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The aim of the study is to assess the consequences of the COVID-19 pandemic on the incomes of households located in various national economies in 2021. The survey of representatives of the economically active adult population (18-64 years old) was conducted in 47 countries in Europe, Asia, Africa, Latin America, and North America within the framework of the Global Entrepreneurship Monitoring Project. The development of mathematical models included the construction of normal distribution density functions in accordance with the authors' methodology. It was proved that almost half of the households (46.6%) had a certain decrease in household income due to the pandemic. Slightly less (45.6%) was the proportion of households in which the income remained stable. An absolute minority (7.8%) of households experienced income growth. Resumen El objetivo del estudio es evaluar las consecuencias de la pandemia de COVID-19 en los ingresos de los hogares de diversas economías nacionales en 2021. La encuesta a representantes de la población adulta económicamente activa (18-64 años) se realizó en 47 países de Europa, Asia, África, América Latina y América del Norte durante el desarrollo del Proyecto Global Entrepreneurship Monitoring. El desarrollo de modelos matemáticos incluyó la construcción de funciones de densidad de distribución normal de acuerdo con la metodología de los autores. Se comprobó que casi la mitad de los hogares (46.6%) tuvieron una cierta disminución de los ingresos familiares debido a la pandemia. Ligeramente menor (45.6%) fue la proporción de hogares en los que se observó estabilidad en los ingresos. Una minoría absoluta (7.8%) de los hogares experimentó un crecimiento de los ingresos.

El estudio se basó en el desarrollo de las funciones de producción que caracterizan las actividades de las empresas agrícolas en las regiones de Rusia. Se utilizó información estadística oficial sobre 65 regiones de Rusia para 2017 y 2018. La investigación realizada permitió identificar factores (inversiones en activos fijos, salarios de empleados y área de tierra cultivable) que afectan el volumen de producción en el sector agrícola en las regiones de Rusia y sugiere utilizar funciones de producción de tres factores de alta calidad para describir esta influencia. Está comprobado que la economía de las regiones del país no ha llegado a la saturación de productos agrícolas y existen importantes reservas para un mayor desarrollo de este sector. Las funciones de producción desarrolladas son herramientas de gestión efectivas que permiten evaluar el nivel de uso de los recursos financieros y laborales. Los nuevos conocimientos y herramientas adquiridos para evaluar las actividades agrícolas en las regiones rusas son de importancia científica y práctica. Pueden ser utilizados en la investigación del sector agrícola de la economía, el seguimiento de los volúmenes de producción, en la determinación de las necesidades de los recursos necesarios para el desarrollo de la agricultura, fundamentando los planes y programas para su desarrollo. The study was based on the development of production functions that characterize the activities of agricultural enterprises in the regions of Russia. Official statistical information on 65 regions of Russia for 2017 and 2018 was used. The conducted research made it possible to identify factors (investments in fixed assets, wages of employees and arable land area) that affect the volume of production in the agricultural sector in the regions of Russia and suggest using three -factor production functions of high quality to describe this influence. It is proved that the economy of the country's regions has not reached saturation with agricultural products and there are significant reserves for further development of this sector. The developed production functions are effective management tools that allow assessing the level of use of financial and labor resources. The acquired new knowledge and tools for assessing the activities of agriculture in the Russian regions are of scientific and practical importance. They can be used in research of the agricultural sector of the economy, monitoring of production volumes, in determining the needs for resources necessary for the development of agriculture, substantiating plans and programs for its development.

The purpose of this study was to examine if it makes sense to further stimulate the development of small and medium-sized businesses in Russia by the State. For this purpose, the authors formulated the following hypotheses: production functions can be used to explore opportunities to promote SMEs in Russia (hypothesis 1). However, if the values of degrees of factors are positive, it can be argued that SMEs development can be achieved by State measures to facilitate an increase in labour costs and investment in fixed assets of SMEs (hypothesis 2). To check formulated hypotheses we have developed production functions, which reflect dependences between SMEs turnover from investments in fixed assets and employees wage. Regression analysis was used to determine the parameters of production functions. While conducting calculations, we used the data of total observation of SMEs activities, provided by the Federal Statistical Service in 83 regions of the Russian Federation for the year 2015. Taking into consideration an important role of SMEs in Russian economy, the results of this research might help government bodies in resource distribution for particular regions and sectors of economy in these regions. From methodological point of view this research shows, that production functions might be used in Development Strategy of SMEs for the period of up to 2030, which establishes double production growth in SMEs.