Harmonization of investment and operational costs of the grain industry in the light of the theory of sustainable development

Approaches to harmonization of methods for determining the optimal level of investment in the renewal of the fleet of combine harvesters and current expenses of agricultural enterprises under conditions of implementation of sustainable development goals in the activities of economic entities are investigated. It is established that the implementation of the concept of sustainable development for the domestic agricultural sector intensifies the processes in it, brings to the fore the problems of ensuring food security of the State, increasing the production of safe products while preserving landscapes and minimizing anthropogenic pressure. At the same time, the seizure of part of the territory, mining of the liberated and adjacent to the combat zone areas raises the issue of rational use of land resources. Under such conditions, only further introduction of innovations aimed at increasing yields and the use of intensive technologies is the most important vector for the development of domestic agriculture. This places strict requirements on the technical condition of its resource potential. Unfortunately, the unsatisfactory technical condition of the grain harvesting machinery fleet and its destruction as a result of hostilities exacerbate the problem of technical support for grain production, in particular for harvesting. Under such conditions, an important task is to develop methodological techniques for determining the optimal, harmonized values of investments in the reproduction of resource potential and operating costs. The tested methodological approach allows determining the optimal level of investment in the renovation of the combine harvester fleet, taking into account the peculiarities of wheat production organization, grain price conditions, material resources, harvesting equipment, and financial factors. The calculations showed that it is economically inexpedient to invest in the renewal of the combine harvester fleet using the most common combine harvester models if one unit has less than 600 hectares of wheat crops. A positive feature of the tested approach is the ability to minimize unproductive costs by taking into account technological and market factors in determining the optimal level of costs. Instead, the introduction of innovations leads to a change in the form of the production function, which should affect the dynamics of the marginal efficiency of investments, and therefore it is promising to expand approaches to modeling and take into account the role of innovations in finding the optimal level of current costs and investments.


Introduction
The functioning of the agrarian sector on the basis of sustainable development implies that it provides three interrelated functions: economic (providing income to agricultural producers), social (ensuring food security, providing productive employment, improving the quality of life) and environmental (maintaining biodiversity, preserving the integrity of the agricultural 1254 (2023) 012122 IOP Publishing doi:10.1088/1755-1315/1254/1/012122 2 landscape, soil fertility, clean air and water resources) [1].Understanding the role of the agricultural sector, in particular the grain industry, through the prism of the Sustainable Development Goals [2] allows us to consider the latter as a guarantor of the country's economic and food security.Ensuring the sustainability of agricultural production and the realization of its social function determines the increase in grain production, which places strict requirements on the fleet of combine harvesters.Problems in this area have been repeatedly discussed during discussions on the prospects for the development of the agricultural sector.In particular, it is worth mentioning the 2.5-fold reduction in the fleet of combine harvesters of Ukrainian agricultural enterprises during 2000-2020, which led to a permanent increase in the amount of operating hours per unit.As a result, the workload per combine harvester reached almost 200 hectares at the end of 2020, while in Germany and France in 2016-2020 it did not exceed 60-70 hectares of wheat crops.
The problem can be solved by simultaneously increasing investments in the renovation of the grain harvester fleet and obtaining harvesting equipment on a land-list basis.The drop of more than 30% in gross domestic product significantly limits the investment opportunities of agricultural companies and significantly increases the cost of borrowed resources.Under such conditions, it is particularly important to justify approaches to determining the optimal level of capital expenditures and their harmonization with the level of current costs caused by the technological process.
Sustainable development is a basic concept for business and policy development that reflects the understanding that progress is impossible without addressing pressing environmental issues such as ecosystem degradation and climate change.This implies that society can only develop on the basis of meeting the needs of the present while protecting the livelihoods of present and future generations [3].Since the laws of nature and social development are unchanging and immutable [4], the solution is for society to respect the limits of "safe workspace" [5,6] and limit environmental damage [7].Although "sustainability is a pluralistic concept" [8], in a broad sense it focuses on simultaneously ensuring economic growth, societal prosperity, and environmental protection [9].In this sense, the concept of sustainable development integrates economic, social, and environmental concerns and offers a new way of thinking that recognizes the world as interconnected between nature, society, and the economy [10].
It should be noted that population growth and changes in the structure and volume of consumption cause an increase in anthropogenic pressure [11].Sustainable land use can reduce the negative impact of these stressors.The Sustainable Development Goals (SDGs) were formulated in 2015 to meet the demands of the present, and they enshrine the commitment of developed countries to end poverty and hunger by 2030.However, climate change poses a challenge to achieving these goals, as slow processes of environmental change, increased climate variability, and extreme weather events negatively affect agricultural productivity [2].That is why innovation strategies, in particular agricultural innovation systems (AIS), are key examples of potential ways to improve the economic, environmental and social performance of the agricultural sector.Not only because agriculture contributes about 30% of the world's gross domestic product and has a high return on investment [12], but also because of the longterm positive impact of agricultural research and development (R&D) on productivity growth, and because new technological solutions contribute to the sustainable use of natural resources.Nevertheless, agriculture receives about 5% of R&D investments [13].
In turn, an important economic problem in economics and econometrics research is the substantiation of approaches to determining the economic and environmental optimum of operating (technological) and capital costs in the context of rapid implementation of R&D results.A significant contribution in this area has been made by scientists who have studied the use of production functions.In particular, we note the works devoted to the identification of production functions [14][15][16][17][18][19].Secondly, studies on industrial organization [20], trade [21][22][23][24] and international economics [25], which aim to measure productivity [26], returns to scale, and more recently, prices [16,27,28] using production functions.Third, a significant contribution has been made in works that focus on the development of methods for estimating multi-product production functions [29][30][31][32][33].And fourth, a whole area of macroeconomic literature, starting with [34], is devoted to the issues of uncertainty in product prices.The approaches of these authors are based on the assumption of the form of the production function, which allows its identification [35].
Investment is a continuous, systematic activity that focuses on the entire organization, including its forms and methods [36].Investing in innovation determines the ability of an agricultural enterprise to maintain competitive advantage and better respond to rapid market and economic changes [37][38][39][40].This process is based on the use of tools and measures that are important for the transition of society and the economy to sustainable development [41,42].Recognition of agricultural innovation as a driving force for addressing environmental issues and social inequalities has led to the emergence of sustainable entrepreneurship in the agricultural sector [43].Sustainable entrepreneurship encompasses business entities that can achieve profitability by exploiting environmental market gaps [44].They address social and environmental challenges through a business approach based on human values and go a step further to mitigate the impact of economic crises while promoting economic growth and social equity [45,46].
However, today's challenges, in particular the complexity and, in some aspects, the impossibility of predicting the development of economic processes, make it important to study approaches to determining the optimal level of investment and their harmonization with the level of current costs of agricultural enterprises.

Results and discussion
The functioning of the agrarian sector on the basis of sustainable development, the realization of its economic and social function, overcoming the challenges caused by the actions of the aggressor, leads to a reorientation of approaches to modeling technological processes to effective principles, maximizing production and profit.In view of this, nonlinear production functions that maximize the output or added value were chosen as the methodological basis for modeling the cost optimum.In turn, there is a need to harmonize approaches to determining the optimal amount of operating costs that maximizes output with the amount of investment to restore the resource potential damaged as a result of hostilities.The harmonization of economic processes is usually interpreted as their mutual coordination, systematization, unification, coordination, streamlining, and compliance.Harmonization of economic processes helps to balance the functioning of a business entity.Its systemic vision switches to the coordination of the formation and use of its resource potential, investment and operating costs.Thus, the methodological basis of our study is a system of models that allows harmonizing the ratio of operating expenses and capital investments.
The first step towards solving the problem was to determine, based on the statistical processing of the 2020 reports of Ukrainian agricultural enterprises, the equation of dependence of wheat yield on variable costs per hectare of harvested area: where f 1 (x) -is the expected yield of wheat, tons/ha; x -variable production costs per 1 ha of harvested wheat area, UAH thousand.The dependence has a high level of statistical reliability, as evidenced by the value of the coefficient of determination (R 2 ), which for function (1) is 0.9106, as well as the excess of the calculated value of the Fisher coefficient (F p = 28.0)over its tabular value (F tab = 0.116).At the same time, based on the values of the Student's t coefficient, the coefficients for the linear and quadratic terms of the formula (1) were also highly reliable.In particular, with the tabular value of this coefficient from -1.72 to 1.72, its actual values with the specified members were equal to 3.2 and 6.17, respectively.
The relevance of the application of function (1) for planning calculations ensures compliance with the optimal wheat harvesting terms, which in the case of single-phase (direct) harvesting should not exceed 6-10 days after the wheat reaches full maturity.At the same time, an analysis of the conditions and timing of early grain harvesting in 2016-2020 shows that due to the insufficient quantity and unsatisfactory technical condition of most of the grain-harvesting equipment, its duration was from 32 to 55 days [47].At the same time, the extension of the duration of the harvesting campaign beyond a ten-day period caused a daily decrease in productivity by 1% [48], as a result of which more than 10% of the potential harvest, i.e. 6-6.5 million tons of grain, was lost.
Considering this circumstance, the question arose -is it possible, by slightly reducing the expected level of yield and the planned level of costs, to minimize crop losses and maximize the financial result, and how to implement such an approach in the production function (1).To solve it, a component was introduced to equation ( 1), which allows to adjust the expected potential yield by the amount of potential losses, proportional to the duration of the harvesting campaign (d ).Taking this into account, the modified form of function ( 1) is as follows: where f 2 (x, d) -is the expected yield of wheat, tons/ha; x -variable production costs per 1 ha of harvested wheat area, UAH thousand; d -duration of the collection campaign, days.
In the future, functions (1) and ( 2) were combined into a system that allows you to determine the expected yield in the event that the harvesting campaign ends in the optimal agrotechnical period or in the event that it is extended beyond a ten-day period: where f 3 (x, d) -is the expected yield of wheat, tons/ha; x -variable production costs per 1 ha of harvested wheat area, UAH thousand; d -duration of the collection campaign, days.The inclusion of the variable d in function (2) necessitated the formalization of approaches to calculating the latter.It is logical to calculate it through the ratio of the expected gross harvest and the total productivity of the combine harvester fleet of the agricultural enterprise.In turn, the expected gross yield is the product of the sown area and the planned yield.The latter, for modeling purposes, can be determined using function (1).In the meantime, the total productivity of the farm's combine harvester fleet is determined by their number, hourly productivity, and shift duration.At the same time, to take into account the production conditions and the technical condition of combine harvesters, it is advisable to introduce a shift time efficiency factor: where pl -is the area from which wheat was harvested, ha; f 1 (x) -expected yield of wheat, tons/ha; W hour -hourly productivity of the grain harvester, centner per hour; T zm -shift duration, hours (according to [49][50][51] the recommended value is 12.0 hours); K vrch -coefficient of use of the working time of the shift (according to [49][50][51] the recommended value is 0.7);kis the number of grain harvesting units, units.
Taking into account the purely individual nature of the formation of the size of wheat sowing areas and the fleet of combine harvesters for each agricultural enterprise, their ratio in formula (4) was replaced by the planned area of wheat threshing by one combine harvester (N ): where N -is the planned area of wheat threshing by one combine harvester, ha.
After that, based on the analysis of statistical reports, it was determined that domestic grain producers mainly have units with an engine power of 330-335 hp.The analysis of the market of grain harvesting equipment shows that the closest to the indicated capacity are the sixth class combines widely represented on it -New Holland CR7.90, John Deere S670, John Deere S770, CASE IH 7140, CASE IH 7240, Gleaner S97, Claas Lexion 740, Massey Ferguson 9540, Massey Ferguson 9545 [52].With this in mind, based on the analysis of the offer of aggregates from this list on the Tractorhouse.comwebsite [53], the model with the largest number of lots -John Deere S670, which has a nominal engine power of 317 hp -was chosen as the base model with hourly productivity of 111.27 centner per hour.
Further, by substituting into function ( 5) the actual and recommended values of the hourly productivity of the John Deere S670 combine (111.27t/ha), the duration of the shift (12 hours), the coefficient of utilization of the working time of the shift (0.7), an analytical expression was formed functions of the dependence of the duration of the harvesting campaign on the planned threshing area with one unit and variable costs per crop unit: where x -variable production costs per 1 ha of harvested wheat area, UAH thousand; N -is the planned area of wheat threshing by one combine harvester, ha.Later, the variable d in the second equation of system (3) was replaced by the right-hand side of expression (6): where, f 3 (x) -is the expected yield of wheat, tons/ha; x -variable production costs per 1 ha of harvested wheat area, UAH thousand; d -duration of the collection campaign, days; N -is the planned area of wheat threshing by one combine harvester, h.A graphic illustration of the dependence of wheat productivity on variable costs at different harvesting areas indicates a reduction in non-productive losses in the case of a reduction in the load on the grain harvester and an increase in the technological efficiency of grain production (figure 1).
The next step was the modeling of the impact on the economic efficiency of grain production of the intensity and load on grain-harvesting equipment during wheat threshing.For this reason, the system of equations ( 7) was transformed.In particular, based on the assumption of one hundred percent marketability of grain production, in order to determine the expected volume of marketable products, the equations were multiplied by the average price of wheat grain sold by agricultural enterprises of Ukraine in 2020, which, according to the official website of the State Statistics Service, was 386.75 UAH/ha.Taking into account the measurement of variable costs per crop unit in the system of equations (7) in thousand UAH, the price of 1 t of wheat grain was converted into the unit of the same name.
After that, to determine the expected profit, the right-hand side of the equations was reduced by the value of variable costs x and the average value of fixed costs in the production of wheat Figure 1.Impact on wheat yield of production intensity and conditions of use of harvesting equipment by agricultural enterprises of Ukraine in 2020 (according to the official website of the State Statistics Service of Ukraine http://www.ukrstat.gov.ua/).Graph of dependence of yield (centner per ha) on variable production costs per 1 ha of crops (UAH thousand) at + + + -annual load on a grain harvester of 1200 hectares; × × × -annual load on a grain harvester of 900 hectares; * * * -annual load on a grain harvester of 600 hectares; ---annual load on a combine harvester of 300 hectares; X -variable production costs per 1 ha of area, UAH thousand; Y -annual load on the grain harvester, ha.grain, which, according to the analysis of the reporting on the costs of agricultural enterprises of Ukraine for 2020, amounted to 2,711 thousand UAH/ha.
where f 6 (x, d) -is the expected yield of wheat, tons/ha; x -variable production costs per 1 ha of harvested wheat area, UAH thousand; d -duration of the collection campaign, days; N -is the planned area of wheat threshing by one combine harvester, h.Graphical interpretation of the behavior of function ( 8) indicates a decrease in the maximum profit, as well as the optimum cost, which guarantees its achievement in case of an excessive increase in the load on the grain harvester (figure 2).So, under the conditions when each harvester of an agricultural enterprise accounts for 300 hectares of wheat crops, the maximum profit of 4.2 thousand UAH/ha is guaranteed by technology with variable costs of 9.0 thousand UAH/ha.Instead, the choice of this technology at a load of 1,200 ha leads to a loss of -2.7 thousand UAH/ha.Under such a load, the technology with variable production costs of 3.9 thousand UAH/ha is optimal, for which the financial result will be equal to +0.4 thousand UAH/ha.Therefore, under the conditions of threshing 1200 hectares of wheat with each combine harvester, it would be more expedient for the farm to use the technology with variable costs per crop unit almost six times lower compared to the technology that allows to achieve maximum productivity.It is clear that the rejection of industrial technologies reduces the efficiency of using the resource potential of agricultural formations, and therefore it is logical to increase investments in the technical base of harvesting operations.But taking into account the effect of agrobiological factors, the payback of such investments has a declining character.Therefore, when determining the optimal amount of capital and current costs, model (8) was transformed by including the increase in depreciation deductions and other fixed costs due to capital investment.
So, to calculate the increase in depreciation deductions, the average costs for the purchase of a combine harvester in the reporting year -UAH 4,845.4thousand were evenly distributed over the 12 years recommended by the John Deere company as a guideline for the productive use of this brand of combine harvester.The obtained value -UAH 403.8 thousand should be distributed to the entire fleet of combines and the planned load during wheat harvesting.For example, in the case of doubling the fleet of combines, the average increase for each combine will be 50% of UAH 403.8 thousand, similarly, in the case of a fourfold increase in the fleet, the share of purchased will reach three quarters, and therefore each combine will account for 75% of 403.8 UAH.
Taking this into account, the formula for calculating the increase in depreciation deductions looks like this: where n -is the share of newly purchased grain harvesters in their total number; N -annual load on the grain harvester, ha.
In addition, a potential increase in fixed costs was formalized under the conditions of payment of interest for the use of a loan taken out to cover the costs of purchasing a combine harvester.Thus, according to the statistical data of the official website of the National Bank of Ukraine, in 2020, agricultural commodity producers attracted long-term loans for the purchase of equipment at an average rate of 16%.Thus, under the conditions of linear accrual of interest payments, the annual cost of paying interest (I) will be equal to: where n -is the share of newly purchased grain harvesters in their total number; N -annual load on the grain harvester, ha.So, taking into account the potential increase in fixed costs, the system of equations for determining the expected profit looks like this: where f 7 (x, d) -is the expected yield of wheat, tons/ha; x -variable production costs per 1 ha of harvested wheat area, UAH thousand; d -duration of the collection campaign, days; N -is the planned area of wheat threshing by one combine harvester, h.Graphical interpretation of the behavior of function (11) shows the non-linearity of changes in the payback of investments (figure 3).
In particular, the reduction of the load from 1,200 ha to 900 ha, due to the expansion of the collection equipment park, leads to an increase in fixed costs by 0.3 thousand UAH/ha.As Figure 3. Impact on the economic efficiency of wheat production of production intensity and conditions of use of existing and newly acquired harvesting equipment by agricultural enterprises of Ukraine in 2020 (according to the official website of the State Statistics Service of Ukraine http://www.ukrstat.gov.ua/).Graph of dependence of yield (centner per ha) on variable production costs per 1 ha of crops (UAH thousand) at + + + -annual load on a grain harvester of 1200 hectares; × × × -annual load on a grain harvester of 900 hectares; * * * -annual load on a grain harvester of 600 hectares; ---annual load on a combine harvester of 300 hectares; X -variable production costs per 1 ha of area, UAH thousand; Y -annual load on the grain harvester, ha. a result, it becomes possible to switch to technology with variable costs of UAH 5,000 with a simultaneous increase in the production intensity indicator by 1,100 UAH/ha (t1).At the same time, the consequence of reducing the duration of the harvesting company and reducing nonproductive costs is an increase in productivity to UAH 23.1 thousand, which, with one hundred percent marketability of production, is equivalent to an increase in revenue by 1.9 thousand UAH /ha (23.1 − 18.3 × 0.3868).As a result, the profit of the agricultural enterprise increases by 0.4 thousand UAH/ha.Similarly, under the conditions of reducing the load from 1,200 to 600 ha, the expected profit increase will reach 1,000 UAH/ha.At the same time, under the conditions of reducing the load from 1,200 to 300 hectares, the financial result will increase by only UAH 0.9 thousand, which indicates a decrease in the marginal efficiency of costs.
Thus, in the case of an increase in the park, which allows to reduce the load from 900 to 600 ha, the increase in fixed costs is 0.7 thousand UAH/ha, the optimal level of variable costs is 1.7 thousand UAH/ha, marketable products -2.9 thousand UAH/ha (30.6 − 23.1 × 0.3868).As a result, the marginal return on costs will be equal to +20.8% ((2.9−(0.7+1.7))/(0.7+1.7)×100).
On the other hand, in the event of a decrease in the load from 600 to 300 ha, fixed and variable costs, as well as marketable products, increase by 2.3, 1.9 and 2.9 thousand UAH/ha, respectively, and the marginal loss of costs is -30.9% .Therefore, under unchanged conditions (production technology, product price situation, production resources, agricultural machinery, interest rates, etc.), the mark of 600 hectares of wheat crops per John Deere S670 combine harvester is the economic limit of the feasibility of investments in the renovation of the combine harvester park of domestic agricultural enterprises by purchasing similar or similar units.

Conclusions and prospects for further research
The implementation of sustainable development goals for Ukraine determines the intensification of processes in the domestic agricultural sector, brings to the fore the problems of ensuring food security of the state, increasing the production of safe products while preserving landscapes and minimizing anthropogenic pressure.In turn, the seizure of part of the territory, contamination of the liberated and adjacent territories with explosive objects further actualize the problem of rational use of land resources.Under such conditions, only further introduction of innovations aimed at increasing yields and the use of intensive technologies is perhaps the only possible way to develop domestic agriculture.The latter places strict requirements on the technical condition of its resource potential.Unfortunately, the unsatisfactory technical condition of the grain harvesting machinery fleet and its destruction as a result of hostilities exacerbate the problem of technical support for grain production, in particular for harvesting.Under such conditions, an important task is to develop methodological techniques for determining the optimal, harmonized values of investments in the reproduction of resource potential and operating costs.
The tested methodological approach allows determining the optimal level of investment in the renovation of the combine harvester fleet, taking into account the peculiarities of wheat production organization, grain price conditions, material resources, harvesting equipment, and financial factors.The calculations showed that it is economically inexpedient to invest in the renewal of the combine harvester fleet with John Deere S670 or similar combine harvesters if one unit has less than 600 hectares of wheat crops.A positive feature of the tested approach is the ability to minimize unproductive costs by taking into account technological and market factors in determining the optimal level of costs.Instead, the introduction of innovations leads to a change in the form of the production function, which should affect the dynamics of the marginal efficiency of investments, and therefore it is promising to expand approaches to modeling and take into account the role of innovations in finding the optimal level of current costs and investments.

Figure 2 .
Figure 2. Impact on the economic efficiency of wheat production of production intensity and conditions of use of available harvesting equipment by agricultural enterprises of Ukraine in 2020 (according to the official website of the State Statistics Service of Ukraine http://www.ukrstat.gov.ua/).Dependence of profit (thousand hryvnias per ha) on production costs per 1 ha of crops (UHA thousand) at + + + -annual load on a grain harvester of 1200 hectares; × × × -annual load on a grain harvester of 900 hectares; * * * -annual load on a grain harvester of 600 hectares; ---annual load on a combine harvester of 300 hectares; X -variable production costs per 1 ha of area, UAH thousand; Y -annual load on the grain harvester, ha.

Table 1 .
The influence of the load on the John Deere S670 combine harvester on the optimal intensity and efficiency of wheat grain production by agricultural enterprises in 2020 (according to the official website of the State Statistics Service of Ukraine http://www.ukrstat.gov.ua/).