## 2 Theoretical Framework and Methodology
### Research Methodology  
The general dynamics and structure of transport use are considered to determine the basis for the study. Significant differences in the general dynamics and structure of  
Figure 2: Methodology for analyzing economic development’s dependence on the transport industry’s functioning. Constructed by the authors. use for various transport systems are possible for different countries. These fundamental differences arise due to differences in the density of logistics infrastructure and natural, climatic, and relief differences. However, to obtain indicators acceptable for comparison, it is necessary to follow the general research methodology. This study uses a productivity metric, the following Factor Model (1), to conduct a qualitative analysis. \[Ft=\sum_{i=1}^{n}Ft_{i}=\sum_{i=1}^{n}(Tv_{i}\cdot Td_{i})=Tv\cdot\sum_{i=1}^{ n}(Sw_{i}\cdot Td_{i}), \tag{1}\]  
where Ft, Ft represent the total volume of freight traffic and for the i-th mode of transport, billion tonne-kilometers; Tv, Tv\({}_{i}\) represent the total volume of freight transport and for the i-th mode of transport, thousand tons; Td, Tdi represent the average distance of freight transportation for all modes of transport and for the i-th mode of transport, thousand kilometers; Swi represents the specific weight of the i-th mode of transport in the total volume of freight transport, %; n represents the number of modes of transport. The functionality of the components of Metric (1) are determined by Formulas (2)-(5). \[\Delta Ft_{Tv}=\Delta Tv\cdot\sum(Sw_{0}\cdot Td_{0}) \tag{2}\]  
\[\Delta Ft_{Sw}=Tv_{1}\cdot\sum(\Delta Sw\cdot Td_{0}) \tag{3}\]  
\[\Delta Ft_{Td}=Tv_{1}\cdot\sum(Sw_{1}\cdot\Delta Td) \tag{4}\]  
\[\Delta Ft=\Delta Ft_{Tv}+\Delta Ft_{Sw}+\Delta Ft_{Td} \tag{5}\]  
Depending on the economic dynamics, in each specific time period, production and consumption indicators Xij, Fi, Xi will take on different values. However, since technological re-equipment in the scale of industries and the national economy occurs slowly due to the high inertia of investment processes, the [PERSON] model assumes the constancy of technological complexity in the medium-term perspective. For this purpose, based on the input data in Table 1, the coefficients of direct expenses are calculated using Formula (6). \[a_{ij}=\frac{X_{ij}}{X_{j}}, \tag{6}\]  
where aij is the coefficient of direct costs of producing one unit of product of the i-th type of economic activity for the production of one unit of product of the j-th type of activity. The calculated coefficients aij are used for the prospective planning of economic development, taking into account interindustry relations and using Equation (7) in matrix form. \[\mathrm{X}=\mathrm{AX}+\mathrm{F}\rightarrow\mathrm{X}=(\mathrm{I}-\mathrm{A} )^{-1}\times\mathrm{F}=\mathrm{BF}, \tag{7}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Freight Turnover by Different Modes of Transport, Billion Tkm** & **Year** \\ \hline
**Total** & **Other** & **Pipeline** & **Road** & **Railway** & **Year** \\ \hline
344.2 & 4.2 & 94.4 & 58.0 & 187.6 & 2016 \\ \hline
364.2 & 4.6 & 105.4 & 62.3 & 191.9 & 2017 \\ \hline
361.3 & 3.7 & 99.2 & 72.1 & 186,3 & 2018 \\ \hline
355.0 & 3.7 & 104.5 & 65.0 & 181,8 & 2019 \\ \hline
313.2 & 3.1 & 69.3 & 65.2 & 175,6 & 2020 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Freight turnover in Ukraine for different types of transport from 2016 to 2020.  
where V is the matrix of total costs, A is the matrix of direct cost coefficients, and I is the identity matrix. Equation (7) considers the \"Cost-Output\" table by rows and allows for prospective calculations of the total output of product X, which satisfies the intermediate consumption of AX and scenario volumes of final demand F. The economic content of the matrix of total costs is a quantitative measure of the efficiency of social production, or the number of times that X exceeds F to cover intermediate costs. Then, we have Equation (8).