Appropriate carbon emission from large-scale breeding based on a binary analysis framework of external environmental costs and resource losses

ABSTRACT

The emission of greenhouse gases is one of the main reasons for climate change, which comes from partially the agricultural production activities, especially livestock and poultry-scale breeding. Massive breeding of livestock and poultry can ensure the safe supply of meat, but it leads to much carbon emission. On the one hand, it is difficult to get zero carbon emissions based on today’s technology level. On the other hand, the emission shouldn’t be too high. Therefore, it is very necessary to determine appropriate carbon emission criteria and then to ensure the sustainable development of scale breeding farms. In this paper, after modelling resource losses, external environmental costs and carbon emissions, the binary analysis framework of resource losses and external environmental costs of scale-breeding farms was built, and then the relationship between the carbon emission and binary analysis framework was analysed in detail. Then, the criteria for determining moderate carbon emissions have been established. Research studies show that carbon emission decreases with the control of external environmental costs and resource losses. And the appropriate carbon emission can be determined when two subsystems of internal resource usage and external environment are in dynamic equilibrium.

KEYWORDS:

• Appropriate carbon emissions
• binary analysis framework
• scale breeding

1. Introduction

As a lot of goods are enjoyed due to industrialization, the environmental and ecological problems are being caused by over-exploitation and resource consumption (Liu et al., 2008; Xia, 2016). The excessive emission of greenhouse gases and the gradual rise of global temperature have become urgent problems. The gases, such as carbon dioxide, methane and nitrous oxide, to cause climate climate change mainly come from human activities, including fossil fuel combustion and agricultural production (Cheng et al., 2022; Tsai, 2019; Zhao & Qian, 2009). According to the data from the United Nations Environment Programme, global carbon emissions in 2022 exceeded 36.8 billion tons (https://www.511ds.com/shark-portal/news388.html; Crippa et al., 2022). Greenhouse gases generated by agricultural and forestry activities, as well as land use changes, account for approximately 21–37% of global greenhouse gases after the emissions from storage, transportation, packaging, processing, sales and consumption in the food production value chain are considered (BCG (Boston Consulting company), Jifei technology company, 2022). According to the Food and Agriculture Organization of the United Nations (FAO), greenhouse gas emissions from animal husbandry account for 18% of the total global greenhouse gas emissions (Su et al., 2022). Today, meat production has changed from traditional free-range breeding to modern large-scale breeding, which alleviates the contradiction between meat supply and demand but brings great pressure on ecological environment resources (Ni et al., 2020).

There are different views on agricultural carbon emission reduction. Some scholars have found that methane and N₂O, an important component of greenhouse gases, mainly comes from the intestinal fermentation of ruminants such as dairy cows and the treatment of livestock and poultry manure (Dong et al., 2008; Du et al. 2021; Huang et al., 2006), and N₂O is discharged from composting and manure treatment (Ban et al., 2017; Chen et al., 2011; Dong et al., 2008; Huang et al., 2006; Olesen et al., 2006). Carbon emissions are affected by many factors. The advanced technique level of agricultural mechanization has a positive impact on carbon emissions, while the accumulation of rural human capital has a negative impact on carbon emissions (Yang, 2012). Production efficiency is the most important factor in curbing carbon emissions, followed by urbanization (Yao et al., 2017). In addition, there is a significant correlation between economic growth, industrial structure, technological level and carbon emissions (Fu, 2019). The Tapio decoupling model was used to analyse the decoupling status between carbon emissions from scale-breeding and the income (such as operational income, wage income, transfer income and property income of rural residents). An SVAR model was constructed, and pulse response methods were used to analyse the dynamic response relationship between carbon emissions and the income of various types of rural residents (Liu & Xiao, 2022). Many scholars use mathematical models to analyse the influencing factors of carbon emissions in the livestock and poultry industry based on specific time series, such as KAYA identity, LMDI decomposition of logarithmic indicators, STIRPAT model, regression model and IPAT model (Guo et al., 2021; Li, 2012). Estimation of carbon emissions is very important to make carbon emission reduction policies. There are some estimation methods, such as index allocation method, life cycle method, process analysis method, input-output method and IPCC standard (Chen et al., 2017; Jing et al., 2019; Ye, 2012; Tang et al., 2019). Many scholars have also explored the carbon emission reduction strategies under different conditions, such as carbon trading, carbon tax, subsidies and carbon quotas (Chen et al., 2019; Guo, 2012; Li & Wang, 2005; Luo & Xiao, 2011; Strobel & Redmann, 2002; Wei & Gu, 2018; Xiao et al., 2008; Xiao et al., 2016)^.

The binary analysis framework study began at the beginning of this century. When the environmental cost innovation was discussed, the resource losses and external environment costs were proposed to be integrated to reflect the economic activities and environment of enterprises comprehensively and uniformly (Xiao et al., 2008). Furthermore, resource losses and external environmental costs were quantified, and then enterprises were prompted to reduce the initial input of resources, improve the utilization rate of resources and reduce the environmental impact. A comprehensive evaluation model of internal resource costs and external environmental damage costs of pig breeding was built, and the internal resource costs of different pig breeding scales in different regions of China were compared (He, 2020). The Tobit model was used to verify the impact of the main cost elements of the binary analysis framework on pig production efficiency. Focusing on the cost elements with obvious impact, the improvement link was compared with the difference in production efficiency before and after the movement of the two-dimensional diagram of internal resource costs and environmental damage costs (Luo & Xiao, 2011; Strobel & Redmann, 2002; Wei & Gu, 2018; Xiao et al., 2016). Chen XL et al used the overall evaluation model of internal resource costs and external environmental costs of pig breeding and studied the pig breeding expenses in different regions of China (Chen et al., 2019). The production efficiency of pig breeding under traditional cost accounting and resource value stream cost accounting was compared and analysed from the perspectives of technical efficiency (static) and total factor productivity (dynamic). It was found that if the external environmental costs are added to the pig breeding costs as an unexpected output, the external environmental costs will cause an obvious impact on the production efficiency of pig breeding, which indicates that the production efficiency of pig breeding is overestimated under the traditional cost accounting method to a certain extent (Li et al., 2011; Li & Li, 2010; Zhang, 2011; Zhao, 2010; Zhao et al., 2010). Li YJ et al. proposed to improve resource utilization efficiency, reduce resource waste and then reduce the impact of livestock and poultry manure pollution on the environment, thereby reducing environmental costs (Li, 2022).

From the above research, after considering internal resource usage costs and external environment damage costs, the binary analysis framework regards the operating organization as a large system focusing on the cost control analysis to improve production efficiency. However, research studies on the carbon emission behaviour of business organizations from the perspective of binary analysis framework have not carried on so far. Many researchers have focused on industrial carbon emissions, but neglected the carbon emissions from agriculture, especially large-scale livestock and poultry breeding industries. In this paper, the coupling and synergy relationship between carbon emission and binary analysis framework was analysed, and then the appropriate carbon emission in line with the current production level of large-scale breeding farms was studied in the system. At last, some useful advice for promoting the sustainable development of low-carbon agriculture was given.

2 Analysis methods

2.1. Normative research methods

In this paper, some research methods were used, such as the theoretical analysis method, modelling analysis method, literature study method, case analysis method and field research method. The literature research method was used to propose the research purpose and content. The binary analysis framework was built by the theoretical analysis method. The resource losses and external environment costs can be quantified by modelling analysis method. The theoretical findings were verified by the case analysis method.

It is necessary to clarify three concepts including resource losses, environmental costs and carbon emissions. The effective use of resources may be reflected by resource losses. Resource losses are defined as the incidental generation of unwanted energy in the production process and links of consumption, namely the waste gas, wastewater, waste residue and negative products. During material flow cost accounting, the products are divided into positive products and negative products. Positive products are produced by enterprises according to pre-design, including finished products, semi-finished products and by-products. Negative products are incidental to the production of positive products, including recyclable parts and non-recyclable parts. Non-recyclable substances cannot be recycled at the current technical level (He, 2020). They will be finally discharged into the ecological environment, and then become resource losses (He, 2020)^. Based on the large-scale breeding characteristics, resource losses include waste gases such as ammonia, hydrogen sulphide, methane and nitric oxide produced in the breeding process, the biogas slurry and biogas residue generated by the treatment of manure exceeds the environmental-carrying capacity of the farm, the unused biogas generated by the treatment of breeding manure, the dead livestock and poultry and other resource losses.

Environmental costs are usually interpreted as environmental degradation costs, which refer to all the expenses to solve the environmental pollution and ecological damages during the production process (He, 2020). They also refer to the costs of taking or being required to deal with the negative impact of enterprise activities on the environment, as well as other costs incurred by enterprises in implementing environmental objectives and requirements (Guo, 2012; Li & Wang, 2005). According to the complete cost method, environmental costs are divided into external environmental costs and internal environmental costs (Li & Wang, 2005). Generally, the internal environmental costs are included in the internal management costs of the enterprise, namely the ‘private costs’ of the enterprise. If the business activities of the enterprise cause external diseconomy to the environment, the private costs are less than the social costs, then the external environmental costs occur. This means that the enterprises or business organizations do not bear legal responsibility.

The resource losses of scale-breeding mainly come from negative products, which include feaces and urine, wastewater, waste gases and dead livestock and poultry. The resource losses are different with treatment methods. After disposal processes, the excess emissions exceeding the environmental carrying capacity of farmland are defined as resource losses. The estimated model of resource losses is as follows (1) $C_{RL}=\sum _{i=1}^4{F}_i\times U_i$(1) where i = 1, 2, 3 and 4 mean unabsorbed feed, urine, waste gases and dead livestock and poultry, respectively. $U_i$ is the ratio of excess waste emissions to the total waste.

The undigested part will be excreted as faeces and urine. The costs of the unabsorbed feed (F₁) accounting model are as follows: (2) $F_1=(Q_n\bullet S_q\bullet D\bullet p_s+Q_b\bullet S_q\bullet D_b\bullet p_s)\times (1-t)\times h$(2) where $Q_n$, $Q_b$, $S_q$, $D$, $D_b$, $p_s$ and $t$ indicate the breeding scale, the number of dead livestock and poultry, the feed consumption per livestock and poultry per day, the breeding days of live livestock and poultry, the breeding days of dead livestock and poultry, the unit price of feed, the feed digestion rate and the feed absorption rate. $h$ is the ratio of faeces to total waste.

For the cost accounting of urine F₂, the model is as follows: (3) $F_2=(Q_n\times D+Q_b\times D_b)\times W_q\times p_w\times t_u$(3) where $W_q$, $p_w$ and$t_u$ refer to the volume of the daily drinking water, the market price of drinking water and the urination proportion. It is difficult to reuse the waste gases, so they may be directly considered as resource losses. Waste gases are the product of decomposition and metabolism of crude protein contained in feed and they may be apportioned from the feed costs. Then the waste gas costs (F₃) may be calculated by multiplying the proportion of waste gases and the total amount of waste as follows. (4) $F_3=F_1\times \sum {\displaystyle \frac{r_l}{\sum _{l=1}^5{r}_l}}$(4) where $r_l$ is the proportion of various waste gases to the total amount of faeces and waste gases, $l=1,2,3,4,5$ mean faeces, $N{H}_3$, $H_{2}S$, $C{H}_4$ and $N_{2}O$, respectively.

The dead livestock and poultry will be chemically treated, and the value of chemical residue is defined as resource losses ($F_4$), which include the purchase price of young livestock and the feed, labour wage, fuel, depreciation, water and electricity expenses.

The environmental pollution caused by livestock and poultry breeding includes water pollution, soil pollution and air pollution. The external environmental costs are also estimated from these three aspects (Guo, 2012; He, 2020): (5) $C_E=C_w+C_S+C_A$(5) where $C_E$, $C_w$, $C_S$ and $C_A$ delegate external environmental (EEC) water pollution, soil pollution and air pollution costs, respectively. Their models have been established in the previous literature (He, 2020).

Carbon emission is the general term for greenhouse gas emission. In this paper, carbon emissions are estimated by taking the pig scale-breeding as an example. Using the national greenhouse gas inventory preparation method, the relevant data in the 2006 IPCC guidelines for national greenhouse gas inventories are selected for estimation.

This paper defined the system boundary of pig carbon emission, which refers to the subsystems directly or indirectly related to the large-scale breeding production process, including the pig production system, the faecal management system, feed planting and the processing system. In the pig production system, carbon emissions come from methane emissions from the pig intestine and energy consumption. In the faecal management system, methane will be produced by faecal degradation under faecal storage and anaerobic conditions. The nitrification and denitrification of nitrogen contained in faeces will emit nitrous oxide. The nitrous oxide will increase when the nitrate concentration increases and water decreases. Piggery cleaning, feed planting and processing systems also indirectly emit greenhouse gases when consuming energy.

The estimated methane from intestinal fermentation and the faecal management system is given by (6) $C{H}_4=Q_n\bullet k_f$(6) where k_f is the emission factor. f = 1 and 2 represent emissions of intestinal fermentation and methane emission, respectively.

The estimation of discharged N₂O from the faecal management system (7) ${\mathrm{N}}_2{\mathrm{O}}_{\mathrm{mm}}=[\sum [\sum Q\bullet Nex\bullet MS]\bullet r]\bullet {\displaystyle \frac{44}{28}}$(7) where Nex is the annual average nitrogen excretion ratio. MS is the direct emission factor of nitrous oxide and 44/28 indicates the emission from (N₂O-N) (mm) to N₂O. (8) $\mathrm{Nex}=N_{\mathrm{rate}}\bullet (\mathrm{TAM}/1000)\bullet 365$(8)

where $N_{\mathrm{rate}}$ is the default N-excretion rate and TAM refers to the quality of pigs.

The greenhouse gas emissions from the consumption of coal, electricity, heat and other energy. (9) $H_c=E\bullet k\bullet n\bullet r$(9) where H_c is the indirect emission of carbon dioxide and E is the consumed energy. k is the effective oxidation fraction and n is the carbon content per ton of standard coal. r is the coefficient of other resource consumption converted into standard coal coefficient.

Different greenhouse gases are converted into carbon dioxide with warming efficiency for statistical analysis.

The binary analysis framework of resource losses and external environmental costs can reflect the internal resource consumption and the impact of scale-breeding on the external environment. A binary analysis model of resource value flow is established and the resource losses and external environmental costs are calculated. At the same time, the synergy relationship between scale-breeding and environment is explored, and then the dynamic transformation process of resource flow is analysed, as shown in Figure 1. According to the resource flow balance principle $\mathrm{raw}\mathrm{materials}+\mathrm{new}\mathrm{input}=\mathrm{positive}\mathrm{products}+\mathrm{negative}\mathrm{products}.$The livestock production process can be divided into many links. The value of the positive and negative products of each link should be calculated. The part of non-recyclable emissions exceeding environmental-carrying capacity is defined as resource losses, which can be divided into resource materialization losses and energy losses. The materialization losses include invalid resource losses and waste. The invalid resource losses will eventually lead to resource depletion. Energy losses include energy consumption losses and waste heat emissions. The energy consumption losses will eventually lead to energy depletion and waste emissions will damage the external ecological environment.

Figure 1. Binary analysis model of external environmental costs and resource losses.

Under the binary analysis framework, the resource losses and EEC are calculated and the key links with high resource losses are found, and the important influencing factors of resource losses and external environmental costs are analysed, then the production and operation plans are adjusted to reduce the resource losses and external environmental costs.

The external environmental costs and resource losses can be placed in the two-dimensional coordinate axis. As shown in Figure 2, A, J, A4 and G are located in four different parts in the quadrant of the coordinate axis, respectively, representing different operation states. A has high external environmental costs and resource losses. G means high external environmental costs but relatively low resource losses. J has high resource losses and low external environmental costs. Obviously, these states are not good and need to be improved. There are four ways to improve management ①F→F1, ②G→G1, ③J→J1, ④A→A1→A2→A3→A4. It is rare to realize the ‘double low’ state of external environmental costs and resource losses directly from point A to A4. The route ④ with a high probability of occurrence is analysed. When the farm is ‘double high’, the operation state should be adjusted from A to A1. Both external environmental costs and resource losses are reduced, but they are still not the best. The pressure on the environment caused by scale-breeding is still high. Continue to improve the management from A1 to A2, gradually the external environmental costs are reduced, but the resource losses increased, which means reducing the external environmental costs will incur more resource losses; so, the farm continues to adjust policies to improve the management from A2 to A3, reducing the external environmental costs and resource losses. If there is room for adjustment, A3 can be moved to A4 and finally tend to the origin, realizing the ‘double low’.

Figure 2. Change track of resource losses and external environmental costs.

The binary analysis framework represents the interaction between the internal resource consumption system and the external environmental system. When these two subsystems are balanced, the binary analysis framework is stable. Carbon emission is the embodiment of resource consumption and environmental pressure, and the relationship between the moderation of carbon emission and the binary analysis framework is key to a farm’s sustainable development.

Table 1. The evaluation value of the internal resource usage system and external environment system.

Date	Internal resource usage system A			External environment system B
	Biogas fertilizer utilization	Biogas utilization	Nitrogen usage utilization	Social evaluation of environment (Score by grade)^a	The land area that can absorb waste (acre)	Compliance rate of waste discharge
2016.7.31	0.386	0.800	0.409	3	8.237	0.6
2017.3.30	0.230	0.800	0.809	2	16.474	0.7
2017.11.30	0.800	0.800	0.733	2	16.474	0.75
2018.6.30	1.000	0.360	1.594	4	16.474	0.8
2019.1.30	1.000	0.500	1.353	4	13.179	0.8
2019.7.30	1.000	0.660	0.977	5	13.179	0.85
2020.1.31	1.000	0.900	0.979	5	13.179	0.9
2020.7.30	1.000	1.000	0.981	5	13.179	1

^a 1 very bad, 2 bad, 3 medium, 4 good, 5 very good.

There is a coupling relationship between the dual integration framework and carbon emissions, including four aspects, namely equipment energy consumption, water resources consumption, faecal sewage treatment and waste gas treatment, as shown in Figure 3. In the process of scale breeding, feed supply, heating and lighting will consume electricity, coal and other resources. If these resources are not fully utilized, they will incur resource losses. At the same time, the heat, light and noise generated by the energy consumption of machinery and equipment will have a negative effect on the external environment. Using equipment and consuming coal, gas and other resources will bring indirect carbon emissions. In the sewage disposal process, nitrous oxide is treated. If the urine, flushing sewage and organic matter produced in the breeding process exceed the carrying capacity of the water environment, it will cause water pollution and water resource losses. Greenhouse gases, such as nitrous oxide and methane, will be produced in faecal sewage management. If the residual material after the faecal management system exceeds the environmental-carrying capacity, it will cause soil pollution and fertilizer resource waste such as nitrogen and phosphorus. With the growth of livestock and poultry, intestinal fermentation will produce methane, nitrogen and ammonia, which will be directly discharged into the air, causing the deterioration of air quality and increasing the greenhouse effect.

Figure 3. Coupling relationship between binary framework and carbon emissions.

Due to the multi-dimensional relationship between the dual integration framework and carbon emissions, there will be an obvious synergy effect. Carbon emissions will be reduced while controlling resource losses and internalizing external environmental costs. The logical relationship is shown in Figure 4. In the three-dimensional diagram, the x-axis represents the resource losses, y the external environmental costs and z the carbon emissions. The points a, b, c and d are in four parts of the first quadrant of the coordinate axis. Point a has high resource losses and high external environmental costs, and produces the most carbon emissions. This state is unsustainable. Ideally, the closer to the remote point, the smaller the impact of breeding activities on the environment. Because of many factors, such as breeding scale, resource endowment, recycling technology, management level market fluctuation and so on, it is difficult to directly adjust a to d. After moderate adjustment, the stage point changed from a to b. And the external environmental costs and resource losses are reduced, and the carbon emissions are also reduced. However, it still exceeds the carrying capacity of the farm's operation environment and needs to be further adjusted to point c. The external environmental costs are reduced, but the resource losses are increased which means, more resources are lost to control the external environmental costs, which is contrary to the goal of maximizing the profits of the farm. Through scale adjustment, technology improvement, mode change and other measures, c is developed to d, to achieve the ideal state of ‘double low’. As shown in Figure 4(a), there are four irregular tetrahedrons and each irregular tetrahedron reflects the interaction results of external environmental costs, resource losses and carbon emissions. The smaller the volume, the smaller the impact on resources environment. Based on the above analysis, it can be concluded that Vaa1a2a3 > Vcc1c2c3 > Vbb1b2b3 > Vdd1d2d3, that is, the volume of irregular Vaa1a2a3 is the largest, followed by Vcc1c2c3, Vbb1b2b3 and Vdd1d2d3. Vdd1d2d3 is the smallest, which means the external environmental costs, resource losses and carbon emissions are the lowest. The stage change trajectory is shown in Figure 4(b) from a to b, then to c, and at last, gets to d, tending to the origin.

Figure 4. Logical change of binary analysis framework and carbon emission.

What’re the appropriate carbon emissions? Whether d is the best decision? It depends on whether it meets the conditions of sustainable operation. Sustainability refers to a sustainable development process or state. The Rio Declaration points out that ‘for sustainable development, environmental protection should be an integral part of the development process and cannot be considered without this process’. Bringing environmental protection into the content of sustainable development is an important difference between sustainable development and traditional development. The sustainable development of the scale-breeding can be analysed from three dimensions: profit maximization (profit is the amount considering the resource losses and external environmental costs of the business entity), environmental impact minimization and the farm’s profit is equal to or larger than opportunity cost, which is the maximum benefit that the farmer gives up breeding and go out for work.

The model of sustainable conditions can be established as follows: (10) $\{\begin{array}{c}C=C_i+RL+EEC+C_c\\ R=Rp+\mathrm{Re}+Rb+R_c\\ L_A=R-C\\ max{L}_A\ge R_0\end{array}$(10) C_i is the production costs of positive products, RL are the resource losses, C_c is the costs of reducing carbon emissions and EEC is the external environmental costs caused by large-scale breeding. R_p is the income obtained from positive products in the breeding link, including sales revenue and deemed sales revenue. R_e refers to the income obtained by adopting the circular operation mode, which includes the production cost saved by resource recycling and the income obtained by beautifying the environment (which can be reflected by the people’s willingness to pay for leisure). R_b is a subsidy given by the government or other institutions to support the circular economy and protect the environment. R_c benefits from reducing carbon emissions. L_A refers to the profit of large-scale breeding under the circular economy mode and using the resource value stream accounting system, and the profit is calculated considering resource losses, external environmental costs and carbon emissions. If the farm or peasant household can continue to operate, the profit L_A should be greater than or equal to R₀ and R₀ includes the risk-free return of investment capital, the opportunity income obtained by operators or employees who give up breeding operation and for other work, the value of low-risk leisure time obtained by giving up large-scale breeding and abandoning the utility value of the achievement sense of entrepreneurial operation. R₀ is the summary of these parts. If the profit obtained by the operator is less than R₀, they will give up operating the farm. When the farm meets sustainable conditions, the appropriate carbon emissions suitable for farm conditions can be achieved. If the appropriate carbon emissions are greater than the amount allocated by the government, it is necessary to purchase carbon emissions right through the carbon emission trading market or construct emission reduction projects. If the appropriate carbon emissions are less than the allocated amount, the remaining carbon emission rights can be sold to obtain emission reduction benefits.

In addition to meeting the conditions of sustainable development, carbon emissions can also be analysed from the perspective of the dynamic equilibrium of the external environment subsystem and internal resource subsystem. When the two subsystems are in dynamic equilibrium, the breeding scale is optimal. The breeding scale is the key factor for carbon emission, the scale of breeding is moderate and the benefits of carbon reduction are maximized. The carbon emissions change with the breeding scale. If the breeding scale is appropriate and the carbon emissions are suitable.

In this paper, the dynamic equilibrium model of two subsystems is built. Internal resource activities affect the external environmental system, and the external environment system can also supply the resource to the internal resource usage system. The general functions of the internal resource system A and the external environmental system B are established, respectively (Liao, 1999). (11) $g(A)=\sum _{i=1}^n{c}_i{x}^i,i=1,2,\cdots ,n$(11) (12) $g(B)=\sum _{j=1}^n{d}_j{x}^j,j=1,2,\cdots ,n$(12) The internal resource systems and external environment come from a large system. Here $g(A)$ and $g(B)$ are the subsystems of this system. w and v are the weights of the function. According to Bertalanffy's general system theory, if A and B are the dominant parts of a system, the system evolution equation can be (13) $\{\begin{array}{c}{E}_s={\displaystyle \frac{dg(A)}{dm}=w_{1}g(A)+w_{2}g(B)}\\ P_y={\displaystyle \frac{dg(B)}{dm}=v_{1}g(A)+v_{2}g(B)}\end{array}$(13) E_s and P_y are the evolutionary states under their own and external influence, and their evolution speed is the partial derivative of their respective functions to scale. (14) $\{\begin{array}{c}{M}_A={\displaystyle \frac{d{E}_s}{dm}}\\ \\ M_B={\displaystyle \frac{d{P}_y}{dm}}\end{array}$(14) $M_A$ and $M_B$ are the change rates of the large system under the influence of the internal resource system and external environment system, which means the speed of change to the internal resource subsystem and external environment subsystem for each additional livestock and poultry. With a limited external environment, internal resource usage activities affect the overall large system and the speed rate of large-scale systems increases. When the resource limit is reached, the rate decreases. The growth of internal resource usage is relatively fast, but it is limited by the bottleneck of the external environmental system’s development speed (Liao, 1999). Suppose H is the angle degree of the arctangent function, and $H=\arctan {\displaystyle \frac{M_A}{M_B}}$, when $M_A=0,M_B\to \mathrm{\infty },$ $H$ equals zero, there is no direct control relationship between the rate changes of the two subsystems. When $0<M_A<M_B$, $H<{45}^{\circ }$, internal resource usage activities are carried out under the inclusion of the external environment system. The impact of the internal resource usage subsystem on the whole large system is greater than that of external environment subsystem. If $H={45}^{\circ }$, the tangent value is 1, and the two subsystems get to the best coordination state, and the breeding scale is optimal and carbon emissions are appropriate to the conditions of farm. When $M_A>M_B>0$ and ${45}^{\circ }<H<{90}^{\circ }$, the growth rate of the external environmental system exceeds the development rate of the internal resource usage system and the impact of external environment on the large system is greater than that of the internal resource usage system. When $H={90}^{\circ }$, under the limit value of environmental resources, the development speed of internal resource usage system is zero, while the development speed of external environment tends to infinity. If ${90}^{\circ }<H<{135}^{\circ }$, the development speed of the internal resource usage system slows down and the speed of external environment system accelerates. The impact of the internal resource usage system on the whole large system exceeds the positive impact of the external environment subsystem. The two subsystems are uncoordinated. When $H={135}^{\circ }$, the impact of the internal resource usage system is on the large system counter balance that of the external environment system. $|M_B|>|M_A|,M_B<0M_A>0$ The internal resource usage system has developed, while the development of the external environment system has greatly slowed down, the system is chaotic and the entropy increases. The impact of the two subsystems on the large system reflects the phenomenon of retrogression. $M_A=0,|M_B|$ is on the Y axis, when $M_B<0$, the internal resource usage system is in a backward state, the growth of environmental resources stops, the whole large system is in a state of entropy increase and the system reaches the extreme value of degradation. If $|M_A|<|M_B|$, $M_B<0,M_A<0$, the resource environment and external environment system decline at the same time, and the decline rate of the external environment system is greater than that of internal resource system. When $|M_A|>|M_B|$, $M_B<0,M_A<0$, the decline rate of internal resources system is greater than that of external environment system, and the whole system is still in decline.

2.2. Empirical analysis

In this paper, pig breeding farms were selected as the research objects and the vertical data were collected from 31st July 2016 to 31st January 2020. The data sources include field visits, questionnaires, face-to-face consultations and statistical data from animal husbandry management departments. The period was divided into seven stages and each stage has eight months based on the production cycle and collected information includes breeding scale, breeding days, farm area, cultivated land and forest area, biogas digestion volume, circulation mode, piglet costs, feed costs, water costs, electricity costs, plant and equipment investment and its service life, residual value, labour costs, medical costs, plant rent, biogas operation costs, the number of live pigs, sales revenue, dead and sick pigs, biogas output rate, biogas utilization rate and profitability, etc.

The breeding site is located in a hilly area. On 31st July 2016, the breeding scale was 1300 pigs, and the breeding days were about 240 on average. The farm area was 1.15 acres, and the total land area of farm-bearing waste was 8.24 acres. The method of faecal cleaning was water flushing and the anaerobic faecal treatment method of biogas. The scale of biogas digestion was 300 m³. Using the pig-biogas-crop cycle mode, the piglet, feed, electricity expense and water were 58445.44, 118086.7, 2690.58 and 538.12 dollars, respectively. The plant and equipment investment was 164424.51 dollars. The expected service life was 20 years. The labour, the medicine, the farm rent and the biogas operation costs were 10762.33, 1943.20, 12556.05, 2073.99, respectively. The number of pigs was 1287 and the sale revenue was 615605.38 dollars. There were 13 dead pigs, so the resource losses caused by dead pigs was 2151.67 dollars. The biogas construction investment was 6726.46 dollars, and the estimated service life was 10 years, so the biogas management costs were 560.54 dollars. The maintenance costs were 840.81 dollars, and the biogas digestion output was 730 m³. The utilization rate of biogas was 80%, so the opportunity costs of breeding work were 9686.098 dollars. The bank interest rate was 2.1%. The minimum wage was USD 269.058/month, the risk-free cost was USD 29.90 and the willingness to pay for extra leisure time was USD 3587.44.

As shown in Figure 5, in July 2016, the external environmental costs were 248844.11 dollars and the resource losses were 17873.03 dollars, so the coordinate point was in ‘double high’ state and located in the first quadrant of the coordinate axis. ‘Double high’ means that a farm’s operation activities brought not only great pressure on the external environment but also wasted more resources, so they should be improved. In August 2016, the forest land increased by 8.24 acres through leasing and transferring land use rights from others. At the end of March 2017, the external environmental costs were reduced by 6.63% and the resource losses were reduced by 44%, but the carbon emissions were not significantly reduced. In April 2017, yucca plants were added to the feed, specially configured feed was adopted and deodorizing forage was added. Although the breeding scale remained stable, the external environmental costs decreased by 5.93%, while the resource losses increased by 4.92%, indicating that the carbon emissions increased. In 2018, the market price of live pigs fell, and the farm adjusted the breeding scale to 600 pigs. As shown in Figure 5, the external environmental costs decreased by a cliff and the resource losses decreased by 20.69%, meaning that the carbon emissions also decreased significantly. To save costs and improve the profit margin of the farms, the breeding scale was maintained in 2018, but the mountainous area was reduced by 3.29 acres and then the biogas utilization rate was improved. The resource losses have decreased significantly, while the reduction of external environmental costs and carbon emissions is not obvious. In July 2019, the pig market recovered, and the farm increased its breeding scale to 800, which signified that the external environmental costs and resource losses decreased slightly, but the carbon emissions increased. In January 2020, the scale is unchanged, but the feed formula is improved. On the other hand, the plant properties were shared, and the epidemic prevention technology was improved. The external environmental costs and resource losses decreased by 26.98% and 40.65%, respectively, so the carbon emissions decreased.

Figure 5. Estimation of resource losses, external environmental costs and carbon emissions.

As shown in Figure 6, take the resource losses as the abscissa and the external environmental costs as the ordinate. With the adjustment of operation policies, the external environmental costs and resource losses gradually change from the ‘double high’ state to the high EEC (external environmental cost) and middle RL (resource losses) and then to middle RL and low EEC and then to low EEC and RL, at last to the origin although there are also cases of increasing resource losses to reduce the external environmental costs and finally both of them develop towards ‘double low’. The trajectory presents an inverse Z-shape.

Figure 6. Change track of external environmental costs and resource losses.

Then put the external environmental costs, resource losses and carbon emissions into three-dimensional coordinates, as shown in Figure 7, the carbon emissions vary with the external environmental costs and resource losses. On the whole, the variation is downward with a little upward. The breeding scale is an important factor. If ignoring carbon tax, carbon subsidy, carbon emissions trading and other factors, the external environmental costs, resource losses and carbon emissions show an obvious downward trend with the scale. With the expansion of the breeding scale, carbon emissions increased.

Figure 7. Three-dimensional diagram of binary analysis framework and carbon emissions.

To make optimal decisions on carbon emissions, in this paper the value L_A and R₀ were compared, and the appropriateness of carbon emissions based on the impact of external environmental costs and resource losses was determined. The appropriate carbon emissions analysis is shown in Figure 8. L_A> R₀ indicates that the external environment costs and resource losses are small, so the carbon emissions under this profit are moderate. Here, the L_A line fluctuates around R₀ and the amplitude is large. On 31 July 2016 and 31 January 2020, the L_A value is both much greater than R₀, but the residual value of L_A minus R₀ in other stages is less than zero, which indicate that the external environment costs and resource losses of farms are high, on 31 July 2016. So, the carbon emissions were also the highest. The farms’ business activities brought great pressure on environmental resources, so the decision-making in July 2016 was not optimal. In January 2020, the external environmental costs, resource losses and carbon emissions were low enough to meet the conditions for farm sustainability, so the decision-making combination is appropriate and conducive to the sustainable development of the farm (Figure 9).

Figure 8. Optimal carbon emissions analysis.

Figure 9. Evaluation indexes of internal resource and the external environment system.

The carbon emissions can be studied from the perspective of the dynamic balance of two subsystems. A is the internal resource usage system and B is the external environment system. With the expert consultation method, the evaluation indexes of internal resources and external environment systems are built as follows Figure 9 and the result can be showed in Table 1.

The data were collected from questionnaires, face-to-face consultation and statistical data of animal husbandry management departments. The value of utilization indexes from questionnaires and field measurement. The data on social evaluation of the environment were obtained from expert consultation and questionnaires. Land area was obtained from statistics of government departments and farm management records. After dimensionless normalization, the data are processed as follows. The chemical reaction rate can be expressed by the change in concentration of reactants or products per unit time (decrease or increase) (Li, 2022; Smith & Lampkin, 2019; Sun et al., 2020; Zhu et al., 2010), The development function with scale as the independent variable is regarded as a continuous function, the system development trajectory can be regarded as the distance of system movement, the per pig is used to replace the unit time and the material movement rate with time as the variable is transformed into the ‘rate’ with scale as the variable. The development rate model of the computing system is established

If $T=tg{\displaystyle \frac{M_A}{M_B}}$, $H=\arctan T$, T is the tangent value. The results are computed as follows in Table 2.

Table 2. T value and angle degree at different dates.

Date	T value	Angle degree
2016.7.31	0.470	25.2°
2017.3.30	10.132	84.36°
2017.11.30	0.879	41.30°
2018.6.30	0.223	12.59°
2019.1.30	−0.498	153.53°
2019.7.30	5.306	79.33°
2020.1.31	1.118	48.18°

As shown in Table 2, the internal resource usage system was developed under the inclusion of the external environment system on 2016, 31 July 2018 and June 30. And impact of the internal resource system on the big system is greater than that of the external environment system. In 2017, 30th March and 2019, 30 July, the growth rate of the external environment system exceeds that of the internal resource system, which is not a good state for farms. In 2019, 30 January, the internal resource system has developed, while the development of the external environment system has slowed down, so the whole big system is chaotic. After 31 January 2020, the T value is close to 1, and the angle degree is 48.18°, which means the internal resource usage system and external environment system are close to the dynamic balance, so the breeding scale is appropriate, and the tolerance of external environment system is larger than that of the internal resource usage system. Therefore, the carbon emission of farms is suitable for farms’ production levels.

3. Results and discussion

Based on the above analysis, business or farms’ operational policies should be made based on the dual integration analysis framework. There are direct logical relationships between EEC and RL. Their comprehensive influence on the environment is inverse Z-shape. It decreases with the improvement of operation. The binary analysis system has a synergistic relationship with carbon emissions. With the decrease in EEC and RL, carbon emissions will decrease. Confined by the technology, it is difficult to decrease carbon emissions to zero. Thus, the appropriate carbon emissions should be determined. With the farm’s business policies alternation, the EEC and RL decrease overall, and then the carbon emissions decrease correspondingly, but the change is inverse Z-shape. The carbon emissions in January 2020 are the lowest and may satisfy the sustainability conditions in that the two subsystems are in approximate dynamic balance. Therefore, the carbon emissions are moderate for the farms.

This study aimed to determine the moderate carbon emission from breeding farms. In this paper, resource losses, external environmental costs and carbon emissions can be quantified and the binary analysis framework of resource losses and external environmental costs can be built. Then the synergistic relationship between carbon emissions and the binary analysis framework is analysed. Finally, the criteria for determining moderate carbon emissions were established, including sustainable development conditions and dynamic equilibrium of the internal resource usage subsystem and external environmental subsystem. Moderate carbon emission can be achieved based on meeting the criteria. These findings support the viewpoints of Li (2022) and Zeng (2022) who insisted that resource utilization and treatment of livestock and poultry manure can eliminate pathogenic bacteria, parasitic eggs, etc., cut off the transmission path of infectious diseases and parasitic diseases, reduce water pollution and land pollution, produce clean energy, provide organic fertilizer for planting. Therefore, improving resource utilization efficiency can reduce resource waste, and then reduce the impact of livestock and poultry manure pollution on the environment, thereby reducing environmental costs (Lin et al., 2022; Zeng, 2022). The results of this study also are consistent with those of Luo et al. (2022) and Sheng (2023) who believe that improving resource utilization efficiency in animal husbandry can reduce pollution, reduce carbon emissions and promote comprehensive green production transformation of the industry (Luo et al., 2022; Sheng, 2023). Thus, there is a synergistic relationship between pollution reduction and carbon reduction (Sheng, 2023).

Previous literature focused on analyzing the accounting, measurement, characteristics and influencing factors of agricultural carbon emissions and proposed that carbon emissions reductions can be obtained in two ways: technical emissions reductions and institutional emission reductions (Cheng, 2022; Lan, 2022; Li & Wang, 2021; Wang et al., 2022). There are a few literature studies on carbon emissions from the perspective of controlling external environmental costs and resource losses. This study proposes the binary analysis framework theory and its synergistic relationship with carbon emissions and establishes criteria for judging the appropriateness of carbon emissions.

4. Implications

Some enlightenments may be put forward based on the above analysis. Firstly, to get appropriate carbon emissions, the livestock and poultry manure pollutants should be recycled to reduce environmental pollution. Secondly, the internal management of farms should be improved to increase the utilization rate of resources, optimize the allocation of resources and then reduce the losses of resources. Thirdly, the external environmental costs should be internalized through environmental regulation, technology upgrading, equipment support and implementation. Fourthly, the appropriate breeding scales should be encouraged to consider resource utilization and environmental impacts. Fifthly, a scientific government subsidy mechanism should be created to ensure necessary subsidies to farms that effectively adopt a circular economy and build emission reduction projects. The number of subsidies may be distributed to farms based on the content of sustainable conditions. Sixthly, the standardized operation of livestock and poultry farms should be encouraged to promote their participation in carbon emission trading markets and emission reduction projects.

5. Limitation and future study

In this study, quantifying the resource losses is important for choosing the appropriate size, and there are many factors to consider for building models, some of which need to be measured in various ways, such as big data, remote sensing technologies, future exploration should approach the changing track of EEC and RL under different environment still need to be studied. The coupling degree of the binary integral system of EEC and RL for special farms or businesses needs to be determined. It is necessary to make clear how to get to a complete dynamic balance. The optimal carbon emissions under the dynamic equilibrium and the key factors that influence the dynamic balance need to be studied.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is supported by the state scholarship fund of the China Scholarship Council (201808505088), the Social Science Planning Project of Chongqing city (2016BS031), Chongqing Educational Science Planning Project (2017GX266), the Social Science Project of Chongqing University of Posts and Telecommunications (2017KZD12) and Doctoral Research Initiation Project of Chongqing University of Posts and Telecommunications (2023).