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This study formulates a mathematical dynamic Computable General Equilibrium (CGE) model within a rational expectations framework, adhering to neo-classical principles. It emphasizes the significant role of agents' expectations in determining the broader economic trajectory over time. The model combines microeconomic and macroeconomic perspectives by merging the concept of intertemporal choice with savings behavior. Its mathematical foundations are derived and calibrated using data from a social accounting matrix to enhance its simulation capabilities. The paper presents a practical simulation investigating the economic implications of a strategic investment impact within an specific European region, Madrid as the case of study. Such demand shock affects sectors such as electronics, food, pharmaceuticals, and education. The study models the long-term effects of heightened investment and persistent demand-side shocks. The research demonstrates the CGE model's ability to forecast economic shifts toward a new equilibrium after an investment shock, proving its utility for assessing the impacts of extensive environmental policies within a European context. The work's originality lies in its detailed mathematical formulation, contributing to theoretical discourse and practical application in business analytics. [ABSTRACT FROM AUTHOR]