Economic and mathematical modelling of innovative development of the agricultural sector.

Purpose: To develop an economic and mathematical model of innovation development in the agricultural sector to quantitatively assess the impact of capital investment, human capital, and energy efficiency on agricultural value added in Ukraine, accounting for energy efficiency factors. Design/Methodology/Approach: The study combined a systematic review of scientific literature with economic-statistical and economic-mathematical modelling. The analysis was based on official data from the State Statistics Service of Ukraine and Eurostat for 2014–2024 to evaluate relationships between investment, human capital, energy efficiency, and agricultural performance. Linear and log-linear regression models were estimated by ordinary least squares (11 annual observations for 2014–2024), with multicollinearity testing (VIF) and residual diagnostics; EU-27 trends were analysed using descriptive and correlation analysis. Research Limitations: The analysis relies on macro-level data and does not examine enterprise-level differences. Future research should incorporate firm-level indicators and institutional factors. Findings: Capital investment promotes technological modernisation and production efficiency, while qualified human capital enhances labour productivity and innovation capacity. Energy-efficient technologies reduce resource consumption, optimise production costs, and strengthen sustainability. Hybrid and digital analytical models improve forecasting accuracy and support management under market and environmental uncertainty. The findings confirm that investment, technology transfer, human capital, and energy efficiency significantly contribute to agricultural competitiveness and sustainable growth in Ukraine and the European Union. Practical Implication: The results support evidence-based policies promoting investment, workforce development, and energy-efficient technologies. Social Implication: Innovation strengthens rural development, environmental sustainability, and food security. Originality/Value: The study provides an integrated quantitative framework linking investment, human capital, and energy efficiency to agricultural value creation. The novelty lies in including energy consumption as an explicit factor alongside capital investment and human capital indicators (employment, personnel costs and wages) in a single value-added model for Ukraine, complemented by an EU-27 analysis of energy productivity and labour dynamics, whereas existing approaches assess these factors separately (Table 1).