FORMATION OF AN INNOVATIVE MODEL OF MANAGEMENT OF THE DEVELOPMENT OF PUBLIC-PRIVATE PARTNERSHIP IN THE CONDITIONS OF POST-WAR RECONSTRUCTION

European Science Economy FORMATION OF AN INNOVATIVE MODEL OF MANAGEMENT OF THE DEVELOPMENT OF PUBLIC-PRIVATE PARTNERSHIP IN THE CONDITIONS OF POST-WAR RECONSTRUCTION Oleg RYBKA PhD. Student Kyiv National University of Technologies and Design, Kyiv, Ukraine Abstract. The article is devoted to the study of the processes of managing the innovative development of public-private partnership as a strategic direction of business development and aims to implement the main management processes in the system of managing innovative activities, forming a strategy for innovative development and innovation systems. Keywords interaction, public-private partnership, innovations, innovation models, integration, management of innovative development, potential, partners-participants in the process of public-private partnership, concession, business interaction strategies, risks of association, technology transfer. Introduction Management of innovative development of business entities should be considered in the context of interrelated elements, which include management bodies at different structural levels, goals, functions, principles, structures, resources, management measures (methods and tools), which are in a certain sequence and function as a single whole, have an impact on increasing innovative activity at all levels of the economy. It is these elements that form an innovative model of management of the development of public-private partnership in the conditions of post-war recovery (Shvets, 2022). The aim of the article is to study formation of an innovative model of management of the development of public-private partnership in the conditions of post-war reconstruction Literature review Paying tribute to the significant achievements of scientific research in the field of forming innovative models of public-private partnership of such Ukrainian scientists as O. Amoshi, I. Hryshchenko, L. Hanushchak-Efimenko, V. M. Geets, I. Hnatenko, V. Gotra, Yu. Danko, Zh. Zhygalkevych, M. Zgurovsky, S. M. Ilyashenko, A. Kasych, T. O. Kokodei, V. Rossokh, S. Solntseva, M. Shkody, as well as foreign scientists such as A. Atkisson, J. Lescure, W. K. Mitchell, B. Santo, B. Twiss, M. Porter, Y. Schumpeter and others, it is worth noting that the concept of defining a comprehensive approach to integration interaction requires further development, since modern scientific research currently lacks integrity and comprehensiveness in the approach to studying relevant theoretical, methodological and practical issues of forming an innovative model of European Science Economy managing the development of public-private partnership in the conditions of post-war recovery. Research methodology The main statistical indicators and financial indicators of the innovative activity of agricultural formations of the Kyiv region over the past five years have been previously formed. For a more in-depth study of the strategic indicators of innovative activity, we will use economic indices and adapt them to the conditions of selected business entities. At the first stage, we will apply the Lerner index to study the market weight of agricultural formations of the Kyiv region (Firm revenue and the Lerner index). The Lerner index is an indicator used in economics to measure the market weight of a company (enterprise). It expresses the percentage by which the price exceeds the marginal revenue. In other words, it is a measure of how much an enterprise can increase the price of its goods (products) without losing customers (consumers) (Firm revenue and the Lerner index). The Lerner index is calculated by the following formula: (P – MC) / P (1) where: P is the monopolist's price, MC is the marginal revenue. The Lerner index is a positive number (L≥0) that increases with the volume of market intensity. The economic interpretation of the Lerner index is expressed as: - If the Lerner index is zero, this means that the enterprise has no market weight and operates in the market as a competitive firm (price equals marginal costs). - If the Lerner index is positive, this means that the enterprise has market weight and can set a price above marginal costs. The higher the index, the greater the market weight of the firm. The Lerner index can be used to: - assess the market weight of an enterprise; - compare the market weight of different enterprises or industries; - assess antitrust regulation. For a competitive firm, the Lerner index is zero, since for it the marginal revenue is equal to the market price of the product, since the marginal revenue and price depend on production, the Lerner index also depends on production; The Lerner index is equal to one if the enterprise's revenue is maximum. In this case, the marginal revenue (derivative of the revenue function) is zero. The Lerner index is less than one if the marginal revenue is positive. In this case, the enterprise's revenue increases with increasing output; The Lerner index is greater than one if the marginal revenue is negative. In this case, the firm's revenue decreases with increasing output. Let's try to adapt the Lerner index to the selected agricultural formations of the Kyiv region. Average purchase prices for grain and leguminous crops were formed from official information sources (Table 1). European Science Economy Table 1 Average purchase prices for grain and leguminous crops, 2020-2024. On average 2020 2021 2022 2023 2024 Purchase prices of grains and legumes, UAH/t 7746 8375 6500 5127 9700 Source: based on (Purchase prices for grain in Ukraine). The calculation of the Lerner index of selected agricultural formations of the Kyiv region according to formula (3.1) was carried out using indicators of average purchase prices for grain and leguminous crops and net income from the sale of products (goods, works, services) of business entities over the last five years (Table 2). Table 2 Calculation of the Lerner index of agricultural formations of the Kyiv region, 2020–2024. Agricultural enterprise Lerner index On average for 2020-2024 2020 2021 2022 2023 2024 FG "Gavryshchuk" 0,991 0,991 0,988 0,984 0,991 0,989 FG "Arhat" 0,917 0,913 0,935 0,884 0,946 0,919 SG "Coop Agribusiness" 0,962 0,986 0,978 1,032 1,211 1,034 STOV "Lyubaretske" 0,666 0,855 0,204 0,117 0,294 0,427 TOV "AF Kyivska" 0,397 0,411 0,955 0,891 0,951 0,721 FG "TVK" 0,992 0,992 0,991 0,984 0,994 0,991 Source: based on (Purchase prices for grain in Ukraine) As we can see, from the calculation of the Lerner index of agricultural formations of the Kyiv region over the past five years in the SG "Coop Agribusiness" this indicator is slightly more than 1, the revenue of the enterprise is maximum. The enterprise is competitive, sells agricultural products to a sufficient extent and has innovative potential. Other agricultural enterprises have a positive Lerner index, it is less than one, the marginal revenue is positive. In this case, the revenue of the enterprise increases with an increase in the volume of output. Also, agricultural enterprises are competitive, sell agricultural products to a sufficient extent and have innovative potential. 1. Next, we will use the Weinberg indicator (Weinberg model), which is not the last factor in the innovative activity of the enterprise. The Weinberg indicator is a method for calculating the advertising budget, which is based on the fact that advertising costs should be proportional to the market share that the enterprise plans to acquire (Methods for determining a company's advertising budget). 2. The purpose of forming the Weinberg model is to capture a certain market share within a certain period of time. The calculation of the Weinberg European Science Economy model is to determine that the advertising budget should be 1.5-2 times larger than the planned market share (in percent) (Methods for determining a company's advertising budget). 3. The author, based on (The essence, features and advantages of the PPP mechanism, 2020) conducted a study to determine what market share the business entity occupies among the leading agricultural formations of the Kyiv region (Table 3). Table 3 Market share among leading agricultural formations in Kyiv region, 2024. Agricultural enterprise Place in the ranking of the 20 leading agricultural formations of the Kyiv region Market share among leading agricultural formations of Kyiv region, % FG "Gavryshchuk" 2 0,90 FG "Arhat" 5 0,75 SG "Coop Agribusiness" 11 0,45 STOV "Lyubaretske" 12 0,40 TOV "AF Kyivska" 16 0,20 FG "TVK" 19 0,05 Source: based on (The essence, features and advantages of the PPP mechanism, 2020). To calculate the Weinberg index, the generated data in Table 3 and the previously presented values of operating expenses, including operating expenses for innovative activities of selected business entities in the Kyiv region over the past five years (Table 4), were used. Table 4 Calculation of the Weinberg index of agricultural formations of the Kyiv region, 2020-2024. Agricultural enterprise Weinberg index, thousand UAH On average for 20202024. 2020 2021 2022 2023 2024 FG "Gavryshchuk" 19435,95 21115,13 24829,88 24447,60 27872,33 23540,18 FG "Arhat" 21595,50 23461,25 27588,75 27164,00 30969,25 26155,75 SG "Coop Agribusiness" 38871,90 42230,25 49659,75 48895,20 55744,65 47080,35 STOV "Lyubaretske" 65894,40 106502,40 102895,20 123802,40 122115,20 104241,92 TOV "AF Kyivska" 45608,00 60964,80 93438,60 108559,00 107116,80 83137,44 FG "TVK" 918,96 998,35 1173,99 1155,91 1317,84 1113,01 Source: based on (Limited Liability Company "Agrofirma "Kyivska". Basic information. Clarity Project. 2025.; TOP 20 farms in Kyiv region, 2023). European Science Economy As a result of calculating the Weinberg indicator of agricultural formations of the Kyiv region for the last five years, the largest value of it was obtained for the Joint-Stock Company "Lyubaretske" 104241.92 thousand UAH, that is, the enterprise can annually invest such an amount in marketing measures of the innovative activity of the business entity. The smallest value of this indicator is for the FG "TVK" 1113.01 thousand UAH, taking into account the size of the agricultural association and the market share it occupies. The essence of determining these indicators of the selected agricultural formations of the Kyiv region is to further form an innovative model of their influence on the management of the development of the business entity from an economic and mathematical perspective. Conclusions. In many cases, when studying the economic situation of an enterprise, the performance characteristic is influenced not by one, but by several factors. There are complex relationships between factors, so their influence on the performance characteristic is complex, and not simply the sum of isolated influences. Multiple correlation-regression analysis makes it possible to assess the degree of influence on the studied performance indicator of each of the factors introduced into the model with a fixed position at the average level of other factors. From practical experience, it is known that dependencies of this type can be described by a multiple linear production function of the type: Ŷ= a0 + a1X1 + a2X2 + …+anXn. (2) The main task of multiple production regression is to study the influence of the main production factors on the results of the enterprise's activities. Based on multiple linear regression, we will study the influence of the main coefficients of innovation activity on the level of profitability of innovation activity of agricultural formations of the Kyiv region over the past five years. The study is conducted using two economic and mathematical models to compare the impact of the main coefficients of innovation activity on the performance indicator of business entities. The factors of influence of the first economic and mathematical model are financial and management indicators of selected agricultural formations of the Kyiv region: - investment activity coefficient, %; - innovation activity coefficient, %; - debt coefficient, %; - net margin, %, - staff turnover coefficient, %; - greening coefficient of innovative agricultural products, %. The factors of influence of the second economic and mathematical model are also financial, management indicators and previously calculated indices of selected business entities: - investment activity coefficient, %; European Science Economy - innovation activity coefficient, %; - autonomy coefficient, %; - Lerner index; - staff turnover coefficient, %; - Weinberg index, thousand UAH. The initial data of agricultural formations of the Kyiv region for the last five years were calculated and formed in advance [53; 81–84; 92; 93; 99]. Calculations are carried out using Microsoft Excel spreadsheets, built-in statistical, mathematical functions and arrays, namely CORREL; MDETERM, MINVERSE, CHIINV, TRANSPOSE, MMULT, FINV and LINEST and the Data Analysis Regression add-in. Research, study, analysis and modeling of factor characteristics and the effective indicator are carried out in several stages. At the initial stage, we bring the factor characteristics and the effective indicator to a mathematical form for further calculation of multiple linear regression, basic statistical indicators and coefficients. Next, we normalize the factor characteristics of the innovative activity of agricultural formations for the last five years in order to further calculate the matrix and check the phenomenon of multicollinearity using the Farrar-Glober method algorithm.When studying the first and second multiple linear models, we check for multicollinearity using the Farrar-Glober method algorithm. The term "multicollinearity" means that in a multiple regression model, two or more independent variables (factors) are related to each other by linear dependence or, in other words, have a high degree of correlation, we can conclude that there is no general multicollinearity of the factor matrix. We take into account that the phenomenon of multicollinearity in econometric analysis is negative and it is necessary to get rid of it, in our research it is absent. The next step of the study is the calculation of paired correlation coefficients, determination of the three best coefficients, their comparison. Paired correlation coefficients indicate the influence of the main factors under study on the indicator Y, that is, the level of profitability of innovative activities of agricultural formations of the Kyiv region. The obtained dependencies are evaluated by the level of indicators of the closeness of the connection. If their absolute value is less than 0.3, the connection is weak; when it is within 0.3-0.7 – average, if more than 0.7 – close and when the absolute value is 1 – this indicates a practical-functional connection. Characterizing the pair correlation coefficients, we observe that each of the factor characteristics affects the level of profitability of innovative activity in different ways. We form a summary table of the three largest pair correlation coefficients of two economic and mathematical models, the factor characteristics of which most affect the performance characteristic of the studied business entities (Table 5). European Science Economy Table 5 Results of determining the largest pairwise correlation coefficients of agrarian formations of Kyiv region, 2020–2024. The first economic and mathematical model of the influence of the main coefficients of innovation activity on the level of profitability of innovation activity of agricultural formations of the Kyiv region, 2020–2024. Agricultural enterprise Investmen t activity ratio, %, Х1 Innovation activity coefficient, %, Х2 Debt ratio,%, Х3 Net margin, %, Х4 Employ ee turnov er rate,% , Х5 The greening coefficient of innovative agricultural products,%, Х6 FG "Gavryshchuk" 0,72 0,70 0,76 FG "Arhat" 0,84 0,76 0,94 SG "Coop Agribusiness" 0,76 0,78 0,98 STOV "Lyubaretske" 0,85 0,82 0,55 TOV "AF Kyivska" 0,64 0,70 0,83 FG "TVK" 0,36 0,97 0,97 The second economic and mathematical model of the influence of the main coefficients of innovative activity on the level of profitability of innovative activity of agricultural formations of the Kyiv region, 2020–2024. Agricultural enterprise Investmen t activity ratio,%, Х1 Innovation activity coefficient, %, Х2 Autonom y coefficie nt,%, Х3 Lerner index,Х 4 Employe e turnover rate, %, Х5 Weinberg indicator, thousand UAH, Х6 FG "Gavryshchuk" 0,72 0,66 0,70 FG "Arhat" 0,84 0,70 0,94 SG "Coop Agribusiness" 0,76 0,88 0,98 STOV "Lyubaretske" 0,53 0,96 0,82 TOV "AF Kyivska" 0,70 0,97 0,94 FG "TVK" 0,36 0,93 0,97 Source: based on (Limited Liability Company "Agrofirma "Kyivska". Basic information. Clarity Project. 2025.; TOP 20 farms in Kyiv region, 2023). So, we see that in the first and second models of the influence of the main coefficients of innovative activity on the level of profitability of innovative activity of agricultural formations of the Kyiv region, the coefficient of staff turnover has a significant impact on the effective characteristic, between this factor and the effective indicator there is a close qualitative relationship, but there is also a significant impact of other studied factors of innovative activity. Next, the stage of calculating the transposed matrix, the product of matrices, the coefficients of the equation of the multiple production function to European Science Economy determine the theoretical values of the level of profitability of innovative activity of agricultural formations of the Kyiv region. As a result of the calculations, the multiple production linear regression of the influence of the main coefficients of innovative activity on the level of profitability of innovative activity of agricultural formations of the Kyiv region has the form (Table 6). Table 6 Multiple production linear regressions of the impact of the main coefficients of innovation activity on the level of profitability of innovation activity of agricultural formations of Kyiv region, 2020– 2024. Agricultural enterprise Multiple production linear regression of the impact of the main coefficients of innovation activity on the level of profitability of innovation activity (first block of production models) FG "Gavryshchuk" Yr=-1,78-2,65X1-1,73Х2+0,001Х3-0,004Х4-0,05Х5+0,11Х6 FG "Arhat" Yr=21,11+ 0,02X1-1,51Х2-4,92Х3+0,004Х4+0,15Х5-0,17Х6 SG "Coop Agribusiness" Yr=- 422,14+219,28X1+11,96Х2+0,003Х3+0,0018Х4+0,78Х5+2,51Х6 STOV "Lyubaretske" Yr=31,36+0,0006X1+9,94Х2+0,0002Х3+19,39Х4+0,00031Х50,63Х6 TOV "AF Kyivska" Yr=-141,33+37,72X1+32,43Х2+0,0004Х3+0,0051Х4-0,26Х50,04Х6 FG "TVK" Yr=7,37-0,98X11,83Х2+0,0015Х3+0,,0027Х4+0,15Х5+0,0064Х6 Agricultural enterprise Multiple production linear regression of the influence of the main coefficients of innovation activity on the level of profitability of innovation activity (second block of production models) FG "Gavryshchuk" Yr=2,56+0,0001X1+0,17Х2+3,33Х3+0,0002Х4+0,2Х5+0,0005Х6 FG "Arhat" Yr=- 1,65+0,0006X1+0,83Х2+6,79Х3+0,00001Х4+0,03Х5+0,00009Х6 SG "Coop Agribusiness" Yr=- 95,20+0,0003X1+12,19Х2+0,00014Х3+20,58Х4+1,39Х5+0,000 081Х6 STOV "Lyubaretske" Yr=92,73+0,0003X1-23,34Х2+0,0001Х3-18,22Х41,83Х5+0,00045Х6 TOV "AF Kyivska" Yr=-69,12+0,000044X1+19,50Х2+0,0022Х3-0,80Х40,10Х5+0,00047Х6 FG "TVK" Yr=7,37-1,05X11,86Х2+0,0003Х3+0,002Х4+0,15Х5+0,000077Х6 Source: based on (Limited Liability Company "Agrofirma "Kyivska". Basic information. Clarity Project. 2025.; TOP 20 farms in Kyiv region, 2023). The obtained statistical coefficients and parameters of multiple production functions of the level of profitability of innovative activity - the parameters of the equations were calculated by the method of least squares. Each coefficient of the equation indicates the degree of influence of the European Science Economy corresponding factor on the effective indicator with a fixed position of the remaining factors, that is, how the effective indicator changes with a change in a separate factor by one unit. The free term of the multiple regression equation has no economic meaning. As a result of data processing, the general coefficient of determination was obtained, in all production linear models it is 1.00. The general coefficient of determination indicates a practical and functional relationship between the main factors of innovative activity and the level of profitability of innovative activity of agricultural formations of the Kyiv region, and also that the variation of the effective indicator is 100% due to the studied factors introduced into the correlation model. This means that the selected factors significantly and qualitatively affect the indicator under study ‒ the level of profitability of innovative activity of the studied agricultural formations. The next stage is a comparative analysis of statistical parameters and coefficients of multiple production linear regressions for the last five years. We use the built-in statistical function LINEST and the Data Analysis Regression tool, which is an add-on for Microsoft Excel spreadsheets. It can be concluded that the use of built-in statistical functions and the Data Analysis Regression add-on for Microsoft Excel spreadsheets for automation, comparison, identity, optimization of processing and analysis of the impact of the main factors of innovative activity on the performance indicator is an alternative optimal solution in economic and mathematical modeling of management processes in the agricultural sector. The obtained results of qualitative production linear models of the level of profitability of innovative activity of agricultural formations of the Kyiv region should be used in the future to forecast factors and the performance indicator for the long-term or short-term period. References 1. Shvets A. I. Public-private partnership as an instrument of postwar recovery and development of the economy of Ukraine. Market infrastructure. 2022. No. 66. С. 83–86. URL: http://www.marketinfr.od.ua/journals/2022/66_2022/17.pdf 2. Firm revenue and the Lerner index. URL: https://stud.com.ua/ 128691/ekonomika/viruchka_firmi_indeks_lernera#goog_rewarded. 3. Purchase prices for grain in Ukraine. URL: https://ukragroconsult.com/grain-prices/ 4. Methods for determining a company's advertising budget. Leosvit Marketing. URL: https://leosvit.com/art/metody_vyznachennia_reklamnogo_budzhetu_ kompanii. 5. The essence, features and advantages of the PPP mechanism. Ministry of Economy of Ukraine. 2020. URL: https://me.gov.ua/Documents/Detail?lang=uk-UA &id=196d3373-eb07-4834a61e-b3608f28eb22&title=SutnistDerzhavnoprivatnogo Partnerstva