Theoretical Analysis and Empirical Study of Urban Expansion Based on the Marginal Principle

Abstract

Rapid urban expansion places unprecedented pressure on urban land management. Optimization of urban spatial layout has become a theoretical proposition and a practical problem associated with urban expansion. Thus, by using the social value measurement model, equivalent factor method, and marginal benefit measurement model, in this paper, we analyze the land resource allocation mechanism, efficiency loss, and reasonable interval. The study results are as follows: (1) Theoretical analysis shows that there are three ranges of land use for urban expansion in China—ideal, moderate and extreme—and it is reasonable to control the amount of land used for urban expansion within the moderate range. (2) Value measurement reveals that the marginal social value and marginal ecological value of cultivated land in Xuzhou show an overall upward trend. From the perspective of the constant price in 2018, the marginal social value increased from CNY 4.91 million/hm² in 2005 to CNY 14.31 million/hm² in 2018, while the marginal ecological value increased from CNY 9513.60/hm² in 2005 to CNY 13,629.70/hm² in 2018. (3) Empirical analysis shows that when the marginal value of land as cultivated land and construction land is equal, the actual scale of occupied agricultural land is 51,887.23 hm², of which 25,686.67 hm² of cultivated land is converted into construction land, sacrificing the social value of farmland, and 12,281.70 hm² of cultivated land is converted into construction land, ignoring the non-market value of land. Based on the perspective of the marginal principle, in this paper, we construct a model of urban expansion land use allocation and define reasonable intervals for urban expansion land use so as to provide a quantitative reference and decision-making basis for urban expansion governance.

1. Introduction

Since the mid-20th century, urban expansion has become a worldwide phenomenon that is difficult to contain, leading to ecological and environmental problems. After the reform and opening up, China’s urbanization level has rapidly increased from 19.7% in 1978 to 65.2% in 2022, with an average annual growth rate of 1%. The construction land area in various regions has significantly increased, and the urban population continues to increase. The urban construction land area in China increased from 6720 square kilometers in 1980 to 58,355 square kilometers by the end of 2021 [1]. However, in the rapid development process of China’s urbanization, a series of problems has emerged that seriously hinder the country’s modernization process, which are summarized as follows:

First, land use is inefficient. From 1978 to 2017, the urban built-up area in China significantly increased, with a yearly average expansion rate of 6.05%. This rate is 1.49 times higher than the growth rate of the urban population during the same period, surpassing the internationally recognized reasonable boundary of 1.12 [2]. According to statistics from the Chinese Academy of Sciences, the built-up area of 75 typical cities in China expanded by 7.46 times from 1972 to 2020, surpassing the growth rate of the urban population. It is evident that as China’s urbanization rapidly advances, the intensification and efficiency of land development and utilization have not been guaranteed, resulting in consistently low efficiency in the use of construction land.

Second, cultivated land resources are constantly lost. From 2000 to 2018, the arable land area in China decreased by 17,000 square kilometers, and the rate of decrease has been consistently declining—from 0.54% in 2000 to 0.11% in 2018 [3]. Urban expansion not only occupies a large amount of arable land, leading to inefficient land use, but also inevitably results in a decline in land quality, affecting production and triggering ecological deterioration. If not given due attention, it will pose a threat to the “red line” of 1.8 billion acres of arable land that the country is committed to protecting.

Third, the government has committed illegal activities. According to a report on cultivated land utilization and protection by the Ministry of Natural Resources published in 2019, the total area of cultivated land illegally occupied by local governments reached 1142,600 acres, of which the proportion of permanent basic farmland reached 12.55%. Some localities and provinces have failed to implement the legal approval and cultivated land balance system in government departments for construction land and other land types covering 94,900 acres [4]. Cultivated land protection is facing all kinds of pressures. Some regions have not fulfilled their responsibility of cultivated land protection, resulting in the serious loss of cultivated land in China and a grim protection situation.

Fourth, urban security risks are rising. In the past decade, China has witnessed several major accidents and sudden incidents that have seriously threatened the safety of Chinese cities, including the Shanghai “12·31” Bund stampede, the Tianjin Port “8·12” explosion, and the Shenzhen “12·20” mountain collapse, which all reveal the underestimated problems in current urban security. With the expansion of cities, hidden urban safety concerns cannot be ignored. This is a daunting task that requires the cultivation of sensitive awareness. If such issues are not identified and properly addressed in a timely manner, immeasurable losses may be experienced.

The rapid expansion of cities has sacrificed the efficiency of land use, accompanied by a sharp decline in cultivated land and ecological deterioration, which has caused unprecedented pressure on urban land management. Therefore, the scientific construction of a theoretical framework for urban space optimization and the optimization of urban space layout based on the economic, social, and ecological benefits of land has become a theoretical proposition and practical problem in the study of urban expansion and space optimization. Therefore, based on the marginal principle, in this paper, we take Xuzhou City as the research area and divides the theoretical interval of urban land quantity through theoretical analysis of the relationship between land price and urban expansion. An optimal allocation model of urban land use was constructed from the perspectives of social benefit, ecological benefit, and economic benefit. The optimal scale of urban land use was determined based on the marginal income of agricultural land and construction land.

2. Theoretical Analysis and Research Framework

2.1. Theoretical Analysis

2.1.1. Literature Combing

How to control a series of problems caused by the disorderly expansion of cities and the sharp decrease in cultivated land and ecological space has become a hot topic of public concern. As early as in the 19th century, scholars abroad began to conduct in-depth theoretical research on the important issue of urban expansion, accumulating experience and mature theories over the years, which can be divided into three categories: research on the characteristics and effects of urban expansion, analysis of driving factors, and research on urban governance and regulation. Regarding theoretical research on the spatial structure of urban expansion, the “concentric circle theory”, “fan theory”, “multi-core mode”, and “central place theory” proposed by foreign scholars have become classic models in the study of the spatial structures of urban areas [5]. Regarding the mechanism of urban sprawl, foreign scholars have made great progress, and their views can be summarized with respect to transportation, culture, market, government, and other levels [6,7,8,9,10]. In order to effectively control the phenomenon of urban expansion, a series of innovative concepts such as “New Urbanism”, “Compact City”, and “Smart Growth” have emerged in Western countries [11,12,13], and governance regulations have shifted, focusing on urban living quality and the ecological environment, with targeted policy research published on urban expansion regulation [14,15,16,17].

China mainly conducts research on urban expansion based on mature theories and experiences from abroad, as well as the flexible application of “3S” technology (collective term for remote sensing technology, geographic information systems, and global positioning systems). Specifically, this research can be divided into three categories: spatial structure exploration, urban expansion mechanism and evaluation, and boundary regulation and governance research. Domestic scholars have conducted extensive research on the structure of urban expansion [18,19,20,21,22] and proposed corresponding urban spatial structure models for different regions, including infilling, extension, corridor, and leapfrog models [5]. Research on urban expansion mechanisms and evaluation can be divided into qualitative and quantitative categories, and scholars have summarized the driving factors of urban expansion as economic, transportation, policy, and geographic/environmental factor, among others [23,24,25,26,27,28,29,30,31]. In terms of boundary regulation and governance research, domestic scholars have taken Western concepts as guidance, mainly proposing urban expansion governance strategies from a planning perspective, focusing son urban functions and food security and proposing strategies such as “connotative growth”, “combining blockage and release with emphasis on release”, and promoting the marketization of land elements [32,33,34,35,36,37].

A few studies have investigated urban expansion from the perspective of marginal analysis; it is more scientific to study the marginal increment of construction land than the absolute increment. Therefore, from the perspective of the marginal principle, in this paper, we take the allocation and loss of land resources as the starting point, analyze the changes in marginal benefits of land during the process of urbanization, and determine the ideal scale of urban expansion.

2.1.2. Concept Definition

Urban expansion is a very common phenomenon. The higher marginal benefits of construction land compared to agricultural land inevitably result in land use change. Due to the non-market value of land, which is difficult to measure in monetary terms, people often choose to ignore it when converting land use. The negative impacts arising from excessive land use changes gradually manifest in people’s daily lives. For example, the livelihoods of displaced farmers are not guaranteed, and the contradiction between humans and land becomes more prominent. How to properly grasp the degree of urban expansion is currently a challenging issue for scholars to study.

Therefore, scholar Futian Qu proposed the theory of non-agriculturalization of agricultural land, analyzing the general laws of economic growth and changes in land use structure. In Figure 1, MR represents the marginal benefits of land used as construction land, while MC represents the marginal costs of converting agricultural land to construction land. There are three special price types of agricultural land in China, which are expressed as follows. Un the process of transforming agricultural land into construction land, P₃ is the price of MC′ with ecological benefit cost included, P₂ is the price of MC′ without ecological benefit cost included, and P₁ is the price of MC′ considering the influence of certain factors (such as government) [38]. The amount of agricultural land (Q₃) is the amount of land that has to be occupied for urban economic development, and the land use efficiency reaches the optimal level at this time, while OQ₂ is the sacrificial loss. When the amount of land grows to Q₂, the excessive occupation of land due to the neglect of the non-market value of agricultural land leads to a decline in land use efficiency, and Q₃Q₂ is excessive loss I. On the basis of the failure of the land market due to government interference, the demand for land resources is too high; the land continues to be occupied, and the amount of land grows to Q₁, while Q₂Q₁ is excessive loss II.

Scholar Xiaoshun Li pointed out that according to particular national conditions, the price of agricultural land resources in China can be divided into three types, which are considered from the perspectives of economy, ecology, and society, respectively. Since the land market itself has certain defects, agricultural land resources are often difficult to trade at their comprehensive price (P₁), which is usually replaced by P₂ (excluding ecological value), whereas P₃ is not conducive to sustainable development because it ignores non-market value; therefore, there are corresponding regulatory boundaries for the expansion of our cities based on these three types of value [20].

2.1.3. Research Hypothesis

The above theory analyzes the allocation and losses of land use in urban expansion through the analysis of marginal social costs and marginal private costs and proposes the goal of rational farmland protection. Accordingly, in this paper, we further divide the analysis into social benefits, ecological benefits, and economic benefits for a more detailed examination.

Land is a non-renewable resource. It is easy to convert agricultural land into construction land, but the transformation from construction land to agricultural land is almost impossible, and the original land quality may not be restored, even at great cost. Therefore, for urban expansion, we should not only conduct analyses from the perspective of economic resource allocation but also balance the social and ecological benefits of agricultural land [39].

With the addition of social benefits, we can obtain a more complete quantity of urban land use allocation, as shown in Figure 2, where MR represents the marginal benefits of land used as construction land, while MC represents the marginal costs of converting agricultural land to construction land. P′₁ is the price at which the marginal benefit of MC₁, which includes social benefits, ecological benefits, and economic costs, is equal to the marginal benefit of being used as construction land, and the corresponding optimal quantity of urban land use is Q′₁. P′₂ is the price at which the marginal benefit of MC₂, which does not include social benefits and costs, is equal to the marginal benefit of being used as construction land, and the corresponding optimal quantity of urban land use is Q′₂. P′₃ is the price at which the marginal cost of developing agricultural land after government intervention is equal to the marginal benefit of construction land, and the corresponding optimal quantity of urban land use is Q′₃.

Accordingly, the urban land use theory interval is divided into three segments: Q′₁, Q′₂, and Q′₃.

OQ′₁ is the quantity of cultivated land that must be occupied in China’s land market under the condition of perfect urbanization. It includes the total economic, social, and ecological benefits of the loss of land in the process of urban expansion, and at this point, the overall efficiency of the comprehensive use of land resources is maximized, meeting the needs of sustainable economic growth and maximizing social welfare. Therefore, OQ′₁ can be regarded as the ideal range under the premise that China’s land system is sound. Currently, China is in the important process of rapid urbanization, and it is necessary to sacrifice a certain amount of land resources to support economic development; however China’s land system needs to be improved. It is difficult to achieve control of urban land quantity within the ideal range at the current stage.

Q′₁Q′₂ is the quantity of land with an estimated value lower than its true value due to excessive consumption of land resulting from imperfect land use systems and other factors, leading to the absence of non-market values such as social security for cultivated land resources. As a result, the overall efficiency of land resource allocation is suboptimal. During the process of urban expansion, occupying farmland without providing reasonable compensation for farmers’ livelihoods has resulted in a significant cost for rural areas and a loss of social welfare, as represented by BDE. In this case, Q′₁Q′₂ can be considered a moderate range under market failure conditions. Although this range sacrifices the social value of farmland resources to meet the demand for urban development land in the new era, it does not damage the regional ecological environment. At a certain stage of economic development, the lost social welfare can be compensated for through other means.

Q′₂Q′₃ represents the excessive consumption of land resulting from government failure and distorted land prices that further reduce the cost of urban expansion land use, overlooking the non-market value of agricultural land. As a result, the overall efficiency of land resource allocation is lower. At this point, the region must pay a huge resource price to maintain economic development, and further social welfare loss is experienced, as represented by DEHF. Under the condition of land market failure and government interference to limit land prices, Q′₂Q′₃ can serve as the basis for the extremum interval within this range [40], where a huge resource cost must be paid. Due to the neglect of the social benefits of cultivated land resources and the failure to consider the ecological benefits of cultivated land resources, the foundation of regional sustainable development is weakened, and it is difficult to find alternative ways to restore or make up for it.

Therefore, based on China’s reality combined with scientific and reasonable prediction, in this paper, we propose that the amount of land used for urban expansion should be regulated in a moderate range for the following reasons:

• In the process of urban expansion, we should always focus on ensuring national food security and maintaining social stability. Excessive expansion can jeopardize arable land, with considerable costs, hindering the sustainable development of the economy. Therefore, the amount of urban expansion land use should be strictly controlled within a moderate range.
• To support sustainable and healthy economic development in the new era of rational urban growth and associated land demand while considering both ecological security and environmental improvement, urban land use quantity should be strictly controlled in a moderate range. The extreme range places too much emphasis on urban development and ignores the maintenance of the regional ecological environment and sustainable economic development, the price of which is difficult to estimate but which does not conform with development requirements of “harmonious coexistence between man and nature”.
• If cultivated land is overprotected and the land use index cannot be supplemented in the process of urban development, slow economic growth or even lag will inevitably result, preventing regional economic development, hindering the modernization process of China, and resulting in additional social cost. The government can make up for the social security function sacrificed by farmers by perfecting the public service.

2.2. Research Framework

Based on the marginal principle, in this paper, we construct a research framework according to a “basic theory combing-non-market value calculation-cost and benefit estimation” to propose “reasonable scale determination”. First, we analyze the relationship between land prices and urban expansion, as well as the special control boundaries in China, from a theoretical perspective. We also analyze the land resource allocation mechanism, efficiency loss, and theoretical range in urban expansion from the perspectives of social benefits, ecological benefits, and economic benefits. Secondly, a model is constructed to measure the social and ecological value of farmland, and an urban land use optimization allocation model is constructed based on the marginal benefits of farmland and construction land, with the optimal scale of urban land use determined accordingly. The overall logical relationship is shown in Figure 3.

3. Empirical Analysis and Hypothesis Validation

3.1. Research Area Overview

Xuzhou City covers an area of 11,765 square kilometers and is located at 33°43′~34°58′ N and 116°22′~118°40′ E. Located southeast of the North China Plain, it is known as the Five-Province Crossroads and is an important transportation hub in China (Figure 4). In 2019, the city’s gross domestic product (GDP) reached CNY 715.135 billion, with an urbanization rate of 66.7%, corresponding to an increase of 1.6% over the previous year. The urban built-up area exhibits an expansion trend to the southeast, making it a typical area of urban land expansion.

3.2. Study Methods

The calculation presented in this section is based on the annual average social benefits and ecological benefits. As they are associated with non-market value, when measuring their values, the total value is a linear function of the cultivated land area, with the total social value equal to the unit social value multiplied by the cultivated land resource area. When calculating the marginal value through differentiation, the resulting derivative is a constant that represents the unit social value per unit area. Therefore, the average value can be seen as the marginal value. Alternatively, it can be understood that the social and ecological benefits lost by converting a unit area of cultivated land resources to construction land are equal to the social and ecological benefits provided by the cultivated land resources.

3.2.1. Marginal Social Benefit Model

In terms of social stability, cultivated land can meet people’s requirements for food and clothing, curb the loss of the agricultural labor force, and provide food security. In terms of social security, cultivated land can provide basic living insurance, old-age insurance, and unemployment insurance to meet the basic living needs of farmers. In the process of calculation, in order to avoid overestimated the social value of cultivated land in the case of the social value of cultivated land, in this paper, we refer to the existing approach.

In terms of social stability, cultivated land can meet people’s requirements for food and provide employment opportunities to prevent the loss of the agricultural labor force, ensuring food security. In terms of social security, cultivated land can provide basic life insurance, pension security, and unemployment insurance for rural residents, satisfying their basic living needs [41]. In the calculation process, in order to avoid overestimating the social value of cultivated land due to incomplete or duplicated estimation of its social value, in this paper, we refers to existing models [42]; the specific formula for estimation is expressed as follows:

$$V_s=V_{s1}+V_{s2}$$

(1)

where V_s represents the social value, V_s1 represents the social stability value, and V_s2 represents the social security value.

(1)

Social stability value model

The specific formula of the social stability value model is expressed as follows:

$$V_{s1}=\frac{S_a}{r}\times m$$

(2)

where S_a represents the per capita urban subsistence allowance, m represents the rural population supported by a unit of cultivated land resources, and r represents the reduction rate of cultivated land.

(2)

Social security value model

The specific formula of the social security value model is expressed as follows:

$$V_{s2}=V_{sy}+V_{sj}$$

(3)

where V_sy represents the basic living security value of cultivated land resources, and V_sj represents the employment security value of cultivated land resources.

The specific formula for the basic living security value of cultivated land resources is expressed as follows:

$$V_{sy}=\frac{Y}{P\times r}$$

(4)

where Y represents the basic pension for rural residents (CNY/person), and P represents the per capita cultivated land area (hectares/person).

The specific formula for the employment security value of cultivated land resources is expressed as follows:

$$V_{sj}=\frac{(K_1/K_2)\times S}{P\times r}$$

(5)

where K₁ represents the per capita productive net income of rural residents (CNY/person), K₂ represents the per capita disposable income of urban residents (CNY/person), S represents the unemployment insurance provided by the government for urban residents (CNY/person), and P represents the per capita cultivated land area (hectares/person).

3.2.2. Marginal Ecological Benefit Model

Considering the feasibility of the research and the availability of data, in this study, we conducted a large-scale estimation of the ecological service value of arable land. Based on the research of Xie Gaodi et al. [43,44], the equivalent factor method was used to calculate the ecological service value of agricultural land in different periods in Xuzhou City. Building upon this, Fu Guanghui et al. revised the equivalent factor table for ecosystem service value in Jiangsu Province [45,46]. In this study, Xuzhou City was taken as the research area, and the table mentioned above was used to objectively reflect the characteristics of the region.

The formula for calculating the value quantity of a unit equivalent factor is expressed as follows:

$$E_a=\frac{1}{7}{\displaystyle {\sum }_{i=1}^n\frac{m_i\times p_i\times q_i}{M}}$$

(6)

where E_a represents the value of the unit equivalent factor of the agricultural ecosystem (CNY/hectare), m_i represents the planting area of crop i (hectares), p_i represents the national average price of crop i (CNY/ton), q_i represents the yield of crop i (tons/hectare), and M represents the total planting area of n crops.

Based on this, the formula for calculating the ecological service value per unit area is expressed as follows:

$$E_i=e_i\times E_a$$

(7)

where e_i represents the equivalent factor.

3.2.3. Marginal Cost–Benefit Model

The problem of land resource allocation ultimately refers to the proportion of land resources allocated to agricultural land and construction land as production factors, requiring a value that maximizes the marginal utility of land. At this point, in theory, the optimal allocation of land resources is achieved as long as the marginal benefits of agricultural land and construction land are equal. In this article, we take Xuzhou City as the research area, organize the supply and demand data of land resources, calculate the marginal returns of agricultural land and urban land, and analyze how to allocate them to achieve equal marginal returns. This determines the degree of rational growth suitable for Xuzhou City. Land resources, as a production factor, have a certain impact on local economic development. By referencing the C-D production function, we can explore the economic output relationship between land and the agricultural and non-agricultural sectors [47,48]. The original function only includes two production factors: capital input and labor input. In this article, we expand the original function it by adding land resource input in order to calculate the marginal output of land as farmland and construction land [47]. The optimal allocation of land resources can be achieved when the marginal outputs of land—both as farmland and construction land—are equal. The specific formula for estimation is expressed as follows:

$$Y_{agr}=A\times K_{\mathrm{agr}}^{\alpha }\times L_{agr}^{\beta }\times Lan{d}_{agr}^{\gamma }$$

(8)

$$Y_{nonagr}=B\times K_{\mathrm{nonagr}}^{\chi }\times L_{nonagr}^{\delta }\times Lan{d}_{nonagr}^{\epsilon }$$

(9)

where Y_agr represents the gross domestic product (GDP) of the primary sector; Y_nonagr represents the GDP of the secondary and tertiary sectors; K_agr, L_agr, and Land_agr represent the capital, labor input, and land resources used in agricultural production, respectively; and K_nonagr, L_nonagr, and Land_nonagr represent the capital, labor input, and land resources used in non-agricultural construction, respectively.

Differentiating the equation with respect to the land factor yields the marginal revenue of land resources. The specific formula for estimation is expressed as follows:

$${MR}_{agr}=A\times \gamma \times K_{\mathrm{agr}}^{\alpha }\times L_{agr}^{\beta }\times Lan{d}_{agr}^{\gamma -1}$$

(10)

$${MR}_{nonagr}=B\times \epsilon \times K_{\mathrm{nonagr}}^{\chi }\times L_{nonagr}^{\delta }\times Lan{d}_{nonagr}^{\epsilon -1}$$

(11)

Referring to the formulas derived for marginal cost and marginal revenue curves, the specific formula for estimation is expressed as follows:

$$\log Q_D=C_1+C_2\times \log MR$$

(12)

$$\log Q_S=C_3+C_4\times \log MC$$

(13)

where Q_D and Q_S represent the actual quantity of agricultural land occupied by construction land.

Estimating the equation yields C₁, C₂, C₃, and C₄, which are then substituting into Formulas (12) and (13), with MC equal to MR. Solving these equations yields the optimal quantity of urban land use for land resource allocation, denoted as Q. The specific formula for estimation is expressed as follows:

$$Q=\exp \left[\frac{\left(C_1\times C_4-C_2\times C_3\right)}{C_4-C_2}\right]$$

(14)

When MC is the marginal economic value, the obtained Q is the limit quantity. When MC corresponds to the marginal ecological value, the obtained Q (the ideal quantity) is the marginal social value including the marginal ecological value. When MC represents marginal economic value, the resulting Q is the optimal quantity or the limit quantity. When MC incorporates marginal ecological value, the resulting Q is the moderate quantity or the appropriate quantity, and when MC combines marginal ecological value with marginal social value, the resulting Q is the ideal quantity.

3.2.4. Data Sources

The land data were sourced from the “Xuzhou Statistical Yearbook” for the years 2005–2018. The annual deposit interest rate published by the People’s Bank of China was obtained through inquiries to the National Bureau of Statistics. Other major socioeconomic data were sourced from the “China Statistical Yearbook”, “Compilation of National Agricultural Cost and Income Data”, “Xuzhou Statistical Yearbook”, “Statistical Data from the Xuzhou Civil Affairs Bureau”, and other relevant sources for the years 2005–2018.

3.3. Results

3.3.1. Calculation of Marginal Social Benefits

This article takes the risk-adjusted value added to the risk-free rate as the discount rate for farmland. The one-year deposit interest rate published by the People’s Bank of China was selected as the risk-free rate. The average change in the Consumer Price Index for residential consumption from 2005 to 2018 was used as the risk adjustment value.

By collecting and organizing the relevant data and inputting them into the formula, the social value of farmland resources in Xuzhou from 2005 to 2018 was calculated. The resulting social value of farmland resources represents the infinite-term income of farmland resources at that time point, which is theoretically different from marginal social benefits. Therefore, it is necessary to multiply the obtained social value by the discount rate of farmland to convert the infinite social benefits of farmland resources into the average social benefits for that year [38]. The Consumer Price Index for residential consumption was used to convert the values into constant prices of 2018, as shown in

Table 1. Social benefit and unchanged price of farmland resources in Xuzhou in 2018 (unit: CNY 10,000/hectare).

Year	Social Benefit	Year	Social Benefit
2005	4.91	2012	8.12
2006	5.19	2013	9.23
2007	5.56	2014	11.77
2008	5.93	2015	12.17
2009	6.38	2016	12.65
2010	6.85	2017	13.35
2011	7.17	2018	14.31

.

3.3.2. Calculation of Marginal Ecological Benefits

When calculating the equivalent ecosystem service value of the farmland system based on the actual situation in Xuzhou, in this study, we selected the main types of food crops, i.e., rice, wheat, and corn. The value of Ea was calculated to be CNY 1972.46/hm². The per unit ecosystem service value of farmland in Xuzhou was calculated utilizing Formula (7). The annual average value of loan interest rates was used to adjust the ecosystem service value over time. Based on this, the ecological value of farmland resources in Xuzhou was calculated and converted into constant prices for 2018, as shown in

Table 2. The constant price of ecological service value of agricultural land resources in Xuzhou City in 2018 (unit: CNY 10,000/hectare).

Year	Ecological Service Value	Year	Ecological Service Value
2005	2.11	2012	2.52
2006	2.19	2013	2.60
2007	2.22	2014	2.70
2008	2.27	2015	2.81
2009	2.39	2016	2.89
2010	2.42	2017	2.97
2011	2.43	2018	3.03

.

3.3.3. Marginal Cost and Benefit Calculation

Formulas (8) and (9) were estimated based on the model established in the previous section. A working file was created in SPSS into which the parameters were input. Then, the variables were transformed into logarithmic form, and a linear regression was performed to obtain the estimated results of the equation, as shown in

Table 3. Equation estimation results.

	Ln A	α	β	γ	R2	DW
Formula (10)	6.48	0.055	−1.394	2.052	0.991	1.799
	Ln B	α	β	γ	R2	DW
Formula (11)	−4.505	0.462	0.140	1.022	0.995	1.933

.

Table 3 shows that the degree of fit of the regression model meets the requirements, indicating that the model is reliable. Substituting the obtained parameters into Formulas (10) and (11), calculations were performed separately to obtain the marginal returns of land resources in Xuzhou for agricultural land and construction land from 2005 to 2018. The results are shown in

Table 4. Marginal income of agricultural land in Xuzhou City (unit: CNY 10,000/a* hm²).

Year	MRagr	Year	MRagr
2005	6.75	2012	9.61
2006	7.04	2013	10.01
2007	7.73	2014	11.05
2008	8.12	2015	11.98
2009	8.40	2016	12.70
2010	8.06	2017	14.66
2011	8.69	2018	17.06

and

Table 5. Marginal income of construction land in Xuzhou City (unit: CNY 10,000/a* hm²).

Year	MRnonagr	Year	MRnonagr
2005	71.59	2012	157.78
2006	74.76	2013	167.46
2007	101.41	2014	186.23
2008	94.78	2015	192.61
2009	116.55	2016	192.51
2010	131.03	2017	213.24
2011	137.73	2018	214.27

.

By substituting the collected values of Q_D and Q_S into Formulas (12) and (13) and adding the marginal social benefits and marginal ecological benefits to MC, we can obtain the three types of marginal values for farmland resources, namely MC₁, MC₂, and MC₃. By estimating the equation, we can obtain the values of C₁, C₂, C₃, and C₄. The results are shown in

Table 6. Parameter estimation.

	C1	C2
MR	5.175	0.236
	C3	C4
MC3	5.868	0.208
MC2	5.840	0.207
MC1	5.730	0.206

.

By substituting the obtained values of C₁, C₂, C₃, and C₄ into Equation (14), the limit quantity can be calculated. Similarly, the ideal quantity and moderate quantity can be obtained.

By completing the estimation of the equation mentioned above, the quantity of land use allocation for urban expansion in Xuzhou from 2005 to 2018 was finally obtained. Rationality loss refers to the ratio of the rational quantity to the actual urban expansion area. Moderation loss refers to the proportion of the moderate range occupying agricultural land compared to the actual urban expansion area. Limit loss refers to the proportion of agricultural land occupying the extreme range compared to the actual urban expansion area. The results are shown in

Table 7. Allocation of land resources for urban expansion in Xuzhou City from 2005–2018.

MC1 = MR	MC2 = MR	MC3 = MR	Actual Urban Expansion Area	Rationality Loss	Moderation Loss	Extreme Loss
13,918.86	39,605.53	60,839.83	51,887.23	26.83%	49.50%	23.67%

.

4. Discussion

Table 7 shows that when both the non-market value and market value of agricultural land are considered in cost–benefit decision making, the optimal allocation quantity is 13,918.86 hectares. At this point, the overall efficiency of land resource utilization is maximized, and both the market value and non-market value of agricultural land are fully reflected, resulting in the maximum social welfare according to welfare economics. Excluding factors such as market failure and government interference, this represents the optimal allocation result. However, it is difficult to achieve this range of land allocation for construction land in Xuzhou at the current stage in China.

When only the market value and ecological value of agricultural land are considered, the optimal allocation quantity is 39,605.53 hectares. At this point, the overall allocation efficiency of land resources is suboptimal, as it neglects the social benefits of farmland resources and leads to a loss in terms of overall social welfare. Excessive occupation of agricultural land is mainly due to the imperfect nature of the land system. Once the economy develops to a certain stage, this can be remedied by improving the land use market.

When only the economic benefits of farmland are considered, leading to an underestimation of its comprehensive value, the optimal allocation quantity is 60,839.83 hectares. At this point, the overall allocation efficiency of land resources is low, as it not only ignores the social benefits of farmland resources but also fails to consider their ecological benefits, resulting in further loss of social welfare. Excessive consumption of land due to government interference in the land market comes at a huge cost and is difficult to recover from. Therefore, the quantity of land used for urban expansion should not exceed 60,839.83 hectares, which represents the limit quantity.

According to the analysis presented above, the quantity of urban land can be divided into three ranges: optimal, moderate, and extreme. Based on China’s basic national conditions and current development situation, the current occupation of agricultural land by urban expansion should not exceed the moderate range. In the future, the conversion of agricultural land to construction land should be kept within the moderate range, which is a reasonable choice. The reasonable loss proportion is 26.83%, which represents the scale of economic growth that must be utilized and is considered a rational scale. This “rational scale” standard is based on achieving a relatively free and competitive market equilibrium for land resources that fully considers the ecological and social costs of land use, thus internalizing the external costs of land use.

The moderate loss proportion is 49.50%, which indicates a market failure in land utilization due to the inherent characteristics of land use. This market failure results in the inability to incorporate the social benefits of farmland utilization into economic decision making, primarily due to the underestimation of farmland benefits and the failure to internalize its external potential, leading to rapid conversion of farmland to construction land. Due to the inherent characteristics of land use, it is currently difficult to eliminate this market failure.

The extreme loss proportion is 23.67%, which is caused by excessive demand for land resources due to the exclusion of market mechanisms. There are two main reasons for this. On one hand, an unscientific and incorrect performance-oriented mindset has driven the use of land as the main tool to promote economic growth at any cost; on the other hand, there are flaws in the planned economy nature of land use planning itself. In conclusion, there is a significant loss when converting farmland to construction land. The disorderly expansion of cities and imbalanced urban spatial structure are the result of incomplete land market development, government exclusion of the land market, and price controls.

Therefore, we believe that the governance and regulation of urban expansion in China should be divided into two steps, the first of which is to correct government failure, as market failure is determined by the characteristics of land use itself and cannot be changed. The government should focus on the quantity of land, reducing the increase in land use. In terms of future urban expansion regulation, the emphasis should be on institutional development, optimizing performance assessment systems, improving property rights systems, setting a reasonable range for urban land quantity, strictly managing and protecting ecological wetlands, implementing farmland protection management systems, monitoring and supervising the implementation of farmland protection measures, reducing illegal land acquisition by the government, and avoiding excessive encroachment on land resources due to government interference in the land market. The second step is to correct market failure by incorporating the ecological and social value of farmland into the public policy decision-making system in order to improve the land system, enhance public services, improve social security for farmers, compensate for the social welfare lost due to excessive use of agricultural land, and promote coordinated urban–rural development.

5. Conclusions

This paper, based on the perspective of marginal principles, differs from pure economics in that it pays more attention to the social benefits of land resources, incorporating social benefits into a new model and theoretically dividing urban expansion into three types: ideal, moderate, and extreme. Our research proposition has been deepened and expanded. By constructing a model for land use allocation in urban expansion, taking Xuzhou City as an example, a reasonable range for land use in urban expansion was delineated. This work provides a reference for the management of urban expansion. The main results and conclusions are summarized as follows:

(1)

Theoretical analysis suggests that agricultural land resources have economic, ecological, and social value, and different allocation methods of land resources result in different overall social welfare. The quantity of agricultural land occupied during urban expansion should be divided into three types according to whether the non-market value of land is considered in cost–benefit decisions: ideal quantity (Q′₁), moderate quantity (Q′₂), and limit quantity (Q′₃). To meet the needs of high-quality development and rational urban growth in the new era and to consider ecological improvement and social stability, the quantity of land occupied during urban expansion should be strictly controlled within the moderate range (Q′₁Q′₂).

(2)

Value assessment reveals an overall increasing trend in the marginal social value and marginal ecological value of farmland in Xuzhou City. From 2005 to 2018, based on constant prices, the marginal social value increased from CNY 4.91 million/hectare to CNY 14.31 million/hectare. It is evident that agricultural land resources have played a positive role in ensuring food security and maintaining social stability. The social security value of agricultural land resources accounts for a large proportion of the social value in Xuzhou City. They constitute the main body of social value, as agricultural land resources can meet the basic needs of farmers and serve as the foundation for their livelihoods. The marginal ecological value also increased from CNY 9513.60/hectare to 13,629.70 yuan/hectare. It is evident that the ecological service function of agricultural land resources is gradually being recognized, but it still lags far behind the social value. This indicates that the ecological function of agricultural land is yet to be fully explored, and its value needs to be increased.

(3)

Empirical analysis shows that when the actual marginal outputs of land used as farmland and construction land are equal, the actual scale of occupied agricultural land is 51,887.23 hectares, among which 25,686.67 hectares of arable land were converted to construction land, sacrificing the corresponding social value, and 12,281.70 hectares of arable land were converted to construction land, neglecting the non-market value of land. Therefore, the quantity of agricultural land occupied during urban expansion should be regulated within the moderate range, which is more reasonable.

(4)

In terms of policy recommendations, we propose that the government should prioritize land stock and reduce land increment. It is necessary to improve institutional development, optimize the performance evaluation system, and strengthen the land system. Providing public services and enhancing social security for farmers will promote coordinated development between urban and rural areas.

It should be noted that in this study, the calculation of the non-market value of agricultural land is based on previous research. However, there is currently no unified assessment standard for this value, and the results may deviate from the actual non-market value of agricultural land. Therefore, the accuracy of the calculated quantity of land use allocation for urban expansion needs improvement. In future research, it is necessary to further evaluate the real value of agricultural land based on specific circumstances in order to provide more detailed guidelines for government decision making.

In this study, we constructed a model of urban land use allocation and examined the theory of urban expansion from the perspective of marginal principles to derive a reasonable strategy for determining the quantity of urban expansion. However, the integration of the quantity of land use for rational urban expansion with spatial layout is a significant issue, and further consideration and exploration are needed in future research.