JEL: Q18, C52, O13 PREREQUISITES AND PROSPECTS FOR SUSTAINABLE DEVELOPMENT OF GRAIN PRODUCTION IN UKRAINE

Purpose. The aim of the article is to identify the benefits of the chosen strategy of agribusiness (profit maximization, or yield maximization) based on the statistical observations of yields and production factors (fertilizers, plant protection products). Methodology / approach. To analyze productivity growth in grain production under the influence of innovative technologies the data of long-term observations of winter wheat yield in Germany and the United States were selected. In this paper, to analyze the prerequisites and prospects for stabilizing of the crop production, mineral fertilizers and plant protection products were selected as production factors affecting the yield of wheat. Methods of time series analysis and nonlinear econometric analysis were used to assess the impact of these factors. Long-term trends of growth of wheat yields in Germany, the USA and Ukraine were analyzed using regression models. The general model of agrarian business profitability in grain production is based on non-linear correlations of individual factors of intensification and panel regression. In order to substantiate the conclusions of the calculation, the estimation of climatic risks is used. For this purpose, dispersion methods, nonlinear optimization methodology are used. Results. Estimates of wheat yield fluctuations due to climate risks show that they will not significantly affect the problem of food security, so there is no need to impose restrictions on the export of wheat. On the choice of optimal strategy, based on analysis using econometric model of decreasing marginal utility of production resources, it is proved that the maximization of yields is achieved at lower costs than profit maximization. Originality / scientific novelty. The main contribution of the article to the level of significantly increases the impact of weather and climate risks. Therefore, a further intensification of crop production while increasing the share of forested land at the expense of less productive land is probably the way to an ecologically balanced development of agriculture.

production. A consequence of these processes was a gradual accumulation of financial resources in the established types of agricultural business for the acquisition of the latest agricultural technologies. This process began around 2000, which, as we know, was the first year of growth of the Ukrainian economy. Since then, along with the growth of Ukrainian agrarian exports there was a growth of agrarian imports, which provided the implementation of innovations into the Ukrainian agricultural sector (Tscharntke et al., 2012; Zaburanna and Poprozman, 2015;Andrieu, 2017). The volume of imports of means of agricultural production in the crop sector has steadily increased from year to year, which contributed to the growth of yields. Over the last few years, Ukrainian grain yields have been steadily increasing and already exceed those of the USA. It should be stressed that this development path is intensive rather than extensive, as the area sown with the main types of grain does not tend to grow. Therefore, the question arises whether the path followed by a significant part of the Ukrainian agricultural business is economically viable. In addition to the average yield indicator, another important indicator is its variability, which can be measured as a deviation from trend or average values. Of course, excessive variability in yields was a major cause of food security risks, both in the years of the planned economy and in the early decades of transition to market relations.
In addition, the issue of climate change is crucial to agricultural development, which can lead to significant losses in agricultural production (Kadiyevskyy and Klymenko, 2014;Babenko et al., 2021). On the other hand, the yield indicator is related to the level of ploughed land, which exceeds all admissible values in Ukraine (Kaminskyi, 2018). This shows that the state is at a stage of social development when economic performance is much more important than the state of the environment. Globally, however, there is a general trend towards an increasing degree of afforestation as a significant factor affecting atmospheric carbon concentrations. Of course, the choice of farming model is a decision for each entrepreneur, but the environment and the ecological and economic use of land is a matter of social utility (FAO, 2018). To date, most researchers (Angelsen and Kaimowitz, 2001;Börjeson, 2007;Pretty and Bharucha, 2014) are proponents of intensive farming theory based on the assumption of getting more production with fewer inputs, which is most commonly interpreted as increased yields per hectare. Most agricultural systems are based on the use of different cultivation methods with crop rotations, have adopted the use of genetically modified varieties of wheat, rice and maize with the use of mineral fertilizers, crop protection products, farm machinery and irrigation systems (Pretty and Bharucha, 2014). In the mid-twentieth century, proponents of intensive farming point to the "miracle" of the "green revolution" in Latin America and Asia, when the first use of high-yielding seed varieties, fertilizers, pesticides led to a doubling of yields of rice, wheat and maize (Pingali, 2012). At the time, the positive impact of agricultural intensification on overcoming hunger became impressive, the reduction in population experiencing malnutrition was measured in billions of people, and economic growth in agriculture became unequivocal (Haddad et al., 2016). Today, the model of agricultural intensification is the dominant one in the world. FAO data show that in recent years, in developing countries, farmers have invested approximately 153 billion USD annually in agricultural development, almost the same as in developed countries, 156 billion USD. Analysis of pesticide use is the mainstay of agricultural intensification, as confirmed by a number of researchers (Silva et al., 2019). Since 1960, the average world yields of rice, wheat and maize have more than doubled as the use of pesticides has increased by 15-20 times and the use of mineral fertilizers, land irrigation systems have increased by 7 and 2 times respectively (Oerke, 2005). Worldwide about 3 million tons of pesticides are used annually, corresponding to a market value of USD 40 billion (Pimentel, 2009). In the European Union (EU) there are almost 500 active substances approved for use as pesticides with annual sales of 374 thousand tones. The results of numerous studies (Ahrends et al., 2018;Bustos, 2016) highlight the need to consider the importance of long-term soil fertilizer management to explore the interaction between genetic potential and management. Research According to the authors (Ickowitz et al., 2019) this fact remains the main justification for the inevitable use of agricultural intensification. In the USA, it has been concluded that increased seeding rates increase weed and plant competition, limited fertilizer limits the availability of nutrients to germinating weeds (Strydhorst et al., 2008). Farmers there have therefore switched to crop rotations, no-tillage, which allow for optimum grain yields, enrich the soil with minerals and optimize costs and increase profits. The purpose of the article. The agricultural sector has focused on yield increasing of the grain to provide the food security in the country. Therefore, the Agricultural and Resource Economics: International Scientific E-Journal http://are-journal.com purpose of the presented work is to identify the benefits of the chosen strategy of agribusiness (profit maximization, or yield maximization) based on the statistical observations of yields and production factors (fertilizers, plant protection products), taking into account climate risk.
Methodology. The paper analyzed the dynamics of grain production, especially winter wheat, as an economically priority market crop for Ukraine in comparison with the USA and Germany. In order to analyze long-term trends, wheat yields were analyzed for the time interval 1961-2019 for the USA and Germany and during 1992-2019 for Ukraine. To bring it to an equivalent time interval, the time series of yields of the former Soviet Union from 1961 to 1990 are extended with a series of yields in Ukraine in the interval 1992-2019. In addition, the time series of yields of the Soviet Union  and Ukraine (1992-2019) were considered separately. Due to that major costs in the total variable costs for grain production are taken by fertilizers and plant protection products, these factors were taken for the model development in the paper. The data of the fertilizers and plant protection products input in Ukraine are from FAOSTAT from 1992 till 2018-time interval.
Regarding the impact of weather conditions, the following factors were investigated: the impact of annual precipitation; the impact of precipitation between September and May (t0) January-May (t1) March-May (t2) in time interval 1992-2018.
Results and discussion. Over the last five years, the average yield of wheat in Ukraine has reached 45 hundreds kg/ha ( Fig. 1), considerably lower than in Germany, but higher by 10 hundreds kg/ha than in the USA. The lowest yields were in 2003 as a result of climate risks in Ukraine. As a large proportion of the crop was not harvested, this resulted in food security risks and led to a grain export quota until 2012.
As far as the USA and Germany are concerned, there are stable yield trends, so this can be presented as a linear trend (1): where − 0  expected yield, hundreds kg/ha in 1960, − 1  expected annual growth of yield of one hectare, −  error. In reference to Ukraine, as the transition to market conditions was accompanied by a certain recession, this was also noticeable in the agricultural sector, so linear growth is replaced by a parabolic time dependence: (2) Let us consider a general model of the profitability of the agricultural business in crop production. We assume that prices for final products and components of the production process (fertilizers, herbicides, pesticides) are fixed and known. Profit  ): where p is the unit price of the Product; y is the yield per hectare, which depends on soil condition, fertilizer and pesticide application and the impact of weather conditions. Since variation in pesticide and fertilizer inputs is the only mechanism that affects profit, a condition for profit growth is that the marginal utility (yield) of a particular component of the production process exceeds the price of that component in the product price: The coefficients of equation (5) can be estimated over a long period with individual farm production cost data using a panel regression technique. The next step could be an optimization solution to maximize profits (3) or maximize yields (5). It should be emphasized that there are price fluctuations in the food grain market and prices for factor of production which have a significant impact on decisions about an individual farm's development strategy. Therefore, for simplicity, output prices and input costs are assumed to be constant.
If the marginal utility is assumed to be a constant, it is possible to increase the profitability of the business within a budget constraint by adjusting the price of the components of the production process. However, if yields are an increasing function of the components of the production process The simplest function corresponding to these properties, which is convenient to use (Green, 2021): The dependence of yields on natural, production and weather factors, given the descending marginal utility of production factors, can be represented in this form, assuming that the marginal utility of each component is known and a constant If we consider fertilizer application as the main production factor, the first order yield equation (6) will have the form: To get a profit: (11) Based on the above equations, maximum profitability is achieved with less fertilizer inputs than maximum yields: fertilization should also be taken into account, then the yield will be as follows: where і  coefficient with fertilizer application in the previous year with index i and, − ij  coefficient with fertilizer effect in years i and j, T is the period of maximum effect after fertilizer application.
Studies show that yields are steadily increasing each year in both Germany and the USA. However, the marginal yield (1) is much higher in Germany than in the USA: 0.86 hundreds kg/ha and 0.26 hundreds kilograms per hectare (Table 1). In addition, the initial grain yield, which characterized soil quality, was higher in Germany (32 hundreds kilograms per hectare) than in the USA (17 hundreds kilograms per hectare). That is, at the beginning of the interval, the yield difference was at the expected value of 15 hundreds kilograms per hectare; hence, at the end of the interval it was 52 hundreds kilograms per hectare for a significant difference in the rate of increase. The yield of the grain since 1961 during the existence of the Soviet Union shows that the marginal yield is almost at the level of the USA (0.26 hundreds kilograms per hectare), but the expected initial value of 9 hundreds kilograms per hectare is much less than in the USA (16.8 hundreds kilograms per hectare), and the deviation from the trend (standard error) is much higher. Due to the fact that the consumption of bread and bakery products took much larger share of the society nutrition in the former Soviet Union than the USA, it is easy to explain how the continuously deviation from the trend towards low yields in time interval form 1981 till 1984 led to the need to import grain in large quantities. Regarding the dynamics of grain yield in Ukraine during the years of its independence and on the initial interval of transformation to the market economy, there is a decrease of grain yield, so we used a parabolic profile of yield dynamics with the expected minimum in 2003. Around 2012, yields in Ukraine exceeded the USA level. However, it is still a long way from the current German level, as the 2020 level (84 hundreds kilograms per hectare) can only be achieved in 40 years, assuming that current growth tendency remain unchanged.
For a comparative analysis of the risks of grain production in each of the three countries, estimates of variability (standard errors) and estimated values of yield for 2020 are used. The coefficient of variation, which for Ukraine turned out to be significantly higher than for Germany or the USA (Table 2), is considered as the main indicator of risk (probability of reduction of the gross fee indicator beyond the established consumption limits). The higher the yield increase, the higher the variability index (standard error). This is also true for the relative risk index (coefficient of variation). That means, the share of variability in the expected grain yield is much higher in Germany than in the USA, but in Ukraine it is even higher. From this it can be concluded that an increase in yields is accompanied by an increase in absolute and relative risk indices.
This assumption is confirmed by estimating the variance by the moving average method for 9-year intervals with a step of 1 year (Fig. 2). The variance over the entire time interval  in Germany is considerably higher than in the USA, it has a clearly pronounced tendency for the amplitude to grow over time. It is possible that the absolute and significant variability in yields in Ukraine is due to the lack of warning about weather risks, and non-usage of weather-resistant technologies. Therefore, the issue of weather risk is increasing due to climate change and this factor must be taken into account in the further analysis.
However, an increase in yields is not the main factor for increasing profits. An interesting fact is that while there has been a steady increase in mineral use per hectare in Ukraine, a steady increase in yield occurs against a downward trend in Germany, and conversely, a significant increase in use does not contribute to an increase in yield in the USA. It is interesting to analyze the relationship between yields and inputs in individual farm enterprises, following econometric models (5,12).
In our study, we used data on the domestic value and import value of inputs (mineral fertilizers and chemicals) for crop production in Ukraine from FAOSTAT. It is assumed that import of inputs is an exogenous variable (x1) and grain yield is an Parameters for estimating regression relationship models are shown in Table 3: ̂= 19.57 + 0.05 1 (14) Table 3 Dependence of grain yields on input factors of production and weather conditions As for the regression coefficients, the null hypothesis for them is rejected at an extremely low level of significance, i.e. we can consider the free term (≈20 hundreds kilograms per hectare) as a natural yield, while the coefficient of imported costs of input factors of production suggests that an increase in the cost of imported inputs by 20 USD will increase in the value of imported inputs, increasing the expected yield by 1 hundred kilograms per hectare. A scatter plot and a plot of the linear dependence of grain yield on the value of imported inputs for their cultivation are shown in Fig. 3.
However, there are a number of points in the scatter plot that deviate significantly from the model plot. Assume that all deviations are greater than ̂ ± σ_ε due to favourable or unfavourable weather conditions. From here, we determine the This results in the following equation for the dependence of grain yields on inputs and climate effects (x2): ̂= 20.12 + 0.05 1 + 6.12 2 (16) All the coefficients are significant and the model adequacy parameters are significantly improved. The standard error is halved from 4.16 to 1.87 hundreds kilograms per hectare (Table 3). It is important to note that the regression coefficients for natural yield and dependence on inputs remain virtually unchanged, while adverse weather conditions can reduce yields by 6 hundreds kilograms per hectare. However, while weather risks were able to induce food insecurity at the beginning of the research interval, such yield changes have almost no effect on food security, as the overall positive yield trend after 2003 has significantly improved the situation The model showed a significant positive contribution to grain yield (Table 3) of average precipitation in the March-May time interval, namely during the second growing season (х3). The null hypothesis (absence of this effect) is rejected at a significance level of 0.05 and a 1 per cent increase in precipitation leads to a yield increase of 0,06 hundreds kilograms per hectare: ̂= 11.99 + 0.05 1 + 0.06 3 (17) The practically oriented case of decreasing marginal utility of an agricultural input factors of production is considered (6,7). The econometric models are based on y = 0.05x 1  data on grain yields and the value of input factors of production (fertilizers, chemicals) for 1992-2017 (Table 4). The results confirmed the hypothesis that the marginal utility value of inputs decreases. If the unit price is known, the question of optimizing yields and profits per hectare can be solved as follows: The maximum profit is achieved: The cost at which the profit is maximized, is determined:  уgrain yield, hundreds kilograms per hectare; x 1total value of inputs import, USD per ha; x 2value of fertilizers import, USD per ha; x 3value of plant protection products import, USD per ha. The calculation of costs is based on maximum yield or maximum (optimum) profit ( Table 5). As expected, the maximum grain yield is achieved at the expense of higher costs, which are not compensated by increased profits. If other costs (wages, depreciation of equipment, transportation costs, etc.) are added to the cost of fertilizer and chemicals, the predicted yield index will be much better in the case of profit maximization rather than yield maximization.