A CRITICAL REVIEW OF MATHEMATICAL MODELS OF ECONOMIC GROWTH
Keywords:
elasticity, production function, economical growth model.Abstract
The article provides a comprehensive analysis of mathematical models widely used in economic theory to model demand, production, and economic growth. In particular, it demonstrates the application of elasticity, as the economic meaning of a derivative, for constructing a production function and its application to models of economic growth research. Special attention is given to the limitations and challenges faced by researchers when developing and implementing these models. The models discussed are powerful tools for studying economic processes, but each has both strengths and weaknesses that determine their effectiveness and applicability under different conditions. The mathematical component of each model provides a clear understanding of the structure of economic processes and allows for quantitative analysis. However, all these models are based on mathematical formulas and certain assumptions and simplifications, which may limit their applicability in real-world economic conditions. The article also addresses the importance of choosing the correct mathematical methods for analyzing these models. An important aspect is the approach to adapting model parameters to real conditions, which often requires modifications to mathematical expressions and consideration of additional factors. In this context, the role of numerical methods in solving complex systems of equations, as well as the use of optimization and approximation techniques to achieve more accurate results, is emphasized. Despite numerous advantages, mathematical models of economic processes have certain limitations. Their application in the real world often requires accounting for multiple external variables that may not be included in the basic mathematical structures of the models. However, for theoretical research and the construction of initial estimates, these models are effective tools for understanding and predicting economic processes. In conclusion, all models have important applications, but to maximize their effectiveness, they need to be adjusted to real economic conditions, supplemented with new variables, and account for the dynamic nature of economic processes.
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