Palizdar, Marzieh2024-12-162024-12-162024-12-13https://hdl.handle.net/10222/84791This research advances economic modeling by extending the Ramsey-Cass-Koopmans (RCK) model through the introduction of an S-shaped production function, which better reflects real-world economic behaviors such as nonlinearity and critical thresholds. Unlike traditional models that prioritize welfare optimization, our approach centers on production, offering a novel perspective on long-term economic growth. Using the calculus of variations, we derive extremal conditions for the functional, employing the second variation to ensure robustness. This framework incorporates key economic factors like depreciation, investment, and taxation, providing a comprehensive tool for analyzing macroeconomic systems. The findings bridge theoretical gaps in economic growth modeling, offering significant implications for policy and research.The main goal of this research is twofold. First, we extend and generalize the renowned Ramsey-Cass-Koopmans (RCK) model in economics by introducing an S-shaped production function in place of the conventional Cobb-Douglas production function. This modification enables the model to address more realistic scenarios. Second, we shift the focus from optimizing consumption or welfare, as in the traditional RCK model, to optimizing production. Our model is developed and analyzed within the framework of the calculus of variations, utilizing the second variation to determine the extremal values of the functional. This approach serves as an analogue to the second derivative test in conventional calculus. The proposed model aims to explain long-term economic growth under the constraints of balance equations that incorporate factors such as depreciation, investment, and taxation. The importance of the model described lies in its potential to address key limitations of the traditional Ramsey-Cass-Koopmans (RCK) model and provide new insights into long-term economic growth.enS-shaped production functionsNon-concave production functionsRamsey-Cass-Koopmans modelOptimization of production functionCalculus of variationsSecond variation analysisConstant returns to scaleMathematical economicsNonlinear economic behaviorsCobb-Douglas production function