated development.

4.3 Parameter solution for urban-rural integration

In the regional system, the key to analyzing the objective function is determining how to connect the urban system and the rural system. In the previous section on basic assumptions, we addressed this problem from production and consumption perspectives. Based on that analysis, the following is a concrete demonstration of additional conditions needed for the objective function to have a solution.

4.3.1 Derivation of the first additional condition

The following two equations can be obtained according to equations (3), (4), (5), and (6):
${{e}_{c}}+{{e}_{v}}=e\left( {{L}_{e}},{{G}_{e}} \right)$
${{b}_{c}}+{{b}_{v}}=b\left( {{L}_{b}},{{G}_{b}} \right)$
For any type of product (e or b), there is a substitution relationship between the amount of resource input (L or G) required to produce the same yield of product. For example, reduced labor input is replaced by increased land input; similarly, reduced land input is substituted by increased labor input. Accordingly, we determine the function or curve of substitutional relationship between labor and land used to produce an equal quantity of products. An intuitive approach is used to explain this using a series of phase diagram analysis techniques. First, Figure 2a describes the isoquant curve of labor and land in producing economic goods or ecological goods. The isoquant curve cluster is convex toward the origin, and has no intersecting lines. The yields on the curve far from the origin are greater than the yields on the curve close to the origin.
Figure 2 (a) The isoquant of economic goods (E) or ecological goods (B); (b) The allocation of labor and land between E and B
However, the resources in any region are limited, and the production of economic and ecological goods cannot infinitely expand. Under the constraints of the total amount of regional land and labor, Figure 2b further depicts how labor resources (L) and land resources (G) are reasonably allocated to produce economic and ecological goods. It is similar to the Edgeworth Box Diagram in form. The figure shows that the optimal point for both full utilization and reasonable distribution of labor and land resources is tangent point H. At that point, the isoquant curve of economic goods meets the isoquant curve of ecological goods. The curve e0Hb0, formed by connecting all such tangent points, is the optimum resource allocation curve.
We choose any other point to compare with point H to verify why the point represents conditions that are more reasonable or better. For example, point N is not a tangent point of two isoquants, but does represent the intersection of two isoquants. Here, we assume it is the intersection of curves e2 and b1. At point N, labor and land resources are fully utilized, but point N is not the optimal resource allocation point. This is because at point N, the production quantities of economic goods and ecological goods are e2 and b1, respectively. Compared with point H, point N only produces ecological goods with quantity b1. In contrast, point H can produce ecological goods with quantity b2 only when the same economic goods with quantity e2 are produced. The value for b2 is larger than b1. Therefore, the production at point N does not meet the optimal allocation of resources, and there remain opportunities for improvement. Eventually, the resource allocations are adjusted to reach point H, where there is no possibility for improvement. In other words, it is in a Pareto optimal state. In summary, curve e0Hb0 is the optimum resource allocation curve, and any point on this curve satisfies the following equation:
$\frac{\partial e\left( {{L}_{e}},{{G}_{e}} \right)/\partial {{L}_{e}}}{\partial e\left( {{L}_{e}},{{G}_{e}} \right)/\partial {{G}_{e}}}=\frac{\partial b\left( {{L}_{b}},{{G}_{b}} \right)/\partial {{L}_{b}}}{\partial b\left( {{L}_{b}},{{G}_{b}} \right)/\partial {{K}_{b}}}$
The left side of the equation is the slope of the isoquant curve of economic goods, and the right side is the slope of the isoquant of ecological goods. This indicates that “the ratio of marginal product of labor to marginal product of land (hereinafter referred to as ‘MPLL’)” of economic goods is equal to the ratio of the MPLL of ecological goods. In short, the marginal rates of substitution of the two production factors are equal.

4.3.2 Derivation of the second additional condition

The first additional condition is to address the optimal allocation of two given quantities of factors (L and G) to produce two products. Here, we further explore the optimal allocation of two given quantities of products (E and B) between urban and rural systems. Equations (7) and (8) indicate that the utility obtained by the urban system or rural system is a function of the quantity of economic and ecological goods consumed by urban areas or rural areas. Likewise, there is a hypothesized substitution relationship between the quantities of economic and ecological goods required to obtain the same utility. For example, to obtain the same utility, a reduced quantity of economic goods is replaced by an increase in ecological goods. As such, we determine the equivalent utility curve of the substitution relationship between the quantity of economic goods and ecological goods when urban and rural areas acquire the same utility, shown in Figure 3a. The equivalent utility curve has similar properties to the isoquant curve.
Figure 3 (a) The equivalent utility curve of cities (C) or villages (V); (b) The allocation of economic goods and ecological goods between C and V
Assuming that the production of economic and ecological goods is constant, Figure 3b describes the allocation of economic goods and ecological goods in the urban-rural system. This figure shows that the optimal point for the full utilization and rational distribution of economic and ecological goods is point J. Point J is the tangent point between the urban and rural equivalent utility curves. The curve C0JV0, formed by connecting all such tangent points, is the curve at which the entire regional system realizes full product utilization, and achieves the rational distribution of products between urban and rural areas.
Any point can be selected as a comparison to point J to verify why that point is better. For example, point K is the intersection of the equivalent utility curves Uc2 and Uv1, however, calculations determine that point K cannot satisfy the optimal allocation of products between urban and rural areas. The urban-rural allocation of products is eventually adjusted to point J, which is the Pareto optimal state. In short, the curve C0JV0 is the optimal product distribution curve. Any point on the curve is the tangent point between urban equivalent utility curve and rural equivalent utility curve, and any point on this curve satisfies the following equation:
$\frac{\partial {{U}_{C}}\left( e,b \right)/\partial e}{\partial {{U}_{C}}\left( e,b \right)/\partial b}=\frac{\partial {{U}_{V}}\left( e,b \right)/\partial e}{\partial {{U}_{V}}\left( e,b \right)/\partial b}$
or $\frac{\partial {{U}_{C}}\left( e,b \right)/\partial {{e}_{C}}}{\partial {{U}_{C}}\left( e,b \right)/\partial {{b}_{C}}}=\frac{\partial {{U}_{V}}\left( e,b \right)/\partial {{e}_{V}}}{\partial {{U}_{V}}\left( e,b \right)/\partial {{b}_{V}}}$
The left side of the equation represents the slope of the urban equivalent utility curve, and the right side represents the slope of rural equivalent utility curve. This equation indicates that the ratio of “the utility of marginal economic goods to the utility of marginal ecological goods (hereinafter referred to as ‘UMEE’)” in the urban system is equal to the ratio of UMEE in rural system. In brief, the marginal rates of substitution of the two products are equal. The parameters ec, bc, ev and bv in the equation are the quantities of products consumed by urban and rural areas, respectively, rather than the quantities produced. As previously noted, the consumption quantities may not coincide with production quantities, but this does not prevent the establishment of Equation (13).

4.3.3 Derivation of the third additional condition

Equations (5) and (6) indicate that the production of economic and ecological goods represents functions of labor input and land input. Conversely, labor and land inputs are inverse functions of the yield of economic and ecological goods. For convenience, the amount of land input is assumed to remain unchanged, and only labor input is used as an example. A certain amount of resource input produces economical products and ecological goods. This allows the construction of a maximum yield substitution curve under certain resource constraints, also called the production possibility curve, as shown in Figure 4a. The production possibility curve shows a transformation or substitution relationship between two optimal outputs. It is downward sloping and convex toward the upper right. The slope at any point on the curve is:
${{S}_{1}}=\frac{\partial e\left( {{L}_{e}},{{G}_{e}} \right)/\partial {{L}_{e}}}{\partial b\left( {{L}_{b}},{{G}_{b}} \right)/\partial {{G}_{b}}}$
Figure 4 (a) The production possibility curve; (b) The equivalent utility curve of the urban system
Different consumption combinations of economic and ecological goods bring different levels of utility to urban and rural areas. Figure 4b describes the equivalent utility curve of the urban system. Another potential assumption is that the yield of the rural system is constant. Here, the changes of ev and bv are essentially changes in e and b. Assume Figure 5 illustrates production and consumption with only one resource (e.g. labor) and one regional subsystem (e.g. city). In the graph, point M is the point where both maximum yield and maximum utility are achieved. At this point, the following equation is obtained:
$\frac{\partial e\left( {{L}_{e}},{{G}_{e}} \right)/\partial {{L}_{e}}}{\partial b\left( {{L}_{b}},{{G}_{b}} \right)/\partial {{G}_{b}}}=\frac{\partial {{U}_{C}}\left( {{e}_{C}},{{b}_{C}} \right)/\partial {{e}_{P}}}{\partial {{U}_{C}}\left( {{e}_{C}},{{b}_{C}} \right)/\partial {{b}_{P}}}=\frac{\partial {{U}_{C}}\left( e,b \right)/\partial e}{\partial {{U}_{C}}\left( e,b \right)/\partial b}$
Figure 5 The relationship between the isoquant and the production possibility curve
The left side of the equation represents the slope of the production possibility curve; the two fractions on the right side represent the slope of the equivalent utility curve of the urban system. This shows that “the ratio of yield of economic goods to ecological goods of marginal labor” is equal to “the ratio of the utility generated by marginal economic goods to the utility generated by marginal ecological goods in the urban system.”
A comparison of point M with points P, L, and E verifies why that point is better. At point P, the urban system obtains the highest utility of UC3. However, it is impossible to achieve such a high yield due to resource constraints: it exceeds the production possibility frontier. At point L, the resources are not fully utilized, and the urban system can only obtain the utility of UC1. At point E, the resources are fully utilized; however, the urban system can only obtain the utility of UC1. Therefore, only point M maximizes resource use, and allows the urban system to obtain the maximum utility of UC2. In brief, point M is the point that conforms to optimal utility and full resource utilization.
We can also consider only the rural regional system and land factor. Regardless of assumptions, we can establish the production and consumption relationship diagram with one type of resource and one regional subsystem, with conclusions that are consistent with the meaning of Equation (15).

4.3.4 Derivation of the forth additional condition

As mentioned earlier, consuming a certain level of economic or ecological goods generates some level of utility. Here, we assume that the yield of ecological goods remains constant, and we only consider changes in the yield of economic goods. When only the yield of economic goods changes, both cities and villages obtain a certain utility. Accordingly, we calculate all the maximum combinations of urban and rural utilities under the product yield constraint. This maximum combination is not a combination, but a set, which is called the maximum utility curve or utility possibility curve, shown in Figure 6a. The slope at any point on the curve is:
${{S}_{2}}=\frac{\partial {{U}_{C}}\left( e,b \right)/\partial e}{\partial {{U}_{V}}\left( e,b \right)/\partial e}$
Figure 6 (a) The utility possibility curve; (b) The equivalent social welfare curve
It is important to consider which point or points on this utility possibility curve maximize the welfare of the entire region. Different combinations of urban and rural utilities create different levels of social welfare. Therefore, at the same level of social welfare, we generate the equivalent social welfare curve of different combinations of urban and rural utility, shown in Figure 6b. This graphically represents the social welfare function, also called the social indifference curve.
Next, we discuss the relationship between the utility possibility curve and the equal social welfare curve without considering changes in the yield of ecological goods. Figure 7 shows that point Q is the only point that satisfies the maximum utility and maximum social welfare. Other points (e.g. S, R, Z) can be compared with point Q; however, only point Q satisfies both maximum utility and optimal social welfare. At this point, the following equation is obtained:
$\frac{\partial {{U}_{C}}\left( e,b \right)/\partial e}{\partial {{U}_{V}}\left( e,b \right)/\partial e}=\frac{\partial w\left( {{U}_{C}},{{U}_{V}} \right)/\partial {{U}_{C}}}{\partial w\left( {{U}_{C}},{{U}_{V}} \right)/\partial {{U}_{V}}}$
Figure 7 The relationship between utility possibility curve and equivalent social welfare curve
The left side of the equation represents the slope of the utility possibility curve, and the right side represents the slope of the equivalent social welfare curve. The equation indicates that “the ratio of utility generated by marginal economic goods in urban and rural areas” is equal to “the ratio of social welfare produced by marginal urban utility and marginal rural utility.” In addition, we can also consider the relationship between the utility possibility curve and equivalent social welfare curve of ecological goods under the condition where there is no change in the yield of economic goods. The resulting conclusion is similar to that associated with Equation (17).
In conclusion, the basic conditions for realizing urban-rural integrated development have been determined. Equations (1) to (17) indicate there are 13 variables and 13 equations, and there is a solution to the optimal social welfare issue for the entire regional system. In other words, when certain conditions are met, urban and rural areas enter into an integrated development pattern, and the social welfare of the entire region is maximized. Therefore, in the context of high-quality development, the urban-rural relationship cannot be understood as the simple overlapping and addition of urban-rural resource factors; it can also not be seen as rural transformation dominated by urbanization. These results highlight the need for a new integration prospect enhanced by the “two-wheel drive” of urbanization and rural revitalization based on equal exchange, balanced allocations, and full development of urban-rural factors. Further, urban and rural development should not be seen as an independent process, but as a product of deep-seated economic and social structural transformation (Yang, 2019). More effort is needed to emphasize the interaction and integrated development of urban and rural areas, change the current urban-rural separation and tradeoff development pattern, and promote the high-quality development of the entire region.

5 Further discussion

The findings above highlight many issues worth further discussion. First, this study introduces several types of isolines, such as isoquants, equivalent utility curves, and social indifference curves. This reflects the specific application of the concept of “equivalence” in the context of different resource factors, different regional systems, and different products (Liu et al., 2015). The concept of “urban-rural equivalence” is used as a value orientation for urban-rural integration, and as a golden key to address the imbalance between urban and rural areas. However, urban-rural integration under equivalence is neither the homogenization of urban and rural areas, nor the attempt to transform the space from being heterogeneous to absolutely homogeneous. Instead, the integration emphasizes the “inhomogeneity but equivalence” in the symbiotic context of urban and rural systems. Urban-rural equivalence does not mean making urban and rural areas identical, nor does it mean eliminating cities or villages. Rather, it acknowledges the differences between urban and rural natural conditions, social forms, production, and lifestyle through the vigorous development of productivity and institutional controls. This facilitates the ability for urban and rural residents to experience the same level of living conditions, job opportunities, quality of life, and social welfare.
Second, the equivalent curves are convex toward the origin and slopes downward to the right. A negative linear relationship provides the most intuitive way to model the fact that one element goes down as the other goes up. Using the urban-rural equivalent utility curve (i.e. Figure 3a) as an example, when urban or rural areas maintain the same level of utility, the increase in the utility of economic goods is at the expense of a reduction in the utility of ecological goods. In other words, there is a substitution relationship in the benefits of social-economic and ecological environment development. Due to differences in urban-rural resource endowments, rural residents’ desire to obtain more ecological products decrease, while their desire to obtain social and economic products increase. Conversely, the desire of urban residents to obtain more ecological products increases. This reflects the law of the diminishing marginal rate of substitution of the two products, and confirms the endogenous demands of urban-rural integration. Besides, Figure 2a shows a substitution relationship between the amount of resource inputs required to produce a product. However, the total outputs of the two products have a limit, as illustrated in Figure 4a. At that point, a trade-off is needed to determine the ratio of two products, to maximize the ability to meet the entire region’s needs. Therefore, both urban and rural regional systems should maximize their own resource endowment advantages, mitigate their shortcomings, and lay a solid material foundation for urban-rural integration.
It is difficult to realize integrated development focused on urban-rural equivalence. Urban and rural regional systems often leverage the system for their own interests. In the absence of certain institutional guarantees, ecological products are usually unable to enter trading market. This may lead to a polarization in development (Huang, 2020). To this end, effective institutional arrangements are needed. Examples include the effective division of labor agreements, cooperation, compensation, and oversight. This is an effective approach for achieving a benign cooperative game between urban and rural areas. In this light, urban-rural integration is a process reflecting the coordinated development of social economy and ecological environment within and between urban and rural areas.
Third, given the constraints of limited resources, the production and consumption of urban and rural areas are restricted by the production possibility curve (Figure 4a) and the utility possibility curve (Figure 6a), respectively. Any yield combination point or utility combination point outside the frontier is not possible. However, this does not make the curves unalterable in the future. When there is an increase in the supply of factors or products, or the technology level improves, the frontiers may expand outward. For example, Figure 8 shows that the production possibilities curve may shift from Y’Y’ to Y’’Y’’. At this point, there may be a larger yield combination of the two products, or a greater utility combination of urban-rural systems. This may elevate the welfare level of the entire region.
Figure 8 The establishment of a new balanced and integrated development pattern
This is also reflected in Figures 2a, 3a, and 6b. The marginal rate of substitution of the isoquant curve, the equivalent utility curve, and the equivalent social welfare curve is diminishing. Within the same cluster of equivalent curves, the farther the equivalent curve is from the origin, the greater its output, utility, or welfare is. Therefore, for a region, as the high-quality development process accelerates, appropriate measures are needed to push these types of isolines from the lower left to the upper right. This results in a new balanced and integrated development pattern based on higher comprehensive development benefits. This is illustrated by the equivalent utility curve of Uc4 and point M’ in Figure 8. Effort is needed to continuously deepen market-oriented reforms, and improve the effective allocation of production factors, such as land, labor, and capital, between urban and rural areas. This would help promote the integrated development of the diffusion effect for cities, and the endogenous power of villages.
Furthermore, there are significant spatial differences in urban-rural development in different regions of China due to the vast territory. This may lead to different patterns and processes for urban-rural integrated development in different regions. Using Figure 9 as an example, some areas may be at point M, while others may already be at point M’. Consequently, realizing urban-rural integrated development has regional asynchrony and temporal dynamics. In this sense, urban-rural integration is a goal, a state, and a process.

6 Conclusions

Promoting the integrated development of urban and rural areas is a key contemporary topic for China’s high-quality development. However, few studies have theoretically or empirically determined whether urban-rural integration can be realized. Drawing on the economic analysis methods of production and consumption, utility and welfare, and general equilibrium, this study develops a scientific and systematic answer and demonstration to address this question. The main conclusions are as follows.
A qualitative analysis at the theoretical level indicates that the core goals of urban-rural integration are to promote the efficient allocation and full utilization of urban-rural factors and outputs, facilitate urban and rural regional systems achieve a higher level of balanced development, and maximize the comprehensive benefits of urban-rural areas. In other words, the goal is to maximize the overall utility of the entire region. We argue that the ideal state of urban-rural integration should reflect a Pareto optimal allocation of urban rural resource factors and outputs, and the maximization of overall social welfare. A systematic demonstration, based on mathematical modeling and transformations, is used to test whether the above ideal state can be realized. This addresses the question of whether there is a solution to the optimal social welfare problem in the regional system. Drawing on the general paradigm of economic research, we propose basic assumptions, and construct the corresponding objective function and its constraints. Detailed analyses and derivations reveal there is a solution to this problem. Urban and rural areas can realize the transformation from binary separation to integrated development, and the entire region can reach an optimal development state.
Achieving urban-rural integration requires some basic conditions. First, the rational flow of urban-rural resource factors and outputs is an important prerequisite for realizing urban-rural integration. For ease of analysis, we consider two representative production factors (i.e. L and G); however, the flow of factors between urban and rural areas is more complicated in the real world. For example, rural land cannot be bought and sold at will, however, land in cities can be (Chen and Long, 2019). Second, the ratio of marginal product of labor to marginal product of land is assumed to be equal for economic and ecological goods produced by the entire region. Third, the ratio of “the utility of marginal economic goods to the utility of marginal ecological goods” is also assumed to be equal for urban and rural regional systems. When only one regional subsystem (e.g. city) and one resource change (e.g. labor) are considered, “the ratio of yield of economic goods to ecological goods of marginal labor” is equal to “the ratio of the utility generated by marginal economic goods to the utility generated by marginal ecological goods in urban system.” The same is true when only rural systems are considered. These conditions, of course, differ in the real world; but the assumptions were needed to conduct the analyses. Finally, when only considering the output change of one product (e.g. economic goods), the ratio of utility generated by marginal economic goods in urban and rural areas is equal to the ratio of social welfare produced by marginal urban utility and marginal rural utility. The same is true when only ecological goods are considered.
This paper verifies that the concept of “urban-rural equivalence” can be used as a value orientation for urban-rural integration, and is a golden key to address the imbalance between urban and rural areas. Urban-rural integration reflects the coordinated development of social economy and ecological environment within and between urban and rural areas. Realizing urban-rural integrated development has regional asynchrony and temporal dynamics. As long as appropriate measures are implemented, a new balanced or integrated development pattern can be established with higher comprehensive development benefits.
In conclusion, this research expands the theoretical depth and perspective of human geography when studying urban-rural integrated development, providing a theoretical basis for understanding the reasons for urban-rural imbalance, and identifying ways to achieve urban-rural integration. However, like all studies, this research has some limitations. For example, the study’s assumptions that there are two resource factors, two products, and homogeneous preferences are not fully consistent with actual circumstances. However, studies about urban-rural equilibrium or integration must be based on core assumptions, because a model that fully reflects the complexity of real urban-rural relationship has no solution. The goal of this study is to inform the future construction of theoretical and empirical models related to urban-rural integration. In addition, this research focuses on the construction, analysis, and derivation of theoretical models; these provide a starting point for subsequent research. Based on China’s actual urban and rural development status, it is very necessary to select specific and appropriate production, consumption, utility, and welfare functions; simulate the threshold for the interaction and integration of urban-rural systems; and provide a quantitative scientific basis for coordinating urban-rural relationships.

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