A Mathematical Optimization Framework for Economic Growth Forecasting Using Multivariate Dynamic Models

Economic forecasting requires a robust framework that captures dynamic interactions between key macroeconomic variables such as GDP, inflation, capital formation, labor productivity, and technological growth. Traditional linear models fail to capture nonlinear behaviors observed in real economic systems. This paper develops a mathematical framework integrating differential equations, regression modeling, and optimization techniques to forecast long-term economic growth. A Multivariate Dynamic Growth Model (MDGM) is proposed, consisting of coupled first-order differential equations that represent relationships among consumption, investment, capital accumulation, and productivity. The model incorporates economic constraints based on utility maximization and budget limitations. Simulated results demonstrate how different policy interventions—such as increasing capital investment or optimizing tax rates—directly influence growth trajectories. The approach is validated with a sensitivity analysis that evaluates how parameter variations affect stability and equilibrium. The developed mathematical–economic framework provides a reliable, adaptable method for policymakers to predict future economic scenarios and evaluate the effect of reforms.